Death by Black Hole: And Other Cosmic Quandaries - Neil deGrasse Tyson (2014)
SECTION 3. WAYS AND MEANS OF NATURE
Chapter 14. ON BEING DENSE
When I was in the 5th grade, a mischievous classmate asked me the question, “Which weighs more, a ton of feathers or a ton of lead?” No, I was not fooled, but little did I know how useful a critical understanding of density would be to life and the universe. A common way to compute density is, of course, to take the ratio of an object’s mass to its volume. But other types of densities exist, such as the resistance of somebody’s brain to the imparting of common sense or the number of people per square mile who live on an exotic island such as Manhattan.
The range of measured densities within our universe is staggeringly large. We find the highest densities within pulsars, where neutrons are so tightly packed that one thimbleful would weigh about as much as a herd of 50 million elephants. And when a rabbit disappears into “thin air” at a magic show, nobody tells you the thin air already contains over 10,000,000,000,000,000,000,000,000 (ten septillion) atoms per cubic meter. The best laboratory vacuum chambers can pump down to as few as 10,000,000,000 (ten billion) atoms per cubic meter. Interplanetary space gets down to about 10,000,000 (ten million) atoms per cubic meter, while interstellar space is as low as 500,000 atoms per cubic meter. The award for nothingness, however, must be given to the space between galaxies, where it is difficult to find more than a few atoms for every 10 cubic meters.
The range of densities in the universe spans forty-four powers of 10. If one were to classify cosmic objects by density alone, salient features would reveal themselves with remarkable clarity. For example, dense compact objects such as black holes, pulsars, and white dwarf stars all have a high force of gravity at their surfaces and readily accrete matter into a funneling disk. Another example comes from the properties of interstellar gas. Everywhere we look in the Milky Way, and in other galaxies, gas clouds with the greatest density are sites of freshly minted stars. Our detailed understanding of the star formation process remains incomplete, but understandably, nearly all theories of star formation include explicit reference to the changing gas density as clouds collapse to form stars.
OFTEN IN ASTROPHYSICS, especially in the planetary sciences, one can infer the gross composition of an asteroid or a moon simply by knowing its density. How? Many common ingredients in the solar system have densities that are quite distinct from one another. Using the density of liquid water as a measuring unit, frozen water, ammonia, methane, and carbon dioxide (common ingredients in comets) all have a density of less than 1; rocky materials, which are common among the inner planets and asteroids, have densities between 2 and 5; iron, nickel, and several other metals that are common in the cores of planets, and also in asteroids, have densities above 8. Objects with average densities intermediate to these broad groups are normally interpreted as having a mixture of these common ingredients. For Earth we can do a little better: the speed of postearthquake sound waves through Earth’s interior directly relates to the run of Earth’s density from its center to the surface. The best available seismic data give a core density of around 12, dropping to an outer crustal density of around 3. When averaged together, the density of the entire Earth is about 5.5.
Density, mass, and volume (size) come together in the equation for density, so if you measure or infer any two of the quantities then you can compute the third. The planet around the sunlike, naked-eye star 51 Pegasus had its mass and orbit computed directly from the data. A subsequent assumption about whether the planet is gaseous (likely) or rocky (unlikely) allows a basic estimate of the planet’s size.
Often when people claim one substance to be heavier than another, the implicit comparison is one of density, not weight. For example, the simple yet technically ambiguous statement “lead weighs more than feathers” would be understood by nearly everybody to be really a question of density. But this implicit understanding fails in some notable cases. Heavy cream is lighter (less dense) than skim milk, and all seagoing vessels, including the 150,000-ton Queen Mary 2, are lighter (less dense) than water. If these statements were false, then cream and ocean liners would sink to the bottom of the liquids upon which they float.
OTHER DENSITY TIDBITS:
Under the influence of gravity, hot air does not rise simply because it’s hot, but because it’s less dense than the surrounding air. One could similarly declare that cool, denser air sinks, both of which must happen to enable convection in the universe.
Solid water (commonly known as ice) is less dense than liquid water. If the reverse were true, then in the winter, large lakes and rivers would freeze completely, from the bottom to the top, killing all fish. What protects the fish is the floating, less dense, upper layer of ice, which insulates the warmer waters below from the cold winter airs.
On the subject of dead fish, when found belly-up in your fish tank, they are, of course, temporarily less dense than their live counterparts.
Unlike any other known planet, the average density of Saturn is less than that of water. In other words, a scoop of Saturn would float in your bathtub. Knowing this, I have always wanted for my bathtub entertainment a rubber Saturn instead of a rubber ducky.
