physics, Space, thought experiment

Hypothetical Nightmares | Black Holes, Part 3



Galaxy Mass Black Hole.png

(Rendered in Universe Sandbox 2.)










The Opposite Extreme


Hobo Sullivan is a Little Black Pinhole






Can’t you just buy a space heater like a normal person?




Back to the Original Extreme






Charlotte vs. The Comet 2: This Time, I Got It Right

A few weeks ago, I posted a scale comparison between comet 67P/Churyumov-Gerasimenko and the city of Charlotte, North Carolina, the city I live in. It was wildly, offensively inaccurate: somehow, I shrank the comet by a factor of five. Well, now that the ESA has finally released their shape model for the comet, I can just import the model into Blender, convert it into a .dae file, scale it until it’s (approximately) the right size, and stick it in Google Earth to get an idea of the comet’s scale.

67 P vs. Charlotte NC

The larger lobe is 4,100 meters long, and the whole comet dwarfs Charlotte. In fact, it looks like Charlotte is being menaced by a legless puppy. There’s an image for you…


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:


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?


The weather in hell.

Neutron stars are horrifying things. They’re born in supernova explosions, which can shine with the light of 10 billion suns for weeks on end. But even after the fireworks, they’re still scary as hell. A neutron star compacts over 1.44 times the sun’s mass into a sphere about 20 kilometers across (about the size of a city). Apart from black holes, they’re the most extreme objects we know about (There may actually be more extreme variants, but none have been conclusively observed, and thank goodness: what we’re dealing with is scary enough.).

Everything about a neutron star is horrifying. Their surfaces broil at temperatures of over 100,000 Kelvin, which is twice as hot as the hottest stars. The young ones can get hotter than 1,000,000 Kelvin. Red-hot metal emits red light because most hot objects emit a so-called blackbody spectrum, with the most intense wavelength (color) of light depending on temperature. Iron near its melting point (1811 Kelvin) emits strongest at a wavelength of 1.6 microns, which is in the near-infrared (which is not the kind of infra-red the Predator used to hunt Arnold Scwharzenegger). To our eyes, the iron would look bright red-orange. The sun, with a blackbody temperature of about 5800 Kelvin, emits most strongly in the blue-green part of the spectrum (it looks yellow on Earth partly because of atmospheric scattering and partly because the human eye is a lot less sensitive to indigo and violet than it is to blue, yellow, orange, and red). At 100,000 to 1,000,000 Kelvin (and above), neutron stars would have about the same purplish-blue color as lightning bolts or the most powerful electric arcs, and they would emit most of their light in the deadly far-ultraviolet and really deadly X-ray. If you replaced the Sun with a 1,000,000-Kelvin neutron star, the Earth would only receive five times less energy than it does from the Sun. That’s ridiculous, considering all that energy is coming from an object the size of downtown Tokyo. (Speaking of which, that gives me an idea for a new Godzilla movie…) Of course, almost all of that energy would be in the x-ray and ultraviolet portions of the spectrum, and therefore would blow off the ozone layer and kill us all. But what would this blog be if I didn’t kill humanity every article?

But let’s handwave the radiation away (in true Star Trek fashion) and say you were able to get close to the neutron star.

Sorry. You’re still dead. Say you replaced Earth with a 2-solar-mass neutron star. If you were in the International Space Station, you’d probably survive the tidal forces, but they would be enough that if you oriented yourself feet-down, you’d feel a noticeable and unpleasant stretch: your head and feet would experience a difference in acceleration of about 0.4 gees. If you were orbiting at 4,000 kilometers, you’d experience a very painful 1.5-gee stretch (and, incidentally, you’d be completing one orbit every 3 seconds, which is ridiculous). By the time you got within 1,000 kilometers of the neutron star, your feet and your head would experience a difference in acceleration of 100 gees, more than enough to pull half your blood to your feet and the other half to your brain, stopping your heart and giving you lethal cerebral hemorrhages at the same time.

But as bad as things are in the neutron star’s neighborhood, they’re even worse on its surface. This is where the “Hell” part comes from. I’ve read through a few papers on neutron star structure (and skimmed many more). It’s hard to get a straight answer on what neutron stars are like on the inside (partly because it’s really hard to simulate the imponderable conditions near the core), but here’s neutron star structure as  I understand it:

Neutron Star Structure

At the top is the atmosphere, crushed to a thickness of between 10 centimeters and 10 meters (definite numbers are hard to find) by a gravity of 200 billion gees. Most neutron star atmospheres are pure hydrogen or pure helium, but sometimes, because of the insane pressures and temperatures, the atoms undergo fusion, leaving behind a carbon atmosphere. Below that is a crust that, thanks to the way nuclei get smashed together in supernovae, is mostly iron ions, their electrons wandering around with little regard for the nuclei.

