Bright stars and an optically thick inactive disk in Sgr A* and other dormant galaxy centers

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. The first of these is the eclipse 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 $\mu$m 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 ${\sim} 30~\mu$m. 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. We estimate the emissivity of the thin layer photo-ionized by the star in Hydrogen Br $\gamma$ line and in the continuum recombination in the 2.2 $\mu$m band, and find that it may be detectable in the future if the disk exists.