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How is the speed of the solar system through the dark matter halo determined?

Direct dark matter detection experiments rely on this speed estimate. Assuming the sun/earth travel through the dark matter halo, the relative speed difference between the sun/earth and the halo would result in a net dark matter 'wind'. As far as I understand, this wind would provide most of the kinetic energy needed for the dark matter to scatter to nuclei in the detector.

But how do we know the dark matter halo is not co-rotating with the luminous disk around the center of the galaxy? If it would, the wind may even be absent, and dark matter would be much harder detect in direct detection experiments.

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There is more than one approach that is used. One way that the velocity of dark matter relative to baryonic matter in a galaxy is inferred is by looking at "tracer" stars and using their dynamics to infer the velocity of the dark matter halo, as was done in a recent pre-print, whose abstract states in part:

We demonstrate how to reconstruct the dark matter velocity distribution from the observed properties of the accreted stellar population by properly accounting for the ratio of stars to dark matter contributed by individual mergers. After demonstrating this method using the Fire-2 simulations, we apply it to the Milky Way and use it to recover the dark matter velocity distribution associated with the recently discovered stellar debris field in the Solar neighborhood.

The review of the literature in the body of that pre-print cites another recent paper's use of a somewhat similar methodology which uses "the RAVE-TGAS dataset to recover the velocity distribution of the local relaxed DM component (Herzog-Arbeitman et al. 2018b)."

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    $\begingroup$ Thank you for the answer! I also found this post: physics.stackexchange.com/q/305983/211576 which I found useful. It explains partly the physics reason why dark matter does not settle into organized rotation like the ordinary matter. So now it seems a reasonable assumption to me; and I understand there are different ways to actually measure it, as you point out. $\endgroup$ – Gevo Nov 1 '18 at 23:22

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