Lyman-$α$ radiation pressure regulates star formation efficiency

TL;DR

This work investigates whether Lyα radiation pressure can fundamentally cap the efficiency of converting gas into stars in primordial clouds before supernova feedback becomes important. By coupling a shell model for Lyα momentum transfer with force multiplier fits that account for dust destruction, and validating against 1D hydrodynamic simulations, the authors show that Lyα feedback disrupts clouds on timescales shorter than the free-fall time across a broad range of surface densities. For metallicities around $\log(Z/Z_\odot)=-2$, the maximum star formation efficiency spans roughly $0.01$ to $0.66$ for $10^3 \lesssim \Sigma_g \lesssim 10^5\,M_\odot\,\mathrm{pc^{-2}}$, with lower values at lower metallicities and near unity only at extreme surface densities and near-solar metallicities. The findings imply Lyα pressure acts as a robust pre-SN feedback mechanism that constrains a hypothetical, feedback-free phase of highly efficient star formation in dense, metal-poor clouds, with important implications for the early growth of galaxies observed by JWST.

Abstract

Order-unity star formation efficiencies (SFE) in early galaxies may explain the overabundance of bright galaxies observed by JWST at high redshift. Here we show that Lyman-$α$ (Ly$α$) radiation pressure limits the gas mass converted into stars, particularly in primordial environments. We develop a shell model including Ly$α$ feedback, and validate it with one-dimensional hydrodynamical simulations. To account for Ly$α$ resonant scattering, we adopt the most recent force multiplier fits, including the effect of Ly$α$ photon destruction by dust grains. We find that, independently of their gas surface density $Σ_g$, clouds are disrupted on a timescale shorter than a free-fall time, and even before supernova explosions if $Σ_g \gtrsim 10^3\,M_{\odot}\ \rm pc^{-2}$. At $\log(Z/Z_{\odot}) = -2$, relevant for high-redshift galaxies, the SFE is $0.01 \lesssim \hatε_{*} \lesssim 0.66$ for $10^3 \lesssimΣ_g [M_{\odot}\ \rm pc^{-2}] \lesssim 10^5$. The SFE is even lower for decreasing metallicity. Near-unity SFEs are possible only for extreme surface densities, $Σ_{g} \gtrsim 10^5\;M_{\odot}\ \rm pc^{-2}$, and near-solar metallicities. We conclude that Ly$α$ radiation pressure severely limits a possible extremely efficient, feedback-free phase of star formation in dense, metal-poor clouds.

Figures (4)

• Figure 1: Left: Shell radius as a function of time normalised to the free-fall time for $\epsilon_* =$ 1% (green), 5% (water green), 10% (blue) and 30% (purple). The cloud surface density and metallicity are $\Sigma_g = 10^4\,M_{\odot}\ \rm pc^{-2}$ and $\log(Z/Z_{\odot}) = -2$, respectively. Both the shell solution (Eq. \ref{['eq:shell_equation']}, solid line) and the simulation predictions (dashed) are shown. Right: Same for the shell velocity.
• Figure 2: Left: Maximum SFE as a function of surface density for metallicity $\log(Z/Z_{\odot}) = -6$ (blue), $-4$ (purple), $-2$ (red), 0 (orange). Solid or dashed curves show where the zero-force ($F_{\rm tot}=0$) or the escape velocity ($\dot R_s = v_{\rm esc}$) conditions are satisfied. The dotted curve shows the time-independent solution (Eq. \ref{['eq:eps_star_analytical']}) for the reference value $\Sigma_{\rm crit}= 2000\,M_{\odot}\ \rm pc^{-2}$ used by Somerville25. Coloured ticks mark the maximum SFE across the surface density range for each metallicity. Middle: Cloud disruption time in units of the free-fall time as a function of the cloud surface density for various metallicities as indicated in the colour bar. Solid or dashed curves show where the zero-force ($F_{\rm tot}=0$) or the escape velocity ($\dot R_s = v_{\rm esc}$) conditions are satisfied. Right: As the middle panel, with $t_d$ in units of Myr.
• Figure 3: Upper: Number density profiles for different snapshots of the simulation. Time in free-fall time units is colour-coded. The surface density of the cloud is $\Sigma_g = 10^4\,M_{\odot}\ \rm pc^{-2}$, with metallicity $\log(Z/Z_{\odot}) = -2$ and SFE $\epsilon_{*} = 30\%$. Lower: Same for the velocity profiles. The black dashed line shows the time evolution of the shell velocity, corresponding to the velocity of the cell with highest density.
• Figure 4: Maximum SFE as a function of cloud surface density for different source extensions: $R_* =$ 0.1 (cyan), 0.25 (light blue), 0.5 (yellow), 0.75 (orange), and 1 (red), shown with dashed lines. The point-source case is shown in solid blue. For reference, the SFE corresponding to $\Sigma_{\rm crit} = 2000\ \rm M_{\odot}\,pc^{-2}$ is indicated by a grey dotted line.