Nobel Lecture: A forty-year journey^*

Figure 1

Near-infrared/radio, color-composite image of the central light years of the Galactic Center. The blue and green colors represent the 1.6 and $3.8\mu \mathrm{m}$ broadband near-infrared emission, at the diffraction limit ($\sim 0.05”$) of the 8 m Very Large Telescope (VLT) of the European Southern Observatory (ESO), and taken with the “NACO” AO camera and an infrared wave-front sensor. Adapted from [56]. Similar work has been carried out at the 10 m Keck telescope ([60], [59]). The red color image is the 1.3 cm radio continuum emission taken with the Very Large Array (VLA) of the U.S. National Radio Astronomy Observatory (NRAO). The red dot in the center of the image is the compact, nonthermal radio source ${\mathrm{SgrA}}^{*}$. Many of the bright blue stars are young, massive $\mathrm{O}/\mathrm{B}$ and Wolf-Rayet (WR) stars that have formed recently. Other bright stars are giants and asymptotic giant branch stars in the old nuclear star cluster. The extended streamers/wisps of $3.8\mu \mathrm{m}$ emission and radio emission are dusty filaments of ionized gas orbiting in the central light years. Adapted from [50].

Figure 2

Total-intensity mm-VLBI of ${\mathrm{SgrA}}^{*}$. Left: normalized, deblurred visibilities at 1.3 mm taken with the Event Horizon Telescope are shown as a function of baseline length; errors are $\pm 1\sigma$. The dashed line shows the best-fit circular Gaussian (FWHM: $52\mu \text{as}$). An annulus of uniform intensity (inner diameter: $21\mu \mathrm{as}$, outer diameter: $97\mu \mathrm{as}$), shown with a solid line, is perhaps the most plausible model that is consistent with the data. Adapted from Fig. S5 in [94], Supplement. Right: 3 mm global mm-VLBI image of ${\mathrm{SgrA}}^{*}$, after removal of the scattering screen. The reconstructed image has an intrinsic Gaussian source diameter of ${\theta }_{\text{maj}}=120\pm 34\mu \mathrm{as}$ and ${\theta }_{\min }=100\pm 18\mu \mathrm{as}$. The ellipses at the bottom indicate half the size of the scatter-broadening kernel (${\theta }_{\text{maj}}=159.9\mu \mathrm{as}$, ${\theta }_{\min }=79.5\mu \mathrm{as}$, $\mathrm{PA}=81.9°$) and of the observing beam. Adapted from Fig. 5 in [91].

Figure 3

Mass distribution in the central parsec of the Galactic Center after phase 2 ($1996/1998$). The left graph shows the projected $1^d$ stellar velocity dispersion as a function of projected distance from ${\mathrm{SgrA}}^{*}$, obtained from proper motions (filled circles) and Doppler velocities (crossed squares). Each point is derived from averaging the motions of 9 to 20 stars. The solid curve is a model assuming that the stars move with an isotropic velocity distribution in the potential of a point mass [M(0)] plus an isothermal star cluster of velocity dispersion $50\mathrm{km}/\mathrm{s}$. The distance of the Galactic Center is assumed to be 8.0 kpc. From [35]. The right graph shows the mass distribution derived from stellar proper motions published by the Keck group in 1998 ([57]) (filled black circles), and compared to the [35], [36] proper motions (open circles), the [54] stellar radial velocities (squares), and the [83] measurement of the rotating gas disk (triangles). From 0.1 to 0.015 pc the enclosed mass appears to be constant with a value of $2.6\times {10}^6{\mathrm{M}}_{\odot }$. For comparison, there are several power law distributions. Adapted from Fig. 7 of [57]. The agreement between the results of the MPE and UCLA groups is excellent.

Figure 4

Summary of the MPE-ESO observational results of monitoring the S2-${\mathrm{SgrA}}^{*}$ orbit from 1992 to the end of 2019. Left: SHARP (black points with large error bars), NACO (black points), and GRAVITY (blue points) astrometric positions of the star S2, along with the best-fitting GR orbit (gray line). The orbit does not close as a result of the Schwarzschild precession (see text). The mass center is at $(0,0)$, marked by the black cross. All NACO and SHARP points were corrected for a zero-point offset and drift of the reference frame in right ascension (RA) and declination (Dec). The red data points mark the positions of the infrared emission from ${\mathrm{SgrA}}^{*}$ during bright states, where the separation of S2 and ${\mathrm{SgrA}}^{*}$ can be directly inferred from differential imaging. Right: RA (top) and Dec (middle) offset of S2 and of the infrared emission from ${\mathrm{SgrA}}^{*}$ relative to the position of ${\mathrm{SgrA}}^{*}$ (assumed to be identical with the mass center) (same symbols as in the left panel). Gray is the best-fitting GR orbit including the Rømer effect (finite speed of light), special relativity, and GR to “parametrized post-Newtonian” approximation PPN1 ([178]). Bottom right: same for the line-of-sight velocity of the star. Position on the sky as a function of time (left) and Doppler velocity (relative to the local standard of rest) as a function of time (right) of the star S2 orbiting the compact radio source ${\mathrm{SgrA}}^{*}$. Blue filled circles denote data taken with the SINFONI, red open circles denote data taken with the Keck telescope as part of the UCLA monitoring project ([31]). Adapted from Fig. 1 of [76].

