Missing Link: How the stars in the center of the Milky Way are measured

Modern astronomical instrumentation allows Einstein’s theory of relativity to be tested at the black hole at the center of the Milky Way. A glimpse.

The near-infrared image of the galactic center with adaptive optics (right) has 20 times more spatial sharpness than the image without adaptive optics (left). (Image: MPE/ESO)

The SINFONI and GRAVITY instruments, deployed at the European Southern Observatory’s Very Large Telescope, have revolutionized the study of exoplanets, supermassive black holes, and star-forming galaxies in the early Universe. Both instruments played an important role in the discovery and characterization of the black hole at the galactic center.

The eminent sky explorers Galileo Galilei, Isaac Newton, Tycho Brahe, William Herschel, and Albert Michelson built the devices themselves with which they observed the sky. Astronomers still follow their example today: Our group at the Max Planck Institute for Extraterrestrial Physics (MPE), headed by Reinhard Genzel, thrives on designing and building new instruments, observing them and thus creating new windows into the cosmos to open.

The advantages of building your own instruments are obvious: we can align the design closely with our scientific goals and use the new apparatus first. We would like to present two of them, SINFONI and GRAVITY, below. One of its applications is observing the galactic center and its black hole.

CCD and infrared detectors are two-dimensional pixel arrays onto which the two-dimensional celestial sphere can be imaged using a camera focused to infinity. The use of filters and multiple exposures allows color information to be obtained. In order to break down the light into its spectral colors, you need one dimension of the detector surface for the wavelength axis. This leaves only one axis for the spatial resolution so that the spectroscopic information is only available along a one-dimensional slit. An astronomical instrument can therefore either “see” – that is, provide good spatial resolution and moderate spectral information – or “hear”, that is, provide good spectral resolution with limited spatial information.

The solution for combining both aspects is strongly reminiscent of how a knitted sweater gets on the other side of a locked door: you thread it on, transport the wool thread through the keyhole into the next room and send the knitting instructions on a piece of paper under the crack in the door with. The basis of “Integral Field Spectroscopy” (IFS) differs only slightly: the image field is cut up into individual rows and optically arranged to form a one-dimensional pseudo-slit.

This can be spectroscopically analyzed in a conventional way so that the spectra of all series are available at once. These individual spectra then have to be reassembled in such a way that their arrangement corresponds to the two-dimensional field of the sky – no problem with computers. The result, a three-dimensional data cube, has two spatial axes and a full spectrum in each pixel.

The field splitter (a) optically splits the image of the astronomical object into individual lines and arranges them in a slit. This is spectrally dispersed and reconstructed in the computer as a data cube. SINFONI’s field splitter (b) splits the square field of view by reflecting the different lines in different directions and combining them with a set of secondary mirrors into a single slit (c).

Because the cutting trick does not provide more detector pixels, the achievable image fields usually remain rather small: SINFONI has 64 × 32 spatial pixels and 2048 spectral ones. The ideal scanning pattern corresponds to a spatial mapping function with a grid of two to four pixels in order to make the best possible use of the captured photons. This results in an image that has approximately 202 to 302 or 400 to 900 independent pixels.

Despite the limited field of view, dozens of stars can be spectroscopically viewed in parallel: This “multiplexing” is one of the great advantages of the IFS. In addition, it is not necessary to determine the orientation of the gap before recording, because the IFS de facto lays all possible gaps at the same time. Accordingly, the orientation of the dynamic axes of a galaxy, for example, does not have to be known a priori in order to measure the Doppler velocities of the stars or the gas along them.

Our team at the MPE has implemented integral field spectroscopy for the first time worldwide – initially with “3D”, which was used in the 1990s on one of the smaller ESO telescopes. 3D was a precursor to SINFONI, which we installed on the Very Large Telescope (VLT) in 2004: SINFONI combines IFS with adaptive optics. This tricky technique compensates for the ever-present, disturbing air turbulence (“seeing”). This makes the images and data cube diffraction limited. The VLT thus achieves a resolution of 60 milliarcseconds in the near-infrared at a wavelength of 2 µm.

To do this, it is necessary to analyze the wavefront of the light from a suitable nearby star in order to bend an optically conjugate, deformable mirror about 100 to 1,000 times per second in such a way that it reverses the effect of the atmosphere and flattens the wavefront. Both the wavefront sensor and the deformable mirror are in the pupil plane of the optical system. A few hundred sensor elements and a corresponding number of actuators ensure the correct deformation if the interaction matrix between sensor signals and actuator impulses is known and can be applied quickly enough.

