Chapters 12, 13 and 14 - Stars: from Birth through Death

This summary presents all three chapters' worth of material as a continuous story, since that is what "life" is like in a group of stars; it also includes some material from chapter 15 where appropriate as background. Tt does not take the place of reading the text, but provides supplemental information, summaries, and alternative explanations.

Use the book and your notes to fill in wherever you are having trouble with understanding something -- and ask your instructor questions! :-)

• All stars start out as part of a cluster. A star cluster starts forming when a large cloud of hydrogen (also helium, and whatever other elements happen to be in that cloud) develops a gravitational instability in one location in the cloud -- usually near the edge, and usually where a supernova remnant or other source of interstellar shock wave action is colliding with the cloud.
  
  
• As the cloud begins to contract under its own self-gravitation, it will tend to: 1) heat up and 2) break into clumps. Each of these clumps, which may be hundreds of times the mass of the Sun or more, will form a star cluster. If the clusters are like the cluster in which our own Sun was formed, the member stars will eventually "smear out" in position as the Galaxy rotates, so that what started as a star cluster will eventually be a widely scattered streak of stars. Such impermanent clusters are called "open clusters." (the Pleiades is a nice example of an open cluster) They are as much as 25 pc in diameter. Since they do smear out over time, if you see one you know its member stars formed fairly recently. Once a cluster has smeared out you can't tell which of the stars in a given area were originally members of a single open cluster. Note that when stars form in a cluster there are dozens of low-mass stars for every high-mass one.
  
  
• In the open cluster there will be tens or hundreds (up to a few thousand) of stars forming; no matter what the mass of each star is, they will all go through the protostar phase first. A protostar is a contracting lump of gas that glows with the heat of its gravitational contraction. It may have one or more sub-lumps -- if any of these is massive enough to eventually be a star (initiate H fusion in its core), then the system will be a binary star system. If not, we might wind up with something like our Solar system. Indeed, if the lump that became Jupiter had been only 100 times more massive than it was, Jupiter would probably have been the smaller member of a binary star system!
  
  
• A much older type of cluster formed at the beginning of our Galaxy's lifetime (see Globular Clusters after the end of the sample stellar evolution paths).
  
  
• Although every star will go through the protostar phase and the main-sequence phase, how fast they do this and how brightly they shine are determined by only one factor: MASS. A star's mass defines its entire lifetime, since the star exists essentially as a fight between its own self-gravitation and its ability to convert mass to energy or otherwise halt its collapse. A higher-mass star will spend less time in every phase of its development, since its greater self-gravity hurries each process along. Although much of what I've told you is observable, the exact processes by which these things take place in the interiors of stars are not directly observable, so astronomers use very complex computer programs and powerful computers to calculate what must be going on, basing these calculations on their knowledge of physics.

Let's look at a typical evolutionary scenario for a three-solar-mass star, so that you get an idea of what's involved in each phase. First comes gravitational collapse, and the protostar glows with the heat from that contraction. Of course the densest part of the contracting protostar is the center, and that gets hotter and hotter until it reaches 10⁷K, the temperature at which Hydrogen fusion can start. Fusion begins and the star starts its main-sequence lifetime. Its position on the main sequence is determined by its mass. The rate of fusion in the core that produces energy with which the star "pushes back" against its own gravity is controlled by the central pressure, which is just the total weight of the material above the core. More material produces higher pressure (and higher temperature: they go together), which produces a higher fusion rate, so a brighter star. Thus a star, once it's on the main sequence, will not move left or right along that sequence, since stars cannot not change their masses enough to make a noticeable change (except under very specific circumstances you'll learn about next term!).

Our sample star is on the main sequence, fusing H into He in its core, and the He is building up in the core. As the He buids up, it acts like ashes, choking fusion in the core, which of course starts to contract (a star's core will always contract until it's stopped by some energy source pushing outward, or by degeneracy pressure preventing further contraction!). As the core contracts and heats up, hydrogen in the region just outside the core, which was formerly not hot enough to fuse, is raised above the H-fusion temperature of 10⁷K, and is ignited in a phase called "Hydrogen Shell Burning." The H shell fusion produces more energy than the star's core did on the main sequence, and so the outer layers of the star are puffed out by the additional radiation pressure until they become very tenuous. Since they're a greater distance from the hot center of the star, they also cool off somewhat, and the star is now brighter, redder, and much less dense at the surface than it was. This is the Red Giant phase of the star's life.

