Superhumps in Cataclysmic Binaries. XXV. q crit , \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $\mathstrut{{\mbox{\boldmath $\varepsilon$}}} $ \end{document} ( q ), and Mass‐Radius

We report on successes and failures in searching for positive superhumps in cataclysmic variables, and show the superhumping fraction as a function of orbital period. Basically, all short‐period system do, all long‐period systems do not, and a 50% success rate is found at P orb = 3.1 ± 0.2 hr. We can use this to measure the critical mass ratio for the creation of superhumps. With a mass‐radius relation appropriate for cataclysmic variables, and an assumed mean white‐dwarf mass of 0.75 M ⊙ , we find a mass ratio q crit = 0.35 ± 0.02. We also report superhump studies of several stars of independently known mass ratio: OU Vir, XZ Eri, UU Aqr, and KV UMa (=XTE J1118+480). The latter two are of special interest, because they represent the most extreme mass ratios for which accurate superhump measurements have been made. We use these to improve the ε( q ) calibration, by which we can infer the elusive q from the easy‐to‐measure ε (the fractional period excess of P superhump over P orb ). This relation allows mass and radius estimates for the secondary star in any cataclysmic variable (CV) showing superhumps. The consequent mass‐radius law shows an apparent discontinuity in radius near 0.2 M ⊙ , as predicted by the disrupted magnetic braking model for the 2.1–2.7 hr period gap. This is effectively the "empirical main sequence" for CV secondaries.

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