The physics of interstellar photon-dominated regions (PDRs) - - PowerPoint PPT Presentation

The physics of interstellar photon-dominated regions (PDRs)

Chemistry I+II (based on lecture notes by E. van Dishoeck, Leiden) SS 2007

Basic Molecular Processes

Formation processes radiative association: X + Y → XY + hν grain surface reaction: X + Y:g → XY:g → XY + g Destruction processes photodissociation: XY + hν → X + Y dissociative recombination: XY+ + e- → X + Y Rearrangement processes ion-molecule reaction: X+ + YZ → XY+ + Z charge transfer reaction: X+ + YZ → X + YZ+ neutral-neutral reactions: X + YZ → X + YZ

Destruction processes

• 4. Dissociative recombination

atomic ions: X+ + e → X + hν radiative ⇒ slow molecular ions: XY+ + e → XY + hν radiative ⇒ slow → X + Y dissociative ⇒ very rapid at low T

energy XY+ XY* X+Y slow XY+ X+Y rapid Need curve crossing between XZ+ and repulsive XY potential for reaction to proceed fast. Occurs for most molecular ions.

Destruction processes

• major uncertainties in models: products

XHn

+ + e → XHn-1 + + H

→ XHn-2

+ + H2

→ ... Example: H3O+ + e → H2O + H → OH + H2 → OH + H + H → OH + H2 + H

branching ratios

33% 5% 18% 36% 48% 29% 1% 30%

Vejby_C et al. ‘97 Williams et al. ‘96 3-body products

Destruction processes

• 5. Collision induced dissociation

If T is high enough (T> 5000K), H2 is destroyed by collisions H + H2 → H + H + H He + H2 → He + H + H H2 + H2 → H2 + H + H H2 has no permanent dipole moment ⇒ significant population in high ν levels at high T ⇒ large dissociation rate CO has small dipole moment ⇒ radiative stabiliyation rapid ⇒ not much pop. in high ν ⇒ small dissociation rate

Rearrangement processes

• 7. Ion-molecule reactions

long-range attraction: ion-(induced) dipole ~ 1/R4 ⇒rapid at low T if reaction is exothermic

X+ + YZ XY+ + Z XYZ+ collision energy in ISM ~ 0.01 eV ⇒ calculation of collision cross section via potential surface calculation requires high precision

Rearrangement processes

+

• +

impact parameter b

Rearrangement processes

+

• +

critical impact parameter bc

Rearrangement processes

• +

critical impact parameter bc + +

Rearrangement processes

R V(R) VL centrifugal potential

2 2 2

v 2

L

b V R μ =

Vel Veff ion induced dipole

2 4

2

el

e V R α = −

2 2 2 4 2

v 2 2R

eff

e b V R α μ = − +

µ: reduced mass α: polarizability (~10-24 cm3) L= m b v : angular momentum in centrifugal potential

Rearrangement processes

R V(R) VL Vel Veff

2 2 2 4 2

v 2 2R

eff

e b V R α μ = − +

2 2 2 2 2 2 2 2

( v ) 2 max : at 2 v

eff M

b e V R e b μ α α μ =

RM centrifugal barrier

barrier can only be surmounted if:

2 2 2 2 2

1 ( v ) v > 2 2 b e μ μ α

1 2 4 2

4 v

c

e b α μ ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ critical impact parameter

Rearrangement processes

R V(R) VL Vel Veff RM centrifugal barrier

1 2 4 2

4 v

c

e b α μ ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠ critical impact parameter: cross section for reaction:

2 c

b σ π = collision frequency: ⇒ k ~ 10-9cm3s-1, independent of T!

1 2 2

v> 2 e k α σ π μ ⎛ ⎞ =< = ⎜ ⎟ ⎝ ⎠

Rearrangement processes

R V(R) VL Vel Veff RM centrifugal barrier

possible processes: X+ + YZ → XY+ + Z exchange → X + YZ+ charge transfer many experiments performed at room T, some at low T. Most reactions proceed at Langevin rate, but some exceptions known! Rate coefficients for ion-polar molecule reactions may be factors of 10-100 larger than Langevin values at low T, because V(R)~R-2 (eg. C+ + OH → CO+ + H H3

+ + CS → HCS+ + H2)

Rearrangement processes

• long range attraction: weak van der Waals

interaction ~1/R6 (Woon & Herbst `97) example: CN + C2H2→H + HC3N

2 6 1 2 6 6

( )

el

C V R R R μ α = − −

µ1: dipole moment of CN α2: polarizability of C2H2 α1: polarizability of CN I : ionization potential

