aa r X i v : . [ a s t r o - ph ] M a y Photoprocesses in protoplanetary disks
Ewine F. van Dishoeck, a Bastiaan Jonkheid a and Marc C. van Hemert ba Leiden Observatory, P.O. Box 9513, 2300 RA Leiden, The Netherlands.E-mail: [email protected] b Leiden Institute of Chemistry, P.O. Box 9502,2300 RA Leiden, The NetherlandsNovember 11, 2018
Circumstellar disks are exposed to intense ultraviolet (UV) radiation from the young star. Inthe inner disks, the UV radiation can be enhanced by more than seven orders of magnitudecompared with the average interstellar radiation field, resulting in a physical and chemicalstructure that resembles that of a dense photon-dominated region (PDR). This intense UV fieldaffects the chemistry, the vertical structure of the disk, and the gas temperature, especially inthe surface layers. The parameters which make disks different from more traditional PDRs arediscussed, including the shape of the UV radiation field, grain growth, the absence of PAHs,the gas/dust ratio and the presence of inner holes. Illustrative infrared spectra from the SpitzerSpace Telescope are shown. New photodissociation cross sections for selected species, includingsimple ions, are presented. Also, a summary of cross sections at the Lyman α µ m. The importance of a proper treatment of the photoprocessesis illustrated for the transitional disk toward HD 141569A which includes grain growth. It is well established observationally and theoretically that many young stars in the solarneighborhood are surrounded by disks, i.e., flattened rotating concentrations of gas and dust(see [18] for a review). In the early phases, up to a few Myr after collapse of the parent cloud,1he disks are rich in gas and dust inherited from the cloud core. Once accretion onto thestar stops and the disk becomes less turbulent, the ∼ µ m interstellar grains coagulate tolarger and larger particles and settle to the midplane, eventually forming km-sized planetesimalswhich interact gravitationally to form protoplanets (e.g., [80]). In this period, between a fewand 10 Myr, also most of the gas may be dissipated from the disk although the precise timescale for gas removal is still uncertain. Dust disks are observed around much older (up to afew Gyr) stars as well, but the grains in these disks are the ‘debris’ produced by collisions andfragmentation of planetesimals and are no longer the original interstellar particles (e.g., [37]).This paper is concerned with young, gas-rich disks up to the transitional stage when the diskbecomes optically thin to UV radiation.Young stars are known to be powerful emitters of UV radiation, with typical intensities at thedisk surface that are orders of magnitude higher than the average interstellar radiation field[23]. For some sources, most of the flux may be contained in the Lyman α line [3]. These UVphotons play a very important role in the physical and chemical structure of the disk, especiallyin the surface and intermediate layers. Many disks are thought to have a flaring structure, inwhich the disk height H and opening angle H/R increase with radius R (e.g., [7, 10]). In such ageometry the disk surface intercepts significantly more UV radiation from the star than in a flatgeometry, heating the surface layers and increasing the scale height further when hydrostaticequilibrium is assumed in the vertical direction. Because the density in the upper layers isbelow that at which gas-grain coupling becomes effective, the gas temperature can be higherthan the dust temperature due to photoelectric heating, affecting both the structure, chemistryand line formation [27, 29]. In the inner disk ( < + to C and CO around A V ≈ H having a significant abundance in the intermediate layers. Inthe cold mid-plane ( <
