A Semi-empirical Mass-loss Rate in Short-period CVs

We present the final results of our study on the mass-loss rate of donor stars in cataclysmic variables (CVs). Observed donors are oversized in comparison with those of isolated single stars of the same mass, which is thought to be a consequence of the mass loss. Using the empirical mass-radius relation of CVs and the homologous approximation for changes in effective temperature T2, orbital period P, and luminosity of the donor with the stellar radius, we find the semi-empirical mass-loss rate M2dot of CVs as a function of P. The derived M2dot is at ~10-9.5-10-10 $M\odot$/yr and depends weakly on P when P > 90 min, while it declines very rapidly towards the minimum period when P < 90 min. The semi-empirical M2dot is significantly different from, and has a less-pronounced turnaround behavior with P than suggested by previous numerical models. The semi-empirical P-M2dot relation is consistent with the angular momentum loss due to gravitational wave emission, and strongly suggests that CV secondaries with 0.075 $M\odot$ < M2 < 0.2 $M\odot$ are less than 2 Gyrs old. When applied to selected eclipsing CVs, our semi-empirical mass-loss rates are in good agreement with the accretion rates derived from the effective temperatures T1 of white dwarfs. Based on the semi-empirical M2dot, SDSS 1501 and 1433 systems that were previously identified as post-bounce CVs have yet to reach the minimal period.