Chemical reactions and dust destructionin protoplanetary accretion disks

F. Finocchi1, I. Bauer2, H.-P. Gail1 and J. P. Schloder2

1 Institut fur Theoretische Astrophysik, Universitat Heidelberg, Tiergartenstraße 15, 69121 Heidelberg, Germany2 Interdisziplinares Zentrum fur Wissenschaftliches Rechnen der Universitat Heidelberg, Im Neuenheimer Feld 368

69120 Heidelberg, Germany

Abstract

A nonequilibrium calculation for the chemistry in a classical protoplanetary accretion disk ispresented. Slow radial particle transport moves a mixture of gas and dust grains from the cold (30 K)outer regions of a protoplanetary accretion disk into its warm (3000 K) central part where the dustgrains are destroyed. We consider the destruction processes for the troilite, silicate and carbon dustcomponent and follow the chemical composition of the gas as a function of the radial distance fromthe protostar. The main result of this calculation is that huge amounts of methane and ammoniaare formed at a distance of ∼ 1 AU1 from the protostar. Methane is a product of the destruction ofcarbon dust and ammonia forms as a direct consequence of the destruction of the nitrogen moleculesby ionisation processes due to the decay of radionuclides.

The simulation of chemical reactions and dust destruction, as in the case of an accretion disk,requires to solve a large and stiff system of differential or differential-algebraic equations. For theintegration of such systems implicit methods are required. We use an efficient BDF-code (DAESOL)which turned out to be more robust and much faster than the more conventional code often used inastrochemistry.

1 Introduction

It is generally believed that stars form by gravitational collapse of a slowly rotating molecular cloudcore from interstellar matter. During such a collapse centrifugal forces prevent the material from fallingdirectly into the stellar embryo but instead a highly flattened configuration is formed: a protostellar disk.The early protostar grows within 104 yr through rapid accretion of material out of the disk by viscousforces associated with turbulent motions. There is observational evidence that the formation of suchaccretion disks around newly formed stars is quite common [5].

In the late stages of the star formation process the disk has become geometrically thin, contains onlya few percent of the mass of the newly born star, and the remaining material only very slowly driftsinwards and enters the star. This phase lasts for at least 1 Myr.

Formation of planetary companions of the star may occur during this phase by a process which startswith agglomeration of micron sized dust grains into millimeter to centimeter sized particles and whichends up after going through a hierarchy of accumulation processes with bodies of planetary size [20].This process probably requires a few times 0.1 Myr. We call such a disk, then, a protoplanetary accretiondisk (cf. Fig. 1). Presently we do not know how often star formation is accompanied by the formationof a planetary system but we do know that this happened to occur at least in the case of our own SolarSystem and there are some observational hints that this is quite a normal event for solar like stars.

The matter falling during the first phase of stellar formation from the molecular cloud onto theprotostellar disk passes a strong shock standing on the surface of the disk close to the star. The infallingmaterial is strongly processed by shock heating in this case. In the protoplanetary phase, however, thecircumstellar region is cleared from material and the feeding of the disk by infalling material has nearlyceased. The material forming the accretion disk in this phase has passed at most only a weak accretionshock far from the star and is likely to be nearly unprocessed material from the molecular cloud.

This material continues to move inwards by the action of viscous forces associated with turbulentmotions in the disk, like in the formation stage of the star, but with a much reduced accretion rate. Asthe material slowly enters into hotter and denser regions of the disk a rich zoo of chemical processesstarts to operate. These chemical processes (e.g. molecule and dust reactions) play an important rolefor the structure and evolution of protoplanetary accretion disks. Chemical reactions together withdust formation and destruction processes on the one hand determine the abundance of the absorbers

11AU(astronomical unit)= 1.5 · 108 km. This is the distance of the earth from the sun

1

Figure 1: Principle structure of a protoplanetary accretion disk. It consists of a flat, thin disk of rapidlyrotating gas mainly H (90%) and He (≈ 10%) with a small admixture of molecules from all otherelements (≈ 0.1% by number) and an admixture of ≈ 1% (by mass) of small (≈ 0.1µm) dust particles.The protosun at the centre has a dimension of ≈ 0.03 AU!