20 K), most molecules are frozen out onto the grains. This layered chem-ical structure is consistent with observations of ions and radicals with abundance ratios thatare similar or higher than those found in PDRs (e.g., [14, 70]). If the UV radiation is energeticenough to dissociate CO, isotope selective processes may occur leading to fractionation of COisotopes which can eventually be incorporated into meteorites [46]. Finally, UV photons canaffect the chemistry through photodesorption of ices brought to the surface by vertical mixingin the disk [82].The above discussion illustrates the need for accurate photodissociation cross sections to de-2cribe the disk chemistry. In this paper, photodissociation rates relevant for disks exposedto different types of radiation fields are presented, including calculations of cross sections forspecies not considered before. Also, a critical evaluation of available cross sections at the Ly-man α wavelength is given. The resulting chemical structure is illustrated for the transitionaldisk around the Herbig Ae/Be star HD 141569A. The PDR structure of a disk differs from that of the more commonly studied PDRs in molecularclouds [24]. First, the spectral shape of the stellar radiation field can differ significantly fromthat of the standard interstellar radiation field (ISRF), especially for the cooler T Tauri stars.Figure 1 compares the standard ISRF cf. [12] with that of a 10000 K (typical Herbig Ae star)and a 4000 K (typical T Tauri star) radiation field, normalized to have the same integratedintensity from 912–2050 ˚A. Below 2000 ˚A where most molecules are photodissociated, the 4000K field has orders of magnitude lower intensity. The figure also includes a NEXTGEN simulatedspectrum of a B9.5 star [22], illustrating that the intensity may be further reduced by stellarabsorption lines in the critical 912–1100 ˚A where H and CO are photodissociated. Thesestellar lines become increasingly important at lower stellar temperatures. Some T Tauri starsare known to have excess UV emission above that of a 4000 K blackbody, either from a hotboundary layer between the accretion disk and the star or from chromospheric stellar activity,bringing the overall shape back closer to that of the ISRF [6, 30]. Specific resonance lines likeLyman α can dominate the spectrum [3]. The key chemical effect is that H and CO are hardlyphotodissociated by ‘cool’ stars at 912–1100 ˚A; only the general ISRF incident on the disksets up the H → H and C + → C → CO transitions [78]. Other molecules with photodissociationchannels primarily at short wavelengths (e.g., N , CN) are equally affected.Second, the UV field can be orders of magnitude higher than that studied in molecular clouds.For example, at 15 AU from an A0 star, the radiation is 10 times that of the ISRF. For suchhigh fluxes, photorates can become comparable to dissociative recombination rates so thatphotodissociation of ions needs to be included in the models.Third, the grain sizes and properties may be very different from those found in clouds. Inparticular, there is strong evidence from infrared observations that grains in the upper disklayers have grown from ∼ . µ m to a few µ m in size regardless of the spectral type of the star(e.g., [71, 32]). Figure 2 illustrates this growth using recent Spitzer Space Telescope spectraof the 10 and 20 µ m silicate feature. Larger grains have significantly lower extinction at UVwavelengths. Also, PAHs may have lower abundances and are detected toward only few T Tauristars [16].Fourth, the gas/dust mass ratio can differ from the interstellar medium value of 100. Currently,it is unclear whether the (small) dust particles disappear before the gas or vice versa. However,3ust-free gaps, rings and holes in disks have been found for some objects including the HD141569A disk (e.g., [2, 8]). Some remaining gas can be present in these dust holes (e.g., [50]).Fifth, the density in the disk PDR varies by orders of magnitude, both in vertical and radialdirection, in contrast with the near constant density assumed for clouds. If ices are released intothe gas due to vertical mixing followed by thermal or photodesorption, the initial conditions forthe PDR are different from those of standard clouds. For example, the presence of enhancedgaseous H O has been shown to modify the PDR chemistry for the case of protostellar envelopes[62].Finally, young stars are known to be powerful X-ray emitters (e.g., [15]). In addition to directionization, the UV radiation resulting from the interaction of the secondary electrons with H has a major effect on the chemistry [19, 63]. This spectrum consists of many discrete linesoriginating from the H B and C electronic states, with peaks at 1500–1600 ˚A and shorterwavelengths. Thus, many of the basic photodissociation processes discussed here are alsorelevant for models which take X-rays into account.
