how does the evolution finally stops of the star
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Answer:
A star remains on the main sequence as long as there is hydrogen in its core that it can fuse into helium. So far we have assumed that a star on the main sequence maintains a constant energy output. In fact, as a main sequence star ages its luminosity increases slightly, resulting in it expanding and its outer layer cooling. This explains why the main sequence is a broad band rather than a narrow line - stars move up and to the right on this band as they age.
Eventually the hydrogen fuel in the core runs out and fusion stops, shutting off the outward radiation pressure. Inward gravitational attraction causes the helium core to contract, converting gravitational potential energy into thermal energy. Although fusion is no longer taking place in the core, the rise in temperature heats up the shell of hydrogen surrounding the core until it is hot enough to start hydrogen fusion, producing more energy than when it was a main sequence star. This so-called shell-burning causes some interesting effects.
Hydrogen shell-burning in a one-solar mass star as it starts to move up the red giant branch.
The new, increased radiation pressure actually causes the outer layers of the star to expand to maintain the pressure gradient. As the gas expands it cools, just as a spray can feels colder after use as the gas has been released. This expansion and cooling causes the effective temperature to drop. Convection transports the energy to the outer layers of the star from the shell-burning region. The star's luminosity eventually increases by a factor of 1000 × or so. During this stage of expansion, the star will move up and to the right on the HR diagram along the Red Giant Branch (RGB). A G (V)-class star may end up as a high-K or low-M luminosity class III giant.
A red giant displays extremes of density. The outer envelope is grossly extended and thus at a density below that of a vacuum on Earth. It is only weakly held by gravitational force to the rest of the star and easily ejected. Mass loss from a giant is typically about 10-7 solar masses per year, compared with only 10-17 solar masses per year currently for the Sun. Whilst the envelope is tenuous and cool, the contracted helium core is incredibly dense. It is only about one-third its original size. Electrons within the core form a degenerate electron gas, they are packed tightly together in a volume governed only by the uncertainty principle. In this state it no longer behaves as an ideal gas.
Comparison in size of Sun as a main sequence star and as a red giant.
When the Sun becomes a red giant its radius will be approximately 0.5 AU, that is about 100 × its current size.