Expected z>5 QSO number counts in large area deep near-infrared surveys

The QSO luminosity function at z>5 provides strong constraints on models of joint evolution of QSO and their hosts. However, these observations are challenging because the low space densities of these objects necessitate surveying of large areas, in order to obtain statistically meaningful samples, while at the same time cosmological redshifting and dimming means that rather deep Near Infrared (NIR) imaging must be carried out. Several upcoming and proposed facilities with wide-field NIR imaging capabilities will open up this new region of parameter space. In this paper we present predictions for the expected number counts of z>5 QSOs, based on simple empirical and semi-empirical models of QSO evolution, as a function of redshift, depth and surveyed area. We compute the evolution of observed-frame QSO magnitudes and colors in a representative photometric system covering the wavelength range 550nm<lambda<1800nm, and combine this information with different estimates for the evolution of the QSO luminosity function. We conclude that planned ground-based surveys such as Pan-STARRS and VISTA should be able to detect a large number of luminous QSOs up to z<7.5, but that space-based missions such as EUCLID (formerly SPACE/DUNE) or SNAP are probably required in order to obtain substantial samples at higher redshift. We also use our models to predict the expected number counts for future X-ray space missions (such as XEUS and Constellation-X), and show that because of their small field-of-view, these telescopes are unlikely to discover significant numbers of AGN at very high redshift. However, X-ray follow-up of objects detected at longer wavelength will be an important means of confirming their identity as AGN and constraining obscuration.