Up to this point we have been considering isolated single stars and their evolution. However, over half of the visible stars are members of binary or multiple star systems. If the stars in a binary system are widely separated then it is not a bad approximation to consider them separately, as if they are isolated stars. However in many binary systems, the stellar evolution can follow new and different paths.
First, what sort of multiple star systems are there? Multiple star systems occur wherever stars are bound together by mutual gravitational attraction. The most common example is the binary star system in which two stars orbit about each other. Multiple star systems entail hierarchical orbital configurations. In a triple system, for example, a third star orbits a tight binary, A quadruple system would have two close binaries orbiting each other and so on. Basically multiple star systems are built as binaries of binaries and so forth. Other orbital configurations are unstable and would not last.
Multiple star systems are fairly common, so they must be easily formed during the star formation process. In the last stages of protostellar collapse, the cloud out of which a solar system is forming can fragment into multiple pieces that are gravitationally bound together in orbits. Each piece goes on to form an individual star. For example, if the planet Jupiter had been a bit more massive it would have turned into a low mass star and our sun would be a binary. It is also possible that very rapidly rotating protostars may fission into two separate pieces that then form a pair of stars in a very close orbit.
What are the different types of binary systems? First there are the visual binaries so called because we can actually see two separate stars when we look through the telescope. Sirius is an example. The bright star called Sirius is actually two stars: an A1 main sequence star (Sirius A) and a white dwarf companion (Sirius B). For a binary to be a visual binary they must both be bright enough and there must be sufficient separation between the two stars so that they each can be resolved separately in the telescopic image.
In other types of binary systems the presence of the companion star is inferred by indirect means. In astrometric binaries only one star is visible but by following its proper motion one can see that its path "wiggles" across the sky, implying that it is in an orbit with an unseen companion. The center of mass of the binary system would move in a straight line but the star orbits around the center of mass. This would be one way to detect planets for example (since planets do not shine and hence would not be visible).
Figure: (a) In a visual binary system one can see two stars
orbiting each other. (b) In an astrometric binary system one sees only
one star but its proper motion follows a curved path. (c) In a
spectroscopic binary the stars are too close to be seen separately but
changes in doppler shifts reveal the orbits.
Not all binaries are visual. There are spectroscopic binaries where the motion of the stars cannot be seen directly but is inferred from the time variable doppler shifts in the absorption lines. For example a hot star of class B or O orbiting with a cool star of class M or K would show helium lines and neutral metals or even molecules, i.e, both spectra would be mixed together. But the two separate spectra would quickly distinguish themselves by their separate doppler shifts. All the lines associated with the hot star would vary as one, and all the lines associated with the cool star would vary as another one. In practice you don't need to have stars of different spectral type, nor do you need to even see the absorption lines from both stars to infer properties of the binary system. The systematic time variation is sufficient.
Perhaps the most interesting of the types of binaries are the eclipsing binaries. These are systems where the light from one star blocks the light from the other at some point in the orbit. This makes the total light from the system seem to vary with time---it is dimmer during eclipse and brighter when the system is out of eclipse. The way that the light changes as a function of time (such a graph of light versus time is known as a "light curve") can give direct information about the size of the stars and the orientation and size of the orbit.
Figure: See Figure 10-14. In an eclipsing binary system changes in the light curve correspond to various points in the binary orbit. The light drops when one or the other of the stars is eclipsed.
There remains one important property of stars that we haven't talked about and that is mass. The problem is that there is no direct way to determine the mass of a star sitting in space in splendid isolation. We need to see something orbiting that star so that we can use Newton's laws and Kepler's third law to derive a mass. Hence the only stars that we can directly obtain masses for are binary stars. All you have to do is determine the period of the orbit and the size of the semi-major axis of the orbit. Recall the formula for this given by:
P2 G (m1+m2) = 4 pi2 a3
If the stars are visual binaries then both stars can be distinguished and followed as they orbit. After mapping out the orbit on the sky, one uses the distance to the system to determine the size of the semi-major axis, and then computes the sum of the stellar masses (m1+m2). If we can determine the center of mass of the system, which is the stationary point about which both stars seem to orbit, then that gives the ratio of the two masses. This allows the individual stellar masses to be determined.
