# Astronomical sources of muons

I am looking for some sources of muon particles (μ) in astronomy. By this, I mean I am interested in any astrophysical event where theoretical presence of muons is suggested.

For instance, does the center of galaxy or supernova emit muons?

I am not interested in the actual detection, just their (expected) presence. I am also aware of atmospheric muons as a byproduct of cosmic ray interactions.

## Primary muons

Muons can be produced in any sufficiently energetic event, but we don't ever see them directly.

The issue is that—though they are long lived by the standards of particle physics—muons still only have a mean lifetime of about 2 microseconds ($\tau = 2.2 \times 10^{-6} \,\mathrm{s}$).

The mean distance they can travel (when highly relativistic) is $$d_\text{mean} \approx \gamma \tau c \;,$$ where $\gamma = [1 - (v/c)^2]^{-1/2}$ is the Lorentz factor. Both $\tau$ and $c$ are constants, so we can re-write this as $$d_\text{mean} = \gamma (660\,\mathrm{m}) \;.$$

But the distance to astrophysical events is measured in light-years, each of which is more than $10^{15}\,\mathrm{m}.$ So for us to have any reasonable chance to capture a muon from a "nearby" astrophysical event it would have to have a energy on order of $10^{12} m_\mu = 10^{20} \,\mathrm{eV}$.1 Now, we do actually see a few cosmic rays at that energy, but they come from active galactic nuclei, so the closest candidate source is the big black hole in the center of our own galaxy about 30,000 light years from us. That puts the energy scale up to something like $10^{24}\,\mathrm{eV}$.

This is simply beyond the energy we've observed concentrated in a single particle.

So, short-short answer part one: there are no observed astrophysical sources of primary muons (meaning that no muons created in astrophysical events reach detector on or around Earth).

## Muon signatures

Now, you might say, well, "That's OK, it would be enough to observe an unmistakable signature of muons."

That means one of a few things

1. Seeing decay products of muons that can not be created in other ways.
2. Seeing other particles that are only generated in reactions in involving muons.
3. Seeing a spectroscopic signature of muon creation or decay.

So let's take those one at a time. The particle data group summary of muon physics (PDF link) will be useful here.

### Muon decay products.

Muons are the second lightest charged lepton and is lighter than all the hadrons. Consequently it's decay products can involve on electrons, positrons and various neutrinos. As all of these are abundant in any enertic event there is no signature here.

### Creation signatures

The only particles that are necessarily created in reaction involving muons are muon flavored neutrinos. Alas neutrino mixing means that we can observe muon-neutrinos from event involving only electrons (for instance we see them from solar fusion events which only create electron flavored neutrinos).

### Spectroscopic signatures

Electron and positron decay products will have their direction and speed radomized by interstellar magnetic and electric field distributions. And positrons will mostly annihilate on the way.

We could try for the neutrino spectrum, but (a) the low neutrino cross-section makes it very hard to collect enough events from an extra-solar source to say "these neutrinos are from that" much less enough to say "and this is the spectrum of neutrinos from the source", and (b) if the muons from which the neutrinos come have relative motion it would blur the distribution.

Similarly muon can be created in so many ways with such a diverse set of partners that the spectrum is unmanagably complex.

So, short-short answer part two: there are no clear signatures of muon creation or decay that can be observed over astrophysical distances.

1 In a highly relativistic regime ($\gamma \ge 100$) it is a very good approximation to relate the Lorentz factor to the mass $m$ and total energy $E$ of the particle by $$\gamma = \frac{E}{m} \;.$$

• Thanks, but I don't mean direct detection of muons. I am looking for astrophysical events where muon presence is suggested. Commented Jul 18, 2018 at 2:27
• Sorry to be so slow in getting back to you. I've been on the road. I can't think of any really clear signal of muon production that would be visible at astrophysical distances. Muon-flavored neutrinos would work if it weren't for neutrino mixing, but all the other products are (a) quite common and (b) are not produced with a sharp spectrum that would be identifiable at long range. Commented Jul 19, 2018 at 6:03
• Presumably $pp\to\pi^\pm$ occurs in supernova remnants shocks (cosmic ray accelerator sites) and the pions then decay to muons & neutrinos. Not sure that we've actually detected the existence, but I'm "out of the game" as it were. Commented Jul 19, 2018 at 16:37
• @Kyle Sure. I imagine that we can make a statistical argument that many (most?) of the UHE neutrinos we see come from decay chains that involve a muon somewhere along the way, but can we looks at a histrogram and say "that structure originates from events involving muons"? Commented Jul 19, 2018 at 16:43
• @dmckee from what I read of OPs wants, showing that CR protons are accelerated in SNR shocks and can interact with ambient protons which lead to a known decay chain of muons probably would suffice. Commented Jul 19, 2018 at 16:51

What measurements exist of the mass and radius of neutron stars do suggest that muons are created in their interior.

The bulk of the interior of a neutron star consists of a neutron fluid that is in equilibrium with a much smaller number density of protons and electrons. Once the Fermi energy of electrons reaches the rest mass energy of a muon then channels open up for neutrons to decay into protons and muons or for direct "muonisation" of electrons e.g. $$\bar{\nu}_e + e \rightarrow \mu + \bar{\nu}_{\mu}$$

The densities required for this to happen are about twice the density of an atomic nucleus (about $5\times 10^{17}$ kg/m$^3$), but such densities should be easily reached among the more massive neutron stars that have been observed and are likely even in the more average neutron star with 1.4 solar masses (see for example the influential review by Douchin & Haensel 2001 - especially Fig.4).

The muons thus created are stabilised against decay by the presence of the degenerate electron gas, which present no lower energy states into which a decay electron can emerge.

• What's a ballpark mass for a neutron star that starts to develop a population of stable muons in the core? The last time we discussed this I was left with the impression that it might be only the very heaviest neutron stars (and thus uncommon), but perhaps that was a misreading or a misremembering on my part.
– rob
Commented Jul 19, 2018 at 20:41
• @rob We didn't discuss it. The critical density for muonisation is about $5\times 10^{17}$ kg/m$^3$. Whether or not a neutron star of a given mass reaches this density in its interior depends on the uncertain equation of state. For an EOS that is just capable of supporting a 2 solar mass MS then I think muonisation should even occur in the core of a more average 1.4 solar mass neutron star. Commented Jul 19, 2018 at 21:59

Cosmic rays are widely believed to be accelerated in supernova remnant shocks (cf. this Q&A of mine). Since the majority of observed cosmic rays are protons, then the interactions of those highly energetic protons with thermal protons can lead to neutral or charged pions: $$p+p\to \begin{cases} p+\pi^\pm \\ p+\pi^0\end{cases}$$ The charged pions can then decay into the muons: $$\pi^+\to\mu^++\nu_\mu$$ which is what you're after (the neutral pions decay to photons, which is what Fermi LAT detects, hence ignoring it).

There is strong interest in the neutrinos in the above reactions (hence IceCube Obs.) in astrophysics, rather than the muons, but I would think that most sources of neutrinos are also going to be generating muons as well. That may be a starting point for further investigations.