and, thus, the opacity of the mixture of gas and dust, and the gas temperature. Temperature changesdue to opacity changes on the other hand influence the rates of the chemical processes and the furtherchemical evolution of the system. This interplay between chemistry, opacity and temperature is of crucialimportance and decides about the stability or instability of the disk, i.e., decides whether a disk mayexist at all. Currently, certain limit cycle instabilities depending on the composition of the matter areunder discussion as possible causes for the luminosity variations of certain classes of variable stars (FUOri stars) suspected to be surrounded by protoplanetary disks.

We determine the chemistry of such a protoplanetary accretion disk by simulating the reaction kineticsin the gas phase and the destruction processes for dust. This leads to a stiff and highly nonlinear systemof differential algebraic equations. For the solution of the system we use the integrator DAESOL (e.g.[6, 15, 2]), a multistep BDF-method with variable coefficients. DAESOL is not only suited for the solutionof ordinary differential equations but also for linear implicit index 1 differential-algebraic equations of thefollowing type

A(t, y, z)y = f(t, y, z)

0 = g(t, y, z) .

Emphasis is laid on the error and stepsize control, based on true variable grid formulas, allowing theorder and step size to change in every step. We describe efficient monitoring strategies that reducethe computational effort for evaluation and decomposition of the Jacobian matrix, used in the implicitmultistep-method. Compared to the code DDRIV3 [19] which is widely used in astrochemistry and alsobased on BDF-formulas with variable coefficients, but with different strategies in error estimation andorder and step size control, simulation showed that DAESOL is not only more robust but also muchfaster [3].

2 Model assumptions for the disk and the chemistry

2.1 Gas phase chemistry

The evolution of the number density ni of each species i is determined by the continuity equation

∂tni + ∂~x(ni~v) = Ri (1)

(~v: gas velocity). Turbulent diffusion in a viscous accretion disk, though probably important for radialand vertical mixing of the disk material, is not yet taken into account. In the present model calculation

2

the continuity equation is solved in a comoving frame for an observer moving inwards with the averageradial inflow velocity of the gas. For this choice the set of rate equations reduces to a system of ordinarydifferential equations.

For the rate coefficients Ri we take into account binary reactions between gas phase species, someternary reactions to allow for H2 formation in the denser parts of the disk, and surface reactions withdust particles to allow for dust particle destruction and growth. The corresponding rate coefficients forthe gas phase reactions are

Ri =∑j,l

kijlnjnl and Ri =∑j,l,m

kijlmnjnlnm . (2)

The rate coefficients for gas phase reactions are approximated by the standard Arrhenius form

k = AT β exp (−T0/T ) . (3)

Currently, we consider neutral-neutral and neutral–ion reactions of ≈ 150 atomic and molecular species ofthe most abundant elements H, C, N, O, S and Si, and ≈ 1200 chemical reactions between these species.The reaction network includes many ionised species and a lot of ion-molecule reactions. The chemicalnetwork for the neutral species of the elements H, C, N and O is nearly identical with that given in [23].Several rate coefficients have been updated using data from [4]. The ion–molecule reactions, part of thesilicon chemistry and the sulfur chemistry are from [22]. The silicon chemistry has been completed withthe reactions from [9].

Additional rate terms account for the injection of molecules into the gas phase when the ice mantleson the dust grains evaporate at a temperature of approximately 150 K and the dust particles themselvesdisappear between 1000 K (carbon dust) and 2000 K (silicate dust) by chemical sputtering or thermaldecomposition.

