Warm gas phase chemistry as possible origin of high HDO/H2O ratios in hot and dense gases: application to inner protoplanetary discs
aa r X i v : . [ a s t r o - ph . E P ] D ec Mon. Not. R. Astron. Soc. , 1–17 (2009) Printed 10 October 2018 (MN L A TEX style file v2.2)
Warm non-equilibrium gas phase chemistry as a possible origin ofhigh HDO/H O ratios in hot and dense gases: application to innerprotoplanetary discs
W.-F. Thi ⋆ , P. Woitke , I. Kamp † SUPA, Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ, UK UK Astronomy Technology Centre, Royal Observatory, Edinburgh, Blackford Hill, Edinburgh EH9 3HJ, UK Kapteyn Astronomical Institute, Postbus 800, 9700 AV Groningen, The Netherlands
Accepted 2009. Received 2009 February 12
ABSTRACT
The origin of Earth oceans is controversial. Earth could have acquired its water either fromhydrated silicates (wet Earth scenario) or from comets (dry Earth scenario). [HDO]/[H O]ratios are used to discriminate between the scenarios. High [HDO]/[H O] ratios are foundin Earth oceans. These high ratios are often attributed to the release of deuterium enrichedcometary water ice, which was formed at low gas and dust temperatures. Observations donot show high [HDO]/[H O] in interstellar ices. We investigate the possible formation of high[HDO]/[H O] ratios in dense ( n H > cm − ) and warm gas ( T = T >
K. The chemicalnetwork is dominated by photodissociation and neutral-neutral reactions. Despite the high gastemperature, deuterium fractionation occurs because of the difference in activation energy be-tween deuteration enrichment and the back reactions. The analytical solutions were confirmedby the time-dependent chemical results in a 10 − M ⊙ disc around a typical TTauri star us-ing the photochemical code P RO D I M O . The P RO D I M O code includes frequency-dependent2D dust-continuum radiative transfer, detailed non-LTE gas heating and cooling, and hydro-static calculation of the disc structure. Both analytical and time-dependent models predict high[HDO]/[H O] ratios in the terrestrial planet forming region ( < O] ratio may not be an unique criterion to discriminate between thedifferent origins of water on Earth.
Key words:
Astrochemistry
The water deuteration abundance ratio [HDO]/[H O] is often used to determine the temperature at which water was synthesised. Currentsub-millimeter observations already provide measurements of [HDO]/[H O] for many astronomical objects including comets, hot-cores, andprotoplanetary discs. In particular, a high [HDO]/[H O] has been observed toward the protoplanetary disc DM Tau (Ceccarelli et al. 2005),although the HDO detection remains controversial (Guilloteau et al. 2006). The Herschel Space Telescope will be capable to detect cool andwarm water in discs while the Atacama Large Millimeter Array (ALMA) will spatially resolve HDO emission.The water deuteration abundance ratio [HDO]/[H O] in hot cores around massive young stellar objects is ∼ × − (Gensheimer et al.1996), around a factor ∼
10 enhancement compared to the cosmic [D]/[H] value set at the Big Bang ( ∼ × − , Linsky 2003). The enrich-ment suggests that the chemistry occurs in a low density, cold medium ( T <
100 K), where HDO synthesis begins with the deuteration of themolecular ion H +3 into H D + (e.g., Roberts & Millar 2000). Further gas-phase reactions lead to a high [HDO]/[H O]. But at temperaturesgreater than 100 K, which is the typical gas temperature of hot cores, the initial deuteration reaction is inefficient and the [HDO]/[H O] is ⋆ E-mail: [email protected] † Scottish Universities Physics Alliancesc (cid:13)
W.-F. Thi et al. close to the cosmic value. Therefore current chemical models need to invoke the evaporation of deuterium enriched water ice when the tem-perature reaches 100 K to explain the deuterium enrichment in water. The observed (HDO/H O)ice ratio is however too low (Dartois et al.2003; Parise et al. 2003). A second difficulty arises from the high observed water ice abundance of 10 − –10 − , which is two orders ofmagnitude larger than the gas phase abundance of water in the hot core around IRAS 16293-2422 (Parise et al. 2005).After decades of research, the origin of water on Earth remains a major subject of debate (e.g., Nuth 2008 for a review). Two majorsmodels exist. In the first model, the Earth accretes dry: the building blocks of the Earth are made of dry rocks, composed only of silicatesand carbonaceous materials. Most of the water is brought afterward by comets during the phase of heavy bombardment. This model issupported by the similarity between the Earth Mean Ocean Water (SMOW ≃ × − ) [HDO]/[H O] and the cometary value, althoughthe later value seems too high. Another support to the ”dry” model is the low [HDO]/[H O] predicted at temperature
T >
