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# Rotation of Spiral Galaxies - Worksheets

## Step 1: Measure the Galaxy Rotations

Table 1: Galaxy Rotation Data
Galaxy m      vleft           vright           vrot      log10 (vrot)
1 11.75
2 11.48
3 11.51
4 13.25
5 12.61
6 12.47

## Step 2: Determine the Distance and Measure the Hubble Constant

Data for M31: m = 1.04, vrot = 275 km/s, dM31 = 770 kpc.

For M31, log10 (vrot) = __________

The apparent magnitude, md, if M31 were at a distance of the 6 galaxies is  __________

How many magnitudes dimmer is this than M31's real apparent magnitude? __________
This is Δm in the formula for d given in the instructions.

The distance is then d = ___________  (See the instructions for the appropriate formula.)

The average vexp for the 6 galaxies = ___________

H0 = vexp/d = __________  (The usual units for this are km/s/Mpc, so convert d to Mpc first.)

For many years, a veritable blood feud has been going on between various astronomers who think that this number is either 50 or 100. More recently there seems to be a consensus developing that it is somewhere in between. Where does your value fit in?

## Step 3: Estimate the Mass of the Galaxies and Check for Dark Matter

Image scale = 90"/(length of 90" line) = __________  arcsec/mm.

Table 2: Mass-to-Light Ratio

 Galaxy # Diam. [mm] Diam. [arcsec] R [kpc] M [Msun] Abs. Mag L [Lsun] M/L 1 2 3 4 5 6

## Concluding Questions

1. Why do you think we are using spiral galaxies that look nearly edge-on? What kind of Doppler shift do you think you would measure if the spiral galaxy were nearly face-on instead?

2. It was mentioned that the six galaxies in this lab are all nearly the same distance from us. Why is this important? How would your graph have looked if the galaxies were all at different distances.

3. Why does the Tully-Fisher relation make sense? Think about how the brightness of a galaxy relates to its mass, and how its mass relates to it rotational velocity.

4. All of the magnitudes that we're using in this lab are infrared magnitudes (measured using infrared light). Why is it advantageous to use the infrared light when studying these edge-on spiral galaxies?

5. You should have found M/L ratios significantly greater than 1. Since stars typically have M/L values of around 1, what does this imply about these galaxies. What kind of objects would increase M/L and why?

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