Repeated faint quasinormal bursts in extreme-mass-ratio inspiral waveforms: Evidence from frequency-domain scalar self-force calculations on generic Kerr orbits

Abstract

We report development of a code to calculate the scalar self-force on a scalar-charged particle moving on generic bound orbits in the Kerr spacetime. The scalar self-force model allows rapid development of computational techniques relevant to generic gravitational extreme-mass-ratio inspirals (EMRIs). Our frequency-domain calculations are made with arbitrary numerical precision code written in Mathematica. We extend spectral source integration techniques to the Kerr spacetime, increasing computational efficiency. We model orbits with nearly arbitrary inclinations 0 ≤ ι < π/2 and eccentricities up to e 0.8. This effort extends earlier work by Warburton and Barack where motion was restricted to the equatorial plane or to inclined spherical orbits. Consistent with a recent discovery by Thornburg and Wardell [1] in time-domain calculations, we observe self-force oscillations during the radially-outbound portion of highly eccentric orbits around a rapidly rotating black hole. As noted previously, these oscillations reflect coupling into the self-force by quasinormal modes excited during pericenter passage. Our results confirm the effect with a frequency-domain code. More importantly, we find that quasinormal bursts (QNBs) appear directly in the waveform following each periastron passage. These faint bursts are shown to be a superposition of the leastdamped overtone (i.e., fundamental) of at least four (l = m ≤ 4) quasinormal modes. Our results suggest that QNBs should appear in gravitational waveforms, and thus provide a gauge-invariant signal. Potentially observable in high signal-to-noise ratio EMRIs, QNBs would provide high-frequency components to the parameter estimation problem that would complement low-frequency elements of the waveform.

Excitation of Kerr quasinormal modes in extreme-mass-ratio inspirals

“…Figures 6-8 show the fitted complex frequencies and their Monte-Carlo error estimates, compared to Kerr QNM frequencies calculated by Berti, Cardoso, and Starinets [66,67]. 10 In each case the fitted frequencies agree with the calculated QNM frequencies, lending further support to the identification of wiggles with QNMs (more precisely, QNMs sampled at the observation points).…”

“…More recently Refs. [8][9][10] of wiggles, demonstrated that wiggles' complex frequencies agree with known Kerr quasinormal-mode (QNM) frequencies, and concluded that wiggles are in fact "just" a sampling at the measurement point(s) of Kerr QNMs excited by the particle.…”

“…Thornburg [8,9] has presented fits of damped-sinusoid models to these wiggles for a range of Kerr spins and particle orbits, found close agreement of the model complex-frequencies with those of known Kerr QNMs, and argued that this agreement shows that wiggles are, in fact, caused by Kerr QNMs excited by the particle's close periapsis passage. Nasipak, Osburn, and Evans [10] calculated the scalarfield self-force and the radiated field at J + for eccentric inclined particle orbits in Kerr spacetime. For one particular (equatorial) orbit configuration they confirmed TW's finding of wiggles in the self-force and also found wiggles in the radiated scalar field at J + , fitting these to a superposition of = m = 1, = m = 2, = m = 3, and = m = 4 Kerr quasinormal modes (QNMs).…”

Scalar self-force for high spin black holes

“…We therefore conjecture that it will remain small throughout the inspiral. Note that even in the case of an excitation of a quasi-normal mode leading to a gravitational wave burst [13], the difference between the actual QNMs (3.21) and the poles associated to the Dirichlet boundary condition will also exhibit the typical suppression ∼ k 2 such that we still expect a small correction. Parametrically in the high spin limit, the exact result is (3.23).…”

“…Progress in gravitational self-force calculations has typically been achieved by first starting with a scalar analogy of the full gravitational problem [13] and with (quasi-)circular orbits [14] around static central black holes [15], and then progressively working to the actual gravitational case, to more general orbits and to rotating black holes. However, simplifications also occur for black holes rotating close to extremality.…”