Astrochimistry Spring 2013

Transcription

1 Astrochimistry Spring 2013 Lecture 3: H2 Formation NGC HST Julien Montillaud 1st February 2013

2 Outline I. The most abundant molecule in the Universe (6 p.) I.1 Relative abundances I.2 Historical milestones I.3 Observational evidence I.4 Destruction of H2 I.5 Chemistry prefers ménages-à-trois II. The inefficient gas-phase formation of H2 (4 p.) II.1 Processes II.2 Astrophysical applications III. Grain-catalyzed formation of H2 (11 p.) III.1 A new partner: dust grains III.2 The Langmuir-Hinshelwood mechanism III.3 The Eley-Rideal mechanism III.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 2

3 I. The most abundant molecule in the Universe I.1 Relative abundance The astronomer's periodic table McCall, Phil. Trans. R. Soc. A (2006) Energy 2s 1s 2px 2py 2pz H: incomplete shell radical H = most abundant chemical element ( 10 x He ; x C, N, O ; ) H = radical a very reactive species 3

4 I. The most abundant molecule in the Universe I.2 Historical 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 H2 formation rate: 3e-17 nh 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 4

5 I. The most abundant molecule in the Universe I.3 Observational evidence: electronic and rotational lines High-resolution UV spectroscopy using HST Meyer et al Mid-IR spectroscopy using Spitzer J=4 J=3 J=2 J=1 J=0 5 Guillard et al. 2010

6 I. The most abundant molecule in the Universe I.3 Observational evidence: electronic and rotational lines H2 can be formed in very various conditions: Hot/cold Dense/not densed Even in some high-uv or X-ray radiation fields Right after shock waves many different formation paths exist H2 6

7 I. The most abundant molecule in the Universe I.4 Destruction of H2 Destruction rate: diss = <pdiss> photoext ~ 4 x 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) In steady-state: diss n(h2) = Rgr nh n(h) with nh = 100 cm-3 and =1: n(h2)/n(h) ~ 10-4 Hollenbach & Tielens

8 I. The most abundant molecule in the Universe I.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 8

9 II. The inefficient gas-phase formation of H2 I. The most abundant molecule in the Universe II. The inefficient gas-phase formation of H2 II.1 Processes II.2 Astrophysical applications III. Grain-catalyzed formation of H2 IV. From processes to interstellar H2 formation rate V. Summary 9

10 II. The inefficient gas-phase formation of H2 II.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) Latter & Black 1991 From electronicaly excited states? A increases when n increases, but still very small : 10

11 II. The inefficient gas-phase formation of H2 II.1 Processes Other processes H + H* H2+ + eh2+ + e- H2 (Rawlings et al. 1993) More efficient than H + H H2 for high n(e-) and low H + e- H- + H- + H H2 + ethe most efficient gas-phase process (Glover 2003) for high n(e-) and low H + H+ H2+ + H2+ + 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 11

12 II. The inefficient gas-phase formation of H2 II.2 Astrophysical application From chemical processes to astrophysical modeling: chemical kinetics H + e- H- + H- + H H2 + e- k1 k2 H + H+ H2+ + H2+ + H H2 + H+ k3 k4 H- + H+ 2H k5 H- + H + e- k6 Glover

13 II. The inefficient gas-phase formation of H2 II.2 Astrophysical application Where there is no dust: Where dust grains are hot, and gas is hot, dense, and with a large enough ionization fraction: X-ray dissociation regions (AGNs, embedded massive protostars,...) Early Universe Latter & Black 1991 Centaurus A Novae ejecta Very specific cases! For all the other cases, gas-phase formation is neglegible wrt catalyzed routes. Wikipedia 13

14 III. Grain-catalyzed formation of H2 I. The most abundant molecule in the Universe II. The inefficient gas-phase formation of H2 III. Grain-catalyzed formation of H2 III.1 A new partner: dust grains III.2 The Langmuir-Hinshelwood mechanism III.3 The Eley-Rideal mechanism III.4 Other mechanisms IV. From processes to interstellar H2 formation rate V. Summary 14

15 III. Grain-catalyzed formation of H2 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 15

16 III. Grain-catalyzed formation of H2 III.2 The Langmuir-Hinshelwood mechanism Potential energy (1) (2) (3) (4) (5) (1) physisorption of one H-atom Distance to surface Physisorption site Chemisorption site (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 interaction Chemisorption = strong covalent bound 16

17 III. Grain-catalyzed formation of H2 III.2 The Langmuir-Hinshelwood mechanism (1) physisorption of one H-atom (2) physisorption of one other H-atom on the same grain (1) (2) (3) (4) (5) Depends on: - surface nature (silicate, carbonaceous, ice) - structure (amorphous, cristaline, porosity) - presence of defects 17

18 III. Grain-catalyzed formation of H2 III.2 The Langmuir-Hinshelwood mechanism (3) traveling of physisorbed H-atom on grain surface (3) Depends (3)on: (4) (5) - surface nature (silicate, carbonaceous, ice) - structure (amorphous, cristaline, porosity) - presence of defects Processes: thermal diffusion (moving over barriers from site to site) quantum tunneling (moving through barriers from site to site) 18

19 III. Grain-catalyzed formation of H2 III.2 The Langmuir-Hinshelwood mechanism (4) encounter chemical binding of H-atoms (5) desorption of the new H2 molecule (4) (5) (3) Depends on: (4) (5) - surface nature (silicate, carbonaceous, ice) - structure (amorphous, cristaline, porosity) - presence of defects A related issue: distribution of the energy released translational kinetic energy grain vibrational energy H2 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+) 19

