Lab 6 HR Diagram (1)
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Spokane Falls Community College *
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Astronomy
Date
Dec 6, 2023
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The H-R Diagram
Background Information
Work through the background material on Spectral Classification, Luminosity, and the Hertzsprung-Russell
Diagram. Then complete the following questions related to the background information.
Remember to type
your answer in blue text.
Question 1:
The table below summarizes the relationship between spectral type, temperature, and color for
stars.
Fill in the blank boxes using the simulator found under the Spectral Classification link in the background
material.
Question 2:
Complete the following table related to stellar luminosities.
All units are expressed in terms of the
sun, or in solar units.
Remember that luminosity is proportional to radius squared and temperature to the fourth
power. (
L
=
R
2
T
4
whensolar unitsareused
).
Star
Surface
Temperature K
Spectral Type
Color
Betelguese
3,530
M2
Orange
Arcturus
4,300
K5
Yellow
Sun
5,380
G2
Yellow
Procyon A
6,530
F5
Yellow-White
Sirius A
9,145
A1
White
Rigel A
11,000
B9
White Blue
Delta Orionis
33,200
O9
Blue
Radius (R
⊙
)
Temperature (T
⊙
)
Luminosity (L
⊙
)
2
1
4
2
2
64
4
1
16
1/2
1/2
.015625
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
3 M
⊙
would have a luminosity of
L
⊙
,
while a star with luminosity of 35,780 L
⊙
would have an
approximate mass of
M
⊙.
H-R Diagram Explorer
Open the
H-R Diagram Explorer
. Begin by familiarizing yourself with the capabilities of the Hertzsprung-
Russell Diagram Explorer through experimentation.
An actual
H-R 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 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.
Drag the active location around on the H-R 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 one box in each row of the table below that corresponds to appropriate region of the H-R
diagram.
45.25
17.46
Description
Top
Right
Bottom
Left
Faint stars are found at the:
X
Luminous stars are found at the:
X
Hot stars are found at the:
X
Cool stars are found at the:
X
Drag the active location around on the H-R Diagram once again.
This time focus on the Size Comparison
panel.
Question 5:
Check the appropriate region of the H-R diagram corresponding to each description below.
Check
show isoradius lines
.
Note that stars have the same radius at each point along a green line.
Use these
isoradius lines to check your answers in the table above.
In addition to the isoradius lines, check
show luminosity classes
.
The green region (Dwarfs V) is known as the
main sequence and contains all stars that are fusing hydrogen into helium in their cores as their primary energy
source.
Over 90% of all stars fall in this region on the H-R diagram.
Move the active cursor up and down the
main sequence to explore the different values of stellar radius.
Question 6:
Investigate the sizes of stars along the main sequence.
Compare the relative sizes of stars near the
top, middle, and bottom of the main sequence.
Top of the main sequence are the hottest stars. These stars are typically large and have relatively small radii compared to their high
luminosities. These are the “blue “ giants / O type stars or the large blue stars from the above diagram. Despite their high temps
are luminosities, their sizes can vary but tend to be larger than average sized stars.
Middle of the main sequence are sun like stars which are intermediate size and temperature. The sizes of the stars are moderate
and are the G type stars. The sun is a G2 star.
Bottom of the main sequence are the smaller and cooler stars. These are the red dwarf or M type stars. These stars are small in size
compared to other main sequence stars.
In summary, Hot massive stars are larger, while cooler smaller stars are found at the bottom.
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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The background page on the Hertzsprung-Russell Diagram detailed the mass-luminosity relationship for stars
on the main sequence:
Question 7:
Note how Luminosity changes on the H-R diagram.
What can you conclude about the relative
masses
of stars as you go from the bottom to the top of the main sequence?
Question 8:
Uncheck
show luminosity classes
and check
show instability strip
.
Note that this region of the H-R Diagram
indicates where pulsating (variable) stars are found, which are extremely important for finding distances.
These
stars vary in brightness because they are pulsating – alternately growing bigger and smaller – which changes
their radii and surface temperatures and resulting luminosities.
Question 8:
Describe the characteristics of stars that are found in the instability strip.
You should describe their
range of temperatures, colors, luminosities, and sizes. (Comparing them to the sun is useful.) What name do we
have for variable stars near the bottom of the instability strip?
