APAS 1040 Spring, 1997

HOMEWORK No. 4

Due date: April 14


1. Suppose the H-R diagram for a star cluster looks like this:

(Note: You must get a paper copy of the assignment, in order to use the drawing here.)

a. How far away is the cluster?

b. How old is it?

Hint: You will need information from the standard H-R diagram (Fig. 19.5 in the text) and from a table of stellar properties as a function of spectral type (e.g. Table 19.2).


2. An x-ray binary is found to have a period of 24.8 days. The visible star has spectral type
K4V, and the periodic Doppler shift of its spectrum has a maximum shift of 3.426Å at the H-a line (rest wavelength 6563.355Å). Is the unseen companion a neutron star or a black hole? (Hints: Use Kepler's third law to determine the sum of the masses, then subtract the mass of a K4V star to estimate the mass of the companion, to see whether it is over the limit for a neutron star. You will have to find the semimajor axis a by assuming a circular orbit and finding the radius from the period and the orbital speed, which you get from the Doppler shift.)


3. The following data were collected on the apparent magnitude (mV) of a Cepheid variable:

Time (days) mV Time (days) mV
0.0 +28.47 43.9 +28.48
4.2 +28.23 48.2 +28.28
5.4 +28.20 54.2 +27.87
11.8 +27.72 56.5 +27.66
14.8 +27.41 57.6 +27.54
15.9 +27.39 58.7 +27.45
18.8 +27.05 62.2 +27.14
20.4 +27.02 63.9 +27.00
24.2 +27.35 65.8 +27.03
26.6 +27.56 68.0 +27.27
32.8 +28.03 74.4 +27.84
38.1 +28.30 78.0 +28.06
39.7 +28.38 79.1 +28.14
40.9 +28.42 83.2 +28.33
42.0 +28.45 88.9 +28.51

Using these data, find the distance to the Cepheid. To do this, you will need to graph the
data listed above, in order to find the period of pulsation and the average apparent magnitude (estimate this by finding the mean between the minimum and maximum values, derived from your graph). Then find the average absolute magnitude, using the period-luminosity relation below, and from that, find the distance using the distance modulus.


(Note: You must get a paper copy of the assignment, in order to use the drawing here.)

How many light years away is this Cepheid? Is it within our own galaxy? Comment on the utility of Cepheids as tools for probing the size scale of the universe.