What is an approximation of the average number of supernovae every century in the Milky Way?

Besides giving out a number and quoted source I would appreciate a short derivation of this number/formula based on our current data and knowledge of supernovae and the Milky Way. Show some traceable reasoning that proofs the source.

Aditionally, how many of these actually (on average) happening supernovae (also in neighbor galaxies) are spotted by amateur and professional astronomers?

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The last one seen in our galaxy was Kepler's supernova in 1604. There have been surely several since then, but unless a supernova is relatively close to us, we won't see it in visual light owing to absorption by interstellar dust near the Milky Way plane. But now, we should definitely see one if it occurs by using infrared, gamma ray, and/or neutrino detectors! –  Pete Jackson Jul 26 '11 at 18:10
This looks suspiciously like an exam question to me –  Pete Jackson Jul 26 '11 at 19:46
I'm trying to ask a fundamental question here. This surely could be an exam question and it is an example how questions fundamental to amateur astronomers are linked to astrophysics/cosmology. As far I know, there are amateur astronomers hunting supernovae though. –  Hauser Jul 26 '11 at 20:16
The real answer is, "They are too sparse for those units to have any meaning, since they are random occurrences subject to considerable stochastic variation. Supernovae per million years, however..." But otherwise, it's about 1 per century. We've had scientific-ish recordings for about a thousand years, and a heaping handful of naked-eye supernovae in that time. 1006, 1054, Brahe's, Kepler's, 1987a (In LMC, not Milky Way, but close enough, IMHO), and some others I can't remember offhand... –  Andrew Jul 27 '11 at 18:44
And Cas A is a supernova remnant in our galaxy whose progenitor star apparently exploded around 1667 but was never detected visually. –  Pete Jackson Jul 28 '11 at 14:25

Diehl et al. (2006) used gamma ray observations to map $^{16}$Al in the galaxy. Because $^{16}$Al has a half-life long compared to the expected rate of supernova, but not so long we expect the SN rate in the galaxy to have changed dramatically over that time, it might be an indicator of the recent SN rate. Actually carrying through this calculation relies on a lot of assumptions and models being correct. Ultimately, they arrive at an answer of about 2 per century.
Another approach is to use Hakobyan et al.'s estimates of the SN rate per $10^{10}$ solar luminosities as a function of galaxy type, and use estimates of the Milky Way luminosity and galaxy type. The Milky Way is probably a SBb (loosely would barred spiral), so the rate from Hakobyan is about 1.5 per year per $10^{10}$ solar luminosities, with large uncertainties. A very rough estimate of the Milky Way luminosity is about $2 \times 10^{10}$ solar luminosities, leading to an estimated rate of about 3 per century. The uncertainties here are huge, so this is completely consistent with Diehl's estimate approach above. (I'm actually quite surprised they are so close.)