H2 ro-vibrational excitation in protoplanetary disks and its effects on the chemistry
DDraft version February 17, 2021
Typeset using L A TEX default style in AASTeX63 H ro-vibrational excitation in protoplanetary disks and its effects on the chemistry Maxime Ruaud
1, 2 NASA Ames Research Center, Moffett Blvd., Mountain View, CA 94035, USA Carl Sagan Center, SETI Institute, Mountain View, CA 94035, USA (Received XX; Revised YY; Accepted ZZ)
Submitted to ApJABSTRACTThe effect of H ro-vibrational excitation on the chemistry of protoplanetary disks is studied using aframework that solves for the disk physical and chemical structure and includes a detailed calculationof H level populations. Chemistry with ro-vibrationally excited H is found to be important forthe formation of several commonly observed species in disks and this work demonstrates the need toaccurately treat PDR chemistry in disks if we are to make inferences on the chemical state of the diskduring planet formation epochs. This is found to be even more critical for molecules like C H, CNor HCN that are commonly used to infer changes in the elemental disk C/O and N/O ratios, withimplications for planetesimal formation and the composition of exoplanet atmospheres. Computedvertical column densities with the full H population calculation are increased by ∼ − . For the commonly used pseudo-level approximation, the computed columns of these molecules areoverestimated by a factor of ∼ − (i.e. 11-13.6 eV), which is not well constrained in disks, and that rate constantsas a function of H ro-vibrational levels for the key reaction N + H → NH are needed for a moreaccurate assessment of CN/HCN chemistry but are currently unavailable.
Keywords:
Protoplanetary disks (1300), Astrochemistry (75), Chemical abundances (224), Star for-mation (1569) INTRODUCTIONChemistry involving ro-vibrationally excited H has long known to be significant for several key reactions in photondominated regions (PDRs) of the interstellar medium (e.g. Ag´undez et al. 2010; Nagy et al. 2013). In these regions,the absorption of FUV photons in Lyman and Werner bands efficiently pumps H in its excited electronic states.Approximately 10% of the absorbed photons lead to H dissociation, while 90% radiatively de-excite to bound ro-vibrational levels of the ground electronic state. These excited ro-vibrational levels decay by means of quadrupoletransitions which result in the emission of infrared photons (e.g. Black & Dalgarno 1976). The energy in these excitedro-vibrational levels is sufficient to overcome the reaction energy barrier of several reactions. Reactions of excited H with C + and S + for instance are responsible for the formation of CH + and SH + ions in PDRs (e.g. Ag´undez et al.2010; Nagy et al. 2013). The efficiency of these reactions critically depends on the levels population of H . For C + forinstance, the reaction with H in ground vibrational state is endothermic by ∼ in v = 1 (Zanchet et al. 2013b). In the case of S + , the reaction is endothermic by ∼ needs to be in v (cid:38) Corresponding author: Maxime [email protected] a r X i v : . [ a s t r o - ph . GA ] F e b Ruaud et al.
Chemistry with ro-vibrationally excited H in disks is often approximated by the so called pseudo-level approxi-mation, in which all the excited vibrational levels of H are grouped together into a single vibrational excited stateH ∗ , corresponding to a pseudo-level v ∗ = 6 and having a weighted averaged energy of ∼ self-shielding and photodissociation as compared to detailed H excitationcalculations (see Fig. 1 & 2 of Draine & Bertoldi 1996, for instance). However, the use of this approximation to solvefor chemistry with excited H may lead to unrealistic results as the rates critically depends on the fractional popula-tions in each ro-vibrational state. In particular, rate coefficients of species reacting with H ∗ are often approximatedusing the rate for reaction with H by reducing the exponential factor by the corresponding energy of the level (i.e. ∼ ∗ , although there is a barrier of 12600K for it to react with ground stateH . Visser et al. (2018) used the same assumption to conclude that most of the observed HCN emission also comesfrom the PDR layer. Kamp et al. (2017) follow a more conservative approach where the rate for reaction with H ∗ isobtained by subtracting the energy corresponding to the first vibrational excited level v = 1 for which E vJ ∼ have been limited to few reactions such as H with C + , He + , S + , O, OH and CN, with important implications