Lab Activity:  Finding Exoplanets

Introduction

The first exoplanet (extra-solar planet) to be detected and confirmed was 51 Pegasi in 1995. This and most of the next 456 exoplanets discovered were detected using the radial velocity (RV) technique. Sometimes called Doppler spectroscopy, this method would detect the slight wobble of a star as the planet orbits it. Understandably, the wobbling stars tended to be less massive and the planets tended to be Jupiter-sized. Planet hunters can detect a star moving as slow as 3 meters per second.

Open the Extrasolar Planets at: http://astro.unl.edu/naap/esp/esp.html

Open and read 1) Introduction, 2) Center of Mass, 3) Doppler Shift, and 4) Detection.

Click on and open “Exoplanet Radial Velocity Simulator.” Click on “Help” and read.

2. Red shift and planetary orbit (19 points)
3. Imagine the three spectra below were taken from the same star but at different times. Red is to the left. “A.” is on top.          Answer the following questions relative to Earth (1 pt @)

Red                                 Blue                (Choices: red, blue, not,      not moving, receding, approaching)

Top is ________ shifted meaning it is ___________.

Middle is ______ shifted meaning it is __________.

Bottom is _____ shifted meaning it is __________.

Scientists use the amount of shift as an indication of how fast the star is moving relative to Earth, the Radial Velocity. As a planet goes around a star, both objects will orbit the center of mass.

1. Label the positions on the star’s orbit (the inner circle below) with the letters corresponding to the labeled positions of the radial velocity RV curve. Remember, the RV is positive when the star is moving away from the Earth and negative when the star is moving towards the earth. (8 pts)
2. Label the positions on the planet’s orbit (the outer circle) with the letters corresponding to the labeled positions of the RV curve. (8 pts)

1. Using the above information circle T for true, F for false for the statements below (1 pt @)

T             F             4. From point “A” to point “C” the planet is moving toward Earth.

T            F            5. At point “A” the stellar spectrum would be greatly blue-shifted.

T            F            6. Point “B” on the RV curve best matches Spectrum B (in #1 above.)

T            F            7. At point “C” the planet is moving away from the Earth.

T            F            8. At point “D” the star is wobbling away from the Earth.

1. How Mass Effects Amplitude (18 points)

Use the Exoplanet Radial Velocity Simulator to complete this task. Select the preset Option A and click set. Change only the features listed below, re-setting on Option A after each system. Determine the peak amplitude (U){\displaystyle \scriptstyle {\hat {U}}}

Table 1: Effect of Mass on RV amplitude (U)

 System Star Mass (suns) Planet Mass (Jupiters) peak U (m/s) notes 9. 0.25 1.00 10. 0.25 2.00 11. 0.50 2.00 12. 1.00 2.00
1. When the mass of the star increases the amplitude of the RV curve ___________________________.
2. When the mass of the planet increases the amplitude of the curve ____________________________.
3. Why does the star appear to wobble less when the star has a greater mass?
1. Why does the star appear to wobble more when the planet has a greater mass?
1. How Orbital Eccentricity Effects the Radial Velocity (18 points)

Use the Exoplanet Radial Velocity Simulator to complete this task. Select the preset Option D and click set. Change only the features listed below, re-setting on Option D after each system.

Table 2: Effect of Eccentricity (e) on RV amplitude (U)

 System Star Mass (suns) Planet Mass (Jupiters) e Peak U (m/s) Trough U (m/s) notes 16. 1.00 0.00315 0.0 17. 1.00 0.00315 0.2 18. 1.50 0.00315 0.2 19. 1.50 0.00630 0.2
1. When an orbit is more eccentric the peak amplitude _______________________________________.
2. When an orbit is more eccentric the trough amplitude _____________________________________.
3. When the star is more massive the peak amplitude ________________________________________.
4. When the star is more massive the trough amplitude ______________________________________.
5. When the planet is more massive the peak amplitude _____________________________________.
6. When the planet is more massive the trough amplitude ___________________________________.
1. Compare and contrast the RV curve for a star with a planet in a circular orbit (Part B) with the RV curve for a star with a planet in an eccentric orbit (Part C). Describe two significant similarities and two significant differences. If all we knew were the RV curves, how could we tell how eccentric the orbit?
1. Inclination (6 points)

Return the simulator to the values of Option A so that we can explore the effects of system orientation.   This is basically a Jupiter-size planet orbiting a Sun-mass star. It may be advantageous to check show multiple views.