100 K bythermochemical equilibrium models. In the second model, most of the water on Earth comes from the release of water vapor trapped insidethe water-entrapped planetesimals like carbonaceous chondrites upon impact or during volcanism. Water-rich planetesimals located at 2-3 AU are perturbed by the giant planets and collide with the young Earth (Morbidelli et al. 2000; Gomes et al. 2005; Raymond et al. 2004,2005). Those planetesimals contain water in form of hydrated silicates. The average D/H in carbonaceous chrondrite is similar to the valuein the Earth ocean (Robert et al. 2000), although the composition of carbonaceous chrondrite does not match the composition of Earth’crust(Righter et al. 2006). The Earth is said to have accreted ”wet” (Drake 2005). Hydrous material does not necessary need to be brought from theasteroid belt area (2-3 AU). Recent study on adsorption of water molecules onto fractal dust grains shows that hydrous material could havebeen present in the vicinity of 1 AU (Stimpfl et al. 2006). In this scenario water in the gaseous solar nebula sticks onto the silicate surface offractal grains, which coagulate and grow into the Earth. The adsorbed water would reflect the deuterium enrichment of the gas-phase water at1 AU. The major difference between the two “wet” scenarios is that water was present in the early-Earth in the latter scenario. Geochemicalfindings suggest that hydrosphere and continental crust were already present in the first ∼
600 million years of Earth history (Hopkins et al.2008). The presence of water and also of organic matter at the formation of the Earth has profound astrobiology implications for the originof life.One major weakness of the “wet” scenario is that the deuterium enrichment predicted by equilibrium chemistry is too low at temperaturesgreater than 100 K. However there are chemical routes to obtain high [HDO]/[H O] ratios at temperatures greater than 100 K in non-equilibrium chemistry. Photodissociation of H O and HDO followed by reformation at the surface of protoplanetary discs and turbulentmixing can also change the [HDO]/[H O] (Yung et al. 1988). Vertical turbulent mixing was invoked by Lyons & Young (2005) to explainthe oxygen anomalies in the early solar nebula. Alternatively Genda & Ikoma (2008) propose that the [HDO]/[H O] ratio on Earth changedduring the evolution of the Earth from its formation. Willacy & Woods (2009) studied the deuterium chemistry of the inner disc around aTTauri star and found relatively high HDO abundance in the warm molecular layer.Four direct physical processes lead to isotopic fractionation in the gas phase. First, heavier isotopologues diffuse slower than the lightermain isotopologue. The diffusion results in zones of varying [HDO]/[H O] ratios. This process is negligible in turbulent media when themixing timescale is much lower than the diffusion timescales. Second, due to their larger reduced mass, isotopologues usually have a lowerzero point energy. The vibrational energy levels are located lower, which increases the density sum of energy and hence reduces the vaporpressure. Hence, the water ice/gas ratios in the interstellar medium is not at equilibrium. Third, heavier isotopologues are chemically morestable because the binding energy between O and D is stronger than between O and H in the water molecule. Fractionation reactionsdominate at low temperature because the inverse reactions have a minimum energy barrier equal to the difference in binding energy. Finally,isotopologues differ in their photodissociation cross section due to changes in the selection rules. A combination of the last two processestogether with chemical diffusion and turbulent mixing probably determine the deuterium fractionation in the inner region of protoplanetarydiscs where terrestrial planets form.Interstellar chemical models often neglect or include only few neutral-neutral reactions because their rates are small at temperaturesbelow ∼
100 K but they become competitively fast with the ion-neutral reactions at a few hundred degrees. For example, in dense and warmgases, the central species is the hydroxyl radical OH, which can react with H to form H O (Thi & Bik 2005).In this paper, we explore neutral-neutral and photochemical reactions relevant to the formation and destruction of H , HD, OH, OH,H O and HDO at gas temperature between 100 and 1000 K. We first focus on steady-state abundances and perform an analytical analysis.Analytical analysis makes it possible to determine the main formation and destruction paths. After establishing the possible reaction paths,we use the photochemical code P RO D I M O to compute a time-dependent chemical structure for a typical TTauri disk to check the validity ofour assumptions in the analytical analysis. In the rest of the paper, the chemical reaction rates are given in Table 4, 5, 6, 7, and 8. In particular,the most important reactions are summarised in Tables 4. O and HDO
