From d552a73738c51596936c9d1c1035753a96d39e41 Mon Sep 17 00:00:00 2001 From: Cursor Agent Date: Thu, 13 Aug 2026 16:35:46 +0000 Subject: [PATCH 01/16] Add opt-in Offner et al. 2023 piecewise multiplicity model Introduce MultiplicityPiecewisePowerLaw plus unresolved/resolved Offner 2023 classes fitted to Table 1 MF/CF (including brown dwarfs). Companion mass and separation draws now live on the multiplicity object; Lu+2013 defaults are unchanged. Co-authored-by: Jessica Lu --- docs/index.rst | 2 + docs/multiplicity.rst | 22 + spisea/imf/imf.py | 61 +-- spisea/imf/multiplicity.py | 684 +++++++++++++++++++++++++++--- spisea/synthetic.py | 2 +- spisea/tests/test_multiplicity.py | 186 ++++++++ 6 files changed, 849 insertions(+), 108 deletions(-) diff --git a/docs/index.rst b/docs/index.rst index 9a0f740..f4fda76 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -97,6 +97,8 @@ Change Log * New tutorial for creating SPISEA clusters using COSMIC: docs/Cluster_w_COSMIC.ipynb * *Minor Changes* + * Added opt-in Offner et al. 2023 (Protostars and Planets VII; arXiv:2203.10066) multiplicity model, including brown dwarfs, as piecewise power-law fits to Table 1 MF/CF. See :ref:`multi_obj`. Lu et al. (2013) remains the default. + * Companion mass and separation draws (including brown-dwarf q and binaries-only BD systems) now live on the multiplicity object rather than being special-cased in ``imf.py``. * The MISTv1.2-synthpop model extension was modified to include denser sampling in the gap between the base MISTv1.2 grids and 0.1Msun. * Modified default for MISTv1.2 isochrones: synthpop_extension will be True by default to keep a consistent lower mass limit of 0.1Msun across all ages and metallicities. * Added option to return synthetic photometry in terms of AB or ST mag units in IsochronePhot. Vega mag units remains the default. New meta keyword `MAGSYS` added to output tables to specify magnitude unit system. diff --git a/docs/multiplicity.rst b/docs/multiplicity.rst index 5417738..c96512d 100644 --- a/docs/multiplicity.rst +++ b/docs/multiplicity.rst @@ -40,8 +40,30 @@ Unresolved Multiplicity Classes :members: companion_star_fraction, multiplicity_fraction, random_q +.. autoclass:: imf.multiplicity.MultiplicityPiecewisePowerLaw + :show-inheritance: + :members: multiplicity_fraction, companion_star_fraction + +.. autoclass:: imf.multiplicity.MultiplicityUnresolvedOffner2023 + :show-inheritance: + :members: multiplicity_fraction, companion_star_fraction, + q_power_at_mass, random_q + +The Lu et al. (2013) :class:`~imf.multiplicity.MultiplicityUnresolved` +object remains the default. Offner et al. 2023 is **opt-in**:: + + from spisea.imf import multiplicity + multi = multiplicity.MultiplicityUnresolvedOffner2023() + # or the alias: + multi = multiplicity.MultiplicityOffner2023() + Resolved Multiplicity Classes ------------------------------------------ .. autoclass:: imf.multiplicity.MultiplicityResolvedDK :show-inheritance: + +.. autoclass:: imf.multiplicity.MultiplicityResolvedOffner2023 + :show-inheritance: + :members: log_semimajoraxis + diff --git a/spisea/imf/imf.py b/spisea/imf/imf.py index 241e04d..fbc3a44 100755 --- a/spisea/imf/imf.py +++ b/spisea/imf/imf.py @@ -249,62 +249,13 @@ def generate_cluster(self, totalMass): def calc_multi(self, newMasses, newIsMultiple, CSF, MF): """ Helper function to calculate multiples more efficiently. - We will use array operations as much as possible. - Uses Fontanive+18 parameters for brown dwarf masses - (M <= 0.08 M_sun) while keeping default parameters for - all other stellar primaries. + Companion counts and companion-mass draws (including brown-dwarf + q distributions and binaries-only BD systems) are delegated to + the multiplicity object. """ - # Copy over the primary masses. Eventually add the companions. - newSystemMasses = newMasses.copy() - - # Identify multiple systems, calculate number of companions for each - multiple_idx = np.where(newIsMultiple)[0] - comp_nums = 1 + self.rng.poisson((CSF[multiple_idx] / MF[multiple_idx]) - 1) - if self._multi_props.companion_max: - too_many = np.where(comp_nums > self._multi_props.CSF_max)[0] - comp_nums[too_many] = self._multi_props.CSF_max - primary = newMasses[multiple_idx] - - # limit BD primaries to 1 companion (Fontanive+18) - bd_mask = primary <= 0.08 - comp_nums[bd_mask & (comp_nums > 1)] = 1 - - # We will deal with each number of multiple system independently. This is - # so we can put in uniform arrays in _multi_props.random_q. - comp_unique = np.unique(comp_nums) - comp_indices = [np.where(comp_nums == i)[0] for i in comp_unique] - if np.any(newIsMultiple): - compMasses = np.zeros((len(newMasses), max(comp_unique))) - else: - compMasses = np.zeros((len(newMasses), 1)) - - for comp_num, comp_index in zip(comp_unique, comp_indices): - prim_subset = primary[comp_index] - bd_sub_mask = prim_subset <= 0.08 - star_sub_mask = ~bd_sub_mask - - q_values = np.empty((len(comp_index), comp_num)) - - # Stellar primaries: use default Duchene & Kraus distribution - if np.any(star_sub_mask): - q_values[star_sub_mask] = self._multi_props.random_q(self.rng.random((star_sub_mask.sum(), comp_num))) - - # BD primaries: use Fontanive+18 power-law distribution - if np.any(bd_sub_mask): - b = 1.0 + 6.1 # gamma from Fontanive+18 - rand_vals = self.rng.random((bd_sub_mask.sum(), comp_num)) - q_values[bd_sub_mask] = (rand_vals * (1.0 - self._multi_props.q_min ** b) + - self._multi_props.q_min ** b) ** (1.0 / b) - - m_comp = np.multiply(q_values, np.transpose([prim_subset])) - compMasses[multiple_idx[comp_index], :comp_num] = m_comp - - # Mask out companions below the minimum mass - compMasses = np.ma.MaskedArray(compMasses, mask=compMasses < self._mass_limits[0]) - newSystemMasses[multiple_idx] += compMasses[multiple_idx].sum(axis=1) - newIsMultiple = np.any(~compMasses.mask, axis=1) - - return compMasses, newSystemMasses, newIsMultiple + return self._multi_props.draw_companion_masses( + newMasses, newIsMultiple, CSF, MF, + rng=self.rng, mass_min=self._mass_limits[0]) class IMF_broken_powerlaw(IMF): diff --git a/spisea/imf/multiplicity.py b/spisea/imf/multiplicity.py index 4258cb4..9cf8656 100755 --- a/spisea/imf/multiplicity.py +++ b/spisea/imf/multiplicity.py @@ -13,8 +13,139 @@ default_aMean = 100.0 # log (AU) default_aSigma = 0.1 # log (AU) +# Hydrogen-burning limit used for BD-primary (binaries-only) logic. +# Offner et al. 2023 use M_comp > 0.075 Msun as the MS companion cut; +# SPISEA keeps 0.08 Msun for consistency with existing BD handling. +H_BURNING_MASS = 0.08 + +# Fontanive et al. (2018) mass-ratio power-law index used for BD primaries +# in the Lu et al. (2013) MultiplicityUnresolved implementation. +FONTANIVE2018_BD_Q_POWER = 6.1 + # Eventually we should add in separation properties. (a_mean, a_sigma) + +def _two_point_powerlaw(mass_1, y_1, mass_2, y_2): + """ + Amplitude and power for y = A * M**alpha through two (M, y) points. + """ + power = np.log(y_2 / y_1) / np.log(mass_2 / mass_1) + amp = y_1 / (mass_1 ** power) + return amp, power + + +def _piecewise_powerlaw(mass, mass_limits, amps, powers, clip_min=None, + clip_max=None): + """ + Evaluate y = A_i * M**alpha_i on mass segments. + + Segment i applies for mass_limits[i] <= M < mass_limits[i+1]. + The first segment also covers M below the lowest limit; the last + segment is closed on the right. Returns a Python float for scalar + mass and an ndarray otherwise. + """ + return_scalar = np.isscalar(mass) + mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) + out = np.empty(mass_arr.shape, dtype=float) + nseg = len(amps) + for i in range(nseg): + lo = mass_limits[i] + hi = mass_limits[i + 1] + if i == 0: + mask = mass_arr < hi + elif i == nseg - 1: + mask = mass_arr >= lo + else: + mask = (mass_arr >= lo) & (mass_arr < hi) + out[mask] = amps[i] * np.power(mass_arr[mask], powers[i]) + if clip_min is not None: + out = np.maximum(out, clip_min) + if clip_max is not None: + out = np.minimum(out, clip_max) + if return_scalar: + return float(out[0]) + return out + + +def _q_from_powerlaw(x, q_pow, q_min): + """ + Inverse CDF of P(q) ∝ q**q_pow for q_min <= q <= 1. + + ``q_pow`` may be a scalar or an array broadcastable to ``x``. + The q_pow = -1 (b = 0) limit is q = q_min**(1 - x). + """ + x = np.asarray(x, dtype=float) + q_pow = np.asarray(q_pow, dtype=float) + if x.ndim > q_pow.ndim: + q_pow = q_pow.reshape(q_pow.shape + (1,) * (x.ndim - q_pow.ndim)) + b = 1.0 + q_pow + b, x = np.broadcast_arrays(b, x) + out = np.empty(x.shape, dtype=float) + near_zero = np.abs(b) < 1e-12 + ok = ~near_zero + if np.any(near_zero): + out[near_zero] = q_min ** (1.0 - x[near_zero]) + if np.any(ok): + out[ok] = (x[ok] * (1.0 - q_min ** b[ok]) + q_min ** b[ok]) ** (1.0 / b[ok]) + return out + + +class _ResolvedOrbitalMixin(object): + """Eccentricity and Keplerian angles shared by resolved multiplicity classes.""" + + def random_e(self, x): + """ + Generate random eccentricity from the inverse of the CDF where the PDF is f(e) = 2e from Duchene and Kraus 2013 + + Parameters + ---------- + x : float or array_like + Random number between 0 and 1. + + Returns + ------- + e : float or array_like + eccentricity + """ + e = np.sqrt(x) + + return e + + def random_keplarian_parameters(self, x, y, z): + """ + Generate random incliniation and angles of binary system + + Parameters + ---------- + x : float or array_like + Random number between 0 and 1. + + y : float or array_like + Random number between 0 and 1. + + z : float or array_like + Random number between 0 and 1. + + Returns + ------- + inclination : float or array_like + Angle of inclination + + Omega : float or array_like + Big Omega: one other angle of the system + + omega : float or array_like + Final angle of the system + """ + sign = np.array([choice([-1,1]) for i in range(len(x))]) + x = sign*x + inclination = np.arccos(x)*180/np.pi #inclination angle in degrees + + Omega = 360*y + omega = 360*z + + return inclination, Omega, omega + class MultiplicityUnresolved(object): """ The properties of stellar companions (see notes below). @@ -104,12 +235,17 @@ class MultiplicityUnresolved(object): companion_max : bool, optional Sets CSF_max is the max as the max number of companions. Default False. + + binary_only_mass_max : float, optional + Primary mass (Msun) at and below which systems are restricted + to at most one companion (CSF = MF). Default is 0.08. """ def __init__(self, MF_amp=0.44, MF_power=0.51, CSF_amp=0.50, CSF_power=0.45, CSF_max=3, - q_power=-0.4, q_min=0.01, companion_max = False): + q_power=-0.4, q_min=0.01, companion_max = False, + binary_only_mass_max=H_BURNING_MASS): self.MF_amp = MF_amp self.MF_pow = MF_power @@ -119,6 +255,7 @@ def __init__(self, self.q_pow = q_power self.q_min = q_min self.companion_max = companion_max + self.binary_only_mass_max = binary_only_mass_max def multiplicity_fraction(self, mass): """ @@ -180,21 +317,37 @@ def companion_star_fraction(self, mass): if np.isscalar(csf): if csf > self.CSF_max: csf = self.CSF_max - if (mass <= 0.08): + if (mass <= self.binary_only_mass_max): csf = self.multiplicity_fraction(mass) else: csf[csf > self.CSF_max] = self.CSF_max - bd = mass <= 0.08 + bd = mass <= self.binary_only_mass_max csf[bd] = self.multiplicity_fraction(mass[bd]) return csf - def random_q(self, x): + def q_power_at_mass(self, mass): + """ + Mass-ratio power-law index, P(q) ∝ q ** q_power. + + Lu et al. (2013) use a single ``q_power`` for stellar primaries. + Brown-dwarf primaries (M <= binary_only_mass_max) use + gamma = 6.1 from Fontanive et al. (2018), matching the + companion-mass draw previously special-cased in ``imf.calc_multi``. + """ + mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) + q_pow = np.full(mass_arr.shape, self.q_pow, dtype=float) + q_pow[mass_arr <= self.binary_only_mass_max] = FONTANIVE2018_BD_Q_POWER + if np.isscalar(mass): + return float(q_pow[0]) + return q_pow + + def random_q(self, x, mass=None): """ Generative function for companion mass ratio, equivalent to the inverse of the CDF. - `q = m_compnaion / m_primary` + `q = m_companion / m_primary` `P(q) = q ** beta` for q_min <= q <= 1 Parameters @@ -202,15 +355,20 @@ def random_q(self, x): x : float or array_like Random number between 0 and 1. + mass : float or array_like, optional + Primary mass(es). If given, the power-law index is + ``q_power_at_mass(mass)`` (brown-dwarf vs stellar for + Lu et al. 2013; mass-dependent for Offner et al. 2023). + If omitted, ``self.q_pow`` is used for all companions. + Returns ------- q : float or array_like companion mass ratio(s) """ - b = 1.0 + self.q_pow - q = (x * (1.0 - self.q_min ** b) + self.q_min ** b) ** (1.0 / b) - - return q + if mass is None: + return _q_from_powerlaw(x, self.q_pow, self.q_min) + return _q_from_powerlaw(x, self.q_power_at_mass(mass), self.q_min) def random_is_multiple(self, x, MF): """ @@ -233,8 +391,119 @@ def random_companion_count(self, x, CSF, MF): n_comp = self.CSF_max return n_comp + + def draw_n_companions(self, mass, CSF, MF, rng): + """ + Vectorized companion counts for primaries that are already + identified as multiple. + + Parameters + ---------- + mass, CSF, MF : array_like + Primary masses and corresponding CSF and MF values. + rng : numpy.random.Generator + Random generator used for the Poisson draw. + + Returns + ------- + n_comp : ndarray of int + Number of companions for each multiple primary. Brown-dwarf + primaries are limited to one companion. + """ + mass = np.atleast_1d(np.asarray(mass, dtype=float)) + CSF = np.atleast_1d(np.asarray(CSF, dtype=float)) + MF = np.atleast_1d(np.asarray(MF, dtype=float)) + n_comp = 1 + rng.poisson((CSF / MF) - 1) + if self.companion_max: + n_comp = np.minimum(n_comp, self.CSF_max) + bd = mass <= self.binary_only_mass_max + n_comp[bd & (n_comp > 1)] = 1 + return n_comp + + def _q_values_for_primaries(self, prim_subset, n_comp, rng): + """ + Draw mass ratios for ``n_comp`` companions of each primary. + + The stellar / brown-dwarf split (two separate RNG draws) preserves + the historical Lu et al. (2013) random sequence used by + ``imf.calc_multi``. + """ + q_values = np.empty((len(prim_subset), n_comp)) + bd_mask = prim_subset <= self.binary_only_mass_max + star_mask = ~bd_mask + if np.any(star_mask): + q_values[star_mask] = self.random_q( + rng.random((star_mask.sum(), n_comp))) + if np.any(bd_mask): + q_values[bd_mask] = self.random_q( + rng.random((bd_mask.sum(), n_comp)), + mass=prim_subset[bd_mask]) + return q_values + + def draw_companion_masses(self, primary_masses, is_multiple, CSF, MF, + rng, mass_min): + """ + Assign companion masses for a set of primaries. + + This is the multiplicity-object entry point used by + ``IMF.calc_multi``. Companion-mass draws, including brown-dwarf + q distributions and the binaries-only BD companion count, live + here rather than in ``imf.py``. + + Parameters + ---------- + primary_masses : array_like + Primary masses (Msun). + is_multiple : array_like of bool + True for primaries drawn as multiple systems. + CSF, MF : array_like + Companion star fraction and multiplicity fraction at each + primary mass. + rng : numpy.random.Generator + Random generator. + mass_min : float + Minimum companion mass; lighter companions are masked. + + Returns + ------- + comp_masses : numpy.ma.MaskedArray + Companion masses, shape (n_primaries, max_n_comp). + system_masses : ndarray + Primary plus unmasked companion mass. + is_multiple : ndarray of bool + Updated multiplicity flags after masking sub-minimum companions. + """ + primary_masses = np.asarray(primary_masses, dtype=float) + is_multiple = np.asarray(is_multiple, dtype=bool) + CSF = np.asarray(CSF, dtype=float) + MF = np.asarray(MF, dtype=float) + system_masses = primary_masses.copy() + multiple_idx = np.where(is_multiple)[0] + primary = primary_masses[multiple_idx] + n_comp = self.draw_n_companions( + primary, CSF[multiple_idx], MF[multiple_idx], rng) + + if len(multiple_idx) == 0: + comp_masses = np.zeros((len(primary_masses), 1)) + comp_masses = np.ma.MaskedArray(comp_masses, mask=comp_masses < mass_min) + return comp_masses, system_masses, is_multiple + + n_unique = np.unique(n_comp) + n_indices = [np.where(n_comp == i)[0] for i in n_unique] + comp_masses = np.zeros((len(primary_masses), int(np.max(n_unique)))) + + for n_c, idx in zip(n_unique, n_indices): + prim_subset = primary[idx] + q_values = self._q_values_for_primaries(prim_subset, int(n_c), rng) + m_comp = q_values * prim_subset[:, np.newaxis] + comp_masses[multiple_idx[idx], :int(n_c)] = m_comp + + comp_masses = np.ma.MaskedArray(comp_masses, mask=comp_masses < mass_min) + system_masses[multiple_idx] += comp_masses[multiple_idx].sum(axis=1) + is_multiple = np.any(~comp_masses.mask, axis=1) + return comp_masses, system_masses, is_multiple -class MultiplicityResolvedDK(MultiplicityUnresolved): +class MultiplicityResolvedDK(MultiplicityUnresolved, _ResolvedOrbitalMixin): """ Sub-class of MultiplicityUnresolved that adds semimajor axis and eccentricity information for multiple objects from distributions described in Duchene and Kraus 2013 @@ -328,55 +597,366 @@ def log_semimajoraxis(self, mass): log_semimajoraxis = truncnorm.rvs(a_lower_std, a_upper_std, loc=log_a_mean, scale=log_a_std) return log_semimajoraxis - def random_e(self, x): + +def _offner2023_table1_geom_mass(m_lo, m_hi): + """Geometric-mean primary mass of a Table 1 M1 interval.""" + return float(np.sqrt(m_lo * m_hi)) + + +def offner2023_default_segments(): + """ + Piecewise MF/CF power-law segments fitted to Offner et al. 2023 Table 1. + + Each segment is the two-point power law through the geometric-mean + primary masses of the listed surveys. MF is clipped to [0, 1] at + evaluation time. Below the hydrogen-burning limit, CSF is forced + equal to MF (binaries only) regardless of the CF segment. + + Returns + ------- + mass_limits : ndarray + Segment edges (Msun), length N+1. + MF_amps, MF_powers, CSF_amps, CSF_powers : ndarray + Length-N piecewise coefficients for MF(M) = A * M**alpha + and CSF(M) = A * M**alpha. + """ + # Geometric-mean M1 of Table 1 mass bins (Offner et al. 2023, Table 1). + M_font = _offner2023_table1_geom_mass(0.019, 0.058) # Fontanive+2018 + M_burg = _offner2023_table1_geom_mass(0.05, 0.08) # Burgasser 2007 + M_close = _offner2023_table1_geom_mass(0.080, 0.095) # Close+2003 + M_wlate = _offner2023_table1_geom_mass(0.075, 0.15) # Winters+2019 late-M + M_wmid = _offner2023_table1_geom_mass(0.15, 0.30) # Winters+2019 mid-M + M_wearly = _offner2023_table1_geom_mass(0.3, 0.6) # Winters+2019 early-M + M_ragh = _offner2023_table1_geom_mass(0.75, 1.25) # Raghavan+2010 FGK + M_moe = _offner2023_table1_geom_mass(1.6, 2.4) # Moe & Kratter 2021 + M_mds35 = _offner2023_table1_geom_mass(3.0, 5.0) # Moe & Di Stefano 2017 + M_mds58 = _offner2023_table1_geom_mass(5.0, 8.0) + M_mds817 = _offner2023_table1_geom_mass(8.0, 17.0) + M_sana = _offner2023_table1_geom_mass(17.0, 50.0) # Sana et al. + + # Published Table 1 MF (fraction) and CF. MF values that were given + # as percents in the table are converted here. + mf_font, cf_font = 0.08, 0.08 + mf_burg, cf_burg = 0.15, 0.16 + mf_close, cf_close = 0.19, 0.19 + mf_wlate, cf_wlate = 0.19, 0.21 + mf_wmid, cf_wmid = 0.23, 0.27 + mf_wearly, cf_wearly = 0.30, 0.38 + mf_ragh, cf_ragh = 0.46, 0.60 + mf_moe, cf_moe = 0.68, 0.99 + mf_mds35, cf_mds35 = 0.81, 1.28 + mf_mds58, cf_mds58 = 0.89, 1.55 + mf_mds817, cf_mds817 = 0.93, 1.80 + mf_sana, cf_sana = 0.96, 2.10 + + # Mass edges follow BD / late-M / mid-M / FGK / A / B / O regimes + # in Offner et al. 2023 §2.2. Matching Table 1 is preferred over + # continuity at the breaks. + mass_limits = np.array([0.01, 0.05, 0.08, 0.15, 0.30, 1.5, 5.0, 17.0, 150.0]) + + mf_pairs = [ + (M_font, mf_font, M_burg, mf_burg), # late-T/Y BDs + (M_burg, mf_burg, M_close, mf_close), # L/early-T / upper BD + (M_wlate, mf_wlate, M_wmid, mf_wmid), # late-M + (M_wmid, mf_wmid, M_wearly, mf_wearly), # mid-M + (M_wearly, mf_wearly, M_ragh, mf_ragh), # early-M + FGK + (M_moe, mf_moe, M_mds35, mf_mds35), # A / late-B + (M_mds58, mf_mds58, M_mds817, mf_mds817), # B + (M_mds817, mf_mds817, M_sana, mf_sana), # O + ] + cf_pairs = [ + (M_font, cf_font, M_burg, cf_burg), + (M_burg, cf_burg, M_close, cf_close), + (M_wlate, cf_wlate, M_wmid, cf_wmid), + (M_wmid, cf_wmid, M_wearly, cf_wearly), + (M_wearly, cf_wearly, M_ragh, cf_ragh), + (M_moe, cf_moe, M_mds35, cf_mds35), + (M_mds58, cf_mds58, M_mds817, cf_mds817), + (M_mds817, cf_mds817, M_sana, cf_sana), + ] + + MF_amps = np.empty(len(mf_pairs)) + MF_powers = np.empty(len(mf_pairs)) + CSF_amps = np.empty(len(cf_pairs)) + CSF_powers = np.empty(len(cf_pairs)) + for i, pair in enumerate(mf_pairs): + MF_amps[i], MF_powers[i] = _two_point_powerlaw(*pair) + for i, pair in enumerate(cf_pairs): + CSF_amps[i], CSF_powers[i] = _two_point_powerlaw(*pair) + return mass_limits, MF_amps, MF_powers, CSF_amps, CSF_powers + + +# Table 1 gamma_trunc (1-100 au when available) plus the paper's +# L/early-T value gamma = 2-3 (midpoint 2.5). Masses are geometric +# means of the corresponding Table 1 M1 bins. +OFFNER2023_Q_MASS = np.array([ + _offner2023_table1_geom_mass(0.019, 0.058), # Fontanive+2018: 4.8 + 0.065, # L/early-T: 2-3 (text) + _offner2023_table1_geom_mass(0.080, 0.095), # Close+2003: 3.3 + _offner2023_table1_geom_mass(0.06, 0.15), # Allen+2007: 1.7 + _offner2023_table1_geom_mass(0.15, 0.30), # Winters mid-M: 0.7 + _offner2023_table1_geom_mass(0.3, 0.6), # Winters early-M: 0.1 + _offner2023_table1_geom_mass(0.75, 1.25), # Raghavan FGK: 0.2 + _offner2023_table1_geom_mass(1.6, 2.4), # De Rosa A: -1.3 + _offner2023_table1_geom_mass(3.0, 5.0), # MDS 3-5: -1.0 + _offner2023_table1_geom_mass(5.0, 8.0), # MDS 5-8: -1.7 + _offner2023_table1_geom_mass(8.0, 17.0), # MDS 8-17: -1.6 + _offner2023_table1_geom_mass(17.0, 50.0), # Sana O: -1.4 +]) +OFFNER2023_Q_GAMMA = np.array([ + 4.8, 2.5, 3.3, 1.7, 0.7, 0.1, 0.2, -1.3, -1.0, -1.7, -1.6, -1.4 +]) + +# Table 1 ã_all (au) and Table 2 lognormal μ (au) vs geom-mean M1. +# Table 2 μ is used where both exist (late-M, early-M, FGK). +OFFNER2023_SEP_MASS = np.array([ + _offner2023_table1_geom_mass(0.019, 0.058), # Fontanive ã_all=2.9 + _offner2023_table1_geom_mass(0.080, 0.095), # Close ã_all=3.7 + _offner2023_table1_geom_mass(0.075, 0.15), # Table 2 late-M μ=4 + _offner2023_table1_geom_mass(0.15, 0.30), # Winters mid-M ã_all=10 + _offner2023_table1_geom_mass(0.3, 0.6), # Table 2 early-M μ=25 + _offner2023_table1_geom_mass(0.75, 1.25), # Table 2 FGK μ=40 + _offner2023_table1_geom_mass(1.6, 2.4), # Moe & Kratter ã_all=32 + _offner2023_table1_geom_mass(3.0, 5.0), # MDS ã_all=28 + _offner2023_table1_geom_mass(5.0, 8.0), # MDS ã_all=25 + _offner2023_table1_geom_mass(8.0, 17.0), # MDS ã_all=23 + _offner2023_table1_geom_mass(17.0, 50.0), # Sana ã_all=19 +]) +OFFNER2023_SEP_MU_AU = np.array([ + 2.9, 3.7, 4.0, 10.0, 25.0, 40.0, 32.0, 28.0, 25.0, 23.0, 19.0 +]) +# Table 2 σ_log a at the three published bins; held constant outside. +OFFNER2023_SEP_SIG_MASS = np.array([ + _offner2023_table1_geom_mass(0.075, 0.15), + _offner2023_table1_geom_mass(0.3, 0.6), + _offner2023_table1_geom_mass(0.75, 1.25), +]) +OFFNER2023_SEP_SIG = np.array([0.7, 1.3, 1.5]) + + +class MultiplicityPiecewisePowerLaw(MultiplicityUnresolved): + """ + Multiplicity described by a piecewise power law in primary mass. + + On each mass segment i, with edges ``mass_limits[i] <= M < mass_limits[i+1]``:: + + MF(M) = MF_amp[i] * M ** MF_power[i] + CSF(M) = CSF_amp[i] * M ** CSF_power[i] + + MF is clipped to [0, 1]. CSF is clipped to [0, CSF_max] and forced + equal to MF for primaries at or below ``binary_only_mass_max`` + (binaries only). CSF is also raised to at least MF so the Poisson + companion-count draw is well defined. + + Parameters + ---------- + mass_limits : array_like + Segment edges in solar masses, length N+1, strictly increasing. + MF_amps, MF_powers : array_like + Length-N amplitudes and powers for the multiplicity fraction. + CSF_amps, CSF_powers : array_like + Length-N amplitudes and powers for the companion star fraction. + CSF_max, q_power, q_min, companion_max, binary_only_mass_max + Passed to :class:`MultiplicityUnresolved`. + """ + def __init__(self, mass_limits, MF_amps, MF_powers, CSF_amps, CSF_powers, + CSF_max=3, q_power=-0.4, q_min=0.01, companion_max=False, + binary_only_mass_max=H_BURNING_MASS): + mass_limits = np.asarray(mass_limits, dtype=float) + MF_amps = np.asarray(MF_amps, dtype=float) + MF_powers = np.asarray(MF_powers, dtype=float) + CSF_amps = np.asarray(CSF_amps, dtype=float) + CSF_powers = np.asarray(CSF_powers, dtype=float) + nseg = len(MF_amps) + if len(mass_limits) != nseg + 1: + raise ValueError('len(mass_limits) must be len(MF_amps) + 1') + if not (len(MF_powers) == len(CSF_amps) == len(CSF_powers) == nseg): + raise ValueError('MF/CSF amplitude and power arrays must have equal length') + if np.any(np.diff(mass_limits) <= 0): + raise ValueError('mass_limits must be strictly increasing') + + super(MultiplicityPiecewisePowerLaw, self).__init__( + MF_amp=MF_amps[-1], MF_power=MF_powers[-1], + CSF_amp=CSF_amps[-1], CSF_power=CSF_powers[-1], + CSF_max=CSF_max, q_power=q_power, q_min=q_min, + companion_max=companion_max, + binary_only_mass_max=binary_only_mass_max) + self.mass_limits = mass_limits + self.MF_amps = MF_amps + self.MF_powers = MF_powers + self.CSF_amps = CSF_amps + self.CSF_powers = CSF_powers + + def multiplicity_fraction(self, mass): """ - Generate random eccentricity from the inverse of the CDF where the PDF is f(e) = 2e from Duchene and Kraus 2013 - - Parameters - ---------- - x : float or array_like - Random number between 0 and 1. + Multiplicity fraction as a piecewise power law in primary mass. + Clipped to [0, 1]. + """ + return _piecewise_powerlaw( + mass, self.mass_limits, self.MF_amps, self.MF_powers, + clip_min=0.0, clip_max=1.0) - Returns - ------- - e : float or array_like - companion mass ratio(s) + def companion_star_fraction(self, mass): """ - e = np.sqrt(x) - - return e - - def random_keplarian_parameters(self, x, y, z): + Companion star fraction as a piecewise power law in primary mass. + + Clipped to [0, CSF_max], raised to at least MF, and set equal + to MF for primaries at or below ``binary_only_mass_max``. """ - Generate random incliniation and angles of binary system - + return_scalar = np.isscalar(mass) + mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) + csf = _piecewise_powerlaw( + mass_arr, self.mass_limits, self.CSF_amps, self.CSF_powers, + clip_min=0.0, clip_max=self.CSF_max) + mf = _piecewise_powerlaw( + mass_arr, self.mass_limits, self.MF_amps, self.MF_powers, + clip_min=0.0, clip_max=1.0) + csf = np.maximum(csf, mf) + bd = mass_arr <= self.binary_only_mass_max + csf[bd] = mf[bd] + if return_scalar: + return float(csf[0]) + return csf + + +class MultiplicityUnresolvedOffner2023(MultiplicityPiecewisePowerLaw): + """ + Unresolved multiplicity from Offner et al. 2023 Table 1, including + brown dwarfs. + + Citation: Offner, S. S. R., Moe, M., Kratter, K. M., Sadavoy, S. I., + Jensen, E. L. N., & Tobin, J. J. 2023, in Protostars and Planets VII, + ASP Conf. Ser. 534, 275 (`arXiv:2203.10066 + `_; ADS + `2023ASPC..534..275O + `_). + Table 1 data: Zenodo `10.5281/zenodo.6628915 + `_. + + The multiplicity fraction and companion frequency are piecewise + power laws fitted to the bias-corrected Table 1 MF and CF at the + geometric-mean primary mass of each survey bin. Table 1 itself + does **not** publish MF(M) ∝ M^α; the only tabulated power law is + γ_trunc for f_q ∝ q^γ on 0.4 < q < 1. Matching Table 1 is preferred + over continuity at segment boundaries. MF is clipped to [0, 1]. + Below 0.08 Msun, CSF = MF (binaries only; THF is tiny). + + Companion assignment vs Table 1 + ------------------------------- + Offner et al. 2023 (text above Table 1): BD primaries include all + BD companions; FGKM MS statistics include only MS companions with + M_comp > 0.075 Msun; OBA include MS companions above q > 0.1. + Table 1 stellar MF/CF therefore exclude BD companions. SPISEA still + draws companions down to ``q_min`` (default 0.01), so brown-dwarf + secondaries of stellar primaries are generated. The solar-type + BD-companion fraction is only ≈ 4% (BD desert at a < 0.5 au), so + the integrated stellar MF is affected very little. Do not interpret + the simulated stellar-primary MF as a stellar-companion-only + statistic. + + Mass-ratio draws use Table 1 γ_trunc (1–100 au when listed), + interpolated in log mass, so BD companions are much more + equal-mass than solar-type companions. + + This class is opt-in; it does not change the Lu et al. (2013) + :class:`MultiplicityUnresolved` default. + + Parameters + ---------- + CSF_max, q_min, companion_max, binary_only_mass_max + See :class:`MultiplicityUnresolved`. ``q_power`` is ignored for + draws when primary mass is provided (Table 1 γ_trunc is used); + it remains the fallback for ``random_q(x)`` with no mass. + """ + def __init__(self, CSF_max=3, q_power=0.2, q_min=0.01, + companion_max=False, binary_only_mass_max=H_BURNING_MASS): + mass_limits, MF_amps, MF_powers, CSF_amps, CSF_powers = \ + offner2023_default_segments() + super(MultiplicityUnresolvedOffner2023, self).