Gas surface density, star formation rate surface density, and the
  maximum mass of young star clusters in a disk galaxy. I. The flocculent
  galaxy M33
  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 M33, 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
is proportional to Sigma_gas^4.7, M_max is proportional Sigma_H2^1.3, and M_max
is proportional to Sigma_SFR^1.0. We rule out that these correlations result
from the size of sample; hence, the change of the maximum cluster mass must be
due to physical causes.
