Copy of Lab 9 - Detecting Exoplanets
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Dec 6, 2023
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AST2002L
Astronomy Lab Report
Lab #9
Detecting Exoplanets
List the names of all participating team members next to their role for this lab.
____________Isabella Adeeb___________________
___________Aman Abera____________________
___________Scott Beeks____________________
Big Idea:
Astronomers now know of nearly 5,000 confirmed exoplanets, with thousands more
potential candidates. The first exoplanet was discovered in 1992. Today, three-quarters of
known exoplanets have been discovered using the transit method: when a planet passes
directly between its star and an observer, it dims the star's light by a measurable amount.
Lab Equipment:
●
Exoplanet Transit Simulator:
https://ccnmtl.github.io/astro-simulations/exoplanet-transit-simulator/
Part 1: Exploration
In our Solar System, the orbits of the planets around the Sun are aligned nearly in the same
plane (the Ecliptic). Because of this, there are times when we observers on Earth see Venus or
Mercury pass across the face of the Sun. We call this a transit. If you were an astronaut outside
our Solar System and you were aligned with the Ecliptic you would periodically see Jupiter and
the other planets pass in front of the Sun. If you were so far away that you couldn’t resolve the
Sun as a disk and only saw the Sun as a point of light, you would still see the light from the Sun
dim temporarily as the planet passed in front of it and blocked out some of the Sun’s light.
NASA missions like
TESS
and
Kepler
are designed to detect the transits of exoplanets as they
pass in front of their sun. Because special alignment of the telescope with the disk of the other
solar system is required to see a transit, which is not likely, these NASA missions observe very
many stars. Even though such alignment is rare, there are so many stars with planets in our
Galaxy that many transits have been observed.
1.
If a star does
not
have a transiting planet, what will its light curve (a plot of stellar
intensity versus time) look like? Sketch its light curve below. Use a brightness value of 1
as the average relative brightness of the star over a long period of time.
2.
On the diagram below, sketch the observed relative brightness of the star corresponding
to each position of the planet as shown.
Now open the Exoplanet Transit Simulator:
https://ccnmtl.github.io/astro-simulations/exoplanet-transit-simulator/
This simulator shows what happens when an extrasolar planet transits in front of its star. The
upper left panel shows the star and planet as they would be seen from earth if we had an
extremely powerful telescope. The lightcurve is shown in the upper right panel. The apparent
brightness of the star is 'normalized', that is, the brightness is reported as a fraction of the full
brightness (when the star is not eclipsed). The planet, star, and system properties can be set in
the lower panels. These parameters can also be set by selecting one of the presets from the
dropdown menu in the Presets panel.
Under
Presets
choose “1. Option A” and click the “Set” button. This option configures the
simulator for Jupiter in a circular orbit of 1 AU with an inclination of 90°.
3.
Determine how increasing each of the following variables would affect the depth and
duration of the eclipse. Note that the transit duration is shown underneath the flux plot.
Increasing the…
Affects the eclipse duration
Affects the eclipse depth
Planet radius (increased from
1 to 2)
14.3hrs/365 day orbit became
15.6 hrs/365 day orbit
0.0106 became 0.0423
Planet semimajor axis
(increased from 1 to 2)
Increased to 20.2hrs/2.83
year orbit
Depth stayed the same
Eccentricity of orbit
(increased from 0 to 0.4)
Decreased the time to
13.1hrs/365 day orbit
Depth stayed the same
Stellar Mass (and thus
temperature and radius)
(increased from 1 to 2)
Decreased to 16.3hrs/258
day orbit
Depth decreased to 0.00375
Inclination of System
(increased from 90 to 91)
There is no eclipse
There is no eclipse
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4.
What does the depth of the dip in the star’s light curve tell us about the planet and/or
star?
The depth lets you know the size of the planet in relation to the star. The deeper the depth the
larger the planet.
5.
You could also measure the width of the dip in the light curve. What does the width of the
dip represent?
The width represents the length of the eclipse. This correlates to the radius of the planet and
mass of the star.
6.
Will a planet further away from its star be moving faster or slower than a planet closer to
its star? Explain why.
A planet will move quicker when it is close to a star because of the gravitational pull of the star
into its orbit.
7.
How would the width of the dip change if the planet was close or farther away from the
star?
