Using 25 years of data from uninterrupted monitoring of stellar orbits in the Galactic Center, we present an update of the main results from this unique data set: a measurement of mass and distance to Sgr A*. Our progress is not only due to the eight-year increase in time base, but also to the improved definition of the coordinate system. The star S2 continues to yield the best constraints on the mass of and distance to Sgr A*; the statistical errors of 0.13 × 10 6 M ⊙ and 0.12 kpc have halved compared to the previous study. The S2 orbit fit is robust and does not need any prior information. Using coordinate system priors, the star S1 also yields tight constraints on mass and distance. For a combined orbit fit, we use 17 stars, which yields our current best estimates for mass and distance: M = 4.28 ± 0.10 ∣ stat . ± 0.21 ∣ sys × 10 6 M ⊙ and R 0 = 8.32 ± 0.07 ∣ stat . ± 0.14 ∣ sys kpc . These numbers are in agreement with the recent determination of R ₀ from the statistical cluster parallax. The positions of the mass, of the near-infrared flares from Sgr A*, and of the radio source Sgr A* agree to within 1 mas. In total, we have determined orbits for 40 stars so far, a sample which consists of 32 stars with randomly oriented orbits and a thermal eccentricity distribution, plus eight stars that we can explicitly show are members of the clockwise disk of young stars, and which have lower-eccentricity orbits.

We derive cosmological constraints using a galaxy cluster sample selected from the 2500 deg² SPT-SZ survey. The sample spans the redshift range 0.25 < z < 1.75 and contains 343 clusters with SZ detection significance ξ > 5. The sample is supplemented with optical weak gravitational lensing measurements of 32 clusters with 0.29 < z < 1.13 (from Magellan and Hubble Space Telescope) and X-ray measurements of 89 clusters with 0.25 < z < 1.75 (from Chandra). We rely on minimal modeling assumptions: (i) weak lensing provides an accurate means of measuring halo masses, (ii) the mean SZ and X-ray observables are related to the true halo mass through power-law relations in mass and dimensionless Hubble parameter E(z) with a priori unknown parameters, and (iii) there is (correlated, lognormal) intrinsic scatter and measurement noise relating these observables to their mean relations. We simultaneously fit for these astrophysical modeling parameters and for cosmology. Assuming a flat νΛCDM model, in which the sum of neutrino masses is a free parameter, we measure Ω_m = 0.276 ± 0.047, σ ₈ = 0.781 ± 0.037, and σ ₈(Ω_m/0.3)^0.2 = 0.766 ±0.025. The redshift evolutions of the X-ray Y _X–mass and M _gas–mass relations are both consistent with self-similar evolution to within 1σ. The mass slope of the Y _X–mass relation shows a 2.3σ deviation from self-similarity. Similarly, the mass slope of the M _gas–mass relation is steeper than self-similarity at the 2.5σ level. In a νwCDM cosmology, we measure the dark energy equation-of-state parameter w = −1.55 ± 0.41 from the cluster data. We perform a measurement of the growth of structure since redshift z ∼ 1.7 and find no evidence for tension with the prediction from general relativity. This is the first analysis of the SPT cluster sample that uses direct weak-lensing mass calibration and is a step toward using the much larger weak-lensing data set from DES. We provide updated redshift and mass estimates for the SPT sample.

Gravitational lensing of the cosmic microwave background generates a curl pattern in the observed polarization. This “$B$-mode” signal provides a measure of the projected mass distribution over the entire observable Universe and also acts as a contaminant for the measurement of primordial gravity-wave signals. In this Letter we present the first detection of gravitational lensing $B$ modes, using first-season data from the polarization-sensitive receiver on the South Pole Telescope (SPTpol). We construct a template for the lensing $B$-mode signal by combining $E$-mode polarization measured by SPTpol with estimates of the lensing potential from a Herschel-SPIRE map of the cosmic infrared background. We compare this template to the $B$ modes measured directly by SPTpol, finding a nonzero correlation at $7.7\sigma$ significance. The correlation has an amplitude and scale dependence consistent with theoretical expectations, is robust with respect to analysis choices, and constitutes the first measurement of a powerful cosmological observable.