A red giant is much larger in diameter, but it has the same mass as it had on the main-sequence. Therefore, the average density of the red giant must be lower than the star's density was on the main sequence, since the mass is spread out over a larger volume. Also, the red giant is much brighter than it was when it was a main-sequence star. This is due to H shell-burning and He core fusion rates producing more total energy than the main-sequence core H fusion. The star's core is becoming more compact than it was on the main sequence, so the fusion rate must fight more of an uphill battle against gravity.

Meanwhile, in the three-solar-mass star's core, the He becomes denser and denser until it is a lattice of Helium nuclei with every possible energy level for the electrons filled. It has become degenerate matter, a lattice of steel-hard Helium held up against further compression by electron degeneracy. A degenerate lattice is a very effective superconductor, so that as the pressure on the core continues to mount and the temperature reaches 100 million Kelvin, the whole core will immediately reach the same temperature, wherever it's degenerate. The result is a sudden huge flash of He fusion, called the Helium Flash, and as fusion is re-established in the core, the core expends a bit -- the degeneracy is "lifted." A more massive core would have reached the temperature for He fusion before degeneracy set in, so there would have been no He flash. All of this action down in the core is reflected eventually in the outer layers of the star by the "blue loop" the star makes on the H-R diagram as it adjusts to its new He fusion rate. Helium is now fusing into Carbon (mostly, and a few side-reactions produce Oxygen as well) in the core. Less energy is liberated per fusion of He than was liberated per fusion by H fusion. This is partly due to the fact that it takes a lot of energy to get a He nucleus moving fast enough to achieve fusion. Since the total energy the star must produce is greater due to the greater compression, the He is used up much faster than the core H was used up -- typically a star is only a red giant for perhaps a tenth as long as it was on the main sequence.

Eventually, the star starts to run out of He in the core. It is buiding up Carbon/Oxygen ashes to choke the He fusion just as previously the He buildup had choked H fusion. Of course the core contracts! Outside the core, in a shell that used to be too cool to fuse Helium, the temperature is now right, so He shell-burning starts. At the same time farther out H shell-burning may also be going on. The star's cross-section is beginning to take on the structure of an onion: layers of different elements produced by different kinds of fusion surround the core. Hydrogen in the outer parts, a H-fusing shell, Helium where H-fusion has run its course, and a He-fusing shell, finally C (and a little O) where He fusion has run its course.

What happens next depends critically on the current mass of the core (which is most of the mass of the star, since the outer layers are puffed 'way out and have very low density). If the mass of the core were under 1.4 solar masses (this is possible; a star can lose a lot of mass in its red giant phase), then there would be insufficient mass to compress the core enough to reach the temperatures needed for C fusion to occur (600 million K). As a result, the core energy generation will cease (choked by C buildup), and the core will contract until it is nothing but a ball of degenerate Carbon -- Carbon atoms supported in the incredibly incompressible lattice of electron degeneracy -- a "diamond" in the sky! Outside the core, there will be a He-fusing shell, an H-fusing shell, and the outer layers of the star will probably be puffed so far out that they detach themselves entirely -- the ring of expanding gas is called a planetary nebula. The exposed inner layers of the star are incredibly hot, so they produce a great deal of UV radiation, which ionizes the expanding gas ring, making a very interesting-looking astronomical object (well, to me!). That central star of the planetary nebula (has nothing to do with planets, it just looked like a planet disk to old-time observers, then some though they formed planets -- they don't -- and the name stuck) will eventually lose most of its remaining "atmosphere" and will become a white dwarf.

A white dwarf formed in this way is supported against gravity by the electron degeneracy of its Carbon core. It glows, but only with "fossil" heat -- there is no more energy production going on. It is very small in radius (diameter of the Earth), and very hot at the start (typically tens of thousands of degrees Kelvin), but it has the mass of a typical star: under 1.4 solar masses. Therefore it is extremely dense (15 tons per teaspoonful!). Its future is that it will cool down slowly and eventually could be called a "black dwarf," but the Universe isn't old enough for that to have happened yet. Some writers prefer to call the white dwarf not a star at all anymore, but a "compact object."

If, on the other hand, the mass of the core is greater than 1.4 solar masses, the Carbon degeneracy will set in, just as with the white dwarf, but the mass of the core has enough self-gravitation to produce sufficient pressure to heat the core above the C-fusion temperature, and once again, when any part of a degenerate gas is at the necessary temperature for fusion, almost immediately ALL of the degenerate gas is at that temperature (that's what "superconductor" means). So fusion initiates all over the degenerate C core at once in a much more ferocious incident called the Carbon Detonation. If the star does not blow itself apart at this point (a distinct possibility), the fusion of Carbon will lift the degeneracy and the core will have its next "stable" energy source. Carbon fuses by various means into many different heavier elements, such as Oxygen, Silicon, Fluorine, Nitrogen, etc., so the core will contain all of these as ashes of the fusion process. Successive fusion of heavy elements will continue until the core produces Iron (chemical symbol: Fe). At that point some serious things can happen: see the evolutionary paths described below...

