Ch. 12: Homework

The following figure displays the evolutionary track of a 1-MSun star. Place each description of the evolutionary stage in its correct location. You may need to use the scrollbar to view all answer options.

A, E, B, D, and C A. A hydrogen-burning shell surrounds a degenerate helium core. E. A hydrogen shell surrounds a helium-burning core. B. Both a hydrogen-burning shell and a helium-burning shell surround a degenerate carbon core. D. Outer layers of stellar atmosphere are ejected into space. C. A degenerate carbon core radiates energy directly into space.

-article- Can this kind of explosion occur in an isolated star? Explain your reasoning.

A. No, a nova requires bursts of hydrogen fusion on the surface.

This figure shows the difference in size between the Sun on the main sequence and the Sun when it will be at its largest size as a red giant star (note that the image of the main-sequence star on the right is a blown-up view of the tiny to-scale Sun to the left of it). A star's size is determined by the relative strength of forces attempting to make it collapse and forces attempting to make it expand. The balance between gravity and pressure causes a star to retain a roughly constant size throughout its main-sequence lifetime. When it runs out of hydrogen and nuclear fusion stops in the core, the pressure drops and the star collapses. Based on this and the descriptions in the figure, why does it then expand in size during the red giant phase?

A. The hydrogen shell burning is producing more total energy than the core hydrogen burning did.

-passage- Ordinarily, the hotter an object is, the more luminous it is. In this case, the temperature has gone down, but the luminosity has gone up. How can this be?

A. The radius is larger.

-passage- As a star leaves the main sequence, it moves up and to the right on the H-R diagram. Grab the cursor (the X on the H-R diagram), and move it up and to the right. How does the test star's temperature change?

A. The test star becomes redder.

This image shows a low-mass star shedding its outer layer. What happens during this process?

B and C B. A planetary nebula is created. C. The star becomes a white dwarf.

An AGB star expands to a much larger size (rAGB) than it did during the red giant phase for our Sun. Recall that the force of gravity between two objects is given by this equation, where m1 and m2 are the masses, and r is the distance between them: How will the gravitational force on a piece of the surface of the star (m1) by the mass of the rest of the star (m2) (effectively located at a point at the center of the star) compare between the AGB and main-sequence phases of a particular star, assuming its mass stays the same?

B. The surface will feel a weaker gravitational force during the AGB phase because it is farther from the center of the star.

We will now specifically consider low-mass stars such as the Sun, which have masses less than 3 solar masses. As the star collapses, it becomes denser and hotter, until the layer just outside the helium ash core reaches the temperatures necessary to burn hydrogen (10 million K). The star moves off the main sequence and enters the next phase in its life, where it is now fusing hydrogen into helium in a shell surrounding a core of nonburning helium. The red line on the H-R diagram here shows the "red giant branch," and describes how the star changes (following the white arrow) as it moves away from the main sequence during this phase. Based on your observations of this diagram, choose all the statements that correctly describe what is happening to the star during this time.

C and D C. The star is getting redder. D. The star is getting larger.

-article- The reporter states that "Such a 'pre-maximum halt' had been theorized before, but evidence for its existence had been inconclusive." Think back to Chapter 1. Is the reporter using the word theory correctly here?

C. No, a theory is a hypothesis that has been verified over and over and has never been contradicted.

-passage- How does the test star's luminosity change?

C. The luminosity increases.

-passage- How does the test star's radius change?

C. The radius increases.

-passage- As a star leaves the main sequence, it moves up and to the right on the H-R diagram. Grab the cursor (the X on the H-R diagram), and move it up and to the right. What changes about the image of the test star next to the Sun?

C. The test star becomes larger, brighter, and redder.

-article- What kind of stellar explosion is being discussed in this article?

C. novae

The figure below shows two scenarios—one that could lead to a nova (left) and another to a Type Ia supernova (right). If a white dwarf is able to gain enough mass to exceed 1.4 solar masses (the Chandrasekhar limit), its self-gravity will be stronger than electron degeneracy pressure, and the star will collapse. As it does so, its temperature increases to the point that carbon can undergo nuclear fusion, and the entire star ignites as a giant carbon bomb. This "Type Ia supernova" explosion always happens at the same mass and, thus, the same luminosity. So much energy is released that the supernovae from very distant galaxies can be easily detected from Earth. Consider this information, and choose the property below that Type Ia supernova can help us measure.

C. the distance to a galaxy

In a white dwarf, electrons are packed in so tightly that they physically cannot get any closer to one another. This provides an overall outward force, similar to the white dwarf's thermal pressure but much stronger, called electron degeneracy pressure, which does not depend on the temperature of the material. A white dwarf no longer has any ongoing energy production from nuclear fusion, so it will continuously cool off with time. Taking into consideration all the forces acting on each piece of the white dwarf, what will happen to it as it cools?

