# Why isn't Dark Matter distributed among ordinary matter?

DM: dark matter; OM: ordinary matter

I know that DM has a distribution which is mostly concentrated in the center of galaxies. This was mainly deduced by accounting for gravitational effects on the motion of galaxies which weren't due to any visible matter.

1) a: What property of DM which isn't present in OM caused it to clump up at the center of galaxies and cause this in-homogeneous distribution of dark and ordinary matter?

b) Is it because DM interacts with itself so weakly compared to OM that allows it to clump up whereas ordinary matter would start repelling itself ? (This would imply that the average density of DM in its clumps would be much higher than that of OM in a galaxy because otherwise even OM would be able to do it.)

2) Also, if interacts so weakly with OM does ordinary matter pass freely through the clumps? Can we study the interactions between OM and DM from objects that have passed through the clumps a long time ago and that are now much nearer to us?

• Why not use SM for "ordinary matter"? Stands for "Standard Model", which describes the kind of particles ordinary matter is made of... – Demosthene May 15 '17 at 13:41

1. Both of them collapse into clumps, the difference between the two processes lies in the inability of DM to interact with radiation. To picture this, imagine a spherical shell of dark matter collapsing under the gravitational influence of a seed galaxy at the center, and separately a shell of baryonic matter. The later interacts with light, and consequently will feel the radiation pressure coming from the center of the galaxy, which will stop the collapse. DM on the other hand does not posses this ability and keeps collapsing.

Because of this, DM structures collapses first at the early stages of galaxy formation. After a DM clump is formed, its gravitational pull can attract baryons and form the visible part of the galaxy. This argument is at the core of the currently accepted model of galaxy formation (Frenk et al. 1988)

2. Interaction indeed plays a crucial role during galaxy formation. In a sense, the collisionless nature of DM certainly affects the way galaxies are assembled. But you are right, the central density of DM clumps is higher than the it is for baryons. As a matter of fact, there's a famously successful model for describing the radial density profile of DM halos (NFW 1997) which predicts

$$\rho_{\rm DM}(r) = \frac{\rho_0}{(r/r_s)(1 + r/r_s)^2}$$

You can immediately see that the density grows without limits when $r\to 0$. This brings other issues into the table, but at a first approach it is a good model. The density of baryons (OM), on the other hand does not follow this behavior, and in general can be described with something like

$$\rho_{\rm bar} \sim \frac{1}{r + r_{c}}$$

3. Interaction between DM and baryons indeed can be tested. Here's an example, because the fraction of baryons is so low (in dwarf galaxies) you can think of them as tracers of the potential generated by DM. So you can reverse-engineer the orbits of the stars in these galaxies to predict the behavior of DM and the results are really interesting (Battaglia et al. 2008)

The issue is that the model $\rho_{\rm DM}$ above has been under the microscope several times because it allows to constraint the nature of dark matter itself (i.e., how 'weakly' two DM particles interact with each other, aka the cross-section). Using these type of experiments we could in principle discern whether this model is right, and under which conditions. The problem is that this is still a heated debate in the community.

Yet another example comes from stellar streams. You can think that a clump of dark matter floating around can poke one of these streams and make noticeable scars on them. By looking with high precision instruments to streams we could for instance conclude on the number of DM clumps in the Milky Way, their distribution, velocity, $\ldots$ all of these, extremely useful quantities when identifying the nature of DM (Sanderson et al. 2016)

• I couldn't understand much from the third reference link, could you explain exactly what interesting results you were referring to in the paper in layman's terms? – alex May 15 '17 at 14:19
• @alex I just updated the last part of my answer. Hopefully it makes more sense now – caverac May 15 '17 at 15:14
• Ohk I get it now... it's indeed pretty interesting – alex May 16 '17 at 7:34