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Measuring a cosmological distance-redshift relationship using only gravitational wave observations of binary neutron star coalescences

Chris Messenger, Jocelyn Read

TL;DR

Using the population of O(10(3)-10(7)) detectable binary neutron star systems predicted for 3rd generation gravitational wave detectors, the luminosity distance-redshift relation can be probed independently of the cosmological distance ladder and independently of electromagnetic observations.

Abstract

Detection of gravitational waves from the inspiral phase of binary neutron star coalescence will allow us to measure the effects of the tidal coupling in such systems. These effects will be measurable using 3rd generation gravitational wave detectors, e.g. the Einstein Telescope, which will be capable of detecting inspiralling binary neutron star systems out to redshift z=4. Tidal effects provide additional contributions to the phase evolution of the gravitational wave signal that break a degeneracy between the system's mass parameters and redshift and thereby allow the simultaneous measurement of both the effective distance and the redshift for individual sources. Using the population of O(10^3-10^7) detectable binary neutron star systems predicted for the Einstein Telescope the luminosity distance--redshift relation can be probed independently of the cosmological distance ladder and independently of electromagnetic observations. We present the results of a Fisher information analysis applied to waveforms assuming a subset of possible neutron star equations of state. We conclude that for our range of representative neutron star equations of state the redshift of such systems can be determined to an accuracy of 8-40% for z<1 and 9-65% for 1<z<4.

Measuring a cosmological distance-redshift relationship using only gravitational wave observations of binary neutron star coalescences

TL;DR

Using the population of O(10(3)-10(7)) detectable binary neutron star systems predicted for 3rd generation gravitational wave detectors, the luminosity distance-redshift relation can be probed independently of the cosmological distance ladder and independently of electromagnetic observations.

Abstract

Detection of gravitational waves from the inspiral phase of binary neutron star coalescence will allow us to measure the effects of the tidal coupling in such systems. These effects will be measurable using 3rd generation gravitational wave detectors, e.g. the Einstein Telescope, which will be capable of detecting inspiralling binary neutron star systems out to redshift z=4. Tidal effects provide additional contributions to the phase evolution of the gravitational wave signal that break a degeneracy between the system's mass parameters and redshift and thereby allow the simultaneous measurement of both the effective distance and the redshift for individual sources. Using the population of O(10^3-10^7) detectable binary neutron star systems predicted for the Einstein Telescope the luminosity distance--redshift relation can be probed independently of the cosmological distance ladder and independently of electromagnetic observations. We present the results of a Fisher information analysis applied to waveforms assuming a subset of possible neutron star equations of state. We conclude that for our range of representative neutron star equations of state the redshift of such systems can be determined to an accuracy of 8-40% for z<1 and 9-65% for 1<z<4.

Paper Structure

This paper contains 3 equations, 1 figure.

Figures (1)

  • Figure 1: The fractional uncertainties in the redshift as a function of redshift obtained from the Fisher matrix analysis for BNS systems using 3 representative EOSs, APR 1998PhRvC..58.1804A, SLY 2001AA...380..151D and MS1 1996NuPhA.606..508M. In all cases the component NSs have rest masses of $1.4M_{\odot}$ and waveforms have a cut-off frequency equal to the ISCO frequency (as defined in the BNS rest-frame). We have used a cosmological parameter set $H_{0} = 70.5$ kms$^{-1}$Mpc$^{-1}$, $\Omega_{m}=0.2736$, $\Omega_{k}=0$,$w_{0} = -1$ to compute the luminosity distance for given redshifts and have assumed detector noise corresponding to the ET-D 2011CQGra..28i4013H2011ETdesigndoc design (a frequency domain analytic fit to the noise floor can be found in ETwebsite).