The photodissociation rate of a molecule can be computed from k contpd = Z σ ( λ ) I ( λ ) dλ s − (1)where σ is the photodissociation cross section in cm and I is the mean intensity of the radiationin photons cm − s − ˚A − . Usually σ is a broad, continuous function with wavelength peakingclose to the vertical excitation energy of the electronic state involved in the process. Forphotodissociation initiated by line absorptions (e.g., predissociation), the rate becomes k linepd = πe mc λ uℓ f uℓ η u I uℓ s − (2)where f uℓ is the oscillator strength for absorption from lower level ℓ to upper level u and η u thedissociation efficiency of state u , which lies between 0 and 1. The numerical value of the factor πe /mc is 8 . × − in the adopted units with λ in ˚A. The total photodissociation rate ofa molecule is obtained by summing over all channels.Overviews of photodissociation cross sections and interstellar photodissociation rates of astro-physically relevant molecules have been given by [40, 73, 57, 26]. Data on cross sections can befound in the chemical physics literature, either from experiments (stable molecules) or theory(radicals, ions). These summaries include only limited data on the photodissociation of smallions which are key to building carbon- and oxygen species. Therefore, a literature search wasperformed and new cross sections were calculated for several species. Also, the first criticalevaluation of cross sections at the Lyman α wavelength is presented. Finally, photodissociationrates are calculated for different radiation fields and grain parameters.4 .1 New photodissociation cross sections For small molecules and ions, quantum chemical calculations of the potential energy curvesand transition dipole moments combined with dynamical calculations of the nuclear motionscan provide accurate photodissociation cross sections and oscillator strengths (see [34] for re-view). All new calculations presented here were performed with the MOLPRO set of programs[81], using the VTZ atomic orbital basis set [13]. For neutral molecules, diffuse s and p func-tions were added to allow for a proper description of molecular Rydberg states. Molecularorbitals were generated in state-averaged complete active space (CAS) calculations. In theultimate contracted multi-reference configuration-interaction (CI) calculation, typically 50 ref-erence configurations per symmetry were used. Thus, around 100000 contracted configurationsout of 300000 uncontracted configurations were generated per symmetry. Orbitals with anorbital energy below -15 eV were kept doubly occupied in all CI calculations.Typically, the lowest 5 electronic states of each symmetry were calculated at the ground-stateequilibrium geometry together with the corresponding transition moments. For diatomics,complete potential energy curves were computed as well. Many of the excited states are boundand the predisssociation efficiencies are often unknown. In the following, individual cases arediscussed in more detail. CH +2 : Accurate CI calculations by Theodorakopoulos & Petsalakis [69] show many dipole-allowed excited states below 13.6 eV. Their 1, 2 and 3 B , 2, 3 and 4 A and 2 B states havebeen included with f =0.008, 0.0001, 0.02, 0.01, 0.06, 0.05 and 0.03, respectively. CH +4 : Detailed studies of the CH +4 photodissociation processes starting from its lowest C v state have been carried out by van Dishoeck et al. [76] indicating that the higher excited statesare likely dissociative. The oscillator strengths into the 2, 3 A and 2 B states computed inthis work are f =0.04, 0.04 and 0.08, respectively. O +2 : Calculations show that all electronic states below 13.6 eV are bound [25]. Our computedoscillator strengths to the A Π u and 2 Π u states —the only dipole allowed states below 13.6eV and above the dissociation limit– are only f =0.005 each. CO + : CO + is strongly bound with a dissociation energy of 8.34 eV, but its higher excited D Π,G, E and F Σ + states are likely (pre-)dissociative [38]. The calculated oscillator strengths tothe D and G states are f =0.01 and 0.02, respectively. Similar values have been assumed forthe higher states. HCO + : The excited electronic states and photodissociation processes of HCO + have beenstudied in detail by Koch et al. [35, 36]. HCO + is remarkably transparent at UV wavelengths:the only dipole-allowed dissociative state is the 1 Π state around 11.5 eV with a small crosssection. H O + : Calculations show that there are no dipole-allowed dissociative electronic states below13.6 eV so that the interstellar H O + photodissociation rate is negligible. SiO:
The electronic structure of SiO is similar to that of CO, but with a lower dissociation5nergy of 8.26 eV implying that even the lower Rydberg states can contribute to SiO photodis-sociation if they are fully predissociated. Our computed oscillator strengths to the 3 Σ + and2, 3, 4 and 5 Π states are f =0.10, 0.32, 0.03, 0.11 and 0.10, respectively. α cross sections The Lyman α line can outshine the continuum radiation, so that it is important to knowwhether a molecule can be photodissociated at 1216 ˚A or not. Table 1 summarizes the crosssections for a number of key molecules, including those that are known to have significantabundances in the inner disk [47]. The table contains references to the original experimentalor theoretical work as well as an assessment of the accuracy of the data, with the notation A( σ known to better than 50%), B ( σ uncertain up to a factor of two) or C ( σ uncertain up toan order of magnitude).The following molecules cannot be dissociated by Lyman α radiation: H , CO, N , CN, H +3 ,OH + , H O + and HCO + . An interesting case is formed by O . The absorption cross section at1215–1216 ˚A is known to be small, of order (1 − × − cm [53], but there are resonancesinto the v ′ = 0 and 1 levels of the 2 Σ − u state at 1245 and 1205 ˚A, with f = 0 .
015 each [5].If the Lyman α line is as wide as observed for some stars (1205–1230 ˚A, ± α are generally accurate to better thana factor of 2, especially when the absorption is continuous. For molecules for which onlytheoretical calculations are available (e.g., CH, CH , C H, C , ...), the cross sections at Lyman α are highly uncertain because the energy level calculations are uncertain by ∼ α . This includes C H , SH,SH + , CS and SiO.Only a few molecules can be photoionized by Lyman α (see Table 2 of [73] for ionizationpotentials). For species like NH and NO, the photoionization cross sections or yields havebeen measured so that the dissociation and ionization parts can be separated. In other casessuch as CH , the branching ratio is unknown. SO has an ionization potential of 10.29 eV, justabove the Lyman α threshold, whereas CS has 10.08 eV, just below. Of the major atoms, C,N, O, and S cannot be photoionized by Lyman α whereas Mg, Si and Fe can. The database on photodissociation and ionization cross sections assembled by van Dishoeck[73] has been used together with the above new input to compute photodissociation rates for6arious radiation fields. No attempt has been made to systematically review the chemicalphysics literature since 1988 for molecules other than those discussed in § , for which the cross sections of [77] are adopted.References to the sources for the cross sections are given in Table 1 of [73], which also includesthe most likely dissociation products. The resulting rates for the standard ISRF cf. [12] aregiven in Tables 2 and 3.In calculating the photodissociation rates, it has been assumed that all states above the dis-sociation limit have 100% dissociation efficiency, thus providing a maximum value ( η u = 1).Even with this assumption, the photodissociation of ions is on average significantly slower thanthat of neutrals. Several ions (e.g., H +3 , H O + ) do not even have any dipole-allowed dissocia-tive electronic transitions below 13.6 eV. Note that CH + dissociates primarily