Bluffton University

NSC111: Physics/Earth/Space
Resource page: Stars

Gee, I always thought they were balls of gas,
burning billions of miles away.
231 KB
audio is exerpted from
this unofficial site
click here for the 1.9MB video clip in RealVideo format

A common mass unit in stellar astronomy is the "solar mass", equal to the mass of our Sun.

You may also want to look at Davison Soper's stellar astronomy lecture notes.

cross section of the Sun

Stars are known to be similar to our Sun (which is itself a star). They are "balls of gas, burning billions of miles away." We know more about the structure of the Sun than of any other star because we're closer!

The Sun is about 75% hydrogen by weight, and 25% helium; other elements ("metals" according to astronomers) make up about 0.1%. If the Sun were allowed to collapse under its own mass, it would shrink to a sphere about the size of the Earth. But it doesn't, because of energy produced by nuclear reactions in its core.

When uranium-238 decays by emitting an alpha-particle, it's because the two daughters (the thorium-234 and helium-4 nuclei) are more stable, take less energy to hold together, than the original 238U. In the same way, when plutonium-239 or uranium-235 fissions, it's because the daughters take less energy to hold together than the original nucleus. You can continue to get energy from knocking apart nuclei until you reach iron-56, although as a practical matter the process stops around bismuth-209 or lead-208. But 56Fe is too stable to knock apart.

In the same way, you can get energy by fusing smaller nuclei into larger ones; it takes more energy to hold the small nuclei together than the larger ones--again until you reach 56Fe. After that, you have to supply energy to get fusion.

These two trends are depicted in Figure 14.27, and explained further on pages 351-353.

The Sun takes advantage of this trend by fusing hydrogen into helium at its core, under tremendous heat and pressure:

4 H-1 to He-4 + energy
The sequence in which this happens is:

solar fusion sequence

We can't perform this particular sequence on Earth because we can't get the temperatures and pressures high enough, so we short-circuit the process by combining 2H (deuterium) and 3H (tritium):

artificial fusion reaction

However, this process produces neutrons, which can make other atoms radioactive (the neutrons hit stable atomic nuclei and produce nuclei which have too many neutrons for the protons).

Gamma rays from the fusion reactions at the Sun's core percolate up through the body of the sun, losing energy and therefore frequency (remember, E = hf ) all the way, until they emerge from the Sun as (mostly) photons of visible light. Stars don't collapse because the large quantities of energy generated at their cores makes them expand (like any other hot gas). This "energy pressure" is what keeps stars so large.

We can know several things about stars from observing them:

  • We can tell the surface temperature from the color (blackbody radiation!).
  • We can tell how bright they look; this is called the apparent magnitude.
  • If we're lucky, we can use triangulation to directly measure how far away they are.
  • If the star has a companion star (this is called a binary star system and was not mentioned in class but is discussed in your textbook) we can get a good handle on its mass.
  • If we know the star's mass and surface temperature, we can make a good estimate of its intrinsic luminosity, or absolute magnitude. This, in turn, allows us to make a good estimate of the distance to the star, because perceived brightness falls off as the square of the distance. (Imagine a 100-watt light bulb 10 feet away. Now put it 300 feet away, the length of a football field. Perceived brightness falls off with distance!)
When we start plotting star colors (or surface temperatures, which is the same thing) against the stars' absolute magnitudes, we get a Herzsprung-Russell diagram (see p. 711 in your textbook).

click here for a discussion of several features of the Hertzsprung-Russell diagram

Click on the H-R diagram for a discussion of several features of stars and how we know them.

Big, massive stars burn faster and hotter, have higher surface temperatures and appear at the upper left; small, light stars burn slower and cooler, have lower surface temperatures and appear at the lower right. This is because the big stars have to generate more energy than the Sun to keep from collapsing--making the surface temperature higher--and small stars don't have to generate as much energy as the Sun--making the surface temperature lower.

The curve joining the upper left and lower right is where most stars fall, and is called the Main Sequence. The Sun is in the yellow portion of the Main Sequence, between Spectral Class F and G, at luminosity = 1. Stars along the main sequence range from red dwarfs at 0.1-0.8 solar mass, to yellow stars like our Sun, to blue giants at 10 solar masses or more. Life along the main sequence is described by Davison Soper.

"Spectral class" corresponds not only to color but to other features of the spectrum, and the classes were named in the early part of the 20th Century. The classes are O, B, A, F, G, K, and M; the mnemonic shows what the culture of astronomy was at the time: "Oh Be A Fine Girl, Kiss Me."

