Factorization and resummation: A new paradigm to improve gravitational wave amplitudes. III. The spinning test-body terms

Abstract

We present new calculations of the energy flux of a spinning test-body on circular orbits around a Schwarzschild black hole at linear order in the particle spin. We compute the multipolar fluxes up to = m = 6 using two independent numerical solvers of the Teukolsky equation, one in the time domain and the other in the frequency domain. After linearization in the spin of the particle, we obtain an excellent agreement (∼ 10 −5 ) between the two numerical results. The calculation of the multipolar fluxes is also performed analytically (up to = 7) using the post-Newtonian (PN) expansion of the Teukolsky equation solution; each mode is obtained at 5.5PN order beyond the corresponding leading-order contribution. From the analytical fluxes we obtain the PN-expanded analytical waveform amplitudes. These quantities are then resummed using new procedures either based on the factorization of the orbital contribution (and resumming it independently from the spin-dependent factor) or on the factorization of the tail contribution solely for odd-parity multipoles. We compare these prescriptions and the resummation procedure proposed in Pan et al. [Phys. Rev. D 83 (2011) 064003] to the numerical data. We find that the new procedures significantly improve over the existing one that, notably, is inconsistent with the numerical data for + m = odd multipoles already at low orbital frequencies. Our study suggests that the approach to waveform resummation used in current effective-one-body-based waveform models should be modified to improve its robustness and accuracy all over the binary parameter space.

Dissipation in extreme mass-ratio binaries with a spinning secondary

“…That comparison is presented in Ref. [42] where we found agreement to within the ∼ 1% level errors bars on the time-domain results.…”

“…This is a seemingly arbitrary choice in this work, but would play a more significant role when working either to higher orders in the mass-ratio, with quantities which are not zero as the mass-ratio goes to zero, with gauge-dependent quantities, or when working with the effective-one-body approach, see for example Refs. [42,55].…”

“…It is important to note that our work is not the first calculation of the radiated flux, F, for a spinning body. These have been carried out before [38][39][40][41][42] (though we perform our calculations to a much higher precision). Our work presents, for the first time, the derivation of a new balance law for spinning bodies; the first calculation of the local dissipative force; an explicit numerical check that this balance law holds; and a comparison with a post-Newtonian expansion at 5.5pN order.…”

Interpreting binary neutron star mergers: describing the binary neutron star dynamics, modelling gravitational waveforms, and analyzing detections

“…The dissipative sector of current EOB models is based on a concise factorized representation of the gravitational waveforms [69,149,153,381,394,399,413,415,513,514] that accurately accounts for the modifications to the GW propagation from the spacetime curvature due to the total mass of the binary. These GW modes are explicit algebraic expressions that depend on the instantaneous EOB dynamics.…”

Setting the cornerstone for a family of models for gravitational waves from compact binaries: The dominant harmonic for nonprecessing quasicircular black holes

“…A recently proposed framework for the factorization and resummation of the residual waveform amplitudes [94][95][96] is expected to improve the self-consistency of the testparticle waveforms and hence the self-consistency of the calibration. A discussion of different approaches to resummation and the radiation reaction in the context of effective one body models can be found in [97,98].…”