The cluster birthline in M 33

Abstract

Aims. The aim of this paper is twofold: (a) to determine the reliability of infrared (IR) emission to trace star formation in individual star-forming sites of M 33, and (b) to outline a new method for testing the distribution function of massive stars in newly formed clusters. Methods. We select 24 μm IR sources from the Spitzer survey of M 33 with Hα counterparts and show that the IR luminosities have a weak dependence on galactocentric radius. The IR and Hα luminosities are not correlated. Complementing the infrared photometry with GALEX-UV data, we estimate the bolometric luminosities to investigate how they are related to the Hα luminosities. We simulate a theoretical diagram for the expected bolometric-to-Hα luminosity ratio, Lbol/ LHα, of young clusters as a function of the cluster luminosity. We then compare the observed Lbol/LHα ratios with the theoretical predictions. Results. In the log(LLbol/L Hα) plane, stellar clusters should be born along a curve that we call the cluster birthline. The birthline depends on the stellar initial mass function (IMF) at the high-mass end, but not on the cluster mass function. For an upper stellar mass limit of 120 M⊙, the birthline is flat for Lbol > 3 × 1039 erg s-1 because all clusters fully sample the IMF. It increases toward lower luminosities as the upper end of the IMF becomes incompletely sampled. Aging moves clusters above the birthline. The observations of M 33 show that young isolated clusters lie close to the theoretical birthline for a wide range of bol. The observed Lbol/LHα ratio increases toward low L bol like the theoretical curve, indicating that luminosity is not proportional to Hα emission for low mass clusters. 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, but can have any value up to the maximum stellar mass with a probability determined by the IMF. We also find that the IR luminosity of young stellar clusters in M 33 is not proportional to their bolometric luminosity. This irregularity could be the result of low and patchy dust abundance. In M 33 dust absorbs and re-radiates in the IR only part of the UV light from young clusters. . © 2009 ESO.