Science

How do we make a picture from the sparse data collected by the EHT?

The Event Horizon Telescope (EHT) collects light from the black hole using a small number of telescopes distributed around the Earth. Once the EHT has measured data from the black hole, we still need to make a picture from it - a process referred to as imaging. The light we collect gives us some indication of the structure of the black hole. However, since we are only collecting light at a few telescope locations, we are still missing some information about the black hole’s image. The imaging algorithms we develop fill in the gaps of data we are missing in order to reconstruct a picture of the black hole.

Since there is a lot of missing data, you may ask how making a picture is even possible. To give you an idea of how this works, you can think about the measurements we make from telescopes in the EHT as a bit like notes in a song. Each pair of telescopes produces a measurement that corresponds to the tone of a just a single note. The tone that is heard is related to the projected distance between the telescopes, as seen from the direction of the black hole; the farther apart the telescopes, the higher the pitch of the note.

Watching the black hole with the EHT is a bit like listening to a song that is played on a piano that has a lot of broken keys. If we had telescopes located everywhere on the globe we would be able to hear all possible notes, and thus hear a perfect rendition of the song. However, as we only have telescopes at a few locations, we must recognize the song being played with just a few notes. Although hearing a song this way is definitely not perfect, often times there is still enough information to follow along.

To make this a bit more clear, listen to the video below (use headphones for the best experience). In this video we play a song as if we were increasing the number of telescopes in the EHT, essentially fixing the broken piano keys. At the beginning you are going to hear only one note of this song, and as you go on you are hear more and more notes until eventually you will start to be able to make out a (hopefully familiar) song. The notes corresponding to the tones we are currently playing on the piano keyboard will be lit up so you can see what you are hearing.

Video credit: Katie Bouman

By close to the end, even before all the notes were playing, you may have been able to start to recognize the song— Vanilla Ice’s "Ice Ice Baby." Even if you don’t know the song, you probably were still starting to get the gist of it. Even though there were still a lot of gaps in the notes near the end, it’s pretty amazing that your brain can fill in holes and you can start to make out the song.  What your brain was doing here is very similar to what the imaging algorithms that we develop for the EHT do. Using the sparse data we collect from the telescopes, our algorithms fill in the missing gaps with the most natural looking image.

But there is one point I want to draw your attention to: there is always some ambiguity in what the true image is. For example, even if many notes are playing, as long as there were some notes missing, it doesn’t have to be "Ice Ice Baby." The more notes missing, the more ambiguity there is. In fact, perhaps close to the beginning you may have thought that the song was Queen and David Bowie’s song "Under Pressure." If those were the only notes we heard we would be in trouble, as there are multiple songs that fit the notes we are hearing fairly well. However, as we increased the number of notes (measurements) the specific song becomes clear.

Image credit: Katie Bouman

Similarly, for the EHT, the data we take only tells us only a piece of the story, as there are an infinite number of possible images that are perfectly consistent with the data we measure. But not all images are created equal— some look more like what we think of as images than others. To chose the best image, we essentially take all of the infinite images that explain our telescope measurements, and rank them by how reasonable they look.  We then choose the image (or set of images) that looks most reasonable.

Image credit: Katie Bouman

Using these algorithms we are able to reconstruct pictures from the very sparse measurements measured with the EHT. Below is a sample reconstruction done using simulated data generated from only 7 telescopes located around the world, and pretending to point at the black hole in the center of our own Milky Way galaxy. Although this is just a simulation, reconstructions such as this give us hope that we soon will be able to to reliably take the first picture of the black hole.

Left square image courtesy of Jason Dexter. Image credit: Katie Bouman

Einstein's theory of general relativity (GR) connects spacetime curvature with distribution and motion of energy. This includes matter, which is just a particular form of energy. Massive objects, such as planets, stars, and black holes, deform spacetime in their vicinity– we interpret this effect as the presence of an attractive gravitational force.

GR theory has been thoroughly tested in a small spacetime curvature limit for astrophysical objects such as the Sun or the Earth. Using atomic clocks, scientists have measured time passing more slowly when the clock is placed closer to the center of the Earth. Scientists have also found that planets do not follow exactly elliptical orbits as predicted by Newton's theory of gravity. This effect is most evident for the Mercury because it is the closest planet to the Sun. Both of these results are predicted by GR theory and can be accurately calculated from Einstein's equations. 

GR is also accounted for in every device that tracks location through GPS signals: during the location computing, the device adjusts its calculations to account for general relativity. In this way, you test GR every time you check your location on a smartphone.

Another consequence of Einstein's theory is the bending of light rays passing through vicinity of a massive body. This effect was famously confirmed in 1919, when Sir Arthur Eddington measured the apparent shifted positions of stars during a total solar eclipse— an illusion caused by light bending around the mass of the Sun, or gravitational lensing.

While all these effects are small in the solar system, the situation looks very different in the vicinity of a black hole, where the spacetime curvature is extremely strong. Whether GR is true in such an environment is still debated by scientists. However, the field of the gravitational waves physics has recently produced evidence that GR holds true around black holes. Every new test of strong GR is essential for our understanding of gravity.

This infographic shows a simulation of the outflow (bright red) from a black hole and the accretion disk around it, with simulated images of the three potential shapes of the event horizon’s shadow. Credit: ESO/N. Bartmann/A. Broderick/C.K. Chan/D. Psaltis/F. Ozel

Testing general relativity using the black hole shadow

GR predicts that photons emitted by the gas falling into a black hole should travel along curved trajectories, forming a ring of light around a “shadow" corresponding to the location of the black hole. While we often use the term “shadow," it isn't technically correct. What we are hoping to observe with the EHT is rather a “silhouette” of a black hole: its dark shape on a bright background of light coming from the surrounding matter, deformed by a strong spacetime curvature.

The size and shape of this image can be predicted from the GR equations. Size and shape depend mostly on black hole mass, and to a smaller degree, on its spin. The “no-hair theorem” tells us that these are the only two parameters describing spacetime around a black hole (apart from the electric charge, which can be neglected). GR predicts a roughly circular shape of the shadow, but there are alternative theories of gravity that predict a slightly different shadow geometry. Therefore, detecting the shadow of a black hole and establishing that it is indeed circular would be an observational test of general relativity.

When people think of a black hole, they might picture it as a giant vacuum cleaner that sucks up all nearby matter. In fact, black holes do grow by eating up nearby matter, but it's actually relatively difficult for matter to fall into a black hole. If matter isn't too close to the black hole and feels only gravity, it can orbit the black hole indefinitely, the way the planets in our solar system orbit the Sun. Something more than gravity is needed to get the matter close enough to the black hole for the black hole to eat it. This process is called accretion, and it is driven by friction. As matter, taking the form of gas, falls into the black hole, it loses gravitational energy and gets heated by friction. Friction causes different parts of the disk that slide by each other to lose energy and heat up, the same way heat is generated when you rub your hands together. The gas then forms a hot disk around the black hole and falls in, causing the black hole to grow.

Because black holes are so massive, but at the same time so compact, matter needs to give up a lot of energy to fall all the way in. As a result, some accretion disks around supermassive black holes are incredibly bright, and can outshine all the billions of stars in their host galaxy put together. The accretion disk around the black hole in the center of the Milky Way, Sgr A*, is comparatively dim— only a few hundred times the brightness of the sun. One of the key goals of the EHT is understanding exactly why the black hole in our galaxy is so dim compared to the bright black holes we can observe across the universe.

