Stellar Atmospheres Part 1 Flashcards by Arthur Morton

What is it called when something transitions between energy states?

Bound-bound transitions.

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What are the 4 quantum numbers?

n, l, s, mz

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What is the quantum state m a function of?

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

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

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

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What is the partition function U(T)?

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

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

-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

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How do electrons create absorption lines?

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

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

A minimum photon energy.

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What does the Saha equation give?

The distribution of atoms in different stages of ionisation.

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

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

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

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

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

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

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What does the Saha equation show?

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

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What does the Boltzmann equation show?

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

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What are the layers of the sun?

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

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

Intensityareatimewavelengthangle subtended by detector.

What is the equation for intensity I(λ)?

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

What is the integral equation for the flux?

F = integral of I(λ)*cosθ dΩ

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

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

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

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

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

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

How is emission related to absorption?

dI(λ)emission = -dI(λ)absorption

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

hv = Em-En

What are the absorption lines in stellar spectra?

They show bb transitions.

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

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

What do fuzzy energy levels mean?

Atoms can absorb photons with slightly different energy.

What is the equation for Δλ?

Δλ = λ^2/2πcΔt

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

v = sqrt(2kT/m)

What is the equation for dopller shift?

Δλ/λ = v/c

What is the difference between natural broadening and doppler broadening?

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

What is pressure/collisional broadening?

Interaction between particles.

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

- Wider lines = main-sequence: small radius, high pressure | - Narrower lines = supergiant: large radius, low pressure

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

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

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

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

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

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

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

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

How do we get the total absorption coefficient?

κ = κ(bb)+κ(bf)+κ(ff)

What kind of transitions are continuous absorption and line absorption?

- Continuous: bf and ff transitions | - Line: bb transitions