On a Source of Systematic Error in Absolute Measurement of Galactocentric Distance from Sol.pdf

a r X i v : 0 8 0 3 .0 8 2 5 v 1 [ a s t r o - p h ] 6 M a r 2 0 0 8 On a Source of Systematic Error in Absolute Measurement of Galactocentric Distance from Solving for the Stellar Orbit Around Sgr A* Igor’ I. Nikiforov Sobolev Astronomical Institute, St. Petersburg State University, Universitetskij pr. 28, Staryj Peterhof, St. Petersburg 198504, Russia, nii@astro.spbu.ru Abstract. Eisenhauer et al. (2003, 2005) derived absolute (geometrical) estimates of the distance to the center of the Galaxy, R0, from the star S2 orbit around Sgr A* on the assumption that the intrinsic velocity of Sgr A* is negligible. This assumption produces the source of systematic error in R0 value owing to a probable motion of Sgr A* relative to the accepted velocity reference system which is arbitrary to some extent. Eisenhauer et al. justify neglecting all three spatial velocity components of Sgr A* mainly by low limits of Sgr A*’s proper motion of 20–60 km/s. In this brief paper, a simple analysis in the context of the Keplerian dynamics was used to demonstrate that neglect of even low (perhaps, formal) radial velocity of Sgr A* leads to a substantial systematic error in R0: the same limits of 20–60 km/s result in R0 errors of 1.3–5.6%, i.e., (0.1–0.45)×(R0/8) kpc, for current S2 velocities. Similar values for Sgr A*’s tangential motion can multiply this systematic error in the case of S2 orbit by factor ≈1.5–1.9 in the limiting cases. 1. Introduction The distance from the Sun to the center of the Milky Way, R0, is a fundamental Galactic constant for solving many astronomical and astrophysical problems (see, e.g., Reid 1993). That is why, in its turn, the problem of determination of R0 remains topical over many years. Absolute (i.e., not using luminosity calibrations) estimates of R0 with a current 3% formal uncertainty from modelling the star S2 orbit around the compact concentration of dark mass, the so-called “supermassive black hole”, associated with the radio source Sgr A* (