for the formation of molecules such as CH + and SH + (Ag´undez et al. 2010, 2018). The goal of this article is to explore the effects of the full vibrational level calculations ofH on the chemistry of protoplanetary disks. Modeling results are presented in Section 2 and Section 3 contains ourconclusions. MODELING RESULTSIn what follows, we consider the fiducial disk model of Ruaud & Gorti (2019) to study the effects of H excitation onthe chemistry. The disk is assumed to have a mass M disk = 5 × − M (cid:12) and a dust-to-gas mass ratio Σ d / Σ g = 0 . M ∗ = 1 M (cid:12) , R ∗ = 2 . R (cid:12) and an X-ray luminosity of 10 erg s − . The stellar spectrum is the TW Hya spectrum taken from the Leiden database (Heays et al. 2017).2.1. H ro-vibrational excitation and level populations The model includes 100 ro-vibrational levels of H in the ground electronic state. The level populations of H arecomputed by including the effects of (1) radiative transitions, (2) collisional processes with He, H, H + and H , (3)FUV radiative pumping (4) X-ray excitation (5) excitation at H formation and (6) the ortho/para conversion ongrains. More details on the implementation of each of these process is given in the appendix. Even though X-raypumping is taken into account, we find that it does not play a significant role in the non-thermal excitation of H when compared to FUV pumping. This result is similar to earlier modeling results of Nomura et al. (2007) where theystudy the relative roles of X-ray and UV excitation of H . Therefore, in what follows, we do not discuss the effects ofX-ray pumping on chemistry any further.Figure 1 shows the model calculated vertical column densities of all H levels included in the model, divided bystatistical weight, at r = 1, 10 and 100 au from the star, and expected LTE values (dashed lines). For r = 1 and 10 au,the lowest rotational levels of the ground vibrational level (i.e. v = 0 and J ≤
8) are at LTE and higher energy levelsare mainly populated by FUV photon pumping. For r = 100 au, only levels up to J = 3 are thermally populated anddeparture from LTE induced by FUV photon pumping occurs at lower energy than for r = 1 and 10 au. This is dueto the the lower temperatures and densities of the outer disk as compared to the inner disk (i.e. radial temperaturegradient). Rotational distributions in vibrationally excited states are characterized by rotational temperatures typicalof fluorescent emission and ranging from T rot ∼ ∼ levels, are colder than regions located in the disk atmosphere.As a result, the LTE curve tends to flatten as the energy of the level increases.Figure 2 shows the computed abundance maps of H in different ( v, J ) states. As seen in this figure (as well as Fig.1), most of the H in the disk is in the ( v = 0 , J = 0) and ( v = 0 , J = 1) ground vibrational states and the abundanceof H in higher ro-vibrational states tends to decrease as the energy levels of the states increase. The abundance of theH ( v = 1 , J = 0) state for instance reaches a peak abundance of few 10 − with respect to the density n H , while higher hemistry of ro-vibrationally excited H in disks E vJ / [K]10 N ( v , J ) / g ( J ) [ c m − ] (0 ,
0) (1 ,
0) (2 ,
0) (3 ,
0) (4 ,
0) (5 ,
0) (6 , r = 1au r = 10au r = 100au Figure 1.
Vertically integrated H column density N ( v, J ) divided by the level degeneracy g ( J ) as a function of the energyof the level at r = 1, 10 and 100 au from the star. Dashed lines are at LTE. energy states have abundances (cid:46) − . As will be discussed below, chemistry with excited H critically depends onthe fractional populations in each of these ro-vibrational states.2.2. Chemistry involving ro-vibrationally excitated H The effects of the full ro-vibrational level calculations of H on the chemistry is explored for species having reactionbarriers with ground state H . In the chemical network used here (i.e. the KIDA network, Wakelam et al. 2015), thereare ∼
80 reactions, including important reactions with species such as C + , S + , N + , C, O, N, and OH that mediatepathways to many other chemical species. Rate constants have been measured and/or calculated for some reactionswith species such as C + , S + and O. For C + ( P ) + H → CH + + H, Gerlich et al. (1987) experimentally derived rateconstants for the reaction with H ( v = 0 , J = 0 −
