Phys. Rev. D 102, 043513 (2020) - Cross-correlation of the astrophysical gravitational-wave background with galaxy clustering

Cross-correlation of the astrophysical gravitational-wave background with galaxy clustering

Guadalupe Cañas-Herrera, Omar Contigiani, and Valeri Vardanyan

Phys. Rev. D 102, 043513 – Published 11 August 2020

Abstract

We investigate the correlation between the distribution of galaxies and the predicted gravitational-wave background of astrophysical origin. We show that the large angular scale anisotropies of this background are dominated by nearby nonlinear structure, which depends on the notoriously hard to model galaxy power spectrum at small scales. In contrast, we report that the cross-correlation of this signal with galaxy catalogues depends only on linear scales and can be used to constrain the average contribution to the gravitational-wave background as a function of time. Using mock data based on a simplified model, we explore the effects of galaxy bias, angular resolution and the matter abundance on these constraints. Our results suggest that, when combined with galaxy surveys, the gravitational-wave background can be a powerful probe for both gravitational-wave merger physics and cosmology.

Received 19 November 2019
Revised 18 June 2020
Accepted 13 July 2020

DOI:https://doi.org/10.1103/PhysRevD.102.043513

Physics Subject Headings (PhySH)

Gravitational waves Large scale structure of the Universe

Galaxies

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Guadalupe Cañas-Herrera ^1,2,*, Omar Contigiani ^1,2,†, and Valeri Vardanyan ^1,2,3,‡

¹Leiden Observatory, Leiden University, PO Box 9506, Leiden 2300 RA, Netherlands
²Lorentz Institute for Theoretical Physics, Leiden University, PO Box 9506, Leiden 2300 RA, Netherlands
³Kavli Institute for the Physics and Mathematics of the Universe (WPI), UTIAS, The University of Tokyo, Chiba 277-8583, Japan

^*canasherrera@lorentz.leidenuniv.nl
^†contigiani@lorentz.leidenuniv.nl
^‡valeri.vardanyan@ipmu.jp

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Vol. 102, Iss. 4 — 15 August 2020

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Figure 1
Left panel: Linear autocorrelation power spectra $C_{ℓ}^{G W}$ of the GWB of a constant $\tilde{K} (r)$ for a set of upper limits of the integral in Eq. (4), in units of ${Mpc}^{- 1}$ . Right panel: The same as in the left panel, but for the cross-correlation between a galaxy sample (centered at $z = 0.5$ ) and the GWB, $C_{ℓ}^{\times}$ . Both of the panels are supposed to be understood as normalized with respect to the amplitude of the fiducial GWB model, to be discussed in detail later.
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Figure 2
Fiducial model as a function of redshift $z$ , of the GW source kernel $\tilde{K} (r (z))$ in Eq. (7). In practice, we cut off the low-redshift sources with comoving distances smaller than 150 Mpc (see the text for details). The galaxy clustering window functions $W_{1}$ and $W_{2}$ are assumed to be Gaussian.
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Figure 3
Effects of the model parameters $b_{GW} K_{0}$ , $z_{*}$ , $Ω_{m}$ and $b_{GW}$ on the cross-correlation signal. The uncertainties are the cosmic variance defined in Appendix pp2. Note particularly that in the case of both of the window functions $W_{1}$ and $W_{2}$ the change in $b_{GW} K_{0}$ induces a significant change in the amplitude of the signal (upper left panel), while when the combination $b_{GW} K_{0}$ is fixed, the signal is not sensitive to the value of the GW bias $b_{GW}$ (lower left panel). Note that mostly the high- $ℓ$ multipoles are sensitive to changes in $z_{*}$ (upper right panel). Note also that the change on $Ω_{m}$ modifies the tilt of the signal, without altering its overall amplitude (lower right panel). All of the panels are supposed to be understood as normalized with respect to the amplitude of the fiducial GWB model.
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Figure 4
Effects of the model parameters $b_{GW} K_{0}$ , $z_{*}$ , $Ω_{m}$ and $b_{GW}$ on the autocorrelation signal. The uncertainties are defined as in Fig. 3. The curves should be understood as normalized with respect to the amplitude of the fiducial GWB model.
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Figure 5
Constraints on the GWB parameters ( $b_{GW} K_{0}$ , $z_{*}$ ) and cosmology ( $Ω_{m}$ ) obtained using the cross-correlation signal with two window functions as a function of the maximum multipole included in the analysis. Cosmic-variance limited measurements are assumed for all the constraints, so these should be understood as the best-case scenario results. Larger values of the signal-to-noise ratio (S/N) correspond to better angular resolution [see Eq. (22)]. We have explored the effect of $Ω_{m}$ on these constraints by either fixing its value (left panel), or setting a Planck-2018-like Gaussian prior (right panel). Remarkably, the combination $b_{GW} K_{0}$ can be constrained even with very limited angular sensitivity. The turnover location $z_{*}$ is practically unconstrained for $ℓ_{\max} ≲ 50$ , and $Ω_{m}$ is prior dominated for these multipoles. In case of $ℓ_{\max} ≳ 50$ all the relevant parameters are tightly constrained, and for $ℓ_{\max} \sim 100$ the constraints are at the level of a few percent. Notably, the cosmology (mimicked by varying $Ω_{m}$ in our analysis) can match and surpass the CMB results only in case of high angular resolution/signal-to-noise. For reference, $ℓ_{\max} = 100$ roughly corresponds to 2 degrees.
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Figure 6
Posterior distributions for the cases of $ℓ_{\max} = 10$ (orange) and $ℓ_{\max} = 100$ (black), with Planck-2018-like Gaussian prior on $Ω_{m}$ (shown in red dashed line). Contours represent the 68% and 95% confidence regions. We can clearly see that $K_{0} b_{GW}$ is constrained even in the case of the limited angular resolution, while $b_{GW}$ is never separately constrained. The turn-over redshift $z_{*}$ is unconstrained for the low-resolution case, while it is tightly constrained for the case of $ℓ_{\max} = 100$ . Finally, $Ω_{m}$ is prior dominated for the low-resolution case, while it beats the prior in the high-resolution scenario. Also noteworthy are the degeneracies between $Ω_{m}$ and $K_{0} b_{GW}$ , as well as between $z_{*}$ and $K_{0} b_{GW}$ .
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Physical Review D

covering particles, fields, gravitation, and cosmology

Cross-correlation of the astrophysical gravitational-wave background with galaxy clustering

Guadalupe Cañas-Herrera, Omar Contigiani, and Valeri Vardanyan

Phys. Rev. D 102, 043513 – Published 11 August 2020

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Physical Review D

covering particles, fields, gravitation, and cosmology

Cross-correlation of the astrophysical gravitational-wave background with galaxy clustering

Guadalupe Cañas-Herrera, Omar Contigiani, and Valeri Vardanyan

Phys. Rev. D 102, 043513 – Published 11 August 2020

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