The Distribution of Mass Surface Densities in a High-Mass Protocluster
  We study the probability distribution function (PDF) of mass surface
densities, $\Sigma$, of infrared dark cloud (IRDC) G028.37+00.07 and its
surrounding giant molecular cloud. This PDF constrains the physical processes,
such as turbulence, magnetic fields and self-gravity, that are expected to be
controlling cloud structure and star formation activity. The chosen IRDC is of
particular interest since it has almost 100,000 solar masses within a radius of
8 parsecs, making it one of the most massive, dense molecular structures known
and is thus a potential site for the formation of a "super star cluster." We
study $\Sigma$ in two ways. First, we use a combination of NIR and MIR
extinction maps that are able to probe the bulk of the cloud structure up to
$\Sigma\sim1\:{\rm{g\:cm}^{-2}}\:$($A_V\simeq200$ mag). Second, we study the
FIR and sub-mm dust continuum emission from the cloud utilizing Herschel PACS
and SPIRE images and paying careful attention to the effects of foreground and
background contamination. We find that the PDFs from both methods, applied over
a $\sim20^\prime$(30 pc)-sized region that contains
$\simeq1.5\times10^5\:M_\odot$ and encloses a minimum closed contour with
$\Sigma\simeq0.013\:{\rm{g\:cm}^{-2}}\:$($A_V\simeq3$ mag), shows a log-normal
shape with the peak measured at
$\Sigma\simeq0.021\:{\rm{g\:cm}^{-2}}\:$($A_V\simeq4.7$ mag). There is
tentative evidence for the presence of a high-$\Sigma$ power law tail that
contains from $\sim3\%$ to 8\% of the mass of the cloud material. We discuss
the implications of these results for the physical processes occurring in this
cloud.
