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The Hertzsprung-Russell Diagram and Stellar Evolution
11/20/2022
The H-R Diagram and Stellar Properties Activity
1. In which corner of the diagram (upper right, upper left, lower right, or lower left) would stars with radii 1000 times larger than that of the Sun be plotted? The stars larger than the that of the Sun would be plotted in the upper right corner of the diagram.
In which corner would stars with radii 1000 times smaller than that of the Sun appear? The stars with smaller than that of the sun appear would be plotted in the lower left Star
Luminosity (solar units)
Radius (solar units)
Surface Temperature
(K)
Sun
1.00
1.00
5800
Star a
0.015
0.10
5800
Star b
18.8
2.00
5800
Star c
20.5
1.00
11600 (or 12000)
Star d
0.0637
1.00
2900
Star e
667
100.00
2900
Star f
0.0018
0.01
11600 (or 12000)
3. (a) Considering the measurement uncertainty inherent in the data, do most of the points lie on (or near to) the Main Sequence line (within the Main Sequence strip)? Yes, most of the points lay on or near to the main sequence line.
(b)
Region A: white dwarfs
Region B: red dwarfs
Region C: giants
Region D: super giants
What object's position is marked by the X? the sun What two lines intersect at this spot? Luminosity and temperature
(c) The "Dwarfs (V)" label for the Main Sequence strip is unfortunate because the most luminous stars at the upper end of this strip have radii roughly 10
times that of the Sun. (d) Of the hundred nearest stars, only 6
are obviously intrinsically brighter than the Sun.
(e) Move the cursor to the middle of the nearest star sample, where many of them are concentrated. This region is labeled red dwarfs
on the diagram. The luminosities for these typical stars are lower
that of the Sun's, their radii are smaller
that of the Sun's, and their surface temperatures are around 2500/5000
K. (f) The nearest star sample shown is technically incomplete; at least five nearby white dwarfs were omitted. The most famous is the companion to the bright, nearby star Sirius A; Sirius B has a luminosity of 0.027 L
Sun
and a surface temperature of 25,000 K. Moving the cursor to where this star would be plotted, its radius is 0.00892
that of the Sun's. (g) Of these 150 brightest stars, only 1
is/are intrinsically fainter than the Sun. While all the nearest stars were predominantly Main Sequence (V) stars, the brightest stars sample also includes many objects of luminosity classes super giants
and giants
.
(h) Move the cursor to the star representing the most luminous star in this sample. Its luminosity is 354010
L
Sun
, its radius is 23.8
R
Sun
, its surface temperature is 28990
K, and its B-V color is blue
. The region where the cursor is now located is labeled blue giants
on the diagram.
(i) Move the cursor to the star representing the largest star in this sample. Its luminosity is 48560 L
Sun
, its radius is 511
R
Sun
, and its surface temperature 3,810
K; its B-V color is red
. The region where the cursor is
now located is labeled super giants
on the diagram. (j) There are 5
stars that are members of both samples (both nearest and brightest stars). (k) In summary, the nearest
star sample is more representative of a typical
volume of stars in our Galaxy, whereas the brightest
star sample is a specially selected sample, heavily weighted towards relatively rare, highly luminous objects.
The H-R Diagram for the Pleiades, a Young Star Cluster
1. If the Sun were to be viewed from larger and larger distances, it would appear fainter
. Its apparent magnitude would remain unchanged
, while its absolute magnitude would increase
2. (a) Identify the seven brightest Pleiades stars from their apparent V magnitudes: 1,2,3,4,5,6,7
(b) The brightest cluster star is #
1
, with an apparent V magnitude of 2.87
If this star also has an apparent B magnitude of 2.78, and a B-V color index
of -0.09, explain how the color index was computed.
Subtract 2.78 from 2.87 and you’ll get -0.09 (c) Star #1 is roughly 3
times brighter than star #4.
(d) Star #
4
is almost 100 times brighter than star #15.
3. If the stars in the Pleiades cluster lay only ten parsecs from Earth, they would appear brighter, though their absolute magnitudes would be
fainter
. Solar-type star #16 would have an apparent V magnitude of 6
and would just be visible to the unaided eye as a faint star. Star #16 is actually much
farther away than ten parsecs (it lies around 130
parsecs away) so it appears much fainter: its actual apparent V magnitude is 10.48
.
4. (a) As a star cluster ages, its Main Sequence turn-off point steadily becomes fainter
and
redder
. The masses of the stars around the turn-off
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point decrease
.