The effort is rewarded with razor-sharp images (see title image). Without adaptive optics, seeing typically limits the resolution to a little less than one arc-second: a value around 20 times worse than an eight-meter telescope theoretically allows.

We mainly used SINFONI for two projects: the study of galaxy dynamics in the early universe and stellar dynamics in the galactic center. The gaseous hydrogen in a galaxy emits, among other things, the well-known Hα line at 656 nm. In distant galaxies, the cosmological redshift z shifts the signal to longer wavelengths: the line is found at z = 2, at a distance of around 9 billion light years in the near-infrared, the astronomical K-band at 2 µm. SINFONI covers such wavelengths: They can be easily corrected with adaptive optics.

The epoch 9 billion years ago is also called “cosmic noon” because most of the galaxies were formed at this time. The spatially resolved spectroscopy with SINFONI allowed us to study the two-dimensional radial velocity fields of the young galaxies for the first time. To our astonishment, most of them showed a field that suggests a very orderly rotation – much like today’s spiral galaxies. Contrary to the previously widespread assumption, galaxies do not grow primarily through chaotic collisions with other galaxies. Rather, it is fed over a long period of time by an orderly flow of gas from the large-scale, cosmic network to the center of mass.

Another reason makes the K-band interesting for observing the galactic center. At optical wavelengths, the interstellar, absorbing dust completely blocks our view of the center of the Milky Way. But the veil lifts at wavelengths beyond 1.5 µm. Since the thermal emission of stars is also evident in the K-band, the images obtained hardly differ from optical ones.

A few years before the development of SINFONI, our diffraction-limited K-band images of the galactic center showed that individual stars can be tracked in their orbits around the central black hole. This system has a similar hierarchical structure to the solar system, with the stars representing the test particles for the potential of a mass around 200,000 times heavier than the sun.

During the completion of SINFONI, events came to a head: The star S2 flew through the pericenter of its orbit in 2002, making it possible to measure it with an orbital period of 16 years and to determine the mass of the black hole at 4 million solar masses without any doubt. This measurement is the basis of the work for which our team leader Reinhard Genzel and the leader of a Californian research team Andrea Ghez received the Physics Nobel Prize in 2020.

Diffraction-limited single telescopes (a, red) measured the orbit of the star S2 from 1992 to 2017, and GRAVITY (blue) contributed interferometrically from 2016 to 2021. Between 2003 and 2019 measurements with SINFONI provided the radial velocities of S2 (b).

Among other things, we optimized the design of SINFONI for the observation of stars in orbits around the black hole with periods of a few decades. The selectable spectral resolutions match the natural line widths possessed by the hydrogen, helium, and carbon monoxide lines in the spectra of the stars. One of the field sizes covers the most exciting part of the central arc second around the black hole, sampling the sharp imaging function of the adaptive optics with 4 × 4 pixels. In this mode, we regularly measured the radial velocities of almost 50 stars between 2003 and 2019.

The radial velocity of S2 is particularly dramatic and best documented: In 2018, the star passed the pericenter of its orbit for the second time in our 30-year observation period. He reached a speed of almost 8000 km/s, which changed significantly within a few weeks. The measurements show that the star reached a Doppler redshift of +4000 km/s before, and after a few weeks, the gravity of the black hole catapulted it to a blueshift of -2000 km/s (Fig. above).

For example, the interaction of astrometry (measured in angular units) and radial velocity (measured in absolute units) allows the constant of proportionality between the two to be determined without further assumptions, and hence the distance to the galactic center.

The maximum speed of S2 is 8000 km/s. This corresponds to 2.5 percent of the speed of light, so the star moves slightly relativistically. In this way, he makes it possible to check the validity of the relativistic formulas in the gravitational field of a black hole. The first detectable effect is spectroscopic: the combination of transverse Doppler effect and gravitational redshift should make the light of S2 appear redder by about 200 km/s when passing through the pericentre – a change that SINFONI measured with a measurement error in the radial velocity of S2 of only 10 km /s not challenged.

However, it is necessary to determine 13 other parameters in addition to the actual effect: the six-phase space coordinates of the star S2 and the black hole, as well as its mass. Some parameters, such as the distance and mass of the black hole, are astrophysically interesting, others less so. This complicates the measurement and requires the astrometric orbit. This can be determined twenty times better with GRAVITY than with adaptive optics.

