# Protostar

 Contents

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 within a giant molecular cloud in the interstellar medium. Observations reveal that giant molecular clouds are approximately in a state of virial equilibrium—on the whole, the gravitational binding energy of the cloud is balanced by the kinetic energy of the cloud's constituent molecules.

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:

[itex] M_j = \frac{9}{4} \times \left( \frac{1}{2 \pi n} \right) ^ \frac{1}{2} \times \frac{1}{m ^ 2} \times \left( \frac{kT}{G} \right) ^ \frac{3}{2} [itex]

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. In fact, as first pointed out by Richard Larson, the giant molecular clouds in which stars are formed are universally observed to have turbulent velocities imposed on all scales within the cloud. These turbulent velocities compress the gas in shocks, and generates filaments and clumpy structures within the giant molecular cloud over a wide range of sizes and densities. This process is referred to as turbulent fragmentation. Some clumpy structures will exceed their Jeans mass and become gravitationally unstable, and may again fragment to form a single or multiple star system.

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 kelvins) 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 in the infrared makes it difficult for us to observe directly what is happening. We must look to longer wavelength radio radiation which does escape even the densest clouds. In addition, we must also use theory and computer modelling to help us understand this phase.de:Protostern it:Protostella ja:原始星

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