Importance of including higher signal harmonics in the modeling of extreme mass-ratio inspirals

TL;DR

This paper demonstrates that including higher signal harmonics in EMRI waveform models significantly improves parameter estimation accuracy for LISA detections, especially for extrinsic parameters, while having minimal impact on intrinsic parameters.

Contribution

It introduces a relativistic flux-based adiabatic waveform model with higher harmonics and quantifies their effect on parameter estimation errors for EMRIs.

Findings

Higher harmonics reduce errors in extrinsic parameters like inclination and distance.

Impact of higher harmonics on intrinsic parameters is negligible across all inclination angles.

Results are consistent regardless of EMRI system mass or spin.

Abstract

Extreme mass-ratio inspirals (EMRIs) are the most potential sources detectable by the Laser Interferometer Space Antenna (LISA). To analyze the influence of higher harmonics on parameter estimation for EMRIs efficiently, we use the waveform model that the phase trajectories are relativistic flux-based adiabatic trajectories and the waveforms are constructed by the augmented analytic kludge method. We perform a Fisher-matrix error analysis of the EMRI parameters using signals taking into account the motion of the LISA constellation and higher harmonics of gravitational waves. Our results demonstrate that including higher harmonics greatly reduces the errors on the exterior parameters such as inclination angle $\iota$, the luminosity distance $d_L$, the polarization angle $\psi$, and the initial phase $\Phi_0$, except for source localization $\Delta \Omega$ when EMRIs face us. However, the influence of higher harmonics on parameters $(\iota,d_L,\psi,\Phi_0)$ can be negligible when the inclination angle is above $1.0$. For intrinsic parameters such as the spin of central black and the masses of binaries, the influence of higher harmonics can be negligible for any inclination angle. Our findings are independent of the mass or spin of the EMRI system.