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Protostar

The protostar period is the period in the evolution of a star after the cloud of hydrogen, helium and dust has started contraction and before the star has reached the main sequence on the Hertzsprung-Russell diagram.

Protostars of around the mass of the Sun typically take 10 million years to evolve from a condensing cloud to a main-sequence star. A protostar of 15 solar masses evolves much more quickly, typically taking only 100,000 years to reach the main sequence.

A protostar forms from the contraction of a dense cloud[?] of interstellar medium. Most of the clouds of interstellar medium are in a state of equilibrium - the force of gravity is balanced by the thermal kinetic energy[?] of the constituent atoms or molecules of the cloud.

Any disturbance to the cloud may upset its state of equilibrium. Examples of disturbances are shock waves from supernovae; spiral density waves[?] within galaxies and the close approach or collision of another cloud. Whatever the source of the disturbance, if it is sufficiently large it may cause the force due to gravity to become greater than the force due to thermal kinetic energy within a particular region of the cloud.

The British physicist Sir James Jeans[?] considered the above phenomenon in detail. He was able to show that, under appropriate conditions, a cloud, or part of one, would start to contract as described above. He derived a formula for calculating the mass and size that a cloud would have to reach as a function of its density and temperature before gravitational contraction would begin. This critical mass is known as the Jeans mass. It is given by the following formula:

$M_j = \frac{9}{4} * \left( \frac{1}{2 \pi n} \right) ^ \frac{1}{2} * \frac{1}{m ^ 2} * \left( \frac{kT}{G} \right) ^ \frac{3}{2}$

where n is the particle number density, m is the mass of the 'average' gas particle in the cloud and T is the gas temperature.

 Fragmentation

Stars are often found in groups known as clusters which appear to have formed at around the same time. This can be explained if it is assumed that as a cloud contracts it does not do so uniformly. As it contracts it is almost certain to break up into areas which continue to contract into individual protostars. This could be due to a number of different reasons. The cloud almost certainly will not be exactly the same density in all areas, denser areas contracting slightly faster than less dense areas. The cloud may be also be rotating.

Whatever the reason, the cloud breaks up unto smaller, denser areas which may again break into still smaller areas - the outcome being a cluster of protostars. This certainly agrees with the observation that star clusters are common.

 Heating due to gravitational energy

As the cloud continues to contract it begins to increase in temperature. This is not caused by nuclear reactions but by the conversion of gravitational energy to thermal kinetic energy. As a particle (atom or molecule) decreases its distance from the centre of the contracting fragment this will result in a decrease in its gravitational energy. The total energy of the particle must remain constant so the reduction in gravitational energy must be accompanied by an increase in the particle's kinetic energy. This can be expressed as an increase in the thermal kinetic energy, or temperature, of the cloud. The more the cloud contracts the more the temperature increases.

Collisions between molecules often leave them in excited states which can emit radiation as those states decay. The radiation is often of a characteristic frequency. At the temperatures we are talking about (10 to 20 Kelvin) the radiation is in the microwave or infrared part of the spectrum. Most of this radiation will escape hence preventing the rapid rise in temperature of the cloud.

As the cloud contracts the number density of the molecules increases. This will eventually make it more difficult for the emitted radiation to escape. In effect, the gas becomes opaque to the radiation and the temperature within the cloud will begin to rise more rapidly.

The fact that the cloud becomes opaque to radiation makes it difficult for us to observe directly what is happening. We have to rely on theory and computer modelling to describe this phase. Another difficulty is that stars spend relatively little time in this phase of their life (compared to their whole lifespan). This means that there are relatively few stars in this phase at any one time.