D. It will stay constant in size.

-article- One of the main advantages of these newly available observations is that they take a picture of the same region of the sky every 102 minutes. Why is that an advantage in studying novae?

D. We can detect the changes of a star's brightness over time.

A puffed-up AGB star is unable to hold onto its outer layers, which expand into a planetary nebula, as shown in the image below: At the center, the very dense carbon-ash core of the star is left behind: a white dwarf. The image below shows the path the star takes on the H-R diagram as it sheds its outer layers and settles down as a white dwarf, which has no fuel left to burn. Based on the white dwarf's position in the H-R diagram, which of the following statements is true?

D. White dwarfs are fainter than stars in other stages at the same temperature because they are smaller.

The following images represent different evolutionary stages of a post-main-sequence star of 1 MSun. Place them in chronological order. You may need to use the arrows to view all of the placement choices.

Earliest to Latest stage: 1) Red giant star 2) He flash 3) H. branch star 4) AGB star 5) Nebula ejection 6)White Dwarf

The star suddenly shifts to the horizontal branch (red dot at the bottom of the upper red line via the blue arrow). Eventually it runs out of helium to burn in the core, and instead begins to burn helium in a shell around the carbon ash core, surrounded by another shell burning hydrogen. As it does this it follows the upper red line (along the white arrow) on the diagram: the asymptotic giant branch. Based on your observations of the H-R diagram and what you have learned of the balance between gravity and pressure, sort each stage of a star's life below in order of increasing energy produced by the peak of its nuclear reactions.

Lowest energy to Highest energy: 1) Main-sequence star 2) Horizontal branch star 3) Red Giant star 4) Asymptotic giant branch star

The following image shows a cross section of a horizontal branch star. Place each label in the correct position on the image.

Top to Bottom: A. Burning helium B. Burning hydrogen C. Non-burning hydrogen

The following image is a cross section of a red giant star. Place each label in the correct position on the image.

Top to Bottom: B, A, and C B. Non-burning helium A. Burning hydrogen C. Non-burning hydrogen

The following image is a cross section of an asymptotic giant branch star. Place each label in the correct position on the image.

Top to Bottom: D, C, B, and A D. Non-burning carbon C. Burning helium B. Burning hydrogen A. Non-burning hydrogen

The following graphs relate the amount of hydrogen (shown as light-blue regions) and helium (shown as light-purple regions) within the Sun at three different moments in time. On each graph, the horizontal axis denotes the fraction of radius (distance from the center), and the vertical axis denotes the percentage of mass (the relative amounts of hydrogen and helium). Match each graph to the appropriate evolutionary stage of the Sun.

When Sun formed: - straight line Sun today: - 60 decline, then constant Sun in future: -

The H-R diagram of five different star clusters is given here. Rank them in age from youngest to oldest based on the appearance of each diagram.

Youngest to Oldest 1) longest white line keep declining 5) Shortest white line

-article- Which figure below (all of them can be found in the chapter) corresponds most closely to the astronomical events being discussed in this article? Scroll down to see all four images.

answer: A first graph with star 1 and 2, all black

The path of evolution of a Sun-like star is shown on this H-R diagram. Match the pictures of the star's changing interior to the proper places on this evolutionary track. Be careful not to overlap images.

start at the sun and follow the red line: B, E, C, A, D (see text book page 319 for the actual image/diagram)

The growth of a red giant can be compared to the growth of a snowball going downhill. Every change in the conditions inside the star leads to even more rapid change and growth. Order these steps in the snowballing growth of a red giant.

start right after the blue box and go clockwise: C, A, D, B, and E C. ...stronger gravitational force, which leads to... A. ...higher pressure in H-burning shell, which leads to... D. ...faster nuclear burning, which leads to... B. ...faster conversion of H to He, which leads to... E. ...faster growth of helium core mass, which leads to...

The following image shows the lifetime of a low-mass star on the H-R diagram. Place each label in the correct position on the image.

start where the sun would be (far light beginning of red line): A, D, E, C, and B A. Main-sequence star D. Horizontal branch star E. Helium flash C. Planetary nebular ejection B. White dwarf

This H-R diagram shows five possible protostar evolutionary tracks, each one ending at the main sequence. Match the given main-sequence lifetimes with the star that would result from each evolutionary track.

top to bottom diagonally: E, A, C, B, and D E. 4 million years A. 20 million years C. 800 million years B. 10 billion years D. 30 billion years

The following image is a schematic of the triple-alpha fusion process. Place each label in the correct position on the image.

top to bottom going diagonally: B, A, D, and C B. Helium A. Beryllium D. Carbon C. Gamma ray