2.2 Evaporation of ice mantles and dust grains

In order to investigate the evaporation of ice mantles and the destruction of dust particles we use thefollowing model:

a) At distances beyond the present position of Jupiter the temperature in the protoplanetary disk isvery low and all molecular species are frozen out, especially H2O and CO, except for the very volatilesH2, He and N2. Less abundant species like CH3OH or NH3 are frozen into the ice mantles [24] and areliberated during their vaporization. Presently they are not considered in the calculation. We assume thatthe dust grains are coated by an outer mantle of CO ice and an inner mantle of H2O ice. This neglectsthat some of the CO is bound into the H2O ice [25]. The rate of injection of such molecules during thevaporization process is included in the rate terms Ri in eq. (1)

b) We assume that there exist three dust components: olivine, carbon dust and some troilite (FeS).Some additional but less abundant dust components like the Al-Ca-silicates are presently neglected.According to [21] all Si initially is bound in olivine and 70 % of the carbon is bound in carbon dust (withthe remaining 30 % in the gas phase as CO). Since the thermodynamical properties of olivine seem notto be known we treat this dust component as Mg2SiO4.

c) Troilite is the first dust component which is destroyed in the slowly heating matter. It decomposesthermally at ≈ 700 K and mainly injects atomic Fe and S into the gas phase. A small amount of FeSmolecules also evaporates from the surface but we neglect this.

Evaporation of carbon at ≈ 1500 K would inject Ci molecules (mainly with i = 1, 2, 3) into the gasphase. These undergo further reactions until they finally are transformed into CO. The correspondingreactions are part of our reaction network and the details are discussed in [3]. It turned out, however,that vaporization is not important since carbon oxidation (see sect. 2.3) occurs already at a temperatureof about 1000 K.

Silicate dust is destroyed by thermal decomposition above ≈ 1650 K. This mainly adds SiO, O, andMg to the gas phase. Details of our treatment of evaporation of silicate dust particles are given in [14].

d) We assume a size distribution of the ensemble of dust particles ∝ a− 52 (a: particle radius) as derived

by Mathis et al. [21]. This does not agree well with the absorption properties of dust in star formingregions, where small particles seem to be much less abundant than in the Mathis–Rumpl–Nordsieckmodel (e.g. [10]). The strong coupling between dust absorption and disk structure during the silicate

3

vaporization depends, however, only on the disappearance of the large grains (see [14]). The troiliteparticles don’t provide a significant contribution to the total opacity. For this reason we assume thatthey all have the same radius.

e) The process of evaporation of ice mantles and of dust is modeled by calculating the change of radiusof the ice layers and of the dust particles, taking properly into account the size distribution of dust grains[3].

2.3 Oxidation of carbon dust

The carbon dust can be eroded by chemical reactions with molecules from the gas phase. From flamechemistry it is known that the most efficient processes are oxidation by oxygen bearing molecular species,especially by OH and O2 (see [17]). However the most promising process in the protoplanetary disk isoxidation by OH radicals and O atoms because O2 does not exist with a significant abundance in thisextremely hydrogen rich environment.

The essential first reaction step in the oxidation of carbon by OH according to [17] is

sootN+2 + OH→ sootN + HCCO (4)

which releases two carbon atoms from the solid. The ketyl radical HCCO then reacts in the gas phaseaccording to

HCCO + H→ CH2 + CO . (5)

This converts one of the two carbon atoms immediately into CO. The subsequent reactions of the CH2

radical are described later.The assumed oxidation process of solid carbon with free O atoms is (see [28]):

sootN+1 + O→ sootN + CO . (6)

CO is directly injected into the gas phase.

2.4 Ionisation processes

Two sources of ionisation are present in the protoplanetary disk. One source is the ever present cosmicradiation. This penetrates into matter no more than up to a depth corresponding roughly to 200 g·cm−2.The minimum surface density Σ of the protoplanetary disk from which our planetary system has formedwas at least 2500 g·cm−2 at the present position of the earth. Cosmic rays, therefore, are not an importantsource of ionisation in the inner part of the accretion disk. They may, however, be important for thechemistry in the outer parts of the disk where Σ is much less. The ionisation rates of the cosmic rays isgiven, e.g., in [13].

