2024ApJ...962...81B

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, $\mathrm{log}({r}_{{\rm{p}}})\sim (1-{e}_{\star })$, 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 $\mathrm{log}({r}_{{\rm{p}}})$ or in the region with low e_⋆ and small $\mathrm{log}({r}_{{\rm{p}}})$. Although the sample is still small, the G-clouds show a very similar distribution. The likelihood $P(\mathrm{log}({r}_{{\rm{p}}}),(1-{e}_{\star }))$ to determine the orbital parameters of S-stars is determined. P is very small for stars with large e_⋆ and large $\mathrm{log}({r}_{{\rm{p}}})$. 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 $\mathrm{log}({r}_{{\rm{p}}})$ 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 $\mathrm{log}({r}_{{\rm{p}}}/\mathrm{AU})\lt 1.57+2.6(1-{e}_{\star })$, the zone of avoidance. Finally, it is shown that the observed frequency of eccentricities and pericenter distances is consistent with a random sampling of $\mathrm{log}({r}_{{\rm{p}}})$ 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_⋆.