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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Uncategorized

A piece of a neutron star.

In the previous article, I talked about neutron stars, and like pretty much everybody else who’s ever tried to describe a neutron star’s absurd density, I explained that a piece of a neutron star the size of a 500-micron grain of sand would weigh as much as a small cargo ship.

That’s the kind of scientific example I like: it uses to comprehensible objects to illustrate something that would otherwise be pretty much impossible to visualize. I know the mass of a cargo ship isn’t exactly intuitive, but it’s more intuitive than saying 2e17 kilograms per cubic meter.

But one thing such examples gloss over is just how hard it is to pack this much mass so close together. In order to reach the pressures and temperatures necessary for fusion, we need the mass of the entire Sun, and that still only compresses the Sun’s core to 1.5e5 kilograms per cubic meter. It takes a truly massive star that has no way to maintain its internal temperature to compress matter the rest of the way and keep it there.

Neutron stars are supported almost entirely by neutron-degeneracy pressure, which, to seriously oversimplify matters, is a product of the fact that neutrons don’t like to occupy the same quantum state, and therefore don’t like to be brought too close together. It produces a lot of pressure. Enough to support 1.38 solar masses or more against a surface gravity of 100 billion gees. It also means that if we got really literal and took an actual piece out of a neutron star, it would not end well.

Let’s say we teleported a cube of neutron fluid, at a density of 2e17 kilograms per cubic meter and 3,000,000 Kelvin, into the air a meter over an empty field on Earth. The pressure exerted by all those neutrons packed too close together is complicated to calculate, but would probably be in the neighborhood of 5e33 pascals, or about 5e18 atmospheres. That’s a million trillion times higher than the pressure during the detonation of a hydrogen bomb.

That’s a lot of energy in one place, but as we’ve learned while trying to kill humanity with a BB gun and contemplating killer asteroids, even when you deposit a ridiculous amount of energy into a small volume, if there’s enough matter around it, eventually, it’ll be converted into a more ordinary form. This is another way of saying that, up to a certain limit, all explosions are going to behave a lot like scaled-up nuclear explosions.

But a whole lot of interesting shit is going to happen very rapidly before we get to that point. First, our grain of neutronium (which, admit it, sounds way cooler than “neutron superfluid,” cool as that one is) will expand rapidly. This will cause its pressure to decrease, and so it’ll be a lot like ascending through the layers of a neutron star, moving from outer core to crust. When the pressure drops low enough, many of the neutrons will decay into protons, emitting electrons and neutrinos. Neutrinos are infamous for carrying off energy, and also for refusing to interact with things. They might heat the ground below them by a few fractions of a degree, but considering that they pass right through the Earth without difficulty, they’re probably not important, except in the fact that they’ll cool the nuclear matter down.

Now, our grain of neutronium is a slightly larger grain of protons and neutrons all mashed together. Without the surrounding pressure to force them unnaturally close, the protons will naturally repel each other. They’ll still be attracted to each other and to the neutrons via the strong force, but once again, without the ridiculous pressures provided by the bulk of a neutron star, their clustering will be limited by the short range of the strong force. That is to say, they’ll stop being a soup of nucleons and go back to being atomic nuclei.

These nuclei will start out quite heavy, but the falling pressure will cause them to rapidly fission and give off a lot of radiation. There’ll be a lot of gamma rays, a lot of stray protons and neutrons, a lot of alpha particles, and probably a lot of beta decays producing protons and electrons from neutrons. It’d take a particle physicist to tell you exactly what elements to expect in the fallout, but I’d wager it’d mostly be lead, iron, hydrogen, and helium, with a smattering of lighter and heavier elements.

By now, we’re dealing with energies too low for massive neutrino emission, so the only way this expanding sphere of plasma can lose energy is by emitting traditional electromagnetic radiation and by expanding. It is now, for all intents and purposes, an extremely hot and extremely small version of a nuclear fireball.

