The Orbital Structure and Selection Effects of the Galactic Center S-star Cluster
Andreas Burkert, S. Gillessen, D. N. C. Lin, Xiaochen Zheng, Philipp Schoeller, F. Eisenhauer, R. Genzel
Abstract
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, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo>∼</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>e</mml:mi> <mml:mo>⋆</mml:mo> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> or in the region with low e ⋆ and small <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> . Although the sample is still small, the G-clouds show a very similar distribution. The likelihood <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>P</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo>,</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>e</mml:mi> <mml:mo>⋆</mml:mo> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo stretchy="false">)</mml:mo> </mml:math> to determine the orbital parameters of S-stars is determined. P is very small for stars with large e ⋆ and large <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> . 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> </mml:msub> <mml:mo stretchy="true">/</mml:mo> <mml:mi>AU</mml:mi> <mml:mo stretchy="false">)</mml:mo> <mml:mo><</mml:mo> <mml:mn>1.57</mml:mn> <mml:mo>+</mml:mo> <mml:mn>2.6</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>e</mml:mi> <mml:mo>⋆</mml:mo> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> , the zone of avoidance. Finally, it is shown that the observed frequency of eccentricities and pericenter distances is consistent with a random sampling of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>log</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi mathvariant="normal">p</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> 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 ⋆ .