Another important unanswered question is: What creates the friction that allows the black hole to grow? Normally, friction is caused by atoms rubbing against each other, but the gas around supermassive black holes is so dilute that atoms rarely collide with each other. Some more complicated mechanism must give rise to the friction that allows the accretion disk to form. The leading hypothesis is that a special type of turbulence is generated by rotating magnetic fields and allows the disk to dissipate energy in a way that can mimic friction without requiring atoms to collide with each other directly. However, this kind of turbulence has never been observed experimentally. By taking a picture of the accretion disk around a black hole, the EHT will test this hypothesis and work toward a better understanding of the processes that allow accretion disks to form and black holes to grow.

As matter falls toward the black hole in the accretion disk, it releases energy and heats up, causing the inner regions of the disk to be hotter and brighter. Image credit: NASA/Goddard Space Flight Center

Relativistic jets are some of the most fascinating astrophysical phenomena. Most galaxies show very large scale jets of very fast moving plasma shooting away from the black hole. Taking the Messier 87 (M87) galaxy as an example: a narrow jet shot at near the speed of light from its center extends to a distance of five thousand light-years. The tip of the the jet diffuses up to 250 thousand light-years.

Although the central black hole is millions of times smaller than the jet, black hole accretion is the only known physical mechanism powerful enough to launch such a jet. State of the art numerical simulations show that, when a spinning black hole sucks in hot plasma, strong magnetic fields are generated around the spin axis. These tightening magnetic fields act as a spring and push the hot plasma out at very high speed.

Angular resolution is the ability of the telescope to distinguish between narrowly separated objects. In astronomy, the mathematical formula for resolution is R (resolution) ~ lambda/D, where lambda is the wavelength and D the size of the telescope. The larger the telescope, the smaller R is, and the better the angular resolution is. Improved angular resolution is one of the two reasons why astronomers want to build bigger and bigger telescopes (the other reason being improved sensitivity). For comparison, the resolution of a human eye is about 60 arcsec of a degree in visible light and that of the Hubble telescope with 2.4-meter diameter is about 0.05 arcsec of a degree. Impressive as it is, such an angular resolution would be grossly inadequate to achieve scientific goals of the Event Horizon Telescope.   The EHT aims to resolve, or be able to distinguish the parts of, the "event horizon" of two galactic center black holes: one at the center of our Milky Way galaxy, the other at the center of nearby galaxy M87 (imaging is one way of doing it, but not necessarily the only way.) The nearest massive black hole, Sgr A*, is in the center of our galaxy, about 26,000 light-years away. Even though the size of this black hole is quite big, about 30 times the size of the Sun, it is at such a large distance from us that it appears about the same size as an orange on the Moon. Farther away is the supermassive black hole at the center of galaxy M87. This black hole is about 1500 times more massive and 2000 times farther away than Sgr A*. As a result, the size of its event horizon is not quite as large as that of Sgr A*, but large enough for the EHT to resolve. M87 is about 22 micro-arc-sec compared to the 53 micro-arc-sec of Sgr A*. The EHT needs a strong enough resolving power, also called angular resolution, to match the small angular size of these black holes.   For the EHT, the D in R ~ lambda/D is the longest distance between any two dishes in the EHT array. This is the reason why antennas of the EHT are spread across the continents— North America, Hawai'i, Europe, South America, and Antarctica. All these EHT antennas act in unison to achieve an unprecedented angular resolution which could be comparable to being able to read a newspaper on the Moon. Without the amazing resolving power of EHT, the black hole would look like a point source, like most stars appear to the naked eye.  

The above images show two distinct light sources. The top image shows a higher angular resolution, while the bottom image shows a lower angular resolution. Credit: Spencer Bliven.

To understand how weak the signal strength of Sgr A* is at the Earth, and how hard it is to detect, consider a home television set before cable and satellite transmission. TV signals were transmitted in analog form and received by rooftop antennas. A typical station might transmit 100 kw in a 4 MHz band. At a distance of 20 miles the incident power density at a user site would be about 10^-15 w m² hz^-1. With a 1 square meter antenna the received power would have been about 10 microwatts. In conditions of weak reception the image became “snowy” and the audio became “staticky” because of extraneous noise— most of which originates in the TV set’s amplifiers, but a small part of which arose from natural radio sources including, the cosmic microwave background from the Big Bang. The sensitivity of the radio telescopes today needed to detect the emission from Sgr A* is very great because, even by the standards of cosmic radio sources, the emission from Sgr A* is weak. 