What name do we have for variable stars near the
top of the instability strip?
As you go from the bottom to the top of the main sequence, where stars are fusing hydrogen into helium, we
can conclude that the relative masses of stars increase. As stars at the top of the main sequence (hot, massive
stars) have greater mass compared to stars at the bottom of the main sequence (cooler, smaller stars)
Stars in the instability strip are a huge group of diverse stars with specific characteristics. This is a region where stars exhibit variability due to the pulsations in
their outer layers.
Range of temperatures: Stars in the instability strip exhibit a wide range of temperatures. They can very from 6,000K to 20,000 K. In comparison with the sun,
which has a surface temperature of approx-5,500K. Stars in the instability strip tend to be hotter. This results in a bluish or blue-white color for these stars
Luminosities: The luminosities of stars in the instability strip can span a significant range encompassing main sequence stars, giants and super giants. Some may
have luminosities greater than the sun (especially super giants) or have lower luminosities such as a main sequence star (Top left to the bottom right in the HR
diagram band). The range of luminosities reflects the diverse evolutionary stages of these stars.
Sizes: The sizes of stars in the instability strip are directly related to their luminosities. Supergiants, which are found in the instability strip tend to be significantly
larger than the sun. While main sequence stars within the strip have sizes comparable to or slightly larger than the sun. The size variations are from he stars
different evolutionary paths.
Variable stars found near the bottom of the instability strip are called RR Lyrae variables. These stars ae cooler and less massive making them
smaller and located near the lower end of the instability strip. The variable stars located near the top of the instability strip are referred as
Cepheid variables. These are hotter and more massive which places them closer to the top of the strip.
3.5
L
M
L
I
n
crea
si
n
g
r
a
d
i
u
s
In
c
reas
in
g Mass
Blue Giants
Large Red Giant stars
Small blue stars
Small red stars
Question 9:
Use the results from the previous questions to construct a “conceptual” H-R Diagram.
Use the
Arrow drawing tool in Shapes under the Insert tab to draw arrows showing the direction in which variables are
increasing.
Use the Scribble drawing tool or insert a text box to label each of the arrows.
a)
Draw and label (with an L) an arrow on the y axis showing the direction of increasing luminosity of the
stars. (This has been completed for you.)
b)
Draw and label (with a T) an arrow on the x-axis showing the direction of increasing surface temperature of
the stars.
c)
Draw and label (with an R) an arrow showing the direction of increasing radius on the diagram.
(hint:
this
must be perpendicular to the isoradius lines.)
d)
Draw and label (with an M) an arrow showing the direction of increasing mass for main sequence stars on
the diagram.
Figure 1: Conceptual H-R Diagram
Luminosity
Increasing
Check the plotted stars option
the nearest stars
.
Note their range of temperatures, colors, luminosities, and
sizes.
Question 10:
Describe the characteristics of the nearest stars (compare them to the sun).
Question 11:
Do you think this type of star (like the nearest) is rare or very common among all of the stars in
our galaxy?
Explain your reasoning
.
Uncheck the plotted stars option
the nearest stars
and check
the brightest stars
. Think about why these are the
brightest stars in the sky.
Three students debate this issue:
Student A: “I think the brightest stars must be very close to us.
That would make them appear brighter to us in
the sky.”
Student B:
“I think the brightest stars are very luminous.
They are putting out a tremendous amount of energy,
which causes them to appear bright even at great distances.”
Student C:
“I think these stars are brightest because they are very close and very luminous.”
Question 12:
Use the tools of the H-R Diagram to support the views of
one
of the three students.
Why are
most of the stars we see as the brightest in the night sky really that bright?
(Hint:
You may find the options
labeled
both the nearest and brightest stars
and
the overlap
useful.)
The nearest stars have different characteristics when comparing to the sun.
Proxima Centauri is smaller, cooler and a red dwarf star with lower mass and luminosity than the sun
Alpha Centauri A is similar to the sun in size and temperature, while Alpha Centauri B is slightly cooler and less massive but still sun like.
Bernards star is a red dwarf star, it is smaller and cooler and less massive than the sun. It is one of the closest single stars to us though.
