› astro › astrokemia › AK13_L3... Astrochimistry – Spring 2013III.3 The Eley-Rideal mechanism 23 Binding and barrier energies can depend on the position of the chemisorption

Astrochimistry – Spring 2013 Lecture 3:

H2 Formation

Julien Montillaud1st February 2013

2

OutlineI. The most abundant molecule in the Universe (6 p.)

I.1 Relative abundancesI.2 Historical milestonesI.3 Observational evidenceI.4 Destruction of H2I.5 Chemistry prefers ménages-à-trois

II. The inefficient gas-phase formation of H2 (4 p.)

II.1 ProcessesII.2 Astrophysical applications

III. Grain-catalyzed formation of H2 (11 p.)

III.1 A new partner: dust grainsIII.2 The Langmuir-Hinshelwood mechanismIII.3 The Eley-Rideal mechanismIII.4 Other mechanisms

IV. From processes to interstellar H2 formation rate (10 p.)

IV.1 Relative contribution to H2 formation rate

IV.2 Implementing H2 formation in astrophysical models

IV.3 Astrochemical application

V. Summary

VI. Some bibliographic references

3

I. The most abundant molecule in the UniverseI.1 Relative abundance

The “astronomer's periodic table”McCall, Phil. Trans. R. Soc. A (2006)

● H = most abundant chemical element( 10 x He ; 10000 x C, N, O ; …)

● H = radical ⇒ a very reactive species

http://en.wikipedia.org/wiki/File:Periodic_Table_2.svg

Ene

rgy

1s

2s2p

x2p

y2p

z

H: incomplete shell ⇒ radical

4

I. The most abundant molecule in the UniverseI.2 Historical milestones

Gould & Salpeter (1963): first model of H2 formation on dust grains (dirty ice, no defects)

H2 never detected yet still a theoretical hypothesis ! ⇒

Hollenbach & Salpeter (1971): first model of H2 formation on dust grains including defects

Jura (1974): determination of the H2 formation rate from UV observations (Copernicus)

Measurement of H2 density from UV absorption lines

Measurement of UV radiation field from UV continuum ⇒ Derivation of H2 destruction rate

Assuming destruction rate = formation rate ⇒ Measure of the H

2 formation rate: 3e-17 n

H n(H) cm3s-1

Launch of ISO (1995): detection of H2 in the IR

Le Bourlot et al. (1995): Rationalization of H2 formation from grain characteristics

1990' – 2000': multiplication of theoretical and experimental studies of catalyzed formation of H2

+ observational evidence for H2 formation in unexpected conditions

(e.g. Habart et al. 2004, 2005, 2011)

Le Bourlot et al. (2012): detailed modeling of H2 formation in a realistic astrophysical model

5

I. The most abundant molecule in the UniverseI.3 Observational evidence: electronic and rotational lines

High-resolution UV spectroscopy using HST

Meyer et al. 2001

http://www.stolaf.edu/depts/chemistry/imt/js/h2energy/h2.htm

Mid-IR spectroscopy using Spitzer

Guillard et al. 2010

J=0

J=1

J=2

J=3

J=4

6

I. The most abundant molecule in the UniverseI.3 Observational evidence: electronic and rotational lines

H2 can be formed in very various conditions:

Hot/coldDense/not densedEven in some high-UV or X-ray radiation fieldsRight after shock waves

⇒ many different formation paths exist

7

I. The most abundant molecule in the UniverseI.4 Destruction of H

2

Destruction rate:

diss = <p

diss>

photoext ~ 4 x 10-11 s-1

diss : photodissociation rate

<pdiss

> : dissociation probability averaged over

the photoexcitation channels

photoext : rate of photoexcitation by UV photons

: scaling factor of the interstellar radiation field (IRSF)

Hollenbach & Tielens 1999

In steady-state:

diss n(H

2) = R

gr n

H n(H)

with nH = 100 cm-3 and =1:

n(H2)/n(H) ~ 10-4

8

I. The most abundant molecule in the UniverseI.5 Chemistry prefers ménages-à-trois

Enough energy to cross the activation barrier from reactants to products<=>

Enough energy to cross the activation barrier from products to reactants

Survival of products if energy is released via a third “body”:- loss of a particle (atom, small molecule, electron)- emission of photons- dilution of the energy in a very large system (=emission of phonons)- 3-body collisions (efficient only at high density)

It has to happen during the collision process ~1e-13 s

9

II. The inefficient gas-phase formation of H2

I. The most abundant molecule in the Universe


II.1 ProcessesII.2 Astrophysical applications

III. Grain-catalyzed formation of H2

IV. From processes to interstellar H2 formation rate

V. Summary

10

II. The inefficient gas-phase formation of H2II.1 Processes

H + H → H2 Collision timescale ~ 1 vibration period ~ 1e-13 s

Energy to be released ~ 4.5 eV (binding energy)

● From electronic ground state ?