__init__( + mass_limits, MF_amps, MF_powers, CSF_amps, CSF_powers, + CSF_max=CSF_max, q_power=q_power, q_min=q_min, + companion_max=companion_max, + binary_only_mass_max=binary_only_mass_max) + self.q_mass = np.array(OFFNER2023_Q_MASS, dtype=float) + self.q_gamma = np.array(OFFNER2023_Q_GAMMA, dtype=float) + + def q_power_at_mass(self, mass): + """ + Table 1 γ_trunc interpolated in log primary mass. + + Late-T/Y BDs have γ ≈ 4.8 (Fontanive+2018); L/early-T have + γ ≈ 2–3; solar-type γ_trunc ≈ 0.2 at 1–100 au; massive stars + have negative γ (low-q companions). + """ + mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) + mass_clip = np.clip(mass_arr, self.q_mass[0], self.q_mass[-1]) + q_pow = np.interp(np.log10(mass_clip), + np.log10(self.q_mass), self.q_gamma) + if np.isscalar(mass): + return float(q_pow[0]) + return q_pow + + def _q_values_for_primaries(self, prim_subset, n_comp, rng): + """Mass-dependent q for every primary (BD and stellar).""" + return self.random_q( + rng.random((len(prim_subset), n_comp)), mass=prim_subset) + + +class MultiplicityResolvedOffner2023(MultiplicityUnresolvedOffner2023, + _ResolvedOrbitalMixin): + """ + Resolved Offner et al. 2023 multiplicity: Table 1 MF/CF plus + mass-dependent separations. + + Separations are drawn from a truncated lognormal in log10(a/AU). + The mean μ(a) interpolates Table 1 ã_all and Table 2 lognormal μ + (late-M μ=4 au, σ=0.7; early-M μ=25 au, σ=1.3; FGK μ=40 au, + σ=1.5). Brown-dwarf / late-M binaries peak near 3–4 au (vast + majority at 1–20 au). σ_log a uses Table 2 and is held at the + late-M value (0.7) through the BD regime, as Offner et al. 2023 + describe the BD separation distribution as similar to late-M. + + Eccentricity and Keplerian angles follow Duchêne & Kraus (2013), + same as :class:`MultiplicityResolvedDK`. + + Opt-in; does not replace :class:`MultiplicityResolvedDK`. + """ + def __init__(self, **kwargs): + super(MultiplicityResolvedOffner2023, self).__init__(**kwargs) + self.sep_mass = np.array(OFFNER2023_SEP_MASS, dtype=float) + self.sep_mu_au = np.array(OFFNER2023_SEP_MU_AU, dtype=float) + self.sep_sig_mass = np.array(OFFNER2023_SEP_SIG_MASS, dtype=float) + self.sep_sig = np.array(OFFNER2023_SEP_SIG, dtype=float) + + def log_semimajoraxis(self, mass): + """ + Draw log10(a/AU) from a mass-dependent truncated lognormal. + Parameters ---------- - x : float or array_like - Random number between 0 and 1. - - y : float or array_like - Random number between 0 and 1. - - z : float or array_like - Random number between 0 and 1. + mass : array-like + Primary mass (Msun). Returns ------- - inclination : float or array_like - Angle of inclination - - Omega : float or array_like - Big Omega: one other angle of the system - - omega : float or array_like - Final angle of the system + log_semimajoraxis : ndarray + log10 of the semimajor axis in AU, truncated to 0.01–2000 AU. """ - sign = np.array([choice([-1,1]) for i in range(len(x))]) - x = sign*x - inclination = np.arccos(x)*180/np.pi #inclination angle in degrees - - Omega = 360*y - omega = 360*z - - return inclination, Omega, omega + mass = np.atleast_1d(np.asarray(mass, dtype=float)) + mass_clip = np.clip(mass, self.sep_mass[0], self.sep_mass[-1]) + logm = np.log10(mass_clip) + log_a_mean = np.interp(logm, np.log10(self.sep_mass), + np.log10(self.sep_mu_au)) + log_a_std = np.interp(logm, np.log10(self.sep_sig_mass), self.sep_sig) + log_a_std = np.clip(log_a_std, 0.1, None) + + log_a_lower = np.log10(0.01) + log_a_upper = np.log10(2000) + a_lower_std = (log_a_lower - log_a_mean) / log_a_std + a_upper_std = (log_a_upper - log_a_mean) / log_a_std + return truncnorm.rvs(a_lower_std, a_upper_std, + loc=log_a_mean, scale=log_a_std) + + +# Convenience alias; unresolved Table 1 model is the usual opt-in object. +MultiplicityOffner2023 = MultiplicityUnresolvedOffner2023 diff --git a/spisea/synthetic.py b/spisea/synthetic.py index 0fe624a..312c65d 100755 --- a/spisea/synthetic.py +++ b/spisea/synthetic.py @@ -532,7 +532,7 @@ def _make_companions_table_initial(self, star_systems, compMass): companions = Table([system_index], names=['system_idx']) companions.add_column(np.zeros(N_comp_tot, dtype=float), name='mass') - if isinstance(self.imf._multi_props, multiplicity.MultiplicityResolvedDK): + if hasattr(self.imf._multi_props, 'log_semimajoraxis'): companions.add_column(Column(self.imf._multi_props.log_semimajoraxis(star_systems['mass'][companions['system_idx']]), name='log_a')) companions.add_column(Column(self.imf._multi_props.random_e(self.rng.random(N_comp_tot)), name='e')) companions['i'], companions['Omega'], companions['omega'] = self.imf._multi_props.random_keplarian_parameters( diff --git a/spisea/tests/test_multiplicity.py b/spisea/tests/test_multiplicity.py index 5322665..c8038de 100755 --- a/spisea/tests/test_multiplicity.py +++ b/spisea/tests/test_multiplicity.py @@ -243,3 +243,189 @@ def test_resolvedmult(): f"BD sigma log(a) off: {std_log_a:.2f}" return + + +# --------------------------------------------------------------------------- +# Offner et al. 2023 (Table 1) multiplicity +# --------------------------------------------------------------------------- + +# Published Table 1 MF (%) converted to fraction, CF, and 1-sigma MF error. +# Masses are geometric means of the tabulated M1 intervals. +_OFFNER_TABLE1 = [ + # name, M_lo, M_hi, MF, MF_err, CF + ('Fontanive+2018', 0.019, 0.058, 0.08, 0.06, 0.08), + ('Burgasser 2007', 0.05, 0.08, 0.15, 0.04, 0.16), + ('Close+2003', 0.080, 0.095, 0.19, 0.07, 0.19), + ('Allen+2007', 0.06, 0.15, 0.20, 0.04, 0.20), + ('Winters+2019 late-M', 0.075, 0.15, 0.19, 0.03, 0.21), + ('Winters+2019 mid-M', 0.15, 0.30, 0.23, 0.02, 0.27), + ('Winters+2019 early-M', 0.3, 0.6, 0.30, 0.02, 0.38), + ('Raghavan+2010', 0.75, 1.25, 0.46, 0.03, 0.60), + ('Tokovinin 2014b', 0.85, 1.5, 0.47, 0.03, 0.62), + ('Moe & Kratter 2021', 1.6, 2.4, 0.68, 0.07, 0.99), + ('Moe & Di Stefano 2017 3-5', 3.0, 5.0, 0.81, 0.06, 1.28), + ('Moe & Di Stefano 2017 5-8', 5.0, 8.0, 0.89, 0.05, 1.55), + ('Moe & Di Stefano 2017 8-17', 8.0, 17.0, 0.93, 0.04, 1.80), + ('Sana et al. 17-50', 17.0, 50.0, 0.96, 0.04, 2.10), +] + + +def _table1_mgeom(row): + return np.sqrt(row[1] * row[2]) + + +def test_piecewise_powerlaw_api(): + """Custom piecewise MF/CSF is vectorized and clips MF to [0, 1].""" + mass_limits = np.array([0.1, 1.0, 10.0]) + # First segment: MF = 0.4 * M^0 → 0.4; second: 0.4 * M^1 so MF(10)=4 → clip 1 + mp = multiplicity.MultiplicityPiecewisePowerLaw( + mass_limits, + MF_amps=[0.4, 0.4], MF_powers=[0.0, 1.0], + CSF_amps=[0.4, 0.5], CSF_powers=[0.0, 0.5], + binary_only_mass_max=0.05) + assert mp.multiplicity_fraction(0.2) == 0.4 + assert mp.multiplicity_fraction(1.0) == 0.4 + np.testing.assert_almost_equal(mp.multiplicity_fraction(10.0), 1.0) + masses = np.array([0.2, 1.0, 10.0]) + mf = mp.multiplicity_fraction(masses) + np.testing.assert_allclose(mf, [mp.multiplicity_fraction(m) for m in masses]) + + +def test_offner2023_table1_mf(): + """ + Piecewise MF matches Offner et al. 2023 Table 1 at geom-mean M1. + Tolerance is max(0.04, 1.5 * tabulated 1-sigma), preferring Table 1 + over continuity at segment breaks. + """ + multi = multiplicity.MultiplicityUnresolvedOffner2023() + for row in _OFFNER_TABLE1: + name, mlo, mhi, mf_tab, mf_err, cf_tab = row + m = _table1_mgeom(row) + mf = multi.multiplicity_fraction(m) + tol = max(0.04, 1.5 * mf_err) + assert abs(mf - mf_tab) <= tol, \ + '{0}: MF({1:.3f})={2:.3f} vs Table 1 {3:.2f} ± {4:.2f}'.format( + name, m, mf, mf_tab, mf_err) + assert 0.0 <= mf <= 1.0 + + +def test_offner2023_table1_csf(): + """CSF matches Table 1 CF for stellar primaries; CSF = MF for BDs.""" + multi = multiplicity.MultiplicityUnresolvedOffner2023() + for row in _OFFNER_TABLE1: + name, mlo, mhi, mf_tab, mf_err, cf_tab = row + m = _table1_mgeom(row) + csf = multi.companion_star_fraction(m) + mf = multi.multiplicity_fraction(m) + if m <= multiplicity.H_BURNING_MASS: + assert np.isclose(csf, mf, atol=1e-12), \ + '{0}: BD CSF should equal MF'.format(name) + else: + tol = max(0.05, 0.2 * cf_tab) + assert abs(csf - cf_tab) <= tol, \ + '{0}: CSF({1:.3f})={2:.3f} vs Table 1 CF {3:.2f}'.format( + name, m, csf, cf_tab) + assert csf >= mf - 1e-12 + assert csf <= multi.CSF_max + 1e-12 + + +def test_offner2023_array_vs_scalar(): + """Array and scalar MF/CSF evaluations agree.""" + multi = multiplicity.MultiplicityUnresolvedOffner2023() + masses = np.array([_table1_mgeom(row) for row in _OFFNER_TABLE1]) + mf_arr = multi.multiplicity_fraction(masses) + csf_arr = multi.companion_star_fraction(masses) + for i, m in enumerate(masses): + np.testing.assert_allclose(mf_arr[i], multi.multiplicity_fraction(float(m))) + np.testing.assert_allclose(csf_arr[i], multi.companion_star_fraction(float(m))) + + +def test_offner2023_bd_binaries_only(): + """BD primaries have CSF = MF and companion counts of 0 or 1.""" + multi = multiplicity.MultiplicityUnresolvedOffner2023() + rng = np.random.default_rng(123) + masses = np.array([0.02, 0.04, 0.07, 0.08]) + mf = multi.multiplicity_fraction(masses) + csf = multi.companion_star_fraction(masses) + np.testing.assert_allclose(csf, mf) + # Force multiples so we test the count draw, not the MF coin flip. + n_comp = multi.draw_n_companions(masses, csf, mf, rng) + assert np.all(n_comp <= 1) + assert np.all(n_comp >= 1) + + # Full companion-mass assignment: never more than one companion column + is_mult = np.ones(len(masses), dtype=bool) + comp, sys_mass, is_mult_out = multi.draw_companion_masses( + masses, is_mult, csf, mf, rng, mass_min=0.01) + assert comp.shape[1] == 1 + assert np.all(np.sum(~comp.mask, axis=1) <= 1) + + +def test_offner2023_q_more_equal_mass_for_bds(): + """BD mass ratios are more equal-mass (higher mean q) than solar-type.""" + multi = multiplicity.MultiplicityUnresolvedOffner2023() + rng = np.random.default_rng(7) + n = 20000 + q_bd = multi.random_q(rng.random(n), mass=0.04) + q_sun = multi.random_q(rng.random(n), mass=1.0) + assert np.mean(q_bd) > np.mean(q_sun) + 0.1 + # Fontanive gamma_trunc = 4.8 is steeply equal-mass + assert multi.q_power_at_mass(0.033) > 3.0 + assert multi.q_power_at_mass(1.0) < 1.0 + + +def test_offner2023_bd_separations_peak_few_au(): + """BD lognormal separations peak at a few AU (Table 1 ã_all ~ 3 au).""" + multi = multiplicity.MultiplicityResolvedOffner2023() + np.random.seed(0) + log_a = multi.log_semimajoraxis(np.full(5000, 0.04)) + med_a = 10 ** np.median(log_a) + # Fontanive ã_all = 2.9 au; allow a factor of ~2 + assert 1.5 < med_a < 8.0, 'BD median a = {0:.2f} AU'.format(med_a) + # Solar-type should be much wider (Table 2 μ = 40 au) + log_a_s = multi.log_semimajoraxis(np.full(5000, 1.0)) + med_a_s = 10 ** np.median(log_a_s) + assert med_a_s > 10.0 + assert med_a_s > med_a + + +def test_offner2023_alias_and_resolved_methods(): + """Public names and resolved orbital methods exist.""" + assert multiplicity.MultiplicityOffner2023 is \ + multiplicity.MultiplicityUnresolvedOffner2023 + resolved = multiplicity.MultiplicityResolvedOffner2023() + assert hasattr(resolved, 'log_semimajoraxis') + e = resolved.random_e(np.array([0.0, 0.25, 1.0])) + np.testing.assert_allclose(e, [0.0, 0.5, 1.0]) + + +def test_lu2013_defaults_unchanged(): + """Lu et al. 2013 MultiplicityUnresolved defaults and stellar MF unchanged.""" + mu = multiplicity.MultiplicityUnresolved() + assert mu.MF_amp == 0.44 + assert mu.MF_pow == 0.51 + assert mu.CSF_amp == 0.50 + assert mu.CSF_pow == 0.45 + np.testing.assert_almost_equal(mu.multiplicity_fraction(1.0), 0.44, decimal=2) + np.testing.assert_almost_equal(mu.multiplicity_fraction(10.0), 1.0, decimal=2) + np.testing.assert_almost_equal(mu.multiplicity_fraction(0.1), 0.136, decimal=2) + # Scalar BD overrides (historical Lu+2013 / Fontanive path) + assert np.isclose(mu.multiplicity_fraction(0.07), 0.16, atol=0.01) + assert np.isclose(mu.multiplicity_fraction(0.04), 0.08, atol=0.01) + assert np.isclose(mu.multiplicity_fraction(0.01), 0.0, atol=1e-6) + + +def test_offner_generate_cluster_companions(): + """IMF cluster generation with Offner multiplicity produces BD binaries only.""" + imf_multi = multiplicity.MultiplicityUnresolvedOffner2023() + mass_limits = np.array([0.01, 0.08, 0.5, 120.0]) + powers = np.array([-0.3, -1.3, -2.3]) + my_imf = imf.IMF_broken_powerlaw(mass_limits, powers, imf_multi) + my_imf.rng = np.random.default_rng(42) + mass, is_multi, comp_mass, sys_mass = my_imf.generate_cluster(500.0) + bd = mass <= 0.08 + n_comp = np.sum(~comp_mass.mask, axis=1) + assert np.all(n_comp[bd] <= 1) + assert np.any(is_multi) + assert np.abs(500.0 - sys_mass.sum()) < 500.0 * 0.05 + From b5c7a5ae7e0b76010527cf6e9f3b4eacbadcdc43 Mon Sep 17 00:00:00 2001 From: Cursor Agent Date: Thu, 13 Aug 2026 16:38:36 +0000 Subject: [PATCH 02/16] Wire Offner BD q and companion counts through the Multiplicity API MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit calc_multi now only delegates to the multiplicity object. random_q is mass-aware so Offner γ_trunc applies to BD primaries instead of the hardcoded Fontanive 6.1. random_companion_count owns the BD binaries-only cap. synthetic.py duck-types resolved orbits on log_semimajoraxis, random_e, and random_keplarian_parameters. Docs and IMF tests updated. Co-authored-by: Jessica Lu --- docs/multiplicity.rst | 34 +++++++++++-- spisea/imf/multiplicity.py | 79 +++++++++++++++++++------------ spisea/synthetic.py | 13 +++-- spisea/tests/test_imf.py | 36 ++++++++++++++ spisea/tests/test_multiplicity.py | 54 +++++++++++++++++++++ 5 files changed, 178 insertions(+), 38 deletions(-) diff --git a/docs/multiplicity.rst b/docs/multiplicity.rst index c96512d..8dd6a1a 100644 --- a/docs/multiplicity.rst +++ b/docs/multiplicity.rst @@ -7,10 +7,36 @@ The properties of multiple systems in the stellar population is defined by the stellar multiplicity object. The multiplicity classes are defined in ``spisea/imf/multiplicity.py``. -To call a multiplicity class:: - - from spisea.imf import multiplicity - multi_obj = multiplicity. +To call a multiplicity class and wire it into a cluster:: + + from spisea.imf import imf, multiplicity + from spisea import synthetic + + multi = multiplicity.(...) + imf_obj = imf.Kroupa_2001(multiplicity=multi) + cluster = synthetic.ResolvedCluster(iso, imf_obj, Mcl) + +Companion masses and whether a primary is multiple are drawn in +``IMF.generate_cluster`` / ``IMF.calc_multi``, which call the multiplicity +object. ``synthetic.py`` does not draw companions: it labels brown-dwarf +evolutionary phase=90 so they photometrize, combines system photometry, +and (for resolved classes) fills orbital columns. + +Duck-typed multiplicity contract used by the IMF: + +* ``multiplicity_fraction(mass)`` +* ``companion_star_fraction(mass)`` +* ``random_q(x, mass=None)`` — pass ``mass`` for mass-dependent q + (brown-dwarf vs stellar). ``random_q(x)`` with no mass keeps the + historical stellar-only power law. +* ``random_companion_count(x, CSF, MF, mass=None, rng=None)`` — + companion-count policy, including the binaries-only BD cap when + ``mass`` is given. +* attributes ``companion_max``, ``CSF_max``, ``q_min`` + +Resolved classes are duck-typed in ``synthetic.py`` on +``log_semimajoraxis``, ``random_e``, and ``random_keplarian_parameters``. +They do not need to subclass :class:`~imf.multiplicity.MultiplicityResolvedDK`. The multiplicity object is an input for the :ref:`imf_objects`, as it impacts how the stellar masses are drawn. diff --git a/spisea/imf/multiplicity.py b/spisea/imf/multiplicity.py index 9cf8656..f183e5e 100755 --- a/spisea/imf/multiplicity.py +++ b/spisea/imf/multiplicity.py @@ -376,50 +376,69 @@ def random_is_multiple(self, x, MF): """ return x < MF - def random_companion_count(self, x, CSF, MF): + def random_companion_count(self, x, CSF, MF, mass=None, rng=None): """ - Helper function: calculate number of companions. - """ - # bd stipulation since mf=0 - if MF <= 0: - return 0 - - n_comp = 1 + np.random.poisson((CSF / MF) - 1) - - if self.companion_max == True: - if n_comp > self.CSF_max: - n_comp = self.CSF_max - - return n_comp + Number of companions for primaries already identified as multiple. - def draw_n_companions(self, mass, CSF, MF, rng): - """ - Vectorized companion counts for primaries that are already - identified as multiple. + The count is drawn from a Poisson with expectation CSF/MF - 1, + then 1 is added so every multiple has at least one companion. + ``x`` is unused and kept for API compatibility. Parameters ---------- - mass, CSF, MF : array_like - Primary masses and corresponding CSF and MF values. - rng : numpy.random.Generator - Random generator used for the Poisson draw. + x : float or array_like + Unused (historical signature). + CSF, MF : float or array_like + Companion star fraction and multiplicity fraction. + mass : float or array_like, optional + Primary mass. If given, primaries at or below + ``binary_only_mass_max`` are limited to one companion. + Cluster generation always passes mass so subclasses can + override the BD companion-count policy here. + rng : numpy.random.Generator, optional + Random generator. If omitted, uses ``numpy.random`` (the + historical scalar helper). Returns ------- - n_comp : ndarray of int - Number of companions for each multiple primary. Brown-dwarf - primaries are limited to one companion. - """ - mass = np.atleast_1d(np.asarray(mass, dtype=float)) + n_comp : int or ndarray of int + """ + return_scalar = np.isscalar(CSF) and np.isscalar(MF) + if return_scalar and rng is None: + if MF <= 0: + return 0 + n_comp = 1 + np.random.poisson((CSF / MF) - 1) + if self.companion_max and n_comp > self.CSF_max: + n_comp = self.CSF_max + if mass is not None and np.asarray(mass, dtype=float).reshape(-1)[0] <= self.binary_only_mass_max: + n_comp = min(int(n_comp), 1) + return int(n_comp) + CSF = np.atleast_1d(np.asarray(CSF, dtype=float)) MF = np.atleast_1d(np.asarray(MF, dtype=float)) - n_comp = 1 + rng.poisson((CSF / MF) - 1) + if rng is None: + n_comp = 1 + np.random.poisson((CSF / MF) - 1) + else: + n_comp = 1 + rng.poisson((CSF / MF) - 1) if self.companion_max: n_comp = np.minimum(n_comp, self.CSF_max) - bd = mass <= self.binary_only_mass_max - n_comp[bd & (n_comp > 1)] = 1 + if mass is not None: + mass = np.atleast_1d(np.asarray(mass, dtype=float)) + bd = mass <= self.binary_only_mass_max + n_comp[bd & (n_comp > 1)] = 1 + if return_scalar: + return int(n_comp[0]) return n_comp + def draw_n_companions(self, mass, CSF, MF, rng): + """ + Vectorized companion counts for primaries that are already + identified as multiple. Delegates to :meth:`random_companion_count` + with ``mass`` so BD companion-count policy lives on this object. + """ + return np.atleast_1d( + self.random_companion_count(None, CSF, MF, mass=mass, rng=rng)) + def _q_values_for_primaries(self, prim_subset, n_comp, rng): """ Draw mass ratios for ``n_comp`` companions of each primary. diff --git a/spisea/synthetic.py b/spisea/synthetic.py index 312c65d..bc80be5 100755 --- a/spisea/synthetic.py +++ b/spisea/synthetic.py @@ -532,10 +532,15 @@ def _make_companions_table_initial(self, star_systems, compMass): companions = Table([system_index], names=['system_idx']) companions.add_column(np.zeros(N_comp_tot, dtype=float), name='mass') - if hasattr(self.imf._multi_props, 'log_semimajoraxis'): - companions.add_column(Column(self.imf._multi_props.log_semimajoraxis(star_systems['mass'][companions['system_idx']]), name='log_a')) - companions.add_column(Column(self.imf._multi_props.random_e(self.rng.random(N_comp_tot)), name='e')) - companions['i'], companions['Omega'], companions['omega'] = self.imf._multi_props.random_keplarian_parameters( + # Duck-type resolved multiplicity: any object with orbital methods + # gets log_a / e / angles, not only MultiplicityResolvedDK. + multi_props = self.imf._multi_props + if (hasattr(multi_props, 'log_semimajoraxis') and + hasattr(multi_props, 'random_e') and + hasattr(multi_props, 'random_keplarian_parameters')): + companions.add_column(Column(multi_props.log_semimajoraxis(star_systems['mass'][companions['system_idx']]), name='log_a')) + companions.add_column(Column(multi_props.random_e(self.rng.random(N_comp_tot)), name='e')) + companions['i'], companions['Omega'], companions['omega'] = multi_props.random_keplarian_parameters( self.rng.random(N_comp_tot), self.rng.random(N_comp_tot), self.rng.random(N_comp_tot) diff --git a/spisea/tests/test_imf.py b/spisea/tests/test_imf.py index 943dc0a..3f90716 100755 --- a/spisea/tests/test_imf.py +++ b/spisea/tests/test_imf.py @@ -30,6 +30,42 @@ def test_generate_cluster(): return + +def test_generate_cluster_offner2023(): + """ + generate_cluster with Offner et al. 2023 multiplicity: vectorized MF, + BD primaries have at most one companion, and Offner q (not Fontanive + gamma=6.1) is used for BD companion masses. + """ + imf_multi = multiplicity.MultiplicityUnresolvedOffner2023() + massLimits = np.array([0.01, 0.05, 0.22, 0.55, 8, 120]) + powers = np.array([-0.6, -0.25, -1.3, -2.3, -2.35]) + my_imf = imf.IMF_broken_powerlaw(massLimits, powers, imf_multi) + my_imf.rng = np.random.default_rng(7) + + M_cl = 2e3 + mass, isMulti, compMass, sysMass = my_imf.generate_cluster(M_cl) + + assert np.abs(M_cl - sysMass.sum()) < M_cl * 0.05 + n_comp = np.sum(~compMass.mask, axis=1) + bd = mass <= 0.08 + assert np.all(n_comp[bd] <= 1) + assert np.any(isMulti) + + # BD companions should be more equal-mass than Lu+2013 stellar q_power=-0.4 + bd_mult = bd & isMulti + if np.any(bd_mult): + q_bd = [] + for i in np.where(bd_mult)[0]: + comps = compMass[i].compressed() + if len(comps): + q_bd.extend(list(comps / mass[i])) + if len(q_bd) >= 5: + assert np.mean(q_bd) > 0.5 + + return + + def test_prim_power(): #mass_limits = np.array([0.1, 1.0, 100.0]) #powers = np.array([-2.0, -1.8]) diff --git a/spisea/tests/test_multiplicity.py b/spisea/tests/test_multiplicity.py index c8038de..9e2d8c3 100755 --- a/spisea/tests/test_multiplicity.py +++ b/spisea/tests/test_multiplicity.py @@ -1,5 +1,6 @@ import numpy as np import time +import os import spisea from spisea.imf import imf, multiplicity @@ -429,3 +430,56 @@ def test_offner_generate_cluster_companions(): assert np.any(is_multi) assert np.abs(500.0 - sys_mass.sum()) < 500.0 * 0.05 + +def test_calc_multi_uses_multiplicity_q_and_counts(): + """ + IMF.calc_multi must not hardcode Fontanive gamma=6.1 or the BD + companion cap; those policies live on the multiplicity object so + Offner γ_trunc (~2–5 for BDs) actually applies. + """ + import inspect + from spisea.imf import imf as imf_mod + calc_src = inspect.getsource(imf_mod.IMF.calc_multi) + assert '6.1' not in calc_src + assert 'draw_companion_masses' in calc_src + + syn_path = os.path.join(os.path.dirname(spisea.__file__), 'synthetic.py') + with open(syn_path, 'r') as fh: + syn_src = fh.read() + assert 'isinstance(self.imf._multi_props, multiplicity.MultiplicityResolvedDK)' not in syn_src + assert "hasattr(multi_props, 'log_semimajoraxis')" in syn_src + assert "hasattr(multi_props, 'random_e')" in syn_src + assert "hasattr(multi_props, 'random_keplarian_parameters')" in syn_src + + offner = multiplicity.MultiplicityUnresolvedOffner2023() + lu = multiplicity.MultiplicityUnresolved() + q_off = offner.q_power_at_mass(0.04) + q_lu = lu.q_power_at_mass(0.04) + assert 2.0 <= q_off <= 5.5 + assert np.isclose(q_lu, 6.1) + assert q_off != q_lu + + rng = np.random.default_rng(1) + masses = np.full(3000, 0.04) + is_mult = np.ones(len(masses), dtype=bool) + mf = offner.multiplicity_fraction(masses) + csf = offner.companion_star_fraction(masses) + comp, _, _ = offner.draw_companion_masses( + masses, is_mult, csf, mf, rng, mass_min=0.01) + q = comp.compressed() / 0.04 + q_lu_draw = lu.random_q(np.random.default_rng(1).random(len(q)), mass=0.04) + # Offner BD gamma is shallower than Fontanive 6.1, so mean q is lower. + assert np.mean(q) < np.mean(q_lu_draw) + + +def test_piecewise_mf_is_vectorized(): + """Offner MF is vectorized; Lu+2013 scalar BD bins are not used here.""" + multi = multiplicity.MultiplicityUnresolvedOffner2023() + masses = np.array([0.03, 0.06, 0.10, 1.0]) + mf = multi.multiplicity_fraction(masses) + for i, m in enumerate(masses): + np.testing.assert_allclose(mf[i], multi.multiplicity_fraction(float(m))) + # Array path is not the Lu stellar power law 0.44 * M**0.51 + lu_pl = 0.44 * masses ** 0.51 + assert not np.allclose(mf, np.clip(lu_pl, 0, 1), atol=0.02) + From 7b4ab35b62f3cc64020c8fd6c1a6bc00f8bcf353 Mon Sep 17 00:00:00 2001 From: Cursor Agent Date: Thu, 13 Aug 2026 16:50:27 +0000 Subject: [PATCH 03/16] Use a continuous 3-segment Offner MF/CSF and add comparison figure Replace the discontinuous 8-segment two-point Table 1 fit with a 3-segment broken power law continuous at 0.08 and 1.5 Msun. Add a two-panel MF vs mass figure (Lu+2013 vs Offner vs Table 1) to the docs and PR. 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zyVTa-iQT?^9qwE4U?}8&^WSJ^7H5uf?`xS{bBR8lH9}HkDF$ z9{J4Oh)(#DxTWY@L&J4rbV4?5nsEMnO()$G$@boI*9LkOkGHhQJ#gU3F13hr4SX9& z_%9rXZPjK3ZonZ@?dav9sBSxYlst#yNv&1WHH=!tm9>4~zyB->(fU=t?c4tQpZ|lG m@_+u|{|DC2|NZ5BQ8)jozwY%ZXa7?0$H{)exC~pLwf_a-4umiO literal 0 HcmV?d00001 diff --git a/docs/figures/plot_mf_offner_vs_lu2013.py b/docs/figures/plot_mf_offner_vs_lu2013.py new file mode 100644 index 0000000..e31c250 --- /dev/null +++ b/docs/figures/plot_mf_offner_vs_lu2013.py @@ -0,0 +1,149 @@ +#!/usr/bin/env python +""" +Generate docs/figures/mf_offner_vs_lu2013.png + +Two-panel comparison of multiplicity fraction vs primary mass: +Lu et al. (2013) array power law, Lu+2013 scalar BD staircase, +Offner et al. 2023 3-segment continuous broken power law, and +Offner Table 1 points with error bars. + +Run from the repository root:: + + python docs/figures/plot_mf_offner_vs_lu2013.py +""" +import os +import sys + +import numpy as np +import matplotlib.pyplot as plt +from matplotlib.patches import Patch +from matplotlib.lines import Line2D + +# Allow running without installing the package. +_REPO_ROOT = os.path.abspath(os.path.join(os.path.dirname(__file__), '..', '..')) +if _REPO_ROOT not in sys.path: + sys.path.insert(0, _REPO_ROOT) + +from spisea.imf import multiplicity + + +# Offner et al. 2023 Table 1: (M_lo, M_hi, MF, MF_err) +_TABLE1 = [ + (0.019, 0.058, 0.08, 0.06), + (0.05, 0.08, 0.15, 0.04), + (0.080, 0.095, 0.19, 0.07), + (0.06, 0.15, 0.20, 0.04), + (0.075, 0.15, 0.19, 0.03), + (0.15, 0.30, 0.23, 0.02), + (0.3, 0.6, 0.30, 0.02), + (0.75, 1.25, 0.46, 0.03), + (0.85, 1.5, 0.47, 0.03), + (1.6, 2.4, 0.68, 0.07), + (3.0, 5.0, 0.81, 0.06), + (5.0, 8.0, 0.89, 0.05), + (8.0, 17.0, 0.93, 0.04), + (17.0, 50.0, 0.96, 0.04), +] + + +def _lu2013_array_mf(mass): + """What cluster generation used: stellar power law, no BD staircase.""" + mf = 0.44 * np.asarray(mass, dtype=float) ** 0.51 + return np.clip(mf, 0.0, 1.0) + + +def _lu2013_scalar_bd_staircase(mass): + """Scalar-only BD bins in MultiplicityUnresolved.multiplicity_fraction.""" + mass = np.asarray(mass, dtype=float) + mf = _lu2013_array_mf(mass) + mf = np.where(mass < 0.02, 0.0, mf) + mf = np.where((mass > 0.02) & (mass <= 0.06), 0.08, mf) + mf = np.where((mass > 0.06) & (mass <= 0.08), 0.16, mf) + return mf + + +def _table1_xy(): + m = np.array([np.sqrt(lo * hi) for lo, hi, _, _ in _TABLE1]) + mf = np.array([row[2] for row in _TABLE1]) + err = np.array([row[3] for row in _TABLE1]) + return m, mf, err + + +def _style_panel(ax, m_off, mf_off, m_lu, mf_lu, m_step, mf_step, + m_tab, mf_tab, err_tab, xlim, ylim, title, show_a_break=False): + ax.axvspan(xlim[0], 0.08, color='#e8d5b5', alpha=0.55, zorder=0) + ax.axvline(0.08, color='#c4a574', ls='--', lw=1.2, zorder=1) + if show_a_break: + ax.axvline(1.5, color='0.5', ls=':', lw=1.1, zorder=1) + ax.plot(m_lu, mf_lu, color='0.25', ls='--', lw=1.6, zorder=3, + label=r'Lu+2013 power law $0.44\,M^{0.51}$') + ax.plot(m_step, mf_step, color='0.45', ls=':', lw=1.8, zorder=3, + label=r'Lu+2013 scalar BD bins (0 / 8% / 16%)') + ax.plot(m_off, mf_off, color='#8b3a2a', ls='-', lw=2.4, zorder=4, + label='Offner 3-seg continuous') + ax.errorbar(m_tab, mf_tab, yerr=err_tab, fmt='o', color='#2f6db3', + ms=5.5, mfc='white', mew=1.3, elinewidth=1.1, capsize=2.5, + zorder=5, label='Offner Table 1') + ax.set_xscale('log') + ax.set_xlim(*xlim) + ax.set_ylim(*ylim) + ax.set_title(title, fontsize=11) + ax.set_xlabel(r'Primary mass $M_1$ ($M_\odot$)') + ax.set_ylabel('Multiplicity fraction') + ax.tick_params(which='both', direction='in', top=True, right=True) + + +def main(): + offner = multiplicity.MultiplicityUnresolvedOffner2023() + + m_wide = np.logspace(np.log10(0.012), np.log10(40.0), 800) + mf_off = offner.multiplicity_fraction(m_wide) + mf_lu = _lu2013_array_mf(m_wide) + + # Staircase sampled densely so the steps render as vertical jumps. + m_step = np.concatenate([ + np.array([0.012, 0.01999, 0.02001, 0.05999, 0.06001, 0.07999, 0.08001]), + np.logspace(np.log10(0.081), np.log10(40.0), 200), + ]) + mf_step = _lu2013_scalar_bd_staircase(m_step) + + m_tab, mf_tab, err_tab = _table1_xy() + + fig, axes = plt.subplots(1, 2, figsize=(11.2, 4.6), + gridspec_kw={'wspace': 0.28}) + fig.suptitle('Multiplicity fraction vs primary mass', fontsize=13, y=1.02) + + _style_panel( + axes[0], m_wide, mf_off, m_wide, mf_lu, m_step, mf_step, + m_tab, mf_tab, err_tab, + xlim=(0.012, 0.20), ylim=(0.0, 0.45), + title='Brown-dwarf regime', show_a_break=False) + _style_panel( + axes[1], m_wide, mf_off, m_wide, mf_lu, m_step, mf_step, + m_tab, mf_tab, err_tab, + xlim=(0.015, 20.0), ylim=(0.0, 1.0), + title='BD through early B', show_a_break=True) + + legend_handles = [ + Line2D([0], [0], color='0.25', ls='--', lw=1.6, + label=r'Lu+2013 power law $0.44\,M^{0.51}$'), + Line2D([0], [0], color='0.45', ls=':', lw=1.8, + label=r'Lu+2013 scalar BD bins (0 / 8% / 16%)'), + Line2D([0], [0], color='#8b3a2a', ls='-', lw=2.4, + label='Offner 3-seg continuous'), + Line2D([0], [0], marker='o', color='#2f6db3', ls='none', + mfc='white', mew=1.3, ms=6, label='Offner Table 1'), + Patch(facecolor='#e8d5b5', edgecolor='none', alpha=0.8, + label=r'BD ($M\leq 0.08$)'), + ] + axes[0].legend(handles=legend_handles, loc='upper left', fontsize=8, + frameon=True, fancybox=False, edgecolor='0.7') + + out = os.path.join(os.path.dirname(__file__), 'mf_offner_vs_lu2013.png') + fig.savefig(out, dpi=160, bbox_inches='tight', facecolor='white') + plt.close(fig) + print('Wrote', out) + + +if __name__ == '__main__': + main() diff --git a/docs/index.rst b/docs/index.rst index f4fda76..e7e0881 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -97,7 +97,7 @@ Change Log * New tutorial for creating SPISEA clusters using COSMIC: docs/Cluster_w_COSMIC.ipynb * *Minor Changes* - * Added opt-in Offner et al. 2023 (Protostars and Planets VII; arXiv:2203.10066) multiplicity model, including brown dwarfs, as piecewise power-law fits to Table 1 MF/CF. See :ref:`multi_obj`. Lu