For the Love of Physics

by Walter Lewin

  If you’re sharp, I know you’re already thinking, “Hold it! You just said black holes don’t emit anything, that nothing can escape their gravitational field—how can they emit X-rays?” Terrific question, which I promise to answer eventually, but here’s a preview: the X-rays emitted by a black hole do not come from inside the event horizon—they’re emitted by matter on the way into the black hole. While a black hole explained our observations of Cyg X-1, it could not explain what was seen in terms of X-ray emission from other binary stars. For that we needed neutron star binaries, which were discovered with the wonderful satellite Uhuru.

  The field of X-ray astronomy dramatically changed in December 1970, when the first satellite totally dedicated to X-ray astronomy went into orbit. Launched from Kenya on the seventh anniversary of Kenyan independence, the satellite was named Uhuru, Swahili for “freedom.”

  Uhuru began a revolution that hasn’t stopped to this day. Think about what a satellite could do. Observations 365 days a year, twenty-four hours a day, with no atmosphere at all! Uhuru was able to observe in ways we could only have dreamed about a half dozen years earlier. In just a little over two years, Uhuru mapped the X-ray sky with counters that could pick up sources five hundred times fainter than the Crab Nebula, ten thousand times fainter than Sco X-1. It found 339 of them (we’d only found several dozen before that) and provided the first X-ray map of the entire sky.

  Freeing us at last from atmospheric shackles, satellite observatories have reshaped our view of the universe, as we learned to see deep space—and the astonishing objects it contains—through every area of the electromagnetic spectrum. The Hubble Space Telescope expanded our view of the optical universe, while a series of X-ray observatories did the same for the X-ray universe. Gamma-ray observatories are now observing the universe at even higher energies.

  In 1971 Uhuru discovered 4.84-second pulsations from Cen X-3 (in the constellation Centaurus). During a one-day interval Uhuru observed a change in the X-ray flux by a factor of ten in about one hour. The period of the pulsations first decreased and then increased by about 0.02 and 0.04 percent, each change of period occurring in about an hour. All this was very exciting but also very puzzling. The pulsations couldn’t be the result of a spinning neutron star; their rotation periods were known to be steady like a rock. None of the known pulsars could possibly change their period by 0.04 percent in an hour.

  The entire picture came together beautifully when the Uhuru group later discovered that Cen X-3 was a binary system with an orbital period of 2.09 days. The 4.84-second pulsations were due to the rotation of the accreting neutron star. The evidence was overwhelming. First, they clearly saw repetitive eclipses (every 2.09 days) when the neutron star hides behind the donor star, blocking the X-rays emissions. And second, they were able to measure the Doppler shift in the periods of the pulsations. When the neutron star is moving toward us, the pulsation period is a little shorter, a little longer when moving away. These earthshaking results were published in March 1972. All this naturally explained the phenomena that seemed so puzzling in the 1971 paper. It was just as Shklovsky had predicted for Sco X-1: a binary system with a donor star and an accreting neutron star.

  Later that very same year, Giacconi’s group found yet another source, Hercules X-1 (or Her X-1, as we like to say), with pulsations and eclipses. Another neutron star X-ray binary!

  These were absolutely stunning discoveries that transformed X-ray astronomy, dominating the field for decades to come. X-ray binaries are very rare; perhaps only one in a hundred million binary stars in our galaxy is an X-ray binary. Even so, we now know that there are several hundred X-ray binaries in our galaxy. In most cases the compact object, the accretor, is a white dwarf or a neutron star, but there are at least two dozen known systems in which the accretor is a black hole.

  Remember the 2.3-minute periodicity that my group discovered in 1970 (before the launch of Uhuru)? At the time we had no clue what these periodic changes meant. Well, we now know that GX 1+4 is an X-ray binary system with an orbital period of about 304 days, and the accreting neutron star spins around in about 2.3 minutes.

  X-ray Binaries: How They Work

  When a neutron star pairs up with the right-size donor star at the right distance, it can create some amazing fireworks. There, in the reaches of space, stars Isaac Newton could never even have imagined perform a beautiful dance, all the while utterly bound by the laws of classical mechanics any undergraduate science major can grasp.

  To understand this better, let’s start close to home. The Earth and the Moon are a binary system. If you draw a line from the center of the Earth to the center of the Moon, there is a point on that line where the gravitational force toward the Moon is equal but opposite to the gravitational force toward Earth. If you were there, the net force on you would be zero. If you were on one side of that point you would fall to Earth; if you were on the other side you would fall toward the Moon. That point has a name; we call it the inner Lagrangian point. Of course, it lies very close to the moon, because the Moon’s mass is about eighty times smaller than that of the Earth.

  Let’s now return to X-ray binaries consisting of an accreting neutron star and a much larger donor star. If the two stars are very close to each other, the inner Lagrangian point can lie below the surface of the donor star. If that is the case, some of the matter of the donor star will experience a gravitational force toward the neutron star that is larger than the gravitational force toward the center of the donor star. Consequently matter—hot hydrogen gas—will flow from the donor star to the neutron star.