How big would the fireball ultimately get? That depends on a lot of things: first, on how much energy was initially contained in our deadly granule. Second, on how much of that energy got carried off by the snobbish non-interacting neutrinos. It’s hard to be certain how much potential energy would have been in the grain to start with, but I’ve read that the neutron degeneracy pressure of neutronium is one third of its mass density. E = m * c^2, so mass density is just energy density. One third of the energy density of our grain of neutronium comes out to about 7.5e23 joules, which is of the same order of magnitude as the Chicxulub impact. So, even though we’re dealing with a very exotic explosion, we know that it’s not the kind of explosion that’s going to blow off the entire atmosphere or boil all the oceans. And actually, since so much energy is likely to be lost to neutrinos (neutrinos carry off 99% of the energy in supernovae, which considering that they still shine as bright as 10 billion suns, is horrifying to contemplate), it could be an almost-ordinary thermonuclear explosion. But, because I don’t know exactly how much energy we’re losing to neutrinos here, I’m going to assume the whole 7.5e23 joules is going to get deposited in the atmosphere.

Using this number, we can estimate the relevant parameters by using the excellent Impact Effects program, written by some very nifty folks. This program is, as far as I’m concerned, justification enough for the existence of the Internet all by itself. By assuming a stony asteroid 12 kilometers across, impacting perpendicular to the ground at 22 kilometers per second, we get an impact energy in the right ballpark.

The fireball would grow to massive proportions. As we learned from nuclear tests, hot plasma is pretty much completely opaque to radiation, since it’s got electrons flying around loose, and since photons like to bounce off of electrons. An initial burst of gamma rays would escape, but much of the radiation from our exploding grain of neutronium would be trapped in the plasma bubble, bouncing around while the bubble expanded at high speed. This bubble would reach a radius of 95 kilometers, reaching vertically to near the edge of space and pushing a massive shockwave out in front of it. Anything that happened to be caught within the fireball wouldn’t be destroyed. It wouldn’t even be vaporized. It would be flash-ionized into hot plasma. But, once the bubble had expanded to 95 kilometers in radius, it would finally have cooled enough to de-ionize and become transparent to ordinary radiation again.

This is very briefly good news for the people in the surrounding area, since it means they’re not going to get smacked in the face with a wall of plasma at 5000 degrees. Then, it becomes very bad news, since there’s a lot of thermal energy in that fireball that can now suddenly escape. The fireball would be visible from 1,100 kilometers away, and possibly farther, if you’re unlucky enough to be in an airliner or on a mountain. And if this fireball is visible to you, that pretty much means you’re dead. We’re looking at flash-fires and third-degree burns for five hundred miles in every direction.

About an hour later, the people at 1,200 kilometers, for whom the fireball was below the horizon, would stop being lucky: the blast wave would arrive, bringing overpressures of almost 2 atmospheres (enough to blow down just about any building) and wind speeds of 610 miles an hour (enough to blow down just about any building).

But the disaster would only just be beginning. Here, the peculiar origin of the explosion would make itself apparent: there would likely be a lot of radioactive fallout, and it would be made of peculiar isotopes generated in a flash when those protons and neutrons were separating into nuclei again. Not only that, with all the ionizing radiation, there would be even more nitric oxide in the plume than usual. Imagine if you will a pancake-shaped incandescent cloud hundreds of kilometers across–the size of a country. This cloud glows from within a larger, dark-red cloud of nitric oxide, ozone, iron, lead, and radioactive dust. Over the course of hours, the upper half of the cloud collapses downward as it cools, while the other half rises buoyantly upward. Within days, there’s a sheet of opaque vapor thousands of kilometers across, trapped in the stratosphere, blowing with the winds, fed from below by a firestorm of a kind not seen for 65 million years. Smoke and dust circle the planet within weeks. Temperatures drop far below freezing. People and animals are poisoned by toxic gases. With the sunlight blotted out, plants die. People starve. There’s a mass extinction. Only the hardiest species survive. After the dust settles out and the climate rebounds, new creatures populate the Earth. The only reminder of the catastrophe is a thin layer of exotic elements, and a crater 160 kilometers across and 2 kilometers deep. Perhaps if Earth ever spawns another species that spawns paleontologists, they will think the crater came from an asteroid impact. But it didn’t. It was created by an object the size of a grain of sand.

So take this as a grim warning: Under no circumstances should you take a useful scientific analogy so literally that you actually remove a piece of an exotic compact star and transport it to a planet. And they say you can’t learn anything from psychotic bloggers!

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