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Transcript
Nebraska Astronomy Applet Project
Student Guide to the
H-R Diagram Applet
_____________________________

Pre-test in EDU
Before working through the student guide, take the pre-test in EDU. Record your
score here
/ 10.
Directions: The next section covers information contained on the HR Diagram background
page and the supplements on luminosity and spectral type. Read those pages, and then
complete the text below by filling in the blanks. Where indicated, open the mini-applets to
answer some questions.
Section 1: Historical Background on the H-R Diagram
The H-R diagram was named after the two discovering astronomers, Ejnar
_________ and Henry Norris _________.
It is a plot of the luminosity vs. surface
temperature of a sampling of stars, such as those in a cluster. The temperature scale along the
bottom axis goes from about 3000 K on the right to about ______ on the left. ___________
(the other axes) is a measure of the total energy radiated by a star each second. The Sun is
nearly in the middle of both the temperature and luminosity scales on the diagram relative to
other stars. Approximately 90% of stars lie along a nearly straight diagonal line known as
the
Spectral classes are one way of categorizing stars by their temperatures. The main
spectral classes in order from hottest to coolest are __, B, __, __, G, __, and __. Stellar
luminosities depend on both the surface temperature and the radius of a star. They are given
by the product of two quantities -- the star's surface area (4R2) and its flux (the amount of
energy coming from each square meter of the star’s surface each second) . The flux is given
by a relation known as the ________-___________ Law (F = T4). Since the 4, , and  are
constants, we can think of luminosity as being equal to L = R2T4 in solar units. So that a star
twice as big as the sun and the same temperature would have a luminosity of __________.
Stars fall into three general categories; ______ ________ stars, ______ ________,
and _______ _______ largely on the basis of size. Bright, cool stars have a very ______
radius. Since they have the same luminosity as main sequence stars, but are cooler, they
must have larger surface areas. Antares is a good example of a bright cool star, known as a
______ ________. Smaller, hot stars are called White Dwarfs and lie below the main
sequence
There is a correlation between a main sequence star's mass and its luminosity. Stars
that have higher ________ and are on the main sequence have a greater mass than fainter
stars. The mass luminosity relation was discovered by __________ in 1924. It says that the
stars luminosity is proportional to the ________ power of its mass. Once you know the mass
and radius of a star you can calculate its average density.
It is important to classify stars so that they can be studied in groups whose members
all have similar properties. This helps astronomers to better understand how each type of star
functions and at what point it is in its evolution. One method is to classify stars into
____________ ____________ based on the thickness of their spectral lines. More luminous
stars have ________ spectral lines than less luminous ones of the same spectral class. Lines
from a _______ star are much narrower than those of a dim star lined up below it on the H-R
Diagram. Our Sun is classified as ____________ class G2 and ___________ class V.
At some points in their life cycle a star may not be in perfect equilibrium. When stars
are in a state of imbalance or instability, they are crossing an area called the ____________
________ on the H-R diagram. Stars called ___________ variables are an important type of
star in this unstable state. They are used as distance indicators (standard candles) because the
________ of their pulsation varies in proportion with their luminosity.
Section 2: Applet Walkthrough
This portion of the student guide is designed to familiarize you with the H-R Diagram
Applet. By reading it and completing the simple exercises you will gain an understanding of
the purpose and functionality of each part of the applet. Take special care to notice how each
action affects different areas of the applet. For example, when you move the temperature
slider, what happens to the size and color of the stars in the Relative Size box? Why does
this occur?
Section 2.1
First, move the temperature slider back and forth. Notice as you move the slider, the white
dot moves horizontally on the H-R diagram matching the temperature you have moved to.
The temperature is in degrees Kelvin, or absolute temperature. It increases from right to left
on the diagram, opposite the motion of the slider.
The luminosity slider is directly below the temperature slider. It shows the luminosity of a
star located where the white dot is on the H-R diagram. Moving the slider will move the dot
vertically on the diagram. The luminosity is given in solar luminosities and increases as you
move up the diagram.
Quick Exercise 2.1: Move the luminosity slider to 1 L (actually1*100 L) and the
temperature slider to near 5770 K. Where does the white dot move to on the diagram? Is it on
the Main Sequence?
