Resolving the nano-hertz gravitational wave sky: The detectability of eccentric binaries with PTA experiments

Pulsar timing array (PTA) collaborations have reported evidence of a nano-hertz (nano-Hz) stochastic gravitational wave background (sGWB) that is compatible with an adiabatically inspiraling population of massive black hole binaries (MBHBs). Despite the large uncertainties, the relatively flat spectral slope of the recovered signal suggests a possible prominent role of MBHB dynamical coupling with the environment and/or the presence of an eccentric MBHB population. This work is aimed at studying the capabilities of future PTA experiments to detect single MBHBs under the realistic assumption that the sGWB is originated from an eccentric binary population coupled with its environment. To this end, we generalised the standard signal-to-noise ratio (S/N) and Fisher information matrix calculations used in PTA for circular MBHBs to the case of eccentric systems. We considered an ideal 10-year MeerKAT and 30-year SKA PTAs and applied our method across a wide number of simulated eccentric MBHB populations. We find that the number of resolvable MBHBs for the SKA (MeerKAT) PTA is ∼30 (4) at S/N > 5 (> 3), featuring an increasing trend for larger eccentricity values of the MBHB population. This is the result of eccentric MBHBs at ≲10−9 Hz emitting part of their power at high harmonics, thus reaching the PTA sensitivity band. Our results also indicate that resolved MBHBs do not follow the eccentricity distribution of the underlying MBHB population; instead, low eccentricity values appear to be preferred (< 0.6). Finally, the recovery of binary intrinsic properties and sky localisation do not depend on the system eccentricity, while orbital parameters such as the eccentricity and initial orbital phase show clear trends. Despite their simplified nature, our results demonstrate that SKA will enable the detection of tens of MBHBs, ushering the community into the era of precision gravitational wave astronomy at nano-Hz frequencies.