# How can the Event Horizon Telescope image Sgr A* when it's not visible from all sites at one time?

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I went to https://eventhorizontelescope.org/array and read about the ten sites listed as part of the EHT, I have a mashed-up screen shot of them below.

I made a little script also shown below with approximate coordinates, and saw that Sgr A* is at a declination of about -29.5 degrees (South). I spun it around the earth, calculated the dot product between each of the sites' position vectors and all normals pointing to Sgr A* as it rotates around the Earth.

I then plotted the elevation angle above the horizon for all ten sites. I was quite surprised!

1. Sgr A* is never above the horizon for the Greenland telescope!
2. Sgr A* is never simultaneously visible even to all of the remaining nine telescopes

Have I made a mistake? If not, how do these ten sites combine their data to image Sgr A*?

class Site(object): def __init__(self, name, lat, lon, alt): self.name = str(name) self.lat = rads * float(lat) self.lon = rads * float(lon) self.alt = km * float(alt) (clat, slat), (clon, slon) = [[f(x) for f in (np.cos, np.sin)] for x in (self.lat, self.lon)] self.norm = np.array([clon*clat, slon*clat, slat]) data = (('Northern Extended Millimeter Array', (44.634, 5.908, 2550.)), ('IRAM 30 meter telescope', (37.066, -3.393, 2850.)), ('The Greenland Telescope now near Thule Air Base', (76.531, -68.703, 10.)), ('Combined Array for Research in Millimeter-wave Astronomy CARMA', (37.280, -118.142, 2196.)), ('Kitt Peak National Observatory 12 meter Submillimeter Telescope (SMT)', (1.9583, -111.5967, 2096.)), ('Mt. Graham International Observatory 12 meter ALMA prototye', (32.701, -109.892, 3191.)), ('The Large Millimeter Telescope Alfonso Serrano', (18.985, -97.315, 4600.)), ('ALMA', (-22.971, -67.703, 4800.)), ('Caltech Submillimeter Observatory', (19.823, -155.476, 4140.)), ('South Pole Telescope', (-90.0, 0.0, 2800.))) # https://eventhorizontelescope.org/array # /questions/26413/math-behind-a-uv-plot-in-interferometry datadict = dict(data) import numpy as np import matplotlib.pyplot as plt from skyfield.api import Topos, Loader, EarthSatellite from mpl_toolkits.mplot3d import Axes3D halfpi, pi, twopi = [f*np.pi for f in (0.5, 1, 2)] degs, rads = 180/pi, pi/180 km = 0.001 sites = [Site(a, *b) for a, b in datadict.items()] Dec = rads * -29.5 # SgrA_star cDec, sDec = [f(Dec) for f in (np.cos, np.sin)] th = twopi * np.linspace(0, 1, 100001)[:-1] cth, sth = [f(th) for f in (np.cos, np.sin)] zth, oth = np.zeros_like(th), np.ones_like(th) SgrA_star = np.stack([cDec*cth, cDec*sth, sDec*oth], axis=1) for site in sites: site.elev = np.arcsin(np.dot(SgrA_star, site.norm)) if True: for site in sites: plt.plot(degs*site.elev) plt.plot(zth, '-k', linewidth=2) plt.ylim(-90, 90) plt.ylabel('elevation (deg)', fontsize=16) plt.show()

I don't think it is necessary for all the telescopes to view the target simultaneously if you can make the assumption that the source you are observing is only varying on timescales longer than it takes the source to be viewable by all the telescopes. Sure, the maximum baseline you can get will be defined by the most distant pair of simultaneously observing telescopes, but that doesn't stop you adding together images taken at other times.

This is very probably the reason why M87 is in the fact the first image presented by the EHT. The timescale for significant variability around this (big) black hole will be of order a few time $$2GM/c^2$$, which is a few days for the M87 black hole. Imaging Sgr A* is going to be more difficult (or at least more blurry) because the variability timescale is minutes.

It looks like (from the data reduction paper) that the first steps involve treating every baseline in a pair-wise way (as I suggested above) and then combining them across the network, with whatever baselines were observing at the time, to give data at the surprisingly (to me) high time-resolution of 10s.

1. Sgr A* is never above the horizon for the Greenland telescope!

Well, Sgr A* is not the only focus of EHT; the website mentions it also studies other objects like the M87 galaxy in Virgo which, at +12° declination, is visible from Greenland.

1. Sgr A* is never simultaneously visible even to all of the remaining nine telescopes

Very Long Baseline Interferometry just combines the results of the telescopes which can (and have been) pointed at a specific target at a specific time (plus or minus a few nanoseconds, because some telescopes might be further away from the target than others, and light takes slightly longer or shorter to reach them). So it will never use the full potential of all the telescopes in the array simultaneously.

At the location of the correlator the data are played back. The timing of the playback is adjusted according to the atomic clock signals on the (tapes/disk drives/fibre optic signal), and the estimated times of arrival of the radio signal at each of the telescopes. A range of playback timings over a range of nanoseconds are usually tested until the correct timing is found.

The recently announced M87 observations only used 8 of the 10 sites. This paper includes this diagram.Even the South Pole instrument seems to have been used only for calibratiom (the dashed lines).

## Scientists unveil first image of black hole in all its dark glory

A virtual telescope the size of planet Earth has captured the first direct image of a black hole a century after Einstein's equations predicted the existence of black holes. Specifically, the image captured by the Event Horizon Telescope was the mysterious region defined by the hole's event horizon, the point beyond which nothing &mdash not even light &mdash can escape.

"We have seen what we thought was unseeable," said Shep Doeleman, a radio astronomer at the Harvard Smithsonian Center for Astrophysics and director of the Event Horizon Telescope project. "We have seen, and taken a picture of, a black hole. This is a remarkable achievement."

The target was an enormous black hole, 6.5 billion times more massive than the sun, in the core of M-87, a giant elliptical galaxy about 55 million light years away in the constellation Virgo. A familiar target for amateur astronomers, M-87 is one of the brightest radio sources in the sky, featuring a huge jet of material extending away from the core, powered by the voracious black hole. The black hole's six-and-a-half billion solar masses are crammed into a region about the size of a solar system.

This image released Wednesday, April 10, 2019, by Event Horizon Telescope shows a black hole. Scientists revealed the first image ever made of a black hole after assembling data gathered by a network of radio telescopes around the world. Event Horizon Telescope Collaboration/Maunakea Observatories via AP

The image captured by the Event Horizon Telescope shows a black central core &mdash the event horizon &mdash surrounded by a lopsided ring of light emitted by particles racing around the black hole at nearly the speed of light. It closely resembles what astronomers expected based on simulations running the equations of Einstein's general theory of relativity.

"We now have visual evidence for a black hole," Doeleman said. "We now know that a black hole that weighs 6.5 billion times what our sun does exists in the center of M-87. This is the strongest evidence we have to date for the existence of black holes. It is also consistent . with Einstein's predictions."