7) and for which we use analytical fits given in Ag´undez et al.(2010). For higher energy levels we use results from quantum calculations carried out by Zanchet et al. (2013b) andfor which fits are available for H ( v = 1 , J = 0) and H ( v = 2 , J = 0) (see Table 3 of Zanchet et al. 2013a). ForS( S ) + H → SH + + H, we use rate constants given in Zanchet et al. (2013a) for reaction with H ( v = 0 , J = 0) and( v = 1 , J = 0) states, and those given in Zanchet et al. (2019) for reaction with H ( v = 2 − , J = 0) states. In thecase of O( P ) + H → OH + H, we use fits to quantum calculations performed by (Sultanov & Balakrishnan 2005)and for which expressions are given in Ag´undez et al. (2010) for reaction with H ( v = 0 − , J = 0). For these threereactions, since rate constants are available for J = 0 only (i.e. except for C + ( P ) + H for which we have rates withH ( v = 0 , J = 0 − J ’s are assumed to be equal to the rate of the corresponding vibrationallevel in J = 0. Moreover, for these reactions, rates for higher energy levels than the last available state are assumedto be equal to the rate in this state. For the remaining reactions having a barrier for reaction with H , reaction ratesare approximated by k vJ = α ( T / β exp( − max[ γ − E vJ , /T ) [cm s − ] (1)where α , β and γ are the usual rate constant parameters. This expression assumes that the reaction proceeds withouta barrier when the energy of the level overcomes the energy barrier of the reaction. Note that this assumption couldbe prone to error as rate constant enhancements are usually specific to each system and difficult to predict (see alsoAg´undez et al. 2010). One such example is O( P ) + H , which has an activation barrier of ∼ is in the v = 3 state, for which E v ∼ is neglected , (2) a model in which all the excited vibrational levels of H are groupedtogether into a single vibrational excited state having a weighted averaged energy of 30160 K corresponding to H ( v = 6) It should however be noted that reaction parameters that are determined experimentally have a temperature dependence that implicitlyconsider the excitation of H . Ruaud et al. . . . . z / r H (0 , l og ( A V ) = − . . . − − − − − − − − − − H (0 , l og ( A V ) = − . . . − − − − − − − − − − H (0 , l og ( A V ) = − . . . − − − − − − − − − − l og ( n ( X )) / n H ) . . . . z / r H (0 , l og ( A V ) = − . . . − − − − − − − − − − H (0 , l og ( A V ) = − . . . − − − − − − − − − − H (0 , l og ( A V ) = − . . . − − − − − − − − − − l og ( n ( X )) / n H ) . . . . z / r H (0 , l og ( A V ) = − . . . − − − − − − − − − − H (0 , l og ( A V ) = − . . . − − − − − − − − − − H (0 , l og ( A V ) = − . . . − − − − − − − − − − l og ( n ( X )) / n H ) . . . . z / r H (1 , l og ( A V ) = − . . . − − − − − − − − − − H (2 , l og ( A V ) = − . . . − − − − − − − − − − H (3 , l og ( A V ) = − . . . − − − − − − − − − − l og ( n ( X )) / n H )
50 100 150 200 r [au]0 . . . . z / r H (4 , l og ( A V ) = − . . . − − − − − − − − − −
10 50 100 150 200 r [au] H (5 , l og ( A V ) = − . . . − − − − − − − − − −
10 50 100 150 200 r [au] H (6 , l og ( A V ) = − . . . − − − − − − − − − − l og ( n ( X )) / n H ) Figure 2.
Computed abundances of H in different ro-vibrational levels as a function of the disk radius r and normalizedheight z/r . Solid line contours show the A V to the star. (the so-called pseudo-level approximation), and (3) a model where the full H ( v, J ) population calculation is takeninto account (see Table 1). For model M2, we follow the treatment described in Tielens & Hollenbach (1985) in whichH ∗ is formed by FUV pumping and destroyed by radiative decay and collisional de-excitation by H and H . The FUVpumping rate is assumed to be 9 times the H photodissociation rate and the radiative decay rate is 2 × − s − .For collisional de-excitation by H and H we use rates given in Equation (A14) of Tielens & Hollenbach (1985). Theserates have recently been updated by Visser et al. (2018) based on more recent calculations. A comparison with therates used in Visser et al. (2018) however shows that the impact of these updated rates is relatively small. This isdue to the fact that radiative decay dominates H ∗ destruction in most of the disk. The only location where the useof these updated rates leads to differences is the inner disk (i.e. r (cid:46)
20 au) where higher densities result in collisionalde-excitation dominating radiative decay. Finally, reaction rates with H ∗ in this model are computed using Eq. 1 and hemistry of ro-vibrationally excited H in disks . . . . z / r H ∗ l og ( A V ) = − . . . − − − − − − − l og ( n ( X )) / n H )
50 100 150 200 r [au]0 . . . . z / r H ( E vJ ≥ l og ( A V ) = − . . . − − − − − − − l og ( n ( X )) / n H ) Figure 3.
