Face on Surface Brightness Profile For Spiral Galaxies

[blumfeld0]

Why does the face on surface brightness profile of spiral galaxies follow an exponential decrease with incresing distance from the center? Why is it exponential as opposed to linear or some power law? seems like 'e' shows up a lot.

I know it is an obervational fact that they exhibit this behavior (it's also been confirmed in numerical simulations) but does anyone know what the mechanism involved here is? I don't know maybe I am asking too deep a question here but I really am curious as to a known explanation.
Is it related to conservation of angular momentum when sprials form maybe?blumfeld0

 

[lippyka]

's answerThe exponential decrease in surface brightness can be explained by the inside-out formation of a galaxy's disk. When the galaxy forms, it begins to form stars at the center first and then slowly moves out in radius as the galaxy's gravitational potential weakens. This is because the gas clouds, which form stars, are able to collapse more easily when the gravity is stronger near the center, allowing for an increased star formation rate. This mechanism explains why the star formation rate decreases with increasing distance from the center, resulting in an exponential decrease in the surface brightness of the galaxy. The exponential decrease is also due to the conservation of angular momentum of the gas clouds. As the gas clouds collapse to form stars, they conserve their angular momentum, preventing them from collapsing too quickly and instead spreading out in a disk. This results in the exponential decrease in surface brightness as the stars are spread out over a larger area.