20 III. Grain-catalyzed formation of H2 III.2 The Langmuir-Hinshelwood mechanism (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 ~ K 20

21 III. Grain-catalyzed formation of H2 III.3 The Eley-Rideal mechanism Potential energy (1) (2) (3) (1) chemisorption of one H-atom Distance to surface Physisorption site Chemisorption site (2) collision between a gas-phase H-atom and the chemisorbed H-atom (3) desorption of the new H2 molecule Physisorption = weak van der Waals interaction Chemisorption = strong covalent bound 21

22 III. Grain-catalyzed formation of H2 III.3 The Eley-Rideal mechanism (1) (2) (3) Depends on: - surface nature (silicate, carbonaceous, ice) - structure (amorphous, cristaline, porosity) - presence of defects no traveling H-atom less efficient than LH Strong bounds robust with temperature 22

23 III. Grain-catalyzed formation of H2 III.3 The Eley-Rideal mechanism Binding and barrier energies can depend on the position of the chemisorption site: Rauls & Hornekaer

24 III. Grain-catalyzed formation of H2 III.3 The Eley-Rideal mechanism Rauls & Hornekaer 2008 Binding and barrier energies also depend on history of the grain: How many H-atoms are already bound to the grain? 24

25 III. Grain-catalyzed formation of H2 III.4 Other mechanisms Intermediate mechanisms: Potential energy physisorbed atoms can tunnel to chemisorption sites gas-phase atoms can strike physisorbed atoms traveling physisorbed atoms can find chemisorbed atoms Distance to surface Physisorption site Chemisorption site 25

26 IV. From processes to interstellar H2 formation rate I. The most abundant molecule in the Universe II. The unefficient gas-phase formation of H2 III. Grain-catalyzed formation of H2 IV. From processes to interstellar H2 formation rate IV.1 Relative contribution to H2 formation rate IV.2 Implementing H2 formation in astrophysical models IV.3 Astrochemical application V. Summary 26

27 IV. From processes to interstellar H2 formation rate IV.1 Relative contributions to H2 formation rate LH versus ER Cazaux et al Modelling H2 formation efficiency on carbonaceous grains Assuming: Tdust = constant Tgas = Tdust K Some particular values for binding and barrier energies LH: dominates at low Tdust ER: significant at high Tdust 27

28 IV. From processes to interstellar H2 formation rate IV.1 Relative contributions to H2 formation rate Grain size and the effect of temperature fluctuations Surface(Small grains) > Surface(Big grains) H2 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) 28

29 IV. From processes to interstellar H2 formation rate IV.2 Implementing H2 formation in astrophysical models Rate equations (example of LH implementation) f W a = surface density of physisorbed H-atoms = flux of impinging H-atoms = desorption rate coefficient = hopping rate ~ H2 formation rate coefficient H(g) H: H: H(g) H: + H: H2(g) (f) (W) (a) The H2 formation rate per unit surface of grain is then given by a 2 BUT: small grains small surface surface density is meaningless 29

30 IV. From processes to interstellar H2 formation rate IV.2 Implementing H2 formation in astrophysical models Master equations (example of LH implementation) Dealing with probabilities: n = number of H atoms physisorbed on one grain P(n) = probability of having n H atoms physisorbed on one grain S = maximum number of physisorption sites closure formula dp(n)/dt = time derivative of P(n) F = flux of impinging H-atoms W = desorption rate coefficient A = hopping rate ~ H2 formation rate coefficient H(g) H: H: H(g) H: + H: H2(g) (F) (W) (A) 30

31 IV. From processes to interstellar H2 formation rate IV.2 Implementing H2 formation in astrophysical models 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: 31

32 IV. From processes to interstellar H2 formation rate IV.2 Implementing H2 formation in astrophysical models Rate equations versus Master equations Biham & Lipshtat 2002 Master equations are more accurate but slower to solve (bigger system of equations) 32

33 IV. From processes to interstellar H2 formation rate IV.2 Implementing H2 formation in astrophysical models Moment equations H2 formation rate for one grain: Depends only on the 2 first moments of n! = A (<n2> - <n>) ( NH is n ) Open system! 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. 33

34 IV. From processes to interstellar H2 formation rate IV.2 Implementing H2 formation in astrophysical models Comparison Lipshtat & Biham

35 IV. From processes to interstellar H2 formation rate IV.3 Astrochemical application Nagy et al Color = CO J=6-5 Black = CH+ J=3-2 White contours=h2* v=1-0 S(1) 35

36 IV. From processes to interstellar H2 formation rate IV.3 Astrochemical application Detailled modelling of H2 formation and excitation (Meudon PDR code) good understanding of CH+ formation and excitation Nagy et al CH+ is a good tracer of the external, warm layers of molecular clouds 36

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,...) 37

38 VI. Some bibliographic references General: - McCall, Phil. Trans. R. Soc. A, 364 : (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 : (1974) - Maloney et al., ApJ, 466 : (1996) Astrophysical aspects: - Glover, ApJ, 584 : (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 : (1998) - Rauls & Hornekaer, ApJ, 679 : (2008) - Latter & Black, ApJ, 372 : (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/ v2 (2002) - Lipshtat & Biham, A&A, 400 : (2003) - Cazaux et al., Journal of Physics: Conference Series, Volume 6, Issue 1, pp (2005) 38