Methylidyne (CH) is one of the most common molecules in the interstellar medium, and is an excellent tracer of molecular hydrogen using optical observations.
Unfortunately, radio observations of CH at $3.3$ GHz require long integration times and, for analysis, the excitation
temperature ($T_{\rm{ex}}$) must be known or assumed.
The excitation temperature of the ground state, hyperfine, main line transition of CH at $3335$ MHz is often assumed to be
$-15$ K (Rydbeck et al. $1976$).
Based on comparisons of radio and optical/uv observations from the literature, using $T_{\rm{ex}}$ = $-15$ K for the $3335$ MHz line may be overestimating the CH column density on average. By comparing the N(CH)/N(H$_2$) ratio and N(CH)/E(B-V) ratio for both data sets, we determine $T_{\rm{ex}}$ may be approximately $-4$ K on average. We calculated the excitation temperature of the CH main line at $3335$ MHz for $16$ lines of sight with optical/UV and radio observations of CH, and we found $T_{\rm{ex}}$ varies significantly between the lines of sight. For example, for HD $24534$, $T_{\rm{ex}}$ = $-3.1$ K, while for HD $24398$ $T_{\rm{ex}}$ = $-27$ K.
CH production in the ISM is closely linked to the production of H$_2$, so we compare CH observations with CO in the diffuse clouds MBM $16$ and MBM $53$. In MBM $16$, CH is able to trace the CO-faint gas which surrounds a CO-bright clump. In CH the molecular gas in the sampled region is roughly uniform, but the CO observations suggests there is a compact clump surrounded by far less dense gas, a suggestion which is not supported by HI and extinction observations. CH and CO observations in MBM $53$ seem to also support that CH is able to trace CO-faint gas, but due to the faint CH $3335$ MHz signal, CH is able to trace gas surrounding CO-bright gas only if the column density of H$_2$ is greater than $\sim 10^{20}$ cm$^{-2}$. In very diffuse regions of MBM $53$, CO was able to be detected, but the signal was too faint for CH to be detected with the integration times used.
Based on comparisons of radio and optical/uv observations from the literature, using $T_{\rm{ex}}$ = $-15$ K for the $3335$ MHz line may be overestimating the CH column density on average. By comparing the N(CH)/N(H$_2$) ratio and N(CH)/E(B-V) ratio for both data sets, we determine $T_{\rm{ex}}$ may be approximately $-4$ K on average. We calculated the excitation temperature of the CH main line at $3335$ MHz for $16$ lines of sight with optical/UV and radio observations of CH, and we found $T_{\rm{ex}}$ varies significantly between the lines of sight. For example, for HD $24534$, $T_{\rm{ex}}$ = $-3.1$ K, while for HD $24398$ $T_{\rm{ex}}$ = $-27$ K.
CH production in the ISM is closely linked to the production of H$_2$, so we compare CH observations with CO in the diffuse clouds MBM $16$ and MBM $53$. In MBM $16$, CH is able to trace the CO-faint gas which surrounds a CO-bright clump. In CH the molecular gas in the sampled region is roughly uniform, but the CO observations suggests there is a compact clump surrounded by far less dense gas, a suggestion which is not supported by HI and extinction observations. CH and CO observations in MBM $53$ seem to also support that CH is able to trace CO-faint gas, but due to the faint CH $3335$ MHz signal, CH is able to trace gas surrounding CO-bright gas only if the column density of H$_2$ is greater than $\sim 10^{20}$ cm$^{-2}$. In very diffuse regions of MBM $53$, CO was able to be detected, but the signal was too faint for CH to be detected with the integration times used.