Muons are naturally generated by cosmic ray protons colliding with atmospheric molecules and creating pions, which then rapidly decay to muons and muon neutrinos.

So in theory they could exist anywhere in the universe somewhat close to a star, if the relevant particles in our atmosphere are around that star? That’s what I meant about the density distribution: are they spherically distributed around (all) stars, or are they only present in very specific situations?

These themselves then decay into a bunch of other things.

I thought they had a small selection of possible decay products. Not particularly relevant to me at the moment, though.

As you say, with a mean lifetime of 2.2 nanoseconds, they shouldn’t be able to hit the surface of the Earth, but because at relativistic speeds time dilation occurs from our frame of reference (or, equivalently, in the muon’s inertial frame, it sees the distance it has to travel be radically shortened via length contraction), they do end up hitting the earth.

I mistyped the mean lifetime, it’s actually 2.2 microseconds. That’s three orders of magnitude different, but from a (non-relativistic) view it would still only travel about 66 centimeters. I’m missing too much information to try to solve the length contraction equation (I don’t know its length, or its velocity) for the observed length. I’m curious here because they’re able to travel on the order of roughly 50 meters into the Earth, and from what I can find they disappear there due to absorption from the many atoms they pass through on that path. So that leads me to a question: If there is not relatively dense earth to get in the way and attenuate the muon, such as if it were produced by a gas cloud beside a star, how far would it realistically be able to travel? Since the muons on Earth “die” from absorption rather than lasting long enough to decay via weak force, they would, in open space, surely be able to travel far enough without enough collisions such that they do end up “dying” by decay.

Thanks for the reply, I am curious here about something that I don’t have enough knowledge to answer for myself.