Evolution of stars
As the cloud condenses, gravitational potential energy is released - half of this released gravitational energy goes into heating the cloud, half is radiated away as thermal radiation. Because gravity is stronger near the center of the cloud (remember Fg ~ 1/distance2) the center condenses more quickly, more energy is released in the center of the cloud, and the center becomes hotter than the outer regions. As a means of tracking the stellar life-cycle we follow its path on the Hertzsprung-Russell Diagram.
The initial collapse occurs quickly, over a period of a few years. As the star heats up, pressure builds up following the Perfect Gas Law:
PV = NRT
where, most importantly P=pressure and T=Temperature. The outward pressure nearly balances the inward gravitational pull, a condition called hydrostatic equilibrium.
• Age: 1--3 yrs
• R ~ 50 Rsun
• Tcore = 150,000K
• Tsurface = 3500K
• Energy Source: Gravity
The star is cool, so its color is red, but it is very large so it has a high luminosity and appears at the upper right in the H-R Diagram.
2. Pre-Main Sequence
Once near-equilibrium has been established, the contraction slows down, but the star continues to radiate energy (light) and thus must continue to contract to provide gravitational energy to supply the necessary luminosity. The star must continue to contract until the temperatures in the core reach high enough values that nuclear fusion reactions begin.
Once nuclear reactions begin in the core, the star readjusts to account for this new energy source Gravity releases its potential energy throughout the star, but due to the very high temperature dependence of the nuclear fusion reactions, the proton-proton chain is highly centrally concentrated. During this phase the star lies above the main sequence; such pre-main sequence stars are observed as T-Tauri Stars, which are going through a phase of high activity.
Material is still falling inward onto the star, but the star is also spewing material outward in strong winds or jets as shown in the HST Photo below.
• Age: 10 million yrs
• R ~ 1.33 Rsun
• Tcore = 10,000,000K
• Tsurface = 4500K
• Energy Source: P-P Chain turns on.
3. Zero Age Main Sequence
It takes another several million years for the star to settle down on the main sequence. The main sequence is not a line, but a band in the H-R Diagram. Stars start out at the lower boundary, called the Zero-Age Main Sequence referring to the fact that stars in this location have just begun their main sequence phases. Because the transmutation of Hydrogen into Helium is the most efficient of the nuclear burning stages, the main sequence phase is the longest phase of a star's life, about 10 billion yrs for a star with 1 solar mass.
• Age: 27 million yrs
• R ~ Rsun
• Tcore = 15,000,000K
• Tsurface = 6000K
• Energy Source: P-P Chain in core.
During the main sequence phase there is a "feedback" process that regulates the energy production in the core and maintains the star's stability. The basic physical principles are:
• The thermal radiation law, L ~ R2T4, determines the energy output, which fixes requirement for nuclear energy production.
• The nuclear reaction rates are very strong functions of the central temperature; Reaction Rate ~ T4 for the P-P Chain.
• The inward pull of gravity is balanced by the gas pressure which is determined by the Ideal Gas Law: PV=NRT.
A good way to see the stability of this equilibrium is to consider what happens if we depart in small ways from equilibrium: Suppose that the amount of energy produced by nuclear reactions in the core is not sufficient to match the energy radiated away at the surface. The star will then lose energy; this can only be replenished from the star's supply of gravitational energy, thus the star will contract a bit. As the core contracts it heats up a bit, the pressure increases, and the nuclear energy generation rate increases until it matches the energy required by the luminosity.
Similarly, if the star overproduces energy in the core the excess energy will heat the core, increasing the pressure and allowing the star to do work against gravity. The core will expand and cool a bit and the nuclear energy generation rate will decrease until it once again balances the luminosity requirement of the star.
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