The present-day formation of cataclysmic variables ( CVs ) with brown dwarf ( BD ) secondaries ( 0.013 M _ { \odot } \leq M _ { s } \leq 0.075 M _ { \odot } ) is investigated using a population synthesis technique .
Results from the latest , detailed models for BDs have been incorporated into the population synthesis code .
The present-day orbital period distribution of zero-age CVs ( ZACVs ) that form with BD secondaries is calculated .
For our models , we find that ZACVs with BD secondaries have orbital periods in the range 46 min to 2.5 hrs .
We also find that ZACVs with BD secondaries comprise 18 % of the total , present-day ZACV population .
In addition , we find that 80 % of ZACVs with BD secondaries have orbital periods less than 78 minutes .
This implies that 15 % of the present-day ZACV population should have orbital periods shorter than the observed orbital period minimum for CVs .
We also investigate the dependence of the present-day formation rate of CVs with BD secondaries on the assumed value of the common envelope efficiency parameter , \alpha _ { CE } , for three different assumed mass ratio distributions in ZAMS binaries .
Surprisingly , we find that the common envelope process must be extremely inefficient ( \alpha _ { CE } < 0.1 ) in order for CVs with BD secondaries not to be formed .
Finally , we find that the progenitor binaries of ZACVs with BD secondaries have ZAMS orbital separations < 3 AU and ZAMS primary masses between \sim 1-10 M _ { \odot } , with \sim 75 % of the primary masses less than \sim 1.6 M _ { \odot } .
Interestingly , these ranges in orbital separation and primary mass place the majority of the progenitor binaries within the so-called “ brown dwarf desert . ” The implications of these results are discussed in the context of V485 Cen and 1RXS J232953.9+062814 , the only known CVs with orbital periods shorter than the period minimum , CVs above the period minimum that are strongly suspected of containing BD secondaries ( such as WZ Sge ) , common envelope evolution involving very low mass secondaries , and the BD mass function in ZAMS binaries .