Convert from Magnitude Density to Mass

[Earnest Guest]

I have data which gives me the magnitude density (mag arcsec-2) of M31 as a function of radius. How can I convert this data to the (enclosed) mass at a given radius (for Velocity Curve analysis)?

 

[Earnest Guest]

I don't know if it's a coincidence or not, but the magnitude density profile looks an awfully lot like a mass density profile:

Is there some very basic relation I'm not seeing or is this just a coincidence?