The goal of this paper is to test whether the formation rate of star clusters is proportional to the star formation rate ( SFR ) in galaxies .
As a first step , we present the mass functions of compact clusters younger than 10 Myr in seven star-forming galaxies of diverse masses , sizes , and morphologies : the Large and Small Magellanic Clouds , NGC 4214 , NGC 4449 , M83 , M51 , and the Antennae .
These cluster mass functions ( CMFs ) are well represented by power laws , dN / dM \propto M ^ { \beta } , with similar exponents \beta = -1.92 \pm 0.27 , but with amplitudes that differ by factors up to \sim 10 ^ { 3 } , corresponding to vast differences in the sizes of the cluster populations in these galaxies .
We then normalize these CMFs by the SFRs in the galaxies , derived from dust-corrected H \alpha luminosities , and find that the spread in the amplitudes collapses , with a remaining rms deviation of only \sigma ( \log A ) = 0.2 .
This is close to the expected dispersion from random uncertainties in the CMFs and SFRs .
Thus , the data presented here are consistent with exact proportionality between the formation rates of stars and clusters .
However , the data also permit weak deviations from proportionality , at the factor of two level , within the statistical uncertainties .
We find the same spread in amplitudes when we normalize the mass functions of much older clusters , with ages in the range 100 to 400 Myr , by the current SFR .
This is another indication of the general similarity among the cluster populations of different galaxies .