Probing the Spin-Induced Quadrupole Moment of Massive Black Holes with the Inspiral of Binary Black Holes (2401.12066v2)

Abstract: One of the most important sources for space-borne gravitational wave detectors such as TianQin and LISA, is the merger of massivie black hole binaries. By analyzing the inspiral signals, we can probe the characteristics of massive black holes, including the spin-induced multipole moments. By verifying the relation among mass, spin, and quadrupole moment, the no-hair theorem can be tested. In this work, we analyed the capability of probing the spin-induced quadrupole moment with the inspiral signal of massive black hole binaries using space-borne gravitational wave detectors. Using the Fisher information matrix, we find that the deviation of the quadrupole moment can be constrained to the level of $10^{-1}$, and events with higher mass ratios will provide a better constraint. We also find that the late inspiral part will dominate the result of parameter estimation. The results of Bayesian analysis indicate that the capability will be significantly enhanced by considering higher modes. We also calculate the Bayes factor, and the results indicate that the model of a black hole and a Boson star can be distinguished without a doubt.