Unveiling the architecture of a pulsar - binary black-hole triple system with pulsar arrival time analysis

TL;DR

This paper proposes a method to detect inner binary black holes in pulsar triple systems using pulsar timing analysis, enabling the identification of systems with very short orbital periods that are relevant for gravitational wave detection.

Contribution

It introduces a novel pulsar timing technique to identify and characterize inner binary black holes in triple systems, including those with sub-hour orbital periods.

Findings

Inner BBHs can be identified via short-term Rømer delay modulation.

Orbital parameters can be determined with relativistic time delay measurements.

Method applicable to BBHs with orbital periods from hours to sub-seconds.

Abstract

A large number of binary black holes (BBHs) with longer orbital periods are supposed to exist as progenitors of BBH mergers recently discovered with gravitational wave (GW) detectors. In our previous papers, we proposed to search for such BBHs in triple systems through the radial-velocity modulation of the tertiary orbiting star. If the tertiary is a pulsar, high precision and cadence observations of its arrival time enable an unambiguous characterization of the pulsar -- BBH triples located at several kpc, which are inaccessible with the radial velocity of stars. The present paper shows that such inner BBHs can be identified through the short-term R{\o}mer delay modulation, on the order of $10$ msec for our fiducial case, a triple consisting of $20~M_\odot$ BBH and $1.4~M_\odot$ pulsar with $P_\mathrm{in}=10$ days and $P_\mathrm{out}=100$ days. If the relativistic time delays are measured as well, one can determine basically all the orbital parameters of the triple. For instance, this method is applicable to inner BBHs of down to $\sim 1$ hr orbital periods if the orbital period of the tertiary pulsar is around several days. Inner BBHs with $\lesssim 1$ hr orbital period emit the GW detectable by future space-based GW missions including LISA, DECIGO, and BBO, and very short inner BBHs with sub-second orbital period can be even probed by the existing ground-based GW detectors. Therefore, our proposed methodology provides a complementary technique to search for inner BBHs in triples, if exist at all, in the near future.