The process of star formation is not well understood but we believe that protostars condense out of the tenuous interstellar gas. With¬out knowing the details we can only make a few general remarks. The material of a typical star smeared out to a typical interstellar density (10~21kgm~3) would occupy a spherical volume about one parsec in radius. Even a very small amount of rotation in a cloud this large would give it a very large angular momentum, so large in fact that during contraction, with angular momentum conservation, the protostar would rotate so fast that the centrifugal force would prevent further gravitational collapse. Since stars manifestly exist there must be some means of disposing of the excess angular momentum. The protostar presumably solves this angular momentum problem by losing angular momentum with a stellar wind or by forming a ring, a binary or multiple star system or a planetary system. Also, in order to become as tightly bound as a star, a protostar must lose a lot of gravitational potential energy. Some of this energy may be radiated away by various cooling pro¬cesses and some of it may go into heating the protostar from inter-stellar-medium temperatures of 100 K to the much higher temperatures of stellar interiors.

An interstellar gas cloud may contain enough material to form several stars or even a star cluster and under certain conditions the cloud will fragment. The fragments will continue contracting, probably fairly rapidly while radiation can leak out easily. When the protostellar cloud becomes largely opaque to its own radiation collapse will proceed more slowly because the internal temperature and pressure start to build up. The cloud will be a dark cloud in the sense that very little optical radiation is emitted. The Ophiucus dark cloud and the Bok globules in Orion may be connected with this phase of evolution. Dust grains in the dark cloud may emit long-wave infrared radiation. Interstellar molecules such as OH, H20 and formaldehyde may be formed by interactions with grains and these molecules may emit maser radiation. The ultimate source of this energy is the gravitational energy release by collapse. The study of protostar evolution is best made at infrared, millimetre and radio wavelengths.

The collapse of an interstellar cloud probably proceeds nonhomologously; that is the central regions collapse faster than the surface ones. The central half of the cloud has contracted to stellar size in a thermal timescale, about 106 yr for a star like the Sun, whereas the outside regions have contracted only a little during this time. When the central region has contracted sufficiently it may become hot enough to commence hydrogen-burning nuclear reactions, the contraction stops, and a star is born. Even before the central nuclear reactions have started burning hydrogen, the protostar is producing a significant amount of energy from gravitational contraction. This energy is being radiated through the cooler in-falling outer layers which absorb much of the blue radiation and reradiate it in the infrared. Indeed even some nuclear reactions occur, mostly of 2H, Li, Be, B, the light elements, which contribute little to the energy but deplete the abundance of these elements

The position that a protostar occupies in the Hertzsprung-Russell diagram is not certain partly because of theoretical problems associated with modifications to the spectrum of the radiation as it passes through the outer layers of the contracting object. After an uncertainrapid phase of evolution the protostar appears to the right of the main sequence as shown in figure 3.3, near the intersection of the Henyey and Hayashi tracks. Henyey and Hayashi were both important contributors to the theory of protostar or pre-main-sequence evolution. The Henyey track is the path that a completely radiative star would follow during protostellar contraction, while the Hayashi track is the same but for a star in which convection is occurring everywhere. At one time each of these tracks was thought to be the route protostars followed to the main sequence, but the realization that the central regions of the contracting protostar collapsed more quickly than the outer layers changed that view. In the latter stages of their contraction protostars probably follow the Henyey track. This is probably what is observed in young stellar clusters, such as NGG 2264, shown in figure 3.11, in which the fainter lower-mass stars above the main sequence are still contracting towards the main sequence, The age of this cluster, as estimated from its main sequence turn-off point, is about 2 x 106yr. The massive stars whose nuclear lifetimes are about 3 x 106yr have (thermal) contraction times of about 104yr.
The contraction time is on the thermal timescale, which is much shorter than the nuclear timescale of a star. In general we do not expect to see a very large proportion of stars in their contracting phase since it is relatively short-lived. However one group of stars, the T Tauri stars, stand out. (See chapter 4 and figure 3.11.) For a variety of reasons these stars, which exhibit peculiar and active spectra including H emission, emit a lot of infrared radiation and are thought to be in a premain-sequence phase. Detailed investigations of their properties may help to unravel the many mysteries remaining in this aspect of stellar evolution

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