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I just read that our galaxy's dark matter halo is estimated to be 1.5m ly across, compared to the visible galaxy's 100k ly across, needed to explain stellar rotation curves.

Why would this be? By which I mean, why would "ordinary" matter have become so localised and comparatively dense in a much smaller space, than the DM whose attraction gave rise to it?

Also, if DM is 4x the amount, but spread across that size it must also be very diffuse, in which case a very large part of the DM would seem to have (almost) zero effect on galactic rotation as it's (probably approximately?) uniform and outside the visible galaxy, hence like being inside a uniform shell, there should be little or no net gravitational effect either.

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  • $\begingroup$ Shouldn't be related to the fact that ordinary matter can 'stick"? At least in part? $\endgroup$ – Alchimista Mar 12 '18 at 10:05
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To answer your two questions:

  1. Almost by definition, dark matter does not interact with itself or other matter at all (or only very weakly). It therefore does not dissipate its energy as, for instance, electromagnetic radiation. "Normal" matter is able to dissipate kinetic energy and as a result can fall deeper into a potential well.

  2. Yes, dark matter is extremely diffuse. Its effects are only felt on very large length scales. The dark matter that exists beyond some particular galactic radius indeed has almost no effect on the rotation of matter inside that radius (it has some, because it not likely to be exactly spherically symmetric). The point is that spiral galaxy rotation curves stay flat out to the edge of where the visible matter is, despite a decline in the visible matter density. The amount of visible mass integrated out to those radii is insufficient to explain the centripetal acceleration observed. The discrepancy can be explained by postulating dark matter that exists inside that radius. However, this dark matter is the minority of the dark matter in a galaxy, most of which is thought to exist in galactic halos and which only (greatly) affects the dynamics of the most distant orbiting objects or satellite galaxies.

The point is made well by this plot from Klypin et al. (2001), which demonstrates how the various components contribute to the Milky Way rotation curve as a function of Galactic radius. Note how the disk+bulge (normal matter) dominate the dark matter (halo) contribution until radii greater than 13 kpc, which is about 4 times the exponential radial density decay scale-length for the Milky Way disk.

Rotation curve modelling of the Milky Way

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    $\begingroup$ Not sure what "the exponential scaling length for the Milky Way disk" means? $\endgroup$ – RBarryYoung Mar 12 '18 at 16:57
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    $\begingroup$ Spot-on answer. To add a bit of cool lore: this is also the reason for the dark matter "wind". The galaxy rotates through the dark matter cloud that is on average "at rest". Why the difference? The diffuse proto-galaxy had some small initial angular momentum. The baryons cooled by emitting photons, which preserves angular momentum. Thus the small angular momentum much more pronounced by the cooling, resulting in rotating galaxies. $\endgroup$ – thegreatemu Mar 12 '18 at 17:12
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    $\begingroup$ RBarryYoung It means the density of the disk drops exponentially in the radial direction, with a scale length of about 3 kpc. $\endgroup$ – Rob Jeffries Mar 12 '18 at 19:12
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    $\begingroup$ Is it worth adding some language that acknowledges the possibility of dynamic cooling in a collision-less gas as it may apply to dark matter systems? $\endgroup$ – dmckee Mar 12 '18 at 20:24

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