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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:

Hurricanes

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:

Superfluid

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.

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2 thoughts on “The weather in hell.

  1. Pingback: A piece of a neutron star. | Sublime Curiosity

  2. Pingback: A great big pile of money. | Sublime Curiosity

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