theorems/distribution functions
states that a star's mass and chemical composition uniquely determine its structure, size, temperature, and luminosity. The distribution of stars on the HR diagram comes from differences in star masses, compositions, and time elapsed since birth.
what is the Vogt-Russell Theorem?
the process by which a star/protostar/PMS star contracts under gravity, converting gravitational potential energy into heat, which is then radiated away. (aka the rate of change of the star's radius is negative, meaning it shrinks as it loses energy)
what is Kelvin-Helmholtz contraction?
Non-degenerate. they behave like a classical gas, roughly following a Maxwell-Boltzmann distribution.
How do electrons behave in the outer layers of MS stars?
Name the four types of novae
What are classical, recurrent, dwarf, and supernovae?
All high-mass stars are destined to burn all the way through to form an iron core. An iron core collapse is the rapid implosion of a massive star's iron core once it can no longer support itself. Electrons are captured by protons, the core collapses to nuclear density, rebounds, and triggers a core-collapse supernova.
What is iron core collapse?
describes how the particles in a system are distributed according to their momentum. It tells you how many particles have a certain momentum at a given time. (f(p)).
you can use this to evaluate the number density and pressure of a star
What is a momentum distribution function?
The time it would take a star to radiate away all its energy if its only source of energy were gravitational contraction.
What is the Kelvin-Helmholtz timescale?
they follow a Fermi-Dirac distribution.
Many low-energy states are filled due to the Pauli exclusion principle. This creates electron degeneracy pressure, which can support the star against gravitational collapse (how WDs exist)
How do electrons behave in dense cores?
describe the differences between the four types of novae
classical: A thermonuclear explosion on the surface of an accreting white dwarf in a binary system, caused by runaway hydrogen fusion in degenerate material
recurrent: nova systems that erupt repeatedly over decades due to a massive, rapidly accreting white dwarf that requires only a thin hydrogen layer for thermonuclear ignition
dwarf novae: Repeated brightness outbursts in cataclysmic variable systems caused by thermal-viscous instabilities in the accretion disk around a white dwarf, not by nuclear explosions.
supernovae: catastrophic stellar explosions
The breakup of atomic nuclei by high-energy gamma-ray photons. In collapsing massive stars, photodisintegration absorbs energy and accelerates iron core collapse.
as the temp approaches 10^10 K, this begins.
What is photodisintegration?
describes how fermions are distributed among energy states at a given temperature.
gives the probability that a fermion occupies a particular energy state at a given temperature, taking into account the Pauli exclusion principle
The Fermi-Dirac distribution/distribution function
a dimensionless form of the equations of hydrostatic equilibrium for a polytropic star, relating pressure, density, and radius. It is used to calculate the structure of stars modeled as polytropes.
what is the Lane-Emden equation?
states that no two fermions (particles with half-integer spin, like electrons, protons, or neutrons) can occupy the same quantum state simultaneously.
What is the Pauli exclusion principle?
The process where electrons are captured by protons to form neutrons and neutrinos during core collapse. It reduces electron pressure, accelerates collapse, and produces a neutron-rich core.
happens at very high densities found in the core.
What is neutronization?
A function that describes how classical particles' speeds or energies are distributed at a given temperature.
What is the Maxwell-Boltzmann distribution?
A model of a star (or gas sphere) in which pressure P and density ρ are related by a simple power law:
P=Kρ^(1+1/n)
What is a polytrope?
electrons that are packed so closely together that their behavior is dominated by the Pauli exclusion principle rather than temperature. Electrons cannot all occupy low-energy states, so they fill up higher-energy states even at low temperatures
What are degenerate electrons?
describe how density and pressure vary with radius in a polytropic star for different polytropic indices n.
Ex: n=0: uniform density sphere
n=1: density decreases linearly with radius
n=5: infinite radius solution (special case)
What are the solutions to the Lane-Emden equation?
Approximate the internal structure of stars without solving full complex equations.
Help understand how pressure supports a star against gravity.
What are polytropes used for?
electrons in a gas where quantum effects are negligible, and their behavior is dominated by temperature rather than the Pauli exclusion principle. Occurs in low-density or high-temperature regions of stars. Electron pressure is thermal pressure, not degeneracy pressure. Follows a classical Maxwell-Boltzmann distribution
BONUS: electrons (or other fermions) are partially affected by the Pauli exclusion principle—some low-energy states are filled, but thermal energy still plays a role in their distribution. Happens in stars or stellar cores that are dense but not extremely dense. The electron pressure comes from a combination of degeneracy and thermal motion
What are non-degenerate electrons?
BONUS: what is partial degeneracy?