SAMPLE EVOLUTIONARY PATHS

• Less than 0.4 solar masses: Protostar -- M-type main sequence star -- ?? -- white dwarf (held up by electron degeneracy in the Helium component of the star)
  
  
• Above 0.4 to 3 solar masses: Protostar -- main sequence star -- H shell-burning phase red giant -- Helium flash! -- He core burning red giant -- central star of planetary nebula -- if final core mass less than 1.4 solar masses -- white dwarf (held up by electron degeneracy in the Carbon/Oxygen core of the star). If core mass > 1.4, see Carbon Detonation, below.
  
  • If white dwarf gains enough mass in a binary system due to mass overflow from its giant-phase neighbor, it may exceed the 1.4-solar-mass limit (called the Chandrasekhar limit), and the result is likely to be one type of supernova.
    
  
  
• Above 3 solar masses: Protostar -- main sequence star -- H shell-burning phase red giant -- He core burning red giant (no degeneracy so no flash) -- if core is between 1.4 and 9 solar masses -- Carbon Detonation! -- if star blows apart in the detonation, this might be another type of supernova (there are at least two different observed types, and probably more: they're rare enough that we've only seen a few actually "going off"), if not, Carbon will fuse into heavier elements in the core and so forth until an Iron (Fe) core develops. Once Iron fuses, the core is doomed, because to fuse Iron takes more energy than the fusion gives back. This is called an endothermic reaction. It "kicks the supports out from under" the core and the core collapses in a few thousandths of a second.
  
  • What happens to the core? If the final core mass is between 1.4 and 3 solar masses, the result is a neutron star (see chapter 15 section of the next study guide). In a neutron star, the protons and electrons of individual atoms have been forced into one another, forming a giant ball of neutrons about 10 km in radius. It is supported by neutron degeneracy, which is stronger than electron degeneracy. Some neutron stars will be pulsars, depending on what angle we see them from.
    
    
  • Meanwhile, what happened to the envelope? Supernova explosion! Shock waves from the collapse of the core blew the outer portions of the star apart, causing all sorts of heavy-element fusion in the onion-layers of the star. What's left behind is a fast-expanding sphere of star-stuff, the body of the star, spiked with heavy elements like gold, lead, uranium, etc., heading out into interstellar space, perhaps to eventually encounter a cold hydrogen cloud and with its blast wave set off the gravitational instabilities that lead to star-formation all over again. If the final core mass is above 3 solar masses, see the next section on black holes!
  
  
  
• If the core mass is above 9 solar masses there is no Carbon Detonation, and if the final core mass is above 3 solar masses, even neutron degeneracy won't be able to hold the star up against its own gravity during the Iron-fusion-induced collapse. The star's extreme mass will push right through the neutron degeneracy and the core will continue to collapse (all this is taking less than a second!). What happens? The escape velocity from the surface, you'll recall, is:
  V_esc=(2GM/R)^1/2,
  so that as R gets smaller and smaller, V_esc gets higher and higher. Eventually at some radius (The "Schwarzschild Radius," which is 3 km for every solar-mass-worth in the star's mass, so a 3-solar-mass black hole has a 9-km Schwarzschild radius), V_esc = c (the speed of light, 3x10⁸ m/sec), and after that we can not know what state the matter might be in -- it can never again communicate with the Universe outside this radius! The star has become a black hole. As for the outer layers, we would still expect a supernova explosion of some kind, but the calculations of supernova explosions still contain enough unknowns that we are not sure exactly what type of supernova explosion we should expect.

Globular Clusters:

Some clusters formed a long time ago, when the Galaxy itself was forming. These clusters formed from much more massive lumps of gas than the gas that forms open clusters -- in these very round clusters there are ten thousand to a million stars! Because they are so beautifully round and compact, they are called globular clusters. The members of the cluster do not "smear out" over time because the cluster is so compact for its mass -- 10 to 30 pc across, the same linear diameters as open clusters, but containing more than 10⁶ solar masses (which on average means about 10⁶ stars -- our Sun having a pretty typical mass). The members of these clusters are in their cluster "for life," and as a result, we can watch what the H-R diagram of a globular cluster looks like and see stellar evolution in action.

