For the Love of Physics

by Walter Lewin

  Its intensity went down in a few weeks by a factor of three, and five months later its intensity had diminished by at least a factor of fifty. Nowadays, we call these sources by the pedestrian name “X-ray transients.”

  McCracken’s group had located the source in the constellation Crux, which you may know better as the Southern Cross. They were very excited about this, and it became something of an emotional thing for them, since that very constellation is in the Australian flag. When it turned out that the source’s location was just outside the Southern Cross, in Centaurus instead, the original name Crux X-1 was changed to Cen X-2, and the Aussies were very disappointed. Scientists can get very emotional about our discoveries.

  On October 15, 1967, George Clark and I observed Sco X-1 in a ten-hour balloon flight launched from Mildura, Australia, and we made a major discovery. This discovery wasn’t anything like you see in pictures of the NASA Space Center in Houston, where they all cheer and hug one another when they have a success. They are seeing things happen in real time. During our observing we had no access to the data; we were just hoping that the balloon would last and that our equipment would work flawlessly. And, of course, we always worried about how to get the telescope and the data back. That’s where all the nerves and the excitement were.

  We analyzed our data months later, back home at MIT. I was in the computer room one night, assisted by Terry Thorsos. We had very large computers at MIT in those days. The rooms had to be air-conditioned because the computers generated so much heat. I remember that it was around eleven p.m. If you wanted to get some computer runs, the evening was a good time to sneak in some jobs. In those days you always needed to have a computer operator to run your programs. I got into a queue and waited patiently.

  So here I was, looking at the balloon data, and all of a sudden I saw a large increase in the X-ray flux from Sco X-1. Right there, on the printout, the X-ray flux went up by a factor of four in about ten minutes, lasted for nearly thirty minutes, and then subsided. We had observed an X-ray flare from Sco X-1, and it was enormous. This had never been observed before. Normally, you’d say to yourself, “Is this flare something that could be explained in a different way? Was it perhaps caused by a malfunctioning detector?” In this case, there was no doubt in my mind. I knew the instrument inside and out. I trusted all our preparation and testing, and throughout the flight we had checked the detector continuously and had measured the X-ray spectrum of a known radioactive source every twenty minutes as a control—the instruments were working flawlessly. I trusted the data 100 percent. Looking at the printout I could see that the X-ray flux went up and down; of all the sources we observed in that ten-hour flight, only one shot up and down, and that was Sco X-1. It was real!

  The next morning I showed George Clark the results, and he nearly fell off his chair. We both knew the field well; we were overjoyed! No one had anticipated, let alone observed, a change in the flux of an X-ray source on a time scale of ten minutes. The flux from Cen X-2 decreased by a factor of three within a few weeks after the first detection, but here we had variability by a factor of four within ten minutes—about three thousand times faster.

  We knew that Sco X-1 emitted 99.9 percent of its energy in the form of X-rays, and that its X-ray luminosity was about 10,000 times the total luminosity of our Sun and about 10 billion times the X-ray luminosity of the Sun. For Sco X-1 to change its luminosity by a factor of four on a time scale of ten minutes—well, there was simply no physics to understand it. How would you explain it if our Sun would become four times brighter in ten minutes? It would scare the hell out of me.

  The discovery of variability on this time scale may have been the most important discovery in X-ray astronomy made from balloons. As I mentioned in this chapter, we also discovered X-ray sources that the rockets couldn’t see, and those were important discoveries as well. But nothing else had the impact of Sco X-1’s ten-minute variability.

  It was so unexpected at the time that many scientists couldn’t believe it. Even scientists have powerful expectations that can be difficult to challenge. The legendary editor of the Astrophysical Journal Letters, S. Chandrasekhar, sent our Sco X-1 article to a referee, and the referee didn’t believe our finding at all. I still remember this, more than forty years later. He wrote, “This must be nonsense, as we know that these powerful X-ray sources cannot vary on a time scale of ten minutes.”

