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

Abstract

The orbital distribution of the S-star cluster surrounding the supermassive black hole in the center of the Milky Way is analyzed. A tight dependence of the pericenter distance r p on orbital eccentricity e ⋆ is found, log(rp)∼(1−e⋆) , which cannot be explained simply by a random distribution of semimajor axis and eccentricities. No stars are found in the region with high e ⋆ and large log(rp) or in the region with low e ⋆ and small log(rp) . Although the sample is still small, the G-clouds show a very similar distribution. The likelihood P(log(rp),(1−e⋆)) to determine the orbital parameters of S-stars is determined. P is very small for stars with large e ⋆ and large log(rp) . 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 ⋆, 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(rp/AU)<1.57+2.6(1−e⋆) , 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(rp) and e ⋆ if one takes into account the fact that no stars exist in the zone of avoidance and that orbital parameters cannot yet be determined for stars with large r p and large e ⋆.