A new clump-based star formation model for galaxy simulations: implications for high-redshift compact star clusters
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 $ε_{\rm SF}$ set by the clump surface density $Σ_{\rm c}$, calibrated against radiation hydrodynamics simulations of star cluster formation. Applying this model to isolated disc galaxies embedded in haloes of $M_{\rm h}=10^{9}$, $10^{10}$ 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 $300\,\mathrm{M_\odot\,pc^{-2}}$ 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 $z \leq 2$ in $10^{10}\,\mathrm{M_\odot}$ haloes, whereas the bound cluster mass fraction reaches $\approx 40$ per cent at $z \geq 8$ 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.