Stellar Evolution Flashcards
What must the gravitational energy be larger than for gravitational binding?
The kinetic energy: GM^2/R >= M/μkT, with ρ = M/((4/3)pi*R^3)
What is the Jeans mass?
The minimum mass: (kT/Gμ)^(3/2) * ρ^(-1/2)
What is the Jeans radius?
Minimum radius: (kT/Gμρ)^(1/2)
Why are stellar clusters important?
Because plotting all stars mixes stars with different ages, compositions etc, and clusters of stars are all at roughly the same distance, made from gas with same composition and have same age.
What is an open cluster?
Groups of few 100 - 100 stars < 10pc across. Wide range of ages from Myr-Gyr
How can we use clusters to look at stellar evolution?
Make a cluster H-R diagram. Key diagnostic is the main-sequence turn-off point. The end of the main-sequence moves steadily to lower masses as a function of age.
What is a globular cluster?
10^5 - 10^6 stars in a spherical cluster 20-50pc across. All very olf (~10^10 yrs)
What are the first two steps in stellar evolution?
- pre-main sequence:collapsing clouds of interstellar gas. Core of this compressing cloud heats up until fusion becomes possible
- Main-sequence: H is converted into He in the core of stars, producing a growing He dominated core
What are the 3rd and 4th steps in stellar evolution?
- Giants: No fusion in the He-core, which contracts. Hydrogen fuses in a shell around the core - envelope expands
- Horizontal branch: If core reaches sufficient T, He can fuse to produce C and O, core expands again. Leads to CO core with He and H burining in shell
What does the graph of log(T(surface)) against log(L/L(solar)) look like? (stellar evolution across the H-R diagram)
- Starts at ~0 L, then slowly increases with slowly increasing temperature
- Constant L with decreasing temperature while H, He shell burns
- L decreases as T increases while C/O cools to White Dwarf
What is a Planetary Nebula?
A planetary nebula is the remnant of the ejected envelope while a star becomes a white dwarf.
What is the White dwarf remnant?
Fusion has stopped in the CO rich core. Small, dense and still hot - thermal pressure can only work for a while, the white dwarf will cool.
What is the equation for the time taken for a white dwarf to cool?
tcool = Etherm/L = (kTc*M/μ)/L
=(GM^2)/(RL) ~ 10^9 yrs
What is the Pauli exclusion principle?
No two fermions (particle with half integer spin) can occupy the same quantum state.
What is degenerate matter?
- Electrons must obey the Pauli exclusion principle
- Number of energy levels is finite, within each energy level electron spin provides two slots
- Once lower energy slots are filled, progressively higher slots are only option for electrons
- Such a fully stacked energy state is called degenerate matter
What is degenerate pressure?
- Pressure in degenerate matter scales with density, but is independent of pressure
- Degenerate pressure keeps the radius constant as the white dwarf continues to cool
What is the Chandrasekhar limit?
The maximum mass of a white dwarf due to relativistic limit: M = 1.33 M(sun)
Why is there a Chandrasekhar limit?
- At very high number of electrons, need to take into account relativistic effects
- For relativistic case, P ∝ n^(4/3) rather than 5/3, so pressure doesn’t grow rapidly enough with density
- Creates a mass limit
What does the graph of radius against mass look like for relativistic and non-relativistic Fermi gas?
- Non-relativistic can have much higher mass as radius decreases
- Relativistic has a maximum mass at 1.33 solar masses
What happens during the shell burning sequence for massive stars?
Shell burning sequence can continue to even heavier elements beyond C, O; Ne, Mg, Si, Fe
Why do massive stars collapse?
Because the heavier elements produced have higher binding energy per nucleon, meaning it costs more energy to fuse them. This energy crisis causes a rapid core collapse.
What is a Type II Supernova explosion?
Driven by core collapse in massive stars, core implodes and the rest of the star explodes.
What is an example of a type II supernova?
Crab nebula
Why does the core collapse in massive stars?
Electrons and protons combine to form neutrons, so creates neutron degeneracy pressure. If star is too big (larger than 30-40 solar masses), there is no pressure force to stop collapse: black hole is formed.
What is the equation for the radius of a black hole?
R = 2GM/c^2
What happens if M < 0.08 M(solar)?
Never initiates fusion (planets and brown dwarfs)
What happens if 0.08 M(solar) < M < 0.8 M(solar)?
Time at main sequence is longer than age of the Universe.
What happens if 0.8 M(solar) < M < 7-9 M(solar)?
Produces white dwarf.
What happens if 7-9 M(solar) < M < 30-40 M(solar)?
Neutron star formed.
What happens if M > 30-40 M(solar)?
Black hole is formed.