Computed abundance of excited H as a function of the disk radius r and normalized height z/r . The top figureshows result obtained in the case of the pseudo-level approximation and the bottom figure shows results obtained with the fullmodel and for levels with E vJ ≥ Table 1.
Model description.Model descriptionM1 Reference model in which the chemistryof excited H is neglectedM2 Chemistry of excited H assumingthe pseudo-level approximationM3 Chemistry of excited H withfull H population calculation assuming E v ∗ = 30160K. A comparison between the computed abundance map of H ∗ calculated with the pseudo-levelapproximation and for all levels with E vJ ≥ z/r < .
2, which trace regions where grain surface chemistry isimportant, is not presented. Readers interested in the chemistry of these regions can refer to papers such as Semenov& Wiebe (2011), Walsh et al. (2014) and Ruaud & Gorti (2019), for detailed models of gas-grain chemistry using largesurface reaction networks. Figs. 4 and 5 show the computed abundance maps of CH + , SH + , OH, H O, C H, CN,HCN, HNC and N H + computed in each of these models and show that the chemistry with ro-vibrationally excitedH is important in the surface layers of the disk (i.e. in regions with z/r > .
2, where H ro-vibrational levels areefficiently populated by the absorption of FUV photons, see Fig. 2). The use of the pseudo-level approximation ascompared to the full H population shows important differences for species such as CN, HCN and HNC for which thecomputed abundances in the PDR layer are overestimated by approximately one order of magnitude in the pseudo-levelapproximation model (M2) as compared to the full H population model (M3). These differences are also seen in Fig.6 which shows vertical column density ratios for models M1 and M2 with respect to the full calculation M3 of someabundant gas-phase species. Details on some important reaction pathways are discussed below.2.2.1. Carbon chemistry
The inclusion of C + + H ( v, J ) has an important impact on the formation of CH + as compared to the referencemodel M1. At r >
20 au, CH + abundance is increased by almost two orders of magnitude in the M2 and M3 modelsas compared to M1, while the M3 model has ∼ + than the M2 model. In the full calculation model,CH + is mainly formed by reaction with H in the ( v = 0 , J = 8), ( v = 1 , J = 0) and ( v = 1 , J = 1) state, for which Ruaud et al.
50 100 150 r [au]0 . . . . . . z / r M1CH + − − − − − − r [au] M2CH + − − − − − − r [au] M3CH + − − − − − − l og ( n ( X )) / n H )
50 100 150 r [au]0 . . . . . . z / r M1SH + − − − − − − − r [au] M2SH + − − − − − − − r [au] M3SH + − − − − − − − l og ( n ( X )) / n H )
50 100 150 r [au]0 . . . . . . z / r M1OH − − − − − − − − r [au] M2OH − − − − − − − − r [au] M3OH − − − − − − − − l og ( n ( X )) / n H ) Figure 4.
Computed abundance map of CH + , SH + and OH as a function of the disk radius r and normalized height z/r formodel M1, M2 and M3 (see Table 1). E vJ (cid:38) + in the irradiated layer is in agreement with Ag´undez et al. (2018), eventhough our computed abundances are lower by a factor of ∼
10. This could be the result of different disk physicalparameters and/or the use of a different stellar spectrum. As seen in Figs. 5 and 6, the enhanced formation of CH + only has a moderate impact on the formation of C H, a bright molecule at millimeter wavelengths in disks for whichmost models fail to reproduce observed emission without invoking enhanced C/O ratios (e.g. Bergin et al. 2016; Cleeveset al. 2018; Miotello et al. 2019). In all three models, C H formation starts with CH + C + which forms C +2 . C +2 thenreacts with H to form successively C H + and C H +2 , which then recombine to form C H. The key molecule in thissequence is CH whose formation is primarily initiated by the radiative association of C + and H to form CH +2 . CH +2 then reacts with H to form CH +3 , which then dissociatively recombine to form CH. In model M2 and M3, the reactionof C with excited H also contributes to the formation of CH. In model M3, enhanced formation of CH + plays a roleon the formation of C H at r (cid:46)
40 au, where C H abundance is enhanced by a factor of ∼ + contributes to the formation of CH through CH + + H whichforms CH +2 and then CH through the sequence described above. In model M2, the decreased abundance of C H at30 (cid:46) r (cid:46)
100 au is found to be linked to the enhanced production of CN in this region which efficiently competes withC H formation. It should however be noted that the enhanced formation of C H due to chemistry with excited H may not be enough to explain observed C H emission using ISM-like C/O ratios and C/O (cid:38) Hobservations as compared to what is predicted with standards C/O ratios (e.g. Bergin et al. 2016; Cleeves et al. 2018;Miotello et al. 2019). It is however still unclear whether this change in disks C/O ratios is induced by the differentialsequestration of oxygen and carbon at the surface of large grains in the disk miplane (e.g. Krijt et al. 2018, 2020) orby photodestruction of carbon grains in disks atmosphere (e.g. Anderson et al. 2017; Bosman et al. 2021).2.2.2.
