Image 1 Caption: An animation of galaxy rotation with inset plots showing galaxy rotation curves.

To see the animation---which is cool--click on the Image 1 and click the next image.

Features:

1. Galaxy rotation is shown WITHOUT dark matter and only baryonic matter (left) and WITH dark matter and baryonic matter (right).

   Note baryonic matter is ordinary matter made of protons, neutrons, and electrons.

2. The WITH-dark matter case is the observationally-verified case.

3. The maker of the computer simulation for animation in Image 1 assumed some plausible model of the distributions of baryonic matter and dark matter.

4. As one can see, without dark matter the galaxy rotation curve declines going outward after a peak. On the other hand, the galaxy rotation curve with dark matter plateaus. The plots have NO scales, but the plateau is typically at rotation velocity ∼ 200 km/s.

   The plateau is illustrated in below Image 2.

   

5. Image 2 Caption: A cartoon of a typical galaxy rotation curve plot. The "naively expected (A) and observed (B) star velocity as a function of distance from the center of mass of the galaxy." (Somewhat edited.)

6. We can understand the galaxy rotation curves from a simple model. Recall, circular orbit velocity formula derived from Newtonian physics:

     v=sqrt[GM(r)/r] , 

   where gravitational constant G = 6.67430(15)*10**(-11) (MKS units), r is the orbital radius, and M(r) is enclosed within a sphere of radius r and distributed with spherically symmetry.

   If the mass is centrally concentrated, then v will fall of as 1/sqrt(r). This behavior is, in fact, what one expects for galaxy rotation curves outside of the central regions if there is only the observed baryonic matter.

   However, what is observed outside of the central region of galaxies is, as aforesaid that, galaxy rotation curve plateaus: i.e.,

     v ≅ constant, 

   which implies

     M(r) ∼∝ r . 

7. In fact, the galaxy rotation curve plateaus extend well beyond almost all observable baryonic matter (typically to tens of kiloparsecs), and so invisible matter extends that far at least.

   Note we do, of course, see some baryonic matter (isolated stars, globular clusters, cold neutral atomic hydrogen gas) out to tens of kiloparsecs in order to the measure the galaxy rotation curves that far.

8. Why CANNOT the invisible dark matter be just baryonic matter?

   Why must it be (exotic) dark matter?

   Two reasons:

   1. The invisible dark matter matter is really, really invisible. The large amounts would be visible in some electromagnetic spectrum band somehow. But we see NOTHING.

   2. Big Bang nucleosynthesis (BBN) in order to match the primordial cosmic composition (fiducial values by mass fraction: 0.75 H, 0.25 He-4, 0.001 D, 0.0001 He-3, 10**(-9) Li-7) combined with viable cosmological models sets a strict limit on the amount of baryonic matter: ∼ 15 % of total matter (Wikipedia: Dark matter: ∼ 85 % dark matter, ∼ 15 % baryonic matter).

   We conclude the dark matter is something exotic: an exotic particle or, in a currently less-favored theory, primordial black holes (PBHs).

9. In fact, almost all large galaxies are embedded in roughly spherically symmetric dark matter halos which cause the gravity wells that hold the galaxies together.

   In a hypothetical universe without dark matter halos, there could still be galaxies, but they would probably be very different from the actual galaxies we see.

10. The cosmic mass-energy distribution (baryonic matter ∼ 5%, dark matter ∼ 27 %, dark energy 68 %) shows that dark matter is ∼ 5 times more abundant in the observable universe as whole than baryonic matter (see also cosmos_energy.html). However, much of the baryonic matter is the rather hard-to-detect baryonic dim matter (which is mainly in intergalactic gas of which much is warm-hot intergalactic medium (WHIM)). The fairly luminous baryonic matter (which is mainly galaxies in the form of stars, compact remnants, brown dwarfs, planets, and interstellar medium (ISM)) is only ∼ 0.4 % of the cosmic mass-energy (see cosmos_energy.html).

    In fact, galaxies have very small baryonic matter to dark matter ratios. One reference suggests the fraction is at most ∼ 1/30 for galaxies of about the golden mass = 10**12 M_☉ and the fraction decreases going to smaller and larger masses (Dekel et al. 2019, Figure 1: see also Cimatti-174--175). These low ratios for galaxies constitute the missing baryon problem of galaxies (AKA missing mass problem galaxies).

11. Note the orbital periods of stars increase with orbital radius from the galaxy center of mass and vary over a large range.

    For orbital radii ∼ 10 kpc, the orbital periods will typically be ∼ 200 Myr.

    This is shorter than the main-sequence lifetimes of stars of ∼≤ 3 M_☉ (lifetime ∼≥ 370 Myr: Wikipedia: Stellar evolution).

    Thus, such stars at orbital radius ∼ 10 kpc (e.g., the Sun) move far from their star formation regions (which typically break up and disperse on time scales of order tens of megayears) in an orbital period. Usually, all traces of their particular star formation regions are erased.

12. Extended Features:

    The extended features are shown in Galaxies file: galaxy_rotation_4.html which may be this file itself.

    EOF

Images:

1. Credit/Permission: © Ingo Berg (AKA User:Eclipse.sx), 2012 / Creative Commons CC BY-SA 3.0.
   Image link: Wikipedia: File:Galaxy rotation under the influence of dark matter.ogv.
   
2. Credit/Permission: © User:PhilHibbs, 2005 / Creative Commons CC BY-SA 3.0.
   Image link: Wikipedia: File:GalacticRotation2.svg.
   
3. Credit/Permission: © HyperPhysics: Orbit Speed Inside and Outside a Mass Distribution, before or circa 2021 / No permission.
   Image link: HyperPhysics: Orbit Speed Inside and Outside a Mass Distribution.
   Image link: Placeholder image alien_click_to_see_image.html.
   
4. Credit/Permission: User:Sjlegg, 2009 / Public domain.
   Image link: Wikimedia Commons: File:Grav field sphere.svg.