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We analyze the relationship between maximum cluster mass, and surfacedensities of total gas (Sigma_gas), molecular gas (Sigma_H_2), neutral gas(Sigma_HI) and star formation rate (Sigma_SFR) in the grand design galaxy M51,using published gas data and a catalog of masses, ages, and reddenings of morethan 1800 star clusters in its disk, of which 223 are above the cluster massdistribution function completeness limit. We find for clusters older than 25Myr that M_3rd, the median of the 5 most massive clusters, is proportional toSigma_HI^0.4. There is no correlation with Sigma_gas, Sigma_H2, or Sigma_SFR.For clusters younger than 10 Myr, M_3rd is proportional to Sigma_HI^0.6, M_3rdis proportional to Sigma_gas^0.5; there is no correlation with either Sigma_H_2or Sigma_SFR. The results could hardly be more different than those found forclusters younger than 25 Myr in M33. For the flocculent galaxy M33, there is nocorrelation between maximum cluster mass and neutral gas, but M_3rd isproportional to Sigma_gas^3.8; M_3rd is proportional to Sigma_H_2^1.2; M_3rdproportional to Sigma_SFR^0.9. For the older sample in M51, the lack of tightcorrelations is probably due to the combination of the strong azimuthalvariations in the surface densities of gas and star formation rate, and thecluster ages. These two facts mean that neither the azimuthal average of thesurface densities at a given radius, nor the surface densities at thepresent-day location of a stellar cluster represent the true surface densitiesat the place and time of cluster formation. In the case of the younger sample,even if the clusters have not yet traveled too far from their birthsites, thepoor resolution of the radio data compared to the physical sizes of theclusters results in measured Sigmas that are likely quite diluted compared tothe actual densities relevant for the formation of the clusters.

astrophysical journal/the astrophysical journal

Gas surface density, star formation rate surface density, and the  maximum mass of young star clusters in a disk galaxy. II. The grand-design  galaxy M51