The Fraction of Stars That Form in Clusters in Different Galaxies

We estimate the fraction of stars that form in compact clusters (bound and unbound), {{{Γ }}}_F, in a diverse sample of eight star-forming galaxies, including two irregulars, two dwarf starbursts, two spirals, and two mergers. The average value for our sample is {{{Γ }}}_F≈ 24 % +/- 9 % . We also calculate the fraction of stars in clusters that survive to ages between {τ }₁ and {τ }₂, denoted by {{{Γ }}}_S({τ }₁,{τ }₂), and find {{{Γ }}}_S(10,100)=4.6 % +/- 2.5 % and {{{Γ }}}_S(100,400)=2.4 % +/- 1.1 % , significantly lower than {{{Γ }}}_F for the same galaxies. We do not find any systematic trends in {{{Γ }}}_F or {{{Γ }}}_S with the star formation rate (SFR), the SFR per unit area ({{{Σ }}}_{SFR}), or the surface density of molecular gas ({{{Σ }}}_{{{H}}₂}) within the host galaxy. Our results are consistent with those found previously from the CMF/SFR statistic (where CMF is the cluster mass function), and with the quasi-universal model in which clusters in different galaxies form and disrupt in similar ways. Our results, however, contradict many previous claims that the fraction of stars in bound clusters increases strongly with {{{Σ }}}_{SFR} and {{{Σ }}}_{{{H}}₂}. We find that the previously reported trends are largely driven by comparisons that mixed {{{Γ }}}_F≈ {{{Γ }}}_S(0,10) and {{{Γ }}}_S(10,100), where {{{Γ }}}_S(0,10) was systematically used for galaxies with higher {{{Σ }}}_{SFR} and {{{Σ }}}_{{{H}}₂}, and {{{Γ }}}_S(10,100) for galaxies with lower {{{Σ }}}_{SFR} and {{{Σ }}}_{{{H}}₂}.