A second source of ionisation are the extinct radio nuclides, i.e. unstable nuclides with half lifes ofthe order of 0.1 to 100 Myr which have all decayed since the formation of our planetary system 4.8 Gyrago. Such nuclei have been present in the early solar system as we know from studies of the isotopiccomposition of pristine material from our solar system found in certain meteorites [26, 29]. The mostimportant source of ionisation by such extinct radio nuclides was the decay of 26Al. The ionisation rateby 26Al is determined in [27].

The ionisation processes are important for the chemistry in the protoplanetary disk since they brakestrong bonds like that of N2 and open reaction channels for the formation of compounds which areotherwise absent from the system.

2.5 The disk structure

Currently we describe the structure of the protoplanetary disk by a semi-analytical model in the approx-imation of a thin, viscous accretion disk. In this approximation all physical quantities are replaced eitherby averages with respect to the vertical variation of such a quantity or by its value in the central planeof the disk. The central plane pressure P , the central plane temperature T , the vertical thickness h ofthe disk, its average viscosity ν and inward drift velocity vs are given in this approximation by [14]

P = 71.65 s−5120

(M

M¯

) 58

(M−7κ)18µ−

12

[ g

cm s2

](7)

4

T = 997 s−910

(M

M¯

) 14

(M−7κ)14 [K] (8)

ν = 2.867.1014 s35 M−7

[cm2

s

](9)

h = 1.446.1012 s2120

(M

M¯

)− 38

(M−7κ)18µ−

12 [cm] (10)

vs = 26.94 s−25 M−7

[cm

s

]. (11)

The symbols have the following meanings: s is the radial distance from the accreting object in AU, M isthe mass of the central accreting object (the Protosun), M¯ is the solar mass, M−7 is the accretion ratein units of 10−7M¯·yr−1, κ is the mass absorption coefficient and µ is the mean molecular weight. Thenumbers correspond to an assumed surface mass density of 2500 g·cm−2 at 1 AU; we assume M−7 = 1.

2.6 Opacity

The dust opacity is calculated simultaneously with the chemical composition of the gas, the destructionprocesses for the dust grains, and the disk structure. The mass absorption coefficient of the silicate andcarbon dust component is calculated from the dust absorption model given by Draine [11, 12] using Mietheory and the size distribution of interstellar dust grains as derived by Mathis et al. [21].

For simplicity, we currently assume that the mass absorption coefficient of the gas component isconstant and equals its typical value of 0.01 cm2·g−1 for the pressure and temperature conditions in thedust free zone of the disk.

The mass absorption coefficient of the gas dust mixture is much higher, approximately 1 cm2·g−1.The presence of the dust component, thus, has a decisive influence on the structure of the disk, especiallyon its central plane temperature.

2.7 Initial conditions

We prescribe initial conditions for the chemistry at a distance s = 30 AU and solve the equations (1)for the particle densities, the disk structure, and the abundance and opacity of grains from this pointinwards. The initial composition of the gas phase is assumed to be: 10−5 of the hydrogen as free atoms,the remaining fraction not bound into molecules is H2, all nitrogen is in N2. All carbon not bound in dustparticles is in CO and all oxygen not bound in CO or dust is in H2O. CO and H2O are frozen out as icemantles on the dust particles. Less abundant species may be present in the gas phase, in the dust grainsor in their ice mantles (see [24]), but these are neglected because they are unlikely to be of significantimportance for the chemistry in the warm inner regions of the disk. All the available sulfur is supposedto be bound in troilite (FeS). We use solar system abundances as given in [1].

We follow the chemical evolution in a gas element which moves from the initial radius inwards towardsthe center of the disk with velocity vs. During this slow inward drift the temperature and pressure bothincrease resulting in changes in the chemical composition of the gas phase and of the amounts of ices anddust present. The temperature is calculated at every time step self-consistently taking into account thecalculated dust opacity and an approximation for the gas opacity.

3 The method of integration

Modeling the reaction kinetics and the destruction processes for dust leads to a system of DifferentialAlgebraic Equations (DAE). With the temperature varying from a few K to 2000 K or more the ordinarydifferential equation system is very stiff and coupled to highly nonlinear equations for the disk structureand the opacity.