Daniel Marrone, an astronomer at the University of Arizona's Steward Observatory said: "Today, general relativity has passed another crucial test. . The object at the heart of M-87 is a black hole like those described by general relativity."

## How the Event Horizon Telescope Showed Us a Black Hole

On April 10, 2019, we were presented with the first-ever close-up image of a black hole by the Event Horizon Telescope (EHT). This remarkable technological achievement was made possible by the collective efforts of hundreds of astrophysics, engineers, and computer scientists. They arranged for simultaneous observations of their target with multiple telescopes around the globe and correlated the data between the instruments to effectively achieve the creation of a planet-sized telescope. The data was then processed to make the image we saw in the news.

But did we really “see” a black hole when we were shown “just” a digital image? And how is it possible to create an Earth-sized telescope?

Let me start by explaining why EHT really needed an Earth-sized telescope. An abundance of dust exists between our telescopes and the observed black holes. This dust absorbs electromagnetic radiation of short wavelengths such as visible light (about 5.5 x 10 -7 m), infrared light (about 10 -6 m), and so on. However, the radiation of wavelengths of about 1 millimeter (10 -3 m) and larger is not affected by the dust. The angular resolution of a telescope is proportional to the observed wavelength divided by the diameter of the telescope. A longer wavelength results in lower resolution, while a bigger telescope mirror ensures higher resolution. ETH, therefore, had to observe a wavelength of around 1 mm. (They observed at 1.3 mm.) However, this wavelength also implied that they needed a telescope similar in size to the diameter of our planet to resolve the black hole shadow. It is not practically possible to construct a mirror of such a size, but we can still achieve the required resolution, using the interferometer technique. To explain it, we will use a series of analogies.

First analogy: Imagine a real telescope mirror equivalent to the size of planet Earth and then placing over it a black cloth with several holes. The cloth would limit the telescope’s capabilities and reduce its light-collecting area, but we still would have a mighty planet-sized telescope with high-resolution capabilities.

Second analogy: Imagine a handful of small mirrors. One can place them together tightly and construct a nice medium-sized telescope mirror. But one can also choose to scatter them across a larger area. Each small mirror represents a place where the fabric from the first analogy has a hole. Thus, if one finds a smart way of connecting the small mirrors and analyzes the data collected by each of them together, one may be able to reproduce the capabilities (in particular, the resolution) of the large mirror similar in size to the area across which the mirrors were scattered. Additionally, in moving the small pieces around, one would cover more and more of the surface of the large mirror and thus get closer and closer to its full capabilities.

This is a toy illustration of how an interferometer works. EHT simultaneously collects the data from multiple telescopes spread across our planet and then correlates and analyzes the data from them jointly. The involved telescopes also change their relative positions with respect to the target due to the Earth’s rotation covering larger parts of the Earth-sized mirror.

Over the history of astronomical observations, we have learned to employ and trust technology to help us study the sky. The first observations were done with unaided eyes only. Then optical telescopes magnified the image and increased the light-collecting area from the pupil size to the size of the lens (and later the mirror) so smaller and fainter objects became visible in detail. The films (and other receivers) afforded us much longer exposures than capable by the human eye. The films and receivers also allowed us to look outside the range of visible spectra, which was extremely useful to the study of celestial objects. (As the product of evolution on our particular planet, our eyes are strategically designed to be sensitive to the radiation from the Sun with a complete disregard of whether it is a good frequency range for the study of the rest of the universe.) Interferometers are just the next step in the evolution of visual aids. Therefore, we indeed “saw” a black hole although we were shown “just” a post-processed digital image.

It is true that science-wise the image of M87’s black hole did not teach us anything unexpected. It looked exactly as predicted. But perhaps this is not a bad thing. When the Large Hadron Collider in CERN started operating, it had to rediscover all the previously discovered particles. Only then, could it be trusted to search for unknown particles and to probe new physics. The first EHT image was proof of the value of new technology, and it passed the test. Should the subsequently released image show something unexpected and new, we will be more inclined to dive into its physical implications rather than questioning what went wrong with the observation. (Such a discovery, which matches predictions so well, has also, hopefully, demonstrated to the world in this age of anti-science that experts likewise should be trusted.)

What is next for the EHT? The other long-anticipated, and I would argue, more exciting target, is our own black hole in the center of our Milky Way galaxy known as Sagittarius A* (Sgr A*)—the subject of my own research at the Institute. Sgr A* is the closest supermassive black hole to Earth. It is located 26,000 light years away and has a mass 4,000,000 times that of the Sun. In contrast, M87’s black hole is 2,000 times further away and is 1,600 times more massive, but the sizes of the shadows of the black holes are similar. The mass of Sgr A* was deduced from the orbits of the nearby stars, which were tracked for twenty-five years, and scientists concluded that the object around which they orbit is so massive and so small that it can be nothing but a black hole. (Professor Scott Tremaine wrote more on this subject in his article “The Odd Couple: Quasars and Black Holes” for the Institute Letter in 2015).

A puzzling side of the behavior of Sgr A* is its accretion, namely, the behavior of in-falling gas. Here I would like to point out that the black hole does not suck in any material. The material falls into it by itself. In the same way, Earth does not suck up the International Space Station, which closely orbits it. The station experiences friction with the outer layers of the planet’s atmosphere, which slows it down causing its orbit to sink lower in order to stay in space, it has to be re-boosted, i.e., moved to a higher orbit, regularly. The gas clouds orbiting the black hole also experience the same kind of friction, get heated, slow down, and move closer and closer to the back hole, until they fall in. They, so to say, accrete onto or feed the black hole. The gas clouds also radiate the excessive heat while spiraling down, thus producing the emission we call black hole radiation. (The Hawking radiation from the black holes is hopelessly overwhelmed by the radiation of the accreting gas.)

The amount of the hot gas (about ten million Kelvin), which is bound to Sgr A*, is well constrained by X-ray observations. If this gas fed the black hole in the usual way, we would see a few orders of magnitude more radiation than we actually observe. It was therefore concluded that it spirals into the black hole faster than it can radiate the heat, because the density of the gas is low, and thus the amount that is getting fed to the black hole can be larger than we would normally infer from the amount of observed radiation. The particular details of the process, however, are still uncertain. We still do not know whether there is a radial outflow from Sgr A* whether it has jets what the velocity of the gas flow around it and the direction of the flow are at the various radii whether the flow forms a disk or not how the density and temperature of the gas and the strength of magnetic fields change with the distance from the black hole and how much of the gas, which is too cool to emit X-rays, is present near the black hole. The last area is the subject of my own studies.

There are several unresolved questions concerning the feeding of our supermassive black hole, which EHT observations will be able to help answer. For instance, we will learn about the presence or absence of Sgr A* jets and confirm the direction of the gas flow rotation and its inclination (it was recently claimed to be face-on). Overall, it would open a completely new chapter in studying black hole physics. All in all, it is a true privilege to live in such an exciting and dynamic time for this wonderful field.

