How long do supernova remnants last?
I'm not sure if this question directly relates to supernovae, but could you tell me how long nebulas last for? I know they are formed when a star goes supernova, but do they ever die or fade?
There are many different types of nebulae in astronomy, none of which actually have much to do with each other! But I'll answer your question specifically in regard to nebulae that come from material ejected in a supernova, which are often called "supernova remnants" (SNR). A famous example of a SNR is the Crab Nebula.
SNR do fade away and eventually become invisible. The time for this to happen is on the order of tens of thousands to a hundred thousand years. The reason that SNR eventually fade is simply that they only have a finite amount of energy input to them at their formation -- this energy comes from the material that was ejected by the central star in the supernova explosion. As this material moves away from the center and collides with gas in the region surrounding the star, it will lose some of its energy as it heats up the gas. The heated gas then releases this energy in the form of light, so eventually all the available energy will be released and the SNR will not shine any more.
We can estimate how long a SNR will shine if we measure the temperature of the gas that is being heated up by the shock wave from the central source. If we know the temperature and can estimate the amount of gas there is, we can calculate the rate at which the gas is emitting energy as well as the total amount of energy available for it to radiate; therefore, we can estimate how long it will shine for.
Another effect to keep in mind is that as the shock wave from the explosion moves farther away from the center of the SNR, it will sweep up a lot of the surrounding gas. Some of the energy of the shock wave goes into accelerating the "new" material that is being swept up, so that overall, the speed of the shock has to go down. This means that eventually, far away from the center of the SNR, the shock wave won't be moving that fast and so it won't heat up the new gas that it encounters too much, and the SNR will not be as bright.
For more discussion of the phases of expansion in a SNR, have a look at this page from Imagine the Universe.
One final complication to the above discussion that is worth pointing out is the effect that the remnant of the exploded star's core, at the center of the SNR, might have on the SNR emission as a whole. If, for example, the supernova explosion left behind a rapidly rotating, magnetized neutron star (i.e. a pulsar), the pulsar can continue to contribute energy to the SNR long after the supernova explosion occurs. Astronomers think that this process is currently going on in the Crab Nebula.
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