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.
