# Do Elliptical Galaxies Have Dark Matter Halos?

Dark Matter in Spiral Galaxies

Kepler’s laws tell us that stars further from the center of their galaxies should have lower rotational velocities. But rotation curves (plots of velocity vs. distance) of stars in spiral galaxies show that the rotational velocities remain constant as distance to the center increases. This tells us that there must be a lot more mass than we can account for based on the light we observe from stars. We call this matter, which has mass but does not give off light, “dark matter.” Rotation curves of satellite galaxies indicate that the distribution of dark matter extends far beyond the edges of the host galaxy. Spiral galaxies appear to be embedded in large dark matter “halos”.

Fig. 1: An example of a galactic rotation curve, plotting the rotational velocities of stars against their distance from the center of a galaxy. The blue dashed line A shows what we would expect if all the mass was concentrated in the center of the galaxy — the velocities decrease further from the center. The red line B shows what we actually observe in galaxies — the velocities stay flat, indicating that mass increases with distance.

We can’t measure rotation curves for elliptical galaxies, which are not flat like spiral galaxies. Instead, we can study the mass-to-light ratio of elliptical galaxies with gravitational lensing. Alice has an excellent explanation of gravitational lensing in her astrobite,  “Gravitational Lensing in the Canary Islands”. As the galaxy passes between us and a quasar, the light from the quasar is bent by the gravity of the galaxy. If the galaxy is directly between us and the quasar, the quasar appears to be smeared out in a ring around the galaxy, usually called an Einstein ring.

Fig. 2: Examples of gravitational lensing from the Hubble Space Telescope.

The angular size of this ring can be calculated with some geometry:

$\theta_E = \sqrt{\frac{4 G M}{c^2}\frac{d_{LS} }{d_L d_S}},$

where G is the gravitational constant, M is the mass of the galaxy, c is the speed of light, and dLS, dL, and dS are the angular diameter distances between the galaxy and the quasar, the galaxy and us, and the quasar and us, respectively. We can measure these distances using redshifts. So if we measure the size of the ring, we can determine the mass! If the galaxy does not quite line up exactly, we see four images of the quasar (see Fig. 3), but these four dots can be used to determine the size of the unseen Einstein ring. If the misalignment is a little bigger, we only see two quasar images, which makes it harder to find the radius of the Einstein ring. However, the mass can still be calculated in these cases to within an accuracy of about 30%.

Fig. 3: Hubble Space Telescope images of the 15 galaxies observed in the article. The white dots are the quasar images. Eight galaxies produced 4 quasar images, while seven were more misaligned and only produced 2.

Observations and Results

The authors used gravitational lensing images from the Hubble Space Telescope to measure the mass-to-light ratio of 15 elliptical galaxies. Eight of these galactic lenses could produce four quasar images, and seven could produce only two. The mass was calculated using the equation above, and the light emitted was measured after removing the light from the quasar images. Observations with larger Einstein rings allowed the authors to measure the mass-to-light ratio further from the galactic centers. This allowed them to build a mass-to-light ratio vs. distance curve, to look for dark matter on the outskirts of the galaxies.

The authors found that the mass-to-light ratio is constant for different sizes of Einstein rings, showing that there is no sign of large amounts of dark matter surrounding these galaxies! If there is dark matter in these galaxies, it’s mixed in with the luminous matter. They measure an average mass-to-light ratio of 1.8, meaning that there is almost twice as much mass present as we would expect based on the amount of light.

Fig. 4: Mass-to-Light ratio versus the size of the Einstein ring for the 15 galaxies in the article. The blue open circles are the misaligned galaxies with only two quasar images. The black closed circles indicate the galaxies with four quasar images. The gold shaded region shows the results expected if a dark matter halo was present. The blue shaded region indicates the results expected if no dark matter halo is present, only stellar matter (dark blue) or stellar matter plus undetected baryonic matter (light blue).

The authors note that according to cosmological models and observations, we think that about 4% of the universe is composed of baryonic (“normal”) matter, but only about 2% can be seen with our current detectors. This isn’t “dark matter” — it’s just very dim, and our telescopes aren’t powerful enough to see it. They suggest that their observed mass-to-light ratio of about 2 could be explained by the missing 2% of baryonic matter. But that still leaves us an open question: why would there be dark matter halos around spiral galaxies but not around elliptical galaxies?

I'm a graduate student in the Physics Department at the University of Maryland, Baltimore County. I do my research at NASA/Goddard Space Flight Center with Marc Kuchner. I'm writing a model of debris disks to understand the way disks and planets interact, which will help us find exoplanets using images of disks. My model includes collisions, so I spend a lot of my day thinking about asteroids smashing into each other.

1. Do measurements of the gravitational lensing of quasars or other luminous objects by spiral galaxies using the formula given yield a more reasonable estimate of the mass of dark matter for spiral galaxies? i.e. does gravitational lensing by spiral galaxies agree with rotation curves with regards to the amount of dark matter present?

• As I understand, the vast majority of galaxy scale strong gravitational lenses are produced by elliptical galaxies. Unfortunately, only very rarely have strong lenses been identified in association with spiral galaxies – then mostly from edge-on viewing angles. As I understand, the properties of those strong lenses suggest that they are produced not by the galactic disks but solely by the elliptical galaxy bulge.

It certainly would be helpful if the total mass of spiral galaxies could be directly determined from strong lensing – so that they could be compared to difficult estimates derived from complex rotation curve studies!

It also seems to beg the question: if spiral galaxies are surrounded by enormous, massive dark matter halos (usually thought to be elliptically shaped) – why don’t their gravitational effects (which are expected to strongly influence disk rotational characteristics) produce strong gravitational lenses?

Also see my brief, informal essay: “Inappropriate Application of Kepler’s Empirical Laws of Planetary Motion to Spiral Galaxies…”
http://fqxi.org/data/essay-contest-files/Dwyer_FQXi_2012__Questionin_1.pdf

• Yes, the mass of spiral galaxies calculated by gravitational lensing shows a large deviation from the one calculated by summing up of individual stars.