Theoretical statistics of zero-age cataclysmic variables

A method is described whereby theoretical distributions of the orbital parameters in newly forming (''zero-age'') cataclysmic variables may be calculated This method is used to calculate the distributions of the white dwarf masses, mass ratios, and orbital periods in zero-age cataclysmic variables (ZACVs) due to binaries present in a stellar population that has undergone continuous star formation for 10(10) yr. We find that the distribution of white dwarf masses in ZACVs has two components-a low-mass component (0.27 M(.) < M(WD) < 0.46 M(.)) composed of helium white dwarfs, and a high-mass component (0.56 M(.) < M(WD) < 1.4 M(.)) composed of carbon-oxygen white dwarfs. The formation of cataclysmic variables (CVs) with oxygen-neon-magnesium white dwarfs is not considered in this calculation. The mean white dwarf mass in ZACVs derived from our models is 0.49 M(.). The distribution of orbital periods in ZACVs reveals several groups of ZACVs, based on the mass and evolutionary state of the secondary. Our models predict that 22% of ZACVs are formed in the period gap. We also predict that about one in 800 ZACVs has orbital periods greater than 18 hr. Such systems contain evolved secondaries, contribute a very long period wing to the orbital period distribution (out to P-orb similar to 2 days), and should secularly evolve to longer orbital periods. Two-dimensional distributions of the CV birthrate over the age of the binary and orbital parameter are also calculated. The youngest binaries present in our population that are able to produce CVs have an age of 2.5 x 10(7) yr. CVs containing helium white dwarfs do not form from binaries that are younger than similar to 10(9) yr. Very long period CVs are formed from binaries having a narrow range of ages, with most having ages in the range 2-5 x 10(9) yr. The birthrate density of CVs predicted from our models is 1.05 x 10(-12) CVs yr(-1) pc(-2). This yields an estimate for the CV space density of 2 x 10(-5) pc(-3). Orbital parameter ranges for CV progenitors are also briefly discussed. Most notably, we find from our models that the mass ratios in the progenitor zero-age main-sequence binaries are less than 0.28 (secondary mass/primary mass). This discrepancy between the progenitor primary and secondary masses explains why the secondaries in the majority of CVs are unevolved.