The Astrophysics of Plasmas
In our second installment, we connect the physics of electrically charged gases to cosmic rays we observe on Earth.
The Kinetic Theory of Gases
What might you say is the most insightful law in theoretical physics? 𝐸 = 𝑚𝑐^2? The general theory of relativity? The quantum nature of the atom? The debates could rage for days. Looking back on my own education, I would emphasize two. The first is Newton’s First Law of Motion:
A body at rest will stay at rest or a body moving in a straight line with a constant speed will not change in its motion unless acted upon by a force.
The second is probably Dalton’s Law of Multiple Proportions, otherwise interpreted as the modern theory of atom
Everything in nature is made of up individual molecules and those molecules are made up of atoms.
These ideas run counter to much of our direct, daily experience1. At least that kind of experience we’ve had in common with our ancestors for thousands of years. Putting those ideas together - which involves a lot of mathematical work - physicists arrived at the modern, kinetic theory of gases.
There are many details and lots of implications from this theory, but one way to understand it goes like this:
Gas - like the air we breathe - is made up of molecules and those molecules move at different speeds. Their average speed tells us the temperature. The higher the temperature, the higher the average speed. But also - and importantly - the higher the temperature the wider the spread on molecular velocities.
Pressure is another phenomena related to the collisions of molecules. We feel their collective impact as air pressure. The individual pressure vary across the gas as the density of molecules varies. Waves of pressure - otherwise known as sound waves - propagate through the gas. The speed of sound depends of course on the individual molecules and their microscopic velocities.
In other words, all around you there are gazillions of tiny molecules. At room temperature, they’re moving at 1000 miles per hour, on average. Some move slowly, some more quickly. A tiny fraction of those molecules are moving, really, really quickly, more than twice as fast as the average.
But we can’t see any of it because they’re just too small.
Plasmas
When a gas get really hot, its individual atoms begin to break down. Their collisions have too much energy and break the atoms to pieces. More precisely, the electrons and nuclei split and form separate components of the gas. This often - but not always - coincides with a very low density of atoms.
When a gas has its charged particles ripped apart, we call that gas a plasma. Plasmas are different from ordinary gases because those newly free charges can source and interact with the electromagnetic field. Plasma’s are kind of a big deal in astrophysics.
If you’ve stood around a bonfire, you’ve seen a plasma. Those tongues of fire are little pockets of air whose atoms have been ripped apart by the intense heat. The intense speeds of electrically charged particles zipping past each other is what causes those tongues of fire to give off electromagnetic radiation - otherwise known as light.
In our podcast miniseries on the 𝛼-particle, we discussed the solar wind and the Earth’s magnetosphere. The outer bits of the sun itself are a plasma, whose glow we see as daylight. Thinking of our Sun as a ball wrapped in plasma also gives an intuitive picture for the source of the solar wind.
From the kinetic theory of gases, it’s easy to see how a few electrically charged particles near the surface of the sun occasionally bounce too far from the Sun and stream out in all directions. That stream impacts all the planets, including the Earth.
Mercifully, the magnetic field generated by our Earth’s spinning core captures much of those charged particles well before they hit the Earth’s atmosphere. Thereby protecting both it and us. Those solar particles are typically confined so the so-called van Allen belts which hold the plasma - a very low density plasma compared to what you’d see in a bonfire - thousands of miles above the Earth’s surface.
Magnetic fields contain that solar wind by bending the trajectories of the individual particles. It curves their motion. That’s just what magnetic fields do! The strength of the magnetic field means that those particles can - at best - move in circles. Roughly speaking, the faster the charged particle, the bigger the circle it makes in the magnetic field.
Like any gas of particles, the van Allen belt plasma has particles moving at very low speeds and very high speeds. Very small circles and very large circles. The average speed - in part - determines the approximate size of those van Allen radiation belts.
Particles moving stupidly fast through a magnetic field - like cosmic rays from space - will also bend, but not enough to get trapped. Instead they fly through the magnetosphere and into the upper atmosphere. Breaking apart by spreading their energy around, leaving us to content with that debris of particles.
Plasmas in Space
You might wonder where those high energy particles from space - those cosmic rays - come from.
There are a lot of stars in space and subsequently a lot of plasma in the universe. Stellar winds blow off particles all the time. But that’s not really enough energy to generate cosmic rays we see on Earth. Those charged particles have more than enough energy to fly past the van Allen belts. But having a lot of stars means more than a few supernovae - the explosive demise of old stars. Supernovae can certainly generate high energy particles.
The aftermath of such explosions often includes clouds of left over gas. These amorphous, interstellar gas clouds are often called nebulae. Nebulae can often find themselves - in part at least - in a plasma state.
These astrophysical plasmas give us beautiful photographs to look at here on Earth. But don’t be fooled. The density of those gorgeous gas clouds - even in star forming reasons like the Horsehead Nebula - aren’t really that visible to the naked eye. Even if you were right up on it, you’d probably have to leave the camera shutter open for a bit to capture all that light.
That is to say, astrophysical plasmas are pretty sparse. By comparison our atmosphere feels like a thick, pea soup. The particles inside those astrophysical plasmas don’t really smash into each other like they do down here on Earth. Rather, the particles interact via the longer range, electromagnetic force.
