The Circumnuclear Disk Revealed by ALMA. I. Dense Clouds and Tides in
  the Galactic Center
  Utilizing the Atacama Large Millimeter/submillimeter Array (ALMA), we present
CS line maps in five rotational lines ($J_{\rm u}=7, 5, 4, 3, 2$) toward the
circumnuclear disk (CND) and streamers of the Galactic Center. Our primary goal
is to resolve the compact structures within the CND and the streamers, in order
to understand the stability conditions of molecular cores in the vicinity of
the supermassive black hole (SMBH) Sgr A*. Our data provide the first
homogeneous high-resolution ($1.3'' = 0.05$ pc) observations aiming at
resolving density and temperature structures. The CS clouds have sizes of
$0.05-0.2$ pc with a broad range of velocity dispersion ($\sigma_{\rm
FWHM}=5-40$ km s$^{-1}$). The CS clouds are a mixture of warm ($T_{\rm k}\ge
50-500$ K, n$_{\rm H_2}$=$10^{3-5}$ cm$^{-3}$) and cold gas ($T_{\rm k}\le 50$
K, n$_{\rm H_2}$=$10^{6-8}$ cm$^{-3}$). A stability analysis based on the
unmagnetized virial theorem including tidal force shows that $84^{+16}_{-37}$ %
of the total gas mass is tidally stable, which accounts for the majority of gas
mass. Turbulence dominates the internal energy and thereby sets the threshold
densities $10-100$ times higher than the tidal limit at distance $\ge 1.5$ pc
to Sgr A*, and therefore, inhibits the clouds from collapsing to form stars
near the SMBH. However, within the central $1.5$ pc, the tidal force overrides
turbulence and the threshold densities for a gravitational collapse quickly
grow to $\ge 10^{8}$ cm$^{-3}$.
