Constraints from Gravitational Recoil on the Growth of Supermassive Black Holes at High Redshift
Zoltan Haiman
TL;DR
This study investigates how gravitational recoil from mergers constrains the growth of supermassive black holes (SMBHs) at high redshift. Using extended Press–Schechter merger trees and a seed-based growth model, it links seed formation to halo mergers and recoil thresholds, requiring seeds in halos with $\sigma < v_{kick}/2$ to be removed, and assuming exponential accretion with $t_{acc}=4\times 10^{7}(\epsilon/0.1)\eta^{-1}$ yr. Applied to the $z=6.43$ quasar SDSS 1054+1024 with $M_{bh} \sim 4.6\times 10^{9}$ M$_{\odot}$, the fiducial model yields a maximum permissible recoil of $v_{kick} \approx 64$ km s^{-1}$, implying that larger kicks would demand super-Eddington growth or different seed demographics. The results underscore a potential tension between gravitational recoil and early SMBH assembly, discuss uncertainties (spin, seed occupation, duty cycles), and suggest observational tests with future facilities to illuminate seed formation and growth histories.
Abstract
Recent studies have shown that during their coalescence, binary supermassive black holes (SMBHs) experience a gravitational recoil with velocities of 100 km/s < v(kick) < 600 km/s. These velocities exceed the escape velocity v(esc) from typical dark matter (DM) halos at high-redshift (z>6), and therefore put constraints on scenarios in which early SMBHs grow at the centers of DM halos. Here we quantify these constraints for the most distant known SMBHs, with inferred masses in excess of 10^9 M(sun), powering the bright quasars discovered in the Sloan Digital Sky Survey at z>6. We assume that these SMBHs grew via a combination of accretion and mergers between pre-existing seed BHs in individual progenitor halos, and that mergers between progenitors with v(esc) < v(kick) disrupt the BH growth process. Our results suggest that under these assumptions, the z=6 SMBHs had a phase during which gained mass significantly more rapidly than under an Eddington-limited exponential growth rate.