We have noted that most stars in our Galaxy are not isolated objects but are actually members of binary-star systems. However, our discussion of stellar evolution has so far focused exclusively on isolated stars. This prompts us to ask how membership in a binary-star system changes the evolutionary tracks we have just described. Indeed, because nuclear burning occurs deep in the core, does the presence of a stellar companion have any significant effect at all? Perhaps not surprisingly, the answer depends on the distance between the two stars in question.

For a binary system whose component stars are very widely separated—that is, the distance between the stars is greater than perhaps a thousand stellar radii—the two stars evolve more or less independently of one another, each following the track appropriate to an isolated star of its particular mass. However, if the two stars are closer, then the gravitational pull of one may strongly influence the envelope of the other. In that case the physical properties of both may deviate greatly from those calculated for isolated single stars.

As an example, consider the star Algol (Beta Persei, the second brightest star in the constellation Perseus). By studying its spectrum and the variation in its light intensity, astronomers have determined that Algol is actually a binary (in fact, an eclipsing double-lined spectroscopic binary, as described in Chapter 17), and they have measured its properties very accurately. (Sec. 17.9) Algol consists of a 3.7—solar mass main-sequence star of spectral type B8 (a blue giant) with a 0.8—solar mass red subgiant companion moving in a circular orbit around it. The stars are 4 million km apart and have an orbital period of about 3 days.

A moment's thought reveals that there is something odd about these findings. On the basis of our earlier discussion, the more massive main-sequence star should have evolved faster than the less massive component. If the two stars formed at the same time (as is assumed to be the case), there should be no way that the 0.8—solar mass star could be approaching the giant stage first. Either our theory of stellar evolution is seriously in error, or something has modified the evolution of the Algol system. Fortunately for theorists, the latter is the case.

As sketched in Figure 20.21, each star in a binary system is surrounded by its own teardrop-shaped "zone of influence," inside of which its gravitational pull dominates the effects of both the other star and the overall rotation of the binary. Any matter within that region "belongs" to the star. It cannot easily flow onto the other component or out of the system. Outside the two regions, it is possible for gas to flow toward either star relatively easily. The two teardrop-shaped regions are called Roche lobes, after Edouard Roche, the French mathematician who first studied the binary-system problem in the nineteenth century and whose work we have already encountered in the context of planetary rings. (Sec. 12.4)

Figure 20.21 Each star in a binary system can be pictured as being surrounded by a "zone of influence," or Roche lobe, inside of which matter may be thought of as being "part" of that star. The two teardrop-shaped Roche lobes meet at the Lagrange point between the two stars. Outside the Roche lobes, matter may flow onto either star with relative ease.

The Roche lobes of the two stars meet at a point on the line joining them—the inner Lagrange point (L₁), which we saw in Chapter 14 when discussing asteroid motions in the solar system. (Sec. 14.1) This Lagrange point is a place where the gravitational pulls of the two stars exactly balance the rotation of the binary system. The greater the mass of one component, the larger is its Roche lobe and the farther from its center (and the closer to the other star) is the Lagrange point.

Normally, both stars lie well within their respective Roche lobes, and such a binary system is said to be detached, as in Figure 20.22(a). However, as a star evolves off the main sequence and moves toward the giant branch, it is possible for its radius to become so large that it overflows its Roche lobe. Its gas begins to flow onto the companion through the Lagrange point. The binary in this case is said to be semidetached (Figure 20.22b). Because matter is flowing from one star onto the other, semidetached binaries are also known as mass-transfer binaries. If, for some reason, the other star also overflows its Roche lobe (either because of stellar evolution or because so much extra material is dumped onto it), the surfaces of the two stars merge. The binary system then consists of two nuclear-burning stellar cores surrounded by a single continuous common envelope—a contact binary, shown in Figure 20.22(c).

Figure 20.22 (a) In a detached binary, each star lies within its respective Roche lobe. (b) In a semidetached binary, one of the stars fills its Roche lobe and transfers matter onto the other, which still lies within its own Roche lobe. (c) In a contact or common-envelope binary, both stars have overflowed their Roche lobes, and a single star with two distinct nuclear-burning cores results.

In a binary system in which the two stars are very close together, neither star has to evolve far off the main sequence before it overflows its Roche lobe and mass transfer begins. In a wide binary, however, both stars may evolve all the way up the giant branch without either surface ever reaching the Lagrange point, and they evolve just as though they were isolated. Depending on the stars involved and their orbital separations, there are many different possibilities for the eventual outcome of the evolution. Binary evolution is a very complex subject. Let's make these ideas more definite by returning to the question of how the binary star Algol may have reached its present state.

Astronomers believe that Algol started off as a detached binary. For reference, let us label the component that is now the 0.8—solar mass subgiant as star 1 and the 3.7—solar mass main-sequence star as star 2. Initially, star 1 was the more massive of the two, having perhaps three times the mass of the Sun. It thus evolved off the main sequence first. Star 2 was originally a less massive star, perhaps comparable in mass to the Sun. As star 1 ascended the giant branch it, overflowed its Roche lobe and gas began to flow onto star 2. This had the effect of reducing the mass of star 1 and increasing that of star 2, which in turn caused the Roche lobe of star 1 to shrink as its gravity decreased. As a result, the rate at which star 1 overflowed its Roche lobe increased, and a period of unstable rapid mass transfer ensued, transporting most of star 1's envelope onto star 2. Eventually, the mass of star 1 became less than that of star 2. Detailed calculations show that the rate of mass transfer dropped sharply at that point, and the stars entered the relatively stable state we see today. These changes in Algol's components are illustrated in Figure 20.23.

Figure 20.23 The evolution of the binary star Algol. (a) Initially, Algol was probably a detached binary made up of two main-sequence stars —a relatively massive blue giant and a less massive companion similar to the Sun. (b) As the more massive component (star 1) evolved off the main sequence it expanded to fill and eventually overflow its Roche lobe, transferring large amounts of matter onto its smaller companion (star 2). (c) Today, star 2 is the more massive of the two, but it is on the main sequence. Star 1 is still in the subgiant phase and fills its Roche lobe, causing a steady stream of matter to pour onto its companion.

Being part of a binary system has radically altered the evolution of both stars in the Algol system. The original high-mass star 1 is now a low-mass subgiant, while the roughly solar mass star 2 is now a massive blue main-sequence star. The removal of mass from the envelope of star 1 may prevent it from ever reaching the helium flash. Instead, its naked core may eventually be left behind as a helium white dwarf. In a few tens of millions of years, star 2 will itself begin to ascend the giant branch and fill its own Roche lobe. If star 1 is still a subgiant or a giant at that time, a contact binary system will result. If, instead, star 1 has by then become a white dwarf, a new mass-transferring period—with matter streaming from star 2 back onto star 1—will begin. In that case (as we will see), Algol may have a very active and violent future in store.

Just as molecules exhibit few of the physical or chemical properties of their constituent atoms, binaries can display types of behavior that are quite different from either of their component stars. The Algol system is a fairly simple example of binary evolution, yet it gives us an idea of the sorts of complications that can arise when two stars evolve interdependently. A significant fraction of all the binary stars in the Galaxy will pass through some sort of mass-transfer or common-envelope phase. In this chapter we have seen one possible result of mass transfer involving main-sequence stars. We will return to this subject in the next two chapters, when we continue our discussion of stellar evolution and the strange states of matter that may result.