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We calculate the properties, occurrence rates and detection prospects ofindividually resolvable 'single sources' in the low frequency gravitationalwave (GW) spectrum. Our simulations use the population of galaxies and massiveblack hole binaries from the Illustris cosmological hydrodynamic simulations,coupled to comprehensive semi-analytic models of the binary merger process.Using mock pulsar timing arrays (PTA) with, for the first time, varyingred-noise models, we calculate plausible detection prospects for GW singlesources and the stochastic GW background (GWB). Contrary to previous results,we find that single sources are at least as detectable as the GW background.Using mock PTA, we find that these 'foreground' sources (also'deterministic'/'continuous') are likely to be detected with $\sim 20 \,\textrm{yr}$ total observing baselines. Detection prospects, and indeed theoverall properties of single sources, are only moderately sensitive to binaryevolution parameters---namely eccentricity & environmental coupling, which canlead to differences of $\sim 5 \,\textrm{yr}$ in times to detection. Red noisehas a stronger effect, roughly doubling the time to detection of the foregroundbetween a white-noise only model ($\sim 10$ - $15 \, \textrm{yr}$) and severered noise ($\sim 20$ - $30 \, \textrm{yr}$). The effect of red noise on the GWBis even stronger, suggesting that single source detections may be more robust.We find that typical signal-to-noise ratios for the foreground peak near $f =0.1 \, \textrm{yr}^{-1}$, and are much less sensitive to the continued additionof new pulsars to PTA.

Single Sources in the Low-Frequency Gravitational Wave Sky: properties and time to detection by pulsar timing arrays