ICW 11 - Extrasolar Planets (1)

Worksheet — Extrasolar Planets Page 1 of 8 Astronomy BPHYS 101 Worksheet — Extrasolar Planets Identify Yourself (Limit 3 people) Background Material Below is an example of a radial velocity curve and some orbital paths of a star and its planet. • The radial velocity is positive when the star is moving away from the Earth. • The radial velocity is negative when the star is moving toward the Earth. On the orbital paths diagram, label the position of the star and planet that correspond to the labeled positions on the radial velocity curve. Use S1, S2, S3, and S4 for the star and use P1, P2, P3, and P4 for the planet. Radial Velocity of the Star Time 1 2 3 4 Name 1: Name 2: Name 3: View from Earth

Worksheet — Extrasolar Planets Page 2 of 8 Part I: Exoplanet Radial Velocity Simulator Introduction Open the exoplanet radial velocity simulator. You should note that there are several distinct panels: • 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: • 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 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. • There are also panels for Animation Controls (start/stop, speed, and phase) and Presets (preconfigured values of the system variables). 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 M sun , planet mass: 1.00 M jup , semimajor axis: 1.00 AU, eccentricity: 0 (effectively Jupiter in the Earth’s orbit).

Worksheet — Extrasolar Planets Page 4 of 8 In general, how does decreasing the orbital inclination affect the amplitude and shape of the radial velocity curve? Explain. 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. 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? 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? Typically, astronomers do not know the inclination of an exoplanet system. What can astronomers say about a planet's mass even if the inclination is not known? Explain. 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 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.

Worksheet — Extrasolar Planets Page 5 of 8 In the orbit view box below, indicate the earth viewing direction. Sketch the shape of the radial velocity curve in the box at right. Now set the longitude to 90°. Again, indicate the E arth’s viewing direction and sketch the shape of the radial velocity curve. Does changing the longitude affect the curve in the example above? Describe what the longitude parameter means. Does longitude matter if the orbit is circular?

Worksheet — Extrasolar Planets Page 7 of 8 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. 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 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 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. Assume you can make 4 measurements per period. A B C D E F G H I J K L Mass (M Jup ) 0.100 0.100 0.100 0.100 1.00 1.00 1.00 1.00 5.00 5.00 5.00 5.00 Radius (AU) 0.100 1.00 5.00 10.0 0.100 1.00 5.00 10.0 0.100 1.00 5.00 10.0 Amplitude (m/s) 8.9 63.4 Period (days) 11.5 4070 Number of Periods in 8 years 254 0.72 Number of Measurements in 8 years 1016 2 Detectable (Yes/No/Maybe) Yes No Not detectable: Amplitude too small ✓ Not detectable: Period too large

Worksheet — Extrasolar Planets Page 8 of 8 Use the table above to summarize the effectiveness of the radial velocity technique. What types of planets is it effective at finding?