No one can predict where the deeper understanding of fundamental laws that rule this world will lead us and what doors they will open, but it is always unexpected and exciting. It is worth remembering that the study of electricity was once considered a completely impractical endeavor, which would never have any useful applications. Now we tax it.

Elena Murchikova, Bezos Member in the School of Natural Sciences, works on the interface between theoretical astrophysics and observational astronomy. Her research interests span studies of the Milky Way’s galactic center black hole with the ALMA telescope, black hole accretion theory, the interiors of neutron stars, and cosmic strings.

## 2. GENERAL DEFINITIONS AND CONSIDERATIONS

### 2.1. The Central Black Hole

Optical/IR observations of the orbits of stars in the vicinity of Sgr A* have led to a measurement of its mass, , and distance from the Earth, D. The uncertainties in the two measurements are significant and highly correlated (Ghez et al. 2008 Gillessen et al. 2009b). Because of the directions of these correlations, however, the uncertainty in the apparent size of the black hole shadow, which is the most relevant quantity for the EHT observations, is significantly smaller. In the following discussion, we set the mass of Sgr A* to and its distance to D = 8.3 kpc (Reid et al. 2014), such that the apparent opening angle of one gravitational radius ( ) at the distance of Sgr A* is equal to as and consistent with the most likely value derived from current observations (Psaltis et al. 2015b).

Because of the large orbital distances of the currently known optical/IR stars around Sgr A*, there have been no dynamical measurements of its spin magnitude, χ, or orientation. Comparisons of accretion flow models with spectroscopic and EHT imaging observations indicate low spins, when semi-analytic models are used (e.g., Broderick et al. 2011), or relatively high spins when GRMHD models are used (e.g., Dexter et al. 2010 Chan et al. 2015). Moreover, the small inferred size of the 1.3 mm image of Sgr A* supports the assumption that the black hole spin is inclined by with respect to the line of sight and is aligned with the angular momentum vector of the stellar disk at

3 arcsec away from the black hole (Psaltis et al. 2015a). For the purposes of the present paper, we set the spin of Sgr A* to , which corresponds to a Kerr quadrupole moment of . We picked these values such that the effects of both the spin and of the quadrupole moment are potentially observable, without being maximal. Clearly, we can perform tests of the no-hair theorem only if the black hole in the center of the Milky Way is spinning.

### 2.2. The Inner Cluster of Stellar-mass Objects

Advances in adaptive optics have revealed a large number of stars in orbit around Sgr A* (see Genzel et al. 2010 Ghez et al. 2012). One of these stars has been followed for at least one fully closed orbit (Ghez et al. 2008 Gillessen et al. 2009a) and the orbital parameters of several others (S0-16, S0-102, and S0-104) will eventually place them within a few thousand gravitational radii from the black hole (e.g., Meyer et al. 2012). Even though monitoring these orbits in the near future will most likely lead to the detection of periapsis precession, additional relativistic effects that will allow for a test of the no hair theorem will either be too small to be detected or masked by other astrophysical complexities.

It is expected that observations with future instruments, such as the adaptive-optics assisted interferometer GRAVITY on the Very Large Telescope (Eisenhauer et al. 2011) and new generation adaptive optics instruments on a 30-m class telescope (Weinberg et al. 2005), will lead to the discovery of stars with closer orbits. Monitoring the precession of their orbits and of their orbital planes will offer the possibility of measuring the spin and the quadrupole moment of the black hole and therefore of testing the no-hair theorem (Will 2008).

The distribution of stellar-mass objects within a few thousand gravitational radii from Sgr A* is very difficult to infer observationally at this point (see the detailed discussion in Merritt 2010). For the purposes of the current study, we will follow Merritt et al. (2010) and set the distribution of the semimajor orbital axes of stellar objects around the black hole such that

We will write our expressions in the general case of , but evaluate them in the corresponding figures for (Merritt et al. 2010) and (Bahcall & Wolf 1976), to quantify the effect of this assumed parameter. Requiring that the total mass of stars inside the characteristic orbital separation a0 is equal to M*, i.e.,

we obtain for the normalization constant

and for the total number of stars inside an orbit with semimajor axis a

The characteristic values for the mass m* of each object and the total mass M* enclosed inside an orbital separation a0 are also poorly constrained from current observations. We will adopt here a conservative set of values (Merritt et al. 2010) for which , pc, and .

We can use this distribution to calculate the mass, angular momentum, and quadrupole moment due to the stellar cluster that is enclosed inside an orbit of a given semimajor axis. The ratio of these quantities to the black hole mass, angular momentum, and quadrupole moment will represent the limiting accuracies to which these black hole properties can be inferred using observations of orbits of stars and pulsars.

The mass of stars inside a circular orbit with semimajor axis a,

and the relative contribution to the mass of the black hole is

where in the last expression we set .

The enclosed angular momentum due to the stellar cluster depends on the relative orientation of the orbits and the distribution of their eccentricities. We can obtain an upper limit to the enclosed angular momentum by assuming that all orbits are circular and aligned. In this case, the enclosed angular momentum is

The dimensional spin angular momentum of the black hole is (cf. Equation (1)) and hence the magnitude of the relative contribution to the angular momentum due to the stellar cluster is

where in the last expression we set .

The enclosed quadrupole moment due to the stellar cluster also depends on the orientation of the orbits. If we add an axisymmetric angular dependence to the distribution of orbits, i.e., denote this distribution by , then the quadrupole mass moment of the stellar cluster becomes

The dimensional quadrupole angular momentum of the black hole is (cf. Equation (2)) and hence the magnitude of the relative contribution to the quadrupole moment due to the stellar cluster is

where in the last expression we set .

The fractional contributions to the mass, angular momentum, and quadrupole moment enclosed inside an orbit of semimajor axis a are shown in Figure 1. Our goal is to use orbits of stars and pulsars to measure the quadrupole moment of the black hole and test the no-hair theorem. Just imposing the requirement that the stellar cluster does not dominate the quadrupole moment of the gravitational field forces us to use circular orbits with orbital separations (or equivalently elliptical orbits with periapsis distances) that are inside a few times (see also Merritt et al. 2010). For pulsars in highly eccentric orbits ( ), as we will demonstrate in Section 4, we have, besides the secular precession of the orbit, an additional probe of the relativistic effects via the near-periapsis periodic contributions, which are less affected by external perturbations.

Figure 1. Fractional contribution to the black hole mass, angular momentum, and quadrupole mass moment inside an orbit due to the enclosed distribution of objects. These fractional contributions represent the limiting accuracies to which the corresponding black hole properties can be inferred using observations of orbits of stars and pulsars. The solid lines correspond to a stellar distribution with while the dashed lines correspond to The various other assumed parameters of the stellar cluster are given in Equations (8), (10), and (13).

