arXiv:1102.3972v1 [astro-ph.EP] 19 Feb 2011 eea hrcmns h utcmoeti only is component pro- dust of has the observations properties shortcomings: 2007, continuum the several dust Natta from inferring g., e. disks however, toplanetary (see, review), disks a of 1984; the for into Willking evolution insight & important and gave Lada and structure g., 1990) e. systems al. (see, et Ob- these 1980s Beckwith years from the 2007). to al. emission million back et dust few date Watson thermal 2006; a 2001, of than al. servations et less Haisch of encom- g., (e. typically timescales found and on and regions are star-forming star disperse in disks of stars chemi- Protoplanetary young processes passing corresponding the and evolution. into cal formation insight system is deeper planetary evolution a molecules. chemical complex to and and key physical simple their of creation Understanding the for ment a etdsraelyr fteinrds e . ie al. et Qi g., 2007). (e. X- al. disk and et inner Carmona the UV- of 2006; the layers surface in heated particularly ray temperatures considerably, dust differ and and gas can 2010), to the Carmona that broad g., e. suggest too (see, observations proper- are kinematics planet disk its features and the spectral and growth study dust dust disk with Also, the change formation. in to expected contained are mass ties total the of t. 0SlmnaR,Klun elntn61,NwZealan New 6012, Wellington Kelburn, Rd, Salamanca 30 Ltd., [email protected] rpittpstuigL using 2018 typeset 5, Preprint June version Draft rtpaeaydssaeantrladatv environ- active and natural a are disks Protoplanetary HMCLEOUINO RTPAEAYDSS–TEEFCSOF EFFECTS THE – DISKS PROTOPLANETARY OF EVOLUTION CHEMICAL 1 urn drs:Mtoooia evc fNwZealand New of Service Meteorological address: Current er n i-nrrdLEln msinsetaadcmaethese compare mo and chemical Astro spectra our emission for use line Database LTE We mid-infrared UMIST interactions. and du the near- gas-grain on detailed from hydrogen added molecular extracted have of effec is formation the chemistry the study We phase for winds. models disk different vertical when and mixing turbulent vertical ihosrain.W n htNH subseq and that th disk find affects the la We mixing from midplane turbulent emission diffusive cold observations. line that the the with show influencing in the we layers, find those hand, molecular We with other significantly. the abundances, increase On molecular surface the disk the influences in abundances OH h ikceityadtersligmlclrln msini iia man similar a in that headings: emission demonstrate line Subject We molecular included. resulting is mixing. the mixing and turbulent chemistry of disk inclusion the the by enhanced u eut hwta fH if that show results Our conside disks protoplanetary of evolution chemical the calculate We eateto srnm,Gaut colo cec,Kyoto Science, of School Graduate Astronomy, of Department 1. srpyisRsac ete colo ahmtc n Ph and Mathematics of School Centre, Research Astrophysics A INTRODUCTION T E tl mltajv 11/10/09 v. emulateapj style X srceity rtpaeaydss crto,aceindis accretion accretion, disks; protoplanetary astrochemistry; rrd lntr systems planetary frared: UBLN IIGADDS WINDS DISK AND MIXING TURBULENT 2 omto nwr risi ae nocnieain h H the consideration, into taken is grains warm on formation .Heinzeller D. .WlhadT .Millar J. T. and Walsh C. 3 rf eso ue5 2018 5, June version Draft CH , efs,B71N UK 1NN, BT7 Belfast, ≈ ABSTRACT 3 1% H C OH, d and 1 n .Nomura H. and 2 e . aete l 06 er ta.20) hysug- They H 2006). of al. as et abundances Geers well 2006; high as al. gest et 2010) (PAHs) Habert al. hydrocarbons g., (e. et aromatic Pontoppidan polycyclic complex 2008; 2008; Najita from & al. Carr et g., Salyk (e. wavelengths. molecules lines organic emission mid-infrared of simple from spectrum at rich spectroscopi- a disk show The to observations inner These 2009). used the al. been study et has Plas cally Telescope der al. van Space 2009; et Spitzer al. Pontoppidan et 2007; Brittain Carr Gemini/Phoenix 2008; g., (e. Keck/NIRSPEC, VLT/CRIRES example, and for using, .g,Njt ta.20,frarve) h 4 The radii review). at detected a been for has 2007, emission (see, line al. regions et CO planet-forming Najita warm the g., e. probe can hand, the of structure chemical disk. and enable physical inner to the proto- regions of of star-forming study direct regions nearby in inner the disks the observe planetary from to lines required emission (ALMA), reso- is (sub)mm Array 2007). construction, spectral Millimeter under Large and (Armitage currently Atacama spatial radii the most and of however, smaller lution sensitivity formation, much superior Planet at The occurs review). likely a for 2007, oainltastoso bnatmlclsi h outer the in molecules ( the abundant target of and transitions facilities res- rotational existing spatial of low sensitivity the and by olution limited is wavelengths (sub)mm at H ≥ er n i-nrrdosrain,o h other the on observations, mid-infrared and Near- h bevto fmlclrln msinfo disks from emission line molecular of observation The 2 0A)rgoso h ik(e,e . urye al. et Dutrey g., e. (see, disk the of regions AU) 50 n upu-otiigseisaegreatly are species sulphur-containing and nvriy yt 0-52 Japan 606-8502, Kyoto University, sc,QensUiest Belfast, University Queen’s ysics, hmsr Rt0)t hc we which to (Rate06) chemistry so h ikceia structure chemical disk the on ts ihrcn pte observations. Spitzer recent with e eut ognrt synthetic generate to results del tgan r dpe.Orgas- Our adopted. are grains st ikceityi h warm the in chemistry disk e ailaceinflwstrongly flow accretion radial igrda icu accretion, viscous radial ring ikwnsptnilyaffect potentially winds disk etyipoigagreement improving uently espriual affected. particularly yers e ota on when found that to ner ICU ACCRETION, VISCOUS 2 s ublne in- turbulence; ks; ,HN C HCN, O, 2 and O 2 H 2 n pro- and < AU, 1 . 7 µ m 2 Heinzeller et al. vide evidence that the disk supports an active chem- culated the effect of accretion along streamlines in steady istry. C2H2 and HCN have also been detected in absorp- 1+1-dimensional α-disk models for chemical networks tion towards IRS 46 and GV Tauri (Lahuis et al. 2006; containing more than 200 species. They found that the Gibb et al. 2007). A particularly interesting case is CO2, chemical evolution is influenced globally by the inward which has been reported to be abundant in the circum- accretion process, resulting in, e. g., enhanced methanol stellar disk of AA Tauri at 1.2 AU (Carr & Najita abundances in the inner disk. Ilgner et al. (2004) also 2008), in IRS46 (Lahuis et al.∼ 2006) and in several other studied vertical mixing using the diffusion approximation sources (e. g., Pontoppidan et al. 2010), but which is not and concluded that vertical mixing changes the abun- detected in the majority of sources observed by Spitzer. dances of the sulphur-bearing species. Their disk model, The recently launched Herschel Space Observatory and however, assumed the gas and dust temperatures were future space telescopes (e.g., the Space Infrared telescope coupled everywhere in the disk and ignored stellar irradi- for Cosmology and Astrophysics (SPICA) and the James ation processes. Semenov et al. (2006) investigated gas- Webb Space Telescope (JWST)) will enable the observa- phase CO abundances in a 2D disk model, allowing for tion of molecular line emission in the mid- to far-infrared radial and vertical mixing using a reduced chemical net- with unprecedented sensitivity and spectral resolution work of 250 species and 1150 chemical reactions, and find and will help address these controversial findings. the mixing processes strongly affect the CO abundances Due to increasing computational power, the theoreti- in the disk. Willacy et al. (2006) studied the effects of cal study of the physical and chemical evolution of pro- vertical diffusive mixing driven by turbulence and found toplanetary disks is entering its Golden Age. As a conse- that this can greatly affect the column density of vari- quence of the observational limitations in the pre-Spitzer ous molecules and increase the size of the intermediate, era, many numerical models focused only on the outer warm molecular layer in the disk. disk (e. g., Aikawa et al. 2002; Willacy 2007). With the In this study, we consider the effects of inward accre- launch of Spitzer, however, the chemistry of the inner tion motion and vertical turbulent mixing to investigate disk has increased in importance (e. g., Woods & Willacy to what extent the abundances of molecules such as H2O, 2009). Unfortunately, complete models, including the CO2 and CH3OH are affected in the inner disk. As an physical and chemical evolution of the gas and the dust alternative driving force for vertical transport, we inves- in the disk, coupled with a consistent treatment of the tigate the effect of upward disk winds on the disk chem- radiative transfer, is still beyond reach and several com- istry. Several kinds of disk wind models, such as mag- promises have to be made. netocentrifugally driven winds (e. g., Blandford & Payne One possibility is to ignore the chemical evolution 1982; Shu et al. 1994) and photoevaporation winds (e. g., and assume chemical equilibrium holds throughout the Shu et al. 1993) have been suggested thus far. Recently, disk to investigate the physical structure in detail Suzuki & Inutsuka (2009) studied disk winds driven by (e. g., Kamp & Dullemond 2004; Jonkheid et al. 2004). MHD turbulence in the inner disk and found that large- Pioneering work by Gorti & Hollenbach (2004) and scale channel flows develop most effectively at 1.5–2 disk Nomura & Millar (2005) combined a basic disk chemistry scale heights, i. e., approximately in those layers where with a self-consistent description of the density and tem- molecular line emission is generated. The disk model perature structure taking into account the gas thermal in our study is from Nomura & Millar (2005) including balance, the stellar irradiation and the dust grain prop- X-ray heating as described in Nomura et al. (2007) and erties. Recently, Woitke et al. (2009a) calculated radi- accounts for decoupling of the gas and dust tempera- ation thermo-chemical models of protoplanetary disks, tures in the disk surface due to stellar irradiation. We including frequency-dependent 2D dust continuum ra- use a large chemical network and allow for adsorption diative transfer, kinetic gas-phase and photochemistry, and desorption onto and from dust grains. We also cal- ice formation and non-LTE heating and cooling. These culate mid-IR dust continuum and molecular line emis- studies show, in accordance with the observations, that sion spectra assuming local thermodynamic equilibrium the stellar UV and X-ray irradiation increases the gas (LTE) and compare our results to recent observations. In temperature considerably in the surface layer of the disk, Section 2 we describe our model in detail. In Section 3, altering the disk chemistry drastically in this region. we present and discuss our results, before drawing our Converse to that described above, several authors in- final conclusions in Section 4. stead focused on combining the physical motion of mate- rial in the disk with time-dependent chemical network 2. MODEL calculations (e. g., Aikawa et al. 1999; Markwick et al. 2.1. Disk structure 2002; Ilgner et al. 2004; Nomura et al. 2009). Radial in- ward motion due to the viscous accretion and vertical Our physical disk model is from Nomura & Millar motion due to inherent turbulent mixing or disk winds (2005) with the addition of X-ray heating as described in have the potential to change the disk chemistry signifi- Nomura et al. (2007). They compute the physical struc- cantly, depending on the timescales of the transport pro- ture of a steady, axisymmetric protoplanetary disk sur- cesses. Molecules, initially frozen out on dust grains, can rounding a typical T Tauri star with mass M = 0.5M⊙, evaporate and increase the gas-phase abundances, pro- radius R = 2R⊙, effective temperature Teff = 4000K vided that accretion and vertical mixing is comparable and luminosity L =0.87L⊙. We adopt the α-disk model to, or faster than, the chemical reactions and the destruc- (Shakura & Sunyaev 1973) to obtain the surface density tion by incident stellar irradiation. First steps towards profile from an equation for angular momentum conser- including the accretion flow in the chemical network have vation (e. g., Pringle 1981, Eq. (3.9)). We assume an −8 −1 been carried out by Aikawa et al. (1999), Markwick et al. accretion rate of M˙ = 10 M⊙yr and a viscosity pa- (2002) and Ilgner et al. (2004). Nomura et al. (2009) cal- rameter of α =0.01. Chemical evolution of protoplanetary disks 3

