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Introduction |
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Energy Generation |
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Main Sequence |
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Low-Mass and Medium-Mass Stars |
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High-Mass Stars |
The Hertzsprung-Russell Diagram
Recall that the Hertzsprung-Russell diagram is a plot of the luminosity of a star versus its surface temperature. This diagram is a useful way to keep track of the way stars change, that is, evolve. As a star ages its luminosity and surface temperature changes and, therefore, so will its position on the H-R diagram.
By studying the H-R diagram we can learn much about stars and the way they evolve. For example, suppose (as is the case) we find most stars clustering in one region of the diagram while in some regions there are relatively few stars. What can we infer from this?
Well, first we must make some assumptions. Let's assume that stars are born and die at the same rate. (That is, the total population of stars is constant in time.) If this is true we can infer that the number of stars in different regions of the diagram is a measure of how long a star remains in the corresponding state of evolution.
Census
This follows from the observation that, if one takes a census, one is more likely to find things in their long-lived state than things in their short-lived state. For example, if you take a snapshot of the population of a town, whose population is stable, it is more likely that you will find people in the worker phase of their lives than in their baby phase, simply because the worker phase lasts about forty times as long as the baby phase.
Most stars lie in a band called the main sequence. We therefore infer that this is the most stable and long-lived phase of a star's life.
Mass, Pressure and Energy
A star's mass is the most important quantity that determines its lifetime. Paradoxically, the more massive a star the shorter its lifetime. Stars are extremely hot at their centers, where the energy is produced by thermonuclear fusion--the same process that occurs when a hydrogen bomb explodes. Yet stars can remain stable. Why? Because the enormous outward pressure, produced by the thermonuclear fusion, is balanced by the inward force of gravity. It is gravity, as it were, that keeps the "lid" on the star and prevents it from exploding.
Hydrostatic Equilibrium
This balance is called hydrostatic equilibrium. If the force of gravity becomes stronger than the gas pressure the star will contract; if the pressure becomes stronger the star will expand.
Sooner or later, every star will exhaust the fuel at its center. When this happens the star will change, because it will no longer be in hydrostatic equilibrium.
Energy Transport
The energy produced in the star's core can reach the surface by: conduction, convection and radiation.
Conduction: energy moves from place to place as heat (motional energy), without the movement of material.
Convection: energy is transported from one place to another by the movement of material.
Radiation: energy is transported by light.
Stellar Models
We cannot actually follow the evolution of a star, because they live far too long compared to human timescales. Instead we see stars at different stages of their evolution, as represented on the H-R diagram.
The only known way to follow the evolution of stars is to simulate the evolution of stars on a computer. A stellar (star) model is a complex calculation in which scientists try to describe the behavior and properties of stars using the best current understanding of the principles of physics. The models are used to make predictions about stellar characteristics that can be measured. That way we can check the validity of the stellar models.
Evolutionary Track
With these models we can trace the evolution of stars and study how the mass, temperature, luminosity and chemical composition of stars change with time. When we plot, as a function of time, the luminosity versus the surface temperature of a stellar model we get an evolutionary track in the H-R diagram. Much of our understanding of how stars evolve is based on the study of stellar models whose predictions have been checked against observations.
Star Clusters
Important clues about stellar evolution can also be had by studying star clusters. The basic assumption made is that the stars in a star cluster were created at about the same time, and began with the same chemical composition. If one observes variations in the chemical composition of the stars in a star cluster this must be due to stars being at different stages of their evolution.
When stars are born as part of a star cluster, about the only variable that can vary across the cluster is the stellar mass: the cluster will have stars of differing mass and, therefore, right from the start, stars of differing luminosity. See the article "How do we determine the life cycles of stars.."
Hydrogen Fusion
Stars like the Sun, with a core temperature of about 10 million K, generate energy by fusing four hydrogen nuclei to one helium nucleus. This is called the proton-proton (PP) reaction. At some point all the hydrogen in the star's core will be converted into helium.
Helium Fusion
If the star's internal temperature can reach about 100 million K, another reaction can happen: the triple-alpha reaction. In this reaction three helium nuclei fuse to form one carbon nucleus. It is this reaction that has produced the carbon in our bodies.
Carbon Fusion
If the star's internal temperature can reach about 600 million K the star can synthesize elements heavier than carbon. At higher and higher temperatures a star can create heavier and heavier elements. At some point the star produces iron at which point this nucleosynthesis (creation of nuclei) ceases.
Stars enter the main sequence when the nuclear fusion (often called nuclear burning) supplies enough energy, and therefore pressure, to stop further gravitational compression. The Sun is currently in its main sequence phase. Stellar models of the Sun predict that the Sun has taken about 30 million years to reach this stage from its proto-star stage. Main sequence stars convert hydrogen to helium. As noted above, how a star evolves depends upon its mass.
Main Sequence Lifetime formula
Every year, the Sun radiates energy equivalent to a mass of about
1.4 x 1017 Kg.
According to stellar models of the Sun (called solar models) only about
1/10
of its total mass is hot enough to participate in thermonuclear reactions. But not all of this mass can be converted to energy, because the hydrogen to helium fusion reaction is not very efficient. In fact, that reaction can convert only 7/1000th of the available mass to energy.
