astronomy, physics, science, Space, thought experiment

If the Sun went Supernova

I have to preface this article by saying that yes, I know I’m hardly the first person to consider this question.

I also have to add that, according to current physics (as of this writing in December 2017), the Sun won’t ever go supernova. It’s not massive enough to produce supernova conditions. But hey, I’ll gladly take any excuse to talk about supernovae, because supernovae are the kind of brain-bending, scary-as-hell, can’t-wrap-your-feeble-meat-computer-around-it events that make astronomy so creepy and amazing.

So, for the purposes of this thought experiment, let’s say that, at time T + 0.000 seconds, all the ingredients of a core-collapse supernova magically appear at the center of the Sun. What would that look like, from our point of view here on Earth? Well, that’s what I’m here to find out!

From T + 0.000 seconds to 499.000 seconds

This is the boring period where nothing happens. Well, actually, this is the nice period where life on Earth can continue to exist, but astrophysically, that’s pretty boring. Here’s what the Sun looks like during this period:

Normal Sun.png

Pretty much normal. Then, around 8 minutes and 19 seconds (499 seconds) after the supernova, the Earth is hit by a blast of radiation unlike anything ever witnessed by humans.

Neutrinos are very weird, troublesome particles. As of this writing, their precise mass isn’t known, but it’s believed that they do have mass. And that mass is tiny. To get an idea of just how tiny: a bacterium is about 45 million times less massive than a grain of salt. A bacterium is 783 billion times as massive as a proton. Protons are pretty tiny, ghostly particles. Electrons are even ghostlier: 1836 times less massive than a proton. (In a five-gallon / 19 liter bucket of water, the total mass of all the electrons is about the mass of a smallish sugar cube; smaller than an average low-value coin.)

As of this writing (December 2017, once again), the upper bound on the mass of a neutrino is 4.26 million times smaller than the mass of an electron. On top of that, they have no electric charge, so the only way they can interact with ordinary matter is by the mysterious weak nuclear force. They interact so weakly that (very approximately), out of all the neutrinos that pass through the widest part of the Earth, only one in 6.393 billion will collide with an atom.

But, as XKCD eloquently pointed out, supernovae are so enormous and produce so many neutrinos that their ghostliness is canceled out. According to XKCD’s math, 8 minutes after the Sun went supernova, every living creature on Earth would absorb something like 21 Sieverts of neutrino radiation. Radiation doses that high have an almost 100% mortality rate. You know in Hollywood how they talk about the “walking ghost” phase of radiation poisoning? Where you get sick for a day or two, and then you’re apparently fine until the effects of the radiation catch up with you and you die horribly? At 21 Sieverts, that doesn’t happen. You get very sick within seconds, and you get increasingly sick for the next one to ten days or so, and then you die horribly. You suffer from severe vomiting, diarrhea, fatigue, confusion, fluid loss, fever, cardiac complications, neurological complications, and worsening infections as your immune system dies. (If you’re brave and have a strong stomach, you can read about what 15-20 Sieverts/Gray did to a poor fellow who was involved in a radiation accident in Japan. It’s NSFW. It’s pretty grisly.)

But the point is that we’d all die when the neutrinos hit. I’m no religious scholar, but I think it’d be appropriate to call the scene Biblical. It’d be no less scary than the scary-ass shit that happens in in Revelation 16. (In the King James Bible, angels pour out vials of death that poison the water, the earth, and the Sun, and people either drop dead or start swearing and screaming.) In our supernova Armageddon, the air flares an eerie electric blue from Cherenkov radiation, like this…

685px-Advanced_Test_Reactor

(Source.)

…and a few seconds later, every creature with a central nervous system starts convulsing. Every human being on the planet starts explosively evacuating out both ends. If you had a Jupiter-sized bunker made of lead, you’d die just as fast as someone on the surface. In the realm of materials humans can actually make, there’s no such thing as neutrino shielding.

But let’s pretend we can ignore the neutrinos. We can’t. They contain 99% of a supernova’s energy output (which is why they can kill planets despite barely interacting with matter). But let’s pretend we can, because otherwise, the only spectators will be red, swollen, feverish, and vomiting, and frankly, I don’t need any new nightmares.

T + 499.000 seconds to 568.570 seconds (8m13s to 9m28.570s)

If we could ignore the neutrino radiation (we really, really can’t), this would be another quiet period. That’s kinda weird, considering how much energy was just released. A typical supernova releases somewhere in the neighborhood of 1 × 10^44 Joules, give or take an order of magnitude. The task of conveying just how much energy that is might be beyond my skills, so I’m just going to throw a bunch of metaphors at you in a panic.

According to the infamous equation E = m c^2, 10^44 Joules would mass 190 times as much as Earth. The energy alone would have half the mass of Jupiter. 10^44 Joules is (roughly) ten times as much energy as the Sun will radiate in its remaining 5 billion years. If you represented the yield of the Tsar Bomba, the largest nuclear device ever set off, by the diameter of a human hair, then the dinosaur-killing (probably) Chicxulub impact would stretch halfway across a football field, Earth’s gravitational binding energy (which is more or less the energy needed to blow up the planet) would reach a third of the way to the Sun, and the energy of a supernova would reach well past the Andromeda galaxy. 1 Joule is about as much energy as it takes to pick up an egg, a golf ball, a small apple, or a tennis ball (assuming “pick up” means “raise to 150 cm against Earth gravity.”) A supernova releases 10^44 of those Joules. If you gathered together 10^44 water molecules, they’d form a cube 90 kilometers on an edge. It would reach almost to the edge of space. (And it would very rapidly stop being a cube and start being an apocalyptic flood.)

Screw it. I think XKCD put it best: however big you think a supernova is, it’s bigger than that. Probably by a factor of at least a million.

And yet, ignoring neutrino radiation (we really can’t do that), we wouldn’t know anything about the supernova until nine and a half minutes after it happened. Most of that is because it takes light almost eight and a quarter minutes to travel from Sun to Earth. But ionized gas is also remarkably opaque to radiation, so when a star goes supernova, the shockwave that carries the non-neutrino part of its energy to the surface only travels at about 10,000 kilometers per second. That’s slow by astronomical standards, but not by human ones. To get an idea of how fast 10,000 kilometers per second is, let’s run a marathon.

At the same moment, the following things leave the start line: Usain Bolt at full sprint (10 m/s), me in my car (magically accelerating from 0 MPH to 100 MPH in zero seconds), a rifle bullet traveling at 1 kilometer per second (a .50-caliber BMG, if you want to be specific), the New Horizons probe traveling at 14 km/s (about as fast as it was going when it passed Pluto), and a supernova shockwave traveling at 10,000 km/s.

Naturally enough, the shockwave wins. It finishes the marathon (which is roughly 42.195 kilometers) in 4.220 milliseconds. In that time, New Horizons makes it 60 meters. The bullet has traveled just under 14 feet (422 cm). My car and I have traveled just over six inches (19 cm). Poor Usain Bolt probably isn’t feeling as speedy as he used to, since he’s only traveled an inch and a half (4.22 cm). That’s okay, though: he’d probably die of exhaustion if he ran a full marathon at maximum sprint. And besides, he’s about to be killed by a supernova anyway.

T + 569 seconds

If you’re at a safe distance from a supernova (which is the preferred location), the neutrinos won’t kill you. If you don’t have a neutrino detector (Ha ha!), when a supernova goes off, the first detectable sign is the shock breakout: when the shockwave reaches the star’s surface. Normally, it takes in the neighborhood of 20 hours before the shock reaches the surface of its parent star. That’s because supernovas (at least the core-collapse type we’re talking about) usually happen inside enormous, bloated supergiants. If you put a red supergiant where the Sun is, then Jupiter would be hovering just above its surface. They’re that big.

