## Dark Matter Worksheet

Table 1: Determining the Masses
(kpc)
(km/s)
Gravitational Mass
(solar masses)
Luminosity
(solar luminosities)
Luminous Mass
(solar masses)
% luminous mass
1.3
2.7
4.0
5.3
6.7
8.0
9.3
10.7

Questions
1. Examine the last column of your table. This column shows the percentage of the gravitational mass that can be accounted for by what we can see. Is there any radius at which we can account for the gravitational mass purely from the mass we can see?

2. Does the problem get better or worse (do we need more or less dark matter) as the radius increases?

3. The last number in the table (% luminous mass at the largest radius) tells you about the percentage of mass that is luminous for the whole galaxy. For this galaxy, what percentage of the gravitational mass can not be accounted for by luminous mass?

4. Galaxies get fainter as you get farther from the center. But in Figure 3, as the radius increases, the luminosity increases! Clearly, the plot is not showing the brightness at a specific radius from the center of the galaxy. What does the plot show instead?

5. We assumed that for every solar luminosity that we see, there is another solar mass of faint stars, so we multiplied by two.
1. How would we change this factor if NGC 2742 has more low mass stars than we thought?

2. Would dark matter be more or less important in this case?

6. These are two galaxies that we cannot use in our search for dark matter.
 M101: The Pinwheel Galaxy M104: The Sombrero Galaxy

Why not?

M101:

M104:

7. Comment on the existence of Dark Matter. Are you convinced that it exists?