2.9

Question 1

Formation of Stellar Absorption Lines

qualitative properties of flux

Answer 1

• Gas particles exhibit strong peaks in τ_ν due to atomic/molecular lines λ
• In stellar atmospheres, F = const
• But F_ν ≠ const
  –> Energy redistribution in frequency
• Grey atmosphere models inadequate for treating line absorption

Question 2

Qualitative Description of Line Absorption

state an equality

Answer 2

• Specific intensity I_ν(0,1) is approximately equal to the Planck function (Blackbody radiation) at τ_ν = 1 for frequency ν
• Derived using a Taylor expansion and considering t_ν = 0 and τ_ν = 1

Question 3

Interpretation for Line Spectrum

relationship of line strength to wavelength

Answer 3

• Continuum:
  – Absorption coefficient 𝛂_C varies for a broad range of 𝛎
  – At τ_C ≈ 1, the temperature T_C relates to the radiation field ≈ B_𝛎(T_C)
• Line: Similar to continuum, but at specific frequency ν_L
• Strong lines: 𝛂_L » 𝛂_C implies T_L < T_C and B_𝛎(T_L) < B_𝛎(T_C).

i dont see where in the notes it says that it varies for broad range

-> lines are stronger at short wavelengths

Question 4

Calculation of Line Absorption

Formula asked

Answer 4

• Absorption coefficient α_ν is given by α_ν = n σ φ(Δν).
• Here, n is the number density of an atom, σ is the absorption cross-section, and φ(Δν) is the normalized profile.
• The optical depth τ_ν then becomes n σ φ(Δν) ds.

it seems to just have taken one of the many formulas, idk if thats the most important one

Question 5

Line Profiles

Interaction of radiation with matter, what are the types?

Answer 5

• Natural line profile: Defined by φ_n(Δν)
• Doppler profile: Described by a Gauss curve φ_D(Δν). Influences include:
  – Maxwell-Boltzmann velocity distribution
  – Atmospheric turbulence
  – Stellar rotation
  – Collisions.
• Voigt profile: A combination of natural and Doppler profiles.

I think the greek letters arent necessary

Question 6

Measurement of a Spectral Absorption Line

/ calculation

formula for equivalent width

Answer 6

Equivalent width W_λ represents the fractional intensity dip of a spectral line. Calculated as:

W_λ = ∫ (I_c - I_λ) / I_c dλ

not sure if we need to know the formula

Question 7

Line Absorption (without Emission)

Answer 7

• Cases like cold or optically thin gas, line emission is negligible
• Line intensity I_L is relative to the continuum intensity I_C
• Equivalent width W_λ is derived considering I_ν = I_ce^-𝛕_𝛎

Question 8

Curve of Growth for Absorption Lines

What are the different regimes?

Answer 8

Describes three regimes for the absorption line equivalent width:

• Linear: weak absorption
• Plateau: doppler core saturation
• Square root: strong damping wings

Question 9

Analysis of Stellar Absorption Lines (4)

what has to be considered?

Answer 9

Analyzing stellar absorption lines involves considering factors like:

• Line emission
• Atomic data accuracy
• Micro-turbulence
• Atmospheric structure

Empirical curves of growth are used for this analysis.