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 BAT have 14--195~keV luminosities of $sim 10^{33} {rm erg s^{-1}}$, there is evidence of a fainter population at $L_X sim 10^{31} {rm erg s^{-1}}$. We find that a population of IPs with this luminosity may have a space density as large as $5times 10^{-6},mathrm{pc^{-3}}$. 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.
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