Oxygen chemistry
The inclusion of O + H ( v, J ) has only a moderate impact on the computed abundances of OH and water in the M3model as compared to M1 (see Fig. 4 and 5). In both models, OH and water formation are mainly driven by X-raysthrough the production of H + and H +3 , and their successive reaction with atomic oxygen. As seen in these figures, M2overestimates slightly the abundance of OH and water (i.e. by a factor of ∼
5) in a thin layer located at z/r ∼ . − . hemistry of ro-vibrationally excited H in disks
50 100 150 r [au]0 . . . . . . z / r M1H O − − − − − − − r [au] M2H O − − − − − − − r [au] M3H O − − − − − − − l og ( n ( X )) / n H )
50 100 150 r [au]0 . . . . . . z / r M1CCH − − − − − − − r [au] M2CCH − − − − − − − r [au] M3CCH − − − − − − − l og ( n ( X )) / n H )
50 100 150 r [au]0 . . . . . . z / r M1CN − − − − − − − − − r [au] M2CN − − − − − − − − − r [au] M3CN − − − − − − − − − l og ( n ( X )) / n H )
50 100 150 r [au]0 . . . . . . z / r M1HCN − − − − − − − r [au] M2HCN − − − − − − − r [au] M3HCN − − − − − − − l og ( n ( X )) / n H )
50 100 150 r [au]0 . . . . . . z / r M1HNC − − − − − − − r [au] M2HNC − − − − − − − r [au] M3HNC − − − − − − − l og ( n ( X )) / n H )
50 100 150 r [au]0 . . . . . . z / r M1N H + − − − − −
10 50 100 150 r [au] M2N H + − − − − −
10 50 100 150 r [au] M3N H + − − − − − l og ( n ( X )) / n H ) Figure 5.
Same as Fig. 4 but for H O, C H, CN, HCN, HNC and N H + . and extending from r = 20 and 100 au as compared to M3. The higher abundance of OH and H O in this layer arefound to be linked to the enhanced production of CN in this model and in particular a slightly lower abundance ofC + which is one of the main destruction channels of OH and water in this layer. The chemistry of other moleculessuch as NO, HNO and NO + are also found to be affected by chemistry with ro-vibrationally excited H (see Fig. 6).For these molecules, this is due to the enhanced formation of NH and NH (see Section 2.2.4) and their subsequentreaction with O. 2.2.3. Sulfur chemistry
Ruaud et al. − − − C o l u m nd e n s i t y r a t i o M1 / M3M2 / M3 SH + CH + OHH OCCH NHNH CNHCNHNC
50 100 150 200 r [au]10 − − − C o l u m nd e n s i t y r a t i o NOHNOCN + NO + CNC +
50 100 150 200 r [au] N H + HCNH + NH +3 NS + Figure 6.
