It seems that we know the rotation curve inside the sun's galactic orbit fairly accurately. Then wouldn't we be able to just take the derivative* of this to get the DM density profile at smaller radii? What then is the primary reason we can't distinguish between different profiles like pseudo-isothermal, NFW etc?
a) Is it uncertainty in the rotation curve? If so what is the source of this uncertainty? b) Uncertainty in the amount of luminous matter? Source?
I can see why the profile is uncertain at larger distances from the galactic center since the rotation curve is uncertain there, but why is it uncertain in the region where the rotation curve is known more precisely?
*Well, square, multiply by r and take the derivative, but you get the idea