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Chapter 17: Problem 29

List the two reasons why each post-helium-burning cycle for high-mass stars (carbon, neon, oxygen, silicon, and sulfur) becomes shorter than the preceding cycle.

Short Answer

Expert verified
Each cycle requires higher core temperatures and has less fuel available, leading to shorter durations.

Step by step solution

01

Identify Post-Helium-Burning Cycles

High-mass stars undergo several burning cycles after helium burning, including carbon, neon, oxygen, silicon, and sulfur burning.
02

Reason 1: Higher Core Temperatures

Each subsequent burning cycle requires a higher core temperature to ignite. As the elements produced in previous cycles have higher fusion thresholds, this increasing temperature leads to faster burning rates.
03

Reason 2: Reduced Fuel Supply

Each burning cycle consumes fuel from the previous cycle, leaving less material for the subsequent cycle. With a reduced amount of fuel available, the time required for each cycle diminishes.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Higher Core Temperatures
In high-mass stars, each post-helium-burning cycle requires higher core temperatures to commence fusion. This happens because the atomic nuclei involved in these cycles have increasing fusion thresholds.
This means that as you move from carbon to neon, then to oxygen, silicon, and finally sulfur, the temperatures needed to ignite these elements become progressively higher.
Here’s why higher core temperatures are crucial:
  • Fusion Thresholds: Different elements require different amounts of energy to start fusion. Carbon, for example, needs a lower temperature than oxygen.
  • Faster Burning Rates: Higher temperatures accelerate the rate at which fusion proceeds, causing the star to burn through its fuel more quickly.
Overall, the rising core temperatures are fundamental to the shorter duration of each subsequent burning cycle.
Fusion Thresholds
Before fusion can occur in high-mass stars, certain conditions must be met, primarily the fusion threshold. Fusion threshold refers to the minimum temperature and pressure required for atomic nuclei to overcome their electrostatic repulsion and fuse together.
Here’s why fusion thresholds matter in the context of post-helium burning cycles:
  • Element Specific: Each element has a unique fusion threshold. Carbon has a lower threshold compared to neon or silicon, meaning less energy is required to start carbon fusion than neon fusion.
  • Energy Requirement: As the star evolves, reaching these higher thresholds becomes a more demanding task. More significant amounts of gravitational energy must be converted into thermal energy.
  • Impact on Cycle Duration: Higher fusion thresholds mean the star reaches the necessary conditions more rapidly, increasing the overall pace of fusion processes. This results in shorter burning cycles.
The fusion thresholds underline why higher core temperatures are vital, and play a significant role in the dwindling time spans of individual burning stages.
Reduced Fuel Supply
Reduced fuel supply is another critical factor in the increasingly shorter post-helium-burning cycles. As each burning cycle progresses, it depletes the available material for the next cycle.
Here’s a closer look at the effect of reduced fuel supply:
  • Cycle-by-Cycle Consumption: Each burning stage consumes the products of the previous cycle. Once the helium burns, carbon is used for the next phase, reducing the quantity of available elements for subsequent cycles.
  • Limited Resources: With each phase, less fuel remains, leading to faster consumption because the star must draw upon the remnants of the previous cycle's products.
  • Shorter Cycles: Due to the reduced amount of fuel, each burning cycle ends more quickly. This reduction in fuel per cycle explains why these stages are brief in duration.
Therefore, reduced fuel supply diminishes the length of each burning cycle and is vital to understanding the overall lifecycle of high-mass stars.

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Most popular questions from this chapter

Arrange the following elements in the order they burn inside the nucleus of a high-mass star during the star's evolution. a. helium b. neon c. oxygen d. silicon e. hydrogen f. carbon

In a large outburst in 1841 , the \(120-M_{\odot}\) star Eta Carinae was losing mass at the rate of \(0.1 M_{\odot}\) per year. Let's put that into perspective. a. The mass of the Sun is \(2 \times 10^{30}\) kg. How much mass (in kilograms) was Eta Carinae losing each minute? b. The mass of the Moon is \(7.35 \times 10^{22}\) kg. How does Eta Carinae's mass loss per minute compare with the mass of the Moon?

Very young star clusters have main-sequence turnoffs a. nowhere. All the stars have already turned off in a young cluster. b. at the top left of the sequence. c. at the bottom right of the sequence. d. in the middle of the sequence.

In a high-mass star, hydrogen fusion occurs via a. the proton-proton chain. b. the CNO cycle. c. gravitational collapse. d. spin-spin interaction.

Iron fusion cannot support a star, because a. iron oxidizes too quickly b. iron absorbs energy when it fuses. c. iron emits energy when it fuses. d. iron is not dense enough to hold up the layers.
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