So the long term careful study of binary systems has allowed us to obtain masses for stars. Fortunately, binaries are numerous so many stellar masses have been thus obtained. The most important result of this study has been the determination that for stars along the main sequence there is a direct relationship between the mass of the star and the luminosity, namely that the more massive a star is the more luminous it is as well. Thus we can associate the O spectral class with the most massive stars, and the M spectral class with the least massive. The sun, a G star, is sort of middling in the mass department.
Now what is it about binary stars that affects their evolution when compared to single stars? Stars in a close binary can transfer mass from one star to the other. Since mass is the major determinant in how a star evolves the loss or addition of significant amounts of mass can substantially change the course of a star's life.
A good example is given by the star Algol which is an eclipsing binary. (During the main eclipse Algol's light drops by 1.2 magnitudes, and amount you can detect with naked eye observations.) The primary star is a B8 V main sequence 5 solar mass star and the secondary star is a K0 III one solar mass giant. This is a mystery: presumably both stars in the binary formed at the same time and yet the lower mass star has already evolved to a giant phase while the high mass star is still on the main sequence. This is inconsistent with our understanding of single star main sequence lifetimes. The answer is that what is now the K0 star was originally more massive (around 9 solar masses) and as it evolved it expanded and transferred a great deal of its mass over to the other star.
To understand close binary systems we have to think about how the stars affect each other. A star influences surrounding things through its gravity. Recall that the gravitational force from an object goes as one over the distance squared. This means that if one were to locate points around a star where the gravitational forces were equal in magnitude those points would all lie on a sphere, that is the gravitational force is "spherically symmetric." Imagine moving two stars together. The gravitational force at any point will be the sum of the gravitational forces of both stars. Now the surfaces of constant force are not spherical, they are distorted into a figure 8 configuration. At some point lying between the two stars the forces from the two stars will be equal in magnitude but opposite in direction. If you move towards one or the other of the stars you will be captured by that star. This point, known as the Lagrange point, is kind of like a low mountain pass between two circularly shaped valleys. Continuing with this analogy imagine the stars to be lakes at the bottom of these valleys. If you were climbing up to that pass and poured out some water you can easily see how the water will flow down to one or the other of the two lakes depending upon which side of the pass you are on. Now imagine one of the lakes having so much water that it completely fills its valley and produces a stream which flows through the pass down into the other lake. In our analogy this is a "water transfer" process.
Figure: Figure 10-15 shows (a) Two stars within a detached binary system. (b) A semi-detached binary system and (c) a contact binary system both stars overflow their "Roche Lobe" and they share common outer layers. In Figure 10-17b we see a semi-detached binary system where the gas stream forms an accretion disk.
In stars it is not water being transferred but gas from the envelope from one of the stars. The transfer generally begins when the star has evolved from a main sequence star up into a giant. The giant star can easily overflow its gravitational basin and dump material onto the other star through the Lagrange point. The figure 8 configuration is known as a Roche lobe so this is often referred to by astronomers as "a star filling its Roche Lobe."
We can classify the state of a binary system by whether or not either of the stars is filling its Roche Lobe. If the two stars are well separated and nowhere near the size of the critical figure 8 surface then they are called a detached binary. If one of the stars is big enough to transfer mass through the Lagrange point then the system is a semidetached binary. If both stars fill their Roche lobes then the system is known as a contact binary. Such a system is almost more like a double-core, figure 8 shaped star.
Figure: In a semidetached binary system, gas from one star can
overflow its Roche lobe and fall into a disk orbiting the other star.
This is known as an accretion disk.
Sometimes in a semidetached binary system the mass transferred from one star to another doesn't actually fall directly down onto the compact star but instead goes into orbit around that star. This material forms a disk orbiting around the compact star known as an accretion disk. Gas in an accretion disk can become very hot and glow in visible, UV and X-ray light. Accretion disks can lead to many interesting types of phenomena, particularly when they are located around neutron stars and black holes. Accretion disks will be discussed more detail later.
Copyright © 1998 John F. Hawley. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 124 at the University of Virginia. Reproduction, distribution, and commercial uses are prohibited.