Dark Matter

Friday, April 22, 2022

Spiral Galaxies

Spiral galaxies, like the Milky Way, are composed of a number on the order of $10^{11}$ stars held together by the gravitational interaction. The diameter of such a galaxy is typically about $10-50~\text{kpc}$ . Most galaxies are spiral galaxies and have a bright region in the middle (most of the galaxy's mass), about which the rest of the galaxy revolves, turning the galaxy into a flat disk.

Our sun is about $8.5~\text{kpc}$ from the center of our galaxy, rotating around its center at about $220~\text{km/s}$ .

Using Kepler's third law, we can relate the period $T$ of orbit to its radius $r$ :

$T^2=\left(\frac{4\pi^2}{GM}\right)r^3$

with $T=2\pi r/v$ , we get

$v=\sqrt{\frac{GM}{r}}$

According to this model, stars farther away from the center of the galaxy should be orbiting with tangential velocity that decrease on the order of $r^{-1/2}$ (just like the planets in our solar system). However, we find that stars' velocities are relatively constant or even increase with increasing radius from the center of the galaxy.

Missing Matter

To explain this discrepancy, we must have some mass $M$ that increases linearly with $r$ . However, this is not found in observations show that stars (which we assume to compose most of the mass) concentrated in the central region. We say that galaxies have some matter that does not interact via the electromagnetic interaction (and is therefore invisible). This is called dark matter, and composes more than 90% of the matter of a galaxy.

We also see discrepancies from Kepler's third law when looking at clusters of galaxies. We therefore propose that there is a large amount of dark matter in between galaxies keeping them together gravitationally.

Gravitational Lensing

By looking at how light bends near galaxies, we see a process called gravitational lensing, where light is bent from massive objects. However, the amount light is bent does not match the level of luminous matter observed, further proposing some dark matter.

Two possibilities of what dark matter could be are massive compact halo objects (MACHOs) or weakly interacting massive particles (WIMPs). WIMPs would include neutrinos, magnetic monopoles, and other types of particles created in the Big Bang. The primary difference between the theories is that MACHOs are composed from baryonic matter whereas WIMPs are composed of more exotic particles.