Chapter 22

Certain stars, like Betelgeuse, have a lower surface temperature than the Sun and yet are more luminous. How do these stars produce so much more energy than the Sun?

Certain stars, like Betelgeuse, have swelled up to be giant stars. They produce more overall energy because of their much larger size (while each piece of the star's surface is cool, there are so many pieces that, overall, the stars give out more energy).

The nuclear process for fusing helium into carbon is often called the "triple-alpha process." Why is it called as such, and why must it occur at a much higher temperature than the nuclear process for fusing hydrogen into helium?

A helium nucleus (two protons and two neutrons) is called an alpha particle by physicists, and it takes three (triple) helium nuclei to simultaneously come together to ultimately form a carbon nucleus. Since each helium nucleus has two positive protons, the six protons repel each other, and it takes a lot of kinetic energy and temperature to get the three helium nuclei to stick together.

What is a planetary nebula? Will we have one around the Sun?

A planetary nebula is the distended outer atmosphere of a giant star as it floats away and is made to glow by ultraviolet light from the hot star that is collapsing inside the nebula. This is a stage that low-mass stars go through. The Sun, which is considered a low-mass star, will eventually have a planetary nebula form around it billions years from now, after it has been a red giant.

Astronomers find that 90% of the stars observed in the sky are on the main sequence of an H-R diagram; why does this make sense? Why are there far fewer stars in the giant and supergiant region?

Being on the main sequence means that the star is converting hydrogen to helium in the core. Since stars are made mostly of hydrogen, this process takes approximately 90% of a star's life. Thus it makes sense that the 90% of the stars observed at some particular time would be undergoing this process. Being a red giant star is a brief stage in the life of each star, when the star is readjusting to the loss of energy from the fusion of hydrogen. In a relatively short time (in the timescale of stars), the core collapses until it is hot enough for the fusion of helium into carbon, restoring the star's equilibrium. Since this is only a brief stage in the life of the star (taking only a few percent of the star's life), it makes sense that only a few percent of stars will be found in the giant stage at any given time.

Referring to the H-R diagrams in Exercise 15, which diagram would more likely be the H-R diagram for an association?

Diagram A, since an association generally consists of very young stars.

Describe the evolution of a star with a mass similar to that of the Sun, from the protostar stage to the time it first becomes a red giant. Give the description in words and then sketch the evolution on an H-R diagram.

During the protostar stage, gravity gathers gas and dust toward a central location, which increases in temperature and pressure. Eventually, the temperature and pressure at the center of the gas and dust will reach critical thresholds and the nuclear fusion of hydrogen into helium will begin in what is now called the core. When this happens, the protostar officially becomes a zero-age main sequence star. For the next 10 billion years or so, the star will stably undergo nuclear fusion as it remains on the main sequence. Once the hydrogen gas runs out in the core, gravity will begin to re-collapse the stellar atmosphere above the core, which in turn increases the temperature and pressure within the core again. While this occurs, a hydrogen shell around the core will begin nuclear fusion, causing the star to swell and become more luminous as it enters the red giant phase. Eventually, the temperature and pressure in the core will reach another set of critical thresholds and the nuclear fusion of helium into carbon will commence in an explosive helium flash, officially beginning a more stable phase.

Describe the evolution of a star with a mass similar to that of the Sun, from just after it first becomes a red giant to the time it exhausts the last type of fuel its core is capable of fusing.

During the red giant phase, the star is swelling up (becoming larger and cooler at the surface) due to the fusion of hydrogen in a shell around the collapsing core. Eventually, the helium gets hot enough to be fused to carbon in the core, and the star regains a temporary equilibrium. When all the helium hot enough to fuse carbon is exhausted in the core, the star swells again as the inert core of carbon tries to reach a temperature and pressure necessary for the next fusion stage. For stars like the Sun, that is not possible after the fusion of helium into carbon (and a bit of oxygen), so this is the last fuel it is capable of using.