Sirius is a binary system with a hotter, more massive A type star and a white dwarf companion.
Tau Ceti is located farther away but it is a sun like star in terms of temperature and size
These stars
provide a range of sizes, temps, masses and luminosities serving as valuable reference for understanding the diversity and properties similar to
our sun
Stars similar to the nearest stars, such as red dwarf, sun like stars, and binary star systems, are actually quite common in our galaxy.
Red Dwarf stars, like Proxima Centarui and Barnard’s star are the most abundant type of star in the milky way. They make up a significant portion of the
stellar population. Their lower mass and longer lifetime contribute to their prevalence. Sun like stars are similar to our sun in terms of size, mass and
temperature. These ones are also common. They are found throughout our galaxy and many of them likely have planetary systems. The sun is a typical G star
and there are numerous stars with similar properties. Binary star systems like Alpha Centauri and Sirius are relatively common as well. Many stars in the
milky way have companions and some are even part of multiple star systems. Over all these type of stars found among the nearest stars are not rare but
represent the diversity of stars in our galaxy. Red dwarf, sun like stars and binary systems are abundant, making up a substantial portion of the milky ways
population of stars.
I am going to support Student B’s view. This view presents the most accurate explanation for why the brightest stars in the night sky ae indeed the brightest.
This student’s view also aligns with the understanding of stellar brightness.
Using the H-R diagram- it reveals that the luminosity of a star is a crucial factor in determining its brightness. Luminous stars emit a tremendous amount of energy which directly influences their apparent
brightness. Stars with higher luminosities will appear brighter in the sky. While student A pointed out that proximity does not affect how bright a star appears, the H-R diagram clarifies that a star’s distance alone
is not the sole determinant of its brightness. The diagram allows us to compare stars of similar luminosities at different distances and we see that more luminous stars will outshine those closer but less luminous.
Student C suggests that both distance and luminosity are important. The H-R diagram demonstrates that some of the brightest stars in the sky are both very close and very luminous. However, it also shows that
high luminosity can compensate for further distances.
By examining the H-R diagram and understanding the relationship between luminosity and brightness, we can conclude that the most significant factor contributing to the brightness of stars in the night sky is their
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Question 13:
Do you think that these brightest stars are very common (do they make up a large percentage of
all
stars in our galaxy)?
Explain your reasoning
.
Summary/Conclusion (5 points):
Roughly 90% of all stars lie along the main sequence but, depending on
their position on the H-R diagram, they spend drastically different amounts of time on the main sequence.
Explain
why bright stars spend a relatively short amount of time
on the main sequence,
why dim stars
spend a very long time
on the main sequence, and
how this affects the relative numbers of bright and dim
stars
found in our galaxy.
The brightest stars that we observe in the night sky are not very common in terms of their numbers
among all of the stars in our galaxy. While the brightest stars in the night sky are remarkable and
conspicuous, they represent a small minority of all stars in the Milky Way. The vast majority of stars in
our galaxy are lower luminosity stars, including red dwarfs which may be individually less bright but are
far more numerous. We have to think of the stellar population, red dwarfs, lower luminosity stars and the
distance in the night sky to determine why the brightest stars in the night sky are not very common.
Bright stars, particularly massive ones, spend a relatively short time on the main sequence because their
high mass results in more rapid consumption of hydrogen fuel in their cores through nuclear fusion. The
increased fusion rate leads to a shorter main sequence lifetime for these stars. Massive stars shine
brightly but have shorter lives.
Dim stars, especially dwarf stars spend a very long time on the main sequence because their lower mass
results in slower nuclear fusion rates. They burn their hydrogen fuel at much slower pace, leading to
extended main sequence lifetimes. Dim stars are more conservative in their energy production which
allows them to remain in this phase for billions of years.
So with this in mind, the longer main sequence of lifetimes of dim stars significantly affect the relative
numbers of bright and dim stars in our galaxy. While bright stars are more luminous and visible, they are
much rarer due to their shorter main sequence lifetimes. Dim stars on the other hand are much more
numerous, contributing to the majority of stars in the milky way. The majority of stars, by virtue of their
extended main sequence lifetimes are dim, low mass stars and this dominance of dim stars are a key
factor in shaping the overall stella population in our galaxy