We can use these numbers to estimate how long a star, like the Sun, will remain as a stable main sequence star if we know how much fuel it has available (which is related to its mass) and the rate at which it uses that fuel (which is determined by its luminosity).
Let us assume that a star that is M times heavier than the Sun will have M times as much fuel available. By definition, a star whose luminosity is L times that of the Sun is using up its fuel L times faster.
If t is the length of time a star will remain on the main sequence then
t = Fuel Available/Rate of Fuel Consumption
= M x 7 x 10-3 x (1/10) x (2 x 1030 kg) /
L x 1.4 x 1017 kg/year
= 1010 x (M/L) yearsFor the Sun we have M = 1 and L = 1; so t = 1010 years!
Mass-Luminosity Relation
The larger the mass of a star the greater the gravitational compression at its core and therefore the hotter it is. The hotter the core the greater the rate of fusion reactions. More fusion reactions means a larger energy release per second, that is, luminosity. Thus we expect the luminosity to increase with mass.
Indeed, that is what is observed. By measuring the mass and luminosity of a large number of stars it has been found that L and M (when measured relative to the luminosity and mass of the Sun) are approximately related as follows
L = M3.5
Eventually, all the hydrogen in the core of a star will be transformed into helium. The enormous pressure of the surrounding material causes the helium core to shrink, thereby increasing the core's temperature and that of the material immediately surrounding the core.
Shell Hydrogen Fusion
In fact, the material surrounding the helium core becomes hot enough for hydrogen to start fusing into helium. This is called shell hydrogen fusion, because the hydrogen fusion reactions occur in a shell about the core. As more and more helium sinks into the core the latter continues to shrink and heat up.
Meanwhile, the hydrogen fusion shell expands away from the core causing the outer layers of the star to heat up and therefore expand. As the outer layers expand they cool, thus turning red. A red giant is formed.
When this happens to the Sun it will probably engulf Mercury and perhaps Venus. The Earth will, for a while, orbit through the Sun's atmosphere at supersonic speeds. But gradually, due to the friction between the Earth and the Sun's atmosphere, the Earth will spiral in towards the Sun and be vaporized.
Degenerate Gas
After about 1 billion years the star shrinks until the temperature of the core is hot enough (about 100 million K) to cause helium to fuse to carbon. But to reach such enormous temperatures the gas within the core must become highly compressed; so compressed in fact that the electrons are forced to fill all the available energy states up to some maximum level.
When all the lowest available energy states are occupied the gas is said to be degenerate. The electrons are so compressed that they are unable to change their speeds: they can't slow down because all the lower energy states are occupied; they cannot speed up because to get to the higher unoccupied energy levels would require the input of an enormous amount of energy.A degenerate gas is one in which the heating of the gas does not raise the pressure of the gas. The pressure cannot increase because of the difficulty in speeding up the electrons.
Helium Flash
Because the pressure does not rise, even as the core is heated, no expansion, and therefore no cooling, occurs. Within a matter of seconds the core grows hotter and hotter and fuses helium to create heavier elements. This explosive destruction of helium is called the Helium Flash.
The star becomes a variable star as the outer layers are periodically re-heated and cooled. This causes the outer layers to pulsate. The star pulsates with a period of between 200 and 600 days and loses matter from its surface in the form of powerful winds that seed space with the newly formed carbon and other elements, thereby setting the stage for the birth of the next generation of stars and planets. See the Ring and Dumbbell Nebulae.
After the helium flash the star becomes again a red giant and then cools to a white dwarf.
Shell Source
When the hydrogen in the core is used up the helium core shrinks, the temperature of the core increases and shell hydrogen fusion occurs. The luminosity increases, the star expands thereby cooling its outer layers. The star becomes a red giant. The shell of fusing hydrogen is called a shell source. Meanwhile, the core contracts, but usually does not become degenerate.
Carbon Detonation
Because the star is so massive the helium in the core begins to fuse with only a little extra compression to form carbon. If the core does, however, become degenerate before the onset of carbon fusion a runaway increase in temperature can occur, similar to what happens in the helium flash of low to medium mass stars, causing an explosive destruction of carbon in what one could call a "carbon flash", but which is usually referred to as a carbon detonation. This is a much more violent explosion than that of the helium flash. Carbon fusion creates oxygen and neon.
Endothermic Reaction
The core burns ever more furiously creating heavier and heavier elements (magnesium, sulfur, silicon) eventually reaching iron (Fe), created by silicon fusion. When that stage is reached the massive star is doomed. The nuclear reactions that produce iron are endothermic, that is, the reactions absorb heat and thus cool the core.
The cooling reduces the pressure in the core to the point where it is insufficient to hold off the crushing force of gravity. In a split second the core collapses and triggers the most powerful explosion in the universe, called supernovae. Within these explosions all the elements heavier than iron are created. The shock waves from these explosions can trigger star formation as the shock compresses nearby molecular clouds.
Last updated October 19, 1999 Harrison
B. Prosper