The total power emitted from Sgr A* in the radio part of the electromagnetic spectrum (0-1000 GHz) is about 2 x 10²⁸ w. However, at the Earth in the part of the radio band of interest to the EHT, the power density is only 3 janskys or 3 x10^-26 w m^-2 hz^-1, more than 10 orders of magnitude less than the TV signal case considered above. A typical antenna of the EHT has a diameter of about 10 m and a receiving bandwidth of 8 GHz.  The power received by an EHT antenna amounts to about 1 x 10^-16 w, about a billion times less than the TV example. 

To place this level of power in a familiar context consider the following examples. To capture enough energy from Sgr A* with an EHT antenna to hypothetically light a 1 watt flashlight bulb for 1 second would require about 250 million years. Not exactly a threat to power from solar panels! To collect enough energy to lift a 6 pound book from the floor to a table would take the age of the universe, 13 billion years. 

The detection problem at radio wavelengths differs from that encountered at optical wavelengths in several important ways. For optical astronomers, detection amounts to counting photons with detectors that have high efficiency. Uncertainty in the measured intensity is due to Poisson counting statistics so the signal-to-noise ratio is proportional to the n^1/2 where n is the number of photons detected. In the radio domain the signals are best thought of as waves that must be amplified before they can be correlated in the EHT signal processors. The signal and the noise added in the amplification are both Gaussian processes. As with any Gaussian type of noise or measurement error, the signal-to-noise ratio improves as n^1/2,  where n here represents the number of independent measurements. According to the Nyquist theorem, the number of independent signal samples exactly equals 2BT, where B is the bandwidth (8 GHZ in the EHT case) and T is the integration time. Hence the signal-to-noise ratio increases both as the square root of the bandwidth and as the square root of the integration time. However, the integration time is limited by the coherence time set by atmospheric fluctuations, so a critical way to improve sensitivity is to increase the bandwidth of the receiving system’s electronics. The ultimate goal is for the ratio of the bandwidth to observing frequency to approach unity.

Black holes are the most compact and energetic objects known in the universe. As a black hole attracts materials from its environment, the gravitational potential energy of the accreted plasma turns into heat and eventually becomes electromagnetic radiation that can be observed by the EHT.

These accretion flows are extremely complex and turbulent. Numerical models of them, therefore, play a key role in understanding black hole physics and in predicting what the EHT would see.

The state-of-the-art simulations use general relativistic magnetohydrodynamics (GRMHD) to solve for the dynamics of the accretion flows. These numerical solutions are then fed to general relativistic ray tracing algorithms to solve for the images of black holes.

By comparing these predicted images with the horizon-scale resolution images taken by the EHT, we will finally be able to answer one of the most important questions in astrophysics: does Einstein's general theory of relativity correctly predict the spacetime near supermassive black hole?

The supermassive black hole at the center of our Milky Way Galaxy is a dynamic source. The light coming from it varies at different timescale across many wavelengths. In addition to the continunig small fluctuations, astronomers observe dramatic flares about once a day. The origin of these flares is a subject of active research. In the above movie, by using a general relativistic magnetohydrodynamics simulation and a general relativistic ray tracing algorithm, we show that strong magnetic flux tubes may be responsible for these flares. The top row of the movie shows images of the black hole and its surrounding accretion flow at, from left to right, radio wave, 1.3 mm, infrared, and x-ray. The second row shows the same images in semi-log scale to bring up the emission in the dimmer regions. Although the accretion flow is optically thick in radio, the black hole shadow is visible in 1.3 mm, infrared, and x-ray. The red, white, green, and blue curves in the bottom panels are the normalized lightcurves at these four wavelengths. The horizontal axis is time in unit of GM/c³ and the vertical axis is normalized flux.  A very strong magnetic flux tube appears around t = 650 GM/c³, creating a strong flare. An Einstein ring is visible during this flare.

