(In the 1970's I started handing out a two page outline of stellar birth and death. Most of the outline has now been turned into more or less satisfactory web pages, and part of it is fleshed out a bit below; but the end of the outline (at the end of this page) is still just an outline, so a future version of this page will be greatly expanded, and broken into several pages to make them more manageable.)
How do stars stop contracting?
Method I (start of "life" for normal stars; see
The Main Sequence): Replace heat being lost by nuclear reactions (Zero Age Main Sequence)
Gradual slowing/ending of contraction; start of Main Sequence
Method II: Destroy Ideal Gas Law (electron degeneracy), -> brown dwarfs (cool electron degenerate stars)
Background Physics: Electron Degeneracy
Inverse relationship between gas temperature and "size" of electrons
Chandrasekhar Diagram: Places limits on temperature, density and radius due to mass
Chandrasekhar Limit = 1.44 solar masses for pure hydrogen
Recent Questions Dec 15, 2002: How do brown dwarfs die?
Brown dwarfs can't die, because they are, so to speak, already dead. As you move down the Main Sequence the density of stars increases, because the lower mass stars have to contract more in order to achieve a given temperature than the higher mass stars do. This means that when they begin nuclear burning, they are much fainter, and therefore don't need to produce as much heat in order to stop their contraction. As a result they are not only much denser but also much cooler (in relative terms) than higher mass stars.
As an example, a massive star may have central temperatures in excess of 30 million Kelvins and central densities only a little greater than that of water, while the Sun has a central temperature of less than 15 million Kelvins and a central density more than 100 times that of water. By the time you get to the bottom of the Main Sequence, the lowest mass stars have central densities of thousands of times that of water and central temperatures of only 6 or 7 million Kelvins.
The higher densities of low mass stars mean that their electrons are pushed closer together, and their lower temperatures mean that the electrons "look" bigger, because of the Heisenberg Uncertainty Principle, than they do in high mass stars. As you go to lower and lower stellar masses the decrease in distance between the electrons and the increase in electron "size" means that the "empty" space between the electrons rapidly decreases. Once the mass gets low enough it becomes so hard for the faint, dense, cool protostar to increase its temperature that as it contracts the electrons begin to fill up its entire interior, and to act like a liquid or as it is technically known, an electron-degenerate gas. This is exactly the same situation which white dwarfs achieve, but at much higher densities, because they are much hotter, so their electrons "act" smaller.
So if the mass of a would-be star is small enough (somewhere below 1/10th the mass of the Sun), as it contracts toward the Main Sequence the electron gas begins to act like a liquid. At first the electron degeneracy is small, and the protostar continues to shrink more or less as it previously did. But as the protostar continues to shrink and the electron degeneracy grows, any further loss of heat becomes less and less important, and it shrinks more and more slowly. Eventually, once the electrons are completely degenerate and the electron gas behaves like a liquid, the protostar stops shrinking.
At this point the protostar has no heat source save the heat stored inside it during its contraction. As that heat is slowly radiated away, the star cools off and becomes gradually fainter and fainter. Such stars are already so cool that most of their heat is in the infrared, and as they cool off further they become almost impossible to observe at interstellar distances, save through their infrared radiation. Once that happens they are called brown dwarfs.
So brown dwarfs never have a life in the sense that the Sun has, as a Main Sequence star. Instead, they are "stillborn" and "die" without ever having lived.
Stellar Death Summary
M < 0.1 Solar Masses -- No Main Sequence Lifetime
As discussed above, very low mass "stars" never become Main Sequence Stars. As they radiate heat and contract, they become so dense that their gas becomes electron-degenerate, and being incompressible they simply cool off and fade out of view as "brown dwarfs".
M > 0.1 Solar Masses -- Main Sequence Stars
Protostars with more than 8 to 10% the mass of the Sun contract until they are hot enough for thermonuclear fusion of hydrogen to helium to replace the heat they are radiating away. This stops their contraction until they run out of fuel. The resulting (very long) stage of visible stellar "life" is represented on the Hertzsprung-Russell Diagram as the "Main Sequence". All Main Sequence stars, such as the Sun, turn hydrogen into helium in the core (using the proton-proton cycle for lower-mass stars such as the Sun, and the carbon cycle of hydrogen burning for higher-mass stars) at a rate exactly equal to the rate at which energy passes from layer to layer throughout the star, and escapes at the surface. Lower-mass stars, which are faint, take a long time to use all their fuel and last for trillions of years, while higher-mass stars, which are very bright, take very little time to use all their fuel, and last for millions of years.
