Periastron shifts of stellar orbits near the Galactic Center

¹ Institut für Theoretische Physik, Universität zu Köln, Zülpicherstraße 77, 50937 Köln, Germany
² I. Physikalisches Institut, Universität zu Köln, Zülpicherstraße 77, 50937 Köln, Germany e-mail: eckart@ph1.uni-koeln.de

Corresponding author: G. F. Rubilar, gr@thp.uni-koeln.de

Received: 22 December 2000
Accepted: 2 May 2001

Abstract

The presence of a million solar mass object in the central stellar cluster of the Milky Way has recently been demonstrated via measurements of the stellar proper motions and radial velocities. This mass is located at the position of the compact radio source Sagittarius A^* (Sgr A^*) at a distance of kpc and is most likely present in the form of a massive black hole (BH). Some of the stars have a projected distance to Sgr A^* of ≤0.005 pc and have proper motion velocities of up to 1400 km s^-1. Recent measurements indicate that their orbits show significant curvatures indicating that the stars indeed orbit the central compact object. Detailed measurements of the stellar orbits close to Sgr A^* will allow us to precisely determine the distribution of this mass. With an increased point source sensitivity due to the combination of large telescope apertures, adaptive optics, and -in the very near future -NIR interferometry it is likely that stars with orbital time scales of the order of one year will be detected. Theses sources, however, will most likely not be on simple Keplerian orbits. The effects of measurable prograde relativistic and retrograde Newtonian periastron shifts will result in rosetta shaped orbits. A substantial Newtonian periastron rotation can already be expected if only a few percent of the central mass are extended. We discuss the conditions under which an extended mass can (over-) compensate the relativistic periastron shift. We also demonstrate that measuring a single periastron shift is not sufficient to determine the distribution of an extended mass component. A periastron shift will allow us to determine the inclination of the stellar orbits and to derive inclination corrected shift values. These have to be acquired for three stars on orbits with different energy or angular momentum in order to unambiguously solve for the compactness, extent and shape of any extended mass contribution.