We consider a gas mixture at a single temperature, density, irradiated by UV photons. In thermochemical equilibrium the deuterium exchangeequilibrium reaction between water and molecular hydrogen (the most abundant reservoir of deuterium) is (e.g., Robert et al. 2000) HD + H O ↔ HDO + H . (1) c (cid:13) , 1–17 igh HDO/H O in warm dense gas The equilibrium constant of this reaction for gas between 273 and 1000 K is (Richet et al. 1977) K = P HDO P H P HD P H O ≃ . × T + 1 . (2)The pressure dependence of K is negligible. At equilibrium, the deuterium enrichment decreases quadratically with temperature. A gasmixture is in thermochemical equilibrium when each chemical reaction is exactly balanced by its reverse reaction. Dissociations uponabsorption of UV photons are not taken into account.A gas is in chemical steady-state (also called stationary state) if the various abundances do not vary with time but the formation anddestruction reactions for a given species are not necessarily the same. An analytical solution to the chemical network for the synthesis ofH O and HDO can be obtained by identifying the main formation and destruction chemical reactions. At high temperature (
T >
100 K) anddensity, it is well established that water is primarily formed via the reactions between the hydroxyl radical OH and molecular hydrogen H (e.g, Thi & Bik 2005; Glassgold et al. 2009). High temperature gases are needed to overcome the large energy barrier of the reaction (reaction5 with rate k , E a =1660 K). The main destruction mechanism is likely photodissociation in low A V regions. Other water destruction mecha-nisms are reactions with atomic hydrogen, and with ionised helium in shielded regions. We assume in this study that the dust temperature T d has equilibrated with the gas temperature. At T d >
100 K most water molecules remain in the gas phase. The rate of water formation is thus: d [ H O ] dt = ( k [ H ] + k [ HD ] + k [ OH ])[ OH ] − ( J + k [ H ] + k [ D ] + k [ He + ] + k cp, )[ H O ] , (3)where k , k , and k are the rates of formation of water via the reactions OH+H , OH+HD, and OH+OH respectively, J is the photodisso-ciation rate, k is the water destruction rate by H, k cp, is the cosmic-ray induced photodissociation of water, and k is the rate of destructionby He + . At steady-state ( d [ H O ] /dt = 0 ), we obtain the ratio [ H O ][ OH ] ≃ k [ H ] J + k [ H ] + k [ He + ] + k cp, , (4)which will be used later in this paper. We have neglected the formation of water via reaction of OH with HD and OH and destruction ofwater via atomic deuterium because the rates are orders of magnitude smaller than the rates of other paths. Deuterated water can be formedvia the reaction of HD with OH as well as via OD + H (Bergin et al. 1998). Destruction occurs via photodissociation, reaction with atomichydrogen and ionised helium. d [ HDO ] dt = k [ OD ][ H ] + k [ OH ][ HD ] − ( J a + J b + ( k + k )[ H ] + ( k + k )[ He + ] + k cp, + k cp, )[ HDO ] . (5)The photodissociation of HDO can either lead to OH + D ( J a ) or to OD + H ( J b ). The sum of the two photorates is the total HDOphotodissociation rate and is similar to the H O photodissociation rate J . The photodissociation of HDO favors cleavage of the O-H bondover O-D bond with a 3 to 1 ratio (Shafer et al. 1989; Vander Wal et al. 1990, 1991), i.e. J b ≃ J a because the binding energy between Oand D is stronger than that between O and H in water. In steady-state, the balance between formation and destruction leads to the ratio X D = [ HDO ][ H O ] = ( k [ OD ][ H ] + k [ OH ][ HD ]) / ( J a + J b + ( k + k )[ H ] + ( k + k )[ He + ] + k cp, + k cp, ) k [ OH ][ H ] / ( J + k [ H ] + k [ He + ] + k cp, ) , (6) X D = [ HDO ][ H O ] = (cid:16) D H O D HDO (cid:17) (cid:18) k ([ OD ] / [ OH ])[ H ] + k [ HD ] k [ H ] (cid:19) , (7)where we define D H O = J + k [ H ] + k [ He + ] + k cp, (8)and D HDO = J a + J b + ( k + k )[ H ] + ( k + k )[ He + ] + k cp, + k cp, (9)to be the total destruction rates of H O and HDO. The total UV photodissociation rates of H O and HDO are similar (Zhang & Imre 1988): J ≃ J a + J b . We further assume that rates with the deuterated species are similar to that of the main isotopologues: k = k + k , k ≃ k + k , and k cp, + k cp, = k cp, . If we can make the assumption that the total destruction rate of H O and HDO are similar,i.e. D H O ≃ D HDO , then the value of [HDO]/[H O] does not depend on the actual destruction mechanisms for H O and HDO. The waterfractionation f (HDO) is defined as f ( HDO ) = [
HDO ] / [ H O ][ HD ] / [ H ] = (cid:16) D H O D HDO (cid:17) (cid:18) k k [ OD ] / [ OH ][ HD ] / [ H ] + k k (cid:19) = (cid:16) D H O D HDO (cid:17) (cid:16) k k f ( OD ) + k k (cid:17) ≃ k k f ( OD ) + k k (10)The ratio k /k is the ratio between the reaction of OH with HD to form HDO compared to the reaction of OH with H to form water.From the values in Table 4 the k /k ratio is lower than 1 for gas temperature greater than 120 K. This term does not enhance the waterdeuteration fractionation. We can write analytically the ratio between rate k and rate k : k k = 1 . × − ( T / . e − /T . × − ( T / . e − /T = 0 . T / . e − /T . (11) c (cid:13) , 1–17 W.-F. Thi et al.
