The Orbital Structure and Selection Effects of the Galactic Center S-star Cluster

The orbital distribution of the S-star cluster surrounding the supermassive black hole in the center of the Milky Way is analyzed. A tight, roughly exponential dependence of the pericenter distance rp on orbital eccentricity e(star) is found, log(r(p))similar to(1-e(star)), which cannot be explained simply by a random distribution of semi-major axes and eccentricities. No stars are found in the region with high e(star) and large log r(p) or in the region with low e(star) and small log r(p). G-clouds follow the same correlation. The likelihood P(log rp,(1-e(star))) to determine the orbital parameters of S-stars is determined. P is very small for stars with large e(star) and large log r(p). S-stars might exist in this region. To determine their orbital parameters, one however needs observations over a longer time period. On the other hand, if stars would exist in the region of low log rp and small e(star), their orbital parameters should by now have been determined. That this region is unpopulated therefore indicates that no S-stars exist with these orbital characteristics, providing constraints for their formation. We call this region, defined by log (r(p)/AU) < 1.57+2.6(1-e(star)), the zone of avoidance. Finally, it is shown that the observed frequency of eccentricities and pericenter distances is consistent with a random sampling of log r(p) and e(star). However, only if one takes into account that no stars exist in the zone of avoidance and that orbital parameters cannot yet be determined for stars with large rp and large e(star).