Rotation curve in spiral galaxy velocity and uniform velocity dispersion

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The rotation curve of spiral galaxies shows uniform velocity dispersion in the outer reaches, which is taken as evidence of the presence and distribution of dark matter. My question: Does uniform velocity dispersion require the diffused distribution of dark matter, or could the distribution be, say, less diffused and more clustered, and there would still be uniform velocity dispersion, as long as there is the presence of dark matter?
 
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I don't think there's a general answer to that question. You'd have to plug a density distribution into the maths and see what orbits were implied.

Bear in mind that dark matter is influenced by gravity. You can probably find other density distributions that reproduce the same velocity curve for visible matter, but you have to show that the density distribution is consistent with the dynamics of dark matter.
 
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Entropy is not an additional form of mass, but in some approaches it can produce an effective extra acceleration at low accelerations (large radii). In an entropic or emergent-gravity picture, space/vacuum/information responds thermodynamically to the presence of baryonic matter, so the gravitational behavior outside the luminous disk deviates from purely Newtonian expectations. This can naturally lead to v_c(r) ≈ constant without invoking a diffuse dark-matter density profile. Importantly, a flat rotation curve tells us that extra gravitational effects are present, not where they physically originate. A roughly uniform velocity dispersion σ(r) is a separate issue, related to random motions and pressure support, and need not increase if the extra contribution mainly affects the mean orbital acceleration. Independent constraints (disk heating, stellar streams) then limit how clumpy any such explanation can be.
 
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FreeResearcher said:
In an entropic or emergent-gravity picture, space/vacuum/information responds thermodynamically to the presence of baryonic matter, so the gravitational behavior outside the luminous disk deviates from purely Newtonian expectations.
Is this deviation also expected for gravitation on the scale of the solar system? Can you cite a technical reference that derives this effect? Thanks.
 
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