- Title: Gravitational lensing evidence against extended dark matter halos
- Authors: Pierre Magain and Virginie Chantry
- First Author’s Institution: Université de Liège
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”.
What about elliptical galaxies?
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.
The angular size of this ring can be calculated with some geometry:
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%.
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.
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?