Astrophysicists will sometimes call them collisionless plasmas to emphasize that fact. The gas behaves less like a game of billiards and more like traffic or a flock of birds.
Shockwaves in Plasma
In a diffuse, astrophysical plasma it helps to think of the three components: the electrons with negative charge, the ions with positive charge and the magnetic field itself.
The importance of the magnetic field can be felt even here in our solar system. Like the Earth, the sun has a magnetic field. A bit one. Unlike the Earth, the sun is constantly producing a large stream of energetic particles, so things are a little hectic. Every once in a while, the sun’s magnetic field gets so twisted up that a little bit pinches off.
That’s right. The magnetic field pinches off. It heads outward into space. Sometimes towards us. And a large chunk of the sun’s outer plasma sometimes goes with it.
These are called coronal mass ejections, and they’re a big concern for satellites and astronauts alike. Like a tsunami of plasma, it can overwhelm Earth’s natural defenses. A coronal mass ejection can wreck havoc on our satellites and other electronics.
On Earth, these kinds of events are experienced as a shockwave in the solar wind. Supernovae can generate even larger shockwaves in astrophysical plasmas. So far as we can tell anyway, shockwaves are the things responsible for accelerating cosmic rays out of astrophysical plasmas.
Sources of Magnetic Shockwaves
Cornoal mass ejections can generate shockwaves near us, in the solar wind. Outside our solar system, in the gas and dust between stars, even larger shockwaves loom. What could generate those?
Supernovae for sure! Those exploding stars can be brighter than entire galaxies, so it’s probably no surprise they’re sending out a lot of sudden shocks during their expansion. Let’s discuss another example.
Neutron stars - city size nuclei (!) left over from one of those supernovae - are really extreme objects. They’re just on the cusp of becoming black holes, and the only thing keeping them from collapsing is the strong nuclear force: you know, gluons and pions and that kind of subnuclear goo.
Neutron stars are very dense. So dense that the force of gravity on their surface is a couple of hundred billion times stronger than on earth. The gravity is so strong that we would be immediately crushed into thin layer of nothing but neutrons.
Just like neutrons themselves have a tiny magnetic field, a neutron star - composed of a gazillion such neutrons - can have a really big magnetic field. A massive one, as it turns out, that spins as the neutron star does, sweeping out a huge wave of electromagnetic energy.
That wild, sweeping motion together with those ginormous magnetic fields surely has a massive impact on any nearby plasmas. Neutron stars, in other words, can generate shockwaves in astrophysical plasmas. Shockwaves that can accelerate cosmic rays.
How to Accelerate Cosmic Rays
Shockwaves accelerate particles in a plasma into cosmic rays, but not all in one go. It’s not like a baseball bat. It’s more convoluted than that.
Some particles pass through the shockwave, back and forth, picking up an an enormous amount of energy as they go. That’s the standard explanation - filed under technical phrases like diffuse shock acceleration or a first order Fermi acceleration.
Passing back and forth through a shockwave is a funny thing to think about. Initiatively, it’s like a surfer passing through a wave, going faster each time. Which of course makes no logical sense. Such an intuitive image of a shockwave is wrong2.
The thing to keep in mind is that the gas of charged particles - the plasma - is very far from the normal, equilibrium thermodynamics we experience down here on Earth. The shockwave is by definition moving faster than the speed of sound in a gas. A shockwave will also very likely be spread out broadly with multiple fronts. Some a little ahead, some a little behind. This texture in the electromagnetic field can give electrically charged particles of the plasma a lot of shock fronts to bounce off of, picking up energy each time. Eventually they can get boosted to such a high energy that they shoot off into space - and eventually - towards us.
Next Time
Once those high energy cosmic rays smash through our magnetosphere and collide with molecules in the upper atmosphere. A cascade of particle debris is formed. But almost all of it decays before it hits the Earth. Almost. On Earth’s surface, the vast majority of those debris particles that we can see are muons.
We don’t normally see muons hanging around in other contexts, like chemistry. Muons are unstable particles. They only live for about 2.2. microseconds. While extremely long lived by particle standards, the muon’s life is still a mere blip by either human or atmospheric standards.
Cosmogenic muons are born at altitudes of nearly 30 miles above sea level, far above where we live or even fly. Created from molecular collisions with extremely fast moving particles, those muons have a lot of energy! They often move close to the speed of light.
These cosmogenic muons are something a curiosity: Light can’t even travel half a mile3 in 2.2 microseconds. So how it these muons can travel well over 10 times that distance without decaying? We’ll resolve this puzzle next time, with a little help from Einstein.
Almost nothing stays in motion from our everyday perspective. Newton’s laws are so ingrained that sometimes its hard to see how novel they were.
There’s also a possible concern from elementary physics that “magnetic fields do no work”, so how could they accelerate particles to higher speeds? The answer is that moving magnetic fields generate induced electric fields, per Maxwell’s theory of electrodynamics. As a result, those induced electric fields can push on charged particles. It’s a complicated story befitting a very complex, dynamical system. For more information, there are some great lecture notes on the topic.
That is, less than 660 meters.