Is Einstein Still Right?

by Clifford M. Will

  Figure 6.2 Accretion of gas from a companion star onto a black hole. The black hole is represented by the black dot, surrounded by an accretion disk of hot gas that can emit light in the X-ray band. Inside the inner edge of the disk (white region), gas can no longer be in a steady circular orbit but instead plunges directly into the black hole.

  This model accounts for the main features of the X-ray source Cygnus X-1, and for many such X-ray sources discovered subsequently. In some cases, in addition to the gas torn from the stellar surface, the massive stellar companion may emit a strong stellar wind, much like the solar wind, but on a much more massive scale. Some of that gas can also find its way to the accretion disk around the black hole. This is thought to be true of HDE 226868, the companion star in Cygnus X-1.

  But what makes us think that Cygnus X-1 involves a black hole? Could it not be a neutron star or a white dwarf? It is here that we combine general relativity with information on the orbital motion of the companion star to identify the compact object. From studying the spectrum of HDE 226868, astronomers concluded that it is of a type of star that typically has a mass between 20 and 40 solar masses. In order to induce the observed orbital motion of the star, the mass of the compact object must therefore be at least 10 solar masses. It cannot be a white dwarf, because, as we remarked in Chapter 5 (page 94), the maximum possible mass for a white dwarf is about 1.4 solar masses, the Chandrasekhar mass. This conclusion does not depend on general relativity, because white dwarfs are not very relativistic. What about a neutron star? General relativity plays an important role in the structure of neutron stars; nevertheless, relativists have determined a maximum possible mass for them as well, in this case about 3 solar masses, and by no means as large as 10 (the maximum observed mass of a neutron star is about 2.2 solar masses). Therefore, it is not a neutron star. The only object left that can be massive enough to induce the orbital wobble of the companion, yet is small enough in size to allow the short-term X-ray fluctuations, is a black hole. Even though this argument is somewhat indirect, it has stood up to further observations of the system, as well as to attempts to propose alternate models that do not invoke black holes. Still, to be safe, scientists customarily call these black hole candidates.

  Many other black hole candidates have been discovered in X-ray binary systems. Interestingly, as we will learn in Chapters 7 and 8, none of them is as massive as the 20 to 50 solar mass black holes detected using gravitational waves by LIGO and Virgo, and this has challenged astrophysicists to come up with scenarios that could produce such heavyweights. There are also numerous X-ray binaries containing neutron stars. In these systems the mass of the compact object is always smaller than the 3 solar mass limit imposed by general relativity, and in many cases the X-rays are pulsed, indicating that the infalling gas is interacting with the strong, rotating magnetic field of the underlying neutron star.

  In addition, there is an intriguing subset of X-ray binaries that shed additional light on the difference between neutron stars and black holes. These are systems in which the rate of accretion of gas from the companion is very low, so that the gas in the disk is thin and friction is much weaker. As a result, the X-ray emission is very faint, but still detectable. However, when one looks at those systems in which the mass of the compact object is less than 3 solar masses, there is an additional X-ray flux superimposed on the disk flux, while for every system where the compact object’s mass is greater than 3 solar masses, there is only the feeble disk flux. Ramesh Narayan and his colleagues at Harvard University have suggested that in the high-mass systems, the gas reaches the inner edge of the disk and plunges into the black hole, emitting no additional radiation. But in the low-mass systems, the gas crashes onto the surface of the neutron star, heats up and emits the additional flux of X-rays. They have suggested that this is the first concrete evidence of general relativity’s prediction of the existence of an event horizon. If this result holds up, it will be a test of a central prediction of Einstein’s theory.

