State-to-state chemistry and rotational excitation of CH+ in photon-dominated regions

We present a detailed theoretical study of the rotational excitation of CH⁺ due to reactive and non-reactive collisions involving C⁺(²P), H₂, CH⁺, H and free electrons. Specifically, the formation of CH⁺ proceeds through the reaction between C⁺(²P) and H_2(ν _H_2 = 1, 2), while the collisional (de)excitation and destruction of CH⁺ is due to collisions with hydrogen atoms and free electrons. State-to-state and initial-state-specific rate coefficients are computed in the kinetic temperature range 10-3000 K for the inelastic, exchange, abstraction and dissociative recombination processes using accurate potential energy surfaces and the best scattering methods. Good agreement, within a factor of 2, is found between the experimental and theoretical thermal rate coefficients, except for the reaction of CH⁺ with H atoms at kinetic temperatures below 50 K. The full set of collisional and chemical data are then implemented in a radiative transfer model. Our non-LTE calculations confirm that the formation pumping due to vibrationally excited H₂ has a substantial effect on the excitation of CH⁺ in photon-dominated regions. In addition, we are able to reproduce, within error bars, the far-infrared observations of CH⁺ towards the Orion Bar and the planetary nebula NGC 7027. Our results further suggest that the population of ν _H_2 = 2 might be significant in the photon-dominated region of NGC 7027.