Section 2.2
In the black box just below the diagram, the radius of a star at the selected position can be
found. In that same box is the name of the last star that was selected, or clicked on, by the
user (either from the provided star list or a user defined list).
Select the 34 Nearest Stars option in the Star Selection area. Now click on the yellow dot set
to indicate the Sun on the H-R diagram. It is labeled underneath with the word Sun. Notice
that the temperature and luminosity sliders read about what they did when you set them to the
Sun's values previously. Now it should say the star name (Sun) and the star's radius in the
black box below the diagram. Now click on a different star. Notice the name and radius, as
well as the temperature and luminosity, change to match the description of the new star. If
you click on the diagram in a place where there is no star, the temperature, luminosity, and
radius will change, but the star name will remain that of the last star selected. Obviously
there are many more stars than can be shown on a single diagram (entering all the data would
take a very long time!), so only a small sampling of stars are provided. While there may be a
star (or many, many stars) in a specific location, the applet can only give the star name for
the stars in its database. Later in this guide you will be shown how to add your own stars to
the diagram.
Quick Exercise 2.2: Click on "25 Brightest Stars". Select the star that is nearest the top right
of the diagram. What is this star called? What is its radius? Notice that this radius is larger
than that of the Sun ( L > 1 *100 L ). How does the temperature compare to the Sun's? The
luminosity? This bright Red Giant star is called Betelgeuse. It is cooler than the Sun and has
a much larger radius.
Section 2.3
The "IsoRadius Lines" button adds lines of constant radius to the diagram. The lines are
labeled in solar radii. Click on "IsoRadius Lines" and look at where the R = 1*100 R line
intersects the main sequence. Again you have found very near the Sun's position on the
diagram. As you can see the radius values increase as you move toward brighter cooler stars.
Find the white dwarf region of the diagram and click anywhere in that area. You can see that
white dwarfs have a much smaller radius than our main sequence Sun.
Right next to the "IsoRadius Lines" button is the "Instability Strip" button. The "Instability
Strip" button adds the instability strip region to the diagram. Stars in this region are in a
period of their life where they are not in equilibrium and therefore vary in brightness with
some periodicity. For example, an RR Lyrae star near the bottom of the instability strip might
vary by anywhere from 0.2 to 1.2 Mv and have a period of ~0.5 days.
By now you have noticed that in the upper left corner of the applet is the Relative Size box.
As you have been using the applet the size and color of those stars in the box have been
varying. The star on the right always represents the Sun. The other star shows the relative
size and the color of the selected star on the diagram. The color represents the effective
temperature of the star, which of course is what determines a star's color in reality. Increasing
or decreasing its luminosity can change the size of the star. This is due to the dependence of a
star’s luminosity on its surface area.
Quick Exercise 2.3: Move the temperature slider until the left star in the Relative Size box is
white or very light blue. Now change its size until it is much smaller than the Sun. What kind
of star is this? Even though the temperature is very high do you think this star would be easy
to see? Why or why not? This type of star is called a White Dwarf. Notice there is a White
Dwarf region on the diagram. Move the dot on the diagram along this region. What
properties do you notice that stay about the same? This almost constant radius for White
Dwarfs is a consequence of how these hot, compact stars were formed.
Section 2.4
As we have seen, in the Star Selection box (lower left) you can choose which stars you want
plotted on the diagram. There is also a Find feature that can be used to locate a specific star
in the database of stars already in the applet (25 brightest stars and 34 nearest stars) or a userdefined star. To use this feature, select a star in the drop down menu and then click Find. To
select a star in the drop down menu you must have something other than No Stars Plotted
selected. Once you have selected a star from the menu, click Find to put a green crosshair on
the star. To select the star's properties you must then click there on the diagram.
If you want to add a new star or group of stars to the plot select one of the User Defined spots
in the Star Selection box. Next adjust the temperature and luminosity to the values you want
for your new star, or click on the diagram where you want the star to be placed. Finally, click
on Adding Star to Plot in the Adding Stars to Groups box and type in the name you want for
the star. Clicking OK will add the new star to the plot. This star will now show up every time
you select that User Defined group in the Star Selection box. Add more stars the same way.