The uppermost layers of the crust are made of almost-normal mater, albeit crushed to insane densities. But as you get deeper, the weight of the crust above puts extreme pressure on the nuclei. Suddenly, nuclei that have half-lives measured in seconds on Earth become as stable as ordinary gold or lead, because the pressure keeps decay products from escaping. The higher the pressure, the easier it is for extra neutrons to slip into nuclei. The nuclei get heavier and heavier and closer and closer together as you go down. Then, a few hundred meters below the surface, you encounter the “neutron drip,” where neutrons start leaking out of nuclei and roaming free. (On Earth, loose neutrons decay with a half-life of about 10 minutes. In the neutron star, once again, the pressure makes them stable.) This region gives us one of the coolest scientific terms ever devised: “nuclear pasta.”

Say it. Nuclear pasta. That sounds like something from an awesomely shitty ’70’s superhero movie. But, according to our current physics, it’s a real thing.

Because like charges repel, a nucleus wants to fly apart, since it’s full of chargeless neutrons (which don’t attract or repel anything) and positive protons (which fiercely repel each other). The strong nuclear force (or Strong Force, which sounds like the name of a badly-translated kung fu movie) provides the glue that holds nuclei together. At small distances, it’s far stronger than the electromagnetic force that causes like charges to repel (thus the name). But it decays very quickly with distance: beyond about a millionth of a nanometer, it gets vanishingly weak. Nuclei that are too large for the strong force to span their whole diameter tend to be unstable.

For this reason, nuclei also repel each other when brought close together. But deep in a neutron star’s crust, the pressure begins to overwhelm the repulsion. The protons still repel each other, but now there are places where they’re forced so close together that the strong force starts winning out. The nuclei grow oblong, and then they fuse into long tubes of protons and neutrons, like subatomic sausage (Subatomic Sausage. Another good band name.). This is the eponymous “pasta phase.” As you go down and the pressure goes up, these tubes get closer together and adjacent ones merge into two-dimensional sheets. This is called the “lasagna phase.” If you go on Google Scholar and type in “nuclear pasta”, you can find an actual peer-reviewed university-supported scientific paper that uses the phrase “lasagna phase” with a straight face. That makes me smile.

Deeper down, parts of the sheets come into contact, and you end up with a weird latticework of nuclear-matter tubes called the “gyroid phase.” Below that is a phase where you have cylindrical holes surrounded by nucleus-stuff, a sort of negative of the pasta phase. Then you get spherical holes. Then, the electromagnetic repulsion just gives up entirely, and the neutron-star matter reaches the density of an atomic nucleus, which is so huge (2 x 10^17 kilograms per cubic meter) that a piece the size of a grain of sand (a cube 500 microns on an edge) would weigh as much as a small cargo ship (25,000 metric tons). Of course, without the pressure provided by a whole neutron star to compress it, that grain would expand rapidly, and you would be spread over a large area. So don’t go removing pieces of neutron stars and carrying them around. Ain’t safe.

This is the outer part of the core. So far, the electrons have pretty much been minding their own business, ignoring the pained cries of the protons and neutrons as they were squeezed unnaturally close (the bastards). Deeper down, the pressures get so high that the electrons and protons combine to form neutrons, releasing a neutrino. Below a certain depth, it’s just a soup of neutrons crammed shoulder-to-shoulder. This soup has some weird properties, which we’ll get to later.

Below the neutron fluid, physicists aren’t quite sure what happens. Funnily enough, we here on Earth don’t have a lot of experience with soups of pure atomic-nucleus fluid. It’s possible that, in the depths, quarks could leak out of the individual neutrons, or even weirder stuff could happen, but we just don’t know. Most diagrams of neutron star structures either just put a question mark at the center or list a bunch of exotic particle names and then put a question mark. I won’t even attempt to guess what’s going on down there. I’ve got hellish weather to talk about.

But would there even be weather on a neutron star? That’s hard to say. Neutron stars have powerful magnetic fields, which could very well hold the plasma in the atmosphere in place, or at least make it awfully hard for it to move around. But, if you think about it, the temperature difference between the bottom and the top of a neutron star atmosphere is between 900,000 and 2,500,000 Kelvin, which is several thousand times the 350-Kelvin temperature difference that drive’s Earth’s weather. I’ll be working under the assumption that the atmosphere of a neutron star is able to circulate. If anybody has better information than me, feel free to set me straight.

