Galaxy brightness and color correlation: what's the equation?

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GleefulNihilism
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So, as you may or may not have known there's an interesting correlation between galaxy brightness and it's color.

Basically, the brighter the absolute luminosity of a galaxy the redder it tends to be when compared to galaxies of the same type. I say "tends" because randomness does give the exact result some leeway.

I was wondering if anyone had the relationships in "mathspeak" as I call it. I'd be very interested in the equation used to derive and display this.
 
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Red giants are much larger - one of the three factors that contribute to the apparent brightness of a star - or collection of stars.
 
Well, Blue Giants can get pretty big too, but they tend to die pretty quick in comparison to Red Giants.

But I was thinking on a larger scale. Mathematical representation on a galactic scale is the goal, if from pure statisitcs alone.