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 () 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) X104 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.
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