In the last article, I talked about “scale height,” which is a nifty number that tells you how high you have to go for the atmosphere on a planet to be e times (about 2.7 times) less dense. Because their gravity is so monstrous, even the superheated plasma in a neutron star’s atmosphere is crushed tight against the surface. The Earth’s scale height is about 8,500 meters. The scale height in a neutron star’s atmosphere (depending on whether it’s made of hydrogen, helium, carbon, or something else, and depending on temperature) can range from a fraction of a millimeter to a few centimeters. On Earth, if you go up two scale heights, you’re higher than most airliners ever fly. If you go up 12 scale heights, you’re in space. I couldn’t find any really reliable numbers on the surface density of neutron-star atmospheres, but let’s assume it’s the same as the density of the sun’s core: 150,000 kilograms per cubic meter. The gravity is so strong that even the deepest neutron star atmospheres reach outer-space densities within half a meter. If I could stand on a neutron star (which, I will remind you, is a bad idea), the atmosphere would just about reach my knees. Right before I evaporated and then collapsed into a one-atom-thin layer of plasma.

Lucky for us, since the density profile of an atmosphere is exponential, many of its features will scale nicely from more familiar examples, like the atmospheres of stars and planets. Here, I’m pretty much making shit up, but the shit I’m making up is informed by some real-world knowledge. It’s also based on a few assumptions. I’m assuming, for one thing, that our neutron star is a pulsar, a neutron star spun up like a top by the infall of matter from a binary companion. I’m further assuming that this neutron star has about the same rotation rate as PSR J1748-2446ad, the fastest-spinning pulsar yet discovered (as of June 2014). It spins 716 times a second. Let’s imagine there was a single spot on the pulsar that emitted radio waves (in reality, there’s one at each magnetic pole, but one spot is usually looks brighter to us on Earth). If you could hear the signal it emitted, it would sound about like this (TURN DOWN YOUR SPEAKERS! It’s not a pretty sound.):

716-Hertz Pulsar

Even for an object like a pulsar, which is small in astronomical terms, spinning 716 times per second is ridiculous. It means that the matter at the equator is moving at 15% of the speed of light. It also means the Coriolis effect is gonna come kick some ass.

For those of you who find the Coriolis effect as confusing as I once did, here’s a brief explanation. Imagine you roll a ball inward from the edge of a frictionless spinning carousel. In the reference frame of the ground, the ball just travels straight to the center, across the other side, and off the edge. But if you were rotating with the carousel, the ball wouldn’t appear to travel in a straight line. This is because, according to you, the ball has both the inward velocity the outside observer sees and a radial velocity tangent to the circle’s circumference, since it’s not moving and the carousel is. This radial velocity is at its highest at the carousel’s edge, so as the ball approaches the center, it’s moving faster than the carousel’s surface, since the inner parts have lower radial velocities. Therefore, it appears to curve across the carousel as though acted upon by a force, pass through the center, and curve back out, describing a (roughly) semicircular trajectory. I know that’s the dunderhead layman’s explanation, but since I’m a dunderheaded layman, what do you expect?

The Coriolis effect is why low-pressure systems swirl anti-clockwise over Earth’s Northern hemisphere (and clockwise over the Southern hemisphere): the Earth is a sphere, so as you move towards the poles, you’re closer to the Earth’s axis of rotation. The faster the rotation of the body in question, the stronger the Coriolis effect and the tighter the circulation. Since our pulsar is spinning so damn fast, the circulation will be very tight, and since the bottom of the atmosphere is so much hotter than the top, the motion will be quite violent. Here’s my guess at what the pulsar’s atmosphere will look like:

Neutron Star Surface Weather Small

Here, I’m calling upon the concept of inertial circles. The radius of an inertial circle is given by:

(speed of the moving fluid) / (2 * angular velocity of planet * sin(latitude, with the poles being plus or minus 90 degrees and the equator 0))

An inertial circle is the path a body would take on a planet’s surface under the influence of the Coriolis effect alone. On Earth, if you assume a wind speed of 100 MPH (about 44 meters per second), then the inertial circle at a latitude of 45 degrees has a radius of about 480 kilometers, which is about right for a hurricane. I’ll make the very naive assumption that the winds on a neutron star will scale up in proportion to the increase in the temperature difference (from about 320 Kelvin (and 44 meters per second) on Earth to as much as 2,500,000 Kelvin on a neutron star). Neutron star winds will therefore have speeds on the order of 1,700 kilometers per second (Dorothy’s not going to make it to Oz in this tornado. Forget an F-5. We’re looking at an F-68000.) At a latitude of 45 degrees, a neutron star hurricane will have a radius of about 250 meters:


Imagine standing up to your knees in glowing gas. Spreading out around you is a brilliant electric-purple hurricane the size of a football stadium. At its center, it has an eye a few meters across, which feeds down into a needle-thin funnel with gas swirling at 0.1% of the speed of light.

