How to Make an Apple Pie from Scratch

by Harry Cliff

  At last, we have a recipe for helium! Even better, the whole process results in a net release of energy, and so it’s also a recipe for starlight. However, there is a problem. Eddington had estimated that the temperature at the center of the Sun was 40 million degrees Celsius, but at that temperature the proton-proton chain would run too fast, resulting in a Sun that shines far more brightly than it actually does. Critchfield and Bethe had come agonizingly close to solving one of the oldest mysteries in science, only to find that the solar oven was too hot for their recipe.

  That all changed at the Washington conference. Bethe’s interest was piqued during a long and detailed talk about the conditions inside the Sun. When Eddington had come up with his 40-million-degree figure, people had thought that the Sun was made of more or less the same stuff as the Earth. However, in 1925 the brilliant young astronomer Cecilia Payne had shown that the Sun and stars were dominated by hydrogen and helium, with only relatively tiny amounts of the heavier elements. When Eddington’s calculations were revised assuming that the Sun was 73 percent hydrogen and 25 percent helium, the temperature in the core plummeted to a far cooler (though still decidedly toasty) 19 million degrees. With the solar oven set at this lower temperature, Bethe found that the proton-proton chain predicted a power output for the Sun that was much closer to the true value.

  At long last, the riddle of why the Sun shines had been solved. Deep inside its core, the crushing force of its own gravity heats hydrogen to a temperature of 15 million degrees Celsius.*8 In this fearsome heat, protons and electrons pinball into one another at terrific speeds, and every so often, in one among unnumbered collisions, two protons come close enough for quantum mechanics to take over, creating a tunnel through the repulsive electrical barrier keeping them apart and allowing them to unite to form a nucleus of deuterium. From here, slowly but surely, the Sun builds helium from hydrogen, gradually transforming its own bulk over billions of years, all the while releasing a steady flow of heat that eventually breaks out from the Sun’s tortured surface and escapes into space as sunlight. The Sun is a vast thermonuclear furnace.

  Our search for the recipe for helium isn’t quite finished, though. During the conference, Bethe realized that something was amiss. The proton-proton chain worked brilliantly for stars smaller than the Sun, but when he applied it to larger stars the reaction didn’t fit.

  Take Sirius, the brightest star in the night sky, a brilliant blue-white jewel in the constellation Canis Major. Sirius’s apparent brightness is a result of two factors: first off, it’s only a short bus ride away in galactic terms, at just a smidge over 8.6 light-years from the Earth. Second, Sirius is about twice as massive as the Sun, which means the crushing force of gravity heats its core to a higher temperature. This higher temperature means that protons are whizzing about faster, which means they can more easily overcome the repulsive electrical forces keeping them apart, boosting the rate of nuclear fusion.

  However, the weird thing is that despite only being twice as massive as the Sun, Sirius is twenty-five times brighter, which couldn’t possibly be explained using the proton-proton chain. There must be something else happening in Sirius’s core that makes it shine so ferociously.

  Bethe started thinking about a completely different sort of reaction. Instead of protons joining together directly to form helium, what if instead they were gobbled up by an existing heavy nucleus, which slowly digested the four protons before spitting them out as a fully formed helium nucleus at the end. The question was, did a heavy nucleus with the right properties to act as a proton digestor exist?

  Starting with helium Bethe worked his way along the first row of the periodic table, considering and then discarding elements one by one. Helium itself was no use at all as there was no element with mass 5 and so no way to get farther by just adding a proton. Lithium, beryllium, and boron were all too scarce and would be burnt up by the reaction too quickly to keep a star shining for very long. Then he came to element six, carbon. It seemed to have just the properties he was after. Bethe caught the train back to Cornell with the outline of a solution already in his mind.

  Just a couple of weeks later, he had come up with a second recipe for helium. It’s known as the “carbon-nitrogen-oxygen (CNO) cycle,” and it goes like this:

  A RECIPE FOR HELIUM— THE CARBON-NITROGEN-OXYGEN CYCLE

  Step 1: A proton tunnels into a carbon-12 nucleus creating a new nucleus of nitrogen-13, which then decays into carbon-13, emitting a positron and a neutrino.

