Stars in the Far Arms of Galaxies Move Just as Quickly as Those in the Mid-Arms

From a Quora Question:
Why are stars in the far arms of galaxies moving just as quickly as those in the mid-arms


It happens to be close the one year anniversary of this video I made last year:

The velocity distribution depends on the matter-distribution.  So if most of the matter is condensed at the center, (like the solar system; more than 99% of the matter lies within the sun) you have one velocity curve.  If you have more uniform matter distribution, you'll have a different velocity curve.

Rigid body:  ω(r)=const;v(r)∝r; 


Uniform mass distribution: ω(r)∝1r√;v∝r√
Google graph of sqrt(x)
(Near the center of galaxies this is close to what you have)

Mass Concentrated at Center : ω(r)=1r3√;v∝1r√
Google graph of 1/sqrt(x) 
(Near the edges of galaxies, this is close to what is expected for the velocity curve, assuming we can actually observe everything that is there.)

What ends up being observed toward the edges is somewhere in between the last two.
Outer Galaxy Observation: ω(r)∝1r;v(r)=const

Now, when physicists credit "Dark Matter" to being the cause of this phenomenon, do they mean by "Dark Matter" simply something they cannot see (For example, could it simply be cold gasses (Though monatomic hydrogen can be detected by the 21 cm line, for instance, diatomic hydrogen might manage to hide, simply by not emitting anything if it is cold enough.) that aren't hot enough to have an emission spectrum,), or do they mean by "Dark Matter" something fundamentally different from ordinary matter?  (Stationary neutrinos, undiscovered noninteracting materieals.)