Hi grav,

I'm having further thoughts on this:

(1) If the area between arms is less dense and cooler, why wouldn't there be less mass. Mass = density x volume, so are you concluding there is more volume in the space between arms, than in the arms?

(2) The papers referenced by SM showed the density variation by a factor of about 2 between arms for M51, so unless volume also changes by about 2, wouldn't there have to be significantly less mass between arms. Then the local gravitational attraction would less and the same rotational velocity would be achieved by less gravity force acting on less mass. What am I missing?

TomT

Yes, less density equals less mass as far as the program is concerned, but I think you are thinking about it like less mass between the rings would mean less mass for the disk overall. But the ratio of densities of the spiral arms and between them is of little consequence, since we are trying to match the same rotation speed curve, which is what matters here. Less mass means less acceleration, which means less rotation speed. So what ends up happening with the reverse process, apparently, in order to match the same rotation speed curve, is that since the same rotations speeds require the same acceleration across the disk, within and between the spiral arms, then the spiral arms just become more dense than average for a uniformly dense disk and less dense between them, at 40%, but it remains about the same average density across the disk overall, and therefore the same mass. Now, with the rings and voids program, I was seeing a big drop in the required mass, and that would be closer to what you are saying, that since there is no mass between the rings, the required mass is also less, only accounting for the mass of the rings themselves, but that case is very different, because I was only accounting for the rotation speed curve within the rings, and not for the spaces in between, but according to what StupendousMan was saying, that would not be the case, so we would have to figure in the same rotation speed curve for between the rings as well.

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To Grav,

I suggest you run a few forward problems first, to see what an acceleration (and rotation speed) pattern would look like for reasonable SMD loadings. A first guess would be an SMD loading like the one resulting in a rotation speed profile of 200(1-e^(-5*r/rmax)) for an ordinary galaxy. Just use that loading along the arms with nothing between.

Ken N

To Grav

Since you pointed out that a disk with 1% thickness can have about a max vd of 2, I have reviewed the comparisons with theory in my paper with the following conclusions:

1. The comparisons are accurate enough. The result in my paper for a 5% thickness disk was a little low, with vd max about 1.704 instead of 1.745, the result for a sphere was close, and also the comparison with Freeman's result was close.

2. My results can be improved by using more rings and more rods. Except for the sphere, an increase in resolution seems to increase vdmax slightly. However the largest difference you noticed between your results and the 5% disk in my paper (2.0 vs 1.704) was because of disk thickness differences. My computer capability at the time my results were first done (late 1990's) was a lot less and thus the low resolution.

3. My paper needs no corrections. It's good enough.


effects of disk thickness:

hd vdmax

0.002 2.147
0.01 2.008
0.05 1.745
0.20 1.468
0.50 1.256
1.00 1.075
2.00 0.888

Ken N