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If the dark matter halo is stationary related to the arms of the galaxy then tidal effects should slow the galaxy rotation.

If it rotates with the normal matter in the galaxy then shouldn't it flatten out into a disk?

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It would probably be more proper to say that the galaxy rotates with the dark matter halo, since the mass of the halo is greater than the baryonic mass of the galaxy that we observe. Generally, dark matter halos have triaxial shapes, and shortest axis of the visible part of the galaxy will also be shortest axis of the dark matter halo.

EDIT: I should have been rather more careful. My answer is generally correct, I think, but there may be some more variation than I thought. A paper looking at spin of dark matter halos in the presence of baryons in the Millennium simulation sees a median misalignment between halo and baryonic (visible) galaxy of 30 degrees, and quite a total distribution. They further note that this misalignment seen in simulations will complicate mapping of dark matter halos with lensing measurements.

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jdmcbr thank you. Kent –  Kent Byerley Feb 1 '12 at 16:20
    
Can you say a few words about the source of this? Model, micro-lensing, other? –  dmckee Feb 1 '12 at 16:44
    
There have been some 2-d density profiles of dark matter halos from gravitational lensing. I'm not sure if anyone has stitched together 3-d halo shapes on the basis of lensing and ... not sure what else would be used. I was mainly referencing the standard models of dark matter halos, which mostly seem to agree with observations in areas where they can currently be compared. –  jdmcbr Feb 1 '12 at 17:36

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