%0 Generic %1 dorazio2020using %A D'Orazio, Daniel J. %A Loeb, Abraham %D 2020 %K tifr %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 = {2020-09-15T18:12:07.000+0200}, author = {D'Orazio, Daniel J. and Loeb, Abraham}, biburl = {https://www.bibsonomy.org/bibtex/2a1273b3327b271b27d1821218bd898ae/citekhatri}, description = {Using Gravitational Wave Parallax to Measure the Hubble Parameter with Pulsar Timing Arrays}, interhash = {249e74d3b724273a262d3bf36b3a8fd5}, intrahash = {a1273b3327b271b27d1821218bd898ae}, keywords = {tifr}, note = {cite arxiv:2009.06084Comment: Submitted to Physical Review D. Comments welcome}, timestamp = {2020-09-15T18:12:07.000+0200}, title = {Using Gravitational Wave Parallax to Measure the Hubble Parameter with Pulsar Timing Arrays}, url = {http://arxiv.org/abs/2009.06084}, year = 2020 }