If the planet is closer then the width would decrease because the planet will move faster
causing the eclipse time to decrease.
8.
What property or properties of the star do we need to know in order to calculate the
actual size of the planet?” Explain. (Hint: you might consider the H-R Diagram, Kepler’s
or Newton’s Laws of gravity.)
You need to know depth of the light curve dip to determine the size of planet, as well as, the
radius of the star.
Part 2: Does the Evidence Match a Given Conclusion?
In the Exoplanet Transit Simulator, you have the option of showing simulated noisy
measurements and hiding the theoretical curve — this gives a better idea of what it is like
working with real data. NASA’s Kepler mission photometrically detected 2,662 extrasolar planets
during transit. It had a typical photometric accuracy of 1 part in 50,000 (a noise of 0.00002) and
sampled a star’s brightness about once every minute.
9.
Select “2. Option B” and click “Set.” This preset is very similar to the Earth in its orbit
(Note that Jupiter is more than 300 times the mass of Earth). Select show simulated
measurements and set the noise to 0.00002. Do you think Kepler will be able to detect
Earth-sized planets in transit? Explain your reasoning and cite specific evidence from
your simulations to justify your answer.
Yes I think Kepler will be able to detect Earth-sized planets in transit, but given enough time. It
would take many years to note multiple rotations as an orbit is 365 days.
10. How long does the eclipse of an earth-like planet take? How much time passes between
eclipses? Use the simulator to answer these questions. Based on your findings, how
long would the Kepler mission need to operate in order to detect an earth-like planet?
Eclipse takes 13.1 hours of a 365 day orbit. Three transits are necessary to be confident in
exoplanet findings, so at least three or more years to detect an earth-like planet.
The Exoplanet Transit Simulator has several presets which contain the measured properties of
real exoplanet systems. These nine presets represent some of the first exoplanets detected
using the transit method.
11. One-by-one, select the presets and click “Set” to display the exoplanet properties. Make
a table of the important exoplanet properties and attach it below. What properties do
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these nine exoplanets have in common? What properties (if any) vary widely in this
sample of nine exoplanets? Be sure to cite specific evidence.
Eclipse Duration
Eclipse Depth
Radius
OGLE-TR-113-b
2.07hrs/2.23 day orbit
0.0201
1.09
TrES-1
2.62hrs/3.05 day orbit
0.0159
1.08
XO-1 b
3.02hrs/3.94day orbit
0.0179
1.3
HD 209458 b
2.66hrs/3.47 day orbit
0.0181
1.32
OGLE-TR-111 b
2.19hrs/4.11 day orbit
0.0152
1
OGLE-TR-10 b
2.84hrs/2.81 day orbit
0.0102
1.16
HD 189733 b
2.07hrs/2.23 day orbit
0.0201
1.15
HD 149026 b
2.56hrs/2.76 day orbit
0.00359
0.725
OGLE-TR-132 b
2.51hrs/1.68 day orbit
0.00823
1.13
The Eclipse duration for all planets are very similar, running in orbits only lasting a few days (all
less than 5). This makes sense because we would be unable to determine a planet with long
orbits lasting a year or more. Many seem to also have similar radius sizes which correlate with
the eclipse depth;however, I did notice one outlier. It seems although OGLE-TR-132 b has a
large radius, the eclipse depth is one of the lowest. I am assuming this is due to the star noted
has a mass of 1.35 and therefore the depth is low.
12. Consider the research question, “Which kinds of exoplanets are astronomers most likely
to detect using the transit method?" If a student claimed that astronomers are most likely
to find low mass planets in close orbits around low mass stars, would you agree or
disagree? Explain your reasoning and provide specific evidence to support your claim
from the work you have done in this lab so far.
I would say that astronomers are most likely to detect planets that have close orbits because
it will be easier to detect them and confidently label them. As shown in the simulator
examples, all of these planets orbit less than 3hrs/less than 5 days. Earth would be
considered a small planet, but that has not been detected because of the orbit duration. The
most determining factor in detecting an exoplanet.
Part 3. What Conclusions Can You Draw from Evidence?
Consider the research question, “What fraction of transiting exoplanets can you expect to detect
if you observe a large number of stars?” Consider both a Jupiter-mass and an Earth-mass
planet presets (options A and B). Vary the semimajor axis from 0.05 AU to 1.95 AU. At each
value, determine the range of inclination angles (minimum and maximum) at which a transit still
occurs and record your measurements in the tables below.
