The Initial Mass Function II: The Luminosity Strikes Back

Continuing the problem from the previous post (and ignoring the lame Star Wars reference), we now have 3 mass categories of stars in the cluster, and the total masses contained in each of these categories in the cluster.

Now suppose we want to find the total luminosity of the cluster. If the luminosity scaled with mass the same way for all masses of stars, then this would be easy. We could just use the total mass and convert it to luminosity using that relation.

It's not quite that simple, though, which is why in the previous post it was necessary to break the stars into categories: different masses of stars have different mass-luminosity relations. Here they are for low, intermediate, and high mass stars, respectively:





So, with each of the masses calculated in the previous post, we can use each of these relations to find the total luminosity for each category. The sum of these will be the total luminosity of the cluster.

I left those masses in terms of the solar mass, so finding the luminosity in erg/s will take some calculation. Help me, WolframAlpha, you are my only hope...

Once the luminosities are found, one can use them and Wien's Displacement Law to find the maximum-intensity wavelengths of the stars. Because younger stars are generally more luminous than older ones (they have more fuel which they use more wuickly), the average output radiation will be toward the blue end of the spectrum; older, cooler stars tend to be red.