http://arxiv.org/abs/2210.09737
Standard sirens — gravitational wave (GW) sources with an electromagnetic (EM) counterpart — can be used to measure the Hubble constant directly which should help to ease the existing Hubble tension. However, if the source is moving, a relativistic redshift affects the redshift of the EM counterpart and the apparent distance of the GW source, and thus it needs to be corrected to obtain accurate measurements. We study the effect of velocity on GWs for a source in an expanding universe showing that the total redshift of the wave is equal to the product of the relativistic redshift and the cosmological redshift. We, further, find that a motion of the source changes its apparent distance by a factor $(1+z_{\rm rel})^2$ in contrast to a linear factor for the cosmological redshift. We discuss that the additional factor for the relativistic redshift is a consequence of a velocity-dependent amplitude for GWs. We consider the effect of the velocity on the chirp mass and the apparent distance of the source an observer would infer when ignoring the velocity. We find that for different astrophysical scenarios the error in the chirp mass can range between 0.1\,\% and 7\,\% while the error in the apparent distance can be between 0.25\,\% and 15\,\%. Furthermore, we consider the error introduced in the measurement of the Hubble constant using standard sirens for two cases: (i) when the effect of velocity on the redshift of the EM counterpart is considered but not on the apparent distance obtained from GWs and (ii) when the effect of the velocity is ignored completely. We find that in the first case the error can reach 1\,\% for a source moving due to the peculiar velocity of its host galaxy and that in the second case the error can be more than 5\,\% for a source at the distance of GW150914 with the same velocity.
A. Torres-Orjuela and X. Chen
Wed, 19 Oct 22
70/87
Comments: 12 pages, 5 figures
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