Gravitational wave astronomy of single sources with a pulsar timing array

The stability of radio millisecond pulsars as celestial clocks allows for the possibility to detect and study the properties of gravitational waves (GWs) when the received pulses are timed jointly in a 'Pulsar Timing Array' (PTA) experiment. Here, we investigate the potential of detecting the GW from individual binary black hole systems using PTAs and calculate the accuracy for determining the GW properties. This is done in a consistent analysis, which at the same time accounts for the measurement of the pulsar distances via the timing parallax. We find that, at low redshift, a PTA is able to detect the nano-hertz GW from super-massive black hole binary systems with masses of similar to 10(8)-10(10)M(circle dot) less than similar to 10(5) yrs before the final merger. Binaries with more than similar to 10(3)-10(4) yr before merger are effectively monochromatic GW, and those with less than similar to 10(3)-10(4) yr before merger may allow us to detect the evolution of binaries. For our findings, we derive an analytical expression to describe the accuracy of a pulsar distance measurement via timing parallax. We consider 5 yr of bi-weekly observations at a precision of 15 ns for close-by (similar to 0.5-1 kpc) pulsars. Timing 20 pulsars would allow us to detect a GW source with an amplitude larger than 5 x 10(-17). We calculate the corresponding GW and binary orbital parameters and their measurement precision. The accuracy of measuring the binary orbital inclination angle, the sky position and the GW frequency is calculated as functions of the GW amplitude. We note that the 'pulsar term', which is commonly regarded as noise, is essential for obtaining an accurate measurement for the GW source location. We also show that utilizing the information encoded in the GW signal passing the Earth also increases the accuracy of pulsar distance measurements. If the GW is strong enough, one can achieve sub-parsec distance measurements for nearby pulsars with distance less than similar to 0.5-1 kpc.