# How does the amount of dark matter in measured galaxies vary?

I have recently viewed two news articles announcing a galaxy composed almost entirely of dark matter and one with hardly any. This made me wonder if there is a "continuum" of percentages of dark matter in galaxies, where it has been measured, or if there is a "preferred" range.

tl;dr: In general, smaller galaxies have relatively more dark matter than larger galaxies. The atypical galaxies that you refer to are discussed in the last paragraph.

## Mass fractions in the Universe

Matter in the Universe is dominated by two components; baryons (i.e. atoms in various forms) and dark matter (DM). The baryons predominantly exist in two forms: gas (including plasma) and stars (some gas condenses to form dust, planets, etc., but that's a minor part).

The fraction of the Universe's total energy in the form of matter is $\Omega_\mathrm{M}\simeq0.31$ (most of the rest is dark energy). The baryons and DM have fractions $\Omega_\mathrm{b}=0.05$ and $\Omega_\mathrm{DM}=0.26$, respectively (numbers from Planck Collaboration et al. 2016).

Hence, the baryons and DM comprise fractions $f_\mathrm{b} = \Omega_\mathrm{b} / \Omega_\mathrm{M} = 16$% and $f_\mathrm{DM} = \Omega_\mathrm{DM} / \Omega_\mathrm{M} = 84$% of the total mass, respectively.

## Galaxies have more dark matter than the average Universe

Galaxies formed when DM+gas overdensities decoupled from the Hubble flow and started collapsing, and so were "born" with the "cosmic" fractions. However, observationally it is found that the baryon fraction in galaxies is much smaller; for instance, a "typical" Milky Way-sized galaxy roughly has $f_\mathrm{b}$ only half of the cosmic average, and the DM fraction is correspondingly larger, >$90$% (e.g. Werk et al. 2014).

### Gas and dark matter dynamics

The reason is the different mechanisms that affect the dynamics of the particles. Whereas the DM is collisionless, the gas particles collide and dissipate their energy, making it easier to cool and contract. Thus, the part of the galaxies that we can observe is much smaller than "whole" galaxy; the typical "half-light radius" is but a few percent of the emcompassing DM halo (Kravtsov 2013, Somerville et al. 2017). The half-light radius is the radius within which half of the light is emitted; when you see an image of a galaxy, it typically looks perhaps 4-5 times larger than this. So, something like this:

A significant fraction of the baryons reside in the halo as well. This is the hot gas of millions of Kelvin, and the high temperature and low density makes it difficult to detect, as it glows only in faint X-rays.

### Feedback blows out gas, but dark matter stays

But various physical processes act so as to try to blow the baryons — but not the DM — out of the galaxies. These processes are known as feedback, and are due to energy being "injected" in the baryons. For massive galaxies with halo masses $M_\mathrm{h}\gtrsim10^{12}\,M_\odot$ this feedback is dominated by their central black hole accreting gas, resulting in extreme luminosities manifesting itself as a quasar, or active galactic nucleus (Silk & Rees 1998; Croton et al. 2006). For smaller galaxies with $M_\mathrm{h}\lesssim10^{12}\,M_\odot$, the feedback is mostly due to stellar winds and exploding stars depositing thermal and kinetic energy in the surrounding gas (Dekel & Silk 1986; Hopkins et al. 2012). At even lower masses, the galaxies are so small that a significant fraction of their gas may be ejected altogether during early epochs of star formation (e.g. Bullock et al. 2000), resulting in galaxies that consist virtually only of DM and a few stars.

The smaller a galaxy is, the shallower its gravitational potential, and thus the easier it is for the gas to escape the galaxy.

Hence, in general the smaller a galaxy is, the larger its amount of dark matter is.

Conversely, the larger a halo is, the more its mass fractions converge toward the cosmic fractions. These are only reached for halos of masses $M_\mathrm{h} \gtrsim 10^{15}\,M_\odot$, which are no longer individual galaxies, but rather groups and clusters. This is seen in the figure below (from a paper from last week by Henden et al. 2018), which shows the stellar mass fraction (left) and gas mass fraction (right) as a function of halo mass:

The baryon fraction is $f_\mathrm{b} = f_\mathrm{stars}+f_\mathrm{gas}$, and the DM fraction — which is what you're asking for — is then given by $f_\mathrm{DM} = 1 - f_\mathrm{stars} - f_\mathrm{gas}$. The stellar fraction is seen to decrease with halo mass, due to the AGN feedback discussed above, but the total star+gas fraction increases.

Note though that although the DM — being collisionless — is not exactly blown out of the galaxy like the baryons, the gravitational attraction between the two components still affects the DM and alters the density profile of the halo (Duffy et al. 2010).

## Galaxies with more gas than dark matter (?)

Thus, a galaxy without baryons is not a huge mystery, as long as it's small. Even larger galaxies are apparently able to rid themselves of most the baryons; van Dokkum et al. (2016) reported a MW-sized halo with 98% DM.

A galaxy with baryons, but without DM is more spectacular, but was reported recently by van Dokkum et al. (2018) (yes, the same guy). In another answer about DF2 I discuss various processes that might lead to such a galaxy, including misinterpretation of the data.

• So, am I right to say that, in general, the smaller the galaxy the higher percentage of dark matter mainly because more of the gas has been "blown away"? Has this been supported by stellar or globular cluster velocity measurements at different radii? – Jack R. Woods Apr 20 '18 at 3:05
• Yes, you're right. I'm not exactly sure what you mean by your second question, but measuring velocities at different radii (using stars, GCs, or gas clouds) is exactly one of the methods used to measure dynamical masses. At higher redshifts, where individual clusters and cloud are not distinguishable, a single emission line from everything in the galaxy may be used, using the width of the line to probe the velocity field. – pela Apr 20 '18 at 9:18
• +1 for a comprehensive answer, and for not saying dark matter is comprised of WIMPs. – John Duffield Apr 20 '18 at 15:13

The basic method used to measure dark matter in a galaxy is to observe the extra gravitational pull coming from matter which is not visible. The effect on orbits of stars in a galaxy (determined by observing galaxy rotational curves) and the bending of light by gravitational lensing are the some of the techniques used for measuring the gravitational pull of a galaxy.

• I've edited for grammar, but this doesn't really answer the question. You've explained how we measure the amount of dark matter in a galaxy. You haven't said how the amount of dark matter in different galaxies varies. – James K Apr 16 '18 at 7:29