Starbursts in low-mass haloes at Cosmic Dawn. I. The critical halo mass for star formation

Abstract

The first stars, galaxies, star clusters, and direct-collapse black holes are expected to have formed in low-mass ($\sim$$10^5-10^9{M}_{\odot }$) haloes at Cosmic Dawn ($z\sim 10-30$) under conditions of efficient gas cooling, leading to gas collapse towards the centre of the halo. The halo mass cooling threshold has been analyzed by several authors using both analytical models and numerical simulations, with differing results. Since the halo number density is a sensitive function of the halo mass, an accurate model of the cooling threshold is needed for (semi-)analytical models of star formation at Cosmic Dawn. In this paper the cooling threshold mass is calculated (semi-)analytically, considering the effects of H${}_2$-cooling and formation (in the gas phase and on dust grains), cooling by atomic metals, Lyman-$\alpha$ cooling, photodissociation of H${}_2$ by Lyman-Werner photons (including self-shielding by H${}_2$), photodetachment of H${}^{-}$ by infrared photons, photoevaporation by ionization fronts, and the effect of baryon streaming velocities. We compare the calculations to several high-resolution cosmological simulations, showing excellent agreement. We find that in regions of typical baryon streaming velocities, star formation is possible in haloes of mass $\gtrsim 1-2\times 10^6{M}_{\odot }$ for $z\gtrsim 20$. By $z\sim 8$, the expected Lyman-Werner background suppresses star formation in all minihaloes below the atomic-cooling threshold ($T_{\mathrm{vir}}=10^4\text{K}$). The halo mass cooling threshold increases by another factor of $\sim$$4$ following reionization, although this effect is slightly delayed ($z\sim 4-5$) because of effective self-shielding.

22 pages, 10 figures. Accepted for publication in MNRAS

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