Molecular Gas Density Measured with H2CO and CS toward a Spiral Arm of M51

Observations of various molecular lines toward a disk region of a nearby galaxy are now feasible, and they are being employed as diagnostic tools to study star formation activities there. However, the spatial resolution attainable for a nearby galaxy with currently available radio telescopes is 10-1000 pc, which is much larger than the scales of individual star-forming regions and molecular-cloud cores. Hence, it is of fundamental importance to elucidate which part of an interstellar medium such spatially unresolved observations are tracing. Here we present sensitive measurements of the H₂CO ({1}₀₁-{0}₀₀) line at 72 GHz toward giant molecular clouds (GMCs) in the spiral arm of M51 using the NRO 45 m and IRAM 30 m telescopes. In conjunction with the previously observed H₂CO (2₀₂ - 1₀₁) and CS (2 - 1 and 3 - 2) lines, we derive the H₂ density of the emitting regions to be (0.6-2.6) × 10⁴ cm^-3 and (2.9-12) × 10⁴ cm^-3 for H₂CO and CS, respectively, by the non-LTE analyses, where we assume the source size of 0.8-1 kpc and the gas kinetic temperature of 10-20 K. The derived H₂ density indicates that the emission of H₂CO and CS is not localized to star-forming cores, but is likely distributed over an entire region of GMCs. Such widespread distributions of H₂CO and CS are also supported by models assuming lognormal density distributions over the 1 kpc region. Thus, contributions from the widespread less dense components should be taken into account for interpretation of the molecular emission observed with a GMC-scale resolution. The different H₂ densities derived for H₂CO and CS imply their different distributions. We discuss these differences in terms of the formation processes of H₂CO and CS.