| MadSci Network: Astronomy |
The best answer to this is one is "probably not, but we just don't know for sure."
The Crab Nebula is a supernova remnant---in A.D. 1054, a star blew up and the Crab Nebula is what was blown into space. This means that any planets in that area would have been blasted with radiation, and any life on them probably died at that time.
[In addition, stars that go supernova are massive and short-lived. It is not clear that such stars last long enough for life to arise on any planets that might be orbiting them. Moderator]
The "we just don't know for sure" part of the answer is that we can't be sure if there are even any planets in or around the Crab Nebula because it's so far away. Most of the planets discovered so far have been found because they are fairly close to the Earth and the planets are very large. This means that, as they circle their star, they tug the star one way and the other, and we can measure that small motion. But, as stars get farther away, the motion is harder to detect, and smaller planets (Earth-sized) don't make the stars wobble as much. We just don't have the technology yet to detect the effects of an Earth-type planet around even a nearby star, let alone around one at the distance of the Crab Nebula. Someday we might, but not yet.
[We can measure the arrival times of pulses from the Crab pulsar, the pulsar at the center of the Crab Nebula. This technique allows us to search for planets around pulsars at large distances from the Earth. Any planets around the Crab pulsar must be less than about 3 times the mass of the Earth or have extremely long orbital periods, otherwise they would have been detected by pulsar timing measurements. Moderator]
If there are any planets around stars in or near the Crab Nebula, they may or may not be able to support life. Some think that any Earth-type planet that's at the right distance to allow liquid water to form will develop life, but that complex life (like us, or cockroaches, or birds) may be very rare. The reasoning behind this was put forth in a book called Rare Earths by Ward and Brownlee, which was published in 2000. It's a good book, although I personally think that they might be a little too pessimistic about the rarity of complex life elsewhere in the Galaxy.
Regardless of your thoughts on the matter, we should all remember that we only know of one type of life---ours. We assume that all the factors that made life on Earth possible are necessary for life elsewhere, and we assume that life elsewhere will look like life on Earth. However, we only have one sample. We don't know for sure that life needs liquid water (or any water), that it will use DNA or similar molecules for storing genetic information, that it needs heavy elements, and so forth. We're like people living in an automobile factory looking for transportation in the jungle---all we know to look for is cars, so we may not recognize a canoe or an elephant as a way of getting around. Similarly, we may be utterly surprised when we discover the first life outside of Earth, or it may look just like life on Earth. With a sample size of one (the Earth) we just can't make any generalizations.
This is a longer way of saying, again, that there's no way to tell if stars in the vicinity of the Crab Nebula may or may not support life. They probably can't support life as we know it, but life as we don't know it may be there in abundance. We probably just won't know until we get there.
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