[Paper Review] Testing the gravitational theory with short-period stars around our Galactic Center

Aurélien Hees, A. M. Ghez+20 more|arXiv (Cornell University)|May 30, 2017

Pulsars and Gravitational Waves Research10 references6 citations

TL;DR

This paper tests gravitational theories using 19 years of high-precision observations of short-period stars S0-2 and S0-38 near the Galactic Center’s supermassive black hole. It constrains a hypothetical fifth force, sets an upper limit on the relativistic advance of periastron for S0-2, and demonstrates that optimized 2018 observations will enable the first direct measurement of relativistic redshift, confirming predictions of general relativity in a strong-field regime.

ABSTRACT

Motion of short-period stars orbiting the supermassive black hole in our Galactic Center has been monitored for more than 20 years. These observations are currently offering a new way to test the gravitational theory in an unexplored regime: in a strong gravitational field, around a supermassive black hole. In this proceeding, we present three results: (i) a constraint on a hypothetical fifth force obtained by using 19 years of observations of the two best measured short-period stars S0-2 and S0-38 ; (ii) an upper limit on the secular advance of the argument of the periastron for the star S0-2 ; (iii) a sensitivity analysis showing that the relativistic redshift of S0-2 will be measured after its closest approach to the black hole in 2018.

Motivation & Objective

• To test general relativity and alternative gravity theories in the strong gravitational field regime near a supermassive black hole.
• To constrain the existence of a hypothetical fifth force using orbital dynamics of short-period stars.
• To place an upper limit on the secular advance of the argument of periastron for S0-2, relevant to relativistic and astrophysical models.
• To design an optimal observation strategy for detecting the relativistic redshift of S0-2 during its 2018 closest approach to the black hole.
• To provide complementary strong-field gravity tests to future instruments like the Event Horizon Telescope.

Proposed method

• Performed a joint orbital fit of S0-2 and S0-38 using 19 years of radial velocity and astrometric data from Keck and VLT telescopes.
• Modelled the gravitational potential using a Yukawa-type modification to Newtonian gravity: $ U = \frac{GM}{r}\left[1 + \alpha e^{-r/\lambda}\right] $, with $\alpha$ and $\lambda$ as free parameters.
• Applied Jackknife resampling to estimate systematic uncertainties in the absolute reference frame, improving robustness of constraints.
• Fitted the relativistic redshift contribution to radial velocity using $[RV]_{\text{rel}} = \frac{v^2}{2c} + \frac{GM}{rc}$, with a dimensionless scaling parameter $\Upsilon$ to test deviations from general relativity.
• Developed an adaptive scheduling tool to identify optimal observation epochs—specifically the turning points of the radial velocity curve—for maximizing signal-to-noise ratio of the relativistic redshift detection.
• Used a Bayesian framework to compute 95% confidence upper limits on $|\alpha|$ and $|\dot{\omega}|$, and to assess the significance of $\Upsilon$-fit results.

Experimental results

Research questions

• RQ1 What is the upper limit on the strength of a hypothetical fifth force in the strong gravitational field near the Galactic Center supermassive black hole?
• RQ2 How large can the secular advance of the argument of periastron be for S0-2, and what does this imply for relativistic and alternative gravity models?
• RQ3 Can the relativistic redshift of S0-2 be measured during its 2018 closest approach, and what observation strategy maximizes detection sensitivity?
• RQ4 How do constraints from the Galactic Center compare with those from Solar System and binary pulsar tests in probing the parameter space of modified gravity?
• RQ5 To what extent do screening mechanisms in alternative gravity theories affect detectability of deviations in the Galactic Center environment?

Key findings

• The 95% confidence upper limit on the fifth force strength is $|\alpha| < 0.016$ at a length scale $\lambda \sim 150$ astronomical units, representing a significant constraint in a strong-field regime.
• An upper limit of $|\dot{\omega}_{\text{S0-2}}| < 1.7 \times 10^{-3}$ rad/yr was placed on the secular advance of the argument of periastron, one order of magnitude larger than the general relativity prediction of $1.6 \times 10^{-4}$ rad/yr.
• The relativistic redshift contribution to S0-2’s radial velocity reaches up to 200 km/s near pericenter, making it a measurable effect with high-precision spectroscopy.
• The adaptive observation scheduling tool identifies the radial velocity turning points as optimal epochs for detecting the relativistic redshift, ensuring a signal-to-noise ratio exceeding 5σ with sufficient data.
• Current data are already compatible with general relativity, excluding the Newtonian model at 1.2σ significance, indicating early consistency with relativistic predictions.
• The study demonstrates that short-period stars like S0-2 provide a unique laboratory for testing gravity in the strong-field regime, complementary to future Event Horizon Telescope observations.