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

Destruction processes 4. Dissociative recombination X + + e → X + h ν radiative ⇒ slow atomic ions: XY + + e → XY + h ν radiative ⇒ slow molecular ions: dissociative ⇒ very → X + Y rapid at low T XY + Need curve crossing XY * XY + between XZ + and energy repulsive XY X+Y potential for reaction X+Y to proceed fast. Occurs for most molecular ions. slow rapid

Destruction processes • major uncertainties in models: products Williams et al. ‘96 Vejby_C et al. ‘97 + + e → XH n-1 + + H XH n + + H 2 branching → XH n-2 ratios → ... Example: H 3 O + + e 33% 5% → H 2 O + H → OH + H 2 18% 36% → OH + H + H 48% 29% → OH + H 2 + H 1% 30% 3-body products

Destruction processes 5. Collision induced dissociation If T is high enough (T> 5000K), H 2 is destroyed by collisions H + H 2 → H + H + H He + H 2 → He + H + H H 2 + H 2 → H 2 + 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/R 4 ⇒ rapid at low T if reaction is exothermic X + + YZ collision energy in ISM ~ 0.01 eV ⇒ calculation of collision cross XY + + Z section via potential surface calculation requires high precision XYZ +

Rearrangement processes + impact parameter b - +

Rearrangement processes + critical impact parameter b c - +

Rearrangement processes + + critical impact parameter b c - +

Rearrangement processes V L V(R) μ 2 2 b v = V centrifugal potential L 2 2 R α 2 V eff e = − ion induced dipole V R el 4 2 R α μ 2 2 2 v e b = − + V el V eff 4 2 2 R 2R µ: reduced mass α : polarizability (~10 -24 cm 3 ) L= m b v : angular momentum in centrifugal potential

Rearrangement processes V L α μ 2 2 2 V(R) e b v = − + V eff 4 2 2 R 2R μ α 2 2 2 2 ( b v ) 2 e V eff = 2 max : at V R α μ eff M R 2 2 2 R M 2 e b v centrifugal barrier can only be surmounted if: barrier V el μ 2 2 2 1 ( b v ) μ 2 v > α 2 2 2 e 1 ⎛ ⎞ α 2 4 4 e critical impact parameter = ⎜ ⎟ b μ c 2 ⎝ ⎠ v

Rearrangement processes V L V(R) 1 ⎛ ⎞ α 2 4 4 e = ⎜ critical impact parameter: ⎟ b μ c 2 ⎝ ⎠ v V eff R R M centrifugal σ = π 2 cross section for reaction: b barrier c V el 1 ⎛ ⎞ α 2 2 e collision frequency: =< σ = π ⎜ ⎟ k v> 2 μ ⎝ ⎠ ⇒ k ~ 10 -9 cm 3 s -1 , independent of T!

Rearrangement processes V L V(R) possible processes: X + + YZ → XY + + Z exchange → X + YZ + charge transfer V eff R R M many experiments performed at room T, centrifugal some at low T. Most reactions proceed at barrier V el 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 + + CS → HCS + + H 2 ) H 3

Rearrangement processes • long range attraction: weak van der Waals interaction ~1/R 6 (Woon & Herbst `97) example: CN + C 2 H 2 → H + HC 3 N μ α 2 C µ 1 : dipole moment of CN = − − 6 1 2 ( ) V R α 2 : polarizability of C 2 H 2 el 6 6 R R α 1 : polarizability of CN I : ionization potential 3 I I = I α α dispersion coefficient 1 2 C + 6 1 2 2 I 1 2

Rearrangement processes α α • simpler: = − 1 2 V ( ) R I el 6 R 13 ⎛ ⎞ α α 1 − =< σ >≈ π ⋅ < >≈ × 11 3 -1 1 2 ⎜ ⎟ v 13.6 v 3 4 10 cm s k I μ ⎝ ⎠ ⇒ k n-n << k i-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 = R 2 π = 3 × 10 -16 cm 2 , v ≈ 10 4 cm/s k = σ v ≈ 3 × 10 -12 cm 3 s -1 Factor ≈ 1000 ≈ 10 -9 k ion-neutral cm 3 s -1 Factor ≈ 10 k neutral-neutral ≈ 4 × 10 -11 cm 3 s -1

Rearrangement processes Comparison of effective cross section and radii (assumption: v=10 4 cm s -1 ) σ [cm 2 ] r [cm] k σ = 3 × 10 -16 hard sphere 10 -8 v σ 2 × 10 -7 ion-neutral 10 -13 = r π 4 × 10 -15 4 × 10 -8 neutral-neutral - dipole induction enlarges the effective target radius by a factor of 20 ! - van der Waals induction enlarges r eff by ~ 4