(Ro-)vibrational emission: nhu in up to 4.5 eV for vibrationally or rotationaly excited H2

But Einstein coefficient: A << 1e-5 s-1 ( << 1e13 s-1 )

“only one in 1e5 collisions would result in the formation Of molecular hydrogen” (Duley & Williams 1984)

● From electronicaly excited states ?

A increases when n increases, but still very small :

Latter & Black 1991

11

II. The inefficient gas-phase formation of H2II.1 Processes

Other processes

H + H* → H2

+ + e- (Rawlings et al. 1993)

H2

+ + e- → H2

More efficient than H + H → H2 for high n(e-) and low

H + e- → H- + H- + H → H

2 + e-

The most efficient gas-phase process (Glover 2003) for high n(e-) and low

H + H+ → H2

+ + H

2

+ + H → H2 + H+

The second most efficient gas-phase process (Glover 2003)

H + H + H → H2 + H (Palla et al. 1983)

Requires nH > 1e8 cm-3

12

II. The inefficient gas-phase formation of H2II.2 Astrophysical application

From chemical processes to astrophysical modeling: chemical kinetics

H + e- → H- + k1

H- + H → H2 + e- k

2

H + H+ → H2

+ + k3

H2

+ + H → H2 + H+ k

4

H- + H+ → 2H k5

H- + → H + e- k6

⇒

Glover 2003

13

II. The inefficient gas-phase formation of H2II.2 Astrophysical application

Where there is no dust:

Early Universe

Latter & Black 1991

Where dust grains are hot, and gasis hot, dense, and with a large enough ionization fraction:→ X-ray dissociation regions(AGNs, embedded massive protostars, ...)

Novae ejecta

Wikipedia

Centaurus A

Very specific cases! For all the other cases, gas-phase formation is neglegible wrt catalyzed routes.

14





III.1 A new partner: dust grainsIII.2 The Langmuir-Hinshelwood mechanismIII.3 The Eley-Rideal mechanismIII.4 Other mechanisms


V. Summary

15


III.1 A new partner: dust grains

Various compositions: C, Si, Mg, Fe, … (+H, O)+ molecular ices according to environments

⇒ various surface properties

Various sizes

16


III.2 The Langmuir-Hinshelwood mechanism

Distance to surface

Chemisorptionsite

Physisorptionsite

Pot

entia

l ene

rgy

(1) (2) (3) (4) (5)

(1) physisorption of one H-atom

(2) physisorption of one other H-atom on the same grain

(3) traveling of physisorbed H-atom on grain surface

(4) encounter chemical binding of H-atoms

(5) desorption of the new H2 molecule

Physisorption = weak van der Waals interactionChemisorption = strong covalent bound

17

(1) (2) (3) (4) (5)

(1) physisorption of one H-atom

(2) physisorption of one other H-atom on the same grain

Depends on:

- surface nature (silicate, carbonaceous, ice) - structure (amorphous, cristaline, porosity)- presence of defects



18

(3) (4) (5)(3)

(3) traveling of physisorbed H-atom on grain surface

Depends on:


Processes:→ thermal diffusion

(moving over barriers from site to site)

→ quantum tunneling(moving through barriers from site to site)



19

(3) (4) (5)(4)

(4) encounter chemical binding of H-atoms


Depends on:


A related issue: distribution of the energy released→ translational kinetic energy→ grain vibrational energy→ H

2 vibrational/rotational energy

Consequences:→ nebula energetics (gas temperature)→ excited-H2 spectroscopic diagnostics→ grain temperature (possible feedback on H2 formation rate)→ chemistry involving excited H2 (e.g. formation of CH+)

(5)



20

(1) (2) (3) (4) (5)

Behaviour with grain temperature:

→ too low T: H-atoms do not move efficiently→ too high T: H-atoms evaporate before encountering an other H-atom

⇒ efficient for T ~ 10 – 50 K



21


III.3 The Eley-Rideal mechanism

(1) (2) (3)

(1) chemisorption of one H-atom

(2) collision between a gas-phase H-atomand the chemisorbed H-atom


Distance to surface

Chemisorptionsite

Physisorptionsite

Pot

entia

l ene

rgy

Physisorption = weak van der Waals interactionChemisorption = strong covalent bound

22

(1) (2) (3)

Depends on:


no traveling H-atom ⇒ less efficient than LHStrong bounds ⇒ robust with temperature



23

Binding and barrier energies can depend on the position of the chemisorption site:

Rauls & Hornekaer 2008



24

Binding and barrier energies also depend on history of the grain:

How many H-atoms are already bound to the grain ?

