Inelastic H + H$^+_3$ Collision rates and their impact in the determination of the excitation temperature of H$^+_3$

Abstract: Context. In dffuse interstellar clouds the excitation temperature derived from the lowest levels of H$^+_3$ is systematically lower than that derived from H2. The differences may be attributed to the lack of state-specific formation and destruction rates of H$^+_3$ needed to thermalize the two species. Aims. In this work, we want to check the role of rotational excitation collisions of H$^+_3$ with atomic hydrogen on its excitation temperature. Methods. A time independent close-coupling method is used to calculate the state-to-state rate coefficients, using a very accurate and full dimensional potential energy surface recently developed for H$^+_4$. A symmetric top approach is used to describe a frozen H$^+_3$ as equilateral triangle. Results. Rotational excitation collision rate coefficients of H$^+_3$ with atomic Hydrogen have been derived in a temperature range appropriate to diffuse interstellar conditions up to $(J; K; \pm) = (7; 6; +)$ and $(J; K; \pm) = (6; 4; +)$ for its ortho and para forms. This allows to have a consistent set of collisional excitation rate coefficients and to improve the previous study where these contributions were speculated. Conclusions. The new state-specific inelastic H$^+_3$ + H rate coeffcients yield differences up to 20% in the excitation temperature, and their impact increases with decreasing molecular fraction. We also confirm the impact of chemical state-to-state destruction reactions in the excitation balance of H$^+_3$ , and that reactive H + H$^+_3$ collisions are also needed to account for possible further ortho to para transitions