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Title: 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 gravitational-wave astronomy in the coming years. Massive (> or approx. 10{sup 8}M{sub {center_dot}}) and low-redshift (< or approx. 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 {approx_equal}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 {approx_equal}20 pulsars; adding more pulsars (up to 1000) to the array reduces the source error box in the skymore » {Delta}{Omega} by a factor {approx_equal}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/SNR{sup 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}{approx_equal}40 deg{sup 2}, a fractional error on the signal amplitude of {approx_equal}30% (which constrains only very poorly the chirp mass-luminosity distance combination M{sup 5/3}/D{sub L}), and the source inclination and polarization angles are recovered at the {approx_equal}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}{approx_equal}10 deg{sup 2}, but has poorer (by an order of magnitude) performance for sources in the northern hemisphere.« less

Authors:
 [1];  [2]
  1. Albert Einstein Institute, Am Muhlenberg 1 D-14476 Golm (Germany)
  2. School of Physics and Astronomy, The University of Birmingham, Edgbaston, Birmingham, B15 2TT (United Kingdom)
Publication Date:
OSTI Identifier:
21409727
Resource Type:
Journal Article
Journal Name:
Physical Review. D, Particles Fields
Additional Journal Information:
Journal Volume: 81; Journal Issue: 10; Other Information: DOI: 10.1103/PhysRevD.81.104008; (c) 2010 The American Physical Society; Journal ID: ISSN 0556-2821
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; AMPLITUDES; APPROXIMATIONS; ASTRONOMY; ASTROPHYSICS; BINARY STARS; BLACK HOLES; CORRELATIONS; FORECASTING; GRAVITATIONAL WAVES; INCLINATION; LUMINOSITY; MASS; MONOCHROMATIC RADIATION; NORTHERN HEMISPHERE; POLARIZATION; PULSARS; RED SHIFT; SIGNAL-TO-NOISE RATIO; SOUTHERN HEMISPHERE; CALCULATION METHODS; COSMIC RADIO SOURCES; DIMENSIONLESS NUMBERS; EARTH PLANET; ELECTROMAGNETIC RADIATION; OPTICAL PROPERTIES; PHYSICAL PROPERTIES; PHYSICS; PLANETS; RADIATIONS; STARS

Citation Formats

Sesana, Alberto, Center for Gravitational Wave Physics, Pennsylvania State University, University Park, Pennsylvania 16802, and Vecchio, Alberto. Measuring the parameters of massive black hole binary systems with pulsar timing array observations of gravitational waves. United States: N. p., 2010. Web. doi:10.1103/PHYSREVD.81.104008.
Sesana, Alberto, Center for Gravitational Wave Physics, Pennsylvania State University, University Park, Pennsylvania 16802, & Vecchio, Alberto. Measuring the parameters of massive black hole binary systems with pulsar timing array observations of gravitational waves. United States. https://doi.org/10.1103/PHYSREVD.81.104008
Sesana, Alberto, Center for Gravitational Wave Physics, Pennsylvania State University, University Park, Pennsylvania 16802, and Vecchio, Alberto. 2010. "Measuring the parameters of massive black hole binary systems with pulsar timing array observations of gravitational waves". United States. https://doi.org/10.1103/PHYSREVD.81.104008.
@article{osti_21409727,
title = {Measuring the parameters of massive black hole binary systems with pulsar timing array observations of gravitational waves},
author = {Sesana, Alberto and Center for Gravitational Wave Physics, Pennsylvania State University, University Park, Pennsylvania 16802 and Vecchio, Alberto},
abstractNote = {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 (> or approx. 10{sup 8}M{sub {center_dot}}) and low-redshift (< or approx. 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 {approx_equal}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 {approx_equal}20 pulsars; adding more pulsars (up to 1000) to the array reduces the source error box in the sky {Delta}{Omega} by a factor {approx_equal}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/SNR{sup 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}{approx_equal}40 deg{sup 2}, a fractional error on the signal amplitude of {approx_equal}30% (which constrains only very poorly the chirp mass-luminosity distance combination M{sup 5/3}/D{sub L}), and the source inclination and polarization angles are recovered at the {approx_equal}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}{approx_equal}10 deg{sup 2}, but has poorer (by an order of magnitude) performance for sources in the northern hemisphere.},
doi = {10.1103/PHYSREVD.81.104008},
url = {https://www.osti.gov/biblio/21409727}, journal = {Physical Review. D, Particles Fields},
issn = {0556-2821},
number = 10,
volume = 81,
place = {United States},
year = {Sat May 15 00:00:00 EDT 2010},
month = {Sat May 15 00:00:00 EDT 2010}
}