Physics and Chemistry of the Interstellar Medium -...

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Physics and Chemistry of theInterstellar Medium

Pierre Hily-Blant

Master2 Lecture, [email protected], Office 53

2012-2013

Pierre Hily-Blant (Master2) The ISM 2012-2013 1 / 229

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I- Production of light in the ISM

1. Electronic spectroscopy

2. Infrared spectroscopy

3. Microwave spectroscopy


1.Electronic spectroscopy

1. Electronic spectroscopyElectronic transition ratesSpectra of atomsSpectra of atoms: Examples


1.Electronic spectroscopy Electronic transition rates

Generalities

• classical electrodynamics: e-m radiation is emitted if a chargedparticle is accelerated, e.g. e− on its orbit around the nucleus.

• Bohr’s model (semi-classical): e-m radiation is emitted when the e−

goes from one quantum orbit to another, quantum jump. Differencein energy is emitted as a light quantum hν = ∆E.

• Quantum mechanics treatment: quantum jump + selection rules



Dipole approximation• Hamiltonian of a charged particle of mass m interacting with

radiation field (in terms of potential vector ~A and electric potential φ)

H =1

2m

[p− q ~A

]2+ qφ

• Assuming an incident plane wave linearly polarized in direction ~ε,~A(~r, t) = ~εA(t) ei~k·~r

• φ(r) = − Ze4πε0r

• With q = −e, and chosing the Coulomb gauge (∇ · ~A = 0), theHamiltonian reads

H = − ~2

2m∇2 − Ze2

4πε0r− i~e

m~A · ∇ = H0 +H1(t)

to first order in ~A• We treat the effect of the radiation field as time-dependent

perturbation H1(t)� H0



• From QM perturbation theory results, the probability that after sometime, the system evolves from an initial state i to a final state f is

Wfi ∝ |〈ψf |H1|ψi〉|2 ∝ |〈ψf |ei~k·~r ~ε∇|ψi〉|2

• Dipole approximation: ei~k·~r = 1 + i(~k · ~r) + 12(i~k · ~r)2 + . . . ≈ 1

• ~k · ~r ∼ ka0 = 2πa0λ ∼ a0∆E

~c ∼Zeα ∼

vc � 1: non-relativistic approx.

• Using p = −i~∇ and properties of r, one finds:

Wfi ∝ |~ε · 〈ψf |r|ψi〉|2

• Recalling that the electric dipole moment is ~d = −er (for H-likeatoms), the probability may be written

Wfi ∝ |〈ψf |~d|ψi〉|2 = |dfi|2

Notes: 1st order in ~k · ~r: quadrupole electric (E2) /dipole magnetic (M1)

2nd order in ~k · ~r: octupole electric (E3) / quadrupole magnetic (M2)



Einstein coefficients

• Spontaneous emission coefficient Aul:

Aul =8π3

3~c2

14πε0

ν3ul|dul|2

• In cgs units:

Aul =64π4

3c3hν3ul|dul|2

• Aul: 10−8 to 108 s−1

• Stimulated absorption Bul:

Aul =2hν3

ul

c2Bul ⇒ (Bul)cgs =

32π4

3ch2|dul|2


1.Electronic spectroscopy Spectra of atoms

Selection rules for the H-like atoms

1 ∆n any2 ∆l = ±13 ∆s = 0 (always satisfied for H)4 ∆j = 0,±15 ∆m = 0,±1

Grotrian diagram for the H atom



Selection rules for complex atoms• We now want to know what transitions are observables• Dipolar transition rates from i to f are ∝ |〈f |~d|i〉|2

• For some {f, i}, |〈f |d|i〉|2 � 1 or even zero• Results: many-electron atoms with total quantities ~L, ~S and total

angular momentum ~J1 ∆J = 0, ±1, 0→ 0 forbidden2 ∆MJ = 0,±13 Parity must change4 ∆S = 05 ∆n any; ∆l = ±1 (for one-electron jumps)6 ∆L = ±1

• Transitions that fulfill all the rules are allowed• Transitions that violate any of (4) to (6) are (semi-)forbidden lines,

and are weaker.• ∆S 6= 0 are intercombination lines



Orders of magnitude

For electronic transitions, typical values for the transition rates are:

Transition type A ( s−1)resonance line ∼ 108 − 109

recombination line ∼ 108 − 109

E-quadrupolar ∼ α2Areson ∼ 104 s−1

Intercombination/intersystem/semi-forbidden ∼ 102 − 103 s−1

M-dipolar ∼ α4Areson ∼ 1 s−1

forbidden ∼ 10−3 s−1



Bound-bound transitions

• Transitions may occur betweenany pair of levels nl following tothe selection rules (∆l = ±1...)

• Such a transition from n′l′ to nlis called a bound-boundtransitions

• For the H atom:hνn′>n = Ry (n−2 − n′−2)



• Transitions to/from a given level form a series• All transitions to/from level n = 1 form the Lyman series• The highest energy of a given series corresponds to n′ →∞:In = Ry/n2. This is the ionization limit.

• Each series has its own ionization limit (see Table values forn′ →∞). It is 13.6 eV (912A) for the Lyman series, 365 nm for theBalmer series, etc...

