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

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 $\text{log}_{10} [\ell(\ell+1)\mathrm{C}_\ell/(2\pi)]$, based on the skymaps of the overdensity $\delta_\mathrm{GW}$ 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.