The descriptions above give a general idea of how linking radio dishes across the Earth can create a virtual planet-sized telescope with a magnifying power capable of imaging black hole event horizons. Here we go into more detail, giving some specifics on the technique used by the EHT: Very Long Baseline Interferometry (VLBI).

It is instructive to start by considering a simple radio interferometer that consists of two dishes pointed at the same position on the sky as shown below. Radio waves from a distant cosmic source (e.g., a star, black hole, galaxy) reach antenna 2 (on the right) a time τ_g before the other. When combined in a ‘correlator’ that multiplies and averages the signals together, the output is a complex number whose magnitude is the intensity of the cosmic source and whose phase is given by (2π τ_g c / λ), where λ is the wavelength of the received radio waves and c is the speed of light. This phase is simply a full rotation for each wavelength of extra path length the radio waves have to travel to reach the second (more distant) antenna. Now we can see the relationship between interferometer phase and position on the sky: if the source changes in position on the sky by an angle of λ/d_p, (where d_p is the distance between the antennas projected in the direction of the source) the phase changes by a full rotation. In this sense, the interferometer has an angular resolution, or magnifying power, of λ/d_p, equivalent to a regular telescope whose diameter is d_p. By adding a compensating delay (τ_g) to the electronic system at antenna 2, we can zero the phase for a particular direction on the sky.

A simple 2-element radio interferometer that achieves an angular resolution (or magnifying power) of λ/d_p. Credit: S. Doeleman

Unlike a regular telescope of diameter d_p, the interferometer only yields spatial information along one dimension of the cosmic source. And because there are only two antennas in the interferometer, it is insensitive to structures on the sky that are larger than λ/d_p. To overcome these limitations, arrays of antennas are constructed to sample many orientations and spatial scales on the sky. An example of such a facility is the Very Large Array in New Mexico (below), which consists of 27 separate radio dishes all linked together to give 27 * 26 / 2 = 351 interferometer pairs at any moment. As the Earth turns, the array changes its orientation with respect to the target source on the sky, so that many more interferometer pairs can be sampled during a night of observing. In this way, an array of dishes can make images of cosmic sources with very high angular resolution without having to build a single large telescope.

The Very Large Array in New Mexico operates as a single telescope consisting of 27 separate radio dishes. Image courtesy of NRAO/AUI

In the case of the VLA, each radio dish is connected to a central processing center that houses the ‘correlator’ shown in the first figure. To reach the highest magnifying power possible from the surface of the Earth, one can separate radio dishes over large geographic distances (see the figure below), but it is then impractical (even impossible) to link the dishes with cables. In this case, the radio waves received by each dish must be recorded and brought together with similar recordings from other sites for correlation, long after the observations are made. This is the fundamental basis for the VLBI technique. Key challenges have to be met to make this distributed array work as an interferometric array in the same was as the VLA:

• Stability: Since there are no direct connections between the radio dishes, the recordings made at each site have to be stable enough so that they can be compared later without ‘jitter’ between the signals. If the signals cannot be precisely compared in time and jitter back and forth, the resulting phase measurements will be washed out. To achieve the required stability, VLBI uses atomic clocks (Hydrogen Masers) to time-stamp the recorded data. These time references are stable losing only about 1 second in every 100 million years.
• Synchronization: To ensure recordings are made simultaneously, VLBI requires synchronization at the level of a millionth of a second. This is easily achieved through use of Global Positioning Service (GPS) clocks located at each geographic location.

The EHT project has taken the VLBI technique to its extreme by extending the observing wavelength to 1.3mm (the shortest wavelength used to date) and by greatly increasing the recording rate of radio waves at each site (now capturing 64 Giga-bits/second as compared to 2 Giga-bits/second for most other VLBI arrays). These breakthrough technical developments now allow us to observe supermassive black holes with an angular resolution and sensitivity that can image the silhouette of the event horizon.

