The evolution of a protostar from being an isolated fragment of an interstellar cloud to becoming a main-sequence star takes hundreds of thousands or even millions of years; astronomers attempting to follow this process must therefore resort to computer calculations rather than direct observations. These calculations are very complicated since they involve estimating simultaneously the density, temperature, velocity, and heat flow in every part of a continually-changing cloud. For this reason, only the simplest protostar models have been considered – namely spherical ones with no rotation or magnetic field. Another difficulty is that the evolution of a protostar depends somewhat on its shape, temperature, and density immediately after its last fragmentation, and since we do not yet have a proper theory of fragmentation, we are forced to start the calculations from conditions which are little more than intelligent guesswork.

The simplest case that has been calculated is that of a 1 MO protostar collapsing from a uniform cloud with an initial density of 6 x 1010 atoms m-3, a temperature of 10K, and a radius of 0.05 pc. As the gravitational forces in the cloud start the collapse, the density at the centre begins to increase. At first the increase is fairly gentle, but after 400000 years the density and temperature at the centre both rise dramatically and a hot core region is formed within the protostar. This core soon itself collapses, forming the nucleus of the future star, and, for another 100000 years the mass of this nucleus steadily increases as the remainder of the protostar falls onto it. The overall appearance of the protostar on an HR diagram is indicated .in When, after 400000 years, the nucleus of the protostar forms, the object appears at point A, with a luminosity about equal to the Sun, but a very 1OW temperature – less than a hundred Kelvins. As the nucleus grows the protostar becomes hotter and more luminous, moving across the HR diagram approximately from A to B. The evolution from B to the main sequence (point C) is very much slower, and takes about 5 x 107 years. During this stage of evolution] (sometimes called the pre-main-sequence or PMS stage), the star as a whole contracts while its centre becomes steadily hotter. When its central temperature reaches about 107K, thermonuclear conversion of hydrogen to helium can begin, and the star can take its place on the main sequence.

Stars more massive than the Sun evolve more rapidly and in a different way. shows the evolution of a protostar which starts off with 60 M0. A nucleus forms in much the same way as for a single solar mass star (point D), but it now grows so quickly that after only 20000 years (point E) it is hot enough for thermonuclear reactions to start. The nucleus now somewhat resembles a main-sequence star except that it is surrounded by the thick gas and dust outer layer of the protostar. The mass and luminosity of the nucleus increase as matter continues to fall on’ ^ until after another 2500 years (point P) the nucleus is so bright that radiation pressure acts to stop any more matter falling inwards. Consequently some 43M0 of the original 60M0 cloud is expelled back into space, and a 17M0 remnant is left behind which, after a very brief luminous period (region G), becomes a normal main-Sequence O star (H).

If a cloud is rotating as it collapses to form a star, the law of conservation of angular momentum requires that the speed of this rotation increases as the cloud becomes smaller. This effect can be very large and is an obstacle to star formation, since a rotational speed increase of a million could be expected during the collapse of a protostar “from a 0.1-pc diameter cloud to a star like the Sun. This rotation leads to centrifugal forces which tend to oppose the contraction of the protostar. As a result of turbulence and of galactic rotation, all interstellar clouds probably possess enough rotation to prevent collapse to stars unless there ip some way of reducing their angular momentum. One way in which a protostar can lose angular momentum is to divide itself into two or more pieces which revolve around each other — in other words it can form a binary or a multiple system. The fact that binary systems are very common emphasizes the importance of this process, but as yet the problem of the evolution of a proto-binary star is nowhere near solved.

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