into C + H + for the radiation fields considered here, not C + + H as listed in UMIST99. In contrast, OH + dissociates primarily into O + + H.The photodissociation rates for larger molecules are uncertain because experimental data aresparse and incomplete. Moreover, often only absorption cross sections are known, not thedissociation yields. For large molecules, absorption is followed by internal conversion to highlyexcited vibrational levels of the ground electronic state, only some of which lead to dissociation.Also, the products of the photodissociation are largely unknown and can vary with wavelength;see [48] for an illustrative example for the case of CH OH.Tables 2 and 3 include the photodissociation and photoionization rates for a T BB = 10000 Kand a 4000 K blackbody radiation field. As noted in §
2, the shapes of the UV fields of HerbigAe and T Tauri stars are thought to lie in between these three extremes. Their intensities havebeen normalized such that the integrated values from 912–2050 ˚A are the same as those of theDraine [12] field, 2 . × − erg cm − s − . The latter value is a factor of 1.7 larger than thatof the integrated Habing [21] field of 1 . × − erg cm − s − used in other normalizations. Theadopted dilution factors are 1 . × − and 1 . × − for 10000 and 4000 K, respectively.For applications in disk chemistry, these rates need to be scaled to the appropriate strength ata certain distance from the star. The photorates for (scaled) fields with T BB = 20000 − , CO, C, CN and N , whichare only dissociated or ionized at < T BB = 4000 K. In contrast, molecules with dissociation channels atwavelengths as long as 3000 ˚A (e.g., CH, HCO, O ) can have enhanced rates in the cooler fieldswith the adopted normalization. Molecules which absorb over a broad wavelength range (e.g.,OH, H O, NO) vary by only a factor of a few between T BB = 30000 and 4000 K.Illustrative examples of the effect of Lyman α radiation on the photorates in disks are given by[3]. The photodissociation and ionization efficiencies corresponding to Lyman α absorption inthe context of X-ray induced chemistry are summarized by [44] for selected species.7 .4 Depth-dependence of photorates With depth into a cloud or disk, the UV radiation is attenuated due to absorption and scatteringby dust grains [56]. For typical 0.1 µ m interstellar grains, the extinction, albedo and scatteringphase function are taken from [57]. The rates are then fitted to a single exponential decay with k pd = k opd exp( − γA V ) s − . (3)The fits of γ are performed over the range A V = 0 − γ vary by ∼ γ for the ISRF differ from those of van Dishoeck [73] due to the adopted grainproperties, which are in between those of grain models 2 and 3 of [56] used previously. Inter-estingly, the values of γ do not change dramatically with T BB for most species, even thoughthere is a general trend for γ to become smaller with cooler fields (see also [61]).When grains grow larger, the main effect on the grain parameters is the smaller extinction atUV wavelengths, which becomes comparable to that at visible wavelengths (e.g., [59]). Thephotorates have been re-computed as a function of depth using the properties for µ m-sizedice-coated grains derived for the HD 141569A disk [45, 28]. For species such as C and COwhich absorb only at the shortest wavelengths, the exponents γ are lowered from > ∼ γ is lowered from 1.1 to 0.47. Other species have exponents γ in between these two values.For T BB = 4000 K, the trends are similar, with values of γ between 0.6 and 0.38. Thus, thedifferences between molecules in the depth dependence of the photorates are minimized forlarge grains. In this work, the effects of different radiation fields and different grain properties are taken intoaccount explicitly by calculating at each point in the disk the UV radiation field from the staras well as the ISRF (either in 1+1D or in full 2D) and then computing the photodissociationrates by integrating the cross sections multiplied by the radiation intensity over wavelength[78, 28]. Self-shielding of H and CO as well as mutual shielding of CO and its isotopes areincluded. X-rays are not included, nor is time-dependence, vertical mixing or photodesorptionof ices.As an example, the disk around the Herbig Ae/Be star HD 141569A (B9.5 V, 22 L ⊙ , 99 pc)is modelled. This ∼ ∼
