Detection of eccentric supermassive black hole binaries with pulsar timing arrays: Signal-to-noise ratio calculations

TL;DR

This paper analyzes how eccentric supermassive black hole binaries affect pulsar timing array signals, providing analytical tools to evaluate detection prospects and the impact on stochastic gravitational-wave background measurements.

Contribution

It extends existing models to include eccentricity effects, offering analytical expressions for SNR calculations and background spectra in pulsar timing array observations.

Findings

Eccentric binaries can increase or decrease SNR depending on harmonic frequency.

Eccentricity suppresses the gravitational-wave background in the PTA band.

Analytical formulas enable rapid SNR and background spectrum estimations.

Abstract

We present a detailed analysis of the expected signal-to-noise ratios of supermassive black hole binaries on eccentric orbits observed by pulsar timing arrays. We derive several analytical relations that extend the results of Peters and Mathews [Phys. Rev. D 131, 435 (1963)] to quantify the impact of eccentricity in the detection of single resolvable binaries in the pulsar timing array band. We present ready-to-use expressions to compute the increase/loss in signal-to-noise ratio of eccentric single resolvable sources whose dominant harmonic is located in the low/high frequency sensitivity regime of pulsar timing arrays. Building upon the work of Phinney (arXiv:astro-ph/0108028) and Enoki and Nagashima [Prog. Theor. Phys. 117, 241 (2007)], we present an analytical framework that enables the construction of rapid spectra for a stochastic gravitational-wave background generated by a cosmological population of eccentric sources. We confirm previous findings which indicate that, relative to a population of quasicircular binaries, the strain of a stochastic, isotropic gravitational-wave background generated by a cosmological population of eccentric binaries will be suppressed in the frequency band of pulsar timing arrays. We quantify this effect in terms of signal-to-noise ratios in a pulsar timing array.