Extrasolar Planets

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Astronomy

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Dec 6, 2023

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Extrasolar Planets Extrasolar planets, also called exoplanets, are planets orbiting other stars than the Sun. This l ab introduces the search for planets outside of our solar system using the Doppler and transit methods. It includes simulations of the observed radial velocities of singular planetary systems and introduces the concept of noise and detection. Part I: Exoplanet Radial Velocity Simulator Open the NAAP Labs program, click on 12. Extrasolar Planets , and under Simulators you will find the link to the Exoplanet Radial Velocity Simulator . You should note that the simulator has several distinct panels: • a 3D Visualization panel in the upper left where you can see the star and the planet (magnified considerably). Note that the orange arrow labeled earth view shows the perspective from which we view the system from Earth. The Visualization Controls panel allows one to check show multiple views . This option expands the 3D Visualization panel so that it shows the system from three additional perspectives: side view , earth view , and orbit view . • a Radial Velocity Curve panel in the upper right where you can see the graph of radial velocity versus phase for the system. The graph has show theoretical curve in default mode. A readout lists the system period , and a cursor allows one to measure radial velocity and thus the curve amplitude (the maximum value of radial velocity) on the graph. The scale of the y-axis renormalizes as needed and the phase of perihelion (closest approach to the star) is assigned a phase of zero. Note that the vertical red bar indicates the phase of the system presently displayed in the 3D Visualization panel. This bar can be dragged and the system will update appropriately. • There are three panels which control system properties. The Star Properties panel allows one to control the mass of the star. Note that the star is constrained to be on the main sequence – so the mass selection also determines the radius and temperature of the star. The Planet Properties panel allows one to select the mass of the planet and the semi-major axis and eccentricity of the orbit. The System Orientation panel controls the two perspective angles. • Inclination is the angle between the Earth’s line of sight and the plane of the orbit. Thus, an inclination of 0º corresponds to looking directly down on the plane of the orbit and an inclination of 90º is viewing the orbit on edge. • Longitude is the angle between the line of sight and the long axis of an elliptical orbit. Thus, when eccentricity is zero, longitude will not be relevant. • There are also panels for Animation Controls (start/stop, speed, and phase) and Presets (preconfigured values of the system variables). Exercises - refer to the previous descriptions if you don’t know where to find something. Note: some of the questions are to guide you; you need to answer all the highlighted questions. Select the preset labeled Option A and click set. This will configure a system with the following parameters – inclination: 90º, longitude: 0º, star mass: 1.00 M sun , planet mass: 1.00 M jup , semimajor axis: 1.00 AU, eccentricity: 0 (This is effectively Jupiter in the Earth’s

orbit). • 1. Describe the radial velocity curve. What is its shape? It starts at 0, goes down to around -28, back up to around 28, etc. It is a curved graph. • • What is its amplitude? 12 m/s • • What is the orbital (system) period? 365 days 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? The amplitudes increase by the mass of the planet, example x1, x2, x3. It is multiplied by the planet mass. • • Does the shape change? The shape does not change. Return the simulator to the values of Option A (and click set). 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? The amplitude of the radial velocity curve seems to have decreased as the mass of the star increased. • Return the simulator to the values of Option A (and click set). • 4. How is the amplitude of the radial velocity curve affected by decreasing the semi- major axis of the planet’s orbit? As you decrease the semi-major axis of the planet’s orbit, the amplitude of the radial velocity curve increases. • • How is the period of the system affected? The period of the system is affected by changing the mass of the stars. Return the simulator to the values of Option A and click set 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? Decreasing the orbital inclination causes the amplitude of the radial velocity curve to increase. The shape remains the same. • • Explain why. This is because systems with greater amplitude are easier to observe. • • 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°? I would say that we are more likely to observe a system with an inclination near 90°. • • Explain why. It has a greater altitude than a system with an inclination of 0°.

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? • 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? Yeah there is enough information to determine the mass of the planet. • 8. Typically astronomers don’t know the inclination of an exoplanet system. What can astronomers say about a planet's mass even if the inclination is not known? They can determine the shape of the radial velocity. • • Select the preset labeled Option B and click set . This will configure a system with the following parameters – inclination: 90º, longitude: 0º, star mass: 1.00 M sun , planet mass: 1.00 M jup , semimajor axis: 1.00 AU, eccentricity: 0.4. Thus, all parameters are identical to the system used earlier except eccentricity. 9. Describe the Earth viewing direction (arrow 2), the shape of the radial velocity curve, and the maximum amplitude of the radial velocity. You can only see the star and planet in the Earth viewing direction. The radial velocity curve starts low, quickly reaches its peak, then goes back down again. The maximum amplitude of the radial velocity is around 43.5. 10. Now set the longitude to 90°. Again, describe the Earth viewing direction (arrow 2), the shape of the radial velocity curve, and the maximum amplitude of the radial velocity. The star is right in front of the planet in the Earth viewing direction. The shape of the radial velocity curve changed to a boomerang shape. It starts around -15, goes up to 30ish, quickly drops to -31.5ish, then goes back up. The maximum amplitude of the radial velocity is now 31. • 11. How does changing the longitude affect the curve in the example above? • Changing the longitude really affected the curve. It is now a new shape. • • 12. What does the longitude parameter tells us? It shows us where the planet is in the orbital plane. • • Does longitude matter if the orbit is circular? Yes, longitude matters if the orbit is circular. Select the preset labeled HD 39091 b and click set . Note that the radial velocity curve has a sharp peak.

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