Spectral Line Strength and Chemical Abundance: Curve of Growth Assumptions Equivalent Width Scaling Models with Observations Spectrum Synthesis with Atmospheres

Simplifying Assumptions lines form by same mechanism: suppose no scattering: lines form in a layer characterized by T, P (poor, lines form over different levels) all lines have the same profile shape damping parameter is a free variable Milne-Eddington approximation for atmosphere with constant

Emergent Flux Source function = Planck function Recall second exponential integral Write in terms of continuum optical depth

Flux for Linear Planck Function Source function: Expression for emergent flux

Line Depth where A0 = depth for strongest lines Grey case Grey, weak line case (same as last time)

Equivalent Width Integral over normalized Doppler shift Express profile as Voigt function Form “reduced equivalent width” Integral depends on # absorbers (in β0) (profile symmetrical about v=0)

Curve of Growth weak: increases with # absorbers (linear) opaque: line reaches A0 limit (saturation, flat) strong: line wings important (damping/square root)

Comparing Observed and Model Curves of Growth y-axis x-axis

Strategy for Temperature measure (Wλ / λ) for lines of given ion/element for each line determine gijk , fij , λ , Χijk plot in curve of growth find excitation temperature that will shift individual points with Χijk into a single curve by shifting by amount –Χijk θexc

Shift (in x,y) observed to match theoretical vertical shift gives Doppler broadening microturbulence vturb delays saturation horizontal shift gives constant get ne , kc from atmosphere model Saha eqtn. to get total number of atoms of element damping part related to line broadening

LTE Spectrum Synthesis with Model Atmospheres model follows depth dependence of accounts for T changes, ionization-excitation, line broadening with depth for discrete set of frequency points find

ATLAS - WIDTH6 Select model parameters Solve for line flux and integrate across profile Iterative approach: trial abundance  Fν  Wλ  compare to obs.  adjust abundance ⏎ Correct for trends of abundance and ... Χijk  fix Teff ... ionization  fix log g (and Teff) ... Wλ  fix microturbulence Spectrum synthesis (moog) if lines are blended