We denote the radius in the cylindrical coordinate sys- (for details, see Nomura et al. 2007). tem with s to distinguish it from the radial distance from The mass density, gas temperature and dust temper- the central star, i. e., r = √s2 + z2, where z represents ature for our disk model are displayed in Figure 1, top, the height from the disk midplane. middle and bottom, respectively. A logarithmic spac- The disk is calculated between s =0.01 AU and 300 AU ing of the grid cells is adopted in radial direction, while in a 1 + 1-dimensional model, which corresponds to a to- the vertical structure is calculated on a linear grid. The −2 tal disk mass of 2.4 10 M⊙ for the values of α and M˙ number of grid cells used in this work is 35 30 for · 0.5 AU s 300AU and 0 z/s 0.8. While× this given above. The steady gas temperature and density ≤ ≤ ≤ ≤ distributions of the disk are obtained self-consistently by resolution is relatively coarse, its consequences for the iteratively solving the equations for hydrostatic equilib- line emission are limited due to the interpolation method rium in the vertical direction and local thermal balance during the line of sight integration (c. f., Section 2.7). between heating and cooling of gas. To solve the equation A more detailed description of the background theory for hydrostatic equilibrium (Nomura et al. 2007, Equa- and calculation of the disk physical model, along with tion (11)), the condition further references, is given in Nomura & Millar (2005), Nomura et al. (2007) and Walsh et al. (2010). +z∞ ρgas(s,z) dz =Σgas(s) (1) 2.2. Dust properties Z−z∞ −18 −3 The dust properties are important as they influence with ρgas(s,z∞) = 10 g cm is imposed the physical and chemical structure of the disk in several (Nomura & Millar 2005). The heating sources of ways. As the dominant source of opacity, they determine the gas are grain photoelectric heating by FUV pho- the dust temperature and the UV radiation field in the tons and X-ray heating by hydrogen ionization, while disk. They also affect the gas temperature, because pho- cooling occurs through gas-grain collisions and by line toelectric heating by UV photons is the dominant heating transitions (for details, see Nomura & Millar 2005, mechanism towards the disk surface. Further, the total Appendix A and Nomura et al. 2007). surface area of the dust grains influences the molecu- The dust temperature is computed assuming radia- lar hydrogen abundance through the H2 formation rates tive equilibrium between the absorption of stellar radia- on grains and determines the freeze-out rate of chemical tion and resulting thermal emission by the dust grains. species onto the grain mantle throughout the disk (see Viscous heating is only taken into account in the disk Section 2.4). Finally, due to their dominant contribution midplane since its effects in the disk surface are com- to the opacity, the dust grain model also determines the parably small for α = 0.01 (Glassgold et al. 2004). In emerging continuum spectrum. the midplane, the density is high and the gas and dust For consistency, we adopt the same dust grain model temperature are tightly coupled. Note that it is often for the spectral calculations as for the underlying pro- assumed that the gas temperature is coupled with the toplanetary disk (Nomura & Millar 2005). We assume dust temperature everywhere in the disk. This is not the dust grains to be compact and spherical, and to con- true in the disk surface which is strongly irradiated by sist of silicate grains, carbonaceous grains and water ice. the parent star. The dust temperature is calculated us- We further assume that the dust and the gas are well ing an iterative radiative transfer calculation by means mixed and that the gas-to-dust mass ratio is uniform of the short characteristic method in spherical coordi- (ρdust/ρgas = 0.01) in the disk. The size distribution is nates, with initial dust temperature profiles obtained taken from Weingartner & Draine (2001a) to reproduce from the variable Eddington factor method (see Nomura the observed extinction in dense clouds, with minimum 2002; Dullemond & Turolla 2000; Dullemond et al. 2002, and maximum sizes for the grains of 3.5 A˚ and 10 µm, for details). ∼ The stellar X-ray and UV radiation fields are based on respectively. The heating of PAHs is included in the spectral observations of TWHydrae, a classical TTauri model for photoelectric heating (Weingartner & Draine star. The X-ray spectrum is obtained by fitting a 2001b). For further details, see also Appendix D in two-temperature thin thermal plasma model to archival Nomura & Millar (2005). 30 −1 XMM-Newton data (mekal model, LX 10 ergs for 2.3. 0.1 keV ... 10 keV) and is slightly softer∼ than that of typ- Gas-phase reaction network ical TTauri stars with temperatures of about 2keV in For the calculation of the chemical evolution in the their quiescent phase (c. f., Wolk et al. 2005). The stellar disk, we use a subset of the UMIST Database for Astro- UV radiation field has three components: photospheric chemistry, or Rate06 (Woodall et al. 2007), neglecting blackbody radiation, hydrogenic thermal bremsstrahlung only those species, and thus reactions, containing flu- 31 −1 radiation and strong Ly α emission (LFUV 10 ergs orine and phosphorus (Walsh et al. 2010). Since we are for 6 eV ... 13 eV). The photochemistry used∼ in this pa- primarily interested in those regions where molecular line per is described in detail in Walsh et al. (2010). Note emission originates and where most molecules are in the that the scattering of Ly α emission by atomic hydrogen gas phase, we neglect grain-surface reactions excepting is not taken into account. On the other hand, the Ly α H2 grain formation (see Section 2.4). In summary, our emission does not affect the molecular abundances sig- gas-phase reaction network contains 375 atomic, molecu- nificantly when the dust grains are well mixed with the lar and ionic species, ranging from atomic hydrogen H to + gas (Fogel et al. 2011). We include the interstellar UV relatively complex molecules such as H3C9N with mass radiation field (Draine (1978) and van Dishoeck & Black m = 125u (see Table 1 for a list of species of particular (1982)), however, the interstellar UV and X-ray radia- interest in this study and their binding energies on dust tion fields are negligible compared to the central star grains). The reaction network consists of 4346 reactions 4 Heinzeller et al.

Fig. 1.— From top to bottom: Gas density, gas temperature and dust temperature for the full disk model (left) and for constant streamlines z/h of the viscous accretion (right), where h denotes the scale height of the disk at radius s. For the gas temperature, inlaid are the vertical profiles as function of z/s in the inner disk region. including 3957 two-body reactions, 214 photochemical mantle species, but allow for adsorption onto and des- reactions, 164 X-ray/cosmic-ray induced photoreactions orption from dust grains. Hence, except for atomic hy- and 11 reactions for direct cosmic-ray ionization. drogen, a particle that hits a dust grain can either detach without change or freeze out and remain in the icy grain 2.4. Gas-grain interactions mantle from where it may eventually evaporate. Atomic hydrogen forms H2, freezes out onto the grain mantle or The formation of molecular hydrogen on the surface evaporates without reaction. of dust grains is thought to be the most efficient means For the H2 grain formation rates, we consider two of forming H2 directly from atomic hydrogen. Except different models. In model A, we refer to early work for this process, we neglect grain-surface reactions of icy Chemical evolution of protoplanetary disks 5 by Gould & Salpeter (1963) and Hollenbach & Salpeter (1971), who derive a grain formation rate for imperfectly TABLE 1 Molecular binding energies Ebind[K] shaped grain surfaces of