The ratio is weakly temperature-dependant. Since k /k = 0 . − between 100 and 1000 K, water and hydroxyl radical deuterium fractionare similar at gas temperature greater than ∼
200 K: f (HDO) ≃ f (OD). Therefore water would be deuterium fractionated if OH is (i.e. f (OD) > The water deuteration fraction f (HDO) is intimately linked to that OH f (OD). The rate limiting reaction for the formation of water is theformation of hydroxyl radical OH: O + H → OH + H with rate k . This reaction has a large energy barrier ( E a =3163 K). The chemistryof OD (and OH) is described in details by Croswell & Dalgarno (1985) for reactions without barrier. The production of OD mostly occursthrough the rapid exchange reaction D + OH → OD + H (12)once OH is present in the gas (reaction 16 with rate from Yung et al. 1988). The forward reaction has no activation barrier but the reversereaction (reaction 13) has a barrier of 810 K because OD is more stable than OH. Thus at T < D + for gas at T <
100 K for the deuterium enrichment. OD can also formed by the reaction HD + O → OD + H. (13)OD is destroyed by reaction with carbon ion C + + OD → CO + D + (14) C + + OD → CO + + D, (15)and by photodissociation (with rate J ) OD + hν → O + D. (16)The steady-state abundance of OH and OD taking into account the most important formation and destruction reactions are [ OH ] = k [ O ][ H ] + ( J + k [ H ] + k [ He + ] + k cp, )[ H O ] + k [ O ][ HD ] + k [ OD ][ H ] + k [ CO ][ H ] + ( J a + k cp, )[ HDO ]( k + k )[ D ] + k [ H ] + k [ H ] + k [ He + ] + k [ O ] + k [ OD ] + k [ CO ] + k [ C ] + k [ C + ] + J + k cp, (17) [ OH ] ≃ k [ O ][ H ] k [ H ] + k [ H ] + k [ CO ] + J + k cp, + k [ C ] + k [ C + ] (18)After some algebra, we obtain the ratio [ OH ][ O ] ≃ k [ H ] J + k [ H ] + k [ CO ] + k cp, + k [ C ] + k [ C + ] + k [ He + ] + k cp, , (19)which would be useful later in the analysis. For the deuterated hydroxyl radical at steady-state: [ OD ] = k [ OH ][ D ] + k [ O ][ HD ] + k [ HDO ][ H ] + k [ O ][ D ] + k [ HDO ][ O ] + k [ CO ][ D ] + ( J b + k cp, )[ HDO ] k [ H ] + k [ H ] + k [ He + ] + k [ O ] + k [ OH ] + k [ CO ] + k [ C ] + k [ C + ] + J + k cp, . (20)The rates are listed in Table 1 to 5. Neglecting the minor formation and destruction reactions (i.e. reactions with C and C + ), we simplify theratio: [ OD ][ OH ] ≃ D OH D OD (cid:18) k [ OH ][ D ] + k [ O ][ HD ] + ( J b + k [ H ] + k cp, )[ HDO ] k [ O ][ H ] + ( J + k [ H ] + k cp, )[ H O ] (cid:19) , (21)where D OH D OD = ( k + k )[ D ] + k [ H ] + k [ H ] + k [ He + ] + k [ O ] + k [ OD ] + k [ CO ] + k [ C ] + k [ C + ] + J + k cp, k [ H ] + k [ H ] + k [ He + ] + k [ O ] + k [ OH ] + k [ CO ] + k [ C ] + k [ C + ] + J + k cp, (22)is the ratio between the sum of all destruction rates of OH and that of OD. The photodissociation rate of OH (rate J ) and OD (rate J ) areclose (van Dishoeck & Dalgarno 1984; van Dishoeck 1988; Croswell & Dalgarno 1985) ( J ≃ J ). From Table 4 reactions 5 and 22 havesimilar rates ( k ≃ k ). Reactions 52 and 53 are ion-molecule reactions and we expect the rates to be of the same order of magnitude. Onlyreactions 4 (OH + H → O + H ) and 17 (OD + H → OH + D) have very different rates, reaction 17 being much faster. But those reactions areimportant at low A V only where photodissociation dominates as destruction process. We assume that k ≃ k .The hydroxyl radical deuterium fractionation reads f ( OD ) = [ OD ] / [ OH ][ HD ] / [ H ] = D OH D OD (cid:18) k ([ OH ] / [ O ])[ D ] + k [ HD ] + ( J b + k [ H ] + k cp, ) X D ([ H O ] / [ O ]) k [ H ] + ( J + k [ H ] + k cp, )([ H O ] / [ O ]) (cid:19) / (cid:18) [ HD ][ H ] (cid:19) . (23)The OD fractionation increases with larger amount of OH and atomic deuterium and decreases if oxygen is in the atomic form anddeuterium is locked in HD. Large amount of OH allows the deuterium exchange reaction to occur.The knowledge of the abundances of H, H , D, and HD is needed to estimate the hydroxyl deuterium fraction f ( OD ) . c (cid:13) , 1–17 igh HDO/H O in warm dense gas The formation of H occurs mostly on grain surface when the grain temperature is below 1000 K and the destruction is caused by photodis-sociation at low A V and cosmic-ray/X-ray induced ionization and reaction with He + in the UV free region. The temperature is low enoughto avoid H destruction by atomic hydrogen. The steady-state balance between formation and destruction is: R ( T g , T d ) n H [ H ] = ( f ss J + k ζ, + k [ He + ])[ H ] , (24)where f ss is the H self-shielding function (Draine & Bertoldi 1996) and R ( T g , T d ) the molecular hydrogen formation rate on grain surfaces(Tielens 2005) R ( T g , T d ) = 4 . × − S ( T g , T d ) (cid:16) T g (cid:17) / , (25)where T g and T d are the gas and dust grain temperature respectively and the sticking coefficient S is defined as S ( T g , T d ) = 11 + 4 × − ( T g + T d ) / + 2 × − T g + 8 × − T g . (26)The sticking coefficient ensures that at high dust temperature atomic hydrogen does not stick onto grain