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


  • Lorenzo Iorio

    Corresponding author
    1. Ministero dell'Istruzione, dell'Università e della Ricerca (M.I.U.R.), Fellow of the Royal Astronomical Society (F.R.A.S.). Viale Unità di Italia 68, 70125 Bari (BA), Italy
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E-mail: lorenzo.iorio@libero.it


We analytically work out the cumulative, i.e. averaged over one orbital revolution, time variations inline image 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 inline image, and the diffuse material distribution, modelled with a Plummer-type mass density profile, with inline image. 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 inline image 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.