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Originally Posted by grav
For a particular shape for a galaxy, there is only one mass distribution that will provide for the rotation curve from the center to the rim.
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That is not correct. In general, there are many possible density distributions which might create very similar rotation curves. That was one of the main points of my previous posting. If someone tells you the distribution of mass, then you can uniquely figure out the rotation curve; that's a "forward problem". However, if someone only provides you with the rotation curve, then it is an "inverse problem" to go back and figure out a mass distribution which could account for it.
At least, that's true in the most general sense. For some particular shapes of rotation curves, it may be true that only one sort of mass distribution will work; but I don't think that's the case for typical galactic rotation curves.
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That is also part of what the iteration does, kind of the point of it also. It gives the density distribution required for stable orbits of the stars at a particular rotation speed at each particular position.
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No, sorry to contradict you again, but your model -- if I understand it correctly -- does not tell you anything about the stability of the orbits. That was another point in my previous post.
For example, if you make a very simple galaxy -- a point mass of 100 units, a star of mass 1 unit at distance 10, and a star of mass 1 unit at distance 20 .... will the system be stable over many orbits of the stars? Your current method, if I understand correctly, does not address this issue. The answer for this simple system is "no", since the two orbits have a commensurate period, so perturbations between the stars will grow with time.
That's the next step in your work, I think. And it requires some new techniques in your code. Fortunately, other people have done this sort of thing already, so if you search through the literature, you can get a lot of tips.
TomT wrote:
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I am not sure of the contention that accounting for the spiral arms shouldn't matter much. This is saying that mass variation in the circumferential direction doesn't matter. So take the case of a 2 armed spiral galaxy. If you observe the light variation in the circumferential direction, would you say there is much variation or very little? It looks like a lot of variation to me. If M/L is important in estimating the mass, then I think circumferential variation of light is important, or should at least be checked out to see.
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Typical spiral arms are much more prominent in light than they are in mass, as images in the infrared (and models) show clearly. Nonetheless, they can have important dynamical effects on timescales of several rotation periods. It is this sort of effect which will require grav to use some new techniques. It _may_ be possible to do some stability analysis of rings or similar simple shapes analytically, but the most general method for dealing with this is to move to N-body calculations.