Two VLBI arrays that link radio dishes across the globe. The GMVA observes at a wavelength of 3mm, and the EHT observes at a wavelength of 1.3mm. The EHT reaches angular resolution (λ/d_p) of about 35 micro arcseconds, equivalent to standing in New York and being able to read the date on a quarter in Los Angeles. Credit: ESO/O. Furtak

At the center of our own Milky Way galaxy lives a very massive black hole which astronomers call Sagittarius A* (pronounced Sagittarius A-star), or Sgr A*, which has a mass approximately 4.3 million times the mass of our sun and is located about 25,000 light years away from the Earth. Even though 4.3 million might seem like a lot, compared to other supermassive black holes at the centers of other galaxies it’s actually fairly small. Astronomers have found black holes at the centers of other galaxies which have masses up to billions of times the mass of our sun. Astronomers have also found various other black holes which are closer to us, but these closer black holes are much smaller and have masses equal to a few times the mass of our sun. However, despite the fact that our supermassive black hole is neither the most massive black hole nor the closest black hole to us, it is the closest supermassive black hole and therefore is the black hole which looks the biggest from our point of view. Because of this, Sgr A* is the primary source for the Event Horizon Telescope.  

In 1974 astronomers Bruce Balick and Robert Brown discovered a bright radio source in the Sagittarius constellation. Although at the time astronomers did not know that the source they had just discovered was in fact a black hole, it was given the name Sagittarius A* in 1982 because it was a bright and exciting source in the constellation Sagittarius. The most compelling evidence that Sgr A* is a black hole comes from studying the motion of stars moving close to the object. By studying the orbits of these stars over many years astronomers can measure the mass of the object that the stars are orbiting. The best explanation that we have for an object with a mass of 4 million times that of the sun contained in the region enclosed by these nearby stars is a black hole. The video below shows the orbits of these stars over a decade.

These images/animations were created by Prof. Andrea Ghez and her research team at UCLA and are from data sets obtained with the W. M. Keck Telescopes.

It might seem a bit counterintuitive that a black hole would be such a bright emission source since light cannot escape the gravitational field of the black hole. In fact the light that we see from Sgr A* does not come from within the black hole but instead comes from gas which is falling into the black hole. As gas falls into Sgr A* it creates a thick puffy disk known as an accretion disk. Accretion disks are very energetic environments with strong magnetic fields which drive turbulence and heat up the gas as it spirals into the black hole. This hot excited gas emits photons at a variety of wavelengths which are then lensed by the gravitational field of the black hole. The details of accretion mechanisms are still a very active area of research, and we hope that the images the EHT will take of the extreme environment of Sgr A* will help us understand them.

M87 is a giant elliptical galaxy in the constellation Virgo. Like Sgr A*, M87 harbors a supermassive black hole living at its center. This black hole is one of the most massive known, 6 billion times more massive than our Sun and 1,500 times more massive than Sgr A*. M87 is 50 million light years from Earth— nearby on a cosmic scale but 2,000 times further away than Sgr A*. More massive black holes have larger event horizons, but, due to distance, the apparent size of the black hole in M87 as viewed from Earth is expected to be slightly smaller than that of Sgr A*.

The most striking feature of M87 is a narrow, one-sided jet emanating from its center and extending for thousands of light years. Only one side of the jet is seen because of relativistic effects; the jet is moving outward at nearly the speed of light and is pointed close to Earth resulting in an increase in brightness from relativistic beaming. The oppositely pointed counter-jet is instead moving away from Earth at near the speed of light and so its brightness is likewise diminished. The mechanisms that form the jet and keep it tightly collimated for thousands of light years are described in the “Understanding Jet Genesis and Collimation” section above.

Jet shooting out of M87. Credit: NASA and The Hubble Heritage Team (STScI/AURA)