OH+ in astrophysical media: state-to-state formation rates, Einstein coefficients and inelastic collision rates with He

Abstract: The rate constants required to model the OH$^+$ observations in different regions of the interstellar medium have been determined using state of the art quantum methods. First, state-to-state rate constants for the H$_2(v=0,J=0,1)$+ O$^+$($^4S$) $\rightarrow$ H + OH$^+(X ^3\Sigma^-, v', N)$ reaction have been obtained using a quantum wave packet method. The calculations have been compared with time-independent results to asses the accuracy of reaction probabilities at collision energies of about 1 meV. The good agreement between the simulations and the existing experimental cross sections in the $0.01-$1 eV energy range shows the quality of the results. The calculated state-to-state rate constants have been fitted to an analytical form. Second, the Einstein coefficients of OH$^+$ have been obtained for all astronomically significant ro-vibrational bands involving the $X^3\Sigma^-$ and/or $A^3\Pi$ electronic states. For this purpose the potential energy curves and electric dipole transition moments for seven electronic states of OH$^+$ are calculated with {\it ab initio} methods at the highest level and including spin-orbit terms, and the rovibrational levels have been calculated including the empirical spin-rotation and spin-spin terms. Third, the state-to-state rate constants for inelastic collisions between He and OH$^+(X ^3\Sigma^-)$ have been calculated using a time-independent close coupling method on a new potential energy surface. All these rates have been implemented in detailed chemical and radiative transfer models. Applications of these models to various astronomical sources show that inelastic collisions dominate the excitation of the rotational levels of OH$^+$. In the models considered the excitation resulting from the chemical formation of OH$^+$ increases the line fluxes by about 10 % or less depending on the density of the gas.