For the integration of the system we use the multistep variable order BDF-method DAESOL (for amore detailed description of the implementations in DAESOL see, e.g., [3]). The code DAESOL solvesinitial value problems for systems of DAEs of index 1 of the following type:

A(t, y, z) y = f(t, y, z)0 = g(t, y, z) .

(12)

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3.1 Backward Differentiation Formulae

BDF-methods are multistep-methods, based on polynomial interpolation of the last, already computedvalues. In step n+ 1 the actual value for the solution is implicitly defined by a polynomial interpolatingthe computed solution at the last k time points tn, . . . , tn+1−k. The idea is to approximate the unknownderivative y(tn+1) by the derivative of the interpolating polynomial at time tn+1:

Pn+1(tn+1) =: − 1

h

k∑i=0

αiyn+1−i = y(tn+1) . (13)

Inserting the derivative of the polynomial into (13) results in

0 = A(tn+1, yn+1, zn+1)k∑i=0

αiyn+1−i +

h f(tn+1, yn+1, zn+1)

0 = g(tn+1, yn+1, zn+1) .

(14)

This set of nonlinear equations defines implicitly the unknown values (yn+1, zn+1) and has to be solvedby an iterative method, e.g., a variant of Newton’s method, which has been proved good for stiff systems.

Solving the nonlinear system (14) via Newton iteration requires a starting guess (y(0)n+1, z

(0)n+1). This is

obtained by evaluating a polynomial, which interpolates the last, already given k + 1 values of y and z,at time tn+1.

The polynomials interpolating and extrapolating the actual value are stored by so-called modifieddivided differences

∇0yn+1 = yn+1 (15)

∇iyn+1 =∇i−1yn+1 −∇i−1yn

tn+1 − tn+1−i.

This reduces the expense of updating and storing the coefficients from step to step.

3.2 Error estimation and stepsize control

Because the global error is not easily accessible, error control of integration methods is based on estimatesof the local error. In contrast to other solvers the error estimates in DAESOL take explicitely into accountthe variability of the grid.

3.2.1 Error estimation

The local error of a discretisation method is defined by the difference between the exact solution of thedifferential equation inserted into the difference equation and the solution itself. In a BDF-method oforder k in step n+ 1 we choose an estimate for the local error

Ek(n+ 1) = hn+1 · (tn+1 − tn) · . . . · (tn+1 − tn+1−k)

· (‖∇k+1yn+1‖+ (tn+1 − tn+1−k) · ‖∇k+2yn+1‖) .(16)

After every step we check whether the so estimated error is less than a user-prescribed tolerance TOL.The error in the next step of integration depends on the one hand on the discretisation of the BDF-

method and on the other hand on evaluating only an approximate solution. The first one is the mainpart of the error and in the following we will only take this one into consideration.

With the error in step n+ 1 estimated by (16), the accumulated error in step n+ 2 is approximatedas

Ek(n+ 2) = hn+2 · (tn+2 − tn+1) · . . . · (tn+2 − tn+2−k)

6

·[‖∇k+1yn+1‖ +

(tn+2 − tn−k+1 + tn+2 − tn−k) · ‖∇k+2yn+1‖].

(17)

3.2.2 Step size and order selection

The step size should be determined such that

Ek(n+ 2) ≤ TOL.

Because it is very difficult to estimate a new step size from formula (17), first a simplified error formulais used:

The analogue to formula (17) on equidistant grids is

Ek(n+ 2) := k!hk+1‖∇k+1yn+1‖ .

With Ek(n+ 2) ≤ TOL , e.g. TOL = 12TOL, one obtains a first guess for the new step size h. It should

also fulfill the more precise non-equidistant error formula (17):

Ek(n+ 2) = (18)

h2 · (h+ tn+1 − tn) · . . . · (h+ tn+1 − tn+2−k)

·[‖∇k+1yn+1‖+

(2h+ tn+1 − tn−k+1 + tn+1 − tn−k) · ‖∇k+2yn+1‖]

≤ TOL.

