Formation of Extremely Low-mass White Dwarfs in Double Degenerates

Abstract

Extremely low-mass white dwarfs (ELM WDs) are helium WDs with a mass less than ∼0.3 M . Most ELM WDs are found in double degenerates (DDs) in the ELM Survey led by Brown and Kilic. These systems are supposed to be significant gravitational-wave sources in the mHz frequency. In this paper, we firstly analyzed the observational characteristics of ELM WDs and found that there are two distinct groups in the ELM WD mass and orbital period plane, indicating two different formation scenarios of such objects, i.e. a stable Roche lobe overflow channel (RL channel) and common envelope ejection channel (CE channel). We then systematically investigated the formation of ELM WDs in DDs by a combination of detailed binary evolution calculation and binary population synthesis. Our study shows that the majority of ELM WDs with mass less than 0.22 M are formed from the RL channel. The most common progenitor mass in this way is in the range of 1.15 − 1.45 M and the resulting ELM WDs have a peak around 0.18 M when selection effects are taken into account, consistent with observations. The ELM WDs with a mass larger than 0.22 M are more likely to be from the CE channel and have a peak of ELM WD mass around 0.25 M which needs to be confirmed by future observations. By assuming a constant star formation rate of 2 M yr −1 for a Milky Way-like galaxy, the birth rate and local density are 5 × 10 −4 yr −1 and 1500 kpc −3 , respectively, for DDs with an ELM WD mass less than 0.25 M .

Gravitational-wave Radiation of Double Degenerates with Extremely Low-mass White Dwarf Companions

“…theoretical result is consistent with the observations that all of the ELM WDs ( 0.3M ) are in binary systems (Brown et al 2016a). Recently, Li et al (2019) have investigated the formation processes of DWDs with ELM WD companions by combining detailed binary evolution calculation with BPS method (Paper I hereafter). We show that DWDs with ELM WD companions can be formed from either stable Roche lobe overflow (RL channel) or common envelope (CE) ejection (CE channel).…”

The Formation of Subdwarf A-type Stars

“…Li et al (2019) had produced several grids of evolution models of ELM WDs in DDs. Following Li et al (2019)'s work, we set the metallicity Z = 0.02 and the hydrogen mass faction X= 0.70, the mixing length parameter is set to be MLT = 1.9. The mass transfer (MT) rate is given by Ritter (1988) as follows:…”

“…We evolve these binary systems that consist of MS + CO WD, where the MS is donor and the CO 2 is accretor. The initial parameter space we selected is similar to Li et al (2019): The initial donor mass (M i d in M ⊙ ) is 1.0, 1.1, 1.2,..., 2.0 (by steps of 0.1 M ⊙ ); the initial accretor mass (M i a in M ⊙ ) is 0.5, 0.6, 0.7,..., 1.1 (by steps of 0.1 M ⊙ ). The M i a = 0.45 M ⊙ , which is usually considered the lowest mass of CO WD, is also be considered.…”

“…Meanwhile, we use BSE to obtain the populations of ELM WDs produced by CE channel. The detailed method we employed are the same with Li et al (2019), but for the CE channal, we set α CE = 1.0. Usually, the larger α CE is, the more easily CE is ejected.…”

A 1201 s Orbital Period Detached Binary: The First Double Helium Core White Dwarf LISA Verification Binary

“…This would be surprising because one expects the cool WD to have evolved first, and thus be more massive than the hot WD. However the models contain a major uncertainty linked to common envelope ejection (Li et al 2019(Li et al , 2020. The thickness of the WD hydrogen envelope, assumptions about elemental diffusion and rotational mixing, the presence or absence of hydrogen shell flashes, and other issues have significant effects on the temperature, radius, and cooling age of a low mass WD (Althaus et al 2013;Istrate et al 2016).…”