Do the stars imaged by a telescope even exist at present?

I know that we now have telescopes which can capture the images of the stars and galaxies millions of light-years away from us.

Does the telescope capture the past image of the star, i.e. the light which it emitted centuries ago?

What guarantee is there that the star is still alive?

What basis do organizations like NASA plan missions for evading such stars?

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What do you mean by "evading such stars"? – Carl Apr 11 '12 at 11:57
@Carl - I want to know about the other missions - the ones aimed at stars :-) – Rory Alsop Apr 11 '12 at 19:26

For a star of a given mass, we can calculate, based on theoretical models, how long it has to live. For example, the Sun is currently 5 Gyr old and will live another 5 Gyr. So if you observe the Sun from, say, Andromeda, the light would be about 2 million years old and you could therefore conclude that the Sun is still alive even though you're observing "old" light. If you flip it around, if we see a Sun-like star in Andromeda, we could safely say it's still alive.

Broadly, while fusing hydrogen in their cores, more massive (and therefore brighter, hotter) stars live shorter lives. On the one hand, it means that we observe some small stars whose lives will be longer than the current age of the Universe. On the other hand, we could theoretically observe stars whose lifetimes are shorter than the distance to them, in light-years. So, a star 80 times as massive as the Sun might have a lifetime of a few million years, so if we currently observe it in Andromeda near the end of its life, that star is probably gone now. Off the top of my head, I'd say most of the stars we presently observe still exist as we see them now. We just can't resolve stars that far away.

For what it's worth, there are some distant phenomena that we see that happen much faster than the light takes to reach us. For example, the 2011 Nobel Prize went to the leaders of two teams that observe Type Ia supernova at redshifts up to about $z=1$. These are events that lasted less than a year that happened nearly 8 billion years ago. Who knows what they look like now!

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2011 Nobel Prize I think... – Chris White Dec 19 '12 at 8:21
Absolutely right. Fixed. – Warrick Dec 19 '12 at 14:43

Any star in our own galaxy is no more than about 100,000 light-years away. Since most stars live for millions or billions of years, the odds of any given star having died in the time it took for its light to reach us are very slim. In most cases, as Warrick's answer points out, the odds are practically zero; Sun-like stars, for example, aren't massive enough to go supernova. It's conceivable that something bad has happened to Alpha Centauri A (4.3 light-years away) in the last 4 years, but there's no known mechanism that would cause it to explode.

The most likely candidate in our galaxy for a relatively nearby star that might have exploded is probably Betelgeuse -- but even it's only about 640 light-years away, and could last another million years, so the odds of it having exploded by now are somewhere around 0.1%. Eta Carinae might be another possible candidate.

There's a supernova in our galaxy roughly once every 50 years (yes, that means we're overdue). Assuming that the average star in the Milky Way is 30,000 light years away (the distance to the core), there are probably about 600 stars in the Milky Way that have already gone supernova, but for which the light from the explosion is still in transit. (That's a very rough estimate.) Probably most of those stars have never been seen individually, even with a telescope. On the other hand, stars that can go supernova tend to be large and bright. It would be interesting to estimate how many of those 600 or so stars have actually been seen; I lack the information to do the calculation.

For stars in other galaxies, the story is nearly the same. Andromeda (M31) is about 2 million light-years away; there are probably some visible stars there that have exploded in the last 2 million years (especially since brighter stars are more likely to do so), but the vast majority are probably still as stable now as they were 2 million years ago.

As you look at more distant galaxies, you're looking further into the past, but it also becomes more difficult to resolve individual stars.

The progenitor star for Supernova 1987a, called Sanduleak -69° 202, was discovered before it exploded, so there's at least one case where we were able (before 1987) to see a star that had already gone supernova.

But stars that explode, even in a supernova explosion, do not simply cease to exist. A remnant of the original star remains, typically as a neutron star or black hole.

Finally, there's a famous Hubble photograph of a formation (not a star) called the Pillars of Creation, part of the Eagle Nebula. The Pillars are about 7000 light-years away, but they are believed to have been destroyed 6000 years ago by the shock wave from a supernova. UPDATE : This interpretation has been disputed; see the linked Wikipedia article for details.

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+1 for all the particular and interesting examples. – Warrick Apr 12 '12 at 7:05