Cepheids - brightness Worksheet
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University of Michigan *
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Course
105
Subject
Astronomy
Date
Dec 6, 2023
Type
docx
Pages
5
Uploaded by BarristerKingfisher3714
Worksheet for Cepheids and the Extragalactic Distance Scale
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 three, look for four. 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).
a.
Once you have identified at least three variables, show your GSI where you think they are.
He/she will
record how many stars you correctly identified here: __________
b.
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?
Part 2: Light Curves
Your GSI will give you a data table and graph for 3 cepheids in a galaxy. The data include the date of the observation, the
apparent magnitude (m) and the brightness (b) of 12 Cepheid variables. The date is a simple count of the days for the year the
data were taken. For example, day 5.5 is noon on January 5. The graphs are the brightness vs. the date.
3.
Record your galaxy number here: ______ Also record it at the top of tables 1 and 2.
4.
Match a couple of the values in the data tables to the points on the graph so you see how the graph was made.
5.
Looking at both the data and graphs, answer the following:
a.
Which star has the most observations? _________
b.
Which star has the longest date range? _________
Page 1 of 5
c.
Which star is the brightest? _________
d.
How many periods are shown for cepheid 2? _________
e.
What are the units of brightness? Enter this value in the appropriate column header of table 1.
f.
What might be the reason for gaps in the dates in the plots?
6.
You will need to determine the period and average brightness for the stars.
Explain how to do that from the light
curve (a sketch of a Cepheid light curve may be helpful.)
7.
Pick one of the three stars. Record its number (1, 2, or 3) in the first column of table 1.
8.
Estimate the period and brightness for that star and record those values in table 1.
9.
Calculate the period raised to the 1.5 power and enter that into the last column of table 1.
Table 1: Light curve results for galaxy number ______
Star
P (days)
b
ave
(___________)
P
1.5
Part 3: Finding the Distance
10.
Your GSI will give you a graph of brightness vs. P
1.5
for your galaxy.
Why is P
1.5
graphed rather than just the period?
11.
Compare your values for b
ave
and P
1.5
in table 1 to the data points on the graph. Which point on the graph
corresponds to your star? Circle one: bottom left;
middle;
top right.
12.
Note there is a best fit line on the graph with an equation in the form y=mx+b. Rewrite the equation in terms of the
Page 2 of 5
brightness b (not the same b as the y-intercept!) and P
1.5
:
13.
Select
two
values of
P
1.5
that fall on the line and are not data points. Record their values in table 2.
Table 2: Brightness and
luminosity for galaxy number ______
P
1.5
(days
1.5
)
b ( L
Sun
/pc
2
)
L (L
Sun
)
d (_______)
Point 1
Point 2
Average
14.
Use the equation of the best fit line you just rewrote to calculate b for each value of P
1.5
. Record the results in table 2.
Show a sample calculation here.
15.
Calculate L from P
1.5
using Leavitt’s law.
Show a sample calculation here.
16.
Record the units of distance in table 2.
17.
Calculate the distance to your galaxy for both points. Record the values in table 2. Show a sample calculation here.
18.
Record your distance in the appropriate row in the table on the board.
19.
Copy the data from the board to table 3. Note you may not use all the rows if there are fewer than eight groups.
While you’re waiting for other groups to post their results, you can work on concluding questions 1 - 4.
20.
Once you have everyone’s distances, average the values for each of the 4 galaxies and record them in the table.
21.
Convert the distances to Mpc for the final column of table 3.
Table 3: Class data and Galactic Distances
galaxy
d (pc)
d
ave
(pc)
d
ave
(Mpc)
1
1
2
2
3
3
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