Anisotropy of Nanohertz Gravitational Wave Background and Source Clustering from Supermassive Binary Black Holes Based on Cosmological Simulation

Several pulsar timing array (PTA) groups have recently claimed the detection of nanohertz gravitational wave background (GWB), but the origin of this gravitational wave (GW) signal remains unclear. Nanohertz GWs generated by supermassive binary black holes (SMBBHs) are one of the most important GW sources in the PTA band. Utilizing data from cosmological simulation, we generate multiple realizations of a mock observable universe that self-consistently incorporates the cosmic large-scale structure, enabling a robust statistical analysis of SMBBH populations and their GW signatures. We systematically investigate the merger event distributions and both the isotropic and anisotropic properties of the resulting GWB signals under different hardening timescales. Specifically, we calculate the characteristic amplitude of the GWB signal, and the angular power spectrum for both the total energy density and energy density in different frequency bins accounting for cosmic variance through different realizations. We also study the clustering pattern of the positional distribution of SMBBHs to examine whether they can reproduce the large-scale structure of galaxies. Furthermore, for the upcoming Chinese Pulsar Timing Array (CPTA) and Square Kilometre Array (SKA)-PTA, we predict the numbers and signal-to-noise ratio (SNR) distributions of resolvable individual GW sources that may be detected with SNR$>$8. We finally investigated the impact of weak lensing effects and found that their influence on the basic characteristics of the GWB signal and individual sources is rather limited.