Using Gravitational Wave Parallax to Measure the Hubble Parameter with
Pulsar Timing Arrays
D. D'Orazio, and A. Loeb. (2020)cite arxiv:2009.06084Comment: Submitted to Physical Review D. Comments welcome.
Abstract
We demonstrate how pulsar timing arrays (PTAs) yield a purely gravitational
wave (GW) measurement of the luminosity distance and co-moving distance to a
supermassive black hole binary source, hence providing an estimate of the
source redshift and the Hubble constant. The luminosity distance is derived
through standard measurement of the chirp mass, which for the slowly evolving
binary sources in the PTA band can be found by comparing the frequency of
GW-timing residuals at the Earth compared to those at distant pulsars in the
array. The co-moving distance can be measured from GW-timing parallax caused by
the curvature of the GW wavefronts. This can be detected for single sources at
the high-frequency end of the PTA band out to ~10 Gpc with a future PTA
containing well-timed pulsars out to ~10 kpc. We estimate that for a future PTA
with ~100 pulsars between 1 and 20 kpc and 1% pulsar-distance errors, the
Hubble constant can be measured to better than 30% for a single source at $0.1
z 2$. At $z 0.1$, the luminosity and co-moving
distances are too similar to disentangle. At $z2$, this measurement
will be restricted by a signal-to-noise ratio threshold.
Description
Using Gravitational Wave Parallax to Measure the Hubble Parameter with Pulsar Timing Arrays
%0 Generic
%1 dorazio2020using
%A D'Orazio, Daniel J.
%A Loeb, Abraham
%D 2020
%K library
%T Using Gravitational Wave Parallax to Measure the Hubble Parameter with
Pulsar Timing Arrays
%U http://arxiv.org/abs/2009.06084
%X We demonstrate how pulsar timing arrays (PTAs) yield a purely gravitational
wave (GW) measurement of the luminosity distance and co-moving distance to a
supermassive black hole binary source, hence providing an estimate of the
source redshift and the Hubble constant. The luminosity distance is derived
through standard measurement of the chirp mass, which for the slowly evolving
binary sources in the PTA band can be found by comparing the frequency of
GW-timing residuals at the Earth compared to those at distant pulsars in the
array. The co-moving distance can be measured from GW-timing parallax caused by
the curvature of the GW wavefronts. This can be detected for single sources at
the high-frequency end of the PTA band out to ~10 Gpc with a future PTA
containing well-timed pulsars out to ~10 kpc. We estimate that for a future PTA
with ~100 pulsars between 1 and 20 kpc and 1% pulsar-distance errors, the
Hubble constant can be measured to better than 30% for a single source at $0.1
z 2$. At $z 0.1$, the luminosity and co-moving
distances are too similar to disentangle. At $z2$, this measurement
will be restricted by a signal-to-noise ratio threshold.
@misc{dorazio2020using,
abstract = {We demonstrate how pulsar timing arrays (PTAs) yield a purely gravitational
wave (GW) measurement of the luminosity distance and co-moving distance to a
supermassive black hole binary source, hence providing an estimate of the
source redshift and the Hubble constant. The luminosity distance is derived
through standard measurement of the chirp mass, which for the slowly evolving
binary sources in the PTA band can be found by comparing the frequency of
GW-timing residuals at the Earth compared to those at distant pulsars in the
array. The co-moving distance can be measured from GW-timing parallax caused by
the curvature of the GW wavefronts. This can be detected for single sources at
the high-frequency end of the PTA band out to ~10 Gpc with a future PTA
containing well-timed pulsars out to ~10 kpc. We estimate that for a future PTA
with ~100 pulsars between 1 and 20 kpc and 1% pulsar-distance errors, the
Hubble constant can be measured to better than 30% for a single source at $0.1
\lesssim z \lesssim 2$. At $z \lesssim 0.1$, the luminosity and co-moving
distances are too similar to disentangle. At $z\gtrsim 2$, this measurement
will be restricted by a signal-to-noise ratio threshold.},
added-at = {2020-09-15T05:51:35.000+0200},
author = {D'Orazio, Daniel J. and Loeb, Abraham},
biburl = {https://www.bibsonomy.org/bibtex/2a1273b3327b271b27d1821218bd898ae/gpkulkarni},
description = {Using Gravitational Wave Parallax to Measure the Hubble Parameter with Pulsar Timing Arrays},
interhash = {249e74d3b724273a262d3bf36b3a8fd5},
intrahash = {a1273b3327b271b27d1821218bd898ae},
keywords = {library},
note = {cite arxiv:2009.06084Comment: Submitted to Physical Review D. Comments welcome},
timestamp = {2020-09-15T05:51:35.000+0200},
title = {Using Gravitational Wave Parallax to Measure the Hubble Parameter with
Pulsar Timing Arrays},
url = {http://arxiv.org/abs/2009.06084},
year = 2020
}