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# Cepheids and the Extra-Galactic Distance Scalef-L version worksheets

## Part 1: Identifying Variable Stars

Get a pair of images from your GSI. These images are a close up of a small region of a galaxy with six simulated variable stars added.  The image pair corresponds to observations of the galaxy at different times.

1. After taking a quick look at the images, figure out what to look for to find the variable stars.  Describe what you will look for and you will identify the variables:

2. There are no fewer than six Cepheid variables in the field.  If you readily find four, look for five. Finding the sixth – quite tricky – earns you the title of ‘Master Variable Star Finder’! This search should give you a taste of what it is like to look for variables in actual data, although you’ve been given “nice” data (fake variables with nice periods were added to an actual image).  Imagine there were 3 variable stars in the field with periods of 5, 10 and 20 days, and the two images were taken 10 days apart.  How many variables would you be able to identify?  Why?

3. Once you have identified at least four variables, show your GSI where you think they are.  He/she will record how many stars you correctly identified here: __________

## Part 2: Light Curves

Please note the data tables and graphs in the rest of this lab may be done in excel if your instructor allows it. In that case, you will need to print and attach your tables and graphs when you hand in the lab. You must still answer all the questions and show your work!
1. Your GSI will give you data tables for stars in 4 different galaxies. They have the Date of the observation, the apparent magnitude and flux of 12 Cepheid variables. The date is a simple count of the days for the year the data were taken.
2. Plot the flux vs the dates for each of the three stars in galaxy 1 (3 graphs).  Be sure to include these plots when you hand in your lab.
3. Why are there gaps in the dates in the plots?

4. Is the light curve of a Cepheid variable a simple sine curve?

5. You will need to determine the period and average flux for the stars.  Explain how to do that from the light curve (a sketch of a Cepheid light curve may be helpful)

6. Fill out the period and average flux for the stars in galaxy 1 in table 1 using the light curves (you may skip the P1.5 colum for now).
7.  Galaxy Star P (days) P1.5 fave (Lsun/pc2) 1 1 2 3 2 1 2 3 3 1 2 3 4 1 2 3
8. You should have the graphs of the light curves for the stars in galaxies 2 – 4.  Use those graphs to fill in the period and average flux for these 9 starrs in table 1.

## Part 3:The Distance Modulus

1. At the end of the document with the light curves is a graph of the P-L relation. Why is P1.5 graphed instead of P?

2. Calculate P1.5 for the 12 stars and record them in table 1.
3. Plot the mean flux vs. P1.5 for the three stars in galaxy 1. Draw a best fit line for the stars.
4. Pick 4 points on the line (not data points). Record the value of P1.5 and f of those points in table 2.
5. Record the luminosity from the P-L graph for the same values of P1.5.
6. Find L/f for all three stars and record the values in table 2. Also calculate the average and record it in table 2.
7. Repeat these last 4 steps for the other 3 galaxies.
 Table 2, Getting the distance. Gal P (days) f (Lsun/pc2) L (Lsun) L/f (________) L/fave(_________) d (__________) 1 2 3 4
8. Should the values of L/f within each galaxy be similar? Should the values be similar in different galaxies? Explain. (Check table 2 to see if your numbers agree to your answer!)

9. Use the average values of L/f to calculate the distance in parsecs to each galaxy. Show your work, including units, below. Enter your final answers in table 2

## Concluding questions

1. Miss Leavitt had to use photographic plates. How do you think astronomers would find variable stars now?

2. You were lucky in having to only find the Cepheids and not having to actually measure their brightnesses on numerous images. How do you think astronomers measure the brightness (aka flux or apparent magnitude) of an object?

3. In this lab, you had to determine the luminosity or absolute magnitude.  Based on what you did and your answer to the previous question, explain why the brightness is generally more accurate than the luminosity/absolute magnitude.

4. Let’s say we can measure Cepheids out to a flux of 2.95x10-14 Lsun/pc2. Using the P-L and inverse-square distance relations, what is the furthest galaxy we could detect Cepheids in if we limit ourselves to a maximum period of 100 days?

5. Put your galaxies in order from closest to farthest.  Which one(s) is/are part of the local group?  Which is/are in the Virgo cluster?  Which is/are father than the Virgo cluster?

6. For a Hubble constant of 70 km/s/Mpc, what recessional velocities would you expect to measure for each of the galaxies used in this lab?