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Precise measurements of the S-stars orbiting SgrA* have set strong constraints on the nature of the compact object at the centre of the Milky Way. The presence of a black hole in that region is well established, but its neighboring environment is still an open debate. In that respect, the existence of dark matter in that central region may be detectable due to its strong signatures on the orbits of stars: the main effect is a Newtonian precession which will affect the overall pericentre shift of S2, the latter being a target measurement of the GRAVITY instrument. The exact nature of this dark matter (e.g., stellar dark remnants or diffuse dark matter) is unknown. This article assumes it to be an scalar field of toroidal distribution, associated with ultra-light dark matter particles, surrounding the Kerr black hole. Such a field is a form of hair expected in the context of superradiance, a mechanism that extracts rotational energy from the black hole. Orbital signatures for the S2 star are computed and shown to be detectable by GRAVITY. The scalar field can be constrained because the variation of orbital elements depends both on the relative mass of the scalar field to the black hole and on the field mass coupling parameter.
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The highly elliptical, 16-year-period orbit of the star S2 around the massive black hole candidate Sgr A* is a sensitive probe of the gravitational field in the Galactic centre. Near pericentre at 120 AU, ~1400 Schwarzschild radii, the star has an orbital speed of ~7650 km/s, such that the first-order effects of Special and General Relativity have now become detectable with current capabilities. Over the past 26 years, we have monitored the radial velocity and motion on the sky of S2, mainly with the SINFONI and NACO adaptive optics instruments on the ESO Very Large Telescope, and since 2016 and leading up to the pericentre approach in May 2018, with the four-telescope interferometric beam-combiner instrument GRAVITY. From data up to and including pericentre, we robustly detect the combined gravitational redshift and relativistic transverse Doppler effect for S2 of z ~ 200 km/s / c with different statistical analysis methods. When parameterising the post-Newtonian contribution from these effects by a factor f, with f = 0 and f = 1 corresponding to the Newtonian and general relativistic limits, respectively, we find from posterior fitting with different weighting schemes f = 0.90 +/- 0.09 (stat) +- 0.15 (sys). The S2 data are inconsistent with pure Newtonian dynamics.
Two recent papers (Ghez et al. 2008, Gillessen et al. 2009) have estimated the mass of and the distance to the massive black hole in the center of the Milky Way using stellar orbits. The two astrometric data sets are independent and yielded consistent results, even though the measured positions do not match when simply overplotting the two sets. In this letter we show that the two sets can be brought to excellent agreement with each other when allowing for a small offset in the definition of the reference frame of the two data sets. The required offsets in the coordinates and velocities of the origin of the reference frames are consistent with the uncertainties given in Ghez et al. (2008). The so combined data set allows for a moderate improvement of the statistical errors of mass of and distance to Sgr A*, but the overall accuracies of these numbers are dominated by systematic errors and the long-term calibration of the reference frame. We obtain R0 = 8.28 +- 0.15(stat) +- 0.29(sys) kpc and M(MBH) = 4.30 +- 0.20(stat) +- 0.30(sys) x 10^6 Msun as best estimates from a multi-star fit.
This paper aims to put constraints on the parameters of the Scalar Field Dark Matter (SFDM) model, when dark matter is described by a free real scalar field filling the whole Universe, plus a cosmological constant term. By using a compilation of 51 $H(z)$ data and 1048 Supernovae data from Panteon, a lower limit for the mass of the scalar field was obtained, $m geq 5.1times 10^{-34} $eV and $H_0=69.5^{+2.0}_{-2.1}text{ km s}^{-1}text{Mpc}^{-1}$. Also, the present dark matter density parameter was obtained as $Omega_phi = 0.230^{+0.033}_{-0.031}$ at $2sigma$ confidence level. The results are in good agreement to standard model of cosmology, showing that SFDM model is viable in describing the dark matter content of the universe.
The star S2 orbiting the compact radio source Sgr A* is a precision probe of the gravitational field around the closest massive black hole (candidate). Over the last 2.7 decades we have monitored the stars radial velocity and motion on the sky, mainly with the SINFONI and NACO adaptive optics (AO) instruments on the ESO VLT, and since 2017, with the four-telescope interferometric beam combiner instrument GRAVITY. In this paper we report the first detection of the General Relativity (GR) Schwarzschild Precession (SP) in S2s orbit. Owing to its highly elliptical orbit (e = 0.88), S2s SP is mainly a kink between the pre-and post-pericentre directions of motion ~ +- 1 year around pericentre passage, relative to the corresponding Kepler orbit. The superb 2017-2019 astrometry of GRAVITY defines the pericentre passage and outgoing direction. The incoming direction is anchored by 118 NACO-AO measurements of S2s position in the infrared reference frame, with an additional 75 direct measurements of the S2-Sgr A* separation during bright states (flares) of Sgr A*. Our 14-parameter model fits for the distance, central mass, the position and motion of the reference frame of the AO astrometry relative to the mass, the six parameters of the orbit, as well as a dimensionless parameter f_SP for the SP (f_SP = 0 for Newton and 1 for GR). From data up to the end of 2019 we robustly detect the SP of S2, del phi = 12 per orbital period. From posterior fitting and MCMC Bayesian analysis with different weighting schemes and bootstrapping we find f_SP = 1.10 +- 0.19. The S2 data are fully consistent with GR. Any extended mass inside S2s orbit cannot exceed ~ 0.1% of the central mass. Any compact third mass inside the central arcsecond must be less than about 1000 M_sun.
[Abridged] The S-stars motion around the Galactic center (Sgr A*) implies the existence of a compact source with a mass of about $4times 10^6 M_odot$, traditionally assumed to be a massive black hole (BH). Important for any model is the explanation of the multiyear, accurate astrometric data of S2 and the challenging G2: its post-pericenter velocity decelerates faster than expected from a Keplerian orbit around the putative BH. This has been reconciled in the literature by acting on G2 a drag force by an accretion flow. Alternatively, we show that the S2 and G2 motion is explained by the core-halo fermionic dark matter (DM) profile of the fully-relativistic Ruffini-Arguelles-Rueda (RAR) model. It has been already shown that for 48-345 keV fermions, it accurately fits the rotation curves of the Milky-Way halo. We here show that, for a fermion mass of 56 keV, it explains the time-dependent data of the position (orbit) and light-of-sight radial velocity (redshift function $z$) of S2 and G2, the latter without a drag force. We find the RAR model fits better the data: the mean of reduced chi-squares of the orbit and $z$ data are, for S2, $langlebar{chi}^2rangle_{rm S2, RAR}approx 3.1$ and $langlebar{chi}^2rangle_{rm S2, BH}approx 3.3$ while, for G2, $langlebar{chi}^2rangle_{rm G2, RAR}approx 20$ and $langlebar{chi}^2rangle_{rm G2, BH}approx 41$. For S2 the fits of the $z$ data are comparable, $bar{chi}^2_{z,rm RAR}approx 1.28$ and $bar{chi}^2_{z,rm BH}approx 1.04$, for G2 only the RAR model fits, $bar{chi}^2_{z,rm RAR}approx 1.0$ and $bar{chi}^2_{z,rm BH}approx 26$. In addition, the critical mass for the gravitational collapse of a degenerate 56 keV-fermion DM core into a BH is $sim 10^8 M_odot$, which may be the initial seed for the formation of the observed central supermassive BH in active galaxies, such as M87.
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