\textit{Euclid}: From Galaxies to Gravitational Waves -- Forecasting Stochastic Gravitational Wave Background Anisotropies and Their Cross-Correlation

TL;DR

This work uses the Euclid Flagship Simulation Galaxy Catalogue to forecast the stochastic gravitational-wave background from compact binaries and its anisotropies, and to explore its cross-correlation with the galaxy distribution. By modeling each galaxy’s star-formation history, metallicity, and delay-time distribution, the authors predict the SGWB angular power spectrum and quantify cross-correlations with Euclid galaxies within a Bayesian, cosmic-variance-limited framework. They find catalogue-based SGWB energy densities about an order of magnitude smaller than semi-analytic GWTC-3 predictions, with most contribution from low redshift, and demonstrate that cross-correlation analyses can constrain the joint astrophysical parameters governing CBC formation. The study outlines a pathway to real data by incorporating survey systematics and LVK noise, highlighting the potential of SGWB–galaxy correlations to shed light on CBC formation channels and the cosmic star-formation history accessible via Euclid.

Abstract

We estimate the amplitude and spatial anisotropy in the stochastic gravitational wave background (SGWB) energy density due to compact binary coalescence (CBC) events: binary black holes (BBH), binary neutron stars (BNS), and black hole-neutron star (BHNS) mergers. Our starting point is the Flagship Simulation Galaxy Catalogue developed by the Euclid Consortium. For each galaxy in the Catalogue, we use the simulated mass and starformation to constrain the galaxy's star-formation history, and predict its contribution to the gravitational-wave energy density through CBC mergers. Combining such contributions from all galaxies in the Catalogue results in a prediction for the frequency spectrum and spatial anisotropy of the CBC SGWB. We also compare this prediction to semi-analytical models of SGWB generated by compact binaries. We identify a set of effective parameters that capture the key features of these models, and we apply a Bayesian framework to infer these parameters assuming an ideal scenario of cosmic variance-limited search. This represents the first step toward developing a comprehensive framework that will eventually enable the correlation of SGWB anisotropy and \textit{Euclid} galaxy data, potentially allowing us to extract valuable astrophysical information from this new observable.

Figures (8)

• Figure 1: The median, 16th and 84th percentile of the delayed star-formation rate computed for minimum time $20$ and $50\ \rm{Myr}$ (corresponding to BNS and BBH or BHNS respectively) using the exponential-flat mixed SFH model for all Euclid Flagship Simulation Galaxy Catalogue galaxies with $H_{\text{E}}$ less than 26.6 in redshift bins of 0.1 width.
• Figure 2: 2D histogram of $H_{\text{E}}$ and redshift with the colour bar being galaxy number count (left) or gravitational wave energy density (right) of all galaxies in Euclid deep region in $5^{\circ}<\rm{Dec}<10^{\circ}, 150^{\circ}<\rm{RA}<155^{\circ}$ with redshift up to 3. The black lines stand for $H_{\text{E}}=26.6$.
• Figure 3: Left: 2D binned histogram of $\log_{10}{\varw^{\text{GW}}_k}$ at 65 Hz and its $\log_{10}(1+z)$ for all Euclid galaxies. The colour bar shows number of galaxies in each bin. Right: sum of total GW energy density in 0.1-wide redshift bins from 0 to 3.
• Figure 4: Total GW energy density summed over all types of binaries (BNS, BBH, BHNS) at 65 Hz for all Euclid Flagship galaxies with $H_{\text{E}}$ less than 26.6 per angular size in HEALPix for pixels of $N_{\text{pix}}=786\,432$ with removal of the edge pixels. The colours are on a log scale. The pixels in purple stand for the edge of the sky coverage, and are removed in all following calculation.
• Figure 5: GW energy density fluctuation $C_\ell$ defined in Eq. (\ref{['eq:gwcl']}) is shown as a solid line, including contributions from all three binary types (BBH, BNS, and BHNS). Two 90% confidence uncertainty regions are shown: the blue region shows the uncertainty due to the uncertainty in the local merger rate, while the orange region shows the total uncertainty in Eq. (\ref{['eq:totsigmaClGW']}).