The Interiors of Stars Flashcards
What is the hydrostatic equilibrium?
Pressure vs gravity balance.
What is the equation for dP/dr at hydrostatic equilibrium? How do you derive this?
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
How do you derive the equation for the central pressure of a star?
- 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
What is the equation for the central pressure of a star?
Pc = (GM/R)ρ = (3/4)(GM^2)/(pi*R^4) ∝ M^2/R^4
What is the equation of state for an ideal gas?
PV = nNkT
How do you derive the equation for the temperate of a stars core?
-Pc = GMρ/R = (ρ/μ)kTc
What is the equation for the temperature of a stars core?
kTc = μGM/R, Tc ∝ M/R
What are the 3 unknowns in stellar structures?
P(r), ρ(r) and T(r)
Why must hydrostatic equilibrium hold at all radii?
Otherwise the star would re-adjust.
What does the graph of density against radial coordinate look like for a star?
- 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.
What does the graph of pressure against radial coordinate look like for a star?
-P curve drops at a much faster rate than T curve, starting high and decreasing as r increases
What makes a star work?
As long as T(r) can provide adequate P(r) to support M(r)
How do you work out the lifetime of a star?
t = Energy of star/luminosity of star
energy of star = Mass of star/mass of H atom times 13.6 times charge of electron
What is the proton-proton chain in the core of the Sun?
4H -> HE + 2e+ + 2ve + 2γ
What does the graph of potential energy against separation look like for power in stellar cores?
Starts at low potential energy and increases steeply till peak, then decreases at a rate of 1/r
How does the percentage of H atoms and He atoms change as you move out of a star?
Starts at 60% H, then goes to equal of both, then % of He slowly decreases as r increases.
What was the Hipparcos H-R diagram?
- 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.
What are the ranges for the H-R diagram of log(T) versus log(L)?
- Temperatures: 1000-100000K
- Luminositites: 0.001 - 100000 L(sun)
How do you work out radius using the log H-R diagram?
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)
What is the main sequence section of the H-R diagram?
What is the ratio of their radius to the suns radius?
Main line going diagonally downwards.
0.1 to 10
Where are the giants located on the H-R diagram? What is the ratio of their radius to the suns radius?
Top right.
10 to 100
Where are the white dwarfs located on the H-R diagram? What is the ratio of their radius to the suns radius?
Bottom left.
0.01
What is the mass-luminosity relation?
L ∝ M^4, so during main sequence they are related, until the star is no longer main sequence.