GRAVITY: combination for precision

The rule of thumb “bigger is better” applies in particular to telescopes: the light-gathering capacity increases quadratically with the telescope diameter and the resolution – limited by the diffraction at the entrance pupil – at least linearly. The cost increases roughly with the third power of the diameter; large conventional telescopes are eight to ten meters in diameter for practical reasons. Four of them stand next to each other on Mount Paranal in the northern Chilean Atacama Desert: Its worn-out dome offers space for the Very Large Telescope (VLT), the flagship of European astronomy.

ESO’s four large 8-meter telescopes are located on a platform on Mount Paranal in Chile; the greatest distance between the two telescopes is 130 meters. In the tunnel system below, the light is delayed before the interferometric combination takes place. (Image: ESO/G.Hüdepohl  atacamaphoto.com)

But how much better would it be to be able to use the entire area of ​​the platform, which is over 130 meters in diameter, as a telescope? Here’s a thought experiment: imagine a mirror of the right size. It would have a spectacular resolution that is around 20 times better than that of a single telescope. If a small black spot of one square meter were applied to the 130-meter mirror at one point, this would hardly disturb the resulting image – just as little would a second black spot. And so more and more parts of the mirror could be colored black until only four holes, every 8 meters in diameter, were still reflecting.

What does the resulting image look like? For one thing, it would of course be much darker, and the mapping function would no longer be a simple Airy function. But the resolution should still be as good as it corresponds to the distance between the telescopes: 130 meters. Therefore, a super-resolution telescope can be synthesized by suitably connecting the four individual telescopes together. In this case, “suitable” means bringing the light together coherently, a single mirror with a diameter of 130 meters would do nothing else. Then the light of each star from the four telescopes interferes with itself. So you have an interferometer in front of you.

For interference to occur, the light from the different telescopes must reach the detector at the same time. There is a tunnel system under the surface of the Paranal. Retroreflectors, which can be moved on very straight rails, compensate for the geometric path difference of the light on delay lines. For exposure times longer than a few milliseconds it is necessary to stabilize the interference against atmospheric turbulence. Similar to adaptive optics, this requires a bright star that allows the phase position to be determined sufficiently quickly. That makes exposures up to a minute workable.

It was only this “fringe tracking” that made it possible to make stars beyond the 19th magnitude (apparent magnitude: 19 mag) in the galactic center visible to the interferometer: they are around 10,000 times darker than objects observed interferometrically up to that point. In addition to the delay lines and fringe tracking, every telescope needs adaptive optics, because this is the only way to deliver coherent light with a sharp imaging function.

In GRAVITY, the light is coupled in fibers: They offer an elegant way of compensating for the small time delay between the fringe tracking star and the object to be examined, and of adjusting the directions of polarization. The fibers guide the light into a micro-optical chip, in which optical waveguides, 50:50 splitters, and phase delay lines interfere in pairs with the light from the four telescopes.

GRAVITY’s vacuum tank (a) contains the optics. The beam combiners (b) are designed as integrated optics and combine the light from the four telescopes into 24 spectra. The output spectra (c) encode the brightness distribution in the sky.

Each interference is measured at four phase positions: In order to obtain the interferometric information, it is necessary to measure 6 × 4 = 24 brightnesses; the spectrally resolved 24 outputs result in 24 spectra. Around ten spectral channels are used for the stars in the galactic center, which are dark according to interferometric standards. This results in around 240 measurements, which are sufficient to describe the contrast and phase position with around 60 complex numbers.

It can be shown mathematically that these numbers correspond to the Fourier transform of the two-dimensional brightness distribution of the source in the sky, measured at 60 points. Since the Earth’s rotation is constantly changing the geometry, if you wait long enough, enough information is collected to reconstruct an image – with the resolution of a 130-meter telescope.

That’s enough to spot cars on the moon. Even more fascinating is the achievable astrometric accuracy of a few tens of microarcseconds: it corresponds to a few centimeters on the moon. If there were a soccer game on the moon, video evidence of whether the ball crossed the goal line could be obtained from Earth. To stay with the picture: The orbit of the star S2 in the sky is about as large as the hypothetical stadium on the moon would appear from Earth.

The infographic (a) shows a section of the orbit of S2 around the pericentre: the redshift is greatest at the closest approach. In May 2018, the spectral lines were up to 200 km/s more redshifted (b) than the orbit alone requires.

In 2018, the measurement accuracy of GRAVITY made it possible to detect a significant redshift signal just a few weeks after the flyby of S2 at the pericenter. The light behaved exactly as the theory of relativity predicted. In addition, the redshift of two different spectral lines could be compared: As expected, they showed the same behavior. This was the first time we had tested the equivalence principle in the gravitational field of a black hole. Another observable relativistic effect is provided by the motion of the body itself: the well-known perihelion rotation of an orbit in the Schwarzschild metric.

