How close must a supernova be to severely harm the Earth?
I did a little looking and it appears stars outside of 10 parsec/33 ly will have very little effect on the Earth.
What it did say was that inside that range the gamma rays would affect our ozone layer which would reduce our radiation protection. How close would it have to be for the actual gamma rays to be a serious primary threat to the Earth, as in the gamma ray burst directly kills a large swath of Earth's life? I've been thinking about a story where this happens.
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Awesome question. I love this kind of thing.
Wikipedia of course has a a page on near-Earth supernovae, and the first body paragraph briefly examines the effects of life on Earth. The only really important thing there is just what you said - that the gamma rays from a supernova could deplete the ozone layer. Not too specific. But look further down the page. In this section, it says
Recent estimates predict that a Type II supernova would have to be closer than eight parsecs (26 light-years) to destroy half of the Earth's ozone layer.
I checked the referenced estimates on the arXiv pre-print used. It starts off with
Estimates made in the 1970's indicated that a supernova occurring within tens of parsecs of Earth could have significant effects on the ozone layer.
They then say that they now have improved tools; later on they say
We find that for the combined ozone depletion from these effects roughly to double the "biologically active" UV flux received at the surface of the Earth, the supernova must occur at <∼ 8 pc.
which they restate later as
Summing our gamma-ray and cosmic ray depletions for DSN = 10 pc, and taking into account that our adopted energy is larger than that found in the latest SN study mentioned earlier, we obtain a fiducial "critical distance" to significantly disrupt ozone of Dcrit ≃ 8 pc for a SN with a total gamma-ray energy ∼ 1.8 × 1047 erg.
And in the conclusion, we again find
Our primary finding is that a core-collapse SN would need to be situated approximately 8 pc away to produce a combined ozone depletion from both gamma-rays and cosmic rays of ∼ 47%, which would roughly double the globally-averaged, biologically active UV reaching the ground.
Not a huge difference at first, but we'd see some pretty bad effects after a while - say, a day or two.
Looking here, we find
A supernova explosion of the order of 10 pc away could be expected every few hundred million years, and could destroy the ozone layer for hundreds of years, letting in potentially lethal solar ultraviolet radiation.
Ouch!
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