Ay 102 Physics of the Interstellar Medium supplemental material - - PowerPoint PPT Presentation

Ay 102 Physics of the Interstellar Medium

supplemental material Hillenbrand – Winter Term 2019-2020

Spectral Line Formation via Electonic Transitions

Source Function for Spectral Lines:

Function describing the shape or profile of the line

ε

Atomic Physics

Atomic Physics – Wave Function Ynlm

Dopita & Sutherland

Electron Population in the Ground State

• No two e- can

have the same four quantum numbers (n – l – ml - s)

• Note in the 2p

level, that 3 e- come in spin-up before any are spin-down.

Atomic Physics – Energy Levels

• 13.6 eV

Dopita & Sutherland

basic hydrogen

• 3.4 eV
• 1.5 eV
• 0.85 eV

“Selection rules” govern permitted, semi-forbidden, and forbidden transitions.

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

• Atoms with more than one electron in outer

shell are (rather) more complex…..

(n=3) ì ì (n=1) (n=2) (n=4)

Atomic Physics – Energy Ordering

From ???

Atomic Physics – Selection Rules

NIST = National Institute of Standards and Technology

Atomic Levels of Hydrogen

Kwok

allowed hydrogen transitions:

• Lyman
• Balmer
• Paschen
• Brackett
• Pfund

Atomic Levels – “Fine” Structure

But wait, there are even more possible energy levels…..

Atomic Levels – “Hyperfine” Structure

drawn to scale (and thus hard to see!) now including electron spin coupling to nucleus spin

aligned spin

Line Transition Types

Tielens Permitted (Electric dipole)

Beyond Hydrogen

Atomic Physics

now helium with 2 electrons è Singlets and Triplets

Atomic Physics

Kwok

helium transitions

Atomic Physics

now nitrogen – NI – with three outer shell electrons è Doublets and Quartets

Atomic Physics

now nitrogen – NII – so back to only two

• uter shell electrons

Atomic Physics

now oxygen – OI – with four outer shell electrons.

Some Important Lines Besides HI

Lequeux

• transition
• wavelength
• spontaneous de-excitation
• collisions strength
• critical density

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 Ωul 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 H2 molecules when between round brackets (for Tk≃100K).

Note Our Imperfect Knowledge

• f Atomic Data

i.e. how well do we know these Aul values, which depend on the gl / gu statistical weights, and the flu

• scillator strengths?

Review (courtesy of K. Dullemond)

Lines of atoms and molecules

4 3 Example: a fictive 6-level atom. 2 1 5 6 E6 E5 E4 E3 E2 E1=0 Energy Energy Levels

Lines of atoms and molecules

4 3 Example: a fictive 6-level atom. 2 1 5 6 g6=2 g5=1 g4=1 g3=3 g2=1 g1=4 Energy Level degeneracies

Lines of atoms and molecules

4 3 Example: a fictive 6-level atom. 2 1 5 6 E6 E5 E4 E3 E2 E1=0 Energy Populating the levels

Lines of atoms and molecules

4 3 Example: a fictive 6-level atom. 2 1 5 6 E6 E5 E4 E3 E2 E1=0 Energy

γ

Spontaneous radiative decay (= line emission)

[sec-1]

Einstein A-coefficient (radiative decay rate):

Lines of atoms and molecules

4 3 Example: a fictive 6-level atom. 2 1 5 6 E6 E5 E4 E3 E2 E1=0 Energy

γ

Spontaneous radiative decay (= line emission) Can be from any pair of levels, provided the transition

• beys selection rules

Lines of atoms and molecules

4 3 Example: a fictive 6-level atom. 2 1 5 6 E6 E5 E4 E3 E2 E1=0 Energy Einstein relations:

Lines of atoms and molecules

4 3 Example: a fictive 6-level atom. 2 1 5 6 E6 E5 E4 E3 E2 E1=0 Energy

γ

Line absorption Einstein B-coefficient (radiative absorption coefficient):

[sec-1]

Lines of atoms and molecules

4 3 Example: a fictive 6-level atom. 2 1 5 6 E6 E5 E4 E3 E2 E1=0 Energy

γ

Stimulated emission Einstein B-coefficient (stimulated emission coefficient):

[sec-1]

γ

Lines of atoms and molecules

4 3 Example: a fictive 6-level atom. 2 1 5 6 E6 E5 E4 E3 E2 E1=0 Energy

Ecollision

Collisional excitation

Our atom free electron

Lines of atoms and molecules

4 3 Example: a fictive 6-level atom. 2 1 5 6 E6 E5 E4 E3 E2 E1=0 Energy

Ecollision

Collisional de-excitation

Our atom free electron

Collision Strength => Ωlu and Ωul values

Atomic Physics

Dopita & 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

Dopita & Sutherland

While collisions determine the population of Electronic states, at high T or n, can also determine the population of Ionization states.

OI OII OIII OVII OIX OVIII

First Ionization Potential

how much energy to free the first (outermost) electron?

consider IP relative to IPH , IPHe

how much energy to free the next electron?

Other Processes: Raman Scattering

Dopita & Sutherland

Inelastic interactions between ions and photons lead to energy level changes. UV photons converted into

• ptical photons

Other Processes: Masers

Dopita & Sutherland

Why Are we Slogging Through all of This Atomic Physics?

Implications of Energy Level Separation

Dopita & Sutherland

Consider a three-level atom: temperature diagnostic !

Example Temperature Probes

Dopita & Sutherland

Dopita & Sutherland

Consider a different three-level atom: density diagnostic !

Implications of Energy Level Separation

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