The Sun is much smaller, and so it only takes a couple minutes for the shock to reach the surface. And when it does, Hell breaks loose. There’s a horrific wave of radiation trapped behind the opaque shock. When it breaks out, it heats it to somewhere between 100,000 and 1,000,000 Kelvin. Let’s split the difference and say 500,000 Kelvin. A star’s luminosity is determined by two things: its temperature and its surface area. At the moment of shock breakout, the Sun has yet to actually start expanding, so its surface area remains the same. Its temperature, though, increases by a factor of almost 100. Brightness scales in proportion to the fourth power of temperature, so when the shock breaks out, the Sun is going to shine something like 56 million times brighter. Shock breakout looks something like this:

Sun Shock Breakout.png

But pretty soon, it looks like this:

Sun Supernova.blend

Unsurprisingly, this ends very badly for everybody on the day side. Pre-supernova, the Earth receives about 1,300 watts per square meter. Post-supernova, that jumps up to 767 million watts per square meter. To give you some perspective: that’s roughly 700 times more light than you’d be getting if you were currently being hit in the face by a one-megaton nuclear fireball. Once again: However big you think a supernova is, it’s bigger than that.

All the solids, liquids, and gases on the day side very rapidly start turning into plasma and shock waves. But things go no better for people on the night side. Let’s say the atmosphere scatters or absorbs 10% of light after passing through its 100 km depth. That means that, after passing through one atmosphere-depth, 90% of the light remains. Since the distance, across the Earth’s surface, to the point opposite the sun is about 200 atmosphere-depths, that gives us an easy equation for the light on the night side: [light on the day side] * (0.9)^200. (10% is approximate. After searching for over an hour, I couldn’t find out exactly how much light the air scatters, and although there are equations for it, I was getting a headache. Rayleigh scattering is the relevant phenomenon, if you’re looking for the equations to do the math yourself).

On the night side, even after all that atmospheric scattering, you’re still going to burn to death. You’ll burn to death even faster if the moon’s up that night, but even if it’s not, enough light will reach you through the atmosphere alone that you’ll burn either way. If you’re only getting light via Rayleigh scattering, you’re going to get something like 540,000 watts per square meter. That’s enough to set absolutely everything on fire. It’s enough to heat everything around you to blowtorch temperatures. According to this jolly document, that’s enough radiant flux to give you a second-degree burn in a tenth of a second.

T + 5 minutes to 20 minutes

We live in a pretty cool time, space-wise. We know what the surfaces of Pluto, Vesta, and Ceres look like. We’ve landed a probe on a comet. Those glorious lunatics at SpaceX just landed a booster that had already been launched, landed, and refurbished once. And we’ve caught supernovae in the act of erupting from their parent stars. Here’s a graph, for proof:

breakout_sim-ws_v6.png

(Source. Funnily enough, the data comes from the awesome Kepler planet-hunting telescope.)

The shock-breakout flash doesn’t last very long. That’s because radiant flux scales with the fourth power of temperature, so if something gets ten times hotter, it’s going to radiate ten thousand times as fast, which means, in a vacuum, it’s going to cool ten thousand times faster (without an energy source). So, that first bright pulse is probably going to last less than an hour. But during that hour, the Earth’s going to absorb somewhere in the neighborhood of 3×10^28 Joules of energy, which is enough to accelerate a mass of 4.959×10^20 kg. to escape velocity. In other words: that sixty-minute flash is going to blow off the atmosphere and peel off the first 300 meters of the Earth’s crust. Still better than a grisly death by neutrino poisoning.

T + 20 minutes to 4 hours

This is another period during which things get better for a little while. Except for the fact that pretty much everything on the Earth’s surface is either red-hot or is now part of Earth’s incandescent comet’s-tail atmosphere, which contains, the plants, the animals, most of the surface, and you and me. “Better” is relative.

It doesn’t take long for the shock-heated sun to cool down. The physics behind this is complicated, and I don’t entirely understand it, if I’m honest. But after it cools, we’re faced with a brand-new problem: the entire mass of the sun is now expanding at between 5,000 and 10,000 kilometers per second. And its temperature only cools to something like 6,000 Kelvin. So now, the sun is growing larger and larger and larger, and it’s not getting any cooler. We’re in deep dookie.

Assuming the exploding sun is expanding at 5,000 km/s, it only takes two and a quarter minutes to double in size. If it’s fallen back to its pre-supernova temperature (which, according to my research, is roughly accurate), that means it’s now four times brighter. Or, if you like, it’s as though Earth were twice as close. Earth is experiencing the same kind of irradiance that Mercury once saw. (Mercury is thoroughly vaporized by now.)

In 6 minutes, the Sun has expanded to four times its original size. It’s now 16 times brighter. Earth is receiving 21.8 kilowatts per square meter, which is enough to set wood on fire. Except that there’s no such thing as wood anymore, because all of it just evaporated in the shock-breakout flash.

At sixteen and a quarter minutes, the sun has grown so large that, even if you ignored the earlier disasters, the Earth’s surface is hot enough to melt aluminum.

The sun swells and swells in the sky. Creepy mushroom-shaped plumes of radioactive nickel plasma erupt from the surface. The Earth’s crust, already baked to blackened glass, glows red, then orange, then yellow. The scorched rocks melt and drip downslope like candle wax. And then, at four hours, the blast wave hits. If you thought things couldn’t get any worse, you haven’t been paying attention.

T + 4 hours

At four hours, the rapidly-expanding Sun hits the Earth. After so much expansion, its density has decreased by a factor of a thousand, or thereabouts. Its density corresponds to about the mass of a grain of sand spread over a cubic meter. By comparison, a cubic meter of sea-level air contains about one and a quarter kilograms.

But that whisper of hydrogen and heavy elements is traveling at 5,000 kilometers per second, and so the pressure it exerts on the Earth is shocking: 257,000 PSI, which is five times the pressure it takes to make a jet of abrasive-laden water cut through pretty much anything (there’s a YouTube channel for that). The Earth’s surface is blasted by winds at Mach 600 (and that’s relative to the speed of sound in hot, thin hydrogen; relative to the speed of sound in ordinary air, it’s Mach 14,700). One-meter boulders are accelerated as fast as a bullet in the barrel of a gun (according to the formulae, at least; what probably happens is that they shatter into tiny shrapnel like they’ve been hit by a gigantic sledgehammer). Whole hills are blown off the surface. The Earth turns into a splintering comet. The hydrogen atoms penetrate a full micron into the surface and heat the rock well past its boiling point. The kinetic energy of all that fast-moving gas delivers 10^30 watts per second, which is enough to sand-blast the Earth to nothing in about three minutes, give or take.

T + 4 hours to 13h51m

And the supernova has one last really mean trick up its sleeve. If a portion of the Earth survives the blast (I’m not optimistic), then suddenly, that fragment’s going to find itself surrounded on all sides by hot supernova plasma. That’s bad news. There’s worse news, though: that plasma is shockingly radioactive. It’s absolutely loaded with nickel-56, which is produced in huge quantities in supernovae (we’re talking up to 5% of the Sun’s mass, for core-collapse supernovae). Nickel-56 is unstable. It decays first to radioactive cobalt-56 and then to stable iron-56. The radioactivity alone is enough to keep the supernova glowing well over a million times as bright as the sun for six months, and over a thousand times as bright as the sun for over two years.

A radiation dose of 50 Gray will kill a human being. The mortality rate is 100% with top-grade medical care. The body just disintegrates. The bone marrow, which produces the cells we need to clot our blood and fight infections, turns to sterile red soup. 50 Gray is equivalent to the deposition of 50 joules of radiation energy per kilogram. That’s enough to raise the temperature of a kilo of flesh by 0.01 Kelvin, which you’d need an expensive thermometer to measure. Meanwhile, everything caught in the supernova fallout is absorbing enough radiation to heat it to its melting point, to its boiling point, and then to ionize it to plasma. A supernova remnant is insanely hostile to ordinary matter, and doubly so to biology. If the Earth hadn’t been vaporized by the blast-wave, it would be vaporized by the gamma rays.

And that’s the end of the line. There’s a reason astronomers were so shocked to discover planets orbiting pulsars: pulsars are born in supernovae, and how the hell can a planet survive one of those?

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All kinds of explosions.