In which of these star groups would you mostly likely find the least heavy-element abundance for the stars within them: open clusters, globular clusters, or associations?

Globular clusters: they have very low heavy-element abundances because they contain very old, first-generation stars that are composed of only hydrogen, helium, and traces of lithium.

Explain how an H-R diagram of the stars in a cluster can be used to determine the age of the cluster.

Initially, most of the stars in a cluster will be distributed all along the main sequence of the H-R diagram. Eventually, the more massive stars will end the hydrogen fusion in the core and move off the main sequence, creating a "turn" in the distribution of the stars in the cluster on the H-R diagram. As more time goes by, stars of even lower mass (and lower on the main sequence) will move toward the giant branch of the diagram, leaving the top of the main sequence without stars on it. The location of the turn thus indicates the age of the cluster.

Why are star clusters so useful for astronomers who want to study the evolution of stars

It is reasonable to assume that the individual stars in a cluster all formed at nearly the same time from the same cloud of gas and dust. As a result, the only initial difference between the stars is their mass (and not their composition or the time that they began). Therefore, as we put all the stars in a cluster on an H-R diagram, we can see how stars of different mass will change their positions in the diagram over time and build up a picture of how stars of different mass go through the stages of their lives. Also, because high-mass stars evolve much more quickly than low mass stars, we can estimate the age of a cluster of stars by observing where its stars are currently leaving the main sequence.

Describe the two "recycling" mechanisms that are associated with stars (one during each star's life and the other connecting generations of stars).

One recycling mechanism is that stars can sometimes use the "ash" from one nuclear fusion process as the "fuel" for the next (i.e., hydrogen fuses into helium, and then helium fuses into carbon). Another recycling mechanism is how all stars eventually end their lives by sending back into the cosmos a considerable part of their mass and all the elements within; this material becomes part of the interstellar medium of gas and dust that can form more stars.

Gravity always tries to collapse the mass of a star toward its center. What mechanism can oppose this gravitational collapse for a star? During what stages of a star's life would there be a "balance" between them?

Outward radiation pressure from gamma rays created by fusion in the core of the star opposes the inward gravitational collapse when a star is in equilibrium. Balances are generally achieved when there is a "fuel" (element) hot enough to fuse in the core, like during the main-sequence stage when hydrogen fusion occurs and during helium core fusion after the helium flash.

Compare the following stages in the lives of a human being and a star: prenatal, birth, adolescence/adulthood, middle age, old age, and death. What does a star with the mass of our Sun do in each of these stages?

Prenatal: A human fetus is still very much dependent on its environment (womb) and receives resources from it. It cannot function on its own. Like a child before birth, the protostar is completely reliant on its environment; a giant cloud of gas and dust begins to collapse from a cloud of cosmic "raw material" due to gravity; the protostar grows in size, temperature, and internal pressure. Birth: A baby is "disconnected" from its mother, and now has to live on its own (eat, breathe, etc. for itself). Similarly, a star is now able to sustain itself by making its own energy. The nuclear fusion of hydrogen into helium begins in the core. Adolescence/Adulthood: A human learns to do whatever it is going to do as an adult and then continues to do those things for the longest part of its life. For a star, nuclear fusion continues in the core while it maintains equilibrium. This is when the star is on the main sequence, and it takes up 90% of each star's life. Middle age: This is when a human being is typically in the prime of his career. The Sun is very much a middle age star right now, in the middle of its main sequence cycle. Old age: Humans are not as healthy as they once were, and don't quite have the energy of their younger selves. Humans sometimes have a late-in-life crisis where they need to (or their health or family forces them to) make a change. For stars, nuclear fusion of hydrogen to helium ends in the core, and the star goes into another fusion stage of converting helium to carbon, swelling up into a red giant. Death: Biological processes begin to fail in a human being, and those failures can quickly cascade, leading to death. In a star, once all nuclear fusion processes cease as the outer part of the star is lost through winds and other processes, the star dies (becoming a planetary nebula) and the hot, inert core begins to cool off.