500 AU disk with a huge inner hole in thedust out to 150 AU and two dust rings at 185 and 325 AU seen in scattered light images (e.g.,82, 8] ∗ ). The outer rings may be explained by tidal interactions with two M-type companions,HD 141569B and C, but other explanations such as a giant planet are not excluded. The originof the inner hole is unknown. The disk is optically thin to UV continuum radiation and thegrains have grown to at least µ m size [45]. Nevertheless, gas is still present since the CO J =2–1 and 3–2 millimeter [11] and the v = 1 − formation rate, and through the photoelectric heating efficiency [31]. Thebest-fitting model to the CO millimeter lines has a total gas mass of 80 M Earth , compared witha total dust mass of 2.2 M Earth in grains up to 1 cm. An important conclusion is that some gasmust be present in the inner hole to provide sufficient H and CO self-shielding in the radialdirection. The PAH abundance with respect to total hydrogen is ∼ − , but even at this lowabundance PAHs are an important site for H formation. Models without PAHs require muchlarger gas masses [28].Figures 3 and 4 present the radial and vertical distributions of various molecules in the HD141569A disk, both with and without the ISRF. Because the stellar radiation field has fewphotons at wavelengths below 1200 ˚A, the photodissociation of CO and H and photoionizationof C occurs mostly by the ISRF in the outer disk. The vertical slices show the typical PDRstructure with atomic H and C + dominant on the surface, and the transition to H taking placein the intermediate layer. However, the CO column never becomes large enough in the verticaldirection for significant self-shielding so that carbon stays in atomic form. Other moleculeslike CH and C H which are not self-shielding and can photodissociate over a large wavelengthrange continue to be dissociated very rapidly by the stellar radiation. Thus, even without theISRF, the CO abundance stays low since its precursor molecules have very low abundances.Neutral atomic carbon is the dominant form of carbon since there are few ionizing photons. Thepredicted peak line intensity of ∼ The main results of this work are as follows. ∗ see http://hubblesite.org/newscenter/newsdesk/archive/releases/2003/02/ for image New photodissociation cross sections are presented for several species not consideredbefore. Also, the first critical evaluation of cross sections at Lyman α is given. • The photodissociation of ions is potentially important in (inner) disk chemistry wherethe radiation field can be 10 times more intense than the standard ISRF. However,the photorates of many ions, especially those containing oxygen, are found to be slowcompared with those of neutrals. • Photorates have been computed for a range of radiation fields appropriate for HerbigAe/Be and T Tauri stars. Molecules such as H , CO, N and CN, which are photodisso-ciated only below 1200 ˚A, have rates that are more than 5 orders of magnitude decreasedfor a T BB = 4000 K blackbody field. • The exponent γ characterizing the depth-dependence of the photorates decreases with T BB but the effect is not large in the 4000–30000 K range for most species. For larger µ m-sized grains, the depth dependence of the photorates becomes much shallower, with γ falling in a narrow range of 0.4–0.6 for all species. • The example of the HD 141569A disk illustrates that both the shape of the stellar radia-tion field and the size of the grains affect the chemistry. Both need to be treated correctlyto derive quantitative conclusions about the gas mass and chemistry from observed lines.Even a small amount of PAHs or small grains can significantly affect dissociation andionization rates, as well as the H formation rate. We are grateful to the Spitzer ‘Cores to Disks’ team, in particular J. Kessler-Silacci and V.Geers, for providing observational data. The HD 141569A modeling is performed in collabo-ration with J.C. Augereau and I. Kamp. Astrochemistry in Leiden is supported by a Spinozagrant from the Netherlands Organization for Scientific Research (NWO).10 eferences [1] Y. Aikawa, G.J. van Zadelhoff, E.F. van Dishoeck and E. Herbst,
