Journal Article

Long-term classical and general relativistic effects on the radial velocities of the stars orbiting Sgr A*

Lorenzo Iorio

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 411, issue 1, pages 453-463
Published in print February 2011 | ISSN: 0035-8711
Published online January 2011 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2010.17701.x
Long-term classical and general relativistic effects on the radial velocities of the stars orbiting Sgr A*

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We analytically work out the cumulative, i.e. averaged over one orbital revolution, time variations of the radial velocity vρ of a typical S star orbiting the supermassive (M≈ 106 M) black hole (SBH) hosted by the Galactic Centre (GC) in Sgr A* caused by several dynamical effects. They are the general relativistic gravitoelectromagnetic (GEM) fields of the SBH, its quadrupole mass moment Q2 and a diffuse dark matter distribution around the SBH. All of them induce non-zero long-term radial accelerations proportional to the eccentricity e of the orbit. By taking the S2 star, orbiting the SBH along a highly eccentric (e= 0.8831) ellipse with a period Pb= 15.9 yr and semimajor axis a= 1031.69 au, we numerically compute the magnitudes of its radial accelerations. The largest effects are due to the general relativistic Schwarzschild-like gravitoelectric (GE) field, with , and the diffuse material distribution, modelled with a Plummer-type mass density profile, with . The effects caused by the general relativistic Kerr-type gravitomagnetic (GM) field and by Q2 are smaller by orders of magnitude. By assuming an uncertainty in measuring the radial velocities of about 15 km s−1, the future accuracy in measuring can be evaluated to be of the order of 2.4 × 10−5 m s−2 over an observational time-span Δt= 20 yr. Currently, the available radial velocity measurements cover just 7 yr.

Keywords: black hole physics; techniques: radial velocities; Galaxy: centre; gravitation

Journal Article.  5635 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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