  Other researchers are asking whether one can test general relativity by examining the details of the emission from such accretion disks, particularly variations with time and unique features in the spectra. After all, near the inner edge of the disk, the gas is orbiting in an extremely warped region of spacetime compared to that in the vicinity of the Sun. For a 10 solar mass black hole, the orbital period just before plunge is about 5 milliseconds and the gas is moving at half the speed of light. The radiation that the gas emits experiences strong Doppler shifts, extreme gravitational redshifts and strong deflections, with some rays encircling the hole a few times before heading out toward the observer. If the black hole is rotating, the dragging of inertial frames will induce a number of observable effects. The hope is to test whether the spacetime geometry around the compact object really is that of either the Schwarzschild solution or the Kerr solution. Unfortunately this is a very complex problem. One must somehow cleanly separate those phenomena arising from spacetime warpage from those arising from the complicated physics associated with the gas and radiation, sometimes called “dirty gastrophysics.” This is currently an extremely active area of research, and may soon provide some remarkable new tests of general relativity.

  The next place you might think to test general relativity using black holes is in quasars. There is widespread agreement that the large redshifts in the spectra of quasars indicate that they are moving away from us at large velocities, and that, according to the picture of the expanding universe, they are therefore at very great distances. The powerhouse of the quasar is believed to be the active and violent central nucleus of a galaxy. The idea that this nucleus involves a relativistic collapsed object has changed little since the first Texas symposium, but now a rotating, supermassive black hole itself is the central engine. The black hole may weigh 100 million solar masses; as large as this is, it may still be only a tenth of a percent of the total mass of the galaxy. The black hole is gobbling up stars and gas at a ferocious rate, perhaps as much as one solar mass of material per year. As the material approaches the hole, friction from collisions with other material heats it up to temperatures high enough to make it radiate the enormous power we see on Earth. The narrow jets of matter that can be seen shooting out at nearly the speed of light on opposite sides of many quasars are believed to be the product of an interaction between magnetic fields embedded in the accreting matter and the strong dragging of inertial frames by the rotating black hole (page 58). There is evidence that quasars were much more prevalent in the early universe than they are at present; as we look farther out in distance, we are also looking farther back in time because the light from the quasar takes a finite time to reach us. It has been found that the number of quasars peaks at a time corresponding to an age of the universe about one-third of its present age. This may be the result of the finite time needed to grow such massive black holes (a problem that is still not fully solved) and the fact that once the black hole has swept up the stars and gas from the core of the galaxy, the quasar phenomenon shuts off.

  Although around 200,000 quasars have been found, the current view is that they are a small and temporary subset of a larger population, derived from the observation that essentially all massive galaxies contain massive black holes, and the fact that there are hundreds of billions of galaxies in the observable universe, far more than the number of quasars. These black hole masses range from 100,000 solar masses to the current world (or should we say, universe) record of 20 billion solar masses in the galaxy NGC 4889. It is still unclear exactly how these supermassive black holes form. One hypothesis is that these monsters form when many smaller black holes merge over the aeons of time. If enough small black holes form early enough in the universe, then they will be gravitationally attracted to each other and will merge. This scenario is aided by astrophysical mechanisms that guarantee that heavy objects tend to sink toward the center of galaxies, thus increasing the chances of mergers, as well as by the fact that mergers of galaxies themselves were r
ather common in the early universe.

  With all these massive black holes around, you might expect a plethora of tests of general relativity. But just as with black holes in binary systems, the complications of gastrophysics make the problem hard, although this is also an area of current research. It turns out, however, that there is one supermassive black hole that may be the perfect laboratory for testing Einstein’s theory. All you have to do is to … look up in the (southern) sky! It’s close! It’s clean! It’s Sagittarius A*!

  We will devote the rest of this chapter to the story of this remarkable, massive black hole, sitting smack dab in the center of our own Milky Way. The story begins with Karl Jansky (1905–1950), the pioneer of radio astronomy, whom we met briefly in Chapter 3.

