The Science of Interstellar
Page 9
Fig. 9.3. Blandford-Znajek mechanism for generating jets. [Drawing by Matt Zimet based on a sketch by me; from my book Black Holes & Time Warps: Einstein’s Outrageous Legacy.]
In 3C273 only one jet was bright enough to see (Figure 9.1), but in many other quasars both are seen.
Blandford and Znajek worked out the full details, relying heavily on Einstein’s relativistic laws. They were able to explain most everything about the jets that astronomers see.
In a second variant of the explanation (Figure 9.4), the whirling magnetic field is anchored in the accretion disk instead of the hole, and is dragged around by the disk’s orbital motion. Otherwise, the story is the same: dynamo action; plasma flung out. This variant works well even if the black hole isn’t spinning. But we’re pretty sure that most black holes spin fast, so I suspect the Blandford-Znajek mechanism (Figure 9.3) is the most common one in quasars. However, I may be prejudiced. I spent much time in the 1980s exploring aspects of the Blandford-Znajek ideas and even coauthored a technical book about them.
Fig. 9.4. Like Figure 9.3 but with magnetic field anchored in the accretion disk. [Drawing by Matt Zimet based on a sketch by me; from my book Black Holes & Time Warps: Einstein’s Outrageous Legacy.]
Whence Comes the Disk? Tidal Forces Tear Stars Apart
Lynden-Bell, in 1969, speculated that quasars live at the centers of galaxies. We don’t see a quasar’s host galaxy, he said, because its light is so much fainter than the quasar’s light. The quasar drowns the galaxy out. In the decades since then, with improving technology, astronomers have found the galaxy’s light around many quasars, confirming Lynden-Bell’s speculation.
In those recent decades we also learned where most of the disk’s gas comes from. Occasionally a star strays so close to the quasar’s black hole that the hole’s tidal gravity (Chapter 4) tears the star apart. Much of the shredded star’s gas is captured by the black hole and forms an accretion disk, but some of the gas escapes.
In recent years, thanks to improving computer technology, astrophysicists simulated this. Figure 9.5 is from a recent simulation by James Guillochon, Enrico Ramirez-Ruiz, and Daniel Kasen (University of California at Santa Cruz) and Stephan Rosswog (University of Bremen).22 At time zero (not shown) the star was headed almost precisely toward the black hole and the hole’s tidal gravity was beginning to stretch the star toward the hole and squeeze it from the sides, as in Figure 6.1. Twelve hours later the star is strongly deformed and at the location shown in Figure 9.5. Over the next few hours, it swings around the hole along the blue gravitational-slingshot orbit and deforms further as shown. By twenty-four hours the star is flying apart; its own gravity can no longer hold it together.
Fig. 9.5. Tidal disruption of a red giant star by a black hole similar to Gargantua.
The star’s subsequent fate is shown in Figure 9.6, from a different simulation by James Guillochon together with Suvi Gezari (Johns Hopkins University). For a movie of this simulation, see http://hubblesite.org /newscenter /archive /releases /2012 /18 /video /a/.
Fig. 9.6. Subsequent fate of the star in Figure 9.5.
The top two images are shortly before the beginning and shortly after the end of Figure 9.5; I enlarged these two images tenfold compared to the others, to make the hole and the disrupting star visible.
As the whole set of images shows, over the subsequent several years much of the star’s matter is captured into orbit around the black hole, where it begins to form an accretion disk. And the remaining matter escapes from the hole’s gravitational pull along a streaming, jetlike trajectory.
Gargantua’s Accretion Disk and Missing Jet
A typical accretion disk and its jet emit radiation—X-rays, gamma rays, radio waves, and light—radiation so intense that it would fry any human nearby. To avoid frying, Christopher Nolan and Paul Franklin gave Gargantua an exceedingly anemic disk.
Now, “anemic” doesn’t mean anemic by human standards; just by the standards of typical quasars. Instead of being a hundred million degrees like a typical quasar’s disk, Gargantua’s disk is only a few thousand degrees, like the Sun’s surface, so it emits lots of light but little to no X-rays or gamma rays. With gas so cool, the atoms’ thermal motions are too slow to puff the disk up much. The disk is thin and nearly confined to Gargantua’s equatorial plane, with only a little puffing.
Disks like this might be common around black holes that have not torn a star apart in the past millions of years or more—that have not been “fed” in a long time. The magnetic field, originally confined by the disk’s plasma, may have largely leaked away. And the jet, previously powered by the magnetic field, may have died. Such is Gargantua’s disk: jetless and thin and relatively safe for humans. Relatively.
Gargantua’s disk looks quite different from the pictures of thin disks that you see on the web or in astrophysicists’ technical publications, because those pictures omit a key feature: the gravitational lensing of the disk by its black hole. Not so in Interstellar, where Chris insisted on visual accuracy.
Eugénie von Tunzelmann was charged with putting an accretion disk into Oliver James’ gravitational lensing computer code, the code I described in Chapter 8. As a first step, just to see what the lensing does, Eugénie inserted a disk that was truly infinitesimally thin and lay precisely in Gargantua’s equatorial plane. For this book she has provided a more pedagogical version of that disk, made of equally spaced color swatches (Inset in Figure 9.7).
