The cosmic ray ionization rate from H3+ observations can be overestimated due to neglect of time-dependent chemistry
The cosmic ray ionization rate (CRIR) is a key parameter governing the physical, chemical and thermal evolution of the interstellar medium. The primary technique for measuring the CRIR in diffuse molecular clouds relies on observations of ${\rm H_3^+}$. Previous analyses of these observations have derived the CRIR under the assumption of steady-state chemistry. Here, we investigate the effect of time-dependent chemistry on the inferred CRIR from ${\rm H_3^+}$ observations. We perform 3D MHD simulations with coupled chemistry and driven turbulence. Following procedures similar to those used in the literature to analyze ${\rm H_3^+}$ observations, we conduct mock CRIR measurements by post-processing our simulations with different values of the CRIR to obtain steady-state abundances of ${\rm H_2}$ and ${\rm H_3^+}$. By comparing those with the abundances from time-dependent chemistry, we determine the best-fitting value of the CRIR. We find that the abundances of both ${\rm H_2}$ and ${\rm H_3^+}$ are higher in time-dependent chemistry simulations than in the steady-state case, especially in low-density regions. Furthermore, the inferred CRIR under the steady-state assumption is a factor of $\sim 2-5$ higher than the true CRIR, with a median value of $\zeta_\mathrm{inferred}/\zeta_\mathrm{true} \approx 3$. This bias increases with stronger magnetic fields, weaker FUV radiation fields, and stronger turbulence. Accounting for time-dependent chemistry, we report an average CRIR per ${\rm H_2}$ of $\zeta_{H_2} = 2\times 10^{-17}~\mathrm{s^{-1}}$ from the ${\rm H_3^+}$ observations. The CRIR is consistent with a constant value over the column density range of $N=(2-6)\times10^{21}~\mathrm{cm^{-2}}$.