1
The stars
The actual process of star formation remains shrouded in mystery because stars form in dense, cold molecular clouds whose dust obscures newly formed stars from our view. For reasons which are not fully understood, but which may have to do with collisions of molecular clouds, or shockwaves passing through molecular clouds as the clouds pass through spiral structure in galaxies, or magnetic-gravitational instabilities (or, perhaps all of the above) the dense core of a molecular cloud begins to condense under its self-gravity, fragmenting into stellar mass clouds which continue to condense forming protostars. 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:
where, most importantly P=pressure and T=Temperature. The outward pressure nearly balances the inward gravitational pull, a condition called hydrostatic equilibrium.
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.
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.
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.
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:
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.
As the Helium core of the star contracts, nuclear reactions continue in a shell surrounding the core. Initially the temperature in the core is too low for fusion of helium, but the core-contraction liberates gravitational energy causing the helium core and surrounding hydrogen-burning shell to increase in temperature, which, in turn, causes an increase in the rate of nuclear reactions in the shell. In this instance, the nuclear reactions are producing more than enough energy to satisfy the luminous energy output. This extra energy output pushes the stellar envelope outward, against the pull of gravity, causing the outer atmosphere to grow by as much as a factor of 200. The star is now cool, but very luminous - a Red Giant.
(You do the arithmetic: 200 x 700,000km = ?; where will the outer radius of the sun be?)
The contraction of the core causes the temperature and density to increase such that, by the time the temperature is high enough for Helium nuclei to overcome the repulsive electrical barrier and fuse to form Carbon, the core of the star has reached a state of electron degeneracy. Degeneracy comes about due to the Pauli Exclusion Principle, which prohibits electrons from occupying identical energy states. The core of the Red Giant is so dense that all available lower energy states are filled up. Because only high-energy states are available, the core resists further compression -- there is a pressure due to the electron degeneracy. This pressure has a significant difference from pressure produced by the Ideal Gas Law -- it is independent of temperature. This removes a key element in the feedback-stability mechanism that regulates hydrogen burning on the main sequence.
Once again the core of the star readjusts to allow for a new source of energy, in this case fusion of Helium to form Carbon via the Triple-Alpha Process. The Triple alpha process releases only about 20% as much energy as hydrogen burning, so the lifetime on the Helium Burning Main Sequence is only about 2 billion years.
During this phase some Carbon and Helium will fuse
12C + 4He --> 16O
resulting in the formation of a Carbon-Oxygen core. When the Helium is exhausted in the core of a star like the sun, no further reactions are possible. Helium burning may occur in a shell surrounding thecore for a brief period, but the lifetime of the star is essentially over.
HST images of Planetary Nebulae: The Ring Nebula and the young Planetary Nebula known as MyCn18, the Hourglass Nebula.
· More about Planetary Nebulare from George Jacoby's (b& w) Planetary Nebula Gallery.
· Planetary Nebulae at the SED's Messier Gallery.
· The Planetary Nebula Observer's HomePage includes more links to Planetary Nebula Resources.
· Univ. of Calgary Planetray Nebula Homepage with theoretical models of PN emission structure.
· Bruce Balick's HST Images of Planetary Nebulae.
As the nebula disperses, the shell nuclear reactions die out leaving the stellar remnant, supported by electron degeneracy, to fade away as it cools down. The white dwarf is small, about the size of the earth, with a density of order 1 million g/cm3, about equivalent to crushing a volkswagen down to a cubic centimeter or a "ton per teaspoonful."
A white dwarf star will take billions of years to radiate away its store of thermal energy because of its small surface area. The white dwarf will slowly move down and to the right in the H-R Diagram as it cools until it fades from view as a "black dwarf". To the right is the white dwarf companion to the nearby star Sirius.
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