The Interiors of Stars

Question 1

What is the hydrostatic equilibrium?

Answer 1

Pressure vs gravity balance.

Question 2

What is the equation for dP/dr at hydrostatic equilibrium? How do you derive this?

Answer 2

dP/dr = (-Gρ(r)M*r))/r^2

Derive by using box of mass dm = ρ dr dA, and then set gravity force equal to pressure force

Question 3

How do you derive the equation for the central pressure of a star?

Answer 3

• Pc = P(r=0), P(r=R) = 0
• dP = P(R) - P(0) = -Pc, dR = R
• So Pc/R = (GM/R^2) ρ, where ρ = M/((4/3)piR^3)
• Rearrange for Pc

Question 4

What is the equation for the central pressure of a star?

Answer 4

Pc = (GM/R)ρ = (3/4)(GM^2)/(pi*R^4) ∝ M^2/R^4

Question 5

What is the equation of state for an ideal gas?

Answer 5

PV = nNkT

Question 6

How do you derive the equation for the temperate of a stars core?

Answer 6

-Pc = GMρ/R = (ρ/μ)kTc

Question 7

What is the equation for the temperature of a stars core?

Answer 7

kTc = μGM/R, Tc ∝ M/R

Question 8

What are the 3 unknowns in stellar structures?

Answer 8

P(r), ρ(r) and T(r)

Question 9

Why must hydrostatic equilibrium hold at all radii?

Answer 9

Otherwise the star would re-adjust.

Question 10

What does the graph of density against radial coordinate look like for a star?

Answer 10

• ρ(r) curve starts at very higher density and curves down ad radial coordinate increases
• M(r) curve starts at 0 density at 0 radial coordinate and increases as r increases, levelling off at the surface.

Question 11

What does the graph of pressure against radial coordinate look like for a star?

Answer 11

-P curve drops at a much faster rate than T curve, starting high and decreasing as r increases

Question 12

What makes a star work?

Answer 12

As long as T(r) can provide adequate P(r) to support M(r)

Question 13

How do you work out the lifetime of a star?

Answer 13

t = Energy of star/luminosity of star

energy of star = Mass of star/mass of H atom times 13.6 times charge of electron

Question 14

What is the proton-proton chain in the core of the Sun?

Answer 14

4H -> HE + 2e+ + 2ve + 2γ

Question 15

What does the graph of potential energy against separation look like for power in stellar cores?

Answer 15

Starts at low potential energy and increases steeply till peak, then decreases at a rate of 1/r

Question 16

How does the percentage of H atoms and He atoms change as you move out of a star?

Answer 16

Starts at 60% H, then goes to equal of both, then % of He slowly decreases as r increases.

Question 17

What was the Hipparcos H-R diagram?

Answer 17

• He measured apparent magnitudes in different filters and determined the parallax
• General shape of H-R diagram with Mv on y-axis and B-V on x-axis, where Mv is the absolute magnitude and B-V is the change in magnitudes.

Question 18

What are the ranges for the H-R diagram of log(T) versus log(L)?

Answer 18

• Temperatures: 1000-100000K

- Luminositites: 0.001 - 100000 L(sun)

Question 19

How do you work out radius using the log H-R diagram?

Answer 19

Use the equation L = 4pi*R^2 * σ * T^4, and find ratio of suns radius by dividing by suns properties (L, R and T of sun)

Question 20

What is the main sequence section of the H-R diagram?

What is the ratio of their radius to the suns radius?

Answer 20

Main line going diagonally downwards.

0.1 to 10

Question 21

Where are the giants located on the H-R diagram? What is the ratio of their radius to the suns radius?

Answer 21

Top right.

10 to 100

Question 22

Where are the white dwarfs located on the H-R diagram? What is the ratio of their radius to the suns radius?

Answer 22

Bottom left.

0.01

Question 23

What is the mass-luminosity relation?

Answer 23

L ∝ M^4, so during main sequence they are related, until the star is no longer main sequence.