Figure: H-R diagram of a globular cluster:

Because they are old, and all their member-stars stayed together with no new star formation, globular clusters tend to be redder in color than open clusters -- all the hot blue stars they were born with have become red giants or even completely finished evolving! Only the lower-mass, redder stars are still on the main sequence.

Since globular clusters formed about the time our Galaxy first started to collapse into stars, the motions of globular clusters around the galactic center are fairly chaotic -- their orbits are elliptical and highly inclined to the plane of our galactic disk. The motion has been described as a sort of "swarming" motion, with the center of our Galaxy at the center of its particular swarm of globular clusters. Other large galaxies also have globular clusters, which show similar characteristics. Within each globular cluster, the stars themselves have "swarming" orbits around the center of mass of the cluster (which makes sense since these clusters are so spherical in shape).

Finally, because they formed so early in our own Galaxy's history, there hadn't been many supernova explosions by the time the globular clusters' stars started forming, so the stars in globular clusters are said to be "metal-poor" (they have much smaller than solar-value amounts of elements heavier than Hydrogen and Helium). Their stars are "Population II stars," which implies low-metal, older stars that formed before many supernova remnants could seed the interstellar medium (gas between the stars in a single galaxy) with heavy elements.

Cepheids and RR Lyrae Variable stars:

A star that varies in brightness over time is called a variable star. There are several different types, but they have in common that they are pulsating -- they are expanding and contracting with a certain period. The length of one expansion and contraction full cycle is the period of pulsation. Some stars do pulsate while still quite near the Main Sequence, but most are already red giants of some kind when they start to pulsate.

For very massive stars that pulsate, more mass has to get turned around, from falling inward to expanding outward, to falling inward again, and more massive stars also are "puffed out" more in the red giant phase, so their atmospheres take longer to "get the message." As a result, the more massive and bright the pulsating red giant, the longer the period of the pulsation. These pulsating red giant stars with a relationship between period and luminosity are called Cepheid variables, after the first one that was well-studied, the star Delta Cephei (fourth brightest in the constellation Cepheus). There are two types, but they both display this period-luminosity relationship. As a result, if we can see a pulsating Cepheid variable in, for example, a globular cluster, we can determine what the Cepheid's absolute magnitude (M_v) must be (by measuring its pulsation period), and use the distance modulus equation: m_v - M_v = 5log(d) - 5 to get the distance to the globular cluster. Cepheids are very useful for finding distances within our Galaxy because they are so bright -- up to -6 in absolute magnitude (the Sun's around +5). We'd have to know whether our star was a Type I or Type II Cepheid, of course.

Another useful kind of variable star is the RR Lyrae variable, which is also fairly bright (M_v = 0 to 0.5), although not as bright as the Cepheids. Where Cepheids have periods from 1 to 100 days or more, RR Lyrae stars pulsate with periods of several hours up to 20 hours or so. Here is the diagram of the period-luminosity relation for these two types of variables:



RR Lyrae stars in globular clusters were used to help calibrate the distances to Cepheids that eventually led to the absolute magnitude scale of the Cepheid period-luminosity relation (figure 13-21 in your text). Cepheids themselves were also used, in a statistical method that you'll read about below (Milky Way).

Mass-transfer Binary systems:

Sometimes a binary system will form in which the two stars are close enough together that interesting things may happen. The more massive star will evolve off the main sequence before the less-massive companion. If it swells to a great enough radius, the outer parts of the star's red giant atmosphere will expand past the point of equal gravitational pull between the two stars (called the "inner Lagrangian point"), and that material will try to fall onto the companion. Since the stars are orbiting one another, the matter falling onto the companion will have to play catch up with the less-massive star, and so a disk is likely to form around the smaller companion. This is called an "accretion disk" and it allows matter to accrete onto the less-massive star, coming from the overflowing more-massive star as it swells. This swelling past the point of equal pull is called "overflowing the star's Roche lobe," where the Roche lobe is the teardrop-shaped 3-dimensional surface inside which matter is gravitationally bound to the star. Outside of that surface, matter will be drawn onto the companion or lost into the surrounding space by the rotation of the binary system. (Imagine how odd a triple-system's Roche lobes might look!) This overflow from a binary "buddy" is virtually the only way that a star may increase its mass during its lifetime.

