What methods can I use to determine the total mass of M31 using rotation curve data (galactocentric radius and rotational velocities)? I've used M(r) = RV^2/G to find the enclosed mass within the orbit of a target body in M31, but I want to use other methods to derive the total mass of the galaxy, including the mass of dark matter within the galaxy. How would I find the ratio of normal matter to dark matter within the galaxy using my rotation curve?
 A: The rotation curve is what gives you the total mass, including dark matter.
A standard, but unsophisticated, method to estimate the total stellar mass, is to measure the total luminosity within some radius and then convert this into stellar mass using an assumed stellar mass to luminosity ratio.
The stellar mass to luminosity ratio is estimated using models of stellar evolution and assumptions about the stellar birth mass distributions and (history of the) star formation rate. A typical figure might be each solar mass of baryonic matter results in about 1 solar luminosity.
The $M/L$ ratio is higher in older and lower-mass stellar populations and lower in very young populations with active star formation.
You then have to add some corrections for the amount of mass in the form of gas and dust (small), which requires measurements at radio wavelengths (e.g. 21 cm surveys).
I don't think there are too many alternatives to measuring the dynamics to estimate what dark matter is there. It's dark.
