Uncovering subdominant multipole asymmetries in binary black-hole mergers

TL;DR

The paper addresses subdominant multipole asymmetries in precessing binary black-hole mergers and their impact on recoil and parameter inference. It combines NR simulations, PN predictions, and perturbative QNM analysis to characterize inspiral-plunge and merger-ringdown behavior, revealing universal scaling of antisymmetric frequencies in the inspiral and the necessity of antisymmetric ringdown amplitudes for accurate modeling. Key findings show that neglecting subdominant asymmetries can bias remnant Kick velocities by up to $\sim210\,\mathrm{km\,s^{-1}}$ and alter inferred masses and spin geometries, with high-SNR ET-like observations highlighting inclination-dependent biases. The work offers guiding principles for future waveform models that incorporate subdominant asymmetries and emphasizes the need for improved NR data and PN corrections to enable robust, high-precision gravitational-wave inferences for next-generation detectors.

Abstract

In dynamically formed binaries, the spins of the black holes tend to be misaligned with the system's orbital angular momentum. This causes the spins to precess and leads to an asymmetric emission of gravitational waves. The resulting gravitational-wave multipole asymmetries directly source the recoil of the remnant black hole and are the critical element in fully describing precession. Recoil and precession are of significant astrophysical importance, but multipole asymmetries contribute only minimally to the overall signal strength. Consequently, most current gravitational-wave models either do not incorporate asymmetries at all, or only consider the dominant ones. Here we highlight the importance of subdominant multipole asymmetries for an accurate recoil velocity calculation and discuss their detectability with third generation detectors. Neglecting subdominant asymmetries leads to velocity differences of up to 210 km/s and can, in particular, introduce systematic biases in the inference of masses and the spin geometry. We further discuss universal characteristics of subdominant multipole asymmetries in order to prepare the ground for potential future asymmetry models. In the inspiral regime, the average antisymmetric frequencies can be described by a multiple of the orbital frequency. During ringdown, however, they become equal to their corresponding symmetric frequencies.

Figures (10)

• Figure 1: SWSH surface illustration. The radial distance from the origin encodes the magnitude $\left| {}^{-2}Y_{\ell m}\right|$ scaled with arbitrary amplitudes such that $\left|h_{\ell,+m}\right| / \left|h_{\ell,-m}\right| = 2/3$ in order to illustrate an enlarged multipole asymmetry. Blue surfaces correspond to $m>0$, whereas red surfaces denote $m<0$.
• Figure 2: Spin–asymmetry–kick correlation, showing the difference between including only dominant multipole asymmetries and including all multipole asymmetries in the kick calculation. Configurations with $q=3$, spin magnitude of $\left|\vec{\chi}_i\right| = 0.8$ and varying spin directions were chosen. Waveforms were generated using NRSur7dq4Varma_2019_NRSur7dq4. Kick computations and coprecessing-frame transformations were performed with scriBoyle_2020_scri.
• Figure 3: Influence of subdominant multipole asymmetries on the kick velocity. The left panel illustrates a case with large subdominant kick amplitudes $\beta$, while the right panel depicts a scenario in which the contribution of the dominant multipole asymmetry to the kick is almost negligible. This occurs because, at the time when most of the linear momentum is radiated (dashed gray line), the dominant antisymmetric and symmetric waveforms are nearly perpendicular, resulting in a cosine value of the phase difference $\psi$ close to zero. The lower panel provides the cumulative kick velocity calculated with all asymmetries, or when the dominant or subdominant asymmetry is deactivated.
• Figure 4: Recovered posteriors of the chirp mass $\mathcal{M}$, the inverted mass ratio $1/q$, the spin magnitudes $a_1$ and $a_2$, the spin tilt angles $\cos\theta_1$ and $\cos\theta_2$, the spin azimuthal angle $\varphi_{12}$, the effective spin $\chi_{\rm eff}$ and the effective spin precession parameter $\chi_{\rm p}$. We use waveform models including all asymmetries, NRSur7dq4, neglecting dominant asymmetries, NRSur7dq4_dom_off and neglecting subdominant asymmetries NRSur7dq4_subdom_off. Black lines shows the injected values of a NRSur7dq4 waveform into the ET-D design sensitivity curve.
• Figure 5: Inclination dependence of the systematic bias between including all asymmetries, NRSur7dq4 (blue), and neglecting the subdominant ones, NRSur7dq4_subdom_off (red). Because the SWSH have a complex structure, it is non-trivial to predict a priori which inclination leads to the largest bias for a given parameter, here exemplified with the spin tilt angle $\cos \theta_1$ and the spin azimuthal angle $\phi_{12}$. Dark, mid, and light colors indicate inclinations of $\iota = \pi/2$, $\pi/3$, and $0$, respectively.