TheseNotes Accompany my
Youtube Lectures
"STELLAR SPECTROPSCOPY"
@StellarSpectroscopyLectures

These notes are hand written for lectures of a introductory graduate level class focused on understanding astronomical spectra, with focus on stellar spectra. The material is compiled from many sources, including several text books and papers from the literature, including many of the figures (however, several figures are original). The notes are by no means complete, and of course are meant to provide a synopsis of material that is then more fully explained in lecture. Anyone is welcome to use these notes; however, I would be appreciative that their use be made known to me (just send me a quick email). Of course, letting me know of any errors (disclaimer- there are errors!), whether conceptual or numerical, would be appreciated. All notes are PDF files.

Chris Churchill
cwc@nmsu.edu

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Chapter 1: Introduction

1.1: What Makes a Stellar Spectrum
- absorption lines in spectra
- optical depth, absorption coefficients, ionization breaks
- equivalent widths, curve of growth
- photospeheric layers of line formation
- anatomy of a stellar spectrum

1.2 HR Diagram, Classification
- the HR diagram, luminosity, temperature, radius
- morgan-keenan spectral classification
- luminosity class
- surface gravity on HR diagram

1.3 Photometric Systems
- filter systems, apparent magnitudes
- AB, vega systems
- johnson UVB, SDSS, stromgren
- color indices

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Chapter 2: Atomic Structure and Transitions

2. From Bohr to Feynman and The Periodic Table
- hydrogenic atoms: Bohr (semi-classic), Schrodinger (wave model)
- damping constants, oscillator strengths, selection rules
- Dirac: fine structure spltting
- Feynman: QED radiative correction shifts
- multi-electronic atoms: spectroscopic notation
- isoelectronic sequences, understanding the periodic table
- grotrian diagrams, NIST atomic data
- some common stellar transitions
- draft book chapters (4) on atomic physics and spectra

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Chapter 3: Gas Physics

3.1 Ideal Gas with Radiation
- thermal equilibrium, LTE
- particle velocity distributions, the Maxwellian
- radiation in equlibrium: the Planck function
- kinetic energy, particle pressure, partial pressures
- number densities, mass densities, mass fractions
- abundances, solar abundances, mass fractions
- mean molecular weights in partially ionized gas
- draft book chapter on gas physics

3.2 Ionization Balance
- bound-bound, bound-free, free-free, scattering absorption/emission
- collisional excitation balance: Boltzmann equation, partition functions
- collisional ionization balance: Saha equation, ionization potentials
- ionization fractions, recursive application of Saha
- combining Boltzmann and Saha: balmer hydrogen densities
- non-equlibrium "temperatures", non-LTE, departure coefficients
- draft book chapter on ionization balance

3.3 Thermo and Hydrodynamics
- equation of state: ideal gas with radiation
- first law: energy density, specific heats, entropy
- adiabatic equations of state, adiabatic index
- hydrostatic equilbirium, pressure gradient, gravity
- temperature gradient: adiabatic gradient, radiative gradient
- superdiabatic gradient (radiative losses during convection)
- mixing length model for convection
- draft book chapter on thermo amd hydro
- draft book chapter on mixing length model

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Chapter 4: Introduction to Radiative Transfer

4. Basic 1D Radiative Transfer
- radiation field, sightlines, specific intensity, solid angle
- mean intensity, flux, astrophysical, eddington, observed
- mean momentum, macroscopic terms of radiative transfer
- the transfer equation, solution, boundary conditions, source function
- microscopic terms: einstein coefficients, absorption, emission
- draft book chapter on radiative transfer

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Chapter 5: Modeling Stellar Atmospheres

5. Eddington and the Grey Approximation
- plane-parallel approximation, reformulating equation of transfer
- Eddington's Treatment: isotropy at each tau layer
- higher moments of specific intensity, Eddingtons's approximation
- the flux integral, exponential integrals
- moments of the transfer equation; no flux gradient
- the grey approximation; relationships between moments of radiation field
- the temperature-tau relation, the Hopf function
- various mean opacities, the Rosseland mean, OPAL, opacity tables
- modeling grey stellar atmospheres, methods, boundary conditions

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Chapter 6: Modeling Absorption Lines

6.1 Natural and Thermal Broadening: Voigt Profiles
- cross sections, absorption corfficients, optical depth
- contributing broadening redistribution functions, convolution of
- "natural" profile, thermal, turbulence, pressure, rotation
- derivation of natural absorption profile, the Lorenzian
- atomic constants: central wavelength, oscillator strengths, damping constants
- thermal redistribution function, Doppler width, b parameters
- the Voigt profile, revisiting the curve of growth
- microturbulence redistribution fucntion, effect on curve of growth

6.2 Pressure and Rotational Broadening and the ISF
- introduction of pressure effects, pressure broadening
- overview of linear Stark, resonance, quadratic Stark, van der Waals
- examples of pressure broadening in stellar lines
- derivation of collisional/pressure braodening: impact theory
- pressure broadening redistribution function, pressure-temperature scaling
- the Weisskppf approximation (ala Mihalas)
- stark splitting in Balmer hydrogen lines
- the total absorption cross section, convolution of redistributions funcs
- modeling absorption lines, chi-square method to obtain parameters
- rotational broadening in fast rotating stars
- derivation of rotational redistribution function
- examples rotational redistribution functions
- the instrumental spread function, the final measured line profile

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Chapter 7: Modeling The Continuum

7. Ionization Edges, The Balmer Decrement, and Continuum Opacities
- overiew of dominant continuum cross sections
- reminder of definitions of absorption cross sections
- computing the total continuum opcacity from continuum cross sections
- examples of total mass absorption coefficients in various stars
- cross section: bound-free (ionization) of neutral hydrogen (HI)
- Kramer's versus full quantum mechanical solution
- the total bound-free HI cross section, Unsold's approximation
- cross section: free-free of neutral hydrogen (HI)
- Menzel's semi-classical expression, the thermally averaged Gaunt factor
- region applicable to stellar atmospheres
- cross section: H- bound-free, Wishart's expression, per HI atom
- cross section: H- free-free, Bell & Berrington's expression
- the Balmer decrement, behavior due to HI verus H- opacities
- continuum scattering: electron, Rayleigh
- cross section: HeII bound-free, converting to per HI atom
- cross section: HeI bound-free, Vardy'as treatment, converting to per HI atom
- cross section: HeII, HeI free-free, the quantum defect factor, per HI atom
- cross section: He- free-free, John's expression, per HI atom

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Chapter 8: Spectral Classification

8. Zoology of Stellar Spectra
- a compendium of examples for fine level classification

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