If there had been no gravitational lensing, the disk would have looked like the inset. The lensing produced huge changes from this (body of Figure 9.7). You might have expected the back portion of the disk to be hidden behind the black hole. Not so. Instead, it is gravitationally lensed to produce two images, one above Gargantua and the other below; see Figure 9.8. Light rays emitted from the disk’s top face, behind Gargantua, travel up and over the hole to the camera, producing the disk image that wraps over the top of Gargantua’s shadow in Figure 9.7; and similarly for the disk image that wraps under the bottom of Gargantua’s shadow.
Fig. 9.7. An infinitesimally thin disk in Gargantua’s equatorial plane, gravitationally lensed by Gargantua’s warped space and time. Here Gargantua spins very fast. Inset: The disk in the absence of the black hole. [From Eugénie von Tunzelmann’s artistic team at Double Negative.]
Fig. 9.8. Light rays (red) bring to the camera images of the back part of the accretion disk, behind Gargantua: one image above the hole’s shadow, the other below the hole’s shadow.
Inside these primary images, we see thin secondary images of the disk, wrapping over and under the shadow, near the shadow’s edge. And if the picture were made much larger, you would see tertiary and higher-order images, closer and closer to the shadow.
Can you figure out why the lensed disk has the form you see? Why is the primary image wrapping under the shadow attached to the thin secondary image wrapping over it? Why are the paint swatches on the over-wrapping and under-wrapping images widened so greatly, and those on the sides squeezed? . . .
Gargantua’s space whirl (space moving toward us on the left and away on the right) distorts the disk images. It pushes the disk away from the shadow on the left and toward the shadow on the right, so the disk looks a bit lopsided. (Can you explain why?)
To get further insight, Eugénie von Tunzelmann and her team replaced their variant of the color-swatch disk (Figure 9.7) with a more realistic thin accretion disk: Figure 9.9. This was much more beautiful, but it raised problems. Chris did not want his mass audience to be confused by the lopsidedness of the disk and black-hole shadow, and the shadow’s flat left edge, and the complicated star-field patterns near that edge (discussed in Chapter 8). So he and Paul slowed Gargantua’s spin to 0.6 of the maximum, making these weirdnesses more modest. (Eugénie had already omitted the Doppler shift caused by the disk’s motion tow
ard us on the left and away on the right. It would have made the disk far more lopsided: bright blue on the left and dim red on the right—totally confusing to a mass audience!)
Fig. 9.9 Gargantua with the infinitesimally thin paint-swatch disk (Fig. 9.7) replaced by a more realistic, infinitesimally thin accretion disk. [From Eugénie von Tunzelmann’s artistic team at Double Negative.]
The artistic team at Double Negative then gave the disk the texture and surface relief that we expect a real, anemic accretion disk to have, puffing it up a bit in a manner that varied from place to place. They made the disk hotter (brighter) near Gargantua and cooler (dimmer) at larger distances. They made it thicker at larger distances because it is Gargantua’s tidal gravity that squeezes the disk into the equatorial plane, and tidal gravity is much weaker farther from the black hole. They added the background galaxy: many layers of artwork (dust, nebulae, stars). And they added lens flare—the haze and glare and streaks of light that would arise from scattering of the disk’s bright light in a camera lens. The results were the wonderful and compelling images in the movie (Figures 9.10 and 9.11).
Fig. 9.10. Gargantua and its accretion disk, with Miller’s planet above the disk’s left edge. The disk is so bright that the stars and nebulae are barely visible. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]
Fig. 9.11 A segment of Gargantua's disk seen up close, with the Endurance passing over it. The black region is Gargantua, framed by the disk and with some white scattered light in the foreground. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]
Eugénie and her team also, of course, made the disk’s gas orbit Gargantua, as it must to avoid falling in. When combined with gravitational lensing, the gas’s orbital motion produced the impressive streaming effects in the movie—streaming effects that are hinted at by the gas’s streamlines in Figure 9.11.
What a joy it was when I first saw these images! For the first time ever, in a Hollywood movie, a black hole and its disk depicted as we humans will really see them when we’ve mastered interstellar travel. And for the first time for me as a physicist, a realistic disk, gravitationally lensed, so it wraps over the top and bottom of the hole instead of being hidden behind the hole’s shadow.
With Gargantua’s disk anemic, though gorgeously beautiful, and with no jet, is Gargantua’s environment truly benign? Amelia Brand thinks so . . .
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21 The friction arises through a complex process where moving gas winds the field up, strengthening it and thereby converting energy of motion into magnetic energy; and then the magnetic field, pointing in opposite directions in neighboring regions of space, reconnects and in the process converts magnetic energy into heat. That’s the nature of friction: a conversion of motion into heat.
22 I changed the size of the hole to that of Gargantua and the size of the star to that of a red giant, and changed the time markers in Figure 9.5 accordingly.
