Density Falloffs and Unpremultiplying RGB for M51

A galaxy is made up of billions of stars.  Thus, there really aren't any alpha or radius differences between each splat in this case.  Instead, there is a falloff in density, or the number of particles (stars) as you move away from the center of the disk.  This indicates that some kind of PDF solution will be needed to create smooth density falloffs.  Also, the bright areas in the initial image indicate areas of greater density, and the dark areas indicate areas of lesser density.

In order to represent this, I'm using a PDF multiplied by the brightness of the particle to cull the density down.  Here's the first image I've gotten out of my code.

Because we're scaling the PDF probability down, much fewer particles are being kept.  I'm going to try a brute force solution to this (a heck of a lot more particles), but another, more elegant solution may be needed.

If a simple PDF is used, and the original alpha is kept, we get the image below.  I have also unpremultiplied the RGB values so that the colors are pure.