surfaces. The number density ofnuclei is n H = [ H ] + 2[ H ] (27)We obtain the atomic and molecular abundances: [ H ] = n H (cid:18) f ss J + k ζ, + k [ He + ]2 R n H + f ss J + k ζ, + k [ He + ] (cid:19) ≃ n H (cid:18) f ss J + k ζ, R n H + f ss J + k ζ, (cid:19) (28)and [ H ] = n H (cid:18) R n H R n H + f ss J + k ζ, + k [ He + ] (cid:19) ≃ n H (cid:18) R n H R n H + f ss J + k ζ, (cid:19) . (29)Atomic and molecular hydrogen abundances are determined by the gas temperature, density, UV flux, extinction, the self-shielding function,and cosmic ray flux. While H is predominately formed on grain surfaces, formation of HD can also occur in the gas phase by reaction between D and H athigh temperature and at density higher than about 5 × cm − (Le Petit et al. 2002). HD is destroyed by photodissociation and reactionwith atomic H while H is mainly photodissociated. H can self-shield against photodissociation, HD is shielded by dust only. Thereforedeuterium remains atomic at higher extinction than H . In hot and dense regions, an important formation route of HD is therefore: H +D → HD + H (reaction 10 with a barrier E a =3820 K). Larger amount of atomic deuterium is needed to obtain high OD over OH ratio.The production of atomic deuterium is enhanced at high temperature via the conversion reaction HD + H → H + D. Another destructionmechanism of HD molecules involves photodissociation: HD + h ν → H + D. Finally, reaction with H exchanges the atomic hydrogen withatomic deuterium: HD + H → H + D. At high A V , cosmic rays destroy HD. Reactions with H + and atomic oxygen also destroy HD. Thesteady-state balance for [HD] then reads [ HD ] = ( k [ H ] + R n H )[ D ] + k [ D + ][ H ] J + k ζ, + k ζ, + k [ H ] + k [ H + ] + ( k + k )[ O ] + k [ OH ] , (30)where R is the formation rate on grain surfaces (Le Petit et al. 2002) density R ( T g , T d ) = 6 . × − S ( T g , T d ) (cid:16) T g (cid:17) / (31)and n H is the total number. This H formation rate does not take into account grain chemisorption sites contrary to more sophisticated H formation model (Cazaux & Tielens 2002). We assume k ζ, + k ζ, ≃ k ζ, and that the sticking coefficient is the same than for H .We neglect the formation of HD via reaction with D + and destruction via reactions with the protons, atomic oxygen and OH radicals.The steady-state balance leads to [ D ][ HD ] = J + k ζ, + k [ H ] k [ H ] + R n H (32)If we can assume that most of the deuterium is locked in H and HD n D ≃ [ D ] + [ HD ] , (33)then we obtain HD and D abundances c (cid:13) , 1–17 W.-F. Thi et al. [ HD ] = n D (cid:18) k [ H ] + R n H J + k ζ, + k [ H ] + k [ H ] + R n H (cid:19) (34)and [ D ] = n D (cid:18) J + k ζ, + k [ H ] J + k ζ, + k [ H ] + k [ H ] + R n H (cid:19) . (35)At low A V , destruction of [HD] is dominated by photodissociation and at gas temperature a few 100 K, the formation of HD via reaction ofatomic deuterium with molecular hydrogen is negligible [ D ][ HD ] ≃ J R n H . (36)Even in obscured ( J ∼ ) and fully molecular regions ( [ H ] ∼ ), cosmic-rays induced photodissociation and deuterium exchange reactionsensure that some atomic deuterium always remains in atomic form: [ D ][ HD ] ≃ k ζ, R n H . (37)The formation of HD on grains decreases dramatically for dust grain temperature above 100 K. Where the steady-state abundance of ionised Helium is given by the expression: [ He + ] = k ζ, [ He ] k [ H ] + k e − , [ e − ] (38)Combining with the element conservation equation: n He = [ He ] + [ He + ] (39)we obtain [ He + ] = k ζ, n He k [ H ] + k e − , [ e − ] − k ζ, (40)The He + abundance can be estimated only if the electron abundance is known. Our simple analytical analysis cannot provide an estimate ofthe He + abundance and we will omit in the rest of the paper reactions with He + . f ( HDO ) The results of the previous sections can be combined to derive an analytical formula of the [HDO]/[H O] ratio: X D = [ HDO ][ H O ] = num/den, (41)where num = k k (cid:16) D OH D OD D H O D HDO (cid:17) k ([ OH ] / [ O ])[ D ] + k [ HD ] k [ H ] + ( J + k [ H ] + k cp, )([ H O ] / [ O ]) + k k [ HD ][ H ] (42)and den = 1 − k k (cid:16) D OH D OD D H O D HDO (cid:17) ( J b + k [ H ] + k cp, )([ H O ] / [ O ]) k [ H ] + ( J + k [ H ] + k cp, )([ H O ] / [ O ]) (43)The abundances and abundance ratios in num and den have been derived earlier: [ OH ][ O ] ≃ k [ H ] J + k [ H ] + k [ CO ] + k [ C ] + k [ C + ] + k [ He + ] + k cp, , (44) [ H O ][ OH ] = k [ H ] J + k [ H ] + k [ He + ] + k cp, , (45)and combining the two equations above, we obtain [ H O ][ O ] = k k [ H ] ( J + k [ H ] + k [ CO ] + k [ C ] + k [ C + ] + k [ He + ] + k cp, )( J + k [ H ] + k [ He + ] + k cp, ) . (46)The water fractionation is composed of 3 terms. At gas temperature greater than 200 K the second term k /k dominates for both low andhigh extinction and the fractionation reaches 10-1000. Our analysis concerns high temperature gas only. In warm and dense region, the main c (cid:13) , 1–17 igh HDO/H O in warm dense gas Figure 1.