I would guess that our pulsar wouldn’t have features like jet streams. For one thing, pretty much any movement in the atmosphere is going to be twisted into a circle by the Coriolis effect and turn into a cyclone. For another thing, the magnetic field would probably put the brakes on big swathes of moving fluid. A neutron star, having such a violent, hot atmosphere, would have hellish weather, and its surface would be paved with hurricanes. I imagine it would look something like this:

Neutron Star Weather

(Yes, I mixed up North and South and scribbled them out. Yes, I do know that I’m an idiot.)

The magnetic poles of neutron stars are often not aligned with the geographic poles (also true of Earth!), so there would probably be spots where the emerging magnetic field, all bunched up and concentrated, would stop the gas from moving much at all, even if the field was weak enough to let it move around everywhere else. These are also the spots where material tends to fall onto neutron stars, so they would have perpetual hot high-pressure systems (much like Louisiana or North Carolina). I took the liberty of adding magnetically-dampened high-pressure cyclones around these poles, and putting hurricanes everywhere else.

But this isn’t the only possible weather on a neutron star. Wherever you have fluid, gravity, and a density and/or temperature gradient, you can have weather-like phenomena. They happen in Earth’s atmosphere, they happen in Earth’s oceans, they happen on Venus, and they happen on the Sun. I’ve just spent quite a while talking about the weather on the surface of a neutron star, but there could also be weather in the interior. Beneath the crust, where the protons and electrons combine and it’s almost all neutrons, the material stops being solid and becomes a neutron liquid. But it’s not just any liquid. It’s a neutron superfluid. Superfluids are weird shit. They behave more or less like liquids, except that they have zero viscosity. Bizarre, but true. Water has a non-zero viscosity: as your pipe gets smaller, it gets harder and harder for water to move at a given velocity. Viscosity is pretty much the internal friction within the moving fluid. Viscosity determines the minimum size a stable vortex can have. Water has a viscosity of about 8.9 x 10^-4 pascal-seconds. But superfluids like liquid helium-4 have a viscosity of zero. The viscosity isn’t just very small, it’s actually zero. Superfluids can slip through any hole (that sounds dirty), and because of capillary action (which allows a wet spot on a paper towel to spread out), and because there’s no viscous friction to oppose it, they can crawl up and out of containers.

That’s all awesome, but, for my money, one of the coolest things about superfluids is what happens when they start swirling. Normally, when you rotate a container of fluid, the fluid starts to rotate with the container. Essentially, the whole container of fluid becomes one giant vortex.

This doesn’t happen in superfluids. No matter how large or small the rotating container, the superfluid forms lots and lots of extremely tiny vortices, their number depending only on the spin rate. If spin a glass of water at 1 revolution per minute, you’ll get one big, slow vortex. If you fill the same glass with superfluid helium-4 and rotate it at 1 RPM, you’ll get thousands of them. Don’t know what the hell I’m talking about? Here’s a truly beautiful video of swirling superfluid helium in action:

And here’s a terrible picture I drew of the same phenomenon:


This is basically quantum mechanics acting on a large scale, which often happens when things get cold enough. Since superfluid helium has zero viscosity, when it has to form vortices, the vortices are infinitely small, or rather, as small as the fact that the helium is made of atoms will allow them to be. This is called “quantization of vortices,” and is extremely weird, and most likely also happens in the superfluid interiors of neutron stars. These tiny vortices will be oriented along the axis of rotation, so they’ll be parallel to the crust near the equator and perpendicular near the poles (with additional changes depending on the magnetic field and whether the rotation is  faster in some regions than in others, which is usually how it works out). So if you look at it from the bottom up, you get knee-deep plasma tornadoes the size of football stadiums. And if you look at it from the top down, you get a field of weird nuclear pasta crawling with trillions and trillions of microscopic tornadoes piercing a neutron sea. I’ve said it before and you know I’ll say it again: astronomy is awesome.