In various fields of physics and astronomy, access to experimental facilities or to telescopes is becoming more and more competitive and limited. It therefore becomes important to optimize the type of measurements and their scheduling to reach a given scientific objective and to increase the chances of success of a scientific project. In this communication, extending the work of Ford and of Loredo et al., we present an efficient adaptive scheduling tool aimed at prioritizing measurements in order to reach a scientific goal. The algorithm, based on the Fisher matrix, can be applied to a wide class of measurements. We present this algorithm in detail and discuss some practicalities such as systematic errors or measurement losses due to contingencies (such as weather, experimental failure, ...). As an illustration, we consider measurements of the short-period star S0-2 in our Galactic Center (GC). We show that the radial velocity measurements at the two turning points of the radial velocity curve are more powerful for detecting the gravitational redshift than measurements at the maximal relativistic signal. We also explicitly present the methodology that was used to plan measurements in order to detect the relativistic redshift considering systematics and possible measurement losses. For the future, we identify the astrometric turning points to be highly sensitive to the relativistic advance of the periastron. Finally, we also identify measurements particularly sensitive to the distance to our GC: the radial velocities around periastron and the astrometric measurements just before closest approach and at the maximal R.A. astrometric turning point.

The late-type stellar population in the Galactic Center was first predicted to reside in a dynamically relaxed cusp (power law slope ranging from 3/2 to 7/4). However, other works - which rely on models to correct for projection effects - have suggested a flat distribution instead. The need for this correction is due to the lack of information regarding the line-of-sight distances. With a two decade long baseline in astrometric measurements, we are now able to measure significant projected radial accelerations, six of which are newly reported here, which directly constrain line-of-sight distances. Here we present a statistical approach to take advantage of this information and more accurately constrain the shape of the radial density profile of the late-type stellar population in the Galactic Center.

We present 3D kinematic observations of stars within the central 0.5 pc of the Milky Way nuclear star cluster using adaptive optics imaging and spectroscopy from the Keck telescopes. Recent observations have shown that the cluster has a shallower surface density profile than expected for a dynamically relaxed cusp, leading to important implications for its formation and evolution. However, the true three dimensional profile of the cluster is unknown due to the difficulty in de-projecting the stellar number counts. Here, we use spherical Jeans modeling of individual proper motions and radial velocities to constrain for the first time, the de-projected spatial density profile, cluster velocity anisotropy, black hole mass ($M_\mathrm{BH}$), and distance to the Galactic center ($R_0$) simultaneously. We find that the inner stellar density profile of the late-type stars, $\rho(r)\propto r^{-\gamma}$ to have a power law slope $\gamma=0.05_{-0.60}^{+0.29}$, much more shallow than the frequently assumed Bahcall $amp;$ Wolf slope of $\gamma=7/4$. The measured slope will significantly affect dynamical predictions involving the cluster, such as the dynamical friction time scale. The cluster core must be larger than 0.5 pc, which disfavors some scenarios for its origin. Our measurement of $M_\mathrm{BH}=5.76_{-1.26}^{+1.76}\times10^6$ $M_\odot$ and $R_0=8.92_{-0.55}^{+0.58}$ kpc is consistent with that derived from stellar orbits within 1$^{\prime\prime}$ of Sgr A*. When combined with the orbit of S0-2, the uncertainty on $R_0$ is reduced by 30% ($8.46_{-0.38}^{+0.42}$ kpc). We suggest that the MW NSC can be used in the future in combination with stellar orbits to significantly improve constraints on $R_0$.

We propose a new approach to Bayesian prior probability distributions (priors) that can improve orbital solutions for low-phase-coverage orbits, where data cover less than ∼40% of an orbit. In instances of low phase coverage - such as with stellar orbits in the Galactic center or with directly imaged exoplanets - data have low constraining power and thus priors can bias parameter estimates and produce underestimated confidence intervals. Uniform priors, which are commonly assumed in orbit fitting, are notorious for this. We propose a new observable-based prior paradigm that is based on uniformity in observables. We compare performance of this observable-based prior and of commonly assumed uniform priors using Galactic center and directly imaged exoplanet (HR 8799) data. The observable-based prior can reduce biases in model parameters by a factor of two and helps avoid underestimation of confidence intervals for simulations with less than ∼40% phase coverage. Above this threshold, orbital solutions for objects with sufficient phase coverage - such as S0-2, a short-period star at the Galactic center with full phase coverage - are consistent with previously published results. Below this threshold, the observable-based prior limits prior influence in regions of prior dominance and increases data influence. Using the observable-based prior, HR 8799 orbital analyses favor low-eccentricity orbits and provide stronger evidence that the four planets have a consistent inclination of ∼30° to within 1σ. This analysis also allows for the possibility of coplanarity. We present metrics to quantify improvements in orbital estimates with different priors so that observable-based prior frameworks can be tested and implemented for other low-phase-coverage orbits.

We present new, more precise measurements of the mass and distance of our Galaxy's central supermassive black hole, Sgr A∗. These results stem from a new analysis that more than doubles the time baseline for astrometry of faint stars orbiting Sgr A∗, combining 2 decades of speckle imaging and adaptive optics data. Specifically, we improve our analysis of the speckle images by using information about a star's orbit from the deep adaptive optics data (2005-2013) to inform the search for the star in the speckle years (1995-2005). When this new analysis technique is combined with the first complete re-reduction of Keck Galactic Center speckle images using speckle holography, we are able to track the short-period star S0-38 (K-band magnitude = 17, orbital period = 19 yr) through the speckle years. We use the kinematic measurements from speckle holography and adaptive optics to estimate the orbits of S0-38 and S0-2 and thereby improve our constraints of the mass (M bh) and distance (R o) of Sgr A∗: M bh = (4.02 ±0.16 ±0.04) x106 M o and 7.86 ±0.14 ±0.04 kpc. The uncertainties in M bh and R o as determined by the combined orbital fit of S0-2 and S0-38 are improved by a factor of 2 and 2.5, respectively, compared to an orbital fit of S0-2 alone and a factor of ∼2.5 compared to previous results from stellar orbits. This analysis also limits the extended dark mass within 0.01 pc to less than 0.13 x106 M o at 99.7% confidence, a factor of 3 lower compared to prior work.

We demonstrate that short-period stars orbiting around the supermassive black hole in our Galactic center can successfully be used to probe the gravitational theory in a strong regime. We use 19 years of observations of the two best measured short-period stars orbiting our Galactic center to constrain a hypothetical fifth force that arises in various scenarios motivated by the development of a unification theory or in some models of dark matter and dark energy. No deviation from general relativity is reported and the fifth force strength is restricted to an upper 95% confidence limit of |α|<0.016 at a length scale of λ=150 astronomical units. We also derive a 95% confidence upper limit on a linear drift of the argument of periastron of the short-period star S0-2 of |ω[over ˙]_{S0-2}|<1.6×10^{-3}  rad/yr, which can be used to constrain various gravitational and astrophysical theories. This analysis provides the first fully self-consistent test of the gravitational theory using orbital dynamic in a strong gravitational regime, that of a supermassive black hole. A sensitivity analysis for future measurements is also presented.

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.