On the mass transfer - orbital period relation in cataclysmic variables.

A simple method to obtain mass transfer rates in cataclysmic variables is discussed. The temperature T(R) of a steady accretion disc varies as R^-3/4, leading to a connection between the accretion rate, the external radius R_e and the mean temperature of the disc, M ∝ R_e³ T_m⁴. We find that if the disc size is a roughly constant fraction of the binary separation then R_e ∝ P^2/3 and < ∝ T_m⁴ P². We argue from theoretical and observational reasons that there is no correlation between T_m and P, leading to the conclusion that M ∝ P₂. Since the radius of the secondary star is a function of the orbital period, we find that the mass transfer is directly proportional to the surface area of the companion star: M ∝ A₈. We use emission lines and photometry to estimate T_m and to calculate mass transfer rates for a large sample of cataclysmic variables, and compare the results with other authors.