arXiv : Projection effects on the observed angular spectrum of the astrophysical stochastic gravitational wave background

Bertacca, Daniele; Matarrese, Sabino; Ricciardone, Angelo; Regimbau, Tania; Bellomo, Nicola; Sakellariadou, Mairi; Jenkins, Alexander C.; Raccanelli, Alvise

doi:10.1103/PhysRevD.101.103513

Article
Report number	arXiv:1909.11627 ; CERN-TH-2019-153 ; KCL-PH-TH 2019-73
Title	Projection effects on the observed angular spectrum of the astrophysical stochastic gravitational wave background
Author(s)	Bertacca, Daniele (U. Padua, Dept. Phys. Astron. ; INFN, Padua ; Padua Observ.) ; Ricciardone, Angelo (INFN, Padua) ; Bellomo, Nicola (ICC, Barcelona U.) ; Jenkins, Alexander C. (King's Coll. London) ; Matarrese, Sabino (U. Padua, Dept. Phys. Astron. ; INFN, Padua ; Padua Observ. ; GSSI, Aquila) ; Raccanelli, Alvise (CERN) ; Regimbau, Tania (Annecy, LAPP) ; Sakellariadou, Mairi (King's Coll. London)
Publication	2020-05-12
Imprint	2019-09-25
Number of pages	15
Note	19 pages, 1 figure. Typos corrected; Minor corrections. Version accepted by Physical Review D
In:	Phys. Rev. D 101 (2020) 103513
DOI	10.1103/PhysRevD.101.103513
Subject category	gr-qc ; General Relativity and Cosmology ; astro-ph.CO ; Astrophysics and Astronomy
Abstract	The detection and characterization of the Stochastic Gravitational Wave Background (SGWB) is one of the main goals of Gravitational Wave (GW) experiments. The observed SGWB will be the combination of GWs from cosmological (as predicted by many models describing the physics of the early Universe) and astrophysical origins, which will arise from the superposition of GWs from unresolved sources whose signal is too faint to be detected. Therefore, it is important to have a proper modeling of the astrophysical SGWB (ASGWB) in order to disentangle the two signals; moreover, this will provide additional information on astrophysical properties of compact objects. Applying the Cosmic Rulers formalism, we compute the observed ASGWB angular power spectrum, hence using gauge invariant quantities, accounting for all effects intervening between the source and the observer. These are the so-called projection effects, which include Kaiser, Doppler and gravitational potentials effect. Our results show that these projection effects are the most important at the largest scales, and they contribute to up to tens of percent of the angular power spectrum amplitude, with the Kaiser term being the largest at all scales. While the exact impact of these results will depend on instrumental and astrophysical details, a precise theoretical modeling of the ASGWB will necessarily need to include all these projection effects.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2020-2025 authors (License: CC-BY-4.0)

$\it Relative contribution of different projection effects on the angular power spectra, for the~$50\ \mathrm{Hz}$ (\textit{left panel}) and~$200\ \mathrm{Hz}$ (\textit{right panel}) channels. In both cases we assume that all the events come from the merger of two 15 $M_\odot$ BHs with no spin, in $M_\mathrm{halo} = 10^{12}\ M_\odot$ dark matter halos, and we consider a second generation network of detectors. The solid thin line at zero indicates intrinsic clustering; the blue dashed line shows the contribution of the Kaiser term, the dot-dashed orange is the Doppler effect, the dotted green shows the contribution of gravitational potential terms, and the red solid line shows the effect of all projection effects combined.$