A new clump-based star formation model for galaxy simulations: implications for high-redshift compact star clusters

Abstract

We develop a new star formation model for galaxy simulations in which star-forming gas clumps are identified on-the-fly and converted into stars with an efficiency ${\epsilon }_{\mathrm{SF}}$ set by the clump surface density ${\Sigma }_{\mathrm{c}}$, calibrated against radiation hydrodynamics simulations of star cluster formation. Applying this model to isolated disc galaxies embedded in haloes of $M_{\mathrm{h}}=10^9$, $10^{10}$ and $10^{11}{\mathrm{M}}_{\odot }$, with disc compactness corresponding to redshift $z=0$--$10$, we find that more compact discs form more massive and denser clumps. The maximum clump mass increases from $\sim 10^5$ to $\sim 10^7{\mathrm{M}}_{\odot }$, and the fraction of clumps exceeding the surface density of $300{\mathrm{M}}_{\odot }\mathrm{p}{\mathrm{c}}^{-2}$ rises from $0.25$ to $0.38$ between $z=0$ and $10$ in $10^{10}{\mathrm{M}}_{\odot }$ haloes. Star formation becomes correspondingly bursty, and the global star formation efficiency after three disc rotations increases from $5\times 10^{-3}$ to $2\times 10^{-1}$ in $10^{10}{\mathrm{M}}_{\odot }$ haloes and from $2\times 10^{-2}$ to $4\times 10^{-1}$ in $10^{11}{\mathrm{M}}_{\odot }$ haloes as the redshift increases from $z=0$ to $10$. The accompanying feedback disrupts the gas discs of the most compact systems, while prominent stellar spiral arms emerge. Self-gravitationally bound star clusters form only in compact discs. We find no bound star clusters at $z\le 2$ in $10^{10}{\mathrm{M}}_{\odot }$ haloes, whereas the bound cluster mass fraction reaches $\approx 40$ per cent at $z\ge 8$ and $\approx 70$ per cent in the most compact $10^{11}{\mathrm{M}}_{\odot }$ halo. These fractions are broadly consistent with those inferred for high-$z$ clumpy galaxies observed by the James Webb Space Telescope.

12 pages, 12 figures, submitted