Lab 9
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University of North Dakota *
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Course
110L
Subject
Astronomy
Date
Dec 6, 2023
Type
Pages
9
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1
Name:__________________________________________
Date:_________________
PHYS 110L Lab # 9
Hertzsprung-Russell Diagram
1
Instructions:
Please read
carefully
and follow the steps
described below and answer
all
questions. If unclear what
to do for various parts, please ask your instructor for help.
Part #1 Introduction
Stars have a number of properties that, at first glance, may
appear to be unrelated, but further analysis shows that they
are related after all. Two astronomers independently of
each other, plotted the luminosities of a number of stars
versus their temperatures to create what is now known as
the “Hertzsprung
-
Russell,” or “H
-
R” diagram (named after
the scientists who invented it), which allows us to study
this relationship between stars.
In this lab you will find that for a majority of stars, there is
a definite relationship between temperature and luminosity.
You will learn that other properties of stars are also related.
In fact, the H-R diagram contains a surprisingly large
amount of information in one simple graph.
In the two tables and the graph that follow, temperatures are in Kelvin (K), and luminosities and
masses
are given in units relative to the Sun; the units are called “Solar Luminosities” and “Solar
Masses,
” respectively, which are abbreviated as L
and M
. Note that the values for the Sun in
these units are 1.0 L
and 1.0 M
by definition. Spectral type is a classification scheme for stars
that depends on their surface temperature. From hottest to coldest, the sequence of spectral types
goes OBAFGKM (which corresponds with the first letter of each entry in the Spectral Type
column).
1
Modified from
Engaging in Astronomical Inquiry
, by S. J. Slater, T. F. Slater, and D. J. Lyons, 2010, W. H. Freeman
and Company.
Learning Objectives:
In this lab assignment you will conduct a series of inquiries to explore correlations of various
stellar properties. The relationship between temperature and luminosity for main sequence
stars will be depicted using the Hertzsprung-Russell diagram.
2
In Table 1, properties of the 25 nearest stars in the sky, starting with the nearest one, are
tabulated.
In Table 2, properties of the 25 visually brightest stars in the sky, starting with the brightest one,
are listed. Note that some of these stars are also found in Table 1.
Table 1:
Properties of the 25 nearest stars to the Earth.
Star
Spectral Type
Temperature
Luminosity
Mass
1 Sun
G2V
5800
1.0
1.0
2 Proxima Cen.
M5V
3042
0.00005
0.1221
3
α Cen A
G2V
5790
1.519
1.100
4
α Cen B
K0V
5260
0.5002
0.907
5
Barnard’s Star
M3V
3134
0.0004
0.144
6 WISE 1049-5319 A
L8
*
1350
0.0000219
0.032
7 WISE 1049-5319 B
T1
*
1210
0.0000209
0.027
8 Wolf 359
M5V
2800
0.00002
0.09
9 Lalande 21185
M2V
3828
0.0055
0.46
10 Sirius A
A1V
9940
25.4
2.063
11 Sirius B
DA2
*
25000
0.056
1.018
12 BL Cet A
M5V
2670
0.00006
0.102
13 UV Cet B
M6V
2650
0.00004
0.100
14 Ross 154
M3V
3340
0.0038
0.17
15 Ross 248
M5V
2799
0.0018
0.136
16
ε Eri
K2V
5084
0.34
0.82
17 CD-36 15693
M1V
3692
0.0367
0.486
18 Ross 128
M4V
3192
0.00362
0.168
19 EZ Aqr A
M5V
1578
0.0001035
0.1187
20 EZ Aqr B
M3V
2600
0.000034
0.11
21 EZ Aqr C
M5V
?
?
0.1
22 61 Cyg A
K5V
4526
0.153
0.70
23 61 Cyg B
K7V
4077
0.085
0.63
24 Procyon A
F5V
6530
6.93
1.499
25 Procyon B
DQZ*
7740
0.00049
0.602
* Not part of the original stellar spectra classification scheme. Sirius B and Procyon B are white
dwarfs.
3
Table 2: Properties of the 25 visually brightest stars in the sky.
