Advice Binary Stars

Advice Binary Stars

In this exercise, you will be finding the masses and the radii of stars in two binary star systems. You will be given two different separate data sets to use.

Each data set includes the speeds of two stars on one plot and the amount of light from the pair of stars on the other. The name of the star(s) are usually two letters, like RS and then the abbreviation for the name of the constellation that it is in e.g. Cas (for Cassiopeia), So the entire name would be RS Cas. It refers to the two stars together, since that is how we have been seeing them.

You will be assigned two different, entirely independent star systems. Follow the directions in the lab write up to find out the properties of each.

One of the things that is different about this lab is that you need to try various things until you get the plot from the computer program to match the plot that you have. You probably will need to try several times, so be patient. The way that astronomer’s get information from binary star systems is to try to match these plots (but with more math). This is one of the very few ways that it is possible to find the masses of stars. It is the way that we can verify our information about the way that stars work.

It is usually easiest to deal with the radial velocity first. You can recognize the radial velocity curve by the fact that the y axis is labeled in km/sec.

It depends on which program you are using, but basically enter the highest and lowest speeds for each star. The plus and minus signs matter a lot. So be sure to use them. The period, time for the stars to complete one orbit also matters. Set eccentricity (e) and the angle (omega, longitude of line of nodes) to zero.

Once you have input the max and min velocities and checked to be certain that the masses you are getting are not crazy (not crazy would be between about 0.2 solar masses and 60 solar masses), change the eccentricity and the angle to match the shape of the light curve.

When the eccentricity is zero, the angle doesn’t matter and the radial velocity curve is very symmetric. As you change the eccentricity (values 0 to .99 are possible), the curves will get less symmetric. And if you change the angle while the eccentricity is non-zero, you can decrease the symmetry further. Take your best shot. Then print it out.

Once you are done with the radial velocity, use the masses that you got and the eccentricity etc to go into the light curve program.

Look at the light curve. The y axis might be in magnitudes or in amount of light. Up is brighter (lower magnitude numbers). The low parts are when one star eclipses the other. The lower of the two, is when the hotter star is in back. These are the eclipses; one star blocking some or all of the light from the other.

Use the spectral types or the temperatures (given on the data sheet, usually). The light curve is VERY sensitive to the difference in temperature, and not sensitive to the overall level of temperature. Changing the temperature changes the difference in depth of the eclipses.

Now guess the radii of the stars and the inclination of the system. The inclination is probably between 75 and 90 degrees. When the angle is 90 degrees, the system is just edge-on and the eclipses are the deepest. As the angle gets smaller, the eclipses get smaller and disappear.

The radii of the stars are given (for most computer programs) in units of the distance between the two stars. So numbers like 0.05, or 0.3 would be appropriate. As the stars get bigger, they become distorted by the gravity from the other one and that makes the light curve have more rounded parts.

You need to experiment with the radii and inclination until the light curve looks like the one given. The idea is to get the idea and a reasonable match. Turn in the plots. And have fun. Just be patient.