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Year 2 Stellar > Stellar > Flashcards

Stellar Flashcards

1
Q

What are the 2 properties of a star?

A
  1. Composed of gas bound by self gravity
  2. It has an internal energy source which radiates through it’s surface
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2
Q

List the 5 stellar assumptions

A
  1. The total mass of a star remains constant
  2. A star can be treated in isolation
  3. We assume stars are perfectly spherical
  4. The hot gas consists of ions and electrons behaving as an ideal gas
  5. Stars begin as 70% Hydrogen, 28% Helium and 2% heavier elements
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3
Q

What is Wein’s Law

A

(Peak Wavelength) * T = 2.9 * 10^(-3) m K

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4
Q

What is the energy density of thermal radiation per frequency interval?

A

u(v) = du/dv = (8πν^2)(hν)/(c^3)(e^{hν/kt} - 1)

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5
Q

How do you find the intensity per frequency interval?

A

(c * u(v))/4π

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6
Q

What is flux per unit frequency at the surface of a star?

A

The integral of f(v), which is B(v)cosθsinθ dθdΦ
f(v) = πB(v)

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7
Q

What is the bolometric flux?

A

Integrating the blackbody over all frequencies gives us bolometric flux. This is the flux at the surface of a star.

f(bol) = σT^4

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8
Q

What is bolometric luminosity?

A

The power:
L(bol) = f(bol)A = 4(π^2)σ(T^4)(R^2)

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9
Q

What is the parallax method?

A

sinθ = 1AU/d

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10
Q

What is a parsec?

A

The distance to a star from earth where the parallax angle is 1 arcsecond. (3.086e16m = 1pc)

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11
Q

What is the relationship between the apparent magnitude of stars and their fluxes?

A

100^{(m1-m2)/5} = F2/F1

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12
Q

how are apparent (m) and absolute (M) magnitudes related?

A

m - M = 5log10(d/10pc)

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13
Q

How are luminosity and temperature related in the main sequence?

A

L ∝ (T^8)

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14
Q

What is the mass fraction?

A

The density of ions/electrons in a gas / the total density

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15
Q

What is the formula for number density of an element?

A

ni = ρi/mi = ρiXi/Ai*mH

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16
Q

How is mean ion weight found?

A

the average ion mass / the mass of hydrogren

The inverse of the sum sum of all Xi/Ai

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17
Q

What is the total ion number density??

A

nI = ρ / μImH

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18
Q

What is the mean weight per electron?

A

The inverse of the sum sum of all Xi*Zi/Ai

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19
Q

What is the total electron number density?

A

ne = (ρ/mH)(sum of all XiZi/Ai)

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20
Q

What makes up most of the energy of particles in an ideal gas in a star during it’s main lifetime?

A

Kinetic energy, (3/2)kT

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21
Q

Where does radiation pressure come from?

A

photons are absorbed or scattered by gas, and the transfer of momentum from photons to the gas particles creates pressure.

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22
Q

What happens when a photon collides with a gas particle?

A

The photon is absorbed, and momentum is transferred to the gas particle. The excited particle emits a photon in a random direction which causes recoil that is normally dominated by the initial forward contribution of momentum transfer.

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23
Q

What is the blackbody number density?

A

The energy density per frequency u(v) divided by hv.

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24
Q

When is radiation pressure significant?

A

for very massive stars

25
Q

What is hydrostatic equilibrium?

A

The constant inward gravitational pressure due to layers of mass within a star required an outward supporting pressure.

26
Q

What is the virial theorem?

A

The total GPE is the integral of the gravitational work done multiplied by the surface area with respect to r.

It is finding the work done over all shells in a star.

27
Q

What is the virial theorem for pressure?

A

P = (1/3)*(Egr/V)

28
Q

What is the eq for thermal energy?

A

Eth = (3/2)*NkT

29
Q

What is the 2nd form of the virial theorem?

A

Eth = -(1/2)*Egr

30
Q

What is the eddington model?

A

The gas pressure is a fraction of the total pressure, so P = Pgas + Prad

31
Q

How does temperature correlate to number of free electrons?

A

Higher temps mean nearly all atoms are ionised and there are more free electrons.

32
Q

In what 2 ways do photons and electrons interact?