Rauls & Hornekaer 2008Rauls & Hornekaer 2008



25


III.4 Other mechanisms

Intermediate mechanisms:

→ physisorbed atoms can tunnel to chemisorption sites→ gas-phase atoms can strike physisorbed atoms→ traveling physisorbed atoms can find chemisorbed atoms

Distance to surface

Chemisorptionsite

Physisorptionsite

Pot

entia

l ene

rgy

26



II. The unefficient gas-phase formation of H2



IV.1 Relative contribution to H2 formation rate



V. Summary

27


IV.1 Relative contributions to H2 formation rate

Cazaux et al. 2005Modelling H

2 formation efficiency

on carbonaceous grains

Assuming:→ Tdust = constant→ Tgas = Tdust + 500 K→ Some particular values for binding and barrier energies

LH: dominates at low Tdust

ER: significant at high Tdust

LH versus ER

28


IV.1 Relative contributions to H2 formation rate

Grain size and the effect of temperature fluctuations

Surface(Small grains) > Surface(Big grains) H⇒2 formation dominated by small grains

BUT: → small grain

⇒ small thermal capacity ⇒ large thermal fluctuations ⇒ stochastic behaviour

→ small grain ⇒ small surface per grain ⇒ higher risk that means

are meaningless (e.g. 0.3 H-atom per grain)

29



Rate equations (example of LH implementation)

= surface density of physisorbed H-atomsf = flux of impinging H-atomsW = desorption rate coefficienta = hopping rate ~ H

2 formation rate coefficient

H(g)

→ H: (f)

H: → H(g)

(W)

H: + H: → H2(g)

(a)

The H2 formation rate per unit surface of grain is then given by a2

BUT: small grains ⇒ small surface ⇒ “surface density” is meaningless

30



Master equations (example of LH implementation)

Dealing with probabilities:n = number of Hatoms physisorbed on one grainP(n) = probability of having n Hatoms physisorbed on one grainS = maximum number of physisorption sites closure formula⇒dP(n)/dt = time derivative of P(n)F = flux of impinging H-atomsW = desorption rate coefficientA = hopping rate ~ H

2 formation rate coefficient

H(g)

→ H: (F)

H: → H(g)

(W)

H: + H: → H2(g)

(A)

31



Master equations (example of LH implementation)

Mean number of H-atoms per grain:

H2 formation rate for one grain:

H2 formation efficiency:

Relation to rate equation:

32



Rate equations versus Master equations

Biham & Lipshtat 2002

Master equations are more accurate but slower to solve (bigger system of equations)

33



Moment equations

H2 formation rate for one grain: = A (<n2> - <n>)

Depends only on the 2 first moments of n !

The system must be closed. Possible for a limited number Nmax of physisorption sites:If Nmax = 2:

… and can be solved much faster than master equations.For Nmax reasonnable, the system must be truncated ⇒ approximate solution.

( “NH” is “n” )

Open system !

34



ComparisonLipshtat & Biham 2003

35



Color = CO J=6-5Black = CH+ J=3-2White contours=H2* v=1-0 S(1)

Nagy et al. 2013

36



Detailled modelling of H2 formation

and excitation (Meudon PDR code)

⇒

good understanding of CH+ formationand excitation

⇒

CH+ is a good tracer of the external, warm layers of molecular cloudsNagy et al. 2013

37

V. Summary

H2 formation still not fully understood

Widely dominated by grain-catalyzed reactions

Many theoretical and experimental studies provide molecular data, but still not enough

Understanding is limited by:

- limited knowledge of dust grains- the huge number of parameters (e.g. grain size, composition, structure, fluffyness, ...)- the observational difficulties

The gas-grain chemistry requieres special care for modelling

In the future, progresses should be achieved from joint studies of H2 formation/excitation

and chemical evolution of other species (molecules, ions, grains) + improvements in modelling the ISM (energetics, morphology, radiative transfer, ...)

38

VI. Some bibliographic references

General:- McCall, Phil. Trans. R. Soc. A, 364 : 2953-2963 (2006)- Hollenbach & Tielens, Reviews of Modern Physics, 71 : 173 (1999)- Gould & Salpeter, ApJ, 138 : 393 (1963)- Hollenbach & Salpeter, ApJ, 163 : 155 (1971)- Jura, ApJ, 191 : 375-379 (1974)- Maloney et al., ApJ, 466 : 561–584 (1996)

Astrophysical aspects:- Glover, ApJ, 584 : 331-338 (2003)- Le Bourlot et al., A&A, 302 : 870 (1995)- Habart et al., A&A, 414 : 531 (2004)- Nagy et al. A&A in press (2013)

Theoretical chemistry aspects- Parneix & Bréchignac, A&A, 334 : 363–375 (1998)- Rauls & Hornekaer, ApJ, 679 : 531–536 (2008)- Latter & Black, ApJ, 372 : 161-166 (1991)

Experimental chemistry aspects- Pirronello et al., ApJ, 475 : L69–L72 (1997)- Islam, PHD thesis, UCL (2009)

Modelling aspects- Le Bourlot et al., A&A 541 : A76 (2012)- Biham & Lipshtat, arXiv:cond-mat/0208550v2 (2002)- Lipshtat & Biham, A&A, 400 : 585–593 (2003)- Cazaux et al., Journal of Physics: Conference Series, Volume 6, Issue 1, pp. 155-160 (2005)

Documents

› astro › astrokemia › AK13_L3... Astrochimistry – Spring 2013III.3 The Eley-Rideal mechanism 23 Binding and barrier energies can depend on the position of the chemisorption