  We had to talk our way into the journal. Rossi had had to do exactly the same thing back in 1962. The editor of Physical Review Letters, Samuel Goudsmit, accepted the article founding X-ray astronomy because Rossi was Rossi and was willing, as he wrote later, to assume “personal responsibility” for the contents of the paper.

  Nowadays, because we have instruments and telescopes that are so much more sensitive, we know that many X-ray sources vary on any timescale, meaning that if you observe a source continuously day by day, its flux will be different every day. If you observe it second by second it will change as well. Even if you analyze your data millisecond by millisecond you may find variability in some sources. But at the time, the ten-minute variability was new and unexpected.

  I gave a talk about this discovery at MIT in February 1968, and I was thrilled to see Riccardo Giacconi and Herb Gursky in the audience. I felt as though I’d arrived, that I had been accepted into the cutting edge of my field.

  In the next few chapters I’ll introduce you to the host of mysteries that X-ray astronomy solved, as well as to some we astrophysicists are still struggling to find answers for. We’ll travel to neutron stars and plunge into the depths of black holes. Hold on to your hats.

  CHAPTER 12

  Cosmic Catastrophes, Neutron Stars, and Black Holes

  Neutron stars are smack dab at the center of the history of X-ray astronomy. And they are really, really cool. Not in terms of temperature, not at all: they can frequently have surface temperatures upward of a million kelvin. More than a hundred times hotter than the surface of our Sun.

  James Chadwick discovered the neutron in 1932 (for which he received the Nobel Prize in Physics in 1935). After this extraordinary discovery, which many physicists thought had completed the picture of atomic structure, Walter Baade and Fritz Zwicky hypothesized that neutron stars were formed in supernova explosions. It turns out that they were right on the money. Neutron stars come into being through truly cataclysmic events at the end of a massive star’s lifetime, one of the quickest, most spectacular, and most violent occurrences in the known universe—a core-collapse supernova.

  A neutron star doesn’t begin with a star like our Sun, but rather with a star at least eight times more massive. There are probably more than a billion such stars in our galaxy, but there are so many stars of all kinds in our galaxy that even with so many, these giants must still be considered rare. Like so many objects in our world—and universe—stars can only “live” by virtue of their ability to strike a rough balance between immensely powerful forces. Nuclear-burning stars generate pressure from their cores where thermonuclear reactions at temperatures of tens of millions of degrees kelvin generate huge amounts of energy. The temperature at the core of our own Sun is about 15 million kelvin, and it produces energy at a rate equivalent to more than a billion hydrogen bombs per second.

  In a stable star, this pressure is pretty well balanced by the gravity generated by the huge mass of the star. If these two forces—the outward thrust of the thermonuclear furnace and the inward-pulling grip of gravity—didn’t balance each other, then a star wouldn’t be stable. We know our Sun, for example, has already had about 5 billion years of life and should continue on that path for another 5 billion years. When stars are about to die, they really change, and in spectacular ways. When stars have used up most of the nuclear fuel in their cores, many approach the final stages of their lives by first putting on a fiery show. This is especially true for massive stars. In a way, supernovae resemble the tragic heroes of theater, who usually end their overlarge lives in a paroxysm of cathartic emo
tion, sometimes fiery, often loud, evoking, as Aristotle said, pity and terror in the audience.

  The most extravagant stellar demise of all is that of a core-collapse supernova, one of the most energetic phenomena in the universe. I’ll try to do it justice. As the nuclear furnace at the core of one of these massive stars begins to wind down—no fuel can last forever!—and the pressure it generates begins to weaken, the relentless, everlasting gravitational attraction of the remaining mass overwhelms it.

  This process of exhausting fuel is actually rather complicated, but it’s also fascinating. Like most stars, the really massive ones begin by burning hydrogen and creating helium. Stars are powered by nuclear energy—not fission, but fusion: four hydrogen nuclei (protons) are fused together into a helium nucleus at extremely high temperatures, and this produces heat. When these stars run out of hydrogen, their cores shrink (because of the gravitational pull), which raises the temperature high enough that they can start fusing helium to carbon. For stars with masses more than about ten times the mass of the Sun, after carbon burning they go through oxygen burning, neon burning, silicon burning, and ultimately form an iron core.