If that is true, the step size is accepted, otherwise it will be reduced using formula (18) (see also Bock etal. [8]).

The order and step size control with step size selection based on variable grids and released orderleads to more reliability and on an average to less rejected steps, which was also shown by Bleser [6] forthe examples of STIFF DETEST [16].

3.3 Solution of the nonlinear system - monitoring strategy

Inserting the BDF-formulas in (12) results in a nonlinear system of equations (14) which defines implicitlythe unknown values xn+1 := (yn+1, zn+1).

We define (14) shortly as

F (xn+1) = 0, with xn+1 = (yn+1, zn+1) .

A Newton-step is given by

x(m+1)n+1 = x

(m)n+1 + ∆x

(m+1)n+1

whereas ∆x(m+1)n+1 solves the linear system of equations

J(x(m)n+1) ·∆x(m+1)

n+1 = −F (x(m)n+1),

with

J(x(m)n+1) =

(Fy Fzgy gz

),

the Jacobian of F , and Fy and Fz are defined as

Fy = α0A+Ay

k∑i=1

αiyn+1−i + h fy (19)

Fz = Az

k∑i=1

αiyn+1−i + h fz (20)

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For many applications, especially when the system is large or the functions of the DAE are verycomplex, evaluation and decomposition of the Jacobian J takes most part of time of the integration. Ingeneral the Jacobian J changes very little during the Newton iteration and even during several steps ofintegration. In order to save computing time, it is advisable to keep the decomposition of J frozen aslong as possible.

In the following we describe a monitoring-strategy that is designed to reduce the total computationaleffort for the integration.

Convergence of Newton-like methods hold on the following assumptions (e.g., [7]):

Let J = ∂F∂x be the Jacobian of F and J−1

the approximate inverse of J . For all τ ∈[0, 1] and all m there are bounds ω and κsuch that

‖J−1(xm+1)(J(xm)− J(xm − τ∆xm)) ·∆xm‖≤ ωmτ‖∆xm‖2, ωm ≤ ω <∞

‖J−1(xm+1)(F (xm)− J(xm)J−1(xm)F (xm))‖≤ κm‖∆xm‖, κm ≤ κ < 1

and the starting point of the iteration has tofulfill

δ0 :=ω0

2‖∆x0‖+ κ0 < 1 . (21)

Then the iteration converges with

‖∆xm+1‖ ≤ (ωm

2‖∆xm‖+ κm)‖∆xm‖

≤ ‖∆xm‖

and for the m-th iterated there is an a prioriestimate

‖xm − x∗‖ ≤ ‖∆x0‖ δm01− δ0

. (22)

ω denotes the nonlinearity of the Jacobian J and κ is a measure for the quality of the approximate inverseJ−1.

We require that maximal three Newton-iterations should be taken in order to reduce the error of thepredictor sufficiently, e.g.,

‖xm − x∗‖ ≤ ‖∆x0‖ δm01− δ0

≤ 1

12‖∆x0‖ .

After two Newton-iterations we get an estimate for the convergence ratio

δ0 =‖∆x(1)‖‖∆x(0)‖

and may decide whether to perform an additional Newton-step or not. If the ratio δ0 is less than 14 , the

Newton-iteration is regarded as convergent, if the ratio is less than 13 , it is regarded as convergent after

one further iteration. Otherwise the Newton-iteration failed to converge.A poor convergence ratio respectively no convergence may have different reasons:

• a big change of the coefficients αi of the BDF-method and of the step size h

• a big change of the matrices ∂f∂x , ∂A

∂x or ∂g∂x

• the predicted starting value for the Newton-method is not sufficiently close to the solution

8

Figure 2: Run of molecular abundances in the accretion disk in the region of dust destruction.

In the first two cases the approximation of J is too inaccurate. The convergence of the Newton-iterationslows down or the computed search direction for the solution is wrong. The Jacobian J has to be (partly)reevaluated and decomposed anew.

In the last case the starting point for the Newton-iteration does not lie in the domain of local conver-gence. The BDF-step has to be repeated with reduced step size.

