The space density of post-period minimum Cataclysmic Variables

Binary evolution theory predicts that accreting white dwarfs with substellar companions dominate the Galactic population of cataclysmic variables (CVs). In order to test these predictions, it is necessary to identify these systems, which may be difficult if the signatures of accretion become too weak to be detected. The only chance to identify such ‘dead’ CVs is by exploiting their close binary nature. We have therefore searched the Sloan Digital Sky Survey (SDSS) Stripe 82 area for apparently isolated white dwarfs that undergo eclipses by a dark companion. We found no such eclipses in either the SDSS or Palomar Transient Factory data sets among our sample of 2264 photometrically selected white dwarf candidates within Stripe 82. This null result allows us to set a firm upper limit on the space density, ρ0, of dead CVs. In order to determine this limit, we have used Monte Carlo simulations to fold our selection criteria through a simple model of the Galactic CV distribution. Assuming a TWD = 7500 K, the resulting 2σ limit on the space density of dead CVs is ρ0 ≲ 2 × 10−5 pc−3, where TWD is the typical effective temperature of the white dwarf in such systems.