Star
Spectral Type
Temperature
Luminosity
Mass
A
Sun
G2V
5800
1.0
1.0
B
Sirius A
A1V
9940
25.4
2.063
C
Canopus
F0I-II
7200
12600
9.8
D
α Cen A
G2V
5790
1.519
1.1
E
Arcturus
K2III
4500
150
1.1
F
Vega
A0V
10800
50
2.135
G
Capella A
G1II
4940
140
2.1
H
Rigel A
B8I
12000
44000
50
I
Procyon A
F5V
6530
6.93
1.499
J
Betelgeuse
M2I
3300
8700
11
K
Achernar
B5V
18800
1260
6.7
L
β Cen A
B1III
25000
12000
10.7
M
Altair
A7IV-V
8200
10.7
1.7
N
α Cru A
B1IV
24000
3500
17.8
O
Aldebaran A
K5III
3800
180
1
P
Spica
B1V
24200
2400
10.3
Q
Antares A
M1I
3400
13000
12
R
Pollux
K0III
4500
30
2.04
S
Formalhaut A
A3V
8590
17
2.3
T
α Cen B
K0V
5260
0.5002
0.907
U
Deneb
A2I
9700
48000
25
V
β Cru
BOIV
27000
5750
16
W
Regulus A
B7V
13000
145
3.5
X
Adhara A
B2II
21900
8300
12.6
Y
Castor A
A1
10300
36.3
2.2
On the next page is a graph showing each star’s
Temperature versus Luminosity. This is an
H-R
Diagram
. Data for the nearest stars have been plotted using a box symbol, while data for the
brightest stars have been plotted using an “
×
”. For the f
our stars that appear on both lists, they
are plotted on the graph using both symbols, so you will see a box with a cross inside, which
looks rather like a filled-in box.
Note that the tick marks on the axes are not evenly spaced. On
the
y
-axis (vertical axis) the numbers are given by a logarithmic scale (
i.e.
powers of ten), while
on the
x
-axis (horizontal axis) the numbers are given by a linear scale (
i.e.
a “normal” scale).
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4
Figure 1. The H-R diagram of the nearest and brightest stars.
Part #2 Main Sequence
Step 1.
Observe the general trend among the majority of stars known as
the “Main
Sequence.”
On Figure 1, circle the Main Sequence
‒
that is, circle the stars which follow the trend that you
observe; the stars are called “Main Sequence stars,” and the trend is
called the Main Sequence.
Question 1:
How many stars does the Main Sequence include for this figure?
Don’t forget stars
that are hotter than 15000 K.
Number of stars:________I counted around 36 stars____________
Sun
Barnard’s
Sirius B
Regulus A
Deneb
Betelgeuse
1.018
25
11
3.5
2.063
1.0
0.144
UV Cet B
0.100
Ross 154
0.17
61 Cyg A
0.70
Spica
10.3
Alpha
Beta
Gamma
Delta
Epsilon
Zeta
5
Step 2.
Briefly describe the trend that defines the Main Sequence, making sure to include the
properties of the stars that are represented and how they are related to one another.
The nearest stars are the ones that are towards the bottom right, which means they have
the least luminosity and the lowest temperature. As the Main Sequence progresses, the
stars turn into the X’s, which means they are getting brighter, which also coincid
es with the
luminosity increasing.
Step 3.
If a main sequence star was measured to have a temperature of 3,500 K, predict, by
examination of your H-R Diagram, the luminosity that you think this star most-likely has.
Explain how you made your prediction, and any assumptions you made.
I would think the star has around 10,000 units of luminosity. The stars kind of started to
plateau out, even with higher temperatures. For example, the star with a temp of 25,000 K
is brighter than the star with 26,500 K.
Step 4.
Find and label by name, using text boxes, the following seven stars on your graph: The
Sun, Barnard
’
s Star, Sirius A, Sirius B, Regulus A, Deneb, and Betelgeuse.
Step 5.
Complete the following table and indicate whether each star is on the Main Sequence.
Star’s
Name
The Sun
Barnard’s
Star
Sirius A
Sirius B
Regulus A
Deneb
Betelgeuse
On the
Main
Sequence?
Yes
Yes
Yes
No
Yes
No
No
Step 6.
Stars in the top right corner of the graph are called Red Giants because their temperature
is cool and thus their color is red, and they are swelled up to a huge
“
giant
”
size, making their
luminosity very large.
6
Question 2:
Which of those seven stars from Step 4 is closest to the top right corner of the
graph?
I would say Betelgeuse is the closest, but Deneb is also very close.
Step 6.
