How Should We Visualize Dark Matter Around Spiral Galaxies?

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ryan albery
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Does it make sense to visualize dark matter as roughly spherical, or oblate, around a spiral galaxy? Perhaps incorrectly, I picture dark matter as analogous to a planet, or star, with the visible disk of the galaxy forming the equatorial plane. Is this reasonable picture of what we observe through lensing, and accounting for the constant rate of rotation? If so, is there thought to be a radial density gradient in the dark matter, something akin to the mostly linear density gradient of Earth's atmosphere, or is the dark matter thought to be more of a constant density? Also, does the dark matter rotate with the galaxy? If the planet analogy is reasonable, insomuch as the dark matter has an axis of rotation, what's the force is that keeps what I'll assume to be 'particles' of dark matter near the poles from simply falling into the center of the galaxy?

Much thanks to anyone who can set me straight, and thanks so much to everyone for making this such a valuable resource for learning about the universe!
 

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The general picture is of a galaxy surrounded by a dark matter halo that goes out to many times the extent of the luminous matter. Haloes definitely have a density gradient, being denser in the centre and becoming more tenuous as you move outwards. I know that some observations support spherically-symmetric density profiles, in which the density depends only on radial distance r, from the the centre. See for example the Navarro-Frenk-White (NFW) profile. On the other hand, I know that triaxial haloes have been found to better match/explain observations in some instances.
 
I usually prefer to think of dark matter as being a large, smoothly-distributed gas of weakly-interacting particles, more dense in the center and tapering slowly out to the edge, with a much smaller galaxy sitting in the center of it. The individual particles of dark matter all have their own orbits around the center of mass. The main reason why they don't just fall to the center and stay at the center is that because they interact so weakly, they have no way to lose energy. So as they fall towards the center of the galaxy, they pick up a large velocity that just pushes them right back out to as far as they came in.

The rotation of dark matter is probably completely unrelated to the rotation of the galaxy that's sitting inside it, because there is so little interaction between the two.