Extracting the unresolved pulsar contribution to the gamma-ray background

We present a statistical framework which can be used to determine the contribution of an unresolved population of pulsars to the gamma-ray background. This formalism is based on the joint analysis of photon time series over extended regions of the sky. We demonstrate the robustness of this technique in controlled simulations of pulsar populations, and show that the Fermi Gamma-ray Space Telescope can be used to detect a pulsar contribution as small as 0.1 per cent of the gamma-ray background. This technique is sensitive to pulsar populations with photon fluxes greater than similar to 10(-10) cm(-2) s(-1). The framework is extensible to arbitrarily complex searches for periodicity and can therefore be tailored to specific applications such as all-sky surveys and studies of the Galactic Centre and globular clusters.