  Since the stars are orbiting their common center of mass, the matter cannot fall directly toward the neutron star. Before it reaches the surface, the matter falls into an orbit around the neutron star, creating a spinning disk of hot gas that we call an accretion disk. Some of the gas on the inner ring of the disk ultimately finds its way down to the surface of the neutron star.

  Now an interesting piece of physics gets involved that you are already familiar with in another context. Since the gas is very hot, it is ionized, consisting of positively charged protons and negatively charged electrons. But since the neutron stars have very strong magnetic fields, these charged particles are forced to follow the star’s magnetic field lines, so most of this plasma ends up at the magnetic poles of the neutron star, like the aurora borealis on Earth. The neutron star’s magnetic poles (where matter crashes onto the neutron star) become hot spots with temperatures of millions of degrees kelvin, emitting X-rays. And as magnetic poles generally do not coincide with the poles of the axis of rotation (see chapter 12), we on Earth will only receive a high X-ray flux when a hot spot is facing us. Since the neutron star rotates, it appears to pulsate.

  Every X-ray binary has an accretion disk orbiting the accretor, be it a neutron star, a white dwarf or, as in Cyg X-1, a black hole. Accretion disks are among the most extraordinary objects in the universe, and almost no one except professional astronomers has ever even heard of them.

  There are accretion disks around all black hole X-ray binaries. There are even accretion disks orbiting supermassive black holes at the center of many galaxies, though probably not, as it turns out, around the supermassive black hole at the center of our own galaxy.

  The study of accretion disks is now an entire field of astrophysics. You can see some wonderful images of them here: www.google.com/images?hl=en&q=xray+binaries&um=1&ie=UTF. There is still lots about accretion disks that we don’t know. One of the most embarrassing problems is that we still don’t understand well how the matter in the accretion disks finds its way to the compact object. Another remaining problem is our lack of understanding of instabilities in the accretion disks, which give rise to variability in the matter flow onto the compact object, and the variability in X-ray luminosity. Our understanding of radio jets present in several X-ray binaries is also very poor.

  A donor star can transfer up to about 1018 grams per second to the accreting neutron star. It sounds
like a lot, but even at that rate it would take two hundred years to transfer an amount of matter equal to the Earth’s mass. Matter from the disk flows toward the accretor in the grip of its intense gravitational field, which accelerates the gas to an extremely high speed: about one third to one half the speed of light. Gravitational potential energy released by this matter is converted into kinetic energy (roughly 5 × 1030 watts) and heats the racing hydrogen gas to a temperature of millions of degrees.

  You know that when matter is heated it gives off blackbody radiation (see chapter 14). The higher the temperature, the more energetic the radiation, making shorter wavelengths and higher frequencies. When matter reaches 10 to 100 million kelvin, the radiation it generates is mostly in X-rays. Almost all 5 × 1030 watts are released in the form of X-rays; compare that with the total luminosity of our Sun (4 × 1026 watts) of which only about 1020 watts is in the form of X-rays. Our Sun’s surface temperature is a veritable ice cube in comparison.

  The neutron stars themselves are much too small to be seen optically—but we can see the much larger donor stars and the accretion disks with optical telescopes. The disks themselves can radiate quite a bit of light partly due to a process called X-ray heating. When the matter from the disk crashes onto the surface of the neutron star, the resultant X-rays go off in all directions and thus also slam into the disk itself, heating it to even higher temperatures. I will tell you more about that in the next chapter, on X-ray bursts.

  The discovery of X-ray binaries solved the first mystery of extrasolar X-rays. We now understand why the X-ray luminosity of a source like Sco X-1 is ten thousand times greater than its optical luminosity. The X-rays come from the very hot neutron star (with temperatures of tens of millions kelvin), and the optical light comes from the much cooler donor star and the accretion disk.

  When we thought that we had a fair understanding of how X-ray binaries work, nature had another surprise in store for us. The X-ray astronomers began making observational discoveries that were outstripping the theoretical models.

  In 1975, the discovery of something truly bizarre led to a high point of my scientific career. I became completely immersed in the effort to observe, study, and explain these remarkable and mysterious phenomena: X-ray bursts.

  Part of the story about X-ray bursts includes a battle I had with Russian scientists who completely misinterpreted their data and also with some of my colleagues at Harvard who believed that X-ray bursts were produced by very massive black holes (poor black holes, they have been unjustly blamed for so much). Believe it or not, I was even called (more than once) to not publish some data on bursts for reasons of national security.

  CHAPTER 14

  X-ray Bursters!

  Nature is always full of surprises, and in 1975 it rocked the X-ray community. Things became so intense that emotions at times got out of control, and I was in the middle of it all. For years I was arguing with a colleague of mine at Harvard (who would not listen), but I had more luck with my Russian colleagues (who did listen). Because of my central role in all of this it may be very difficult for me to be objective, but I’ll try!

  The new thing was X-ray bursts. They were discovered independently in 1975 by Grindlay and Heise using data from the Astronomical Netherlands Satellite (ANS) and by Belian, Conner, and Evans, using data from the United States’ two Vela-5 spy satellites designed to detect nuclear tests. X-ray bursts were a completely different animal from the variability we discovered from Sco X-1, which had a flare-up by a factor of four over a ten-minute period that lasted tens of minutes. X-ray bursts were much faster, much brighter, and they lasted only tens of seconds.

