Feedback-Free Star Formation in Clusters within a Galaxy Simulated at High Resolution in Cosmic Dawn

We perform a cosmological zoom-in simulation of a massive galaxy ($M_s\sim {10}^{10}{\mathrm{M}}_{\odot }$ at $z\sim 10$) using the GIZMO code. By employing $\le 3\mathrm{p}\mathrm{c}$ resolution and a $3.4\mathrm{M}\mathrm{y}\mathrm{r}$ supernova feedback delay, we capture the feedback-free starbursts (FFB) in clusters. The simulation reproduces FFB model predictions and super-bright galaxies observed by JWST. At $z\sim 10$, cold streams feed a compact galaxy ($R_{\mathrm{e}}\sim 1\mathrm{k}\mathrm{p}\mathrm{c}$), with stellar and surface densities ($>{10}^5\mathrm{c}{\mathrm{m}}^{-3}$, $>{10}^5{\mathrm{M}}_{\odot }\mathrm{p}{\mathrm{c}}^{-2}$) exceeding FFB thresholds. The global star-formation efficiency (SFE) is ${\epsilon }_s\sim 0.2\text{–}0.3$, associated with a fluctuating star-formation history. We identified over ${10}^5$ star clusters ($M_{\star }>{10}^{4.5}{\mathrm{M}}_{\odot }$) with a nearly scale-free mass distribution ($\mathrm{d}N\mathrm{/}\mathrm{d}\log M\propto M^{-1.06}$). Approximately 90% of star formation occurs in clusters, which at a given time constitute $30\text{–}40\mathrm{\%}$ of the total stellar mass. The star formation in most of the clusters of masses $<{10}^7{\mathrm{M}}_{\odot }$, occurs in bursts of $<3\mathrm{M}\mathrm{y}\mathrm{r}$ and a local SFE $\sim 0.5\pm 0.2$. Cluster metallicities ($-2.01<\log (Z\mathrm{/}{Z}_{\odot })<-0.45$) indicate rapid baryon recycling. Feedback-driven outflows exhibit typical temperature of ${10}^7\mathrm{K}$ and typical velocities of $\sim 2000\mathrm{k}\mathrm{m}{\mathrm{s}}^{-1}$. In the highly dynamic central $1\mathrm{k}\mathrm{p}\mathrm{c}$, clusters undergo rapid orbital decay and merge to assemble the oblate nuclear stellar cluster. Cluster shapes range from oblate to prolate, with a triaxial median. These clusters are consistent with JWST observations, and a fraction of them may survive to yield the globular clusters (GCs) at low redshifts.