STELLAR STRUCTURE AND EVOLUTION
Stars are gaseous fluids governed by the forces of nature. At all times, the gravitational pull of every atom, ion, electron, or molecule in a star is pulling on every other such particle in the star, and if this were the only force present it would cause all the matter to collapse down to a small point. For the Sun and other stars to have any size at all, there must be a force which counters gravity. In fact, since most stars are not rapidly expanding nor shrinking, the other force must be equal in size and opposite in direction. It is the internal pressure in the star that provides this hydrostatic equilibrium.
At the core of the star, the entire weight of the star must be balanced by very high pressure, which in most cases also requires high temperature. It is also under these conditions that thermonuclear reactions can occur.
In stars like the Sun, the core can sustain hydrogen fusion, what astronomers call "hydrogen burning". Note that this is not burning in the usual sense, which is a chemical reaction. This is a nuclear reaction, which is much more powerful. The specific set of reactions is called the proton-proton chain, or PP chain for short. Here two protons (1H nuclei) fuse to form deuterium (2H), a heavy isotope of hydrogen. If hit with another proton, the deuterium becomes light helium (3He). Finally, two of these will fuse to make the common form of helium (4He) plus two protons. The net effect is:
The mass of the 4 H nuclei is greater than the He nucleus, and the mass difference appears in the form of energy - mechanical heat, neutrinos, and especially photons (gamma rays):
In main sequence stars more massive than the Sun, another reaction dominates the energy generated by the star, the CNO Cycle. This is a series of reactions that use the12C nucleus as a catalyst, an agent that helps the reaction go which would otherwise be unfavorable energetically, and which is not itself consumed. The net effect is:
The C can be used over and over.
In the middle of this reacation14N, due to its great stability, builds up to high levels.
The luminosity (wattage) of most of the stars in the sky is the result of these two reactions.
The distance (or length of time) a car can travel is determined by the size of its fuel tank and how many miles per gallon it gets (for time, how many gallons per hour it uses). Similarly, the length of time a star can remain a main sequence star is determined by it mass (that's its fuel supply) and how quickly it consumes its fuel. The luminosity of the star is a direct measure of how fast its nuclear reactions are running, consuming its fuel, so the lifetime of a star on the main sequence is
But, we know that from measuring the masses and luminosities of main sequence stars, the luminosity is very dependent on the mass. For stars with masses close to 1 solar mass,
so that the lifetime is
This means that the main sequence stars with more mass (fuel) actually run out of fuel faster than the lower-mass stars, because they are "gas-guzzlers". As a consequence, massive MS stars must be relatively young.
The Sizes of Stars
Back in Section 2 of these notes, we discovered that:
And above I implied that we could measure the masses of the stars (more on this later on).
What else can we find out? Well, the physical size of the stars can be determined, if L and T are known! The full-blown version of the S-B Law is:
or, in mathematical terms:
We can rearrange this, algebraically, to solve for R if T and L are known:
The equation can be written for the Sun, which is a star we use as a standard unit of measure for L, M, and R (almost never T). By dividing the above equation by the same one for the Sun:
From this, we find that the red giant stars are much bigger than MS stars, supergiants are REALLY BIG stars, and white dwarf stars are tiny stars, about the size of the Earth. As it happens, most of these stars are post-main sequence stars. Lets look at how star get on the MS first.
Pre-MS Evolution and the HR Diagram
Because they are governed by the laws of physics, stars must form along predetermined paths of life, so to speak. Theoretical calculations indicate that a star of a particular mass will follow a path on the HR diagram as it goes from being a protostellar blob to being a MS star. (Remember that the HR Diagram is a plot of L versus T, so that when we say, "a star moves on the HR Diagram" this has nothing to do with its physical motion in space. It is simply easier to say this phrase than " the locus of points in a plot of the luminosity versus surface temperature of the star at different times "). Stars of different masses follow slightly different paths. And the location of the star on its path, its evolutionary track, depends on time, how long since the star began to form. The TTS and HAEBEs are very young, indeed, usually only a few million years old (the sun is about 4.6 billion years old).
We often draw these evolutionary tracks on the HR Diagram and compare them with the observed locations of stars on the plot. In this way, we can estimate the mass and age of a PMS star! Sometimes, it is useful to plot a line where all the stars of a particular age will be, what we call an isochrone.
Post-MS Evolution and the HR Diagram
When a star uses up all the fuel in its core (where the conditions are extreme enough for fusion to occur), it cannot maintain its current structure. The laws of physics say that something different must happen. No fuel means no luminosity means temperature and pressure loss in the core, leading to loss of hydrostatic equilibrium. And since higher-mass MS stars run out of fuel faster than low-mass ones, them must do something sooner!
