Chapter 17: Problem 18
Why does the core of a high-mass star not become degenerate, as the core of a low-mass star does?
Short Answer
Expert verified
High-mass stars maintain high core temperatures and thermal pressure from nuclear fusion, which prevents core degeneracy, unlike low-mass stars.
Step by step solution
01
Understand Star Mass Differences
High-mass stars (greater than about 8 times the mass of the Sun) and low-mass stars (less than about 8 times the mass of the Sun) have different core behaviors. Understanding these mass differences is key to understanding their core development.
02
Define Degenerate Matter
Degenerate matter occurs when electrons are packed so closely together that quantum mechanical effects, specifically the Pauli exclusion principle, dominate and prevent further compression.
03
High-Mass Star Core Temperatures
High-mass stars have cores that achieve extremely high temperatures, which exceed the threshold needed to sustain continuous nuclear fusion.
04
Nuclear Fusion and Pressure
In high-mass stars, the ongoing nuclear fusion reactions produce an immense amount of thermal pressure. This pressure counteracts gravitational forces, preventing the core from compressing to the point of degeneracy.
05
Cooling and Contraction in Low-Mass Stars
Low-mass stars, on the other hand, do not achieve these high core temperatures. As their nuclear fuel depletes, the core cools and contracts, leading to electron degeneracy pressure taking over to counteract gravity.
06
Conclusion
Thus, the core of a high-mass star doesn't become degenerate because its extreme core temperatures sustain nuclear fusion and produce enough thermal pressure to oppose gravitational contraction, unlike low-mass stars.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Degenerate Matter
In the hearts of stars, 'degenerate matter' is a key concept. It usually shows up in low-mass stars as they age. When electrons are smashed together in extremely tight spaces, they start to behave according to quantum mechanical rules. One of these rules is the Pauli exclusion principle, which says no two electrons can occupy the same state at the same time. This principle stops the core from being compressed further, even if more gravitational pressure is applied. This resistance against further compression is known as electron degeneracy pressure. It's crucial because it marks a stage where normal gas behaviors, like increased pressure with higher temperature, no longer apply. So, degenerate matter in low-mass stars acts as a safeguard against gravitational collapse.
Nuclear Fusion
Nuclear fusion is the process that powers stars, including high-mass stars. At extreme temperatures and pressures found in their cores, lighter atomic nuclei such as hydrogen fuse to form heavier nuclei like helium. This process releases immense amounts of energy. In high-mass stars, the core temperatures are so high that fusion can continue to occur even as the star ages. This constant nuclear fusion generates significant energy and keeps the star stable. Unlike low-mass stars, high-mass stars can cycle through different types of nuclear fusion, fusing elements heavier than helium when the core temperature rises further. Each stage of fusion produces thermal pressure, which helps control the gravitational forces trying to compress the core.
Thermal Pressure
Thermal pressure is the force exerted by particles moving at high speeds due to the intense heat in a star's core. In high-mass stars, this pressure is extraordinarily high because of the extreme temperatures caused by continuous nuclear fusion. The thermal pressure pushes outward, balancing the inward pull of gravity. This dynamic equilibrium keeps the star from collapsing in on itself.
Without sufficient thermal pressure, as happens in low-mass stars when their nuclear fuel depletes, the core starts to contract. This contraction raises the core's density until degeneracy pressure takes over. However, high-mass stars maintain high thermal pressure throughout much of their lifetimes, avoiding this degenerate state.
Without sufficient thermal pressure, as happens in low-mass stars when their nuclear fuel depletes, the core starts to contract. This contraction raises the core's density until degeneracy pressure takes over. However, high-mass stars maintain high thermal pressure throughout much of their lifetimes, avoiding this degenerate state.
Gravitational Forces
Gravitational forces are the inward-pulling forces exerted due to the mass of the star. For stars, gravity is always working to compress the core. In both high-mass and low-mass stars, gravity aims to pull the core material inward. However, the counterbalance to this force comes from the pressures inside the core.
In high-mass stars, the extreme temperatures from nuclear fusion create enough thermal pressure to push back against gravity. This prevents the core from reaching the point where it would become degenerate. Conversely, in low-mass stars, once the nuclear fuel is run out and thermal pressure drops, gravitational forces dominate, leading to core contraction and the emergence of electron degeneracy pressure to balance the gravitational forces once again.
This balancing act between gravitational forces and internal pressures shapes the life and fate of stars.
In high-mass stars, the extreme temperatures from nuclear fusion create enough thermal pressure to push back against gravity. This prevents the core from reaching the point where it would become degenerate. Conversely, in low-mass stars, once the nuclear fuel is run out and thermal pressure drops, gravitational forces dominate, leading to core contraction and the emergence of electron degeneracy pressure to balance the gravitational forces once again.
This balancing act between gravitational forces and internal pressures shapes the life and fate of stars.