Measuring the parameters of massive black hole binary systems with pulsar timing array observations of gravitational waves

The observation of massive black hole binaries with pulsar timing arrays (PTAs) is one of the goals of gravitational-wave astronomy in the coming years. Massive (greater than or similar to 10(8)M(circle dot)) and low-redshift (less than or similar to 1.5) sources are expected to be individually resolved by upcoming PTAs, and our ability to use them as astrophysical probes will depend on the accuracy with which their parameters can be measured. In this paper we estimate the precision of such measurements using the Fisher-information-matrix formalism. For this initial study we restrict ourselves to monochromatic'' sources, i.e. binaries whose frequency evolution is negligible during the expected approximate to 10 yr observation time, which represent the bulk of the observable population based on current astrophysical predictions. In this approximation, the system is described by seven parameters and we determine their expected statistical errors as a function of the number of pulsars in the array, the array sky coverage, and the signal-to-noise ratio (SNR) of the signal. At fixed SNR (regardless of the number of pulsars in the PTA), the gravitational-wave astronomy capability of a PTA is achieved with approximate to 20 pulsars; adding more pulsars (up to 1000) to the array reduces the source error box in the sky Delta Omega by a factor approximate to 5 and has negligible consequences on the statistical errors on the other parameters, because the correlations among parameters are already removed to a large extent. If one folds in the increase of coherent SNR proportional to the square root of the number of pulsars, Delta Omega improves as 1/SNR2 and the other parameters as 1/SNR. For a fiducial PTA of 100 pulsars uniformly distributed in the sky and a coherent SNR = 10, we find Delta Omega approximate to 40 deg(2), a fractional error on the signal amplitude of approximate to 30% (which constrains only very poorly the chirp mass-luminosity distance combination M-5/3/D-L), and the source inclination and polarization angles are recovered at the approximate to 0.3 rad level. The ongoing Parkes PTA is particularly sensitive to systems located in the southern hemisphere, where at SNR 10 the source position can be determined with Delta Omega approximate to 10 deg(2), but has poorer (by an order of magnitude) performance for sources in the northern hemisphere.