Statistics of supermassive black hole gravitational wave background anisotropy

We investigated the statistical properties of the anisotropy in the gravitational wave (GW) background originating from supermassive black hole (SMBH) binaries. Considering scenarios that include environmental effects and eccentricities of the SMBH binaries, we derived the distribution of the GW anisotropy power spectrum coefficients, C l ≥ 1 / C 0 . Although the mean of C l ≥ 1 / C 0 is the same for all multipoles, we show that their distributions vary, with the low l distributions being the widest. This study finds a strong correlation between spectral fluctuations and anisotropy in the GW signal and shows that the GW anisotropy can break the degeneracy between scenarios that include environmental effects or eccentric binaries. We find that existing NANOGrav constraints on GW anisotropy begin to constrain SMBH scenarios with strong environmental effects.