(b) The difference between absolute and apparent magnitude is the same for all members of the Pleiades cluster, because it is purely a function of the cluster distance from Earth. Use the absolute magnitude of the Sun and the apparent magnitude of solar-type star #16 to estimate this difference, and then determine the absolute magnitude of star #1, Alcyone
(the brightest star in the Pleiades). Show your work, as well as stating your final answer. For solar-type star #16 in the Pleiades cluster, absolute magnitude M
ab
=4.8 and apparent magnitude M
ap
= 10.48
For all stars in the Pleiades cluster the difference Δ between absolute and apparent magnitude is defined as M
ab
M
﹣
ap
= Δ. For star #16, M
ab
M
﹣
ap
= -5.68, and so Δ = -5.68 for all Pleiades stars.
For star #1, M
ap
= 2.87
If M
ab
M
﹣
ap
= Δ, then we can solve this expression for M
ab
, defining M
ab
in terms of M
ap
and Δ. M
ab
= -5.68+2.87 (write M
ab
in terms of M
ap
and Δ).
For star #1, M
ab
= 8.55
The brightest, bluest star still remaining on the Main Sequence is sometimes used to define a cluster's turn-off point. The term “
turn-off
” comes from recognizing that this star will be the next one to leave (or turn off) the Main Sequence, and become a red giant. For the Pleiades, this turn-off point is currently at absolute magnitude 8.55
and B-V color red
. (c) Locate star #1
4
(resembling Sirius) in Figure 6.4. There are only 4
stars on the diagram that are brighter and bluer than it.
An H-R Diagram for M67, an Older Star Cluster
3. Insert your first figure here containing a copy of your list of 12 stars. Add a figure caption stating which star (identified by ID) is the solar-type star, and which stars fall into each of the other four categories of brightness and color.
6. (a) What happens if an aperture is too small? Where will the associated star appear on the H-R diagram, relative to its correct position?
If the aperture decreases then that will increase the magnitude, and decrease the luminosity.
(b) What happens if an aperture is too large? Does it matter whether the extra space is dark sky, or contains a neighboring object?
If it too large that means the magnitude decreases and the luminosity increases. It doesn’t really matter if the extra space is dark or if it contains a neighboring object.
(c) What happens if the aperture is offset from the center of the star?
Luminosity increases and the magnitude decreases if the aperture is offset from the center of the star
(d) What happens if you place an aperture directly between two stars?
If you place it directly between two stars you get two even counts and two even peaks.
Insert any extra figures here showing radial plots of counts to help with your answers to the following four questions. Be sure to add figure captions explaining each figure.
7. Discuss your results (your age estimate) for M67 below, explaining how you came to your conclusion. Note the particular features on the H-R diagram which were most important to your decision-making process. Replace this text.
8. Compare your results for M67 with those for the Pleiades, with respect to the following five factors:
(a) Cluster turn-off point: Replace this text.
(b) Presence of red giants: Replace this text.
(c) Presence of red dwarfs: Replace this text.
(d) Presence of massive blue Main Sequence stars: Replace this text.
(e) Age of cluster: Replace this text.
Insert your second figure here showing the final H-R diagram. Be sure to add a figure caption explaining the figure.
Final (post-lab) Questions
1. How does the Sun compare to the other members of the nearest star sample? If one assumes this sample is representative of typical stars found throughout the universe, to what extent is the Sun a typical star?
The sun would not be a typical star if the sample we used represented those stars and since it is not in the group of typical stars. The sun is towards the end of the group of the nearest stars. While there are a few of the stars in that group that have the luminosity and hot temperature of the
sun, most of those stars members in the group of the nearest stars are cooler in temperature and fainter than the sun. 2. Consider the brightest stars in the sky, and why they appear so bright. Three students debate this issue. Student A: "These stars must be very close to us. That would make them appear brighter to us in the sky." Student B: "These stars are intrinsically very luminous, so they emit a tremendous amount of energy.'' Student C: "I think it's because these stars are very close and very luminous.'' Use what you've learned in this lab to support the views of one of the three students and answer the question "Why do the stars which appear the brightest in the night sky seem so bright?'' I think student B’s hypothesis is correct and the information from this lab will back that up. The brighter stars are actually the stars that are further
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from us and they are the hotter stars, also putting off the most energy. Meanwhile the stars that are closer to us are dimmer, cooler in temperature, and they put off less energy compared to the stars that are further away. 3. Are these apparently bright stars very common (do stars like them make
up a large percentage of all stars)? Explain your reasoning. The really bright stars are not that common, and the bright stars do not make up a large percentage of all stars. According to the H-R diagram, most stars are under the luminosity of 10.
4. Consider how the H-R diagram of the Pleiades would look far in the future. (a) Suppose all of the Main Sequence stars above solar-type star #16 had run out of fuel and left the Main Sequence. What other regions in the diagram (besides the Main Sequence) would now be populated?
