Seeding Cores: A Pathway for Nuclear Star Clusters from Bound Star Clusters in the First Billion Years

TL;DR

The paper demonstrates that using a physically motivated, cloud-dependent star formation efficiency (SFE) model within a cosmological radiation-hydrodynamics simulation yields a bursty star formation history and a populous, bound star cluster system in a dwarf galaxy progenitor during the first 700 Myr. A central nuclear star cluster (NSC) is seeded by $z\sim8$ primarily through the mergers of massive, bound clusters formed in high-SFE clouds, with in-situ central star formation contributing a smaller fraction. The results reveal a time-dependent cluster mass function (CMF) that is initially broad and becomes steeper as metallicity evolves, and they show substantial metallicity spreads within clusters due to pre-enrichment inhomogeneities. These findings have implications for the early growth of NSCs and potential seeds for supermassive black holes, and they provide a framework to interpret JWST observations of compact, high-redshift clusters and the little red dots population.

Abstract

We model the formation of star clusters in a dwarf galaxy progenitor during the first $700 ~{\rm Myr}$ of cosmic history using a cosmological radiation-hydrodynamic simulation with a sub-grid star formation efficiency (SFE) model calibrated from AU-scale radiation-MHD simulations of molecular clouds with varying mass, density, and metallicity. In comparison to a constant SFE model, our model yields more bursty star formation, a more abundant massive star cluster population, and overall a higher stellar mass. Clouds reach SFEs up to $80\%$, forming bound star clusters (densities $\sim10^{2-4} ~{\rm M_\odot\:pc^{-2}}$, radii $\lesssim 3~{\rm pc}$) resembling those observed by the James Webb Space Telescope (JWST) in strongly lensed galaxies. Star clusters follow a flat power-law mass function ${\rm d}N/{\rm d}\log M \propto M^Γ$ with slope $Γ\sim -0.4$. The most massive star clusters ($10^{4-5} ~{\rm M_\odot}$) grow through mergers and have metallicity spreads of $0.05 - 0.1$ dex that roughly scale with mass. The second burst of star formation produce loosely bound star clusters with higher metallicities: $-1.95 < \log(Z/{\rm Z_\odot}) < -1.50$ at lower SFEs ($2 - 20\%$). At $z \sim 8.7$, a nuclear star cluster (NSC) is seeded, growing $83\%$ of its mass ($ 2.4 \times 10^5 ~{\rm M_\odot}$, $20\%$ of the galaxy's stellar mass) through mergers with pre-existing clusters and the rest through in-situ star formation. The early formation of NSCs has interesting implications for seeding supermassive black holes and the population of $\textit{little red dots}$ recently discovered by JWST at $z \gtrsim 5$

Figures (13)

• Figure 1: Snapshot of a dwarf galaxy simulation at high redshift with SFEs in gas clouds calibrated from cloud-scale simulations of star formation, shown just after starburst (a) in Figure \ref{['fig: SF History']}. The star clusters are shown according to their rest-frame UV surface brightness (at $\lambda = 1500 \text{\AA}$) assuming a Salpeter IMF and a metallicity of $10^{-3}~\rm{Z_\odot}$ using Starburst99. The green hues show the gas density while the redder hues show the density-weighted gas temperatures; the colour bars are at the bottom right of the figure. The panels progressively zoom into the star clusters (scale bars shown in physical units), with the bottom panel showing two of the most massive star clusters. The most massive star cluster, shown near the top right corner of the inset, comprises roughly 10% of the galaxy's total stellar mass.
• Figure 2: Pop II star formation histories of the simulations presented in this paper (see also Fig. 2 (left) in garcia_star_2023). The top panel shows the mass of stars produced under the different assumed star formation efficiencies throughout each simulation (see legend). The following panels (top to bottom) show the corresponding star formation rates (same colours as the legend) in 1 Myr bins. In the top left of each panel, we show the duty cycle $f_{\rm duty}$ of star formation, defined as the ratio between times when the SFR $> 5$% of the peak SFR, and the total time elapsed since the onset of Pop II star formation through the end of each simulation run. Note that we also label starbursts (a) - (h) across all simulations, shading regions where the SFRs roughly reach at least 5% of the peak SFR during the starburst. We will use these in the text to refer to star-forming periods (e.g., starburst (a) and (b) for the first and second starbursts in the VSFE model, respectively).
• Figure 3: SFEs for the star-forming clouds in the VSFE simulation as a function of cloud mass. The circle markers are clouds that produced star clusters before starburst (b) ($t \lesssim 500$ Myr) while the square markers are for clouds that formed stars during and after starburst (b). The markers themselves are coloured by the mean cloud surface density $\Sigma_{\rm cloud}$ assuming a spherically symmetric, constant-density cloud. For comparison, we also show two dashed lines indicating the two constant efficiency runs: low SFE (35%) and high SFE (70%). The right panel shows the distribution of SFEs for these two time periods weighted by the stellar mass. The red histogram refers to the first burst (circle markers) and the green histogram refers to the second burst (square markers).
• Figure 4: We show the Pop II star-forming cloud metallicity as a function of mass for the different star-forming periods: see top colour bar where we also indicate (with two thicker lines) the times when the SFRs peak for staburst (a) and (b). For each row, the right panel shows the metallicity function for the clouds for a given model (see lower right of each left panel). The very bottom panel shows the mass function of the clouds, coloured according to the sub-grid SFE for each run. Note, that the metallicity of the star clusters is identical to their natal clouds'.
• Figure 5: At-birth (solid) and current (hatched) star cluster mass function for the VSFE run. The simulation progresses from left to right and we see how the star cluster population evolves after starburst (a) from the first column and second column ($t_{\rm univ} = 512$ Myr corresponds to the snapshot shown in Figure \ref{['fig: vsfe run render']}), right after the second starburst (the third column), and the latest snapshot (fourth column). We also show reference lines for power laws used to fit the CMF with power law index $\Gamma$ which also evolves. Note that the NSC seeded by the starburst (b) is indicated in red. Furthermore, we show the cumulative ICMF fitted with a Gaussian in log-log space to find the mean ($\mu$) and standard deviation ($\sigma$). The top row corresponds to all the star clusters, both bound and unbound (see text for definition), while the second row only shows those we consider bound.