  Step 2: A second proton tunnels into the carbon-13 nucleus creating nitrogen-14.

  Step 3: A third proton tunnels into the nitrogen-14 nucleus to create oxygen-15, which then decays into nitrogen-15, emitting a positron and a neutrino.

  Step 4: Finally, a fourth proton tunnels into the nitrogen-15 nucleus, breaking it apart to form a helium-4 nucleus and the same carbon-12 nucleus we started with.

  Bethe’s reaction was almost miraculous. Through a series of successive collisions, a carbon-12 nucleus was able to effectively swallow up protons and convert them into helium. And best of all at the end of it you got back the original carbon-12 nucleus, allowing the whole process to start again.

  Now, as a carbon-12 nucleus contains six positively charged protons, its repulsive barrier is six times higher than hydrogen’s. As a result, for a proton to have a chance of tunneling into a carbon nucleus it has to be moving at a hell of a lick, making the reaction incredibly sensitive to temperature. In fact, if you double the temperature at the center of a star, the CNO cycle blasts out 65,000 times more power, explaining why Sirius shines twenty-five times more brilliantly than the Sun despite only being twice as big and a little bit hotter. The CNO cycle is now thought to be the dominant source of starlight for all stars more than 1.2 times as heavy as the Sun.*9

  So there you have it—at last we have the recipes needed to make helium inside stars. But there is one big challenge left to face: How do we actually know this is what is going on inside the Sun?

  Until relatively recently, our understanding of how the Sun fuses hydrogen to make helium was based on two different bits of science. From the 1930s onward, physicists started to use particle accelerators to fire protons at various targets, recreating the nuclear fusion reactions dreamed up by Hans Bethe and his colleagues. These pioneering experiments gave physicists a direct handle on how fast each helium cooking process should run depending on the temperature of the stellar oven. Meanwhile, astrophysicists produced ever-more accurate theoretical models that could make increasingly precise estimates of the core temperatures of stars. With these two pieces of crucial scientific knowledge, physicists could infer that stars the size of the Sun were powered mostly by the proton-proton chain, while larger stars like Sirius relied on the CNO cycle.

  However, all the evidence was really only indirect. To know for sure, we need to look straight into a star’s burning core and witness the nuclear reactions firsthand. But looking inside a star is impossible, right? When we look at the Sun (with the appropriate equipment of course, not directly please) all we can see is its shining surface. The core is hidden, forever beyond our reach.

  Or so it seems at first. In fact, it is only in the last few decades that physicists have finally been able to peel back the outer layers of the Sun and stare straight into its heart. Deep inside an Italian mountain a couple of hours’ drive from Rome, a team of physicists have built a gigantic detector that patiently watches for ghostly messengers that come to us direct from the Sun’s thermonuclear furnace. Their goal is to prove once and for all that the nuclear reactions first proposed in the late 1930s really are the ultimate source of the Sun’s awesome power.

  SUNSHINE UNDER A MOUNTAIN

  On a stiflingly hot August day, I turned off Autostrada A24 near the Italian village of Assergi and onto an unmarked road running across the lower slopes of the towering Gran Sasso mountains. Wh
ether it was the lack of road markings or the fact that I’d gotten up at three that morning to catch the early flight to Rome, I had briefly relapsed into driving on the left, only realizing my mistake when another car rounded the corner ahead of me. After a panicked swerve and an apologetic wave to the startled-looking driver, I turned the corner to find the road full of Italian police.

  The officers were gathered outside the gates of LNGS, the Laboratori Nazionali del Gran Sasso, the largest underground research facility in the world. Hoping that they hadn’t witnessed my eccentric driving I cruised gingerly past the assembled cops, who to my relief made no moves to arrest me. Nonetheless, I was more than a little concerned—had something happened underground? I had read that the lab had been involved in some recent legal trouble that was threatening to shut down some of its experiments but hadn’t realized for a second that it was this serious. After parking my rental car out of sight just around the next bend I presented myself at security and asked for Aldo Ianni, the physicist who had agreed to be my guide inside the mountain, hoping that the whole thing wasn’t about to be called off.

