Statistics of supermassive black hole gravitational wave background anisotropy

¹ Keemilise ja Bioloogilise Füüsika Instituut Rävala pst. 10 10143 Tallinn, Estonia
² Department of Cybernetics, Tallinn University of Technology Akadeemia tee 21 12618 Tallinn, Estonia
³ Dipartimento di Fisica e Astronomia, Università degli Studi di Padova Via Marzolo 8 35131 Padova, Italy
⁴ Istituto Nazionale di Fisica Nucleare, Sezione di Padova Via Marzolo 8 35131 Padova, Italy

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Received: 19 December 2024
Accepted: 9 October 2025

Abstract

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/C₀. Although the mean of C_l ≥ 1/C₀ 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.