  Jansky was born in the Territory of Oklahoma to parents of Czech and French–English descent. He finished his undergraduate physics degree at the University of Wisconsin in 1927 and then moved to New Jersey to work for Bell Telephone Laboratory. At the time, the company wanted to investigate the use of electromagnetic waves with a short wavelength (of about 10 meters) in trans-Atlantic telephone services. In 1931 Jansky was tasked with studying what else could produce such waves on Earth and interfere with communication signals. To do this, he built a radio antenna designed to detect waves with a wavelength of about 15 meters (with a corresponding frequency of 20 megahertz), and mounted it on a large turntable. Jansky’s “carousel” was about 30 meters wide and stood about 6 meters tall, allowing him to rotate the antenna and pinpoint the direction of any signals he detected.

  Over several months, he collected data. The main sources of radio static were thunderstorms, but in addition to weather effects, roughly once per day his antenna also detected a faint but steady radio “hiss” of unknown origin. Whenever a scientist detects a signal that repeats once per day the usual suspect is the Sun, and Jansky at first reasoned that he was recording radio waves from the Sun.

  Upon further study, however, Jansky realized that the signal repeated once every 23 hours and 56 minutes and not every 24 hours. The latter is the time it takes the Earth to complete a full rotation so that the Sun appears in the same position in the sky. This period is called the solar day. But 23 hours and 56 minutes is the time it takes the Earth to complete a full rotation so that the stars appear in the same position in the night sky. This is called the sidereal day. The roughly 4 minute difference is due to Earth’s motion around the Sun, which of course affects when the Sun rises but has no effect on when the stars appear in the night sky. If the signal Jansky had detected had something to do with the Sun, then it should have repeated with the solar day and not the sidereal day. The data indicated an origin far outside the solar system.

  By carefully rotating his antenna and taking many more months of data, Jansky was able to show that the signal was strongest in the direction of the center of the Milky Way galaxy. This coincides with the direction of the Sagittarius constellation, near a feature denoted Sagittarius A by astronomers. He published a paper on his discovery in the Proceedings of the Institute of Radio Engineers in 1933.

  A New York Times article entitled “New Radio Waves Traced to Centre of the Milky Way” catapulted Jansky to brief public stardom. But despite this, he could not convince other astronomers that there was important science in this “star noise” he had detected. It did not help either that the United States was going through the Great Depression in the early 1930s, followed by World War II. The field of astronomy would eventually recognize Jansky as the father of radio astronomy and name a unit of radio flux, the jansky, after him, but only after his death in 1950 from a heart condition.

  For decades, Jansky’s mysterious radio source in the Sagittarius constellation remained mostly unexplored, until in 1974 astronomers Bruce Balick and Robert Brown used radio interferometry to explore the region. Recall from Chapter 3 (page 39) that combining pairs or groups of radio telescopes can enable pinpointing the direction of a radio source with very high precision. In addition, this technique can resolve the size and shape of such sources with good resolution. Working at the National Radio Astronomy Observatory, Balick and Brown tried to resolve the patch of the sky from which Jansky had earlier detected radio waves. To their surprise, they found that most of the emission was confined to a very small area in the sky that was coincident with the Galactic Center. The size was about a tenth of an arcsecond as seen from Earth, or about 800 astronomical units at the source (later observations would narrow the size down to 50 microarcseconds, or about half an astronomical unit).

  Balick invented the name Sagittarius A* for the radio source in 1982, arguing that in quantum mechanics the excited states of atoms are sometimes denoted with an asterisk, and this radio source was indeed very “exciting.” Other names were later proposed for Sagittarius A*, but none of them stuck, and a standard abbreviation Sgr A* (pronounced “saj-ay-star”) was soon adopted.

  The fact that the radio emission was coming from such a compact region was a hint that a black hole might be there, but confirmation was difficult to come by. It was impossible to observe the region using optical telescopes, because of enormous bands of dust that lie between the solar system and the center of the galaxy, which absorb light in the visible band. However, in a band of wavelengths just beyond the red end of the visible spectrum, called the near infrared, light passes right through the dust, making the Galactic Center “visible” (albeit not by eye, but using special infrared sensors that had been developed to enable this branch of astronomy). Numerous astronomers trained their infrared telescopes on the Galactic Center to try to see what was going on there.

