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Hertzsprung-Russell Diagram – Student Guide
Pretest Score:
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, use the online demos to answer
some questions.
Background Material
The HR 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
4
(F = T ). 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
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below it on the HR 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 HR 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.
HR Diagram Explorer
This portion of the student guide is designed to familiarize you with the HR Diagram
Explorer. By reading it and completing the simple exercises you will gain an
understanding of the purpose and functionality of each part of the explorer. Take special
care to notice how each action affects different areas of the explorer. 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?
Temperature and Luminosity
First, move the temperature slider back and forth. Notice as you move the slider, the
white dot moves horizontally on the HR 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 HR 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.
Question 1: Move the luminosity slider to 1 L⊙ (actually 1×100 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?
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 HR 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
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stars are provided. While there may be a star (or many, many stars) in a specific location,
the explorer 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.
Question 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 ( R > 1 × 100 R⊙ ). 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.
Radius
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 M⊙ and have a period of ~0.5
days.
By now you have noticed that in the upper left corner of the explorer is the Relative Size
box. As you have been using the explorer 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.
Question 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
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that stay about the same? This almost constant radius for White Dwarfs is a consequence
of how these hot, compact stars were formed.
Adding a User Defined Star
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 explorer (25 brightest stars and 34
nearest stars) or a user-defined 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 explorer by default.
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.
Stefan-Boltzmann Law
The purpose of this exercise is to gain some insight into how the Stefan-Boltzmann law
relates to the HR Diagram.

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.

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
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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.

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.
Question 4: Which changed the luminosity the most: step 2 or step 3?
Question 5: 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?
Question 6: Did your “experimental” values obtained in steps 2 and 3 agree with this?
Why or why not?
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 explorer to plot the stars.

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 explorer allows.

From this table each star can be placed on the HR diagram. Before using the
explorer 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.
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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)
5754
3890
3890
13183
13183
9120
4467
Prediction of Type
main sequence
Now that you have filled in the table above, select Both Groups from the star
selection box on the explorer and add these stars to the HR diagram. Go back and
make sure that your predictions were correct. All of these stars are fairly typical
for their type.
Question 7: What is the name of a star near Star 2 on the diagram? Near Star 3?
Question 8: 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?
Posttest Score:
NAAP – HR Diagram 6/6