Hard spectrum ROSAT sources. I.

Such sources must be the dominant contributors to the X-ray background at faint fluxes. We have used Monte Carlo simulations to verify that our technique is very efficient at selecting hard sources: the survey has >=10 times as much effective area for hard sources as it has for soft sources above a 0.5-2keV flux level of 10^-14^erg/cm^2^/s.

The distribution of best-fitting spectral slopes of the hard sources suggests that a typical ROSAT hard source in our survey has a spectral slope {alpha}~0. The hard sources have a steep number flux relation (dN/dS_{mu}_S^-{gamma}^ with a best-fitting value of {gamma}=2.72+/-0.12) and make up about 15 per cent of all 0.5-2keV sources with S>10^-14^erg/cm^2^/s. If their N(S) continues to fainter fluxes, the hard sources will comprise ~40 per cent of sources with 5x10^-15^<S<10^-14^erg/cm^2^/s.