Anisotropy of Nanohertz Gravitational Wave Background and Individual Sources from Supermassive Binary Black Holes: Probe of Cosmic Large Scale Structure

Several pulsar timing array (PTA) groups have recently claimed the detection of nanohertz gravitational wave (GW) background, but the origin of this 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 numerical cosmology simulation, we generate mock SMBBHs within the observable universe and treat them as PTA band GW sources. We present their statistical properties, and analyze the isotropic and anisotropic characteristics of the gravitational wave background (GWB) signal they produce. Specifically, we derive the characteristic amplitude and spectrum of the GWB signal, and calculate the angular power spectrum for both GW strains/energy density and the position distribution of GW sources. We predict that the angular power spectrum of GWB energy density has $C_1/C_0\approx0.40\pm0.32$, and $C_l/C_0\simeq \frac{1}{2(2l+1)}$ (for $l>1$). Furthermore, for the upcoming Chinese Pulsar Timing Array (CPTA) and Square Kilometre Array (SKA) PTA, we predict the spatial distribution, numbers and signal-to-noise ratio (SNR) distribution of individual GW sources that may be detected with SNR>8, and study the anisotropy property in the spatial distribution of these individual GW sources.