For Educators

An Eclipsing Binary System with a Precessing Accretion Disk

By James Humphreys


Introduction, Requirements, Lesson Plan, References



Some X-ray bright objects in the sky show regular, long-term changes in intensity that can best be explained as due to the source, a neutron star being eclipsed by a companion star. (Typically the companion is a spectral type B-F star, relatively very weak in X-ray emission.) In such a system, it is likely that some material from the companion star is being pulled into an accretion disk by the gravitational attraction of the neutron star.

The combination of forces arising from the gravity and rotation of the two stars may cause the disk to slowly precess like a spinning top. Due to the tilt and precession of its rotational axis, the disk may periodically come between the neutron star and the observer, causing fluctuations in the number of X-ray photons received.

The orbital plane of the system may be so little inclined to the line of sight that the neutron star, along with its accretion disk may pass behind the companion star, giving rise to dramatic periodic variations in the light curve.

The total light curve is then modulated by the combined periods of the rotation of the neutron star, the precession of the accretion disk and the occultation of the neuron star by its companion.


In this segment the student uses X-ray data to identify multiple periodic variations in a binary star system.


Using data of the object Hercules X-1 taken by the All Sky Monitor aboard RXTE, the student will be able to:

  1. Identify this object as a binary source.

  2. Determine an approximate value for the orbital period of the object.

  3. Notice the distinct, long-term intensity changes, and interpret them in terms of emergence from occultation by the accretion disk.

  4. Determine an approximate value for the period of precession of the accretion disk.


  • Grade level: 11th or 12th

  • Prerequisites: Algebra, physics, chemistry or physical science.

  • Preparation: The teacher must download and distribute copies of the Light Curve of Hercules X-1 (or be able to instruct the student to do so).

  • Materials (per lab group): One copy of the graph, calculator, pencil.

  • Setup: Be sure to know how the student groups will obtain the necessary graph.

  • Estimated class time: Once the graph is obtained, approximately 25 minutes.

Lesson Plan


  1. Sketch a light curve (graph of intensity vs. time) for a solar eclipse.

  2. Why don't we see an eclipse of the sun every month?


Distribute the graph with the following directions/questions:

The graph you have is of the 2-12 keV photon count rate vs time in days of Hercules X-1 as measured by the All Sky Monitor aboard RXTE. Each individual data point represents the average count rate take over a half a day.

  1. Identify any periodic variations in the count rate that show up on your graph, and estimate the period of each. (Note that there may more than one overlapping periodic fluctuations on the same graph. If this seems to be the case, find a portion of the graph that shows distinctly the shortest period, and try to show that same period throughout the graph.)

  2. What explanation might you offer for each of the periodic variations that you identified above?

  3. Why do you suppose that the pulse period (the rotational period of the neutron star) is not identifiable in this graph?

  4. How would you interpret the occasional negative values for the count rate?

The student should find two periodic variations in the light curve: the shorter 1.7 day variation corresponds to the orbital period of the neutron star and the normal star; the longer 35 day variation is due to a warped, precessing accretion disk around the central neutron star. A segment of a video (created by Dr. William Priedhorsky (Los Alamos National Lab)) illustrating how this 35 day variation arises is available in .avi and .mov format for PCs and MACs.


Kepler's third law can be modified to

(m + M) P2 = a3

where: m, M are the masses of the two stars (in solar masses); P is the orbital period (in years); and a is the semi-major axis (in astronomical units)

  1. For Her X-1, the masses of the two stars are about 1.2 and 2.5 solar masses respectively. Use your result for the orbital period (see number 2 above) and this form of Kepler's third law to calculate the distance between the neutron star and its companion (assuming zero eccentricity for an orbit centered on the center of the companion star).

  2. Some of the details of binary systems that astronomers try to discover include:

    • number and type of bodies in the system
    • size and mass of each member of the system
    • orbital period
    • inclination of the orbital plane to the line of sight
    • eccentricity of the orbit

    Choose large and small reasonable values for each of the above quantities and describe (verbally or graphically) the effects of each on the light curve of the system as seen from earth.


  1. Zeilik, Michael. Astronomy: The Evolving Universe. John Wiley & Sons, Inc., New York (1991, 6th ed.) pp.303-308

  2. Arny, Thomas. Explorations: an Introduction to Astronomy. Mosby, St. Louis (1994) pp.336-340

  3. Cannizzo, John K. and Ronald H. Kaitchuck. "Accretion Disks in Interacting Binary Stars." Scientific American 266 (January 1992): 92

  4. Verbunt, F. "Origin and Evolution of X-Ray Binaries and Binary Radio Pulsars." Annual Review of Astronomy and Astrophysics 31 (1993): 93-127