Understanding the fate of merging supermassive black holes

TL;DR

Understanding the fate of merging supermassive black holes is central to LISA science and to constraining galaxy evolution. The authors implement the Lazarus hybrid approach, blending full numerical relativity with black-hole perturbation theory to model the final plunge and associated gravitational radiation, enabling estimates of the remnant spin and recoil for SMBH mergers. They report a final spin relation $a/M \approx 0.72 + 0.32\, (s/m_H)$ for equal-mass, moderately spinning binaries and discuss recoil velocities that peak at intermediate mass ratios, with spin effects likely to modify these values. These results provide theoretical predictions to interpret LISA waveforms and inform growth and retention of SMBHs in galaxies, while underscoring the need for more extensive simulations at higher spins and mass ratios.

Abstract

Understanding the fate of merging supermassive black holes in galactic mergers, and the gravitational wave emission from this process, are important LISA science goals. To this end, we present results from numerical relativity simulations of binary black hole mergers using the so-called Lazarus approach to model gravitational radiation from these events. In particular, we focus here on some recent calculations of the final spin and recoil velocity of the remnant hole formed at the end of a binary black hole merger process, which may constraint the growth history of massive black holes at the core of galaxies and globular clusters.

Figures (3)

• Figure 1: Real part of the plunge waveforms from the coalescence of several spinning black holes for the $l=2$ multipole, as viewed by an observer located along the polar axis. The waveforms have been rescaled by a factor $q=\omega_{QN}^{s}/\omega_{QN}^{s=0}$. $T$ indicates the time after which one can treat each system perturbatively as described in the Lazarus approach.
• Figure 2: Instantaneous frequency $\omega$ of waveforms described in Fig. \ref{['fig:rescala']} normalized to quasinormal frequencies $\omega_{QN}$ of the remnant Kerr holes. We see that the quasinormal ringing frequency is approached similarly in each case with a slightly delayed approach for the counter-aligned cases. This is expected for these plunge waveforms since the anti-aligned spin initial data starts with black holes with larger separations than the aligned spin configurations.
• Figure 3: Recoil velocity as a function of the mass ratio for perturbative and full numerical calculations. The perturbative values are from Ref.Favata:2004wz. The error bars in the numerical calculations are computed taking the maximum and the minimum of the values of the total linear momentum as a function of the transition time $T$ from non-linear to linear evolution. The minus sign convention is because we actually compute the momentum carried out by the gravitational waves.