A stellar fly‐by close to the Galactic center: Can we detect stars on highly relativistic orbits?

Abstract

The Galactic center Nuclear Star Cluster is one of the densest stellar clusters in the Galaxy. The stars in its inner portions orbit the supermassive black hole associated with the compact radio source Sgr A* at the orbital speeds of several thousand kilometers per second. The B‐type star S2 is currently the best case to test the general relativity as well as other theories of gravity, based on its stellar orbit. Yet, its orbital period of ∼16 years and the eccentricity of ∼0.88 yields the relativistic pericenter shift of ∼11′, which is observationally still difficult to reliably measure due to possible Newtonian perturbations as well as reference‐frame uncertainties. A naive way to solve this problem is to find stars with smaller pericenter distances, rp ≲ 1529 Schwarzschild radii (120 AU), and thus with more prominent relativistic effects. In this paper, we show that to detect stars on relativistic orbits is progressively less likely, given the volume shrinkage and the expected stellar density distributions. Finally, one arrives at a sparse region where the total number of bright stars is expected to fall below 1. One can, however, still potentially detect stars crossing this region. In this paper, we provide a simple formula for the detection probability of a star crossing a sparse region. We also examine an approximate timescale in which the star reappears in the sparse region, i.e., a “waiting” timescale for observers.

Selected Chapters on Active Galactic Nuclei as Relativistic Systems

“…Subsequently, the measured proper motions and relative velocities have been used to derive accelerations and stellar orbits for several S stars (Eckart et al, 2002;Schödel et al, 2002;Ghez et al, 2008;Gillessen et al, 2009;Boehle et al, 2016;Gillessen et al, 2017). In the future, this will allow to test the General Theory of Relativity based on the determined orbits of S stars (mainly S2) and potentially stars that will be found on even tighter orbits (Eckart et al, 2017;Parsa et al, 2017;Waisberg et al, 2018;Zajaček and Tursunov, 2018). In fact, the NIR-observations of S2 star moving around Sgr A* on a highly elliptical orbit with the period of ∼ 16 yr led to successful measurements of two relativistic effects -the combined gravitational redshift and relativistic transverse Doppler effect of ∼ 200 km s −1 (Gravity Collaboration et al, 2018a) and an indication of the periastron shift (Parsa et al, 2017) being consistent with the predicted value of 12 arcminutes per orbital period.…”

“…6 for an illustration. The number of stars can thus fall below one at a certain radius, which marks the volume which lacks stars or one can refer to it as a sparse region, see also Zajaček and Tursunov (2018) for a detailed discussion. As a consequence, it is quite implausible to detect a cluster of stars in the strong-gravity regime, i.e.…”

“…To quantify the length-scale, on which the number of stars is expected to fall below one for a certain stellar type T , it is straightforward to calculate the radius r 1T at which this is expected to happen. One can obtain the radius r 1T from the integral N (< r) = r 0 4πr 2 n (r)dr by setting N (< r) = 1 (see also Hopman and Alexander, 2006;Zajaček and Tursunov, 2018),…”

Stellar transits across a magnetized accretion torus as a mechanism for plasmoid ejection

“…Stars on long-period, higheccentricity orbits, which result from dynamical scattering into a loss cone, can in principle be located inside r for a short period of time. The probability of detecting such stars in a sparse region close to the SMBH was considered and estimated by Zajaček & Tursunov (2018).…”

S62 and S4711: Indications of a population of faint fast moving stars inside the S2 orbit -- S4711 on a 7.6 year orbit around Sgr~A*

“…The three-body interaction including the massive black hole can effectively fill the 'sparse region' around Sgr A*. In the classical quasi-spherical stellar cluster around Sgr A* with the power-law distribution of stellar number densities, there is a well-defined radius below which the number of stars statistically drops below one (Zajaček & Tursunov 2018),…”