How close does a supernova need to be to damage the Earth's environment?
How close to Earth would a supernova need to be before it caused significant damage to our ecosystem?
Phil Plait's Bad Astronomy page has a nice, detailed discussion of this question.
The conclusion seems to be that a supernova would need to be within tens or hundreds of light-years from us to cause significant damage to the Earth and life on our planet.
Luckily, the closest star that is massive enough to undergo a "type II" supernova explosion is farther away than that! (A type II supernova occurs when a massive star runs out of fuel in its nucleus, then collapses and explodes; the exact time when these supernovae will occur is difficult for us to predict. An alert reader has pointed out that there is a nearby star system which may be capable of undergoing a type I supernova -- in this type of supernova, a compact white dwarf star accretes matter from a companion until an explosion is triggered. However, it is likely that it will be hundreds of millions of years before the supernova actually occurs, at which point the system will have moved much farther away than it is now -- see the above link for details.)
As for the damage that a supernova would cause, the x-ray and gamma ray light emitted by the supernova would probably be our biggest concern. Without the Earth's atmosphere to protect us, x-rays and gamma rays can do significant damage to the molecules that make up living organisms. And supernovae do put out a huge number of x-rays and gamma rays; even if a supernova is thousands of light years away, it will still dump gamma rays on us at a faster rate than the sun does during its most active periods (i.e. when it is undergoing solar flares).
Luckily, though, our atmosphere easily protects us against solar flares and would probably do a good job against much larger gamma ray fluxes as well. You'd have to get to the point where the gamma ray flux was so high that it was destroying a significant percentage of the molecules in the protective layer of our atmosphere before you could really say that the supernova was damaging our environment.
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