Lab 8 Packet, Pruyn

Name: ______________________________ Extrasolar Planets A NNA ‘C AT ’ P RUYN 10/27/2023 E XTRASOLAR P LANETS  P ROCEDURES C OMPUTER SIMULATIONS : This lab makes use of a number of computer simulations created as part of the Nebraska Astronomy Applet Project (NAAP). You will use two different simulation programs, which can be found at the following URLs: HELPFUL HINT: I can only successfully run these simulators in Microsoft Internet Explorer/Edge. Be sure you have flash enabled. Exoplanet Radial Velocity Simulator – http://astro.unl.edu/naap/esp/animations/radialVelocitySimulator.html It should look like THIS when you launch it:  This lab is adapted from the NAAP lab “Extrasolar Planets”

Extrasolar Planets Exoplanet Transit Simulator, which looks like this when you launch it – http://astro.unl.edu/naap/esp/animations/transitSimulator.html 2

Extrasolar Planets 1.00 M jup , semimajor axis: 1.00 AU, eccentricity: 0 (effectively Jupiter in the Earth’s orbit). 1. Describe the radial velocity curve. What is its shape? What is its amplitude? What is the orbital period? The radial velocity curve is sinusoidal in shape with an amplitude of 29 miles per second. The orbital period is one year. Increase the planet mass to 2.0 M jup and note the effect on the system. Now increase the planet mass to 3.0 M jup and note the effect on the system. 2. In general, how does the amplitude of the radial velocity curve change when the mass of the planet is increased? Does the shape change? Explain. The shape of the curve does not change, however as the mass of the planet increases, the amplitude of the curve increases. In this instance, increasing the mass of the planet at 1.0Mjup resulted in the amplitude increased from 29 miles per second at 2.0Mjup, to 58 miles per second at 3.0Mjup. Return the simulator to the values of Option A. Increase the mass of the star to 1.2 M sun and note the effect on the system. Now increase the star mass to 1.4 M sun and note the effect on the system. 3. How is the amplitude of the radial velocity curve affected by increasing the star mass? Explain. The amplitude of the radial velocity curve decreases as the mass of the star increases. When the mass of the star increased from 1.0Msun, the amplitude of the curve decreased from 29 miles per second at 1.0Msun to 26 miles per second at 1.2Msun, and 24 miles per second at 1.4Msun. Return the simulator to the values of Option A. 4. How is the amplitude of the radial velocity curve affected by decreasing the semi- major axis of the planet’s orbit? How is the period of the system affected? Explain. As the semi-orbital major axis of the planet’s orbit is decreased, the amplitude increases and the orbital period decreases. 4

Extrasolar Planets Return the simulator to the values of Option A so that we can explore the effects of system orientation. It is advantageous to check show multiple views . Note the appearance of the system in the earth view panel for an inclination of 90º. Decrease the inclination to 75º and note the effect on the system. Continue decreasing inclination to 60º and then to 45º. 5. In general, how does decreasing the orbital inclination affect the amplitude and shape of the radial velocity curve? Explain. As the orbital inclination decreases the amplitude decreases. When inclination was decreased from 90 degrees the amplitude decreased from 29 miles per second to 28 miles per second at 75 degrees, 25 miles per second at 60 degrees, and 20 miles per second at 45 degrees. The shape of the radial velocity curve becomes flatter the smaller the degree of orbital inclination. 6. Assuming that systems with greater amplitude are easier to observe are we more likely to observe a system with an inclination near 0° or 90°. Explain. It would be more likely for us to observe a system with an inclination of 90 degrees. A system with a 90-degree inclination will have a greater amplitude than a system near 0 degrees. At 0 or near zero degrees, the radial velocity curve becomes nearly flat with an amplitude nearly 0 miles per second. Return the simulator to Option A. Note the value of the radial velocity curve amplitude. Increase the mass of the planet to 2 M Jup and decrease the inclination to 30°. What is the value of the radial velocity curve amplitude? Can you find other values of inclination and planet mass that yield the same amplitude? At a mass of 2.0 Mjup and an inclination of 30 degrees, the amplitude is 29 miles per second. The same can be said for a planet with a mass of 1.0 Mjup and inclination of 90 degrees. 7. Suppose the amplitude of the radial velocity curve is known but the inclination of the system is not. Is there enough information to determine the mass of the planet? 5

