The Evolution of Cataclysmic Variables as Revealed by their Donor Stars

We reconstruct the evolutionary path followed by cataclysmic variables (CVs) from the observed mass-radius relationship of their donor stars. Along the way, we update the semi-empirical CV donor sequence of Knigge (2006) and present a comprehensive review of the link between CV evolution and donor physics. After calibrating state-of-the art stellar models for use in the CV setting, we fit self-consistent theoretical evolution sequences to the observed donor masses and radii. In the standard model of CV evolution, AML below the period gap is assumed to be driven solely by gravitational radiation (GR), while AML above the gap is usually described by a magnetic braking prescription due to Rappaport, Verbunt & Joss (1983). We find that simple scaled versions of these recipes match the data quite well. However, the optimal scaling factors turn out to be f_GR = 2.47 +/- 0.22 below the gap and f_MB = 0.66 +/- 0.05 above. The implications and applications of our results include: (1) The revised evolution sequence yields correct locations for the CV minimum period and the upper edge of the period gap; the standard sequence does not. (2) A comparison of predicted and observed WD temperatures suggests an even higher value for f_GR, but this is sensitive to the assumed WD mass. (3) The absolute donor magnitudes predicted by our sequences can be used to set firm lower limits on the distances toward CVs. (4) Both standard and revised sequences predict that short-period CVs should be susceptible to dwarf nova (DN) eruptions, consistent with observations. However, both sequences also predict that the DNe fraction among long-period CVs should decline with P_orb. Observations suggest the opposite behaviour. (5) The ratio of long-period CVs to short-period, pre-bounce CV is about 3x higher for the revised sequence than the standard one. This may resolve a long-standing problem in CV evolution. [abridged]