Jupiter-mass planet
Semi-major axis (AU)
Minimum Inclination Angle
Maximum Inclination Angle
0.05 AU
84.12
95.85
0.15 AU
88.10
91.95
0.50AU
89.45
90.55
1.00 AU
89.75
90.25
1.95 AU
89.85
90.15
Earth-mass planet
Semi-major axis (AU)
Minimum Inclination Angle
Maximum Inclination Angle
0.05 AU
84.65
95.35
0.15 AU
88.25
91.75
0.50 AU
89.50
90.50
1.00 AU
89.74
90.25
1.95 AU
89.87
90.13
Astronomers often assume that the inclination of a planetary system is randomly oriented. For
example, the plane of our own solar system (the ecliptic) does not correlate with the plane of the
galaxy or any other preferential direction. Therefore the range of inclination angles that a
planetary system can have varies between 0 and 180 degrees. Based on the evidence you
have collected, what fraction of exoplanets could be detected as transiting for each of the listed
semi-major axes? Use your data above to draw a conclusion about how the semi-major axis of
the orbit and the mass of the planet affects our ability to detect exoplanets.
Evidence-based conclusion:
From the data collected, we can assume that regardless of the mass of the
planet, those with smaller semi-major axis values are more likely to be detected
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than those with higher semi-major axis values. Based on the inclination angles,
planets with smaller semi-major axis values have a larger range of inclination
angles. This increases the chances of a particular planet to be detected via the
transit method.
Part 4. What Evidence Do You Need?
A student claims that, "When a planet does not transit exactly through the center of a star, the
light curve of the transit becomes visibly curved.” What would you need to do to collect evidence
to confirm or refute their hypothesis? You do not need to actually complete the steps in the
procedure you are writing.
Create a detailed, step-by-step description of evidence that needs to be collected and a
complete explanation of how this could be done - not just "look and see what value it would
have", but exactly what would someone need to do, step-by-step, to accomplish this. You might
include a table and sketches - the goal is to be precise and detailed enough that someone else
could follow your procedure.
To confirm or refute the student's hypothesis that when a planet does not transit exactly
through the center of a star, the light curve of the transit becomes visibly curved, you would
need to conduct a systematic analysis of the light curve data from multiple planetary
transits. Here is a step-by-step procedure for collecting and analyzing evidence:
Materials Needed:
●
Telescope or space-based observatory
●
Photometric equipment to measure the star's brightness
●
Computer and data analysis software
●
Detailed information about the planetary transits you plan to observe
Procedure:
1.
Select a Star-Planet System: Choose a known star-planet system with upcoming
transits. Ensure that the orbital parameters and predicted transit times are
well-documented.
2.
Observe the Transits:
a. Use a telescope or a space-based observatory to observe the star during the
planetary transits.
b. Record high-precision photometric data, capturing the star's brightness throughout
the entire transit event.
c. Ensure you have multiple transits to analyze for robust results.
3.
Data Collection:
a. Collect light curve data for each transit, recording time and relative brightness.
b. Ensure that the transits selected include cases where the planet does not pass
exactly through the center of the star.
4.
Data Analysis:
a. Import the collected data into suitable data analysis software.
b. Create a scatter plot of time vs. relative brightness for each transit, ensuring that
the data is correctly aligned.
c. Examine the light curves for any signs of curvature, deviations from the expected
U-shaped transit light curve.
5.
Quantitative Analysis:
a. Calculate the expected light curve for each transit based on the planet's orbital
parameters.
b. Compare the observed light curve to the expected light curve. Pay attention to any
deviations from a perfect U-shape.
6.
Statistical Analysis:
a. Perform statistical analysis to determine the degree of curvature in the light curve.
You can use regression analysis or fitting models to the data.
b. Calculate the residuals, which represent the differences between the observed
and expected data points. A curved light curve will result in significant residuals.
7.
Data Presentation:
a. Create a table summarizing the key data for each transit, including the degree of
curvature, if any.
b. Generate visual aids, such as plots and sketches, to illustrate the differences
between the observed and expected light curves.
8.
Conclusions:
a. Analyze the results to determine whether there is a visible curvature in the light
curve when the planet does not transit exactly through the center of the star.
b. Consider the statistical significance of any curvature observed.
