# Week 10 Dark Matter Reading: Dark Matter: 16.1, 16.5d (4 pages)

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Week 10 Dark Matter Reading: Dark Matter: 16.1, 16.5d (4 pages)

Sometimes even when galaxies do not look like they are interacting – they really are. That is, the matter extends beyond the visible light.

Dark Matter It turns out that it is even more dramatic than that. We now have evidence that there is 10x more matter than we can actually see (i.e., that gives off light) This used to be called the “missing matter” problem.

Dark vs Non-Dark Matter Dark Matter Not Dark Matter

If we can’t see it, why do we think it’s there? Three Reasons: 1.Galaxy Rotation Curves 2.Existence of Galaxy Clusters 3.Gravitational Lensing

Kepler’s Laws I&II The orbital period [P] (time per complete orbit) of a planet is related to its average distance [a] by: P 2 in years = a 3 in A.U. III

Galaxy Rotation Curves

The orbital speed of an object only depends on the amount of mass between it and the Galactic center:

The Sun orbits the Galaxy at ~230 km/s. The Sun takes ~230 million years to orbit the Galaxy. Using Kepler’s Law and the mass and speed of the Sun, we estimate the mass of the Galaxy to be 1.1x10 11 solar masses. Dark Matter and The Sun’s Orbit Around the Galaxy

At very large distances from the Galactic center, the velocity should diminish with distance, as the dashed curve shows. It doesn’t; more than twice the mass of the galaxy would have to be outside the visible part to reproduce the observed curve.

Since there must be more mass in the Galaxy than we can see, we refer to this mass as “Dark Matter”.

Other galaxies have rotation curves similar to ours, which means that they have dark matter too.

Galaxy mass measurements show that galaxies need between 3 and 10 times more mass than can be observed to explain their rotation curves. The discrepancy is even larger in galaxy clusters, which need 10 to 100 times more mass. The total needed is more than the sum of the dark matter associated with each galaxy. How Much Dark Matter?

Another way to measure the average mass of galaxies in a cluster is to calculate how much mass is required to keep the cluster gravitationally bound.

Dark Matter in Galaxy Clusters In short, galaxies in clusters are moving so fast that they should fly away from each other. That they don’t suggests that there is more gravitational force than we thought.

On the left is a visible image of a cluster of galaxies. On the right, to the same scale, is the dark matter distribution inferred from galaxy motion.

The Bullet Cluster: A Spectacular Example

Bullet Cluster Gas Collision

Bullet Cluster: Proof of Dark Matter

Gravitational Lensing

Gravitational Lensing: Examples

Here, the intervening galaxy has made four images of the distant quasar.

These are two spectacular images of gravitational lensing. On the left are distant galaxies being imaged by a whole cluster. On the right is a cluster with images of what is probably a single galaxy.

So What is Dark Matter Really? We don’t know.

Neutrinos, WIMPs, MACHOs But we have some good guesses. These include massive neutrinos, WIMPs (Weakly Interacting Massive Particles) and MACHOs (MAssive Compact Halo Objects)

Neutrinos and WIMPs

MACHOs Massive Compact Halo Objects For example, planets, dim white dwarfs, etc. Can detect these via gravitational lensing.

MACHOS vs WIMPS MACHOS are likely to account for only a small fraction of the total dark matter. Most likely candidate for dark matter is, as of yet undiscovered particle called the neutralino (which is a WIMP) So WIMPS win!

Dark Matter Fraction