Water deuteration fraction f (HDO). The upper panels show models with UV enhancement of factor 100 w.r.t. the standard interstellar UV filed andfor three increasing gas densities. The four curves correspond to the various dust extinctions. The lower panels are models with UV enhancement of 10 . oxygen carrier is water and that of carbon is methane CH and not CO at high A V and C + at low A V . As state before, we further neglectreactions with He + .At temperature below 100 K, the only fast chemical reactions are between ions and neutral species, which are not taken into account inour analysis. The starting point of water formation is H +3 . Deuterium enrichment occurs via the deuterated equivalent of H +3 , H D + . H D + has a lower zero-point energy, which favors the deuteration reaction H +3 + HD → H D + + H . The rate of the back reaction has an energybarrier of 230 K.The water deuteration fraction enhancement is caused by the fast deuterium exchange reaction with OH (D+OH → OD + H). The inversereaction has an energy barrier of 717 K. Significant amount of atomic deuterium is possible at low and intermediate extinction. We plottedin Fig. 1 the ratio [HDO]/[H O] as function of the gas temperature for an impinging UV enhanced by a factor 10 and 10 , for differentextinctions (A V =1, 5, 10, 15), and for two gas densities ( n H = and 10 cm − ). Disc surfaces around young accreting T Tauri starsreceive ∼ to 10 times the amount of standard interstellar UV. The UV field, extinction, density, and gas temperature values are typicallyfound in regions of discs where water is abundant. In the following section, we will use a time-dependent thermo-photochemical code tosupport our assumed values for the parameters. The figure shows that large f (HDO)=[HDO]/[H O] ratios (up to a few 100) are possiblefor gas temperatures up to 500-600 K and up to extinction of 10, although the average value for f is lower than 10. At T > → OH+D starts to destroy efficiently OD. The figure also shows the large range of values for f (HDO) (0.1–10 ). The f (HDO)curves testify of the sensitivity of the abundances on the gas temperature, which reflects the exponential nature of the Arrhenius’ law forneutral-neutral reactions. c (cid:13) , 1–17 W.-F. Thi et al.
Table 1.
Stellar and disc parametersStellar mass M ∗ ⊙ Stellar luminosity L ∗ ⊙ Effective temperature T eff M d − M ⊙ Disc inner radius R in R out
300 AUVertical column density power law index ǫ ρ dust − minimum dust particle size a min µ mmaximum dust particle size a max µ mdust size distribution power law p CR × − s − ISM UV filed w.r.t. Draine field χ f PAH α viscosity parameter α P RO D I M O photochemical code We modelled the chemical abundances of a 10 − M ⊙ disc around a typical TTauri star ( T eff log g =4.0, Z =1.0) using the pho-tochemical code P RO D I M O . P RO D I M O combines frequency-dependent 2D dust-continuum radiative transfer, kinetic gas-phase and UVphotochemistry, ice formation, and detailed non-LTE heating and cooling balance. The major improvement over previous studies is that thedensity structure is determined by the gas pressure that is computed by detailed chemistry and energy balanced and not by assuming thatthe gas and dust have the same temperature. Detailed description of the code are given by Woitke et al. (2009) and in Kamp et al. (2009).The code has been used to determine the water abundance in the inner disc around a typical Herbig Ae star (Woitke et al. 2009). The mostrecent additions to the code includes PAH chemistry, time-dependent chemistry, deuterium chemistry, and generation of Spectral EnergyDistribution and spectral lines. The last two features are not used in the modelling performed for this paper. Table 1 summarized the inputparameters to the model. The stellar spectrum was generated using P HOENIX (Brott & Hauschildt 2005) with the addition of chromosphericflux from HD 129333 (Dorren & Guinan 1994). Although the model extends to 300 AU, we focus here only on the inner 3 AU as we areinterested in the [HDO]/[H O] ratio in the terrestrial planet forming region of discs.The chemical network includes a total of 187 deuterated and non-deuterated gas and ice species. Most reaction rates are taken fromthe UMIST
DATABASE (Woodall et al. 2007). Additional reaction rates were compiled from the NIST chemical kinetic database. The ratesinvolving deuterated species are described in e.g., Roberts et al. (2004), Roberts & Millar (2000), Charnley et al. (1997), and Brown & Millar(1989). Species can freeze-out onto grain surfaces and desorb thermally or upon absorption of a cosmic-ray or a UV photon (photodesorption).Grain surface reactions were omitted apart from the grain surface formation of H and HD (Cazaux & Tielens 2002). The photodissociationcross-sections are taken from the L EIDEN DATABASE described in van Dishoeck et al. (2008).The chemical abundances in the disc were established in three stages. First P RO D I M O determined the UV field, hydrostatic density,gas and dust temperature, and chemical abundance structure self-consistently assuming steady-state chemistry. Second we computed thechemical abundances of gas and solid species for a 1 Myr old molecular cloud with density of 5 × cm − and gas and dust temperature of15 K from diffuse cloud initial abundances, where the elements are in neutral or ionized atomic form (see Table 2). Third we ran P RO D I M O in the time-dependent chemical mode to simulate the chemical structure of a 1 Myr old disc using the results of the molecular cloud run asinitial chemical abundances and the disc properties computed in the first stage. All other disc properties (UV field, density and temperaturestructure) were fixed in this last stage.The three-stage method mimics the incorporation of molecular cloud materials and their subsequent evolution in the disc. It also makesit possible to compare the chemical abundances obtained with the time-dependent model and at steady-state. Our approach differs fromVisser et al. (2009) who solve the chemistry in a Lagrangian frame and their disc evolves according to viscous spreading. However theirnumber of species and reactions are limited. Figure 2 show the UV field, density, and gas and dust temperature structure in the inner 3 AU. The disc structure is discussed in Woitke et al.(2009). In this paper we focus on the water and HDO abundances. Figure 3 show the water and HDO abundances at steady-state on the leftand for a disc of 1 Myr old on the right. Apart from the H O HDO in the midplane beyond ∼ c (cid:13) , 1–17 igh HDO/H O in warm dense gas Table 2.
