Temperature structures in Galactic Center clouds - Direct evidence for
  gas heating via turbulence
  The Central Molecular Zone (CMZ) at the center of our Galaxy is the best
template to study star formation processes under extreme conditions, similar to
those in high-redshift galaxies. We observed on-the-fly maps of para-H$_{2}$CO
transitions at 218 GHz and 291 GHz towards seven Galactic Center clouds. From
the temperature-sensitive integrated intensity line ratios of
H$_{2}$CO(3$_{2,1}-$2$_{2,0}$)/H$_{2}$CO(3$_{0,3}-$2$_{0,2}$) and
H$_{2}$CO(4$_{2,2}-$3$_{2,1}$)/H$_{2}$CO(4$_{0,4}-$3$_{0,3}$) in combination
with radiative transfer models, we produce gas temperature maps of our targets.
These transitions are sensitive to gas with densities of $\sim$10$^{5}$
cm$^{-3}$ and temperatures <150 K. The measured gas temperatures in our sources
are all higher (>40 K) than their dust temperatures ($\sim$25 K). Our targets
have a complex velocity structure that requires a careful disentanglement of
the different components. We produce temperature maps for each of the velocity
components and show that the temperatures of the components differ, revealing
temperature gradients in the clouds. Combining the temperature measurements
with the integrated intensity line ratio of
H$_{2}$CO(4$_{0,4}-$3$_{0,3}$)/H$_{2}$CO(3$_{0,3}-$2$_{0,2}$), we constrain the
density of this warm gas to 10$^{4}-$10$^{6}$ cm$^{-3}$. We find a positive
correlation of the line width of the main H$_{2}$CO lines with the temperature
of the gas, direct evidence for gas heating via turbulence. Our data is
consistent with a turbulence heating model with a density of n = 10$^5$
cm$^{-3}$.
