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Originally Posted by RussT
BUT, since there can be no transverse component to its velocity it MUST be a straight line.
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No, you are mistaken. As Kaptain K pointed out, dark matter is accelerated by gravity, just as ordinary matter is.
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SO those spheres (If they really exist) MUST form somehow...How?
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Gravitational interactions between clumps of dark matter can cause some clumps to lose angular momentum and energy. In addition, gravitational interactions between dark matter and _regular_ matter -- which can dissipate energy and angular momentum -- can lead the dark matter to coalesce, to some extent. It's not an efficient process, which is one of the reasons that dark matter halos are so extended compared to baryonic matter.
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So, are you saying that the spherical halo is rotating with the influence of the SMBH in the center of the galaxy as its main source of gravitational influence?
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No, the influence of a SMBH at the center of a galaxy on the non-baryonic dark matter in that galaxy's halo will be minimal. The regular matter distributed throughout the galaxy will have a larger effect. The non-baryonic dark matter itself will have the largest effect. Halos need not be rotating, by the way; they may be triaxial.
Why don't you spend a few days reading some recent papers describing the formation of structure on galactic scales? There are plenty of papers on the topic freely available on astro-ph.