On the late spectral types of cataclysmic variable secondaries

We investigate why the spectral type of most cataclysmic variable (CV) secondaries is significantly later than that of a ZAMS star with the same mean density. Using improved stellar input physics, tested against observations of low-mass stars at the bottom of the main sequence, we calculate the secular evolution of CVs with low-mass donors. We consider sequences with different mass transfer rates and with a different degree of nuclear evolution of the donor prior to mass transfer. Systems near the upper edge of the gap ($P \sim 3 - 6$ h) can be reproduced by models with a wide range of mass transfer rates from $1.5 \times 10^{-9} \msolyr$ to $10^{-8} \msolyr$. Evolutionary sequences with a small transfer rate and donors that are substantially evolved off the ZAMS (central hydrogen content $0.05-0.5$) reproduce CVs with late spectral types above $P \simgr$ 6 h. Systems with the most discrepant (late) spectral type should have the smallest donor mass at any given $P$. Consistency with the period gap suggests that the mass transfer rate increases with decreasing donor mass for evolved sequences above the period gap. In this case, a single-parameter family of sequences with varying $\xc$ and increasing mass transfer rate reproduces the full range of observed spectral types. This would imply that CVs with such evolved secondaries dominate the CV population.

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