Modelling Binary Light Curves

Binary stars are of great importance to astronomers as they provide virtually the only means of directly determining the masses of stars other than our Sun. On this page you will find two Java based exercises that allow you to investigate binaries using computer simulations to together with links to other binary star software for download or online use. The first two exercises have been adapted with kind permission from originals by Sandra Woodward. You can download her original worksheets and web links presented at the Science Teachers Workshop at University of Sydney in 2004 as a pdf file here.

Exercise 1: Binary Stars

For this exercise you need to open a Java applet hosted at Cornell University. Click here to open the site (another window will open automatically). To change your view quickly between the two pages you can use ALT+TAB keys held down simultaneously. If the first site does not open, click here for a mirror site at Melbourne University.

This exercise allows you to alter parameters to see the effect on a binary star system. You can see privileged and Earth views of the system, the orbit of each of the stars (blue for star 1 and red for star 2), the spectrum from the system and the radial velocity plot. Your applet window gives you control over the following parameters:

Symbol Quantity Explanation
M1 or M2
 Mass 1 or Mass 2 The mass of each of the two stars
a
 Separation The distance between the two stars in solar radii
e
 Eccentricity Eccentricity of the orbit (e = 0 is a circular orbit).
i
 Inclination angle

Angle of the orbital plane of the stars to our line-of-sight.

  • 0° - face on
  • 90° - edge on
Note that this is the opposite from the Eclipse simulation (2nd exercise below).
w
 Node angle Angle of the major axis as measured in the orbital plane (see privileged view).

Read the instructions on the applet page before proceeding to work through the steps and questions below.

Procedure and Questions

  1. Set the parameters to: M1 = 1, M2 = 1, a = 0.7, e = 45, i = 45 and w = 0.
  2. Describe the view from Earth in terms of motion and position of the two stars.
  3. How does this convert to the graph?
  4. Explain the effect on the motion if the masses are changed. Try the following combinations:
    M1 M2
    1
    2
    2
    1
    4
    1
    1
    8
  5. Explain what the spectra is telling you about the stars in this system. Relate your description to the positions of the stars in their orbits.
  6. How can the period of the stars be determined?
  7. Define what is mean by the term spectroscopic binary stars.
  8. Using Kepler's Laws explain how the mass of the system can be determined.

Exercise 2: Eclipsing Binary Stars

For this exercise you need to open a Java applet hosted at Cornell University. Click here to open the site (another window will open automatically). To change your view quickly between the two pages you can use ALT+TAB keys held down simultaneously.

This exercise allows you to investigate an eclipsing binary system, altering its parameters to examine their effect on the simulated light curve. The simulation provides you with the following parameters:

  • Angle; a value of 0° gives an edge-on view, a value of 90.0° gives a top-down view. (Note this is the opposite to the previous binary star simulation).
  • Separation; the distance between the two stars in solar radii, from 0 to 25.
  • Spectral class of each of the two stars.

Read the instructions on the applet page before proceeding to work through the steps and questions below.

Procedure and Questions

  1. Define what is meant by an eclipsing binary.
  2. What do the axes of the graph represent?
  3. Set the values a follows:
    angle = 10
    separation = 10
    Star 1 type A
    Star 2 type F
  4. Describe the shape of the graph.
  5. Relate the features of the graph to specific positions in the orbit of the two stars.
  6. Change the values to see the effect that each of the following has:
    Star Type - eg What happens when the types are the same?
    Separation - separate the stars by differing amounts and make a general observation.
  7. What effect does the angle of inclination have on the graph? Can you put forward an explanation for this?
  8. Discuss the conditions under which a primary and a secondary eclipse will take place.

Other Binary Star Simulations

There are several other simulations that help you explore binary stars. Some of these are online Java applets whilst others require you to download and install software.

  1. Binary Stars has four free programs for Mac computers that can be downloaded from the site. Manuals are also available and useful for classroom or self-education use.
  2. Eclipsing Binary Simulator (EBS) is a free executable program for Win98 or higher PCs. With it you can visualise the orbit and light curve for an eclipsing binary system.
  3. Eclipsing Binary Stars is an extensive site that provides free software downloads for Windows PCs plus detailed information on eclipsing binaries. There is a free program, StarLightPro and a range of Excel spreadsheets that allow you to investigate various properties of binaries. The page also has extensive categorised links for binary stars.
  4. Orbital Characteristics of Spectroscopic Binaries is an activity where you can explore, using the online Java applet, how the parameters effect the radial velocity plots for a spectroscopic binary. There are several questions on the worksheet which can be printed out.