SOFIA {\it FORCAST} Photometry of 12 Extended Green Objects in the Milky
  Way
  Massive young stellar objects are known to undergo an evolutionary phase in
which high mass accretion rates drive strong outflows. A class of objects
believed to trace this phase accurately is the GLIMPSE Extended Green Object
(EGO) sample, so named for the presence of extended 4.5 $\mu$m emission on
sizescales of $\sim$0.1 pc in \textit{Spitzer} images. We have been conducting
a multi-wavelength examination of a sample of 12 EGOs with distances of 1 to 5
kpc. In this paper, we present mid-infrared images and photometry of these EGOs
obtained with the SOFIA telescope, and subsequently construct SEDs for these
sources from the near-IR to sub-millimeter regimes using additional archival
data. We compare the results from greybody models and several
publicly-available software packages which produce model SEDs in the context of
a single massive protostar. The models yield typical \rstar\/$\sim$10 \rsun,
\tstar\/$\sim$10$^3$ to 10$^4$ K, and \lstar\/$\sim$1~$-$~40~$\times$~10$^3$
\lsun; the median $L/M$ for our sample is 24.7 \lsun/\msun. Model results
rarely converge for \rstar\/ and \tstar, but do for \lstar, which we take to be
an indication of the multiplicity and inherently clustered nature of these
sources even though, typically, only a single source dominates in the
mid-infrared. The median $L/M$ value for the sample suggests that these objects
may be in a transitional stage between the commonly described ``IR-quiet'' and
``IR-bright'' stages of MYSO evolution. The median $T_{dust}$ for the sample is
less conclusive, but suggests that these objects are either in this
transitional stage or occupy the cooler (and presumably younger) part of the
IR-bright stage.
