Common Envelope Evolution — WD Binary Reconstruction

A pipeline for reconstructing the common envelope (CE) evolution of white dwarf (WD) binary systems. Given observed binary parameters (WD mass, companion mass, orbital period), it infers the progenitor donor mass and CE efficiency parameter α via a grid search followed by MCMC sampling.

Method

1. SSE grid — evolves a grid of single-star progenitors using COSMIC/BSE to identify giant-phase snapshots whose core mass matches the observed WD mass.
2. CE grid — for each snapshot, computes the CE envelope-binding-energy parameter λ (Claeys et al. 2014 prescription) and inverts the α–λ energy formalism to find the pre-CE orbital separation.
3. MCMC — samples the posterior over (M₁, α) using emcee, initialised from grid survivors.
4. Plots — walker traces, a corner plot, and a COSMIC best-fit evolution plot.

Installation

pip install -r requirements.txt

Usage

python main.py --config example.ini

Configuration file

All run parameters are set in an .ini file. See example.ini for a template.

Section	Key	Description
[binary]	stage_name	Label used for logging
	log_file	Path to the output log file
	m_wd	Observed WD mass (M☉)
	sigma_mwd	Uncertainty on WD mass (M☉)
	m_bd	Companion mass (M☉)
	p_obs	Observed orbital period (days)
	a_f	(optional) Final separation (R☉); derived from p_obs if omitted
[paths]	output_csv	Grid results CSV
	chain_csv	MCMC chain CSV
	walkers_plot	Walker trace PNG
	corner_plot	Corner plot PNG
	evolution_plot	Best-fit COSMIC evolution PNG
[mcmc]	n_burnin	Burn-in steps (default 500)
	n_steps	Production steps (default 2000)
	t_max_plot	Max time for evolution plot in Myr (default 14000)

Output

File	Description
results/grid_results.csv	All (M₁, α) grid solutions that pass physical bounds
results/chain.csv	Flattened MCMC chain: columns M1, alpha
results/walkers.png	Walker trace for each parameter
results/corner.png	Corner plot of the posterior
results/best_fit_evolution.png	COSMIC evolution for the median posterior solution

Module overview

File	Description
main.py	Entry point: argument parsing, MCMC, and plotting
grid_runner.py	Orchestrates the CE parameter grid over (M₁, α)
sse_grid.py	Builds the SSE grid of giant-phase snapshots via COSMIC
lambda_claeys2014.py	λ prescription from Claeys et al. (2014)
ce_energy_inversion.py	α–λ energy-balance inversion for the pre-CE separation
logger.py	Rotating file + console logger
example.ini	Example configuration file

References

• Theoretical uncertainties of the Type Ia supernova rate J. S. W. Claeys, O. R. Pols, R. G. Izzard, J. Vink and F. W. M. Verbunt A&A, 563 (2014) A83 DOI: https://doi.org/10.1051/0004-6361/201322714
• Monica Zorotovic, MatthiasR Schreiber, Close detached white dwarf + brown dwarf binaries: further evidence for low values of the common envelope efficiency, Monthly Notices of the Royal Astronomical Society, Volume 513, Issue 3, July 2022, Pages 3587–3595, https://doi.org/10.1093/mnras/stac1137
• Post-common-envelope binaries from SDSS - IX: Constraining the common-envelope efficiency -M. Zorotovic, M. R. Schreiber, B. T. Gänsicke and A. Nebot Gómez-Morán A&A, 520 (2010) A86 DOI: https://doi.org/10.1051/0004-6361/200913658