Exploring the anisotropic gravitational wave background from all-sky mock gravitational wave event catalogues

Abstract

Anisotropic stochastic gravitational wave background (SGWB) serves as a potential probe of the large-scale structure (LSS) of the universe. In this work, we explore the anisotropic SGWB from local ($z<\sim 0.085$) merging stellar mass compact binaries, specifically focusing on merging stellar binary black holes, merging neutron-star-black-hole binaries, and merging binary neutron stars. The analysis employs seven all-sky mock lightcone gravitational wave event catalogues, which are derived from the Millennium simulation combined with a semi-analytic model of galaxy formation and a binary population synthesis model. We calculate the angular power spectra ${\mathrm{C}}_{\ell }$ at multipole moments $\ell$, expressed as ${\text{log}}_{10}[\ell (\ell +1){\mathrm{C}}_{\ell }/(2\ddot{I}€)]$, based on the skymaps of the overdensity $\hat{I}{´}_{\mathrm{GW}}$ in the anisotropic SGWB. The spectra for all three source types exhibit an approximately linear increase with ${\text{log}}_{10}\ell$ at higher $\ell$ (e.g., $\ell >\sim 30-300$) in seven catalogues, with a characteristic slope of $\sim 2$. The spectra of seven catalogues exhibit considerable variations, arising from fluctuations in spatial distribution, primarily in the radial distribution, of nearby sources (e.g., $<50$ Mpc/h). After subtracting these nearby sources, the variations become much smaller and the spectra for the three source types become closely aligned (within discrepancies of a factor of $\sim 2$ across $\ell =1-1000$ for all catalogues). We also find that including further sources results in a rapid decrease in the anisotropy.

13 pages 5 figures