Typical diffuse cloud abundances used as initial abundances for the molecular cloud chemical calculation. Species with ionization potential (IP)higher than 13.6 eV are neutral while species with IP below 13.6 eV are ionized. The other species have negligible initial abundance.Species log ( n (X)/ n H )H 0.0D -5.0He -1.125C + -3.886O -3.538N -4.67S + -5.721Si + -5.1Mg + -5.377Fe + -5.367PAH -6.52 Table 3.
Mass and average gas and dust temperature for the three gas-phase water and HDO locations. The paper focuses mostly on the inner midplane.Location Mass < T gas > < T dust > (M ⊙ ) (K) (K)H OInner midplane 2.6 × −
178 177Cold belt 1.1 × −
16 16Hot layer 2.1 × − × −
140 140Cold belt 3.8 × −
16 16Hot layer 2.6 × −
474 102 are similar for the steady-state and time-dependent chemistry models. The differences stem from the fact that at steady-state even very slowreactions will impact the chemistry. In this case, the dust temperature is low enough ( T d <
150 K) such that all water and HDO should befrozen-out. In the time-dependent model, significant amount of water and HDO remains in the gas-phase in the inner 1 AU or above the icezone. The differences between the steady-state and time-dependent abundances occur in low gas-phase water abundance regions and thus donot impede our analysis of deuterium enrichment for gas-phase water either outside the water freeze-out zone.The [HDO]/[H O] ratio for the time-dependent model is plotted in Figure 4. The water abundance levels at 10 − and 10 − are overlaid.Water is abundant as soon as hydrogen is in molecular form. In our model, water and HDO are frozen onto grain surfaces in the midplanebeyond ∼ O] ratio decreases with radius. At 0.5–1.5 AU in the mid-plane, the ratiois a few 10 − –10 − . Gas-phase water and HDO are located in three zones: the inner midplane, the cold belt, and the hot layer (Woitke et al.2009). The mass and average gas and dust temperature are given in Table 3.Most of the gas-phase water (n(H O)/n H =10 − –10 − ) is located in the inner plane close to the star ( R < A V is between 1 and 10. Although of insignificantmass, the molecules are hot and emit strongly (e.g. Carr & Najita 2008; Salyk et al. 2008). In the outer disc, gas-phase water is found ina cold belt, which is sandwiched between A V ∼ O have similar adsorption energy, the gas-phase abundance of both species are co-located (seeFig.3). We plotted the vertical column densities for H, D, OH, OD, H O, HDO, H O , and HDO in Fig. 6. This figure shows that thecolumn density ratios HDO/H O, HDO /H O , and OD/OH stay relatively constant in the inner disc, with values much higher than theelemental D/H ratio of 10 − .In the high water abundance region, the [HDO]/[H O] ratio is higher than 10 − . Using the mass of H O and HDO in the inner midplanelisted in Table 3, we derived an average [HDO]/[H O] ratio of 4.6 × − , which is 30 times higher than the Earth Mean Ocean Water value( ≃ × − ) and close to cometary values. The actual [HDO]/[H O] values in our models depend on the disc parameters. Future studieswith focus on the effect of disc properties (disc mass, radius, ...) on the [HDO]/[H O] ratios.Overall, the [HDO]/[H O] ratios in the inner disc midplane by the time-dependent code P RO D I M O are consistent with the analyticalresults. Our results contradict the simple decrease in [H O]/[HDO] with increasing temperature if thermochemical equilibrium ratios areassumed. c (cid:13) , 1–17 W.-F. Thi et al.
Figure 2.
The four panels show the gas density n < H > (upper left), strength of the UV field with respect to the Draine field χ (upper right), the dust temperature T d (lower left), and the gas temperature T g with dust and gas temperature overlaid (lower right) for the inner 3 AU computed by P RO D I M O . The structure isconsistent with the chemical abundances. A simple analytical analysis shows that high water fraction is possible in a simple deuteration chemical network for gas hotter than 100Kelvin if neutral-neutral reactions are included. The analytical results are supported by the time-dependent photochemical model results. Intheir study Willacy & Woods (2009) also found that HDO can be abundant in the inner disc.The water deuterium fractionation is determined by the ratio between the rate of formation of OD via O + HD and the rate of for-mation of OH via O + H . Lower zero-point energy for HD makes the first reaction faster than the second one above 200 K. At lowtemperature ( T <
100 K), fast deuteration of H +3 , the main driver of cold gas-phase chemistry ensures that main molecules are deuterium-enriched. Another reason for higher HDO/H O is the preferential branching into OD + H when HDO is photodissociated (Shafer et al. 1989;Vander Wal et al. 1990, 1991).From our work, it is also theoretically possible to have high water deuterium fractionation from gas-phase photo-chemistry above 200 K.Deuterium enrichment can also occur at high temperature because of the energy difference in activation barrier for deuterium exchange andthe back reactions. Finally, water deuterium enrichment is not as stringent a constraint as thought for the origin of water on Earth. Deuterium- c (cid:13) , 1–17 igh HDO/H O in warm dense gas Figure 3.
