Phases of Mass Transfer from Hot Subdwarfs to White Dwarf Companions and Their Photometric Properties

Binary systems of a hot subdwarf B (sdB) star + a white dwarf (WD) with orbital periods less than 2-3 hours can come into contact due to gravitational waves and transfer mass from the sdB star to the WD before the sdB star ceases nuclear burning and contracts to become a WD. Motivated by the growing class of observed systems in this category, we study the phases of mass transfer in these systems. We find that because the residual outer hydrogen envelope accounts for a large fraction of an sdB stars radius, sdB stars can spend a significant amount of time ($sim$10s of Myr) transferring this small amount of material at low rates ($sim 10^{-10}$-$10^{-9} M_odot,rm yr^{-1}$) before transitioning to a phase where the bulk of their He transfers at much faster rates ($gtrsim 10^{-8} M_odot,rm yr^{-1}$). These systems therefore spend a surprising amount of time with Roche-filling sdB donors at orbital periods longer than the range associated with He star models without an envelope. We predict that the envelope transfer phase should be detectable by searching for ellipsoidal modulation of Roche-filling objects with $P_{rm orb}=30$-$100$ min and $T_{rm eff}=20{,}000$-$30{,}000$ K, and that many ($geq$10) such systems may be found in the Galactic plane after accounting for reddening. We also argue that many of these systems may go through a phase of He transfer that matches the signatures of AM CVn systems, and that some AM CVn systems associated with young stellar populations likely descend from this channel.