### 2.3. Pulsars in the Galactic Center

For a number of observational and theoretical considerations, we expect a large number of neutron stars in the central part of the Galaxy. For a comprehensive review of the observational evidence and related theoretical considerations, we refer to Wharton et al. (2012) and references therein. Based on evidence for, e.g., the past star formation rate, the expected initial stellar mass function in the Galactic Center environment, and the observations of massive stars and stellar remnants, overall up to 100 normal pulsars and 1000 millisecond pulsars should be expected in the inner parsec. Earlier, Faucher-Giguère & Loeb (2011) pointed out that the high stellar density in the region also allows the effective creation of exotic binaries, like millisecond pulsar-stellar black hole binaries, which would be exciting laboratories in their own right (Wex & Kopeikin 1999 Liu et al. 2014).

Millisecond pulsars are old, recycled pulsars, which show typical periods between 1.4 and 30 ms, while normal pulsars have average periods of 0.5–1 s. Millisecond pulsars also have spin-down rates and estimated magnetic field strengths that are typically three orders of magnitude smaller than those of normal (unrecycled) pulsars. These properties make Millisecond pulsars superior—and hence preferred—clocks in pulsar timing experiments. For a normal pulsar, a typical timing precision is around 100 μs, while for the best Millisecond pulsars one can achieve a timing precision as good as 100 ns or better. In both cases, the final timing precision depends on the pulsar itself (e.g., the sharpness of its pulse shape, the intrinsic rotational stability) and the strength of the pulsar, as the error on an individual TOA measurement scales with the signal-to-noise ratio (S/N) of the observation (see Lorimer & Kramer 2004 for further details on pulsar properties and timing methods).

Despite concentrated efforts and dedicated searches in the Galactic Center region, the yield has been disappointingly low given the estimates. Until 2013, only five pulsars had been found within of Sgr A*, with the closest of these away, i.e., at a projected distance of about 25 pc (Johnston et al. 2006 Deneva et al. 2009 Bates et al. 2011). All of these were slow pulsars with dispersion measures up to 1500 pc cm −3 . Given their distances to Sgr A*, none of these are suitable for the experiments described below.

The resulting perceived paucity of Galactic Center pulsars had been explained as a consequence of hyper-strong scattering of the radio waves at the turbulent inhomogeneous interstellar plasma in the region. The scattering leads to temporal broadening of the pulses with expected timescales of at least 2000 (ν/1 GHz) −4 s (Cordes & Lazio 2002), rendering their detection impossible at typical search frequencies, around 1–2 GHz. For this reason, a number of high-frequency searches were conducted in the past (Kramer et al. 2000 Klein et al. 2004 Johnston et al. 2006 Deneva et al 2009 Macquart et al. 2010 Bates et al. 2011 Eatough et al. 2013 Siemion et al. 2013) at frequencies as high as 26 GHz. However, even in these searches, no pulsar in the central parsec was found. The currently best limit ( Jy for a ) is provided by observations with the 100-m Effelsberg telescope at 19 GHz (R. P. Eatough et al. 2015, in preparation).

The recent discovery of radio emission from the magnetar SGR J1745–29 by Eatough et al. (2013 see also Shannon & Johnston 2013), which had been first identified at X-rays (Kennea et al. 2013 Mori et al. 2013), provides an unexpected probe of the Galactic Center medium and the local pulsar population. The source that, with improved positional precision, is now named PSR J1745–2900, is located within 24 (or 0.1 pc projected) of Sgr A* (Bower et al. 2015) and is strong enough that even single pulses can be detected from a frequency of a few GHz (Spitler et al. 2014) up to an unprecedented 154 GHz (Torne et al. 2015). Below 1.1 GHz, the temporal broadening prevents a detection of the source (Spitler et al. 2014), while pulsed radio emission is detected up to 225 GHz, which is the highest frequency at which radio emission from a neutron star has been detected so far (Torne et al. 2015). The dispersion measure and the rotation measure of PSR J1745–2900 are the largest in the Galaxy (only the rotation measure of Sgr A* itself is larger Eatough et al. 2013 Shannon & Johnston 2013), while the angular broadening of the source is consistent with that of Sgr A* (Bower et al. 2014, 2015), providing evidence for the proximity of the magnetar to the Galactic Center. While its rotational stability is unfortunately not sufficiently good to conduct precision timing experiments, it allows us to revisit the question of the hidden pulsar population.

Radio-emitting magnetars are a very rare type of neutron star and previously only three of them were known to exist in the Galaxy, i.e., less than 0.2% of all radio-loud neutron stars (Olausen & Kaspi 2014). The discovery of such a rare object adjacent to Sgr A* thereby supports the notion that many more ordinary radio pulsars should be present (Eatough et al. 2013 Chennamangalam & Lorimer 2014). A surprising aspect of the magnetar discovery is the relatively small scatter broadening that is observed (Spitler et al. 2014). With a pulse period of 3.75 s, its radio emission should not be detectable at frequencies as low as 1.1 GHz, if hyper-strong scattering were indeed present.

Imaging observations (Bower et al. 2015) resulted in the measurement of a proper motion that does not allow us yet to conclude as to whether the pulsar is bound to Sgr A*. It is possible that PSR J1745–2900 and the other five nearby pulsars originated from a stellar disk (see also Johnston et al. 2006) and that a central population of pulsars is still hidden. Indeed, Chennamangalam & Lorimer (2014) argue that, even if the lower-than-expected scattering in the direction of PSR J1745–2900 is representative of the entire inner parsec, the potentially observable population of pulsars in the inner parsec still has a conservative upper limit of members. They conclude that it is premature to assume that the number of pulsars in this region is small.

In contrast, Dexter & O'Leary (2014) come to a different conclusion. They also revisited the question about the central pulsar population given the new constraints provided by the magnetar and the non-detection of previous high-frequency surveys. Considering various effects like depletion of the pulsar population due to kick velocities exceeding the central escape velocity, pulsar spectra, and the apparent reduced scattering indicated by the magnetar observations (Spitler et al. 2014), they argue in favor of a "missing pulsar problem." They also concluded that the magnetar discovery in the center may imply, in turn, an efficient birth process for magnetars in the central region. Similarly, others suggested that normal pulsars are not formed since they may collapse into black holes on comparably short timescales by accreting of dark matter (Bramante & Linden 2014).