bind gr 1 th 2 species E [K] reference n˙ (H2)A = nH vH (Tgas)ndustπ a αH 2 · h i H 350 (5) 1/2 H2 450 (5) −18 −1 Tgas = nH 2 10 s ntot . (2) CO2 2690 (3) · · 300K H2O 4820 (4)   CO 960 (1) th In Equation (2), vH (Tgas) is the thermal relative velocity OH 1260 (5) of hydrogen atoms, CH4 1080 (2) NH3 3080 (4) 8k T 1/2 HCN 4170 (2) th B gas CH3OH 2140 (5) vH (Tgas)= , (3) πmH C2H2 2400 (2)   SO2 3070 (5) 2 and ndustπ a the cross section of the dust grains per H2S 1800 (5) h i −10 2 unit volume, with ndust 6 10 ntot and a = References. — (1) Sandford & Allamondola (1988), (2) 4.84 10−12cm2 for the dust∼ grain· model adoptedh here.i Yamamoto et al. (1983), (3) Sandford & Allamondola (1990), (4) · Sandford & Allamondola (1993), (5) Hasegawa & Herbst (1993) Further, ntot and nH denote the total number density of hydrogen nuclei and the number density of atomic hydro- number density of all ice species (ntot = ngas + nice). In gen, respectively. The total number density of hydrogen the following, we summarize the expressions for the rate nuclei is calculated from the mass density, ρgas, using coefficients and we refer readers to Woitke et al. (2009a) ρ ρ for a detailed discussion. n = gas = gas , tot The adsorption rate for species k with mass mk and (1+4yHe)mH 1.4mH th thermal velocity vk is where yHe = 0.1 is the fractional elemental abundance ads 2 th of helium. Here, we neglect the mass contained in other, Rk = π a ndustαkvk , (8) less abundant elements. h i where we assume a sticking coefficient of unity for all Alternatively, in model B, the H2 grain formation is calculated according to Cazaux & Tielens (2002), species excepting hydrogen (c. f., αH in Equation (5)). The desorption rates are gr gr n˙ (H2) =n ˙ (H2) ε(Tdust) B A · Ebind 1 des, th osc k th 2 Rk = νk exp , (9) = nH vH (Tgas)ndustπ a αHε(Tdust) , (4) − T 2 · h i  dust  with several updates for the efficiency ε(T ) (Woitke des, cr des, th ζCR dust R = f70 KR , (10) 2009, private communication). The sticking coefficient, k k,70 K 5 10−17s−1 · αH, is taken from Hollenbach & McKee (1979), and ap- des, ph 2 ndust proximated to first order, i. e., Rk = π a YkFFUV . (11) h i nact 1 αH . (5) bind ≈ 1+0.4 (T + T )/100 K) The binding energies Ek [K], for the most important gas dust species are listed in Table 1. The vibrational frequency The model for adsorptionp of gaseous species onto dust of species k in the surface potential well is grains and desorption of ice species from dust grains 15 bind 1/2 is taken from Woitke et al. (2009a), who consider col- osc 3 10 kBEk νk = · 2 . (12) lisional adsorption together with thermal desorption, π mk cosmic-ray induced desorption and UV photodesorption.   We calculate the ice formation rates for all neutral and The expression for cosmic-ray induced desorption is negatively charged species k in our reaction network, adopted from Hasegawa & Herbst (1993), who evalu- ate the rate coefficient at a temperature of 70K with ads −19 n˙ k ice = nkRk (6) a duty cycle of the grains of f70 = 3.16 10 . The photo-desorption yields Y are simply set· to 10−3 per ndesorb Rdes, th + Rdes, cr + Rdes, ph , k − k ice · k k k UV photon (Westley et al. 1995). Finally, the cosmic   ray ionization rate ζCR and the FUV field FFUV in where nk ice denotes the number density of ice species k 2 desorb units [photons/cm /s] are calculated from the density and nk ice its fraction located in the uppermost surface desorb profile and the dust opacity adopted in the disk model layers of the ice mantle. This fraction nk ice is given by (Nomura et al. 2007). The calculation of the FUV field is (Aikawa et al. 1996) based on Nomura & Millar (2005, Equations (6) and (7)) nk ice nice

(see below for the calculation of these coefficients for the TABLE 2 different transport processes). The chemical evolution of Initial fractional abundances in the chemical network, including the entire disk is calculated in parallel for time steps that the gas and ice component of each satisfy the CFL condition and the transport coefficients species. are updated each iteration. This step is repeated until a 6 a total age of the disk of 10 yr is reached. species xk,0 In the following, we describe each process we consider H 2.00e-07 in this study. A detailed discussion of the numerical H+ 1.00e-10 methods used to compute the chemical evolution is given + H3 1.00e-08 in Appendix A. He+ 2.50e-11 He 1.00e-01 2.6.1. Radial transport by viscous accretion CH4 2.00e-07 NH3 1.00e-05 Firstly, we allow for the radial inward transport of H2O 1.00e-05 material through the disk via accretion. The main pa- C2H2 5.00e-07 rameter describing this effect is the accretion rate M˙ = Si 3.60e-08 −8 −1 N2 2.00e-05 10 M⊙yr , which relates the radial inflow velocity vs C2H4 1.00e-08 with the column density Σ at radius s, CO 5.00e-05 H2CO 4.00e-08 M˙ =2πsvsΣ (vs > 0 for radial inflow) . (14) CH3OH 5.00e-07 O2 1.00e-06 We assume that inward accretion occurs along stream- H2S 1.00e-06 √ 2 2 Fe+ 2.40e-08 lines l = s + z , with z/h = const. Here, h is the scale a height of the disk defined by h = cs/ΩK, cs is the sound The initial fractional abundance is de- speed at the disk midplane and Ω is the Keplerian an- fined as x = n /n . K k,0 k,0 tot gular frequency. abundances for each species nk,k ice,0 include both the ice We denote the net accretion rate of species k, i. e., the and the gas component. net change in its number density, withn ˙ k, acc. In steady ads state, the net accretion rate of species k can be written We compare the freeze-out timescale τk and evapo- des as (see Appendix A.1 for the numerical implementation) ration timescale τk for each species in a simple model to determine whether it exists initially as gas or ice only: ∂(An˜ kvl) n˙ k, acc = , (15) ads ads −1 des des −1 ∂l τk = Rk , τk = Rk . (13) where A˜ is a geometrical factor and corresponds to For τ ads < τ des, the species
is initially frozen
out, n = k k k ice ρi+1/ρi in (A2). The boundary conditions for the ac- nk,0 and nk = 0. Otherwise, it exists in the gas phase cretion process at the inner and outer disk radii are set only, nk = nk,0 and nk ice = 0. as follows: due to the purely inward motion, all ma- 2.6. terial that flows inwards from the innermost grid cell Physicochemical interactions: viscous accretion, is removed from the disk, whereas at the outer radius turbulent mixing and disk winds s = 300 AU, the accretion timescales become sufficiently Modeling the physicochemical interaction is the key long that we can safely assumen ˙ k, acc = 0 for all species. aspect of our study. Even with the steady increase in In Section 2.6.4, we compare the timescales for viscous computational power, this is still a challenging problem accretion with the chemical timescale and also with cor- which can only be overcome by massive parallel comput- responding values for the other physical processes con- ing and by accepting several simplifications. In the con- sidered here. text of a steady disk model, for example, it is a reasonable 2.6.2. Vertical transport by turbulent mixing assumption to describe the interaction between the disk physics and chemistry as a one-way process. Hence, we Although the mechanism is not yet fully clear, it is consider the influence of physical processes on the disk commonly understood that the source of viscosity in as- chemistry, but neglect the feedback of the chemistry on trophysical disks is turbulence. Hence, a sufficiently large the physical disk structure. viscosity, as is the case in our model (α = 0.01) implies Despite this simplification, the calculation of the disk’s that the effect of turbulent mixing is strong, particularly chemical evolution with interaction is still considerably in the inner disk region. While this turbulent mixing, more computationally expensive, the reason being that in principle, occurs in the radial and vertical directions, adjacent grid cells are chemically coupled through the ra- we ignore the radial turbulent motion and focus on the dial and vertical exchange of material. Accordingly, their vertical mass fluxes only. Furthermore, we assume that evolution must be calculated in parallel with integration the turbulent velocity is independent of the distance z time steps that can be shorter than the the time scale from the midplane and thus only a function of radius. of the chemical reaction network, due to the Courant- We calculate the mixing in a diffusion-type approach. Friedrichs-Lewy (CFL) condition (Courant et al. 1928) The diffusion coefficient is set as K = vz dz, where of the fluid (see Section 2.6.4). More precisely, to com- v = v = α′c , (16) pute the models with interaction, we adopt the following z z,mix s procedure: all grid cells are initialized at the starting in analogy to the expression for the turbulent velocity time with their initial conditions (Section 2.5) and the in a Shakura-Sunyaev disk model, where the turbulent transfer coefficients between the grid cells are evaluated viscosity is Chemical evolution of protoplanetary disks 7

