How Does a Dark Matter Halo Relate to the Clusters of Galaxies We Observe?

[sketos]

I can undurstand that a dark matter halo is an area that surrounds galaxies and cluster of galaxies.

dark matter haloes can be constructed using N-body simulations, but what is the relation between the haloes and the cluster which we observe. Running a simulation for a cosmology profile ( LCDM cosmology ) and generating points of data in an area of the sky [φ1<azim-angle<φ2, θ1<polar-angle<θ2, z1<redshift<z2] what information do i get.

 

[marcus]

I can undurstand that a dark matter halo is an area that surrounds galaxies and cluster of galaxies.

dark matter haloes can be constructed using N-body simulations, but what is the relation between the haloes and the cluster which we observe. Running a simulation for a cosmology profile ( LCDM cosmology ) and generating points of data in an area of the sky [φ1<azim-angle<φ2, θ1<polar-angle<θ2, z1<redshift<z2] what information do i get.

It's interesting how two methods come together: (A) we can detect and make density contour MAPS of DM clouds surrounding galaxies and clusters, by the "weak lensing" method.
(B) we can PREDICT that during the expansion history DM should have CONDENSED somewhat to form wispy cobwebby strands and slightly denser clots where strands happen to cross.

And there is a rough qualitative agreement between what B predicts and the condensation structure we see with A. You probably have seen these density contour maps (google "bullet cluster" ). Made by plotting the distortion of background galaxy images by gravitational effect of DM density concentrations in foreground.

Part B involves what you mentioned, namely N-body simulations. To see the results of simulations of this "structure formation" google "TED design universe".

Part of what makes the part B simulations so interesting is that the cobwebby slimy-looking mess of DM provided a FRAMEWORK WHERE ORDINARY MATTER COULD CONDENSE. The framework helped pull the OM together. It provided regions of overdensity with enough pull to gather the OM into where it could start condensing on its own.

DM could do this because there was MUCH MORE of it, 10-fold more dark matter.

On the other hand OM is better at condensing in the final stages because it can radiate away surplus energy---the heat of particle collision that appears as a gas cloud contracts.
DM does not have this ability to expel contraction energy by radiation, so DM is limited in the extent to which it can contract.

The N-body simulations take account of this. During the initial stages of structure formation you can actually ignore OM because there is so little of it compared with DM. Then once the largescale structures are in place the OM begins to condense on that framework and you get galaxies and stars beginning to form.

When you google "TED design universe" you get a wide audience slideshow talk by Nobelist George Smoot called "The Design of the Universe". It has the images from the N-body simulations of DM condensation.

 

[Chronos]

Keep in mind that dark matter, unlike ordinary baryonic matter, does not clump. That makes its abundance in halos entirely logical. As it yo-yo's back and forth through the local center of gravity, it has its least velocity at aphelion, hence, spends a lot more time in the halo region than near the center of gravity.