At the core of deciding between these possibilities is our ability to properly model and account for all selection effects in the previous surveys. There are in fact indications that this is not the case. First, continued monitoring of the scattering timescales for the magnetar indicates that the scattering time is highly variable. While it remains well below the prediction of hyper-strong scattering, it varies by a factor of 2–4 on timescales of months at frequencies between 1.4 and 8 GHz (L. G. Spitler et al. 2015, in preparation). This suggests that local "interstellar weather" certainly plays a role and that nearby scattering screens also affect the observed emission, making the resulting ability to observe sources overall line of sight dependent, especially at lower frequencies. This is not unexpected given the properties of the turbulent interstellar medium in the Galactic Center. Rather than dealing with a uniform single screen, it is likely that we see the effects of multiple finite screens. In this case, second, one expects a much shallower frequency dependence of the scattering time than the canonical values (Cordes & Lazio 2001). This is indeed seen for high-DM pulsars (Löhmer et al. 2001, 2004), where the scattering index is typically around for large dispersion measures. L. G. Spitler et al. (2015, in preparation) find similar values for the magnetar. If this is indeed representative for a possible central pulsar or millisecond pulsar population, then the remaining scattering at 5, 14, or even 19 GHz would be underestimated in the analysis by Macquart et al. (2010) or Dexter & O'Leary (2014) by factors of 2.2, 3.7, or 4.3 respectively, when extrapolating from 1 GHz. Löhmer et al. (2001) measured even flatter frequency dependencies, which would make the discrepancy between real and estimated scattering times even larger. Unless more scatter broadening times in the Galactic Center are measured, this issue is difficult to settle. However, there is yet another, third effect that has usually been neglected in sensitivity calculations of pulsar surveys. As shown very recently by Lazarus et al. (2015) for the P-ALFA survey, red noise present in pulsar search data due to radio interference (RFI), receiver gain fluctuations, and opacity variations of the atmosphere cause a significant decrease in sensitivity for pulsars with periods above 100 ms or so, when compared to the standard radiometer-based equation (see their Figure 11). This would affect in particular a search for young pulsars, but also, of course, magnetars, which are nevertheless still easier to detect at high frequencies due to their much flatter flux density spectrum (Torne et al. 2015). This selection effect in particular would favor the detection of magnetars over that of normal, young pulsars and may explain in some respects the peculiarities of the current observational situation pointed out by Dexter & O'Leary. The work by Lazarus et al. demonstrates that the various selection effects are highly dependent on the individual surveys and that much more work is needed to understand the impact on the resulting search sensitivities.

Finally, none of the previous high-frequencies surveys has, to our knowledge, applied a fully coherent acceleration search. Such an acceleration search may be needed to account both for the movement of the pulsar around the central black hole, as well as for the presence of a binary companion. Indeed, due to the high stellar density, even exotic systems (e.g., millisecond pulsar-stellar mass BH binary) may be expected (Faucher-Giguère & Loeb 2011). An acceleration search is usually very computationally expensive, especially for long integration times as employed in the high frequency searches (e.g., by Macquart et al. 2010 or R. P. Eatough et al. 2015, in preparation), since the parameter range to be searched scales as . The lack of such an acceleration search contributes as a selection effect to the present non-detection of fast-spinning pulsars.

In order to model the selection effects (red noise, acceleration, scattering etc.) a more detailed study, taking the orientation of the possible orbits and the change in acceleration into account, is needed. This is beyond the scope of this paper and will be presented elsewhere. It is clear, however, that selection effects are not adequately modeled so far and that more work is required.

We conclude that three scenarios are still possible: (a) the scattering seen for the Galactic Center magnetar is representative of the inner parsec. In this case, the pulsar population may be dominated by Millisecond pulsars, for which this moderate scattering would still have prevented their detection at previous search frequencies. Higher frequency searches may therefore even allow the discovery and hence the exploitation of Millisecond pulsars orbiting Sgr A* (see also Macquart & Kanekar 2015). We note in passing that the discovery of a Millisecond pulsar population may settle an ongoing debate about a possible excess of GeV gamma ray photons from the Galactic Center. It is being discussed whether such an excess could arise from the presence of dark matter or a central population of unresolved young or Millisecond pulsars (see e.g., O'Leary et al. 2015 and references therein). Any pulsar discovery in the Galactic Center would make a dark matter discovery less likely. (b) There is a reduced number of pulsars in the Galactic Center region that is consistent with selection effects. For example, the lack of dispersion makes the discovery of unknown pulsars actually more difficult at high frequencies, as the signals are more difficult to distinguish from radio interference (see R. P. Eatough et al. 2015, in preparation), or (c) PSR J1745–2900 is indeed in front of a much more severe scattering screen but the scattering properties for particular lines of sight are changing with time due to "local weather" effects, signs of which have been already detected (L. G. Spitler et al. 2015, in preparation). In this case, search observations at even higher frequencies are required and still promising.

Given that we cannot distinguish between these scenarios based on the available data, high frequency searches will continue. The use of more sensitive instruments than available in the past, e.g., ALMA or the Square Kilometre Array (SKA), may therefore lead to the discovery of normal pulsars and even Millisecond pulsars. In considering how they can be used to measure the properties of Sgr A*, we will therefore assume a variety of obtainable timing precisions. For details, we refer the reader to Liu et al. (2012), who demonstrated possible precision levels as a function of observing frequency for the SKA and 100-m class telescopes. In their arguments, Liu et al. (2012) only considered normal pulsars and also assumed a hyper-strong scattering. If the latter is not present as we have discussed above, Millisecond pulsars may be detectable (although this may require proper acceleration searching). Hence, for the discussion of the measurable effects, we will also allow for this possibility that Millisecond pulsars will be detected.

There are a number of Millisecond pulsars in globular clusters at distances that are signifantly larger than that of the Galactic Center. It is not uncommon to achieve a timing precision of about 10 μs for these distant sources. The exact precision mainly depends on the strength of the pulsar signal and the sensitivity of the telescope, as well as the sharpness of some of the detetable profile features. If we need to go to high radio frequencies in order to beat interstellar scattering to see pulsars in the center of the Milky Way, the flux density decreases and timing precision decreases accordingly. This can be compensated by larger bandwidth or bigger telescopes. As shown in Eatough et al. (2015), a timing precision of 1 μs should be routinely possible with the SKA, even at distances of the Galactic Center at higher frequencies. Such a precision is certainly more challenging with existing instruments. Overall, in order to cover all three plausible scenarios discussed above, we will assume, in the following, that a Galactic Center pulsar can be timed with a precision of 1, 10, and 100 μs. As, in principle, only one pulsar is needed to extract the black hole parameters, we consider this to be a useful range to demonstrate the effects that we can expect to measure.

### 2.4. Relativistic Orbital Effects

In describing the orbit of a stellar-mass object around Sgr A*, we will use the coordinate system and notation shown in Figure 2. In particular, we will denote by m* the mass of the orbiting object and by a and e the semimajor axis and eccentricity of its orbit. We will use the vector to define the black hole spin and the vector to denote the line of sight unit vector pointing from the Earth to the black hole. We will also denote the longitude of the periapsis of the orbit with respect to the equatorial plane of the black hole by ω, the location of the ascending node by , and the inclination of the orbit with respect to the black hole spin axis by Θ.

