chapters 4-7 Flashcards
Why is the assumption of blackbody radiation valid within stars, even though photon transport is not strictly isotropic?
A: Because the average distance a photon travels (mean free path) is extremely small compared to the stellar radius, and the temperature changes negligibly over such small distances.
How does the opacity (ΞΊ) relate to the mean free path of a photon, and why does this matter for energy transport?
A: Opacity is inversely proportional to the mean free path. A higher opacity reduces the mean free path, making radiative transport less efficient and favoring convection.
Why is free-free absorption dominant in high-temperature stellar cores, and how does it differ from Thompson scattering?
A: Thomson scattering occurs when photons interact with free electrons without changing their energy, whereas free-free absorption transfers energy to the electrons.
Explain why the optical depth πβ2/3 at the starβs photosphere is significant.
At πβ2/3 approximately 50% of photons can escape the star without further scattering, making this the effective surface where radiation escapes.
Q: Why is radiative diffusion an appropriate model for energy transport in stellar interiors?
A: Because photons undergo numerous random scatterings, and the net energy flow resembles a diffusion process due to the small mean free path.
Q: How does a steep temperature gradient affect the mode of energy transport within a star?
A: A steeper gradient increases the likelihood of convection becoming dominant, as radiative transport alone cannot carry energy efficiently.
Q: Why does radiative energy flux decrease with increasing opacity in a star?
A: Higher opacity reduces the mean free path, slowing down the rate at which photons diffuse outward, thus reducing the flux.
Q: How does the mean free path depend on the number density of free electrons and the cross-section?
The mean free path π decreases as the number density π or the cross-section π increases, since more interactions occur.
Q: Why are photon-matter interactions crucial for energy transport in stars?
These interactions dictate the opacity and determine how efficiently energy can flow outward through radiation or convection.
Why is the stellar core described as optically thick, and what are the consequences for energy escape?
A: In the core, optical depth πβ«1 so photons are continuously scattered and absorbed, causing energy to move outward very slowly.
Q: Why does the observed spectrum of stars resemble a blackbody spectrum?
A: The photosphere emits radiation like a blackbody because photons that escape have interacted enough to reach local thermodynamic equilibrium.
Q: How does the energy flow depend on the temperature gradient in a star?
A: Energy flux is proportional to the temperature gradient, as a steeper gradient drives a larger flux of energy.
Q: Why does radiative transport dominate in some stellar regions while convection dominates in others?
A: Radiative transport dominates when opacity is low, and the temperature gradient is shallow. Convection dominates when the temperature gradient is steep.
Q: How does opacity influence the overall structure and stability of a star?
A: Opacity determines energy transport efficiency, which in turn affects the temperature gradient and stability of stellar regions.
Q: Why does nuclear fusion require extremely high temperatures to occur?
A: High temperatures give particles enough kinetic energy to overcome the Coulomb barrier and allow the strong nuclear force to bind nuclei together.
Q: What is the Gamow energy, and why is it significant for fusion?
A: The Gamow energy represents the quantum tunneling threshold for fusion. It determines the likelihood of nuclei overcoming the Coulomb barrier.
Q: Why does the fusion rate depend on both temperature and quantum tunneling?
A: High temperatures increase particle velocities, but quantum tunneling allows fusion even when classical energies are insufficient.
Q: Why is the pp-chain the dominant fusion process in solar-mass stars?
A: Lower core temperatures (~15 million K) favor the slower proton-proton reactions over the CNO cycle.
- Does not require catalysts.
- The dominance of the pp-chain in solar-mass stars explains their relatively steady and long-lasting energy production, as the process is slow and efficient at moderate temperatures.
- T^4
Q: Why does the CNO cycle become dominant in more massive stars?
Higher core temperatures (>20 million K) make the CNO cycle more efficient despite the lower abundance of carbon, nitrogen, and oxygen.
- carbon, nitrogen, and oxygen are catalysts providing the cycles efficiency
- The high energy production rate from the CNO cycle explains why massive stars burn their fuel quickly and have shorter lifetimes compared to solar-mass stars.
- T^16
- due to this temp dependence CNO produces more power per nit mass
Q: Why does nuclear fusion release energy, and how does the binding energy per nucleon explain this?
A: Fusion releases energy because the final products are more tightly bound (lower total mass) than the initial reactants.
Q: Why does the Q value differ between fusion processes like the pp-chain and the CNO cycle?
A: The Q value depends on the specific nuclei involved and the binding energy differences between reactants and products.
Q: Why do neutrinos escape from the stellar core, and what do they tell us about fusion?
A: Neutrinos have extremely low interaction cross-sections, so they escape directly, providing evidence of ongoing fusion.
Q: Why does quantum tunneling make fusion possible at lower energies than predicted classically?
A: Tunneling allows particles to penetrate coulomb energy barrier which they would not overcome classically.
- classically repelling electrons must overcome coulomb force
- quantum mechanics says that particles act as waves and have a finite probability of tunneling through a barrier
- in stellar cores the temp is not high enough for fusion via overcoming coulomb barrier so tunneling allows a star to sustain energy production
Q: What does the solar neutrino problem reveal about neutrinos and fusion?
A: Neutrino oscillations (flavor changes) explain why fewer electron neutrinos are detected than expected.
- electron neutrons are a byproduct of fusion
- a predicted number of neutrinos should reach earth
- 1/3 of this number was observed
- as ns travel from the sun to the earth they oscillate meaning they have non zero mass
Q: How does the Coulomb barrier change with increasing nuclear charge?
A: The Coulomb barrier increases with the product of nuclear charges, making fusion harder for heavier nuclei.
Why does fusion efficiency depend strongly on particle densities and velocities
A: Higher densities increase collision rates, and higher velocities increase the likelihood of tunneling.
Q: What triggers convective instability in a stellar region?
A: A steep temperature gradient where the actual temperature drop with radius exceeds the adiabatic gradient. This causes gas elements to rise and transfer energy via bulk motion.
- temp decreases with increasing radius
- steep temp gradient means temp drops rapidly over a small radial distance
- gas element rises, it expands adiabatically, bc the pressure surrounding it decreases
- after expanding the temperature drops
- if the surrounding gas cools faster than the rising element (due to gradient) the displaced element remains hotter and less dense than its surroundings creating buoyancy
Why is the heat capacity ratio
πΎ=πΆπ/πΆπ£ significant for convection in stars?
A: It determines the adiabatic temperature gradient, which sets the condition for convective instability.
Q: Why does the temperature gradient steepen in the outer layers of a solar-type star?
A: The opacity increases sharply in cooler regions, reducing radiative transport efficiency and forcing the temperature gradient to steepen.
Q: Why must a rising gas element in a star maintain pressure equilibrium with its surroundings?
A: The timescale for pressure adjustments is much shorter than that for temperature changes, so pressure equalizes almost instantaneously.
Why are convective zones more common in the outer layers of lower-mass stars but in the cores of massive stars?
In lower-mass stars, the outer layers have high opacity.
In massive stars, the core has high temperature gradients due to intense energy production.
Q: Why is convection considered βbulk motionβ energy transport?
A: Energy is carried as gas elements physically move, rather than relying on photon diffusion.
Q: Derive the mathematical condition for convection in terms of the temperature gradient.
Convection occurs when:
(ππ/ππ)>(ππ/ππ)ad
where the adiabatic gradient depends on πΎ and the pressure.
Q: How does convection affect the structure of a star, and how is it observed in the Sun?
A: Convection creates granulation patterns on the Sunβs surface due to rising and sinking gas elements.
