He-star donor AM CVn stars and their progenitors as LISA sources

Ultracompact cataclysmic variables (CVs) of the AM CVn type are deemed to be important verification sources for the future space gravitational wave detectors such as the Laser Interferometer Space Antenna (LISA). We model the present-day Galactic population of AM CVn stars with He-star donors. Such a population has long expected to exist, though only a couple of candidates are known. We applied the hybrid method of binary population synthesis (BPS) which combines a simulation of the population of immediate precursors of AM CVn stars by a fast BPS code with subsequent tracking of their evolution by a full evolutionary code. The model predicts that the present birthrate of He-donor AM CVn stars in the Galaxy is $4.6\times 10^{-4}$ per yr and the Galaxy may harbour about 112000 objects of this class which have orbital periods less than 42-43 min. The foreground confusion limit and instrumental noise of LISA prevent the discovery of longer periods systems in gravitational waves. We find that about 500 He-star AM CVns may be detected by LISA with signal-to-noise ratio (S/N)>5 during a 4 yr mission. Within 1 Kpc from the Sun, there may exist up to 130 He-star AM CVns with the periods in the same range, which may serve as verification binaries, if detected in the electromagnetic spectrum. In the Milky Way, there are also about 14800 immediate precursors of AM CVn stars. They are detached systems with a stripped low-mass He-star and a white dwarf companion, out of which about 75 may potentially be observed by LISA during its mission.