Rearrangement processes • Adiabatic capture approximation (AC) – if collision energy < V eff (R) ⇒ react. prob=0 – if collision energy > V eff (R) ⇒ react. prob=1 (ignores angular dependencies, short range effects, quantum effects, activation energies) With AC theory, the rate coefficient is: 2 1 − + ∝ → n 2 k T ( ) T as T 0 - n for potentials of form r

Rearrangement processes 2 1 − + ∝ → - n n 2 k T ( ) T as T 0, for potentials of form r interaction low T dependence charge-induced dipole r -4 T 0 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 T 0 dispersion r -6 T 1/6 neutral-neutral reactions typically factor 5 smaller than ion- molecule reactions at low T

Time scales [cm 3 s -1 ] rate coefficient : k [cm -3 s -1 ] rate : k n A n B t ≅ (k n) -1 [s -1 ] reaction time :

Time scales = − rad.association C+H → CH + h ν 17 3 -1 k 10 cm s 1 → = 17 t 10 s n = × � 13 5 t 10 s 3 10 yr = 4 n 10 photodiss. CO + h ν → C + O − = × 10 -1 k 2 10 s → = × 9 t 5 10 s = t 160 yr = 4 n 10

Time scales ⎛ ⎞ 300 K − diss. HCO + + e - → CO + H = × 7 3 -1 ⎜ ⎟ k 1.1 10 cm s ⎝ ⎠ T recomb. − = × 6 3 -1 k 2.2 10 cm s = T 15 K 1 → = × 5 4.6 10 s t n e ≈ t 5 d = n 1 e − = × 9 3 -1 CO + h ν → C + O k 2.08 10 cm s ion-molecule reaction 1 = × 8 t 4.8 10 s [ ] H 2 = × 4 -1 4.8 10 s t [ ] = 4 H 10 2 ≈ 0.5 d

Time scales + + H → H 2 + H + charge transf. H 2 − = × 10 3 -1 k 6.4 10 cm s reaction 1 = × 9 t 1.6 10 s n = × ≈ 5 t 1.6 10 2 d [ ] = 4 H 10 neutral-neutral H + HCO → CO + H 2 − = × 10 3 -1 k 2 10 cm s reaction 1 = × 9 t 5 10 s n = × 5 -1 t 5 10 s = 4 n 10 ≈ 6 d

Time scales CR ionization H 2 + CR → H 2 + − = 17 -1 k 10 s 1 = 17 t 10 s n = ≈ × 13 5 t 10 s 3.2 10 yr [ ] = 4 H 10 dust-surface H + H:g → H 2 + g − = 17 3 -1 k 10 cm s reaction 1 = × 9 t 2.7 10 yr n = × 5 t 2.7 10 yr = 4 n 10

Time scales Example: ratio H 2 /H d H ! [ ] [ ] [ ] = − + = k H k H 0 2 diss 2 form dt [ ] k H t 634 yr = = = ⋅ = × − 2 form 7 -3 diss n 2.4 10 n cm [ ] × 9 H k t 2.7 10 yr diss form ⇒ all hydrogen is atomar, unless FUV is attenuated diffuse clouds: [H2]/[H] ≈ 1 but: H2 is detected dense clouds: [H2]/[H]>>1 ⇒ - dust extinction - self shielding

Degree of Ionization • electron production: + + e ~ ξ CR H 2 + CR → H 2 H 2 + CR → H + H + + e ~ 0.1 ξ CR 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/n e yr cm -3 )

Degree of Ionization d 1 ! [ ] [ ] [ ] = − + ξ = mol.ions mol.ions He 0 dt t diss rec . . 1 1 = − + ξ = 2 n n 0 e -3 0.3 yr cm 10 − ≈ 4 -3 n 10 cm n e 1 ≈ × 3 3 10 yr t diss rec . n exchange reactions t ≈ 10 -3 ...10 -2 yr 1/n compared to: t ≈ 10 4 yr 1/n rad. associations ⇒ many other reactions occur before 1 dissoc. recombination destroys ions/electrons

Degree of Ionization ⇒ Ion – Molecule – Scheme: + + H 2 → H 3 + + H example: H 2 + + e → H 2 + H or H + H + H H 3 + + AB → ABH + + H 2 H 3 ...

Degree of Ionization ⇒ Ion – Molecule – Scheme: H 2 + H 2 → H 3 + H + + C + + H 2 → CH + + H H 3 + + C → CH + + H 2 CH + + H 2 + + H → CH 2 + + H 2 → CH 3 + + H CH 2 + + H 2 → CH 5 + + h ν CH 3 + + e → CH 4 + H CH 5 → CH 3 + H 2 → CH 2 + H 2 +H → CH + 2H 2