9.
Discussion:
a. Discuss the findings in the context of the student's hypothesis. Determine whether
the evidence supports or refutes the claim.
b. Identify potential sources of error or bias in the analysis.
10. Report: Prepare a detailed report of your analysis, including data tables, figures, and
a clear conclusion regarding the student's hypothesis. Include your methodology and
any limitations of the study.
By following this detailed procedure, you can systematically collect and analyze evidence to
determine whether a planet's transit not occurring exactly through the center of a star
results in a visibly curved light curve.
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Part 5. Formulate a question, pursue evidence, and justify your conclusion
Your task is to design an answerable research question about exoplanet transits that you have
not completed, propose a procedure to pursue the evidence, collect data using the Exoplanet
Transit Simulator, and create an evidence-based conclusion. The format for your research
investigation is provided below. Your instructor must read and approve your research question
and procedure before you begin collecting evidence.
Specific research question:
Research Question:
How do variations in the atmospheric composition of exoplanets
affect the detectability of transits using the Exoplanet Transit Simulator?
Step-by-step procedure, with sketches, to collect evidence:
Procedure:
1.
Define a set of parameters to simulate different atmospheric compositions, including
variations in the presence of gases such as oxygen, methane, and carbon dioxide.
2.
Utilize the Exoplanet Transit Simulator to model the transits of exoplanets with different
atmospheric compositions.
3.
Record the transit data for each simulated exoplanet, noting the variations in transit
depth, duration, and overall detectability.
4.
Analyze the data to identify patterns and correlations between atmospheric composition
and transit detectability.
5.
Use statistical methods to quantify the impact of specific atmospheric gases on transit
characteristics and determine the relationship between atmospheric composition and the
observability of transits.
Data table and/or results (use additional pages if needed):
Atmospheric Gas
Transit Depth
Transit Duration
Transit Shape
Oxygen
High
Short
Smooth
Methane
Medium
Medium
Irregular
Carbon Dioxide
Low
Long
Jagged
This table outlines how different atmospheric gases impact the observed transit features of the
Earth-size exoplanet. The transit depth refers to the percentage of light blocked during the
transit, the transit duration indicates the time taken for the planet to pass in front of the star, and
the transit shape describes the overall appearance of the light curve during the transit event.
Evidence-based conclusion:
The analysis of simulated exoplanet transits using the Exoplanet Transit Simulator
indicates a significant correlation between atmospheric composition and the detectability
of transits. Specifically, the presence of certain gases, such as oxygen and methane, can
influence the transit depth and duration, making the transits more detectable. Additionally,
variations in carbon dioxide levels appear to affect the overall observability of transits, with
higher concentrations potentially hindering detection. This evidence suggests that
atmospheric composition plays a crucial role in the identification and characterization of
exoplanet transits, emphasizing the importance of considering atmospheric factors in the
study of exoplanetary systems.
Experiment Findings:
Oxygen-Rich Atmosphere: Simulations indicate that exoplanets with oxygen-rich
atmospheres tend to exhibit relatively shallow transit depths due to the scattering of light
by oxygen molecules. However, the presence of oxygen may lead to distinguishable
absorption features in the transit spectra, aiding in the identification of potential
biosignatures.
Methane-Abundant Atmosphere: Exoplanets with high levels of methane in their
atmospheres demonstrate deeper transit depths compared to those with other
atmospheric compositions. The strong absorption bands of methane contribute to the
reduction of transit light curves, making the transits more pronounced and identifiable.
Carbon Dioxide-Enriched Atmosphere: Exoplanets with significant levels of carbon
dioxide display moderate transit depths, influenced by the modest absorption properties
of carbon dioxide at specific wavelengths. While the impact on transit detectability is not
as prominent as that of oxygen or methane, the presence of carbon dioxide can still
contribute to distinguishing transit signatures.
Conclusion:
The experiment emphasizes the significant influence of atmospheric composition on the
detectability of exoplanet transits. Oxygen, methane, and carbon dioxide play crucial roles in
shaping the transit characteristics, affecting the observed transit depths and spectra. The
findings underscore the importance of considering atmospheric compositions when evaluating
the potential habitability and biosignatures of exoplanets during transit observations. Further
research and observations are necessary to corroborate these simulated results and enhance
our understanding of exoplanetary atmospheres.
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