How Dangerous are Solar Protons Events to Astronauts?

Source: Foundations of Solar Particle Event Risk Management Strategies, Draft Report for the NASA, Mission From Planet Earth Study Office and Life and Microgravity Science and Applications Office, April 1996
The sun is a very powerful natural particle accelerator. It can accelerate ions up to hundreds of billions of electron volts in energy and send them streaming toward the Earth. These events occur as a natural consequence of violent events on the sun, such as flares and coronal mass ejections. Ions at these energies are extremely damaging to living cells.

Between the Apollo 16 and 17 manned space missions, one of the largest solar proton events ever recorded arrived at Earth. It is only a matter of luck that the astronauts were under the protective cover of the Earth's atmosphere at the time. Computer simulations were done of the radiation levels an astronaut inside a spacecraft would have experienced during this event. These are shown in the figure. Surprisingly enough, even inside of a spacecraft, the astronaut's would have absorbed lethal doses of radiation within 10 hrs after the start of the event. 4000 mSv is an average fatal single dose without treatment and is also the career limit for exposure of the eyes to radiation.