Extrasolar Planets 7

Extrasolar Planets 9. Does changing the longitude affect the curve in the example above? Yes. 10. Describe what the longitude parameter means. Does longitude matter if the orbit is circular? The longitude parameter determines the angle between the observer and the minor-axis of the orbit. The radial velocity curve of a planet with a circular orbit is unaffected by longitude. Select the preset labeled HD 39091 b and click set . Note that the radial velocity curve has a sharp peak. 11. Determine the exact phase at which the maximum radial velocity occurs for HD 39091 b. Is this at periastron? Does the minimum radial velocity occur at apastron? Explain. (Hint: Using the show multiple views option may help you.) The maximum radial velocity occurs at 0.017, at periastron, when HD 30901 b is closest to its parent star. The minimum radial velocity occurs near apastron when HD 39091 b is farthest from its parent star. This is due to the fact that when a planet nears its planet star its velocity will increase due to gravitational force. This simulator has the capability to include noisy radial velocity measurements. What we call ‘noise’ in this simulator combines noise due to imperfections in the detector as well as natural variations and ambiguities in the signal. A star is a seething hot ball of gas and not a perfect light source, so there will always be some variation in the signal. Select the preset labeled Option A and click set once again. Check show simulated measurements , set the noise to 3 m/s, and the number of observations to 50. 12. The best ground-based radial velocity measurements have an uncertainty (noise) of about 3 m/s. Do you believe that the theoretical curve could be determined from the measurements in this case? (Advice: check and uncheck the show theoretical curve checkbox and ask yourself whether the curve could reasonably be inferred from the measurements.) Explain. 8

Extrasolar Planets Mass Radius Amplitude Period Detectable Rationale (M Jup ) (AU) (m/s) (days) Y N M A too small P too big 0.1 0.1 8.9 11 X 1 0.1 89.9 11.5 X 5 0.1 450 11.5 X 0.1 1 2.86 365 X X 1 1 28.8 365 X 5 1 144.1 364 X 0.1 5 1.28 4,080 X X X 1 5 12.82 4,080 X X 5 5 63.4 4070 X X 0.1 10 0.898 11,500 X X X 1 10 8.99 11,500 X X 5 10 44.9 11,500 X X 15. Use the table above to summarize the effectiveness of the radial velocity technique. What types of planets is it effective at finding? Specifically, the radial velocity technique is very useful for discovering exoplanets.. However, it has proven to be problematic when attempting to discover every other kind of planet. Using the table it is apparent that radial velocity can easily detect planets with large masses and orbital periods, but has more difficulty detecting planets with smaller masses and long orbital periods. PART II: E XOPLANET T RANSIT S IMULATOR I NTRODUCTION Open the exoplanet transit simulator. Note that most of the control panels are identical to those in the radial velocity simulator. However, the panel in the upper right now shows the variations in the total amount of light received from the star. The visualization panel in 10

Extrasolar Planets the upper left shows what the star’s disc would look like from earth if we had a sufficiently powerful telescope. The relative sizes of the star and planet are to scale in this simulator (they were exaggerated for clarity in the radial velocity simulator.) Experiment with the controls until you are comfortable with their functionality. E XERCISES Select Option A and click set. This option configures the simulator for Jupiter in a circular orbit of 1 AU with an inclination of 90°. 16. Determine how increasing each of the following variables would affect the depth and duration of the eclipse. (Note: the transit duration is shown underneath the flux plot.) Radius of the planet: When increased, the duration and the depth of the eclipse increases. When decreased, the duration and depth of the eclipse also decreases. Semimajor axis: When increased, the duration of the eclipse as well as the orbital period will increase. When decreased, the duration of the eclipse as well as the orbital period will decrease. However, it doesn’t have an effect on the depth of the eclipse. Mass (and thus, temperature and radius) of the Star: When increased, the duration of the eclipse increases but the depth of the eclipse decreases. Similarly, when decreased, the duration of the eclipse decreases while the depth increases. Inclination: Changing the inclination would result in there being no eclipse. The Kepler space probe ( http://kepler.nasa.gov , launched in 2009) photometrically detects extrasolar planets during transit. It has a photometric accuracy of 1 part in 50,000 (a noise of 0.00002). 17. Select Option B and click set . This preset is very similar to the Earth in its orbit. 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? Yes. He would be able to detect them using the transit method. 11