Wobbling Stars: Discovering Extrasolar Planets with Doppler Shift

11 WOBBLING STARS: HOW EXTRASOLAR PLANETS ARE DISCOVERED GOALS = Discover how Doppler shift is used to detect the presence of extrasolar planets = Analyze graphical data to interpret extrasolar planet motion = Compare the orbital distance and mass of extrasolar planets PART A: THE MOTION OF THE SUN Astronomers have made astounding progress in discovering planets orbiting stars outside our solar system. In fact, they have identified a vastly larger number of these planets, called extrasolar planets, than currently exist in our own solar system. There is more than one technique for detecting extrasolar planets. But with current technology, the most effective technique for detection has been the radial velocity of Doppler shift technique. In this activity, you will learn how astronomers use this technique to infer the presence of planets around other stars. Let’s begin by looking at the radial velocity technique applied to our own solar system. In Figures I and 2, there are two different depictions of our solar system. Since the Sun and Jupiter account for nearly all the mass of our solar system, our solar system is modeled here as a two-body problem involving only the Sun and Jupiter. Note that these representations are not drawn to the proper scale for the size or distance of the objects shown.* Our solar system as seen from above (not to scale) Our solar system as seen edge-on or from the side (not to scale) Center of Mass Center of Mass Sun Jupiter Figure 1 Figure 2 *The center of mass of the solar system is located within the Sun. We 've exaggerated the Sun's orbit about the center of mass. Prather, Offerdahl, and Slater 131 Life in the Universe — Activities Manual, 2nd Edition

Activity 11 1. Is Jupiter coming toward or going away from you in Figure 27 2. Is the Sun coming toward or going away from you in Figure 2? 3. Draw a stick figure in Figure 1 to indicate where an observer would need to be in relationship to the solar system to see the view shown in Figure 2. Now examine the four drawings in Figure 3 below. Each of the four drawings shows the positions of the Sun and Jupiter at a different time during a single orbit. March 1985 Observer . Observer March 1991 Observer Observer March 1988 s Jupltfy Figure 3 4. In Figure 3, does the Sun always appear to remain in the same position? If not, describe its motion. Life in the Universe — Activities Manual, 2nd Edition Prather, Offerdahl, and Slater

Extrasolar Planeis What form of interaction or force causes the orbital motions of the Sun and Jupiter? Estimate the time (in Earth years) for the Sun to complete one orbit (this time is known as the orbital period). How does this time compare to the orbital period of Jupiter? use the boxes below to draw what the For each of the four drawings in Figure 3, he or she was observing the solar system observer would see at each time period if edge-on. See the example in Figure 2. March 1985 March 1988 March 1991 March 1994 Life in the Universe _ Activities Manual, 2nd Edition Prather, Offerdahl, and Slater 133 —4

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Activity 11 8. Make two sketches below (using representations in Figures 1 and 2) depicting what you would see in September 1992 from the observer location. Your drawings need to include the positions of the Sun and Jupiter. September 1992 September 1992 When studying motion it is useful to consider the object’s velocity as being made of two parts or components. The component of velocity that is directed toward (negative) or away from (positive) the observer’s line of sight is known as the radial velocity. 9. Jmagine that you are at the observer location shown in the drawings you made in Question 8 for September 1992, and that you are located much farther away from the Sun and Jupiter’s orbital paths than is depicted in your drawing. a. From your point of view and line of sight at the observer location, would the Sun appear to be moving with a radial velocity? If so, is it positive or negative? Explain your reasoning. b. From your point of view and line of sight at the observer location, does Jupiter appear to be moving with a radial velocity? If so, is it positive or negative? Explain your reasoning. 10. Now consider the entire interval shown in Figure 3 from March 1985 all the way through March 1994. a. During which range of dates would the Sun appear to be moving with a radial velocity? When is the radial velocity positive and when is the radial velocity negative? b. During which range of dates would Jupiter appear to be moving with a radial velocity? When is the radial velocity positive and when is the radial velocity negative? Life in the Universe — Activities Manual, 2nd Edition Prather, Offerdahl, and Slater 134 '

