Excitation and Abundance of C3 in star forming cores:Herschel/HIFI
  observations of the sight-lines to W31C and W49N
  We present spectrally resolved observations of triatomic carbon (C3) in
several ro-vibrational transitions between the vibrational ground state and the
low-energy nu2 bending mode at frequencies between 1654-1897 GHz along the
sight-lines to the submillimeter continuum sources W31C and W49N, using
Herschel's HIFI instrument. We detect C3 in absorption arising from the warm
envelope surrounding the hot core, as indicated by the velocity peak position
and shape of the line profile. The sensitivity does not allow to detect C3
absorption due to diffuse foreground clouds. From the column densities of the
rotational levels in the vibrational ground state probed by the absorption we
derive a rotation temperature (T_rot) of ~50--70 K, which is a good measure of
the kinetic temperature of the absorbing gas, as radiative transitions within
the vibrational ground state are forbidden. It is also in good agreement with
the dust temperatures for W31C and W49N. Applying the partition function
correction based on the derived T_rot, we get column densities N(C3)
~7-9x10^{14} cm^{-2} and abundance x(C3)~10^{-8} with respect to H2. For W31C,
using a radiative transfer model including far-infrared pumping by the dust
continuum and a temperature gradient within the source along the line of sight
we find that a model with x(C3)=10^{-8}, T_kin=30-50 K, N(C3)=1.5 10^{15}
cm^{-2} fits the observations reasonably well and provides parameters in very
good agreement with the simple excitation analysis.
