AstroTutor - Eclipsing Binary Star Systems

When we refer to the amount of material making up an object--the number and type of atoms and molecules--we are referring to the mass of the object. It is tempting to use the word "weight" interchangeably with mass, but to do so, strictly speaking, is incorrect. Mass under the influence of another mass has weight. That influence for large objects such as stars is of course gravity. That influence for atomic particles like electrons and protons is the electromagnetic force. The mass of your body has weight while you remain on Earth. But as you venture away from Earth, you gradually lose your weight even though you retain your mass. We cannot bring stars to Earth in order to weigh them, so we instead refer to their masses. Unfortunately, it is not easy to determine the mass of a star. "

Consider this situation: a star is all alone in space, with nothing close enough to be influenced by its gravity. How can we determine the amount of material (mass) in this star from our distant location?

There is an example within our solar system. The masses of the planets are fairly accurately known, because their influences on one another are easily determined by measuring the changes in their orbits as they pass one another. But Pluto's mass was a mystery for a long time, because we were unable to detect anything close to it. But in 1978 an object was discovered close to Pluto on a photographic plate taken of Pluto itself. By taking consecutive photographs of the position of the object relative to Pluto from week to week, it became obvious that it was a moon (now named Charon) in orbit around Pluto. At the same time, its plotted orbit around the planet allowed astronomers to determine Pluto's influence on Charon's orbit and therefore Pluto's mass.

Similar techniques can be used with stars. We find stars in the presence of other stars, close enough to one another that they influence one another. Stars found in close company to one another are what astronomers refer to as binary star systems. If there are three or more stars orbiting one another, astronomers refer to it as a multiple star system. By measuring the stars' movements with respect to one another, we determine their masses. It turns out that at least 50% of the stars we observe in the sky at night are members of such binary or multiple star systems, although it is anything but obvious to the casual observer. So how do astronomers locate these systems of stars? Let's take a familiar example.

Would you be surprised to learn that there is a naked-eye star in the sky whose apparent visual magnitude changes from (+ 2.1) to (+ 3.4) every couple of days, and that a reward of $200,000 awaits anyone who locates that star? Assuming that you are not allowed to use star maps or astronomical instruments, are you willing to invest the time necessary to find the star? "

Before you get stirred up for action, consider the task at hand. You must first record the positions and the apparent brightness of all of the stars in the sky. Then you must return to each star on a schedule to find the one that has changed in brightness. To do that, you must become familiar with each star in comparison to its neighboring stars in order to recognize the mystery star when its brightness has changed. And of course, the star isn't necessarily going to be visible on any particular night. Different stars appear in the sky at different times of the year (seasonal stars). It appears that the task will take you at least several months. (I'll pass.)

There is such a star--it is called Algol, which in Arabic means "the demon's head." The prefix "Al" in Arabic means "the." The English word "ghoul," commonly used during our celebration of Halloween, derives from the Arabic "gol." Although officially first detected in 1669, there is reason to believe that long before the Arabs had noticed its variation in brightness, and therefore assigned a name appropriate to its behavior. After all, early cultures considered the sky to be permanent and unchanging and eternal.

Having discovered a star with variable brightness, astronomers first obtain a spectrum of the star in order to determine its properties and characteristics. In the case of Algol, the spectrum reveals all of the characteristics of a binary star system.

But why the light variations? That becomes obvious when we use a photometer to determine the apparent visual magnitude of the star over a long period of time. Plotting the observations made with the photometer on graph paper gives us a light curve, a plot of light received against time. The data reveals an interesting pattern in the light variation.

Our interpretation is that in addition to two stars alternately moving away from and toward us, their orbital plane just happens to lie along our line of sight. The two stars alternately eclipse one another. This is called an eclipsing binary system. Let's look a little closer at the manner in which we conclude that Algol consists of two stars. The Animation illustrates how the pattern of apparent visual magnitude plots is explained. Astronomers interpret the light curve of Algol by suggesting that two stars of different temperatures are orbiting one another. When the two stars are not aligned, we receive the combined light emitted by both. When an eclipse occurs, the light from one is absorbed by the back of the nearest star, and the amount of light we get is less. When the hotter of the two stars passes in front of the cooler star, there is a decrease of light, but not as much as when the cooler star passes in front of the hotter star. That is how we explain the two unequal dips in the light curve. In addition to determining the orbital period of the two stars by knowing the time interval between successive dips, we can also calculate the diameters of the two stars in an eclipsing binary system. By knowing the orbital velocities of the stars (from measuring the Doppler effect in the spectral lines), and the times required for each star to pass in front of each other (the width of each dip in the light curve), the diameters are easily calculated.