Einstein himself had calculated the effect for the planet Mercury to be 43 arc seconds per century and thus explained the observed Mercury orbit. For S2, the effect is about twelve arc minutes per 16-year cycle. Projected on the sky, this results in a deviation of about 0.5 milliarcseconds, corresponding to about 25 centimeters in the image of the stadium on the moon. With a highly elliptical orbit like that of S2, almost all of the rotation occurs at the pericenter, and the star exits on a slightly twisted orbit.

By the end of 2019, GRAVITY had collected enough data from the slightly twisted orbit. These clearly showed that the orbit of S2 was processed – the amount and direction of the rotation are consistent with the theory of relativity. Our 2021 data also shows the effect when compared to the 16-year-old data recorded with adaptive optics.

Comparing the 2005 adaptive optics data with the 2021 interferometric data (a) shows that the orbit of S2 rotated slightly during the May 2018 pericenter flyby – in best agreement with predictions of the theory of relativity. A veritable ballet of stars could be followed around the black hole in 2021 (b).

The S2 data make it possible to estimate the proportion of the measured approximately 4 million solar masses that is in the black hole: If part of the mass reached the orbit of S2, a different precession would be present. An invisible swarm of neutron stars or dark matter comes into question. According to the GRAVITY data, a maximum of 0.1 percent of the mass is outside the S2 train: 99.9 percent is within 120 astronomical units, the pericenter distance of the S2 train.

In addition to the mass of the black hole, we also want to measure its rotation very precisely. The stellar orbits also serve this purpose, because a rotating black hole pulls the space-time around it somewhat, so that the orbits rotate around the axis of rotation of the black hole. However, this effect is significantly smaller than redshift or pericenter rotation. That’s why we’re looking for other darker stars that orbit the black hole with even shorter periods and that have a correspondingly stronger influence on its spin. The 2021 observations reveal a new star that sets an interferometer brightness record: S300, a 19th-magnitude star. Work is now underway on an upgrade project: Among other things, GRAVITY+ is intended to further increase the sensitivity of the interferometer.

The high resolution of GRAVITY allows seeing the emission from the accretion disk around the black hole. Their faint glow outshines neighboring stars in adaptive optics data. This gives GRAVITY another invaluable advantage: we can use it to reference stellar positions directly to the center of mass so that four of the 13 parameters mentioned above are omitted when determining the orbit.

But the accretion disk doesn’t always glow faintly. About once a day, it shines unpredictably much brighter for about an hour. Our team had already discovered this in 2003, but the associated model could only be confirmed by GRAVITY data from 2018: In a small, limited space, electrons heat up and emit the detected synchrotron radiation. This could be due to a mechanism similar to the radiation bursts on the sun’s surface: magnetic short circuits. The GRAVITY data unequivocally showed that during the outburst, the emission rotates around the black hole, with the radius and orbital period matching exactly.

GRAVITY observed a black hole burst of radiation in 2018. The astrometric positions complete a circular motion within an hour (a). At the same time, the linear polarization also rotates during the burst of radiation (b).

“Hotspots” run directly around the event horizon and make it possible, for example, to determine the system’s axis of rotation: We can see the accretion disk roughly “from above” – ​​a real stroke of luck. The now-published EHT image confirms this geometry.

In an observational science like astronomy, the systems being studied cannot be manipulated. However, almost all of the impressive progress of recent decades is based on the fact that astronomers also do experimental physics and have built new observation instruments. We hope that this exciting journey will continue for a long time.

Stefan Gillessen and Frank Eisenhauer: Highest resolution. Physics Journal. 2022. 21/2022. 32-37. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission.

THE AUTHORS

Stefan Gillessen received his doctorate from the University of Heidelberg in 2004 with a thesis on the alignment control of the Cherenkov telescopes of the HESS experiment in Namibia. He then joined the group of Reinhard Genzel at the Max Planck Institute for Extraterrestrial Physics (MPE). Since then he has been researching stellar motion in the galactic center and is part of the team developing new instruments for use on ESO telescopes.

Frank Eisenhauer received his doctorate from the LMU Munich in 1998 and was already involved in the development of novel astronomical instruments: a near-infrared camera for adaptive optics for observing the star-forming region NGC 3603. At the MPE he leads the development and scientific elaboration of large astronomical instruments and experiments such as SINFONI and GRAVITY. Eisenhauser was awarded the Stern-Gerlach Medal in 2022 for his groundbreaking work on the development and use of instruments in infrared astronomy and on adaptive optics.

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