  At MIT we had our own satellite (launched in May 1975) known as the Third Small Astronomy Satellite, or SAS-3. Its name wasn’t as romantic as “Uhuru,” but the work was the most absorbing of my entire life. We had heard about bursters and began looking for them in January 1976; by March we’d found five of our own. By the end of the year we’d found a total of ten. Because of the sensitivity of SAS-3, and the way it was configured, it turned out to be the ideal instrument to discover burst sources and to study them. Of course, it wasn’t specially designed to detect X-ray bursts; so in a way it was a bit of luck. You see what a leading role Lady Luck has played in my life! We were getting amazing data—a bit of gold pouring out of the sky every day, twenty-four hours a day—and I worked around the clock. I was dedicated, but also obsessed. It was a once in a lifetime opportunity to have an X-ray observatory you can point in any direction you want to and get data of high quality.

  The truth is that we all caught “burst fever”—undergraduates and graduate students, support staff and postdocs and faculty—and I can still remember the feeling, like a glow. We ended up in different observing groups, which meant that we got competitive, even with one another. Some of us didn’t like that, but I have to say that I think it pushed us to do more and better, and the scientific results were just fantastic.

  That level of obsession was not good for my marriage, and not good for my family life either. My scientific life was immeasurably enhanced, but my first marriage dissolved. Of course it was my fault. For years I’d been going away for months at a time to fly balloons halfway around the globe. Now that we had our own satellite, I might as well still have been in Australia.

  The burst sources became a kind of substitute family. After all, we lived with them and slept with them and learned them inside out. Like friends, each one was unique, with its own idiosyncrasies. Even now, I recognize many of these telltale burst profiles.

  Most of these sources were about 25,000 light-years away, which allowed us to calculate that the total X-ray energy in a burst (emitted in less than a minute) was about 1032 joules, a number that’s almost impossible to grasp. So look at it this way: it takes our Sun about three days to emit 1032 joules of energy in all wavelengths.

  Some of these bursts came with nearly clocklike regularity, such as the bursts from MXB 1659-29, which produced bursts at 2.4-hour intervals, while others changed their burst intervals from hours to days, and some showed no bursts at all for several months. The M in MXB stands for MIT, the X for X-rays, and the B for burster. The numbers indicate the source’s celestial coordinates in what’s known as the equatorial coordinate system. For the amateur astronomers among you, this will be familiar.

  The key question, of course, was what caused these bursts? Two of my colleagues at Harvard (including Josh Grindlay, who was one of the codiscoverers of X-ray bursts) got carried away and proposed in 1976 that the bursts were produced by black holes with a mass greater than several hundred times the mass of the Sun.

  We soon discovered that the spectra during X-ray bursts resemble the spectra from a cooling black body. A black body is not a black hole. It’s an ideal construct to stand in for an object that absorbs all the radiation that strikes it, rather than reflecting any of it. (As you know, black absorbs radiation, while white reflects it—which is why in summer in Miami a black car left in a beach parking lot will always be hotter inside than a white one.) The other thing about an ideal black body is that since it reflects nothing, the only radiation it can emit is the result of its own temperature. Think about a heating element in an electric stove. When it reaches a cooking temperature, it begins to glow red, emitting low-frequency red light. As it gets hotter it reaches orange, then yellow, and usually not much more. When you turn off the electricity, the element cools, and the radiation it emits has a profile more or less like the tail end of bursts. The spectra of black bodies are so well known that if you measure the spectrum over time, you can calculate the temperature as it cools.

  Since black bodies are very well understood, we can deduce a great deal about bursts based on elementary physics, which is quite amazing. Here we were, analyzing X-ray emission spectra of unknown sources 25,000 light-years away, and we made breakthroughs using the same physics that first-year college students learn at MIT!

  We know that the total luminosity of a black body (how much e
nergy per second it radiates) is proportional to the fourth power of its temperature (this is by no means intuitive), and it is proportional to its surface area (that’s intuitive—the larger the area, the more energy can get out). So, if we have two spheres a meter in diameter, and one is twice as hot as the other, the hotter one will emit sixteen times (24) more energy per second. Since the surface area of a sphere is proportional to the square of its radius, we also know that if an object’s temperature stays the same but triples in size, it will emit nine times more energy per second.

  The X-ray spectrum at any moment in time of the burst tells us the blackbody temperature of the emitting object. During a burst, the temperature quickly rises to about 30 million kelvin and decreases slowly thereafter. But since we knew the approximate distance to these bursters, we could also calculate the luminosity of the source at any moment during the burst. But once you know both the blackbody temperature and the luminosity, you can calculate the radius of the emitting object, and that too can be done for any moment in time during the burst. The person who did this first was Jean Swank of NASA’s Goddard Space Flight Center; we at MIT followed quickly and concluded that the bursts came from a cooling object with a radius of about 10 kilometers. This was strong evidence that the burst sources were neutron stars, not very massive black holes. And if they were neutron stars, they were probably X-ray binaries.