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.
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).
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
So let's take those one at a time. The particle data group summary of muon physics (PDF link) will be useful here.
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.
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).
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 $$ \gamma = \frac{E}{m} \;.$$
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.
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.
