The Shape of Cold Dark Matter Haloes

Title: The Structure of Cold Dark Matter Halos

Also referenced: Small-Scale Challenges to the Lambda-CDM Paradigm

Authors: Julio F. Navarro, Carlos S. Frenk, Simon D. White

First Author’s Current Institution: University of Victoria

Status: Published in ApJ

Since the late 1970s, when Vera Rubin et al. confirmed the existence of dark matter via galaxy rotation curves, astronomers have known that dark matter, or matter which does not emit electromagnetic radiation, makes up a significant portion of the mass in a galaxy. This means that the dark matter component of a galaxy is a major contributor to the physics behind the galaxy’s star formation history, chemical enrichment. More generally, this suggests that the distribution of dark matter also plays a role in processes of galaxy formation and interaction. Thus, it’s paramount that we investigate the shape, or matter distribution, of dark matter halos in order to understand the gravitational conditions under which galaxies form and evolve.

In “The Structure of Cold Dark Matter Halos,” the authors Navarro, Frenk and White use numerical, dark-matter-only simulations to understand the shape of dark matter halos in cold dark matter (CDM) cosmology. The “cold” aspect of CDM cosmology comes from the idea that dark matter particles in this paradigm are kinematically cold. That is, they move at speeds slower than the speed of light. Dark matter particles (and objects more generally) that are moving slower relative to each other have a higher chance of clumping into larger blobs, or “halos.”

Takeaway 1: Dark matter halos have the same general shape

            Figure 4 from a recent review paper on the challenges to the Lambda-CDM paradigm (Bullock & Boylan-Kolchin 2017) illustrates the results from the NFW paper. For both of these panels, the x axis is the radius away from the galaxy. The color of each line corresponds to the mass of the galaxy halo (color bar on the right). On the left panel, the y axis is the matter density at a given radius. The left panel shows that dark matter halos across seven orders of magnitude have the same shape. In a gravity-only simulation, we should expect this general result because gravity is a scale-invariant property.

The right panel communicates the same result, but with circular velocity on the y axis. We expect circular velocity to increase with mass because the circular velocity of a star orbiting the halo increases with the amount of mass enclosed in its orbit. Mapping the results of the left panel to circular velocity provides us with an observational method of verifying this result, because we measure the circular velocity around a galaxy using Doppler shift spectroscopy. In fact, that’s how Rubin et al. deduced that there was dark matter: they found that circular velocities of galaxies at large radii were larger than expected from simply the mass contribution due to luminous matter!

Takeaway 2: Lower-mass halos are more centrally concentrated than higher-mass halos

In general, dark matter halos have the same profile. However, there are subtle differences between low-mass and high-mass halos. Figure 4 (left) and Figure 6 (right) from the NFW1996 paper are shown above. Unlike the previous plot, the density and circular velocities here are normalized between the low-mass and high-mass halos. The left panel shows the scaled density on the y axis, and the right panel shows the logarithm of the scaled circular velocity on the y axis.

In the left panel, the lower-mass halo is the lower line. This figure shows that small and large halos have the same shape at large radii (past log radius/r₂₀₀ ~ -1.0). At small radii, however, smaller halos are more centrally concentrated than larger halos. The right panel shows what we would should observe if this were the case. Again, the larger halo corresponds to the lower line on the y axis. For smaller halos, their maximum circular velocity for should be higher, and occur closer to the center of the halo, than for larger halos.

Takeaway 3: Larger galaxies have greater light-to-total mass ratio

            In Figure 11 of the paper, NFW match their results to observed rotation curves of spiral galaxies. The dotted straight lines are observed rotation curves of spiral galaxies. The solid line is the rotation curve of the galaxy that results from the combined mass contribution of dark matter and luminous matter (baryons). The dashed line is the velocity rotation curve that the dark matter halo contributes to. From bottom to top, the curves correspond to galaxies of increasing mass. The ratio of mass to light in the disk increases with mass. The more massive a galaxy is, the more its luminous matter component contributes to the rotation curve in comparison to the halo.

On the end of lower-mass galaxies, their rotation curves are almost entirely dark matter dominated. Although these results are for spiral galaxies, we also see a similar phenomenon in the Milky Way’s dwarf spheroidal galaxies.