We combine two complete , X-ray flux-limited surveys , the ROSAT Bright Survey ( RBS ) and the ROSAT North Ecliptic Pole ( NEP ) survey , to measure the space density ( \rho ) and X-ray luminosity function ( \Phi ) of non-magnetic CVs .
The combined survey has a flux limit of F _ { X } \ga 1.1 \times 10 ^ { -12 } \mathrm { erg cm ^ { -2 } s ^ { -1 } } over most of its solid angle of just over 2 \pi , but is as deep as \simeq 10 ^ { -14 } \mathrm { erg cm ^ { -2 } s ^ { -1 } } over a small area .
The CV sample that we construct from these two surveys contains 20 non-magnetic systems .
We carefully include all sources of statistical error in calculating \rho and \Phi by using Monte Carlo simulations ; the most important uncertainty proves to be the often large errors in distances estimates .
If we assume that the 20 CVs in the combined RBS and NEP survey sample are representative of the intrinsic population , the space density of non-magnetic CVs is 4 ^ { +6 } _ { -2 } \times 10 ^ { -6 } \mathrm { pc ^ { -3 } } .
We discuss the difficulty in measuring \Phi in some detail—in order to account for biases in the measurement , we have to adopt a functional form for \Phi .
Assuming that the X-ray luminosity function of non-magnetic CVs is a truncated power law , we constrain the power law index to -0.80 \pm 0.05 .
It seems likely that the two surveys have failed to detect a large , faint population of short-period CVs , and that the true space density may well be a factor of 2 or 3 larger than what we have measured ; this is possible , even if we only allow for undetected CVs to have X-ray luminosities in the narrow range 28.7 < \mathrm { log } ( L _ { X } / \mathrm { erg s ^ { -1 } } ) < 29.7 .
However , \rho as high as 2 \times 10 ^ { -4 } \mathrm { pc ^ { -3 } } would require that the majority of CVs has X-ray luminosities below L _ { X } = 4 \times 10 ^ { 28 } \mathrm { erg s ^ { -1 } } in the 0.5–2.0 keV band .