HR diagram
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Utah State University *
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1040
Subject
Astronomy
Date
Dec 6, 2023
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docx
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HR Diagram – Student Guide
Background Information
Work through the background sections on Spectral Classification, Luminosity, and the
Hertzsprung-Russell Diagram. Then complete the following questions related to the background
information.
Question 1: The table below summarizes the relationship between spectral type, temperature, and
color for stars.
Note that the surface temperature of the stars in the table increases.
Question 2: Complete the following table related to stellar luminosities in solar units using the
equation
2
4
L
R T
.
NAAP – HR Diagram Explorer 1/7
Star
Surface
Temperature K
Spectral Type
Color
Betelguese
3,500
M2
Red
Arcturus
4,300
K5
Orange
Sun
5,800
G2
Yellow
Procyon A
6,500
F5
Yellow-White
Sirius A
9,100
A1
White
Rigel A
11,000
B9
Blue-White
Delta Orionis
33,000
O9
Blue
Radius (R
⊙
)
Temperature (T
⊙
)
Luminosity (L
⊙
)
1
1
1
1
2
16
3
1
9
1
1/2
0.0625
Question 3: The mass luminosity relation
3.5
L
M
describes the mathematical relationship
between luminosity and mass for main sequence stars.
It describes how a star with a mass of
2 M
⊙
would have a luminosity of ____11.31_________ L
⊙
while a star with luminosity of
3,160 L
⊙
would have an approximate mass of _______10_________ M
⊙.
HR Diagram Explorer
Open the
HR Diagram Explorer
. Begin by familiarizing yourself with the capabilities of the
Hertzsprung-Russell Diagram Explorer through experimentation.
An actual
HR Diagram
is provided in the upper right panel with an active location
indicated by a red x.
This active location can be dragged around the diagram.
The
options panel
allows you to control the variables plotted on the x-axis: (temperature, B-
V, or spectral type) and those plotted on the y-axis (luminosity or absolute magnitude).
One can also show the main sequence, luminosity classes, isoradius lines, or the
instability strip.
The
Plotted Stars
panel allows you to add various groups of stars to the
diagram.
The
Cursor Properties
panel has sliders for the temperature and luminosity of the active
location on the HR Diagram.
These can control the values of the active location or move
in response to the active location begin dragged. The temperature and luminosity (in solar
units) are used to solve for the radius of a star at the active location.
The
Size Comparison
panel in the upper left illustrates the star corresponding to the
active location on the HR Diagram.
Note that the size of the sun remains constant.
NAAP – HR Diagram Explorer 2/7
Exercises
Drag the active location around on the HR Diagram.
Note the resulting changes in the
temperature and luminosity sliders.
Now manipulate the temperature and luminosity
sliders and note the corresponding change in the active location.
Question 4: Check the appropriate region of the HR diagram corresponding to each description
below.
Drag the active location around on the HR Diagram once again.
This time focus on the
Size Comparison panel.
Question 5: Check the appropriate region of the HR diagram corresponding to each description
below.
Check show isoradius lines.
Note that at each point on a green line, stars have the same
value of radius.
Use these isoradius lines to check your answers in the table above.
NAAP – HR Diagram Explorer 3/7
Description
Top
Right
Bottom
Left
Hot stars are found at the:
x
Faint stars are found at the:
x
Luminous stars are found at the:
x
Cool stars are found at the:
x
Description
Upper
Left
Upper
Right
Lower
Right
Lower
Left
Large Blue stars are found at the:
x
Small Red stars are found at the:
x
Small Blue stars would be found at the:
x
Really Large Red stars are found at the:
x
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Question 6: The equation below describes the luminosity of a star in terms of its radius and
temperature.
Use this equation to explain the results you found in the table of the previous
question.
I found that when you increase the temperature or the radius which also is relating to the
color it will increase the luminosity of the star, and I can see that when you decrease either one it
will decrease the luminosity as well.
In addition to the isoradius lines, check
show luminosity classes
.
This green region
(dwarfs V) is known as the main sequence and contains all stars that are fusing hydrogen
into helium as their primary energy source.
Over 90% of all stars fall in this region on
the HR diagram.