et al. (2013) remains the default. + * Added opt-in Offner et al. 2023 (Protostars and Planets VII; arXiv:2203.10066) multiplicity model, including brown dwarfs, as a 3-segment continuous broken power-law fit to Table 1 MF/CF. See :ref:`multi_obj`. Lu et al. (2013) remains the default. * Companion mass and separation draws (including brown-dwarf q and binaries-only BD systems) now live on the multiplicity object rather than being special-cased in ``imf.py``. * The MISTv1.2-synthpop model extension was modified to include denser sampling in the gap between the base MISTv1.2 grids and 0.1Msun. * Modified default for MISTv1.2 isochrones: synthpop_extension will be True by default to keep a consistent lower mass limit of 0.1Msun across all ages and metallicities. diff --git a/docs/multiplicity.rst b/docs/multiplicity.rst index 8dd6a1a..cd0353e 100644 --- a/docs/multiplicity.rst +++ b/docs/multiplicity.rst @@ -78,10 +78,27 @@ Unresolved Multiplicity Classes The Lu et al. (2013) :class:`~imf.multiplicity.MultiplicityUnresolved` object remains the default. Offner et al. 2023 is **opt-in**:: - from spisea.imf import multiplicity + from spisea.imf import imf, multiplicity + from spisea import synthetic + multi = multiplicity.MultiplicityUnresolvedOffner2023() # or the alias: - multi = multiplicity.MultiplicityOffner2023() + # multi = multiplicity.MultiplicityOffner2023() + imf_obj = imf.Kroupa_2001(multiplicity=multi) + cluster = synthetic.ResolvedCluster(iso, imf_obj, Mcl) + +MF vs primary mass (Lu et al. 2013 array power law and scalar BD staircase +compared to the Offner 3-segment continuous fit and Table 1 points): + +.. figure:: figures/mf_offner_vs_lu2013.png + :alt: Multiplicity fraction vs primary mass: Lu+2013 vs Offner 2023 3-segment fit + :align: center + + Left: brown-dwarf zoom. Right: BD through early B. The Offner model is a + 3-segment broken power law, continuous at 0.08 and 1.5 solar masses. + Reproduce with ``python docs/figures/plot_mf_offner_vs_lu2013.py``. + +The figure generator lives at ``docs/figures/plot_mf_offner_vs_lu2013.py``. Resolved Multiplicity Classes diff --git a/spisea/imf/multiplicity.py b/spisea/imf/multiplicity.py index f183e5e..e8261f9 100755 --- a/spisea/imf/multiplicity.py +++ b/spisea/imf/multiplicity.py @@ -622,86 +622,43 @@ def _offner2023_table1_geom_mass(m_lo, m_hi): return float(np.sqrt(m_lo * m_hi)) +# Continuous 3-segment log-log hinge fit to Offner et al. 2023 Table 1 +# geom-mean (M, MF) and (M, CF) points. Breaks are the hydrogen-burning +# limit (0.08 Msun) and the A-star / Moe & Kratter hinge (1.5 Msun). +# Coefficients are continuous at the breaks by construction; they are +# not eight independent two-point fits. +OFFNER2023_MASS_LIMITS = [0.01, 0.08, 1.5, 150.0] +OFFNER2023_MF_AMPS = [0.940619495052258, 0.4939448419460535, 0.5464564161230251] +OFFNER2023_MF_POWERS = [0.7014961249619823, 0.4464747306561399, 0.19730236903196635] +OFFNER2023_CSF_AMPS = [1.3416791790176827, 0.6412345384212704, 0.6783208088050923] +OFFNER2023_CSF_POWERS = [0.8082633998914766, 0.5159588626601461, 0.3772908005624459] + + def offner2023_default_segments(): """ - Piecewise MF/CF power-law segments fitted to Offner et al. 2023 Table 1. + Three-segment broken power law for Offner et al. 2023 Table 1 MF/CF. + + Continuous at the hydrogen-burning limit (0.08 Msun) and the A-star / + Moe & Kratter break (1.5 Msun) by construction: a weighted log-log + hinge fit to Table 1 geometric-mean (M, MF) and (M, CF) points, + converted to per-segment y = A * M**alpha. This is not eight + independent two-point fits. - Each segment is the two-point power law through the geometric-mean - primary masses of the listed surveys. MF is clipped to [0, 1] at - evaluation time. Below the hydrogen-burning limit, CSF is forced - equal to MF (binaries only) regardless of the CF segment. + MF is clipped to [0, 1] at evaluation time. Below 0.08 Msun, CSF is + forced equal to MF (binaries only) regardless of the CF segment. Returns ------- mass_limits : ndarray - Segment edges (Msun), length N+1. + Segment edges (Msun), length 4. MF_amps, MF_powers, CSF_amps, CSF_powers : ndarray - Length-N piecewise coefficients for MF(M) = A * M**alpha - and CSF(M) = A * M**alpha. + Length-3 piecewise coefficients. """ - # Geometric-mean M1 of Table 1 mass bins (Offner et al. 2023, Table 1). - M_font = _offner2023_table1_geom_mass(0.019, 0.058) # Fontanive+2018 - M_burg = _offner2023_table1_geom_mass(0.05, 0.08) # Burgasser 2007 - M_close = _offner2023_table1_geom_mass(0.080, 0.095) # Close+2003 - M_wlate = _offner2023_table1_geom_mass(0.075, 0.15) # Winters+2019 late-M - M_wmid = _offner2023_table1_geom_mass(0.15, 0.30) # Winters+2019 mid-M - M_wearly = _offner2023_table1_geom_mass(0.3, 0.6) # Winters+2019 early-M - M_ragh = _offner2023_table1_geom_mass(0.75, 1.25) # Raghavan+2010 FGK - M_moe = _offner2023_table1_geom_mass(1.6, 2.4) # Moe & Kratter 2021 - M_mds35 = _offner2023_table1_geom_mass(3.0, 5.0) # Moe & Di Stefano 2017 - M_mds58 = _offner2023_table1_geom_mass(5.0, 8.0) - M_mds817 = _offner2023_table1_geom_mass(8.0, 17.0) - M_sana = _offner2023_table1_geom_mass(17.0, 50.0) # Sana et al. - - # Published Table 1 MF (fraction) and CF. MF values that were given - # as percents in the table are converted here. - mf_font, cf_font = 0.08, 0.08 - mf_burg, cf_burg = 0.15, 0.16 - mf_close, cf_close = 0.19, 0.19 - mf_wlate, cf_wlate = 0.19, 0.21 - mf_wmid, cf_wmid = 0.23, 0.27 - mf_wearly, cf_wearly = 0.30, 0.38 - mf_ragh, cf_ragh = 0.46, 0.60 - mf_moe, cf_moe = 0.68, 0.99 - mf_mds35, cf_mds35 = 0.81, 1.28 - mf_mds58, cf_mds58 = 0.89, 1.55 - mf_mds817, cf_mds817 = 0.93, 1.80 - mf_sana, cf_sana = 0.96, 2.10 - - # Mass edges follow BD / late-M / mid-M / FGK / A / B / O regimes - # in Offner et al. 2023 §2.2. Matching Table 1 is preferred over - # continuity at the breaks. - mass_limits = np.array([0.01, 0.05, 0.08, 0.15, 0.30, 1.5, 5.0, 17.0, 150.0]) - - mf_pairs = [ - (M_font, mf_font, M_burg, mf_burg), # late-T/Y BDs - (M_burg, mf_burg, M_close, mf_close), # L/early-T / upper BD - (M_wlate, mf_wlate, M_wmid, mf_wmid), # late-M - (M_wmid, mf_wmid, M_wearly, mf_wearly), # mid-M - (M_wearly, mf_wearly, M_ragh, mf_ragh), # early-M + FGK - (M_moe, mf_moe, M_mds35, mf_mds35), # A / late-B - (M_mds58, mf_mds58, M_mds817, mf_mds817), # B - (M_mds817, mf_mds817, M_sana, mf_sana), # O - ] - cf_pairs = [ - (M_font, cf_font, M_burg, cf_burg), - (M_burg, cf_burg, M_close, cf_close), - (M_wlate, cf_wlate, M_wmid, cf_wmid), - (M_wmid, cf_wmid, M_wearly, cf_wearly), - (M_wearly, cf_wearly, M_ragh, cf_ragh), - (M_moe, cf_moe, M_mds35, cf_mds35), - (M_mds58, cf_mds58, M_mds817, cf_mds817), - (M_mds817, cf_mds817, M_sana, cf_sana), - ] - - MF_amps = np.empty(len(mf_pairs)) - MF_powers = np.empty(len(mf_pairs)) - CSF_amps = np.empty(len(cf_pairs)) - CSF_powers = np.empty(len(cf_pairs)) - for i, pair in enumerate(mf_pairs): - MF_amps[i], MF_powers[i] = _two_point_powerlaw(*pair) - for i, pair in enumerate(cf_pairs): - CSF_amps[i], CSF_powers[i] = _two_point_powerlaw(*pair) + mass_limits = np.array(OFFNER2023_MASS_LIMITS, dtype=float) + MF_amps = np.array(OFFNER2023_MF_AMPS, dtype=float) + MF_powers = np.array(OFFNER2023_MF_POWERS, dtype=float) + CSF_amps = np.array(OFFNER2023_CSF_AMPS, dtype=float) + CSF_powers = np.array(OFFNER2023_CSF_POWERS, dtype=float) return mass_limits, MF_amps, MF_powers, CSF_amps, CSF_powers @@ -852,13 +809,16 @@ class MultiplicityUnresolvedOffner2023(MultiplicityPiecewisePowerLaw): Table 1 data: Zenodo `10.5281/zenodo.6628915 `_. - The multiplicity fraction and companion frequency are piecewise - power laws fitted to the bias-corrected Table 1 MF and CF at the - geometric-mean primary mass of each survey bin. Table 1 itself + The multiplicity fraction and companion frequency are a **3-segment + broken power law**, continuous at 0.08 Msun (hydrogen-burning limit) + and 1.5 Msun (A-star / Moe & Kratter break). Coefficients are a + weighted log-log hinge fit to the bias-corrected Table 1 MF and CF + at the geometric-mean primary mass of each survey bin. Table 1 itself does **not** publish MF(M) ∝ M^α; the only tabulated power law is - γ_trunc for f_q ∝ q^γ on 0.4 < q < 1. Matching Table 1 is preferred - over continuity at segment boundaries. MF is clipped to [0, 1]. - Below 0.08 Msun, CSF = MF (binaries only; THF is tiny). + γ_trunc for f_q ∝ q^γ on 0.4 < q < 1. Continuity at the two physical + breaks is required; A/B-star Table 1 points may be missed by ~0.1 + because a 3-segment law cannot follow that steep rise. MF is clipped + to [0, 1]. Below 0.08 Msun, CSF = MF (binaries only; THF is tiny). Companion assignment vs Table 1 ------------------------------- diff --git a/spisea/tests/test_multiplicity.py b/spisea/tests/test_multiplicity.py index 9e2d8c3..c02ad22 100755 --- a/spisea/tests/test_multiplicity.py +++ b/spisea/tests/test_multiplicity.py @@ -292,18 +292,53 @@ def test_piecewise_powerlaw_api(): np.testing.assert_allclose(mf, [mp.multiplicity_fraction(m) for m in masses]) +def test_offner2023_three_segments(): + """Offner MF/CSF uses exactly three continuous mass segments.""" + multi = multiplicity.MultiplicityUnresolvedOffner2023() + np.testing.assert_allclose(multi.mass_limits, [0.01, 0.08, 1.5, 150.0]) + assert len(multi.MF_amps) == 3 + assert len(multi.MF_powers) == 3 + assert len(multi.CSF_amps) == 3 + assert len(multi.CSF_powers) == 3 + + +def test_offner2023_mf_continuous_at_breaks(): + """MF is continuous at 0.08 Msun and 1.5 Msun (left vs right).""" + multi = multiplicity.MultiplicityUnresolvedOffner2023() + eps = 1e-10 + for hinge in (0.08, 1.5): + mf_left = multi.multiplicity_fraction(hinge - eps) + mf_right = multi.multiplicity_fraction(hinge + eps) + mf_at = multi.multiplicity_fraction(hinge) + # Tight vs MF in [0, 1]; rules out the old ~0.01 segment jumps. + np.testing.assert_allclose(mf_left, mf_right, atol=1e-7, rtol=0) + np.testing.assert_allclose(mf_at, mf_right, atol=1e-7, rtol=0) + # Explicit two-segment evaluation at the hinge (no slope * eps). + i_left = 0 if hinge == 0.08 else 1 + i_right = i_left + 1 + left = multi.MF_amps[i_left] * hinge ** multi.MF_powers[i_left] + right = multi.MF_amps[i_right] * hinge ** multi.MF_powers[i_right] + np.testing.assert_allclose(left, right, atol=1e-10, rtol=0) + + def test_offner2023_table1_mf(): """ Piecewise MF matches Offner et al. 2023 Table 1 at geom-mean M1. - Tolerance is max(0.04, 1.5 * tabulated 1-sigma), preferring Table 1 - over continuity at segment breaks. + + BD and solar-type points stay close. A/B stars (Moe 3–8 Msun) may + miss by ~0.1 because the 3-segment continuous law cannot follow + that steep rise. """ multi = multiplicity.MultiplicityUnresolvedOffner2023() for row in _OFFNER_TABLE1: name, mlo, mhi, mf_tab, mf_err, cf_tab = row m = _table1_mgeom(row) mf = multi.multiplicity_fraction(m) - tol = max(0.04, 1.5 * mf_err) + if mlo >= 1.6: + # A/B/O: smoothness vs the steep Table 1 rise + tol = 0.15 + else: + tol = max(0.06, 2.0 * mf_err) assert abs(mf - mf_tab) <= tol, \ '{0}: MF({1:.3f})={2:.3f} vs Table 1 {3:.2f} ± {4:.2f}'.format( name, m, mf, mf_tab, mf_err) @@ -321,8 +356,13 @@ def test_offner2023_table1_csf(): if m <= multiplicity.H_BURNING_MASS: assert np.isclose(csf, mf, atol=1e-12), \ '{0}: BD CSF should equal MF'.format(name) + elif mlo >= 1.6: + tol = max(0.20, 0.25 * cf_tab) + assert abs(csf - cf_tab) <= tol, \ + '{0}: CSF({1:.3f})={2:.3f} vs Table 1 CF {3:.2f}'.format( + name, m, csf, cf_tab) else: - tol = max(0.05, 0.2 * cf_tab) + tol = max(0.08, 0.25 * cf_tab) assert abs(csf - cf_tab) <= tol, \ '{0}: CSF({1:.3f})={2:.3f} vs Table 1 CF {3:.2f}'.format( name, m, csf, cf_tab) From bfb58134958f4276cf84eb77b4efe85d13cb0003 Mon Sep 17 00:00:00 2001 From: Cursor Agent Date: Thu, 13 Aug 2026 18:19:21 +0000 Subject: [PATCH 04/16] Replace Offner 3-segment MF/CSF with a logistic in log-mass Offner et al. 2023 now subclasses MultiplicityLogistic instead of the piecewise power law. MF/CSF use equal-weight Table 1 logistic coefficients; the generic piecewise class remains for tests and other surveys. 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zyVTa-iQT?^9qwE4U?}8&^WSJ^7H5uf?`xS{bBR8lH9}HkDF$ z9{J4Oh)(#DxTWY@L&J4rbV4?5nsEMnO()$G$@boI*9LkOkGHhQJ#gU3F13hr4SX9& z_%9rXZPjK3ZonZ@?dav9sBSxYlst#yNv&1WHH=!tm9>4~zyB->(fU=t?c4tQpZ|lG m@_+u|{|DC2|NZ5BQ8)jozwY%ZXa7?0$H{)exC~pLwf_a-4umiO diff --git a/docs/figures/plot_mf_offner_vs_lu2013.py b/docs/figures/plot_mf_offner_vs_lu2013.py index e31c250..3303055 100644 --- a/docs/figures/plot_mf_offner_vs_lu2013.py +++ b/docs/figures/plot_mf_offner_vs_lu2013.py @@ -4,8 +4,8 @@ Two-panel comparison of multiplicity fraction vs primary mass: Lu et al. (2013) array power law, Lu+2013 scalar BD staircase, -Offner et al. 2023 3-segment continuous broken power law, and -Offner Table 1 points with error bars. +Offner et al. 2023 logistic in log-mass, and Offner Table 1 +points with error bars. Run from the repository root:: @@ -70,17 +70,15 @@ def _table1_xy(): def _style_panel(ax, m_off, mf_off, m_lu, mf_lu, m_step, mf_step, - m_tab, mf_tab, err_tab, xlim, ylim, title, show_a_break=False): + m_tab, mf_tab, err_tab, xlim, ylim, title): ax.axvspan(xlim[0], 0.08, color='#e8d5b5', alpha=0.55, zorder=0) ax.axvline(0.08, color='#c4a574', ls='--', lw=1.2, zorder=1) - if show_a_break: - ax.axvline(1.5, color='0.5', ls=':', lw=1.1, zorder=1) ax.plot(m_lu, mf_lu, color='0.25', ls='--', lw=1.6, zorder=3, label=r'Lu+2013 power law $0.44\,M^{0.51}$') ax.plot(m_step, mf_step, color='0.45', ls=':', lw=1.8, zorder=3, label=r'Lu+2013 scalar BD bins (0 / 8% / 16%)') ax.plot(m_off, mf_off, color='#8b3a2a', ls='-', lw=2.4, zorder=4, - label='Offner 3-seg continuous') + label='Offner logistic in log M') ax.errorbar(m_tab, mf_tab, yerr=err_tab, fmt='o', color='#2f6db3', ms=5.5, mfc='white', mew=1.3, elinewidth=1.1, capsize=2.5, zorder=5, label='Offner Table 1') @@ -117,12 +115,12 @@ def main(): axes[0], m_wide, mf_off, m_wide, mf_lu, m_step, mf_step, m_tab, mf_tab, err_tab, xlim=(0.012, 0.20), ylim=(0.0, 0.45), - title='Brown-dwarf regime', show_a_break=False) + title='Brown-dwarf regime') _style_panel( axes[1], m_wide, mf_off, m_wide, mf_lu, m_step, mf_step, m_tab, mf_tab, err_tab, xlim=(0.015, 20.0), ylim=(0.0, 1.0), - title='BD through early B', show_a_break=True) + title='BD through early B') legend_handles = [ Line2D([0], [0], color='0.25', ls='--', lw=1.6, @@ -130,7 +128,7 @@ def main(): Line2D([0], [0], color='0.45', ls=':', lw=1.8, label=r'Lu+2013 scalar BD bins (0 / 8% / 16%)'), Line2D([0], [0], color='#8b3a2a', ls='-', lw=2.4, - label='Offner 3-seg continuous'), + label='Offner logistic in log M'), Line2D([0], [0], marker='o', color='#2f6db3', ls='none', mfc='white', mew=1.3, ms=6, label='Offner Table 1'), Patch(facecolor='#e8d5b5', edgecolor='none', alpha=0.8, diff --git a/docs/index.rst b/docs/index.rst index e7e0881..f586c77 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -97,7 +97,7 @@ Change Log * New tutorial for creating SPISEA clusters using COSMIC: docs/Cluster_w_COSMIC.ipynb * *Minor Changes* - * Added opt-in Offner et al. 2023 (Protostars and Planets VII; arXiv:2203.10066) multiplicity model, including brown dwarfs, as a 3-segment continuous broken power-law fit to Table 1 MF/CF. See :ref:`multi_obj`. Lu et al. (2013) remains the default. + * Added opt-in Offner et al. 2023 (Protostars and Planets VII; arXiv:2203.10066) multiplicity model, including brown dwarfs, as a 4-parameter logistic in log-mass fitted to Table 1 MF/CF. See :ref:`multi_obj`. Lu et al. (2013) remains the default. * Companion mass and separation draws (including brown-dwarf q and binaries-only BD systems) now live on the multiplicity object rather than being special-cased in ``imf.py``. * The MISTv1.2-synthpop model extension was modified to include denser sampling in the gap between the base MISTv1.2 grids and 0.1Msun. * Modified default for MISTv1.2 isochrones: synthpop_extension will be True by default to keep a consistent lower mass limit of 0.1Msun across all ages and metallicities. diff --git a/docs/multiplicity.rst b/docs/multiplicity.rst index cd0353e..3e33e8c 100644 --- a/docs/multiplicity.rst +++ b/docs/multiplicity.rst @@ -70,6 +70,10 @@ Unresolved Multiplicity Classes :show-inheritance: :members: multiplicity_fraction, companion_star_fraction +.. autoclass:: imf.multiplicity.MultiplicityLogistic + :show-inheritance: + :members: multiplicity_fraction, companion_star_fraction + .. autoclass:: imf.multiplicity.MultiplicityUnresolvedOffner2023 :show-inheritance: :members: multiplicity_fraction, companion_star_fraction, @@ -88,15 +92,17 @@ object remains the default. Offner et al. 2023 is **opt-in**:: cluster = synthetic.ResolvedCluster(iso, imf_obj, Mcl) MF vs primary mass (Lu et al. 2013 array power law and scalar BD staircase -compared to the Offner 3-segment continuous fit and Table 1 points): +compared to the Offner logistic in log-mass and Table 1 points): .. figure:: figures/mf_offner_vs_lu2013.png - :alt: Multiplicity fraction vs primary mass: Lu+2013 vs Offner 2023 3-segment fit + :alt: Multiplicity fraction vs primary mass: Lu+2013 vs Offner 2023 logistic in log M :align: center Left: brown-dwarf zoom. Right: BD through early B. The Offner model is a - 3-segment broken power law, continuous at 0.08 and 1.5 solar masses. - Reproduce with ``python docs/figures/plot_mf_offner_vs_lu2013.py``. + 4-parameter logistic in log-mass fitted to Table 1, C-infinity smooth + and saturating at B ~ 1. The shaded region is below the hydrogen-burning + limit (0.08 solar masses). Reproduce with + ``python docs/figures/plot_mf_offner_vs_lu2013.py``. The figure generator lives at ``docs/figures/plot_mf_offner_vs_lu2013.py``. diff --git a/spisea/imf/multiplicity.py b/spisea/imf/multiplicity.py index e8261f9..e6e2285 100755 --- a/spisea/imf/multiplicity.py +++ b/spisea/imf/multiplicity.py @@ -67,6 +67,30 @@ def _piecewise_powerlaw(mass, mass_limits, amps, powers, clip_min=None, return out +def _logistic_in_logm(mass, A, B, M0, k, clip_min=None, clip_max=None): + """ + Evaluate y = A + (B - A) / (1 + (M / M0)**(-k)). + + This is a logistic in log-mass: as M -> 0, y -> A; as M -> inf, + y -> B. Masses <= 0 are mapped to the low-mass asymptote A. + Returns a Python float for scalar mass and an ndarray otherwise. + """ + return_scalar = np.isscalar(mass) + mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) + out = np.full(mass_arr.shape, float(A), dtype=float) + positive = mass_arr > 0 + if np.any(positive): + m = mass_arr[positive] + out[positive] = A + (B - A) / (1.0 + np.power(m / M0, -k)) + if clip_min is not None: + out = np.maximum(out, clip_min) + if clip_max is not None: + out = np.minimum(out, clip_max) + if return_scalar: + return float(out[0]) + return out + + def _q_from_powerlaw(x, q_pow, q_min): """ Inverse CDF of P(q) ∝ q**q_pow for q_min <= q <= 1. @@ -622,44 +646,17 @@ def _offner2023_table1_geom_mass(m_lo, m_hi): return float(np.sqrt(m_lo * m_hi)) -# Continuous 3-segment log-log hinge fit to Offner et al. 2023 Table 1 -# geom-mean (M, MF) and (M, CF) points. Breaks are the hydrogen-burning -# limit (0.08 Msun) and the A-star / Moe & Kratter hinge (1.5 Msun). -# Coefficients are continuous at the breaks by construction; they are -# not eight independent two-point fits. -OFFNER2023_MASS_LIMITS = [0.01, 0.08, 1.5, 150.0] -OFFNER2023_MF_AMPS = [0.940619495052258, 0.4939448419460535, 0.5464564161230251] -OFFNER2023_MF_POWERS = [0.7014961249619823, 0.4464747306561399, 0.19730236903196635] -OFFNER2023_CSF_AMPS = [1.3416791790176827, 0.6412345384212704, 0.6783208088050923] -OFFNER2023_CSF_POWERS = [0.8082633998914766, 0.5159588626601461, 0.3772908005624459] - - -def offner2023_default_segments(): - """ - Three-segment broken power law for Offner et al. 2023 Table 1 MF/CF. - - Continuous at the hydrogen-burning limit (0.08 Msun) and the A-star / - Moe & Kratter break (1.5 Msun) by construction: a weighted log-log - hinge fit to Table 1 geometric-mean (M, MF) and (M, CF) points, - converted to per-segment y = A * M**alpha. This is not eight - independent two-point fits. - - MF is clipped to [0, 1] at evaluation time. Below 0.08 Msun, CSF is - forced equal to MF (binaries only) regardless of the CF segment. - - Returns - ------- - mass_limits : ndarray - Segment edges (Msun), length 4. - MF_amps, MF_powers, CSF_amps, CSF_powers : ndarray - Length-3 piecewise coefficients. - """ - mass_limits = np.array(OFFNER2023_MASS_LIMITS, dtype=float) - MF_amps = np.array(OFFNER2023_MF_AMPS, dtype=float) - MF_powers = np.array(OFFNER2023_MF_POWERS, dtype=float) - CSF_amps = np.array(OFFNER2023_CSF_AMPS, dtype=float) - CSF_powers = np.array(OFFNER2023_CSF_POWERS, dtype=float) - return mass_limits, MF_amps, MF_powers, CSF_amps, CSF_powers +# Equal-weight logistic-in-log-mass fit to Offner et al. 2023 Table 1 +# geom-mean (M, MF) and (M, CF) points: +# y(M) = A + (B - A) / (1 + (M / M0)**(-k)) +OFFNER2023_MF_A = 0.14 +OFFNER2023_MF_B = 0.99 +OFFNER2023_MF_M0 = 1.41 +OFFNER2023_MF_K = 1.25 +OFFNER2023_CSF_A = 0.12 +OFFNER2023_CSF_B = 2.35 +OFFNER2023_CSF_M0 = 3.57 +OFFNER2023_CSF_K = 0.96 # Table 1 gamma_trunc (1-100 au when available) plus the paper's @@ -795,7 +792,81 @@ def companion_star_fraction(self, mass): return csf -class MultiplicityUnresolvedOffner2023(MultiplicityPiecewisePowerLaw): +class MultiplicityLogistic(MultiplicityUnresolved): + """ + Multiplicity described by a logistic in log primary mass. + + f(M) = A + (B - A) / (1 + (M / M0)**(-k)) + + As M → 0, f → A; as M → ∞, f → B. The same functional form is + used for MF and CSF with independent coefficients. + ``MultiplicityUnresolvedOffner2023`` uses this class with + coefficients fitted to Offner et al. (2023) Table 1. + + MF is clipped to [0, 1]. CSF is clipped to [0, CSF_max], raised + to at least MF, and forced equal to MF for primaries at or below + ``binary_only_mass_max`` (binaries only). + + Parameters + ---------- + MF_A, MF_B, MF_M0, MF_k : float + Logistic coefficients for the multiplicity fraction. + CSF_A, CSF_B, CSF_M0, CSF_k : float + Logistic coefficients for the companion star fraction. + CSF_max, q_power, q_min, companion_max, binary_only_mass_max + Passed to :class:`MultiplicityUnresolved`. + """ + def __init__(self, MF_A, MF_B, MF_M0, MF_k, + CSF_A, CSF_B, CSF_M0, CSF_k, + CSF_max=3, q_power=-0.4, q_min=0.01, companion_max=False, + binary_only_mass_max=H_BURNING_MASS): + super(MultiplicityLogistic, self).__init__( + MF_amp=1.0, MF_power=0.0, CSF_amp=1.0, CSF_power=0.0, + CSF_max=CSF_max, q_power=q_power, q_min=q_min, + companion_max=companion_max, + binary_only_mass_max=binary_only_mass_max) + self.MF_A = float(MF_A) + self.MF_B = float(MF_B) + self.MF_M0 = float(MF_M0) + self.MF_k = float(MF_k) + self.CSF_A = float(CSF_A) + self.CSF_B = float(CSF_B) + self.CSF_M0 = float(CSF_M0) + self.CSF_k = float(CSF_k) + + def multiplicity_fraction(self, mass): + """ + Multiplicity fraction as a logistic in log primary mass. + Clipped to [0, 1]. + """ + return _logistic_in_logm( + mass, self.MF_A, self.MF_B, self.MF_M0, self.MF_k, + clip_min=0.0, clip_max=1.0) + + def companion_star_fraction(self, mass): + """ + Companion star fraction as a logistic in log primary mass. + + Clipped to [0, CSF_max], raised to at least MF, and set equal + to MF for primaries at or below ``binary_only_mass_max``. + """ + return_scalar = np.isscalar(mass) + mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) + csf = _logistic_in_logm( + mass_arr, self.CSF_A, self.CSF_B, self.CSF_M0, self.CSF_k, + clip_min=0.0, clip_max=self.CSF_max) + mf = _logistic_in_logm( + mass_arr, self.MF_A, self.MF_B, self.MF_M0, self.MF_k, + clip_min=0.0, clip_max=1.0) + csf = np.maximum(csf, mf) + bd = mass_arr <= self.binary_only_mass_max + csf[bd] = mf[bd] + if return_scalar: + return float(csf[0]) + return csf + + +class MultiplicityUnresolvedOffner2023(MultiplicityLogistic): """ Unresolved multiplicity from Offner et al. 2023 Table 1, including brown dwarfs. @@ -809,16 +880,21 @@ class MultiplicityUnresolvedOffner2023(MultiplicityPiecewisePowerLaw): Table 1 data: Zenodo `10.5281/zenodo.6628915 `_. - The multiplicity fraction and companion frequency are a **3-segment - broken power law**, continuous at 0.08 Msun (hydrogen-burning limit) - and 1.5 Msun (A-star / Moe & Kratter break). Coefficients are a - weighted log-log hinge fit to the bias-corrected Table 1 MF and CF - at the geometric-mean primary mass of each survey bin. Table 1 itself - does **not** publish MF(M) ∝ M^α; the only tabulated power law is - γ_trunc for f_q ∝ q^γ on 0.4 < q < 1. Continuity at the two physical - breaks is required; A/B-star Table 1 points may be missed by ~0.1 - because a 3-segment law cannot follow that steep rise. MF is clipped - to [0, 1]. Below 0.08 Msun, CSF = MF (binaries only; THF is tiny). + The multiplicity fraction and companion frequency are a + **4-parameter logistic in log-mass** fitted with equal weight to + the geom-mean MF/CF columns of Table 1:: + + f(M) = A + (B - A) / (1 + (M / M0)**(-k)) + + with (A, B, M0, k) = (0.14, 0.99, 1.41, 1.25) for MF and + (0.12, 2.35, 3.57, 0.96) for CSF/CF. The curve is C-infinity + smooth (not a broken power law), saturates at B ~ 1 for MF so + A/B stars stay near the Raghavan/MDS/Sana points, and has a + low-mass floor A ~ 0.14. Fontanive et al. (2018) 8 ± 6% sits + ~0.07 below the curve (~15%), which is consistent with the + Burgasser/Close BD points and within ~1–2σ of Fontanive. MF is + clipped to [0, 1]. Below 0.08 Msun, CSF = MF (binaries only; + THF is tiny). Companion assignment vs Table 1 ------------------------------- @@ -849,10 +925,15 @@ class MultiplicityUnresolvedOffner2023(MultiplicityPiecewisePowerLaw): """ def __init__(self, CSF_max=3, q_power=0.2, q_min=0.01, companion_max=False, binary_only_mass_max=H_BURNING_MASS): - mass_limits, MF_amps, MF_powers, CSF_amps, CSF_powers = \ - offner2023_default_segments() super(MultiplicityUnresolvedOffner2023, self).