Clicking the Clearing Stars from Group will erase all the stars in the selected user defined
group. Stars may also be added to other selected groups in this manner, by clicking on the
desired group and adding the star. Clearing the stars from a group cannot erase stars already
in the applet by default.
Quick Exercise 2.4: Click on User Defined group #1. Move the temperature slider to 9550 K
and the luminosity slider to 2.6*100 L. Next, click on Adding Star to Plot. Enter the name
Vega and click OK. Now, click anywhere on the diagram. Go to the drop down menu in the
Star Selection box and select your newly added star. Click on Find. Now your new star has a
green crosshair on it on the diagram. To select this star you must click on the crosshair. You
can add other stars in this manner to create your own diagram. If you use a random sampling
of stars for this you will find that most of the stars lie along a smooth curve. This curve will
agree with the Main Sequence.
Section 3: The Applet Exercises
Exercise 1: Exploring the Stefan-Boltzmann Law
The purpose of this exercise is to gain some insight into how the Stefan-Boltzmann law
relates to the H-R Diagram.
Step 1:
First select the Sun on the diagram by clicking the 34 Nearest Stars option and then clicking
on the spot that represents the Sun on the diagram. Make sure the luminosity slider reads
1*100 (we will call this luminosity L). Now, by moving the temperature slider a small
amount, make the radius as close to 1*100 as possible (label this R). The purpose of this
was to make the numbers in this exercise as easy as possible (so we are starting at R = 1R 
and L = 1L). Also take note of the temperature (T) once you have the other two values set.
Step 2:
Next, turn on the IsoRadius Lines. Drag your star along the R = 1R line until the
temperature has doubled. What has happened to the luminosity? Write down this new
luminosity and label it Lstar1. Add a star at this location named Star 1 in case you want to
reference it at the end of this exercise.
Step 3:
Move your star position back to the original values for the Sun (L, R, T). This time move
the star so that T stays the same while the radius doubles (to make R = 2R  try moving the
luminosity slider). Once you have done this note the luminosity and label it Lstar2. Add a star
named Star2 here for future reference.
Questions:
1.) Which changed the luminosity the most step 2 or step 3?
2.) These results are due to the luminosity relation L = 4R2)(T4), where  is a constant. If
we consider this equation in solar luminosities and solar radii we get L = (R2)(T4). Given
this and assuming you used exactly L = 1*100and R = 1*100, what values would you
expect to find for Lstar1 and Lstar2?
3.) Did your “experimental” values obtained in steps 2 and 3 agree with this? Why or why
not?
Exercise 2: Predicting Star Types
For this exercise the main goal is for you to understand how to categorize a star using its
temperature and luminosity. What makes a star a main sequence star, a white dwarf, or a red
giant? It is important that you really think about your predictions before moving on to using
the applet to plot the stars.
Step 1:
Below is a table listing temperatures (in Kelvin) and luminosities (in solar luminosities) for
some unknown types of stars. The first star listed is the Sun. It is a main sequence star and
its temperature and luminosity are listed as closely to the actual values as this applet allows.
From this table each star can be placed on the H-R diagram. Before using the applet to place
the stars, can you predict where they might go? In the spaces provided, predict whether the
star is a main sequence star, a white dwarf, a giant or a super giant. Remember, the Sun is a
main sequence star. Use this to help you guess what the others are.
Star Name
Sun
Star 1
Star 2
Star 3
Star 4
Star 5
Star 6
L(L)
1.0*100
1.0*10-1
2.0*102
2.0*102
5.01*10-3
3.16*101
1.58*105
T(K) Prediction of Type
5754 main sequence
3890
3890
13183
13183
9120
4467
Step 2:
Now that you have filled in the table above, select Both Groups from the star selection box
on the applet and add these stars to the H-R diagram. Go back and make sure that your
predictions were correct. All of these stars are fairly typical for their type.
Questions:
1.) What is the name of a star near Star 2 on the diagram? Near Star 3?
2.) What property of Stars 1-6 were we really trying to determine in our predictions? Which
stars had the most extreme values of this property?
Post-test in EDU
Before working through the student guide, take the post-test in EDU. Record your
score here
/ 10.