If you feed a black hole, its event horizon (that boundary beyond which light cannot escape) grows in direct proportion to its mass, which means that as a black hole’s mass increases, the average density within its event horizon actually decreases. Meanwhile, as far as we can tell from our equations, the material content of a black hole has collapsed to a single point of near-infinite density at its center.
And behold the greatest mystery of them all: an unopened can of diet Pepsi floats in water while an unopened can of regular Pepsi sinks.
IF YOU WERE to double the number of marbles in a box, their density would, of course, remain the same because both the mass and the volume would double, which in combination has no net effect on the density. But objects exist in the universe whose density relative to mass and volume yields unfamiliar results. If your box contained soft, fluffy down, and you doubled the number of feathers, then ones on the bottom would become flattened. You would have doubled the mass but not the volume, and you would be left with a net increase in density. All squishable things under the influence of their own weight will behave this way. Earth’s atmosphere is no exception: we find half of all its molecules packed into the lowest three miles above Earth’s surface. To astrophysicists, Earth’s atmosphere forms a bad influence on the quality of data, which is why you often hear about us escaping to mountaintops to conduct research, leaving as much of Earth’s atmosphere below us as possible.
Earth’s atmosphere ends where it blends indistinguishably with the very low density gas of interplanetary space. Normally, this blend lies several thousand miles above Earth’s surface. Note that the space shuttle, the Hubble telescope, and other satellites that orbit within only a few hundred miles of Earth’s surface would eventually fall out of orbit from the residual atmospheric air resistance if they did not receive periodic boosts. During peak solar activity, however (every 11 years) Earth’s upper atmosphere receives a higher dose of solar radiation, forcing it to heat and expand. During this period the atmosphere can extend an extra thousand miles into space, thus decaying satellite orbits faster than usual.
BEFORE LABORATORY VACUUMS, air was the closest thing to nothing that anyone could imagine. Along with earth, fire, and water, air was one of the original four Aristotelian elements that composed the known world. Actually, there was a fifth element known as the “quint”-essence. Otherworldly, yet lighter than air and more ethereal than fire, the rarefied quintessence was presumed to comprise the heavens. How quaint.
We needn’t look as far as the heavens to find rarefied environments. Our upper atmosphere will suffice. Beginning at sea level, air weighs about 15 pounds per square inch. So if you cookie cut a square inch of atmosphere from thousands of miles up all the way down to sea level and you put it on a scale, it would weigh 15 pounds. For comparison, a square-inch column of water requires a mere 33 feet to weigh 15 pounds. On mountaintops and high up in airplanes, the cookie-cut column of air above you is shorter and therefore weighs less. At the 14,000-foot summit of Mauna Kea, Hawaii, home to some of the world’s most powerful telescopes, the atmospheric pressure drops to about 10 pounds per square inch. While observing on site, astrophysicists will intermittently breathe from oxygen tanks to retain their intellectual acuity.
Above 100 miles, where there are no known astrophysicists, the air is so rarefied that gas molecules move for a relatively long time before colliding with one another. If, between collisions, the molecules are slammed by an incoming particle, they become temporarily excited and then emit a unique spectrum of colors before their next collision. When the incoming particles are the constituents of the solar wind, such as protons and electrons, the emissions are curtains of undulating light that we commonly call aurora. When the spectrum of auroral light was first measured, it had no counterpart in the laboratory. The identity of the glowing molecules remained unknown until we learned that excited, but otherwise ordinary, molecules of nitrogen and oxygen were to blame. At sea level, their rapid collisions with each other absorb this excess energy long before they have had a chance to emit their own light.
Earth’s upper atmosphere is not alone in producing mysterious lights. Spectral features in the Sun’s corona long puzzled astrophysicists. An extremely rarefied place, the corona is that beautiful, fiery-looking outer region of the Sun that’s rendered visible during a total solar eclipse. The new feature was assigned to an unknown element dubbed “coronium.” Not until we learned that the solar corona is heated to millions of degrees did we figure out that the mystery element was highly ionized iron, a previously unfamiliar state where most of its outer electrons are stripped away and floating free in the gas.
The term “rarefied” is normally reserved for gases, but I will take the liberty to apply it to the solar system’s famed asteroid belt. From movies and other descriptions, you would think it was a hazardous place, wrought with the constant threat of head-on collisions with house-sized boulders. The actual recipe for the asteroid belt? Take a mere 2.5 percent of the Moon’s mass (itself, just 1/81 the mass of Earth), crush it into thousands of assorted pieces, but make sure that three-quarters of the mass is contained in just four asteroids. Then spread them all across a 100-million-mile-wide belt that tracks along a 1.5-billion-mile path around the Sun.