4 Extrasolar Plarnets If an observer and a star being studied are both stationary then the wavelength of the light traveling from a star to an observer will remain unchanged. However, if the star is moving toward an observer (with a negative radial velocity), then the light’s wavelength will appear to be shifted to a shorter wavelength (or blue shifted). Furthermore, if a star is moving away from an observer (with a positive radial velocity), the light’s wavelength will appear to be shifted to a longer wavelength (or red shifted). This shifting in the wavelength of light due to the motion toward or away from a light source (like a star) is known as the Doppler shift. 11. During which range of dates would the light from the Sun have a Doppler shift to a longer wavelength? Explain your reasoning. 12. During which range of dates would the light from the Sun have a Doppler shift to a shorter wavelength? Explain your reasoning. 13. If, instead of viewing the solar system edge-on (like in Figure 2), an observer was very far away from the solar system and looking directly down on the solar system, during what time interval, if ever, would the observer see the Sun have a Doppler shift to shorter wavelengths? Explain your reasoning. PART B: DISCOVERING NEW PLANETS Astronomers measure the change in radial velocity using the Doppler shift of the light coming from a star. They can graph this change in radial velocity versus time. Figure 4 shows a radial velocity versus time graph for a star that has an extrasolar planet orbiting it. A 50 + 2 Q L o J| Il 1 1 ! 4> B 1 3 5 7 9 = t; .50 4 Time (days) Figure 4 Life in the Universe — Activities Manual, 2nd Edition Prather, Offerdahl, and Slater 135

o | . Activity 11 1. At what time(s) is the star moving with a radial velocity that is zero? 2. Imagine you are observing this star edge-on (like in Figure 2 from Part A). Sketch how it would look when the radial velocity is zero. 3. At what time(s) would the star be moving toward the observer with the greatest radial velocity? How fast would it be moving? 4. At what time(s) would the star be moving away from the observer with the greatest radial velocity? How fast would it be moving? 5 What do astronomers observe about the light of stars that makes it possible to determine the stars are moving with a changing radial velocity? Now let’s examine actual data gathered by astronomers in their pursuit to find planets orbiting distant stars outside our solar system. Below are the radial velocity versus time graphs for three stars (47 Ursae Majoris, 49 Sengir V Cdc, and HD 11964).* Two of the graphs come from measurements of stars with companion planets; the other is a graph of a star without a companion planet. Note that the dots shown in each graph represent the actual measured radial velocities for these stars, and the curves provide a “best fit” to the data points. Use these best fit curves to answer the questions regarding the motion of these three stars. * The original versions of the rcal graphs can be found at http://cannon.sfsu.edu/~gmarcy/planetsearch/doppler.html i Life ir the Universe — Activities Manual, 2nd Edition Prather, Offerdahl, and Slater 136 '

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Extrasolar Planets 47 Ursae Majoris 100 | = N b o N I . g 50F = N~ L A o 0 A L o e L 3 > : 50 F N " 2 A s 1 L 1 3 1288 1950 1992 1994 1996 1998 Time (Years) Sengir V Cdc 100 ~ 7] S~ g 50 N z (] o | o] g 0 -50 1990 1992 1994 Time (Years) Life in the Universe _ Activities Manual, 2nd Edition Prather, Offerdahl, and Slater 137

Activity 11 HD 11964 40§ T T T 3 Y3 ; E E + w R IR S L 8 05 + {+ . +r ++ = CR A T > H _ggz_ { _ _30E_. 1996 1998 000 2002 2004 2006 Time (Years) 6. At what time(s) was each star measured to be moving toward Earth with the greatest radial velocity? Note that you are to use a point on the best fit curve in each graph and not the individual data points. How fast was the star moving? 47 Ursae Majoris Sengir V Cdc HD 11964 7. For each star, state whether or not you think the star has a companion planet and, if so, estimate the orbital period of the planet. If not, explain why not. 47 Ursae Majoris Sengir V Cdc HD 11964 Life in the Universe — Activities Manual, 2nd Edition Prather, Offerdahl, and Slater 138 ;

