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I am attempting to pin down the data on just how many Super Nova have occurred in the history of our Milky Way solar system. How can scientist detect the remains of a Supernova and for how long after that Supernova occurres can we reliably detect that it happened? Is there a way that Astronomers can tell just how many Supernova have occurred in our galaxy?

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Supernova remnants do not remain visible for very long (if by that you mean the expanding debris from the supernova). It depends how you look for them, how close they are etc. but a rough guesstimate would be 100,000 years. However many such remnants in our own Galaxy would be obscured by dust, since supernovae tend to occur in the Galactic plane. Likewise, we only see a fraction of the neutron star remnants, since the pulsar phenomenon lasts again, perhaps only 100,000 years and observing the pulses is orientation dependent.

Nevertheless, such measurements and observations suggest the supernova rate in the Milky Way might be about 1 every 50 years, but is uncertain by a factor of two at least (see What is an approximation of the average number of supernovae every century in the Milky Way? ) . Extrapolating this to the $\sim 10^{10}$ year age of the Milky Way would suggest $2\times 10^8$ supernovae during its history.

However, it is thought that the star formation rate was much higher in the past than now. For a standard Salpeter initial mass function of say $N(m) \propto m^{-2.35}$ above $0.1M_{\odot}$ and an estimated Galactic stellar population of $10^{11}$ stars, one would estimate that perhaps $2\times 10^9$ stars were born with masses above $8M_{\odot}$ and would have exploded as supernovae. The idea of a billion supernovae or more in our Galaxy is consistent with calculations of supernova yields of various characteristic chemical elements and the abundance of those chemical elements (e.g.Europium) in the interstellar medium.

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