STELLAR EVOLUTION is the study of how a star changes with time. There are three important distinct timescales on which a star may change. These are dynamical, thermal and nuclear timescales.

The DYNAMICAL TIMESCALE is the time it would take for the whole star to feel seriously and to react to an absence “of-pressure support. It is the time it takes a sound wave, or pressure wave moving at the speed of sound, to cross a star

The THERMAL TIMESCALE (or KBLVIN-HBLMHOLTZ TIMBSCALE) IS the time it takes for the whole star to feel seriously an absence of thermal equilibrium. It is the time it takes energy to diffuse from the centre to the surface, and it is equivalently the time it takes for the star to radiate away a significant amount of its thermal or heat energy

The NUCLEAR TIMESCALE is the time it takes for significant changes of chemical composition to occur in a star on account of nuclear transmutation, and the time for a significant amount of the nuclear fuel to be converted into energy. In this equation one tenth of the total mass (0.1M) is usually taken for a significant amount of fuel and s is the energy release per kg (6 X 1014 joules kg-1 for conversion of hydrogen to helium).

These timescales are purposely left a little imprecise as they are designed only to give rough estimates. The important fact is that the three timescales are very different, and this is a useful feature when making computer simulations of stellar evolution. For example, when we consider the pulsations of a Cepheid variable star, which take place on a timescale of days, it is not necessary to worry about any nuclear evolution of the central regions as that only changes significantly on a much longer timescale. Conversely when considering the long-timescale nuclear evolution of the central regions of a Cepheid, the short-term outer layer pulsations can be averaged over, as a great many will occur while the interior changes only slightly.

When thinking about the evolution of stars one must keep in mind two factors: (i) the timescale on which physical conditions are changing and (ii) the source of the stellar energy.

The main part and the longest part of the life of nearly all stars is their MAIN-SEQUENCE PHASE, during which they convert hydrogen into helium on a nuclear timescale. Most stars spend a major part of their lives in the main-sequence phase; this fact accounts for the well-populated main-sequence band in the Hertzsprung-Russell diagram. The main-sequence lifetime of a star is essentially the time that it takes to process all the hydrogen in the core to helium. Only the core is hot enough for the occurrence of the nuclear reactions. The remainder of a star’s life is relatively short in comparison to the main-sequence time, typically about 20 per cent. The actual life¬time of a star on the main sequence depends on the amount of its nuclear fuel and the rate at which it is consumed. The amount of fuel depends on M, the mass, and the rate of consumption on L, the luminosity. The lifetime therefore depends on the quantity M/L. From two forms of the mass-luminosity law we see that the lifetime is proportional to 1/M2 or 1/M3’5 on substituting M3 or M4’5 for L in M/L. Therefore higher-mass stars have shorter lives; to be sure, they have more nuclear fuel available but they consume it faster.

We have now reached the point in our story where we can ex¬plain a feature of the observed Hertzsprung- Russell diagram for star clusters. Let us consider a star cluster, in which initially all stars of different masses were burning hydrogen in their cores. The Hertzsprung-Russell diagram of such a cluster would then consist of a main sequence, with the more massive, more luminous stars at the top end. There would be no red-giant stars to start with. As time proceeds, the higher-mass, more luminous stars exhaust their central hydrogen. The adjustments that then take place in the star’s structure cause it to move away from the main sequence. The stars peel off the top of the main sequence first. The point in the Hertzsprung-Russell diagram of a cluster where stars are just Raving the main sequence is called the TURN-OFF POINT of the cluster main sequence. Observations of where it is can be used as an estimate of the age of a star cluster; the age is such that stars of and luminosity above the turn-off have had time to evolve 3.10 clearly shows the effect of age.

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