We calculate the full stellar-structural evolution of donors in AM CVn systems formed through the 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 P _ { \mathrm { orb } } 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 P _ { \mathrm { orb } } \approx 45–55 minutes 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 \sim 10 ^ { 4 } - 10 ^ { 6 } yrs , significantly longer than prior estimates .
We predict the donor ’ s luminosity , L , and effective temperature , T _ { \mathrm { eff } } .
During the adiabatic expansion phase ( ignoring irradiation effects ) , L \approx 10 ^ { -6 } – 10 ^ { -4 } { L } _ { \odot } and T _ { \mathrm { eff } } \approx 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 P _ { \mathrm { orb } } , 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 \approx 10 ^ { -2 } { L } _ { \odot } .
We argue that the turn-on and cooling phases both will leave significant imprints on the AM CVn population ’ s P _ { \mathrm { orb } } -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 .