The Evolution of Close Binary Stars

If the components of a binary star are well separated, they do not significantly perturb one another. When studying their evolution, one can regard them as two single stars evolving independently, as described above.

Fig. 11.9a-c. The types of close binary systems: (a) detached,

(b) semidetached and

(c) contact binary

Fig. 11.9a-c. The types of close binary systems: (a) detached,

(b) semidetached and

(c) contact binary

However, in close binary pairs, this will no longer be the case.

Close binary stars are divided into three classes, as shown in Fig. 11.9: detached, semidetached and contact binaries. The figure-eight curve drawn in the figure is an equipotential surface called the Roche surface. If the star becomes larger than this surface, it begins to lose mass to its companion through the waist of the Roche surface.

During the main sequence phase the stellar radius does not change much, and each component will remain within its own Roche lobe. When the hydrogen is exhausted, the stellar core will rapidly shrink and the outer layers expand, as we have seen. At this stage a star may exceed its Roche lobe and mass transfer may set in.

Close binary stars are usually seen as eclipsing binaries. One example is Algol in the constellation Perseus. The components in this binary system are a normal main sequence star and a subgiant, which is much less massive than the main sequence star. The sub-giant has a high luminosity and thus has apparently already left the main sequence. This is unexpected, since the components were presumably formed at the same time, and the more massive star should evolve more rapidly. The situation is known as the Algol paradox: for some reason, the less massive star has evolved more rapidly.

In the 1950's a solution to the paradox proposed that the subgiant was originally more massive, but that it had lost mass to its companion during its evolution.

11.7 Comparison with Observations

2 Mq j

1 Mq

>--o

2 i ^----

1

r

xo;

Fig. 11.10a-f. Evolution of a low-mass binary: (a) both components on the main sequence; (b) mass transfer from the more massive component; (c) light subgiant and massive main sequence star; (d) white dwarf and main sequence star; (e) mass transferred to the white dwarf from the more massive component leads to nova outbursts; (f) the white dwarf mass exceeds the Chandrasekhar mass and explodes as a type I supernova

Since the 1960's mass transfer in close binary systems has been much studied, and has turned out be a very significant factor in the evolution of close binaries.

As an example, let us consider a close binary, where the initial masses of the components are 1 and 2 solar masses and the initial orbital period 1.4 days (Fig. 11.10). After evolving away from the main sequence the more massive component will exceed the Roche limit and begin to lose mass to its companion. Initially the mass will be transferred on the thermal time scale, and after a few million years the roles of the components will be changed: the initially more massive component has become less massive than its companion.

The binary is now semidetached and can be observed as an Algol-type eclipsing binary. The two components are a more massive main sequence star and a less massive subgiant filling its Roche surface. The mass transfer will continue, but on the much slower nuclear time scale. Finally, mass transfer will cease and the less massive component will contract to a 0.6 Me white dwarf.

The more massive 2.4 Me star now evolves and begins to lose mass, which will accumulate on the surface of the white dwarf. The accumulated mass may give rise to nova outbursts, where material is ejected into space by large explosions. Despite this, the mass of the white dwarf will gradually grow and may eventually exceed the Chandrasekhar mass. The white dwarf will then collapse and explode as a type I supernova.

As a second example, we can take a massive binary with the initial masses 20 and 8 Me and the initial period 4.7 days (Fig. 11.11). The more massive component evolves rapidly, and at the end of the main sequence phase, it will transfer more than 15 Me of its material to the secondary. The mass transfer will occur on the thermal time scale, which, in this case, is only a few ten thousand years. The end result is a helium star, having as a companion an unevolved main sequence star. The properties of the helium star are like those of a Wolf-Rayet star.

Helium continues to burn to carbon in the core of the helium star, and the mass of the carbon core will grow. Eventually the carbon will be explosively ignited, and the star will explode as a supernova. The consequences of this explosion are not known, but let us suppose that a 2 Me compact remnant is left. As the more massive star expands, its stellar wind will become stronger, giving rise to strong X-ray emission as it hits the compact star. This X-ray emission will only cease when the more massive star exceeds its Roche surface.

The system will now rapidly lose mass and angular momentum. A steady state is finally reached when the system contains a 6 Me helium star in addition to the 2 Me compact star. The helium star is seen as a Wolf-Rayet star, which, after about a million years, explodes as a supernova. This will probably lead to the breakup of the binary system. However, for certain values of the mass, the binary may remain bound. Thus a binary neutron star may be formed.

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