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Fifty Years of IMF Variation: The Intermediate-Mass Stars

I track the history of star count estimates of the Milky Way field star and open cluster IMFs, concentrating on the neglected mass range from 1 to 15 M${_\odot}$. The prevalent belief in a universal IMF appears to be without basis for this mass range. Two recent estimates of the field star IMF using different methods and samples give values of the average logarithmic slope $Γ$ between -1.7 and -2.1 in the mass range 1.1 to 4 M${_\odot}$. Two older estimates between 2 and 15 M${_\odot}$ disagree severely; the field IMF in this range is essentially unknown from star counts. Variations in $Γ$ among open cluster IMFs in this mass range have not decreased despite numerous detailed studies, even for studies using homogeneous data and reduction procedures and including only clusters with a significant mass range. These cluster variations \textit{might} be due to the combined effects of sampling, systematic errors, stellar evolution uncertainties, dynamical evolution, and unresolved binaries. If so, then the cluster data are consistent with a universal IMF, but are also consistent with sizeable variations. The cluster data do not allow an estimate of an average IMF or $Γ$ because the average depends on the choice of weighting procedure and other effects. If the spread in cluster IMFs is in excess of the effects listed above, real IMF variations must occur that do not depend much on physical conditions explored so far. The complexity of the star formation process seen in observations and simulations suggests that large realization-to-realization differences might be expected, in which case an individual cluster IMF would be in part the product of evolutionary contingency in star formation, and the function of interest is the probability distribution of IMF parameters.