AST1120-lab8
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Astronomy
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Apr 3, 2024
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AST 1120: Stellar Astronomy
Name:
Lab 8 (40 points) Dark Matter & Gravity on Large Scales
Learning Goals
Summarize the evidence for dark matter in most galaxies
Explain how we know that galaxy clusters are dominated by dark matter
Describe how gravitational lensing can be used to detect dark matter
THIS ONE MAY BE NEAR PERFECT AS IS Part 1 – Dark Matter
Read thru 28.4 The Challenge of Dark Matter
. Visit the Dark Matter Simulator
from Foothill College and click on the link What is Dark Matter? at the top right of the screen for more background information on Dark Matter.
Figure 1- Spiral Galaxy NGC 1232
1.
It may seem obvious but, which region of a galaxy emits the most light? 2.
Which region of a galaxy should have the strongest gravity? Explain your answer.
Figure 2 - Orbital speed vs Mean distance from Sun
3.
In our solar system, describe how orbital speed varies with distance from the Sun. (Recall Kepler’s Laws from Chapter 3). 4.
Assuming that most of a galaxy’s mass is at its center, what should happen to
the speed of objects as orbital distance gets farther and farther from the center?
5.
On Figure 3, estimate the expected velocity at a distance of 30,000 ly from the center of the galaxy: 2
Figure 3 - Velocity vs Distance from Center of Milky Way
6.
The observed velocity at 30,000 ly from the center of the Milky Way is about 250 km/s. Determine the percent error in this measurement of the velocity at 30,000 ly from the center of the galaxy. %
error
=
|
(
(
observed
−
expected
)
expected
)
|
×
100
7.
On Figure 3, draw a curve that obeys Kepler’s Laws. 3
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Figure 4 - Rotation Curves for Several Spiral Galaxies
8.
Now imagine that every single galaxy you measure has an observed velocity that is many times higher than expected (a few examples are shown in Figure
4). Should you conclude that Kepler’s Laws are wrong? Explain your answer. Think about what Kepler’s Laws were originally used for. Visit the Dark Matter Simulator
from Foothill College
9.
What is the default galaxy? Look in the Orbital Velocity (km/s) window. 10.What is the Total Mass Enclosed (Solar Masses) given at a radius of 50,000 light-years out? _____________________
4
11.When you first open the animation, look at the central graph (Orbital Velocity (km/s) versus Radius (Thousands of light-years). How many of the red dots fall on the blue line? 12.What is the orbital velocity shown for a distance of 30,000 ly from center? 13.Now adjust the Dark Matter Density by clicking and dragging the red circles in
the top right graph until the red dots on the orbital velocity graph all line up with the blue line. Hint – move from left to right. What is the orbital velocity now for a distance of 30,000 ly from center? 14.Insert a screenshot that includes the 3 graphs for the Milky Way (dark matter density, orbital velocity, and total mass enclosed), showing the red dots on the orbital velocity graph lined up with the blue line. 15.Overall, did you increase or decrease the total mass of the Milky Way? Look at the total mass enclosed now at a distance of 50,000 light-years in radius. Rest the animation and select Andromeda Galaxy using the window in the Orbital Velocity graph. 16.What is the initial Total Mass Enclosed for Andromeda (at 50,000 light-years radius)?
5
17.Adjust the Dark Matter Density until all the red dots on the Orbital Velocity Graph line up with the blue line. What is the Total Mass Enclosed for Andromeda now (at 50,000 light-years)? 18.Assume that the initial mass of Andromeda is everything that emits light (stars, nebulas, etc), normal matter. The final adjusted mass included dark matter. What percentage of Andromeda is normal matter vs dark matter? Part 2 – Gravitational Lensing Visit the Gravitational Lensing Simulator
from Foothill College Astronomy.
Click Create cluster in the upper right corner. 19.Click and drag the bar below Source Distance. Describe how the View from Earth (shown in center of browser window) changes as you vary the Source distance. 20.Reset/Refresh the animation. Create a cluster. Now describe how the View form Earth varies as you change the Source offset. 21.Reset/refresh the animation. Create a cluster. Describe how the View from Earth varies as you change the Cluster distance. 6
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22.Reset/refresh the animation. Create a cluster. Describe how the View from Earth varies as you change the Cluster mass. Figure 5 - Two real examples of gravitational lensing. Cluster A on the left and Cluster B on the right
23.Figure 5 shows two real images of galaxy clusters where gravitational lensing is occurring. Which cluster is more massive? Explain how you can tell. Check out this Astronomy Picture of the Day
of a Supernova being gravitationally lensed. 24.How many times have we seen this supernova so far? 7
25.When will we see this supernova again? Use the Cosmological Redshift simulator
from Foothill College
26.With the default settings when you open the page, click play animation in the lower right corner. Let the animation play, then fill in the table below. 27.Reset the animation. Use the slider bar to decrease the Universe Expansion Rate to zero. Let the animation play, then fill in the table below.
28.Reset the animation. Use the slider bar to set the Universe Expansion Rate to
5. Let the animation play, then fill in the table below.
29.Reset the animation. Use the slider bar to set the Universe Expansion Rate to
13. Let the animation play, then fill in the table below.
Hubble Constant (km/s/Mpc)
Initial Separation
Distance (light-
years)
Current Separation
Distance (light-
years)
Time Elapsed (billions of years)
26
27
28
29
30.Our universe is 13.77 billion years old, but the most distant objects are greater than 13.77 billion light-years away. Explain why it is possible for objects to be farther apart than the age of the universe. 8