Theoretical models indicate that the majority of stars undergo shrinkage of their cores, and the expansion of their envelopes. Their sizes increase. Stars like the Sun become red giant stars after spending about 10 billion years as an MS star. High-mass stars do it sooner, low-mass ones take their jolly good time about it, and can last 100 billion years or more! Again, we can plot both evolutionary tracks and isochrones on the HR Diagram to estimate the ages and masses of these other stars.
For stars like the Sun and more massive, this post-MS core contraction eventually raises the core T and pressure sufficiently high that another nuclear reaction is possible, the so-called triple-alpha reaction, or "He-burning".
To make any fusion reaction work, you need a lot of nuclei in a small space - high density - and they must have high thermal speeds - high T. (density, pressure and T are also related to one another). The He nuclei have two protons each, so the electrical repulsion is much higher than for H nuclei, with only one proton each. This is why the core T must be higher for He-burning than for H-burning - you need high collision speeds to overcome the large electrical repulsion. And you need to have three He nuclei hitting at almost the same instant, requiring very high densities. It is for these reasons that He-burning does not occur until after the star has left the MS. The core T and density are too low on the MS, and it helps to have all that He made from the H-burning first!
Note that we are getting a glimmer of where the elements came from:
What are the most abundant elements in the universe? You guessed it! In order of abundance, they are: H, He, O, C, and N. What are the most abundant elements in living systems? H, O, C, and N. He, being a noble (inert) gas, does not form molecules under most conditions present in the universe. So the most abundant molecule-forming elements are also the ones that are most abundant. This should not be a big surprise to anyone!
What about the rest?
Supernovae & Other Mass Outflow Objects
Really massive stars can go far beyond He-burning. Especially important is the slow buildup of heavier and heavier elements by way of He-capture, which produces "even number nuclei". A plot of the abundances of the elements in nature exhibits this even-number nuclei pattern.
It is the very massive stars that build up the heavy elements. The abundances we see in the Sun and other stars today is the result of these stars incorporating recycled material. The stars "cook up" the heavy elements and return this processed material back out into space.
Red giants eventually eject their outer layers in a wind that forms a "planetary nebula" (PN). (This term has nothing to do with the formation of planets. It derived from the fact that some of them look like a planet when seen though small telescopes). We find these nebulae enriched in C and O
M57, the Ring Nebula in Lyra, a well-known example of a planetary nebula.
The Hourglass Nebula
The Egg Nebula
M2-9, "Minkowski's Footprint"
Massive stars often have PN-like nebulae due to massive winds. Some are rich in N, others enriched in C and O. The former have apparently ejected CNO-processed material. The latter, He-burning products.
And the Type II supernovae, which can build elements all the way to Fe by "slow" He-capture (and a bunch of heavier ones in other reactions during the explosion itself) also eject this enriched material into space. The explosion process also generates COSMIC RAYS, highly energetic atomic nuclei and gamma-ray photons.
Stars like the sun are fated to become white dwarf stars after PN-ejection. These stars are usually about the size of the Earth. The laws of nature requires that they have masses no greater than 1.4 solar masses, the Chandrasekhar Limit.
Stars much more massive than the Sun have a denser fate - to become neutron stars roughly the size of a city, and no more than 3 solar masses is allowed.
The most massive stars can have a weirder fate - as a black hole! They have no real size, in the strictest sense, but an effective size determined by the event horizon, whose value is roughly 3 km per solar mass.
Over three decades ago, astronomers began to discover stars, pulsars, emitting regular pulses of light with periods as long as a couple seconds, down to a few milliseconds. Although such regular pulses might be produced by a technical civilization (the LGM - Little Green Men - hypothesis), it became clear that it was a natural process of magnetized neutron stars. The ionized material in the magnetic fields emits light via the synchrotron process (as opposed to a thermal process) which is preferentially emitted outward from the magnetic poles of the star. When rotating, the beam of light act as searchlights that flash on and off as viewed from a distance.
As billions of years pass, our galaxy becomes more enriched in heavy elements - those required to form terrestrial planets, life, computers, etc. Furthermore, the younger "heavy-rich" (astronomers use the term "metal-rich") stars are better places to look for life than those poor in heavies.
The photographic images included here are from the Space Telescope Science Institute, operated by the Association for Universities for Research in Astronomy, Inc., from NASA contract NAS5-26555 and are reproduced here under the conditions specified for educational use by AURA/STScI.
The line drawings are strictly my own.