Formation of Extremely Low-mass White Dwarf Binaries

Abstract

Motivated by the discovery of a handful of pulsating, extremely low mass\nwhite dwarfs (ELM WDs, mass $M \\lesssim 0.17\\, M_\\odot$) which likely have WD\ncompanions, this paper discusses binary formation models for these systems.\nFormation of an ELM WD by unstable mass transfer (MT) or a common envelope (CE)\nevent is unlikely. Stable Roche-lobe overflow with conservative MT produces\nonly $M \\gtrsim 0.2\\, M_\\odot$. This paper discusses the formation of ELM WD\nusing angular momentum losses by magnetic braking. The initially more massive\nstar becomes the companion WD through a CE event. The initially less massive\nstar becomes the ELM WD as an evolved donor in a Cataclysmic Variable binary.\nEvolutionary models are constructed using the Modules for Experiments in\nStellar Astrophysics (MESA), with ELM WD progenitors in the range\n$M_d=1.0-1.5\\, M_\\odot$ and WD companions in the range $M_{\\rm a} \\simeq\n0.4-0.9\\, M_\\odot$. A prescription to reduce magnetic braking for thin surface\nconvection zones is included. Upon the thinning of the evolved donor's\nenvelope, the donor star shrinks out of contact and MT ceases, revealing the\nELM WD. Systems with small masses have previously been suggested as possible AM\nCVN's. Systems with large masses, up to the limit $M \\simeq 0.18\\, M_\\odot$ at\nwhich shell flashes occur on the WD cooling track, will tend to expand out to\norbital periods $P_{\\rm orb} \\gtrsim 15\\, {\\rm hr}$. In between this range, ELM\nWD may become pulsators both as pre-WD and on the WD cooling track. Brickhill's\ncriterion for convective mode driving is used to estimate the location of the\nblue edge of the g-mode instability strip.\n