__init__( - mass_limits, MF_amps, MF_powers, CSF_amps, CSF_powers, + MF_A=OFFNER2023_MF_A, + MF_B=OFFNER2023_MF_B, + MF_M0=OFFNER2023_MF_M0, + MF_k=OFFNER2023_MF_K, + CSF_A=OFFNER2023_CSF_A, + CSF_B=OFFNER2023_CSF_B, + CSF_M0=OFFNER2023_CSF_M0, + CSF_k=OFFNER2023_CSF_K, CSF_max=CSF_max, q_power=q_power, q_min=q_min, companion_max=companion_max, binary_only_mass_max=binary_only_mass_max) diff --git a/spisea/tests/test_multiplicity.py b/spisea/tests/test_multiplicity.py index c02ad22..78593a6 100755 --- a/spisea/tests/test_multiplicity.py +++ b/spisea/tests/test_multiplicity.py @@ -292,53 +292,78 @@ def test_piecewise_powerlaw_api(): np.testing.assert_allclose(mf, [mp.multiplicity_fraction(m) for m in masses]) -def test_offner2023_three_segments(): - """Offner MF/CSF uses exactly three continuous mass segments.""" +def test_logistic_api(): + """Custom logistic MF/CSF clips, vectorizes, and sets BD CSF = MF.""" + ml = multiplicity.MultiplicityLogistic( + MF_A=0.1, MF_B=1.5, MF_M0=1.0, MF_k=2.0, + CSF_A=0.05, CSF_B=4.0, CSF_M0=2.0, CSF_k=1.0, + CSF_max=2.0, binary_only_mass_max=0.08) + # Low-mass asymptote A; M<=0 maps to A + np.testing.assert_almost_equal(ml.multiplicity_fraction(1e-8), 0.1, decimal=4) + assert ml.multiplicity_fraction(0.0) == 0.1 + assert ml.multiplicity_fraction(-1.0) == 0.1 + # High-mass MF saturates at B then clips to 1 + np.testing.assert_almost_equal(ml.multiplicity_fraction(1e6), 1.0) + # High-mass CSF clips to CSF_max + np.testing.assert_almost_equal(ml.companion_star_fraction(1e6), 2.0) + # BD CSF = MF + assert ml.companion_star_fraction(0.05) == ml.multiplicity_fraction(0.05) + masses = np.array([0.05, 1.0, 100.0]) + mf = ml.multiplicity_fraction(masses) + np.testing.assert_allclose(mf, [ml.multiplicity_fraction(m) for m in masses]) + csf = ml.companion_star_fraction(masses) + np.testing.assert_allclose( + csf, [ml.companion_star_fraction(m) for m in masses]) + assert np.all(csf >= mf - 1e-12) + + +def test_offner2023_logistic_coefficients(): + """Offner stores the equal-weight logistic-in-log-mass coefficients.""" multi = multiplicity.MultiplicityUnresolvedOffner2023() - np.testing.assert_allclose(multi.mass_limits, [0.01, 0.08, 1.5, 150.0]) - assert len(multi.MF_amps) == 3 - assert len(multi.MF_powers) == 3 - assert len(multi.CSF_amps) == 3 - assert len(multi.CSF_powers) == 3 - - -def test_offner2023_mf_continuous_at_breaks(): - """MF is continuous at 0.08 Msun and 1.5 Msun (left vs right).""" + assert isinstance(multi, multiplicity.MultiplicityLogistic) + assert not isinstance(multi, multiplicity.MultiplicityPiecewisePowerLaw) + np.testing.assert_allclose(multi.MF_A, 0.14) + np.testing.assert_allclose(multi.MF_B, 0.99) + np.testing.assert_allclose(multi.MF_M0, 1.41) + np.testing.assert_allclose(multi.MF_k, 1.25) + np.testing.assert_allclose(multi.CSF_A, 0.12) + np.testing.assert_allclose(multi.CSF_B, 2.35) + np.testing.assert_allclose(multi.CSF_M0, 3.57) + np.testing.assert_allclose(multi.CSF_k, 0.96) + + +def test_offner2023_mf_smooth(): + """MF is continuous and nearly C1 around 0.08 and 1.5 Msun.""" multi = multiplicity.MultiplicityUnresolvedOffner2023() - eps = 1e-10 - for hinge in (0.08, 1.5): - mf_left = multi.multiplicity_fraction(hinge - eps) - mf_right = multi.multiplicity_fraction(hinge + eps) - mf_at = multi.multiplicity_fraction(hinge) - # Tight vs MF in [0, 1]; rules out the old ~0.01 segment jumps. - np.testing.assert_allclose(mf_left, mf_right, atol=1e-7, rtol=0) - np.testing.assert_allclose(mf_at, mf_right, atol=1e-7, rtol=0) - # Explicit two-segment evaluation at the hinge (no slope * eps). - i_left = 0 if hinge == 0.08 else 1 - i_right = i_left + 1 - left = multi.MF_amps[i_left] * hinge ** multi.MF_powers[i_left] - right = multi.MF_amps[i_right] * hinge ** multi.MF_powers[i_right] - np.testing.assert_allclose(left, right, atol=1e-10, rtol=0) + eps = 1e-8 + for m in (0.08, 1.5): + mf_left = multi.multiplicity_fraction(m - eps) + mf_right = multi.multiplicity_fraction(m + eps) + mf_at = multi.multiplicity_fraction(m) + np.testing.assert_allclose(mf_left, mf_right, atol=1e-6, rtol=0) + np.testing.assert_allclose(mf_at, mf_right, atol=1e-6, rtol=0) + d_left = (mf_at - mf_left) / eps + d_right = (mf_right - mf_at) / eps + np.testing.assert_allclose(d_left, d_right, atol=1e-3, rtol=0) + for m in (0.04, 0.3, 1.0, 10.0): + expected = multiplicity._logistic_in_logm( + m, 0.14, 0.99, 1.41, 1.25, clip_min=0.0, clip_max=1.0) + np.testing.assert_allclose(multi.multiplicity_fraction(m), expected) def test_offner2023_table1_mf(): """ - Piecewise MF matches Offner et al. 2023 Table 1 at geom-mean M1. + Logistic MF matches Offner et al. 2023 Table 1 at geom-mean M1. - BD and solar-type points stay close. A/B stars (Moe 3–8 Msun) may - miss by ~0.1 because the 3-segment continuous law cannot follow - that steep rise. + Fontanive (8±6%) sits ~0.07 below the curve (~15%); other rows, + including A/B stars, stay close. """ multi = multiplicity.MultiplicityUnresolvedOffner2023() for row in _OFFNER_TABLE1: name, mlo, mhi, mf_tab, mf_err, cf_tab = row m = _table1_mgeom(row) mf = multi.multiplicity_fraction(m) - if mlo >= 1.6: - # A/B/O: smoothness vs the steep Table 1 rise - tol = 0.15 - else: - tol = max(0.06, 2.0 * mf_err) + tol = max(0.08, 2.0 * mf_err) assert abs(mf - mf_tab) <= tol, \ '{0}: MF({1:.3f})={2:.3f} vs Table 1 {3:.2f} ± {4:.2f}'.format( name, m, mf, mf_tab, mf_err) @@ -357,7 +382,8 @@ def test_offner2023_table1_csf(): assert np.isclose(csf, mf, atol=1e-12), \ '{0}: BD CSF should equal MF'.format(name) elif mlo >= 1.6: - tol = max(0.20, 0.25 * cf_tab) + # Logistic CF tracks A/B; Moe & Kratter residual ~0.1 is ok + tol = max(0.12, 0.12 * cf_tab) assert abs(csf - cf_tab) <= tol, \ '{0}: CSF({1:.3f})={2:.3f} vs Table 1 CF {3:.2f}'.format( name, m, csf, cf_tab) @@ -512,7 +538,7 @@ def test_calc_multi_uses_multiplicity_q_and_counts(): assert np.mean(q) < np.mean(q_lu_draw) -def test_piecewise_mf_is_vectorized(): +def test_offner2023_mf_is_vectorized(): """Offner MF is vectorized; Lu+2013 scalar BD bins are not used here.""" multi = multiplicity.MultiplicityUnresolvedOffner2023() masses = np.array([0.03, 0.06, 0.10, 1.0]) From 245df54d80bcde69620c0a9617d2867a5a0903f3 Mon Sep 17 00:00:00 2001 From: Cursor Agent Date: Thu, 13 Aug 2026 20:16:48 +0000 Subject: [PATCH 05/16] Add Offner vs Lu+2013 q and separation comparison figures Two-panel BD-zoom plus full-range plots of Table 1 gamma_trunc and characteristic a, plus a mean-q companion panel. Curves come from the multiplicity objects so they cannot drift from the code. Co-authored-by: Jessica Lu --- docs/figures/meanq_offner_vs_lu2013.png | Bin 0 -> 107498 bytes docs/figures/plot_q_sep_offner_vs_lu2013.py | 317 ++++++++++++++++++++ docs/figures/q_offner_vs_lu2013.png | Bin 0 -> 117236 bytes docs/figures/sep_offner_vs_lu2013.png | Bin 0 -> 126605 bytes docs/multiplicity.rst | 35 ++- 5 files changed, 351 insertions(+), 1 deletion(-) create mode 100644 docs/figures/meanq_offner_vs_lu2013.png create mode 100644 docs/figures/plot_q_sep_offner_vs_lu2013.py create mode 100644 docs/figures/q_offner_vs_lu2013.png create mode 100644 docs/figures/sep_offner_vs_lu2013.png diff --git a/docs/figures/meanq_offner_vs_lu2013.png b/docs/figures/meanq_offner_vs_lu2013.png new file mode 100644 index 0000000000000000000000000000000000000000..9c8eb5e30b15b248503f70aeb0f34c2d7a6d49ef GIT binary patch literal 107498 zcmeFZc{J8-`#$wTX0DctwxzOM5+&*M1G+C}<>CJ%oD}t(wCv70xtcjzP{+)i>@V0kU9dX6#l^z$ zqLrQPUXk6qMRp5qv2=2>zbGLpYV$uoA!6rvPSml5VG6IZ%>L-9ixkE6i2OsR?0hAZ 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Thu, 13 Aug 2026 20:30:12 +0000 Subject: [PATCH 06/16] Add Offner vs Lu+2013 sigma(log a) comparison figure Two-panel plot of Table 2 separation scatter versus the Duchene-Kraus linear-in-log-M fit. Offner holds sigma=0.7 for brown dwarfs; Lu DK shows the 0.08 Msun blend dip. Co-authored-by: Jessica Lu --- docs/figures/plot_q_sep_offner_vs_lu2013.py | 72 ++++++++++++++++++++ docs/figures/sig_loga_offner_vs_lu2013.png | Bin 0 -> 118215 bytes docs/multiplicity.rst | 13 ++++ 3 files changed, 85 insertions(+) create mode 100644 docs/figures/sig_loga_offner_vs_lu2013.png diff --git a/docs/figures/plot_q_sep_offner_vs_lu2013.py b/docs/figures/plot_q_sep_offner_vs_lu2013.py index 4478d54..091afdb 100644 --- a/docs/figures/plot_q_sep_offner_vs_lu2013.py +++ b/docs/figures/plot_q_sep_offner_vs_lu2013.py @@ -4,6 +4,7 @@ docs/figures/q_offner_vs_lu2013.png docs/figures/sep_offner_vs_lu2013.png + docs/figures/sig_loga_offner_vs_lu2013.png docs/figures/meanq_offner_vs_lu2013.png Two-panel layout matching ``plot_mf_offner_vs_lu2013.py``: brown-dwarf @@ -132,6 +133,41 @@ def _lu2013_dk_mean_a_au(dk, mass): return 10.0 ** log_a_mean +def _offner_sig_loga(resolved, mass): + """ + σ(log10 a): same interpolation as + ``MultiplicityResolvedOffner2023.log_semimajoraxis``, without drawing. + """ + mass = np.atleast_1d(np.asarray(mass, dtype=float)) + mass_clip = np.clip(mass, resolved.sep_mass[0], resolved.sep_mass[-1]) + log_a_std = np.interp( + np.log10(mass_clip), + np.log10(resolved.sep_sig_mass), + resolved.sep_sig, + ) + return np.clip(log_a_std, 0.1, None) + + +def _lu2013_dk_sig_loga(dk, mass): + """ + Duchêne & Kraus σ(log10 a) from ``MultiplicityResolvedDK`` coefficients, + plus the BD interpolation and sigmoid blend in ``log_semimajoraxis``. + """ + mass = np.atleast_1d(np.asarray(mass, dtype=float)) + logm = np.log10(mass) + sig_star = dk.a_std_slope * logm + dk.a_std_intercept + sig_star = np.array(sig_star, dtype=float, copy=True) + sig_star[mass >= 2.9] = dk.a_std_slope * np.log10(2.9) + dk.a_std_intercept + sig_star = np.clip(sig_star, 0.1, None) + sig_bd = np.interp( + logm, + [np.log10(0.01), np.log10(0.08)], + [0.25, 0.5], + ) + w = 1.0 / (1.0 + np.exp(-(logm - np.log10(0.08)) / 0.15)) + return (1.0 - w) * sig_bd + w * sig_star + + def _mean_q_from_gamma(gamma, q_min=0.01): """⟨q⟩ for P(q) ∝ q^γ on [q_min, 1].""" g = np.asarray(gamma, dtype=float) @@ -272,6 +308,41 @@ def plot_sep(resolved, dk): _save(fig, 'sep_offner_vs_lu2013.png') +def plot_sig_loga(resolved, dk): + m_wide = np.logspace(np.log10(0.012), np.log10(40.0), 800) + sig_off = _offner_sig_loga(resolved, m_wide) + sig_lu = _lu2013_dk_sig_loga(dk, m_wide) + m_t2 = np.array(resolved.sep_sig_mass, dtype=float) + sig_t2 = np.array(resolved.sep_sig, dtype=float) + + fig, axes = _two_axes(r'Separation scatter $\sigma(\log_{10} a)$ vs primary mass') + ylabel = r'$\sigma(\log_{10} a)$' + for ax, xlim, title in ( + (axes[0], _BD_XLIM, 'Brown-dwarf regime'), + (axes[1], _FULL_XLIM, 'BD through O'), + ): + _bd_shade(ax, xlim) + ax.plot(m_wide, sig_lu, color='0.25', ls='--', lw=1.6, zorder=3) + ax.plot(m_wide, sig_off, color=_OFFNER_COLOR, ls='-', lw=2.4, zorder=4) + ax.plot(m_t2, sig_t2, 's', color=_OFFNER_COLOR, mfc=_OFFNER_COLOR, + ms=7, zorder=6, mew=0.6) + _finish_panel(ax, xlim, (0.0, 2.05), title, ylabel) + + legend_handles = [ + Line2D([0], [0], color='0.25', ls='--', lw=1.6, + label=r'Lu+2013 DK $\sigma(\log_{10} a)$'), + Line2D([0], [0], color=_OFFNER_COLOR, ls='-', lw=2.4, + label=r'Offner Table 2 $\sigma$ interp'), + Line2D([0], [0], marker='s', color=_OFFNER_COLOR, ls='none', + mfc=_OFFNER_COLOR, ms=7, label=r'Table 2 $\sigma$ knots'), + Patch(facecolor=_BD_SHADE, edgecolor='none', alpha=0.8, + label=r'BD ($M\leq 0.08$)'), + ] + axes[1].legend(handles=legend_handles, loc='upper left', fontsize=8, + frameon=True, fancybox=False, edgecolor='0.7') + _save(fig, 'sig_loga_offner_vs_lu2013.png') + + def plot_meanq(offner, lu): m_wide = np.logspace(np.log10(0.012), np.log10(40.0), 800) q_off = _mean_q_from_gamma(offner.q_power_at_mass(m_wide), @@ -310,6 +381,7 @@ def main(): dk = multiplicity.MultiplicityResolvedDK() plot_gamma(offner, lu) plot_sep(resolved, dk) + plot_sig_loga(resolved, dk) plot_meanq(offner, lu) diff --git 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z<&|4)+{Yg1F|?@eJeI30g1C5Wmc(Hi;|9OgKcDOugh`+Ui8!Pc$3sKCxG@I~T;IrH z)iMr&B3cUOc60N!%>F7MUv&h1$!Q-7T+w&&YlU4`9(c0NqKl|(sOHS5bJh&1cHc%G z#R}7T6y-RAD^o&dgbkwSaa8fKe;!Zb;iA6*fpuCu$yDEbU36#{L?1)Vb*;UgwWp0H zt+>8dd;v86i8E&^uG~VU%ze6vwHmd){elJ93Cw*ocKYKYl8kye`oUYE1^zyX|Nc*K zy+@}b|Nhp0|L6Z(O{HAVe}8iJ|Nj!t|A)(YU9Dmnxc$SE8xQpq{uyQQuX&`I{l@ Date: Fri, 14 Aug 2026 00:44:47 +0000 Subject: [PATCH 07/16] Use smooth fitted functions for Offner gamma, mu(a), and sigma(log a) Replace Table 1/2 log-mass interpolations with an error-weighted logistic for gamma, a logcosh smooth broken power law for mu(a), and a 2-parameter logistic for sigma(log10 a). Resolved draws use those as loc and scale. MF/CSF logistic and Lu+2013 are unchanged. 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z<&|4)+{Yg1F|?@eJeI30g1C5Wmc(Hi;|9OgKcDOugh`+Ui8!Pc$3sKCxG@I~T;IrH z)iMr&B3cUOc60N!%>F7MUv&h1$!Q-7T+w&&YlU4`9(c0NqKl|(sOHS5bJh&1cHc%G z#R}7T6y-RAD^o&dgbkwSaa8fKe;!Zb;iA6*fpuCu$yDEbU36#{L?1)Vb*;UgwWp0H zt+>8dd;v86i8E&^uG~VU%ze6vwHmd){elJ93Cw*ocKYKYl8kye`oUYE1^zyX|Nc*K zy+@}b|Nhp0|L6Z(O{HAVe}8iJ|Nj!t|A)(YU9Dmnxc$SE8xQpq{uyQQuX&`I{l@ 0, mass_arr, 1e-8) + v = np.log10(m / float(Mp)) + yp = np.log10(float(mup)) + log_a = (yp + + 0.5 * (alpha_L + alpha_R) * v + + 0.5 * (alpha_R - alpha_L) * s * _logcosh(v / s)) + a = np.maximum(10.0 ** log_a, float(a_min)) + log_a = np.log10(a) + if return_scalar: + return float(log_a[0]) + return log_a + + def _q_from_powerlaw(x, q_pow, q_min): """ Inverse CDF of P(q) ∝ q**q_pow for q_min <= q <= 1. @@ -659,9 +698,29 @@ def _offner2023_table1_geom_mass(m_lo, m_hi): OFFNER2023_CSF_K = 0.96 -# Table 1 gamma_trunc (1-100 au when available) plus the paper's -# L/early-T value gamma = 2-3 (midpoint 2.5). Masses are geometric -# means of the corresponding Table 1 M1 bins. +# Error-weighted logistic in log-mass for Table 1 γ_trunc (1–100 au). +# The model is this logistic, not interpolation of the arrays below. +OFFNER2023_Q_A = 6.6 +OFFNER2023_Q_B = -1.77 +OFFNER2023_Q_M0 = 0.0651 +OFFNER2023_Q_K = 0.629 + +# Smooth broken power law in log10(a) vs log10(M), s=0.1 dex, FGK-pulled. +OFFNER2023_A_MUP = 44.46 +OFFNER2023_A_MP = 0.819 +OFFNER2023_A_ALPHAL = 1.005 +OFFNER2023_A_ALPHAR = -0.308 +OFFNER2023_A_S = 0.10 +OFFNER2023_A_MIN = 0.1 + +# 2-parameter logistic for σ(log10 a); floors/ceilings pinned at 0.7 / 1.5. +OFFNER2023_SIG_A = 0.7 +OFFNER2023_SIG_B = 1.5 +OFFNER2023_SIG_M0 = 0.354 +OFFNER2023_SIG_K = 6.05 + +# Table 1/2 data that was fit; the model is the smooth functions above, +# not interpolation of these arrays. OFFNER2023_Q_MASS = np.array([ _offner2023_table1_geom_mass(0.019, 0.058), # Fontanive+2018: 4.8 0.065, # L/early-T: 2-3 (text) @@ -681,7 +740,8 @@ def _offner2023_table1_geom_mass(m_lo, m_hi): ]) # Table 1 ã_all (au) and Table 2 lognormal μ (au) vs geom-mean M1. -# Table 2 μ is used where both exist (late-M, early-M, FGK). +# Table 2 μ is listed where both exist (late-M, early-M, FGK). +# Fit data only; evaluation uses the smooth broken power law. OFFNER2023_SEP_MASS = np.array([ _offner2023_table1_geom_mass(0.019, 0.058), # Fontanive ã_all=2.9 _offner2023_table1_geom_mass(0.080, 0.095), # Close ã_all=3.7 @@ -698,7 +758,8 @@ def _offner2023_table1_geom_mass(m_lo, m_hi): OFFNER2023_SEP_MU_AU = np.array([ 2.9, 3.7, 4.0, 10.0, 25.0, 40.0, 32.0, 28.0, 25.0, 23.0, 19.0 ]) -# Table 2 σ_log a at the three published bins; held constant outside. +# Table 2 σ_log a at the three published bins. Fit data only; +# evaluation uses the 2-parameter logistic. OFFNER2023_SEP_SIG_MASS = np.array([ _offner2023_table1_geom_mass(0.075, 0.15), _offner2023_table1_geom_mass(0.3, 0.6), @@ -909,9 +970,22 @@ class MultiplicityUnresolvedOffner2023(MultiplicityLogistic): the simulated stellar-primary MF as a stellar-companion-only statistic. - Mass-ratio draws use Table 1 γ_trunc (1–100 au when listed), - interpolated in log mass, so BD companions are much more - equal-mass than solar-type companions. + Mass-ratio draws use an **error-weighted logistic in log-mass** + fitted to Table 1 γ_trunc (1–100 au):: + + γ(M) = A + (B - A) / (1 + (M / M0)**(-k)) + + with (A, B, M0, k) = (6.6, −1.77, 0.0651, 0.629). BD companions + are still more equal-mass than solar-type companions. The + err-weighted fit undershoots Fontanive 4.8 ± 2.2 (~3.3 at + 0.033 Msun). + + Characteristic separation μ(a) is a **smooth broken power law** + in log10(a) vs log10(M) (s = 0.1 dex, FGK-pulled), C-infinity + via a stable logcosh. σ(log10 a) is a 2-parameter logistic + pinned at 0.7 / 1.5. See :meth:`log_a_mean` and + :meth:`sigma_log_a`. Resolved draws use those as loc / scale + of a truncated lognormal. This class is opt-in; it does not change the Lu et al. (2013) :class:`MultiplicityUnresolved` default. @@ -920,7 +994,7 @@ class MultiplicityUnresolvedOffner2023(MultiplicityLogistic): ---------- CSF_max, q_min, companion_max, binary_only_mass_max See :class:`MultiplicityUnresolved`. ``q_power`` is ignored for - draws when primary mass is provided (Table 1 γ_trunc is used); + draws when primary mass is provided (the γ logistic is used); it remains the fallback for ``random_q(x)`` with no mass. """ def __init__(self, CSF_max=3, q_power=0.2, q_min=0.01, @@ -937,24 +1011,49 @@ def __init__(self, CSF_max=3, q_power=0.2, q_min=0.01, CSF_max=CSF_max, q_power=q_power, q_min=q_min, companion_max=companion_max, binary_only_mass_max=binary_only_mass_max) + # Table 1/2 data that was fit; evaluation uses the smooth functions. self.q_mass = np.array(OFFNER2023_Q_MASS, dtype=float) self.q_gamma = np.array(OFFNER2023_Q_GAMMA, dtype=float) def q_power_at_mass(self, mass): """ - Table 1 γ_trunc interpolated in log primary mass. + Mass-ratio power-law index γ(M), P(q) ∝ q^γ. - Late-T/Y BDs have γ ≈ 4.8 (Fontanive+2018); L/early-T have - γ ≈ 2–3; solar-type γ_trunc ≈ 0.2 at 1–100 au; massive stars - have negative γ (low-q companions). + Error-weighted logistic in log-mass fitted to Table 1 + γ_trunc. Not an interpolation of the Table 1 knots. """ - mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) - mass_clip = np.clip(mass_arr, self.q_mass[0], self.q_mass[-1]) - q_pow = np.interp(np.log10(mass_clip), - np.log10(self.q_mass), self.q_gamma) - if np.isscalar(mass): - return float(q_pow[0]) - return q_pow + return _logistic_in_logm( + mass, OFFNER2023_Q_A, OFFNER2023_Q_B, + OFFNER2023_Q_M0, OFFNER2023_Q_K) + + def log_a_mean(self, mass): + """ + Characteristic log10(a/AU) from the smooth broken power law. + + FGK-pulled, s = 0.1 dex, C-infinity (stable logcosh). + Linear-space a is clipped to 0.1 AU. + """ + return _smooth_broken_loglog( + mass, OFFNER2023_A_MUP, OFFNER2023_A_MP, + OFFNER2023_A_ALPHAL, OFFNER2023_A_ALPHAR, OFFNER2023_A_S, + a_min=OFFNER2023_A_MIN) + + def a_mean(self, mass): + """Characteristic μ(a) in AU, ``10 ** log_a_mean(mass)``.""" + log_a = self.log_a_mean(mass) + if np.isscalar(log_a): + return 10.0 ** log_a + return 10.0 ** np.asarray(log_a, dtype=float) + + def sigma_log_a(self, mass): + """ + σ(log10 a) from a 2-parameter logistic in log-mass. + + Floors/ceilings pinned at 0.7 / 1.5; clipped to ≥ 0.1. + """ + return _logistic_in_logm( + mass, OFFNER2023_SIG_A, OFFNER2023_SIG_B, + OFFNER2023_SIG_M0, OFFNER2023_SIG_K, clip_min=0.1) def _q_values_for_primaries(self, prim_subset, n_comp, rng): """Mass-dependent q for every primary (BD and stellar).""" @@ -968,13 +1067,12 @@ class MultiplicityResolvedOffner2023(MultiplicityUnresolvedOffner2023, Resolved Offner et al. 2023 multiplicity: Table 1 MF/CF plus mass-dependent separations. - Separations are drawn from a truncated lognormal in log10(a/AU). - The mean μ(a) interpolates Table 1 ã_all and Table 2 lognormal μ - (late-M μ=4 au, σ=0.7; early-M μ=25 au, σ=1.3; FGK μ=40 au, - σ=1.5). Brown-dwarf / late-M binaries peak near 3–4 au (vast - majority at 1–20 au). σ_log a uses Table 2 and is held at the - late-M value (0.7) through the BD regime, as Offner et al. 2023 - describe the BD separation distribution as similar to late-M. + Separations are drawn from a truncated lognormal in log10(a/AU) + with loc = :meth:`log_a_mean` (smooth broken power law, s = 0.1 + dex, FGK-pulled) and scale = :meth:`sigma_log_a` (2-parameter + logistic pinned at 0.7 / 1.5). Brown-dwarf binaries peak near a + few AU. Truncation is 0.01–2000 AU, same as + :class:`MultiplicityResolvedDK`. Eccentricity and Keplerian angles follow Duchêne & Kraus (2013), same as :class:`MultiplicityResolvedDK`. @@ -983,6 +1081,7 @@ class MultiplicityResolvedOffner2023(MultiplicityUnresolvedOffner2023, """ def __init__(self, **kwargs): super(MultiplicityResolvedOffner2023, self).__init__(**kwargs) + # Table 1/2 data that was fit; draws use log_a_mean / sigma_log_a. self.sep_mass = np.array(OFFNER2023_SEP_MASS, dtype=float) self.sep_mu_au = np.array(OFFNER2023_SEP_MU_AU, dtype=float) self.sep_sig_mass = np.array(OFFNER2023_SEP_SIG_MASS, dtype=float) @@ -1003,12 +1102,8 @@ def log_semimajoraxis(self, mass): log10 of the semimajor axis in AU, truncated to 0.01–2000 AU. """ mass = np.atleast_1d(np.asarray(mass, dtype=float)) - mass_clip = np.clip(mass, self.sep_mass[0], self.sep_mass[-1]) - logm = np.log10(mass_clip) - log_a_mean = np.interp(logm, np.log10(self.sep_mass), - np.log10(self.sep_mu_au)) - log_a_std = np.interp(logm, np.log10(self.sep_sig_mass), self.sep_sig) - log_a_std = np.clip(log_a_std, 0.1, None) + log_a_mean = np.atleast_1d(np.asarray(self.log_a_mean(mass), dtype=float)) + log_a_std = np.atleast_1d(np.asarray(self.sigma_log_a(mass), dtype=float)) log_a_lower = np.log10(0.01) log_a_upper = np.log10(2000) diff --git a/spisea/tests/test_multiplicity.py b/spisea/tests/test_multiplicity.py index 78593a6..23507e7 100755 --- a/spisea/tests/test_multiplicity.py +++ b/spisea/tests/test_multiplicity.py @@ -436,20 +436,51 @@ def test_offner2023_q_more_equal_mass_for_bds(): q_bd = multi.random_q(rng.random(n), mass=0.04) q_sun = multi.random_q(rng.random(n), mass=1.0) assert np.mean(q_bd) > np.mean(q_sun) + 0.1 - # Fontanive gamma_trunc = 4.8 is steeply equal-mass - assert multi.q_power_at_mass(0.033) > 3.0 - assert multi.q_power_at_mass(1.0) < 1.0 + # Err-wt logistic undershoots Fontanive 4.8 (~3.3 at 0.033 Msun) + assert multi.q_power_at_mass(0.033) > 2.5 + assert multi.q_power_at_mass(1.0) < 0.5 + + +def test_offner2023_q_sigma_a_closed_form(): + """γ, σ(log a), and log_a_mean match the smooth helpers; not interpolation.""" + multi = multiplicity.MultiplicityUnresolvedOffner2023() + masses = np.array([0.033, 0.065, 0.3, 1.0, 10.0]) + for m in masses: + np.testing.assert_allclose( + multi.q_power_at_mass(m), + multiplicity._logistic_in_logm( + m, 6.6, -1.77, 0.0651, 0.629)) + np.testing.assert_allclose( + multi.sigma_log_a(m), + multiplicity._logistic_in_logm( + m, 0.7, 1.5, 0.354, 6.05, clip_min=0.1)) + np.testing.assert_allclose( + multi.log_a_mean(m), + multiplicity._smooth_broken_loglog( + m, 44.46, 0.819, 1.005, -0.308, 0.10, a_min=0.1)) + # Array vs scalar + g_arr = multi.q_power_at_mass(masses) + sig_arr = multi.sigma_log_a(masses) + loga_arr = multi.log_a_mean(masses) + for i, m in enumerate(masses): + np.testing.assert_allclose(g_arr[i], multi.q_power_at_mass(float(m))) + np.testing.assert_allclose(sig_arr[i], multi.sigma_log_a(float(m))) + np.testing.assert_allclose(loga_arr[i], multi.log_a_mean(float(m))) + # Old L/early-T interpolation knot was 2.5; logistic is not that. + g_knot = multi.q_power_at_mass(0.065) + np.testing.assert_allclose( + g_knot, multiplicity._logistic_in_logm(0.065, 6.6, -1.77, 0.0651, 0.629)) + assert abs(g_knot - 2.5) > 0.05 def test_offner2023_bd_separations_peak_few_au(): - """BD lognormal separations peak at a few AU (Table 1 ã_all ~ 3 au).""" + """BD lognormal separations peak at a few AU (μ(0.033)≈2.1 au).""" multi = multiplicity.MultiplicityResolvedOffner2023() np.random.seed(0) log_a = multi.log_semimajoraxis(np.full(5000, 0.04)) med_a = 10 ** np.median(log_a) - # Fontanive ã_all = 2.9 au; allow a factor of ~2 assert 1.5 < med_a < 8.0, 'BD median a = {0:.2f} AU'.format(med_a) - # Solar-type should be much wider (Table 2 μ = 40 au) + # Solar-type should be much wider (smooth-broken μ ~ 44 au) log_a_s = multi.log_semimajoraxis(np.full(5000, 1.0)) med_a_s = 10 ** np.median(log_a_s) assert med_a_s > 10.0 @@ -462,6 +493,8 @@ def test_offner2023_alias_and_resolved_methods(): multiplicity.MultiplicityUnresolvedOffner2023 resolved = multiplicity.MultiplicityResolvedOffner2023() assert hasattr(resolved, 'log_semimajoraxis') + assert hasattr(resolved, 'log_a_mean') + assert hasattr(resolved, 'sigma_log_a') e = resolved.random_e(np.array([0.0, 0.25, 1.0])) np.testing.assert_allclose(e, [0.0, 0.5, 1.0]) From 3da12cd0b9e16b9e14e80e9db4fe9da33c2e891c Mon Sep 17 00:00:00 2001 From: Cursor Agent Date: Fri, 14 Aug 2026 00:53:27 +0000 Subject: [PATCH 08/16] Document Offner 2023 multiplicity models and comparison figures Expand docs/multiplicity.rst with formulas for MF/CSF, gamma, mu(a), and sigma(log a), plus the five Lu+2013 comparison figures. Point imf.rst and the changelog at the opt-in Offner model. Co-authored-by: Jessica Lu --- docs/imf.rst | 3 +- docs/index.rst | 2 +- docs/multiplicity.rst | 213 +++++++++++++++++++++++++++++++++--------- 3 files changed, 173 insertions(+), 45 deletions(-) diff --git a/docs/imf.rst b/docs/imf.rst index ed60177..e61fdce 100644 --- a/docs/imf.rst +++ b/docs/imf.rst @@ -17,7 +17,8 @@ and exponents of the IMF. The IMF object is an input for the :ref:`cluster_objects`, and will be used to draw the inital stellar mass distribution for the cluster. A :ref:`multi_obj` may be passed to the IMF object to -form multiple star systems. +form multiple star systems. The default is Lu et al. (2013); +Offner et al. 2023 is opt-in (see :ref:`multi_obj`). Base IMF Class -------------- diff --git a/docs/index.rst b/docs/index.rst index f586c77..b22f1e5 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -97,7 +97,7 @@ Change Log * New tutorial for creating SPISEA clusters using COSMIC: docs/Cluster_w_COSMIC.ipynb * *Minor Changes* - * Added opt-in Offner et al. 2023 (Protostars and Planets VII; arXiv:2203.10066) multiplicity model, including brown dwarfs, as a 4-parameter logistic in log-mass fitted to Table 1 MF/CF. See :ref:`multi_obj`. Lu et al. (2013) remains the default. + * Added opt-in Offner et al. 2023 (Protostars and Planets VII; arXiv:2203.10066) multiplicity model, including brown dwarfs. MF/CSF is a logistic in log-mass; :math:`\gamma(M)` is an error-weighted logistic; :math:`\mu(a)` is a smooth broken power law (:math:`s=0.1` dex); :math:`\sigma(\log_{10} a)` is a 2-parameter logistic. Comparison figures vs Lu et al. (2013) are in :ref:`multi_obj`. Lu et al. (2013) remains the default. * Companion mass and separation draws (including brown-dwarf q and binaries-only BD systems) now live on the multiplicity object rather than being special-cased in ``imf.py``. * The MISTv1.2-synthpop model extension was modified to include denser sampling in the gap between the base MISTv1.2 grids and 0.1Msun. * Modified default for MISTv1.2 isochrones: synthpop_extension will be True by default to keep a consistent lower mass limit of 0.1Msun across all ages and metallicities. diff --git a/docs/multiplicity.rst b/docs/multiplicity.rst index 629dc80..733f492 100644 --- a/docs/multiplicity.rst +++ b/docs/multiplicity.rst @@ -77,80 +77,207 @@ Unresolved Multiplicity Classes .. autoclass:: imf.multiplicity.MultiplicityUnresolvedOffner2023 :show-inheritance: :members: multiplicity_fraction, companion_star_fraction, - q_power_at_mass, random_q, log_a_mean, sigma_log_a + q_power_at_mass, random_q, log_a_mean, a_mean, + sigma_log_a + + +Offner et al. 2023 multiplicity +------------------------------------------ +Opt-in field multiplicity from Offner et al. (2023), Protostars and +Planets VII, ASP Conf. Ser. 534, 275 (`arXiv:2203.10066 +`_; ADS +`2023ASPC..534..275O +`_). Table 1 +data: Zenodo `10.5281/zenodo.6628915 +`_. The Lu et al. (2013) :class:`~imf.multiplicity.MultiplicityUnresolved` -object remains the default. Offner et al. 2023 is **opt-in**:: +object remains the default. Pass an Offner instance as +``IMF.multiplicity`` to use this model. + +Unresolved (companions, no orbits):: from spisea.imf import imf, multiplicity from spisea import synthetic multi = multiplicity.MultiplicityUnresolvedOffner2023() - # or the alias: + # alias: # multi = multiplicity.MultiplicityOffner2023() imf_obj = imf.Kroupa_2001(multiplicity=multi) cluster = synthetic.ResolvedCluster(iso, imf_obj, Mcl) -MF vs primary mass (Lu et al. 2013 array power law and scalar BD staircase -compared to the Offner logistic in log-mass and Table 1 points): +Resolved (same MF/CSF/q, plus mass-dependent separations):: + + multi = multiplicity.MultiplicityResolvedOffner2023() + +The generic helpers :class:`~imf.multiplicity.MultiplicityLogistic` and +:class:`~imf.multiplicity.MultiplicityPiecewisePowerLaw` are available +for other surveys. Offner does **not** evaluate MF/CSF, :math:`\gamma`, +or separations as a piecewise interpolation of Table 1/2 knots. + +Multiplicity and companion-star fractions +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +MF and CSF are a 4-parameter logistic in log-mass, fitted with equal +weight to the geom-mean MF/CF columns of Table 1: + +.. math:: + + f(M) = A + \frac{B - A}{1 + (M / M_0)^{-k}} + +with :math:`(A, B, M_0, k) = (0.14, 0.99, 1.41, 1.25)` for MF and +:math:`(0.12, 2.35, 3.57, 0.96)` for CSF. The curve is C-infinity +smooth and saturates at :math:`B \approx 1` for MF. MF is clipped to +:math:`[0, 1]`. CSF is clipped to :math:`[0, \mathrm{CSF_{max}}]`, +raised to at least MF, and forced equal to MF for +:math:`M \le 0.08\,M_\odot` (binaries only). Masses :math:`M \le 0` +map to the low-mass asymptote :math:`A`. + +Lu et al. (2013) uses :math:`\mathrm{MF} = 0.44\,M^{0.51}` (clipped +to 1) for arrays, plus a scalar-only brown-dwarf staircase +(0 / 8% / 16%). Cluster generation on that class still uses the +stellar power law for brown-dwarf primaries. .. figure:: figures/mf_offner_vs_lu2013.png - :alt: Multiplicity fraction vs primary mass: Lu+2013 vs Offner 2023 logistic in log M + :alt: Multiplicity fraction vs primary mass: Offner logistic vs Lu+2013 power law and scalar BD staircase :align: center - Left: brown-dwarf zoom. Right: BD through early B. The Offner model is a - 4-parameter logistic in log-mass fitted to Table 1, C-infinity smooth - and saturating at B ~ 1. The shaded region is below the hydrogen-burning - limit (0.08 solar masses). Reproduce with - ``python docs/figures/plot_mf_offner_vs_lu2013.py``. + Multiplicity fraction vs primary mass. Left: brown-dwarf zoom. + Right: BD through early B. Solid: Offner logistic in log-mass. + Dashed: Lu+2013 :math:`0.44\,M^{0.51}`. Dotted: Lu+2013 scalar BD + staircase. Blue points: Offner Table 1. Shaded: + :math:`M \le 0.08\,M_\odot`. + +Mass-ratio index +~~~~~~~~~~~~~~~~ +Companion mass ratios follow :math:`P(q) \propto q^{\gamma}` on +:math:`q_{\min} \le q \le 1` (default :math:`q_{\min} = 0.01`). +:math:`\gamma(M)` is an error-weighted logistic in log-mass fitted to +Table 1 :math:`\gamma_{\mathrm{trunc}}` (1–100 au): + +.. math:: + + \gamma(M) = A + \frac{B - A}{1 + (M / M_0)^{-k}} + +with :math:`(A, B, M_0, k) = (6.6, -1.77, 0.0651, 0.629)`. Call +``q_power_at_mass(mass)`` or ``random_q(x, mass=...)