Transverse Doppler effect and parameter estimation of LISA three-body systems

TL;DR

This paper investigates how relativistic three-body effects, especially the transverse Doppler effect, influence gravitational wave signals from binary black holes orbiting supermassive black holes, enabling precise parameter estimation of the system.

Contribution

It introduces a second-order Doppler effect analysis that breaks degeneracies in waveform modeling, improving parameter estimation accuracy for LISA-detectable systems.

Findings

Can measure SMBH mass with better than 30% accuracy for systems with orbital periods under 100 years.

Second-order Doppler effects help break degeneracies in waveform parameters.

Parameter estimation improves significantly with the inclusion of relativistic three-body effects.

Abstract

Some binary black hole systems potentially observable in LISA could be in orbit around a supermassive black hole (SMBH). The imprint of relativistic three-body effects on the waveform of the binary can be used to estimate all the parameters of the triple system, in particular the mass of the SMBH. We determine the phase shift in the waveform due to the Doppler effect of the SMBH up to second order in velocity, which breaks a well-known exact degeneracy of the lowest-order Doppler effect between the mass of the SMBH and its inclination. We perform several parameter estimations for LISA signals including this additional dephasing in the wave, showing that one can determine accurately all parameters of the three-body system. Our results indicate that one can measure the mass of a $10^8\,$M$_{\odot}$ SMBH with an accuracy better than $\sim 30\%$ (resp. $\sim 15\%$) by monitoring the waveform of a binary system whose period around the SMBH is less 100 yr (resp. 20 yr).