Stellar Atmospheres Part 1

Question 1

What is it called when something transitions between energy states?

Answer 1

Bound-bound transitions.

Question 2

What are the 4 quantum numbers?

Answer 2

n, l, s, mz

Question 3

What is the quantum state m a function of?

Answer 3

m = m(n, l, s, mz)

Question 4

What is the equation for Nm, the particle density at level m?

Answer 4

Nm = N1/g1 * gm*exp(Em/kT)

Question 5

What is the partition function U(T)?

Answer 5

U(T) = sum from m=1 to inf of gm*exp(_em/kT)

Question 6

How do we incorporate the partition function into the equation for Nm?

Answer 6

-Change Nm to N and add a 
sum infront of the exponential
-Sub in U(T)
-Rearrange for N1
-Sub back into equation for Nm

Question 7

How do electrons create absorption lines?

Answer 7

Free electrons can have range of kinetic energies, so bound free transitions produce continuous opacity (absorption)

Question 8

What is needed to ionise an atom from a given level.

Answer 8

A minimum photon energy.

Question 9

What does the Saha equation give?

Answer 9

The distribution of atoms in different stages of ionisation.

Question 10

What is the equation for the energy difference between ground state and free electron having velocity u?

Answer 10

ΔE = χ1 + 1/2 * m(e)*(v^2), where χ1 is the ionization potential and the second part is the KE of electron.

Question 11

What is the difference between the Saha and the Boltzmann equation?

Answer 11

Saha gives the ionisation equilibrium, whereas Boltzman gives the excitation equilibrium.

Question 12

What is the equation for the statistical weight of an electron, ge?

Answer 12

ge = 2dx1dx2dx3dp1dp2dp3/h^3, where dx1dx2dx3 = 1/Ne (Ne = electron density)

Question 13

What does the Saha equation show?

Answer 13

The number of electrons which are completely disassociated with its original atom and now travelling freely through a star.

Question 14

What does the Boltzmann equation show?

Answer 14

Used to calculate the distribution of a specific ion/atom over the available energy levels.

Question 15

What are the layers of the sun?

Answer 15

Core, radiative zone, interface layer, convective zone, surface.

Question 16

What is the equation for energy in terms of radiation transfer?

Answer 16

Intensityareatimewavelengthangle subtended by detector.

Question 17

What is the equation for intensity I(λ)?

Answer 17

I(λ) = B(T) = 2hc^2/λ^5 * 1/(exp(hc/λkT)-1)

Question 18

What is the integral equation for the flux?

Answer 18

F = integral of I(λ)*cosθ dΩ

Question 19

What is the equation for the absorption of intensity dI(λ)?

Answer 19

dI(λ) = -κ(λ)*I(λ) dz, where κ(λ) is the absorption coefficient and dz is the path length.

Question 20

What is the equation for the scattering of intensity dI(λ)?

Answer 20

dI(λ) = -σ(λ)*I(λ) dz, where σ(λ) is the scattering coefficient

Question 21

What is the equation for the emission of intensity, dI(λ)?

Answer 21

dI(λ) = ε(λ) dz, where ε(λ) is the emission coefficient. ε(λ) = κ(λ)*B(T)

Question 22

How is emission related to absorption?

Answer 22

dI(λ)emission = -dI(λ)absorption

Question 23

What is the energy of a photon released when a BB transition occurs equal to?

Answer 23

hv = Em-En

Question 24

What are the absorption lines in stellar spectra?

Answer 24

They show bb transitions.

Question 25

What is the equation for ΔE, the uncertainty principle in natural broadening? What does this mean?

Answer 25

ΔE ~ h/(2π*Δt). The energy levels are ‘fuzzy’.

Question 26

What do fuzzy energy levels mean?

Answer 26

Atoms can absorb photons with slightly different energy.

Question 27

What is the equation for Δλ?

Answer 27

Δλ = λ^2/2πcΔt

Question 28

What is the equation for velocity distribution of atoms (Maxwell-Boltzmann)?

Answer 28

v = sqrt(2kT/m)

Question 29

What is the equation for dopller shift?

Answer 29

Δλ/λ = v/c

Question 30

What is the difference between natural broadening and doppler broadening?

Answer 30

Natural is due to the fuzziness of the energy, whereas doppler is due to the doppler shifted frequencies.

Question 31

What is pressure/collisional broadening?

Answer 31

Interaction between particles.

Question 32

What do wide/narrow absorption lines represent on Flux-wavelength graphs?

Answer 32

• Wider lines = main-sequence: small radius, high pressure

- Narrower lines = supergiant: large radius, low pressure

Question 33

How does the rotation of the star effect the absorption lines?

Answer 33

There is a constant Doppler shift along stripes parallel to the projected rotation axis. Faster the rotation, the broader the absorption lines.

Question 34

What is bound-free transition and what is the equation for hv?

Answer 34

Produces continuous absorption. Ionisation: produces ‘absorption edges’ at ionisation points.
hv = E(inf)-En + 1/2 * mv^2

Question 35

What does a graph of κ/ρ againt wavelength look like for different temperatures?

Answer 35

Linearly upwards with shard ‘ionisation edges’. Ionisation edges go further down for lower temperature.

Question 36

What is the equation for hv for free-free absorption?

Answer 36

hv = 1/2me(v2^2-v1^2)

Question 37

How do we get the total absorption coefficient?

Answer 37

κ = κ(bb)+κ(bf)+κ(ff)

Question 38

What kind of transitions are continuous absorption and line absorption?

Answer 38

• Continuous: bf and ff transitions

- Line: bb transitions