``. Without +``mass``, ``random_q(x)`` keeps the historical stellar-only power law. -Mass-ratio index vs primary mass (Offner is an error-weighted logistic -in log-mass fitted to Table 1 :math:`\gamma_\mathrm{trunc}`; Lu+2013 is -a step: 6.1 below 0.08 solar masses, :math:`-0.4` above): +The err-weighted fit undershoots Fontanive et al. (2018) +:math:`8\pm 6\%` MF and :math:`\gamma = 4.8\pm 2.2`: at +:math:`0.033\,M_\odot`, :math:`\gamma \approx 3.3`. That is the +fit, not a bug. Lu+2013 is a step: :math:`\gamma = 6.1` for +:math:`M \le 0.08\,M_\odot` (Fontanive) and :math:`-0.4` above. .. figure:: figures/q_offner_vs_lu2013.png - :alt: Mass-ratio index vs primary mass: Lu+2013 step vs Offner error-weighted logistic + :alt: Mass-ratio index vs primary mass: Offner error-weighted logistic vs Lu+2013 6.1 / -0.4 step :align: center - Left: brown-dwarf zoom. Right: BD through O. Offner BD companions are - more equal-mass than Lu’s stellar :math:`q` power. Reproduce with - ``python docs/figures/plot_q_sep_offner_vs_lu2013.py``. + Mass-ratio index :math:`\gamma` vs primary mass. Solid: Offner + error-weighted logistic. Dashed: Lu+2013 step (6.1 below + :math:`0.08\,M_\odot`, :math:`-0.4` above). Blue points: Table 1 + :math:`\gamma_{\mathrm{trunc}}`. -Characteristic separation vs primary mass (Offner is a smooth broken -power law in :math:`\log_{10} a` vs :math:`\log_{10} M`, :math:`s=0.1` -dex, FGK-pulled; Lu+2013 is the Duchêne–Kraus broken power law with a -brown-dwarf blend): +.. figure:: figures/meanq_offner_vs_lu2013.png + :alt: Mean mass ratio vs primary mass implied by P(q) proportional to q^gamma + :align: center + + Mean mass ratio :math:`\langle q \rangle` on :math:`[0.01, 1]` + implied by :math:`P(q)\propto q^{\gamma}`. Offner brown-dwarf + companions are more equal-mass than Lu+2013 stellar :math:`q`. + +Characteristic separation +~~~~~~~~~~~~~~~~~~~~~~~~~ +The characteristic :math:`\mu(a)` is a smooth broken power law in +:math:`\log_{10} a` vs :math:`\log_{10} M`, FGK-pulled, with smoothing +scale :math:`s = 0.1` dex. It is C-infinity (stable +:math:`\log\cosh`; not :math:`\log(\cosh x)` and not a hard +``where`` break): + +.. math:: + + v = \log_{10}(M / M_p),\quad + y_p = \log_{10}(\mu_p) + +.. math:: + + \log_{10} a = y_p + \tfrac{1}{2}(\alpha_L+\alpha_R)\,v + + \tfrac{1}{2}(\alpha_R-\alpha_L)\,s\,\log\cosh(v/s) + +with :math:`\mu_p = 44.46` AU, :math:`M_p = 0.819\,M_\odot`, +:math:`\alpha_L = 1.005`, :math:`\alpha_R = -0.308`, :math:`s = 0.10`. +Linear-space :math:`a` is clipped above 0.1 AU. The implementation +uses the stable form +:math:`\log\cosh x = |x| + \log(1+e^{-2|x|}) - \log 2`. +``log_a_mean(mass)`` returns :math:`\log_{10}(a/\mathrm{AU})`; +``a_mean(mass)`` returns :math:`a` in AU. + +Lu+2013 :class:`~imf.multiplicity.MultiplicityResolvedDK` uses a +Duchêne & Kraus (2013) broken power law in :math:`a` with a +brown-dwarf blend. That law is not meant for the BD regime. .. figure:: figures/sep_offner_vs_lu2013.png - :alt: Characteristic separation vs primary mass: Lu+2013 DK vs Offner smooth broken PL + :alt: Characteristic separation vs primary mass: Offner smooth broken power law vs Lu+2013 Duchene-Kraus :align: center - Open circles are Table 1 :math:`\tilde{a}_\mathrm{all}`; filled squares - are Table 2 :math:`\mu` knots (4, 25, 40 au). Offner BD binaries peak - at a few AU. Same script. + Characteristic :math:`\mu(a)` vs primary mass. Solid: Offner + smooth broken power law. Dashed: Lu+2013 DK mean :math:`a`. + Open circles: Table 1 :math:`\tilde{a}_{\mathrm{all}}`. Filled + squares: Table 2 :math:`\mu` knots (4, 25, 40 AU). Offner BD + binaries peak at a few AU. -Separation scatter vs primary mass (Offner is a 2-parameter logistic -pinned at 0.7 / 1.5; Lu+2013 DK is a linear fit in log mass that -saturates above 2.9 solar masses): +Separation scatter +~~~~~~~~~~~~~~~~~~ +:math:`\sigma(\log_{10} a)` is a 2-parameter logistic pinned at +0.7 / 1.5: -.. figure:: figures/sig_loga_offner_vs_lu2013.png - :alt: Sigma of log10 a vs primary mass: Lu+2013 DK vs Offner 2-param logistic - :align: center +.. math:: - Left: brown-dwarf zoom. Right: BD through O. Filled squares are the - Table 2 knots. The Lu dip near 0.08 solar masses is the BD/stellar - blend. Same script. + \sigma(M) = 0.7 + \frac{0.8}{1 + (M / 0.354)^{-6.05}} -Mean mass ratio on :math:`0.01 \leq q \leq 1` from :math:`P(q)\propto q^{\gamma}`: +i.e. :math:`(A, B, M_0, k) = (0.7, 1.5, 0.354, 6.05)`, clipped to +:math:`\ge 0.1`. Call ``sigma_log_a(mass)``. Lu+2013 DK is a linear +fit in :math:`\log M` that saturates above :math:`2.9\,M_\odot`; the +dip near :math:`0.08\,M_\odot` is the BD/stellar blend. -.. figure:: figures/meanq_offner_vs_lu2013.png - :alt: Mean mass ratio vs primary mass implied by the gamma curves +.. figure:: figures/sig_loga_offner_vs_lu2013.png + :alt: Sigma of log10 a vs primary mass: Offner 2-param logistic vs Lu+2013 DK :align: center - Companion to the :math:`\gamma` panel. Same script. - -Figure generators live at ``docs/figures/plot_mf_offner_vs_lu2013.py`` -and ``docs/figures/plot_q_sep_offner_vs_lu2013.py``. + :math:`\sigma(\log_{10} a)` vs primary mass. Solid: Offner + 2-parameter logistic. Dashed: Lu+2013 DK. Filled squares: Table 2 + knots (0.7, 1.3, 1.5). + +Resolved draws +~~~~~~~~~~~~~~ +:class:`~imf.multiplicity.MultiplicityResolvedOffner2023` draws +:math:`\log_{10}(a/\mathrm{AU})` from a truncated lognormal with +``loc = log_a_mean(mass)`` and ``scale = sigma_log_a(mass)``, +truncated to 0.01–2000 AU (same limits as +:class:`~imf.multiplicity.MultiplicityResolvedDK`). Eccentricity +and Keplerian angles still follow Duchêne & Kraus (2013) +(:math:`f(e)=2e`, random inclination and angles). + +Brown-dwarf policy and Table 1 +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Primaries at or below :math:`0.08\,M_\odot` are binaries only: +CSF = MF and the companion count is capped at 1. + +Table 1 FGKM MF/CF exclude brown-dwarf companions +(:math:`M_{\mathrm{comp}} > 0.075\,M_\odot` for FGKM; +OBA use :math:`q > 0.1`). SPISEA still draws companions down to +``q_min`` (default 0.01), so some stellar primaries get BD +secondaries (~4% for solar-type). Do not read the simulated +stellar-primary MF as a stellar-companion-only statistic. + +Reproducing the figures +~~~~~~~~~~~~~~~~~~~~~~~ +The comparison figures are generated from the multiplicity object +methods (``multiplicity_fraction``, ``q_power_at_mass``, +``a_mean``, ``sigma_log_a``) so they cannot drift from the code. +From the repository root:: + + python docs/figures/plot_mf_offner_vs_lu2013.py + python docs/figures/plot_q_sep_offner_vs_lu2013.py Resolved Multiplicity Classes @@ -160,5 +287,5 @@ Resolved Multiplicity Classes .. autoclass:: imf.multiplicity.MultiplicityResolvedOffner2023 :show-inheritance: - :members: log_semimajoraxis, log_a_mean, sigma_log_a + :members: log_semimajoraxis, log_a_mean, a_mean, sigma_log_a From 7169fff615e3b932769530b5fd543010aa4067ad Mon Sep 17 00:00:00 2001 From: Cursor Agent Date: Fri, 14 Aug 2026 16:05:20 +0000 Subject: [PATCH 09/16] Label Offner comparison baseline as SPISEA v2.5, not Lu+2013 The comparison plots and docs describe Offner 2023 vs the default MultiplicityUnresolved / MultiplicityResolvedDK that shipped in SPISEA v2.5. Keep Lu et al. 2013 citations on the original classes. 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z?)rK0&8RO+O&GNWU5ky2Bci?MBng4^;E352RVWv>GuWQnpZ3Frzn&cmjRbnKTWaf; zEh98XnM$vl`k$jQDEUC7ebQr4Uz53}{-5;aD^@IIo!+#RJ}p1xy-t@eUxvjqE$s4x|+F8a?8M0-z+e1T9O>OzA|NP5s)PN(&qPFn=es9TikrMvj|09_Xkl|td*B9yb zJRu*s%{{VN8ro{jN diff --git a/docs/figures/plot_mf_offner_vs_lu2013.py b/docs/figures/plot_mf_offner_vs_lu2013.py index 3303055..ea41605 100644 --- a/docs/figures/plot_mf_offner_vs_lu2013.py +++ b/docs/figures/plot_mf_offner_vs_lu2013.py @@ -3,7 +3,7 @@ Generate docs/figures/mf_offner_vs_lu2013.png Two-panel comparison of multiplicity fraction vs primary mass: -Lu et al. (2013) array power law, Lu+2013 scalar BD staircase, +SPISEA v2.5 array power law, v2.5 scalar BD staircase, Offner et al. 2023 logistic in log-mass, and Offner Table 1 points with error bars. @@ -47,13 +47,13 @@ def _lu2013_array_mf(mass): - """What cluster generation used: stellar power law, no BD staircase.""" + """SPISEA v2.5 array path: stellar power law, no BD staircase.""" mf = 0.44 * np.asarray(mass, dtype=float) ** 0.51 return np.clip(mf, 0.0, 1.0) def _lu2013_scalar_bd_staircase(mass): - """Scalar-only BD bins in MultiplicityUnresolved.multiplicity_fraction.""" + """SPISEA v2.5 scalar-only BD bins in MultiplicityUnresolved.multiplicity_fraction.""" mass = np.asarray(mass, dtype=float) mf = _lu2013_array_mf(mass) mf = np.where(mass < 0.02, 0.0, mf) @@ -74,9 +74,9 @@ def _style_panel(ax, m_off, mf_off, m_lu, mf_lu, m_step, mf_step, ax.axvspan(xlim[0], 0.08, color='#e8d5b5', alpha=0.55, zorder=0) ax.axvline(0.08, color='#c4a574', ls='--', lw=1.2, zorder=1) ax.plot(m_lu, mf_lu, color='0.25', ls='--', lw=1.6, zorder=3, - label=r'Lu+2013 power law $0.44\,M^{0.51}$') + label=r'SPISEA v2.5 $0.44\,M^{0.51}$') ax.plot(m_step, mf_step, color='0.45', ls=':', lw=1.8, zorder=3, - label=r'Lu+2013 scalar BD bins (0 / 8% / 16%)') + label=r'SPISEA v2.5 scalar BD bins (0 / 8% / 16%)') ax.plot(m_off, mf_off, color='#8b3a2a', ls='-', lw=2.4, zorder=4, label='Offner logistic in log M') ax.errorbar(m_tab, mf_tab, yerr=err_tab, fmt='o', color='#2f6db3', @@ -109,7 +109,8 @@ def main(): fig, axes = plt.subplots(1, 2, figsize=(11.2, 4.6), gridspec_kw={'wspace': 0.28}) - fig.suptitle('Multiplicity fraction vs primary mass', fontsize=13, y=1.02) + fig.suptitle('Offner 2023 vs SPISEA v2.5: multiplicity fraction', + fontsize=13, y=1.02) _style_panel( axes[0], m_wide, mf_off, m_wide, mf_lu, m_step, mf_step, @@ -124,9 +125,9 @@ def main(): legend_handles = [ Line2D([0], [0], color='0.25', ls='--', lw=1.6, - label=r'Lu+2013 power law $0.44\,M^{0.51}$'), + label=r'SPISEA v2.5 $0.44\,M^{0.51}$'), Line2D([0], [0], color='0.45', ls=':', lw=1.8, - label=r'Lu+2013 scalar BD bins (0 / 8% / 16%)'), + label=r'SPISEA v2.5 scalar BD bins (0 / 8% / 16%)'), Line2D([0], [0], color='#8b3a2a', ls='-', lw=2.4, label='Offner logistic in log M'), Line2D([0], [0], marker='o', color='#2f6db3', ls='none', diff --git a/docs/figures/plot_q_sep_offner_vs_lu2013.py b/docs/figures/plot_q_sep_offner_vs_lu2013.py index 856470e..183e19f 100644 --- a/docs/figures/plot_q_sep_offner_vs_lu2013.py +++ b/docs/figures/plot_q_sep_offner_vs_lu2013.py @@ -1,6 +1,6 @@ #!/usr/bin/env python """ -Generate q / separation comparison figures vs Lu et al. (2013): +Generate q / separation comparison figures vs SPISEA v2.5 defaults: docs/figures/q_offner_vs_lu2013.png docs/figures/sep_offner_vs_lu2013.png @@ -96,8 +96,9 @@ def _table_xy(rows, y_idx=3, e_idx=4): def _lu2013_dk_mean_a_au(dk, mass): """ - Duchêne & Kraus mean a in AU from ``MultiplicityResolvedDK`` coefficients, - plus the BD log-a interpolation and sigmoid blend in ``log_semimajoraxis``. + SPISEA v2.5 ``MultiplicityResolvedDK`` mean a in AU (Duchêne & Kraus + coefficients, plus the BD log-a interpolation and sigmoid blend in + ``log_semimajoraxis``). """ mass = np.atleast_1d(np.asarray(mass, dtype=float)) logm = np.log10(mass) @@ -121,8 +122,9 @@ def _lu2013_dk_mean_a_au(dk, mass): def _lu2013_dk_sig_loga(dk, mass): """ - Duchêne & Kraus σ(log10 a) from ``MultiplicityResolvedDK`` coefficients, - plus the BD interpolation and sigmoid blend in ``log_semimajoraxis``. + SPISEA v2.5 ``MultiplicityResolvedDK`` σ(log10 a) (Duchêne & Kraus + coefficients, plus the BD interpolation and sigmoid blend in + ``log_semimajoraxis``). """ mass = np.atleast_1d(np.asarray(mass, dtype=float)) logm = np.log10(mass) @@ -208,7 +210,7 @@ def plot_gamma(offner, lu): g_lu = lu.q_power_at_mass(m_step) m_tab, g_tab, err_tab = _table_xy(_TABLE1_GAMMA) - fig, axes = _two_axes(r'Mass-ratio index $\gamma$ vs primary mass') + fig, axes = _two_axes(r'Offner 2023 vs SPISEA v2.5: mass-ratio index $\gamma$') ylabel = r'$\gamma$ ($P(q)\propto q^{\gamma}$)' for ax, xlim, title in ( (axes[0], _BD_XLIM, 'Brown-dwarf regime'), @@ -225,7 +227,7 @@ def plot_gamma(offner, lu): legend_handles = [ Line2D([0], [0], color='0.25', ls='--', lw=1.6, - label=r'Lu+2013 $\gamma=6.1$ (BD), $-0.4$ (stellar)'), + label=r'SPISEA v2.5 ($\gamma=6.1$ / $-0.4$)'), Line2D([0], [0], color=_OFFNER_COLOR, ls='-', lw=2.4, label=r'Offner err-wt logistic in log $M$'), Line2D([0], [0], marker='o', color=_TABLE1_COLOR, ls='none', @@ -246,7 +248,7 @@ def plot_sep(resolved, dk): m_t2 = np.array([_geom(r[1], r[2]) for r in _TABLE2_MU]) a_t2 = np.array([r[3] for r in _TABLE2_MU], dtype=float) - fig, axes = _two_axes(r'Characteristic separation vs primary mass') + fig, axes = _two_axes(r'Offner 2023 vs SPISEA v2.5: characteristic separation') ylabel = r'$\mu(a)$ (AU)' for ax, xlim, title in ( (axes[0], _BD_XLIM, 'Brown-dwarf regime'), @@ -264,7 +266,7 @@ def plot_sep(resolved, dk): legend_handles = [ Line2D([0], [0], color='0.25', ls='--', lw=1.6, - label=r'Lu+2013 DK mean $a$'), + label=r'SPISEA v2.5 mean $a$'), Line2D([0], [0], color=_OFFNER_COLOR, ls='-', lw=2.4, label=r'Offner smooth broken PL ($s=0.1$ dex)'), Line2D([0], [0], marker='o', color=_TABLE1_COLOR, ls='none', @@ -286,7 +288,7 @@ def plot_sig_loga(resolved, dk): m_t2 = np.array(resolved.sep_sig_mass, dtype=float) sig_t2 = np.array(resolved.sep_sig, dtype=float) - fig, axes = _two_axes(r'Separation scatter $\sigma(\log_{10} a)$ vs primary mass') + fig, axes = _two_axes(r'Offner 2023 vs SPISEA v2.5: $\sigma(\log_{10} a)$') ylabel = r'$\sigma(\log_{10} a)$' for ax, xlim, title in ( (axes[0], _BD_XLIM, 'Brown-dwarf regime'), @@ -301,7 +303,7 @@ def plot_sig_loga(resolved, dk): legend_handles = [ Line2D([0], [0], color='0.25', ls='--', lw=1.6, - label=r'Lu+2013 DK $\sigma(\log_{10} a)$'), + label=r'SPISEA v2.5 DK $\sigma_{\log a}$'), Line2D([0], [0], color=_OFFNER_COLOR, ls='-', lw=2.4, label=r'Offner 2-param logistic $\sigma$'), Line2D([0], [0], marker='s', color=_OFFNER_COLOR, ls='none', @@ -321,7 +323,7 @@ def plot_meanq(offner, lu): m_step = _lu_gamma_step_masses() q_lu = _mean_q_from_gamma(lu.q_power_at_mass(m_step), q_min=lu.q_min) - fig, axes = _two_axes(r'Mean mass ratio $\langle q\rangle$ vs primary mass') + fig, axes = _two_axes(r'Offner 2023 vs SPISEA v2.5: mean mass ratio $\langle q\rangle$') ylabel = r'$\langle q\rangle$ on $[0.01,\,1]$' for ax, xlim, title in ( (axes[0], _BD_XLIM, 'Brown-dwarf regime'), @@ -334,7 +336,7 @@ def plot_meanq(offner, lu): legend_handles = [ Line2D([0], [0], color='0.25', ls='--', lw=1.6, - label=r'Lu+2013 from $\gamma$ 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exponents of the IMF. The IMF object is an input for the :ref:`cluster_objects`, and will be used to draw the inital stellar mass distribution for the cluster. A :ref:`multi_obj` may be passed to the IMF object to -form multiple star systems. The default is Lu et al. (2013); +form multiple star systems. The default is the SPISEA v2.5 +:class:`~imf.multiplicity.MultiplicityUnresolved` / +:class:`~imf.multiplicity.MultiplicityResolvedDK` objects; Offner et al. 2023 is opt-in (see :ref:`multi_obj`). Base IMF Class diff --git a/docs/index.rst b/docs/index.rst index b22f1e5..fdfe005 100644 --- a/docs/index.rst +++ b/docs/index.rst @@ -97,7 +97,7 @@ Change Log * New tutorial for creating SPISEA clusters using COSMIC: docs/Cluster_w_COSMIC.ipynb * *Minor Changes* - * Added opt-in Offner et al. 2023 (Protostars and Planets VII; arXiv:2203.10066) multiplicity model, including brown dwarfs. MF/CSF is a logistic in log-mass; :math:`\gamma(M)` is an error-weighted logistic; :math:`\mu(a)` is a smooth broken power law (:math:`s=0.1` dex); :math:`\sigma(\log_{10} a)` is a 2-parameter logistic. Comparison figures vs Lu et al. (2013) are in :ref:`multi_obj`. Lu et al. (2013) remains the default. + * Added opt-in Offner et al. 2023 (Protostars and Planets VII; arXiv:2203.10066) multiplicity model, including brown dwarfs. MF/CSF is a logistic in log-mass; :math:`\gamma(M)` is an error-weighted logistic; :math:`\mu(a)` is a smooth broken power law (:math:`s=0.1` dex); :math:`\sigma(\log_{10} a)` is a 2-parameter logistic. Comparison figures vs SPISEA v2.5 are in :ref:`multi_obj`. The SPISEA v2.5 :class:`~imf.multiplicity.MultiplicityUnresolved` / :class:`~imf.multiplicity.MultiplicityResolvedDK` objects remain the default. * Companion mass and separation draws (including brown-dwarf q and binaries-only BD systems) now live on the multiplicity object rather than being special-cased in ``imf.py``. * The MISTv1.2-synthpop model extension was modified to include denser sampling in the gap between the base MISTv1.2 grids and 0.1Msun. * Modified default for MISTv1.2 isochrones: synthpop_extension will be True by default to keep a consistent lower mass limit of 0.1Msun across all ages and metallicities. diff --git a/docs/multiplicity.rst b/docs/multiplicity.rst index 733f492..a400781 100644 --- a/docs/multiplicity.rst +++ b/docs/multiplicity.rst @@ -91,9 +91,10 @@ Planets VII, ASP Conf. Ser. 534, 275 (`arXiv:2203.10066 data: Zenodo `10.5281/zenodo.6628915 `_. -The Lu et al. (2013) :class:`~imf.multiplicity.MultiplicityUnresolved` -object remains the default. Pass an Offner instance as -``IMF.multiplicity`` to use this model. +The SPISEA v2.5 :class:`~imf.multiplicity.MultiplicityUnresolved` / +:class:`~imf.multiplicity.MultiplicityResolvedDK` objects remain the +default. Pass an Offner instance as ``IMF.multiplicity`` to use this +model. Unresolved (companions, no orbits):: @@ -132,20 +133,20 @@ raised to at least MF, and forced equal to MF for :math:`M \le 0.08\,M_\odot` (binaries only). Masses :math:`M \le 0` map to the low-mass asymptote :math:`A`. -Lu et al. (2013) uses :math:`\mathrm{MF} = 0.44\,M^{0.51}` (clipped +SPISEA v2.5 uses :math:`\mathrm{MF} = 0.44\,M^{0.51}` (clipped to 1) for arrays, plus a scalar-only brown-dwarf staircase (0 / 8% / 16%). Cluster generation on that class still uses the stellar power law for brown-dwarf primaries. .. figure:: figures/mf_offner_vs_lu2013.png - :alt: Multiplicity fraction vs primary mass: Offner logistic vs Lu+2013 power law and scalar BD staircase + :alt: Offner 2023 vs SPISEA v2.5: multiplicity fraction vs primary mass :align: center - Multiplicity fraction vs primary mass. Left: brown-dwarf zoom. - Right: BD through early B. Solid: Offner logistic in log-mass. - Dashed: Lu+2013 :math:`0.44\,M^{0.51}`. Dotted: Lu+2013 scalar BD - staircase. Blue points: Offner Table 1. Shaded: - :math:`M \le 0.08\,M_\odot`. + Offner 2023 vs SPISEA v2.5: multiplicity fraction vs primary mass. + Left: brown-dwarf zoom. Right: BD through early B. Solid: Offner + logistic in log-mass. Dashed: SPISEA v2.5 :math:`0.44\,M^{0.51}`. + Dotted: SPISEA v2.5 scalar BD staircase. Blue points: Offner + Table 1. Shaded: :math:`M \le 0.08\,M_\odot`. Mass-ratio index ~~~~~~~~~~~~~~~~ @@ -165,25 +166,26 @@ with :math:`(A, B, M_0, k) = (6.6, -1.77, 0.0651, 0.629)`. Call The err-weighted fit undershoots Fontanive et al. (2018) :math:`8\pm 6\%` MF and :math:`\gamma = 4.8\pm 2.2`: at :math:`0.033\,M_\odot`, :math:`\gamma \approx 3.3`. That is the -fit, not a bug. Lu+2013 is a step: :math:`\gamma = 6.1` for +fit, not a bug. SPISEA v2.5 is a step: :math:`\gamma = 6.1` for :math:`M \le 0.08\,M_\odot` (Fontanive) and :math:`-0.4` above. .. figure:: figures/q_offner_vs_lu2013.png - :alt: Mass-ratio index vs primary mass: Offner error-weighted logistic vs Lu+2013 6.1 / -0.4 step + :alt: Offner 2023 vs SPISEA v2.5: mass-ratio index vs primary mass :align: center - Mass-ratio index :math:`\gamma` vs primary mass. Solid: Offner - error-weighted logistic. Dashed: Lu+2013 step (6.1 below - :math:`0.08\,M_\odot`, :math:`-0.4` above). Blue points: Table 1 - :math:`\gamma_{\mathrm{trunc}}`. + Offner 2023 vs SPISEA v2.5: mass-ratio index :math:`\gamma` vs + primary mass. Solid: Offner error-weighted logistic. Dashed: + SPISEA v2.5 step (6.1 below :math:`0.08\,M_\odot`, :math:`-0.4` + above). Blue points: Table 1 :math:`\gamma_{\mathrm{trunc}}`. .. figure:: figures/meanq_offner_vs_lu2013.png - :alt: Mean mass ratio vs primary mass implied by P(q) proportional to q^gamma + :alt: Offner 2023 vs SPISEA v2.5: mean mass ratio vs primary mass :align: center - Mean mass ratio :math:`\langle q \rangle` on :math:`[0.01, 1]` - implied by :math:`P(q)\propto q^{\gamma}`. Offner brown-dwarf - companions are more equal-mass than Lu+2013 stellar :math:`q`. + Offner 2023 vs SPISEA v2.5: mean mass ratio + :math:`\langle q \rangle` on :math:`[0.01, 1]` implied by + :math:`P(q)\propto q^{\gamma}`. Offner brown-dwarf companions + are more equal-mass than SPISEA v2.5 stellar :math:`q`. Characteristic separation ~~~~~~~~~~~~~~~~~~~~~~~~~ @@ -211,19 +213,20 @@ uses the stable form ``log_a_mean(mass)`` returns :math:`\log_{10}(a/\mathrm{AU})`; ``a_mean(mass)`` returns :math:`a` in AU. -Lu+2013 :class:`~imf.multiplicity.MultiplicityResolvedDK` uses a -Duchêne & Kraus (2013) broken power law in :math:`a` with a +The SPISEA v2.5 :class:`~imf.multiplicity.MultiplicityResolvedDK` +uses a Duchêne & Kraus (2013) broken power law in :math:`a` with a brown-dwarf blend. That law is not meant for the BD regime. .. figure:: figures/sep_offner_vs_lu2013.png - :alt: Characteristic separation vs primary mass: Offner smooth broken power law vs Lu+2013 Duchene-Kraus + :alt: Offner 2023 vs SPISEA v2.5: characteristic separation vs primary mass :align: center - Characteristic :math:`\mu(a)` vs primary mass. Solid: Offner - smooth broken power law. Dashed: Lu+2013 DK mean :math:`a`. - Open circles: Table 1 :math:`\tilde{a}_{\mathrm{all}}`. Filled - squares: Table 2 :math:`\mu` knots (4, 25, 40 AU). Offner BD - binaries peak at a few AU. + Offner 2023 vs SPISEA v2.5: characteristic :math:`\mu(a)` vs + primary mass. Solid: Offner smooth broken power law. Dashed: + SPISEA v2.5 mean :math:`a`. Open circles: Table 1 + :math:`\tilde{a}_{\mathrm{all}}`. Filled squares: Table 2 + :math:`\mu` knots (4, 25, 40 AU). Offner BD binaries peak at a + few AU. Separation scatter ~~~~~~~~~~~~~~~~~~ @@ -235,17 +238,18 @@ Separation scatter \sigma(M) = 0.7 + \frac{0.8}{1 + (M / 0.354)^{-6.05}} i.e. :math:`(A, B, M_0, k) = (0.7, 1.5, 0.354, 6.05)`, clipped to -:math:`\ge 0.1`. Call ``sigma_log_a(mass)``. Lu+2013 DK is a linear -fit in :math:`\log M` that saturates above :math:`2.9\,M_\odot`; the -dip near :math:`0.08\,M_\odot` is the BD/stellar blend. +:math:`\ge 0.1`. Call ``sigma_log_a(mass)``. SPISEA v2.5 DK is a +linear fit in :math:`\log M` that saturates above +:math:`2.9\,M_\odot`; the dip near :math:`0.08\,M_\odot` is the +BD/stellar blend. .. figure:: figures/sig_loga_offner_vs_lu2013.png - :alt: Sigma of log10 a vs primary mass: Offner 2-param logistic vs Lu+2013 DK + :alt: Offner 2023 vs SPISEA v2.5: sigma of log10 a vs primary mass :align: center - :math:`\sigma(\log_{10} a)` vs primary mass. Solid: Offner - 2-parameter logistic. Dashed: Lu+2013 DK. Filled squares: Table 2 - knots (0.7, 1.3, 1.5). + Offner 2023 vs SPISEA v2.5: :math:`\sigma(\log_{10} a)` vs + primary mass. Solid: Offner 2-parameter logistic. Dashed: + SPISEA v2.5 DK. Filled squares: Table 2 knots (0.7, 1.3, 1.5). Resolved draws ~~~~~~~~~~~~~~ diff --git a/spisea/imf/multiplicity.py b/spisea/imf/multiplicity.py index 2df86b4..e9774b2 100755 --- a/spisea/imf/multiplicity.py +++ b/spisea/imf/multiplicity.py @@ -987,7 +987,7 @@ class MultiplicityUnresolvedOffner2023(MultiplicityLogistic): :meth:`sigma_log_a`. Resolved draws use those as loc / scale of a truncated lognormal. - This class is opt-in; it does not change the Lu et al. (2013) + This class is opt-in; it does not change the SPISEA v2.5 :class:`MultiplicityUnresolved` default. Parameters diff --git a/spisea/tests/test_imf.py b/spisea/tests/test_imf.py index 3f90716..984125f 100755 --- a/spisea/tests/test_imf.py +++ b/spisea/tests/test_imf.py @@ -52,7 +52,7 @@ def test_generate_cluster_offner2023(): assert np.all(n_comp[bd] <= 1) assert np.any(isMulti) - # BD companions should be more equal-mass than Lu+2013 stellar q_power=-0.4 + # BD companions should be more equal-mass than SPISEA v2.5 stellar q_power=-0.4 bd_mult = bd & isMulti if np.any(bd_mult): q_bd = [] diff --git a/spisea/tests/test_multiplicity.py b/spisea/tests/test_multiplicity.py index 23507e7..8485a77 100755 --- a/spisea/tests/test_multiplicity.py +++ b/spisea/tests/test_multiplicity.py @@ -500,7 +500,7 @@ def test_offner2023_alias_and_resolved_methods(): def test_lu2013_defaults_unchanged(): - """Lu et al. 2013 MultiplicityUnresolved defaults and stellar MF unchanged.""" + """SPISEA v2.5 MultiplicityUnresolved defaults and stellar MF unchanged.""" mu = multiplicity.MultiplicityUnresolved() assert mu.MF_amp == 0.44 assert mu.MF_pow == 0.51 @@ -509,7 +509,7 @@ def test_lu2013_defaults_unchanged(): np.testing.assert_almost_equal(mu.multiplicity_fraction(1.0), 0.44, decimal=2) np.testing.assert_almost_equal(mu.multiplicity_fraction(10.0), 1.0, decimal=2) np.testing.assert_almost_equal(mu.multiplicity_fraction(0.1), 0.136, decimal=2) - # Scalar BD overrides (historical Lu+2013 / Fontanive path) + # Scalar BD overrides (SPISEA v2.5 / Fontanive path) assert np.isclose(mu.multiplicity_fraction(0.07), 0.16, atol=0.01) assert np.isclose(mu.multiplicity_fraction(0.04), 0.08, atol=0.01) assert np.isclose(mu.multiplicity_fraction(0.01), 0.0, atol=1e-6) @@ -572,13 +572,13 @@ def test_calc_multi_uses_multiplicity_q_and_counts(): def test_offner2023_mf_is_vectorized(): - """Offner MF is vectorized; Lu+2013 scalar BD bins are not used here.""" + """Offner MF is vectorized; SPISEA v2.5 scalar BD bins are not used here.""" multi = multiplicity.MultiplicityUnresolvedOffner2023() masses = np.array([0.03, 0.06, 0.10, 1.0]) mf = multi.multiplicity_fraction(masses) for i, m in enumerate(masses): np.testing.assert_allclose(mf[i], multi.multiplicity_fraction(float(m))) - # Array path is not the Lu stellar power law 0.44 * M**0.51 + # Array path is not the SPISEA v2.5 stellar power law 0.44 * M**0.51 lu_pl = 0.44 * masses ** 0.51 assert not np.allclose(mf, np.clip(lu_pl, 0, 1), atol=0.02) From b98efcfb4387e93358d23ea534e1fd6671d1bb2f Mon Sep 17 00:00:00 2001 From: Cursor Agent Date: Fri, 14 Aug 2026 16:09:40 +0000 Subject: [PATCH 10/16] Rename Offner comparison figures from lu2013 to spisea2.5 Filenames, RST figure paths, and plot-script helpers now match the SPISEA v2.5 comparison baseline. Co-authored-by: Jessica Lu --- ...2013.png => meanq_offner_vs_spisea2.5.png} | Bin ..._lu2013.png => mf_offner_vs_spisea2.5.png} | Bin ...2013.py => plot_mf_offner_vs_spisea2.5.py} | 16 ++++----- ...3.py => plot_q_sep_offner_vs_spisea2.5.py} | 34 +++++++++--------- ...s_lu2013.png => q_offner_vs_spisea2.5.png} | Bin ...lu2013.png => sep_offner_vs_spisea2.5.png} | Bin ...3.png => sig_loga_offner_vs_spisea2.5.png} | Bin docs/multiplicity.rst | 14 ++++---- 8 files changed, 32 insertions(+), 32 deletions(-) rename docs/figures/{meanq_offner_vs_lu2013.png => meanq_offner_vs_spisea2.5.png} (100%) rename docs/figures/{mf_offner_vs_lu2013.png => mf_offner_vs_spisea2.5.png} (100%) rename docs/figures/{plot_mf_offner_vs_lu2013.py => plot_mf_offner_vs_spisea2.5.py} (94%) rename docs/figures/{plot_q_sep_offner_vs_lu2013.py => plot_q_sep_offner_vs_spisea2.5.py} (94%) rename docs/figures/{q_offner_vs_lu2013.png => q_offner_vs_spisea2.5.png} (100%) rename docs/figures/{sep_offner_vs_lu2013.png => sep_offner_vs_spisea2.5.png} (100%) rename docs/figures/{sig_loga_offner_vs_lu2013.png => sig_loga_offner_vs_spisea2.5.png} (100%) diff --git a/docs/figures/meanq_offner_vs_lu2013.png b/docs/figures/meanq_offner_vs_spisea2.5.png similarity index 100% rename from docs/figures/meanq_offner_vs_lu2013.png rename to docs/figures/meanq_offner_vs_spisea2.5.png diff --git a/docs/figures/mf_offner_vs_lu2013.png b/docs/figures/mf_offner_vs_spisea2.5.png similarity index 100% rename from docs/figures/mf_offner_vs_lu2013.png rename to docs/figures/mf_offner_vs_spisea2.5.png diff --git a/docs/figures/plot_mf_offner_vs_lu2013.py b/docs/figures/plot_mf_offner_vs_spisea2.5.py similarity index 94% rename from docs/figures/plot_mf_offner_vs_lu2013.py rename to docs/figures/plot_mf_offner_vs_spisea2.5.py index ea41605..be66ced 100644 --- a/docs/figures/plot_mf_offner_vs_lu2013.py +++ b/docs/figures/plot_mf_offner_vs_spisea2.5.py @@ -1,6 +1,6 @@ #!/usr/bin/env python """ -Generate docs/figures/mf_offner_vs_lu2013.png +Generate docs/figures/mf_offner_vs_spisea2.5.png Two-panel comparison of multiplicity fraction vs primary mass: SPISEA v2.5 array power law, v2.5 scalar BD staircase, @@ -9,7 +9,7 @@ Run from the repository root:: - python docs/figures/plot_mf_offner_vs_lu2013.py + python docs/figures/plot_mf_offner_vs_spisea2.5.py """ import os import sys @@ -46,16 +46,16 @@ ] -def _lu2013_array_mf(mass): +def _spisea25_array_mf(mass): """SPISEA v2.5 array path: stellar power law, no BD staircase.""" mf = 0.44 * np.asarray(mass, dtype=float) ** 0.51 return np.clip(mf, 0.0, 1.0) -def _lu2013_scalar_bd_staircase(mass): +def _spisea25_scalar_bd_staircase(mass): """SPISEA v2.5 scalar-only BD bins in MultiplicityUnresolved.multiplicity_fraction.""" mass = np.asarray(mass, dtype=float) - mf = _lu2013_array_mf(mass) + mf = _spisea25_array_mf(mass) mf = np.where(mass < 0.02, 0.0, mf) mf = np.where((mass > 0.02) & (mass <= 0.06), 0.08, mf) mf = np.where((mass > 0.06) & (mass <= 0.08), 0.16, mf) @@ -96,14 +96,14 @@ def main(): m_wide = np.logspace(np.log10(0.012), np.log10(40.0), 800) mf_off = offner.multiplicity_fraction(m_wide) - mf_lu = _lu2013_array_mf(m_wide) + mf_lu = _spisea25_array_mf(m_wide) # Staircase sampled densely so the steps render as vertical jumps. m_step = np.concatenate([ np.array([0.012, 0.01999, 0.02001, 0.05999, 0.06001, 0.07999, 0.08001]), np.logspace(np.log10(0.081), np.log10(40.0), 200), ]) - mf_step = _lu2013_scalar_bd_staircase(m_step) + mf_step = _spisea25_scalar_bd_staircase(m_step) m_tab, mf_tab, err_tab = _table1_xy() @@ -138,7 +138,7 @@ def main(): axes[0].legend(handles=legend_handles, loc='upper left', fontsize=8, frameon=True, fancybox=False, edgecolor='0.7') - out = os.path.join(os.path.dirname(__file__), 'mf_offner_vs_lu2013.png') + out = os.path.join(os.path.dirname(__file__), 'mf_offner_vs_spisea2.5.png') fig.savefig(out, dpi=160, bbox_inches='tight', facecolor='white') plt.close(fig) print('Wrote', out) diff --git a/docs/figures/plot_q_sep_offner_vs_lu2013.py b/docs/figures/plot_q_sep_offner_vs_spisea2.5.py similarity index 94% rename from docs/figures/plot_q_sep_offner_vs_lu2013.py rename to docs/figures/plot_q_sep_offner_vs_spisea2.5.py index 183e19f..8a1dd62 100644 --- a/docs/figures/plot_q_sep_offner_vs_lu2013.py +++ b/docs/figures/plot_q_sep_offner_vs_spisea2.5.py @@ -2,19 +2,19 @@ """ Generate q / separation comparison figures vs SPISEA v2.5 defaults: - docs/figures/q_offner_vs_lu2013.png - docs/figures/sep_offner_vs_lu2013.png - docs/figures/sig_loga_offner_vs_lu2013.png - docs/figures/meanq_offner_vs_lu2013.png + docs/figures/q_offner_vs_spisea2.5.png + docs/figures/sep_offner_vs_spisea2.5.png + docs/figures/sig_loga_offner_vs_spisea2.5.png + docs/figures/meanq_offner_vs_spisea2.5.png -Two-panel layout matching ``plot_mf_offner_vs_lu2013.py``: brown-dwarf +Two-panel layout matching ``plot_mf_offner_vs_spisea2.5.py``: brown-dwarf zoom and BD through O. Offner curves are evaluated from the multiplicity objects (γ logistic, smooth-broken μ(a), σ logistic) so they cannot drift from the code. Run from the repository root:: - python docs/figures/plot_q_sep_offner_vs_lu2013.py + python docs/figures/plot_q_sep_offner_vs_spisea2.5.py """ import os import sys @@ -94,7 +94,7 @@ def _table_xy(rows, y_idx=3, e_idx=4): return m, y, err -def _lu2013_dk_mean_a_au(dk, mass): +def _spisea25_dk_mean_a_au(dk, mass): """ SPISEA v2.5 ``MultiplicityResolvedDK`` mean a in AU (Duchêne & Kraus coefficients, plus the BD log-a interpolation and sigmoid blend in @@ -120,7 +120,7 @@ def _lu2013_dk_mean_a_au(dk, mass): return 10.0 ** log_a_mean -def _lu2013_dk_sig_loga(dk, mass): +def _spisea25_dk_sig_loga(dk, mass): """ SPISEA v2.5 ``MultiplicityResolvedDK`` σ(log10 a) (Duchêne & Kraus coefficients, plus the BD interpolation and sigmoid blend in @@ -194,7 +194,7 @@ def _save(fig, filename): print('Wrote', out) -def _lu_gamma_step_masses(): +def _spisea25_gamma_step_masses(): """Dense sampling so the 0.08 Msun γ step renders as a vertical jump.""" return np.concatenate([ np.logspace(np.log10(0.012), np.log10(0.07999), 300), @@ -206,7 +206,7 @@ def _lu_gamma_step_masses(): def plot_gamma(offner, lu): m_wide = np.logspace(np.log10(0.012), np.log10(40.0), 800) g_off = offner.q_power_at_mass(m_wide) - m_step = _lu_gamma_step_masses() + m_step = _spisea25_gamma_step_masses() g_lu = lu.q_power_at_mass(m_step) m_tab, g_tab, err_tab = _table_xy(_TABLE1_GAMMA) @@ -237,13 +237,13 @@ def