Unveiling the solution to the final-parsec problem by combining milli-Hertz gravitational-wave observation and AGN survey

TL;DR

This paper proposes a statistical method to test the correlation between massive black hole binaries and active galactic nuclei using gravitational-wave observations, aiming to address the final-parsec problem.

Contribution

It introduces a novel statistical approach to identify MBHB-AGN correlations with gravitational-wave data, enhancing understanding of black hole merger environments.

Findings

Detecting one MBHB at z<0.5 can distinguish merger scenarios.

Future GW detectors and surveys can test MBHB-AGN correlation up to z~2.

Constraints can help resolve the final-parsec problem.

Abstract

Massive black hole binaries (MBHBs) could be the loudest gravitational-wave (GW) sources in milli-Hertz (mHz) GW band, but their dynamical evolution may stall when the black holes reach the innermost parsec of a galaxy. Such a "final-parsec problem" could be solved if MBHB forms in a gas-rich environment, such as an active galactic nucleus (AGN), but other solutions not involving AGNs also exist. Testing the correlation between these mHz GW sources and AGNs is difficult in real observation because AGNs are ubiquitous. To overcome this difficult, we use a statistical method, first designed to constrain the host galaxies of stellar-mass binary black holes, to search for a MBHB-AGN correlation in different astrophysical scenarios. We find that by detecting only one MBHB at $z \lesssim 0.5$, a mHz GW detector, such as the Laser Interferometer Space Antenna (LISA), can already distinguish different merger scenarios thanks to the precise localization of the source. Future detector networks and deeper AGNs surveys can further testify the MBHB-AGN correlation up to a redshift of $z\sim 2$ even if only a small fraction of MBHBs merge inside AGNs. These constraints will help settle the long-standing debate on the possible solutions to the final-parsec problem.