As you’ve probably worked out by now, I’m a big fan of explosions. Since this ridiculous blog began, I’ve blown up rabbits (don’t worry–hypothetical rabbits), stellar-mass balls of gold, grains of neutronium, and I’ve nearly blown up the earth with an ultrarelativistic BB gun. As you’ve probably also figured out, I’m a big fan of bizarre thought experiments, thought experiments based on ideas boiled and distilled down to their absolute essentials. With that in mind, let’s blow some more shit up!

But before we can get started, we have to decide what an explosion is. For the purpose of this thought experiment, we’re going to use a one-meter-diameter sphere of space anchored to the surface of the Earth, just touching the ground. The explosions will consist of energy (in the form of photons of an appropriate wavelength) magically teleported into this sphere. (I still haven’t decided what symbol to use for the magic teleporter in my Feynman diagrams.) With that cleared up, let’s get blastin’.

The smallest possible explosion.

It’s pretty difficult to decide on the lower limit for the size of a one-meter-diameter explosion. First of all, that one-meter sphere is already full of all kinds of energy: solar photons, the kinetic energy of air molecules moving at high speeds, the rest-mass energy of those air molecules, et cetera. But even if the sphere were completely evacuated, quantum mechanics tells us that the lowest amount of energy that a volume of space can possess is greater than zero: its zero-point energy or vacuum energy.

To simplify things (and to keep me from having to learn the entirety of gauge field theory while writing a blog post), we’re going to say that the lowest-energy explosion we can create has the energy of the longest-wavelength (and therefore lowest-energy) photon we can fit in the sphere: 1 meter. That’s towards the high-frequency (short-wavelength) end of the radio spectrum. It’s not quite a microwave (those have wavelengths on the order of a centimeter), but it’s shorter than the photons used to transmit FM radio signals. Needless to say, it would impart a pretty much un-measurable quantity of energy to our sphere of air. A 1-meter photon carries 1.986×10e-25 joules of energy, the same energy as an oxygen molecule puttering along at a grandmotherly 6 miles per hour (10 kph).

The most efficient possible explosion.

But while we’re using our magic vacuum-fluctuation laser (lots of magic in this article…), we might as well see how big an explosion we can make with a single photon. We know the minimum is 1.986×10e-25 joules. But what’s the highest-energy photon we can stick in there? (Sounds like a plot to a horrible science porno…) I’m not a physicist, but I would guess that it’s a photon with a wavelength of 1 Planck length. Here’s my logic: the Planck length is the smallest length that makes sense according to our current laws of physics. To carry energy, an electromagnetic wave must change over time (or space, which work out to be part of the same thing). In order to take two different values, the wave’s crest and trough must be at least 1 Planck length apart. Of course, weird things happen on the Planck scale, so who knows if an electromagnetic field varying by a large quantity over 1 planck length would even make sense, or even behave like a photon, but you can say this with some certainty: a photon with a wavelength shorter than that doesn’t make a lot of sense.

A photon with a wavelength this short would be off-scale, as far as the electromagnetic spectrum goes. By definition, it would be a hard gamma ray, but that’s only because we humans don’t have access to the high-energy regions of the spectrum, so we say “Anything with a wavelength between A and B is an X-ray. Anything with a wavelength between B and zero is a gamma ray. Stupid gamma rays. Who needs ’em?”

This is a gross oversimplification, but photons tend to prefer to interact with objects that are roughly their same size. Visible photons interact with the electron clouds of  large molecules (like chlorophyll, which is good if you like oxygen). Infrared photons interact with large molecules directly, making them rotate or move. Radio-frequency photons interact only with big crowds of mobile electrons, like you find in plasma or radio antennas. In the other direction, ultraviolet photons interact with atoms and their bonds, either knocking outer electrons loose or breaking the bonds. X-ray photons interact with the tightly-bound electrons in lower energy states (I’m afraid to say “closer to the nucleus,” because that’s not quite right, and people smarter than me will make fun of me; but we’ll pretend that’s how it works to speed things along). Gamma-ray photons interact with the nucleus directly. They can push the nucleus into strange high-energy states or, if they’re the right wavelength, pelt protons and neutrons loose.

The physics of extremely short-wavelength gamma rays is much more complicated. That’s partly because, once a gamma ray passes an energy greater than 1022 keV (the kinds of energies you get when you heat something to several billion Kelvin) have enough mass-energy that they can spontaneously turn into matter: a 1023 keV gamma ray can briefly become an electron and a positron, which rapidly annihilate to re-form the gamma ray. The higher your photon’s energy gets, the more important these bizarre transformations become. Basically, once you get above 1022 keV, your photons start behaving less and less like light and more and more like matter.

Our Planck-length photon would (probably) be small enough to pass through all ordinary matter. It might pop a quark loose of a proton or a neutron, but I don’t really know. This photon would carry an energy far greater than 1022 keV. Indeed, its energy wouldn’t be measured in the peculiar particle-physics unit of the electronvolt, but rather in freakin’ megawatt-hours. This photon would add as much energy to our sphere as the explosion of three tons of TNT, which would form a cube large enough to contain our sphere with room to spare. From one…single…photon. Physics is scary.

Explosions, both conventional and nuclear (ain’t I posh?).

If you Google the phrase “largest conventional explosion,” you’ll probably dig up an article on Operation Sailor Hat, in which the U.S. Navy built a 500-ton Minecraft-style sphere of TNT:

It made a real mess of the decommissioned test ships anchored just offshore, and left a crater in Hawai’i that still exists to this day. It remains one of the largest intentional non-nuclear explosions humans have ever created. This isn’t relevant to our thought experiment, but I’m easily distracted by 500-ton piles of TNT.

In everyday life, a “conventional explosion” is one created by a chemical reaction of some kind. This ranges from the rapid burning of a lot of wheat dust in a grain silo to the bizarre high-tech cube-shaped molecule octanitrocubane. An explosion that gets most of its power from the fission of radioactive elements (or the fusion of light elements) is a nuclear explosion. Simple.

But you can think of it another way: the difference between conventional chemical explosions and nuclear explosions is a matter of temperature. Explosives like TNT produce gases with temperatures of thousands of degrees Kelvin. Nuclear explosions produce temperatures in the million to hundred million Kelvin range.

Since we’ve got a magic sphere of air we can pump energy into (how convenient!), let’s make one of each kind of explosion!

For the conventional explosion, we’ll heat the air to a temperature of 5,000 Kelvin (about as hot as the surface of the sun). Our sphere has a volume of 0.52 cubic meters, and air has a volumetric heat capacity of about 0.001 joules per cubic centimeter per Kelvin. Therefore, heating the air to 5,000 kelvin will require 2.6 million joules. We’re talking about a decent-sized bang here, equivalent to just over half a kilogram of TNT. Not exactly spectacular, but certainly not the kind of explosion you want to hold in your hand. (Actually, thinking about it, why would you want to hold any explosion in your hand? That was silly of me.)

For the nuclear explosion, we’ll heat our sphere to 10 million Kelvin, which is a compromise, since nuclear explosions are complicated beasties and their temperature varies very rapidly in the span of microseconds. I should point out that I’m still using a volumetric heat capacity of 0.001 joules per cubic centimeter per Kelvin, which is absurd. At these temperatures, we’re not just making molecules move faster–we’re breaking them apart. And blasting electrons off the individual atoms. Both of these things take energy, so heating the plasma to 10 million Kelvin will actually require more energy input than my idealized equation suggests. But I digress. We’re looking at an explosive energy of about 5.2 billion Joules, which is about one and a quarter tons of TNT. I’m disappointed. Even the smallest nuclear weapon ever made had a yield larger than that. (Incidentally, the smallest nuclear weapon ever made (by the U.S., at least) was the W54 warhead. This is what they used in the “Davy Crockett,” which was a nuclear warhead launched from a fucking bazooka. Think about that.)

But the real temperature of a young nuclear fireball (good name for a band) is probably higher than this. After the fission of the nuclear material is complete, there’s a brief period where the nuclear explosion is mostly made up of high-energy nuclear radiation (hard x-rays, gamma rays, and particles). Then, it gets absorbed by the evaporating bomb casing and the surrounding air and (mostly) turns into heat. It’s not unreasonable to assume that the temperature in a baby nuclear fireball (bad idea for a child’s doll) is closer to 100 million Kelvin, which works out to almost twelve and a half tons of TNT. Still not nuclear in the traditional sense, but certainly more than enough to bust up a whole city block.

