Dark Matter — part 2
Introduction
Yesterday we looked at the pre WWII discovery of dark matter. Today we’ll be focusing on the post WWII discovery and how it pretty much caused a paradigm shift in how we understood dark matter.
“The missing link in cosmology is the nature of dark matter and dark energy.”
- Stephen Hawking
Vera Rubin, an American astronomer, was studying the Andromeda Galaxy (NGC 224). She analysed the spectra of stars within this galaxy to measure their rotational velocities and spotted an anomaly.
I’m going to digress here, it’ll be worth it. We know that the Earth has an elliptical orbit around the Sun. However for our purposes, we’ll assume it has a circular orbit. You can skip towards the bottom if you don’t want to go through the Maths.
This means that the Earth has some centripetal acceleration which helps keep it in circular orbit. This is given by:
We also know that there is a force of Gravity between the Earth and the Sun, this is given by:
Now based on Newton’s second law (F=ma), we can multiply the Earth’s centripetal acceleration by its mass to get the centripetal force”
By equating Eq 2. and Eq 3. and solving for the orbital velocity of the Earth, we get:
Notice how the mass of the Earth isn’t in this equation? This tells us that the mass of the Earth and its orbital velocity (the velocity with which the Earth orbits around the Sun) is independent of each other.
Basically, the further you are away from the Sun, the slower you’ll take to orbit. The reason for this is because the only variable in the above equation is r, it changes based on what planet you are looking at while the other two are always gonna remain constant, thus we can say that:
If we were to draw a graph of all the planets in our solar system where r is on the x-axis and v is on the y-axis, we’d get something like this:
This graph is known as a rotation curve and the data used to plot this graph will be available below. Essentially, this graph shows that the further you are away from the Sun, the slower you orbit around the Sun.
Even though Jupiter has a greater mass than Neptune, it doesn’t matter; Neptune is further away from the Sun and so will take longer to complete one orbit.
Now, Vera Rubin wanted to confirm if this was true for a macroscopic object like a galaxy. She wanted to see if the stars at the edge of the galaxy moved much slower than the stars towards the centre of the galaxy.
She plotted a rotation curve of NGC 224 but it looked something like this:
The red line is what it is supposed to look like whereas the white line is what was observed. The white line essentially tells us that the orbital velocity of the stars at the edge of the galaxy is somewhat equal to those of the stars towards the galactic centre. This is basically what Fritz Zwicky discovered.
This means that there had to be some additional mass unaccounted for. For the sake of accuracy, Vera Rubin surveyed sixty different galaxies and found that this trend persisted. Thus the idea that Zwicky posited, could actually be the one missing piece in the puzzle.
If you skipped to the bottom, basically what happens is that the stars at the edge of the galaxy were moving too fast than they should. Thus there had to be additional mass which is what we call dark matter. In the next post, I’ll actually cover what dark matter is; it’s a bit more abstract than just “mass”.
Citations:
- Data for graph: https://nssdc.gsfc.nasa.gov/planetary/factsheet/
- Image of Vera Rubin: https://static01.nyt.com/images/2016/12/28/us/28rubin-obit-1/28rubin-obit-1-superJumbo.jpg
- Image of Andromeda Galaxy: https://earthsky.org/upl/2019/08/andromeda-galaxy-9-18-10-Adam-Evans-Flickr-e1565883339297.jpg
- Image of galactic rotation curve: https://scx2.b-cdn.net/gfx/news/hires/2011/coulddarkmat.jpg