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J. Quant. Spect.Rad. Transf. , 1996, , 53 14able 1: Photodissociation and ionization cross sections at Lyman α a Species σ pd Accuracy b Ref(cm − )CH 5.0(-20) C [72] TCH H 1.0(-18) C [60] TC H ≥ c B [65] EC H O 1.2(-17) A [42] EO b C [53] ECO CO 1.0(-17) B [67] ECH OH 1.4(-17) A [52] ENH 1.0(-18) B [33] TNH N 2.5(-17) B [9] ECH CN 2.0(-17) A [66] ENO 4.0(-19) B [20] EH S 3.3(-17) B [40] ESO 1.0(-16) C [51] ESO p.i. 2.0(-18) B [79] ENO p.i. 1.6(-18) B [20] ECS p.i. 2.0(-16) B [40] E a See text for list of species that cannot be dissociated or ionized by Lyman α b See text for discussion c f =0.013 15able 2: Photodissociation rates for various radiation fields a,b Species k opd (s − ) γ ISRF c d d ISRF 10000 K 4000 KH +2 + +2 +4 H 5.2(-10) 1.9(-10) 7.2(-12) 2.30 2.16 2.10C H H c − C H + O 8.0(-10) 4.3(-10) 1.2(-10) 2.20 1.97 1.90O +2 O + + CO 1.0(-9) 6.7(-10) 1.8(-10) 2.16 1.99 1.90CH OH 1.4(-9) 5.9(-10) 7.0(-11) 2.28 2.07 1.9516able 3: Photodissociation rates for various radiation fields a,b (Table 2 cont’d)Species k opd (s − ) γ ISRF c d d ISRF 10000 K 4000 KNH 5.0(-10) 1.6(-10) 3.0(-12) 2.33 2.24 2.12NH + O 1.9(-9) 4.8(-10) 2.0(-11) 2.44 2.32 2.02CN 2.9(-10) 2.1(-11) 2.0(-15) 3.54 3.49 3.23HCN 1.6(-9) 2.5(-10) 3.7(-12) 2.69 2.44 2.02HC N 5.6(-9) 3.0(-9) 2.5(-10) 2.16 2.12 2.12CH CN 2.5(-9) 4.8(-10) 8.5(-12) 2.58 2.38 2.01SH 9.8(-10) 1.3(-9) 1.6(-8) 2.04 1.85 1.34SH + S 3.1(-9) 2.0(-9) 3.2(-9) 2.27 2.12 2.16CS 9.8(-10) 2.7(-10) 3.7(-12) 2.43 2.33 2.14CS + a See van Dishoeck [73] for products and references to cross section data b H +3 , HeH + and H O + cannot be photodissociated by radiation with λ >
912 ˚A, so k opd =0 c ISRF according to [12] with extension at > d Scaled blackbody radiation field with temperature T BB (see text)17able 4: Photoionization rates for various radiation fields a (Table 3)Species k opd (s − ) γ ISRF b c c ISRF 10000 K 4000 KC 3.1(-10) 2.5(-11) 4.2(-15) 3.33 3.27 3.10Mg 7.9(-11) 5.9(-11) 6.9(-12) 2.08 2.00 1.96Si 3.1(-9) 1.2(-9) 4.1(-11) 2.27 2.17 2.09S 6.0(-10) 5.9(-11) 4.0(-14) 3.08 2.95 2.76Fe 2.8(-10) 1.3(-10) 5.8(-12) 2.20 2.14 2.05CH 7.6(-10) 6.4(-11) 1.6(-14) 3.28 3.20 2.97CH H H H O 3.1(-11) 2.0(-12) 3.6(-17) 3.90 3.90 3.88NH O 1.7(-10) 1.1(-11) 1.4(-16) 3.93 3.93 3.92H S 7.3(-10) 7.2(-11) 3.5(-14) 3.09 3.01 2.86CS CO 4.8(-10) 4.1(-11) 1.2(-14) 3.21 3.13 2.96 a See van Dishoeck [73] for references to cross section data b See footnote c Table 2 c See footnote d Table 2 18 ig. 1
Comparison of the interstellar radiation field (ISRF) according to [12] (with theextension by [74] for > Fig. 2
Evidence for grain growth in disks around T Tauri stars. Top: Spitzer Space Tele-scope observations of the 10 and 20 µ m silicate Si-O stretching and O-Si-O bendingmode features of two T Tauri stars, shifted by +0.4 and +0.2 for clarity. Bottom:normalized absorption efficiencies Q abs for models of spherical amorphous olivineswith various sizes, calculated using the distribution of hollow spheres (DHS) methodof [49]. The models are offset by +0.4, +0.25 and +0.1, respectively. Figure basedon [32]. Fig. 3
Left: Radial distribution in the midplane of the HD 141569A disk of the tempera-ture and density (top), and various chemical species (middle and bottom). Right:Vertical slice at R = 300 AU. This model includes both the stellar radiation (Figure1) and the ISRF. Fig. 4