Modelling the ArH+ emission from the Crab nebula

We have performed combined photoionization and photodissociation region (PDR) modelling of a Crab nebula filament subjected to the synchrotron radiation from the central pulsar wind nebula, and to a high flux of charged particles; a greatly enhanced cosmic-ray ionization rate over the standard interstellar value, zeta(0), is required to account for the lack of detected [CI] emission in published Herschel SPIRE FTS observations of the Crab nebula. The observed line surface brightness ratios of the OH+ and ArH+ transitions seen in the SPIRE FTS frequency range can only be explained with both a high cosmic-ray ionization rate and a reduced ArH+ dissociative recombination rate compared to that used by previous authors, although consistent with experimental upper limits. We find that the ArH+/OH+ line strengths and the observed H-2 vibration-rotation emission can be reproduced by model filaments with n(H) = 2 x 10(4) cm(-3), zeta = 10(7)zeta(0) and visual extinctions within the range found for dusty globules in the Crab nebula, although far-infrared emission from [OI] and [CII] is higher than the observational constraints. Models with n(H) = 1900 cm(-3) underpredict the H-2 surface brightness, but agree with the ArH+ and OH+ surface brightnesses and predict [OI] and [CII] line ratios consistent with observations. These models predict HeH+ rotational emission above detection thresholds, but consideration of the formation time-scale suggests that the abundance of this molecule in the Crab nebula should be lower than the equilibrium values obtained in our analysis.