Extragalactic source counts in the 20-50 keV energy band from the deep observation of the Coma region by INTEGRAL/IBIS

We present the analysis of serendipitous sources in a deep, 500 ksec, hard X-ray observation of the Coma cluster region with the IBIS instrument onboard INTEGRAL. In addition to the Coma cluster, the final 20-50 keV image contains 12 serendipitous sources with statistical significance >4sigma. We use these data (after correcting for expected number of false detections) to extend the extragalactic source counts in the 20-50 keV energy band down to a limiting flux of 1.0e-11 erg/s/cm^2 (~ 1mCrab). This is a more than a factor of 10 improvement in sensitivity compared to the previous results in this energy band obtained with the HEAO-1 A4 instrument. The derived source counts are consistent with the Euclidean relation, N(>f) ~ f**(-3/2). A large fraction of identified serendipitous sources are low-redshift, z<0.02, AGNs, mostly of Seyfert 1 type. The surface density of hard X-ray sources is 0.014 +- 0.005 per square degree above a flux threshold of 1e-11 erg/s/cm^2. These sources directly account for ~3% of the cosmic X-ray background in the 20-50 keV energy band. Given the low redshift depth of our sample, we expect that similar sources at higher redshifts account for a significant fraction of the hard X-ray background. Our field covers only 3% of the sky; a systematic analysis of other extragalactic INTEGRAL observations can produce much larger source samples and is, therefore, critically important.