The evolution of a cloud of interstellar gas depends on a balance between internal gravitational forces tending to make it contract and thermal pressure tending to make it expand. James Jeans, in 1926, first showed that a cloud of given temperature and density can collapse only if its mass is above a certain minimum value. Large, dense, cool clouds contract, while small, low density, warm ones expand. The Jeans mass (Mj) can be calculated in solar units from a simple formula :

Mj > 3 x 104 -v/T3/n solar masses

The density of the cloud (n) is expressed as the number of hydrogen atoms per cubic meter, while the temperature (T) is measured in Kelvins. The Jeans mass as calculated for various components of the interstellar medium.

The fact that the Jeans mass for these different types of cloud is much more than the mass of a typical star (1MO) explains why stars generally form in groups; only large accumulations of gas have sufficient gravitational pressure to contract. Since the Jeans mass in the first line of the table is larger than any collection of stars in the Galaxy, it is clear that stars do not form out of the intercloud medium. On the other hand the Jeans mass for atomic clouds 3000 M0, corresponds to the typical mass of an open cluster or association, suggesting that it is out of such regions of interstellar space that new stars begin to form. Smaller groups oi stare can subsequently be formed in dark clouds.

The metamorphosis of an interstellar cloud into a cluster of stars must involve the breaking up of the cloud into smaller pieces as it collapses. This process is called FRAGMENTATION and can also be explained by the simple theory of collapse under gravity. As a cloud collapses, its density must increase as its radius decreases. A 3000 M0 cloud such as the one in table 14.1 would start with a diameter of 13 pc. Over a period of some 10 million years it would collapse to about 3pc, increasing its density from 108 m-3 to 1010 atoms m-3. The Jeans mass for a cloud with density 1010 atoms m-3 and the same temperature is only 300 M0, so it would be possible for small fragments of the cloud to collapse themselves, and for the cloud to separate into up to ten pieces. The fragmentation process would then continue , with each fragment having the possibility of subsequently breaking into yet smaller fragments as its density increases and its Jeans mass gets less.

The process of fragmentation can only take place if the temperature of the cloud stays cool. In a low-density cloud, heat can easily escape, but as the fragments become denser and denser the heat is trapped by the dust in the fragments, and their temperatures start to rise. A fragment then no longer breaks up into smaller fragments but becomes instead a PROTOSTAR. One of the current unsolved problems hi astrophysics is to predict into how many pieces a cloud will fragment at each stage in its collapse. The importance of this calculation is that it is the fragmentation process which primarily determines the ratio of the numbers of each different type of star in the Galaxy.

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