If our galaxy's dark matter halo is so large and diffuse, why is the ordinary matter in it so much more localised and compactly located?

Question

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.

Answer 1

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.