Figure 2. Coordinate system and notation used in defining an orbit of a stellar-mass object around Sgr A*. The vector denotes the spin of Sgr A* and is the line of sight unit vector pointing from the Earth to the black hole. The longitude of the periapsis of the orbit is ω, the location of the ascending node is , and the inclination of the orbit with respect to the black hole spin axis is Θ. The angle i, between and the orbital angular momentum is the inclination of the orbit with respect to the observer.

With these definitions, the Newtonian period of the orbit is

Eccentric orbits of stars and pulsars precess on the orbital plane (relativistic periapsis precession). The leading term comes from the mass-monopole and corresponds to the relativistic precession of the Mercury orbit (Einstein 1915). The advance of periapsis per orbit is , where

This corresponds to a characteristic timescale for this precession of (see Merritt et al. 2010 for the definition, who denote this by )

In this expression, we have neglected the small contributions of the spin and of the quadrupole of the black hole.

Orbits with angular momenta that are not parallel to the spin of the black hole show a precession of the orbital angular momentum around the direction due to frame dragging (Lense–Thirring precession of the nodes). The location of the ascending node of the orbit, , advances per orbit by

is the Lense–Thirring frequency. The characteristic timescale for this process is (Merritt et al. 2010)

Finally, tilted orbits also precess because of the quadrupole moment of the spacetime with a characteristic timescale (Merritt et al. 2010)

Figure 3 shows the characteristic timescales of these relativistic orbital effects as a function of the semimajor axes and orbital periods of the orbits. A number of additional relativistic effects related to time dilation and photon propagation (Shapiro delay) can also be detected during timing observations of pulsars. We will discuss these effects and their dependence on the pulsar orbital parameters in Section 4.

Figure 3. Characteristic timescales for various relativistic and astrophysical effects that alter the orbits of stars around Sgr A*. The three blue lines correspond to the periapsis precession ( ), and orbital plane precession due to frame dragging ( ) and due to the quadrupole of the black hole ( ), for orbits with eccentricities of e = 0.5 (solid) and e = 0.8 (dashed), respectively the spin of Sgr A* is set to The green line corresponds to the orbital decoherence timescale ( ) due to the interactions with other objects in the stellar cluster. The black curve ( ) corresponds to the orbital evolution timescale due to the launching of a stellar wind. The red curves correspond to the orbital evolution due to the tidal dissipation of orbital angular momentum for two eccentricities. Stars in orbits with semimajor axes comparable to 1000 gravitational radii are optimal targets for observing post-Schwarzschild relativistic effects.

### 2.5. Optimal Orbital Parameters for Stars and Pulsars

Performing tests of the no-hair theorem with orbits is hampered by a number of astrophysical complexities caused by non-relativistic phenomena that affect, in principle, the orbits. These included the self-interaction between the stars in the stellar cluster (Merritt et al. 2010 Sadeghian & Will 2011), the hydrodynamic drag between the stars and the accretion flow (Psaltis 2012), as well as stellar winds and tidal deformations (Psaltis et al. 2013). In order to identify the orbital parameters of stars that are optimal for performing the test of the no-hair theorem, we will first summarize and combine the results of these studies.

Interactions with Other Stars. Merritt et al. (2010) and Sadeghian & Will (2011) explored the decoherence of the orbit of a star (or pulsar) due to Newtonian gravitational interactions within the inner stellar cluster. They obtained an approximate expression for the decoherence timescale given by

where is the average ratio of the mass of a star (or compact object) in the cluster to that of Sgr A*, and N(a) is the number of stars inside the orbit of the object under consideration.

Using Equations (6), (14), and (21), we obtain for the decoherence timescale of orbits due to the self interaction between objects in the stellar cluster

Figure 3 compares the Newtonian decoherence timescale with those of the three relativistic effects discussed in Section 2. For the parameters of Sgr A* and of the stellar cluster around it, stars with orbital periods less than year are required in order for the Newtonian interactions not to mask the orbital plane precession due to frame dragging (see a more detailed discussion and simulations in Merritt et al. 2010).

Hydrodynamic Interactions with the Accretion Flow. In Psaltis (2012) we investigated the changes in the orbits of stars and pulsars caused by the hydrodynamic and gravitational interactions between them and the accretion flow around Sgr A*. For all cases of interest, we found that the hydrodynamic drag is the dominant effect. However, as we will show below, even the hydrodynamic drag is negligible for the orbital separations considered here.

When a star of mass m* and radius R* plows through the accretion flow of density ρ with a relative velocity , it feels an effective acceleration equal to

We can use this acceleration to define a characteristic timescale for the change of the orbital parameters as

Setting the relative velocity equal to the orbital velocity of a circular orbit, and the density of the accretion flow to

which has been inferred observationally (see discussion in Psaltis 2012), we obtain

Here, is the mass of the proton and we assumed for simplicity that the orbit is circular. This timescale is significantly larger than all other timescales shown in Figure 3.

Stellar Winds. In Psaltis (2012) we explored the change in the orbital parameters of stars due to the launching of a wind that carries a fraction of the orbital energy and angular momentum. The semimajor axis and the eccentricity of the orbit change at a timescale comparable to , where is the rate of wind mass loss, i.e.,

where we have used the subscript " " to denote the exponent in the wind mass loss rate. As shown in Figure 3, the evolution of the stellar orbit due to the launching of a stellar wind is always negligible compared to the effects of the Newtonian interactions with the other stars in the cluster.

Tidal Evolution. Finally, in Psaltis (2013) we also explored the evolution of a stellar orbit due to the tidal dissipation of orbital energy during the periapsis passages. Even though tidal dissipation does not cause a significant precession in the orbit (see Sadeghian & Will 2011), it leads to an evolution of the semimajor axis that may be misinterpreted (due to the expected low signal-to-noise in the observations) as a change in the projected orbital separation caused by orbital precession.

The characteristic timescale for orbital evolution due to tidal dissipation is

where the quantity is defined and calculated in Psaltis et al. (2013). Also, if the star at periastron reaches inside the tidal radius

it gets disrupted. Both these effects, for two different orbital eccentricities, are shown in Figure 3.

Optimal parameters. Comparing the various constraints shown in Figure 3 to the characteristic timescales of the three relativistic effects allows us to identify the optimal orbital parameters of stars and pulsars for measuring the black hole spin and for testing the no-hair theorem.

Using the orbital precession of stellar orbits to measure the spin of Sgr A* simply requires sub-year orbital periods for the effects of the stellar perturbations to become negligible (as previously discussed in Merritt et al. 2010). On the other hand, measuring the black hole quadrupole requires stars in much tighter orbits ( yr), for the stellar perturbations to be negligible, but with moderate eccentricities ( ), for tidal effects to not interfere with the measurements of the relativistic precessions (see also Will 2008).

