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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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
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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
orbit view radial velocity 4 6 8 00 2 Now set the longitude to 90°. Again indicate the earth’s viewing direction and sketch the shape of the radial velocity curve. orbit view radial velocity | | 40 L A 6 8 00 2 Question 11: Does changing the longitude affect the curve in the example above? Yes, when you alter the longitude, the curvature of the planet shifls to the opposite direction from _its initial orientation. Question 12: Describe what the longitude parameter means. Does longitude matter if the orbit is circular? The longitude of the ascending node serves as one of the key orbital elements for specifying_an_object’s path in space. It denotes the angle from the origin of longitude to the direction of the ascending node within a specified reference plane. The ascending node significs the point where the object's orbit intersects the reference plane. Yes, it is important to consider whether the orbit is circular or not. NAAP — ExteaSalag Planets 6/10 Scanned with CamScanner
Select the preset labeled HD 39091 b and click set. Note that the radial velocity curve has a sharp peak. Question 13: Determine the exact phase at which the maximum radial velocity occurs for HD 39091 b. Is this at perihelion? Does the minimum radial velocity occur at aphelion? Explain. (Hint: Using the show multiple views option may help you.) At phase 0.0, the object reaches perihelion, its closest point to the sun. Yet, the lowest radial velocity doesn't coincide with aphelion. During perihelion, the object is nearest to Earth, while it's furthest from Earth, almost halfway between aphelion locations. 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 secthing 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. Question 14: 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. Yes, I think that's the case. I find that most of the points align closely with the designated line. Therefore, if you were to draw a line connecting as many dots as possible, you'd likely arrive at a very similar conclusion. To me, this method seems highly accurate. Select the preset labeled Option C and click set. This preset effectively places the planet Neptune (0.05 My) in the Earth’s orbit. Question 15: Do you believe that the theoretical curve shown could be determined from the observations shown? Explain. In this case I do not believe that the theoretical curve could be shown because the observations are way to spread out and to make a line off that would be complicated. Scanned with CamScanner
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Select the preset labeled Option D and click set. This preset effectively describes the Earth (0.00315 My at 1.0 AU). Set the noise to 1 m/s. Question 16: Suppose that the intrinsic noise in a star’s Doppler shift signal — the noise that we cannot control by building a better detector — is about 1 m/s. How likely are we to detect a planet like the earth using the radial velocity technique? Explain. I belicve detecting a planet similar to Earth would be quite challenging because everything is dispersed, making it difficult to pinpoint its exact location. The lack of distinct details makes it challenging to provide a confident answer regarding its whereabouts You have been running an observing program hunting for extrasolar planets in circular orbits using the radial velocity technique. Suppose that all of the target systems have inclinations of 90°, stars with a mass of 1.0 My, and no eccentricity. Your program has been in operation for 8 years and your cquipment can make radial velocity measurements with a noise of 3 m/s. Thus, for a detection to occur the radial velocity curve must have a sufficiently large amplitude and the orbital period of the planet should be less than the duration of the project (astronomers usually need to observe several cycles to confirm the existence of the planet). Use the simulator to explore the detectability of each of the following systems. Describe the detectability of the planet by checking Yes, No, or Maybe. If the planet is undetectable, check a reason such as “period too long™ or “amplitude too small”. Complete the following table. Two examples have been completed for you. NAAP ~ LxtoaSwug Planets 8/10 Scanned with CamScanner
Rationale A too P too Period (days) Detectable YNM Mass Radius Amplitude Mup) | (AU) (w/s) > H. us. el wn | s | R 4080 [ I sl [T Question 17: Use the table above to summarize the effectiveness of the radial velocity technique. 115 365 365 4080 X » > What types of planets is it effective at finding2 2 It appears that the radial velocity technique is particularly effective_in_detecting planets with_higher mass. Those with greater mass and semimajor axes are more easily detected using this method. Overall, the radial velocity technique demonstrates significant success, especially when applied to larger celestial bodies. Scanned with CamScanner
Part II: Exoplanet Transit Simulator Introduction 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 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. Exercises 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°. Question 18: 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: It would increase the depth and the duration. Semimajor axis: It would increase the duration but do nothing to the depth. Mass (and thus, temperature and radius) of the Star: [t would decrease the duration and do nothing to the depth. Inclination: It would get rid of the eclipse all together. The Kepler space probe (http:/kepler.nasa.gov, scheduled for launch in 2008) will attempt to photometrically detect extrasolar planets during transit. It is predicted to have a photometric accuracy of 1 part in 50,000 (a noise of 0.00002). Question 19: 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, [ believe it has the potential to achieve that. The possibility is quite narrow, but there is a chance it might happen. Question 20: How long does the eclipse of an earth-like planet take? How much time passes between eclipses? What obstacles would a ground-based mission to detect earth-like planets face? The duration spans up to seven minutes and thirty-one seconds. Generally, there are around four cclipses annually, meaning one occurs approximately every three months. However, not all of them are full, and visibility varies. I belicve there would be significant challenges in terms of technology and funding to consistently observe eclipses. Additionally, identifying smaller objects like Earth might require more time and resources for detection. NAAP — faSadag Planets 10710 Scanned with CamScanner
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