Astronauts often see flashes when they are in space. How often these particles make their ways down to the Earth and hit us? What's the chance they hit our eyes and see flashes?
[Physics] How often does a cosmic ray hit our eyes when we are on Earth
cosmic-rays
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OK, here is something concrete and quantitative, "Guidelines for predicting single-event upsets in neutron environments":
Neutrons in the atmosphere result from cosmic-ray spallation interactions with nitrogen and oxygen nuclei. A typical reaction is a 1 GeV proton fragmenting a nitrogen necleus into lighter charged particles and simultaneoously emitting a couple of neutrons.
From "Cosmic ray induced ionization in the atmosphere: Full modeling and practical applications":
... full numerical model, which computes the cosmic ray induced ionization in the entire atmosphere, from the ground level up to the stratosphere, all over the Globe. The model computations reproduce actual measurements of the atmospheric ionization in the full range of parameters, from equatorial to polar regions and from the solar minimum to solar maximum. A detailed numerical recipe is given in section 2.5 together with the precalculated tabulated ionization yield function (Tables 1 and 2). Using this method, one can easily compute the CRII for any desired location and conditions, instead of using, e.g., a neutron monitor count rate as a proxy.
It does not describe it, but the CORSIKA (Cosmic Ray Simulations for Kascade) simulation tool is used.
Google-fu: quantitative neutrons cosmic rays atmosphere
It has to do with something called the Doppler effect. Looking at it from the cosmic ray's point of view, the light it hits head on has a really high energy, and the light that hits it from behind is even colder/lower energy than what we see ($2.7$ Kelvin).
If you want to stick to our point of view, then yes a photon hitting it from behind would boost it, but when you balance out the conservation of energy and momentum the head on hit takes away far more energy than the rear-ending gives. The way the math works on those conservation laws, it's basically changing perspective to the person who sees the cosmic ray and photon having the same momentum in opposite directions ("center of mass" frame), seeing what happens, and then translating back to our perspective. When the cosmic ray is being hit from behind there is very little energy left in either the photon or the cosmic ray after the change in perspective. When they hit head on, though, there is also less energy, overall, but far more than in the other case. This happens because in both cases the change in perspective needed is to be moving almost as fast as the cosmic ray in the same direction. By the Doppler effect, this will boost the frequency of the head on photon, and further reduce that of the rear-end collision photon.
This becomes really important when there's enough energy in the center of momentum frame to start doing something called pair production. For every type of particle the cosmic ray has enough energy to produce with the CMB, the faster it will lose energy to collisions with it. There is even a hypothesis that the distance cosmic rays can travel above a certain kinetic energy is severely limited by the fact that they should produce pions when it runs into the CMB. The name for this limit is the GZK cutoff. If you want to know why that is the limit, and not the production of electron-positron pairs, muon-anti muon pairs, or some other process, I don't know those details.
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Muons are the main cosmic rays reaching sea level with a possibility of interacting with matter. Neutrinos interact very weakly and need special detectors to be seen at all.
Rule of thumb when I was working with counters is that the flux of muons at sea level is 1 per cm^2 per second, wikipedia gives this number for over 1 Gev
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For energies above 1 GeV see this link.
The question then becomes biophysical, can the eye detect ionizing deposition which lasts much less than a second as the velocities are very high? The answer is no, unless there is an interaction with nuclei in the eye and there is a shower in the eye. The flux at sea level is predominantly muons which interact weakly with nuclei so there is very small probability that a shine in the dark is a cosmic interaction.
In the stratosphere and where the astronauts are living the flux is composed mainly by hadrons, and those have a high probability of interacting with nuclei in the eye.