A mean density of $112\, M_{\odot}\,\rm pc^{-3}$ for Central Molecular
  Zone clumps -- Evidences for shear-enabled pressure equilibrium in the
  Galactic Center
  We carry out a systematic study of the density structure of gas in the
Central Molecular Zone (CMZ) in the Galactic center by extracting clumps from
the APEX Telescope Large Area Survey of the Galaxy survey at 870 $\mu$m. We
find that the clumps follow a scaling of $m = \rho_0 r^3$ which corresponds to
a characteristic density of $n_{\rm H_2} = 1.6 \times 10^3\,\rm cm^{-3}$
($\rho_0 =112\;M_{\odot}\;\rm pc^{-3}$) with a variation of $\approx 0.5\,\rm
dex$, where we assumed a gas-to-dust mass ratio of 100. This characteristic
density can be interpreted as the result of thermal pressure equilibrium
between the molecular gas and the warm ambient interstellar medium. Such an
equilibrium can plausibly be established since shear has approximately the same
strength as self-gravity. Our findings may explain the fact that star formation
in the CMZ is highly inefficient compared to the rest of the Milky Way disk. We
also identify a population of clumps whose densities are two orders of
magnitudes higher in the vicinity of the Sgr B2 region, which we propose are
produced by collisions between the clumps of lower densities. For these
collisions to occur, processes such as compressive tides probably have created
the appropriate condition by assembling the clumps together.