  I was there to visit what has got to be the most extraordinary solar observatory in the world. For one, a cavern a kilometer and a half under a mountain isn’t an obvious place to study the Sun. But this is no ordinary observatory. The instrument I was here to see doesn’t look at the Sun in light, or even radio waves, but in neutrinos.

  Neutrinos are the most elusive of all the fundamental particles. They have almost no mass and no electric charge. This makes detecting them fiendishly difficult. Most particle detectors rely on the fact that charged particles interact with the material of the detector through the electromagnetic force, creating a telltale flash of light or an electric current. However, neutral particles don’t interact electromagnetically and so are much harder to spot. For exactly the same reason, James Chadwick had had to struggle through a decade of frustration and failure before he finally cornered the neutron. But even though the neutron has no electric charge, it does at least feel the strong nuclear force, which makes it more likely to collide with other atomic nuclei and make its presence known. Neutrinos, on the other hand, don’t even feel the strong nuclear force. The only way they can interact directly with ordinary matter is through the third force that governs the quantum realm, the so-called weak force. As its name suggests, the weak force is, well, weak, which means that the chances of a neutrino bumping into an atom are vanishingly small.

  However, while this makes detecting neutrinos extremely challenging, it also makes them the perfect tool to probe the inner workings of the Sun. Deep within its core, nuclear fusion reactions are constantly generating a vast flood of photons (particles of light) as well as neutrinos. Unfortunately for solar physicists, those photons endlessly collide with the superheated gas of protons and electrons that make up the body of the Sun, taking tens of thousands of years to pinball their way to the surface, by which time all the information they originally carried about the nuclear reactions that created them has been lost. Neutrinos, on the other hand, face no such obstacle. To them the Sun’s enormous bulk is almost completely invisible; they escape to the surface traveling at the speed of light in a little over two seconds, reaching the Earth around eight minutes and twenty seconds later.

  By the time you have finished reading this sentence, around two thousand trillion of these neutrinos will have passed straight through you. Fortunately, we are blissfully unaware of this constant barrage as the weakness of the weak nuclear force ensures hardly any will ever so much as glance off an atom of your body. Still, each of these neutrinos carries precious information about the nuclear reactions going on at the center of the Sun, if only they could be captured.

  The experiment I had come to Italy to see does just that. It’s called Borexino, a gigantic tank containing a liquid hydrocarbon housed in a cavern deep within the Gran Sasso mountain range. The principle of the experiment is easy to understand, even if it is unbelievably hard to pull off in practice. Among the uncountable trillions of neutrinos that constantly pass through the tank, a tiny fraction will collide with electrons, giving them a kick as they pass by. As an electron recoils from the invisible blow, it excites the surrounding liquid, creating a tiny flicker of light, which is captured by an array of detectors encircling the tank. By counting the number of neutrinos and measuring their energies, the physicists at Borexino are able to watch the Sun fusing hydrogen into helium in real time.

  After a few minutes waiting by the security hut in the midday sunshine, Aldo pulled up in his car and greeted me with a handshake. He explained that the heavy police presence was due to an impromptu visit by the Italian finance minister, and all systems were go for our tour of the experiment. To reach Borexino, we first had to drive back onto Autostrada A24 and then straight into the mountainside through the 10-kilometer freeway tunnel. As we drove, Aldo explained that the Gran Sasso laboratory had first been proposed back in the 1970s while the freeway tunnel was being built, with the three huge experimental halls completed in 1987. Meanwhile I did my best to explain to a slightly bemused-looking Aldo what neutrino physics had to do with apple pie; it turns out Carl Sagan isn’t a household name in Italy.

  With the lofty peaks of Gran Sasso towering above us, we passed from the bright Italian afternoon sunshine into the darkness of the mountain. Above us was a gigantic mass of dolomite rock more than a kilometer thick, without which the Borexino experiment would be totally impossible. The Earth is under constant bombardment from high-energy cosmic rays from deep space. When they strike the upper atmosphere, they produce a shower of electrically charged particles, many of which get all the way to ground level. This cosmic avalanche would completely swamp the rare neutrino interactions studied by Borexino were it not for the mighty shield of the Gran Sasso mountain range, which absorbs them almost entirely while allowing neutrinos from the Sun to pass straight through.

