|Orbital Characteristics of Binary Stars and Extra-Solar
To investigate the effect that changes in mass, separation, eccentricity, and inclination angle have on the characteristics of the radial velocity or photometric light curves of binary stars and stars with extra-solar planets.
The most important property of a star is its mass, but stellar masses are much harder to measure than luminosities or surface temperatures. The most dependable method for "weighing" a star relies on Newton's version of Kepler's third law. This law allows us to calculate the masses of orbiting objects by measuring both the period and average distance (semimajor axis) of their orbit. We must be able to determine the orbital properties of the two stars in order to derive the masses and radii of the system.
There are three main classes of binary systems: visual binary, eclipsing binary, and spectroscopic binary. In this exercise, we examine the characteristics of a) spectroscopic binaries by noting the effects changes in mass, separation, eccentricity, and inclination angle have on the shapes of the radial velocity curves and the Doppler shifts of the lines in their spectra; b) eclipsing binaries by comparing the changes in the light curves depending on the masses of the two stars, their spectral type, and the inclination angle; and c) the orbits of stars with suspected Jupiter-like planets and compare them to "normal" binary systems.
Also check out:
You've been given a handout containing the phased data for changes in the magnitudes of 4 eclipsing binary stars (seemingly a biased selection as all of the curves indicate contact binaries). Work with the following java applet demonstrating Eclipsing Binaries, and try to duplicate this curves by manipulating the inclination angle, separation, and spectral types of the stars.
Note: I tried to figure out the units for "L" in the program, trying to translate them to a change in magnitude for a direct comparison with the actual light curves. I was not successful and there seems to be no explanation at all on the web site itself. The corresponding lecture seems to indicate that this is apparent magnitude, only upside down for astronomers.
Take a look at the image to the right of each of the following definitions and find the corresponding parameters on the simulation:
|M1 or M2||The mass of each of the two stars.|
|The distance between the two stars in solar radii.|
|Eccentricity of the orbit|
|Angle of the orbital plane of the stars to our line-of-sight.
0o = face on
90o = edge on
This is the opposite from the standard notation.
|Angle of the major axis as measured in the orbital plane|
Do some trial investigation to see how you can adjust each of the parameters for the simulation:
Adjust each of the star parameters -- masses, separation, eccentricity, inclination, and node angle.
Click "enter" to update the simulation parameters.
Use "pause" to start and stop the simulation, if desired.
If the picture is messed up at anytime, use "enter"to redraw it.
The number between the "<=" and "=>"buttons, is the rough time (in seconds) it takes the simulation to complete an orbit. Make this number larger or smaller by clicking the "arrow" buttons.
Now for a real astronomical treat! Visit the California & Carnegie Planet Search web page. On this home page you will note the distribution of extrasolar planets as a function of distance from the primary star, and as a function of the metallicity of the primary star. If this stuff is new to you, be sure to take some time to study these results. They are significant.
Click on the Almanac of Planets link. There you will see the entire list of extrasolar planets with the primary star name, planet mass (times sin i), peiod of the orbit, semi-major axis, eccentricity, and semi-amplitude of the radial velocity variations of the primary star. Pick 5 stars to investigate further. Try to get a wide range of planet masses, semi-major axes (a), and eccentricities (e ). What we are going to do is try to duplicate these radial velocity curves with the "spectroscopic binary" java simulation to better understand how astronomers determine all of the parameters of these star-planet systems. Fill in the following table for the "questions for this part."
|a||e||Values for Simulation Variables|
Comment on these results (pretty much anything that comes to mind).