The star S0-2, orbiting the Galactic central massive black hole candidate Sgr A * , passed its pericenter in May 2018. This event is the first chance to detect the general relativistic (GR) effect of a massive black hole, free from non-gravitational physics. The observable GR evidence in the event is the difference between the GR redshift and the Newtonian redshift of photons coming from S0-2. Within the present observational precision, the 1st post-Newtonian (1PN) GR evidence is detectable. In this paper, we give a theoretical analysis of the time evolution of the 1PN GR evidence, under a presupposition that is different from used in previous papers. Our presupposition is that the GR/Newtonian redshift is always calculated with the parameter values (the mass of Sgr A * , the initial conditions of S0-2, and so on) determined by fitting the GR/Newtonian motion of S0-2 with the observational data. It is then revealed that the difference of the GR redshift and the Newtonian one shows two peaks before and after the pericenter passage. This double-peak-appearance is due to our presupposition, and reduces to a single peak if the same parameter values are used in both GR and Newtonian redshifts as considered in previous papers. In addition to this theoretical discussion, we report our observational data obtained with the Subaru telescope by 2018. The quality and the number of Subaru data in 2018 are not sufficient to confirm the detection of the double-peak-appearance.

The stellar distribution derived from an H and K S -band survey of the central region of our Galaxy is compared with the Fe XXV Kα (6.7 keV) line intensity observed with the Suzaku satellite. The survey is for the Galactic coordinates |l| < ∼ 3 • .0 and |b| < ∼ 1 • .0 (equivalent to 0.8 kpc × 0.3 kpc for R 0 = 8 kpc), and the number-density distribution N (K S,0 ; l, b) of stars is derived using the extinction-corrected magnitude K S,0 = 10.5. This is deep enough to probe the old red giant population and in turn to estimate the (l, b) distribution of faint X-ray point sources such as coronally active binaries and cataclysmic variables. In the Galactic plane (b = 0 • ), N (10.5; l, b) increases to the Galactic center as |l| −0.30±0.03 in the range of −0 • .1 ≥ l ≥ −0 • .7, but this increase is significantly slower than the increase (|l| −0.44±0.02 ) of the Fe XXV Kα line intensity. If normalized with the ratios in the outer region 1 • .5 ≤ |l| ≤ 2 • .8, where faint X-ray point sources are argued to dominate the diffuse Galactic X-ray ridge emission, the excess of the Fe XXV Kα line intensity over the stellar number density is at least a factor of two at |l| = 0 • .1. This indicates that a significant part of the Galactic center diffuse emission arises from a truly diffuse optically-thin thermal plasma, and not from an unresolved collection of faint X-ray point sources related to the old stellar population.

During the next closest approach of the orbiting star S2/S0-2 to the Galactic supermassive black hole (SMBH), it is estimated that RV uncertainties of ∼ 10 km/s allow us to detect post-Newtonian effects throughout 2018. To evaluate an achievable uncertainty in RV and its stability, we have carried out near-infrared, high resolution (R ∼ 20,000) spectroscopic monitoring observations of S2 using the Subaru telescope and the near-infrared spectrograph IRCS from 2014 to 2016. The Br-γ absorption lines are used to determine the RVs of S2. The RVs we obtained are 497 km/s, 877 km/s, and 1108 km/s in 2014, 2015, and 2016, respectively. The 1 statistical uncertainties are derived using the jackknife analysis. The wavelength calibrations in our three-year monitoring are stable: short-term (hours to days) uncertainties in RVs are < ∼ 0.5 km/s, and a long-term (three years) uncertainty is 1.2 km/s. The uncertainties from different smoothing parameter, and from the partial exclusion of the spectra, are found to be a few km/s. The final results using the Br-γ line are 497 ± 17(stat.) ± 3(sys.) km/s in 2014, 877 ± 15(stat.) ± 4(sys.) km/s in 2015, and 1108 ± 12(stat.) ± 4(sys.) km/s in 2016. When we use two He I lines at 2.113 µm in addition to Br-γ, the mean RVs are 513 km/s and 1114 km/s for 2014 and 2016, respectively. The standard errors of the mean are 16.2 km/s (2014) and 5.4 km/s (2016), confirming the reliability of our measurements. The difference between the RVs estimated by Newtonian mechanics and general relativity will reach about 200 km/s near the next pericenter passage in 2018. Therefore our RV uncertainties of ≈ 13 − 17 km/s with Subaru enable us to detect the general relativistic effects in the RV measurements with more than 10 σ in 2018.

We have determined the wavelength dependence of the extinction in the near-infrared bands (J, H, K S ) toward the Galactic center from the VVV (VISTA Variables in the Vía Láctea) aperture photometry of the stars in the region |l| < ∼ 2 • .0 and 0 • .5 < ∼ |b| < ∼ 1 • .0; this region consists of 12 VVV tiles. We have found significant systematic discrepancy up to ∼ 0.1 mag between the stellar magnitudes of the same stars in overlapping VVV tiles. However, by carefully using the positions of red clump stars in color-magnitude diagrams as a tracer of the extinction and reddening, we are able to determine the average of the ratios of total to selective extinction to beH, K S wavelength range is estimated. The obtained wavelength dependence is consistent with those obtained with the Mauna Kea Observatory (MKO) photometric system employed in the Simultaneous 3-color InfraRed Imager for Unbiased Survey (SIRIUS) camera attached to the Infrared Survey Facility (IRSF) telescope in previous studies. Such a steep decline of extinction toward the longer wavelengths is also in line with recent results based on deep imaging surveys. The determined extinction law seems to be variable in the VVV tile to tile, and it is not clear how much of this is due to real sight line variations and due to observational systematic effects. Thus, there might be room for improvement of the 1 extinction law determination from the existing VVV data, but this steep extinction law tends to locate heavily reddened objects in the Galactic plane more distant from us when their distance moduli are calculated from the observed reddening values.