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Transition-to-plunge self-force waveforms with a spinning primary

Loïc Honet, Lorenzo Küchler, Adam Pound, Geoffrey Compère

Abstract

With the upcoming third-generation gravitational-wave detectors comes the need to build complete, faithful, and fast waveform models for asymmetric-mass-ratio compact binaries. Most efforts within the self-force community have focused on modeling these binaries' inspiral regime, but for ground-based detectors the systems' final merger can represent the dominant part of the signal. Recent work by three of us has extended the multiscale self-force framework through the transition-to-plunge and merger-ringdown regimes for nonspinning binaries. In this paper, we generalize the next-to-next-to-leading-order transition-to-plunge waveform model to include the spin of the primary black hole. We also improve the construction of composite inspiral-transition waveform models by performing a change of variables on the binary's mechanical phase space during the transition to plunge. We provide detailed discussions of our numerical implementation and comparisons with numerical relativity simulations.

Transition-to-plunge self-force waveforms with a spinning primary

Abstract

With the upcoming third-generation gravitational-wave detectors comes the need to build complete, faithful, and fast waveform models for asymmetric-mass-ratio compact binaries. Most efforts within the self-force community have focused on modeling these binaries' inspiral regime, but for ground-based detectors the systems' final merger can represent the dominant part of the signal. Recent work by three of us has extended the multiscale self-force framework through the transition-to-plunge and merger-ringdown regimes for nonspinning binaries. In this paper, we generalize the next-to-next-to-leading-order transition-to-plunge waveform model to include the spin of the primary black hole. We also improve the construction of composite inspiral-transition waveform models by performing a change of variables on the binary's mechanical phase space during the transition to plunge. We provide detailed discussions of our numerical implementation and comparisons with numerical relativity simulations.
Paper Structure (29 sections, 150 equations, 9 figures, 1 table)

This paper contains 29 sections, 150 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction and outline
  2. Forced motion, circular geodesics, and field equations
  3. Setup and conventions
  4. Orbital motion
  5. Study of circular geodesics
  6. Einstein field equations
  7. The inspiral's post-adiabatic expansion
  8. Perturbative expansion
  9. Re-expansion in the symmetric mass ratio
  10. The transition-to-plunge expansion
  11. Perturbative expansion
  12. Re-expansion in the symmetric mass ratio
  13. Asymptotically matching the inspiral with the transition
  14. Match of the mode amplitudes and self-force
  15. Match of the forcing functions of the orbital frequency
  16. ...and 14 more sections

Figures (9)

  • Figure 1: Left panel: the function $D(\Omega; \mathring\chi)$ in Eq. \ref{['eq:D']} plotted in terms of the orbital frequency $\Omega$ and the primary's spin $\mathring\chi$. The blue level set corresponds to $D(\Omega_\star(\mathring\chi); \mathring\chi)=0$, where $\Omega_\star(\mathring\chi)$ is the ISCO frequency. The region below the blue curve corresponds to $D>0$ (inspiral), while the region above it corresponds to $D<0$ (plunge). Right panel: phase diagram of quasicircular motion around a primary Kerr black hole of spin $\mathring\chi$. The dashed blue curve corresponds to the ISCO radius $r_\star(\mathring\chi)$. Above that curve, circular orbits are stable, while below it they are unstable. We qualitatively depict the region of validity of the inspiral (green region above the ISCO), the transition to plunge (orange band around the ISCO) as well as the plunge (red region below the ISCO). The gray region corresponds to the primary black hole's interior. All quantities have been adimensionalized using the primary mass $\mathring M$. The numbers in square brackets next to a quantity correspond to its mass dimension as defined in Appendix \ref{['app:massdimension']}.
  • Figure 2: Normalized 0PLT and 2PLT forcing functions. The solution to the normalized Painlevé equation \ref{['eq:y0PLT']} with boundary condition \ref{['0PLTnormalizedmatchingcondition']} is shown in black. The solutions $z_i$ to the sourced linearized Painlevé equations \ref{['eq:zi2PLT']} with boundary solutions \ref{['2PLTASmatch']} are shown in yellow, green, and blue, respectively. Here $u=0$ corresponds to the location of the ISCO, while $u<0$ ($u>0$) corresponds to an orbital frequency below (above) the ISCO frequency.
  • Figure 3: Values of the coefficients $\alpha^{1/4}$ and $\beta$, as defined in Eqs. \ref{['alphabetadef']}, as a function of the primary black hole's spin ${\mathring\chi}$.
  • Figure 4: Dependence on the primary's spin ${\mathring\chi}$ of the coefficients $\gamma(\Omega_\star)$, $\eta(\Omega_\star)$, and $\tau(\Omega_\star)$ defined in Eqs. \ref{['gammaetataudef']}.
  • Figure 5: Solid curves: relative error between the 0PA-2PLT composite \ref{['0PA2PLTcomposite']} and the 0PA forcing functions \ref{['FOmega0PA']} when the two bodies are separated by twice the ISCO radius, $2r_\star(\mathring\chi)$, for different values of the mass ratio. Dashed curves: the same quantity but using the re-expanded 0PA-2PLT forcing function \ref{['eq:0PA2PLTcomposite_reexp']}.
  • ...and 4 more figures