The nature of dark matter is one of the biggest open questions in modern cosmology. Dark matter is believed to be substantially different from ordinary luminous matter in composition – no atoms or quarks are allowed, since dark matter particles do not “feel” the electromagnetic force nor the strong nuclear force. The only way we can understand more about dark matter is by investigating its gravitational pull on ordinary matter.
How did scientists come to believe that this elusive form of matter makes up so much of the Universe?

This is the question we are trying to answer in this lab. By plotting the rotation curve of a galaxy, you will be able to draw your own conclusions about whether dark matter is a necessary to explain how stars in spiral galaxies move around the center. The material in this lab is partly based on the lab developed by Professor Dalcaton at the University of Washington and by faculty at the University of Syracuse.

An object in a circular orbit around a mass will have a velocity given by

$M(\lt R) = {V^2 R \over{G}} $

Here G is Newton’s constant which in units of solar masses, kpc and km/s is given by G = 4.3 × 10^-6 kpc (km/s)² Msun^-1.

Laboratory Tools

In this lab we will make use of rotation curve data obtained for M33 a nearby low mass galaxy seen above.  The data can be found here. We will then make use of Google Sheets to make a rotation curve from this data (you may use Microsoft Excel or other software if you choose).  Download or copy the data for your use. The result of our efforts should be a rotation curve plot like the one below.

 

Assignment

Create a plot of the data like the above plot.  Make sure it is a scatter plot and that you label the axes and have a legend for the points. Include this plot in your report. Using the plot estimate the values of the observed velocity and the contribution from stars and gas at the following radii: 2, 4, 6 and 8. Convert the velocity into a mass enclosed using the formula above. Finally subtract the stellar and gas masses from the observed mass to find the mass of dark matter.  Report your results in a table like this one.

Radius	Vstars	Vgas	Vobs	Massstars	Massgas	Massobs	Massdm
2
4
6
8

 

Questions

1. If the mass of the Sun suddenly doubled, would the planets of the Solar System move faster or slower? Why?
2. When does the contribution of gas become important to the total mass?
3. What is the problem with claiming that maybe there is no dark matter and the stars are just more massive then we have estimated them to be?