Ch 20 Homework

If the luminosity of a main-sequence star is proportional to the fourth power of the star's mass, what is the mass of a star that is just now leaving the main sequence in a cluster that formed 4 billion years ago? Express your answer using two significant figures. M = ________ solar units

M = (10^10 years/4 × 10^9 years)^(1/3) M = 1.4 solar units

On the main sequence, massive stars

burn their hydrogen fuel more rapidly than the Sun.

Compared to other stars on the H-R diagram, red-giant stars are so named because they are

cooler.

Compared to the Sun, stars plotted near the bottom left of the H-R diagram are much

denser.

A star will evolve "off the main sequence" when it uses up

most of the hydrogen in the core.

If the evolutionary track in Overlay 3, showing a Sun-like star, were instead illustrating a significantly more massive star, its starting point (stage 7) would be

up and to the left.

When the Sun is on the red-giant branch, it will be found at the

upper right of the H-R diagram.

A star like the Sun will end up as a

white dwarf.

Evolutionary changes and hydrostatic equilibrium. A star is in hydrostatic equilibrium when the outward push of pressure due to core burning is exactly in balance with the inward pull of gravity. When the hydrogen in a star's core has been used up, burning ceases, and gravity and pressure are no longer in balance. This causes the star to undergo significant changes. Which of the following evolutionary changes would bring a star back into hydrostatic equilibrium? Check all that apply. - A small increase in the star's internal pressure and temperature causes the star's outer layers to expand and cool. - A small increase in the star's internal pressure and temperature causes the star's outer layers to contract and heat up. - A small decrease in the star's internal pressure and temperature causes the star's outer layers to expand and cool. - A small decrease in the star's internal pressure and temperature causes the star's outer layers to contract and heat up.

- A small increase in the star's internal pressure and temperature causes the star's outer layers to expand and cool. - A small decrease in the star's internal pressure and temperature causes the star's outer layers to contract and heat up. Feedback: Correct Hydrostatic equilibrium keeps a star balanced and stable. When a star stops burning hydrogen in its core, evolutionary changes must take place in order for the star to regain stability. For instance, if the internal pressure and temperature of a star decrease, then gravity takes over and causes the star to contract and heat up, restoring equilibrium. Conversely, if the internal pressure and temperature of a star increase, then the extra pressure causes the star to expand and cool, restoring equilibrium.

Confirming our understanding of stellar evolution Depending on its mass, it can take millions to trillions of years for a star to evolve from a main-sequence star to a red giant. Despite this astronomical length of time, astronomers are confident in their models of stellar evolution. Which of the following statements best describe why astronomers firmly believe that their models of stellar evolution are correct? Check all that apply. - Astronomers can observe many stars at different evolutionary stages. - Astronomers have been collecting data for millions of years and have data from a single star as it evolved from a main-sequence star to a red giant. - Astronomers can observe many galaxies at different evolutionary stages. - Astronomers have well-tested theoretical models that explain how a star evolves over the course of its life.

- Astronomers can observe many stars at different evolutionary stages. - Astronomers have well-tested theoretical models that explain how a star evolves over the course of its life. Feedback: Correct Astronomers are able to observe stars at many different stages of stellar evolution within star clusters and can therefore gather information about how stars of different masses evolve over time. Such observational data is used to test and refine theoretical models of stellar evolution. Astronomers are confident that their models of stellar evolution are correct because they are supported by direct observational evidence.

The Sun will leave the main sequence when roughly 10 percent of its hydrogen has been fused into helium. Using the data given in Section 16.6 and Table 16.2 in the textbook, calculate the total amount of mass destroyed (i.e., converted into energy.) Express your answer using one significant figure.

10% of Sun's Mass (2x10^30 kg) = 2x10^29 kg When hydrogen fuses into helium a fraction of 0.7% of the mass is converted to energy. = 1×10^27 kg

Compare each of the two densities with the central density of the Sun ρSun=1.5×105kg/m3. (Sec. 16.2 in the textbook) Express your answers using two significant figures. Enter your answers numerically separated by a comma. density of core / density of sun, density of envelope / density of sun

150,1.1*10^−9

Use the radius-luminosity-temperature relation to calculate the radius of a red supergiant with temperature 3000 K and total luminosity 60000 times that of the Sun. (Sec. 17.3 in the textbook) Express your answer using two significant figures. R= ___________ AU

18 AU

How many planets of our solar system would this star engulf? Express your answer as an integer.

4

Refer to the figure above. At what numbered point on the graph above does the helium flash occur?

9

Structural changes in a star after core hydrogen burning ceases When a star's core hydrogen has been fully depleted via hydrogen burning, the star becomes unstable. The internal structure of the star changes as a result of the new instabilities within its interior. Which of the diagrams below shows the internal structure of a star immediately after running out of its core hydrogen? Pictures: https://s30.postimg.org/q9xiqgj5d/MA_1330914_B_MC.jpg

C. Feedback: Correct When a main-sequence star runs out of hydrogen in its core, hydrogen burning ceases. The internal pressure decreases, and gravity causes the nonburning helium core to contract. The helium core and overlying layers heat up as they contract. As the helium core increases in temperature, a shell of hydrogen surrounding the nonburning helium core ignites, and the star becomes a subgiant. Above the hydrogen-burning shell is a large envelope of hydrogen that remains too cool to ignite hydrogen burning.

Calculate the total energy released by the fusion of that amount of matter. Express your answer using one significant figure.

