Close Binary Systems ( Binary Stars)
As a star evolves and burns its nuclear fuel its radius slowly in-creases If, therefore, the star is in a binary system it is possible for it, during the course of evolution, to swell up and inter¬act with and possibly even to engulf a companion star. If the two stars are near enough together for this possibility to occur we call them a CLOSE BINARY SYSTEM. When we consider the evolution of a single star we can assume, for the most part, that the mass of the star is a constant. We see immediately that the evolution of stars in close binary systems is fraught with additional complications, since it is possible for matter to be transferred from one star to another. Before proceeding further we consider more precisely the manner in which the two stars interact.
A single star is spherical; in other words, the equipotential surfaces (that is, surfaces over which the gravitational field is constant) around a point mass are spheres. To see this more clearly, imagine that space can be represented by a stretched rubber sheet (we sup¬press the third dimension for the moment). A point mass stretches to form a POTENTIAL WELL. We may imagine a star as being a point mass surrounded by a massless fluid. Then however much fluid is put into the potential well, the surface of the fluid is always a circle. If we could imagine the same process in three dimensions with the ‘sheet’ being stretched in the fourth dimension, the surface would be a sphere contours of the well. known as the EQUIPOTENTIAL SURFACES.
When two stars are close to each other it is clear that the i q potential surfaces cannot he spheres. The gravitational potential well of each star interferes with that of the other. The shapes of the equipotential surfaces in this case were first calculated by Roche and they are therefore known as the ROCHE POTENTIALS. We see that close to each mass point the surfaces are almost spherical, and that as we start to fill the wells with our massless fluid the stars are initially almost spheres. Such a system is called a DETACHED BINARY SYSTEM. If the stars eclipse they give rise to the Algol-type light curve described above.
If we continue to fill one of the wells we find that the surfaces become less spherical and the star more distorted. Eventually the star cannot get any larger; it starts spilling matter on to its companion at the INNER LAGRANGIAN POINT, marked L1 .If such a distorted star is eclipsed it gives rise to the ? -Lyrae-type light curve. We call this type a semi-detached binary system; the star which is losing mass is said to fill its ROCHE LOBE. The material tipped off the surface of the star starts to fall towards the companion, but, because the system is rotating, it is deflected by Coriolis force. The path it follows This gas stream from the larger star may either strike the companion star directly, or orbit the star until it strikes itself. In the latter case it interacts with itself to form a ring or a disc around the companion star.These circumstellar rings are observed in many systems .In the dwarf novae it is possible to see a luminous patch called the hot spot, where the incoming gas stream crashes into theTBBF In certain binary systems the disc can emit intense X-ray radiation.
If we continue to fill both of the potential wells, we find even¬tually that the stars are immersed in a common envelope of gas. We term this type of binary a CONTACT BINARY, of which the prototype is W Ursae Majoris. If the filling process continues we see that the system must spill matter eventually, through the outer Lagrangian point L2