Faint blue galaxies as a probe of the X-ray background at high redshift

We present a formalism describing the physical content of cross-correlation functions between a diffuse background and a population of discrete sources. The formalism is used to interpret cross-correlation signals between the unresolved X-ray background and a galaxy population resolved to high redshift in another spectral band. Specifically, we apply it to the so-called faint blue galaxy population and constrain their X-ray emissivity and clustering properties. A model is presented which satisfies the recently measured constraints on all three correlation functions (galaxy/galaxy, background/background and galaxy/background). This model predicts that faint galaxies in the magnitude range B = 18-23 (covering redshifts z less than or equal to 0.5) make up similar to 22 per cent of the X-ray background in the 0.5-2 keV band. At the mean redshift of the galaxy sample, (z) over bar similar to 0.3, the comoving volume emissivity is rho(X) similar to (6-9) x 10(38) h erg s(-1) Mpc(-3). When extrapolated to fainter magnitudes, the faint blue galaxy population can account for most of the residual background at soft X-ray energy. We show how the measurement of the angular and zero-lag crosscorrelation functions between increasingly faint galaxies and the X-ray background can in principle allow us to map the X-ray emissivity as a function of redshift.