# Constraints on the binary black hole nature of GW151226 and GW170608 from the measurement of spin-induced quadrupole moments

## TL;DR

This paper develops a Bayesian method to measure spin-induced quadrupole moments in gravitational wave signals, testing whether binary mergers are consistent with Kerr black holes or exotic objects, using GW151226 and GW170608 data.

## Contribution

It introduces a new Bayesian framework for testing the black hole nature of compact binaries through spin-induced quadrupole measurements, focusing on the inspiral phase.

## Key findings

- GW151226 and GW170608 are consistent with binary black hole mergers in general relativity.
- The method can constrain deviations from Kerr black holes with future data.
- Simulations show the approach's effectiveness across different binary parameters.

## Abstract

According to the "no-hair" conjecture, a Kerr black hole (BH) is completely described by its mass and spin. In particular, the spin-induced quadrupole moment of a Kerr BH with mass $m$ and dimensionless spin $\chi$ can be written as $Q=-\kappa\,m^3\chi^2$, where $\kappa_{\rm BH}=1$. Thus by measuring the spin-induced quadrupole parameter $\kappa$, we can test the binary black hole nature of compact binaries and distinguish them from binaries comprised of other exotic compact objects, as proposed in [N. V. Krishnendu et al., PRL 119, 091101 (2017)]. Here, we present a Bayesian framework to carry out this test where we measure the symmetric combination of individual spin-induced quadrupole moment parameters fixing the anti-symmetric combination to be zero. The analysis is restricted to the inspiral part of the signal as the spin-induced deformations are not modeled in the post-inspiral regime. We perform detailed simulations to investigate the applicability of this method for compact binaries of different masses and spins and also explore various degeneracies in the parameter space which can affect this test. We then apply this method to the gravitational wave events, GW151226 and GW170608 detected during the first and second observing runs of Advanced LIGO and Advanced Virgo detectors. We find the two events to be consistent with binary black hole mergers in general relativity. By combining information from several more of such events in future, this method can be used to set constraints on the black hole nature of the population of compact binaries that are detected by the Advanced LIGO and Advanced Virgo detectors.