Extrasolar Planets PART C: EXPLORING SYSTEM PROPERTIES As was mentioned in Part A, the number of extrasolar planets discovered to date is far greater than the total number of planets within our solar system. However, we have not yet discussed the nature of these extrasolar planets. How close do they orbit their parent star? What are their orbital periods? How massive are they? In this part of the activity, you will look at real data of extrasolar planets discovered using the radial velocity technique showing how these extrasolar planets compare to planets within our solar system. Figure 5 shows a histogram for 167 extrasolar planets. A histogram is a type of graph that shows information sorted into bins. Notice that the last bin on the far right represents the number of extrasolar planets with a mass 15 times that of Jupiter. The height of the bar in each bin represents how many extrasolar planets have that particular planetary mass. It is important to note that all of the planet masses are represented in units of Jupiter mass, M, so that the mass of the planet in the last bin on the right would be written 15 My,,. Mass Distribution of Extrasolar Planets LACIL Suu B NN DL NN N EDEL UL BN JNNE BEEL BENL NN LN Suun S L LI | L B e : " 167 Planets Number of Planets 0 2 4 6 8 10 12 14 Planet Mass (M ) Figure 5 1. What is the mass of the planets, in units of Jupiter mass, indicated by that bar corresponding to the number 9? Life in the Universe — Activities Manual, 2nd Edition Prather, Offerdahl, and Slater 139

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Activity 11 2. If Jupiter is approximately 300 times more massive than Earth, how many times greater than the mass of Earth are the smallest planets on the chart in Figure 57 3. You overhear two students in class having the following conversation: Student #1: 1don’t know why people say that it will be difficult to find Earth-size planets orbiting around other stars. I mean, if you look at the bar on the far left in Figure 5, you can clearly see that there are at least 30 planets with a mass about the same as Earth. Student #2: 1 think the graph shows that we are finding planets that are way bigger than Earth. The masses shown in the graph are based on the mass of Jupiter, not Earth. So even the bar that is less at a value less than 1 will be hundreds of times more massive than Earth. Do you agree or disagree with one, both, or neither of the students? Why? Figure 6 is another histogram, this time showing the number of planets that orbit at a particular distance from their central star (as determined by their semimajor axis). 40F ™ 167 Planets Number of Planels 0.1 1.0 Distance from Star (AU) Figure 6 10.0 Life in the Universe — Activities Manual, 2nd Edition 140 Prather, Offerdahl, and Slater

Extrasolar Planets 4. Approximately how many extrasolar planets orbit at the same distance that Earth orbits the Sun (1 AU)? 5. Jupiter orbits our Sun at a distance of 5 AU. Are the majority of extrasolar planets orbiting closer to their stars or farther from their stars than Jupiter orbits the Sun? Explain why you think so. 6. A family friend calls you and says she has read the most astounding headline in the newspaper. The headline reads, “Much Like Our Solar System, Scientists Are Finding Jupiter-Sized Extrasolar Planets at Very Large Distances from Their Star.” What would you correct about this headline for your friend? Life in the Universe _ Activities Manual, 2nd Edition Prather, Offerdahl, and Siater 141

Activity 11 Figure 7 is a histogram showing the number of extrasolar planets that have a particular orbital period. Note that the orbital periods of these planets are recorded in units of days. Number of Planets llllll-llljll.l-ll.llllllll 10 25 Orbital Period (d) Figure 7 7. How long will it take a planet represented by a 10 on the X-axis of the histogram above to complete one orbit of its central star? 8. Approximately how many times more quickly would the planet in Question 7 orbit its star as compared to Earth (circle one)? 3 times faster 30 times faster 300 times faster 3,000 times faster Life in the Universe _ Activities Manual, 2nd Edition Prather, Offerdahl, and Slater 142 '

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Extrasolar Planets 9. All of the extrasolar planets shown in Figures 5 through 7 above were detected using the radial velocity technique. In just a few sentences, describe how these extrasolar planets compare in general to Jupiter in terms of mass, orbital distance, and orbital period. 10. Imagine you and your classm velocity technique. Which of t ates set out to detect the next extrasolar planet using the radial he following planets would you most likely discover? Why? Planet A Planet B Planet C Mass 2 Myyp 7.5 Myyp 11 Myyp Distance from Star 1 AU 10 AU 0.5 AU Orbital Period 3 days 12 days 23 days 11. What do the distributions in Figures 5, 6, and 7 above tel | us about the likelihood that we will find Earth-like planets with the radial velocity technique? Explain your reasoning. Life in the Universe — Activities Manual, 2nd Edition Prather, Offerdahl, and Slater 143

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