Download Rotation curves for galaxies: student activity

Rotation curves for the Galaxies (Student Activity)
"Fame is fleeting. My numbers mean more to me than my name. If astronomers are still using my
data years from now, that's my greatest compliment."
Vera Rubin
Methods
We can weigh a spiral galaxy by measuring the gravitational effects of the galaxy's mass on the
orbits of objects in its disk. Even beyond the point in the disk at which starlight fades into the
blackness of intergalactic space, we can still see radio waves from atomic hydrogen gas. We can
therefore use Doppler shifts of the 21-cm emission line of atomic hydrogen to determine how quickly
this gas moves toward us or away from us. Galaxies beyond the Local Group have cosmological
redshifts affecting all their spectral lines. However, on one side of a spiral galaxy the gas is rotating
away from us, so its 21-cm line is redshifted a little more than the redshift of the galaxy as a whole.
On the other side, the 21-cm line is blueshifted relative to the redshift of the galaxy as a whole
because the gas is rotating toward us. From the Doppler shifts of these clouds, we can construct a
rotation curve--a plot showing orbital velocities of gas clouds and stars--just as we did for the Milky
Way. A rotation curve contains all the information we need to measure the mass contained within the
orbits of the outermost gas clouds. (Because the Doppler effect tells us only about the velocity of
material directly toward or away from us, we must also take into account the tilt of the galaxy before
we construct the rotation curve.)
Measuring the rotation of a spiral galaxy with the 21-cm line of atomic hydrogen. Blueshifted lines
on the left side of the disk show how fast that side is rotating toward us. Redshifted lines on the right
side show how fast that side is rotating away from us.
A rotation curve shows the orbital velocities of stars or gas clouds at different distances from a
galaxy's center.
1. Use the data below to plot a rotation curve for the Milky Way Galaxy.
r[kpc]
r[ly]
2
6520
2.5
8150
3.5
11410
4.5
14670
5.5
17930
6.7
21842
7
22820
7.5
24450
9.5
30970
10.3
33578
11.5
37490
12.5
40750
13.3
43358
14.5
47270
15.5
50530
16.5
53790
17.5
57050
18.5
60310
What are the differences between this rotation curve and the those of the solar system?
2. Other data for other Galaxies can be found below. The data is taken from Vera's Rubin's Work
(The Astrophysical Journal 238, 471-487), 1980.
NGC 801
r (kpc)
r(ly)
v(km/s)
9
29340
212
10
32600
218
12
39120
222
14
45640
218
16
52160
218
18
58680
225
20
65200
228
22
71720
225
24
78240
221
26
84760
216
28
91280
212
32
104320
207
36
117360
205
40
130400
202
NGC 2998
r (kpc)
r(ly)
v(km/s)
10
32600
189
12
39120
200
14
45640
203
16
52160
206
18
58680
209
20
65200
211
22
71720
213
26
84760
214
30
97800
215
34
110840
216
3. Astronomers have studied galaxy UGC 128 for many years. They have measured its
brightness and calculated that the mass of stars within a radius of 1.30 x 1021 m is 3.34 x
1040 kg. Stars orbiting at this radius has been measured travelling at a speed of 1.30 x 105
m/s. What percentage of the mass within this radius is dark matter? (From Perimeter
Institute DVD).
4. Our sun is located in the Milky Way galaxy which is shown in the figure below.
Its distance from the galaxy center is 8kpc (1 parsec is equal to 3.26 light year) and its orbital velocity
around the galaxy center is 220 km/s. Use your former answer to calculate the Calculate the mass of
the Milky Way Galaxy within the solar circle.