Measuring the parameters of massive black hole binary systems with pulsar timing array observations of gravitational waves
Abstract
The observation of massive black hole binaries with pulsar timing arrays (PTAs) is one of the goals of gravitationalwave astronomy in the coming years. Massive (≳10^{8}M_{⊙}) and lowredshift (≲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 Fisherinformationmatrix formalism. For this initial study we restrict ourselves to “monochromatic” sources, i.e. binaries whose frequency evolution is negligible during the expected ≈10yr 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 signaltonoise ratio (SNR) of the signal. At fixed SNR (regardless of the number of pulsars in the PTA), the gravitationalwave 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 ΔΩ by a factor ≈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, ΔΩ 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 ΔΩ≈40deg^{2}, a fractional error on the signal amplitude of ≈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 ≈0.3rad 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 ΔΩ≈10deg^{2}, but has poorer (by an order of magnitude) performance for sources in the northern hemisphere.
 Publication:

Physical Review D
 Pub Date:
 May 2010
 DOI:
 10.1103/PhysRevD.81.104008
 arXiv:
 arXiv:1003.0677
 Bibcode:
 2010PhRvD..81j4008S
 Keywords:

 04.30.Db;
 95.85.Sz;
 97.60.Gb;
 97.60.Lf;
 Wave generation and sources;
 Gravitational radiation magnetic fields and other observations;
 Pulsars;
 Black holes;
 Astrophysics  Cosmology and Extragalactic Astrophysics;
 General Relativity and Quantum Cosmology
 EPrint:
 20 pages, 12 figures, 2 color figures, submitted to Phys. Rev. D