A
  1. Electron scattering, when the photon scatters off a free electron and it’s energy remains almost unchanged.
  2. Free-free absorption, when the photon is absorbed and the electron transitions to a higher energy state in the presence of an ion.
33
Q

What are the conditions for Thompson scattering?

A

When the photons energy is lower than the electron’s rest mass, as is the case in stars.

34
Q

How to find the average number of interactions of a photon travelling through target electrons?

A

Nint = nσdx

n: num density of electrons
σ: cross section

35
Q

How is opacity defined?

A

nσ/ρ

36
Q

How is photon intensity defined?

A

I(X) = I0 * e^(-τ)

where τ = the integral of ρκ between x and 0.

37
Q

what is kramer’s opacity law?

A

κ = 4.3*10^21 Z(X + 1)ρT^{-7/2} m^2kg^-1

38
Q

What is the dominant form of opacity in stars similar to the sun?

A

free-free absorption.

39
Q

What is the case for opacity in very high temps in cores?

A

The dominant form is electron scattering, and the cross section doesn’t depend on ρ or T, so the opacity is given by:

κ = 2*10^-2 (X + 1) m^2kg^-1

40
Q

How is radiation transported through a star?

A

Diffusion

41
Q

How is the energy density of blackbody photons found?

A

Integrating the energy density per frequency interval over all frequencies.

u = 4σT^4 / c

42
Q

What happens to the energy density as the radius increases?

A

it decreases

43
Q

What is the nuclear force?

A

The residual of the strong force which binds together quarks within nucleons.

44
Q

what is the range of the nuclear force?

A

Roughly the radius of the nucleus. So beyond this range, the potential energy goes from negative to positive due to the repulsive coulomb force.

45
Q

What is the scaling relation between the atomic weight of the nucleus, A, and the radius, R?

A

1.2 A ^{1/3}

46
Q

What stars become red giants vs supergiants?

A

below 8 solar mass : red giants, follow low mass evolution

above: SUPERGIANTS YAY, different composition in core and higher luminosity.

47
Q

What is the eddington luminosity?

A

The largest stable luminosity, when hydrostatic equilib starts to be overcome by radiation pressure.

48
Q

How is Ledd found?

A

Taking the derivative of radiation pressure and inserting dT/dr and then equating it to hydrostatic gradient.

49
Q

When does fusion stop?

A

when iron is produced as it has the highest binding energy per nucleon of any element.

50
Q

How does fusion occur for massive stars?

A

The higher temp enables fusion to procede to more massive elements. Fusion continues in shells surrounding the core until the degenerate core grows to the chandrasekhar mass limit of 1.4Msolar.

51
Q

What is the chandrasekhar mass limit

A

When the iron core can no longer be supported by degen pressure.

52
Q

What is photodisintegration and neutronization?

A

Iron core contracts to 10^9 K, photons have large enough energies to photodisintegrate, where the photon + iron turns into helium and neutrons.

53
Q

What is photodisintegration ex?

A

Gamma + 56Fe = 13 * 4He + 4n

Gamma + 4He = 2p + 2n

54
Q

What happens after photodisintegration?

A

The high energy loss, high temperatures and densities leads to neutronization, where:

e + p = n + neutrino

and less frequently:
n + n = n + p + e + neutrino

55
Q

What happens after neutronization?

A

So many neutrons, 10x larger than protons or electrons. The core is depleted of electrons, so electron degen pressure is removed and neutrinos escape.

56
Q

What happens in core collapse?

A

Near free-fall collapse, where neutrino scattering slows the collapse to a few seconds.

The material falls faster than speed of sound, so the core decouples from surrounding layers.

Neutron degeneracy only way to halt collapse since density in core is so high.

57
Q

What defines a neutron star?

A

During core collapse, if the mass is less than 3 M solar. Supported by neutron pressure.

58
Q

What happens after formation of neutron star?

A

The falling decoupled layers strike the neutron core and cause an outwards travelling shock wave, the high flux of neutrinos interacting with the layers, pushing them outwards.

Creates a supernova remnant.

59
Q

What happens when the core is more massive than 3 Msolar?

A

The relativistic KE dominates particles rest energy, black hole is formed.

Year 2 Stellar (1 decks)

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