Science with the TianQin Observatory: Preliminary Results on Testing the No-hair Theorem with EMRI

TL;DR

This paper evaluates TianQin's capability to test the no-hair theorem by measuring the quadrupole moment of massive black holes through EMRI gravitational wave signals, demonstrating high measurement precision under various scenarios.

Contribution

It provides the first detailed analysis of TianQin's potential to constrain the black hole quadrupole moment using EMRI signals with quadrupole corrections.

Findings

TianQin can measure the quadrupole moment with an accuracy of 10^{-5}.

Waveform cutoff choice significantly affects measurement accuracy.

Simultaneous observations with other detectors like LISA enhance testing capabilities.

Abstract

Constituted with a massive black hole and a stellar mass compact object, Extreme Mass Ratio Inspiral (EMRI) events hold unique opportunity for the study of massive black holes, such as by measuring and checking the relations among the mass, spin and quadrupole moment of a massive black hole, putting the no-hair theorem to test. TianQin is a planned space-based gravitational wave observatory and EMRI is one of its main types of sources. It is important to estimate the capacity of TianQin on testing the no-hair theorem with EMRIs. In this work, we use the analytic kludge waveform with quadrupole moment corrections and study how the quadrupole moment can be constrained with TianQin. We find that TianQin can measure the dimensionless quadrupole moment parameter with accuracy to the level of $10^{-5}$ under suitable scenarios. The choice of the waveform cutoff is found to have significant effect on the result: if the Schwarzschild cutoff is used, the accuracy depends strongly on the mass of the massive black hole, while the spin has negligible impact; if the Kerr cutoff is used, however, the dependence on the spin is more significant. We have also analyzed the cases when TianQin is observing simultaneously with other detectors such as LISA.