factor κ = 10−3 in Equation (19) to reduce the wind ve- νturb = vturblturb = αcsh . (17) locities such that the dispersal time scales, Σ/(ρgasvz) (where Σ is the surface density of the disk), become We assume α′ = 10−3 to account for the turbulence in 106yr. The resulting wind profiles reproduce the re- vertical direction only. For our numerical model, the sults∼ of Suzuki & Inutsuka (2009) in the sense that the length scale dz corresponds to the vertical extent of the disk wind is most effective at 2 disk scale heights, grid cells ∆z h/30. The mixing timescales are dis- where the gas density and therefore∼ the gas pressure cussed in Section≈ 2.6.4. decreases steeply and any potential magnetic pressure The usual diffusion equation for species k (c.f., Equa- would become comparable with it. tion (3) in Willacy et al. 2006) reduces to The wind rates are calculated from the vertical con- tinuity equation for species k, using the wind velocity ∂ ∂(n /n ) n˙ = Kn k tot . (18) profile (Equation (19)): k, mix ∂z tot ∂z   ∂(n v ) n˙ = k z . (20) In Appendix A.2, we describe the numerical implemen- k, wind − ∂z tation of calculating the chemistry accounting for the The wind rates for the discrete grid of the disk are given mixing rates. in Appendix A.3. The boundary conditions are set at the disk midplane The boundary conditions are set as follows: since we and surface. Due to the symmetry with respect to the adopt small wind velocities so that the disk dispersal midplane, the net exchange rate at z = 0 is zero. Like- time becomes long enough, we can assume that the mass wise, we assume that there is no exchange of material loss is negligible at the midplane and thereforen ˙ k, wind = between the uppermost disk layer and any potential at- 0, whereas at the upper boundary, we simply allow all mosphere on top of it. material transported by the disk wind to be lost. 2.6.3. Vertical transport by disk winds 2.6.4. Timescales We consider vertical disk winds as an alternative de- The grid crossing times for the mass transport by vis- scription of the vertical motion in the chemical model cous accretion, turbulent mixing and disk winds are dis- of the disk. Contrary to turbulent mixing, which im- played in Figure 2. These are set by the CFL-condition plies upward and downward motion, the disk wind trans- for the discrete grid of our disk model: ports material upwards only (c. f. Figure 11(c) in Ap- ∆s ∆z ∆z pendix A.2). τacc = , τmix = , τwind = . We refer to the wind solutions of Suzuki & Inutsuka vs vz, mix vz, wind (2009) to describe the vertical disk wind in our protoplan- The radial and vertical size of the grid cells are given by etary disk model. They investigated disk winds driven by ∆s and ∆z, respectively, and depend on distance s from MHD turbulence in local three-dimensional MHD simu- the star. For reference, we display the accretion, mixing lations of stratified accretion disks and found that large- and wind velocities in Figure 2 (left panel). scale channel flows develop most effectively at 1.5–2 disk In the right panel of Figure 2, we also plot the timescale scale heights, where the magnetic pressure is comparable of photochemistry given by (Duley & Williams 1984): to the gas pressure (here, we refer to their model with initial plasma β = 106). The breakup of these channel 3 FFUV,ISRF τphotochem = 10 yr , (21) flows drives structured disk winds, which might play an · FFUV(s,z) essential role in the dynamical dispersal of protoplan- where FFUV,ISRF is the FUV photon flux of the interstel- etary disks. While Suzuki & Inutsuka (2009) perform lar radiation field. In the upper layers of the disk, the UV local three-dimensional simulations at radius s = 1 AU radiation field is strong and the timescale for the photo- which lead to quasi-periodic cycles of 5–10 rotations and chemistry is shorter than the dynamical timescales. Be- strong mass outflows, our disk model is steady and does low the transition layer, z/s / 0.2, the incident FUV ra- not allow for a dispersal of the disk. diation is highly attenuated and the chemical timescales We therefore adopt their solutions for the wind veloc- are controlled by two-body reactions, which are sensitive ityv ˆwind,0 at the midplane at 1 AU and calculate the ra- to the temperature and density. The chemical timescale dial and vertical profile according to Suzuki & Inutsuka in this region is generally longer than the photochemical (2009) and the vertical continuity equation in steady timescale for the interstellar radiation field, 103yr. The state, ∂(ρvz)/∂z = 0, accretion and mixing timescales become comparable to this limit at 0.5 and 10 AU, respectively. The disk wind cs(s) v0 = vwind(s,z =0) = κvˆwind,0 , timescales are longer than the chemical timescales for all · cs(1 AU) z/s for the entire disk in this model. ρ(s,z = 0) v = v (s,z)= v , (19) 2.7. Infrared molecular line spectra z wind 0 · ρ(s,z) Using the results of our chemical evolution calcula- wherev ˆ = 8.5 10−5c (1 AU) (Suzuki & Inutsuka tions, we compute emergent mid-infrared spectra from wind,0 · s 2009). For large values ofv ˆwind,0, the midplane layers the disk. We include the dust continuum, which is the disperse over timescales shorter than the typical disk dominant source of opacity in protoplanetary disks, along lifetime of 106yr, which contradicts the assumption of with molecular line emission and absorption, assuming a steady disk model. We therefore introduce an ad-hoc local thermodynamic equilibrium (LTE). 8 Heinzeller et al. Accretion, mixing and wind velocities Chemical and physical timescales τ photochem. accretion 105 107 mixing wind 103 104

101 1 [yr]

[cm/s] 10 τ v

10–1 10–2

10–3 10–5 100 101 102 100 101 102 s [AU] s [AU] Fig. 2.— Velocities (left) and timescales (right) for the transport processes of accretion (radial), mixing (vertical) and wind (vertical). Typical timescales of the photochemical reactions are also shown in the right panel (see text for details). Solid lines denote midplane values, i. e., z/s = 0, (accretion, mixing, wind), or the timescale of the photochemistry for the interstellar radiation field (photochem.), respectively. Dashed lines correspond to z/s = 0.2 and dotted-dashed lines to z/s = 0.5. The dust continuum opacities are taken from the emissivity and the line opacity, respectively. The Ein- Jena opacity tables, using routines contained within stein coefficients A and B are listed in the HITRAN the RATRAN package (Ossenkopf & Henning 1994; database or determined using the principle of detailed Hogerheijde & van der Tak 2000). In accordance with balance. The database also provides statistical weights the dust properties of the disk model, we use the ta- g and partition functions Q for a wide range of tempera- bles for spherical dust grains (parameter “e5” in the tures. We calculate Voigt profiles including natural line RATRAN routines) with thin ice coating (parameter broadening, pressure broadeningV and thermal broaden- “thin”). ing. A Doppler profile at a temperature, Tgas, is assumed The HITRAN’2004 molecular spectroscopic database for the thermal broadening. Turbulent broadening is ne- (Rothman et al. 2005) provides a large set of energy lev- glected, since it is negligible compared to thermal broad- els and line transitions in the infrared for 39 molecules, ening for subsonic turbulent velocities. The half-widths focussing on terrestrial atmospheric species. Neverthe- for natural broadening γn and pressure broadening γp less, the overlap of species of interest between the HI- are provided by the HITRAN database at a tempera- TRAN and UMIST databases is sufficient for our pur- ture of 296K. The temperature dependence of pressure poses. Since isotopes are not currently included in our broadening is approximated by chemical reaction network, we neglect spectroscopic in- formation for minor isotopes in the HITRAN database. 296K np The major issue concerning the calculation of line in- γp = γp(296 K) , (26) · Tgas tensities in the infrared is the limited availability of col-   lisional coefficients, in particular, for the large set of lev- where np is the temperature-dependent exponent in the els and transitions contained in the HITRAN database HITRAN database. (e. g., more than 180000 transitions for the main isotope We adopt a simple, one-dimensional line-of-sight inte- of CH4 for wavelengths between 1 and 40 µm). Since the gration to calculate the emergent disk spectra for a disk main purpose of this work is the calculation of the disk’s viewed face-on, i. e., with an inclination i = 0, relative to chemical evolution, a detailed non-LTE radiative transfer the observer. The radial resolution for the spectral calcu- calculation of the emergent spectra is beyond the scope lation is identical to the chemical model. Along each ray, of this paper. We therefore assume local thermal equilib- the intensity is integrated following the one-dimensional rium to model the line emission and absorption strengths equation of radiative transfer, accounting for the thermal for the species of interest. For a species k, the transition dust continuum emission and the molecular line emission, j i (E < E ) is calculated from the standard equa- → i j tions dI ′ ν = (ν′/ν)2 j κ I . (27) E dz ν − ν ν Q (T )= g exp k,i , (22) k gas k,i −T h i i gas Quantities on the right hand side of (27) are evaluated X   gk,i/j Ek,i/j in the moving frame of a fluid element of the observed nk,i/j = nk exp , (23) object, while those on the left hand side are given in the Q (T ) · − T ′ k gas  gas  rest frame of the observer (denoted with ). The observed frequency is given by ν′ = ν(1 + (v/c)cos θ), where v j = hνA n , (24) k,ij k,ji k,j Vk is the velocity of the fluid element and θ is the angle between the directions of the velocity and the observer. κ = hν(B n B n ) . (25) The emission and absorption coefficients are given by k,ij k,ij k,i − k,ji k,j Vk Here, n, j and κ denote the level populations, the line jν = jk,ij + κν,dustBν (Tdust) , (28) Xk EXi

κν = κk,ij + κν,dust , (29) photodestruction region, i. e., the surface layers of the

