------------------------------------------------------------------------
 paper "On PN orbits and GC stars", ApJ, Oct 2009, in press
Message-ID: <Pine.LNX.4.56.0908191705490.26348@bootes>
MIME-Version: 1.0
Content-Type: TEXT/PLAIN; charset=US-ASCII
X-MailScanner-Information: Please contact the postmaster@aoc.nrao.edu for more information
X-MailScanner: Found to be clean
X-MailScanner-SpamCheck: not spam, SpamAssassin (not cached, score=-4,
	required 5, autolearn=disabled, RCVD_IN_DNSWL_MED -4.00)
X-MailScanner-From: miguelp@ari.uni-heidelberg.de
X-Spam-Status: No



%arXiv:0906.2226

\documentclass[12pt,preprint]{aastex}

\begin{document}
\title{On post-Newtonian orbits \\ and the Galactic-center stars}
author{Miguel Preto}
\affil{Astronomisches Rechen-Institut, Zentrum f\"{u}r Astronomie, \\
University of Heidelberg, D-69120 Heidelberg, Germany}
\and
\author{Prasenjit Saha}
\affil{Institute for Theoretical Physics, University of Z\"{u}rich, \\
Winterthurerstrasse 190, CH-8057 Z\"{u}rich, Switzerland}

\begin{abstract}
  Stars near the Galactic center reach a few percent of light speed
  during pericenter passage, which makes post-Newtonian effects
  potentially detectable.  We formulate the orbit equations in
  Hamiltonian form such that the $O(v^2/c^2)$ and $O(v^3/c^3)$
  post-Newtonian effects of the Kerr metric appear as a simple
  generalization of the Kepler problem. A related perturbative
  Hamiltonian applies to photon paths. We then derive a symplectic
  integrator with adaptive time-steps, for fast and accurate numerical
  calculation of post-Newtonian effects.  Using this integrator, we
  explore relativistic effects.  Taking the star S2 as an example, we
  find that general relativity would contribute tenths of mas in
  astrometry and tens of $\rm km\;s^{-1}$ in kinematics.  (For
  eventual comparison with observations, redshift and time-delay
  contributions from the gravitational field on light paths will need
  to be calculated, but we do attempt these in the present paper.) The
  contribution from stars, gas, and dark matter in the Galactic center
  region is still poorly constrained observationally, but current
  models suggest that the resulting Newtonian perturbation on the
  orbits could plausibly be of the same order as the relativistic
  effects for stars with semi-major axes $\gtrsim 0.01$~pc (or
  250~mas).  Nevertheless, the known and distinctive {\it time
  dependence\/} of the relativistic perturbations may make it possible
  to disentangle and extract both effects from observations.
\end{abstract}

\end{document}