We measure the peak U at 28.8 m/s.

1. If the system inclination is edge-on (90 degrees) from our point of view, what would be the mass of the planet?
2. If the system inclination is almost face-on (one degree) from our point of view, what would be the mass of this planet?
3. Two students are discussing the implication of their answers to # 25 and 26.

Student 1: The mass of this planet is about 25 MJup since that’s half-way

between 1 and 50..

Student 2: The mass of the planet is somewhere between 1 and 50 Mjup

Do you agree or disagree with either or both? Explain your reasoning.

1. Determining the Mass of Exoplanets (3 points)

Use the Semi-major axis slider to change the length of the orbital period for the planets.

 Table 2 : Determining the mass of planets System Star Mass (suns) Orbital period (days) Amplitude of RV curve (m/s) Planet Mass (Jupiters) 28. 0.519 467 19 29. 1.0 1.03 2361.7 30. 2.0 10 373

1. Transit method

In 2002 the first exoplanet was discovered using the transit method. The Polish astronomical project OGLE detected a slight dimming of the light from the star OGLE-TR-56. If the orbital plane of the exoplanet is in line with the Earth, we can measure the decrease in light received from the star as the exoplanet eclipses, or transits the star. In 2009 NASA’s Kepler mission was launched to measure the light from some stars in the constellation Cygnus looking for evidence of transits. As of May 2016 the Kepler mission had discovered 1,284 exoplanets.

Open the Exoplanet Transit Simulator. Note that most of the control panels are identical to those in the Radial Velocity Simulator. Click on Help and read about the difference. Experiment with the controls until you are comfortable with their functionality.

1. Depth and Duration of the Eclipse (23 points)
2. In the Exoplanet Transit Simulator. select Option A and click set. This option configures the simulator for Jupiter in a circular orbit of 1 AU with an inclination of 90o. Depth is a measure of how much light is being blocked by the planet. Duration is how long the eclipse lasts (hours? days?) compared to the orbital period. (Always include units.)

Depth of Transit:   ________________________     Duration ___________________of ____________________

 32.   Situation Depth Duration Increase radius to 1.5 Increase radius to 2 Reset to Option A Semi-major axis 1.6 AU Semi major axis to 2 AU

1. If a planet has a larger radius, the depth ________is deeper____________.
2. If a planet has a larger radius the eclipse will take _______________________ time.
3. If planet is further from its star, the eclipse will take _____________________time.
4. Reset to Option A. What’s the most tilted inclination at which you can still detect an eclipse?
1. Which factor presents more of an obstacle to detecting exoplanets by transit, a) size of the planet, b) orbital period or c) inclination? Explain your reasoning. Can you offer some ways to surmount those obstacles?
1. Detecting an Earth-size planet (12 points)
2. Select option B and click set. This preset is very similar to the Earth in its orbit. Now under the plot of flux, unselect show theoretical curve and select show simulated measurements. Then find the slider to adjust the noise level and slide it around. Describe what happens. At approximately what noise level does an Earth-sized planet first become detectable to you? How can you tell?
1. The Kepler space probe was designed to detect exoplanets during transit. Its accuracy is 1 part in 50,000 (which means it has noise of 0.00002).Now set the noise level to 0.00002. Do you think the Kepler probe would have been able to detect Earth-sized planets in transit? Why or why not? Supply details.
1. How long does it take the eclipse of an Earth-sized planet about 1 AU from its star.                   to take place? How much time passes between eclipses? What timing obstacle would a space telescope have in trying to detect such a planet? What extra timing obstacle would a ground based telescope face?  Why are they obstacles? Describe possible solutions to those obstacles..