  After several minutes driving through the long autostrada tunnel, we took a turn off into a smaller passage that you could easily miss if you didn’t know it was there. In front of us was the entrance to the underground lab, a large stainless-steel door that slowly slid open after Aldo buzzed the intercom. The whole thing felt like entering a Bond villain’s mountain lair.

  We parked in a side tunnel. Stepping out of the car I was hit by the coolness of the air and that particular damp, mineral aroma that I’ve only ever smelled in deep caves. Water dripped from the moss-covered walls of the tunnel as we walked the short distance to present ourselves at security. After signing in and passing me a rather fetching blue hard hat, Aldo led me along another long curving tunnel before we stepped through a steel door into a soaring cavern. We had entered Hall C, the home of Borexino, a huge barrel-vaulted concrete chamber 20 meters across, 18 meters high, and 100 meters long. The low hum of machinery was punctuated by a rhythmic high-pitched chirrup, like the mating call of some giant mechanical cricket. This, Aldo reassured me, was just the sound of the vacuum pumps.

  In front of us were two huge cylindrical tanks, each several stories high, part of the complex plumbing system that feeds Borexino. As we walked toward the towering mass of machinery, Aldo explained that the key challenge that he and his colleagues face comes from natural background radiation. The ground we walk on, the objects that surround us, and even the air we breathe all contain tiny traces of radioactive elements, from uranium and radon to carbon-14. These substances emit a constant background of alpha particles, electrons, and gamma rays. Such low levels are harmless to us but would be fatal to an experiment like Borexino.

  Despite its huge size, Borexino only sees a few dozen neutrinos each day thanks to the weakness of their interaction with ordinary matter. Such a tiny signal would be totally overwhelmed by normal levels of background radiation, and so Aldo and his colleagues wage a constant war against radioactive impurities in the system. The job of the huge network of tanks and pipes that we stood
beneath is to endlessly clean and purify the various liquids inside the Borexino tank, which are distilled and then cleansed of radioactive contaminants using bubbles of highly purified nitrogen gas, before at last being allowed into the experiment. More than that, the material of every component in Borexino had to be carefully selected, manufactured, and tested to produce as little radioactivity as possible. The result of this enormous effort is one of the lowest levels of radiation ever achieved on Earth.

  Climbing a steel gantry, we reached one of Borexino’s control rooms, where Aldo stopped to talk with a colleague who was busy working on the experiment. I had no idea what they were saying—my Italian is barely good enough to order a coffee—but his colleague seemed agitated. Aldo explained afterward that the system used to cool the electronics that read out the data had broken down, and they were working to bring them back online as quickly as possible. Every day of data collecting is precious when you are working with such rare events, and the Borexino team are in a race against time.

  Just a few months earlier, at the end of 2018, the Borexino collaboration had published a comprehensive study of the neutrinos produced by the proton-proton chain, the reaction that provides 99 percent of the Sun’s power. As the proton-proton chain slowly builds helium from hydrogen, neutrinos are released whose energies reveal the stage in the process that they came from. After almost two decades of measuring the numbers and energies of the arriving neutrinos in painstaking detail, the scientists at Borexino had found that the fusion reactions first proposed by Hans Bethe and Charles Critchfield way back in 1938 were going on deep in the heart of the Sun just as they had predicted.

  However, one piece of the puzzle remains—the CNO cycle, the fusion reaction where carbon gradually swallows protons before spitting out a fully formed helium nucleus. This second reaction only produces 1 percent of the Sun’s power, which makes it much harder to see. The prize, though, is huge. If Aldo and his colleagues can detect neutrinos from the CNO cycle, it would be the final verification of one of the oldest mysteries in science: namely, why the Sun shines. More than that, since the CNO cycle is thought to be the main power supply of all stars 1.2 times heavier than the Sun, seeing it going on in nature in real time would be a spectacular coup.