A High Resolution Study of Carbon Radio Recombination Lines towards
  Cassiopeia A
  Carbon Radio Recombination Lines trace the interface between molecular and
atomic gas. We present GMRT observations of Carbon Radio Recombination Lines
(CRRL), C$\alpha$244-C$\alpha$250 towards Cassiopeia A. We use a novel
technique of stacking the emission lines in the visibility domain to obtain,
for the first time, sub-pc resolution optical depth maps of these CRRLs. The
emission shows a wide range of spatial and velocity structures, some of which
are unresolved within our synthesis beam of 0.29 pc and velocity channel of
0.55 km/s. These variations in the emission optical depth and line width are
indicative of inhomogeneity and fragmentation in the intervening Perseus Arm
gas. We compare the distribution of the CRRL emission with that of diffuse and
dense molecular gas using existing CO and H$_2$CO studies. We find that the CO
emission in the -47 km/s Perseus Arm component is primarily concentrated along
an elongated structure detected in our CRRL maps, to the south of which lies
the high-density molecular clumps traced by H$_2$CO. This spatial distribution
of CRRL and molecular tracers is similar to what one would observe for a Photo
Dissociation Region (PDR). In the other Perseus Arm component centered at -37
km/s, there is evidence for high column density (N$_{H_2}$ ~
$10^{22}$cm$^{-2}$) molecular clumps embedded in diffuse CO as well as CRRL
emission towards the center of Cassiopeia A. We propose that the CRRL emissions
coincident with molecular tracers originates from the line of sight integrated
component of the C$^{+}$ envelope of the molecular gas.
