Extra Credit Assignments

Cepheid Variable Stars

Purpose: To find a relationship between the periods and luminosities of cepheid variable stars and use it to determine distances.

 Procedure: Cepheid variables are giant and super­giant stars that expand and contract. As they do so (we measure this change by the Doppler shift), their luminosities vary in a regular fashion. The time interval from peak brightness to the next peak brightness defines the period of light variability. The name "cepheid" comes from the star that is the pro­totype of the group, Delta Cephei (fourth brightest star in the constellation Cepheus). The cepheid vari­ability marks a stage late in a star's evolution, as it burns helium (to carbon) in its core. These stars are more massive than the sun, typically a few to ten solar masses.

 Table 1 provides the periods and luminosities (to two or three significant figures) of selected cepheid variables. These luminosities are the average values, since these stars vary! (You will probably not recog­nize the names of any of these stars.) Use the Graph Template to plot these data. Notice that the x-axis (period in days) has an increment of 1 day; the y-axis (luminosity in solar luminosities) has an increment of 500. Once you have plotted the values for the stars, draw a "best fit" straight line through the data points. (Position the line so that it goes through most of the points, and it has about as many points above it as below it. A region of many points should influ­ence the line more than a region of few points.) Using your graph, answer the following questions:

 1. What is the general trend of period versus luminosity?

 2. Using your line, estimate the luminosity of a cepheid variable with a period of 25 days.

 2b. What of one with a period of 30 days?

 3. Suppose you measure the flux at the earth of a cepheid whose period is 30 days. What procedure could you use to find out the distance to this cepheid?

 Go HERE for Table 1 and Graph Template in PDF format.

Hubble's Law

Purpose: To visualize the relationship between distances and recessional velocities for galaxies and find

a value for the Hubble constant.

 Procedure: You will make "Hubble plots" of the dis­tances and recessional velocities for selected groups of galaxies. The distances are found by a variety of ways, including the period-luminosity relationship for cepheids. The recessional speeds are found from the red shifts in the spectra of the galaxies. If this red shift is interpreted as a Doppler shift, it provides the radial velocity along the line of sight-a recessional velocity for a red shift.

 1. First make a plot using Graph Template 1 from the data in Table 1. These galaxies are selected from the brightest ones in the sky (but you probably won't recognize their names). (What can you infer from the fact that they are among the brightest?) Graph Tem­plate 1 has the horizontal axis as the distance in mil­lions of light years, from the closest to the farthest galaxies. On the vertical axis is the radial velocity in kilometers per second.

Plot the points for all the galaxies and draw a straight line through them with a ruler. DO NOT "CONNECT THE DOTS"! Try to draw a straight line so that about as many galaxies fall above and below the line as on the line. Now measure the slope of the line, which is the rise (y -axis) over the run (x -axis). Use the complete length of this "best fit" line, not just a part of it.

 2. Find the slope from the difference in the value of the y-axis over the difference in the value of the x-axis. What value do you get? This is your value of Hubble's constant from the information in the graph.

3. All velocities for these galaxies are recessional – they are red shifts. What does this tell you about the universe: is it static, expanding, or contracting?

 4. Now turn to Table 2, which lists a different sample of galaxies. Each one is chosen from a cluster of galaxies. Use Graph Template 2 and the plotted data to find the slope. What is it?

 5. How do your values compare? Do they differ significantly? If so, why?

Go HERE for Tables and Graph Templates in PDF format.