When stars which have a Main Sequence lifetime less than the current age of the Universe get old and die, they swell up to become red giants or supergiants. In this process their surface gravities become much lower, and the convective motions in their outer layers drive part of their outer layers into space, which can reduce their masses by a substantial amount during the last stages of their life.
If the giant star is a single star such as the Sun, all that happens as a result of the mass loss is that it becomes less massive and ends its red giant lifetime and its life as a whole a little sooner. But if it is a member of a binary star system, as almost half the stars are, then there can be a transfer of mass from the dying star to its companion, resulting in a number of interesting possibilities.
When the other star is a Main Sequence star
the transfer of mass increases the weight compressing the core of the smaller star, and as the core becomes denser and hotter its nuclear reactions go faster and faster, producing an ever larger amount of heat, and making the star swell up to a larger hotter brighter structure which corresponds to its now larger mass. In other words it remains a Main Sequence star, but moves up the Main Sequence to a position corresponding to its new mass. This sort of thing must have happened to the star Sirius, which is the brightest star in our sky other than the Sun, partly because it is one of the closest stars to our Sun, and partly because it is a little over twice the mass and twenty times the brightness of the Sun. Such stars only last about two billion years as Main Sequence stars, but Sirius has a companion, Sirius B, which is a white dwarf about the same mass as the Sun. Since a star like the Sun can last for over ten billion years as a Main Sequence star, it is impossible for the less massive star to have already died, while the more massive star still lives. At one time the star which is now less massive must have been the more massive one, and as it grew old it swelled up, dumped material onto its companion, and in the process became a less massive star, while its companion became a more massive one.
But suppose that the companion is not a Main Sequence star
, but a white dwarf, the most common type of dead stellar object we know about. In this case, as the dying star transfers material to the white dwarf the nuclear reactions in its core will not go faster, because white dwarfs cannot have any nuclear reactions inside them. In a normal star, if nuclear reactions go a little too fast, the gas will heat up, increase its and expand, which reduces the temperature and damps down the nuclear reactions, forcing them toward a value closer to the average heat loss of the core. If the nuclear reactions go too slowly the gas will cool off, decrease its pressure and contract, which will increase the temperature and increase the nuclear reactions. In either casenthe relationship between temperature and pressure which applies to normal gases will guarantee that the nuclear reactions cannot go too fast or too slow, at least on the average. But in the electron-degenerate material which makes up a white dwarf, pressure and temperature are not linked. If nuclear reactions go too fast the temperature will rise, but the pressure will not be significantly changed, and the increase in temperature will simply make the nuclear reactions go faster and faster until, as in a chain reaction, the region which contains nuclear fuel simply undergoes a catastrophic explosion. (Note: This is discussed in the text under such topics as the Helium Flash which occurs during the red giant lifetime of the Sun.)
Because of this it is not possible for a white dwarf to have any nuclear burning going on inside it. So when new material is dumped onto the surface of the star by a companion the mass of the star increases and the pressure inside the star increases, but otherwise, nothing much happens, at least for a while. Over a long period of time, however, as more and more material is dumped onto the star, the pressures and temperatures within the electron-degenerate gas do begin to rise, and if they reach values where nuclear burning can begin, will result in an explosion of considerable violence.
How violent the explosion is depends upon the size and mass of the white dwarf. Since white dwarfs, unlike Main Sequence stars, are smaller the more massive they are, a white dwarf with a mass near but not too near the limit of mass for white dwarfs (the Chandrasekhar Limit) will be relatively small and have a relatively large gravity. This means that material falling onto the star will very quickly reach high pressures and temperatures, and so only a little material will accumulate before an explosion occurs, and the explosion will be 'relatively' minor. This is believed to be the reason for so-called recurrent novae
, such as RS Ophiuchi (shown below). Over a period of a few dozens to a few hundreds of years material piles up on a massive white dwarf then explodes, making the object millions of times brighter for a short while. After the explosion is over more material has to accumulate before another explosion can take place, and so there will be another few decades or centuries before the nova recurs. (For white dwarfs with masses extremely close to the Chandrasekhar Limit
, see the note following neutron stars, below.)