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Physics LibreTexts

9.5 Helmholtz Contraction

As a cloud of gas and dust collapses, a new force comes into play. In the free-fall phase of the contraction, gas and dust particles stream freely toward the center of gravity. The density is so low that collisions are rare. But as the gas gets denser, the distance between particles gets smaller, and the rate of collisions gets higher. Compress a gas, and the pressure and temperature will rise. This is one of the laws that govern the behavior of gases. When you push on a bicycle pump with the valve covered, the gas will shrink, but it will also exert a pressure that can counter your entire weight. In the forming solar system, gas pressure competes against the inward force of gravity.
 


Hermann von Helmholtz. Click here for original source URL.

German astrophysicist Hermann von Helmholtz showed how these competing forces shape the contraction and evolution of a collapsing cloud. He published his first calculations in 1871, which was even before the energy source that powers the Sun had been discovered. Helmholtz showed that pressure and heat would build up in the contracting cloud. This is an example of the conservation of energy. Gravitational potential energy is converted into thermal energy. He used physical principles to calculate the rate at which temperature increased inside the contracting proto-Sun. Gravitational contraction, in which the shrinkage is slowed by outward pressure like this, is called Helmholtz contraction.
 


A small area of the Orion Nebula showing little pockets of gas forming new stars. The sun started out as a small pocket of gas about 4.6 billion years ago. Click here for original source URL.

Calculations based on the Helmholtz theory describe the evolution of the collapsing solar nebula. The shrinkage of the disk is eventually halted by the increasing pressure of the hot gas at a temperature of a few thousand Kelvin. The main disk of material stabilized at a size corresponding to the size of the present-day Solar System. Meanwhile, the bulk of the gas continued to collapse under strong gravity. Eventually the cloud's central temperature rose to 10 million Kelvin or more, starting the nuclear reactions that made it a star and not just a ball of inert gas. 

You might wonder how sure we can be about events that took place so long ago. This theory is a plausible scenario that is based on simple physics. Our confidence in it is bolstered by actual observations of newly forming stars surrounded by clouds of gas and dust. The limitation of matching theory and observations is that the theory deals with idealized situations of spherical symmetry and a single cloud collapsing into a star. In practice, the gas that forms stars has chaotic motions and is not spherical in shape, and one large gas cloud may simultaneously form many stars.