The cluster birthline in M33

We test the reliability of infrared (IR) emission to trace star formation in individual star-forming sites of M33, and outline a new method for testing the distribution function of massive stars in newly formed clusters. We select IR sources from the Spitzer survey of M33 and show that the IR and Halpha luminosities are not correlated. Complementing the infrared photometry with GALEX-UV data, we estimate the source bolometric luminosities. For a given stellar IMF we simulate a theoretical curve for the expected bolometric-to-Halpha luminosity ratio, along which stellar clusters are born. We call this the cluster birthline in the Lbol--Lbol/LHal plane. The birthline is flat for Lbol>3x10^{39}erg/s because all clusters fully sample the IMF and it increases toward lower luminosities as the upper end of the IMF becomes incompletely sampled. The observations of M33 show that young isolated clusters lie close to the theoretical birthline for a wide range of Lbol. The luminosity is not proportional to Halpha emission for low mass clusters and aging moves clusters above the birthline. The best fit to the birthline is for a randomly sampled IMF, in which the mass of most massive star in a cluster is not strictly limited by the cluster's mass. We also find that the IR luminosity of young stellar clusters in M33 is not proportional to their bolometric luminosity. This irregularity could be the result of low and patchy dust abundance in M33.