k Ei

Fig. 3.— Gas-phase fractional abundances of H2, CO, H2O and OH for models A and B. Chemical evolution of protoplanetary disks 11 tion signatures are generated at radii / 2 AU, where the tween the two states that fall into this wavelength range temperature increases near the midplane due to viscous have even higher critical densities. Hence, the conditions heating (c. f., the inlay in Figure 1). Since the abun- for LTE are partly violated and a proper non-LTE cal- dances of CO2 and H2O in model A are high near the culation of the disk spectra should be considered. In the disk midplane, but low in the disk surface where the gas following sections, we ignore the enhanced H2 formation temperature increases towards an observer, absorption rates of model B and study the effects of accretion, tur- lines rather than emission lines are generated. Emission bulent mixing and wind on model A only. or absorption from other molecules included in the spec- 3.2. Accretion, mixing, disk winds – single column tral calculation (e. g., NH3, CH4) is very weak in the spectrum. solutions Model B, on the other hand, produces a spectrum with To investigate the effects of including physicochemical enormous emission features from OH, H2O and CO. The interaction, we first focus on one vertical column of the CO2 absorption feature is not affected by the H2 forma- disk at radius s =1.3AU. Here, the temperatures of gas tion model, since it is destroyed very efficiently in the and dust are high enough, in particular in the upper lay- upper layers of the disk, where the main differences in ers of the disk, to allow for an active chemistry. Further, the molecular abundances arise between model A and near- and mid-infrared observations derive characteris- B. Comparing the two-dimensional abundances of OH, tic radii for molecular line emission around 1 AU (c. f., H2O and CO in model A and B (Figure 3) allows us Section 3.4). to constrain the origin of the emission lines to roughly In the following, we discuss in detail the modeled 3–20AU, where the gas temperature is high enough to molecular abundances for a number of species of interest. contribute to the total flux (c. f., Figure 1). Such strong For a better understanding, in particular for interpreting emission features are certainly in disagreement with ob- the resulting fractional abundances xk = nk/ntot, we servations. The enhanced formation rate of H2 on grains display the physical properties of the disk column at this from Cazaux & Tielens (2002) might simply produce too radius in Figure 6. The gas and dust temperatures are much H2 due to the choice of the variety of parameters tightly coupled in the dense midplane with values around used for this model, however, we should note here the 200 K. Hence, practically all species have desorbed from limitations of our simple dust model. Firstly, we assume the dust grains and the ice abundances are negligible. In that gas and dust are well mixed in the disk, with a the warm molecular layer (z 0.2 AU), the gas and dust ≈ constant mass density ratio of ρgas/ρdust 100. Numer- temperatures begin to decouple due to the lower den- ous studies show that dust grains will settle≈ towards the sity. In the photodestruction layer, the gas is heated up midplane instead of residing in the upper disk layers (see, to 4000 K because of the strong stellar irradiation, while e. g., Dominik et al. 2007, for a review). Less dust grains the dust temperature is around a factor of 10 lower. in these layers lead to lower H2 abundances and thus to In Figure 7, we plot the fractional abundances as a lower abundances of water and OH. Aikawa & Nomura function of vertical distance from the midplane for the (2006) demonstrated that less dust grains will also lead model without physicochemical interaction (model A) to a lower gas temperature at the disk surface, which and for models with either accretion, turbulent mixing reduces the line intensities. Since the same line of ar- or disk winds (models ACR, MIX, WND). The gas-phase gument applies to model A, it implies even lower abun- abundances are shown together with the – mostly neg- dances and thus weaker emission lines for H2O in this ligible – ice abundances. All four models make use of model. Secondly, the spectral calculations in our study the simple H2 formation rates on grains (Eq. (2)), while assume LTE level populations, which may overestimate model B (not displayed) includes the enhanced H2 for- the strength of the emission lines. Meijerink et al. (2009) mation rates on grains (Eq. (4)) without physicochemical studied the effects of non-LTE radiative transfer on the interaction. Table 3 at the end of this section compares molecular emission lines of water: they assume fractional the column densities of the most important species at −10 −4 H2O abundances between 10 and 10 throughout radius 1.3 AU for all models A, B, ACR, MIX, WND. In the disk. Interestingly, they conclude that a strong de- the following, we discuss in detail the effects of turbulent pletion at s < 1AU is required to account for observed mixing on the vertical chemical stratification at a radius emission line spectra, and such a depletion is found in s = 1.3 AU, since this model has the largest effects on our model A. There, the H2O abundance is low in the the chemical structure of the disk. surface layer, because of the efficient destruction of wa- 3.2.1. ter due to the stellar irradiation and the high tempera- Turbulent mixing ture. Most important, however, is that Meijerink et al. Turbulent mixing has important effects on the disk’s (2009) find drastic differences between LTE and non-LTE chemical composition, in particular in the upper layers. spectral calculations: the LTE calculations overestimate Generally, diffusive mixing tries to homogenize the frac- the strength of the emission lines by a factor of 10 for tional abundances of molecules over the depth of the disk. the strongest transitions (i. e., the largest Einstein coef- Figure 7 illustrates this effect, for example in the case of ficients). In model B, the line emission is generated in H2, the fractional abundances are slightly increased in the upper layers of the disk, where the gas number den- the transition region, with only negligible changes in the sity is of the order of 108cm−3. The water line transi- column density (c. f., Table 3 at the end of this section). tions between 10 and 40µm reported from Spitzer obser- This effect is more pronounced for CO2: in model A, vations (e. g., Carr & Najita 2008) are mainly rotational CO2 is abundant close to the midplane only, since it is transitions in the ground vibrational state and in the first removed from the upper layers by reactions with H and vibrational state with critical densities of 1012cm−3 or H+ and by photo-dissociation due to the incident UV larger (Meijerink et al. 2009). Vibrational transitions be- and X-ray radiation: 12 Heinzeller et al. Model A: column number densities Model B: column number densities H2 H2O 24 24 10 10 CO OH 1021 1021 ] ] -2 -2 1018 1018 [cm [cm N N 1015 1015

1012 1012 100 101 102 100 101 102

s [AU] s [AU] Fig. 4.— Column densities for the species of interest in models A and B. Solid lines correspond to gas-phase species, dashed lines to ices.

Fig. 5.— Emergent LTE disk spectra for models A and B for dust continuum and molecular line emission.

1014 104 MIX, CO2 diffuses upwards and its abundance is reduced near the midplane. n T tot gas The H2O, OH, and CO abundances are correlated with ]

-3 12

10 temperature that of molecular hydrogen and are enhanced in model MIX in the region where H2 is more abundant. The ef- [cm

tot fect of diffusion of H2O leads to reduced fractional abun- n 1010 103 dances for z < 0.15AU and increased abundances be-

T tween 0.15AU and 0.2 AU. Water is destroyed easily Tdust [K] at high temperatures and through photodissociation by 8 10 UV and X-ray photons. The H2O abundance has a dip at z 0.22 AU, where both the gas temperature and

number density ≈ 2 density are relatively low (c. f., Woitke et al. 2009b, Fig- 106 10 0.0 0.2 0.4 0.6 0.8 1.0 ure 1). Here, UV and X-ray photodestruction become strong, while at the same time the temperature is still too z [AU] low to activate the main formation reactions for H2O, Fig. 6.— Gas and dust temperature Tgas and T , and total dust H2 +O OH+H number density ntot as function of vertical distance from the disk −→ midplane at a radius s = 1.3 AU. OH+H H O + H . 2 −→ 2 H+CO CO+OH In the case of methane, diffusion also increases the frac- 2 −→ tional abundances in the surface layers. At the same H+ + CO HCO+ +O 2 −→ time, the formation of CH4 close to the midplane is effi- CO + γ CO+O cient enough to maintain its initial fractional abundance, 2 UV −→ CO2 + γX−ray CO+O . leading to an overall increase in the column density of −→ methane. For z 0.3 AU, methane is destroyed quickly At z 0.2 AU, the reactions with H+ and the X-ray by UV and X-ray≥ photons. photochemistry≈ are dominant, while in the upper layers, A similar mechanism is responsible for the considerable the UV photochemistry is most important. In model increase in ammonia for z 0.3 AU. The formation of ≤ Chemical evolution of protoplanetary disks 13

0 10 10–4 model A –6 10–1 model ACR 10 model MIX 10–8 –2 model WND tot tot 10 n n / / 2 2 10–10 H CO n –3 n = 10 2 =

2 –12 H 10 x CO 10–4 x 10–14

10–5 10–16 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8

z [AU] z [AU]

10–4 10–4

10–6 10–6

10–8 10–8 tot tot n n / /

O –10 –10 2 10 10 CO H n n = = –12 O 10–12 10 CO 2 x H x 10–14 10–14

10–16 10–16 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8

z [AU] z [AU]

–4 10–4 10

–6 10–6 10

–8 10–8 tot 10 n / 4 tot n / –10 –10 CH 10

10 n OH = 4 n

= –12 10–12 CH 10 x OH x –14 10–14 10

–16 10–16 10 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8

z [AU] z [AU]

–4 10–4 10 w/o reaction NH3 to CH3OH –6 10–6 10

–8 10–8

10 tot tot n / n / 3 10–10 10–10 HCN NH n n = = 3 10–12 10–12 NH HCN x x 10–14 10–14

10–16 10–16 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8

z [AU] z [AU] Fig. 7.— Fractional abundance profiles of gas-phase species (solid) and ices (dashed) as a function of vertical distance from the midplane at s = 1.3 AU in model A (black), and in models with accretion (ACR, blue), mixing (MIX, red) or disk winds (WND, green). 14 Heinzeller et al.

10–4 ammonia near the disk midplane is driven by a change w/o reaction NH3 to CH3OH in the oxygen chemistry, with O2 being overabundant in 10–6 model MIX (see also Section 3.3). The differences in the oxygen abundance between model A and model MIX is

tot –8 n 10 / caused by the continuous diffusion of O2 from the warm

OH molecular layer towards the midplane. This implies a de- 3 10–10 crease in the column density of HCN, whose formation CH n

= is competing with NH3 for the available nitrogen. Since 10–12

OH the number of nitrogen atoms over the full column is con- 3 served and since the formation of NH is more efficient, CH 10–14 3 x HCN is depleted by one order of magnitude close to the 10–16 midplane, compared with that in model A. Its column 0.0 0.2 0.4 0.6 0.8 density decreases by approximately the amount required z [AU] for the formation of the additional ammonia molecules. The most pronounced effect arises in the case of 10–4 methanol as a consequence of the increase in ammonia. w/o reactions CH3/NH3 to C2H2 Its fractional abundance increases for z 0.3 AU by one 10–6 to six orders of magnitude, resulting in a≤ column density of 1.2 1019cm−2 compared with 4.7 1017cm−2 in model –8

tot 10 · · n A. This is due to an enhanced production of CH3OH by / 2

H –10 the reaction (Rodgers & Charnley 2001) 2 10 C n + + =

2 –12 CH3OH2 + NH3 NH4 + CH3OH .

