ASTRO 801
Planets, Stars, Galaxies, and the Universe

Binary Stars

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Additional reading from www.astronomynotes.com


Stars do not form in isolation. When clumps of gas in a GMC begin to collapse, the clumps usually fragment into smaller clumps, each of which forms a star. After the formation process ends, many stars wind up gravitationally bound to one or more partner stars. The fraction of stars that are found in multiple star systems is actually a difficult measurement to make, but the fractions are likely higher than you might expect. For massive stars, we think a large fraction may be in multiple systems—for Sun-like stars it may be about half of all stars, and for low mass stars, less than half.

For example, take some famous bright stars in the sky: Albireo (we saw an image of Albireo in Lesson 4) appears in a telescope to be a pair of stars. The brightest star in the winter sky, Sirius, also has a companion (an X-ray image of the Sirius pair is available at Astronomy Picture of the Day). Also, there is a star in the handle of the Big Dipper known as Mizar, which can be resolved into a double star, too.

Try this with Starry Night!

There are a number of "visual binary" stars that you can observe with small telescopes or with Starry Night. Using the "find" feature on Starry Night, search for the stars listed below. You may have to vary the date and time so they are visible at night. Once you have them centered in your field of view, use the zoom feature to zoom in to see how they would appear magnified through a telescope. Also, read the descriptions that pop up when you mouse over them.

  1. Mizar & Alcor (be sure to zoom in even further on Mizar)
  2. Albireo
  3. Algieba (gamma Leonis)
  4. Castor
  5. Epsilon Lyrae (to find this in Starry Night, go first to Vega, and Epsilon Lyrae is one of the bright stars in Lyra near Vega)
Finally, look at Sirius, which is a binary, as seen in the APOD image linked above. Is the Starry Night description for Sirius any different than the others? Is its appearance in Starry Night any different?

Stars classified as visual binaries are rare examples of stars that are close enough to the Earth that in images we can directly observe that they have a companion. In most cases, however, stars are so far away and their companions are so close that images taken by even the most powerful telescopes in the world cannot tell if there is one star or two present. However, we have observational methods to determine if a star is in a binary system even if an image appears to show only one point of light. Three of these techniques are:

  1. Spectroscopy: Recall that stars were originally separated into different spectral types by their spectral lines. Occasionally, the spectrum of what appears to be a single star will contain absorption lines from two different spectral types (e.g., G and K), indicating that this is really a binary star system, not a single star. Just like the planets in our Solar System orbit the center of mass of the Solar System, the two stars in a binary star system will orbit the common center of mass of the binary system as shown in this animation:

    As demonstrated in the animation, we can also occasionally observe the motion of the stars in a binary star system by observing periodic changes in their spectral lines. This is explained in a bit more detail in the spectroscopic binary movie at an Ohio State astronomy course website. (Once you click on the link, you will see three links at the top of the new window. You can click on any of the links because they all show the same animation. They are just different file formats.)

    As you can see, when one of the stars is moving away from us, the other is moving towards us. Thus, because of the Doppler shift, we know that the lines from one of the stars will be blueshifted while the lines from the other star are redshifted. As the two stars orbit each other, each set of lines will appear to shift back and forth. In some cases, you can only see the lines from one of the stars, but those lines will still oscillate back and forth as the star orbits the center of mass of the binary system.
  2. Eclipses: If we are fortunate enough to be observing a binary system in the same plane as the stars' orbit (an edge-on view of the system), we can actually see them eclipse each other. In this case, we can observe the periodic dimming of the system as one star passes in front of the other, and then passes behind the other star. Richard Pogge has an animation of this type of system, too. In this case, you do not need to observe the spectrum of the binary system; instead, you simply take frequent images and measure the apparent brightness of the system. If you plot brightness on the y-axis and time on the x-axis, you will see the periodic eclipses show up as periodic dips in the total brightness. This type of plot is referred to as a "light curve."
  3. Astrometry: Instead of observing the stars from a side view, occasionally a binary system is oriented so that it is closer to a top view from our point of view (we do not have to be observing the system from exactly top down, but nearly top down). In this case, the motion of the stars in their orbit is in the plane of the sky, instead of towards and away from us. Thus, we might observe a star slowly wobbling back and forth on the sky. This is the motion of the brighter star in its orbit around the companion that is too dim to observe.

Binary stars are very useful tools in the study of the properties of stars. In the previous lesson, we discussed that we can measure a star's luminosity, distance, and velocity, but we did not discuss any methods for measuring the mass or radius of a star. You might be curious how those properties correlate with the other properties we did discuss, like luminosity, for example. Our knowledge of the masses and radii of stars comes mostly from the study of stars in binary systems. For example, we can use Kepler's third law to derive the masses of the stars in a binary system. Recall that when two objects orbit each other the following equation applies:

P 2  = (4π   2  *  a 3 ) / G( m 1  +  m 2 ) This equation is not rendering properly due to an incompatible browser. See Technical Requirements in the Orientation for a list of compatible browsers.

If we measure the separation between the objects (a) and the period of their orbit (P), we can calculate their masses. Unfortunately, depending on the type of binary (e.g., spectroscopic, eclipsing, astrometric), we are often unable to directly measure its orbital properties unambiguously. Since the inclination angle of a binary star's orbit with our line of sight (that is, is it edge-on, face-on, or somewhere in between?) is often unknown or only able to be estimated, in many cases what you measure is not the mass of the star, but the mass times sin (i) where i is the inclination angle of the orbit. Thus, you get a limit on the mass, but not the true value. If you have a spectroscopic binary that is also eclipsing, you can measure the velocities, period, separation, and inclination angle, because you know that the orbital plane has to be edge-on or nearly edge-on for us to witness eclipses from Earth. Thus, it is these systems that really help us measure stellar masses quite accurately.

Eclipsing binaries also provide us with a tool for measuring the radius of a star.

Try this!

  1. Go to the UNL NAAP "Eclipsing Binary Simulator."
  2. Click on the "start animation" button, and watch the binary stars orbit their center of mass several times, then pause the animation.
  3. Set the inclination using the slider to 85 degrees.
  4. Set the orbital eccentricity using the slider (lower right) to 0.0.
  5. Start the animation again, and note the stars' orientation to each other at the beginning of the deep eclipse and at the end of the deep eclipse.
The duration of the primary eclipse (the one that causes the larger amount of dimming) is the time from the star first beginning to pass in front of the second star until it is completely past the second star. So, the time from the beginning of the dimming to total eclipse is equal to the diameter of the star passing in front multiplied by its velocity. If you can measure the orbital velocity of the stars and the duration of the eclipse, you can then determine the diameter of the stars. This is our primary method for determining stellar radii.

Want to learn more?

In the interests of time and space, I am skipping the details of making the calculations of stellar mass and stellar radii using binary systems, but you can read about these topics in more detail in the online astronomy textbook Astronomy Notes: