GAS SURFACE DENSITY, STAR FORMATION RATE SURFACE DENSITY, AND THE MAXIMUM MASS OF YOUNG STAR CLUSTERS IN A DISK GALAXY. I. THE FLOCCULENT GALAXY M 33

We analyze the relationship between maximum cluster mass M-max and surface densities of total gas (Sigma(gas)), molecular gas (Sigma(H2)), and star formation rate (Sigma(SFR)) in the flocculent galaxy M 33, using published gas data and a catalog of more than 600 young star clusters in its disk. By comparing the radial distributions of gas and most massive cluster masses, we find that M-max alpha Sigma(4.7 +/- 0.4)(gas), M-max alpha Sigma(1.3 +/- 0.1)(H2), and M-max alpha Sigma(1.0 +/- 0.1)(SFR). We rule out that these correlations result from the size of the sample; hence, the change of the maximum cluster mass must be due to physical causes.