I would guess that the stars in the O region look like they slowly drift towards the M region, and with that they grow in size over time
(b) How old would this cluster be? Explain.
In the lab 6 video that is linked it mentions that this group would be about 125 millions years old. All of these stars are aorunf the same age because it takes around the same time for the gas and dust to form a star. That being said it takes millions of years for that to happen.
5. The best explanation for why the H-R diagram for M67 does not include any white dwarf stars is (a) this cluster is not old enough for any of its stars
to have evolved to this stage, or (b) the data this H-R diagram is based on only includes stars brighter than an apparent V magnitude of 16, and we expect any white dwarfs in M67 to be fainter than this. Explain your choice
of answer. I think option B is the best answer for this explanation/question. If we look at the placement of white dwarf stars youll notice the positions are off the main sequence and are in a magnitude of > 10. The data we have does not
relate to white dwarf stars, our data shows larger values than white dwarf
stars.
6. When measuring apparent magnitudes for stars in M67, if two equal-
mass stars were tightly clustered in a binary system and could not be separated (they appeared as one star), where would their combined properties place them on the H-R diagram (versus where they would be placed if they were separable)? The combined properties would put them towards the lower end of the magnitude scale because when combined they record a brighter data. Together they record around 10 on the scale but when its just one star you
can see its not as bright.
7. The constellation of Cancer contains the star cluster M44, which, like the
Pleiades, is visible to the unaided eye on a clear night. (a) Using its H-R diagram in Figure 6.5, compare this cluster's age with that
of of the Pleiades and M67 clusters. Explain how you arrived at your conclusion. The stars in the figure 6.5 cluster are much younger than those in the Pleiades and M67 groups because of the space and lack of clusters. The more stars in the cluster usually means that the cluster is older and that’s how I got that conclusion. (b) Is M44 closer to or farther away from us than the Pleiades, and closer to
or farther away from us than M67? Explain your answer.
The M44 is actually farther away from us than the Pleiades and we knows this because of the magnitude. Pleiades is around 1.6 magnitude and M44 is around 3.10. that also means the Pleiades stars are brighter in comparison to the M44 stars.
Summary
(300 to 500 words)
This lab was about the Main Sequence and where star clusters are formed. As the stars get older, their positions start to move further away from the main sequence. The Hertzsprung-Russell diagram is a diagram that plots the star's temperature against the star’s luminosity. You can also plot the color
of the star against the stars magnitude. We can also see the changes and evolutions a star goes through over time. Another cool thing we can do with the H-R diagram is compare those stars to the star we are the most familiar with. The sun is the most important star to us here on Earth and this a great way to measure up other stars using luminosity and temperature. This way we can get a better visual of the position, age, and size without having to actual travel to each star. The magnitude scale was something I never knew about and now knowing how useful it is I can see why it is mentioned and used so often. When I think
of magnitude scale, I only think of measuring magnitude of earthquakes and so on. Using this scale, you can measure the brightness and distance of clusters away from Earth and other planets. N this lab we focused on a few specific star clusters, M44, M67, and Pleiades. Using these clusters as models, we were able to learn about the brightness of stars and the correlation of distance with brightness. We were able to learn about different types of stars like white dwarfs, red dwarfs, giants, and so on. Each cluster has their own stars in that specific cluster, as the M67 had red giants.
We used the scale to estimate the age of the clusters too, for example, we estimate the M67 group are about 2 billion years old and the Pleiades group to be around 160 million years old.
Scientist believe that the sun has about 5 billion years left of stable well-
behaved existence on the main sequence. To which many people are skeptic
of that statement and wonder how we could possibly be correct is that assumption. Scientist are able to come to this conclusion due to the sun’s position on the main sequence. We can compare the sun to other stars that are similar in luminosity and magnitude to get an idea of the possible Sun lifespan. There are other similar stars, and it takes billions of years for the stars to fall off the main sequence and transition into giants. By observing the patterns of other similar stars, we were able to come to this time line and conclusion for the sun
.
Extra Credit
Astronomers were able to use the hubble to measure the size of Sirius B, it is a white dwarf and using the Hubble allowed them to precisely meausure it’s mass. Scientist were able to measure the change in wavelengths and the use of Einstein’s theory of general relativity to figure out the mass of Sirius B. Even though Sirius B is a little smaller than the earth, it has greater gravitational field at almost 350,000 times greater.
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“’Weighing’ the dog star’s companion”. Science and Exploration
,21/12/2005
https://www.esa.int/Science_Exploration/Space_Science/
Weighing_the_Dog_Star_s_companion#:~:text=The%20astronomers
%20used%20Hubble%20to,light%20emitted%20by%20the%20star.