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We investigate the potential of detecting the gravitational wave from
individual binary black hole systems using pulsar timing arrays (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 \sim10^8 -
10^{10}\,M_{\sun} less than ∼105\,years before the final merger, and
those with less than ∼103−104 years before merger may allow us to
detect the evolution of binaries.
We derive an analytical expression to describe the accuracy of a pulsar
distance measurement via timing parallax. We consider five years of bi-weekly
observations at a precision of 15\,ns for close-by (∼0.5−1\,kpc)
pulsars. Timing twenty pulsars would allow us to detect a GW source with an
amplitude larger than 5×10−17. 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 are 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
gravitational wave is strong enough, one can achieve sub-parsec distance
measurements for nearby pulsars with distance less than ∼0.5−1\,kpc.Comment: 16 pages, 5 figure,, accepted by MNRA