Dissecting the nanoHz gravitational wave sky: frequency-correlated anisotropy induced by eccentric supermassive black hole binaries

Revealing the nature of the nanoHz gravitational wave (GW) signal recently reported by Pulsar Timing Arrays (PTAs) collaborations around the world is the next goal of low-frequency GW astronomy. The signal likely originates from the incoherent superposition of GWs emitted by a cosmological population of supermassive black hole binaries (SMBHBs). Those binaries can be highly eccentric and/or strongly coupled to their nuclear environment, resulting in an attenuation of the overall GW signal at low frequencies. In this paper, we propose to use the correlation properties of the distributed GW power in the sky across the frequency spectrum as a smoking gun for eccentric SMBHBs thus allowing to break the spectral degeneracy between eccentricity and environmental effect. The simple underlying idea is that, contrary to circular binaries, eccentric ones emit a broadband spectrum thus resulting in similar sky maps at different frequencies. We first demonstrate the applicability of this simple concept on sky maps constructed directly from the theoretical sky distribution of the GWB power induced by realistic populations of SMBHBs. We then demonstrate the viability of this analysis on simulated SKA-like PTA data. By statistically comparing sky maps reconstructed from hundreds injected circular and highly eccentric SMBHB populations, we find that eccentricity can be detected at $3σ$ in more than $50\%$ of cases.