Move the active cursor up and down the main sequence and explore the
different values of stellar radius.
Question 7: Describe the sizes of stars along the main sequence.
What are stars like near the top
of the main sequence, the middle, and the bottom?
The bottom stars of the main sequence are very little and as you move towards through the
middle to the top they increase in size which leads to the stars at the top being very large.
The background pages of this module talked about the mass-luminosity relationship for
stars on the main sequence:
Question 8: What can you conclude about the masses of stars along the main sequence?
I can conclude that the mass increase with the size of the stars in the main sequence, so
we can see it increases from the bottom right to the upper left.
NAAP – HR Diagram Explorer 4/7
2
4
4
L
R
T
3.5
L
M
L
Use the results from the previous 5 questions to construct a “conceptual” HR Diagram.
You
simply want to draw arrows showing the direction in which variables are increasing.
a)
Draw in an arrow on the y axis showing the direction of increasing “intrinsic luminosity” of
the stars. (This is complete for you.)
b)
Draw in an arrow on the x-axis showing the direction of increasing surface temperature of the
stars.
c)
Draw in an arrow showing the direction of increasing radius on the diagram.
(hint:
this must
be perpendicular to the isoradius lines.)
d)
Draw in an arrow showing the direction of increasing mass for main sequence stars on the
diagram.
(Note that his arrow only applies to main sequence stars, but that is over 90% of stars.)
Figure 1: Conceptual HR Diagram
NAAP – HR Diagram Explorer 5/7
Uncheck show luminosity classes and check
show instability strip
.
Note that this region
of the HR Diagram indicates where pulsating stars are found such as RR Lyrae stars and
Cepheid variable stars.
These stars vary in brightness because they are pulsating –
alternately growing bigger and smaller – which changes their radii and surface
temperatures and resulting their luminosities.
Question 9: Describe the characteristics of stars that are found in the instability strip.
You should
cover their range of temperatures, colors, luminosities, and sizes. (Hint: Comparing them to the
sun is useful.) Are variable stars necessarily on the main sequence?
These stars temperatures range from about 5,000 to about 8,000 Kelvin, their radii range
from about 2.5 to about 50, and their luminosities range from about 25 to 1,500. Their colors
have a wide range but that is from lighter blue-white to yellow, and these are not always
necessarily on the main sequence.
Check the plotted stars option
the nearest stars
.
You should cover their range of
temperatures, colors, luminosities, and sizes.
Question 10: Describe the characteristics of the nearest stars.
These stars are all on the bottom half of the main sequence. These stars temperature range
from 2,300 to about 10,000, their luminosities go all the way up to about 23, and their radii goes
up to about 1.8, and the colors all range from blue-white to red.
Question 11: Do you think these stars are rare or very common among all of the stars of our
galaxy?
Explain your reasoning.
Are any assumptions involved in your reasoning?
To me I think for the most part all these stars are pretty common throughout the stars in
our galaxy. I think this because they are all for the most part located in the main sequence, which
for the most part this means the majority of stars.
NAAP – HR Diagram Explorer 6/7
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Uncheck the plotted stars option
the nearest stars
and check
the brightest stars
. Why
are these stars the brightest in the sky?
Three students debate this issue:
Student A: “I think it’s because these stars must be very close to us.
That would make them
appear brighter to us in the sky.”
Student B: “I think it’s because these stars are very luminous.
They are putting out a tremendous
amount of energy.”
Student C:
“I think it’s because these stars are very close and very luminous.”
Question 12: Use the tools of the HR Diagram to support the views of one of the three students.
Why are the stars we perceive as bright in the night sky really bright?”
(hint:
You may find the
options labeled
both the nearest and brightest stars
and
the overlap
useful.)
I think the stars are the brightest when they are very luminous. Which most of the stars that we
are closest to are not even the brightest, there is a very small overlap which happens between the
two groups. The brightest stars are higher up on the diagram, which means they have higher
luminosities.
Question 13: Do you think that these bright stars are very common (make up a large percentage
of all stars in general)? Explain your reasoning.
It looks like there is a lot of these stars on the diagram that I can see so because of
that I think that these bright stars are pretty common for the most part.
NAAP – HR Diagram Explorer 7/7