Obviously massless photons and the almost massless neutrinos escape all the time into interstellar space and beyond even without the assistance of a solar flare, but do electrons, protons, neutrons and even atoms ejected from the Sun, ever reach the escape velocity of our solar system?
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The solar plasma breaks down into Protons and Electrons that can easily reach our planet. I have no idea if they would be able to reach outside of our solarsystem. Interesting. I giant star or binary star systems could theoretically be ejecting protons and electrons further into their galaxies.
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The do not eject neutrinos. Neutrinos are generated by the nuclear reactions in the core of the Sun and every other star and emerge from the Sun is a pretty constant stream. The story that flares eject neutrinos comes from an excuse for a movie called "2012". It has no reality in fact. Solar flares only emit hydrogen, helium and a few other elements in the form of a plasma or charged particles, which may fall back into the Sun or may form part of the solar wind, which is different from the neutrino stream.