Turning it up to 10.

I’m tired of messing around. I want a real boom. We’re sticking a full megaton into that sphere, and damn the consequences!

Well, with energy densities this high, you can’t really even pretend that the volumetric heat capacity equation applies. Even at 100 million Kelvin, we were getting into the region where atoms are stripped of most or all of their electrons, which is where matter stops behaving even remotely the way it does at ambient temperatures. Much hotter, and we’re going to start splitting the atoms themselves.

Instead, to describe the conditions in our magic sphere when 1 megaton is pumped into it, I’m going to make two assumptions: the energy is deposited over the course of 1 nanosecond, and the superheated sphere radiates like a thermodynamic blackbody, which is to say the same way red-hot steel does and stars (mostly) do.

An energy release of 1 megaton over 1 nanosecond gives us 4.184 trillion trillion watts of radiated power. The sphere will very briefly shine as bright as a small star, and will have a surface temperature of 69 million Kelvin. Then, ba-boom, say goodbye to your city. Next time you build a city, don’t go letting people like me build magic energy-spheres in the middle. I hope you’ve learned your lesson.

This thing goes to 11.

Sorry. Couldn’t help myself.

Let’s stick in 50 megatons now. That’s about the energy released by the Tsar Bomba, a Soviet hydrogen bomb that produced a mushroom cloud that rose above the top of the stratosphere. For comparison, really impressive explosions and big thunderstorms and volcanic eruptions and such are lucky if they can make it into the stratosphere at all, let alone breaking all the way through the damn thing.

I can do all the math here just like before: 210 trillion trillion watts, a temperature of 185 million Kelvin, yadda yadda yadda. The thing is, as I wrote in “A Piece of a Neutron Star“, up to a point, an explosion is an explosion. The energy of an explosion gets spread over a large volume fairly quickly, and ordinary fluid dynamics and thermodynamics take over. Ever notice how a conventional explosive produces a mushroom cloud that looks an awful lot like the mushroom from a nuclear explosion? That’s because both are powered by the same thing: a rising plume of hot air. While it’s true that in the nuclear explosion there’s a lot more air and it’s a hell of a lot hotter, it’s easy to see that the two are related. They’re part of the same spectrum. A nuclear explosion is like a conventional explosion, only it’s larger, and it produces a lot more radiant heat.

This thing goes to 111.

This scaling law (which real physicists have investigated in great detail) seems to hold for larger and larger energies. Small asteroid impacts create explosions that are very much like nuclear explosions (with some extra effects from high-velocity ejecta and from the entry trail and so on). Even impacts like Chicxulub (which may or may not have helped kill off the dinosaurs, but certainly ruined everybody’s day for several thousand years) produce a fairly ordinary shockwave, and then a fireball that reaches an enormous, but reasonable, size before cooling to ordinary temperatures. The excellent Impact Effects Calculator tells me that a Chicxulub-like impact would produce a visible fireball with a radius of about 66 kilometers. This would reach up through the stratosphere, and about halfway to the edge of space, so it would probably be flattened, with a blurry, undefined edge at the top, but it would still be very much like what it is: a 100 million megaton explosion.

But like all scaling laws, the explosion spectrum eventually gives out. Once you start imagining blasts with the same kinetic energy as, say, a 100-kilometer-wide stone asteroid, you’ve passed over a threshold. Beyond this threshold, the assumptions that let us imagine our earlier explosions break down. Assumptions like “Shockwaves and heat plumes travel through the atmosphere, but the atmosphere doesn’t go flying off or anything” and “The crust is firmly attached to the rest of the Earth.” (It’s nice that we live in a time when we can make assumptions like that. Not that we could live in a time when the crust wasn’t attached, but it’s nice to know we (probably) have that kind of stability). We move out of the realms of meteorology and geology and into the realms of astrophysics. When you talk about 100-kilometer asteroid impacts, you’re no longer talking about “an asteroid hitting the Earth.” You’re talking about “two celestial bodies colliding.” Things like organic life and atmospheres crumble (and burn and evaporate) before energies like this.

Which is a (very) roundabout way of saying that a 90-billion-megaton explosion isn’t really an explosion anymore. It’d blow the atmosphere off a pretty big portion of the planet, peel back the crust, and pave some or all of the Earth in magma. Larger explosions could put sizeable dents in the Earth, or blow off enough material to push it into a different orbit. Not that we care: we’ll all be dead. Again. Sorry. Planet-killing is a bad addiction to have.

Hey! Where’d my explosion go?

This transition from fluid dynamics to astrodynamics has an ultimate limit. You can only squeeze so much energy into a 1-meter-diameter sphere and have it come back out. For this, you have Albert Einstein and Karl Schwarzschild to thank.

Energy and mass are equivalent. Not only can one be converted into the other, but they also produce and react to gravity in the same way. Because of this, if you try to cram more than 3.029e43 Joules (7239 trillion trillion megatons) of energy into a sphere 1 meter across, you won’t get an explosion at all. Your energy, no matter what form it’s in, will vanish behind an event horizon. This is bad news for the Earth. Partly because this energy will weigh 56 times as much as the Earth (over a fifth the mass of Jupiter), and will therefore screw up its orbit and either freeze us or boil us. Of course, the slow and painful destruction of the entire human race, all of our infrastructure and achievements, everything you and I and everybody else cares about, and also all life on earth, is the least of our problems. Because now we’ve got a 1-meter black hole sitting in the middle of a public park somewhere (I moved it away from downtown, to be nice. Sorry.) The Earth will swirl into the hole like a sinkful of water down a drain. That’s not just me failing to be poetic, that’s about how it’ll be. The whole Earth wont’ fall into the hole in an instant, nor will it be instantly spaghettified. Remember that, until you get close to it, a black hole behaves like any other object of the same mass. So the bulk of the Earth will fall towards the hole (thereby putting the hole at the middle of the planet) and everything else will collapse around it. We will, briefly, have a planet cracked and hollowed like a broken Kinder egg. Then we will have a ball of incandescent gas around a tiny black hole. Then we will have an accretion disk whose molecules do not resemble the farmers, sailors, priests, road signs, eggs benedict, and fire ants they were once part of. This is the point at which the explosion stops being an explosion. This is the limit.

Hey, this thing goes to 10.999.

That’s no fun. Well, I tell a lie–black holes are great fun to play with. (From a large distance.) But we want explosions, not black holes! We can talk about black holes some other time (hint hint). What if we put a little less than 3.029e43 Joules into our magic sphere? If that happens, boy oh boy do we get some fireworks!

The first thing that’ll happen is that the spacetime around the sphere will go from the gentle curvature (gravity) produced by the Earth, Sun, and other celestial bodies to a violent light-bending time-warping curvature. This does not end well for us. (why would you think it would? You’re silly.) A single powerful pulse of gravity waves races out at the speed of light, turning the Earth to gravel in a few milliseconds. Right on its heels comes a wave of radiation with almost the power of a supernova (almost, as in, 0.3 times as energetic as a supernova. Serious shit.) The Earth does not have time to fall into the region of ridiculous energy density and turn it into a black hole. That’s because the Earth is busy turning into a pancake of purple-white plasma and racing outwards at high speed. If the pancake hits anything, the flash will destroy the solar system. (Which sounds like it should be a line from Spaceballs). If it doesn’t hit anything, the supernova will destroy the solar system.

The moral of today’s story is: Don’t trust a man who says he has a magic sphere. He might kill everything.

The other moral of today’s story is: If you study a little physics, you can take any thought experiment to its absolute logical limit. Which, as I’m discovering, is pretty damn fun.

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A great big pile of money.

