Stellar Structure Part 1

Question 1

What is the H-R diagram?

Answer 1

A diagram showing the absolute magnitudes of stars and their spectral types: shows clear areas of similar stars such as main sequence and giants etc.

Question 2

What does the theoretical H-R diagram show the main sequence as?

Answer 2

A single line, rather than a line with thickness.

Question 3

For main sequence stars, what does the Mass Luminosity equation mean?

Answer 3

That luminous stars are much more massive.

Question 4

What is the luminosity of a star proportional to in terms of mass?

Answer 4

L∝M^3

Question 5

What can we observe on an H-R diagram of the open cluster Pleiades?

Answer 5

Most luminous stars are just leaving the main sequence, and there are no low luminosity stars, so they have not yet evolved into main sequence.

Question 6

What can we observe on an H-R diagram of the open cluster Hyades?

Answer 6

Most luminous stars evolved off main sequence to red giant, and have the lowest mass stars on main sequence.

Question 7

What can we infer from the HR diagrams of Pleiades and Hyades?

Answer 7

That Hyades is a much older open cluster than Pleiades.

Question 8

Where do galactic and globular clusters lie in the galaxy?

Answer 8

Galactic clusters: lie in galaxy disc, globular clusters: lie in galaxy halo

Question 9

Approximately how many stars are in galactic and globular clusters?

Answer 9

Galactic: few thousand, globular: millions

Question 10

What is the turn off point of the main sequence related to?

Answer 10

The age of the cluster you’re looking at.

Question 11

What is the equation for mass Mr, the mass within the radius r?

Answer 11

Mr = integral from 0 to r of 4πr^2ρ dr, so dMr/dr = 4πr^2ρ and dr/dMr = 1/that

Question 12

What is balanced in hydrostatic equilibrium?

Answer 12

The change in pressure is balanced by mg.

Question 13

What is the equation for dP/dr in hydrostatic equilibrium?

Answer 13

dP/dr = -ρ*GMr/r^2

Question 14

What is the equation for dP/dMr in hydrostatic equilibrium?

Answer 14

dP/dMr = -GMr/4πr^4

Question 15

What is the equation of energy conservation dL/dr?

Answer 15

dL/dr = 4πr^2 * ε(N)*ρ, where ε(N) is the nuclear energy production per unit mass and L is the luminosity

Question 16

What is the equation for dL/dMr?

Answer 16

dL/dMr = ε(N)

Question 17

What is the equation for dT/dr in energy transport?

Answer 17

dT/dr = -3κρL/(16acπr^2 *T^3), where κ is the absorption coefficient, a is the radiation constant

Question 18

What is the equation for dT/dMr?

Answer 18

dT/dMr = -3κL/(64acπ^2r^4 *T^3)

Question 19

Describe the Convection I model for energy transport (stellar model).

Answer 19

• Displace upward gas with T1, ρ1
• Gas stays in hydrostatic equilibrium
• Bubble stays at same pressure s surroundings
• Pressure is less, bubble expands and cools

Question 20

In the energy transport model convection I, what is the energy exchange like?

Answer 20

No energy exchange, so adiabatic process - get T2, ρ2 from PV = const

Question 21

Describe the Convection II model for energy transport.

Answer 21

• If ρ2’>ρ2, bubble sinks back and atmosphere is stable against convection
• If bubble remains warmer despite adiabatic cooling, ρ2’ < ρ2and continues to rise, so convection sets in

Question 22

When is there no convection in the convection II model?

Answer 22

No convection if T2’ < T2

Question 23

What is the equation for the dynamical timescale of a star?

Answer 23

τ(dyn) = sqrt(R^3/2GM)

Question 24

What is the equation for the time needed to radiate total energy contained at current L? (Kelvin-Helmholtz)

Answer 24

τ(KH) = 1/2 * E(pot)/L

Question 25

What is the equation for the time needed for the total mass of fuel to be converted at present rate?

Answer 25

τ(nuc) = εMc^2/L

Question 26

What are the 4 forces involved with nuclear energy production?

Answer 26

Gravity, coulomb, strong nuclear force and weak nuclear force

Question 27

What needs to be overcome for nuclear fusion to occur?

Answer 27

Coulomb force needs to be overcome so the strong force can bring the protons together.

Question 28

What is the tunnel effect?

Answer 28

Where particles are described by wave functions that have a finite probability to tunnel through a potential barrier.

Question 29

What is the equation for the mass defect?

Answer 29

ΔM = Zm(proton) + (A-Z)*m(neutron) - M(A,Z)

Question 30

What is the equation for the binding energy?

Answer 30

E(B) = ΔMc^2

Question 31

Which quantities are conserved in the proton-proton chain?

Answer 31

• Electric charge
• Number of Baryons
• Number of particles and anti-particles

Question 32

Describe the first stage of the PPI chain.

Answer 32

• 2 hydrogens go to one hydogen with 2 atomic number plus positron plus neutrino
• add another hydrogen to get hydrogen with 3 atomic number plus gamma ray
• Add 2 of these hydrogens to get He-4 plus 2 normal hydrogens

Question 33

Describe the second stage of the PPI chain.

Answer 33

• He-3 + He-4 goes to Be-7 plus gamma
• Be-7 plus electron goes to Li-7 plus neutrino
• Li-7 plus hydrogen goes to 2 He-4’s

Question 34

Describe the third stage of the PPI chain.

Answer 34

• Be-7 plus one H goes to B-8 plus gamma
• B-8 goes to Be-8 plus positron plus neutrino
• Be-8 goes to 2 He-4

Question 35

Why must the triple α process occur quickly?

Answer 35

As Be-8 decays quickly

Question 36

What is Carbon-Oxygen burning?

Answer 36

• 2 carbons added together makes magnesium which then decays to oxygen-16
• 2 oxygen-16’s makes S-32 which then decays to Mg-24