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.
