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 (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 ΔΩby a factor ~5 and has negligible consequences on the statistical errors on the other parameters. ΔΩimproves 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~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 ΔΩ~10 deg^2, but has poorer performance for sources in the northern hemisphere. (Abridged)

20 pages, 12 figures, 2 color figures, submitted to Phys. Rev. D

References in corpus (14)

• Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects
• The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays
• Upper bounds on the low-frequency stochastic gravitational wave background from pulsar timing observations: current limits and future prospects
• The Population of Viscosity- and Gravitational Wave-Driven Supermassive Black Hole Binaries Among Luminous AGN
• Gravitational waves from resolvable massive black hole binary systems and observations with Pulsar Timing Arrays
• Supermassive black hole binaries in gaseous and stellar circumnuclear discs: orbital dynamics and gas accretion
• The imprint of massive black hole formation models on the LISA data stream
• Black Hole Growth in Hierarchical Galaxy Formation
• Models for jet power in elliptical galaxies: A case for rapidly spinning black holes
• Localizing coalescing massive black hole binaries with gravitational waves
• The Parkes Pulsar Timing Array
• Pre-Merger Localization of Gravitational-Wave Standard Sirens With LISA I: Harmonic Mode Decomposition
• Probing white dwarf interiors with LISA: periastron precession in double white dwarfs
• The Most Massive Black Holes in the Universe: Effects of Mergers in Massive Galaxy Clusters

Cited by in corpus (2)

• Assessing the Role of Spin Noise in the Precision Timing of Millisecond Pulsars
• Self consistent model for the evolution of eccentric massive black hole binaries in stellar environments: implications for gravitational wave observations