An analytic approach to the secular evolution of cataclysmic variables

Details An analytic approach to the secular evolution of cataclysmic variables An analytic approach to the secular evolution of cataclysmic variables

Mar 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996mnras.279..581s&link_type=abstract

Monthly Notices of the Royal Astronomical Society, Volume 279, Issue 2, pp. 581-590.

Astronomy and Astrophysics

Astronomy

33

Stars: Evolution, Stars: Mass-Loss, Novae, Cataclysmic Variables

Scientific paper

We investigate the reaction of low-mass stars to mass loss within the context of the evolution of cataclysmic 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 function of the mass-transfer time-scale tau_M=--M/M_solar-- and the stellar mass M. The main property of the differential equation is the convergence of solutions which differ only in the initial conditions. The solutions converge on an e-folding time-scale tau_per. A linearized analysis yields tau_per<~1/20 tau_KH (with tau_KH 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, which explains the similarity of secular evolution tracks previously found by Paczynski & Sienkiewicz and Kolb & Ritter in numerical studies. This is why the detached phase (M_solar=0) in the life of a single CV can still be seen in the CV population as a period gap. An analytic 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.

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