Diadem wrote:That is considerably more than I expected. And judging from your figures it sounds like a pretty low estimate. Only a factor 2.5 increase in supernova rate seems rather low. I always thought star formation was much, much higher in young galaxies? Also, why would heavy elements from the galactic centre not reach us? Their velocity is a significant fraction of the speed of light, well above the escape velocity. And there's plenty of time. Traversing a 100K lightyears at relativistic speed does not take long, on the time scales involved.
Remember, I quoted a (completely made up) average
SFR over the lifetime of the galaxy. It has for the most part been slowly, constantly decreasing over the lifetime of the galaxy, and was indeed much higher when the Milky Way was young. And SNR goes hand-in-hand linearly with SFR, assuming the initial mass function1
(IMF) is essentially universal. All signs so far point to the idea that it is.
Now, starburst galaxies do exist that can have SFRs stretching up into the hundreds of solar masses/yr (this might not sound like it, but it is a truly prodigious SFR - it means there are at least 1-2 SNe every year in that galaxy!), but this is not sustainable. They very quickly exhaust most of their star formation capable gas (usually within a few tens of Myr), and essentially shut off. For that reason, I think it is fairly reasonable to assume an average SFR only a few times higher than the current Milky Way SFR.
As for supernova ejecta, while it is going much faster than galactic escape velocity, it runs into the ISM and slows down fairly quickly; we can see remnants due to the shock waves that they generate as they expand. IIRC, significant amounts of ejecta don't get more than a couple of kpc away from the initial explosion site. Also remember that most supernovae, especially core-collapse supernovae, occur in giant molecular clouds (GMCs) and their immediate remains, regions where the ISM is much denser than normal. The supernovae blow bubbles in the ISM that are typically a few hundred pc across, and the majority of the progenitor star's mass remains within the bubble. I suppose, however, I should not have categorically declared that absolutely no material from bulge star formation makes it out to the solar neighborhood and beyond, but it isn't a very high fraction of the material that does. For the purposes of the order of magnitude calculation, it can shuffled under the rug.
Now, as a separate question, if you just want to ask how many SNe it takes to just make the amount of heavy elements we find in the solar system, that's much smaller. To get the correct abundances, you need a combination of core collapse and Type Ia SNe, plus a few AGB stars to make the s-process elements. But if you just want to have enough material to make our solar system, without caring about getting the absolute right abundances, it's probably only one, since core collapse SNe spew out many solar masses worth of ejecta, quite a bit of which is heavy elements. If you want to hedge your bets, make it two to throw in a 1a for a solar mass or two of iron peak elements.
lorb wrote:I think this assumption is too much of a stretch, especially since supernovae are known to be asymmetric, and there may be plenty of objects/forces around which do have an impact where the matter goes.
Nah, Diadem's got it. They're symmetric enough that it all averages out, especially when you have a lot of them going off in a relatively short time (~10 Myr or so). Most of the SNe in the galaxy, like 70-75%, occur in OB associations, 1
The IMF is basically the distribution of stellar masses. It describes quantitatively how many stars of a given mass are formed in a given volume. The first good estimate of this was done by Salpeter in the 50's. A Salpeter IMF has N(M)dM, the number of stars with mass between M and M+dM, proportional to M2.35
. More recent IMFs have a shallower slope at the low mass end below 1 solar mass; this better fits the observed stellar populations we see.