A new method for determining the sensitivity of X-ray imaging observations and the X-ray number counts

We present a new method for determining the sensitivity of X-ray imaging observations, which correctly accounts for the observational biases that affect the probability of detecting a Source of a given X-ray flux, without the need to perform a large number of time-consuming simulations. We use this new technique to estimate the X-ray source counts in different spectral hands (0.5-2, 0.5-10, 2-10 and 5-10 keV) by combining deep pencil-beam and shallow wide-area Chandra observations. The sample has a total of 6295 unique sources over an area of 11.8 deg(2) and is the largest used to date to determine the X-ray number Counts. We determine, for the first time, the break flux in the 5-10keV band, in the case of a double power-law Source count distribution. We also find an upturn in the 0.5-2keV counts at fluxes below about 6 x 10(-17) erg s(-1) cm(-2). We show that this can be explained by the emergence of normal star-forming galaxies which dominate the X-ray population at faint fluxes. The fraction of the diffuse X-ray background resolved into point sources at different spectral bands is also estimated. It is argued that a single population of Compton thick active galactic nuclei (AGN) cannot be responsible for the entire unresolved X-ray background in the energy range 2-10 keV.