E = mc^2 = 1.4 x x10^27 kg x (3x10^8 m/s)^2 = 9 x 10^43 J

Provided following are various elements that can be produced during fusion in the core of a high mass main sequence star. Rank these elements based on when they are produced, from first to last.

First Produced - helium - carbon - oxygen - iron Last Produced Feedback: Correct During their main-sequence lives, all stars fuse hydrogen into helium in their cores. During the late stages of their lives, massive stars fuse helium into carbon, and ongoing reactions create successively heavier elements, including oxygen. Iron is the last product of fusion in a massive star's core; iron fusion does not release energy, so the production of iron is the event that provokes the stellar crisis that ends (within seconds) in a supernova.

The following figures show various stages during the life of a star with the same mass as the Sun. Rank the stages based on when they occur, from first to last.

First Stage - contracting cloud of gas and dust - protostar - main sequence G star - red giant, planetary nebula - white dwarf Last Stage Feedback: Correct Remember that these stages take very different amounts of time. A one-solar-mass star spends about ten billion years as a hydrogen-burning main-sequence star, making this by far the longest stage of its life.

Provided following are various stages during the life of a high-mass star. Rank the stages based on when they occur, from first to last.

First Stage - contracting cloud of gas and dust - protostar - main-sequence O star - red supergiant - supernova - neutron star Last Stage Feedback: Correct Remember also that high-mass stars progress through all these stages at a much faster rate than lower-mass stars. The highest-mass stars may be born, live, and die in only a few million years. Note also that while this particular high-mass star leaves behind a neutron star after its supernova, an even higher-mass star may instead leave behind a black hole.

Assume that all four H-R diagrams below represent a star in different stages of its life, after it starts to fuse hydrogen in its core. Rank the HR diagrams based on when each stage occurs, from first to last. Pictures: http://s17.postimg.org/dt4i8xsu7/Untitled_1_copy.jpg

First Stage 1 (Main Sequence) 4 (Red Giant) 2 (Super Giant) 3 (White Dwarf) Last Stage Feedback: Correct The diagram at the left represents the Sun (or any other one-solar-mass star) as a hydrogen-burning main-sequence star, with spectral type G and one solar luminosity. The next diagram shows the Sun after it has exhausted its core hydrogen and left the main sequence, making it a subgiant with energy generated by hydrogen burning in a shell around an inert helium core. The third diagram shows the Sun a little later; its energy source is still hydrogen shell burning, but at this point it has expanded in size so much that it is a red giant. The final diagram (far right) shows the white dwarf corpse of a one-solar-mass star; it is hot because it is the exposed core of the dead star, but dim because it is small in size.

Calculate the average density of a red-giant core of 0.28 solar mass and radius 18000 km . Express your answer using two significant figures. density of core = ___________ kg/m^3

First convert .28 solar mass to kg .28 * 1.98892000114 E30 = 5.568976 E29 Now plug in to d=m/v, volume of sphere = 4/3 * (pi) * r^3, and convert 18,000 km to m d= ( 5.568976 E29 ) / ((4/3)(pi)(18,000,000 ^3)) = 2.3*10^7 kg/m3

Listed following are characteristics that describe either high-mass or low-mass stars. Match these characteristics to the appropriate category.

High-Mass Stars (>8 Msun) - late in life fuse carbon into heavier elements - have higher fusion rate during main sequence life - end life as a supernova Low-Mass Stars (<2 Msun) - have longer lifetimes - final corpse is a white dwarf - end life as a planetary nebula - the Sun is an example

The evolution from subgiant to red giant As you learned in Part B, a nonburning helium core surrounded by a shell of hydrogen-burning gas characterizes the subgiant stage of stellar evolution. As time goes on, the star continues to evolve, and eventually, it becomes a red giant. Rank the stages a star goes through as it evolves from a subgiant into a red giant, from latest to earliest. Rank the stages a star goes through as it evolves from a subgiant into a red giant, from latest to earliest.

Latest Stage - The star becomes a red giant. - The surface of the star becomes brighter and cooler. - Pressure from the star's hydrogen-burning shell causes the nonburning envelope to expand. - The shell of hydrogen surrounding the star's nonburning helium core ignites. - The star's nonburning helium core starts to contract and heat up. - Pressure in the star's core decreases. Earliest Stage Feedback: Correct A star moves off the main sequence once its core runs out of hydrogen to fuse into helium. The pressure that was once supplied by hydrogen burning decreases, and the core starts to contract under the force of gravity. This contraction causes the core and the surrounding layers to heat up. The shell of hydrogen surrounding the core eventually becomes hot enough to ignite hydrogen burning. The resulting pressure from hydrogen shell burning causes the star to expand, cool, and become brighter. At this point, the star is considered a red giant.

The Sun will reside on the main sequence for 10^10 years. If the luminosity of a main-sequence star is proportional to the fourth power of the star's mass, what is the mass of a star that is just now leaving the main sequence in a cluster that formed 500 million years ago? Express your answer using two significant figures. M = _________ solar units

M = (10^10 years/500 × 10^6 years)^(1/3) M = 2.7 solar units

Compare your answer with the average density of the giant's envelope, if it has a 0.6 solar mass and its radius is 0.8 AU . Express your answer using two significant figures. density of envelope = _________ kg/m^3

Repeat process above. 1.6*10^−4 kg/m3

When the Sun leaves the main sequence, it will become

brighter.

A white dwarf is supported by the pressure of tightly packed

electrons.

After the core of a Sun-like star starts to fuse helium on the horizontal branch, the core becomes

hotter with time.

Which of the following elements contained in your body is NOT formed in the cores of stars during thermonuclear fusion?

hydrogen.