COMET TAILS, as tenuous and rarefied as they are, represent an increase in density by a factor of 1,000 over the ambient conditions in interplanetary space. By reflecting sunlight and re-emitting energy absorbed from the Sun, a comet tail possesses remarkable visibility given its nothingness. Fred Whipple, of the Harvard-Smithsonian Center for Astrophysics, is generally considered to be a parent of our modern understanding of comets. He has succinctly described a comet’s tail as the most that has ever been made of the least. Indeed, if the entire volume of a 50-million-mile-long comet tail were compressed to the density of ordinary air, all the tail’s gas would fill a half-mile cube. When the astronomically common yet deadly gas cyanogen (CN) was first discovered in comets, and when it was later announced that Earth would pass through the tail of Halley’s comet during its 1910 visit to the inner solar system, gullible people were sold anticomet pills by pharmaceutical charlatans.
The core of the sun, where all its thermonuclear energy is generated, is not a place to find low-density material. But the core comprises a mere 1 percent of the Sun’s volume. The average density of the entire Sun is only one-fourth that of Earth, and only 40 percent higher than ordinary water. In other words, a spoonful of Sun would sink in your bathtub, but it wouldn’t sink fast. Yet in 5 billion years the Sun’s core will have fused nearly all its hydrogen into helium and will shortly thereafter begin to fuse helium into carbon. Meanwhile, the luminosity of the Sun will increase a thousandfold while its surface temperature drops to half of what it is today. We know from the laws of physics that the only way an object can increase its luminosity while simultaneously getting cooler is for it to get bigger. As will be detailed in Section 5, the Sun will ultimately expand to a bulbous ball of rarefied gas that will completely fill and extend beyond the volume of Earth’s orbit, while the Sun’s average density falls to less than one ten-billionth of its current value. Of course Earth’s oceans and atmosphere will have evaporated into space and all life will have vaporized, but that needn’t concern us here. The Sun’s outer atmosphere, rarefied though it will be, would nonetheless impede the motion of Earth in its orbit and force us on a relentless spiral inward toward thermonuclear oblivion.
BEYOND OUR SOLAR SYSTEM we venture into interstellar space. Humans have sent four spacecraft with enough speed to journey there: Pioneer 10 and 11, and Voyager 1 and 2. The fastest among them, Voyager 2, will reach the distance of the nearest star to the Sun in about 25,000 years.
Yes, interstellar space is empty. But like the remarkable visibility of rarefied comet tails in interplanetary space, gas clouds out there, with a hundred to a thousand times the ambient density, can readily reveal themselves in the presence of nearby luminous stars. Once again, when the light from these colorful nebulosities was first analyzed their spectra revealed unfamiliar patterns. The hypothetical element “nebulium” was proposed as a placeholder for our ignorance. In the late 1800s, there was clearly no spot on the periodic table of elements that could possibly be identified with nebulium. As laboratory vacuum techniques improved, and as unfamiliar spectral features became routinely identified with familiar elements, suspicions grew—and were later confirmed—that nebulium was ordinary oxygen in an extraordinary state. What state was that? The atoms were each stripped of two electrons and they lived in the near-perfect vacuum of interstellar space.
When you leave the galaxy, you leave behind nearly all gas and dust and stars and planets and debris. You enter an unimaginable cosmic void. Let’s talk empty: A cube of intergalactic space, 200,000 kilometers on a side, contains about the same number of atoms as the air that fills the usable volume of your refrigerator. Out there, the cosmos not only loves a vacuum, it’s carved from it.
Alas, an absolute, perfect vacuum may be impossible to attain or find. As we saw in Section 2, one of the many bizarre predictions of quantum mechanics holds that the real vacuum of space contains a sea of “virtual” particles that continually pop in and out of existence along with their antimatter counterparts. Their virtuality comes from having lifetimes that are so short that their direct existence cannot ever be measured. More commonly known as the “vacuum energy,” it can act as antigravity pressure that will ultimately trigger the universe to expand exponentially faster and faster—making intergalactic space all the more rarefied.
What lies beyond?
Among those who dabble in metaphysics, some hypothesize that outside the universe, where there is no space, there is no nothing. We might call this hypothetical, zero-density place, nothing-nothing, except that we are certain to find multitudes of unretrieved rabbits.