Authors: Aurelien Hees, Andrea M. Ghez, Tuan Do
Galactic Center Group, University of California Los Angeles, USA
Our current understanding of fundamental physics is based on four interactions: electromagnetism, the weak interaction, the strong interaction and gravitation. The first three ones are unified in a common framework, the Standard Model of particle physics based on a relativistic quantum field theory. On the other hand, Einstein’s theory of General Relativity, the gravitational theory, has not been successfully included in this quantum framework so far. The development of a quantum theory of gravity is important to understand phenomena that take place in very strong gravitational fields like for example in our very early universe or around black holes.
In addition, Dark Matter and Dark Energy are contributing to 26% and 69% to the mass-energy content of our Universe . These two components of our Universe, essential to explain some cosmological and astrophysical observations, have not been directly observed so far and are also challenging General Relativity (see e.g. ).
For these reasons, in the last decades, theoreticians have developed many modified gravitational theories (see  and references therein). On the other hand, there has been a tremendous effort to confront General Relativity with different observations and to search for a deviation from General Relativity using a large number of experiments (see the review ). Historically, tests of gravitation have been first performed in the Solar System and in laboratories on Earth where extremely good accuracy in the measurements can be achieved. In these low gravitational fields, the agreement between General Relativity’s predictions and observations is extremely good. It is therefore highly interesting to perform such tests in other environments, such as in strong gravitational fields.
The motion of short-period stars orbiting around the supermassive black hole in the center of our Galaxy, the Milky Way, has been tracked since 1995 at the W. M. Keck Observatory in Hawaii by the UCLA Galactic Center Group. The stars observed close to the black hole have orbital periods of the orders of 10-50 years, allowing us to measure quasi-Keplerian motion (similar to
the motion of the planets around our Sun). These observations have led to many great discoveries, the most important one being the evidence for a supermassive black hole at the center of our Galaxy . Two types of observations are made at the Keck observatory: (i) astrometric observations which give the 2-dimensional position of the stars in the plane of the sky and (ii) spectroscopic measurements which give the radial velocity of the stars. Nowadays, the typical accuracy of these measurements is at the level of 0.2 milliarcsecond for astrometry and of 30 km/s for radial velocity for a bright star. Recently, observations of two of these stars, S0-2 (period: 16 years) and S0-38 (period: 19 years), have been used to measure our distance to the Galactic Center and the mass of the central supermassive black hole with an accuracy of 5%  (Fig. 1 shows the orbit of these two stars).
Fig 1 : Orbital motion of two stars, S0-2 and S0-38, orbiting around the supermassive black hole at the center of our Galaxy. Observations of these two stars have been used to test the gravitational theory and to constrain the presence of a hypothetical 5th force. Credit: S. Sakai and A. Ghez, W. M. Keck Observatory/UCLA Galactic Center Group.
In a recent work , we used these observations to perform a test of the gravitational theory using orbital dynamics in a strong gravitational field generated by a supermassive black hole. The main novelty in using these measurements to test General Relativity comes from the fact that we are probing the gravitational theory in a gravitational field much stronger than for example in the Solar System, around a central mass which is much more massive (the black hole mass is 4 x 106 the mass of the Sun) and around an extremely interesting body: a black hole.
More precisely, short-period stars are constraining the presence of a hypothetical fifth force in our Galactic Center. A fifth interaction is predicted by many modifications of General Relativity developed in order to unify it with the Standard Model of particle physics and by models of Dark Matter and Dark Energy. This fifth force is parametrized by a length of interaction λ and a strength of interaction α, both of these parameters being constrained observationally by Solar System observations and by laboratory measurements (see e.g. ). We used observations of S0-2 and S0-38 to search for a fifth force in a strong gravitational field generated by a black hole . No deviation from General Relativity has been observed and new constraint on this scenario has been derived (see Fig. 2).
Two main factors are expected to improve such an analysis in the future. First, in 2018, the star S0-2 will experience its closest approach to the supermassive black hole. At that time, the gravitational effects experienced by the star are the strongest and the possibility to measure relativistic effects and to test General Relativity is enhanced. Observations during S0-2’s closest approach in 2018 will be the most sensitive to a hypothetical deviation from General Relativity. The UCLA Galactic Center Group is currently actively preparing this wonderful event. On the other hand, the development of the next generation of extremely large telescope, such as the Thirty Meter Telescope, will allow us to detect and to track stars that are even closer to the black hole. On the long-term, this will improve significantly tests of General Relativity.
Fig 2: (click on the image to view with higher resolution) Constraints on a hypothetical fifth interaction. In green are constraints coming from Earth observations or from the LAGEOS satellites, in blue the constraints coming from Lunar Laser Ranging observations, in orange constraints from planetary ephemerides and in red the new constraint obtained using observations of stars around our Galactic Center. Our current analysis probed the 5th interaction in a strong gravity field as emphasized in the right panel (red region).
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