Extreme mass-ratio inspirals in the effective-one-body approach: Quasicircular, equatorial orbits around a spinning black hole

We construct effective-one-body waveform models suitable for data analysis with the Laser Interferometer Space Antenna for extreme mass-ratio inspirals in quasicircular, equatorial orbits about a spinning supermassive black hole. The accuracy of our model is established through comparisons against frequency-domain, Teukolsky-based waveforms in the radiative approximation. The calibration of eight high-order post-Newtonian parameters in the energy flux suffices to obtain a phase and fractional amplitude agreement of better than 1 rad and 1%, respectively, over a period between 2 and 6 months depending on the system considered. This agreement translates into matches higher than 97% over a period between 4 and 9 months, depending on the system. Better agreements can be obtained if a larger number of calibration parameters are included. Higher-order mass-ratio terms in the effective-one-body Hamiltonian and radiation reaction introduce phase corrections of at most 30 rad in a 1 yr evolution. These corrections are usually 1 order of magnitude larger than those introduced by the spin of the small object in a 1 yr evolution. These results suggest that the effective-one-body approach for extreme mass-ratio inspirals is a good compromise between accuracy and computational price for Laser Interferometer Space Antenna data-analysis purposes.

Figure 1

Fractional difference between PN and Teukolsky-based fluxes as a function of velocity for spins $q=(0.5,0.9)$ (top) and $q=(-0.9,-0.5,0.0)$ (bottom). The dotted curves employ the Taylor-expanded PN flux with BH absorption terms, while the dashed and solid curves use the uncalibrated and calibrated $\rho$-resummed fluxes with BH absorption terms, respectively.

Figure 2

Fractional difference between $\rho$-resummed and Teukolsky-based fluxes as a function of velocity for spins $q=(-0.9,-0.5,0.0,0.5,0.9)$. The dotted curves do not include the Taylor-expanded BH absorption contributions, while the solid lines do.

Figure 3

Absolute value of the dephasing (left) and relative, fractional amplitude difference (right) computed in the calibrated EOB model and the Teukolsky-based waveforms for the dominant $(\ell ,m)=(2,2)$ mode. Different curves correspond to different background spin values.

Figure 4

Fractional difference between the calibrated $\rho$-resummed and Teukolsky-based fluxes for spins $q=(-0.9,-0.5,0.0,0.5,0.9)$ as a function of velocity. We plot here only the range of velocities sampled by Sys. I.

Figure 5

Absolute value of the dephasing computed for the dominant mode in different PN models and the Teukolsky-based waveforms. Different curve colors/shades correspond to different background spin values, while different curve types correspond to different PN models.

Figure 6

Absolute value of the dephasing (left) and relative, fractional amplitude difference (right) computed in the calibrated EOB model and the Teukolsky-based waveforms. The solid curve corresponds to the dominant (2, 2) mode, while the dashed curve is for the (3, 3) mode and the dotted curve for the (4, 4) mode. Different curves stand for different background spins.

Figure 7

Relative fraction between the squared of the SNR computed with only the $(\ell ,m)$ mode and that computed with all $(\ell ,m)$ modes. The lines connecting points are only meant to group points with $\ell =m$ (dotted line), $\ell =m+1$ (dashed line), and $\ell =m+2$ (dot-dashed line).

Figure 8

Mismatch between Teukolsky and EOB waveforms as a function of waveform duration for Systems I and II and a background spin of $q=0.9$.