Analyzing clustering of astrophysical gravitational-wave sources: Luminosity-distance space distortions. (arXiv:2007.04359v2 [astro-ph.CO] UPDATED)

<a href="http://arxiv.org/find/astro-ph/1/au:+Namikawa_T/0/1/0/all/0/1">Toshiya Namikawa</a>

We present a formulation of observed number density fluctuations of

gravitational-wave (GW) sources in a three dimensional space. In GW

observations, redshift identification for each GW source is a challenging

issue, in particular, for high redshift sources. The use of observed luminosity

distance as a distance indicator will be a simple yet optimal way for measuring

the clustering signal. We derive the density fluctuations of GW sources

estimated from observed luminosity distance and sky position of each source.

The density fluctuations are distorted as similar to the so-called redshift

space distortions in galaxy surveys but with several differences. We then show

the two-point correlation function and multipole power spectrum in the presence

of the distortion effect. We find that the line-of-sight derivative of the

lensing convergence, which does not appear in the redshift-space distortions,

leads to significant distortions in the observed correlation function. In

addition, the lensing effect affects higher-order multipole power spectra and

its signal-to-noise at high redshifts.

We present a formulation of observed number density fluctuations of

gravitational-wave (GW) sources in a three dimensional space. In GW

observations, redshift identification for each GW source is a challenging

issue, in particular, for high redshift sources. The use of observed luminosity

distance as a distance indicator will be a simple yet optimal way for measuring

the clustering signal. We derive the density fluctuations of GW sources

estimated from observed luminosity distance and sky position of each source.

The density fluctuations are distorted as similar to the so-called redshift

space distortions in galaxy surveys but with several differences. We then show

the two-point correlation function and multipole power spectrum in the presence

of the distortion effect. We find that the line-of-sight derivative of the

lensing convergence, which does not appear in the redshift-space distortions,

leads to significant distortions in the observed correlation function. In

addition, the lensing effect affects higher-order multipole power spectra and

its signal-to-noise at high redshifts.

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