An analytic approach to the secular evolution of cataclysmic variables

We investigate the reation of low-mass stars to mass loss in the ction of low-mass stars to mass loss in the context of atacataclysmi variables (CVs). Based on homology we derive a first order differential equation for the radius reac variables (CVs). Based on homology we derive a first order differential equation for the radius reaction of a low-mass star upon mass loss. The solution of the differential equation yields the stellar radius as a funtion of the mass transfer timesction of the mass transfer timescale #tau#_M = vertical stroke M/M vertical stroke and the stellar mass M. The main property of the differential equation is the onvergenconvergence of solutions whih differ only in the initial ch differ only in the initial conditions on an e-folding timesale #tau#_p_e_r. A linearized analysis yields #tau#_p_e_r <or#approx# 1/20#tau#_K_H (with #tau#_K_H the Kelvin-Helmholtz time of the star). Applying our model to CV evolution we furthermore show that after a short turn-on phase the CV evolution is independent of its initial cale #tau#_p_e_r. A linearized analysis yields #tau#_p_e_r <or#approx# 1/20#tau#_K_H (with #tau#_K_H the Kelvin-Helmholtz time of the star). Applying our model to CV evolution we furthermore show that after a short turn-on phase the CV evolution is independent of its initial conditions whih explains the similarity of sech explains the similarity of secular evolution traks previously found by Packs previously found by Paczynski and Sienkiewiz (1983) and Kolb and Ritter (1992) in numericz (1983) and Kolb and Ritter (1192) in numerical studies. It is therefore why the detahed phase (M=0) in the life of a single CV ched phase (M=0) in the life of a single CV can still be seen in the whole CV population as a period gap. An analyti solution of the linearized differential equation near thermal equilibrium is applied to the period flag subsequent to the turn-on of mass transfer after the detac solution of the linearized differential equation near thermal equilibrium is applied to the period flag subsequent to the turn-on of mass transfer after the detached phase of CV evolution. (orig.)Available from TIB Hannover: RR 4697(888) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman