Cloud formation modelling in exoplanetary atmospheres

Transcription

1 Cloud formation modelling in exoplanetary atmospheres Christiane Helling Centre for Exoplanet Science University of St Andrews leap2010.wp.st-andrews.ac.uk Cloud Academy, Les Houches, September 2018

2 We know it. What we perceive as clouds Cloud(s) noctilucent clouds in Earth s mesosphere detached haze in Titan s mesosphere Rain no condensation seeds available in Earth s mesosphere at 76-85km in 520km height in Titan s mesosphere 2

3 We know it. on Earth. What we perceive as clouds Cloud(s) noctilucent clouds in Earth s mesosphere detached haze in Titan s mesosphere Rain Why not simply apply no condensation seeds available what has been developed and tested in Earth s mesosphere at 76-85km in 520km height in Titan s for years in meteorology and planetary science? mesosphere 3

4 Exoplanets are different from Earth 3824 extrasolar planets, 2859 extrasolar planetary systems no exoplanet resembles any solar system planet Challenge: These are mean bulk abundances. What atmosphere is associated with the planet? Universally applicable cloud formation model required 4

5 Cloud formation in exoplanet atmospheres H - H 2 O gas phase cluster formation cold (T gas < 500K) gravitational settling nucleation by gas-gas reactions element depletion bulk growth by gas-surface reactions element replenishment bulk material changes due to changing thermal stability element enrichment bulk evaporation due to decreasing thermal stability with increasing T gas warm (T gas > 2500K) gas phase

6 elements (O, Ti, Si, Mg, Fe, N, He, ) atoms & ions e.g. Fe / Fe + molecules e.g. FeO, MgH, TiO 2 clusters e.g. (Fe) N, (TiO 2 ) N, (Al 2 O 3 ) N (TiO 2 ) 5 (Al 2 O 3 ) 2 (H 2 SO 4 )-(H 2 O) 50 binary clusters 6

7 H-rich and ~ solar element abundance atmosphere Most abundant molecules in thermochemical equilibrium (at 1bar): H2O CO CH4 HCN NH3 N2 Photo-chemistry will change upper atmosphere Life-chemistry will change whole atmosphere on evolutionary timescales 7

8 H-rich and ~ solar element abundance atmosphere H Li C N O Fl Na Mg Al Si S Cl K Ca Ti Cr Mn Fe 8

9 H-rich and ~ solar element abundance atmosphere Clusters Cloud particles H Li C N O Fl Na Mg Al Si S Cl K Ca Ti Cr Mn Fe 9

10 Clusters Cloud particles Mg(OH)2 Mg 1 bar 10

11 Cloud formation in exoplanet atmospheres H - H 2 O gas phase cluster formation cold (T gas < 500K) element replenishment gravitational settling element depletion nucleation by gas-gas reactions bulk growth by gas-surface reactions bulk material changes due to changing thermal stability exoplanet cloud particles change in size and change their composition of mixed materials element enrichment bulk evaporation due to decreasing thermal stability with increasing T gas warm (T gas > 2500K) gas phase

12 Then: processing First: formation Microphysics of cloud formation processes: cluster formation & element depletion bulk growth & element depletion fractal formation crystallisation, rearrangement. 12

13 Coagulation: particle-particle collisional processes a 1 =a 2 a 1 <<a 2 (Güttler et al. 2010) 13

14 Coagulation: particle-particle collisional processes How many? What omposition? Exoplanet/brown dwarf cloud particles -- composed of material material that changes with height (locally) -- height-dependent particle size distribution f(a, (x, y, z)) Protoplanetary disk particles -- given f(a, z) and material composition 14

15 Seed formation (nucleation): the chemical path cloud particle Critical cluster = lowest stability Bottle neck: = slowest reaction rate leading to point of no return 15

16 Seed formation: silica (SiO 2 ) clusters homogeneous reaction path silica nanocluster structures SiO 2 + (SiO 2 ) N à (SiO 2 ) N+1 red: oxygen atom grey/yellow: silicon atom Bromley et al. (2009) 16

17 Seed formation (nucleation): (SiC)N-cluster & isomers (Gobrech et al. 2017) (SiC)2 SiC2 (SiC)10 (SiC)16 17

18 Seed formation (nucleation): add small, get large heterogeneous reaction path MgO 3 þ SiO 2! MgSiO 3 þ O 2 FeO 3 þ SiO 2! FeSiO 3 þ O 2 As shown in Fig. 6, these Dust seeds form from small gas-phase molecules (nucleation) Saunders & Plane (2011) 18

19 Seed formation (nucleation): What about Al 2 O 3, MnS, ZnS, Na 2 S, KCl? (Lee, Belcic, Helling 2017) /n tot AlO 2 H AlO 2 AlOH Al AlCl Al 2 O 3 (corundum) - not as monomer in gas-phase - Al x O x more stable than (Al 2 O 3 ) X (Patzer et al. 2005) - additional cluster simulations for (Al 2 O 3 ) N in Decin et al. (2017) 19

20 Thermal stability / phase equilibrium 20

21 Clouds form in phase-non-equilibrium thermal stability S=1 τ ev τ gr Rates: τ gr = τ ev S>>1 growth τ ev τ gr Rates: τ gr > τ ev 21

22 Thermal stability of critical cluster τ gr τ ev phase equilibrium: T=T s => τ gr = τ ev (T s sublimation temperature) (Goeres 1996) 22

23 Thermal stability of critical cluster τ gr τ ev τ gr τ ev phase equilibrium: T=T s => τ gr = τ ev (T s sublimation temperature) surface energy decreases for decreasing cluster size è cluster evaporation because: T=T s => τ gr < τ ev for smaller clusters (Goeres 1996) 23

24 Thermal stability of critical cluster τ gr τ ev τ gr τ ev phase equilibrium: T=T s => τ gr = τ ev (T s sublimation temperature) surface energy decreases for decreasing cluster size è cluster evaporation because: T=T s => τ gr (N) < τ ev (N) for smaller clusters τ for ê T, ê exponentially gr τ ev but ê τ gr only ~ T τ ev è point of phase equilibrium where τ gr (N) = τ ev (N) shift to smaller cluster (Goeres 1996) 24

25 Basic concept for seed formation: homogeneous nucleation = linear reaction chain: Flux through cluster space J(N, t) [s -1 cm -3 ] (effective transition rate): stationary process => J(N,t) =const and J(N,t)=J(N+1,t)=J * nucleation rate + detailed balance + define reference equilibrium state See also Chapter 13 in Gail & Sedlmayr: Physics and Chemistry of Circumstellar Dust Shells Sect 4a(ii) in Helling & Fomins (2013) 25

26 Basic concept for seed formation: cluster growth time scale of size N (in an ref equilibrium state), with N=1 the monomer number density of cluster of size N (in an ref equilibrium state), Gibbs free energy of formation of cluster of size N (in a reference state) 26

27 Seed formation: chasing the thermodynamic properties TiO2 cluster data 1 TiO2 cluster abundances 2 3a 4a 3b 4b 5a 5b log p1 6a 6b log p (Lee, Helling, Giles, Bromley 2015) log p10 TixCy in Patzer, Change, Sülzle (2014) 27

28 Seed formation: Taking the short-cut 28

29 Phase equilibrium cloud formation τ ev τ gr Where J * >>1 => S>> 1 for plenty materials Clouds form at lower temperatures (higher in atmosphere!!) than stability curves suggest. Mg/Si/Fe/O/ -materials grow cloud particle bulk through surface reactions 29

30 Continuing cloud formation by surface growth: super-cooling makes dirty cloud particles Clouds form at lower temperatures (higher in atmosphere!!) than stability curves suggest. S=1 S>>1 Within a few 100 K, many refractory solid materials become thermodynamically stable. (homog.) nucleation requires strongly supersaturated gas => efficient nucleation occurs at much lower temperatures, where different solid species can grow simultaneously on the surface of seed particles. => Formation of dirty and/or core-mantle cloud particles expected 30

31 Basic concept for modelling cloud particle formation: Moment method for nucleation, growth/evap & drift assumptions: spherical grains with macroscopic properties (e. g. reactive surface a 2 ), neglection of coagulation ( V r V ), T d (a)=const, S r (a)=const V i+1 V i L j (applex, t) = Z f(v,applex, t) V j/3 dv V V i-1 t f(v ) dv + t L j + applev gas L j = applevgas + applev dr (V ) f(v ) dv Z X R k V j/3 dv k V` {z } e ect of surface reactions R 4 a 2 V r n r r (1 1 ) S r = R R + R R dv (1) Z f(v ) V j/3 applev dr (V ) dv V` {z } e ect of size-dependent particle drift (2) 31

32 Equations that describe cloud formation Master equations: f(v ) dv t + vgas + v dr (V ) f(v ) dv = X X k Moment equations: t L j + v gas L j = (Helling & Fomins 2013) Z X R k V j/3 dv k V` {z } e ect of surface reactions V /3 l Z Vl 3 + D g L j L j St min {z St min } di usive term for St >1 f(v) -- grain size distribution function L j (applex, t) = R k dv Z V j dust dv f(v,applex, t) V j/3 dv f(v ) V j/3 v dr (V ) dv V` {z } e ect of sizedependent particle drift (Stokes number) (4) 32

33 Gravitational Settling equation of motion m s v dr = gm s + F fric (a,,t,v dr ) equilibrium drift g s 43 a3 = F fric (a,,t,v dr ) (quick relaxation) Knudsen number Kn = /(2a) Reynolds number Re = 2a v dr /µ kin F fric = 8 3 a 2 c T v dr (Kn 1,v dr c T ) subsonic free molecular flow = a 2 vdr 2 (Kn 1,v dr c T ) supersonic free molecular flow =6 aµ kin v dr (Kn 1, Re 1000) laminar viscous flow (Stokes) =1.3 a 2 vdr 2 (Kn 1, Re 1000) turbulent flow (Newton) implicit equation for v dr = v dr (g, a, s,,t) (Woitke & Helling 2003, A&A) 33

34 Gravitational Settling turbulent laminar K>>1 K<<1 di erent regimes e. g. at =10 5 gcm 3 : sink = H p /v dr =... 8 months (a=0.1 µm) 1/4 hour (a=100µm) e ects of s, T, porosity, non-spherical shapes... K<<1: viscous flow K>>1: free molecular flow (Woitke & Helling 2003, A&A) 34

35 Growth & Evaporation for example SiO + H 2 O SiO 2 [s] + H 2 Kn 1, v dr c S : Kn 1, Re 1000 : dv dt =4 a2 r dv dt =4 a r V r n r v rel r r 1 V r D r n r 1 1 S r 1 S r (Woitke & Helling 2003, A&A) 35

36 nucleation growth / evap. drift growth velocity [cm/s] gravitational force density [dyn/cm 3 ] (Woitke & Helling 2003; Helling & Woitke 2006) 36

37 nucleation growth / evap. drift growth velocity [cm/s] gravitational force density [dyn/cm 3 ] drift mixing nucleation growth / evap. (Woitke & Helling 2003; Helling & Woitke 2006) 37

38 Cloud formation summary Model equations for nucleation, growth/evap & gravitation settling: j=0, 1, 2 s=1, 2, #condensates Model equations for element conservation: Eqs. 4, 8, 9 10 in Helling, Woitke, Thi 2008 i=1, 2, #elements 38

39 Cloud formation summary Required input / material equations: local gas temperature, T gas [K], and gas pressure, p gas [dyn/cm 2 ] (undepleted) element abundances ε i 0 (i=o, Fe, Ti, #elements; e.g. Asplund 2009) local gas composition n r (T gas, p gas ) [cm -3 ] vapor pressure data for condensing species p vap [dyn/cm 2 ] for s=1,2, #condensates if 1D stationary cloud formation: τ mix [1/s] Output: τ mix = const H p2 (z)/k zz with K zz (z)=hp(z)v z or K zz =const [cm 2 s -1 ] or local gas composition n(t gas, p gas ) [cm -3 ] based on depleted ε i ε i 0 cloud properties: J * -- nucleation rate [s -1 cm -3 ] n d = ρ gas L 0 -- local number density of cloud particles [cm -3 ] <a> = (3/(4π)) 1/3 L 1 /L 0 -- local mean cloud particle size [cm] V s = ρ gas L s 3 -- local volume of condensate s (Vtot = Σ V s ) [cm 3 ] v dr = 0.5 (π) 1/2 g ρ d / (ρ gas c T ) local cloud particle drift velocity [cm s -1 ] (Kn>>1, subsonic) 39

40 Cloud formation summary Approach / how to utilize pre-calculated (T gas, p gas, v z, z) structure solve in thermochemical equilibrium, e.g. with GGChem (Woitke et al. 2018)) solve cloud formation model plot cloud properties nicely (e.g. as maps) 40

41 Cloud formation summary Approach / how to utilize pre-calculated (T gas, p gas, v z, z) structure: 1D trajectories from a 3D GCM model (Parmentier et al.) for HAT-P-7b 41

42 Cloud formation summary Approach / how to utilize pre-calculated (T gas, p gas, v z, z) structure 1D trajectories from a 3D GCM model (Parmentier et al.) for HAT-P-7b solve in thermochemical equilibrium, e.g. with GGChem (Woitke et al. 2018)) solve cloud formation model 42

43 Results: cloud structures of exoplanet atmosphere nightside SiO TiO 2 n d J * tot higher latitude <a> V s /V tot equator 43

44 Results: cloud and chemistry structure of exoplanet atmosphere cloudy nightside higher latitude SiO TiO2 cloud-free dayside nd <a> J*tot Al+ Al (C/O) HAlH AlOH Vs/Vtot Al2O Al equator Al+ 44

45 45

46 Lecture end 46

47 Element replenishment / mixing for 1D K diffusion constant (also: D) q -- concentrations f sed gravitational settling parameter (Ackerman & Marley 2001) τ mix convective mixing time scale ε -- element abundances overshooting (Woitke & Helling 2004) τ mix = const H p2 /K 47

48 Element replenishment / mixing for 1D Results from 3D RHD simulations in-cloud convection gravity waves overshooting convection D=H p v 2 /c sound (Freytag et al. 2010) 48

49 Element replenishment / mixing for 1D in-cloud convection gravity waves Results from 3D RHD simulations overshooting convection hydrodynamic mixing D=H p v 2 /c sound (Freytag et al. 2010) (Parmentier et al. 2015) 49

50 Element replenishment / mixing for 1D D = D micro + D macro = 1/3 v th l MFP + v HD H p molecular diffusion HD diffusion 50

51 Mixted-material cloud particles with particle size distributions nucleation, growth, evaporation, drift, mixing, element cons. cloud particles contain a mixture of materials Conclusions particle sizes vary inside each layer and with height + a selective effect on the element abundances

52 Element replenishment / mixing for 1D Results from 3D RHD simulaltions Mass flux beyond convectively unstable region (Ludwig et al. 2006) Tracer particles in upper atmosphere (Parmentier et al. 2015) 52

53 Growth & Evaporation SiO + H 2 O SiO 2 [s] + H 2 gr = 4 3 a3 dv dt sink < gr only for a < 100µm (deeper layers) a < 1µm (upper layers) maximum particle size a max in BD atmospheres a<a max, but not a a max! supersonic and turbulent regimes not relevant (Woitke & Helling 2003, A&A) 53

54 Cloud particle energetics Q cond + Q fric = Q rad + Q coll implicit equation for T = T d T g Q cond = dv dt s fh Q fric = fric F apple fric applev dr Q rad =4 a 2 Q abs (a, ) B (T d ) J d a 2 n v th acc 2k(T d T g ), Kn 1 Q coll = 4 a (T d T g ), Kn 1 a < a max : dust temperature increase T < 3K negligible: T d T g growth not limited by the need to eliminate the heat of condensation log(g)=5, T g =1500 K, SiO 2 grains, J =B (T g ) (Woitke & Helling 2003, A&A) 54

55 Bulk growth through surface reactions Solid s Surface reaction TiO 2 [s] TiO 2 TiO 2 [s] rutile TiO + H 2 O TiO 2 [s] + H 2 Ti + 2 H 2 O TiO 2 [s] + 2 H 2 TiS + 2 H 2 O TiO 2 [s] + H 2 S+H 2 SiO 2 [s] SiO 2 SiO 2 [s] silica SiO + H 2 O SiO 2 [s] + H 2 SiS + 2 H 2 O SiO 2 [s] + H 2 S+H 2 SiO[s] SiO SiO[s] SiO 2 +H 2 SiO[s] + H 2 O SiS + H 2 O SiO[s] + H 2 S Fe[s] Fe Fe[s] solid iron FeO + H 2 Fe[s] + H 2 O FeS + H 2 Fe[s] + H 2 S Fe(OH) 2 +H 2 Fe[s] + 2 H 2 O FeO[s] FeO FeO[s] Fe + H 2 O FeO[s] + H 2 FeS + H 2 O FeO[s] + H 2 S Fe(OH) 2 FeO[s] + H 2 O FeS[s] FeS FeS[s] Fe + H 2 S FeS[s] + H 2 FeO + H 2 S FeS[s] + H 2 O Fe(OH) 2 +H 2 S FeS[s] + 2 H 2 O Fe 2 SiO 4 [s] 2Fe+SiO+3H 2 O Fe 2 SiO 4 [s] + 3 H 2 fayalite 2Fe+SiS+4H 2 O Fe 2 SiO 4 [s] + H 2 S+3H 2 2FeO+SiO+H 2 O Fe 2 SiO 4 [s] + H 2 2FeO+SiS+2H 2 O Fe 2 SiO 4 [s] + H 2 S+H 2 2FeS+SiO+3H 2 O Fe 2 SiO 4 [s] + H 2 +2H 2 S 2FeS+SiS+4H 2 O Fe 2 SiO 4 [s] + H 2 S+3H 2 2 Fe(OH) 2 +SiO Fe 2 SiO 4 [s] + H 2 O+H 2 2 Fe(OH) 2 +SiS Fe 2 SiO 4 [s] + H 2 S+H 2 Surface Reactions Solid s Surface reaction MgO[s] MgO MgO[s] periclase Mg + H 2 O MgO[s] + H 2 2MgOH 2MgO[s]+H 2 Mg(OH) 2 MgO[s] + H 2 O MgSiO 3 [s] Mg + SiO + 2 H 2 O MgSiO 3 [s] + H 2 enstatite Mg + SiS + 3 H 2 O MgSiO 3 [s] + H 2 S+2H 2 2MgOH+2SiS+4H 2 O 2MgSiO 3 [s] + 2 H 2 S+3H 2 2MgOH+2SiO+2H 2 O 2MgSiO 3 [s] + 3 H 2 Mg(OH) 2 +SiO MgSiO 3 [s] + H 2 Mg(OH) 2 +SiS+H 2 O MgSiO 3 [s] + H 2 S+ H 2 Mg 2 SiO 4 [s] 2Mg+SiO+3H 2 O Mg 2 SiO 4 [s] + 3 H 2 forsterite 2Mg+SiS+H 2 O Mg 2 SiO 4 [s] + H 2 S+3H 2 2MgOH+SiO+H 2 O Mg 2 SiO 4 [s] + 2 H 2 2MgOH+SiS+2H 2 O Mg 2 SiO 4 [s] + H 2 S+2H 2 2 Mg(OH) 2 +SiO Mg 2 SiO 4 [s] + H 2 O+H 2 2 Mg(OH) 2 +SiS Mg 2 SiO 4 [s] + H 2 +H 2 S Al 2 O 3 [s] 2 AlOH + H 2 O Al 2 O 3 [s] + 2 H 2 aluminia 2 AlH + 3 H 2 O Al 2 O 3 [s] + 4 H 2 Al 2 O+2H 2 O Al 2 O 3 [s] + 2 H 2 2 AlS + 3 H 2 O Al 2 O 3 [s] + 2 H 2 S+H 2 2 AlO 2 H Al 2 O 3 [s] + H 2 O CaTiO 3 [s] Ca + TiO + 2 H 2 O CaTiO 3 [s] + 2 H 2 Ca + TiO 2 +H 2 O CaTiO 3 [s] + H 2 CaO + TiO + H 2 O CaTiO 3 [s] + H 2 CaO + TiO 2 CaTiO 3 [s] CaS + TiO + 2 H 2 O CaTiO 3 [s] + H 2 S+H 2 CaS + TiO 2 +H 2 O CaTiO 3 [s] + H 2 S Ca(OH) 2 +TiO CaTiO 3 [s] + H 2 Ca(OH) 2 +TiO 2 CaTiO 3 [s] + H 2 O 12 compounds contributing to the bulk growth with 12 different monomer volumes at different rates (see Appendix B in Helling & Woitke 2006, A&A 455) 55

56 cloudy Hydrodynamics: ( ) t + ( v) = 0 (1) 1 ( v) t + ( v v) = M 2 P M2 g (2) Fr ( e) t + (v[ e + P ]) = Rd (T 4 RE T 4 ) (3) Dust formation: Element conservation: Gas compositions: Opacities: ( L j ) t + (v L j ) = Da nuc ( x ) t + (v x ) = d R r=1 Se j J + Da gr d ( nuc r El Da nuc d j net + gr r El Da gr d n x,rv rel,x r L 2 ) + law of mass action for all gas-phase species - coupling between dust and hydrodynamics χ dust (z) =κ dust (z)+σ dust (z) = 3 36π 0 3 L j 1 (4) 3 36 Nl J (5) j=1 J x=1 X (Q abs (V, b s )+Q sca (V, b s ))f(v, b s,z)v 2/3 dv( (Woitke & Helling 2003, 2004; Helling et al. 2006, 2011; Helling et al 2008; Helling, Woitke, Thi 2008, Helling & Fomins 2013, Helling & Casewell 2014) Christiane Helling, University of St Andrews 56

57 Solve system of equations with: J(N) (N=1 N max -1) number of equations f(2) f(n max ), J * number of unknowns 57