Gravitational waves and pulsar timing: stochastic background, individual sources and parameter estimation

Massive black holes are key ingredients of the assembly and evolution of cosmic structures. Pulsar Timing Arrays (PTAs) currently provide the only means to observe gravitational radiation from massive black hole binary systems with masses ∼> 107Mo-dot. The whole cosmic population produces a signal consisting of two components: (i) a stochastic background resulting from the incoherent superposition of radiation from the all the sources, and (ii) a handful of individually resolvable signals that raise above the background level and are produced by sources sufficiently close and/or massive. Considering a wide range of massive black hole binary assembly scenarios, we investigate both the level and shape of the background and the statistics of resolvable sources. We predict a characteristic background amplitude in the interval hc(f = 10-8 Hz) ∼ 5 x 10-16-5 x 10-15, within the detection range of the complete Parkes PTA. On average, at least one resolvable source produces timing residuals that integrated over the typical time of observation lay in the range ∼5-50 ns. We also quantify the capability of PTAs of measuring the parameters of individual sources, focusing on the astrophysically more likely monochromatic signals produced by binaries in circular orbit. We investigate how the results depend on the number and distribution of pulsars in the array, by computing the variance-covariance matrix of the parameter measurements. For plausible Square Kilometre Array (SKA) observations (100 pulsars uniformly distributed in the sky), and assuming a coherent signal-to-noise ratio of 10, the sky position of massive black hole binaries can be located within an ∼40 deg2 error box, opening promising prospects for detecting a putative electromagnetic counterpart to the gravitational wave emission. The planned SKA can plausibly observe these unique systems, although the number of detections is likely to be small. These observations would naturally complement on the high-mass end of the black hole distribution function future surveys carried out by the Laser Interferometer Space Antenna (LISA).