Mass transfer stability for AM CVn binaries with white dwarf donors

TL;DR

This work argues that the traditional stability criterion for mass transfer in double white dwarf binaries, which assumes completely cold and degenerate donors, underestimates the stability of systems with hot Helium white dwarfs. By incorporating finite-temperature effects through both analytical fits (e.g., $R(m,T_\mathrm{eff})$) and non-equilibrium transfer models, the authors show that mass transfer is more stable than previously thought, leading to fewer DWDB mergers and more AM CVn progenitors than cold models would predict. The findings help explain tensions between observed AM CVn birth rates and merger rates and highlight the importance of thermal structure in shaping binary evolution; they also point to upcoming gravitational wave observations (e.g., LISA) as crucial to constraining these rates in the Galactic DWDB population.

Abstract

Double white dwarf binaries (DWDBs) with Helium components are progenitors to AM CVn binary systems. Their Galactic production rate may be given by the number of stably mass transferring DWDBs in the Milky Way. The theoretical criteria for stable mass transfer in DWDBs is calculated assuming that component white dwarfs are completely cold and degenerate. Respective fractions of surviving AM CVn and DWDB which merge are then calculated by applying this criteria to population synthesis estimates for Galactic DWDB. However, emerging observations of the local DWDB population suggest that Helium white dwarf (He WD) components are typically hot, and only partially degenerate when they begin mass transferring. Using recent numerical simulations of He WD donors in DWDBs, we qualitatively describe a temperature dependent stable mass transfer criteria for Galactic DWDBs. Mass transfer is even more stable than previously thought, or equivalently, DWDB mergers are even rarer. Realistic finite temperature treatments will deepen the dearth in observed AM CVn binaries compared to DWDB merger products.

Figures (1)

• Figure 1: Temperature in K as a function of mass in $M_\odot$ (horizontal axis) and radius in $0.01 R_\odot$ (vertical axis) for a variety of theoretical stellar models and observations of He WD donors. The contours in the background approximate the finite temperature single He WD models from Panei2000. The thick track with the purple outline is the $0.18M_\odot$ donor from Wong2021 being stripped to $0.15M_\odot$ by stable mass transfer, which is referred to as Md18-Tc3e7-Ma0p75. Notably, unlike a completely degenerate WD, the donor shrinks as a response to mass transfer. The two stars are different candidate properties of J0127+5258 in Burdge2023. Compared to the single He WD models, both the mass transfer model (track) and candidate J0127+5258 donors (stars) are cooler for a given mass and radius.