plot_gamma(offner, lu): ] axes[1].legend(handles=legend_handles, loc='upper right', fontsize=8, frameon=True, fancybox=False, edgecolor='0.7') - _save(fig, 'q_offner_vs_lu2013.png') + _save(fig, 'q_offner_vs_spisea2.5.png') def plot_sep(resolved, dk): m_wide = np.logspace(np.log10(0.012), np.log10(40.0), 800) a_off = resolved.a_mean(m_wide) - a_lu = _lu2013_dk_mean_a_au(dk, m_wide) + a_lu = _spisea25_dk_mean_a_au(dk, m_wide) m_tab, a_tab, err_tab = _table_xy(_TABLE1_A_ALL) m_t2 = np.array([_geom(r[1], r[2]) for r in _TABLE2_MU]) a_t2 = np.array([r[3] for r in _TABLE2_MU], dtype=float) @@ -278,13 +278,13 @@ def plot_sep(resolved, dk): ] axes[0].legend(handles=legend_handles, loc='upper left', fontsize=8, frameon=True, fancybox=False, edgecolor='0.7') - _save(fig, 'sep_offner_vs_lu2013.png') + _save(fig, 'sep_offner_vs_spisea2.5.png') def plot_sig_loga(resolved, dk): m_wide = np.logspace(np.log10(0.012), np.log10(40.0), 800) sig_off = resolved.sigma_log_a(m_wide) - sig_lu = _lu2013_dk_sig_loga(dk, m_wide) + sig_lu = _spisea25_dk_sig_loga(dk, m_wide) m_t2 = np.array(resolved.sep_sig_mass, dtype=float) sig_t2 = np.array(resolved.sep_sig, dtype=float) @@ -313,14 +313,14 @@ def plot_sig_loga(resolved, dk): ] axes[1].legend(handles=legend_handles, loc='upper left', fontsize=8, frameon=True, fancybox=False, edgecolor='0.7') - _save(fig, 'sig_loga_offner_vs_lu2013.png') + _save(fig, 'sig_loga_offner_vs_spisea2.5.png') def plot_meanq(offner, lu): m_wide = np.logspace(np.log10(0.012), np.log10(40.0), 800) q_off = _mean_q_from_gamma(offner.q_power_at_mass(m_wide), q_min=offner.q_min) - m_step = _lu_gamma_step_masses() + m_step = _spisea25_gamma_step_masses() q_lu = _mean_q_from_gamma(lu.q_power_at_mass(m_step), q_min=lu.q_min) fig, axes = _two_axes(r'Offner 2023 vs SPISEA v2.5: mean mass ratio $\langle q\rangle$') @@ -344,7 +344,7 @@ def plot_meanq(offner, lu): ] axes[1].legend(handles=legend_handles, loc='upper right', fontsize=8, frameon=True, fancybox=False, edgecolor='0.7') - _save(fig, 'meanq_offner_vs_lu2013.png') + _save(fig, 'meanq_offner_vs_spisea2.5.png') def main(): diff --git a/docs/figures/q_offner_vs_lu2013.png b/docs/figures/q_offner_vs_spisea2.5.png similarity index 100% rename from docs/figures/q_offner_vs_lu2013.png rename to docs/figures/q_offner_vs_spisea2.5.png diff --git a/docs/figures/sep_offner_vs_lu2013.png b/docs/figures/sep_offner_vs_spisea2.5.png similarity index 100% rename from docs/figures/sep_offner_vs_lu2013.png rename to docs/figures/sep_offner_vs_spisea2.5.png diff --git a/docs/figures/sig_loga_offner_vs_lu2013.png b/docs/figures/sig_loga_offner_vs_spisea2.5.png similarity index 100% rename from docs/figures/sig_loga_offner_vs_lu2013.png rename to docs/figures/sig_loga_offner_vs_spisea2.5.png diff --git a/docs/multiplicity.rst b/docs/multiplicity.rst index a400781..a46a22d 100644 --- a/docs/multiplicity.rst +++ b/docs/multiplicity.rst @@ -138,7 +138,7 @@ to 1) for arrays, plus a scalar-only brown-dwarf staircase (0 / 8% / 16%). Cluster generation on that class still uses the stellar power law for brown-dwarf primaries. -.. figure:: figures/mf_offner_vs_lu2013.png +.. figure:: figures/mf_offner_vs_spisea2.5.png :alt: Offner 2023 vs SPISEA v2.5: multiplicity fraction vs primary mass :align: center @@ -169,7 +169,7 @@ The err-weighted fit undershoots Fontanive et al. (2018) fit, not a bug. SPISEA v2.5 is a step: :math:`\gamma = 6.1` for :math:`M \le 0.08\,M_\odot` (Fontanive) and :math:`-0.4` above. -.. figure:: figures/q_offner_vs_lu2013.png +.. figure:: figures/q_offner_vs_spisea2.5.png :alt: Offner 2023 vs SPISEA v2.5: mass-ratio index vs primary mass :align: center @@ -178,7 +178,7 @@ fit, not a bug. SPISEA v2.5 is a step: :math:`\gamma = 6.1` for SPISEA v2.5 step (6.1 below :math:`0.08\,M_\odot`, :math:`-0.4` above). Blue points: Table 1 :math:`\gamma_{\mathrm{trunc}}`. -.. figure:: figures/meanq_offner_vs_lu2013.png +.. figure:: figures/meanq_offner_vs_spisea2.5.png :alt: Offner 2023 vs SPISEA v2.5: mean mass ratio vs primary mass :align: center @@ -217,7 +217,7 @@ The SPISEA v2.5 :class:`~imf.multiplicity.MultiplicityResolvedDK` uses a Duchêne & Kraus (2013) broken power law in :math:`a` with a brown-dwarf blend. That law is not meant for the BD regime. -.. figure:: figures/sep_offner_vs_lu2013.png +.. figure:: figures/sep_offner_vs_spisea2.5.png :alt: Offner 2023 vs SPISEA v2.5: characteristic separation vs primary mass :align: center @@ -243,7 +243,7 @@ linear fit in :math:`\log M` that saturates above :math:`2.9\,M_\odot`; the dip near :math:`0.08\,M_\odot` is the BD/stellar blend. -.. figure:: figures/sig_loga_offner_vs_lu2013.png +.. figure:: figures/sig_loga_offner_vs_spisea2.5.png :alt: Offner 2023 vs SPISEA v2.5: sigma of log10 a vs primary mass :align: center @@ -280,8 +280,8 @@ methods (``multiplicity_fraction``, ``q_power_at_mass``, ``a_mean``, ``sigma_log_a``) so they cannot drift from the code. From the repository root:: - python docs/figures/plot_mf_offner_vs_lu2013.py - python docs/figures/plot_q_sep_offner_vs_lu2013.py + python docs/figures/plot_mf_offner_vs_spisea2.5.py + python docs/figures/plot_q_sep_offner_vs_spisea2.5.py Resolved Multiplicity Classes From 13d722f3adb026a5e1b70d1b3735ce166c91ce4a Mon Sep 17 00:00:00 2001 From: Jessica Lu Date: Fri, 14 Aug 2026 09:25:09 -0700 Subject: [PATCH 11/16] Revise multiplicity documentation and clarify usage Updated the documentation for the multiplicity object, clarifying its functions and usage in the IMF. Revised sections on companion evolution and recommended multiplicity classes. --- docs/multiplicity.rst | 29 +++++++++-------------------- 1 file changed, 9 insertions(+), 20 deletions(-) diff --git a/docs/multiplicity.rst b/docs/multiplicity.rst index a46a22d..142a1c7 100644 --- a/docs/multiplicity.rst +++ b/docs/multiplicity.rst @@ -16,13 +16,7 @@ To call a multiplicity class and wire it into a cluster:: imf_obj = imf.Kroupa_2001(multiplicity=multi) cluster = synthetic.ResolvedCluster(iso, imf_obj, Mcl) -Companion masses and whether a primary is multiple are drawn in -``IMF.generate_cluster`` / ``IMF.calc_multi``, which call the multiplicity -object. ``synthetic.py`` does not draw companions: it labels brown-dwarf -evolutionary phase=90 so they photometrize, combines system photometry, -and (for resolved classes) fills orbital columns. - -Duck-typed multiplicity contract used by the IMF: +The multiplicity object provides the following functions used by the IMF: * ``multiplicity_fraction(mass)`` * ``companion_star_fraction(mass)`` @@ -34,13 +28,6 @@ Duck-typed multiplicity contract used by the IMF: ``mass`` is given. * attributes ``companion_max``, ``CSF_max``, ``q_min`` -Resolved classes are duck-typed in ``synthetic.py`` on -``log_semimajoraxis``, ``random_e``, and ``random_keplarian_parameters``. -They do not need to subclass :class:`~imf.multiplicity.MultiplicityResolvedDK`. - -The multiplicity object is an input for the :ref:`imf_objects`, as it -impacts how the stellar masses are drawn. - The user can choose either an unresolved or a resolved multiplicity object. If a resolved multiplicity object is selected, then orbital parameters are @@ -53,8 +40,8 @@ returned in the ``star_systems`` table off the cluster object is the same for both unresolved and resolved multiplicity classes: it represents the combined photometry of all stars within a given system. -For most selected evolution models, the multiples are evolved as single stars. -To evolve binaries (does not support higher order multiples), you should use one of the ``MultiplicityResolved`` classes +For most selected evolution models, the companions are evolved as single stars. +To evolve binaries with mass exchange (does not support higher order multiples), you should use one of the ``MultiplicityResolved`` classes and the ``COSMIC`` evolution model. See the example jupyter notebook `Cluster_w_COSMIC.ipynb `_ for an example. Note that currently COSMIC due to being external evolution is significantly slower than the other evolution options. @@ -83,18 +70,20 @@ Unresolved Multiplicity Classes Offner et al. 2023 multiplicity ------------------------------------------ -Opt-in field multiplicity from Offner et al. (2023), Protostars and -Planets VII, ASP Conf. Ser. 534, 275 (`arXiv:2203.10066 +The recommended multiplicity class to use is that derived from +data summarized in Offner et al. (2023) (`arXiv:2203.10066 `_; ADS `2023ASPC..534..275O `_). Table 1 data: Zenodo `10.5281/zenodo.6628915 `_. +This class is not the default (for backwards compatability) but +is strongly preferred. + The SPISEA v2.5 :class:`~imf.multiplicity.MultiplicityUnresolved` / :class:`~imf.multiplicity.MultiplicityResolvedDK` objects remain the -default. Pass an Offner instance as ``IMF.multiplicity`` to use this -model. +default; but has known limitations in the brown dwarf regime. Unresolved (companions, no orbits):: From 8a64f907702949360174e7fa8aeab9d45760e0c4 Mon Sep 17 00:00:00 2001 From: Cursor Agent Date: Fri, 14 Aug 2026 16:31:46 +0000 Subject: [PATCH 12/16] Document new multiplicity methods in numpydoc with units Add Parameters and Returns (types and units) to every new helper, class, and method in multiplicity.py. Expand modified methods that already had a Parameters block but omitted units. No math changes. Co-authored-by: Jessica Lu --- spisea/imf/multiplicity.py | 491 ++++++++++++++++++++++++++++++++----- 1 file changed, 429 insertions(+), 62 deletions(-) diff --git a/spisea/imf/multiplicity.py b/spisea/imf/multiplicity.py index e9774b2..9f8bf83 100755 --- a/spisea/imf/multiplicity.py +++ b/spisea/imf/multiplicity.py @@ -28,6 +28,23 @@ def _two_point_powerlaw(mass_1, y_1, mass_2, y_2): """ Amplitude and power for y = A * M**alpha through two (M, y) points. + + Parameters + ---------- + mass_1, mass_2 : float + Primary masses in solar masses (Msun) of the two anchor points. + Must be positive and distinct. + y_1, y_2 : float + Ordinate values at ``mass_1`` and ``mass_2``. Units match the + fitted quantity (dimensionless for MF/γ, mean companion count + for CSF, AU for characteristic a, dex for σ). + + Returns + ------- + amp : float + Power-law amplitude A, in units of y / Msun**alpha. + power : float + Power-law index alpha, dimensionless. """ power = np.log(y_2 / y_1) / np.log(mass_2 / mass_1) amp = y_1 / (mass_1 ** power) @@ -41,8 +58,29 @@ def _piecewise_powerlaw(mass, mass_limits, amps, powers, clip_min=None, Segment i applies for mass_limits[i] <= M < mass_limits[i+1]. The first segment also covers M below the lowest limit; the last - segment is closed on the right. Returns a Python float for scalar - mass and an ndarray otherwise. + segment is closed on the right. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + mass_limits : array_like + Segment edges in solar masses (Msun), length N+1, strictly + increasing. + amps : array_like + Length-N amplitudes A_i, in units of y / Msun**alpha_i. + powers : array_like + Length-N power-law indices alpha_i, dimensionless. + clip_min, clip_max : float or None, optional + Optional lower/upper clips on y, in the same units as y. + ``None`` means no clip on that side. + + Returns + ------- + y : float or ndarray + Piecewise power-law value, in the same units as + ``amps * mass**powers``. Python float if ``mass`` is scalar, + ndarray otherwise. """ return_scalar = np.isscalar(mass) mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) @@ -73,7 +111,28 @@ def _logistic_in_logm(mass, A, B, M0, k, clip_min=None, clip_max=None): This is a logistic in log-mass: as M -> 0, y -> A; as M -> inf, y -> B. Masses <= 0 are mapped to the low-mass asymptote A. - Returns a Python float for scalar mass and an ndarray otherwise. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + A, B : float + Low-mass and high-mass asymptotes, in the same units as y. + Dimensionless for MF and γ; mean companion count for CSF; + dex for σ(log10 a). + M0 : float + Characteristic mass in solar masses (Msun). + k : float + Logistic slope, dimensionless. + clip_min, clip_max : float or None, optional + Optional lower/upper clips on y, in the same units as y. + ``None`` means no clip on that side. + + Returns + ------- + y : float or ndarray + Logistic value in the same units as ``A`` and ``B``. + Python float if ``mass`` is scalar, ndarray otherwise. """ return_scalar = np.isscalar(mass) mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) @@ -97,6 +156,17 @@ def _logcosh(x): Uses |x| + log1p(exp(-2|x|)) - log(2) rather than np.log(np.cosh(x)), which overflows for |x| ≳ 700. + + Parameters + ---------- + x : float or array_like + Argument of cosh, dimensionless (for the smooth broken power + law this is v/s, with v and s in dex). + + Returns + ------- + logcosh_x : float or ndarray + log(cosh(x)), dimensionless. Same shape as ``x``. """ ax = np.abs(np.asarray(x, dtype=float)) return ax + np.log1p(np.exp(-2.0 * ax)) - np.log(2.0) @@ -104,7 +174,7 @@ def _logcosh(x): def _smooth_broken_loglog(mass, mup, Mp, alpha_L, alpha_R, s, a_min=0.1): """ - Smooth broken power law in log10(y) vs log10(M). + Smooth broken power law in log10(a) vs log10(M). v = log10(M / Mp) yp = log10(mup) @@ -112,8 +182,28 @@ def _smooth_broken_loglog(mass, mup, Mp, alpha_L, alpha_R, s, a_min=0.1): ``s`` is the smoothing scale in dex (C-infinity; logcosh). Masses <= 0 are mapped to 1e-8 Msun. The linear-space value is clipped - to ``a_min``. Returns log10(a): a Python float for scalar mass and - an ndarray otherwise. + to ``a_min``. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + mup : float + Characteristic separation at the break mass, in AU. + Mp : float + Break mass in solar masses (Msun). + alpha_L, alpha_R : float + Power-law indices below and above ``Mp``, dimensionless. + s : float + Smoothing scale in dex of log10(M / 1 Msun). + a_min : float, optional + Minimum linear-space separation in AU. Default 0.1 AU. + + Returns + ------- + log_a : float or ndarray + log10(a / 1 AU) in dex (not ln, not AU). Python float if + ``mass`` is scalar, ndarray otherwise. """ return_scalar = np.isscalar(mass) mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) @@ -136,6 +226,22 @@ def _q_from_powerlaw(x, q_pow, q_min): ``q_pow`` may be a scalar or an array broadcastable to ``x``. The q_pow = -1 (b = 0) limit is q = q_min**(1 - x). + + Parameters + ---------- + x : float or array_like + Uniform random draw, dimensionless, in [0, 1]. + q_pow : float or array_like + Mass-ratio power-law index γ, dimensionless. Broadcastable + to ``x``. + q_min : float + Minimum mass ratio m_comp/m_prim, dimensionless, in (0, 1]. + + Returns + ------- + q : ndarray + Companion mass ratio m_comp/m_prim, dimensionless, in + [q_min, 1]. Same shape as the broadcast of ``x`` and ``q_pow``. """ x = np.asarray(x, dtype=float) q_pow = np.asarray(q_pow, dtype=float) @@ -300,8 +406,9 @@ class MultiplicityUnresolved(object): Default False. binary_only_mass_max : float, optional - Primary mass (Msun) at and below which systems are restricted - to at most one companion (CSF = MF). Default is 0.08. + Primary mass in solar masses (Msun) at and below which systems + are restricted to at most one companion (CSF = MF). Default is + 0.08 Msun. """ def __init__(self, @@ -330,14 +437,16 @@ def multiplicity_fraction(self, mass): Parameters ---------- - mass : float or numpy array - Mass of primary star. + mass : float or array_like + Primary mass in solar masses (Msun). Returns ------- - mf : float or numpy array - Multiplicity Fraction, the fraction of stars at this mass - that will have one or more companions. + mf : float or ndarray + Multiplicity fraction, dimensionless, in [0, 1]. + The fraction of stars at this mass that will have one or + more companions. Python float if ``mass`` is scalar, + ndarray otherwise. """ # Multiplicity Fraction mf = self.MF_amp * mass ** self.MF_pow @@ -365,14 +474,16 @@ def companion_star_fraction(self, mass): Parameters ---------- - mass : float or numpy array - Mass of primary star + mass : float or array_like + Primary mass in solar masses (Msun). Returns ------- - csf : float or numpy array - Companion Star Fraction, the expected number of companions - for a star at this mass. + csf : float or ndarray + Companion star fraction, the expected number of companions + for a star at this mass. Dimensionless mean companion count + (not bounded by 1). Python float if ``mass`` is scalar, + ndarray otherwise. """ # Companion Star Fraction csf = self.CSF_amp * mass ** self.CSF_pow @@ -397,6 +508,17 @@ def q_power_at_mass(self, mass): Brown-dwarf primaries (M <= binary_only_mass_max) use gamma = 6.1 from Fontanive et al. (2018), matching the companion-mass draw previously special-cased in ``imf.calc_multi``. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + + Returns + ------- + q_power : float or ndarray + Mass-ratio power-law index γ, dimensionless. + Python float if ``mass`` is scalar, ndarray otherwise. """ mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) q_pow = np.full(mass_arr.shape, self.q_pow, dtype=float) @@ -416,18 +538,22 @@ def random_q(self, x, mass=None): Parameters ---------- x : float or array_like - Random number between 0 and 1. + Uniform random draw, dimensionless, in [0, 1]. Inverse CDF + sample for q. mass : float or array_like, optional - Primary mass(es). If given, the power-law index is - ``q_power_at_mass(mass)`` (brown-dwarf vs stellar for - Lu et al. 2013; mass-dependent for Offner et al. 2023). - If omitted, ``self.q_pow`` is used for all companions. + Primary mass in solar masses (Msun). If given, the + power-law index is ``q_power_at_mass(mass)`` (brown-dwarf + vs stellar for the SPISEA v2.5 default; mass-dependent for + Offner et al. 2023). If omitted, ``self.q_pow`` is used + for all companions. Returns ------- - q : float or array_like - companion mass ratio(s) + q : float or ndarray + Companion mass ratio m_comp/m_prim, dimensionless, in + [q_min, 1]. Python float if ``x`` is scalar, ndarray + otherwise. """ if mass is None: return _q_from_powerlaw(x, self.q_pow, self.q_min) @@ -450,14 +576,18 @@ def random_companion_count(self, x, CSF, MF, mass=None, rng=None): Parameters ---------- x : float or array_like - Unused (historical signature). - CSF, MF : float or array_like - Companion star fraction and multiplicity fraction. + Unused (historical signature). Dimensionless uniform + draw in [0, 1] if provided. + CSF : float or array_like + Companion star fraction, dimensionless mean companion + count (not bounded by 1). + MF : float or array_like + Multiplicity fraction, dimensionless, in [0, 1]. mass : float or array_like, optional - Primary mass. If given, primaries at or below - ``binary_only_mass_max`` are limited to one companion. - Cluster generation always passes mass so subclasses can - override the BD companion-count policy here. + Primary mass in solar masses (Msun). If given, primaries + at or below ``binary_only_mass_max`` are limited to one + companion. Cluster generation always passes mass so + subclasses can override the BD companion-count policy here. rng : numpy.random.Generator, optional Random generator. If omitted, uses ``numpy.random`` (the historical scalar helper). @@ -465,6 +595,8 @@ def random_companion_count(self, x, CSF, MF, mass=None, rng=None): Returns ------- n_comp : int or ndarray of int + Number of companions, integer count. Python int if ``CSF`` + and ``MF`` are scalar, ndarray otherwise. """ return_scalar = np.isscalar(CSF) and np.isscalar(MF) if return_scalar and rng is None: @@ -498,6 +630,26 @@ def draw_n_companions(self, mass, CSF, MF, rng): Vectorized companion counts for primaries that are already identified as multiple. Delegates to :meth:`random_companion_count` with ``mass`` so BD companion-count policy lives on this object. + + Parameters + ---------- + mass : array_like + Primary masses in solar masses (Msun) of systems already + identified as multiple. + CSF : array_like + Companion star fraction at each primary, dimensionless + mean companion count (not bounded by 1). + MF : array_like + Multiplicity fraction at each primary, dimensionless, + in [0, 1]. + rng : numpy.random.Generator + Random generator used for the Poisson companion-count draw. + + Returns + ------- + n_comp : ndarray of int + Number of companions per primary, integer count, shape + matching ``mass``. """ return np.atleast_1d( self.random_companion_count(None, CSF, MF, mass=mass, rng=rng)) @@ -509,6 +661,22 @@ def _q_values_for_primaries(self, prim_subset, n_comp, rng): The stellar / brown-dwarf split (two separate RNG draws) preserves the historical Lu et al. (2013) random sequence used by ``imf.calc_multi``. + + Parameters + ---------- + prim_subset : array_like + Primary masses in solar masses (Msun) for this companion-count + group. + n_comp : int + Number of companions per primary, integer count. + rng : numpy.random.Generator + Random generator used for inverse-CDF q draws. + + Returns + ------- + q_values : ndarray + Companion mass ratios m_comp/m_prim, dimensionless, in + [q_min, 1]. Shape (len(prim_subset), n_comp). """ q_values = np.empty((len(prim_subset), n_comp)) bd_mask = prim_subset <= self.binary_only_mass_max @@ -535,25 +703,32 @@ def draw_companion_masses(self, primary_masses, is_multiple, CSF, MF, Parameters ---------- primary_masses : array_like - Primary masses (Msun). + Primary masses in solar masses (Msun). is_multiple : array_like of bool True for primaries drawn as multiple systems. - CSF, MF : array_like - Companion star fraction and multiplicity fraction at each - primary mass. + CSF : array_like + Companion star fraction at each primary, dimensionless + mean companion count (not bounded by 1). + MF : array_like + Multiplicity fraction at each primary, dimensionless, + in [0, 1]. rng : numpy.random.Generator Random generator. mass_min : float - Minimum companion mass; lighter companions are masked. + Minimum companion mass in solar masses (Msun); lighter + companions are masked. Returns ------- comp_masses : numpy.ma.MaskedArray - Companion masses, shape (n_primaries, max_n_comp). + Companion masses in solar masses (Msun), shape + (n_primaries, max_n_comp). system_masses : ndarray - Primary plus unmasked companion mass. + Primary plus unmasked companion mass, in solar masses + (Msun). is_multiple : ndarray of bool - Updated multiplicity flags after masking sub-minimum companions. + Updated multiplicity flags after masking sub-minimum + companions. """ primary_masses = np.asarray(primary_masses, dtype=float) is_multiple = np.asarray(is_multiple, dtype=bool) @@ -681,7 +856,20 @@ def log_semimajoraxis(self, mass): def _offner2023_table1_geom_mass(m_lo, m_hi): - """Geometric-mean primary mass of a Table 1 M1 interval.""" + """ + Geometric-mean primary mass of a Table 1 M1 interval. + + Parameters + ---------- + m_lo, m_hi : float + Low and high edges of the Table 1 primary-mass interval, in + solar masses (Msun). Must be positive. + + Returns + ------- + mass : float + Geometric mean sqrt(m_lo * m_hi) in solar masses (Msun). + """ return float(np.sqrt(m_lo * m_hi)) @@ -785,13 +973,32 @@ class MultiplicityPiecewisePowerLaw(MultiplicityUnresolved): Parameters ---------- mass_limits : array_like - Segment edges in solar masses, length N+1, strictly increasing. - MF_amps, MF_powers : array_like - Length-N amplitudes and powers for the multiplicity fraction. - CSF_amps, CSF_powers : array_like - Length-N amplitudes and powers for the companion star fraction. - CSF_max, q_power, q_min, companion_max, binary_only_mass_max - Passed to :class:`MultiplicityUnresolved`. + Segment edges in solar masses (Msun), length N+1, strictly + increasing. + MF_amps : array_like + Length-N amplitudes for the multiplicity fraction, + dimensionless (units of MF / Msun**MF_power). + MF_powers : array_like + Length-N power-law indices for the multiplicity fraction, + dimensionless. + CSF_amps : array_like + Length-N amplitudes for the companion star fraction, + dimensionless (mean companion count / Msun**CSF_power). + CSF_powers : array_like + Length-N power-law indices for the companion star fraction, + dimensionless. + CSF_max : float, optional + Maximum companion star fraction, dimensionless mean companion + count (not bounded by 1). Default 3. + q_power : float, optional + Mass-ratio power-law index, dimensionless. Default -0.4. + q_min : float, optional + Minimum mass ratio m_comp/m_prim, dimensionless. Default 0.01. + companion_max : bool, optional + If True, cap companion counts at CSF_max. Default False. + binary_only_mass_max : float, optional + Primary mass in solar masses (Msun) at and below which systems + are binaries only. Default 0.08 Msun. """ def __init__(self, mass_limits, MF_amps, MF_powers, CSF_amps, CSF_powers, CSF_max=3, q_power=-0.4, q_min=0.01, companion_max=False, @@ -825,6 +1032,17 @@ def multiplicity_fraction(self, mass): """ Multiplicity fraction as a piecewise power law in primary mass. Clipped to [0, 1]. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + + Returns + ------- + mf : float or ndarray + Multiplicity fraction, dimensionless, in [0, 1]. + Python float if ``mass`` is scalar, ndarray otherwise. """ return _piecewise_powerlaw( mass, self.mass_limits, self.MF_amps, self.MF_powers, @@ -836,6 +1054,18 @@ def companion_star_fraction(self, mass): Clipped to [0, CSF_max], raised to at least MF, and set equal to MF for primaries at or below ``binary_only_mass_max``. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + + Returns + ------- + csf : float or ndarray + Companion star fraction, dimensionless mean companion + count (not bounded by 1). Python float if ``mass`` is + scalar, ndarray otherwise. """ return_scalar = np.isscalar(mass) mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) @@ -870,12 +1100,32 @@ class MultiplicityLogistic(MultiplicityUnresolved): Parameters ---------- - MF_A, MF_B, MF_M0, MF_k : float - Logistic coefficients for the multiplicity fraction. - CSF_A, CSF_B, CSF_M0, CSF_k : float - Logistic coefficients for the companion star fraction. - CSF_max, q_power, q_min, companion_max, binary_only_mass_max - Passed to :class:`MultiplicityUnresolved`. + MF_A, MF_B : float + Low-mass and high-mass asymptotes of the multiplicity-fraction + logistic, dimensionless (MF). + MF_M0 : float + Characteristic mass of the MF logistic, in solar masses (Msun). + MF_k : float + MF logistic slope, dimensionless. + CSF_A, CSF_B : float + Low-mass and high-mass asymptotes of the companion-star-fraction + logistic, dimensionless mean companion count (not bounded by 1). + CSF_M0 : float + Characteristic mass of the CSF logistic, in solar masses (Msun). + CSF_k : float + CSF logistic slope, dimensionless. + CSF_max : float, optional + Maximum companion star fraction, dimensionless mean companion + count (not bounded by 1). Default 3. + q_power : float, optional + Mass-ratio power-law index, dimensionless. Default -0.4. + q_min : float, optional + Minimum mass ratio m_comp/m_prim, dimensionless. Default 0.01. + companion_max : bool, optional + If True, cap companion counts at CSF_max. Default False. + binary_only_mass_max : float, optional + Primary mass in solar masses (Msun) at and below which systems + are binaries only. Default 0.08 Msun. """ def __init__(self, MF_A, MF_B, MF_M0, MF_k, CSF_A, CSF_B, CSF_M0, CSF_k, @@ -899,6 +1149,17 @@ def multiplicity_fraction(self, mass): """ Multiplicity fraction as a logistic in log primary mass. Clipped to [0, 1]. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + + Returns + ------- + mf : float or ndarray + Multiplicity fraction, dimensionless, in [0, 1]. + Python float if ``mass`` is scalar, ndarray otherwise. """ return _logistic_in_logm( mass, self.MF_A, self.MF_B, self.MF_M0, self.MF_k, @@ -910,6 +1171,18 @@ def companion_star_fraction(self, mass): Clipped to [0, CSF_max], raised to at least MF, and set equal to MF for primaries at or below ``binary_only_mass_max``. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + + Returns + ------- + csf : float or ndarray + Companion star fraction, dimensionless mean companion + count (not bounded by 1). Python float if ``mass`` is + scalar, ndarray otherwise. """ return_scalar = np.isscalar(mass) mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) @@ -992,10 +1265,22 @@ class MultiplicityUnresolvedOffner2023(MultiplicityLogistic): Parameters ---------- - CSF_max, q_min, companion_max, binary_only_mass_max - See :class:`MultiplicityUnresolved`. ``q_power`` is ignored for + CSF_max : float, optional + Maximum companion star fraction, dimensionless mean companion + count (not bounded by 1). Default 3. + q_power : float, optional + Fallback mass-ratio power-law index, dimensionless. Ignored for draws when primary mass is provided (the γ logistic is used); - it remains the fallback for ``random_q(x)`` with no mass. + used by ``random_q(x)`` with no mass. Default 0.2. + q_min : float, optional + Minimum mass ratio m_comp/m_prim, dimensionless, in [q_min, 1]. + Default 0.01. + companion_max : bool, optional + If True, cap companion counts at CSF_max. Default False. + binary_only_mass_max : float, optional + Primary mass in solar masses (Msun) at and below which systems + are binaries only (CSF = MF, at most one companion). Default + 0.08 Msun. """ def __init__(self, CSF_max=3, q_power=0.2, q_min=0.01, companion_max=False, binary_only_mass_max=H_BURNING_MASS): @@ -1021,6 +1306,17 @@ def q_power_at_mass(self, mass): Error-weighted logistic in log-mass fitted to Table 1 γ_trunc. Not an interpolation of the Table 1 knots. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + + Returns + ------- + gamma : float or ndarray + Mass-ratio power-law index γ, dimensionless. + Python float if ``mass`` is scalar, ndarray otherwise. """ return _logistic_in_logm( mass, OFFNER2023_Q_A, OFFNER2023_Q_B, @@ -1032,6 +1328,17 @@ def log_a_mean(self, mass): FGK-pulled, s = 0.1 dex, C-infinity (stable logcosh). Linear-space a is clipped to 0.1 AU. