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Revised rate coefficients for H$_2$ and H$^-$ destruction by realistic stellar spectra

Understanding the processes that can destroy H$_2$ and H$^-$ species is quintessential in governing the formation of the first stars, black holes and galaxies. In this study we compute the reaction rate coefficients for H$_2$ photo--dissociation by Lyman--Werner photons ($11.2 - 13.6$ eV), and H$^-$ photo--detachment by 0.76 eV photons emanating from self-consistent stellar populations that we model using publicly available stellar synthesis codes. So far studies that include chemical networks for the formation of molecular hydrogen take these processes into account by assuming that the source spectra can be approximated by a power-law dependency or a black-body spectrum at 10$^4$ or $10^5$ K. We show that using spectra generated from realistic stellar population models can alter the reaction rates for photo-dissociation, $\rm k_{\rm{di}}$, and photo-detachment, $\rm k_{\rm{de}}$, significantly. In particular, $\rm k_{\rm{de}}$ can be up to $\sim 2-4$ orders of magnitude lower in the case of realistic stellar spectra suggesting that previous calculations have over-estimated the impact that radiation has on lowering H$_2$ abundances. In contrast to burst modes of star formation, we find that models with continuous star formation predict increasing $\rm k_{\rm{de}}$ and $\rm k_{\rm{di}}$, which makes it necessary to include the star formation history of sources to derive self-consistent reaction rates, and that it is not enough to just calculate J$_{21}$ for the background. For models with constant star formation rate the change in shape of the spectral energy distribution leads to a non-negligible late-time contribution to $\rm k_{\rm{de}}$ and $\rm k_{\rm{di}}$, and we present self-consistently derived cosmological reaction rates based on star formation rates consistent with observations of the high redshift Universe.