Mass-to-light ratio and rotation curve from brightness profile This should probably be basic but I've been looking for days and I can't find how to (I'm probably over complicating, but still).
I want to calculate a rotation curve for some spiral galaxies.
From what I understand I need to use the brightness profile (which I have) to determine the mass distribution and then use that with Poisson to calculated the $g$.
Then I can get the rotation curve.
My problem (for now) is how do I convert the brightness profile to mass-distribution?
the units are $mag/pc^2$ and the $y$-axis scale is 24-->18. it's not a direct relation because the distribution $y$-axis scale goes from small to large (10-->10^2 for example) so I can't just use $100 L/pc^2 = 22.05$ 
been finding all kind of different equations for different things, just not this.
would appreciate any help. 
 A: This presentation might be helpful to you.
Based on dust density and mass density in each pixel of an image, the luminosity is calculated as
$$L=L_0 \cdot \exp \left( \int \kappa \rho ds\right)$$
where $\kappa$ is a constant and $\rho$ is the density of the interstellar medium (I believe).
A more helpful relation for pixel-mass-to-luminosity is
$$\frac{dn}{d \log (m)} \propto m^{- \Gamma}$$
where
$$\Gamma= \left\{ 
  \begin{array}{l l}
    0.5 & \quad 0.1M_{\odot} \leq m \leq 0.5M_{\odot}\\
    1.15 & \quad 0.5M_{\odot} \leq m \leq 120_{\odot}
  \end{array} \right.$$
From this, you should be able to generate a rotation curve.
I'm not sure how well this will work for you; another option is the Tully-Fisher relation (for spiral galaxies); the Faber-Jackson relation is used for elliptical galaxies.

(source: noao.edu)
Scholarpedia has a helpful article.
A: It is probably best to start with a simple/crude estimate which you can then refine as you see fit.
Start by converting your surface brightness profile to units of $L_\odot/{\rm pc}^2$. Very crudely:
$$M - M_\odot = -2.5\log_{10}\frac{L}{{\rm L}_\odot}$$
Note $M_\odot$ is the absolute magnitude of the Sun, not its mass!
Then turn this into a (stellar) mass profile. You'll need a mass-to-light ratio $\Upsilon$ for this. These ratios are a whole sub-discipline unto themselves, so you can refine this endlessly, but a very crude estimate is $\Upsilon\sim1 {\rm M}_\odot/{\rm L}_\odot$ (note that here ${\rm M}_\odot$ is the solar mass - standard notation is messy in this case, sorry). The most useful mass profile for a rotation curve is the cumulative mass profile, which is:
$$M(<R)=2\pi\Upsilon\int_0^R \sigma(R')R'dR'$$
where $\sigma(R)$ is the surface density profile.
Once you have the cumulative mass profile, the rotation curve is trivial to compute:
$$V_{\rm rot} = \sqrt{\frac{GM(<R)}{R}}$$
This assumes that the mass distribution is approximately spherically symmetric (it probably isn't) and that the stars are all on approximately circular orbits (they probably aren't), but it's a start. Hopefully that's enough to get you started, from there it's a matter of reading a big chunk of literature and probably consulting experts to figure out all the details of how to refine your estimate.
Oh and as a bonus I'll save you 5 minutes of unit conversion and give $G$ in useful units:
$$G = 4.031\times 10^{-3} \frac{({\rm km~s^{-1}})^2\,{\rm pc}}{{\rm M}_\odot}$$
