Ay 102 Physics of the Interstellar Medium supplemental material Hillenbrand – Winter Term 2019-2020
Spectral Line Formation via Electonic Transitions
Function describing the shape or profile of the line Source Function for Spectral Lines:
ε
Atomic Physics
Atomic Physics – Wave Function Y nlm Dopita & Sutherland
Electron Population in the Ground State • No two e- can have the same four quantum numbers ( n – l – m l - s ) • Note in the 2p level, that 3 e- come in spin-up before any are spin-down.
Atomic Physics – Energy Levels basic hydrogen “Selection rules” govern permitted, semi-forbidden, and forbidden transitions. -0.85 eV -1.5 eV -3.4 eV -13.6 eV Dopita & Sutherland
Atomic Physics – Spectroscopic Terms
Atomic Physics – Spectroscopic Terms Dopita & Sutherland
Atomic Physics – Outer Shell is What Matters • Atoms with single-electron outer shells are “hydrogen-like” so the terms look like (n=2) (n=1) ì (n=3) ì (n=4) • Atoms with more than one electron in outer shell are (rather) more complex…..
Atomic Physics – Energy Ordering From ???
Atomic Physics – Selection Rules NIST = National Institute of Standards and Technology
Atomic Levels of Hydrogen allowed hydrogen transitions: - Lyman - Balmer - Paschen - Brackett - Pfund Kwok
Atomic Levels – “Fine” Structure But wait, there are even more possible energy levels…..
Atomic Levels – “Hyperfine” Structure now including electron spin coupling to nucleus spin aligned spin drawn to scale (and thus hard to see!)
Line Transition Types Permitted (Electric dipole) Tielens
Beyond Hydrogen
Atomic Physics now helium with 2 electrons è Singlets and Triplets
Atomic Physics helium transitions Kwok
Atomic Physics now nitrogen – NI – with three outer shell electrons è Doublets and Quartets
Atomic Physics now nitrogen – NII – so back to only two outer shell electrons
Atomic Physics now oxygen – OI – with four outer shell electrons.
The most important forbidden lines in the interstellar medium. Only CI, CII, OI, SiII, SII, and FeII are present in the neutral medium. They are also present in the ionised medium, but generally in smaller amounts than more ionised species. The collision strengths Ω ul are for collisions with electrons at a temperature of 104 K. The critical densities correspond to collisions either with electrons (for Te ≃ 104 K), or with H 2 molecules when between round brackets (for T k ≃ 100K). Some Important Lines Besides HI - transition - wavelength - spontaneous de-excitation - collisions strength - critical density Lequeux
Note Our Imperfect Knowledge of Atomic Data i.e. how well do we know these A ul values, which depend on the g l / g u statistical weights, and the f lu oscillator strengths?
Review (courtesy of K. Dullemond)
Lines of atoms and molecules E 6 6 Example: 5 E 5 a fictive 6-level atom. E 4 4 Energy Energy Levels E 3 3 2 E 2 1 E 1 =0
Lines of atoms and molecules g 6 =2 6 Example: 5 g 5 =1 a fictive 6-level atom. g 4 =1 4 Energy Level degeneracies g 3 =3 3 2 g 2 =1 1 g 1 =4
Lines of atoms and molecules E 6 6 Example: 5 E 5 a fictive 6-level atom. E 4 4 Energy Populating the levels E 3 3 2 E 2 1 E 1 =0
Lines of atoms and molecules E 6 6 Example: 5 E 5 a fictive 6-level atom. E 4 4 γ Energy Spontaneous radiative decay E 3 3 (= line emission) 2 E 2 1 E 1 =0 Einstein A-coefficient (radiative decay rate): [sec -1 ]
Lines of atoms and molecules E 6 6 Example: 5 E 5 a fictive 6-level atom. E 4 4 γ Energy Spontaneous radiative decay E 3 3 (= line emission) 2 E 2 1 E 1 =0 Can be from any pair of levels, provided the transition obeys selection rules
Lines of atoms and molecules E 6 6 Example: 5 E 5 a fictive 6-level atom. E 4 4 Energy E 3 3 2 E 2 1 E 1 =0 Einstein relations:
Lines of atoms and molecules E 6 6 Example: 5 E 5 a fictive 6-level atom. E 4 4 Energy γ Line absorption E 3 3 2 E 2 1 E 1 =0 Einstein B-coefficient (radiative absorption coefficient): [sec -1 ]
Lines of atoms and molecules E 6 6 Example: 5 E 5 a fictive 6-level atom. E 4 4 γ Energy γ Stimulated emission E 3 3 2 E 2 1 E 1 =0 Einstein B-coefficient (stimulated emission coefficient): [sec -1 ]
Lines of atoms and molecules E 6 6 Example: 5 E 5 a fictive 6-level atom. E 4 4 Energy E collision Collisional excitation E 3 3 2 E 2 1 E 1 =0 Our atom free electron
Lines of atoms and molecules E 6 6 Example: 5 E 5 a fictive 6-level atom. E 4 4 Energy E collision Collisional de- excitation E 3 3 2 E 2 1 E 1 =0 Our atom free electron
Collision Strength => Ω lu and Ω ul values
Dopita & Atomic Physics Sutherland Collisions do not need to obey the “selection rules” like for energy level changes involving photons. This means that photons can “scatter” into other frequency photons.
Spectral Line Radiation • Emission of a photon via radiative de-excitation requires the higher energy level to be populated. • Getting electrons above the ground can occur by: – Collisional Excitation; also Collisional Ionization – Photo-Ionization followed by Recombination+Cascade – Photon Scattering (Raman not Rayleigh) – Masers
OI OII OIII OVII OVIII OIX Dopita & Sutherland While collisions determine the population of Electronic states, at high T or n, can also determine the population of Ionization states.
First Ionization Potential how much energy to free the first ( outermost ) electron?
how much energy to free the next electron? consider IP relative to IP H , IP He
Other Processes: Raman Scattering Inelastic interactions between ions and photons lead to energy level changes. UV photons converted into optical photons Dopita & Sutherland
Other Processes: Masers Dopita & Sutherland
Why Are we Slogging Through all of This Atomic Physics?
Implications of Energy Level Separation Consider a three-level atom: temperature diagnostic ! Dopita & Sutherland
Example Temperature Probes Dopita & Sutherland
Implications of Energy Level Separation Consider a different three-level atom: density diagnostic ! Dopita & Sutherland
Example Density Probes Dopita & Sutherland
Ideally, Find Line Ratios that Probe Both Density and Temperature Dopita & Sutherland
(Almost) Enough Atomic Physics! We will come back to these concepts as needed over the rest of the • term – focussing on the practical applications. Over next few weeks , we will discuss: • – Atomic gas (typical diffuse HI, plus HI clouds) – right now in fact – Molecular gas (GMCs) – Dust (nearly everywhere the gas is) – Ionized gas (HII and “photon dominated” regions) – Hot “coronal” gas (half the volume of the galaxy) Goal is to understand: • – Appropriate temperature and density probes – Role of major constituents in heat and cooling – Formation and destruction mechanisms
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