Rotation Curves As Evidence of A Dark Matter Halo
The presence of dark matter in the halo is demonstrated by its gravitational effect on a spiral galaxy's rotation curve. Without large amounts of mass throughout the (roughly spherical) halo, the rotational velocity of the galaxy should decrease at large distance from the galactic core, just like the velocity of the outer planets decrease with distance from the Sun. However, observations of spiral galaxies, particularly radio observations of line emission from neutral atomic hydrogen (known, in astronomical parlance, as HI), show that the rotation curve of most spiral galaxies flattens out, meaning that rotational velocities do not decrease with distance from the galactic center. The absence of any visible matter to account for these observations implies the presence of unobserved (i.e. dark) matter. Asserting that this dark matter does not exist would mean that the accepted theory of gravitation (General Relativity) is incomplete, and while that could be possible, most scientists would require extensive amounts of compelling evidence before seriously considering it.
The Navarro-Frenk-White profile:
is often used to model the distribution of mass in dark matter halos. Theoretical dark matter halos produced in computer simulations are best described by the Einasto profile:
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