But there are some anomalies:

  • There are stars in the lower left: they have high surface temperatures and thus high brightness per unit area; but their absolute magnitudes are very small. Therefore their surface areas must be much smaller than normal, and these stars are called white dwarf stars.
  • There are stars in the middle right: they have low surface temperatures and thus low brightness per unit area; but their absolute magnitudes are large. Therefore their surface areas must be larger than normal, and these stars are called red or yellow giant stars.
  • There are stars along the top of the diagram, particularly the upper right: they have lower surface temperatures and thus lower brightness per unit area; but their absolute magnitudes are huge. Therefore their surface areas must be much larger than normal, and these stars are called supergiant stars.
These stars don't fit into the tidy scheme we've worked up for the Main Sequence; small stars ought to be cool and red; large ones hot and blue! But it makes sense if we make one assumption: Stars are not eternal.

A star works by fusing hydrogen to helium in its core. It may do so rather slowly (like a red dwarf, which may burn for 100 billion years) or very rapidly (like a blue giant, which lives only 1-100 million years). But eventually the star will run low on hydrogen. What then?

Helium, being denser than hydrogen, has been accumulating at the star's core; hydrogen burns in a shell around the core, making the star hotter at the surface. As the helium core compresses, it gets hotter; this makes the hydrogen shell burn hotter, and the outer layers begin to expand.

Eventually, the helium may get so hot and dense that it will begin to fuse, into carbon and oxygen. Because the core is now hotter, the outer layers of the star expand, and as they expand they cool; the result is a red giant star.

For a somewhat different discussion, see Davison Soper's description.

Incidentally, carbon and oxygen are required for life. They are formed by a series of three successive fusions in the cores of red giant stars:

  1. 4He + 4He → 8Be
  2. 8Be + 4He → 12C
  3. 12C + 4He → 16O
8Be is not a very stable nucleus, but it lives just long enough to get hit by another 4He, so that carbon is formed. But carbon is a stable nucleus, and so it can wait indefinitely for another 4He collision. Why isn't all the carbon converted into oxygen?

It so happens that the energy in the core of the typical red giant is not quite enough to make a helium nucleus stick to carbon; it takes a little extra oomph, which is less common than the collisions which form carbon. So carbon accumulates.

Much carbon finds its way to the surface of the star, by convection, and is blown away in strong stellar winds, so that many red giants ("carbon stars") are surrounded by clouds of carbon-rich gas. Others, less common, called "oxygen stars," have enough oomph to make carbon into oxygen and blow out clouds of oxygen. This carbon and oxygen, as the molecule carbon monoxide, is very common indeed in interstellar space, and forms part of the matter for making new stars, and new solar systems.

But if stars had to be even a little bit larger to burn helium, there would be no carbon--and therefore no life--because all carbon would be converted to oxygen. If beryllium-8 didn't hold together even for a short time, there would be no carbon either... see Al Schroeder's discussion of this particular process.

Stars the size of the Sun stop at carbon; stars larger than the Sun may burn carbon and oxygen to form magnesium, silicon and sulfur, all the way up to 56Fe (iron-56). But it stops there. You get energy from fusion of light elements. But if you try to fuse 56Fe, you have to put energy in. So fusion stops.
See Davison Soper's description of Old Stars.
When fusion stops, there is nothing left to keep the star from collapsing under its own weight, and so it does: a star the mass of the Sun may shrink to a ball the size of the Earth! It doesn't stop until the electrons of its atoms are in contact with the atomic nuclei. The rapid compression results in heating, just as your bike tire gets hot when you inflate it, and the surface of these small objects glow white-hot. In fact, they are white dwarfs. The outer layers of the former red giant are typically ejected during the compression process, resulting in beautiful objects called planetary nebulae.

What happens to stars at the end of their lives? As we noted above, a star will start building up helium "ashes" in its core, with hydrogen fusing in a shell around the core. As the core accumulates more helium, it gets heavier and denser, therefore hotter, and the heat makes the hydrogen in the shell burn faster. The star puts out more energy.

As a matter of fact, our Sun is brighter now than it was long ago, and will get brighter yet; the Earth is expected to become uninhabitable in about 2 billion years, long before the Sun enters the red giant stage.
Eventually, the helium core will get hot enough to ignite, fusing helium to carbon and/or oxygen. The outer layers of the star get much hotter, expand enormously, and cool from the expansion; the result is a red giant star.
Presumably, really small red dwarf stars will not be able to burn helium; they'll just eventually run out of hydrogen and collapse into white dwarfs. But a red dwarf that small has not had time to run out of hydrogen yet, not in the whole history of the universe!
For stars about the mass of the sun, carbon is the limit; and for stars up to about 2 solar masses or so, oxygen is the limit. Carbon/oxygen "ashes" just accumulate in the core as the helium runs out. Toward the end, the helium is thought to burn in bursts; these explosions (firecrackers on a stellar scale!) blow off the outer layers of the star, forming a beautiful ball of gas called a planetary nebula. What remains is called a stellar remnant.

