## Discovering Dark Matter

Purpose
Examine the evidence for Dark Matter in NGC 2742.

Background
Dark Matter is matter that does not produce light. We can detect it using gravitational methods, but not by looking for shiny objects. Many astronomers are trying all sorts of clever observing schemes (if you can think of any, let us know) to find observational evidence for this stuff. As yet, no experiment has been able to account for the 'missing mass' in the Universe. On the theory side, physicists have a lot of fun coming up with ideas for new particles to explain dark matter.

The total mass of a galaxy can be found by measuring how fast the galaxy rotates around its center. We will compare this mass with the mass of the stars in the galaxy, to determine how much of the mass is Dark Matter.

One note about the galaxy we selected: If we are looking at the "side" of a galaxy, most of the light is blocked by dust, and we can't figure out how many stars there are. When we are looking at the galaxy “face-on” (you might think of this as from above), we see almost all the light that is coming out of a galaxy, but we can't figure out how fast it spins! We choose galaxies that are viewed at an angle to maximize our ability to find both the amount of light and the spin, and make a trigonometric correction to account for the angle.

Procedure
Part A: Finding the Gravitational Mass
At right is a "rotation curve" of NGC 2742, measured from the Doppler shift of stellar spectral lines. The y-axis is the radial velocity (how fast stuff is moving in the line of sight direction) of a star in the galaxy. The x-axis is the radius of the star's orbit. In Part A, we will determine the gravitational mass interior to different radii of the galaxy, using Newton's Law of Gravity.

1. Table 1 on the worksheet lists eight radii, which correspond to positions on the x-axis in the graph at right. Determine the radial velocity (from the y-axis) at each of these radii. Record those values in Table 1.

2. For a circular orbit, we use Newton's Law of Gravity to find that:
,
where G = 4.31 x 10-6 , and “M” is the mass contained inside of radius “R”.

Use your values for Radius and Velocity to determine the mass interior to each radius. Record your results in the “Gravitational Mass” column in Table 1. Your numbers should be big. This is a galaxy, after all. It contains a lot of stars.

Part B: Finding the Luminous Mass
Now that we’ve found the gravitational mass of the galaxy, we wonder how much of that mass comes from stuff we can see (i.e. stars and gas). At right is a graph of the luminosity profile of NGC 2742. The x-axis is the distance from the center, the y-axis is the brightness contained within a circle of that radius.

1. At the same radii that you used for Part A, determine a value for the luminosity of the galaxy and record it in Table 1.
2. Now that we've measured how much light is coming from NGC 2742, we need to estimate the mass of the stuff that produced that light. In order to take into account different brightnesses of stars, faint ones that are difficult to see, dust and gas that hides some stars, we will assume that there are two solar masses of stars for each solar luminosity of light.

Calculate the lumionous mass by counting 2 solar masses for each observed solar luminosity, and record the number in the “Radiation Mass” column of Table 1. (In other words, multiply the total luminosity by 2.)

Part C: What's Missing?
There's one last step to figuring out how much of the galaxy can be understood by things we know (luminous stuff like stars and gas), and how much of the galaxy can't be detected this way.
1. Divide the luminous mass by the gravitational mass at each radius, and enter this number in the last column on the table.
2. Answer the questions on the worksheet.