The densities in diffuse and translucent molecular clouds: estimates from observations of C$_2$ and from 3-dimensional extinction maps

Newly-computed collisional rate coefficients for the excitation of C$_2$ in collisions with H$_2$, presented recently by Najar and Kalugina (2020), are significantly larger than the values adopted previously in models for the excitation of the C$_2$ molecule, a widely used probe of the interstellar gas density. With these new rate coefficients, we have modeled the C$_2$ rotational distributions inferred from visible and ultraviolet absorption observations of electronic transitions of C$_2$ towards a collection of 46 nearby background sources. The inferred gas densities in the foreground interstellar clouds responsible for the observed C$_2$ absorption are a factor 4 to 7 smaller than those inferred previously, a direct reflection of the larger collisional rate coefficients computed by Najar and Kalugina (2020). These lower density estimates are generally in good agreement with the peak densities inferred from 3D extinction maps for the relevant sightlines. In cases where H$_3^+$ absorption has also been observed and used to estimate the cosmic-ray ionization rate (CRIR), our estimates of the latter will also decrease accordingly because the H$_3^+$ abundance is a function of the ratio of the CRIR to the gas density.