When I was little, there was always that one kid on the playground who thought he was clever. We’d be drawing horrifying killer monsters (we were a weird bunch). I would say “My monster is a thousand feet high!” Then Chad would say “My monster is a mile high!” Then I would say “Nuh-uh, my monster is a thousand miles high!” Then Taylor would break in, filling us with dread, because we knew what he was going to say: “My monster is infinity miles high!” There would then follow the inevitable numeric arms race. “My monster is infinity plus one miles high!” “My monster is infinity plus infinity miles high!” “My monster is infinity times infinity miles high!” Our shortsighted teachers hadn’t taught us about Georg Cantor, or else we would have known that, once you hit infinity, pretty much all the math you do just gives you infinity right back.

But that’s not what I’m getting at here. As we got older and started (unfortunately) to care about money, the concept of “infinite money” inevitably started coming up. As I got older still and descended fully into madness, I realized that having an infinite amount of printed money was a really bad idea, since an infinite amount of mass would cause the entire universe to collapse into a singularity, which would limit the number of places I could spend all that money. Eventually, my thoughts of infinite wealth matured, and I realized that what you really want is a machine that can generate however much money you want in an instant. With nanomachines, you could conceivably assemble dollar bills (or coins) with relative ease. As long as you didn’t create so much money that you got caught or crashed the economy, you could live really well for the rest of your life.

But that’s not what I got hung up on. I got hung up on the part where I collapsed the universe into a Planck-scale singularity. And that got me thinking about one of my favorite subjects: weird objects in space. I’ve been mildly obsessed with creating larger and larger piles of objects ever since. Yes, I do know that I’m weird. Thanks for pointing that out.

Anyway, I thought it might be nice to combine these two things, and try to figure out the largest pile of money I could reasonably accumulate. My initial thought was to make the pile from American Gold Eagle coins, but I like to think of myself as a man of the world, and besides, those Gold Eagles are annoyingly alloyed with shit like copper and silver, and I like it when things are pure. So, instead, I’m going to invent my own currency: the Hobo Sullivan Dragon’s Egg Gold Piece. It’s a sphere of 24-karat gold with a diameter of 50 millimeters, a mass of 1,260 grams, and a value (as of June 29, 2014) of $53,280. The Dragon’s Egg bears no markings or portraits, because when your smallest unit of currency is worth $53,280, you can do whatever the fuck you want. And you know what? I’m going to act like a dragon and pile my gold up in a gigantic hoard. But I don’t want any arm-removing Anglo Saxon kings or tricksy hobbitses or anything coming and taking any of it, so instead of putting it in a cave under a famous mountain, I’m going to send it into space.

Now, a single Dragon’s Egg is already valuable enough for a family to live comfortably on for a year, or for a single person to live really comfortably. But I’m apparently some kind of ridiculous royalty now, so I want to live better than comfortably. As Dr. Evil once said, I want one billion dollars. That means assembling 18,769 Dragon’s Eggs in my outer-space hoard. Actually, now that I think about it, I’m less royalty and more some kind of psychotic space-dragon, which I think you’ll agree is infinitely cooler. 18,769 Dragon’s Eggs would weigh in at 23,649 kilograms. It would form a sphere with a diameter of about 1.46 meters, which is about the size of a person. Keen-eyed (or obsessive) readers will notice that this sphere’s density is significantly less than that of gold. That’s because, so far, the spheres are still spheres, and the closest possible packing, courtesy of Carl Friedrich Gauss, is only 74% sphere and 26% empty space.

You know what? Since I’m being a psychotic space-dragon anyway, I think I want a whole golden planet. Something I can walk around while I cackle. A nice place to take stolen damsels and awe them with shining gold landscapes.

Well, a billion dollars’ worth of Dragon’s Eggs isn’t going to cut it. The sphere’s surface gravity is a pathetic 2.96 microns per second squared. I’m fascinated by gravity, and so I often find myself working out the surface gravity of objects like asteroids of different compositions. Asteroids have low masses and densities and therefore have very weak gravity. The asteroid 433 Eros, one of only a few asteroids to be visited and mapped in detail by a space probe (NEAR-Shoemaker), has a surface gravity of about 6 millimeters per second squared (This varies wildly because Eros is far from symmetrical. Like so many asteroids, it’s stubbornly and inconveniently peanut-shaped. There are places where the surface is very close to the center of mass, and other places where it sticks way up away from it.) The usual analogies don’t really help you get a grasp of how feeble Erotian gravity is. The blue whale, the heaviest organism (living or extinct, as far as we know) masses around 100 metric tons. On Earth, it weighs 981,000 Newtons. You can also say that it weighs 100 metric tons, because there’s a direct and simple equivalence between mass and weight on Earth’s surface. Just be careful: physics dorks like me might try to make a fool out of you. Anyway, on Eros, a blue whale would weigh 600 Newtons, which, on Earth, would be equivalent to a mass of 61 kilograms, which is about the mass of a slender adult human.

But that’s really not all that intuitive. It’s been quite a while since I tried to lift 61 kilograms of anything. When I’m trying to get a feel for low gravities, I prefer to use the 10-second fall distance. That (not surprisingly) is the distance a dropped object would fall in 10 seconds under the object’s surface gravity. You can calculate this easily: (0.5) * (surface gravity) * (10 seconds)^2. I want you to participate in this thought experiment with me. Take a moment and either stare at a clock or count “One one thousand two one thousand three one thousand…” until you’ve counted off ten seconds. Do it. I’ll see you in the next paragraph.

In those ten seconds, a dropped object on Eros would fall 30 centimeters, or about a foot. For comparison, on Earth, that dropped object would have fallen 490 meters. If you neglect air resistance (let’s say you’re dropping an especially streamlined dart), it would have hit the ground after 10 seconds if you were standing at the top of the Eiffel Tower. You’d have to drop it from a very tall skyscraper (at least as tall as the Shanghai World Financial Center) for it to still be in the air after ten seconds.

But my shiny golden sphere pales in comparison even to Eros. Its 10-second fall distance is 148 microns. That’s the diameter of a human hair (not that I’d allow feeble humans on my golden dragon-planet). That’s ridiculous. Clearly, we need more gold.

Well, like Dr. Evil, we can increase our demand: 1 trillion US dollars. That comes out to 18,768,769 of my golden spheres. That’s 23,649,000 kilograms of gold. My hoard would have a diameter of 14.6 meters and a surface gravity of 29.6 microns per second squared (a 10-second fall distance of 1.345 millimeters, which would just barely be visible, if you were paying close attention.) I am not impressed. And you know what happens when a dragon is not impressed? He goes out and steals shit. So I’m going to go out and steal the entire world’s economy and convert it into gold. I’m pretty sure that will cause Superman and/or Captain Planet to declare me their nemesis, but what psychotic villain is complete without a nemesis?

It’s pretty much impossible to be certain how much money is in the world economy, but estimates seem to be on the order of US$50 trillion (in 2014 dollars). That works out to 938,438,439 gold balls (you don’t know how hard I had to fight to resist calling my currency the Hobo Sullivan Golden Testicle). That’s a total mass of 1.182e9 kilograms (1.182 billion kilograms) and a diameter of 54 meters (the balls still aren’t being crushed out of shape, so the packing efficiency is still stuck at 74%). 54 meters is pretty big in human terms. A 54-meter gold ball would make a pretty impressive decoration outside some sultan’s palace. If it hit the Earth as an asteroid, it would deposit more energy than the Chelyabinsk meteor, which, even though it exploded at an altitude of 30 kilometers, still managed to break windows and make scary sounds like this:

This golden asteroid would have a surface gravity of 0.108 millimeters per second squared, and a 10-second fall distance of 0.54 centimeters. Visible to the eye if you like sitting very still to watch small objects fall in weak gravitational fields (and they say I have weird hobbies), but still fairly close to the kind of micro-gravity you get on space stations. I can walk across the room, get my coffee cup, walk back, and sit down in 10 seconds (I timed it), and my falling object would still be almost exactly where I left it.

Obviously, we need to go bigger. Most small asteorids do not even approach hydrostatic equilibrium: they don’t have enough mass for their gravity to crush their constituent materials into spheres. For the majority of asteroids, the strength of their materials is greater than gravitational forces. But the largest asteroids do start to approach hydrostatic equilibrium. Here’s a picture of 4 Vesta, one of the other asteroids that’s been visited by a spacecraft (the awesome ion-engine-powered Dawn, in this case.)