Would the Sun more likely have been a member of a globular cluster or open cluster in the past?

The Sun more likely would have been a member of an open cluster with other stars that would have formed from the same cloud of gas and dust. Stars in an open cluster can have a range of ages, whereas stars in a globular cluster are all very old—much older than the current age of the Sun. Also, if we had been born in a crowded (dense) globular cluster, all the stars in the cluster would still be around us and with us. In contrast, stars in a loose open cluster can disperse with time, leaving a star like the Sun alone later in its life (just as we now are).

Where did the carbon atoms in the trunk of a tree on your college campus come from originally? Where did the neon in the fabled "neon lights of Broadway" come from originally

The carbon could have come from the product of helium fusion (the triple-alpha process) in a high-mass star. Neon must have come from fusion inside of a high-mass star, as its atomic number is higher than that of carbon and therefore could not be produced in low-mass stars. ]

Suppose you were handed two H-R diagrams for two different clusters: diagram A has a majority of its stars plotted on the upper left part of the main sequence with the rest of the stars off the main sequence; and diagram B has a majority of its stars plotted on the lower right part of the main sequence with the rest of the stars off the main sequence. Which diagram would be for the older cluster? Why?

The crucial idea here is that the more massive the star, the more quickly it goes through each stage of its life. The older cluster would be represented by diagram B, which indicates that higher-mass stars have already evolved past the main-sequence stage of their lives, while the lower-mass stars continue to be on the main sequence. Diagram A indicates a young cluster, as only the higher-mass stars have reached the main-sequence stage and the lower mass stars are still protostars and have yet to reach zero-age main sequence.

On which edge of the main sequence band on an H-R diagram would the zero-age main sequence be?

The zero-age main sequence would be on the left edge of the main sequence band.

Pictures of various planetary nebulae show a variety of shapes, but astronomers believe a majority of planetary nebulae have the same basic shape. How can this paradox be explained

There is a variety of planetary nebula shapes because astronomers are looking at the same basic shape (a thicker torus right around the star or stars and outflows through the hole in the torus in opposite directions) from different points of view.

A star is often described as "moving" on an H-R diagram; why is this description used and what is actually happening with the star?

What is actually happening is that the star is progressing into different evolutionary stages, during which various properties of the star (mass, luminosity, radius, etc.) change. The H-R diagram plots a star's luminosity versus its surface temperature. As the star evolves, these characteristics change. When the star is plotted on an H-R diagram as it goes through these evolutionary stages, the star's "dot" on the diagram moves from one location to another.

What is the first event that happens to a star with roughly the mass of our Sun that exhausts the hydrogen in its core and stops the generation of energy by the nuclear fusion of hydrogen to helium? Describe the sequence of events that the star undergoes.

When all the hydrogen that's hot enough to fuse into helium has been turned into helium, the star's core no longer has a source of energy. The inert core begins to collapse due to gravity and to increase in temperature and pressure. The increasing temperature then heats the surrounding layers of hydrogen until nuclear fusion can start within them. Energy from all the fusion in this growing layer (or shell) then pours outward. The result is a star that begins to swell in size; as it grows, its outer layers cool off and the star becomes a red giant.

How do stars typically "move" through the main sequence band on an H-R diagram? Why

When nuclear fusion begins, a star is plotted on the left edge of the main sequence band (the zero-age main sequence) and then makes a slow progression up and to the right edge of the main sequence band. As a star converts hydrogen to helium in its core, it gradually increases in luminosity and size. Note that this is a very short distance for the star to travel, and it takes 90% of its lifetime to do so. Because the main sequence is a fairly narrow band of properties, for most practical purposes, astronomers state that a star is nearly fixed in place on the H-R diagram and undergoes only minimal changes during its hydrogen core fusion stage.