H 10 −→ 2

C In Figure 7, we display the ammonia and methanol abun- x 10–14 dances for an additional model calculation with diffusive mixing, but where this reaction is switched off. The am- 10–16 0.0 0.2 0.4 0.6 0.8 monia abundances remain unchanged, but the methanol abundances drop by one order of magnitude, which is z [AU] comparable to the midplane abundances in model A. Significant changes are also found for acetylene, C H . 10–4 2 2 At z = 0.2 AU, it is mainly produced from NH3 by the 10–6 reactions + + NH3 +C2H C2H2 + NH 10–8 3 4 tot + −→ + n / NH3 +C2H C2H2 + NH , 2 2 3 10–10 −→ SO n as well as by a reaction of C and CH3 at z < 0.2 AU, = 2 10–12 SO C+CH3 C2H2 + H . x −→ 10–14 Switching off these reactions leads to a significant de- crease in C2H2 (c. f., Figure 7). Hence, acetylene profits 10–16 0.0 0.2 0.4 0.6 0.8 from the increase in ammonia abundances and is over- abundant by two orders of magnitude at z 0.2 AU. ≤ z [AU] Higher up in the disk, it is destroyed efficiently by photo- chemical reactions and reactions with atomic hydrogen. –4 10 Finally, we inspect the sulphur-bearing species SO2 and H2S. Initially, sulphur is locked in H2S only, with 10–6 −6 a fractional abundance of 10 (c. f., Table 2). H2S is easily destroyed by atomic hydrogen due to the small ac- 10–8 tot tivation barrier of this reaction. Provided the O and n 2 / S 2 10–10 OH abundances are sufficiently high, this drives a chain H n of reactions (Charnley 1997; Millar et al. 1997) which = S 2 10–12 forces large amounts of H2S into SO2 in both models H x at z 0.25 AU. The now highly abundant SO2 near the 10–14 midplane≤ is destroyed on timescales longer than its for- mation timescales and therefore provides a steady reser- 10–16 0.0 0.2 0.4 0.6 0.8 voir to maintain the enhanced H2S abundances in com- parison to model A. At the midplane, the destruction of z [AU] H2S is less efficient, but still sufficient to produce OCS from CO and S (Hatchell et al. 1998). After 106yr, sul- Fig. 7.— (cont.) Gas and ice fract. abundances at s = 1.3 AU. phur is locked in SO2 and OCS in equal amounts. Contrarily, in model A, the formation of SO2 is ineffi- cient in the lower layers due to the missing OH and the missing O at z 0. Thus, the slower reaction path 2 ≈ Chemical evolution of protoplanetary disks 15 of S with CO is preferred and OCS is built up over the TABLE 3 lifetime of the disk, eventually locking all sulphur. − Calculated column densities N[cm 2] at radius 3.2.2. Disk winds s = 1.3 AU of selected species for the disk models considered in this study. The resulting chemical abundances for model WND are displayed in Figure 7. For all species, the effects of species A B ACR MIX WND the disk wind on the vertical stratification of the chem- H2 1.7e+25 1.7e+25 1.7e+25 1.7e+25 1.7e+25 ical species are much less pronounced than in the case CO2 2.5e+19 2.6e+19 2.5e+19 8.3e+18 2.4e+19 of turbulent mixing. In the cases of CO2, NH3, CH3OH H2O 4.2e+20 4.2e+20 4.0e+20 3.5e+20 4.2e+20 and C H , slight increases in the fractional abundances OH 1.5e+15 9.3e+15 1.5e+15 5.3e+15 1.8e+15 2 2 CO 1.6e+21 1.6e+21 1.6e+21 1.7e+21 1.6e+21 are found around z =0.2 AU, in particular where narrow CH4 5.4e+18 5.4e+18 6.5e+17 7.1e+18 5.7e+18 dips occur in the abundances from model A. Protected NH3 2.5e+20 2.5e+20 3.4e+20 3.0e+20 2.6e+20 by the upper layers against the UV and X-ray irradia- HCN 4.3e+19 3.8e+19 1.1e+19 4.7e+18 4.0e+19 tion, molecules transported upwards from the midplane CH3OH 4.7e+17 4.8e+17 1.4e+16 1.2e+19 5.6e+17 C2H2 1.6e+16 1.6e+16 1.3e+14 2.2e+18 1.6e+16 fill these sinks on timescales comparable to their removal SO2 2.7e+17 2.6e+17 1.2e+19 1.4e+19 2.9e+17 by chemical reactions. H2S 9.6e+14 8.3e+17 6.2e+15 2.8e+18 9.4e+14 The reason for the inefficiency of the disk wind lies in OCS 3.3e+19 3.2e+19 2.0e+19 1.6e+19 3.3e+19 the steady disk model assumption considered here: to avoid disk dispersal over the lifetime of the disk, which would contradict the steady state assumption, we in- troduced a scaling factor κ = 10−3 for the resulting wind speeds of Suzuki & Inutsuka (2009) at the midplane layer. Hence, the upward velocities near the midplane are low in model WND, compared to the turbulent velocities in model MIX (c. f., Figure 2). At radii s 10 AU, the ≤ wind velocities become very large in the photodestruc- On the contrary, NH3 shows higher abundances at z < tion region of the disk (z/s > 0.3), due to the continuity 0.15 AU. As discussed for the case of diffusive mixing equation in vertical direction in steady state. But there, above, the total amount of nitrogen atoms is conserved the timescales of the photochemistry are extremely short and determined by the initial abundances of N2 and NH3 so that the effect of the disk wind is small (c. f., Figure 2). (c. f., Table 2). An increase in the column density of NH3 For a scaling factor κ = 10−3, the midplane grid cell from 2.5 1020cm−2 in model A to 3.4 1020cm−2 in model at radius s = 1.3AU evaporates in about 2 105yr, cor- ACR leads· to a decrease in HCN from· 4.3 1019cm−2 to responding to a mass loss of 20% of the total· mass con- 1.1 1019cm−2 at this radius. · tained in this disk ring. Hence, in a stationary model, In· contrast to the results from model MIX, methanol κ should be lower than 10−3, which would lead to even shows lower abundances close to the disk midplane, de- less efficient disk winds. spite the increase in ammonia. Since its fractional abun- We thus conclude that in a steady disk model, the disk dance is even lower than those from model A, the reason, winds have only negligible effects. Due to the neces- therefore, is not only the lack of vertical diffusion, but the sary downscaling of the wind speeds by a factor of 1000 fact that the formation and evaporation timescales (from (κ = 10−3), the vertical mass transport becomes small dust grains) of methanol at around 10AU are longer than and causes only small changes in the disk’s chemical com- its destruction timescale (c. f., Section 3.3). The accre- position. Nonetheless, it is worth noting that in a time- tion flow propagates this depletion inwards over time. dependent physical disk model, where evaporation and Compared to model A, this reduces the CH3OH column dynamical refueling by the accretion flow are allowed, density from 4.7 1017cm−2 to 1.4 1016cm−2. the disk wind may become significant. The simple model One should bear· in mind that· the location of the considered here suggests that it will affect molecules that snow line for methanol and hence its gas-phase abun- also show an enhancement in the upper layers in the dif- dance is sensitive to its binding energy on dust grains, fusive mixing model (e. g., NH3, CH3OH). which varies across the literature. Here, we adopt the theoretical value from Hasegawa & Herbst (1993), 3.2.3. Viscous accretion Ebind = 2140 K. Sandford & Allamondola (1993) and The chemical abundances from model ACR at a radius more recently Brown & Bolina (2007) find much higher of 1.3 AU are displayed in Figure 7. As in the previous values between 4000 and 5000K based on the results cases, at the disk surface photochemistry dominates and of temperature-programmed desorption (TPD) experi- the accretion flow does not affect the chemical composi- ments on pure methanol ice. Higher binding energies tion. Close to the disk midplane, the accretion time scale would imply lower gas-phase abundances and a shift of is comparable to the chemical timescale and the effects the snow line to smaller radii. Here, the NH3 abundances of the radial inflow of material become visible. Whether are higher and the formation of methanol more efficient, the accretion flow leads to an increase or a decrease in which would imply higher gas-phase abundances within the abundance of a particular species depends on the the snow line. formation and destruction timescales of that species. In A similar decrease in the abundances in the innermost the case of H2O, for example, the chemical reactions are disk can be found particularly for C2H2, where the ac- fast enough to compensate for the effects of the accretion cretion flow removes a considerable fraction of acetylene flow and the abundances and column density are similar close to the midplane (c. f., Table 3 for the resulting col- to those from model A. umn densities of C2H2 and other species). 16 Heinzeller et al.

