lab 9

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University of Nebraska, Omaha *

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001

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Astronomy

Date

May 2, 2024

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pdf

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9

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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. Radial Velocity 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 Radial Velocity be moving. Part I: Exoplanet Radial Velocity Simulator Introduction Qpen up the exoplanet radial velocity simulator. You should note that there are several distinct panels: NAAP — ExtraSalax, Planets 2/10 Scanned with CamScanner
e 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 peried 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. o 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 0° corresponds to looking directly down on the plane of the orbit and an inclination of 90° 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. o There are also panels for Animation Controls (start/stop, speed, and phase) and Presets (preconfigured values of the system variables). Scanned with CamScanner
Exercises Select the preset labeled Option A and click set. This will configure a system with the following parameters — inclination: 90°, longitude: 0°, star mass: 1.00 Mss, planet mass: 1.00 M, 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 plot exhibits a cycle spanning 365 days. It depicts a consistent upward trend followed by a downward trend, featuring a significant amplitude of 29 /s, with its lowest point reaching -29 m/s. Jupiter's orbit around the Earth appears notably circular in shape. Increase the planet mass to 2.0 Mo, and note the effect on the system. Now increase the planet mass to 3.0 Mg 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 mass is augmented, there is a considerable increase in the amplitude of the radial velocity curve. Consequently, the shape of the planetary orbit exhibits a more pronounced fluctuation between high and low points, while still maintaining a circular motion around the Earth. Return the simulator to the values of Option A. Increase the mass of the star to 1.2 Mgp and note the effect on the system. Now increase the star mass to 1.4 Mg 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. The orbital duration becomes shorter, and the planet's orbit around Earth becomes more compact and closer to Earth. Additionally, the magnitude of the amplitude decreases. As the star accumulates mass, its pace diminishes, leading to a reduction_in the distance between the two entities because the increased mass exerts a stronger gravitational pull, drawing the objects closer together. Return the simulator to the values of Option A. Question 6: 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. The magnitude of the amplitude experiences a significant increase, leading to a considerable reduction in the orbital period. Decreasing the semimajor axis results in a shorter distance traveled by the object around Earth, NAAP - Eaxwasalag Plancts 4/10 Scanned with CamScanner
Retumn 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 90°. Decrease the inclination to 75° and note the effect on the system. Continue decreasing inclination to 60° and then to 45°. Question 7: In general, how does decreasing the orbital inclination affect the amplitude and shape of the radial velocity curve? Explain. As the inclination decreases. the amplitude also decreases, and the radial velocity curve tends to flatten out further, displaying less pronounced peaks and troughs. The decreasing inclination brings the objects closer together, leading to the emergence of longer but shorter wavelengths. 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. You would be more likely to observe an object closer to 90 degrees, because as the inclination decreases the amplitude becomes less visible to us. §g if the object has a great inclination we will see greater short wave lengths with a higher amplitude. Return the simulator to Option A. Note the value of the radial velocity curve amplitude. Increase the mass of the planet to 2 My 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? Not exactly. With this information they could set a range of possible masses, but not identify the exact one. 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. With this information they can set a range of possible masses, by judging the effect the planet is having on the star. If they have the mass of one of the objects, they may be able to find the others mass without inclination Select the preset labeled Option B and click set. This will configure a system with the following parameters — inclination: 90°, longitude: 0°, star mass: 1.00 Mo, planet mass: 1.00 My, 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 - bauaSadar Planets 5/10 Scanned with CamScanner
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