  After each burning cycle the core shrinks, its temperature increases, and the next cycle starts. Each cycle produces less energy than the previous cycle and each cycle is shorter than the previous one. As an example (depending on the exact mass of the star), the hydrogen-burning cycle may last 10 million years at a temperature of about 35 million kelvin, but the last cycle, the silicon cycle, may only last a few days at a temperature of about 3 billion kelvin! During each cycle the stars burn most of the products of the previous cycle. Talk about recycling!

  The end of the line comes when silicon fusion produces iron, which has the most stable nucleus of all the elements in the periodic table. Fusion of iron to still heavier nuclei doesn’t produce energy; it requires energy, so the energy-producing furnace stops there. The iron core quickly grows as the star produces more and more iron.

  When this iron core reaches a mass of about 1.4 solar masses, it has reached a magic limit of sorts, known as the Chandrasekhar limit (named after the great Chandra himself). At this point the pressure in the core can no longer hold out against the powerful pressure due to gravity, and the core collapses onto itself, causing an outward supernova explosion.

  Imagine a vast army besieging a once proud castle, and the outer walls begin to crumble. (Some of the battle scenes in the Lord of the Rings movies come to mind, when the apparently limitless armies of Orcs break through the walls.) The core collapses in milliseconds, and the matter falling in—it actually races in at fantastic speeds, nearly a quarter the speed of light—raises the temperature inside to an unimaginable 100 billion kelvin, about ten thousand times hotter than the core of our Sun.

  If a single star is less massive than about twenty-five times the mass of the Sun (but more than about ten times the mass of the Sun), the collapse creates a brand new kind of object at its center: a neutron star. Single stars with a mass between eight and about ten times the mass of the Sun also end up as neutron stars, but their nuclear evolution in the core (not discussed here) differs from the above scenario.

  At the high density of the collapsing core, electrons and protons merge. An individual electron’s negative charge cancels out a proton’s positive charge, and they unite to create a neutron and a neutrino. Individual nuclei no longer exist; they have disappeared into a mass of what is known as degenerate neutron matter. (Finally, some juicy names!) I love the name of the countervailing pressure: neutron degeneracy pressure. If this would-be neutron star grows more massive than about 3 solar masses, which is the case if the single star’s mass (called the progenitor) is larger than about twenty-five times the mass of the Sun, then gravity overpowers even the neutron degeneracy pressure, and what do you think will happen then? Take a guess.

  That’s right. I figured you guessed it. What else could it be but a black hole, a place where matter can no longer exist in any form we can understand; where, if you get close, gravity is so powerful that no radiation can escape: no light, no X-rays, no gamma rays, no neutrinos, no anything. The evolution in binary systems (see the next chapter) can be very different because in a binary the envelope of the massive star may be removed at an early stage, and the core mass may not be able to grow as much as in a single star. In that case even a star that originally was forty times more massive than the Sun may still leave a neutron star.

  I’d like to stress that the dividing line between progenitors that form neutron stars and black holes is not clear cut; it depends on many variables other than just the mass of the progenitor; stellar rotation, for instance, is also important.

  But black holes do exist—they aren’t the invention of feverish scientists and science fiction writers—and they are incredibly fascinating. They are deeply involved in the X-ray universe, and I’ll come back to them—I promise. For the moment, I’ll just say this: not only are they real—they probably make up the nucleus of every reasonably massive galaxy in the universe.

  Let’s go back to the core collapse. Once the neutron star forms—remember, we’re talking milliseconds here—the stellar matter still trying to race into it literally bounces off, forming an outward-going shock wave, which will eventually stall due to energy being consumed by the breaking apart of the remaining iron nuclei. (Remember that energy is released when light elements fuse to form an iron nucleus, therefore breaking an iron nucleus apart will consume energy.) When electrons and protons merge during core collapse to become neutrons, neutrinos are also produced. In addition, at the high core temperature of about 100 billion kelvin, so-called thermal neutrinos are produced. The neutrinos carry about 99 percent (which is about 1046 joules) of all energy released in the core collapse. The remaining 1 percent (1044 joules) is largely in the form of kinetic energy of the star’s ejected matter.