For the seven Main Sequence stars that you labeled on the graph from Step 4, consult the
two tables near the beginning of the lab assignment and write their mass next to their label on the
graph using text boxes.
Step 7.
Label the location and mass of the following additional four main sequence stars: UV
Cet B, Ross 154, 61 Cyg A, and Spica. Write them directly on the graph using text boxes.
Step 8.
Rank the labeled Main Sequence stars (the proceeding
four
stars from Step 7 plus the
seven
stars from Step 4) from highest to lowest luminosity.
Highest Luminosity
Lowest Luminosity
Deneb, Betelgeuse, Spica, Regulus A, Sirius A, Sun, 61 Cyg A, Sirius B, Ross 154, Barnard’s, UV Cet B
Step 9.
Describe any trend in the progression of masses that you just labeled along the Main
Sequence.
The more luminosity, the higher mass.
Part #3 Stellar Radius
Step 10.
The most luminous stars have either a very high temperature (hot things glow brightly),
or a very large radius (the more glowing surface area there is, the more the total luminosity given
off), or both.
Consider the research question, “How does a star’s radius change with its
temperature and
luminosity?” Use the following six hypothetical stars to explore this property of
the H-R Diagram.
Star Name
Temperature (K)
Luminosity (Solar Units)
Radius
Alpha
3,000
0.00001
the same as star Beta
Beta
30,000
0.1
the same as star Alpha
Gamma
3,000
0.001
10× bigger than star Alpha
Delta
30,000
10
10× bigger than star Alpha
Epsilon
3,000
0.1
100× bigger than star Alpha
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7
Zeta
30,000
1000
100× bigger than star Alpha
Step 11.
Label the location of the six stars, in the table above, on the previous H-R Diagram
from Figure 1 (Part #2) using text boxes.
Step 12.
Star Alpha and Star Beta have the same radius. Connect the points representing stars
Alpha and Beta with a straight line. This line represents a line of constant radius on the diagram.
All stars on this line have the same radius!
Step 13.
Stars Gamma and Delta also have the same radius as one another. Draw a straight line
connecting these two stars.
Step 14.
Stars Epsilon and Zeta have equal radii. Draw a line connecting those two stars.
Step 15.
You should now have three lines of constant radius on your H-R diagram. Each line you
drew represents a radius that is ten times larger than the previous line you drew. Label the lines
on your diagram accordingly,
e.g.
“
Radius = 1 × Alpha,
”
“
Radius = 10 × Alpha,
”
and
“
Radius =
100 × Alpha
”
using text boxes.
Question 3:
The Sun should fall almost exactly along one of the lines you drew. How does the
Sun
’
s radius compare to that of star Alpha?
It’s about 100 x Alpha
Question 4:
Given the three lines drawn, what conclusions and generalizations can you make
regarding the direction on the H-R diagram in which the radii of stars increase?
The larger radius, the higher luminosity.
Step 16.
Continue drawing several more lines of constant radius (or size) on your H-R diagram
following the established pattern, where each line represents a change of radius by a factor of 10
as before, until you have encompassed all the labeled stars on your diagram. (You will have to
draw lines representing both larger and smaller radius than before.) Label each line with the
corresponding radius as before, relative to star Alpha.
8
Question 5:
Consider the research question “
How does the radius of a given star compare to the
radius of the Sun?
” If s
omeone claimed that the star Betelgeuse has a radius 500 times that of the
Sun, would you agree or disagree? Explain your reasoning and provide specific evidence to
support your claim.
If we’re looking at the relationships in the stars in the chart, I’d disagree and say that 500
times isn’t enough. Betelgeuse’s luminosity is almost 10,000, whereas the Sun’s is only 1. If
we look at Delta and Zeta, Zeta’s radius is 100 times Delta’s.
Question 6:
If someone claimed the Sun has a radius 500 times that of the star Sirius B, would
you agree or disagree? Explain your reasoning and provide specific evidence to support your
claim.
I would say that it’s only about 10 times bigger, because Sirius B is almost .1 in luminosity
and the Sun is 1, and that’s 10 times.
9
Conclusion.
Please provide feedback regarding the lab assignment. Are there things that you
liked or disliked? Thanks!!
Step 16 was mildly confusing; I couldn’t tell if we were supposed to connect any star to
each other, or the previously labeled stars to the new hypothetical ones.
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