Multipolar analysis of spinning binaries

TL;DR

This work extends multipolar analyses of gravitational radiation to spinning black-hole binaries, examining how spin alters energy distribution across multipoles and the final remnant spin. It uses two simulation sequences, including non-spinning and spinning binaries, with high-order numerical relativity tools to benchmark against post-Newtonian predictions, including leading-order spin-orbit and spin-spin terms. The results show that incorporating spin corrections can improve PNQC frequency agreement in some cases, identify a Schwarzschild remnant at a critical initial spin near -0.842, and quantify ringdown energy fractions via EMOP while highlighting frame-dependent mode mixing in tilted-spin configurations. The findings provide benchmarks for analytical models and have practical implications for gravitational-wave data analysis and parameter estimation.

Abstract

We present a preliminary study of the multipolar structure of gravitational radiation from spinning black hole binary mergers. We consider three different spinning binary configurations: (1) one "hang-up" run, where the black holes have equal masses and large spins initially aligned with the orbital angular momentum; (2) seven "spin-flip" runs, where the holes have a mass ratio q=4, the spins are anti-aligned with the orbital angular momentum, and the initial Kerr parameters of the holes j_1=j_2=j_i are fine-tuned to produce a Schwarzschild remnant after merger; (3) three "super-kick" runs where the mass ratio q=M_1/M_2=1, 2, 4 and the spins of the two holes are initially located on the orbital plane, pointing in opposite directions. For all of these simulations we compute the multipolar energy distribution and the Kerr parameter of the final hole. For the hang-up run, we show that including leading-order spin-orbit and spin-spin terms in a multipolar decomposition of the post-Newtonian waveforms improves the agreement with the numerical simulation.

Figures (3)

• Figure 1: Convergence analysis of the $(l=2,m=2)$ mode of $M_{\rm ADM}r\Psi_4$ for simulations sk1 and sk2 of Table \ref{['tab:\n models']}. The difference between the high-resolution runs has been rescaled by 1.72, as expected for sixth-order convergence.
• Figure 2: Left: Energy $E_l$ in different multipoles for the unequal-mass binaries of sequence 1 as a function of $q$ (from Berti:2007fi). Right: $E_l$ for some spinning binary configurations belonging to sequence 2, as a function of the multipole index $l$. Continuous (black) lines refer to equal-mass binaries, the dotted (red) line to a binary with $q=2$, and dashed (blue) lines to binaries with $q=4$.
• Figure 3: Convergence of the PNQC expansion. Left: non-spinning binaries; right: spinning binaries. In the right panel, thick lines estimate the PNQC frequency including the spin terms of Eq. (\ref{['c22e']}), and thin lines omit the spin terms.