  Two teams in particular took advantage of the latest advances in telescope technology. These included the ability to do interferometry at infrared wavelengths, extending a method that had been routine at radio wavelengths (see Chapter 3). Another advancement was a technique called “adaptive optics,” whereby information about disturbances in the Earth’s atmosphere is used to alter the shape of the mirrors of the telescopes in order to achieve the sharpest images. They also had the advantage of working at dry, high-altitude sites. Being high and dry is important because water vapor absorbs near-infrared light. One group, based at the Max Planck Institute for Extraterrestrial Physics in Garching, Germany, headed by Reinhard Genzel, used the Very Large Telescope Interferometer. This is an array of four instruments located on a mountaintop in Chile at about 8,600 feet above sea level, some 1,200 kilometers north of Santiago. The other group, led by Andrea Ghez of the University of California, Los Angeles, used the two telescopes of the 13,000 foot altitude Keck Observatory near the peak of the extinct Mauna Kea volcano in Hawaii.

  But when they looked near the location of Sgr A* they saw something astounding. Stars! You might think that this should not be a big deal, since stars are what astronomers are usually paid to see. But these were neither foreground stars, between us and the Galactic Center, nor background stars, on the far side of the central region. Such stars are easy to identify and account for. These stars seemed to be in the close neighborhood of the Sgr A* object itself. The spectra of the light they emitted showed them to be of a class of massive, cool, young stars known as S-stars, around ten times more massive than our Sun. Accordingly, they gave the stars the highly original names S1, S2, S3, and so on (the UCLA group called them SO-1, SO-2, and so on; in 20 years the two groups have sadly been unable to agree on a common set of names). Ghez called this the “paradox of youth,” because these stars could not possibly have formed there from the usual collapse of a large cloud of gas and dust, the way most stars such as our Sun formed. This is because the gravitational field of the central object would have disrupted the cloud before the star could form. So where did they come from and how did they get so close to the central object?

  Even more interesting was that within a few years of observing the S-stars, the astronomers could see them move! The Munich group reported the first detections of motion in 1996 and the UCLA group followed two years later. There is a
reason why ancient astronomers referred to the “fixed stars.” They are so far away that it’s nearly impossible to see them move. Even in the modern era, it takes careful long-term monitoring of stars with the utmost precision to detect their transverse motion, and even then it works only for stars in our immediate solar neighborhood (detecting their motion along the line of sight using the Doppler shift is much easier, of course). To see a star change its sky position at the Galactic Center after only a few years implied that the star was moving extraordinarily fast. Very soon it was realized that these motions were not random, they were orbital. These stars were in orbit around the spot that had been established for Sgr A*.

  The star S2 was particularly important, because it had a relatively short orbital period of around 16 years, and was in a highly elliptical orbit (see Figure 6.3). By 2002, S2 had reached its pericenter, or point of closest approach to Sgr A*, and there was data covering more than half of its orbit.1 With this information, the teams were able to use Newton’s theory of gravity to determine that the point about which S2 was orbiting, whatever it might be, had to be several million times more massive than the Sun. Einstein’s theory is not needed here because the closest approach of S2 to Sgr A* is still distant enough that relativistic effects are unimportant for this calculation. A material object with such a mass, such as a hypothetical supermassive star or a dense cluster of stars, would have been visible in multiple bands. As we have seen, radio measurements had confined Sgr A* to a region several hundred astronomical units in radius. A tremendously massive object confined to such a very small region of space, that emits almost no light, has to be a black hole. Genzel’s team announced this conclusion in Nature in October 2002, and Ghez’s team made a similar announcement in early 2003. Improved measurements indicate that what is now called “the black hole Sgr A*” has the mass of 4.3 million suns.