  The nearly massless and neutral neutrinos ordinarily sail through nearly all matter, and most do escape the core. However, because of the extremely high density of the surrounding matter, they transfer about 1 percent of their energy to the matter, which is then blasted away at speeds up to 20,000 kilometers per second. Some of this matter can be seen for thousands of years after the explosion—we call this a supernova remnant (like the Crab Nebula).

  The supernova explosion is dazzling; the optical luminosity at maximum brightness is about 1035 joules per second. This is 300 million times the luminosity of our Sun, providing one of the great sights in the heavens when such a supernova occurs in our galaxy (which happens on average only about twice per century). Nowadays, with the use of fully automated robotic telescopes, many hundreds to a thousand supernovae are discovered each year in the large zoo of relatively nearby galaxies.

  A core-collapse supernova emits two hundred times the energy that our Sun has produced in the past 5 billion years, and all that energy is released in roughly 1 second—and 99 percent comes out in neutrinos!

  That’s what happened in the year 1054, and the explosion produced the brightest star in our heavens in the past thousand years—so bright that it was visible in the daytime sky for weeks. A true cosmic flash in the interstellar pan, the supernova fades within a few years, as the gas cools and disperses. The gas doesn’t disappear, though. That explosion in 1054 not only produced a solitary neutron star; it also produced the Crab Nebula, one of the more remarkable and still-changing objects in the entire sky, and a nearly endless source of new data, extraordinary images, and observational discoveries. Since so much astronomical activity takes place on an immense time scale, one we more often think of as geological—millions and billions of years—it’s especially exciting when we find something that happens really fast, on a scale of seconds or minutes or even years. Parts of the Crab Nebula change shape every few days, and the Hubble Space Telescope and the Chandra X-Ray Observatory have found that the remnant of Supernova 1987A (located in the Large Magellanic Cloud) also changes shape in ways we can see.

  Three differen
t neutrino observatories on Earth picked up simultaneous neutrino bursts from Supernova 1987A, the light from which reached us on February 23, 1987. Neutrinos are so hard to detect that between them, these three instruments detected a total of just twenty-five in thirteen seconds, out of the roughly 300 trillion (3 × 1014) neutrinos showering down in those thirteen seconds on every square meter of the Earth’s surface directly facing the supernova. The supernova originally ejected something on the order of 1058 neutrinos, an almost unimaginably high number—but given its large distance from the Earth (about 170,000 light-years), “only” about 4 × 1028 neutrinos—thirty orders of magnitude fewer—actually reached the Earth. More than 99.9999999 percent go straight through the Earth; it would take a light-year (about 1013 kilometers) of lead to stop about half the neutrinos.

  The progenitor of Supernova 1987A had thrown off a shell of gas about twenty thousand years earlier that had made rings around the star, and the rings remained invisible until about 8 months after the supernova explosion. The speed of the expelled gas was relatively slow—only around 8 kilometers per second—but over the years the shell’s radius had reached a distance of about two-thirds of a light-year, about 8 light-months.

  So the supernova went off, and about eight months later ultraviolet light from the explosion (traveling at the speed of light, of course) caught up with the ring of matter and turned it on, so to speak—and the ring started to emit visible light. You can see a picture of SN 1987A in the insert.

  But there’s more, and it involves X-rays. The gas expelled by the supernova in the explosion traveled at roughly 20,000 kilometers per second, only about fifteen times slower than the speed of light. Since we knew how far away the ring was by now, we could also predict when, approximately, the expelled matter was going to hit the ring, which it did a little over eleven years later, producing X-rays. Of course, we always have to remember that even though we talk about it as though it happened in the last few decades, in reality, since SN 1987A is in the Large Magellanic Cloud, it all happened about 170,000 years ago.