High Rydberg state carbon recombination lines toward Cassiopeia A: Physical conditions and a new class of models

We present models of physical conditions in Perseus arm clouds observed in the direction of Cas A. Theoretical predictions of carbon radio recombination line intensities are compared with observations spanning the frequency range 14 to 775 MHz. Best-fitting model parameters are then combined with the results of lambda 21 cm H I absorption line observations, and low-frequency hydrogen recombination line observations, to evaluate the thermal and pressure balance in these clouds. A critical reexamination of the available recombination line data shows that the lowest frequency carbon line observations have underestimated the integrated optical depths in the line by up to a factor of 3. This is due to the removal of large Lorentzian wings from the pressure broadened line profiles during baseline subtraction. Models where some or all of the recombination line optical depth originates in molecular clouds do not give satisfactory results. Models based on standard calculations of recombination line intensites (Salem & Brocklehurst 1979; Walmsley & Watson 1982) have high pressures and are out of thermal balance. We modified the theoretical calculation of line intensities, described by Salem & Brocklehurst (1979) and Walmsley & Watson (1982), by imposing a different boundary condition at large principal quantum number n. Instead of assuming an infinite number of levels populated according to thermodynamic equilibrium, we impose a cutoff in level populations above a critical principal quantum number ncr, as suggestd b y Gulyaev & Nefedov (1989). We followed the occupation probability formalism presented by Hummer & Mihalas (1988) to calculate ncr. Using these new line intensity calculations, we find that, with the exception of the recombination line width, all of the Cas A recombination line and lambda 21 cm H I absorption line data can be attributed to a region where the physical conditions are typical of the cold neutral medium of the interstellar medium. We show a model in which this region is in thermal balance at a temperature near 36 K and has a reasonable interstellar pressure. In this model, the photoionization of polycyclic aromatic hydrogen molecules is the dominant mechanism for heating the region