1 2 6 1 2 1 2

3 2 I I C I I α α = + dispersion coefficient

Rearrangement processes

• simpler:

1 2 6

( )

el

V R I R α α = −

13 1 11 3 -1 1 2 3

v 13.6 v 4 10 cm s k I α α σ π μ

−

⎛ ⎞ =< >≈ ⋅ < >≈ × ⎜ ⎟ ⎝ ⎠ ⇒ kn-n << ki-n ⇒neutral-neutral reactions unimportant (exception: reactions with radicals)

Rearrangement processes

• comparison:

simple hard sphere collision without electromagnetic interaction

Rearrangement processes

• comparison:

simple hard sphere collision without electromagnetic interaction (Bohr‘s radius: r = 5.3×10-11 m = 5.3×10-9 cm) R≈10-10 m=10-8 cm ⇒ σ = R2π = 3×10-16 cm2, v ≈104 cm/s k = σv ≈ 3×10-12 cm3s-1 kion-neutral ≈ 10-9 cm3s-1 kneutral-neutral ≈ 4×10-11 cm3s-1

Factor≈1000 Factor≈10

Rearrangement processes

Comparison of effective cross section and radii (assumption: v=104 cm s-1) σ [cm2] r [cm] hard sphere 3×10-16 10-8 ion-neutral 10-13 2×10-7 neutral-neutral 4×10-15 4×10-8

v k r σ σ π = =

• dipole induction enlarges the effective target

radius by a factor of 20 !

• van der Waals induction enlarges reff by ~ 4

Rearrangement processes

• Adiabatic capture approximation (AC)

– if collision energy < Veff(R) ⇒ react. prob=0 – if collision energy > Veff(R) ⇒ react. prob=1 (ignores angular dependencies, short range effects, quantum effects, activation energies) With AC theory, the rate coefficient is:

2 1 2

• ( )

as for potentials of form

n n

k T T T r

− +

∝ →

Rearrangement processes

2 1

• 2

( ) as 0, for potentials of form

n n

k T T T r

− +

∝ → interaction low T dependence charge-induced dipole r-4 T0 charge-dipole r-2 T-1/2 charge-quadrupole r-3 T-1/6 dipole-dipole r-3 T-1/6 dipole-quadrupole r-4 T0 dispersion r-6 T1/6 neutral-neutral reactions typically factor 5 smaller than ion- molecule reactions at low T

Time scales

rate coefficient : k [cm3 s-1] rate : k nA nB [cm-3 s-1] reaction time : t ≅ (k n)-1 [s-1]

Time scales

rad.association C+H → CH + hν

• photodiss. CO + hν → C + O

4

17 3 -1 17 13 5 10

10 cm s 1 10 s 10 s 3 10 yr

n

k t n t

− =

= → = = ×

• 4

10

• 1

9 10

2 10 s 5 10 s 160 yr

n

k t t

− =

= × → = × =

Time scales

• diss. HCO+ + e- → CO + H

recomb. ion-molecule CO + hν → C + O reaction

7 3 -1 6 3 -1 15 5 1

300 K 1.1 10 cm s T 2.2 10 cm s 1 4.6 10 s 5 d

e

T K e n

k k t n t

− − = =

⎛ ⎞ = × ⎜ ⎟ ⎝ ⎠ = × → = × ≈

[ ]

[ ]

4 2

9 3 -1 8 2 4

• 1

H 10

2.08 10 cm s 1 4.8 10 s H 4.8 10 s 0.5 d k t t

− =

= × = × = × ≈

Time scales

charge transf. H2

+ + H → H2 + H+

reaction neutral-neutral H + HCO → CO + H2 reaction

[ ]

4

10 3 -1 9 5 10

6.4 10 cm s 1 1.6 10 s 1.6 10 2 d

H

k t n t

− =

= × = × = × ≈

4

10 3 -1 9 5

• 1

n 10

2 10 cm s 1 5 10 s n 5 10 s 6 d k t t

− =

= × = × = × ≈

Time scales

CR ionization H2 + CR → H2

+

dust-surface H + H:g → H2 + g reaction

[ ]

4

17

• 1

17 13 5 10

10 s 1 10 s 10 s 3.2 10 yr

H

k t n t

− =

= = = ≈ ×

4

17 3 -1 9 5 n 10

10 cm s 1 2.7 10 yr n 2.7 10 yr k t t

− =

= = × = ×

Time scales

Example: ratio H2/H

[ ] [ ] [ ] [ ] [ ]