Gas-phase H O and HDO abundance in the inner 3 AU computed by P RO D I M O . The left panels show the steady-state abundances while the rightpanels show the time-dependent abundances for a 1 Myr old disc. enriched water may have been synthesised at ∼ RO D I M O do not include effects of turbulent mixing in protoplanetary discs, both radial and vertical. WFT is supported by a Scottish Universities Physics Alliance (SUPA) fellowship in Astrobiology. We thank the referee for his/her comments. c (cid:13) , 1–17 W.-F. Thi et al.
Table 4.
Principal reactionsReaction A B E a Reference(cm s − ) (K) k O + H → OH + H 3.14 × − k OH + H → H O+ H 2.05 × − k H + D → HD + H 7.50 × − – 3820 Zhang & Millar 1989 k HD + H → H + D 7.50 × − – 4240 Zhang & Millar 1989 k O + HD → OD + H 1.57 × − k OH + D → OD + H 9.07 × − -0.63 – Yung et al. 1988 k OH + HD → HDO + H 0.60 × − k OD + H → HDO + H 1.55 × − γ Reference(s − ) J HD + h ν → H + D 2.6 × − J OH + h ν → O + H 3.5 × − Table 5.
Neutral-neutral and radical-neutral reactionsReaction A B E a Reference(cm s − ) (K) (K) R H + H + M → H – – – see text R H + D + M → HD – – – see text k O + H → OH + H 3.14 × − k O + H → OH + H 2.61 × − – 8156 UMIST k O + H → OH + OH 3.16 × − – 21890 UMIST k OH + H → O + H × − k OH + H → H O+ H 2.05 × − k OH + O → O + H 1.77 × − – -178 UMIST k OH + OH → O + H O 3.87 × − k H O + H → OH + H × − k H O+ O → OH + OH 1.85 × − k H + D → HD + H 7.50 × − – 3820 Zhang & Millar 1989 k HD + H → H + D 7.50 × − – 4240 Zhang & Millar 1989 k O + HD → OD + H 1.57 × − k OD + H → O + HD – – – k = k is assumed k O + HD → OH + D 9.01 × − k OH + D → O + HD – – – k = k is assumed k OH + D → OD + H 9.07 × − -0.63 – Yung et al. 1988 k OD + H → OH + D 1.26 × − -0.63 717 Yung et al. 1988 k OH + HD → H O + D 2.12 × − k H O + D → OH + HD – – – k = k is assumed k OH + HD → HDO + H 0.60 × − k HDO + H → OH + HD – – – k = 0 . × k is assumed k OD + H → HDO + H 1.55 × − k HDO + H → OD + H – – – k = 0 . × k is assumed k OD + O → O + D – – – k = k is assumed k O + D → OD + O – – – k = k is assumed k OD + OH → O + HDO – – – k = k is assumed k HDO + O → OD + OH – – – k = k is assumed k OH + CO → CO + H 1.17 × − k OH + C → CO + H 1.10 × − k CO + H → OH + C 1.10 × − k OD + CO → CO + D – – – k = k is assumed k OD + C → CO + D – – – k = k is assumed k CO + D → OD + C – – – k = k is assumedRef. UMIST: Woodall et al. (2007) c (cid:13) , 1–17 igh HDO/H O in warm dense gas Figure 4. [HDO]/[H O] in the 3 AU of a 10 − disc as computed by the photochemical code P RO D I M O . The contours indicate the regions where gas-phasewater abundance is 10 − and 10 − . REFERENCES
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Photodissociation and photoionisation reactionsReaction q γ Reference(s − ) J H + h ν → H + H 3.4 × − J HD + h ν → H + D 2.6 × − J CO + h ν → C + O 2.0 × − J OH + h ν → O + H 3.5 × − J OD + h ν → O + D 4.0 × − J H O + h ν → H + OH 5.9 × − J a HDO + h ν → OH + D – – J a = 0 . J , see text J b HDO + h ν → OD + H – – J b = 0 . J , see text J C + h ν → C + + e UMISTRef. UMIST: Woodall et al. (2007) Table 7.
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Figure 6.
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Cosmic-ray induced ionisation and recombination reactions ( ζ = 5 × − s − ).Reaction k Reference(cm s − ) k ζ, H + cr → H + + e − × ζ UMIST k ζ, D + cr → D + + e − × ζ UMIST k ζ, He + cr → He + + e − × ζ UMIST k ζ, H + cr → H + + H + e − × ζ UMIST k ζ, HD + cr → H + + D + e − – k ζ, = 0 . k ζ, is assumed k ζ, HD + cr → D + + H + e − – k ζ, = 0 . k ζ, is assumed k e − , H + + e − → H + h ν . × − ( T/ − . Prasad & Huntress (1980) k e − , D + + e − → D + h ν – k e − , = k e − , is assumed k e − , He + + e − → He + h ν . × − ( T/ − . Prasad & Huntress (1980) k cp, OH + CRPhot → O + H 1.3 × − (509 / (1 − w )) UMIST k cp, OD + CRPhot → O + D 1.3 × − (509 / (1 − w )) k cp, = k cp, is assumed k cp, H O + CRPhot → OH + H 1.3 × − (971 / (1 − w )) UMIST k cp, HDO + CRPhot → OD + H . × . × − (971 / (1 − w )) UMIST k cp, HDO + CRPhot → OH + D . × . × − (971 / (1 − w )) UMISTRef. UMIST: Woodall et al. (2007)
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