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I have been given the task of synthesising an elliptical galaxy, a starburst galaxy and a spiral galaxy (considering the arms and the bulge separately and adding them) using stellar spectra which I have classified. I need to add different weightings of five types of stars to produce a normalised spectrum of each of these galaxies. I have spectra for giants, main sequence stars and sub-giants with varying stellar types (O, B, A, F, G, K, M). I know that Spiral arms and the starburst are going to be primarily young stars, while the spiral bulge and the elliptical will be of older stars, but I have no idea which types or luminosity classes of stars I would use and their weightings in each. Can anyone offer any information or resources where I would find good information on adding different types of star to 'create' a galaxy?

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This is an old one, but just in case you still need an answer, or someone else does:

The key realization here seems to be: what are the typical lifetimes of different stellar types? You might know that the hot and big (O/B) type stars are short-lived (their main sequence lifetime is in the order of a couple of million years) but the smaller, cooler stars (such as G stars like our Sun) can live for much longer - typically, $10$ billion years in the case of a Sun-like star.

In ellipticals (and likewise the spiral bulge), not many stars are created (low Star Formation Rate, SFR). As such, O/B stars will soon cease to exist in these. This causes reddening of the spectrum, since not the hot, blue stars will dominate, but rather cooler, redder stars. And in general, the older, the redder.

This is of course a consequence of Wienn's law / the Planck spectrum: cooler stars peak at greater wavelength.

Now, synthesising galaxy spectra is a whole field of astronomy in itself, dating back to the '60s and starting to make significant progress after the work of Tinsley (and others) in the '80s. All sorts of things need to be assumed, such as the Initial Mass Function (how many stars of each kind are created), Star Formation History (do stars form in bursts, or continuously? At what rate?), but also things like the dust content and temperature. This is actually a topic of ongoing research.

For your purposes, I would select an age for each of your galaxy types, and look up which stars will be still on the main sequence and which ones will not: if they're not on the main sequence I would set their weight to zero*. If they're still on the MS, you can couple first the number of stars of a given type (which you can get from an IMF; a Salpeter IMF is easiest to work with) to their average luminosity, to get a weight factor.

*Setting the post-MS luminosity to zero would be a very poor approximation in a proper SPS model, but again: to me this seems to be coursework where a general outline is of foremost importance.

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