The Field Guide to Particle Physics
https://pasayten.org/the-field-guide-to-particle-physics
©2021 The Pasayten Institute cc by-sa-4.0
The definitive resource for all data in particle physics is the Particle Data Group: https://pdg.lbl.gov.

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The Particle Data Group's write up on cosmic rays. See Figure 29.8 for a representation of the "ankle" feature in the spectrum.
https://pdg.lbl.gov/2019/reviews/rpp2019-rev-cosmic-rays.pdf

Another representation of the power laws can be found in Professor Peter Gorham's Coursework on Ultra High Energy Cosmic Rays: http://www2.hawaii.edu/~gorham/UHECR.html

Cosmic Rays
Part 1 - Particles from Space

Well before the gigantic particle accelerators like the Large Hadron Collider at CERN or the Tevatron at Fermilab, particle physics was studied with balloons.

Well. It still is. I don’t want to give an overly simplified take on the history of particle physics - but it’s fair to say that physicists will study high energy particles WHEREVER they can find them. And it just so happens that  a large number of really high energy particles are constantly bombarding us from space.

In our prior series on the ALPHA PARTICLE, we learned about the solar wind and how the Earth’s magnetic field catches much of that ionizing radiation, which we occasionally see displayed as the Aurora.

Well. That magnetic field is no match for these cosmic rays, which come flying at us from deeper in space with much higher velocities than anything in the solar wind. These particles smash right though the magnetosphere and into the molecules of the upper atmosphere.

From our perspective on Earth, these cosmic rays appear as showers of debris left over from those high altitude collisions. But they’re happening all the time.

There’s so much debris out there that hundreds of particles - particles of that debris - have passed through you since you first hit play on this episode.

### Cosmic Rays

On the 15th of October, 1991, a particle with enormous energy entered our upper atmosphere.

A particle with this much energy had never been seen before on Earth. At least by humans. It had tens of millions of times more energy than anything produced at the Large Hadron Collider or FermiLab. 

All told. It had the kinetic energy of a baseball moving at around 60 miles per hour. All Packed. Into. A single. Particle. And it was heading right for us.

The first thing it found upon arrival at Earth was the magnetic field. Traveling at such a high speed, it barely noticed the deflecting force and smashed through through into the atmosphere.

Even in the rarified air of our upper atmosphere, tens of kilometers above the Earth’s surface, there are plenty of molecules to go around. Way more than you’d find in outer space. And what do particles from space with a lot of energy do when suddenly surrounded by a bunch of molecules? They spend it.

That poor first molecule it encountered didn’t stand a chance. Whether it simply lost an electron or got completely blown apart is hard to say, but that incident cosmic ray quickly broke apart into a shower of particles high above the Earth. 

Pions were certainly created, but with that much energy - 50ish Joules of energy - all kinds of particles - from Lambda Zero to Kaons to the Cascades and Sigma baryons - could have been present. 

And all of them decayed as they usually do.

The resulting shower of decays grew wider and wider, until the final, resultant charged pions decayed into muons. And the neutral pions decayed into photons. And any high energy photons decayed into electron-positron pairs who would in turn radiate the rest of the energy away.

That final blast of radiation filled a circle kilometers wide that slammed into the US Army’s Dugway Proving ground in Utah desert and - as luck would have it - right into the detectors of a physics experiment.

The detectors measured resultant spray and were able to back-calculate the energy of the original, impinging particle from space.

This aptly-named Oh-my-god particle was far and away the highest energy particle ever detected. To date, it’s not entirely clear what could accelerate a particle to such outrageous speeds.

And the current candidates are, frankly, terrifying.

## The Power Law
In some respects, cosmic rays are kind of like earthquakes. There’s a lot more little ones than there are big ones. For earthquakes, big ones with lots of shaking - magnitude 7 or 8 - are, mercifully, fairly uncommon around the world. Small ones, like magnitude 1’s or 2’s happen almost every day.

Cosmic rays follow a similar law.

Cosmic rays with an energies around 1000 MeV arrive almost continuously, from every direction, where as cosmic rays with energies a million times that might strike near you a few times per year.  Those ultra high energy cosmic rays, a bit like the oh my god particle, whose energies can be measured macroscopic units like Joules? They might strike your whole TOWN maybe once a year, if that.

As scientists would say, the frequency depends inversely on energy.

More precisely, the frequency is derived from a POWER LAW.  A power law for cosmic rays implies that the relative likelihood of two events, with energy E1 and E2 is proportional to their ratio, raised to some exponent. 

Power laws are simple enough to understand, but difficult to explain.  Bigger cosmic rays are less common, sure. But what’s difficult to explain about a power laws is that little number. The scaling exponent. Where does it come from?

It’s a collective effect. All the things inside and outside our galaxy that throw cosmic rays at us contribute to that effect. Other stars and planets sometimes get in the way and capture some of them. Cosmic rays in interstellar space sometimes decay or interact en route, turning into other particles with somewhat lower energy, muddying things a bit. Magnetic fields in space - like the one surrounding our Earth - deflect cosmic rays ever so slightly. 

It’s a bit like studying Earthquakes. There are just so many moving parts and we don’t know all the details.

## The Ankle

Despite all this complexity, the shape of the cosmic ray power law can tell us a LOT about the nature of cosmic rays.

For example. 

At the highest end, for those particles coming in with the HIGHEST energies, the power law for cosmic rays actually changes a bit. It flattens out. It becomes slightly less sensitive to Energy. 

Ultra high energy Cosmic Rays aficionados call this change the “ankle”.

The ankle represents a cut in the cosmic ray spectrum at about half a joule of kinetic energy. There’s a pretty good plot physicists who study these things have made. I’ll include links to a picture in the show notes.

It’s a small effect on a small fraction of the total number cosmic rays we see on Earth. But to astrophysicists who study these things, it says a lot.

Namely, this “kink” or “ankle” in the power law suggests a possible change in where those cosmic rays are coming form. The leading explanation is that those ultra high energy cosmic rays - those cosmic rays with kinetic energy greater than half a Joule or so - are coming from OUTSIDE our galaxy.

Which is just as well. Becau...