Lab 5 Extrasolar Planets complete

Extrasolar Planets Remember to type your answers in blue text Background Material Complete the following after reviewing everything in the links under Background Materials. Question 1: The left side of the diagram below depicts the radial velocity curve of a star that is orbited by an extrasolar planet. The right side is a top-down view of the orbital motion of the star and planet. The small circle represents the star’s motion, and the larger circle represents the planet’s motion as both objects move around a common center of mass. The view from Earth is in the plane of the page, so we are viewing the system edge-on from the left side of the page. Radial velocity is positive when the star is moving away from Earth and negative when the star is moving towards Earth. In the boxes provided, label the positions on the star’s orbit with the letters corresponding to the labeled positions of the radial velocity curve. NAAP – ExtraSolar Planets 1/9 + -

Question 2: Label the positions on the planet’s orbit with the letters corresponding to the labeled positions of the radial velocity curve. 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 you 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 you 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 you to select the mass of the planet, the semi- major axis, and the 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 NAAP – ExtraSolar Planets 2/9 - +

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: What is the amplitude of the radial velocity curve? Remember that the amplitude in this case is the speed of the star. What is the orbital (system) period? 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? Explain why the amplitude changes. 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’s mass? Explain why the amplitude changes. 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 why these values change. NAAP – ExtraSolar Planets 4/9 The Amplitude of the radial velocity curve is 28.5 and the orbital period is one year-365 days. The amplitude of the radical velocity curve increases when you increase the planets mass. The amplitude changes because if the planet is more massive then the center of mass moves closer to the planet and the star moves more, so it increases the velocity overall. As the mass of the star increases the amplitude of the radical velocity curve decreases. And when you increase the mass of the star its speed or velocity will decrease. As you decrease the semi-major axis of the planets orbit the amplitude of the radial velocity curve will increase. The period of the system decreases when you decrease the semi-major axis of the planets orbit. Changing the way the planet orbits cause the amplitude of the radial velocity to change.

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 why. 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 why. 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°. Again, note 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? Explain why or why not. 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 NAAP – ExtraSolar Planets 5/9 When your decrease the orbital inclination below 90 the amplitude of the radial velocity decreases. Also, if you increase it over 90 the amplitude of the radial velocity will also increase. The velocity will change depending on changing the angle between the earths line of sight and the plane of the orbit. We are more likely to observe a system with an inclination near 90 degrees. When you put the inclination on 90 degrees it is at its highest amplitude of 33.1 m/s. When you go below 90 towards 0 the amplitude decreases and the bigger the amplitude the easier it is to observe. I don’t think there is enough information to determine the mass of the planet. You can get the same radical velocity curve with a different mass by adjusting the inclination of the orbit. Astronomers can say that we get the minimum mass since we know the star is probably moving more than we are measuring it.

Question 14: Question 14: Suppose you have been running an observing program hunting for extrasolar planets 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 radial velocity measurements with a noise of 3 m/s. Thus, for a detection to occur, the radial velocity curve must have a amplitude larger than 3 m/s, and the orbital period of the planet must be less than the duration of the project (in practice, astronomers need to observe several complete orbits 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 table below. Two examples have been completed for you. Mass (M Jup ) Orbital Radius (AU) Amplitude (m/s) Period (days) Detectable Y N M Rationale A too P too Small long 0.1 0.1 9.0 11.5 X 1 0.1 90 11.5 x 5 0.1 445 11.5 x 0.1 1 2.78 365 X x 1 1 28.8 365 x 5 1 142.5 364 x 0.1 5 1.25 4080 X X x 1 5 13.02 4080 X x 5 5 63.4 4070 X X 0.1 10 .86 11,500 X X x 1 10 9.1 11,500 X X NAAP – ExtraSolar Planets 7/9

5 10 45.6 11,500 X x Question 15: Judging from your results from the previous question, what type of planet (high or low mass) in what kind of orbit (close to or far from the star) is the radial velocity technique most effective at finding? Explain. 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 drop in the amount of light received from the star as a planet passes in front of the star. This is called a light curve. 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. You must click and drag the phase slider button in the lower right to move the planet. 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 16: Describe how increasing each of the following variables would affect the depth and duration of the transit (eclipse). (Note: the eclipse duration is shown underneath the plot.) Radius of the planet: Semimajor axis: NAAP – ExtraSolar Planets 8/9 When the radius is he lower the planet is easier to detect. The detectability depends mostly on the radius. When the radius is high then the more days are in that period, and it cannot be detected. Increasing the radius of the planet increases the hour of duration of the eclipse . As you increase the semimajor axis, the duration of the eclipse increases dramatically.