|MadSci Network: Astronomy|
The great majority of stars lie on the main sequence. The excellent hyperphysics website includes an HR diagram with the main sequence marked. The sequence defines those stars that fuse hydrogen to form helium. Given the preponderence of hydrogen (73% by mass) and helium (25% by mass) in the universe - everything else is only about 2% by mass - it's no wonder that most stars are made of these elements.
A star's position along the narrow sequence depends solely on the mass of the star. More massive stars are positioned at the hotter, brighter and short-lived end of the sequence, while low mass stars are redder, cooler and have longer lifetimes. Stars that don't primarily fuse hydrogen alone (such as old stars like the red giants and white dwarfs) lie away from the main sequence.
As a star ages, its core (where high temperatures and pressures allows fusion to take place) becomes hydrogen-depleted: we can see this on the main sequence as stars move slowly across the narrow sequence (not along it - few star lose enough mass during their lives to substantially travel along the sequence).
For stars like the sun, the increasingly helium-rich core means that hydrogen fusion eventually takes place in a shell of purer hydrogen surrounding the core. The helium core eventually undergoes a helium flash when conditions reach temperatures and pressures where helium can be fused into heavier elements such as carbon.
Only the heaviest and most short-lived stars contain enough mass for conditions in the core to reach the stage at which iron can be fused. These massive stars can eventually resemble onions, where a core of iron is surrounded by layers of lighter-fusing elements, up to a hydrogen-fusing shell. The production of iron is the end of the line for normal energy-producing fusion - elements heavier than iron require energy to be formed and are a net drain on the star. In the universe, these heavier elements (such as silver and gold) are the by-products of supernovae, in which really massive stars explode at the end of their lives.
For all stars, only about 10% of the hydrogen available to fuse is actually used during the lifetime of the star. Some is blown off in solar winds, some in expanding shells of gas that mark the end of many stars' lives on the main sequence, while some never reacts in the inner core of the star (this is a complicated topic: you might wish to Google for resources detailing and modelling stellar convection if you want to follow this up.)
To answer your question: assuming that a massive star had depleted its initial core fuel-stock of hydrogen and had begun the iron-core stage of development, and it was to receive an massive influx of hydrogen (perhaps from a younger, less evolved main sequence star impacting a growing red giant in a close binary system), what would happen?
We can see that the red giant would increase in mass, which might make us think that the influx would simply produce a new, rejuvenated, but metal-rich star "further up" the main sequence. However, any addition of new matter would release a load of potential energy into the red giant, and while we might think that this might prolong the life of the star, the shock to an iron core of a red giant might not be survivable. That said, assuming the star survived receiving a mass of hydrogen, the convective zones around a star (as alluded to earlier) might or might not transfer this fresh hydrogen to depths where new fusion could occur.
As you can see, it's a complicated question, and one with several potential outcomes, partly depending on the size of the star, its age and the means by which new material is added to it. The addition of new material to a star is not well-modelled by astrophysics - current programs modelling "normal" stars throughout their lives often have problems with short-term events (such as the onset of the helium flash, and the processes that lead to supernovae), so in this instance it's not possible to say precisely what might occur.
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