On the Newtonian and Spin-Induced Perturbations Felt by the Stars Orbiting Around the Massive Black Hole in the Galactic Center

Abstract

The S-stars discovered in the Galactic center (GC) are expected to provide unique dynamical tests of the Kerr metric of the massive black hole (MBH) orbited by them. In order to obtain unbiased measurements of its spin and the related relativistic effects, a comprehensive understanding of the gravitational perturbations of the stars and stellar remnants around the MBH is quite essential. Here, we study the perturbations on the observables of a typical target star, i.e., the apparent orbital motion and the redshift, due to both the spin-induced relativistic effects and the Newtonian attractions of a single or a cluster of disturbing object(s). We find that, in most cases, the Newtonian perturbations on the observables are mainly attributed to the perturbed orbital period of the target star, rather than the Newtonian orbital precessions. The Newtonian perturbations have their unique features when they peak around the pericenter passage in each revolution, which is quite different from those of the spin-induced effects. Looking at the currently detected star S2/S0-2, we find that its spin-induced effects on both the image position and redshift are very likely obscured by the gravitational perturbations from the star S0-102 alone. We also investigate and discuss the Newtonian perturbations on a hypothetical S-star located inside the orbits of the currently detected ones. By considering a number of possible stellar distributions near the central MBH, we find that the spin-induced effects on the apparent position and the redshift dominate over the stellar perturbations for target stars with orbital semimajor axis smaller than 100 − 400 AU if the MBH is maximally spinning. Our results suggest that, in principle, the stellar perturbations can be removed as they have distinctive morphologies comparing to those of the relativistic Kerr-type signatures.

What stellar orbit is needed to measure the spin of the Galactic centre black hole from astrometric data?

“…In order to detect black hole spin, closer stars are needed to overcome gravitational perturbations from other stars/remnants Zhang & Iorio 2017). For average black hole spin angle parameters, we found that the hypothetical star would have to satisfy a orb (1−e 2 ) 3/4 300RS T 4years N obs 120 0.25 10µas σx χ 0.9 (6.1) in order to allow detection of black hole spin.…”

“…Even though these two effects could potentially be separated (e.g. astrometric deviations due to spin are maximum at apastron whereas Newtonian perturbations peak during periastron, Zhang & Iorio 2017), disentangling them with limited observations and without prior knowledge on the perturbers would be very challenging. From the diffuse light background from faint stars that cannot be currently resolved, Schödel et al (2018) estimated a total enclosed stellar mass of ∼ 180M within 250 mas.…”

“…Both Merritt et al (2010) and Zhang & Iorio (2017) consider a variety of stellar/remnant distributions with different perturber masses, total masses and density profiles to compare the effect of Newtonian perturbations to black hole precession. While Merritt et al (2010) used N-body simulations to study the overall evolution of an entire cluster, Zhang & Iorio (2017) studied the detailed evolution of a test star in response to the perturbers. We can use their results to assess how much a black hole spin measurement for our two example stars in §5 with (a orb , e) = (500RS, 0.3) and (1600RS, 0.9) would suffer from Newtonian perturbations for different cluster properties.…”

“…We approximate the potential near the black hole as a Kerr spacetime and stars as test particles. This is appropriate in the range 100RS a 5000RS, where the lower and upper limits are set by the tidal disruption radius and Newtonian perturbations from the underlying stellar/remnant distribution, respectively (Psaltis et al 2013;Merritt et al 2010;Zhang & Iorio 2017). We can then use geodesic ray tracing to follow the orbits of stars.…”

“…As mentioned above, for S2 the time scale associated with Newtonian perturbations due to an underlying stellar/remnant distribution is still shorter than the one associated with Lense-Thirring precession Zhang & Iorio 2017). Nevertheless, several works have estimated the astrometric effect of frame-dragging on the orbit of S2 (e.g.…”