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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

We analyze the relationship between maximum cluster mass, and surface densities 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 more than 1800 star clusters in its disk, of which 223 are above the cluster mass distribution function completeness limit. We find for clusters older than 25 Myr that M_3rd, the median of the 5 most massive clusters, is proportional to Sigma_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_3rd is proportional to Sigma_gas^0.5; there is no correlation with either Sigma_H_2 or Sigma_SFR. The results could hardly be more different than those found for clusters younger than 25 Myr in M33. For the flocculent galaxy M33, there is no correlation between maximum cluster mass and neutral gas, but M_3rd is proportional to Sigma_gas^3.8; M_3rd is proportional to Sigma_H_2^1.2; M_3rd proportional to Sigma_SFR^0.9. For the older sample in M51, the lack of tight correlations is probably due to the combination of the strong azimuthal variations in the surface densities of gas and star formation rate, and the cluster ages. These two facts mean that neither the azimuthal average of the surface densities at a given radius, nor the surface densities at the present-day location of a stellar cluster represent the true surface densities at 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, the poor resolution of the radio data compared to the physical sizes of the clusters results in measured Sigmas that are likely quite diluted compared to the actual densities relevant for the formation of the clusters.