The Main Sequence Phase

The main sequence phase is that evolutionary stage in which the energy released by the burning of hydrogen in the core is the only source of stellar energy. During this stage, the star is in stable equilibrium, and its structure changes only because its chemical composition is gradually altered by the nuclear reactions. Thus the evolution takes place on a nuclear time scale, which means that the main sequence phase is the longest part of the life of a star. For example, for a solar mass star, the main sequence phase lasts for about 10,000 million years. More massive stars evolve more rapidly, because they radiate much more power. Thus the main sequence phase of a 15 solar mass star is only about 10 million years. On the other hand, less massive stars have a longer main sequence lifetime: a 0.25 Me star spends about 70,000 million years on the main sequence.

11.3 The Main Sequence Phase

Since stars are most likely to be found in the stage of steady hydrogen burning, the main sequence in the HR diagram is richly populated, in particular at its low-mass end. The more massive upper main sequence stars are less abundant because of their shorter main sequence lifetimes.

If the mass of a star becomes too large, the force of gravity can no longer resist the radiation pressure. Stars more massive than this upper limit cannot form, because they cannot accrete additional mass during the contraction phase. Theoretical computations give a limiting mass of about 120 Me; the most massive stars observed are claimed to be about 150 Me.

There is also a lower-mass limit of the main sequence. Stars below 0.08 Me never become hot enough for hydrogen burning to begin. They can still generate some luminosity from the burning of deuterium, but this energy source is rapidly exhausted. These brown dwarfs have surface temperatures in the range of 1000-2000 K Hundreds of brown dwarfs have now been found in dedicated surveys. The lower limit for brown dwarf mass is sometimes taken to be about 0.015, Me, corresponding to the minimum mass for deuterium burning.

If the mass is even lower there are no nuclear sources of energy. The smallest protostars therefore contract to planet-like dwarfs. During the contraction phase they radiate because potential energy is released, but eventually they begin to cool. In the HR diagram such stars first move almost vertically downwards and then further downwards to the right.

Is there a difference between the lowest-mass brown dwarfs and the most massive planets? If brown dwarfs have formed by gravitational collapse and fragmentation as described in the previous section and in Abschn. 15.4, there is no reason not to count them as stars, although they are not producing energy by nuclear reactions. Planets in contrast are thought to form much more slowly by the clumping of solids and accretion of gas in a protoplanetary disc. The objects formed by this mechanism start out with a quite different structure. Whether such a clear-cut distinction between the formation mechanisms of dark stars and planets really can be made still remains an open question.

The Upper Main Sequence. The stars on the upper main sequence are so massive and their central temperature so high that the CNO cycle can operate. On

the lower main sequence the energy is produced by the pp chain. The pp chain and the CNO cycle are equally efficient at a temperature of 18 million degrees, corresponding to the central temperature of a 1.5 Me star. The boundary between the upper and the lower main sequence corresponds roughly to this mass.

The energy production in the CNO cycle is very strongly concentrated at the core. The outward energy flux will then become very large, and can no longer be maintained by radiative transport. Thus the upper main sequence stars have a convective core, i.e. the energy is transported by material motions. These keep the material well mixed, and thus the hydrogen abundance decreases uniformly with time within the entire convective region.

Outside the core, there is radiative equilibrium, i. e. the energy is carried by radiation and there are no nuclear reactions. Between the core and the envelope, there is a transition region where the hydrogen abundance decreases inwards.

The mass of the convective core will gradually diminish as the hydrogen is consumed. In the HR diagram the star will slowly shift to the upper right as its luminosity grows and its surface temperature decreases (Fig. 11.3). When the central hydrogen supply becomes exhausted, the core of the star will begin to shrink rapidly. The surface temperature will increase and the star will quickly move to the upper left. Because of the contraction of the core, the temperature in the hydrogen shell just outside the core will increase. It rapidly becomes high enough for hydrogen burning to set in again.

The Lower Main Sequence. On the lower main sequence, the central temperature is lower than for massive stars, and the energy is generated by the pp chain. Since the rate of the pp chain is not as sensitive to temperature as that of the CNO cycle, the energy production is spread over a larger region than in the more massive stars (Fig. 11.4). In consequence, the core never becomes convectively unstable, but remains radiative.

In the outer layers of lower main sequence stars, the opacity is high because of the low temperature. Radiation can then no longer carry all the energy, and convection will set in. The structure of lower main sequence stars is thus opposite to that of the upper main sequence: the centre is radiative and the envelope is convective. Since there is no mixing of material in

Fig. 11.3. Stellar evolutionary paths in the HR diagram at the main sequence phase and later. On the main sequence, bounded by dashed curves, the evolution is on the nuclear time scale. The post-main sequence evolution to the red giant phase is on the thermal time scale. The point marked He corresponds to helium ignition and in low-mass stars the helium flash. The straight line shows the location of stars with the same radius. (Iben, I. (1967): Annual Rev. Astron. Astrophys. 5, 571; data for 30 Me from Stothers, R. (1966): Astrophys. J. 143, 91)

the core, the hydrogen is most rapidly consumed at the very centre, and the hydrogen abundance increases outwards.

As the amount of hydrogen in the core decreases, the star will slowly move upwards in the HR diagram, almost along the main sequence (Fig. 11.3). It becomes slightly brighter and hotter, but its radius will not change by much. The evolutionary track of the star will then bend to the right, as hydrogen in the core nears its end. Eventually the core is almost pure helium. Hydrogen will continue to burn in a thick shell around the core.

Stars with masses between 0.08 MQ and 0.26 Me have a very simple evolution. During their whole main sequence phase they are fully convective, which means

Fig. 11.4a-c. Energy transport in the main sequence phase. (a) The least massive stars (M < 0.26 Mq) are convec-tive throughout. (b) For 0.26 Mq < M < 1.5 Mq the core is radiative and the envelope convective. (c) Massive stars (M > 1.5 Mq) have a convective core and a radiative envelope that their entire hydrogen content is available as fuel. These stars evolve very slowly toward the upper left in the HR diagram. Finally, when all their hydrogen has burned to helium, they contract to become white dwarfs.

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