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

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-year Laser Interferometer Space Antenna 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 $M\ensuremath{\gtrsim}{10}^{6}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, (ii) the SNR has a maximum for $M\ensuremath{\approx}{10}^{6}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, and (iii) the SNR increases as the initial eccentricity increases for $M={10}^{6}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$. We also show that incorporating the contribution from the higher multipole modes of gravitational waves is crucial for enhancing the detection rate.