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It is well-known that measurements of the velocity profile in galaxies are not compatible with Newtonian laws. A way to circumvent the problem is to assume that galaxies are surrounded by a spherical halo of Dark Matter. The density of mass of this Dark Matter can then be computed from the velocity profile with Newton's laws.

My question is the following: the formation of a galaxy involves essentially only the gravitational interaction. According to Newton (and General Relativity too), the trajectory of a particle does not depend on its mass. As a consequence, I do not understand how usual matter and Dark Matter could have followed different trajectories leading to such different mass distributions nowadays. Can somebody explain this (apparent) paradox ?

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one plausible explanation is that dark matter was not "dark" since the conception of universe! According to what i heard about dark matter, they are black holes and neutron stars which were present as ordinary matter. But then this also doesn't explain your answer... :( –  Vineet Menon Sep 29 '11 at 12:09
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The theory of dark matter as neutron stars and black holes has, for the most part, been shown not true. Look at the EROS, MACHO, and OGLE studies. –  Benjamin Horowitz Sep 29 '11 at 12:38

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Because normal matter can radiate (and therefore lose) energy when it gets hot, it is able to collapse into more compact configurations, like the stars that form galaxies. The real hold up in forming a galactic disk, I believe, is angular momentum. Dark matter, on the other hand, has no efficient way of releasing energy, so it keeps moving around quickly on large orbits, which leads to a more spherical halo.

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Wouldn't it possible to imagine that energy excess is transferred from Dark Matter to "normal" matter through the gravitational field and then dissipated by radiation. I would expect that because the gravitation field provides an interaction between Dark Matter and normal matter, they would reach an equilibrium state. –  Christophe Sep 29 '11 at 14:40
    
@Christophe: Yes it is, but the mechanism of such an interaction must be exceedingly weak (otherwise particle physicists would have seen evidence of it in our various low background detectors), and that weakness makes the time scale for such transfers longer than the current age of the galaxy. Efforts aimed explicitly at observing dark matter--ordinary matter interaction are now underway at a small scale and ramping up. Check again in a few years. –  dmckee Sep 29 '11 at 14:58

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