Lab B Katie A

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May 6, 2024

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Name: Katie Avalo ExtraSolar Planets – Student Guide Background Material Complete the following sections after reviewing the background pages entitled Introduction, Doppler Shift, Center of Mass, and ExtraSolar Planet Detection. Question 1: Label the positions on the star’s orbit with the letters corresponding to the labeled positions of the radial velocity curve. Remember, the radial velocity is positive when the star is moving away from the earth and negative when the star is moving towards the earth. Question 2: Label the positions on the planet’s orbit with the letters corresponding to the labeled positions of the radial velocity curve. Hint: the radial velocity in the plot is still that of the star, so for each of the planet positions determine where the star would be and in which direction it would be moving.

NAAP – ExtraSolar Planets 1/10 Part I: Exoplanet Radial Velocity Simulator Introduction Open up the exoplanet radial velocity simulator. You should note that there are 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. o 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: • 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. o 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. o The Planet Properties panel allows one to select the mass of the planet and the semi-major axis and eccentricity of the orbit. o 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). NAAP – ExtraSolar Planets 2/12

Exercises 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 (effectively Jupiter in the Earth’s orbit). Question 3: Describe the radial velocity curve. What is its shape? What is its amplitude? What is the orbital period ? The radial velocity curve indicates how fast a star is moving around the center of mass. It is a horizontal S shape with an amplitude of 28 and it orbits for a 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. Question 4: 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. When the planet mass increases, the amplitude increases. When the planet is larger, the center of mass moves closer to the planet. 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. Question 5: How is the amplitude of the radial velocity curve affected by increasing the star mass? Explain. When you increase the star mass, the amplitude of the radial velocity curve decreases. NAAP – ExtraSolar Planets 3/12

Return the simulator to the values of Option A. Question 6: How is the amplitude of the radial velocity curve affected by decreasing the semimajor axis of the planet’s orbit? How is the period of the system affected? Explain. When the semi-major axis of the planet’s orbit decreases, the amplitude of the radial velocity curve increases. The period of the system decreases when you decrease the semi- major axis of the planets orbit. 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. Question 7: In general, how does decreasing the orbital inclination affect the amplitude and shape of the radial velocity curve? Explain . It affects the amplitude because when you decreases the inclination it decreases the amplitude of the radial velocity curve and it makes the shape more circular. Question 8: 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. A system with an inclination of 90 degrees is more likely to be observed because it has a greater amplitude than one with a system near 0 degrees. NAAP – ExtraSolar Planets 4/12

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? Question 9: 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 ? No, there isn’t enough information to determine that. Question 10: 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? Explain. Astronomers can still determine its minimum mass through the Doppler spectroscopy method . 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. In the orbit view box below indicate the earth viewing direction. Sketch the shape of the radial velocity curve in the box at right. NAAP – ExtraSolar Planets 5/12

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