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

Abstract

Astrometric and spectroscopic monitoring of individual stars orbiting the supermassive black hole in the Galactic Center offer a promising way to detect general relativistic effects. While low-order effects are expected to be detected following the periastron passage of S2 in Spring 2018, detecting higher-order effects due to black hole spin will require the discovery of closer stars. In this paper, we set out to determine the requirements such a star would have to satisfy to allow the detection of black hole spin. We focus on the instrument GRAVITY, which saw first light in 2016 and which is expected to achieve astrometric accuracies $10-100\mu$as. For an observing campaign with duration $T$ years, $N_{obs}$ total observations, astrometric precision ${\sigma }_x$ and normalized black hole spin $\chi$, we find that $a_{orb}(1-e^2{)}^{3/4}\lesssim 300R_S\sqrt{\frac{T}{4\text{years}}}{\left(\frac{N_{obs}}{120}\right)}^{0.25}\sqrt{\frac{10\mu as}{{\sigma }_x}}\sqrt{\frac{\chi }{0.9}}$ is needed. For $\chi =0.9$ and a potential observing campaign with ${\sigma }_x=10\mu$as, 30 observations/year and duration 4-10 years, we expect $\sim 0.1$ star with $K<19$ satisfying this constraint based on the current knowledge about the stellar population in the central 1". We also propose a method through which GRAVITY could potentially measure radial velocities with precision $\sim 50$ km/s. If the astrometric precision can be maintained, adding radial velocity information increases the expected number of stars by roughly a factor of two. While we focus on GRAVITY, the results can also be scaled to parameters relevant for future extremely large telescopes.

Accepted to MNRAS

References in corpus (14)

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• The S-Star Cluster at the Center of the Milky Way: On the nature of diffuse NIR emission in the inner tenth of a parsec
• Probing the spinning of the massive black hole in the Galactic Center via pulsar timing: A Full Relativistic Treatment
• On the Newtonian and Spin-induced Perturbations felt by the Stars Orbiting around the Massive Black Hole in the Galactic Center
• Measuring the effects of General Relativity at the Galactic Center with Future Extremely Large Telescopes

Cited by in corpus (27)

• Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole
• The mass distribution in the Galactic Centre from interferometric astrometry of multiple stellar orbits
• Testing General Relativity with the Event Horizon Telescope
• ALMA Polarimetry of Sgr A*: Probing the Accretion Flow from the Event Horizon to the Bondi Radius
• 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*
• Scalar field effects on the orbit of S2 star
• The dark mass signature in the orbit of S2
• Improving constraints on the extended mass distribution in the Galactic Center with stellar orbits
• Test of Einstein equivalence principle near the Galactic center supermassive black hole
• Detection of faint stars near SgrA* with GRAVITY
• Gravitational redshift/blueshift of light emitted by geodesic test particles, frame-dragging and pericentre-shift effects, in the Kerr-Newman-de Sitter and Kerr-Newman black hole geometries
• Unveiling the nature of SgrA* with the geodesic motion of S-stars
• Deep Images of the Galactic Center with GRAVITY
• The short-period S-stars S4711, S62, S4714 and the Lense-Thirring effect due to the spin of Sgr A${}^{\ast }$
• PPN motion of the S-stars around Sgr A*
• The impact of gravitational lensing in the reconstruction of stellar orbits around Sgr A*
• Is it possible to measure the Lense-Thirring orbital shifts of the short-period S-star S4716 orbiting Sgr A${}^{\ast }$?
• The former companion of the hyper-velocity star S5-HVS1
• Dynamical Measurement of Supermassive Black Hole Masses: QPE Timing Method
• Revisiting Stellar Orbits and the Sgr A${}^{\ast }$ Quadrupole Moment
• Selected Chapters on Active Galactic Nuclei as Relativistic Systems
• Dark Matter reconstruction from stellar orbits in the Galactic Centre
• Detecting Black Hole Occultations by Stars with Space Interferometric Telescopes
• Analytic Post-Newtonian Astrometric and Spectroscopic Models of Orbits around Black Holes
• Impact of a granular mass distribution on the orbit of S2 in the Galactic center
• The effects of the spin and quadrupole moment of SgrA* on the orbits of S stars
• PPN--spin degeneracies in mock S62-like stellar-orbit inference