Recent papers have found that the inferred slope of the high-mass ( > 1.5 M _ { \odot } ) IMF for field stars in the solar vicinity has a larger value ( \sim 1.7 - 2.1 ) than the slopes ( \sim 1.2 - 1.7 ; Salpeter= 1.35 ) inferred from numerous studies of young clusters .
We attempt to reconcile this apparent contradiction .
Stars mostly form in Giant Molecular Clouds , and the more massive stars ( \raise 1.29 pt \hbox { $ > $ } \kern - 7.5 pt \lower 3.01 pt \hbox { $ \sim$ } 3 M _ { \odot } ) may have insufficient time before their deaths to uniformly populate the solar circle of the Galaxy .
We examine the effect of small sample volumes on the apparent slope , \Gamma _ { app } , of the high-mass IMF by modeling the present day mass function ( PDMF ) over the mass range 1.5 - 6 M _ { \odot } .
Depending on the location of the observer along the solar circle and the size of the sample volume , the apparent slope of the IMF can show a wide variance , with typical values steeper than the underlying universal value \Gamma .
We show , for example , that the PDMFs observed in a small ( radius \sim 200 pc ) volume randomly placed at the solar circle have a \sim 15 - 30 % likelihood of resulting in \Gamma _ { { app } } \raise 1.29 pt \hbox { $ > $ } \kern - 7.5 pt \lower 3.01 pt \hbox { $ \sim% $ } \Gamma + 0.35 because of inhomogeneities in the surface densities of more massive stars .
If we add the a priori knowledge that the Sun currently lies in an interarm region , where the star formation rate is lower than the average at the solar circle , we find an even higher likelihood ( \sim 50 - 60 \% ) of \Gamma _ { { app } } \raise 1.29 pt \hbox { $ > $ } \kern - 7.5 pt \lower 3.01 pt \hbox { $ \sim% $ } \Gamma + 0.35 , corresponding to \Gamma _ { { app } } \raise 1.29 pt \hbox { $ > $ } \kern - 7.5 pt \lower 3.01 pt \hbox { $ \sim% $ } 1.7 when the underlying \Gamma = 1.35 .