ASP Astrophysics Fundamentals 2 — Questions and Answers
Question 1: What is the Schwarzschild radius?
- The radius at which a star begins hydrogen fusion
- The critical radius at which an object becomes a black hole (its escape velocity equals the speed of light) (Correct answer)
- The radius of the Sun's photosphere
- The distance from the Sun beyond which solar wind becomes subsonic
Correct answer: The critical radius at which an object becomes a black hole (its escape velocity equals the speed of light)
The Schwarzschild radius is the radius to which a mass must be compressed to form a black hole, where the escape velocity equals the speed of light (rs = 2GM/c²); for the Sun it is about 3 km.
Question 2: What is nuclear binding energy?
- The energy released when an electron is removed from an atom
- The energy required to completely separate the nucleons (protons and neutrons) in an atomic nucleus (Correct answer)
- The energy stored in stellar magnetic fields
- The kinetic energy of protons in a stellar core
Correct answer: The energy required to completely separate the nucleons (protons and neutrons) in an atomic nucleus
Nuclear binding energy is the energy required to disassemble an atomic nucleus into its constituent protons and neutrons; fusion of lighter elements releases energy when the products have higher binding energy per nucleon.
Question 3: What is the mass-luminosity relationship for main-sequence stars?
- L ∝ M (linear)
- L ∝ M² (squared)
- L ∝ M³·⁵ to M⁴ (approximately) (Correct answer)
- L ∝ M¹/² (square root)
Correct answer: L ∝ M³·⁵ to M⁴ (approximately)
For main-sequence stars, luminosity scales approximately as L ∝ M³·⁵ to M⁴, meaning a star twice as massive as the Sun is roughly 10–16 times more luminous and consequently lives much shorter.
Question 4: What is escape velocity?
- The velocity needed for an object to maintain a circular orbit
- The minimum velocity needed for an object to escape a body's gravitational pull without further propulsion (Correct answer)
- The velocity at which a planet's atmosphere escapes to space
- The maximum velocity of particles in a stellar wind
Correct answer: The minimum velocity needed for an object to escape a body's gravitational pull without further propulsion
Escape velocity is the minimum speed an object needs to escape a gravitational field without additional thrust, equal to v = √(2GM/r); for Earth it is about 11.2 km/s.
Question 5: What is the hydrostatic equilibrium condition in stars?
- The balance between nuclear fusion rate and stellar luminosity
- The balance between the inward gravitational force and the outward pressure gradient that keeps a star stable in size (Correct answer)
- The balance between magnetic field pressure and thermal pressure
- The equilibrium between fusion products and raw hydrogen
Correct answer: The balance between the inward gravitational force and the outward pressure gradient that keeps a star stable in size
Hydrostatic equilibrium is the condition where the outward pressure gradient force (thermal + radiation pressure) exactly balances the inward gravitational force at every point within a star, maintaining a stable structure.
Question 6: What is the Eddington luminosity?
- The luminosity at which a star leaves the main sequence
- The maximum luminosity at which radiation pressure balances gravity, above which material is blown away (Correct answer)
- The minimum luminosity for a star to be visible to the naked eye
- The luminosity at which a star becomes a red giant
Correct answer: The maximum luminosity at which radiation pressure balances gravity, above which material is blown away
The Eddington luminosity is the theoretical maximum luminosity at which the outward radiation pressure force exactly balances the inward gravitational force, with more luminous sources blowing away accreting material.
ASP Astrophysics Fundamentals 2
What is the Schwarzschild radius?