Extreme mass ratio inspirals on the equatorial plane in the adiabatic order

TL;DR

This paper models gravitational waves from stellar-mass objects inspiraling into supermassive spinning black holes on the equatorial plane, analyzing how parameters like black hole spin, mass, and eccentricity affect the signal-to-noise ratio for LISA observations.

Contribution

It introduces an interpolation method for adiabatic orbital evolution and evaluates gravitational wave signals, including higher multipole modes, for extreme mass ratio inspirals.

Findings

SNR increases with black hole spin and compact object mass for M > 10^6 M_sun.

SNR peaks around M ≈ 10^6 M_sun.

Higher initial eccentricity boosts SNR for M=10^6 M_sun.

Abstract

We compute gravitational waves from inspiraling stellar-mass compact objects on the equatorial plane of a massive spinning black hole (BH). Our inspiral orbits are computed by taking into account the adiabatic change of orbital parameters due to gravitational radiation in the lowest order in mass ratio. We employ an interpolation method to compute the adiabatic change at arbitrary points inside the region of orbital parameter space computed in advance. Using the obtained inspiral orbits and associated gravitational waves, we compute power spectra of gravitational waves and the signal-to-noise ratio (SNR) for several values of the BH spin, the masses of the binary, and the initial orbital eccentricity during a hypothetical three-yrs LISA observation before final plunge. We find that (i) the SNR increases as the BH spin and the mass of the compact object increase for the BH mass $M \agt 10^6M_\odot$, (ii) the SNR has a maximum for $M \approx 10^6M_\odot$, and (iii) the SNR increases as the initial eccentricity increases for $M=10^6M_\odot$. We also show that incorporating the contribution from the higher multipole modes of gravitational waves is crucial for enhancing the detection rate.