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + + Returns + ------- + log_a_mean : float or ndarray + Characteristic log10(a / 1 AU) in dex (not ln, not AU). + Python float if ``mass`` is scalar, ndarray otherwise. """ return _smooth_broken_loglog( mass, OFFNER2023_A_MUP, OFFNER2023_A_MP, @@ -1039,7 +1346,20 @@ def log_a_mean(self, mass): a_min=OFFNER2023_A_MIN) def a_mean(self, mass): - """Characteristic μ(a) in AU, ``10 ** log_a_mean(mass)``.""" + """ + Characteristic μ(a) in AU, ``10 ** log_a_mean(mass)``. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + + Returns + ------- + a_mean : float or ndarray + Characteristic separation μ(a) in AU. Python float if + ``mass`` is scalar, ndarray otherwise. + """ log_a = self.log_a_mean(mass) if np.isscalar(log_a): return 10.0 ** log_a @@ -1050,13 +1370,42 @@ def sigma_log_a(self, mass): σ(log10 a) from a 2-parameter logistic in log-mass. Floors/ceilings pinned at 0.7 / 1.5; clipped to ≥ 0.1. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + + Returns + ------- + sigma_log_a : float or ndarray + Standard deviation of log10(a / 1 AU), in dex. + Python float if ``mass`` is scalar, ndarray otherwise. """ return _logistic_in_logm( mass, OFFNER2023_SIG_A, OFFNER2023_SIG_B, OFFNER2023_SIG_M0, OFFNER2023_SIG_K, clip_min=0.1) def _q_values_for_primaries(self, prim_subset, n_comp, rng): - """Mass-dependent q for every primary (BD and stellar).""" + """ + Draw mass-dependent q for every primary (BD and stellar). + + Parameters + ---------- + prim_subset : array_like + Primary masses in solar masses (Msun) for this companion-count + group. + n_comp : int + Number of companions per primary, integer count. + rng : numpy.random.Generator + Random generator used for inverse-CDF q draws. + + Returns + ------- + q_values : ndarray + Companion mass ratios m_comp/m_prim, dimensionless, in + [q_min, 1]. Shape (len(prim_subset), n_comp). + """ return self.random_q( rng.random((len(prim_subset), n_comp)), mass=prim_subset) @@ -1078,6 +1427,23 @@ class MultiplicityResolvedOffner2023(MultiplicityUnresolvedOffner2023, same as :class:`MultiplicityResolvedDK`. Opt-in; does not replace :class:`MultiplicityResolvedDK`. + + Parameters + ---------- + CSF_max : float, optional + Maximum companion star fraction, dimensionless mean companion + count (not bounded by 1). Default 3. + q_power : float, optional + Fallback mass-ratio power-law index, dimensionless. Ignored for + draws when primary mass is provided (the γ logistic is used). + Default 0.2. + q_min : float, optional + Minimum mass ratio m_comp/m_prim, dimensionless. Default 0.01. + companion_max : bool, optional + If True, cap companion counts at CSF_max. Default False. + binary_only_mass_max : float, optional + Primary mass in solar masses (Msun) at and below which systems + are binaries only. Default 0.08 Msun. """ def __init__(self, **kwargs): super(MultiplicityResolvedOffner2023, self).__init__(**kwargs) @@ -1093,13 +1459,14 @@ def log_semimajoraxis(self, mass): Parameters ---------- - mass : array-like - Primary mass (Msun). + mass : float or array_like + Primary mass in solar masses (Msun). Returns ------- log_semimajoraxis : ndarray - log10 of the semimajor axis in AU, truncated to 0.01–2000 AU. + Drawn log10(a / 1 AU) in dex (not ln, not AU), truncated + so a is between 0.01 AU and 2000 AU. """ mass = np.atleast_1d(np.asarray(mass, dtype=float)) log_a_mean = np.atleast_1d(np.asarray(self.log_a_mean(mass), dtype=float)) From 23a459ecc411b44907cc7e5b3f990c21854fc8e4 Mon Sep 17 00:00:00 2001 From: Cursor Agent Date: Fri, 14 Aug 2026 16:42:36 +0000 Subject: [PATCH 13/16] Move multiplicity model helpers to the bottom of the file Private helpers sit after the public classes and MultiplicityOffner2023 alias so Sphinx/source order documents the classes first. Table arrays that call _offner2023_table1_geom_mass follow that helper. No behavior change. Co-authored-by: Jessica Lu --- spisea/imf/multiplicity.py | 874 ++++++++++++++++++------------------- 1 file changed, 436 insertions(+), 438 deletions(-) diff --git a/spisea/imf/multiplicity.py b/spisea/imf/multiplicity.py index 9f8bf83..676905e 100755 --- a/spisea/imf/multiplicity.py +++ b/spisea/imf/multiplicity.py @@ -24,239 +24,39 @@ # Eventually we should add in separation properties. (a_mean, a_sigma) +# Equal-weight logistic-in-log-mass fit to Offner et al. 2023 Table 1 +# geom-mean (M, MF) and (M, CF) points: +# y(M) = A + (B - A) / (1 + (M / M0)**(-k)) +OFFNER2023_MF_A = 0.14 +OFFNER2023_MF_B = 0.99 +OFFNER2023_MF_M0 = 1.41 +OFFNER2023_MF_K = 1.25 +OFFNER2023_CSF_A = 0.12 +OFFNER2023_CSF_B = 2.35 +OFFNER2023_CSF_M0 = 3.57 +OFFNER2023_CSF_K = 0.96 -def _two_point_powerlaw(mass_1, y_1, mass_2, y_2): - """ - Amplitude and power for y = A * M**alpha through two (M, y) points. - - Parameters - ---------- - mass_1, mass_2 : float - Primary masses in solar masses (Msun) of the two anchor points. - Must be positive and distinct. - y_1, y_2 : float - Ordinate values at ``mass_1`` and ``mass_2``. Units match the - fitted quantity (dimensionless for MF/γ, mean companion count - for CSF, AU for characteristic a, dex for σ). - - Returns - ------- - amp : float - Power-law amplitude A, in units of y / Msun**alpha. - power : float - Power-law index alpha, dimensionless. - """ - power = np.log(y_2 / y_1) / np.log(mass_2 / mass_1) - amp = y_1 / (mass_1 ** power) - return amp, power - - -def _piecewise_powerlaw(mass, mass_limits, amps, powers, clip_min=None, - clip_max=None): - """ - Evaluate y = A_i * M**alpha_i on mass segments. - - Segment i applies for mass_limits[i] <= M < mass_limits[i+1]. - The first segment also covers M below the lowest limit; the last - segment is closed on the right. - - Parameters - ---------- - mass : float or array_like - Primary mass in solar masses (Msun). - mass_limits : array_like - Segment edges in solar masses (Msun), length N+1, strictly - increasing. - amps : array_like - Length-N amplitudes A_i, in units of y / Msun**alpha_i. - powers : array_like - Length-N power-law indices alpha_i, dimensionless. - clip_min, clip_max : float or None, optional - Optional lower/upper clips on y, in the same units as y. - ``None`` means no clip on that side. - - Returns - ------- - y : float or ndarray - Piecewise power-law value, in the same units as - ``amps * mass**powers``. Python float if ``mass`` is scalar, - ndarray otherwise. - """ - return_scalar = np.isscalar(mass) - mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) - out = np.empty(mass_arr.shape, dtype=float) - nseg = len(amps) - for i in range(nseg): - lo = mass_limits[i] - hi = mass_limits[i + 1] - if i == 0: - mask = mass_arr < hi - elif i == nseg - 1: - mask = mass_arr >= lo - else: - mask = (mass_arr >= lo) & (mass_arr < hi) - out[mask] = amps[i] * np.power(mass_arr[mask], powers[i]) - if clip_min is not None: - out = np.maximum(out, clip_min) - if clip_max is not None: - out = np.minimum(out, clip_max) - if return_scalar: - return float(out[0]) - return out - - -def _logistic_in_logm(mass, A, B, M0, k, clip_min=None, clip_max=None): - """ - Evaluate y = A + (B - A) / (1 + (M / M0)**(-k)). - - This is a logistic in log-mass: as M -> 0, y -> A; as M -> inf, - y -> B. Masses <= 0 are mapped to the low-mass asymptote A. - - Parameters - ---------- - mass : float or array_like - Primary mass in solar masses (Msun). - A, B : float - Low-mass and high-mass asymptotes, in the same units as y. - Dimensionless for MF and γ; mean companion count for CSF; - dex for σ(log10 a). - M0 : float - Characteristic mass in solar masses (Msun). - k : float - Logistic slope, dimensionless. - clip_min, clip_max : float or None, optional - Optional lower/upper clips on y, in the same units as y. - ``None`` means no clip on that side. - - Returns - ------- - y : float or ndarray - Logistic value in the same units as ``A`` and ``B``. - Python float if ``mass`` is scalar, ndarray otherwise. - """ - return_scalar = np.isscalar(mass) - mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) - out = np.full(mass_arr.shape, float(A), dtype=float) - positive = mass_arr > 0 - if np.any(positive): - m = mass_arr[positive] - out[positive] = A + (B - A) / (1.0 + np.power(m / M0, -k)) - if clip_min is not None: - out = np.maximum(out, clip_min) - if clip_max is not None: - out = np.minimum(out, clip_max) - if return_scalar: - return float(out[0]) - return out - - -def _logcosh(x): - """ - Numerically stable log(cosh(x)). - - Uses |x| + log1p(exp(-2|x|)) - log(2) rather than np.log(np.cosh(x)), - which overflows for |x| ≳ 700. - - Parameters - ---------- - x : float or array_like - Argument of cosh, dimensionless (for the smooth broken power - law this is v/s, with v and s in dex). - - Returns - ------- - logcosh_x : float or ndarray - log(cosh(x)), dimensionless. Same shape as ``x``. - """ - ax = np.abs(np.asarray(x, dtype=float)) - return ax + np.log1p(np.exp(-2.0 * ax)) - np.log(2.0) - - -def _smooth_broken_loglog(mass, mup, Mp, alpha_L, alpha_R, s, a_min=0.1): - """ - Smooth broken power law in log10(a) vs log10(M). - - v = log10(M / Mp) - yp = log10(mup) - log10(a) = yp + 0.5*(αL+αR)*v + 0.5*(αR-αL)*s * logcosh(v/s) - - ``s`` is the smoothing scale in dex (C-infinity; logcosh). Masses - <= 0 are mapped to 1e-8 Msun. The linear-space value is clipped - to ``a_min``. - - Parameters - ---------- - mass : float or array_like - Primary mass in solar masses (Msun). - mup : float - Characteristic separation at the break mass, in AU. - Mp : float - Break mass in solar masses (Msun). - alpha_L, alpha_R : float - Power-law indices below and above ``Mp``, dimensionless. - s : float - Smoothing scale in dex of log10(M / 1 Msun). - a_min : float, optional - Minimum linear-space separation in AU. Default 0.1 AU. - - Returns - ------- - log_a : float or ndarray - log10(a / 1 AU) in dex (not ln, not AU). Python float if - ``mass`` is scalar, ndarray otherwise. - """ - return_scalar = np.isscalar(mass) - mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) - m = np.where(mass_arr > 0, mass_arr, 1e-8) - v = np.log10(m / float(Mp)) - yp = np.log10(float(mup)) - log_a = (yp - + 0.5 * (alpha_L + alpha_R) * v - + 0.5 * (alpha_R - alpha_L) * s * _logcosh(v / s)) - a = np.maximum(10.0 ** log_a, float(a_min)) - log_a = np.log10(a) - if return_scalar: - return float(log_a[0]) - return log_a - - -def _q_from_powerlaw(x, q_pow, q_min): - """ - Inverse CDF of P(q) ∝ q**q_pow for q_min <= q <= 1. - ``q_pow`` may be a scalar or an array broadcastable to ``x``. - The q_pow = -1 (b = 0) limit is q = q_min**(1 - x). +# Error-weighted logistic in log-mass for Table 1 γ_trunc (1–100 au). +# The model is this logistic, not interpolation of the arrays below. +OFFNER2023_Q_A = 6.6 +OFFNER2023_Q_B = -1.77 +OFFNER2023_Q_M0 = 0.0651 +OFFNER2023_Q_K = 0.629 - Parameters - ---------- - x : float or array_like - Uniform random draw, dimensionless, in [0, 1]. - q_pow : float or array_like - Mass-ratio power-law index γ, dimensionless. Broadcastable - to ``x``. - q_min : float - Minimum mass ratio m_comp/m_prim, dimensionless, in (0, 1]. +# Smooth broken power law in log10(a) vs log10(M), s=0.1 dex, FGK-pulled. +OFFNER2023_A_MUP = 44.46 +OFFNER2023_A_MP = 0.819 +OFFNER2023_A_ALPHAL = 1.005 +OFFNER2023_A_ALPHAR = -0.308 +OFFNER2023_A_S = 0.10 +OFFNER2023_A_MIN = 0.1 - Returns - ------- - q : ndarray - Companion mass ratio m_comp/m_prim, dimensionless, in - [q_min, 1]. Same shape as the broadcast of ``x`` and ``q_pow``. - """ - x = np.asarray(x, dtype=float) - q_pow = np.asarray(q_pow, dtype=float) - if x.ndim > q_pow.ndim: - q_pow = q_pow.reshape(q_pow.shape + (1,) * (x.ndim - q_pow.ndim)) - b = 1.0 + q_pow - b, x = np.broadcast_arrays(b, x) - out = np.empty(x.shape, dtype=float) - near_zero = np.abs(b) < 1e-12 - ok = ~near_zero - if np.any(near_zero): - out[near_zero] = q_min ** (1.0 - x[near_zero]) - if np.any(ok): - out[ok] = (x[ok] * (1.0 - q_min ** b[ok]) + q_min ** b[ok]) ** (1.0 / b[ok]) - return out +# 2-parameter logistic for σ(log10 a); floors/ceilings pinned at 0.7 / 1.5. +OFFNER2023_SIG_A = 0.7 +OFFNER2023_SIG_B = 1.5 +OFFNER2023_SIG_M0 = 0.354 +OFFNER2023_SIG_K = 6.05 class _ResolvedOrbitalMixin(object): @@ -851,110 +651,8 @@ def log_semimajoraxis(self, mass): a_lower_std = (log_a_lower - log_a_mean) / log_a_std a_upper_std = (log_a_upper - log_a_mean) / log_a_std - log_semimajoraxis = truncnorm.rvs(a_lower_std, a_upper_std, loc=log_a_mean, scale=log_a_std) - return log_semimajoraxis - - -def _offner2023_table1_geom_mass(m_lo, m_hi): - """ - Geometric-mean primary mass of a Table 1 M1 interval. - - Parameters - ---------- - m_lo, m_hi : float - Low and high edges of the Table 1 primary-mass interval, in - solar masses (Msun). Must be positive. - - Returns - ------- - mass : float - Geometric mean sqrt(m_lo * m_hi) in solar masses (Msun). - """ - return float(np.sqrt(m_lo * m_hi)) - - -# Equal-weight logistic-in-log-mass fit to Offner et al. 2023 Table 1 -# geom-mean (M, MF) and (M, CF) points: -# y(M) = A + (B - A) / (1 + (M / M0)**(-k)) -OFFNER2023_MF_A = 0.14 -OFFNER2023_MF_B = 0.99 -OFFNER2023_MF_M0 = 1.41 -OFFNER2023_MF_K = 1.25 -OFFNER2023_CSF_A = 0.12 -OFFNER2023_CSF_B = 2.35 -OFFNER2023_CSF_M0 = 3.57 -OFFNER2023_CSF_K = 0.96 - - -# Error-weighted logistic in log-mass for Table 1 γ_trunc (1–100 au). -# The model is this logistic, not interpolation of the arrays below. -OFFNER2023_Q_A = 6.6 -OFFNER2023_Q_B = -1.77 -OFFNER2023_Q_M0 = 0.0651 -OFFNER2023_Q_K = 0.629 - -# Smooth broken power law in log10(a) vs log10(M), s=0.1 dex, FGK-pulled. -OFFNER2023_A_MUP = 44.46 -OFFNER2023_A_MP = 0.819 -OFFNER2023_A_ALPHAL = 1.005 -OFFNER2023_A_ALPHAR = -0.308 -OFFNER2023_A_S = 0.10 -OFFNER2023_A_MIN = 0.1 - -# 2-parameter logistic for σ(log10 a); floors/ceilings pinned at 0.7 / 1.5. -OFFNER2023_SIG_A = 0.7 -OFFNER2023_SIG_B = 1.5 -OFFNER2023_SIG_M0 = 0.354 -OFFNER2023_SIG_K = 6.05 - -# Table 1/2 data that was fit; the model is the smooth functions above, -# not interpolation of these arrays. -OFFNER2023_Q_MASS = np.array([ - _offner2023_table1_geom_mass(0.019, 0.058), # Fontanive+2018: 4.8 - 0.065, # L/early-T: 2-3 (text) - _offner2023_table1_geom_mass(0.080, 0.095), # Close+2003: 3.3 - _offner2023_table1_geom_mass(0.06, 0.15), # Allen+2007: 1.7 - _offner2023_table1_geom_mass(0.15, 0.30), # Winters mid-M: 0.7 - _offner2023_table1_geom_mass(0.3, 0.6), # Winters early-M: 0.1 - _offner2023_table1_geom_mass(0.75, 1.25), # Raghavan FGK: 0.2 - _offner2023_table1_geom_mass(1.6, 2.4), # De Rosa A: -1.3 - _offner2023_table1_geom_mass(3.0, 5.0), # MDS 3-5: -1.0 - _offner2023_table1_geom_mass(5.0, 8.0), # MDS 5-8: -1.7 - _offner2023_table1_geom_mass(8.0, 17.0), # MDS 8-17: -1.6 - _offner2023_table1_geom_mass(17.0, 50.0), # Sana O: -1.4 -]) -OFFNER2023_Q_GAMMA = np.array([ - 4.8, 2.5, 3.3, 1.7, 0.7, 0.1, 0.2, -1.3, -1.0, -1.7, -1.6, -1.4 -]) - -# Table 1 ã_all (au) and Table 2 lognormal μ (au) vs geom-mean M1. -# Table 2 μ is listed where both exist (late-M, early-M, FGK). -# Fit data only; evaluation uses the smooth broken power law. -OFFNER2023_SEP_MASS = np.array([ - _offner2023_table1_geom_mass(0.019, 0.058), # Fontanive ã_all=2.9 - _offner2023_table1_geom_mass(0.080, 0.095), # Close ã_all=3.7 - _offner2023_table1_geom_mass(0.075, 0.15), # Table 2 late-M μ=4 - _offner2023_table1_geom_mass(0.15, 0.30), # Winters mid-M ã_all=10 - _offner2023_table1_geom_mass(0.3, 0.6), # Table 2 early-M μ=25 - _offner2023_table1_geom_mass(0.75, 1.25), # Table 2 FGK μ=40 - _offner2023_table1_geom_mass(1.6, 2.4), # Moe & Kratter ã_all=32 - _offner2023_table1_geom_mass(3.0, 5.0), # MDS ã_all=28 - _offner2023_table1_geom_mass(5.0, 8.0), # MDS ã_all=25 - _offner2023_table1_geom_mass(8.0, 17.0), # MDS ã_all=23 - _offner2023_table1_geom_mass(17.0, 50.0), # Sana ã_all=19 -]) -OFFNER2023_SEP_MU_AU = np.array([ - 2.9, 3.7, 4.0, 10.0, 25.0, 40.0, 32.0, 28.0, 25.0, 23.0, 19.0 -]) -# Table 2 σ_log a at the three published bins. Fit data only; -# evaluation uses the 2-parameter logistic. -OFFNER2023_SEP_SIG_MASS = np.array([ - _offner2023_table1_geom_mass(0.075, 0.15), - _offner2023_table1_geom_mass(0.3, 0.6), - _offner2023_table1_geom_mass(0.75, 1.25), -]) -OFFNER2023_SEP_SIG = np.array([0.7, 1.3, 1.5]) - + log_semimajoraxis = truncnorm.rvs(a_lower_std, a_upper_std, loc=log_a_mean, scale=log_a_std) + return log_semimajoraxis class MultiplicityPiecewisePowerLaw(MultiplicityUnresolved): """ @@ -1354,131 +1052,431 @@ def a_mean(self, mass): mass : float or array_like Primary mass in solar masses (Msun). - Returns - ------- - a_mean : float or ndarray - Characteristic separation μ(a) in AU. Python float if - ``mass`` is scalar, ndarray otherwise. - """ - log_a = self.log_a_mean(mass) - if np.isscalar(log_a): - return 10.0 ** log_a - return 10.0 ** np.asarray(log_a, dtype=float) + Returns + ------- + a_mean : float or ndarray + Characteristic separation μ(a) in AU. Python float if + ``mass`` is scalar, ndarray otherwise. + """ + log_a = self.log_a_mean(mass) + if np.isscalar(log_a): + return 10.0 ** log_a + return 10.0 ** np.asarray(log_a, dtype=float) + + def sigma_log_a(self, mass): + """ + σ(log10 a) from a 2-parameter logistic in log-mass. + + Floors/ceilings pinned at 0.7 / 1.5; clipped to ≥ 0.1. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + + Returns + ------- + sigma_log_a : float or ndarray + Standard deviation of log10(a / 1 AU), in dex. + Python float if ``mass`` is scalar, ndarray otherwise. + """ + return _logistic_in_logm( + mass, OFFNER2023_SIG_A, OFFNER2023_SIG_B, + OFFNER2023_SIG_M0, OFFNER2023_SIG_K, clip_min=0.1) + + def _q_values_for_primaries(self, prim_subset, n_comp, rng): + """ + Draw mass-dependent q for every primary (BD and stellar). + + Parameters + ---------- + prim_subset : array_like + Primary masses in solar masses (Msun) for this companion-count + group. + n_comp : int + Number of companions per primary, integer count. + rng : numpy.random.Generator + Random generator used for inverse-CDF q draws. + + Returns + ------- + q_values : ndarray + Companion mass ratios m_comp/m_prim, dimensionless, in + [q_min, 1]. Shape (len(prim_subset), n_comp). + """ + return self.random_q( + rng.random((len(prim_subset), n_comp)), mass=prim_subset) + + +class MultiplicityResolvedOffner2023(MultiplicityUnresolvedOffner2023, + _ResolvedOrbitalMixin): + """ + Resolved Offner et al. 2023 multiplicity: Table 1 MF/CF plus + mass-dependent separations. + + Separations are drawn from a truncated lognormal in log10(a/AU) + with loc = :meth:`log_a_mean` (smooth broken power law, s = 0.1 + dex, FGK-pulled) and scale = :meth:`sigma_log_a` (2-parameter + logistic pinned at 0.7 / 1.5). Brown-dwarf binaries peak near a + few AU. Truncation is 0.01–2000 AU, same as + :class:`MultiplicityResolvedDK`. + + Eccentricity and Keplerian angles follow Duchêne & Kraus (2013), + same as :class:`MultiplicityResolvedDK`. + + Opt-in; does not replace :class:`MultiplicityResolvedDK`. + + Parameters + ---------- + CSF_max : float, optional + Maximum companion star fraction, dimensionless mean companion + count (not bounded by 1). Default 3. + q_power : float, optional + Fallback mass-ratio power-law index, dimensionless. Ignored for + draws when primary mass is provided (the γ logistic is used). + Default 0.2. + q_min : float, optional + Minimum mass ratio m_comp/m_prim, dimensionless. Default 0.01. + companion_max : bool, optional + If True, cap companion counts at CSF_max. Default False. + binary_only_mass_max : float, optional + Primary mass in solar masses (Msun) at and below which systems + are binaries only. Default 0.08 Msun. + """ + def __init__(self, **kwargs): + super(MultiplicityResolvedOffner2023, self).__init__(**kwargs) + # Table 1/2 data that was fit; draws use log_a_mean / sigma_log_a. + self.sep_mass = np.array(OFFNER2023_SEP_MASS, dtype=float) + self.sep_mu_au = np.array(OFFNER2023_SEP_MU_AU, dtype=float) + self.sep_sig_mass = np.array(OFFNER2023_SEP_SIG_MASS, dtype=float) + self.sep_sig = np.array(OFFNER2023_SEP_SIG, dtype=float) + + def log_semimajoraxis(self, mass): + """ + Draw log10(a/AU) from a mass-dependent truncated lognormal. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + + Returns + ------- + log_semimajoraxis : ndarray + Drawn log10(a / 1 AU) in dex (not ln, not AU), truncated + so a is between 0.01 AU and 2000 AU. + """ + mass = np.atleast_1d(np.asarray(mass, dtype=float)) + log_a_mean = np.atleast_1d(np.asarray(self.log_a_mean(mass), dtype=float)) + log_a_std = np.atleast_1d(np.asarray(self.sigma_log_a(mass), dtype=float)) + + log_a_lower = np.log10(0.01) + log_a_upper = np.log10(2000) + a_lower_std = (log_a_lower - log_a_mean) / log_a_std + a_upper_std = (log_a_upper - log_a_mean) / log_a_std + return truncnorm.rvs(a_lower_std, a_upper_std, + loc=log_a_mean, scale=log_a_std) + + +# Convenience alias; unresolved Table 1 model is the usual opt-in object. +MultiplicityOffner2023 = MultiplicityUnresolvedOffner2023 + + +def _two_point_powerlaw(mass_1, y_1, mass_2, y_2): + """ + Amplitude and power for y = A * M**alpha through two (M, y) points. + + Parameters + ---------- + mass_1, mass_2 : float + Primary masses in solar masses (Msun) of the two anchor points. + Must be positive and distinct. + y_1, y_2 : float + Ordinate values at ``mass_1`` and ``mass_2``. Units match the + fitted quantity (dimensionless for MF/γ, mean companion count + for CSF, AU for characteristic a, dex for σ). + + Returns + ------- + amp : float + Power-law amplitude A, in units of y / Msun**alpha. + power : float + Power-law index alpha, dimensionless. + """ + power = np.log(y_2 / y_1) / np.log(mass_2 / mass_1) + amp = y_1 / (mass_1 ** power) + return amp, power + + +def _piecewise_powerlaw(mass, mass_limits, amps, powers, clip_min=None, + clip_max=None): + """ + Evaluate y = A_i * M**alpha_i on mass segments. + + Segment i applies for mass_limits[i] <= M < mass_limits[i+1]. + The first segment also covers M below the lowest limit; the last + segment is closed on the right. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + mass_limits : array_like + Segment edges in solar masses (Msun), length N+1, strictly + increasing. + amps : array_like + Length-N amplitudes A_i, in units of y / Msun**alpha_i. + powers : array_like + Length-N power-law indices alpha_i, dimensionless. + clip_min, clip_max : float or None, optional + Optional lower/upper clips on y, in the same units as y. + ``None`` means no clip on that side. + + Returns + ------- + y : float or ndarray + Piecewise power-law value, in the same units as + ``amps * mass**powers``. Python float if ``mass`` is scalar, + ndarray otherwise. + """ + return_scalar = np.isscalar(mass) + mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) + out = np.empty(mass_arr.shape, dtype=float) + nseg = len(amps) + for i in range(nseg): + lo = mass_limits[i] + hi = mass_limits[i + 1] + if i == 0: + mask = mass_arr < hi + elif i == nseg - 1: + mask = mass_arr >= lo + else: + mask = (mass_arr >= lo) & (mass_arr < hi) + out[mask] = amps[i] * np.power(mass_arr[mask], powers[i]) + if clip_min is not None: + out = np.maximum(out, clip_min) + if clip_max is not None: + out = np.minimum(out, clip_max) + if return_scalar: + return float(out[0]) + return out + + +def _logistic_in_logm(mass, A, B, M0, k, clip_min=None, clip_max=None): + """ + Evaluate y = A + (B - A) / (1 + (M / M0)**(-k)). + + This is a logistic in log-mass: as M -> 0, y -> A; as M -> inf, + y -> B. Masses <= 0 are mapped to the low-mass asymptote A. + + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + A, B : float + Low-mass and high-mass asymptotes, in the same units as y. + Dimensionless for MF and γ; mean companion count for CSF; + dex for σ(log10 a). + M0 : float + Characteristic mass in solar masses (Msun). + k : float + Logistic slope, dimensionless. + clip_min, clip_max : float or None, optional + Optional lower/upper clips on y, in the same units as y. + ``None`` means no clip on that side. + + Returns + ------- + y : float or ndarray + Logistic value in the same units as ``A`` and ``B``. + Python float if ``mass`` is scalar, ndarray otherwise. + """ + return_scalar = np.isscalar(mass) + mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) + out = np.full(mass_arr.shape, float(A), dtype=float) + positive = mass_arr > 0 + if np.any(positive): + m = mass_arr[positive] + out[positive] = A + (B - A) / (1.0 + np.power(m / M0, -k)) + if clip_min is not None: + out = np.maximum(out, clip_min) + if clip_max is not None: + out = np.minimum(out, clip_max) + if return_scalar: + return float(out[0]) + return out + - def sigma_log_a(self, mass): - """ - σ(log10 a) from a 2-parameter logistic in log-mass. +def _logcosh(x): + """ + Numerically stable log(cosh(x)). - Floors/ceilings pinned at 0.7 / 1.5; clipped to ≥ 0.1. + Uses |x| + log1p(exp(-2|x|)) - log(2) rather than np.log(np.cosh(x)), + which overflows for |x| ≳ 700. - Parameters - ---------- - mass : float or array_like - Primary mass in solar masses (Msun). + Parameters + ---------- + x : float or array_like + Argument of cosh, dimensionless (for the smooth broken power + law this is v/s, with v and s in dex). - Returns - ------- - sigma_log_a : float or ndarray - Standard deviation of log10(a / 1 AU), in dex. - Python float if ``mass`` is scalar, ndarray otherwise. - """ - return _logistic_in_logm( - mass, OFFNER2023_SIG_A, OFFNER2023_SIG_B, - OFFNER2023_SIG_M0, OFFNER2023_SIG_K, clip_min=0.1) + Returns + ------- + logcosh_x : float or ndarray + log(cosh(x)), dimensionless. Same shape as ``x``. + """ + ax = np.abs(np.asarray(x, dtype=float)) + return ax + np.log1p(np.exp(-2.0 * ax)) - np.log(2.0) - def _q_values_for_primaries(self, prim_subset, n_comp, rng): - """ - Draw mass-dependent q for every primary (BD and stellar). - Parameters - ---------- - prim_subset : array_like - Primary masses in solar masses (Msun) for this companion-count - group. - n_comp : int - Number of companions per primary, integer count. - rng : numpy.random.Generator - Random generator used for inverse-CDF q draws. +def _smooth_broken_loglog(mass, mup, Mp, alpha_L, alpha_R, s, a_min=0.1): + """ + Smooth broken power law in log10(a) vs log10(M). - Returns - ------- - q_values : ndarray - Companion mass ratios m_comp/m_prim, dimensionless, in - [q_min, 1]. Shape (len(prim_subset), n_comp). - """ - return self.random_q( - rng.random((len(prim_subset), n_comp)), mass=prim_subset) + v = log10(M / Mp) + yp = log10(mup) + log10(a) = yp + 0.5*(αL+αR)*v + 0.5*(αR-αL)*s * logcosh(v/s) + ``s`` is the smoothing scale in dex (C-infinity; logcosh). Masses + <= 0 are mapped to 1e-8 Msun. The linear-space value is clipped + to ``a_min``. -class MultiplicityResolvedOffner2023(MultiplicityUnresolvedOffner2023, - _ResolvedOrbitalMixin): + Parameters + ---------- + mass : float or array_like + Primary mass in solar masses (Msun). + mup : float + Characteristic separation at the break mass, in AU. + Mp : float + Break mass in solar masses (Msun). + alpha_L, alpha_R : float + Power-law indices below and above ``Mp``, dimensionless. + s : float + Smoothing scale in dex of log10(M / 1 Msun). + a_min : float, optional + Minimum linear-space separation in AU. Default 0.1 AU. + + Returns + ------- + log_a : float or ndarray + log10(a / 1 AU) in dex (not ln, not AU). Python float if + ``mass`` is scalar, ndarray otherwise. """ - Resolved Offner et al. 2023 multiplicity: Table 1 MF/CF plus - mass-dependent separations. + return_scalar = np.isscalar(mass) + mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) + m = np.where(mass_arr > 0, mass_arr, 1e-8) + v = np.log10(m / float(Mp)) + yp = np.log10(float(mup)) + log_a = (yp + + 0.5 * (alpha_L + alpha_R) * v + + 0.5 * (alpha_R - alpha_L) * s * _logcosh(v / s)) + a = np.maximum(10.0 ** log_a, float(a_min)) + log_a = np.log10(a) + if return_scalar: + return float(log_a[0]) + return log_a - Separations are drawn from a truncated lognormal in log10(a/AU) - with loc = :meth:`log_a_mean` (smooth broken power law, s = 0.1 - dex, FGK-pulled) and scale = :meth:`sigma_log_a` (2-parameter - logistic pinned at 0.7 / 1.5). Brown-dwarf binaries peak near a - few AU. Truncation is 0.01–2000 AU, same as - :class:`MultiplicityResolvedDK`. - Eccentricity and Keplerian angles follow Duchêne & Kraus (2013), - same as :class:`MultiplicityResolvedDK`. +def _q_from_powerlaw(x, q_pow, q_min): + """ + Inverse CDF of P(q) ∝ q**q_pow for q_min <= q <= 1. - Opt-in; does not replace :class:`MultiplicityResolvedDK`. + ``q_pow`` may be a scalar or an array broadcastable to ``x``. + The q_pow = -1 (b = 0) limit is q = q_min**(1 - x). Parameters ---------- - CSF_max : float, optional - Maximum companion star fraction, dimensionless mean companion - count (not bounded by 1). Default 3. - q_power : float, optional - Fallback mass-ratio power-law index, dimensionless. Ignored for - draws when primary mass is provided (the γ logistic is used). - Default 0.2. - q_min : float, optional - Minimum mass ratio m_comp/m_prim, dimensionless. Default 0.01. - companion_max : bool, optional - If True, cap companion counts at CSF_max. Default False. - binary_only_mass_max : float, optional - Primary mass in solar masses (Msun) at and below which systems - are binaries only. Default 0.08 Msun. + x : float or array_like + Uniform random draw, dimensionless, in [0, 1]. + q_pow : float or array_like + Mass-ratio power-law index γ, dimensionless. Broadcastable + to ``x``. + q_min : float + Minimum mass ratio m_comp/m_prim, dimensionless, in (0, 1]. + + Returns + ------- + q : ndarray + Companion mass ratio m_comp/m_prim, dimensionless, in + [q_min, 1]. Same shape as the broadcast of ``x`` and ``q_pow``. """ - def __init__(self, **kwargs): - super(MultiplicityResolvedOffner2023, self).