Vertical column density ratios of a selection of gas-phase molecules as a function of the distance from the star.Solid lines correspond to ratios between column densities computed in model M1 (no chemistry with excited H ) and M3 (fullmodel) while dashed lines show ratios between results obtained from model M2 (pseudo-level approximation) and M3. The grayshaded area indicate a factor of 5 deviation compared to results obtained from the full model. Even though the abundance of SH + is low throughout the disk, the inclusion of S + + H ( v, J ) has an importantimpact on its formation (see Fig. 4). As seen in this figure, models M2 and M3 give relatively different results withSH + being overestimated in the vertical directions of model M2 and slightly underestimated in the inner part of thedisk (i.e. at r (cid:46)
100 au). Quantum calculations show that H needs to be in v ≥ ( v ≥
2) states. Inmodel M3, H ( v ≥
2) states are more efficiently populated in the inner disk (the abundance of H ( v ≥
2) is on theorder of few 10 − − − up to r ∼
100 au, see Fig. 2). At greater distance from the star, the populations in thesestates decrease significantly hence lowering the formation efficiency of SH + . Except for SH + , sulfur chemistry is notparticularly affected by chemistry with excited H .2.2.4. Nitrogen chemistry
Nitrogen chemistry is strongly affected by the chemistry with ro-vibrationally excited H . In particular, the abun-dance of species such as CN, HCN and HNC is increased by a factor of ∼
100 in model M3 as compared to thereference model M1 (see Fig. 5). For model M2, the abundance of these species is increased by almost a factor of ∼ ( v, J ) toform NH for which the reaction barrier is 12650 K. NH then reacts with C + to form CN + . CN is then formed bycharge exchange with H while HCN/HNC are formed through reaction of CN + with H to form successively HCN + and HCNH + , which then recombines with electrons to form HCN and HNC. The overestimation of CN and HCN/HNCin model M2 as compared to model M3 comes from the fact that the fractional population of H in ( v >
2) states, forwhich E ( v, J ) > ∗ (see Fig. 2 and 3). As seen in Fig.5 and 6, the increased formation of CN and HCN also impacts N H + for which the computed vertical column densitiesare increased by a factor of at least 3 in models M2 and M3 as compared to model M1. The increased production ofNH is also found to impact the formation of molecules such as NH , NO, HNO, NO + , CN + , HCNH + , CNC + , NS + ,SiN and SiN + (see Fig. 6). Recently, Cazzoletti et al. (2018) used the pseudo-level approximation to explain CN hemistry of ro-vibrationally excited H in disks
50 100 150 200 r [au]10 N ( X ) [ c m − ] G − . = 10 G − . = 1 G − . = 0 . + SH + N H +
50 100 150 200 r [au]10 N ( X ) [ c m − ] G − . = 10 G − . = 1 G − . = 0 . Figure 7.
Computed vertical column densities of CH + , SH + , N H + , C H, CN and HCN as a function of the disk radius r formodel M3 and where the FUV flux in the 11 to 13.6eV photons range was varied by a factor of 10. G − . = 1 used for thereference model corresponds to a photon flux of 4 × photons cm − s − in the 11-13.6 eV range and at 1 au from the star. emission around the well studied disk TW Hya as originating from the PDR surface and being formed by the samereaction of N with excited H , where they assumed no barrier (i.e. similar to our model M2). Visser et al. (2018) usedthe same assumption to conclude that most of the observed HCN emission also comes from the PDR layer. While theimpact of this reaction on the formation of CN and HCN is confirmed by models shown here, it is however found thatthe use of the pseudo-level approximation lead to a factor of 3 to 5 overestimation in their computed vertical columndensities (see Fig. 6). 2.3. Sensitivity to the stellar FUV photons flux
In this section we study the effect of the FUV flux on the modeling results. As seen previously, the chemistry ofexcited H sensitively depends on the fractional populations in each ro-vibrational state of H which in turn dependon FUV pumping. We focus on the 11 to 13.6eV photons range which is poorly constrained in disks (e.g. Franceet al. 2014) but yet fundamental for H excitation and disk photochemistry. In particular, it is important to notethat most H fluorescent lines only depend on the photon flux in this energy range. This is because FUV pumpingtends to be dominated by electronic transitions from the lower vibrational levels of the ground state X Σ + g , (e.g.electronic Lyman and Werner transitions from H ( v = 0 , J <
8) all lie at λ < + , SH + , CN and HCN vary by a factor of ∼
10 when the FUV flux in the 11-13.6 eV rangevaries by a factor of 10. C H is found to be relatively insensitive to the FUV flux, except in a small region locatedat 30 (cid:46) r (cid:46)
100 au where its computed vertical column density varies by at most a factor of ∼ G − . = 1). Increased CN, HCN and C H column densities with FUV flux could explainsome of the positive correlations found in the emission of these molecules (e.g. Bergner et al. 2019). CONCLUSIONThe effect of H ro-vibrational excitation on the chemistry of protoplanetary disks is studied using a frameworkthat solves for the disk physical and chemical structure and includes a detailed calculation of H level populations.Chemistry with ro-vibrationally excited H is found to be efficient in the irradiated surface layer of disks where H is efficiently pumped by FUV photons and its efficiency sensitively depends on the fractional populations in eachro-vibrational state of H . Chemistry with excited H is found to play an important role on the formation of severalcommonly observed species in disks and in particular CN, HCN and HNC, for which the computed vertical columndensities are increased by 1 to 2 orders of magnitude for the full H population calculation compared to calculationswith no treatment of ro-vibrationally excited H , and by factors of ∼ − is considered to be at a single energy. Chemistry with ro-vibrationallyexcited H also enhances the formation of molecules such as SH + , CH + , N H + , NH, NH , NO, HNO, NO + , CN + ,0 Ruaud et al.
