Stellar Evolution

Question 1

What must the gravitational energy be larger than for gravitational binding?

Answer 1

The kinetic energy: GM^2/R >= M/μkT, with ρ = M/((4/3)pi*R^3)

Question 2

What is the Jeans mass?

Answer 2

The minimum mass: (kT/Gμ)^(3/2) * ρ^(-1/2)

Question 3

What is the Jeans radius?

Answer 3

Minimum radius: (kT/Gμρ)^(1/2)

Question 4

Why are stellar clusters important?

Answer 4

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.

Question 5

What is an open cluster?

Answer 5

Groups of few 100 - 100 stars < 10pc across. Wide range of ages from Myr-Gyr

Question 6

How can we use clusters to look at stellar evolution?

Answer 6

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.

Question 7

What is a globular cluster?

Answer 7

10^5 - 10^6 stars in a spherical cluster 20-50pc across. All very olf (~10^10 yrs)

Question 8

What are the first two steps in stellar evolution?

Answer 8

1. pre-main sequence:collapsing clouds of interstellar gas. Core of this compressing cloud heats up until fusion becomes possible
2. Main-sequence: H is converted into He in the core of stars, producing a growing He dominated core

Question 9

What are the 3rd and 4th steps in stellar evolution?

Answer 9

3. Giants: No fusion in the He-core, which contracts. Hydrogen fuses in a shell around the core - envelope expands
4. 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

Question 10

What does the graph of log(T(surface)) against log(L/L(solar)) look like? (stellar evolution across the H-R diagram)

Answer 10

• 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

Question 11

What is a Planetary Nebula?

Answer 11

A planetary nebula is the remnant of the ejected envelope while a star becomes a white dwarf.

Question 12

What is the White dwarf remnant?

Answer 12

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.

Question 13

What is the equation for the time taken for a white dwarf to cool?

Answer 13

tcool = Etherm/L = (kTc*M/μ)/L

=(GM^2)/(RL) ~ 10^9 yrs

Question 14

What is the Pauli exclusion principle?

Answer 14

No two fermions (particle with half integer spin) can occupy the same quantum state.

Question 15

What is degenerate matter?

Answer 15

• 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

Question 16

What is degenerate pressure?

Answer 16

• 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

Question 17

What is the Chandrasekhar limit?

Answer 17

The maximum mass of a white dwarf due to relativistic limit: M = 1.33 M(sun)

Question 18

Why is there a Chandrasekhar limit?

Answer 18

• 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

Question 19

What does the graph of radius against mass look like for relativistic and non-relativistic Fermi gas?

Answer 19

• Non-relativistic can have much higher mass as radius decreases
• Relativistic has a maximum mass at 1.33 solar masses

Question 20

What happens during the shell burning sequence for massive stars?

Answer 20

Shell burning sequence can continue to even heavier elements beyond C, O; Ne, Mg, Si, Fe

Question 21

Why do massive stars collapse?

Answer 21

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.

Question 22

What is a Type II Supernova explosion?

Answer 22

Driven by core collapse in massive stars, core implodes and the rest of the star explodes.

Question 23

What is an example of a type II supernova?

Answer 23

Crab nebula

Question 24

Why does the core collapse in massive stars?

Answer 24

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.

Question 25

What is the equation for the radius of a black hole?

Answer 25

R = 2GM/c^2

Question 26

What happens if M < 0.08 M(solar)?

Answer 26

Never initiates fusion (planets and brown dwarfs)

Question 27

What happens if 0.08 M(solar) < M < 0.8 M(solar)?

Answer 27

Time at main sequence is longer than age of the Universe.

Question 28

What happens if 0.8 M(solar) < M < 7-9 M(solar)?

Answer 28

Produces white dwarf.

Question 29

What happens if 7-9 M(solar) < M < 30-40 M(solar)?

Answer 29

Neutron star formed.

Question 30

What happens if M > 30-40 M(solar)?

Answer 30

Black hole is formed.