Constraints on ultra-low-frequency gravitational waves from an eccentric supermassive black hole binary

TL;DR

This paper develops a formalism to extend pulsar timing array constraints to ultra-low-frequency gravitational waves from eccentric supermassive black hole binaries, applying it to hypothetical cases including M87.

Contribution

It introduces a new waveform formalism for eccentric SMBH binaries at ultra-low frequencies and applies it to real galaxy data, expanding PTA sensitivity.

Findings

Upper limit on SMBH binary mass ratio at M87 is 0.16 for high eccentricity.

Waveform differences due to eccentricity are significant for ultra-low-frequency GW detection.

Formalism allows constraints on SMBH binaries beyond conventional PTA frequency range.

Abstract

Milli-second pulsars with highly stable periods can be considered as very precise clocks and can be used for pulsar timing array (PTA) which attempts to detect nanoheltz gravitational waves (GWs) directly. Main sources of nanoheltz GWs are supermassive black hole (SMBH) binaries which have sub-pc-scale orbits. On the other hand, a SMBH binary which is in an earlier phase and has pc-scale orbit emits ultra-low-frequency ($\lesssim 10^{-9}\,\mathrm{Hz}$) GWs cannot be detected with the conventional methodology of PTA. Such binaries tend to obtain high eccentricity, possibly $\sim 0.9$. In this paper, we develop a formalism for extending constraints on GW amplitudes from single sources obtained by PTA toward ultra-low frequencies considering the waveform expected from an eccentric SMBH binary. GWs from an eccentric binaries are contributed from higher harmonics and, therefore, have a different waveform those from a circular binary. Furthermore, we apply our formalism to several hypothetical SMBH binaries at the center of nearby galaxies, including M87, using the constraints from NANOGrav's 11-year data set. For a hypothetical SMBH binary at the center of M87, the typical upper limit on the mass ratio is $0.16$ for eccentricity of $0.9$ and semi-major axis of $a=1~\mathrm{pc}$, assuming the binary phase to be the pericenter.