Lyman-alpha Radiation Pressure in Dense Star Clusters: Implications for Star Formation and Winds at Cosmic Dawn

Observations with the JWST in lensed fields have revealed that galaxies at cosmic dawn may concentrate their star formation in highly dense, compact, star clusters. The high columns and low metallicities encountered in their birth environments suggest that Lyman-alpha (Ly$\alpha$) radiation pressure may be crucial to their formation and evolution. In this study, we address this question by post-processing snapshots from radiation hydrodynamic simulations of dense star cluster-forming clouds ($\Sigma_*\gtrsim10^3{M_\odot{pc}^{-2}}$) with a range of dust abundances ($Z_d=0-0.1Z_{d,\odot}$) using the COLT Monte Carlo code. We infer that Ly$\alpha$ is likely to have mild (~10%) effects on the gas-to-star conversion efficiencies ($\epsilon_*\gtrsim60$%) for $Z_d\gtrsim0.01Z_{d,\odot}$, and even in dust-free environments, $\epsilon_*\gtrsim25$% - much higher than the <10% values typical of star-forming regions in the local Universe. This is because the densest filaments dominating stellar mass assembly ($n\gtrsim10^4{cm}^{-3}$) remain sub-Eddington ($f_{Edd}<1$). On the other hand, the bulk of the gas volume ($n\lesssim10^3{cm}^{-3}$) has $f_{Edd}>1$, with noticeable fractions having $f_{Edd}\gtrsim10$, implying that Ly$\alpha$ can launch dynamically significant winds from these systems rapidly ($\lesssim$4Myr), with possible implications for ionizing photon escape and galactic outflows. The Ly$\alpha$ force multiplier $M_F$ is highly sensitive to $Z_d$, with $M_F\lesssim3$ ($\lesssim 500$) for $0.1Z_{d,\odot}$ (dust-free) environments respectively. Nevertheless, Ly$\alpha$ dominates over UV and IR radiation pressure at all values of $Z_d\lesssim0.1Z_{d,\odot}$, by factors of ~3-500. Our results suggest that Ly$\alpha$ radiation pressure reinforces the emerging picture of locally efficient, bursty star formation accompanied by rapid outflows in galaxies at cosmic dawn.