Range [µm]n Name Symbol Spectral region n′ =∞ n′ = n+ 11 Lyman Ly UV 0.0912 0.1212 Balmer H Vis. 0.365 0.6563 Paschen P IR 0.820 1.8084 Brackett Br IR 1.459 4.052



Bound-free transitions

• Transition between a bound state n and continuum state• Continuous range of frequency• Photoionization: absorption of a photon with ν > νn = Ry/n2

• liberates an electron with kinetic energy mev2/2 = h(ν − νn)

(heating of the gas)• Inverse process is Radiative recombination: an electron is captured

by an ion into a bound state n, with emission of a photon• Note: detailed balance applied to photoionization/recombination

lead to relations between the cross-sections of both processes(Milne relations).


1.Electronic spectroscopy Spectra of atoms: Examples

Spectra of atoms: Examples

WHAM sky survey of ionized gas, Haffner et al ApJSS 2003

Hα (n = 3→ 2) at 6562.8 A



H spectra towards a X-ray binary (Soria et al 2000)

Lyman forest and recombination lines towards QSOs



Ionization and recombination of Hatoms

• Below the Balmer discontinuity(λ < 365A), continuum spectra:stellar photons partiallyabsorbed by bound-freetransitions

• Above: recombination linestowards n = 2

• Idem for the Paschendiscontinuity

• Continuum/Line is sensitive toTe

Liu et al 1993, 1995



Fine-structure lines

Time variation of the fine structure constant

• In super string theory, fundamental constants are predicted to varyslowly over cosmological timescales. Fine structure splittingdepends only on α: ∆En/En = α2Z2/(nl(l + 1)). Idea: observefine structure lines at different redshifts:∆αα (z) = 1/2 [(∆λ/λ)z/(∆λ/λ)0 − 1]

• Results: using many fine structure lines (e.g. alkali ions): only upperlimits for ∆α/α up to z ≈ 3.5 (Uzan, Rev. Mod. Phys. 75 403 2003)



Fine-structure lines

• Genzel et al 1985• Schematic infrared and radio

spectrum of line and continuumemission in the central 2 pc ofSgr A.


2.Infrared spectroscopy

2. Infrared spectroscopyExamples


2.Infrared spectroscopy

Vibration-Rotation molecular spectra• Dipole electric vibrations transitions (∆v = ±1) are usually

accompanied by a change in J with selection rule ∆J = 0,±1(depending on electronic state)

• Example: ∆v = −1, J ′′ → J ′ = J ′′ ± 1• ∆J = 1: ∆E = ~ωv + 2B(J ′′ + 1), R-branch, R(J ′′ = 0, 1, . . .)• ∆J = −1: ∆E = ~ωv + 2B(J ′′ − 1), P-branch, P (J ′′ = 1, 2, . . .)• ∆J = 0: Q-branch (B(v′) 6= B(v′′))


2.Infrared spectroscopy Examples


2.Infrared spectroscopy Examples

ISO-SWS spectrum towards Massive–star-forming regions (vanDishoeck et al 1998)

Vibration−rotation spectrum


3.Microwave spectroscopy

3. Microwave spectroscopyPure rotational spectra of molecules


3.Microwave spectroscopy Pure rotational spectra of molecules

Molecular spectra: Pure Rotational

Dipole electric transitions

Selection rules:1 Dipole moment non-zero2 ∆J = −1: emission3 ∆J = +1: absorption

• Total angular momentum ~J

• No electric-dipole rotationaltransitions in homonuclearmolecules (weak spectra dueto higher order radiation)

J ′ → J = J ′ − 1 : ∆EJ = B[J ′(J ′ + 1)− J(J + 1)]~2 = 2B(J + 1)~2

For quadrupole electric transitions (H2): ∆J = ±2



Spectral surveys in the sub-mm

Herschel/HIFI HEXOS program (Bergin et al 2010)Pierre Hily-Blant (Master2) The ISM 2012-2013 52 / 229


Hyperfine structures

Hyperfine structures of ND, NH, and NH2 in a protostar’s envelope (Bacmann et al 2010, Hily-Blant et al 2010)



The Milky Way seen in the rotational transition 12CO(J = 1→ 0)

+30°

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Galactic Longitude

Gal

acti

c L

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180° 160° 140° 120° 100° 80° 60° 40° 20° 0° 340° 320° 300° 280° 260° 240° 220° 200° 180°170° 150° 130° 110° 90° 70° 50° 30° 10° 350° 330° 310° 290° 270° 250° 230° 210° 190°

Beam

S235

Per OB2

Polaris Flare

Cam CepheusFlare

W3

Gr e a t R i f t

NGC7538Cas A Cyg

OB7 Cyg XW51 W44

AquilaRift

R CrA

Ophiuchus

Lupus

GalacticCenter G317−4

Chamaeleon

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CarinaNebula

Vela

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Mon R2

Maddalena’sCloud

CMaOB1

MonOB1

Rosette

GemOB1

S147S147CTA-1

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Tau-Per-Aur Complex

AquilaSouth

Pegasus

Lacerta GumNebula S. Ori

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Galactic Longitude

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Orion Complex

Ursa Major

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log Tmb dv (K km s−1)∫

FIG. 2.–Velocity-integrated CO map of the Milky Way. The angular resolution is 9´ over mostof the map, including the entire Galactic plane, but is lower (15´ or 30´) in some regions outof the plane (see Fig. 1 & Table 1). The sensitivity varies somewhat from region to region,since each component survey was integrated individually using moment masking or clippingin order to display all statistically significant emission but little noise (see §2.2). A dotted linemarks the sampling boundaries, given in more detail in Fig. 1.

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