10
Accident Is the First Building Block of Evolution
In Interstellar, upon finding Miller’s planet sterile, Amelia Brand argues for going next to a planet very far from Gargantua, Edmunds’ planet, instead of the closer Mann’s planet: “Accident is the first building block of evolution,” she tells Cooper. “But when you’re orbiting a black hole, not enough can happen—it sucks in asteroids and comets, other events that would otherwise reach you. We need to go further afield.”
This is one of the few spots in Interstellar where the characters get the science wrong. Christopher Nolan knew that Brand’s argument was wrong, but he chose to retain these lines from Jonah’s draft of the screenplay. No scientist has perfect judgment.
Although Gargantua tries to suck asteroids and comets into itself, and planets and stars and small black holes too, it rarely succeeds. Why?
When far from Gargantua, any object has a large angular momentum,23 unless its orbit is headed almost directly toward the black hole. That large angular momentum produces centrifugal forces that easily overwhelm Gargantua’s gravitational pull whenever the object’s orbit carries it near the black hole.
A typical orbit has a form like that in Figure 10.1. The object travels inward, pulled by Gargantua’s strong gravity. But before it reaches the horizon, centrifugal forces grow strong enough to fling the object back outward. This happens over and over again, almost endlessly.
The only thing that can intervene is an accidental near encounter with some other massive body (a small black hole or star or planet). The object swings around the other body on a slingshot trajectory (Chapter 7), and thereby is thrown into a new orbit around Gargantua with a changed angular momentum. The new orbit almost always has a large angular momentum, like the old one did, with centrifugal forces that save the object from Gargantua. Very rarely the new orbit carries the object almost directly toward Gargantua, with a small enough angular momentum that centrifugal forces can’t win, so the object plunges through Gargantua’s horizon.
Astrophysicists have carried out simulations of the simultaneous orbital motions of millions of stars around a gigantic black hole like Gargantua. Slingshots gradually change all the orbits and thereby change the density of stars (how many stars there are in some chosen volume). The star density near Gargantua does not go down; it grows. And the density of asteroids and comets will also grow. Random bombardment by asteroids and comets will become more frequent, not less frequent. The environment near Gargantua will become more dangerous for individual life forms, including humans, promoting faster evolution if enough individuals survive.
Fig. 10.1. Typical orbit of an object around a fast-spinning black hole like Gargantua. [From a simulation by Steve Drasco.]
With Gargantua and its dangerous environment under our belts, let’s make a brief change of direction: to Earth and our solar system; to disaster on Earth and the extreme challenge of escaping disaster via interstellar travel.
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23 The angular momentum is the object’s circumferential speed multiplied by its distance from Gargantua; and this angular momentum is important because it is constant along the object’s orbit, even if the orbit is complicated.
III
DISASTER ON EARTH
11
Blight
In 2007, when Jonathan (Jonah) Nolan joined Interstellar as screenwriter, he set the movie in an era when human civilization is a pale remnant of today’s and is being dealt a final blow by blight. Later, when Jonah’s brother Christopher Nolan took over as director, he embraced this idea.
But Lynda Obst, Jonah, and I worried a bit about the scientific plausibility of Cooper’s world, as envisioned by Jonah: How could human civilization decline so far, yet seem so normal in many respects? And is it scientifically possible that a blight could wipe out all edible crops?
I don’t know much about blight, so we turned to experts for advice. I organized a dinner at the Caltech faculty club, the Athenaeum, on July 8, 2008. Great food. Superb wine. Jonah, Lynda, me, and four Caltech biologists with the right mixture of expertise: Elliot Meyerowitz, an expert on plants; Jared Leadbetter, an expert on the diverse microbes that degrade plants; Mel Simon, an expert on the cells that make up plants and how they are affected by microbes; and David Baltimore, a Nobel laureate with a broad perspective on all of biology. (Caltech is a wonderful place. Named the top university in the world by the Times of London in each of the last three years, it is small enough—just 300 professors, 1000 undergrads, and 1200 graduate students—that I know Caltech experts in all branches of science. It was easy to find and recruit the experts we needed for our Blight Dinner.)
As dinner began I placed a microphone at the center of our round table and recorded our two-and-a-half-hour, free-wheeling conversation. This chapter is based on that recording, but I’ve paraphrased what people said—and they checked and approved my paraphrasin
g.
Our final consensus, easily reached, is that Cooper’s world is scientifically possible, but not very likely. It is very unlikely to happen, but it could. That’s why I labeled this chapter for speculative.
Cooper’s World
Over wine and hors d’oevres, Jonah described his vision for Cooper’s world (Figure 11.1): Some combination of catastrophes has reduced the population of North America tenfold or more, and similarly on all other continents. We have become a largely agrarian society, struggling to feed and shelter ourselves. But ours is not a dystopia. Life is still tolerable and in some ways pleasant, with little amenities such as baseball continuing. However, we no longer think big. We no longer aspire to great things. We aspire to little more than just keeping life going.
Fig. 11.1. Aspects of life in Cooper’s world. Top: A baseball game with a dust storm on the horizon. Bottom: Cooper’s home and truck after the storm. [From Interstellar, used courtesy of Warner Bros. Entertainment Inc.]