The High Mass Slope of the IMF
  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 ($\gtrsim 3$ 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 {\it apparent} slope, $\Gamma_{\rm app}$,
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 $\Gamma_{\rm app} \gtrsim \Gamma+
0.35$ 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
$\Gamma_{\rm app} \gtrsim \Gamma+0.35$, corresponding to $\Gamma_{\rm app}
\gtrsim 1.7$ when the underlying $\Gamma= 1.35$.