For the case of pulsar timing, tidal effects do not alter the orbits and therefore only stellar perturbations can limit our ability to observe relativistic precessions. If we were to use pulsar timing to measure the black hole quadrupole by observing the pulsar orbital plane precess, we would still be limited to using only rather tight orbits ( yr). However, in defining the characteristic timescale for quadrupole effects on the pulsar orbits (Equation (20)), we have only considered the secular precession of the orbit. The most promising way to extract the quadrupole moment from timing observations is through the periodic effects in the orbital motion of the pulsar caused by the quadrupolar structure of the gravitational field of Sgr A* (Wex & Kopeikin 1999 Liu et al. 2012). This is not only the case for the quadrupole but also for the relativistic precession of the periapsis due to the mass monopole (Damour & Deruelle 1985) and the precession of the orbit due to the frame dragging (Wex 1995). (See also the discussion in Angélil & Saha 2014). As argued by Liu et al. (2012), such unique periodic features in the timing of a pulsar around Sgr A* provide a powerful handle to correct for external perturbations. As we will demonstrate with mock data simulations in Section 4, timing a pulsar only during a small number of successive periapses passages is sufficient to measure both the spin and the quadrupole moment of Sgr A*.

## New analysis of black hole reveals a wobbling shadow

In 2019, the Event Horizon Telescope Collaboration delivered the first image of a black hole, revealing M87*—the supermassive object in the center of the M87 galaxy. The team has now used the lessons learned last year to analyze the archival data sets from 2009-2013, some of them not published before.

The analysis reveals the behavior of the black hole image across multiple years, indicating persistence of the crescent-like shadow feature, but also variation of its orientation—the crescent appears to be wobbling. The full results appeared today in The Astrophysical Journal.

The Event Horizon Telescope is not one singular telescope, but a global partnership of telescopes—including the UChicago-led South Pole Telescope—which performs synchronized observations using the technique of Very Long Baseline Interferometry. Together they form a virtual Earth-sized radio dish, providing a uniquely high image resolution.

"The Event Horizon Telescope is giving us a new tool to study black holes and gravity in ways that were never before possible," said Bradford Benson, an associate professor of astronomy and astrophysics at UChicago. "As members of the South Pole Telescope (SPT) collaboration and the EHT network, we look forward to contributing to future studies—in particular on Sgr A*, the black hole at the center of the Milky Way galaxy, which we have a unique view of given SPT's location at the geographical South Pole."

The first image of a black hole, revealed in 2019, has helped researchers analyze archival data sets. Those findings could help scientists formulate new tests of the theory of general relativity. Credit: EHT Collaboration

"With the incredible angular resolution of the Event Horizon Telescope, we could observe a billiard game being played on the Moon and not lose track of the score!" said Maciek Wielgus, an astronomer at Center for Astrophysics | Harvard & Smithsonian, Black Hole Initiative Fellow, and lead author of the new paper.

"Last year we saw an image of the shadow of a black hole, consisting of a bright crescent formed by hot plasma swirling around M87*, and a dark central part, where we expect the event horizon of the black hole to be," said Wielgus. "But those results were based only on observations performed throughout a one-week window in April 2017, which is far too short to see a lot of changes."

But from 2009 to 2013, researchers had taken data of M87* with early prototype arrays before the full complement of telescopes joined. They could tap that data to find out if the crescent size and orientation had changed.

The 2009-2013 observations consist of far less data than the ones performed in 2017, making it impossible to create an image. Instead, the EHT team used statistical modeling to look at changes in the appearance of M87* over time.

Snapshots of the M87* black hole obtained through imaging / geometric modeling, and the EHT array of telescopes in 2009-2017. The diameter of all rings is similar, but the location of the bright side varies. Credit: M. Wielgus, D. Pesce and the EHT Collaboration

Expanding the analysis to the 2009-2017 observations, scientists have shown that M87* adheres to theoretical expectations. The black hole's shadow diameter has remained consistent with the prediction of Einstein's theory of general relativity for a black hole of 6.5 billion solar masses.

But while the crescent diameter remained consistent, the EHT team found that the data were hiding a surprise: The ring is wobbling, and that means big news for scientists. For the first time they can get a glimpse of the dynamical structure of the accretion flow so close to the black hole's event horizon, in extreme gravity conditions. Studying this region holds the key to understanding phenomena such as relativistic jet launching, and will allow scientists to formulate new tests of the theory of general relativity.

The gas falling onto a black hole heats up to billions of degrees, ionizes and becomes turbulent in the presence of magnetic fields. "Because the flow of matter is turbulent, the crescent appears to wobble with time," said Wielgus. "Actually, we see quite a lot of variation there, and not all theoretical models of accretion allow for so much wobbling. What it means is that we can start ruling out some of the models based on the observed source dynamics."

An animation representing one year of M87* image evolution according to numerical simulations. Measured position angle of the bright side of the crescent is shown, along with a 42 microarcsecond ring. For a part of the animation, image blurred to the EHT resolution is shown. Credit: G. Wong, B. Prather, C. Gammie, M. Wielgus & the EHT Collaboration

"These early-EHT experiments provide us with a treasure trove of long-term observations that the current EHT, even with its remarkable imaging capability, cannot match," said Shep Doeleman, the founding director of EHT. "When we first measured the size of M87 in 2009, we couldn't have foreseen that it would give us the first glimpse of black hole dynamics. If you want to see a black hole evolve over a decade, there is no substitute for having a decade of data."

EHT project scientist Geoffrey Bower added: "Monitoring M87* with an expanded EHT array will provide new images and much richer data sets to study the turbulent dynamics. We are already working on analyzing the data from 2018 observations, obtained with an additional telescope located in Greenland. In 2021 we are planning observations with two more sites, providing extraordinary imaging quality. This is a really exciting time to study black holes!"

## How can the Event Horizon Telescope image Sgr A* when it's not visible from all sites at one time? - Astronomy

The center of the Milky Way galaxy, with the supermassive black hole Sagittarius A* (Sgr A*) located in the middle, is revealed in these images. As described in our press release, astronomers have used NASA's Chandra X-ray Observatory to take a major step in understanding why gas around Sgr A* is extraordinarily faint in X-rays.

The large image contains X-rays from Chandra in blue and infrared emission from the Hubble Space Telescope in red and yellow. The inset shows a close-up view of Sgr A* only in X-rays, covering a region half a light year wide. The diffuse X-ray emission is from hot gas captured by the black hole and being pulled inwards. This hot gas originates from winds produced by a disk-shaped distribution of young massive stars observed in infrared observations (mouse over the image for the distribution of these massive stars).

These new findings are the result of one of the biggest observing campaigns ever performed by Chandra. During 2012, Chandra collected about five weeks worth of observations to capture unprecedented X-ray images and energy signatures of multi-million degree gas swirling around Sgr A*, a black hole with about 4 million times the mass of the Sun. At just 26,000 light years from Earth, Sgr A* is one of very few black holes in the Universe where we can actually witness the flow of matter nearby.

