[Paper Review] Population synthesis for double white dwarfs I.Close detached systems

G. Nelemans, L. R. Yungelson+2 more|arXiv (Cornell University)|Oct 23, 2000

Gamma-ray bursts and supernovaePhysics and Astronomy56 references205 citations

TL;DR

This paper presents a refined population synthesis model for close detached double white dwarfs in the Galaxy, improving agreement with observations by incorporating angular momentum-conserving common envelope evolution and updated white dwarf cooling models. The key result is a predicted Galactic merger rate of 0.003 yr⁻¹ for double CO white dwarfs exceeding the Chandrasekhar mass, consistent with the observed SNe Ia rate, and a local sample of 855 white dwarfs with 220 close pairs, including 10 double CO systems, one of which will merge within a Hubble time.

ABSTRACT

We model the population of double white dwarfs in the Galaxy and find a better agreement with observations compared to earlier studies, due to two modifications. The first is the treatment of the first phase of unstable mass transfer and the second the modelling of the cooling of the white dwarfs. A satisfactory agreement with observations of the local sample of white dwarfs is achieved if we assume that the initial binary fraction is ~ 50% and that the lowest mass white dwarfs (M < 0.3 Msun) cool faster than the most recently published cooling models predict. With this model we find a Galactic birth rate of close double white dwarfs of 0.05 yr^{-1}, a birth rate of AM CVn systems of 0.005 yr^{-1}, a merger rate of pairs with a combined mass exceeding the Chandrasekhar limit (which may be progenitors of SNe Ia) of 0.003 yr^{-1} and a formation rate of planetary nebulae of 1 yr^{-1}. We estimate the total number of double white dwarfs in the Galaxy as 2.5 10^8. In an observable sample with a limiting magnitude V_lim = 15 we predict the presence of ~855 white dwarfs of which ~220 are close pairs. Of these 10 are double CO white dwarfs of which one has a combined mass exceeding the Chandrasekhar limit and will merge within a Hubble time.

Motivation & Objective

• To improve agreement between theoretical models and observed properties of close double white dwarfs by refining binary evolution and cooling physics.
• To resolve the discrepancy between observed and predicted low-mass white dwarfs (M < 0.3 M☉), which are underrepresented in surveys.
• To test the consistency of the model with observed orbital period and mass ratio distributions of double white dwarfs.
• To estimate the local number density of close double white dwarfs and the formation rate of planetary nebulae, SNe Ia progenitors, and AM CVn systems.
• To constrain the initial binary fraction and cooling rates of low-mass white dwarfs using observational constraints.

Proposed method

• Modeling the first phase of unstable mass transfer via angular momentum conservation rather than energy balance in common envelopes, using a parameter γ to account for angular momentum loss.
• Incorporating detailed white dwarf cooling models, particularly for low-mass white dwarfs (M < 0.3 M☉), which cool faster than previous models (DSBH98).
• Using a population synthesis code based on Portegies Zwart & Verbunt (1996) and Portegies Zwart & Yungelson (1998), with updated core mass tracking and binary evolution prescriptions.
• Applying a star formation history consistent with the Milky Way's disk and halo components to compute the present-day population of double white dwarfs.
• Correcting model predictions for observational selection effects using the method of Moran et al. (2000) to compare with observed mass ratio distributions.
• Calculating observable quantities such as the number of white dwarfs in a V < 15 magnitude-limited sample and the expected merger rates of massive double white dwarf systems.

Experimental results

Research questions

• RQ1 Why are low-mass white dwarfs (M < 0.3 M☉) underrepresented in observed samples, and can this be explained by faster cooling than predicted by existing models?
• RQ2 How does the treatment of common envelope evolution—specifically angular momentum conservation instead of energy balance—affect the predicted orbital period and mass ratio distributions of double white dwarfs?
• RQ3 What initial binary fraction is required to reproduce the observed fraction of close double white dwarf systems among all white dwarfs in the solar neighborhood?
• RQ4 What is the predicted merger rate of double CO white dwarfs with total mass exceeding the Chandrasekhar limit, and how does it compare to the observed SNe Ia rate?
• RQ5 How well do the model-predicted numbers of white dwarfs in a V < 15 magnitude-limited sample match the observed count of ~855 white dwarfs?

Key findings

• The model achieves good agreement with observations by assuming that low-mass white dwarfs (M < 0.3 M☉) cool faster than predicted by Driebe et al. (1998), which resolves the discrepancy in their observed underabundance.
• The predicted mass ratio distribution of double white dwarfs peaks at q ≈ 1, consistent with observations after correcting for selection effects, unlike earlier models that peaked at q ≈ 0.7 or q > 1.5.
• The Galactic birth rate of close double white dwarfs is estimated at 0.05 yr⁻¹, with a formation rate of AM CVn systems at 0.005 yr⁻¹ and a merger rate of massive double CO white dwarfs at 0.003 yr⁻¹.
• In a magnitude-limited sample with V < 15, the model predicts 855 white dwarfs, of which 220 are close pairs, including 10 double CO white dwarfs, one of which will merge within a Hubble time.
• The total number of double white dwarfs in the Galaxy is estimated at 2.5 × 10⁸, and the model predicts a planetary nebula formation rate of 1 yr⁻¹, consistent with observations.
• The model's consistency with the observed SNe Ia rate supports the hypothesis that merging massive double CO white dwarfs are viable progenitors of SNe Ia.