! 2 2 2 7

• 3

9

634 yr 2.4 10 cm 2.7 10 yr

diss form form diss diss form

d H k H k H dt k H t n n H k t

−

= − + = = = = ⋅ = × × ⇒ all hydrogen is atomar, unless FUV is attenuated but: H2 is detected diffuse clouds: [H2]/[H]≈1 dense clouds: [H2]/[H]>>1 ⇒

• dust extinction
• self shielding

Degree of Ionization

• electron production:

H2 + CR → H2

+ + e

~ ξCR H2 + CR → H + H+ + e ~ 0.1 ξCR He + CR → He+ + e ~ ξ

radiative recombination of atomic ions too slow ⇒ charge exchange from H+,He+ → moelcular ions (10-100 1/n yr cm-3) followed by dissociative recombination of molecular ions (0.3 1/ne yr cm-3)

Degree of Ionization

[ ] [ ] [ ]

! . . 2 e

• 3

4

• 3

3 .

1 mol.ions mol.ions He 1 1 n 0.3 yr cm 10 10 cm 1 3 10 yr

diss rec e diss rec

d dt t n n n t n ξ ξ

−

= − + = = − + = ≈ ≈ × compared to: exchange reactions t≈10-3...10-2 yr 1/n

• rad. associations

t≈104 yr 1/n ⇒many other reactions occur before 1 dissoc. recombination destroys ions/electrons

Degree of Ionization

⇒ Ion – Molecule – Scheme: example: H2

+ + H2 → H3 + + H

H3

+ + e → H2 + H or H + H + H

H3

+ + AB → ABH+ + H2

...

Degree of Ionization

⇒ Ion – Molecule – Scheme: H2

+

+ H2 → H3

+

+ H H3

+

+ C → CH+ + H2 CH+ + H2 → CH2

+ + H

CH2

+ + H2 → CH3 + + H

CH3

+ + H2 → CH5 + + hν

CH5

+ + e → CH4 + H

→ CH3 + H2 → CH2 + H2 +H → CH + 2H2

C+ + H2 → CH+ + H

C+ CO C CH+ CH2

+

CH3

+

CH2 CH CO+

HCO+

CH4

+

CH5

+

CH3 CH4

H H H2,H2

*

H H H2 H2 H2 H2 e , C O e e ν,H+ OH H3

+

e O2 He+ ν OH ν H e, S e ν ν ν,C+ ν e e e e e H3

+

H2,H2

*

ν ν H ν ν H3

+

O H2 O ν, νCR O O O O O

The carbon roadmap

• Like any roadmap, this

network describes how to get from A to B.

• Like on any roadmap,

some paths are quick some are slow.

• Unlike any normal

roadmap some slow paths may become very quick under certain conditions

C+ CO C CH+ CH2

+

CH3

+

CH2 CH CO+

HCO+

CH4

+

CH5

+

CH3 CH4

H H H2,H2

*

H H H2 H2 H2 H2 e , C O e e ν,H+ OH H3

+

e O2 He+ ν OH ν H e, S e ν ν ν,C+ ν e e e e e H3

+

H2,H2

*

ν ν H ν ν H3

+

O H2 O ν, νCR O O O O O

Example: Diffuse Cloud starting point: C+ collision with H2: C+ + H2 → CH+ + H instead: C+ + H2 → CH2+ + ν CH2+ + H2 → CH3+ + H then: CHn+ + e → CHn-1 + H and: CHn + O → CO +n H

C+

ΔE=4600K H H2,H2

*

CH+

H2 k ≈ 10-15 cm3s-1 k ≈ 10-9 cm3s-1

CH3

+

H2 e e

CH2 CH CH2

+

k ≈ 10-7 cm3s-1 e O O

CO

k ≈ 10-10 cm3s-1

CH5

+

H2 very slow

C+ CO C CH+ CH2

+

CH3

+

CH2 CH CO+

HCO+

CH4

+

CH5

+

CH3 CH4

H H H2,H2

*

H H H2 H2 H2 H2 e , C O e e ν,H+ OH H3

+

e O2 He+ ν OH ν H e, S e ν ν ν,C+ ν e e e e e H3

+

H2,H2

*

ν ν H ν ν H3

+

O H2 O ν, νCR O O O O O

Example: PDR high FUV intensity heats the gas at the surface → some slow routes become quick C+ + H2 → CH+ + H C+ + H2* → CH+ + H endothermic reactions become possible activation energy barriers become surmountable

