Extreme mass-ratio inspirals in the effective-one-body approach: Quasicircular,equatorial orbits around a spinning black holeNicola´s Yunes,1,2,3Alessandra Buonanno,4Scott A. Hughes,2Yi Pan,4Enrico Barausse,4M. Coleman Miller,5and William Throwe21Department of Physics, Princeton University, Princeton, New Jersey 08544, USA2Department of Physics and MIT Kavli Institute, MIT,77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA3Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138, USA4Maryland Center for Fundamental Physics & Joint Space-Science Institute, Department of Physics,University of Maryland, College Park, Maryland 20742, USA5Maryland Astronomy Center for Theory and Computation & Joint Space-Science Institute, Department of Astronomy,University of Maryland, College Park, Maryland 20742, USA(Received 29 September 2010; published 24 February 2011)We construct effective-one-body waveform models suitable for data analysis with the LaserInterferometer Space Antenna for extreme mass-ratio inspirals in quasicircular, equatorial orbits abouta spinning supermassive black hole. The accuracy of our model is established through comparisonsagainst frequency-domain, Teukolsky-based waveforms in the radiative approximation. The calibration ofeight high-order post-Newtonian parameters in the energy flux suffices to obtain a phase and fractionalamplitude agreement of better than 1 rad and 1%, respectively, over a period between 2 and 6 monthsdepending on the system considered. This agreement translates into matches higher than 97% over aperiod between 4 and 9 months, depending on the system. Better agreements can be obtained if a largernumber of calibration parameters are included. Higher-order mass-ratio terms in the effective-one-bodyHamiltonian and radiation reaction introduce phase corrections of at most 30 rad in a 1 yr evolution. Thesecorrections are usually 1 order of magnitude larger than those introduced by the spin of the small object ina 1 yr evolution. These results suggest that the effective-one-body approach for extreme mass-ratioinspirals is a good compromise between accuracy and computational price for Laser Interferometer SpaceAntenna data-analysis purposes.DOI: 10.1103/PhysRevD.83.044044 PACS numbers: 04.25.Nx, 04.30.Db, 04.30.w, 04.30.TvI. INTRODUCTIONExtreme mass-ratio inspirals (EMRIs) are one of themost promising sources of gravitational waves (GWs)expected to be detected with the proposed LaserInterferometer Space Antenna (LISA) [1–4]. Thesesources consist of a small compact object, such as a neu-tron star or stellar-mass black hole (BH), in a close orbitaround a spinning, supermassive BH [5]. Gravitationalradiation losses cause the small object to spiral closer tothe supermassive BH and eventually merge with it. Hence,the GW signal from such events encodes information aboutstrong gravity, allowing tests of general relativity [6] and ofthe Kerr metric [7–17], as well as measurements of thespins and masses of massive BHs [18].Unfortunately, EMRIs are very weak sources of GWs attheir expected distances from us, and thus, they must beobserved over many cycles to be detectable [5]. For ex-ample, a typical EMRI at a distance of 3 Gpc wouldproduce GWs with signal-to-noise ratios (SNRs) on theorder of 10–200 depending on the observation time.Therefore, matched filtering is essential to extract EMRIsfrom LISA noise and the foreground of unresolved GWsfrom white dwarf binaries in our galaxy.Matched filtering consists of cross-correlating the datastream with a certain noise-weighted waveform template[19]. If the latter is similar to a GW event hidden in thedata, then this cross-correlation filters it out of the noise. Ofcourse, for matched filtering to be effective, one mustconstruct accurate template filters. Otherwise, real eventscan be missed, or if an event is detected, parameter esti-mation can be strongly biased [20]. The construction ofaccurate EMRI waveforms is extremely difficult due to thelong duration of the signal and the strong-field nature of theorbits. A one-year EMRI signal contains millions of radi-ans in phase information. To avoid significant dephasing,its waveform modeling must be accurate to at least one partin 105–106[21].Such an exquisite accuracy requirement is complicatedfurther by the strong-field nature of the orbit. An EMRI canreach orbital velocities of two-thirds the speed of light andorbital separations as small as a few times the mass of thesupermassive companion. This automatically implies thatstandard, post-Newtonian (PN) Taylor-expanded wave-forms fail to model such EMRI orbits [22]. PN theoryrelies on the assumptions that all orbital velocities aremuch smaller than the speed of light and that all objectsare at separations much larger than the total mass of thePHYSICAL REVIEW D 83, 044044 (2011)1550-7998=2011=83(4) =044044(21) 044044-1 Ó 2011 American Physical Societysystem [23]. A better approximation scheme to modelEMRIs is BH perturbation theory, where one only assumesthat the mass ratio of the system is much less than unity[24]. This is clearly the case for EMRIs, as the mass ratio isin the range 104–106. Perturbation theory, however, iscomputationally and analytically expensive. Only recentlyhave generic orbits been computed around a nonspinningBH to linear order in the mass ratio [ 25–27], and it isunlikely that these will be directly used for EMRI dataanalysis [4].EMRIs involve complicated inspiral analysis, but unlikecomparable-mass coalescences, the merger and ringdownphase can be completely neglected. To see this, note thatthe instantaneous amplitude of the waves from a binaryscales as , where  ¼ m1m2=M is the reduced mass, M isthe total mass and m1;2are the component masses. Theinspiral lasts for a time 1= and releases an energy flux2=  . In contrast, the merger and ringdown last fora time M (independent of ), and thus, release an energyflux 2. For an EMRI,  M and the inspiral clearlydominates the signal. Based on this argument, we neglectthe merger and ringdown, focusing on the inspiral for ouranalysis.A. Summary of previous workThe modeling of EMRIs has been attempted in the pastwith various degrees of success. One approach is to com-pute the self-field of the test particle to understand how itmodifies the orbital trajectory. This task, however, is quiteinvolved, both theoretically and computationally, as