This principle strategy is realized in DAESOL in the following way:

1) As long as‖∆x1‖‖∆x0‖ ≤ δ, e.g., δ = 1

3 , the decomposition of J is frozen.

2) If the convergence ratio is too poor, keep the matrices ∂f∂x , ∂A∂x and ∂g

∂x frozen but decompose J anewwith actual BDF-coefficients αi and actual stepsize h.

3) If J is still too inaccurate, reevaluate the matrices ∂f∂x , ∂A

∂x and ∂g∂x and decompose J anew.

4) If there is still no convergence repeat the step with reduced step size.

In most solvers step 2) is omitted. But experience showed that it results in one third to one half evaluationsof the matrices ∂f

∂x , ∂A∂x and ∂g

∂x .The step size reduction in DAESOL after a failure of the Newton-convergence is also based on estimates

on variable grids and the step size is not only decreased, e.g., by a constant factor as in other codes.The step size is reduced such that the Newton-method of the next step converges after two (or three)iterations. This is achieved using the above given error estimation (18).

9

Figure 3: Run of molecular abundances in the innermost region of the protoplanetary accretion diskwhere molecular dissociation occurs.

4 Results and interpretation

We present in this section the most significant chemical processes operating in our accretion disk model.For a complete description see [18].

Figure 2 shows the chemical composition of the gas phase in the disk’s central plane in the radial rangewhere the carbon and silicate dust is destroyed. At larger radii (not shown here) first CO ice evaporatesat ≈ 21 AU where T ≈ 30 K, and then water ice evaporates at ≈ 8 AU where T ≈ 150 K. The first dustcomponent to be destroyed is troilite. Between 2 and 1 AU (T ≈ 700 K) the sulfur injected into the gasphase rapidly reacts with the molecular hydrogen and produces H2S by the following reaction sequence

S+H2←→ HS

+H2−→ H2S

Between 1 and 0.5 AU, in the temperature regime between T ≈ 1 000 and ≈ 1 300 K (see Fig. 4), thecarbon is oxidised by OH radicals and atomic O resulting ultimately in an increase of the CO abundancein the gas phase and a corresponding decrease of the water steam abundance. In principle, the carbonis destroyed in the protostellar disk by the process of water gas production which converts carbon intoCO and H2. The first steps of this process are the two reactions (4) and (5). The CH2 resulting from

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reaction (5) reacts with molecular hydrogen to form CH3 and CH4

CH2 + H2 ↔ CH3 + H , CH3 + H2 ↔ CH4 + H .

From several possible reaction paths from this to CO, the most efficient one in the protoplanetary diskaccording to the results of our model calculation is the condensation reaction

CH3 + CH3 → C2H4 + H2 (23)

followed by

C2H4+H←→ C2H3

+H−→ C2H2+H←→ C2H

+OH−→ CO + CH2

This sequence of reactions converts the second carbon atom released in reaction (4) into CO. The inter-mediate products CH4 and CH3 accumulate to considerable abundances in the gas phase (cf. Fig. 2)since reaction (23) becomes fast only if the abundance of CH3 has increased to a significant level. Thisdelays the conversion of the second carbon atom into CO to a temperature where already most of thecarbon is gasified.

The ionisation processes have a decisive influence on the nitrogen chemistry. At the outer edge of thedisk about 50% of the nitrogen molecules are dissociated into N and N+ according to the reaction

N2 + He+ −→ N+ + N + He . (24)

The He+ results from cosmic ray ionisations or ionisation following nuclear decays (Al 26). The N+ ionsreact in the gas phase with H2 and form the molecular ions NHi

+ (i=1, . . . ,4). These recombine withelectrons and finally form ammonia. The large amounts of HCN found in our model calculation are dueto a reaction between NH2 and the ion C+

NH2 + C+ −→ HCN+ + H . (25)

The main pathway to neutral HCN is a charge transfer reaction between HCN+ and water. The C+ ionsalso are the result of cosmic ray ionisation and decay of 26Al. If there are no ionisation processes the N2

entering the protoplanetary disk from the molecular cloud cannot be broken up until the material entersthe innermost and hottest part of the disk where N2 is thermally dissociated. The formation of largeamounts of NH3 and HCN would be impossible in this case.