(Image courtesy of NASA via Wikipedia.)

You’re probably saying “Hobo, that’s not very fucking spherical.” Well first of all, that’s a pretty damn rude way to discuss asteroids. Second of all, you’re right. That’s partly because of its gravity (still weak), partly because its fast rotation (once every 5 hours) deforms it into an oblate spheroid, and partly because of the massive Rheasilvia crater on one of its poles (which also hosts the solar system’s tallest known mountain, rising 22 kilometers above the surrounding terrain). But it’s pretty damn spherical when you compare it to ordinary asteroids, like 951 Gaspra, which is the shape of a chicken’s beak. It’s also large enough that its interior is probably more similar to a planet’s interior than an asteroid’s. Small asteroids are pretty much homogenous rock. Large asteroids contain enough rock, and therefore enough radioactive minerals and enough leftover heat from accretion, to heat their interiors to the melting point, at least briefly. Their gravity is also strong enough to cause the denser elements like iron and nickel to sink to the center and form something approximating a core, with the aluminosilicate minerals (the stuff Earth rocks are mostly made of) forming a mantle. Therefore, we’ll say that once my golden asteroid reaches the same mass as 4 Vesta, the gold in the center will finally be crushed sufficiently to squeeze out the empty space.

It would be convenient for my calculations if the whole asteroid melted so that there were no empty spaces anywhere. Would that happen, though? That’s actually not so hard to calculate. What we need is the golden asteroid’s gravitational binding energy, which is the amount of energy you’d need to peel the asteroid apart layer by layer and carry the layers away to infinity. This is the same amount of energy you’d deposit in the asteroid by assembling it one piece at a time by dropping golden balls on it. A solid gold (I’m cheating there) asteroid with Vesta’s mass (2.59e20 kg) would have a radius of 147 kilometers and a gravitational binding energy of about 1.827e25 Joules, or about the energy of 37 dinosaur-killing Chicxulub impacts. That’s enough energy to heat the gold up to 546 Kelvin, which is less than halfway to gold’s melting point.

But, you know what? Since I don’t have access to a supercomputer to model the compressional deformation of a hundred million trillion kilograms of close-packed gold spheres, I’m going to streamline things by melting the whole asteroid with a giant draconic space-laser. I’ll dispense with the gold spheres, too, and just pour molten gold directly on the surface.

You know where this is going: I want a whole planet made of gold. But if I’m going to build a planet, it’s going to need a name. Let’s call it Dragon’s Hoard. Sounds like a name Robert Forward would give a planet in a sci-fi novel, so I’m pleased. Let’s pump Dragon’s Hoard up to the mass of the Earth.

Dragon’s Hoard is a weird planet. It has the same mass as Earth, but its radius is only 66% of Earth’s. Its surface gravity is 22.64 meters per second squared, or 2.3 earth gees. Let’s turn off the spigot of high-temperature liquid gold (of course I have one of those) for a while and see what we get.

According to me, we get something like this:

Gold Tectonics

The heat content of a uniform-temperature sphere of liquid gold depends on its volume, but since it’s floating in space, its rate of heat loss depends on surface area (by the Stefan-Boltzmann law). The heat can move around inside it, but ultimately, it can only leave by radiating off the surface. Therefore, not only will the sphere take a long time to cool, but its upper layers will cool much faster than its lower layers. Gold has a high coefficient of thermal expansion: it expands more than iron when you heat it up. Therefore, as the liquid gold at the surface cools, it will contract, lose density, and sink beneath the hotter gold on the surface. It will sink and heat up to its original temperature, and will eventually be displaced by the descent of cooler gold and will rise back to the surface. When the surface cools enough, it will solidify into a solid-gold crust, which is awesome. Apparently, my fantasies are written by Terry Pratchett, which is the best thing ever. I’ve got Counterweight Continents all over the place!

Gold is ductile: it’s a soft metal, easy to bend out of shape. Therefore, the crust would deform pretty easily, and there wouldn’t be too many earthquakes. There might, however, be volcanoes, where upwellings of liquid gold strike the middle of a plate and erupt as long chains of liquid-gold fountains. It would behave a bit like the lava lake at Kilauea volcano, in Hawai’i. See below:

What a landscape this would be! Imagine standing (in a spacesuit) on a rumpled plain of warm gold. To your right, a range of gold mountains glitter in the sun, broken here and there by gurgling volcanoes of shiny red-hot liquid. Flat, frozen puddles of gold fill the low spots, concave from the contraction they experienced as they cooled. To your right , the land undulates along until it reaches another mountain range. In a valley at the foot of this range is an incandescent river of molten gold, fed by the huge shield volcano just beyond the mountains. Then a psychotic space-dragon swoops down, flying through the vacuum (and also in the face of physics), picks you up in his talons, carries you over the landscape, and drops you into one of those volcanoes.

Yeah. It would be something like that.

As fun as my golden planet is, I think we could go bigger. Unfortunately, the bigger it gets, the more unpredictable its properties become. As we keep pouring molten gold on it, its convection currents will become more and more vigorous: it will have more trapped heat, a larger volume-to-surface area ratio, and stronger gravity, which will increase the buoyant force on the hot, low-density spots. Eventually, we’ll end up with convection cells, much like you see in a pot of boiling water. They might look like this:

Benard Cells

Those are Rayleigh-Bénard cells, which you often get in convective fluids. I used that same picture in my Endless Sky article. But there, I was talking about supercritical oxygen and nitrogen. Here, it’s all gold, baby.

Eventually, the convection’s going to get intense enough and the heat’s going to get high enough that the planet will have a thin atmosphere of gold vapor. If it rotates, the planet will also develop a powerful magnetic field: swirling conductive liquid is believed to be the thing that creates the magnetic fields of Earth, the Sun, and Jupiter (and all the other planets). This planet is going to have some weird electrical properties. Gold is one of the best conductors there is, second only to copper, silver, graphene, and superconductors. Therefore, expect some terrifying lightning on Dragon’s Hoard: charged particles and ultraviolet radiation from the Sun will ionize the surface, the gold atmosphere (if there is one) or both, and Dragon’s Hoard will become the spherical terminal in a gigantic Van de Graaff generator. As it becomes more and more charged, Dragon’s Hoard will start deflecting solar-wind electrons more easily than solar-wind protons (since the protons are more massive), and will soak up protons, acquiring a net positive charge. It’ll keep accumulating charge until the potential difference explosively equalizes. Imagine a massive jet or bolt of lightning blasting up into space, carrying off a cloud of gold vapor, glowing with pink hydrogen plasma. Yikes.

After Dragon’s Hoard surpasses Jupiter’s mass, weird things will begin happening. Gold atoms do not like to fuse. Even the largest stars can’t fuse them. Therefore, the only things keeping Dragon’s Hoard from collapsing altogether are the electrostatic repulsion between its atoms and the thermal pressure from all that heat. Sooner or later, neither of these things will be enough, and we’ll be in big trouble: the core, compressed to a higher density than the outer portions by all that gold, will become degenerate: its electrons will break loose of their nuclei, and the matter will contract until the electrons are squeezed so close together that quantum physics prevents them from getting any closer. This is electron degeneracy pressure, and it’s the reason white dwarf stars can squeeze the mass of a star into a sphere the size of a planet without either imploding or exploding.

