Extrasolar Planets

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°.

• 13. Determine the exact phase at which the maximum radial velocity occurs for HD 39091 b. Is this at perihelion (closest approach)? 307 m/s. Yes it is the closest approach. • • Does the minimum radial velocity occur at aphelion (farthest position)? No the minimum radial velocity does not occur at aphelion. • • Explain. (Hint: Using the show multiple views option may help you. Move the latitude slider until the red bar on the graph matched with the peak. Hint 2: Kepler’s Laws) • The maximum radial velocity occurred at perihelion but the minimum radial velocity did not occur at aphelion. • • 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. • 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? I believe that the theoretical curve could be determined from the measurements. • • Why? (Advice: check and uncheck the show theoretical curve checkbox and ask yourself whether the curve could reasonably be inferred from the measurements.) • The curve lines up with the dots, so you could determine the theoretical curve from the measurements. Select the preset labeled Option C and click set . This preset effectively places the planet Neptune (0.05 M Jup ) in the Earth’s orbit. • 15. Do you believe that the theoretical curve shown could be determined from the observations shown? No • • Why? The scatter plot is across the entire screen. There is no way you could justify anything from just those dots. Select the preset labeled Option D and click set. This preset effectively describes the Earth (0.00315 M Jup at 1.0 AU). Set the noise to 1 m/s. • 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. 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 M sun , and no eccentricity. Your program has been in operation for 8 years, and your equipment can make measurements with a noise of 3 m/s. 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. Use the simulator to explore the detectability of each of the following systems. Manually input mass and distance into the planet properties panel. Describe the detectability of the planet by checking Yes, No, or Maybe. If the planet is undetectable, check a reason such as ‘Amplitude too small’ or ‘Period too long’. Complete the following table. Two have been completed for you. Mass (M Jup ) Radius (AU) Amplitude (m/s) Period (days) Detectable Y N M Rationale A small / P long 0.1 0.1 9.3 11.5 X 1 0.1 91 11.5 X 5 0.1 450 11.5 X 0.1 1 3 365 X X 1 1 28.5 365 X 5 1 142 265 X 0.1 5 1.5 4080 X X 1 5 12.7 4080 X X 5 5 63.5 4080 X X 0.1 10 1 11550 X X X 1 10 9 11550 X X 5 10 45 11550 X X • • 17. Based on your observations in the table, what types of planets is the radial velocity technique effective at finding? Earth-like in size and red dwarf stars. • Part II: Exoplanet Transit Simulator