3.3. Accretion, mixing – full disk solutions monia is a result of a fundamental change in the oxy- In the previous section, we inspected in detail the gen chemistry. In model ACR and model MIX, atomic chemical abundances for the different disk models as a oxygen is reduced by orders of magnitude between 2 and function of height at a single radial position. The chemi- 10 AU, with an increase in O2 and a decrease in OH. The cal composition varies between the individual models due drastic decrease in atomic oxygen practically switches off to mass transport in the radial and vertical directions. the the main destruction reaction of NH3, The results thereby depend strongly on the species con- O + NH3 OH + NH2 . sidered, in particular, on its formation and destruction −→ timescales relative to the dynamical timescales. Since The overabundant regions are located below the warm these timescales vary with radial distance from the star molecular layer in model ACR and reach slightly into it for accretion, turbulent mixing and disk winds, we expect in model MIX (see also Figure 7). Hence, ammonia is significant changes in the effects of these mass transport found in absorption in the spectrum of model MIX due phenomena at different radial positions in the disk. to the same reasons as CO2 in model ACR. Here, we focus on the radial accretion and vertical mix- Another species of interest is methanol, whose gas- ing and neglect the disk wind. At a radius, s = 1.3 AU, phase abundance is high in regions where the ammonia the influence of the disk wind on the chemistry is small, abundances are high in all the models. In model MIX, compared with diffusive mixing, due to the low wind this implies an increase in methanol within 5 AU com- speed required to impede the evaporation of the disk pared to model A. Viscous accretion increases its abun- in our model. At larger radii, the wind velocities are dance between 2 and 5AU and decreases it further inside. even smaller, leading to longer timescales of the upward As in model MIX, CH3OH is produced efficiently from wind motion. At the same time, however, the chemical NH3, however, its gas-phase formation and evaporation timescales increase (c. f., Section 2.6.4), so that we do from dust grains at 5–10AU is slower than its destruc- not find significant changes to the disk chemistry due to tion and the accretion flow transports less material into the inclusion of a disk wind. the inner disk than is removed from it. Methanol is lo- We compare the resulting fractional gas-phase abun- cated below the transition region of the disk, even in dances and the gas and ice column densities for model model MIX, hence, the line opacities are so small that ACR and model MIX with model A in Figure 8. The the absorption features are negligible in the spectra. results for water differ only slightly between the mod- The abundance profile of acetylene can be explained els, and the only difference arises in a narrow stripe as follows: in model MIX, its abundance is increased be- z/s 0.2–0.4, where the gas-phase abundances of wa- tween 1 and 10 AU. Further inside, the diffusion leads to ≈ ter are increased in model MIX due to the enhanced H2 a depletion of C2H2. In model ACR, C2H2 is increased abundances (see also the discussion in Section 3.1). This between 2 and 10AU and decreased further inside, simi- leads to an increase in the gas-phase column density be- lar to CO2. Since the overall abundance of C2H2 is low tween 2 and 10 AU. Since the H2O abundances are in- and since it is located below the transition region, the creased in the transition layer, turbulent mixing affects absorption lines are negligibly small in the spectra of the the strength of the H2O line emission from the disk. This disks in model A and model ACR. The stark increase in can be seen in Figure 9, where we compare the emerging C2H2 in model MIX leads to a weak absorption feature disk spectra for model A, model ACR and model MIX. seen at 13–13.5µm (Figure 9). Apart from H2O, the species dominating the molecular line emission are CO and OH. Both show slightly stronger 3.4. Theory versus observations emission lines in model MIX and in model ACR, although We refer to the observations of the protoplanetary disks the effect is more pronounced in the case of diffusive mix- of AA Tauri (Carr & Najita 2008), DR Tauri and AS 205 ing. (Salyk et al. 2008). AA Tauri is a classical T Tauri star In the case of CO2, turbulent mixing reduces the gas- −8 −1 with mass 0.8M⊙, accretion rate 10 M⊙yr and incli- phase column density inside 10 AU: turbulent mixing nation 75◦ (Bouvier et al. 1999). Carr & Najita (2008) leads to the diffusion of CO from the lower, protected 2 observed the disk around AA Tauri with the Infrared layers into the upper disk, where it is efficiently destroyed Spectrograph (IRS) on the Spitzer Space Telescope over by incident radiation, compared with its production. For the wavelength range of 9.9–37.2µm. They found a rich radii 1 AU, CO is strongly depleted. Viscous accre- 2 spectrum of molecular emission lines dominated by ro- tion,≤ on the other hand, enhances the CO gas-phase 2 tational transitions of H O and OH. Between 10 and abundances at radii 1 AU due to a net inward transport 2 15µm, they detected ro-vibrational emission bands of from radii 10 AU.≤ This leads to changes in the disk C H , HCN and CO , plus the atomic [Ne II] transition spectra for≤ both models ACR and MIX: inside 2 AU, the 2 2 2 at 12.8µm. Fundamental ro-vibrational emission bands gas and dust temperature first decrease with increasing of CO have been detected in Keck/NIRSPEC observa- distance from the midplane (see Figure 1). This is due tions between 3 and 5µm. Fitting model spectra to the to the viscous heating near the midplane. Since CO is 2 observations, Carr & Najita (2008) derive a high column concentrated near the midplane and since it is abundant density for these species and characteristic emission radii in model ACR (depleted in model MIX), the absorption in the inner disk (s< 2.5 AU). feature at 15µm is enhanced (reduced). DRTauri and AS205, both classical TTauri stars, Ammonia shows the largest variations between the dif- have been observed with IRS on Spitzer and with ferent models. Compared to model A, model ACR and Keck/NIRSPEC by Salyk et al. (2008). DR Tauri has model MIX lead to a similar increase in the gas and ice a mass of 0.76M⊙ and a variable accretion rate of [0.3– abundances between 1 and 10AU. The increase in am- −7 −1 79] 10 M⊙yr , much higher than in our model or that · Chemical evolution of protoplanetary disks 17

Fig. 8.— Two-dimensional fractional gas-phase abundances and column densities (solid: gas; dashed: ice) of H2O and CO2 for model A (black), model ACR (blue) and model MIX (red). 18 Heinzeller et al.

Fig. 8.— (cont.) Two-dimensional fractional gas-phase abundances and column densities (solid: gas; dashed: ice) of NH3 and CH3OH for model A (black), model ACR (blue) and model MIX (red). Chemical evolution of protoplanetary disks 19

Fig. 8.— (cont.) Two-dimensional fractional gas-phase abundances and column densities (solid: gas; dashed: ice) of C2H2 for model A (black), model ACR (blue) and model MIX (red). observed in AA Tauri. AS 205 is the primary component and abundance ratios are derived from the photodestruc- of a triple system with mass 1.2M⊙ and accretion rate tion layer and the warm molecular layer, i. e., from the −7 −1 ◦ 7.2 10 M⊙yr . The inclinations are 67 for DR Tauri disk surface down to an optical depth of about unity. and· 47◦ for AS205A, respectively. Both systems show The total molecular column densities in our model are a large number of transitional emission lines from water mainly determined by the dense midplane layers and are and require high temperatures and column densities to therefore larger by orders of magnitude and not compa- explain this emission, similar to AA Tauri. Further, CO, rable to the observed column densities. Thus, we cal- OH and CO2 are required to fit the observed spectra in culate the column densities of the observed species from the near- to mid-infrared. In the following, we discuss the disk surface down to a continuum optical depth of how our models relate to, and compare with, these ob- unity at each wavelength and compare them to the ob- servational results. servations (Figure 10). At s = 1.3 AU and wavelengths The calculated spectra for our models show emission λ = 5, 10, 20, 40 µm, the disk becomes optically thick and absorption features different from the observed spec- at z/s{ = 0.14, 0}.15, 0.14, 0.11 , respectively. For the tra (Figure 9). Firstly, the molecular line emission in unusually strong{ OH lines, a continuum} optical depth of our models is dominated by rotational transitions of OH. unity corresponds to a maximum optical depth of τ 20 ∼ Weak emission from H2O is detected in model MIX. In (see discussion below for large discrepancy between the model ACR and in model A, water is found mainly in ab- models and the observations of OH lines). For all other sorption. Model WND leads to results similar to model molecules, the maximum optical depth of the lines is A due to the limitations of our disk model. These mod- τ 2. ∼ els make use of the simple H2 formation rates on grains, If we compare the H2O and CO column densities of the Eq. (2). Model B, which accounts for the enhanced H2 upper layers at disk radius 1.3 AU, we find an abundance formation rates on grains, Eq. (4), leads to huge emis- ratio of 0.02 for model A and model ACR, while model sion lines from OH and H2O. The near-infrared emission MIX shows an abundance ratio of 0.18. Carr & Najita bands of CO at 5µm are reproduced in model A, model (2008) derive an abundance ratio of H2O to CO of 1.3, MIX and also in model ACR. while Salyk et al. (2008) find water to be less abundant The modeled line intensities depend strongly on the gas than carbon monoxide with an abundance ratio for H2O temperature and molecular abundances profiles, i. e., the to CO of 0.1 for both systems. Note that Carr & Najita detailed thermal balance and the chemistry. It is there- (2008) calculate the abundance ratio for different radii of fore more favorable to compare the molecular column the H2O and CO column densities (2.1AU and 0.7 AU), densities from our model calculations to the observed while Salyk et al. (2008) obtain their results for the same ones. In the inner disk, the observed column densities radius (3 AU). It is important to note that the ob- 20 Heinzeller et al.

Fig. 9.— LTE line spectra for model A, model ACR and model MIX for an observer at inclination i = 0. For model MIX, we also show the spectrum normalized by the continuum flux in the lower right panel (for a better illustration, the color coding in the normalized spectrum is different from the other spectra and listed in lower right legend). served systems differ from our model in their central ob- UV radiation, efficient turbulent mixing can increase the jects, disk masses, inclination angles and accretion rates, abundances in the upper layers of the disk (c. f., Fig- with AA Tauri being the closest match. Further, the ure 10). derived column densities in Carr & Najita (2008) and CO2 is found in absorption instead of in emission in Salyk et al. (2008) contain considerable uncertainties in model A, model ACR and model MIX. The absorption their values and their characteristic radii. is strongest in model ACR and weakest in model MIX. The resulting column densities of the upper disk lay- Contrary to this, the observations detect CO2 in emission ers are displayed in Figure 10 for model A and for model at a characteristic radius of 1.2 AU in AA Tauri. It is MIX only, since it leads to the largest changes in the ver- also detected in emission towards DRTauri and AS205 tical distribution of the chemical species. In model MIX, (with large uncertainties on the column densities and the the H2O to CO abundance ratio is of the order of 0.2 emission radii). The column densities derived from the inside the snow line, while in model A, it is reduced by observations of AA Tauri are lower than in model A and at least a factor of 10. Model MIX reproduces the H2O model MIX, although the latter one gives a better fit. abundance in AA Tauri at a radius of 2.1 AU. In the Since CO2 is destroyed quickly in the upper layers of the case of DRTauri and AS205, the central star is more lu- disk, stronger mixing will lead to lower CO2 abundances. minous than in AA Tauri and in our model, hence, the HCN is detected in weak emission in AA Tauri snow line is located further outwards and gas-phase H2O and a number of other sources (see, for example, remains abundant with derived column densities of the Pontoppidan et al. 2010), but not detected in our mod- same order as in our model or in AATauri at radii of eled spectra. The column density in AA Tauri is slightly 2 AU. The modeled CO abundances agree with the ob- higher than in our models, and model MIX again gives a servations for both models. Both models fail to repro- better fit. Turbulent mixing increases the column density duce the high OH abundances, although the calculated in the upper layers, although the total column density is line emission is much stronger than that of the observa- reduced. Stronger mixing will help to improve the fit of tions. This adds further support to the call for non-LTE the model calculations to the observations. spectral calculations and gas temperature profile calcula- In the case of C2H2, the characteristic radius in tions accounting for dust-grain settling and grain growth AA Tauri could not be determined and was set to that (c. f., Section 3.1). Since the binding energy of OH on derived for HCN. Assuming that the C2H2 emission is lo- dust grains is low and considering it is robust against cated at larger radii (e. g., 1 AU instead of 0.6 AU), model Chemical evolution of protoplanetary disks 21

Column densities of the upper disk layers In addition, the observed objects have inclination an- gles of 67◦ for DR Tauri and 47◦ for AS 205A, while our theoretical spectra are calculated for a disk seen face-on. 1019 This affects the observed line emission and the derived column densities, since the chemical composition is differ-