The equations involved here are complicated, and were designed for bodies made of hydrogen, carbon, and oxygen instead of gold (Those short-sighted physicists never consider weird thought experiments when they’re unraveling the secrets of the universe. The selfish bastards.) The result is that I’m not entirely sure how large Dragon’s Hoard will be when this happens. It’s a good bet, though, that it’ll be somewhere around Jupiter’s mass. This collapse won’t be explosive: at first, only a fraction of the matter in the core will be degenerate.As we add mass, the degenerate core will grow larger and larger, and more and more of it will become degenerate. It will, however, start to get violent after a while. Electron-degenerate matter is an excellent conductor of heat, and its temperature will equalize pretty quickly. That means that we’ll have a hot ball of degenerate gold (Degenerate Gold. Add that to the list of possible band names.) surrounded by a thin layer of hot liquid gold. Because of the efficient heat transfer within the degenerate core, it will partly be able to overcome the surface-area-versus-volume problem and radiate heat at a tremendous rate.  The liquid gold on top, though, will have trouble carrying that heat away fast enough, and will get hotter and hotter, and thanks to its small volume, will eventually get hot enough to boil. Imagine a planet a little larger than Earth, its surface white-hot, crushed under a gravity of 500,000 gees, bubbles exploding and flinging evaporating droplets of gold a few kilometers as gaseous gold and gold plasma jet up from beneath. Yeah. Something like that.

But in a chemical sense, my huge pile of gold is still gold. The nuclei may be uncomfortably close together and stripped of all of their electrons, but the nuclei are still gold nuclei. For now. Because you know I’m going to keep pumping gold into this ball to see what happens (That’s also a line from a really weird porno movie.)

White dwarfs have a peculiar property: the more massive they are, the smaller they get. That’s because, the heavier they get, the more they have to contract before electron degeneracy pressure balances gravity. Sirius B, one of the nearest white dwarfs to Earth, has a mass of about 1 solar mass, but a radius similar to that of Earth. When Dragon’s Hoard reached 1.38 solar masses, it would be even smaller, having a radius of around 3000 kilometers. The stream of liquid gold would fall towards a blinding white sphere, striking the surface at 3% of the speed of light. The surface gravity would be in the neighborhood of 2 million gees. If the gravity were constant (which it most certainly would not be), the 10-second fall distance would be 2.7 times the distance between Earth and moon. Now we’re getting into some serious shit.

Notice that I specified three significant figures when I gave that mass: 1.38 solar masses. That is not by accident. As some of you may know, that’s dangerously close to 1.39 solar masses, the Chandrashekar limit, named after the brilliant and surprisingly handsome Indian physicist Subrahmanyan Chandrasekhar. (Side note: Chandrashekhar unfortunately died in 1995, but his wife lived until 2013. Last year. She was 102 years old. There’s something cool about that, but I don’t know what it is.) The Chandrasekhar limit is the maximum mass a star can have and still be supported by electron degeneracy pressure. When you go above that, you’ve got big trouble.

When ordinary white dwarfs (made mostly of carbon, oxygen, hydrogen, and helium) surpass the Chandrasekhar limit by vacuuming mass from a binary companion, they are unable to resist gravitational contraction. They contract until the carbon and oxygen nuclei in their cores get hot enough and close enough to fuse and make iron. This results in a Type Ia supernova, which shines as bright as 10 billion suns. It’s only recently that our supercomputers have been able to simulate this phenomenon. The simulations are surprisingly beautiful.

I could watch that over and over again and never get tired of it.

Unfortunately, even though it’s made of gold (which, as I said, doesn’t like to fuse), the same sort of thing will happen to Dragon’s Hoard. When it passes the Chandrasekhar limit, it will rapidly contract until the nuclei are touching. This will trigger a bizarre form of runaway fusion. The pressure will force electrons to combine with protons, releasing neutrinos and radiation. Dragon’s Hoard will be heated to ludicrous temperatures, and a supernova will blow off its outer layers. What remains will be a neutron star, which, as I talked about in The Weather in Hell, is mostly neutrons, with a thin crust of iron atoms and an even thinner atmosphere of iron, hydrogen, helium, or maybe carbon. Most or all of the gold nuclei will be destroyed. The only thing that will stop the sphere from turning into a black hole is that, like electrons, neutrons resist being squeezed too close together, at least up to a limit.

But you know what? That tells us exactly how much gold you can hoard in one place: about 1.38 solar masses. So fuck you, Taylor from kindergarten! You can’t have infinity dollars! You can only have 0.116 trillion trillion trillion dollars (US, and according to June 2014 gold prices) before your gold implodes and transmutes itself into other elements! So there!

But while I’m randomly adding mass to massive astronomical objects (that’s what space dragons do instead of breathing fire), let’s see how much farther we can go.

The answer is: Nobody’s exactly certain. The Chandrasekhar limit is based on pretty well-understood physics, but the physics of neutron-degenerate matter at neutron star pressures and temperatures (and in highly curved space-time) is not nearly so well understood. The Tolman-Oppenheimer-Volkoff limit (Yes, the same Oppenheimer you’re thinking of.) is essentially a neutron-degenerate version of the Chandrasekhar limit, but we only have the TOV limit narrowed down to somewhere between 1.5 solar masses and 3 solar masses. We’re even less certain about what happens above that limit. Quarks might start leaking out of neutrons, the way neutrons leak out of nuclei in a neutron star, and we might get an even smaller, denser kind of star (a quark star). At this point, the matter would stop being matter as we know it. It wouldn’t even be made of neutrons anymore. But to be honest, we simply don’t know yet.

Sooner or later, though, Karl Schwarzschild is going to come and kick our asses. He solved the Einstein field equations of general relativity (which are frightening but elegant, like a hyena in a cocktail dress) and discovered that, if an object is made smaller than its a certain radius (the Schwarzschild radius), it will become a black hole. The Schwarzschild radius depends only on the object’s mass, charge, and angular momentum. Dragon’s Hoard, or rather what’s left of it, doesn’t have a significant charge or angular momentum (because I said so), so its Schwarzschild radius depends only on mass. At 3 solar masses, the Schwarzschild radius is 8.859 kilometers, which is only just barely larger than a neutron star. Whether quark stars can actually form or not, you can bet your ass they’re going to be denser than neutron stars. Therefore, I’d expect Dragon’s Hoard to fall within its own Schwarzschild radius somewhere between 3 and 5 solar masses. Let’s say 5, just to be safe. There are suspected black holes with masses near 5.

That’s the end of Dragon’s Hoard. The physics in the center gets unspeakably weird, but the gold-spitting space dragon doesn’t get to see it. He’s outside the event horizon, which means the collapse of his hoard is hidden to him. He just sees a black sphere with a circumference of 92.77 kilometers, warping the images of the stars behind it. It doesn’t matter how much more gold we pour into it now: it’s all going to end up inside the event horizon, and the only noticeable effect will be that the event horizon’s circumference will grow larger and larger. But fuck that. If I wanted to throw money down a black hole, I’d just go to Vegas. (Heyo!) Dragon’s Hoard isn’t getting any more of my draconic space-gold.

But one last thing before I go. Notice how I suddenly went from saying Schwarzschild radius to talking about the event horizon’s circumference. That’s significant. Here’s a terrible picture illustrating why I did that:

CurvedSpacetime

Massive objects create curvature in space-time. Imagine standing at the dot on circle B, in the top picture. If you walk to the center-point along line A, you’ll measure a length a. If you then walk around circle B, you’ll get the circle’s circumference. You’ll find that that circumference is 2 * pi * a. The radius is therefore (circumference) / (2 * pi) But that only holds in flat space. When space is positively curved (like it is in the vicinity of massive objects), the radius of a circle will always be larger than (circumference) / (2 * pi). That is to say, radius C in the bottom picture is significantly longer than radius A in the top one, and longer than you would expect from the circumference of circle D.

In other words, the radius of a massive object like a star, a neutron star, or a black hole, differs from what you would expect based on its circumference. The existence of black holes and neutron stars has not actually been directly confirmed (because they’re so small and so far away). It is merely strongly suspected based on our understanding of physics. The existence of spacetime curvature, though, has been confirmed in many experiments.

Imagine you’re standing in a field that looks flat. There’s a weird sort of bluish haze in the center, but apart from that, it looks normal. You walk in a circle around the haze to get a better look at it. It only takes you fifteen minutes to walk all the way around and get back to your starting point. The haze makes you nervous, so you don’t walk straight into it. Instead, you walk on a line crossing the circle so that it passes halfway between the haze and the circle’s edge at its closest approach. Somehow, walking that distance takes you twenty minutes, which is not what you’d expect. When you walk past the haze at a quarter-radius, it takes you an hour. When you walk within one-eighth of a radius, it takes you so long you have to turn back and go get some water. Each time, you’re getting closer and closer to walking along the circle’s radius towards its center, but if you actually tried to walk directly into its center, where the haze is (the haze is because there’s so much air between you and the stuff beyond the haze, which is the same reason distant mountains look blue), you would find that the distance is infinite.