Between 0.5 and 0.1 AU corresponding to the temperature regime T ≈ 1 650 . . . 2 100 K the olivinedust evaporates. This injects the decomposition products Mg, SiO, and O into the gas phase. SiO isdissociated at a much higher temperature by collisions with H2 and H. In our current calculations Si andMg remain unchanged in the gas phase because no reactions of these species are taken into account. Theoxygen released by silicate decomposition is rapidly converted into H2O.

HCN, NH3 and H2S react fast with oxygen bearing molecules and, thus, all disappear as the olivineparticles start to vaporize. HCN is converted into CO

HCN + O −→ CO + NH , (26)

ammonia reacts with OHNH3 + OH −→ NH2 + H2O , (27)

and H2S reacts in a more complex reaction sequence to SO2

H2S+OH←→ HS

+O−→ SO+OH←→ SO2 .

Figure 3 shows an enlargement of the inner part of the disk where a huge number of new molecularspecies occurs, especially carbon compounds. This is due to the fact that some of the carbon is liberatedby CO dissociation. Most of the molecules dissociate in the inner part of the disk at s < 0.06 AU.Dissociation of molecular hydrogen occurs at s ≈ 0.09 AU. Close to the center of the disk only the freeatoms H, C, N, O, S, Fe, Mg, and Si remain.

As a direct consequence of the oxidation process of carbon dust by OH and of the ionisation of N2,we obtain a huge concentration of methane, ammonia and cyanide in the disk in the region between 1.4and 0.8 AU i.e. where the terrestrial planets are presently located. The earth is just in the middle partof this region. This means that the earth has formed in an environment where huge amounts of these

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Figure 4: Radial run of midplane temperature in the accretion disk. The full line shows the result of themodel calculation. The dotted line shows, for comparison, the run of temperature in a model withoutdust.

precursors of organic compounds were present. We expect that a large variety of more complex organicmolecules are formed in this region as well, but such molecules are not yet implemented in the presentsimulation. The carbon dust oxidation by HCCO formation in the surface reaction (4) is the key processleading to these huge amounts of methane. A calculation which omits the oxidation and the ionisationprocesses leads to formation of small amounts of methane and organics only [3].

It is interesting to compare the central plane temperature for two models with and without dustopacities, see Fig. 4. The dotted line corresponds to a model without dust opacity (i.e. only with anestimated gas extinction coefficient of 0.01 cm2·g−1). The temperature in a model with dust opacity (fullline in Fig. 4) shows two plateaus corresponding to the destruction of carbon (1 - 0.5 AU) and of olivine(0.5 - 0.1 AU) dust grains. The plateaus are due to the decrease of opacity during dust destruction whichcounteracts a temperature raise with decreasing distance. The two curves merge where the last dustgrains disappear.

Figure 5 shows the thickness of the accretion disk. The reduction of the thickness with decreasingabsorption can be clearly seen. The figure shows an additional short plateau in the disk around s=0.05AUwhere H2 dissociates. The increase in particle density in this region prevents the further shrinkage of thedisk over a short radius interval.

The asterisks in Figs. 4 and 5 indicate the present positions of the planets from Jupiter to Mercury.

Acknowledgements

We grateful acknowledge stimulating discussions with W.J. Duschl, W. M. Tscharnuter, J. Warnatz andespecially H. G. Bock, who has decisively influenced the development of DAESOL over the last 10 years.This work has been supported by the Deutsche Forschungsgemeinschaft (DFG), Sonderforschungsbereich359 “ Reaktive Stromungen, Diffusion und Transport”.

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Figure 5: Radial run of disk height (in units AU) in the accretion disk. The full line shows the result ofthe model calculation. The dotted line shows, for comparison, the disk height in a model without dust.

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