It is reasonable to assume that the two stars in a binary system formed at the same time. The chance of a collision between two single stars in the Galaxy is very small; t he chance of the capture of one by another of a different age to form a binary system smaller still. It is, therefore, usual to assume that the two stars formed simultaneously as a binary system and that they began burning their nuclear fuel at the same instant. A more massive star burns its nuclear fuel at a much faster rate than a less massive one and its radius therefore expands at a faster rate as well (figure 5.20). We therefore expect the more massive star to be the first one to fill its Roche lobe and to start transferring mass on to its less massive companion. This initial stage of mass transfer is separated into three types which depend on how far the more massive star has evolved before it has expanded to rill its Roche lobe and mass trans¬fer begins.

If mass transfer begins while the star is still burning hydrogen in its core, the expanding star transfers most of its mass to its companion in a relatively short-lived but possibly spectacular burst of mass flow. By short-lived, we here mean about ten thousand years, that is short compared to the total lifetime of the binary system. 1 he star that was originally less massive is now the more massive one and it becomes a bright main-sequence star with luminosity corresponding to its new mass. The star filling its Roche lobe is now the less massive and continues to burn nuclear fuel and expand slowly, trickling matter on to its companion. What happens next depends on the parameters of the binary system. There are essentially two possibilities:

Either the (now) less-massive star runs out of hydrogen in its core and begins a phase described below.

With this outline of mass transfer we now consider further the Algol system. Algol itself, and a number of similar binary systems, consists of a small bright blue star well inside its Roche lobe and a less massive, but larger, red star that fills its Roche lobe and is losing mass from its surface. Before the process of mass transfer had been studied, astronomers were puzzled by this behaviour, since it seemed that the less massive star had evolved arid expanded to fill its Roche lobe more rapidly than its more massive companion. This seemed flatly to contradict the theories of stellar evolution. The reader may have noticed that the resolution of the paradox is already at hand. The initial burst of mass transfer takes place very rapidly and therefore the probability of our seeing it is correspond¬ingly small. It may be, however, that ? -Lyrae-type systems are examples of this. After this transfer, the now less massive but evolved star continues to trickle matter on to its now more massive, but unevolved,
companion for a considerable length of time. It is this process we are witnessing in Algol-type systems. It is these binaries that give us some confidence that our ideas on mass transfer are at least qualitatively correct.

Now we consider what happens when the hydrogen fuel is exhausted in the core of an evolving star. The core collapses until it has reached a temperature and density at which helium can be burnt. As the core contracts, the outer envelope of the star expands. If the star fills its Roche lobe during this phase of expansion, another kind of mass transfer begins. This case is relatively easier to understand because once the star has formed a dense helium-burning core (and therefore becomes a red giant), this core is fairly oblivious of how much material is in the diffuse envelope surrounding it. Therefore as much of this envelope is lost as is necessary to bring the star completely within the Roche lobe .If the helium core is less than about four solar masses it is able, eventually, to become a white dwarf once nuclear burning has ceased. The binary system then consists of a massive bright main-sequence star (which was originally the less massive but is now rejuvenated by acquiring matter from its companion) and a less massive white dwarf. We note that Sirius is just such a system – Sirius A is a 2.25 solar mass main-sequence star and Sirius B is a white dwarf of about one solar mass. If the helium core is more than about four solar masses it probably cannot shed enough mass to become a white dwarf and may well eventually collapse to form a neutron star or a black hole.

When a star, now a red giant, has exhausted its helium fuel, its core collapses until carbon burning can start. If mass transfer begins during the corresponding expansion of the stellar envelope, when the outer layers are now diffuse, very little energy is required to drive the mass transfer and the flow takes place very rapidly. The subsequent history of such systems is uncertain. It is probably similar in many respects to that described in the previous Paragraph.

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