Analyzing clustering of astrophysical gravitational-wave sources: Luminosity-distance space distortions

Abstract

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.

25 pages, 10 figures, matches the version to be published in JCAP

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• The Science of the Einstein Telescope
• Probing gravity and growth of structure with gravitational waves and galaxies' peculiar velocity
• Signatures of primordial black holes in gravitational wave clustering
• Clustering of Gravitational Wave and Supernovae events: a multitracer analysis in Luminosity Distance Space
• The observed number counts in luminosity distance space
• Magnification and evolution bias of transient sources: GWs and SNIa
• Gravitational waves and galaxies cross-correlations: a forecast on GW biases for future detectors
• Relativistic imprints on dispersion measure space distortions
• Probing the large-scale structure of the universe through gravitational-wave observations
• Angular power spectrum of gravitational-wave transient sources as a probe of the large-scale structure
• Exploring future synergies for large-scale structure between gravitational waves and radio sources
• Calibrating systematic errors in the distance determination with the luminosity-distance space large scale structure of dark sirens and its potential applications
• Detector induced anisotropies on the angular distribution of gravitational wave sources and opportunities of constraining horizon scale anisotropies