H H2,H2

*

CH+ C+

C+ CO C CH+ CH2

+

CH3

+

CH2 CH CO+

HCO+

CH4

+

CH5

+

CH3 CH4

H H H2,H2

*

H H H2 H2 H2 H2 e , C O e e ν,H+ OH H3

+

e O2 He+ ν OH ν H e, S e ν ν ν,C+ ν e e e e e H3

+

H2,H2

*

ν ν H ν ν H3

+

O H2 O ν, νCR O O O O O

Example: Dark Cloud cold and dense: T=10 K, n=104-105 cm-3 carbon locked in CO He + c.r → He+ + e He+ + CO → C+ + O + He FUV fully absorbed some roads vanish some roads become slow e.g. reactions with e- but: CH5+ +CO → CH4 + HCO+

CO C+

He+

CH5

+

CH4

e , C O

C+ CO C CH+ CH2

+

CH3

+

CH2 CH CO+

HCO+

CH4

+

CH5

+

CH3 CH4

H H H2,H2

*

H H H2 H2 H2 H2 e , C O e e ν,H+ OH H3

+

e O2 He+ ν OH ν H e, S e ν ν ν,C+ ν e e e e e H3

+

H2,H2

*

ν ν H ν ν H3

+

O H2 O ν, νCR O O O O O

Looks ‘simple’, but: CH+ a factor 100 too low H2 formation not fully understood …

CH+

H H2,H2

*

H H2 H2 H2 H2 H2,H2

*

H2

Dust

• chemical reactions, that are impossible or unlikely in the

gas phase, might occur on grain surfaces → dust evidence for dust:

– extinction (dark clouds) – reddening of starlight – polarization (aligned, non-spherical grains) – depletion of some elements from the gas – thermal emission at far infrared wavelength – interstellar grains in primitive meteorites and interplanetary dust particles – discrete absorption and emission features

Dust

NGC 891

Dust

Davis Greenstein Effect

Dust

Magnetic field

• rientation in the

Galaxy M51 (Berkhuijsen et

• al. 1975).

Elemental depletions as a function of condensation temperature (the temperature at which 50% of element condenses out in solid form)

Dust

silicate core

Dust

What is this dust composed of?

• amorphous silicates

– observed depletion: most of Si, Mg, Fe, and 20% of O is contained in silicates (e.g. MgFeSiO4, i.e. Olivine) – shape of 9.7µm Si_O stretch and 18 µm O_Si_O bending modes (Gillel &Forrest, ’79), absorption features – optical extinction + polarization ⇒ typical size ~ 0.1 µm, elongated – wavelength dependence of extinction ⇒ size distribution, e.g. n(a)~a-3.5 50Å-2500Å (MRN)

silicate core icy mantle H2O CO

W33A

Dust

• crystalline silicates

– discrete, relatively sharp emission features found in spectra of old (post) AGB stars, PNe, and young stars with circumstellar disks, but not in ISM! (photons and ions tend to destroy lattice order) – features can be identified with Mg-rich cyrstalline silicates, e.g. Mg2SiO4 fosterite MgSiO3 enstatite

Molster et al. 2000

PAHs Molster et al. 2000

Dust

• crystalline silicates

– fraction crystalline/anorphous ranges from few % to ~ 50%, vs. ≤ few % in interstelar clouds

Dust

• carbonaceous material

– 2175Å extinction bump ⇒ ‘graphitic’ material – 3.4µm absorption diffuse ISM ⇒ ‘aliphatic’ C_H (aliphatic means chain-like, i.e. does not contain ring structures) – mass extinction coefficient (opacity) ⇒ ~60%

• f C in solid form

Bless&Savage 1972

graphite silicates

Hydrogenated carbon grains Mennella et al. 2001 Galactic center source IRS 6E vs laboratory

Dust

• PAHs

– Series of discrete emission bands at 3.29 µm, 6.2µm, 7.7µm, 8.6µm, 11.3 µm, ... – best fit by Polycyclic Aromatic Hydrocarbons with 20-100 carbon atoms containing ~1% of carbon abundance.

PAH spectral features in IR spectra

• f

NGC7027 (PN) & Orion Bar (PDR)

Dust

• Ices

– discrete absorption features in dense, cold clouds: 3.1, 6.0 µm H2O ice 4.27, 15.2µm CO2 ice 4.67 µm CO ice 3.53, 9.75 µm CH3OH ice 7.68 µm CH4 ice

W33A

Dust

• Ices

– ices can be distinguished from gas-phase by:

• lack of rotational structure bands
• broadening bands

– shape of ice bands provides constraints on environmental molecules, e.g.:

• H2O-rich ices: “polar” ices
• H2O-poor ices: “apolar” ices

Review: Boogert &Ehrenfreund, astro-ph/0311163

Fraction of photons emitted by a star above 13.6eV increases rapidly with stellar temperature from 10-10 (Sun), to 10-5 (A0V, 104K), 10% (B0V, 3.104K), ~50% (O3V, 5.105K).