RR Lyrae Stars and the Distance to M4: Worksheet

Table 1: Magnitude vs. Time for Star #42
Framet (days)D1 (mm)D2 (mm)D (ave)apparent
magnitude
10.24
20.15
30.18
40.52
50.53
60.38
70.05
80.26
90.08
100.07
110.37
120.36
130.11
140.48
150.09
160.32
170.22
180.40
190.44
200.02

1. Is there more than one cycle in the data? How long is the period of the variable star in a fraction of a day? In hours?

2. What is the mean apparent magnitude of #42? To calculate this, take 1/2 the value between the brightest and dimmest magnitudes. Remembering that the mean absolute magnitude of an RR Lyrae star is 0.75, calculate the distance to the RR Lyrae star, and thus M4, using the distance-magnitude relation.

3. Qualitatively, how would your distance to M4 change if you found out that an accurate parallax value had been obtained for a Galactic RR Lyrae star and its mean absolute magnitude is really 0.6 rather than 0.75?

4. What do you estimate is your error in determining the magnitude of Star #42 in each frame? To determine this, decide how accurate your slope is drawn for the sizes-vs-magnitudes of your standard stars. If your measurements of the diameter of each star is 1/2 mm wrong, how different would your inferred magnitude be?

5. Cepheid variables have periods that range from a few days to a few hundreds of days. This makes for more difficult observing, but, on the other hand, their mean absolute magnitudes range from about -1 to -6.

1. What do you think would be the advantages of searching for RR Lyrae variables over Cepheids? (Hint: Where are Cepheids and RR Lyrae stars usually found in a galaxy?)

2. What do you think would be some disadvantages of using RR Lyrae variables?

6. Suppose you were given unlimited time on a telescope to monitor RR Lyrae variables in all of the globular clusters of the Milky Way. What would you learn? How would you apply this knowledge to help us learn more about the Milky Way?