We construct a complete , hard X-ray flux-limited sample of intermediate polars ( IPs ) from the Swift /BAT 70-month survey , by imposing selection cuts in flux and Galactic latitude ( F _ { X } > 2.5 \times 10 ^ { -11 } \mathrm { erg cm ^ { -2 } s ^ { -1 } } at 14–195 keV , and |b| > 5 ^ { \circ } ) .
We then use it to estimate the space density ( \rho ) of IPs .
Assuming that this sample of 15 long-period systems is representative of the intrinsic IP population , the space density of long-period IPs is 1 ^ { +1 } _ { -0.5 } \times 10 ^ { -7 } \mathrm { pc ^ { -3 } } .
The Swift /BAT data also allow us to place upper limits on the size of a hypothetical population of faint IPs that is not included in the flux-limited sample .
While most IPs detected by Swift /BAT have 14–195 keV luminosities of \sim 10 ^ { 33 } { ergs ^ { -1 } } , there is evidence of a fainter population at L _ { X } \sim 10 ^ { 31 } { ergs ^ { -1 } } .
We find that a population of IPs with this luminosity may have a space density as large as 5 \times 10 ^ { -6 } \mathrm { pc ^ { -3 } } .
Furthermore , these low-luminosity IPs , despite appearing rare in observed samples , are probably at least as intrinsically common as the brighter systems that are better represented in the known IP sample .