Detecting Eccentric Supermassive Black Hole Binaries With Pulsar Timing Arrays: Resolvable Source Strategies

Abstract

The couplings between supermassive black hole binaries (SMBHBs) and their environments within galactic nuclei have been well studied as part of the search for solutions to the final parsec problem. The scattering of stars by the binary or the interaction with a circumbinary disk may efficiently drive the system to sub-parsec separations, allowing the binary to enter a regime where the emission of gravitational waves can drive it to merger within a Hubble time. However, these interactions can also affect the orbital parameters of the binary. In particular, they may drive an increase in binary eccentricity which survives until the system's gravitational-wave (GW) signal enters the pulsar-timing array (PTA) band. Therefore, if we can measure the eccentricity from observed signals, we can potentially deduce some of the properties of the binary environment. To this end, we build on previous techniques to present a general Bayesian pipeline with which we can detect and estimate the parameters of an eccentric SMBHB system with PTAs. Additionally, we generalize the PTA  e -statistic to eccentric systems, and show that both this statistic and the Bayesian pipeline are robust when studying circular or arbitrarily eccentric systems. We explore how eccentricity influences the detection prospects of single GW sources, as well as the detection penalty incurred by employing a circular waveform template to search for eccentric signals, and conclude by identifying important avenues for future study.

Amplification of superkicks in black-hole binaries through orbital eccentricity

“…For the case of supermassive BH binaries, eccentric sources are commonly invoked to explain current PTA limits. Orbital eccentricity shifts some of the emitted power to higher frequencies, causing a turnover in the predicted spectrum [78][79][80][81]. The presence of this feature allows current astrophysical formation models calibrated on galaxy counts to more easily accommodate the measured upper limits.…”

Detection and localization of continuous gravitational waves with pulsar timing arrays: the role of pulsar terms

“…In the former case, a successful search can provide estimation of the binary chirp mass (Taylor et al 2014). Data analysis techniques for eccentric binaries have been developed in Zhu et al (2015) and Taylor et al (2016), both of which consider only the Earth terms. How the sky localization is biased in such searches and how to correct for/remove such a bias should be addressed in future studies.…”

“…The Earth term is coherent for all pulsars being monitored in the array, while the phase of the pulsar term depends on pulsar distance which is poorly known for most pulsars. A majority of previous work on searches for GWs from individual SMBHBs treated pulsar terms as a source of self-noise and thus ignored them in the search and parameter estimation algorithms (e.g., Sesana & Vecchio 2010;Babak & Sesana 2012;Petiteau et al 2013;Zhu et al 2015;Madison et al 2016;Taylor et al 2016). However, a coherent inclusion of pulsar terms has been suggested to be critical for improving detection probability and sky localization (Lee et al 2011;Boyle & Pen 2012).…”

Synthetic model of the gravitational wave background from evolving binary compact objects

“…The signal from inspiraling SMBH which take longer than the age of the Universe to merge falls in the frequency range accesible with PTA (10 −9 − 10 −8 Hz), while merging SMBH will be observable with eLISA. The evolution of the eccentricity of these systems may be affected by their environment and some of the SMBH binaries may enter the observable frequency band while still retaining a non-negligible eccentricity which will have an imprint on the GW background [29,33,56]. These questions can be treated within the formalism described in this paper and we plan to study them in future work.…”