HCNH + , CNC + , NS + , SiN and SiN + . For most of these molecules, except CH + and SH + , the key reaction is N +H → NH which has a barrier of 12650 K with ground state H . Even though few studies exist on this particularsystem (e.g Pascual et al. 2002), rate constants as a function of H ro-vibrational levels are missing. Here it wasassumed that the reaction proceeds without a barrier when the energy of the level overcomes the energy barrier ofthe reaction (see Eq. 1). However this could be a strong over simplification of the problem and rate constants shouldtherefore be obtained for a more accurate assessment of CN/HCN chemistry. This is even more critical that moleculessuch as C H, CN or HCN are now commonly used to infer changes in the elemental disk C/O and N/O ratios (e.g.Bergin et al. 2016; Cleeves et al. 2018; Miotello et al. 2019), with implications for planetesimal formation and thecomposition of exoplanet atmospheres. It is also shown that the formation of these molecules is greatly affected bya change in the FUV flux in the 11 to 13.6eV energy range. In particular we find a positive correlation between theincrease in the FUV flux and the computed vertical column densities of molecules such as CN, HCN and to a lesserextent C H. However, the strength of the FUV photon flux at energies that pump H in protoplanetary disks (i.e.mostly 11-13.6 eV) is not well constrained and this further impacts our ability to make inferences on the chemical stateof the disk during planet formation epochs. With the upcoming launch of JWST, it will soon be possible to probeexcited H which will help to further constrain disks chemistry and potential molecular tracers of planet formationprocesses. Finally, it is found that computed vertical column densities from the common pseudo-level approximationfor H chemistry for most species agree within a factor (cid:46) A. RADIATIVE TRANSITIONSDue to its homonuclearity and symmetry, H has no permanent dipole moment. As a result, electric dipole ro-vibrational transitions of H are forbidden and only weak quadrupole transitions are allowed. For ro-vibrationallevels within the ground electronic state we use energy levels compiled in Dabrowski (1984) and quadrupole radiativetransition probabilities from Wolniewicz et al. (1998). For radiative transitions of the Lyman and Werner band systems(i.e. B Σ u → X Σ + g and C Π u → X Σ + g ), we use energy levels and transition probabilities calculated by Abgrallet al. (1993a,b, 2000). B. COLLISIONAL PROCESSESCollision excitation are included for collisions with H (Wrathmall & Flower 2007), He (Flower et al. 1998), H (Flower & Roueff 1998) and H + (Gerlich 1990). For collisions with He and H we use fit to collisional de-excitationrates provided by Le Bourlot et al. (1999) in the range 100 (cid:46) T gas (cid:46) q ( v (cid:48) J (cid:48) → vJ ) = g J g (cid:48) J q ( vJ → v (cid:48) J (cid:48) ) exp (cid:32) − E vJ − E v (cid:48) J (cid:48) T (cid:33) (B1)where g J is the statistical weight of the level J and E vJ its energy. Statistical weights are given by g J = (2 J + 1) forpara-H and g J = 3(2 J + 1) for ortho-H . C. FUV RADIATIVE PUMPINGThe FUV pumping rate from a ro-vibrational level ( v, J ) of the ground electronic sate to level ( v ∗ , J ∗ ) of an upperelectronic state is given by (e.g van Dishoeck & Black 1986; Sternberg & Dalgarno 1989) P ( vJ → v ∗ J ∗ ) = (cid:90) I ν σ ν ( vJ → v ∗ J ∗ ) exp (cid:0) − N vJ σ ν ( vJ → v ∗ J ∗ ) (cid:1) dν (C2) hemistry of ro-vibrationally excited H in disks ν is the transition frequency, I ν is the FUV photon intensity (in photons.cm − .s − .Hz − ), σ ν is the photonabsorption cross section of the transition, and N vJ is the column density of H molecule in level ( v, J ). Assuming thatthe FUV intensity is constant over the line profile and