Expected properties of the first gravitational wave signal detected with pulsar timing arrays

In this paper, we attempt to investigate the nature of the first gravitational wave (GW) signal to be detected by pulsar timing arrays (PTAs): will it be an individual, resolved supermassive black hole binary (SBHB), or a stochastic background made by the superposition of GWs produced by an ensemble of SBHBs? To address this issue, we analyse a broad set of simulations of the cosmological population of SBHBs that cover the entire parameter space allowed by current electromagnetic observations in an unbiased way. For each simulation, we construct the expected GW signal and identify the loudest individual sources. We then employ appropriate detection statistics to evaluate the relative probability of detecting each type of source as a function of time for a variety of PTAs; we consider the current International PTA, and speculate into the era of the Square Kilometre Array. The main properties of the first detectable individual SBHBs are also investigated. Contrary to previous work, we cast our results in terms of the detection probability (DP), since the commonly adopted criterion based on a signal-to-noise ratio threshold is statistic-dependent and may result in misleading conclusions for the statistics adopted here. Our results confirm quantitatively that a stochastic signal is more likely to be detected first (with between 75 and 93 per cent probability, depending on the array), but the DP of single-sources is not negligible. Our framework is very flexible and can be easily extended to more realistic arrays and to signal models including environmental coupling and SBHB eccentricity.