Lab 7 Eclipsing Binary Stars

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Eclipsing Binary Stars- Leah Andersen Remember to use blue text for your answers Background Material Complete the following section after reviewing all the Background Material. Question 1: Describe where the center of mass is located relative to the two stars that make up a binary system. Question 2: Complete the following table related to the location of the center of mass. The distance between the stars is always measured from the center of Star 1, so the separation between the stars (x) is the location of Star 2. The center of mass (x CM ) of the system is the distance from Star 1 to the center of mass. Star Star 1 Star 2 x CM Mass (M ⊙ ) x Mass (M ⊙ ) x System A 5 0 5 10 5 System B 2 0 4 6 4 System C 3 0 6 12 8 Question 3: If a small, very hot star is completely obscured by a large, cool star, the drop in total luminosity of the binary system would be best described as … (highlight your answer in blue) a) very small b) around 50% c) very large Question 4: Complete the following table related to stellar luminosities. Star Luminosity (L ⊙ ) Radius (R ⊙ ) Temperature(T ⊙ ) Star A 16 4 1 Star B 9 3 1 Star C 1 4 1/2 NAAP – Eclipsing Binary Simulator 1/10 The center of mass is always found on the line between the two objects and is located closer to the more massive object. If the two masses are equal, the center of mass must be halfway between the two masses. When one object is considerably more massive than the other, the center of mass may be inside the more massive object.

Figure : Light Curve Visualization Panel for Example 1 at phase = 0.5. Part 1: Exploration with Presets Open up the Eclipsing Binary simulator. You should note that there are four distinct panels:  a Perspective from Earth panel in the upper left where you can see the binary system in motion.  a Light Curve panel in the upper right where you can see the light variations of the system graphed in either flux or magnitude.  a Presets panel in the lower right which contains settings to configure the simulator to Student Guide Examples, Datasets with Complete Parameters (real eclipsing binary light curve data will be displayed and the simulator will be configured so as to mimic this system), and Datasets with Incomplete Parameters (real eclipsing binary light curve data will be displayed and students will be asked to configure the system to match). There is also a System Properties sub-panel where you can set the semi-major axis and eccentricity.  a System Orientation panel in the lower left that allows you to adjust the inclination at which the system is viewed, as well as the viewing longitude. The Animation and Visualization control allows you to start and stop the animation, and view it from different phases of the orbit. This panel also contains a button that allows you to see the stars’ location on the HR Diagram. Spend some time experimenting with the simulator, and make sure that you are experimenting in a systematic matter. Make adjustments to one variable exclusively until you develop a good grasp of how it affects the light curve. It is difficult to develop physical intuition if you hop from one variable to another in a haphazard fashion. Set the system to Example 1 . This preset has stars of the same size, radius, and temperature in circular orbits. Click on the start animation button to show the stars in simulated orbit around their common center of mass. After you have watched the system through several orbits click the pause animation button when the system is near a phase of 0.5 (if the light curve is not exactly at 0.5 you can drag the vertical red line cursor in the light curve display to the appropriate phase, or use the phase slider under the Animations and Visualization Controls sub panel). This phase represents the instant when one star completely covers the other from the Earth’s perspective. A “pointed” eclipse on a light curve typically reflects a partial eclipse when one star doesn’t completely NAAP – Eclipsing Binary Simulator 2/10

obscure the other. This system is a special case in that the two stars are exactly the same size so that a total eclipse occurs – yet it only happens for an instant and thus resembles a partial eclipse. Now move the vertical red cursor to a phase of 0.25. Note that a large portion of the light curve has this “flat top” reflecting the total luminosity of both stars. This occurs because the two stars are relatively small compared to their separation so an eclipse only occurs for a small fraction of the time. Set the system to Example 2 . This system is very similar to Example 1 except that one star is now twice as big as the other. Note that the eclipses now have flat bottoms corresponding to the time when one star completely eclipses or is encompassed by the other. You should also note that the eclipse depths (the decrease in light level) are much smaller in this system. Whereas Example 1 dropped to a normalized flux of 0.5 during eclipse, the minimum flux here is about 77% of the peak value when both stars are completely visible. However, in both of these examples the eclipse depths for both eclipses are the same. Question 5: Use the vertical red cursor to advance the system to a phase of 0.03. What is the physical significance of this phase (describe the position of the stars relative to each other)? Set the system to Example 3 . The two stars once again have the same mass, same radius, and are in circular orbits, but have different surface temperatures. This causes the eclipse at phase 0.0 to be deeper than the eclipse at phase 0.5. This deeper eclipse is known as the primary eclipse while the shallower is referred to as the secondary eclipse. Question 6: Is the hotter or cooler star closer to Earth during the deeper eclipse? How do you know? Question 7: What is the depth of the secondary eclipse in visual light (what fraction of light is lost during this eclipse)? Set the system to Example 4 . The two stars once again have the same radius, same temperature, and are in circular orbits, but now have different masses. There is no difference between this light curve and that of example 1. We will have to change our vantage point to see the change in the system. NAAP – Eclipsing Binary Simulator 3/10 The small star is eclipsing the big star, but a part of the small star is not eclipsing the big star. The colder the star is closer to earth during the deep eclipse because the star, is less luminous. Depth is 0.25

Figure : 3D Visualization panel for Example #4 looking down onto the plane of the binary system. In the 3D Visualization panel deselect lock on perspective from Earth . You may now click and drag anywhere in the 3D Visualization Panel to change the viewer’s perspective. Note that the Lightcurve Visualization panel still illustrates the light curve as detected from the Earth’s perspective. Thus, the 3D Visualization panel is allowing you to leave the Earth and view the system from any vantage point. The red arrow indicates the direction to Earth. Manipulate the panel until you are looking directly down onto the plane of the binary system as is shown in the figure to the right. The green cross represents the center of mass of the system. You are encouraged to open up the Star 1 Properties sub-panel and play with the mass of Star 1. Note that as the stars’ distances from the center of mass change the mean separation of the stars is still 6R ⊙ and the light curve shape is also unchanged. NAAP – Eclipsing Binary Simulator 4/10

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