Once the "red giant" star has become a white dwarf, neutron star, or black hole (depending on its final core mass), it may become the companion's turn to overflow its Roche lobe, and dump mass from its red giant envelope into an accretion disk around the w.dw., n.s., or B.H. When it does that, more interesting things can happen. If the recipient is a white dwarf, the system may become a nova, brightening greatly when sufficient hydrogen has been deposited on the dwarf's surface to initiate a burst of surface fusion. Novae are fairly common. If enough mass is transferred onto the white dwarf to raise it above the Chandrasekhar limit (1.4 solar masses), there may be a Type I supernova explosion and the white dwarf will collapse through its electron degeneracy into a neutron star. This is not a very commmon ocurrence!

If the recipient is already a neutron star, chances are very good that an accretion disk will form (the stars smaller radius and larger mass means incoming matter will be moving faster and will need the disk, to allow it to lose angular momentum and fall onto the neutron star). There will most likely be X-ray bursts and gamma-ray bursts from the accretion of matter onto the million-degree surface of the neutron star. Hercules X-1 is an X-ray source in which the accreting neutron star is also a pulsar.

If the recipient is a black hole, the accretion disk will get so hot (due to orbital velocity) in its inner regions that it will radiate strongly in X-rays. These systems are called X-ray binaries, and while they do sometimes have outbursts, they also flicker on very short timescales and display masses greater than 3 solar masses for the "unseen" disk-surrounded companion. All of these are indicative of the small size and intense gravitation of a black hole.

Jets and disks: Some very hot disks, or systems with strong magnetic fields, can form jets perpendicular to the accretion disk. These sorts of bipolar outflows are fairly common at all size scales in our Galaxy and in the Universe. Disks, too, are extremely commonly encountered.

1. Complete the following table:

PHASE		energy source		support against gravity			sizeprotostar									light-hours (1012 m)main sequence 									light-seconds (109 m)red giant									light-minutes (1011 m)white dwarf									Earth-sized (107 m)neutron star									city-sized (> 10 km)black hole									a little "smaller"

2. Which is the end state likeliest for a 0.8 solar-mass star? For an 80 solar-mass star?

3. Using the diagram (figure 13-21) on page 260, find the distance to a Type I Cepheid with an apparent magnitude of 12 and a period of 10 days. (Use a corner of a piece of paper to read off the absolute magnitude at a right angle to the edge up from the period. Estimate to the nearest .5 mag or better!)

4. Find the approximate distance to an RR Lyrae variable with an apparent magnitude of 5.

5. A red giant is much brighter than the main sequence star it came from. It also has a larger size. Is it more massive, and if so, how did it get that way? If not, why is it larger?

6. What is the expected luminosity of a ten-solar-mass star? What is its expected lifetime?

7. If a neutron star has a radius of 10 km (1x10^-8 solar radii) and a surface temperature of 10⁶K (500 times solar), use the Luminosity-Radius-Temperature equation (in formulas section at end) to find its luminosity. Why don't we see any neutron stars except as pulsars?

8. What causes the Helium Flash? What causes the Carbon Detonation? Why do really massive stars never have either a Helium Flash or a Carbon Detonation? For what core mass is it possible to have BOTH (assuming the star doesn't blow up entirely)?

9. Why does the H-R diagram of a globular cluster have a clearly-defined turn-off point from the main sequence?

10. Would you expect to find any white dwarfs in an open cluster?

11. What makes a planetary nebula glow? Can we determine any limits (upper or lower) on the mass of the central star of a planetary nebula?

12. Why does the Earth have heavy elements such as Uranium, Gold, and Lead in it? If all of the Universe started as a gas of almost-pure Hydrogen with a little Helium, where did the heavier elements come from?

13. Approximately when will our planet be engulfed by the Sun? (hint: the Sun is currently about 5 billion years old)

14. A star is fusing Carbon in its core for about 600 yrs, Neon for one year, Oxygen for 6 months, and Silicon fusion (produces Nickel through Iron) supports it for only one day. What happens then?

15. For a globular cluster and an open cluster give their typical characteristics: diameter? number of stars? is it gravitationally bound, or will it be smeared out by Galactic rotation? how about age? heavy elements?

16. How can you tell a star cluster's age?

17. What single property of a (single) star most strongly determines its entire future?

18. What type of star can be described as having a structure like a "rigid crystalline lattice," or "diamond in the sky"? What else can it be rightly called, other than "star"?

19. What's dangerous about a black hole? Will a black hole eventually suck up everything in the Universe, like an unplugged leak in space-time?

20. Name three common ways to get X-rays from binary star systems.

21. What's an accretion disk?

22. Can a white dwarf ever become a neutron star? If so, how? Is this a common ocurrence?

You can reach me by e-mail at: hpreston@grits.valdosta.peachnet.edu
Return to Heather's Homepage