The thermal evolution of the donors in AM Canum Venaticorum binaries

Abstract

We calculate the full stellar structural evolution of donors in AM CVnAM Canum Venaticorum (AM CVn) systems formed through the white dwarf (WD) channel coupled to the binary's evolution. Contrary to assumptions made in prior modelling, these donors are not fully convective over much of the AM CVn phase and do not evolve adiabatically under mass loss indefinitely. Instead, we identify three distinct phases of evolution: a mass-transfer turn-on phase (during which Porb continues to decrease even after contact, the donor contracts, and the mass-transfer rate accelerates to its maximum), a phase in which the donor expands adiabatically in response to mass loss, and a cooling phase beginning at Porb ≈ 45-55 min during which the donor contracts. The physics that determines the behaviour in the first and third phases, both of which are new outcomes of this study, are discussed in some detail. We find the overall duration of the turn-on phase to be between ∼104 and ∼106 yr, significantly longer than prior estimates. We predict the donor's luminosity, L, and effective temperature, Teff. During the adiabatic expansion phase (ignoring irradiation effects), L ≈ 10-6-10-4 L⊙ and T eff ≈ 1000-1800 K. However, the flux generated in the accretion flow dominates the donor's intrinsic light at all times. The impact of irradiation on the donor extends the phase of adiabatic expansion to longer Porb, slows the contraction during the cooling phase, and alters the donor's observational characteristics. Irradiated donors during the adiabatic phase can attain surface luminosities up to ≈10-2 L ⊙. We argue that the turn-on and cooling phases both will leave significant imprints on the AM CVn population's Porb-distribution. Finally, we show that the eclipsing AM CVn system SDSS J0926+3624 provides evidence that WD channel systems with non-zero entropy donors contribute to the AM CVn population, and we discuss the observational signature of the donor in this system. © 2007 RAS.