Figure 5

Left: the ESO-Very Large Telescope (VLT) on Cerro Paranal (Chile), where most of the observations by our group were obtained. The Observatory in the Atacama desert is at 2,635 m altitude and $-24.7^0$ latitude. It hosts $4\times 8.2\mathrm{m}$ telescopes (large silvered structures) as well as $4\times 1.8\mathrm{m}$ Auxiliary Telescopes (white round domes). Both arrays can be combined optically as a spatial interferometer (VLTI) through mirror trains, where the relative geometric path lengths to a given celestial source can be compensated by movable delay line mirrors in the linear white structure underneath the platform ([69]). The final combined set of four beams finally arrives at the beam combiner facility structure underneath the rectangular building in the center of the array. Here, the light beams are brought together in the cryogenic beam combiner instrument GRAVITY [built by a French-German-Portuguese consortium of six institutions (logos above the VLT image), plus ESO itself]. In GRAVITY, we calibrate and optimize the data and extract the visibilities and relative phases of the science object as well as that of a nearby, fringe-tracking reference object, as a function of wavelength, guiding and manipulating the infrared light in single-mode fibers and combining the six two-telescope combinations in a microchip ([71]). Bottom right: after calibration of the phases using laser metrology, images with $2\times 4$ mas FWHM resolution are reconstructed by Fourier transformation. In the case shown, the VLTI science fibers were placed on the star $\mathrm{S}2/\mathrm{Sgr}{\mathrm{A}}^{*}$ in the left image, while the interferometer phases were tracked on the bright star IRS16C 1” NE of ${\mathrm{SgrA}}^{*}$, in the top left of the AO image. All four telescopes are equipped with infrared adaptive optics, which uses the $K=7$ bright star IRS7 5” north of ${\mathrm{S}2/\mathrm{SgrA}}^{*}$ as a natural guide star to flatten the wave fronts. The image at the bottom right was taken in March 2018, about two months before the peri-passage of S2, and both S2 and ${\mathrm{SgrA}}^{*}$ can be clearly detected and its $\sim 22$ mas separation measured to $\sim 40–100\mu \text{as}$ precision. Top right: during the peri-passage in 2018, the motion of S2 can be easily detected night for night, then moving at $\sim 7,700\mathrm{km}/\mathrm{s}$ at $\sim 1,400$ Schwarzschild radii from ${\mathrm{SgrA}}^{*}$. Adapted from Fig. 2 of [72].

Figure 6

Testing GR and the MBH paradigm with relativistic effects near ${\mathrm{SgrA}}^{*}$. Top left: residuals between the SINFONI $\mathrm{HeI}/\mathrm{HI}$ $\mathrm{Br}\gamma$ line centroid velocities in the local standard of rest (filled red circles with $1\sigma$ uncertainties) and the best-fitting Newton/Kepler orbit of all spectroscopic and astrometric data over the past three decades (gray horizontal line at 0). The blue line is the best-fitting relativistic orbit including all PPN1 terms (as well as the Rømer effect), and fitting a free parameter $f_{gr}$ to the PPN1 wavelength term including gravitational redshift and transverse Doppler effect. GR has $f_{gr}=1$ and our best fit yields $f_{gr}=1.02\pm 0.04$ ([72], [74], [76]). Bottom plots: residuals in RA (left) and angle on the sky $\phi$ (right) between the GRAVITY (filled cyan circles and $1\sigma$ uncertainties) and average NACO astrometry before 2017 (gray bar) and the best-fitting relativistic orbit without precession ($f_{SP}=0$, blue dotted horizontal line at 0). The best-fitting relativistic orbit including precession has $f_{SP}=1.1\pm 0.19$. Adapted from Figs. 3 and B2 in [76]. Top right: residual motion of the $2\mu \mathrm{m}$ light centroid of ${\mathrm{SgrA}}^{*}$ originating from polarized synchrotron emission from $\gamma >1,000$ accelerated electrons in the inner accretion zone in a bright “flare” on July 22, 2018, cf. [50] as a function of time over about 30 minutes, and relative to the location of the mass as estimated from the S2 orbit (dark gray asterisk and $1\sigma$ errors). The blue curve denotes a circular particle orbit at $3.5{\mathrm{R}}_{\mathrm{S}}$ around a nonspinning MBH of 4.3 million solar masses, inclined at 160°. From Fig. 1 in [73], [77], [78].

Figure 7

Status of the Galactic Center mass distribution after phase 4. Constraints on the enclosed mass in the central 10 pc of the Galaxy. The blue, black and red circles, the pink, green and red triangles are estimates of the enclosed mass at different radii obtained from stellar and gas motions [see [50] and [80] for details]. The filled black rectangle comes from the clockwise loop motions of synchrotron near-infrared flares ([73]). The cyan double arrow denotes current VLBI estimates of the 3 mm size of ${\mathrm{SgrA}}^{*}$ ([91]). The continuous magenta line shows the total mass model from all stars and stellar remnants ([4]). The gray line marks the distribution of $\mathrm{K}<18.5$ subgiants and dwarfs from [155]. The gray dashed lines indicate the distribution of stellar black holes and neutron stars from theoretical simulations of [4] and [12], which span a range of roughly factor 5. Red, black and green upper limits denote upper limits on giants, main-sequence B stars and $\mathrm{K}<19$ GRAVITY sources. The Schwarzschild radius of a $4.26\times {10}^6{\mathrm{M}}_{\odot }$ black hole and the innermost stable circular orbit radius for a nonspinning black hole are given by orange and dark green vertical lines. The pericenter radius of S2 is the dashed vertical blue line and the sphere of influence of the black hole is given by the vertical light green line. The blue horizontal line denotes the $2\sigma$ upper limit of any extended mass around ${\mathrm{SgrA}}^{*}$ obtained from the lack of retrograde precession in the S2 orbit. Adapted from Fig. D1 in [76].