Black hole mass function shift in proto-stellar-clusters driven by gas accretion

Abstract

The James Webb Space Telescope (JWST) has observed compact, massive proto-stellar clusters of low metallicity in the Cosmic Gems arc galaxy at high redshift, which represent likely precursors to globular clusters. We model the mass growth of stellar black holes (BHs) during the first few Myr of the life of a massive, compact, gaseous stellar cluster before stellar feedback expels the primordial gas. At high redshift, in a lower metallicity environment stellar winds get weaker allowing for larger gas-depletion time-scales in the cluster despite of energetic pair-instability supernova (PISN) feedback for sufficiently compact clusters. Mass segregation drives the massive stellar progenitors of BHs in the center of the cluster where gas is most dense. We estimate the conditions for which the initial black hole mass function (BHMF), with a PISN-induced cut-off $<55{\rm M}_\odot$, gets shifted to values within the upper BH mass gap, $\sim 60-130{\rm M}_\odot$, or higher, as observed by Gravitational Wave (GW) experiments LIGO-Virgo-KAGRA. We find that the BHs are shifted by the end of gas depletion to values within and above the mass gap, well within the range of BH components of the recent GW-signal GW231123, depending on total mass, star formation efficiency, metallicity and compactness. The individual BH mass increase follows approximately a surprisingly steep power law with respect to initial BH mass with an exponent in the range $\approx 4-6$. This occurs in gaseous proto-stellar clusters that are sufficiently massive and compact, with typical values of total mass $\sim 10^6{\rm M}_\odot$ and size $\sim 1{\rm pc}$. Our analysis suggests that proto-stellar clusters at high redshift such as Cosmic Gems arc clusters have generated through early gas accretion, BHs as heavy as $\sim 10^2-10^3{\rm M}_\odot$.

Figures (7)

• Figure 1: Our estimated depletion timescale, $\tau$, with respect to the compactness, $C$, of a gaseous stellar cluster of any total mass. We considered three possible star formation efficiencies, $\varepsilon$. Each sub-figure $(a)$, $(b)$, $(c)$ corresponds, respectively, to solar, subsolar ($\sim 0.1 Z_\odot$), and low ($\sim 0.01 Z_\odot$) metallicity. We assume that at subsolar metallicity PPISN operates, and that in the low-metallicity case both PPISN and PISN do.
• Figure 2: BH-remnant mass with respect to the ZAMS progenitor's mass, reproduced from 2017MNRAS.470.4739S, used here in determining the BH entry time in our simulation.
• Figure 3: Shifted BH masses, after stellar feedback expels $99\%$ of the gas, with respect to the initial BH masses for a gaseous stellar cluster with total initial mass $M = 10^6{\rm M}_\odot$ containing $\sim 1000$ BHs, for several star formation efficiency and half-mass radius, i.e., compactness, values of the cluster. Each subfigure was generated by a set of ten simulations. The left column corresponds to subsolar metallicity ($\sim 0.1 Z_\odot$), the right column to low metallicity ($\sim 0.01 Z_\odot$). The solar metallicity case, not shown here, requires about double or higher compactness to have the same effect as the subsolar case.
• Figure 4: BHMF shift, after stellar feedback expels $99\%$ of the gas, for a gaseous stellar cluster as in Figure \ref{['fig:BHmass_scatter_M1.0e6']}. In the legend we depict the power exponent, $\alpha$, of several fits, namely of the BH IMF and of the shifted BHMF for several ranges; the whole range of values, the low-mass range up to the initial PISN cutoff, the range within the upper BH mass gap, and if applicable the tail of heavy BHs.
• Figure 5: Range of parameters in which the proto-BHMF-shift operates. The rows correspond to different stellar-cluster total masses and the columns to different metallicities. The solid shaded blue region in the $\varepsilon$-$r_{\rm h}$ plane signifies their range in which the most massive BH grows by at least $10{\rm M}_\odot$. The diagonally hatched region signifies additionally the $\varepsilon$-$r_{\rm h}$ range for which an IMBH with a mass of $\sim 10^3{\rm M}_\odot$ can be generated. Notice that the subsolar and low-metallicity cases require an almost identical cluster compactness for the BHMF-shift to operate, but the solar metallicity case requires about double or higher compactness (x axis).