Repopulating the pair-instability mass gap without sustained growth to massive IMBHs: the case of 47\,Tuc

TL;DR

This study models the formation and retention of massive black holes in 47 Tuc, showing hierarchical mergers and primordial seeds can produce black holes up to about 1100 solar masses, consistent with observational limits.

Contribution

It introduces a comprehensive simulation of black hole formation in 47 Tuc, incorporating primordial seeds and hierarchical mergers, to explain the observed black hole mass distribution.

Findings

Hierarchical mergers produce black holes up to 70 M_sun with moderate spins.

Primordial seeds lead to a bimodal mass distribution, with some seeds surviving as massive black holes.

Retained black holes can reach masses of 500-1100 M_sun, consistent with observational constraints.

Abstract

We model the formation and retention of the most massive black hole (BH) in 47~Tuc using the semi-analytical code \texttt{cBHBd}, coupling cluster evolution with binary BH dynamics and computing merger-remnant masses, spins, and gravitational-wave recoil kicks via numerical-relativity surrogate prescriptions. We evolve 80\,000 cluster realisations spanning initial masses, densities, IMFs, and metallicities, in both a baseline scenario ($m_{\rm max} = 130\,\mathrm{M}_{\odot}$) and an extended-IMF scenario with ${\sim}\,50-110$ primordial BH seeds above the pair-instability gap ($M_{\rm BH} \sim 130-700\,\mathrm{M}_{\odot}$). Selecting models reproducing 47~Tuc's present-day mass and half-mass radius, we find hierarchical mergers alone yield a most massive retained BH of $M_{\rm BH} \sim 45-70\,\mathrm{M}_{\odot}$ with spin $\chi_{\rm BH} \sim 0.65$, limited to ${\sim}\,1-3$ mergers, as second-generation remnants acquire spin $\chi \sim 0.7$ that amplifies recoil kicks in subsequent generations. When primordial seeds are included, the retained-mass distribution becomes bimodal -- in ${\sim}\,90\%$ of realisations all seeds are ejected, but in ${\sim}\,10\%$ a massive seed ($M_{\rm BH} \gtrsim 450\,\mathrm{M}_{\odot}$) survives -- while the joint mass-spin distribution is trimodal; seeds surviving via stellar-mass BH mergers retain low spin ($\chi \lesssim 0.3$), whereas seed-seed mergers produce high-mass, high-spin remnants ($\chi \sim 0.65-0.7$), yielding 90th-percentile retained masses of ${\sim}\,500-1100\,\mathrm{M}_{\odot}$. Both scenarios are consistent with the $3\sigma$ dynamical upper limit of $578\,\mathrm{M}_{\odot}$. Our results favour a dark-remnant subsystem over a single massive IMBH and provide a spin-mass diagnostic testable with LIGO-Virgo-KAGRA, the Einstein Telescope, Cosmic Explorer, and LISA.