The authors infer that less than 1% of the material initially within the black hole's gravitational influence reaches the event horizon, or point of no return, because much of it is ejected. Consequently, the X-ray emission from material near Sgr A* is remarkably faint, like that of most of the giant black holes in galaxies in the nearby Universe.

The captured material needs to lose heat and angular momentum before being able to plunge into the black hole. The ejection of matter allows this loss to occur.

This work should impact efforts using radio telescopes to observe and understand the "shadow" cast by the event horizon of Sgr A* against the background of surrounding, glowing matter. It will also be useful for understanding the impact that orbiting stars and gas clouds might make with the matter flowing towards and away from the black hole.

## Title: HIGH-RESOLUTION LINEAR POLARIMETRIC IMAGING FOR THE EVENT HORIZON TELESCOPE

Images of the linear polarizations of synchrotron radiation around active galactic nuclei (AGNs) highlight their projected magnetic field lines and provide key data for understanding the physics of accretion and outflow from supermassive black holes. The highest-resolution polarimetric images of AGNs are produced with Very Long Baseline Interferometry (VLBI). Because VLBI incompletely samples the Fourier transform of the source image, any image reconstruction that fills in unmeasured spatial frequencies will not be unique and reconstruction algorithms are required. In this paper, we explore some extensions of the Maximum Entropy Method (MEM) to linear polarimetric VLBI imaging. In contrast to previous work, our polarimetric MEM algorithm combines a Stokes I imager that only uses bispectrum measurements that are immune to atmospheric phase corruption, with a joint Stokes Q and U imager that operates on robust polarimetric ratios. We demonstrate the effectiveness of our technique on 7 and 3 mm wavelength quasar observations from the VLBA and simulated 1.3 mm Event Horizon Telescope observations of Sgr A* and M87. Consistent with past studies, we find that polarimetric MEM can produce superior resolution compared to the standard CLEAN algorithm, when imaging smooth and compact source distributions. As an imaging framework, MEM is highlymore » adaptable, allowing a range of constraints on polarization structure. Polarimetric MEM is thus an attractive choice for image reconstruction with the EHT. « less

## Photographing a Black Hole: Historic Campaign Now Underway

The campaign to capture the first-ever image of a black hole has begun.

From today (April 5) through April 14, astronomers will use a system of radio telescopes around the world to peer at the gigantic black hole at the center of the Milky Way, a behemoth called Sagittarius A* (Sgr A*) that's 4 million times more massive than the sun.

The researchers hope to photograph Sgr A*'s event horizon — the "point of no return" beyond which nothing, not even light, can escape. (The interior of a black hole can never be imaged, because light cannot make it out.) [The Strangest Black Holes in the Universe]

"These are the observations that will help us to sort through all the wild theories about black holes — and there are many wild theories," Gopal Narayanan, an astronomy research professor at the University of Massachusetts Amherst, said in a statement. "With data from this project, we will understand things about black holes that we have never understood before."

The project, known as the Event Horizon Telescope (EHT), links up observatories in Hawaii, Arizona, California, Mexico, Chile, Spain and Antarctica to create the equivalent of a radio instrument the size of the entire Earth. Such a powerful tool is necessary to view the event horizon of Sgr A*, which lies 26,000 light-years from our planet, EHT team members said.

"That's like trying to image a grapefruit on the surface of the moon," Narayanan said.

During the current campaign, EHT is also eyeing the supermassive black hole at the core of the galaxy M87, which lies 53.5 million light-years from Earth. This monster black hole's mass is about 6 billion times that of the sun, so its event horizon is larger than that of Sgr A*, Narayanan said.

These observations should help astronomers determine the mass, spin and other characteristics of supermassive black holes with better precision, team members said. The researchers also aim to learn more about how material accretes into disks around black holes, and the mechanics of the plasma jets that blast from these light-gobbling giants.

EHT could also reveal more about the "information paradox" — a long-standing puzzle about whether information about the material gobbled up by black holes can be destroyed — and other deep cosmological mysteries, team members said.

"At the very heart of Einstein's general theory of relativity, there is a notion that quantum mechanics and general relativity can be melded, that there is a grand, unified theory of fundamental concepts," Narayanan said. "The place to study that is at the event horizon of a black hole."

Though the current observing campaign will be over soon, it will take a while for astronomers to piece together the images. For starters, so much information will be collected by the participating telescopes around the world that it will be physically flown, rather than transmitted, to the central processing facility at the Massachusetts Institute of Technology's Haystack Observatory.

Then, the data will have to be calibrated to account for different weather, atmospheric and other conditions at the various sites. The first results from the campaign will likely be published next year, EHT team members said.

## Title: A GENERAL RELATIVISTIC NULL HYPOTHESIS TEST WITH EVENT HORIZON TELESCOPE OBSERVATIONS OF THE BLACK HOLE SHADOW IN Sgr A*

The half opening angle of a Kerr black hole shadow is always equal to (5 ± 0.2)GM/Dc, where M is the mass of the black hole and D is its distance from the Earth. Therefore, measuring the size of a shadow and verifying whether it is within this 4% range constitutes a null hypothesis test of general relativity. We show that the black hole in the center of the Milky Way, Sgr A*, is the optimal target for performing this test with upcoming observations using the Event Horizon Telescope (EHT). We use the results of optical/IR monitoring of stellar orbits to show that the mass-to-distance ratio for Sgr A* is already known to an accuracy of ∼4%. We investigate our prior knowledge of the properties of the scattering screen between Sgr A* and the Earth, the effects of which will need to be corrected for in order for the black hole shadow to appear sharp against the background emission. Finally, we explore an edge detection scheme for interferometric data and a pattern matching algorithm based on the Hough/Radon transform and demonstrate that the shadow of the black hole at 1.3 mm can be localized, in principle, to within ∼9%. All these results suggest thatmore » our prior knowledge of the properties of the black hole, of scattering broadening, and of the accretion flow can only limit this general relativistic null hypothesis test with EHT observations of Sgr A* to ≲10%. « less

## Title: THE EVENT HORIZON OF SAGITTARIUS A*

Black hole event horizons, causally separating the external universe from compact regions of spacetime, are one of the most exotic predictions of general relativity. Until recently, their compact size has prevented efforts to study them directly. Here we show that recent millimeter and infrared observations of Sagittarius A* (Sgr A*), the supermassive black hole at the center of the Milky Way, all but require the existence of a horizon. Specifically, we show that these observations limit the luminosity of any putative visible compact emitting region to below 0.4% of Sgr A*'s accretion luminosity. Equivalently, this requires the efficiency of converting the gravitational binding energy liberated during accretion into radiation and kinetic outflows to be greater than 99.6%, considerably larger than those implicated in Sgr A*, and therefore inconsistent with the existence of such a visible region. Finally, since we are able to frame this argument entirely in terms of observable quantities, our results apply to all geometric theories of gravity that admit stationary solutions, including the commonly discussed f(R) class of theories.