M < 1/4 - 1/3 Solar Masses -- Complete convection leads to helium brown dwarfs
The least massive stars reach the Main Sequence by sliding down the Hayashi Line, becoming fainter and fainter as they contract despite the fact that they are getting hotter and brighter on the inside. Despite their increasing temperature and brightness in the deep interior, their increasing density makes it harder and harder for heat to escape, so the amount of heat reaching the surface gradually decreases, causing the surface temperature to remain low. This also causes the star to remain completely convective, so that even though once nuclear "burning" starts it only occurs in the core of the star, the thorough mixing of the star's gases carries the ashes of nuclear burning throughout the star and fresh fuel into the core, and until there is no fuel left anywhere in the star, nuclear burning can continue in the core. This lengthens the star's already trillions of years long Main Sequence lifetime (primarily due to the low brightness of the star). It also means that when these stars run out of fuel in the core they are out of fuel everywhere, and all they can do to replace the heat they continue to radiate away is to resume the same slow contraction they had before their Main Sequence life. Within a few tens of millions of years they become, like the lowest mass stars that never reach the Main Sequence, so dense that their gases are electron degenerate, and being incompressible they are no longer able to contract, and simply cool off and become brown dwarfs like their lower-mass siblings. However, although these stars eventually become brown dwarfs, they are not the same as the lower-mass brown dwarfs in various ways:
(1) Since the lowest-mass brown dwarfs never burn hydrogen, they are made mostly of hydrogen; while the thoroughly convective Main Sequence stars will turn all their hydrogen into helium, so they will be made almost entirely of helium.
(2) Since turning hydrogen into helium destroys half the electrons in the star, and regardless of their composition more massive electron-degenerate stars are smaller than less massive ones, when they finally contract to become brown dwarfs, the low-mass Main Sequence stars will be even smaller and fainter than the hydrogen brown dwarfs.
(3) Since these stars are Main Sequence stars for trillions of years, no such star has ever died. Every star of this mass range (about 10% to about 30% of the mass of the Sun) is still shining just as faintly as ever, even if among the first stars formed, close to 13 billion years ago.
M > 1/4 - 1/3 Solar Masses -- Partially convective stars become Red Giants
All stars bright enough to have died or even reached middle age either have no outer convective zone, or it doesn't reach down into the core (e.g., the Sun's convective zone only mixes the outer third of its radius). In these stars there is still plenty of fuel left on the outside of the star when the fuel supply is exhausted in the core. As discussed in
The Main-Sequence Life of the Sun, the gradual reduction in the quality of the fuel in the core of an unmixed Main Sequence star causes the core to contract and become brighter, and its outer regions to expand. Once the fuel is completely exhausted the rate of contraction of the core increases, and the changes in the star's brightness become more rapid and extreme, and it swells to many times its former size, becoming a Red Giant.
(more to follow)
Stellar Death Part 2: Red Giant Phases
Accelerated changes leading to second Red Giant stage
Death of the Earth
Effect of Mass on Nuclear Processes Available: Chandrasekhar Revisited
Effect of Mass Loss on Nuclear Processes Available: Chandrasekhar Revised
M < 1/2: No Helium Burning -> rapid shrinkage to helium white dwarf
Slow cooling of white dwarf to brown/black dwarf
(None exist yet because lifetime on Main Sequence too long)
M > 1/2: Helium Burning possible
Helium flash in degenerate core, or possible carbon detonation in a more massive degenerate core
M < 2?: Eventual demise as white dwarf (includes our Sun); original mass limit uncertain due to mass loss in old age
M > 2?: Unlimited nuclear burning: H -> He, He -> C, C -> heavier and heavier nuclei
Impossibility of burning iron due to negative energy production leads to massive iron core
Even iron-core collapse leads to catastrophic implosion/explosion = supernova
Stellar Death Part III: Remnants
White Dwarves: Internal and external characteristics; observations
Neutron Stars: Internal and external characteristics; pulsars, X-ray bursters
Black holes: Internal and external characteristics; Cygnus X-1; SS 433
