The Contraction of Stars Towards the Main Sequence

The formation and subsequent gravitational collapse of condensations in the interstellar medium will be considered in a later chapter. Here we shall follow the behaviour of such a protostar, when it is already in the process of contraction.

When a cloud contracts, gravitational potential energy is released and transformed into thermal energy of the gas and into radiation. Initially the radiation can propagate freely through the material, because the density is low and the opacity small. Therefore most of the liberated energy is radiated away and the temperature does not increase. The contraction takes place on the dynamical time scale; the gas is falling freely inwards.

The density and the pressure increase most rapidly near the centre of the cloud. As the density increases, so does the opacity. A larger fraction of the released energy is then turned into heat, and the temperature begins to rise. This leads to a further increase in the pressure that is resisting the free fall. The contraction of the central part of the cloud slows down. The outer parts, however, are still falling freely.

At this stage, the cloud may already be considered a protostar. It consists mainly of hydrogen in molec ular form. When the temperature reaches 1800 K, the hydrogen molecules are dissociated into atoms. The dissociation consumes energy, and the rise in temperature is slowed down. The pressure then also grows more slowly and this in turn means that the rate of contraction increases. The same sequence of events is repeated, first when hydrogen is ionized at 104 K, and then when helium is ionized. When the temperature has reached about 105 K, the gas is essentially completely ionized.

The contraction of a protostar only stops when a large fraction of the gas is fully ionized in the form of plasma. The star then settles into hydrostatic equilibrium. Its further evolution takes place on the thermal time scale, i. e. much more slowly. The radius of the protostar has shrunk from its original value of about 100 AU to about 1 /4 AU. It will usually be located inside a larger gas cloud and will be accreting material from its surroundings. Its mass therefore grows, and the central temperature and density increase.

The temperature of a star that has just reached equilibrium is still low and its opacity correspondingly large. Thus it will be convective in its centre. The convective energy transfer is quite efficient and the surface of the protostar will therefore be relatively bright.

We now describe the evolution in the HR diagram. Initially the protostar will be faint and cool, and it will reside at the lower far right in the HR diagram (outside Fig. 11.1). During the collapse its surface rapidly heats up and brightens and it moves to the upper right of Fig. 11.1. At the end of the collapse the star will settle at a point corresponding to its mass on the Hayashi track. The Hayashi track (Fig. 11.1) gives the location in the HR diagram of completely convective stars. Stars to its right cannot be in equilibrium and will collapse on the dynamic time scale.

The star will now evolve almost along the Hayashi track on the thermal time scale. In the HR diagram it moves almost vertically downwards, its radius decreases and its luminosity drops (Fig. 11.1). As the temperature goes on increasing in its centre, the opacity diminishes and energy begins to be transported by radiation. The mass of the radiative region will gradually grow until finally most of the star is radiative. By then the central temperature will have become so large that nuclear reactions begin. Previously all the stellar energy had been released potential energy, but now the nuclear reactions make a growing contribution and the luminosity

11.2 The Contraction of Stars Towards the Main Sequence

Hayashi Track
Fig. 11.1. The paths in the HR diagram of stars contracting to the main sequence on the thermal time scale. After a rapid dynamical collapse the stars settle on the Hayashi track and evolve towards the main sequence on the thermal time scale. (Models by Iben, I. (1965): Astrophys. J. 141, 993)

increases. The stellar surface temperature will also increase and the star will move slightly upwards to the left in the HR diagram. In massive stars, this turn to the left occurs much earlier, because their central temperatures are higher and the nuclear reactions are initiated earlier.

For solar mass stars, the rapid collapse of the proto-stellar cloud only lasts for a few hundred years. The final stage of condensation is much slower, lasting several tens of millions of years. This length of time strongly depends on the stellar mass because of the luminosity dependence of the thermal time scale. A15 M0 star condenses to the main sequence in 60,000 years, whereas for a 0.1 M0 star, the time is hundreds of millions of years.

Some of the hydrogen burning reactions start already at a few million degrees. For example, lithium, beryllium and boron burn to helium in the ppII and ppIII branches of the pp chain long before the complete chain has turned on. Because the star is convective and thus

Fig. 11.2. Herbig-Haro object number 555 lies at the end of the "elephant's trunk" in Pelican Nebula in Cygnus. The small wings are shockwaves, which give evidence for powerful outflows from newly formed stars embedded within the clouds. (Photo University of Colorado, University of Hawaii and NOAO/AURA/NSF)

Fig. 11.2. Herbig-Haro object number 555 lies at the end of the "elephant's trunk" in Pelican Nebula in Cygnus. The small wings are shockwaves, which give evidence for powerful outflows from newly formed stars embedded within the clouds. (Photo University of Colorado, University of Hawaii and NOAO/AURA/NSF)

well mixed during the early stages, even its surface material will have been processed in the centre. Although the abundances of the above-mentioned elements are small, they give important information on the central temperature.

The beginning of the main sequence phase is marked by the start of hydrogen burning in the pp chain at a temperature of about 4 million degrees. The new form of energy production completely supersedes the energy release due to contraction. As the contraction is halted, the star makes a few oscillations in the HR diagram, but soon settles in an equilibrium and the long, quiet main sequence phase begins.

It is difficult to observe stars during contraction, because the new-born stars are usually hidden among dense clouds of dust and gas. However, some condensations in interstellar clouds have been discovered and near them, very young stars. One example are the TTauri stars. Their lithium abundance is relatively high, which indicates that they are newly formed stars in which the central temperature has not yet become large enough to destroy lithium. Near the T Tauri stars, small, bright, star-like nebulae, Herbig-Haro objects, have been discovered. These are thought to be produced in the interaction between a stellar wind and the surrounding interstellar medium.

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