Beyond Jcrit: a critical curve for suppression of H2-cooling in protogalaxies

TL;DR

This paper introduces a critical curve in the (kLW, kH^-) parameter space that determines H2-cooling suppression in protogalaxies, considering realistic spectra and detailed chemistry, impacting early universe structure formation.

Contribution

It presents a new critical curve for H2-cooling suppression based on realistic stellar spectra and frequency-dependent chemistry, improving previous idealized models.

Findings

Derived an analytical fit for the critical curve in (kLW, kH^-) space.

Calculated the minimum stellar mass needed for suppression at various distances.

Provided critical M_star/d^2 values with analytic fits for future research.

Abstract

Suppression of H2-cooling in early protogalaxies has important implications for the formation of supermassive black holes seeds, the first generation of stars, and the epoch of reionization. This suppression can occur via photodissociation of H2 (by ultraviolet Lyman-Werner [LW] photons) or by photodetachment of H-, a precursor in H2 formation (by infrared [IR] photons). Previous studies have typically adopted idealised spectra, with a blackbody or a power-law shape, in modeling the chemistry of metal-free protogalaxies, and utilised a single parameter, the critical UV flux, or Jcrit, to determine whether H2-cooling is prevented. This can be misleading, and that independent of the spectral shape, there is a critical curve in the (kLW , kH^- ) plane, where kLW and kH^- are the H2-dissocation rates by LW and IR photons, which determines whether a protogalaxy can cool below ~1000 Kelvin. We use a one-zone model to follow the chemical and thermal evolution of gravitationally collapsing protogalactic gas, to compute this critical curve, and provide an accurate analytical fit for it. We improve on previous works by considering a variety of more realistic Pop III or Pop II-type spectra from population synthesis models and perform fully frequency-dependent calculations of the H2-photodissociation rates for each spectrum. We compute the ratio kLW/kH^- for each spectrum, as well as the minimum stellar mass M_star, for various IMFs and metallicities, required to prevent cooling in a neighboring halo a distance d away. We provide critical M_star/d2 values for suppression of H2-cooling, with analytic fits, which can be used in future studies.