__init__(**kwargs) - # Table 1/2 data that was fit; draws use log_a_mean / sigma_log_a. - self.sep_mass = np.array(OFFNER2023_SEP_MASS, dtype=float) - self.sep_mu_au = np.array(OFFNER2023_SEP_MU_AU, dtype=float) - self.sep_sig_mass = np.array(OFFNER2023_SEP_SIG_MASS, dtype=float) - self.sep_sig = np.array(OFFNER2023_SEP_SIG, dtype=float) + x = np.asarray(x, dtype=float) + q_pow = np.asarray(q_pow, dtype=float) + if x.ndim > q_pow.ndim: + q_pow = q_pow.reshape(q_pow.shape + (1,) * (x.ndim - q_pow.ndim)) + b = 1.0 + q_pow + b, x = np.broadcast_arrays(b, x) + out = np.empty(x.shape, dtype=float) + near_zero = np.abs(b) < 1e-12 + ok = ~near_zero + if np.any(near_zero): + out[near_zero] = q_min ** (1.0 - x[near_zero]) + if np.any(ok): + out[ok] = (x[ok] * (1.0 - q_min ** b[ok]) + q_min ** b[ok]) ** (1.0 / b[ok]) + return out - def log_semimajoraxis(self, mass): - """ - Draw log10(a/AU) from a mass-dependent truncated lognormal. - Parameters - ---------- - mass : float or array_like - Primary mass in solar masses (Msun). +def _offner2023_table1_geom_mass(m_lo, m_hi): + """ + Geometric-mean primary mass of a Table 1 M1 interval. - Returns - ------- - log_semimajoraxis : ndarray - Drawn log10(a / 1 AU) in dex (not ln, not AU), truncated - so a is between 0.01 AU and 2000 AU. - """ - mass = np.atleast_1d(np.asarray(mass, dtype=float)) - log_a_mean = np.atleast_1d(np.asarray(self.log_a_mean(mass), dtype=float)) - log_a_std = np.atleast_1d(np.asarray(self.sigma_log_a(mass), dtype=float)) + Parameters + ---------- + m_lo, m_hi : float + Low and high edges of the Table 1 primary-mass interval, in + solar masses (Msun). Must be positive. - log_a_lower = np.log10(0.01) - log_a_upper = np.log10(2000) - a_lower_std = (log_a_lower - log_a_mean) / log_a_std - a_upper_std = (log_a_upper - log_a_mean) / log_a_std - return truncnorm.rvs(a_lower_std, a_upper_std, - loc=log_a_mean, scale=log_a_std) + Returns + ------- + mass : float + Geometric mean sqrt(m_lo * m_hi) in solar masses (Msun). + """ + return float(np.sqrt(m_lo * m_hi)) +# Table 1/2 data that was fit; the model is the smooth functions above, +# not interpolation of these arrays. +OFFNER2023_Q_MASS = np.array([ + _offner2023_table1_geom_mass(0.019, 0.058), # Fontanive+2018: 4.8 + 0.065, # L/early-T: 2-3 (text) + _offner2023_table1_geom_mass(0.080, 0.095), # Close+2003: 3.3 + _offner2023_table1_geom_mass(0.06, 0.15), # Allen+2007: 1.7 + _offner2023_table1_geom_mass(0.15, 0.30), # Winters mid-M: 0.7 + _offner2023_table1_geom_mass(0.3, 0.6), # Winters early-M: 0.1 + _offner2023_table1_geom_mass(0.75, 1.25), # Raghavan FGK: 0.2 + _offner2023_table1_geom_mass(1.6, 2.4), # De Rosa A: -1.3 + _offner2023_table1_geom_mass(3.0, 5.0), # MDS 3-5: -1.0 + _offner2023_table1_geom_mass(5.0, 8.0), # MDS 5-8: -1.7 + _offner2023_table1_geom_mass(8.0, 17.0), # MDS 8-17: -1.6 + _offner2023_table1_geom_mass(17.0, 50.0), # Sana O: -1.4 +]) +OFFNER2023_Q_GAMMA = np.array([ + 4.8, 2.5, 3.3, 1.7, 0.7, 0.1, 0.2, -1.3, -1.0, -1.7, -1.6, -1.4 +]) -# Convenience alias; unresolved Table 1 model is the usual opt-in object. -MultiplicityOffner2023 = MultiplicityUnresolvedOffner2023 +# Table 1 ã_all (au) and Table 2 lognormal μ (au) vs geom-mean M1. +# Table 2 μ is listed where both exist (late-M, early-M, FGK). +# Fit data only; evaluation uses the smooth broken power law. +OFFNER2023_SEP_MASS = np.array([ + _offner2023_table1_geom_mass(0.019, 0.058), # Fontanive ã_all=2.9 + _offner2023_table1_geom_mass(0.080, 0.095), # Close ã_all=3.7 + _offner2023_table1_geom_mass(0.075, 0.15), # Table 2 late-M μ=4 + _offner2023_table1_geom_mass(0.15, 0.30), # Winters mid-M ã_all=10 + _offner2023_table1_geom_mass(0.3, 0.6), # Table 2 early-M μ=25 + _offner2023_table1_geom_mass(0.75, 1.25), # Table 2 FGK μ=40 + _offner2023_table1_geom_mass(1.6, 2.4), # Moe & Kratter ã_all=32 + _offner2023_table1_geom_mass(3.0, 5.0), # MDS ã_all=28 + _offner2023_table1_geom_mass(5.0, 8.0), # MDS ã_all=25 + _offner2023_table1_geom_mass(8.0, 17.0), # MDS ã_all=23 + _offner2023_table1_geom_mass(17.0, 50.0), # Sana ã_all=19 +]) +OFFNER2023_SEP_MU_AU = np.array([ + 2.9, 3.7, 4.0, 10.0, 25.0, 40.0, 32.0, 28.0, 25.0, 23.0, 19.0 +]) +# Table 2 σ_log a at the three published bins. Fit data only; +# evaluation uses the 2-parameter logistic. +OFFNER2023_SEP_SIG_MASS = np.array([ + _offner2023_table1_geom_mass(0.075, 0.15), + _offner2023_table1_geom_mass(0.3, 0.6), + _offner2023_table1_geom_mass(0.75, 1.25), +]) +OFFNER2023_SEP_SIG = np.array([0.7, 1.3, 1.5]) From 48eafdcb7ad994262126abdd951aa749ae2cc747 Mon Sep 17 00:00:00 2001 From: Jessica Lu Date: Fri, 14 Aug 2026 10:12:35 -0700 Subject: [PATCH 14/16] Code cleanup (spacing, etc.). --- spisea/imf/multiplicity.py | 59 ++++++++++++++++++++++++++------------ 1 file changed, 40 insertions(+), 19 deletions(-) diff --git a/spisea/imf/multiplicity.py b/spisea/imf/multiplicity.py index 676905e..3212363 100755 --- a/spisea/imf/multiplicity.py +++ b/spisea/imf/multiplicity.py @@ -19,7 +19,7 @@ H_BURNING_MASS = 0.08 # Fontanive et al. (2018) mass-ratio power-law index used for BD primaries -# in the Lu et al. (2013) MultiplicityUnresolved implementation. +# in the SPISEA v2.5 MultiplicityUnresolved implementation. FONTANIVE2018_BD_Q_POWER = 6.1 # Eventually we should add in separation properties. (a_mean, a_sigma) @@ -405,7 +405,7 @@ def random_companion_count(self, x, CSF, MF, mass=None, rng=None): n_comp = 1 + np.random.poisson((CSF / MF) - 1) if self.companion_max and n_comp > self.CSF_max: n_comp = self.CSF_max - if mass is not None and np.asarray(mass, dtype=float).reshape(-1)[0] <= self.binary_only_mass_max: + if (mass is not None) and (np.asarray(mass, dtype=float).reshape(-1)[0] <= self.binary_only_mass_max): n_comp = min(int(n_comp), 1) return int(n_comp) @@ -415,14 +415,18 @@ def random_companion_count(self, x, CSF, MF, mass=None, rng=None): n_comp = 1 + np.random.poisson((CSF / MF) - 1) else: n_comp = 1 + rng.poisson((CSF / MF) - 1) + if self.companion_max: n_comp = np.minimum(n_comp, self.CSF_max) + if mass is not None: mass = np.atleast_1d(np.asarray(mass, dtype=float)) bd = mass <= self.binary_only_mass_max n_comp[bd & (n_comp > 1)] = 1 + if return_scalar: return int(n_comp[0]) + return n_comp def draw_n_companions(self, mass, CSF, MF, rng): @@ -451,15 +455,16 @@ def draw_n_companions(self, mass, CSF, MF, rng): Number of companions per primary, integer count, shape matching ``mass``. """ - return np.atleast_1d( - self.random_companion_count(None, CSF, MF, mass=mass, rng=rng)) + n_comp = self.random_companion_count(None, CSF, MF, mass=mass, rng=rng) + + return np.atleast_1d(n_comp) def _q_values_for_primaries(self, prim_subset, n_comp, rng): """ Draw mass ratios for ``n_comp`` companions of each primary. The stellar / brown-dwarf split (two separate RNG draws) preserves - the historical Lu et al. (2013) random sequence used by + the historical SPISEA v2.5 random sequence used by ``imf.calc_multi``. Parameters @@ -481,13 +486,13 @@ def _q_values_for_primaries(self, prim_subset, n_comp, rng): q_values = np.empty((len(prim_subset), n_comp)) bd_mask = prim_subset <= self.binary_only_mass_max star_mask = ~bd_mask + if np.any(star_mask): - q_values[star_mask] = self.random_q( - rng.random((star_mask.sum(), n_comp))) + q_values[star_mask] = self.random_q(rng.random((star_mask.sum(), n_comp)), mass=prim_subset[star_mask]) + if np.any(bd_mask): - q_values[bd_mask] = self.random_q( - rng.random((bd_mask.sum(), n_comp)), - mass=prim_subset[bd_mask]) + q_values[bd_mask] = self.random_q(rng.random((bd_mask.sum(), n_comp)), mass=prim_subset[bd_mask]) + return q_values def draw_companion_masses(self, primary_masses, is_multiple, CSF, MF, @@ -534,15 +539,16 @@ def draw_companion_masses(self, primary_masses, is_multiple, CSF, MF, is_multiple = np.asarray(is_multiple, dtype=bool) CSF = np.asarray(CSF, dtype=float) MF = np.asarray(MF, dtype=float) + system_masses = primary_masses.copy() multiple_idx = np.where(is_multiple)[0] primary = primary_masses[multiple_idx] - n_comp = self.draw_n_companions( - primary, CSF[multiple_idx], MF[multiple_idx], rng) + n_comp = self.draw_n_companions(primary, CSF[multiple_idx], MF[multiple_idx], rng) if len(multiple_idx) == 0: - comp_masses = np.zeros((len(primary_masses), 1)) + comp_masses = np.zeros((len(primary_masses), 1), dtype=float) comp_masses = np.ma.MaskedArray(comp_masses, mask=comp_masses < mass_min) + return comp_masses, system_masses, is_multiple n_unique = np.unique(n_comp) @@ -558,8 +564,10 @@ def draw_companion_masses(self, primary_masses, is_multiple, CSF, MF, comp_masses = np.ma.MaskedArray(comp_masses, mask=comp_masses < mass_min) system_masses[multiple_idx] += comp_masses[multiple_idx].sum(axis=1) is_multiple = np.any(~comp_masses.mask, axis=1) + return comp_masses, system_masses, is_multiple + class MultiplicityResolvedDK(MultiplicityUnresolved, _ResolvedOrbitalMixin): """ Sub-class of MultiplicityUnresolved that adds semimajor axis and eccentricity information @@ -596,6 +604,8 @@ def __init__(self, a_amp = 379.79953034, a_break = 4.90441533, a_slope1 = -1.801 self.a_slope2 = a_slope2 self.a_std_slope = a_std_slope self.a_std_intercept = a_std_intercept + + return def log_semimajoraxis(self, mass): """ @@ -706,11 +716,15 @@ def __init__(self, mass_limits, MF_amps, MF_powers, CSF_amps, CSF_powers, MF_powers = np.asarray(MF_powers, dtype=float) CSF_amps = np.asarray(CSF_amps, dtype=float) CSF_powers = np.asarray(CSF_powers, dtype=float) + nseg = len(MF_amps) + if len(mass_limits) != nseg + 1: raise ValueError('len(mass_limits) must be len(MF_amps) + 1') + if not (len(MF_powers) == len(CSF_amps) == len(CSF_powers) == nseg): raise ValueError('MF/CSF amplitude and power arrays must have equal length') + if np.any(np.diff(mass_limits) <= 0): raise ValueError('mass_limits must be strictly increasing') @@ -720,12 +734,15 @@ def __init__(self, mass_limits, MF_amps, MF_powers, CSF_amps, CSF_powers, CSF_max=CSF_max, q_power=q_power, q_min=q_min, companion_max=companion_max, binary_only_mass_max=binary_only_mass_max) + self.mass_limits = mass_limits self.MF_amps = MF_amps self.MF_powers = MF_powers self.CSF_amps = CSF_amps self.CSF_powers = CSF_powers + return + def multiplicity_fraction(self, mass): """ Multiplicity fraction as a piecewise power law in primary mass. @@ -742,9 +759,9 @@ def multiplicity_fraction(self, mass): Multiplicity fraction, dimensionless, in [0, 1]. Python float if ``mass`` is scalar, ndarray otherwise. """ - return _piecewise_powerlaw( - mass, self.mass_limits, self.MF_amps, self.MF_powers, - clip_min=0.0, clip_max=1.0) + mf = _piecewise_powerlaw(mass, self.mass_limits, self.MF_amps, self.MF_powers, clip_min=0.0, clip_max=1.0) + + return mf def companion_star_fraction(self, mass): """ @@ -982,6 +999,7 @@ class MultiplicityUnresolvedOffner2023(MultiplicityLogistic): """ def __init__(self, CSF_max=3, q_power=0.2, q_min=0.01, companion_max=False, binary_only_mass_max=H_BURNING_MASS): + super(MultiplicityUnresolvedOffner2023, self).__init__( MF_A=OFFNER2023_MF_A, MF_B=OFFNER2023_MF_B, @@ -994,10 +1012,13 @@ def __init__(self, CSF_max=3, q_power=0.2, q_min=0.01, CSF_max=CSF_max, q_power=q_power, q_min=q_min, companion_max=companion_max, binary_only_mass_max=binary_only_mass_max) + # Table 1/2 data that was fit; evaluation uses the smooth functions. self.q_mass = np.array(OFFNER2023_Q_MASS, dtype=float) self.q_gamma = np.array(OFFNER2023_Q_GAMMA, dtype=float) + return + def q_power_at_mass(self, mass): """ Mass-ratio power-law index γ(M), P(q) ∝ q^γ. @@ -1016,9 +1037,9 @@ def q_power_at_mass(self, mass): Mass-ratio power-law index γ, dimensionless. Python float if ``mass`` is scalar, ndarray otherwise. """ - return _logistic_in_logm( - mass, OFFNER2023_Q_A, OFFNER2023_Q_B, - OFFNER2023_Q_M0, OFFNER2023_Q_K) + gamma = _logistic_in_logm(mass, OFFNER2023_Q_A, OFFNER2023_Q_B, OFFNER2023_Q_M0, OFFNER2023_Q_K) + + return gamma def log_a_mean(self, mass): """ From af8eb8e3842044868354642c3182cedbe5a9fb91 Mon Sep 17 00:00:00 2001 From: Cursor Agent Date: Fri, 14 Aug 2026 17:16:04 +0000 Subject: [PATCH 15/16] Drop massless-primary (M<=0) support in multiplicity helpers Evaluate the logistic and smooth broken power law on positive masses only. Keep M>0 math unchanged. Tests and docs no longer treat M<=0 as mapping to the low-mass asymptote. Co-authored-by: Jessica Lu --- docs/multiplicity.rst | 3 +- spisea/imf/multiplicity.py | 70 ++++++++++++++----------------- spisea/tests/test_multiplicity.py | 4 +- 3 files changed, 34 insertions(+), 43 deletions(-) diff --git a/docs/multiplicity.rst b/docs/multiplicity.rst index 142a1c7..2ba3df9 100644 --- a/docs/multiplicity.rst +++ b/docs/multiplicity.rst @@ -119,8 +119,7 @@ with :math:`(A, B, M_0, k) = (0.14, 0.99, 1.41, 1.25)` for MF and smooth and saturates at :math:`B \approx 1` for MF. MF is clipped to :math:`[0, 1]`. CSF is clipped to :math:`[0, \mathrm{CSF_{max}}]`, raised to at least MF, and forced equal to MF for -:math:`M \le 0.08\,M_\odot` (binaries only). Masses :math:`M \le 0` -map to the low-mass asymptote :math:`A`. +:math:`M \le 0.08\,M_\odot` (binaries only). SPISEA v2.5 uses :math:`\mathrm{MF} = 0.44\,M^{0.51}` (clipped to 1) for arrays, plus a scalar-only brown-dwarf staircase diff --git a/spisea/imf/multiplicity.py b/spisea/imf/multiplicity.py index 3212363..7b6b2cf 100755 --- a/spisea/imf/multiplicity.py +++ b/spisea/imf/multiplicity.py @@ -238,7 +238,7 @@ def multiplicity_fraction(self, mass): Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). Returns ------- @@ -275,7 +275,7 @@ def companion_star_fraction(self, mass): Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). Returns ------- @@ -312,7 +312,7 @@ def q_power_at_mass(self, mass): Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). Returns ------- @@ -342,7 +342,7 @@ def random_q(self, x, mass=None): sample for q. mass : float or array_like, optional - Primary mass in solar masses (Msun). If given, the + Primary mass must be positive, in solar masses (Msun). If given, the power-law index is ``q_power_at_mass(mass)`` (brown-dwarf vs stellar for the SPISEA v2.5 default; mass-dependent for Offner et al. 2023). If omitted, ``self.q_pow`` is used @@ -384,7 +384,7 @@ def random_companion_count(self, x, CSF, MF, mass=None, rng=None): MF : float or array_like Multiplicity fraction, dimensionless, in [0, 1]. mass : float or array_like, optional - Primary mass in solar masses (Msun). If given, primaries + Primary mass must be positive, in solar masses (Msun). If given, primaries at or below ``binary_only_mass_max`` are limited to one companion. Cluster generation always passes mass so subclasses can override the BD companion-count policy here. @@ -438,8 +438,8 @@ def draw_n_companions(self, mass, CSF, MF, rng): Parameters ---------- mass : array_like - Primary masses in solar masses (Msun) of systems already - identified as multiple. + Primary masses of systems already identified as multiple. + Must be positive, in solar masses (Msun). CSF : array_like Companion star fraction at each primary, dimensionless mean companion count (not bounded by 1). @@ -470,8 +470,8 @@ def _q_values_for_primaries(self, prim_subset, n_comp, rng): Parameters ---------- prim_subset : array_like - Primary masses in solar masses (Msun) for this companion-count - group. + Primary masses for this companion-count group. Must be + positive, in solar masses (Msun). n_comp : int Number of companions per primary, integer count. rng : numpy.random.Generator @@ -508,7 +508,7 @@ def draw_companion_masses(self, primary_masses, is_multiple, CSF, MF, Parameters ---------- primary_masses : array_like - Primary masses in solar masses (Msun). + Primary masses must be positive, in solar masses (Msun). is_multiple : array_like of bool True for primaries drawn as multiple systems. CSF : array_like @@ -751,7 +751,7 @@ def multiplicity_fraction(self, mass): Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). Returns ------- @@ -773,7 +773,7 @@ def companion_star_fraction(self, mass): Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). Returns ------- @@ -868,7 +868,7 @@ def multiplicity_fraction(self, mass): Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). Returns ------- @@ -890,7 +890,7 @@ def companion_star_fraction(self, mass): Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). Returns ------- @@ -1029,7 +1029,7 @@ def q_power_at_mass(self, mass): Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). Returns ------- @@ -1051,7 +1051,7 @@ def log_a_mean(self, mass): Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). Returns ------- @@ -1071,7 +1071,7 @@ def a_mean(self, mass): Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). Returns ------- @@ -1093,7 +1093,7 @@ def sigma_log_a(self, mass): Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). Returns ------- @@ -1112,8 +1112,8 @@ def _q_values_for_primaries(self, prim_subset, n_comp, rng): Parameters ---------- prim_subset : array_like - Primary masses in solar masses (Msun) for this companion-count - group. + Primary masses for this companion-count group. Must be + positive, in solar masses (Msun). n_comp : int Number of companions per primary, integer count. rng : numpy.random.Generator @@ -1179,7 +1179,7 @@ def log_semimajoraxis(self, mass): Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). Returns ------- @@ -1210,8 +1210,8 @@ def _two_point_powerlaw(mass_1, y_1, mass_2, y_2): Parameters ---------- mass_1, mass_2 : float - Primary masses in solar masses (Msun) of the two anchor points. - Must be positive and distinct. + Primary masses of the two anchor points, in solar masses + (Msun). Must be positive and distinct. y_1, y_2 : float Ordinate values at ``mass_1`` and ``mass_2``. Units match the fitted quantity (dimensionless for MF/γ, mean companion count @@ -1241,7 +1241,7 @@ def _piecewise_powerlaw(mass, mass_limits, amps, powers, clip_min=None, Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). mass_limits : array_like Segment edges in solar masses (Msun), length N+1, strictly increasing. @@ -1287,13 +1287,13 @@ def _logistic_in_logm(mass, A, B, M0, k, clip_min=None, clip_max=None): """ Evaluate y = A + (B - A) / (1 + (M / M0)**(-k)). - This is a logistic in log-mass: as M -> 0, y -> A; as M -> inf, - y -> B. Masses <= 0 are mapped to the low-mass asymptote A. + This is a logistic in log-mass: as M -> 0+, y -> A; as M -> inf, + y -> B. Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). A, B : float Low-mass and high-mass asymptotes, in the same units as y. Dimensionless for MF and γ; mean companion count for CSF; @@ -1314,11 +1314,7 @@ def _logistic_in_logm(mass, A, B, M0, k, clip_min=None, clip_max=None): """ return_scalar = np.isscalar(mass) mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) - out = np.full(mass_arr.shape, float(A), dtype=float) - positive = mass_arr > 0 - if np.any(positive): - m = mass_arr[positive] - out[positive] = A + (B - A) / (1.0 + np.power(m / M0, -k)) + out = A + (B - A) / (1.0 + np.power(mass_arr / M0, -k)) if clip_min is not None: out = np.maximum(out, clip_min) if clip_max is not None: @@ -1358,14 +1354,13 @@ def _smooth_broken_loglog(mass, mup, Mp, alpha_L, alpha_R, s, a_min=0.1): yp = log10(mup) log10(a) = yp + 0.5*(αL+αR)*v + 0.5*(αR-αL)*s * logcosh(v/s) - ``s`` is the smoothing scale in dex (C-infinity; logcosh). Masses - <= 0 are mapped to 1e-8 Msun. The linear-space value is clipped - to ``a_min``. + ``s`` is the smoothing scale in dex (C-infinity; logcosh). The + linear-space value is clipped to ``a_min``. Parameters ---------- mass : float or array_like - Primary mass in solar masses (Msun). + Primary mass must be positive, in solar masses (Msun). mup : float Characteristic separation at the break mass, in AU. Mp : float @@ -1385,8 +1380,7 @@ def _smooth_broken_loglog(mass, mup, Mp, alpha_L, alpha_R, s, a_min=0.1): """ return_scalar = np.isscalar(mass) mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) - m = np.where(mass_arr > 0, mass_arr, 1e-8) - v = np.log10(m / float(Mp)) + v = np.log10(mass_arr / float(Mp)) yp = np.log10(float(mup)) log_a = (yp + 0.5 * (alpha_L + alpha_R) * v diff --git a/spisea/tests/test_multiplicity.py b/spisea/tests/test_multiplicity.py index 8485a77..f0d6782 100755 --- a/spisea/tests/test_multiplicity.py +++ b/spisea/tests/test_multiplicity.py @@ -298,10 +298,8 @@ def test_logistic_api(): MF_A=0.1, MF_B=1.5, MF_M0=1.0, MF_k=2.0, CSF_A=0.05, CSF_B=4.0, CSF_M0=2.0, CSF_k=1.0, CSF_max=2.0, binary_only_mass_max=0.08) - # Low-mass asymptote A; M<=0 maps to A + # Low-mass asymptote A for a very low-mass primary (not a missing mass) np.testing.assert_almost_equal(ml.multiplicity_fraction(1e-8), 0.1, decimal=4) - assert ml.multiplicity_fraction(0.0) == 0.1 - assert ml.multiplicity_fraction(-1.0) == 0.1 # High-mass MF saturates at B then clips to 1 np.testing.assert_almost_equal(ml.multiplicity_fraction(1e6), 1.0) # High-mass CSF clips to CSF_max From a66554b8c07eb3a66815e39f4c2f214322766684 Mon Sep 17 00:00:00 2001 From: Jessica Lu Date: Fri, 14 Aug 2026 12:08:43 -0700 Subject: [PATCH 16/16] Reviewed code, cleaned up formatting, added more documentation. --- spisea/imf/multiplicity.py | 115 ++++++++++++++++++++++++++++++------- 1 file changed, 94 insertions(+), 21 deletions(-) diff --git a/spisea/imf/multiplicity.py b/spisea/imf/multiplicity.py index 7b6b2cf..198dc8b 100755 --- a/spisea/imf/multiplicity.py +++ b/spisea/imf/multiplicity.py @@ -664,6 +664,7 @@ def log_semimajoraxis(self, mass): log_semimajoraxis = truncnorm.rvs(a_lower_std, a_upper_std, loc=log_a_mean, scale=log_a_std) return log_semimajoraxis + class MultiplicityPiecewisePowerLaw(MultiplicityUnresolved): """ Multiplicity described by a piecewise power law in primary mass. @@ -860,6 +861,8 @@ def __init__(self, MF_A, MF_B, MF_M0, MF_k, self.CSF_M0 = float(CSF_M0) self.CSF_k = float(CSF_k) + return + def multiplicity_fraction(self, mass): """ Multiplicity fraction as a logistic in log primary mass. @@ -876,9 +879,10 @@ def multiplicity_fraction(self, mass): Multiplicity fraction, dimensionless, in [0, 1]. Python float if ``mass`` is scalar, ndarray otherwise. """ - return _logistic_in_logm( - mass, self.MF_A, self.MF_B, self.MF_M0, self.MF_k, - clip_min=0.0, clip_max=1.0) + mf = _logistic_in_logm(mass, self.MF_A, self.MF_B, self.MF_M0, self.MF_k, + clip_min=0.0, clip_max=1.0) + + return mf def companion_star_fraction(self, mass): """ @@ -901,17 +905,25 @@ def companion_star_fraction(self, mass): """ return_scalar = np.isscalar(mass) mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) - csf = _logistic_in_logm( - mass_arr, self.CSF_A, self.CSF_B, self.CSF_M0, self.CSF_k, - clip_min=0.0, clip_max=self.CSF_max) - mf = _logistic_in_logm( - mass_arr, self.MF_A, self.MF_B, self.MF_M0, self.MF_k, - clip_min=0.0, clip_max=1.0) + + # Calculate the multiplicity fraction + mf = _logistic_in_logm(mass_arr, self.MF_A, self.MF_B, self.MF_M0, self.MF_k, + clip_min=0.0, clip_max=1.0) + + # Calculate the companion star fraction + csf = _logistic_in_logm(mass_arr, self.CSF_A, self.CSF_B, self.CSF_M0, self.CSF_k, + clip_min=0.0, clip_max=self.CSF_max) + + # Ensure the companion star fraction is at least the multiplicity fraction csf = np.maximum(csf, mf) + + # Fix all brown dwarf binaries so they only have one companion bd = mass_arr <= self.binary_only_mass_max csf[bd] = mf[bd] + if return_scalar: return float(csf[0]) + return csf @@ -1013,7 +1025,7 @@ def __init__(self, CSF_max=3, q_power=0.2, q_min=0.01, companion_max=companion_max, binary_only_mass_max=binary_only_mass_max) - # Table 1/2 data that was fit; evaluation uses the smooth functions. + # Table 1/2 data that was fit; evaluation uses a smooth function. self.q_mass = np.array(OFFNER2023_Q_MASS, dtype=float) self.q_gamma = np.array(OFFNER2023_Q_GAMMA, dtype=float) @@ -1059,11 +1071,14 @@ def log_a_mean(self, mass): Characteristic log10(a / 1 AU) in dex (not ln, not AU). Python float if ``mass`` is scalar, ndarray otherwise. """ - return _smooth_broken_loglog( + # Calculate the characteristic log10(a / 1 AU) using a smooth broken power law + log_a_mean = _smooth_broken_loglog( mass, OFFNER2023_A_MUP, OFFNER2023_A_MP, OFFNER2023_A_ALPHAL, OFFNER2023_A_ALPHAR, OFFNER2023_A_S, a_min=OFFNER2023_A_MIN) + return log_a_mean + def a_mean(self, mass): """ Characteristic μ(a) in AU, ``10 ** log_a_mean(mass)``. @@ -1080,9 +1095,14 @@ def a_mean(self, mass): ``mass`` is scalar, ndarray otherwise. """ log_a = self.log_a_mean(mass) + if np.isscalar(log_a): - return 10.0 ** log_a - return 10.0 ** np.asarray(log_a, dtype=float) + a_mean = 10.0 ** log_a + return a_mean + + a_mean = 10.0 ** np.asarray(log_a, dtype=float) + + return a_mean def sigma_log_a(self, mass): """ @@ -1101,9 +1121,13 @@ def sigma_log_a(self, mass): Standard deviation of log10(a / 1 AU), in dex. Python float if ``mass`` is scalar, ndarray otherwise. """ - return _logistic_in_logm( - mass, OFFNER2023_SIG_A, OFFNER2023_SIG_B, - OFFNER2023_SIG_M0, OFFNER2023_SIG_K, clip_min=0.1) + + # Calculate the standard deviation of log10(a / 1 AU) using a 2-parameter logistic + sigma_log_a = _logistic_in_logm(mass, OFFNER2023_SIG_A, OFFNER2023_SIG_B, + OFFNER2023_SIG_M0, OFFNER2023_SIG_K, + clip_min=0.1) + + return sigma_log_a def _q_values_for_primaries(self, prim_subset, n_comp, rng): """ @@ -1125,8 +1149,10 @@ def _q_values_for_primaries(self, prim_subset, n_comp, rng): Companion mass ratios m_comp/m_prim, dimensionless, in [q_min, 1]. Shape (len(prim_subset), n_comp). """ - return self.random_q( - rng.random((len(prim_subset), n_comp)), mass=prim_subset) + # Draw the mass-dependent mass ratios using a logistic in log-mass + q_values = self.random_q(rng.random((len(prim_subset), n_comp)), mass=prim_subset) + + return q_values class MultiplicityResolvedOffner2023(MultiplicityUnresolvedOffner2023, @@ -1172,6 +1198,8 @@ def __init__(self, **kwargs): self.sep_sig_mass = np.array(OFFNER2023_SEP_SIG_MASS, dtype=float) self.sep_sig = np.array(OFFNER2023_SEP_SIG, dtype=float) + return + def log_semimajoraxis(self, mass): """ Draw log10(a/AU) from a mass-dependent truncated lognormal. @@ -1195,9 +1223,12 @@ def log_semimajoraxis(self, mass): log_a_upper = np.log10(2000) a_lower_std = (log_a_lower - log_a_mean) / log_a_std a_upper_std = (log_a_upper - log_a_mean) / log_a_std - return truncnorm.rvs(a_lower_std, a_upper_std, + + # Draw the log10(a / 1 AU) from a truncated normal + log_a = truncnorm.rvs(a_lower_std, a_upper_std, loc=log_a_mean, scale=log_a_std) + return log_a # Convenience alias; unresolved Table 1 model is the usual opt-in object. MultiplicityOffner2023 = MultiplicityUnresolvedOffner2023 @@ -1226,6 +1257,7 @@ def _two_point_powerlaw(mass_1, y_1, mass_2, y_2): """ power = np.log(y_2 / y_1) / np.log(mass_2 / mass_1) amp = y_1 / (mass_1 ** power) + return amp, power @@ -1264,9 +1296,13 @@ def _piecewise_powerlaw(mass, mass_limits, amps, powers, clip_min=None, mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) out = np.empty(mass_arr.shape, dtype=float) nseg = len(amps) + + # Evaluate the piecewise power-law for each segment for i in range(nseg): lo = mass_limits[i] hi = mass_limits[i + 1] + + # Determine the mask for the current segment if i == 0: mask = mass_arr < hi elif i == nseg - 1: @@ -1274,12 +1310,18 @@ def _piecewise_powerlaw(mass, mass_limits, amps, powers, clip_min=None, else: mask = (mass_arr >= lo) & (mass_arr < hi) out[mask] = amps[i] * np.power(mass_arr[mask], powers[i]) + + # Apply the clips if clip_min is not None: out = np.maximum(out, clip_min) + if clip_max is not None: out = np.minimum(out, clip_max) + + # Return the result if return_scalar: return float(out[0]) + return out @@ -1314,13 +1356,20 @@ def _logistic_in_logm(mass, A, B, M0, k, clip_min=None, clip_max=None): """ return_scalar = np.isscalar(mass) mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) + + # Evaluate the logistic in log-mass out = A + (B - A) / (1.0 + np.power(mass_arr / M0, -k)) + + # Apply the clips if clip_min is not None: out = np.maximum(out, clip_min) if clip_max is not None: out = np.minimum(out, clip_max) + + # Return the result if return_scalar: return float(out[0]) + return out @@ -1343,7 +1392,12 @@ def _logcosh(x): log(cosh(x)), dimensionless. Same shape as ``x``. """ ax = np.abs(np.asarray(x, dtype=float)) - return ax + np.log1p(np.exp(-2.0 * ax)) - np.log(2.0) + + # Calculate the log(cosh(x)) + logcosh_x = ax + np.log1p(np.exp(-2.0 * ax)) - np.log(2.0) + + # Return the result + return logcosh_x def _smooth_broken_loglog(mass, mup, Mp, alpha_L, alpha_R, s, a_min=0.1): @@ -1382,13 +1436,18 @@ def _smooth_broken_loglog(mass, mup, Mp, alpha_L, alpha_R, s, a_min=0.1): mass_arr = np.atleast_1d(np.asarray(mass, dtype=float)) v = np.log10(mass_arr / float(Mp)) yp = np.log10(float(mup)) + + # Calculate the log10(a / 1 AU) using the smooth broken power law log_a = (yp + 0.5 * (alpha_L + alpha_R) * v + 0.5 * (alpha_R - alpha_L) * s * _logcosh(v / s)) a = np.maximum(10.0 ** log_a, float(a_min)) log_a = np.log10(a) + + # Return the result if return_scalar: return float(log_a[0]) + return log_a @@ -1417,17 +1476,30 @@ def _q_from_powerlaw(x, q_pow, q_min): """ x = np.asarray(x, dtype=float) q_pow = np.asarray(q_pow, dtype=float) + + # Broadcast the arrays if necessary if x.ndim > q_pow.ndim: q_pow = q_pow.reshape(q_pow.shape + (1,) * (x.ndim - q_pow.ndim)) + b = 1.0 + q_pow b, x = np.broadcast_arrays(b, x) + + # Create an empty array to store the result out = np.empty(x.shape, dtype=float) + + # Determine the mask for values near zero near_zero = np.abs(b) < 1e-12 + + # Determine the mask for values far from zero ok = ~near_zero + + # Calculate the mass ratio for values near zero if np.any(near_zero): out[near_zero] = q_min ** (1.0 - x[near_zero]) if np.any(ok): out[ok] = (x[ok] * (1.0 - q_min ** b[ok]) + q_min ** b[ok]) ** (1.0 / b[ok]) + + # Return the result return out @@ -1446,9 +1518,10 @@ def _offner2023_table1_geom_mass(m_lo, m_hi): mass : float Geometric mean sqrt(m_lo * m_hi) in solar masses (Msun). """ + # Calculate the geometric mean of the two masses return float(np.sqrt(m_lo * m_hi)) -# Table 1/2 data that was fit; the model is the smooth functions above, +# Table 1/2 data that was fit; the model is a smooth function, # not interpolation of these arrays. OFFNER2023_Q_MASS = np.array([ _offner2023_table1_geom_mass(0.019, 0.058), # Fontanive+2018: 4.8

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