  Cold inactive disks are believed to exist in Low Luminosity AGN (LLAGN). They
may also exist in the nuclei of inactive galaxies and in the center of our own
Galaxy. These disks would then be embedded in the observed dense nuclear
stellar clusters. Making the simplest assumption of an optically thick disk, we
explore several ways to detect the disk presence through its interaction with
the cluster. First of these is the eclipses of close bright stars by the disk.
The second is the increase in the infrared flux of the disk due to illumination
of its surface by such stars during close passages. Finally the surface
brightness of the star cluster should show an anisotropy that depends on the
inclination angle of the disk. We apply the first two of the methods to Sgr A*,
the super massive black hole in our Galactic Center. Using the orbital
parameters of the close star S2, we strongly rule out a disk optically thick in
the near infrared unless it has a relatively large inner hole. For disks with
no inner holes, we estimate that the data permit a disk with infrared optical
depth no larger than about 0.01. Such a disk could also be responsible for the
detected 3.8 microns excess in the spectrum of S2. The constraints on the disk
that we obtain here can be reconciled with the disk parameters needed to
explain the observed X-ray flares if dust particles in the disk have sizes
greater than ~ 30 microns. The destruction of small dust particles by strong UV
heating and shocks from star passages through the disk, and grain growth during
"quiescent" times, are mentioned as possible mechanisms of creating the unusual
grain size distribution. (...)