A small stellar remnant (less than 1.4 solar masses) will collapse into a white dwarf. The collapse of a star under its own weight is stopped by the fact that its electrons want to stay outside its nuclei. But what happens to stars that are bigger than that?

1.4 solar masses is called the Chandrasekhar limit; Subrahmanyan Chandrasekhar shared the 1983 Nobel Prize in Physics for his work on the theory of white dwarf stars.
Stellar remnants larger than 1.4 solar masses have too much gravitational pressure at their cores. The electrons are squeezed right into the protons and what remains is a giant atomic nucleus made almost entirely of neutrons (there are some protons and electrons at the surface). This is called a neutron star. Most small stars (less than 2-5 solar masses) blow off enough mass during the final stages of red-gianthood to keep themselves under the Chandrasekhar limit of 1.4 solar masses. Larger stars do something else... they explode!

 A very large star (10-100 solar masses or even larger!) has enough mass that it doesn't stop by burning helium. Eventually, as the carbon/oxygen ash builds up in its core (and helium burns in a shell around the carbon/oxygen core, with hydrogen burning in a shell around that), temperatures and pressures rise to the point at which carbon and oxygen will also burn; the ash from this burning builds up until it ignites, and the ash from that builds up until it ignites, until you have shells of progressively heavier nuclei burning around (and pressing in on) a core of 56Fe (iron-56).

But, as noted above, 56Fe won't burn. To burn 56Fe, you need to put energy in, so fusion stops in the core of the star. As the 56Fe ash builds up, it compresses more and more (and there is no fusion to provide outward pressure!) until it finally collapses. The core may develop enough pressure to ignite the 56Fe (absorbing gravitational energy and hastening the collapse!) or not, but in either case there is a sudden, catastrophic collapse of the core.

With the core collapsed, each subsequent layer also collapses inward. But the major effect comes from the fact that in some ways the core behaves like a rubber ball. As the core falls in on itself, electrons and nuclei are squeezed together into neutrons, and even the neutrons are squeezed into each other--but they push back! and the core actually bounces outward. The shockwaves from the collapse and the bounce (both are spherical) meet and reinforce, and the star very rapidly tears itself apart in what is called a Type II Supernova. During the explosion, enough energy is available to fuse iron into all the elements up to uranium and beyond. This matter gets distributed, with at least 80% of the star's original mass, in a huge nebula called a supernova remnant.

The Crab Nebula through the Palomar 200-inch telescope
The Crab Nebula
the neutron star at the core of the Crab Nebula, seen with the Hubble Space Telescope
the neutron star at the core of the Crab Nebula
The Crab Nebula, in the constellation Taurus, is the remnant of a supernova which was sighted on Earth in 1054 AD. The supernova was recorded by Chinese astronomers, and the nebula itself was first noticed by Messier. Images (courtesy of the Palomar Observatory and the Hubble Space Telescope) were taken from this page.

If the stellar remnant (really just the core of the former star) is small, it will become a white dwarf or a neutron star. But if the stellar remnant is bigger than 3 solar masses, gravity overcomes everything and the star collapses to nothing! Only the gravity remains! This mighty odd-sounding state of affairs is called a black hole. Black holes are discussed in your text.

Robert Nemiroff has posted several virtual trips to neutron stars and black holes with explanations of what causes the rather odd things you would see.
But what if the stellar remnant is part of a multiple star system? Well, stellar remnants have pretty intense surface gravity (again, see your textbook, Chapter 29!). This means that they usually attract at least some material from the other star onto their surfaces.
  1. If the stellar remnant is in a close binary relationship with another, normal star, the remnant's gravity will suck matter from the surface of its companion. This usually produces an accretion disk, as shown at right.
  2. If the stellar remnant companion is a black hole, that's pretty much all you see. You get a steady flow of X-rays, with occasional bursts of X-rays as larger clumps of matter from the accretion disk fall into the black hole.
  3. But if the remnant is a white dwarf or neutron star, you build up matter (mostly hydrogen, since it came from the companion's outer layers!) on the surface of the stellar remnant. Eventually, you have enough of the stuff that it ignites under its own gravitational pressure (and the heat from the stellar remnant). This ignition is called a nova.

  4. If the remnant is a white dwarf, enough matter may build up on its surface that the dwarf's carbon core becomes hot and dense enough to ignite. This causes a massive explosion, a Type Ia Supernova, that blows the white dwarf apart.
Eventually, almost all the elements forged in the cores of stars find their way back into the universe at large in one way or another, and that's why our Solar System is not just made of hydrogen and helium.

return to index
Copyright © 2001 by Daniel J. Berger. This work may be copied without limit if its use is to be for non-profit educational purposes. Such copies may be by any method, present or future. The author requests only that this statement accompany all such copies. All rights to publication for profit are retained by the author.