LAB 9 HR DIAGRAM
pdf
keyboard_arrow_up
School
University Of Dallas *
*We aren’t endorsed by this school
Course
2302
Subject
Astronomy
Date
Apr 3, 2024
Type
Pages
12
Uploaded by MasterFang13191
Name: Faith Berry
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.
Star
Surface
Temperature K
Spectral Type
Color
Betelguese
3500
M2
Orange-red
Arcturus
4,300
K2
Orange
5770
G2
Yellow
Procyon A
6530
F5
Yellow-White
Sirius A
9940
A1
White
Rigel A
11,000
B8
Blue-white
Delta Orionis
18,400
O9
Blue-white
Question 2: Complete the following table related to stellar luminosities in solar units using the
equation
2 4
L RT
∝
.
Radius (R
⊙
)
Temperature (T
⊙
)
Luminosity (L
⊙
)
1
1
1
1
2
16.8
3
1
9
1
1/2
1/16
NAAP – HR Diagram Explorer 1/9
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 _____16________ 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 2/9
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.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
Question 4: Check the appropriate region of the HR diagram corresponding to each description
below.
HOT STARS ARE FOUND AT THE:
Left
FAINT STARS ARE FOUND AT THE:
Bottom
LUMINOUS STARS ARE FOUND AT THE
:
Top
COOL STARS ARE FOUND AT THE:
Right
∙
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.
Description
Upper
Left
Upper
Right
Lower
Right
Lower
Left
Large Blue stars are found at the:
Yes
Small Red stars are found at the:
Yes
Small Blue stars would be found at the:
Yes
Really Large Red stars are found at the:
Yes
∙
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 3/9
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.
Radius, temperature, and luminosity determine the placement on the HR and is used to
determine where stars fall on the HR diagram. Luminosity is dependent on the size and
temperature of the star itself.
2 4
L
=
4
π
R T
σ
∙
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 top is the big blue hot stars. The middle is yellow-whiteish cooler stars. The bottom is
organeish-red cooler stars. They get smaller as you go down.
∙
The background pages of this module talked about the mass-luminosity relationship for
stars on the main sequence:
3.5
L M
∝
Question 8: What can you conclude about the masses of stars along the main sequence?
As mass decreases, luminosity decreases.
NAAP – HR Diagram Explorer 4/9
Question 9: 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.)
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
NAAP – HR Diagram Explorer 5/9
∙
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 10: 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?
Stars on the instability strip vary in color, temperature, and luminosity. They are larger, more
luminous, and hotter than the sun.
∙
Check the plotted stars option
the nearest stars
. You should cover their range of
temperatures, colors, luminosities, and sizes.
Question 11: Describe the characteristics of the nearest stars.
They are the coolest and smallest stars on the HR diagram.
Question 12: 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?
They are very common among all stars in our galaxy. There are very many of them in a dense area,
whereas the bigger stars seem to be fewer and far between within the galaxy.
∙
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:
NAAP – HR Diagram Explorer 6/9
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 13: 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.)
C. These stars are the rare ones that are both near and fairly luminous.
Question 14: Do you think that these bright stars are very common (make up a large percentage
of all stars in general)? Explain your reasoning.
They are not as common because, on the HR graph, there were a lot of less luminous stars.
NAAP – HR Diagram Explorer 7/9
Deriving the Isoradius Lines
(optional, mathematical section)
2 4
L RT
=
2 4
log L log R T
=
Question 15: The HR Diagram is a log-log plot of
the solar units
( )
2 4
equation L=R
2
T
4
. Use the boxed equations to
argue that isoradius lines on the HR Diagram
must be parallel lines.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
log L log R log T
= +
2 4
log L log R log T
= +
Question 16: Complete the table below. Then add the points to the following HR Diagram and
use them to draw in the isoradius lines for 1, 10, and 100 solar radii.
Symbol
L (L
u
)
R (R
u
)
T (T
u
)
x
1
1
1
A
10
1
4
√
10
B
100
1
√
10
C
100
10
1
D
1,000
10
1
E
10,000
10
√
10
F
10,000
100
1
G
160,000
100
2
H
625
100
0.5
NAAP – HR Diagram Explorer 8/9
NAAP – HR Diagram Explorer 9/9
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help