Measuring the parameters of massive black hole binary systems with
  Pulsar Timing Array observations of gravitational waves
  The observation of massive black hole binaries (MBHBs) with Pulsar Timing
Arrays (PTAs) is one of the goals of gravitational wave astronomy in the coming
years. Massive (>10^8 solar masses) and low-redshift (< 1.5) sources are
expected to be individually resolved by up-coming 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. We restrict to
"monochromatic" sources. 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, the gravitational wave
astronomy capability of a PTA is achieved with ~20 pulsars; adding more pulsars
(up to 1000) to the array reduces the source error-box in the sky \Delta\Omega
by a factor ~5 and has negligible consequences on the statistical errors on the
other parameters. \Delta\Omega improves as 1/SNR^2 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~40 deg^2, a fractional error on the
signal amplitude of ~30% (which constraints only very poorly the chirp mass -
luminosity distance combination M_c^{5/3}/D_L), and the source inclination and
polarization angles are recovered at the ~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 ~10 deg^2,
but has poorer performance for sources in the northern hemisphere. (Abridged)
