Your Name: TA:
Partner’s Names:
Astronomy 1101
Transiting Exoplanets Activity
Part 1: Discovery and Orbital Period of an Exoplanet
Using a network of telescopes at different locations around the globe, you observe the apparent brightness of a star every 10 minutes for 40 days.
At the end of these 40 days you make the following plot of your observations. Here the vertical (y) axis shows the measured apparent brightness of the star relative to its average value and the horizontal (x) axis shows time. Thus, a “brightness” of 0.99 means that the star appears 1% fainter than average. Individual points scatter up and down because there is inevitably some noise in your measurements.
You look at this plot and conclude with enthusiasm that you have discovered a transiting exoplanet!
The diagram above illustrates an “overhead” view of the system: when the planet (small circle) passes in front of the star (large solid circle) it blocks a small portion of the star’s light. An “edge-on” view of this system appears in Part 3.
Answer the following questions:
What is the orbital period of the planet around its parent star, in days?
To get a data set like the one shown, why would you have needed to have a network of many telescopes located around the globe instead of a single telescope at one location?
Part 2: Properties of the Parent Star from Light
Conveniently, the distance to this star is known to be D=10 light years = 9.48´1016 meters.
Observations show that the apparent brightness of the star is B = 3.39´10-9 watts/m2 (watts per square meter).
Using the equation below to answer the following questions:
Luminosity(L) = Brightness(B) ´ 4 ´ p ´ (Distance (D))2
What is the luminosity of the star in watts?
How does this compare to the luminosity of the Sun, 3.83´1026 watts?
The equation that relates a star’s luminosity (L) to its radius (R) and surface temperature (T) is
L = (4 ´ p ´ R2) ´ s ´ T4
The symbol s is a constant, like G for gravity – it’s just a number. For two stars of the same surface temperature, the luminosity is proportional to the star’s area, and thus to R2. The radius and mass of the Sun are: Rsun=7.0´105 km, Msun=2.0´1030 kg.
You measure the color of the star and find that it has exactly the same color as the Sun, meaning the two stars have the same temperature (Tsun = Tstar). From Question 4, you found that the star’s luminosity is also the same as the Sun (Lsun = Lstar). For the next two questions use the reasoning of “If it looks like a Duck and quacks like a Duck it is most likely a Duck.”
What is the radius of the star in km? DO NOT calculate anything. Just use logic.
Rstar =
What is the mass of the star in kg? Again, just use logic.
Mstar =
Part 3: A Detailed Transit Light Curve
Now that you can predict when the transits are going to occur, you get time on the Hubble Space Telescope to get better observations of your star during one transit. You now get one exposure every 100 seconds, and because Hubble is a bigger telescope it collects more light and gives you more precision on each measurement.
The light curve (plot of brightness vs. time) below shows the result of your observation, where time is now marked in seconds rather than days. Several times are marked on this diagram, t1 through t7.
The diagram below shows a schematic view of the transit, with the planet moving from left to right as it transits the star. This is the “edge-on” view of the system
Which time on the top diagram corresponds to each lettered location on the lower diagram? (Give your answers as, e.g., “t1” or “t5”, not a time in seconds.)
A:
B:
C:
D:
E:
F:
G:
The distance that the planet travels between times t2 and t5, is the diameter of the star. Calculate the diameter of the star using your value of Rstar from Part 2 and remember that the diameter of the star is twice the radius.
Using the Python notebook linked on Carmen or here, https://go.osu.edu/ast1101-transitingplanets, go to the webpage and read the instructions while it compiles and loads. You will estimate the start and end times t2, t3, t5, t6, and the transit depth from the data on the website. The model should go through the data points, not above or below. You will then run the program which will draw your model and give a resulting X2 value measuring how good your model is. You will modify your input parameters until you find a model that has a X2 less than 1.2. When you do, the transit time will be given on your graph.
Copy your graph into the activity here:
Calculate the orbital speed of the planet, in km/sec using the time on your graph and the diameter calculated in question 8.
Understanding measurement error. Start by reducing your ingress start time. As the X2 value goes up your model is less likely to be supported by the data until it becomes highly improbable. Discuss with your group what this means for the range of probable models. How much are you able to change the ingress value in seconds without the X2 going above 1.5? 100s, 1000s of seconds? Write about what you found and discussed. Use complete sentences for full points.
Part 4: The Mass of the Star
The orbital period from part 1 is 864,000 seconds. If the orbit is a circle, then the orbital speed you found in Part 3 should be v = 2πr / P, where r is the orbital radius and P is the orbital period. This equation can be rewritten as
r = v × P / (2 × π)
Assuming that the planet is in a circular orbit, what is the orbital radius, in km? Show your calculation and USE PARENTHESES in your calculator or you will get this answer wrong.
Just as you determined the mass of Jupiter from the orbital speed and orbital radius of its moons in the previous activity, you can determine the mass of this star using the formula from Newtonian gravity,
M = (v2 × r) / G
where v is now the orbital speed, r is the orbital radius, and Newton’s gravitational constant is
– Gravitational Constant with km, kg, sec
What is the mass of the star in kg? Show your calculation and USE PARENTHESES.
Mstar =
How does this approximately compare to mass of the Sun (2.0 × 1030 kg)?
Does this value for the mass of the star, agree with the mass of the star estimated from its observed properties in part 2?
2
1