That’s how black holes are. They’re so strongly-curved that there’s way more space inside than there should be. The radius is effectively infinite, which is why it’s better to talk about circumference. As long as the black hole is spherically symmetric, circumferences are still well-behaved.

But the radius isn’t actually infinite. When you consider distance scales close to the Planck length, Einstein’s equations butt heads with quantum mechanics, and physicists don’t really know what the fuck’s going on. We still don’t know what happens near a black hole’s central singularity.

Incidentally, the Planck length compared to the diameter of an atom is about the same as the diameter of an atom compared to the diameter of a galaxy. The Universe is a weird place, isn’t it?

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Decibels of DEATH!

Ear Protection

When I see the word “decibel,” I think two things. First, I think “Noise.” Then, I think “Oh god, decibels confuse the hell out of me…”

Well, I think I finally understand the decibel. It’s kind of a weird unit, but it’s also nifty, and it showcases one of the coolest things in mathematics: the logarithm.

Here’s how you compute the decibel-level of a sound. First, you figure out the acoustic power of that sound, probably using a microphone (or using a sound engineer who has a microphone and understands better than I do the difference between “acoustic power” and “sound amplitude.”) The acoustic power tells you the maximum pressure the sound wave exerts on things (say, your eardrums). Most of the time, you measure that sound pressure in pascals. Take that sound pressure and divide it by 20 micro-pascals. 20 micro-pascals is a semi-arbitrary reference point. It’s about the sound pressure where a 1000-Hertz sine wave first becomes audible to a human ear. It’s not a lot of pressure. The pressure 10 meters underwater is about twice what it is at sea level, which means the overpressure is about 1 atmosphere (1000 hectopascals. I’d like to note that Hectopascal would be a good name for a movie villain.) Well, the depth of water it would take to get an overpressure of 20 micropascals is 2 nanometers, which is about the diameter of a strand of DNA. Did you know human ears were that sensitive? I didn’t.

Anyway, you can use decibels to express a wide range of noise levels without using too many digits (Because, let’s face it, we all start zoning out after you get beyond about six digits, give or take.) To get the decibel number, you divide your sound pressure by 20 micropascals, take the base-10 logarithm of that, and multiply the result by 20. For example: a sound pressure of 20 micropascals gives you 20 * log10(20/20) = 20 * log10(1) = 20 * 0 = 0 dB.

With a title like Decibels of Death, you knew this article was going to be all about extremes. The quietest officially-measured place in the world is the anechoic chamber at Orfield Laboratories. It’s a room encased in a foot-thick concrete vault. The room itself sits on I-beams which are on springs to isolate external vibration. The inside of the room is full of wedge-shaped foam blocks which prevent echoes and dampen the sound from outside even further. The Guinness Book of World Records measured the sound level in the Orfield anechoic chamber at -9.4 decibels. That works out to a sound pressure level of 6.8 micropascals. To produce an overpressure that small, you’d only need a layer of water 0.612 nanometers thick. At that point, it’s less a puddle and more a molecular stack. That’s pretty damn quiet.

It’s actually intolerably quiet, apparently. The longest anybody’s ever spent in the chamber is 45 minutes, according to that Daily Mail article I linked above. I’ve heard stories about people who freaked out in the chamber because, all of a sudden, they can hear their heartbeats. And some people have auditory hallucinations when deprived of sound long enough, which probably makes the Orfield chamber even scarier.

So -9.4 dB is quiet enough to make you crazy. 0 dB is the threshold of hearing. 10 dB is about the quietest environment you or I will ever experience, and that’s only if we don’t breathe too loud. 25 dB is a very quiet room. According to a funky app I’ve got on my smartphone, the noise level at this desk is 51 dB. The EPA (the US environmental agency) recommends your everyday environment not exceed 70 dB. 85 dB can cause hearing damage over the long-term. 130 dB is painful. 150 dB can rupture your eardrums. This is what I was talking about earlier: logarithmic scales allow you to convert numbers orders of magnitude apart into nice numbers with low digit counts, which makes it easier to compare them side-by-side. When we started out, back at -9.4 decibels, the pressures were so low they were almost impossible to measure. Now, they’re so high they’re doing organ damage.

And speaking of organ damage… The strength of a blast wave is measured by its overpressure, just like the strength of a sound wave. In this fascinating and unnerving paper, some doctors report the effects of 62,000-pascal blast waves on rats. They speak of “minimal to mild alveolar hemorrhages,” as though there were such a thing as a mild case of bleeding fucking lungs. The upshot of all this is that, although 150 dB may burst your eardrums, 189.9 decibels (which is the decibel equivalent of 62,000 pascals overpressure) can actually damage your guts.

But if you’re catching a 190-decibel blast, you’ve got more serious things to worry about than bleeding lungs. Yes, really. There are a lot of reports of soldiers who have been hit by blasts from roadside bombs and car bombs and other such nasty things. Some of these soldiers, although they didn’t hit their heads on anything and nothing hit them in the head, developed serious cognitive problems: difficulty concentrating and short-term memory loss, enough to pretty much spoil their day-to-day lives. In another experiment, rats exposed to a blast overpressure of 20 kilopascals (180 decibels) experienced similar symptoms, and when they were dissected, had lots of dying brain cells. Which is all really pretty damn sad.

As it turns out, there’s actually technically a maximum sound pressure, at least if you want an undistorted sound wave. A pure tone has the shape of a sine wave: the pressure rises a certain amount above atmospheric, drops in a graceful sinusoidal curve, falls that same amount below atmospheric pressure, returns to atmospheric pressure, rinse and repeat. The thing about these kinds of sine waves is that, after their maximum overpressure, they have to drop that far below atmospheric pressure. And if the sound pressure of your sine wave happens to be greater than atmospheric pressure, that can’t happen: pressure is a number that doesn’t go any lower than zero, which is a vacuum. So a sine wave with a sound pressure larger than 1013 hectopascals (1 atmosphere) will sound all right when the pressure goes up, but will get cut off (“clipped,” the sound-engineer people call it) when it goes down. (And when I say “Will sound all right” I mean “Will rupture your aorta, destroy your lungs, tear your limbs off, and knock your house down,” as we learned from nuclear tests.) The maximum for unclipped sound, therefore, is 194.1 decibels.

But since we’re already blowing everything up, why worry about a little distortion? You know the Barrett M82? The big-ass .50-caliber sniper rifle? That one from that movie The Hurt Locker? The big scary one? Well, when that thing fires, its cartridge sees a blast wave of 265.5 decibels, which is just one more reason not to live in a rifle barrel.

You would experience 270 decibels if you were standing about 100 meters (350 feet) from a 1-megaton nuclear bomb when it went off. I use “experience” loosely here, since you wouldn’t have long to enjoy the racket before you were spread over an alarmingly large area.

Now, let’s say you were standing on the surface of a star just as it went supernova. Well, you’d be exposed to a blast pressure of something in the (very rough) neighborhood of 476 decibels, which I’m pretty sure the EPA would classify as “potentially hazardous.”

As it turns out, there’s a maximum pressure that is still physically meaningful, at least according to our current understanding of physics. It’s called the Planck Pressure, and it’s very large. It’s the kind of pressure you get inside black holes. It’s the kind of pressure the universe experienced (we think) right after the Big Bang. The Big Bang had a noise rating of 2,367.3 decibels. The explosion that set the current universe in motion had a pressure which can be quantified in five significant digits.

That’s what I mean about logarithmic scales being awesome. They turn unimaginable cosmic numbers into nice, manageable, comprehensible numbers. You’d better believe I’m going to be playing with logarithmic scales again soon. Which sounds way dirtier than I intended.

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