] ent along the line of sight. Robust conclusions therefore -2 1017 require spectral calculations accounting for the different inclination angles. = 1) [cm τ ( 15 4. CONCLUSION

N 10 We studied the chemical evolution of a steady proto- planetary disk, investigating different models for the for- mation rate of H on dust grains and the effects of includ- 1013 2 100 101 102 ing viscous accretion, turbulent mixing and disk winds. 1019 Using our chemical results, we calculated the emergent s near- and mid-infrared spectrum from the disk, includ- ing contributions from the dust continuum and molecular 1017 line emission. ]

-2 Our results show that the abundances of water and the hydroxyl radical are very sensitive to the H2 for- 1015 mation rates on grains, with the resulting spectra dif-

= 1) [cm fering considerably. The enhanced H2 formation rates of τ ( Cazaux & Tielens (2002) lead to a drastic increase in the N 1013 gas-phase abundances of water and OH in the upper disk layers and to strong emission lines. We concluded that dust grain settlement towards the midplane and non-LTE 1011 calculations of the molecular line emission are required 100 101 102 to obtain meaningful results for models using these en- s [AU] hanced H2 formation rates. We investigated the effects of physical mass transport CO HCN AA Tauri phenomena in the radial direction by viscous accretion H2O C2H2 DR Tauri and in the vertical direction by diffusive turbulent mix- OH CO AS 205 ing and disk winds. Due to the steady state assump- 2 tion of the underlying protoplanetary disk model, the Fig. 10.— Column densities of the gas-phase species in the upper wind velocities are limited to impede the evaporation of layers in model A (dashed) and model MIX (dotted). The derived column densities for AA Tauri, DR Tauri and AS 205 are indicated the disk over its lifetime and consequently, the effects at their characteristic radii (Carr & Najita 2008; Salyk et al. 2008). of the disk winds on the chemistry are small. On the contrary, vertical diffusive mixing has a considerable im- MIX fits the observed column density, while model A pact on the disk chemistry and increases the abundance predicts much lower values. Adversely, the spectrum of of many observed species in the warm molecular layer model MIX shows C2H2 in weak absorption instead of of the disk. Species which are produced efficiently in a emission. From the previous discussion in Sections 3.2 particular layer and which are stable in lower (or up- and 3.3, we can assume that stronger turbulence will per) layers can experience a significant enhancement due transport C2H2 higher up in the disk, leading to emis- to the diffusive motion. Including the radial accretion sion instead of absorption signatures. flow in the chemical network calculation leads to large The abundances of NH3 are enhanced in model MIX, changes in the chemical composition of the disk, particu- leading to absorption signatures in the spectrum between larly in the cold and dense midplane layer. The effect of 8 and 13µm. To date, there has been no published detec- the accretion flow on a particular species depends on the tion of ammonia from protoplanetary disks, but NH3 has accretion timescale and the formation and destruction been found in absorption towards the hot core associated timescales of that species. For example, inside 10 AU, with the massive protostar NGC7538IRS1 (Knez et al. the gas-phase water abundances are not overly affected 2009), using the Texas Echelon Cross Echelle Spectro- by the accretion flow, while ammonia is greatly enhanced graph (TEXES). Observing NH3 emission from disks and methanol, greatly depleted. with high resolution and high sensitivity will allow us Since the accretion flow affects mainly the midplane to draw important conclusions on the efficiency of tur- layers, the infrared molecular line emission is basically bulent mixing in protoplanetary disks. unchanged. Contrarily, turbulent mixing alters the Taking into account the model uncertainties, e. g. the chemical composition of the warm molecular layer, where H2 formation rates on grains, the gas temperature pro- the molecular line emission is generated. We thus con- files (which are related to the dust model adopted, e. g., trasted two models with and without turbulent mixing to the dust growth and settling), as well as the uncertain- to observations of protoplanetary disks around classical ties in deriving molecular column densities and charac- TTauri stars. We compared the modeled disk spectra teristic radii from the observations, further investigations and column densities of the upper layers of the disk to are needed to strengthen the significance of our results. the observed spectra and the derived column densities. 22 Heinzeller et al.

In summary, a model with turbulent mixing repro- duces the observations of AA Tauri, DR Tauri and AS 205 better than a model without mixing, although the dis- cussion of the column densities in the upper layers and of the spectra suggests a more efficient vertical mass transport mechanism. In the models considered here, turbulent mixing provides an efficient way of transport- ing material from the midplane into the transition layer. Due to the constant mixing velocity in each vertical col- umn, the turbulent timescales become longer than the chemical timescales at larger distances from the mid- plane. But these are the layers where the disk winds studied by Suzuki & Inutsuka (2009) become most effec- tive (the transition layer coincides roughly with 1.5 disk scale heights) and drive large-scale channel flows. Hence, a combination of turbulence in the cold midplane layers and disk winds in the transition layer, both generated by the magneto-rotational instability, might account for the observations better than turbulent mixing or disk winds alone. In the latter case, the steady state assumption would have to be abandoned to allow for stronger disk winds. An interesting aspect for future studies will be the com- bination of radial and vertical transport processes. In this work, we showed that the radial accretion flow al- ters predominantly the midplane abundances, while tur- bulent mixing affects the midplane and warm molecular layers. We therefore expect that a combination of ra- dial and vertical motion will have a strong impact on the chemical abundances in the molecular layer, which will be reflected in the emission line spectrum.

The authors would like to thank Dr. Inutsuka and Dr. Suzuki from Nagoya University for providing the data of their MHD simulations and for useful discussions. DH and HN were supported by the Grant-in-Aid for the Global COE Program “The Next Generation of Physics, Spun from Universality and Emergence” from the Min- istry of Education, Culture, Sports, Science and Technol- ogy (MEXT) of Japan. DH received further support from the Kyoto University Startup Grants, and HN from the Grant-in-Aid for Scientific Research 2174 0137, MEXT. CW acknowledges DEL for a studentship and JSPS for the award of a short-term fellowship to conduct research in Japan. Astrophysics at QUB is supported by a grant from the STFC. The numerical calculations were carried out on Al- tix3700 BX2 at the Yukawa Institute for Theoretical Physics, Kyoto University, and on the Cray XT4C at the Center for Computational Astrophysics, National Astro- nomical Observatory of Japan. Chemical evolution of protoplanetary disks 23

Fig. 11.— Schematic view of (a) accretion, (b) mixing and (c) wind modeling in our model.

APPENDIX A. PHYSICOCHEMICAL INTERACTIONS – NUMERICS Modeling the physical mass transport phenomena in combination with calculating the chemical evolution is the key aspect of this study. Here, we discuss in detail the numerical techniques used to compute the chemistry accounting for transport mechanisms in relation to the grid of our protoplanetary disk model. The general expression for the rate of change in the abundance of gas-phase species k in grid cell (i, j) at radius si and vertical distance zj from the midplane is given by ∆ni,j n˙ i,j = k = P i,j Li,j n˙ i,j +n ˙ i,j , (A1) k ∆t k − k − k ice k, acc/mix/wind where Pk and Lk denote the production and loss terms due to gas-phase chemical reactions,n ˙ k ice the adsorp- tion/desorption rate (> 0 for net freeze-out, < 0 for net evaporation) andn ˙ k, acc/mix/wind the rates arising from mass transport due to accretion, mixing or disk winds. In the case of molecular hydrogen, an additional (positive) termn ˙ H2 is added to the right-hand side to account for the H2 formation on grains. Accordingly, in the case of atomic hydrogen, an additional term 2n ˙ is required. − H2 A.1 Radial transport by viscous accretion We assume that inward accretion occurs along constant streamlines z/h. (see Figure 11(a) for an illustration of the coupling between the grid cells at different radii). The net accretion rate along constant streamlines is given in Equation (15), where the differentiation with respect to l needs to be translated into a differentiation with respect to s. Accordingly, on the discrete grid of the disk model, the net accretion rate for cell (i, j) can be expressed as

i,i+1 i+1,j1,j2 i,j v¯s i,j ρ˜ i+1,j1,j2 n˙ k, acc = i nk + i,j n˜k (A2) ∆s (− ρ ) whereρ ˜ andn ˜ represent the average mass and number density of the outer grid cells, weighed by their relative mass i,i+1 transfer into cell (i, j). The accretion velocityv ¯s is evaluated at the interface between the grid cells i and i +1 1 2 and is introduced to improve the accuracy of the finite calculation. The additional factorρ ˜i+1,j ,j /ρi,j arises from the i,j i+1,j1,j2 requirement of mass conservation. In the context of a steady disk model, all variables except nk andn ˜k are constant with time.

A.2 Vertical transport by turbulent mixing Figure 11(b) demonstrates the grid-cell mass transfer by turbulent mixing in the diffusion-type model. Starting from Equation (18), we replace the differentials by finite differences over the vertical extent ∆z of the grid cells. Additionally, we introduce mean densitiesρ ¯ and velocitiesv ¯ at the interface of the grid cells as before. The exchange rates of species k between grid cell (i, j) and the adjacent grid cells (i, j 1) and (i, j + 1) then become − ρ¯i,j−1,j v¯i,j−1,j ρi,j−1 ρ¯i,j,j+1 v¯i,j,j+1 ρi,j n˙ i,j = z ni,j−1 ni,j + z ni,j+1 ni,j . (A3) k, mix ρi,j−1 · ∆zi,j · k − ρi,j k ρi,j · ∆zi,j · ρi,j+1 k − k     A.3 Vertical transport by disk winds The model of the upward disk wind is shown in Figure 11(c). In the finite case, the differential equation for the wind rate (Equation (20)) of grid cell (i, j) translates into vi,j−1,j vi,j,j+1 n˙ i,j = z ni,j−1 z ni,j . (A4) k, wind ∆zi,j · k − ∆zi,j k

In both the wind and the mixing scenarios, the only variable changing with time is nk. 24 Heinzeller et al.

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