Chapter 1-3 Flashcards
Why does the black-body spectrum for a star shift toward shorter wavelengths as the temperature increases?
Higher temperatures mean particles have more thermal energy, producing photons with higher energy. According to Wien’s Law,
𝜆max T∝1 the peak wavelength shifts inversely with temperature.
How does the concept of bolometric luminosity resolve the issue of wavelength-dependent observations?
Bolometric luminosity includes energy emitted across all wavelengths, providing a complete measure of a star’s energy output without reliance on specific wavelength observations.
Why are some stars bright in apparent magnitude but have low absolute magnitudes?
Stars can appear bright (low
𝑚
m) if they are nearby, even if their intrinsic brightness (low
𝑀
M) is low. Apparent magnitude depends on distance, while absolute magnitude does not.
If two stars have the same luminosity but different temperatures, which star is larger and why?
The cooler star must be larger because luminosity
𝐿∝𝑅^2 𝑇^4 L∝A lower temperature requires a larger radius to maintain the same L
Why does the intensity of radiation decrease with distance?
Intensity follows the inverse square law I ∝ 1/d^2 because the same amount of energy is spread over an increasingly larger area as distance increases.
Q: Explain why stars with higher absolute magnitudes tend to have shorter lifetimes.
A: Higher absolute magnitudes indicate more luminous, massive stars, which burn through their nuclear fuel more rapidly due to higher core temperatures and pressures.
Q: Why is the Stefan-Boltzmann law critical in modeling stars as black bodies?
It connects surface temperature to the radiative energy flux enabling calculation of a star’s total energy output when combined with its radius.
Q: Why are stars not perfect black bodies?
Stars deviate from ideal black-body behavior due to atmospheric effects like absorption, scattering, and emission from specific chemical elements.
Why do smaller stars have lower surface temperatures?
A: Smaller stars have less gravitational pressure, resulting in lower core temperatures and slower fusion rates, which produce less heat and lower surface temperatures.
Q: How can the distance to a star be measured using parallax?
A: Parallax measures the apparent shift in a star’s position against the background stars as Earth orbits the Sun. The distance is inversely proportional to the parallax angle.
Q: How does interstellar dust affect apparent magnitude?
A: Interstellar dust absorbs and scatters light, dimming a star’s apparent magnitude and reddening its observed color.
Q: Explain why stars radiate energy primarily through electromagnetic waves.
A: Fusion in the core produces high-energy photons, which transport energy outward through radiation and convection.
Q: How does the H-R diagram link temperature, luminosity, and stellar evolution?
A: The H-R diagram places stars by temperature and luminosity, showing evolutionary paths such as main sequence, red giant, and white dwarf phases.
How does hydrostatic equilibrium influence a star’s size over time?
A: As nuclear fuel depletes, gravity overcomes outward pressure, causing contraction. This increases core temperature and pressure until equilibrium is re-established.
Q: How does the Virial Theorem explain energy release during gravitational contraction?
A: Half of the gravitational energy is converted into thermal energy, heating the star, while the other half is radiated away.
Q: Why is the temperature gradient steeper in convective regions of a star?
Convection requires a steeper temperature gradient to overcome buoyancy and transport energy efficiently compared to radiation.
Q: Why does the core of a star become hotter as it contracts?
A: Gravitational potential energy converts into thermal energy during contraction, increasing the core temperature.
Q: Explain how the pressure gradient in a star is maintained.
The pressure gradient is determined by the balance between gravity pulling inward and pressure pushing outward, as described by
Q: Why do more massive stars have shorter main-sequence lifetimes?
A: Their higher core temperatures cause faster fusion rates, depleting hydrogen fuel more quickly despite having more of it.
Q: How does radiation transport dominate in massive stars but not in smaller stars?
A: Massive stars have lower densities in their outer layers, allowing photons to transfer energy efficiently without frequent scattering.
Q: What happens if a star’s core temperature drops below the threshold for fusion?
A: Fusion ceases, and the core collapses, potentially leading to a white dwarf, neutron star, or black hole depending on the mass.
Q: How does gravitational potential energy act as an energy source for stars?
A: During contraction or collapse, gravitational energy is converted into heat, powering the star when nuclear fusion is insufficient.
Q: Why is the total energy of a star negative in equilibrium?
A: The binding gravitational potential energy (U) is negative and twice as large in magnitude as the internal energy (𝐸kin) resulting in E_tot = -U/2
How does the mean molecular weight (𝜇) affect pressure?
Lower 𝜇 (e.g., for ionized hydrogen) increases the number density of particles, raising the gas pressure for a given temperature.
Q: Why does opacity play a critical role in energy transport?
A: High opacity increases resistance to radiation flow, favoring convection, while low opacity allows efficient radiative transfer.
Q: How does ionization influence the pressure in a star’s core?
A: Ionization frees electrons, increasing the number of particles, which raises the pressure according to P=nkT
Q: Explain the role of degenerate pressure in white dwarfs.
A: Degenerate pressure arises from the Pauli exclusion principle and prevents further collapse in white dwarfs, independent of temperature.
Q: How does the gravitational force balance the radiation pressure in massive stars?
A: Radiation pressure provides an outward force that counters gravity. This balance determines the maximum luminosity (Eddington limit) a star can sustain without blowing away its outer layers.
Q: What happens when energy transport by radiation becomes inefficient in a star’s interior?
A: Convection takes over as the dominant energy transport mechanism, redistributing heat through bulk motion of material.
Q: How does the central pressure of a star relate to its total mass?
Higher mass stars require greater central pressure to counteract the stronger gravitational forces, as determined by dp/dr = GMρ/r^2
Q: Why does the energy produced in the core of a star not escape immediately?
A: Photons undergo multiple scatterings due to the high opacity of stellar material, taking thousands to millions of years to reach the surface.
Q: What would happen to a star if it exceeded the Eddington luminosity?
A: The outward radiation pressure would overpower gravity, causing mass loss from the star’s outer layers or disrupting the star entirely.
Q: How does the pressure contribution from ions compare to that from electrons in a fully ionized gas?
A: Ion pressure dominates because ions have greater mass, but electron pressure contributes significantly due to their larger number density.
Q: How does the number density of electrons depend on the ionization state of the gas?
A: Higher ionization increases the number density of free electrons, which in turn raises the pressure and opacity of the gas.
Q: Why does degeneracy pressure depend on density rather than temperature?
A: Degeneracy pressure arises from quantum mechanical principles (Pauli exclusion), which depend on particle density and not thermal motion.
How is the opacity 𝜅 of a star related to its energy transport?
High opacity traps photons, slowing radiative transfer and favoring convection. Low opacity enables efficient radiation transport.
Q: How does the transition from ideal gas pressure to degenerate pressure affect the behavior of a star?
A: When degeneracy pressure dominates, the star’s pressure becomes independent of temperature, halting further contraction and leading to stable configurations like white dwarfs.