defining the equivalent width of the absorption line W ( vJ → v ∗ J ∗ ) = (cid:90) (cid:104) − exp (cid:0) − N vJ σ ν ( vJ → v ∗ J ∗ ) (cid:1)(cid:105) dν (C3)as well as the line self-shielding function θ ( vJ → v ∗ J ∗ ) = (cid:32) πe m e c f osc ( vJ → v ∗ J ∗ ) (cid:33) − dW ( vJ → v ∗ J ∗ ) dN vJ (C4)equation C2 may be rewritten P ( vJ → v ∗ J ∗ ) = πe m e c I ν f osc ( vJ → v ∗ J ∗ ) θ ( vJ → v ∗ J ∗ ) (C5)where f osc ( vJ → v ∗ J ∗ ) is the oscillator strength of the transition. The line self-shielding function is calculatedfollowing the analytical treatment of Federman et al. (1979). D. EXCITATION BY X-RAYSFast electrons created by X-rays ionization can excite H ro-vibrational levels via collisions. This can occur eitherby direct collisional excitation within the ground vibrational level or by cascade following excitation of the electronicstates (e.g. Gredel & Dalgarno 1995; Tin´e et al. 1997). Tin´e et al. (1997) provide entry probabilities for excitation ratesby X-rays for H in the ground vibrational state to H ( v = 0 − , J = 0 −
11) and use tabulated entry probabilitiesobtained for a fractional ionization of 10 − . E. EXCITATION AT FORMATION AND O/P CONVERSION ON GRAINSFor the excitation at formation, we follow an approach similar to Le Petit et al. (2006) and consider an equipartitionof the energy released at formation (i.e. 4.5 eV) with 1/3 of the energy being used as internal excitation of H ,1/3 being transferred to the grain and 1/3 being converted into kinetic energy. The fraction of H formed in eachro-vibrational levels follows f vJ ( T ) = g J exp( − E vJ /T ) (cid:80) g J exp( − E vJ /T ) (E6)where T = 8734K. As noted in Le Petit et al. (2006), this is different than assuming a Boltzmann distribution at T = 17322 K (i.e. ∼ . ∼ . . For the ortho/para conversion on grains, we followthe approach of Le Bourlot (2000) and consider that conversion occurs with an efficiency set by η c = exp (cid:0) − τ c k ev ) (E7)where τ c is the conversion timescale and k ev the evaporation rate of H from the grains. The o/p conversion rate isthen calculated by k o/p = α H v H (cid:104) σ d n d (cid:105) η c (E8)where α H is the H sticking probability taken from Matar et al. (2010) and Chaabouni et al. (2012), v H is thethermal speed of H molecules and (cid:104) σ d n d (cid:105) the product of the dust cross sectional area and the dust density averagedover the grain size distribution. REFERENCES Abgrall, H., Roueff, E., & Drira, I. 2000, A&AS, 141, 297,doi: 10.1051/aas:2000121 Abgrall, H., Roueff, E., Launay, F., Roncin, J. Y., & Subtil,J. L. 1993a, A&AS, 101, 323 Ruaud et al. —. 1993b, A&AS, 101, 273Ag´undez, M., Goicoechea, J. R., Cernicharo, J., Faure, A.,& Roueff, E. 2010, ApJ, 713, 662,doi: 10.1088/0004-637X/713/1/662Ag´undez, M., Roueff, E., Le Petit, F., & Le Bourlot, J.2018, A&A, 616, A19, doi: 10.1051/0004-6361/201732518Anderson, D. E., Bergin, E. A., Blake, G. A., et al. 2017,ApJ, 845, 13, doi: 10.3847/1538-4357/aa7da1Bergin, E. A., Du, F., Cleeves, L. I., et al. 2016, ApJ, 831,101, doi: 10.3847/0004-637X/831/1/101Bergner, J. B., ¨Oberg, K. I., Bergin, E. A., et al. 2019, ApJ,876, 25, doi: 10.3847/1538-4357/ab141eBlack, J. H., & Dalgarno, A. 1976, ApJ, 203, 132,doi: 10.1086/154055Bosman, A. D., Alarcon, F., Zhang, K., & Bergin, E. A.2021, arXiv e-prints, arXiv:2101.12502.https://arxiv.org/abs/2101.12502Cazzoletti, P., van Dishoeck, E. F., Visser, R., Facchini, S.,& Bruderer, S. 2018, A&A, 609, A93,doi: 10.1051/0004-6361/201731457Chaabouni, H., Bergeron, H., Baouche, S., et al. 2012,A&A, 538, A128, doi: 10.1051/0004-6361/201117409Cleeves, L. I., ¨Oberg, K. I., Wilner, D. J., et al. 2018, ApJ,865, 155, doi: 10.3847/1538-4357/aade96Dabrowski, I. 1984, Canadian Journal of Physics, 62, 1639,doi: 10.1139/p84-210Draine, B. T., & Bertoldi, F. 1996, ApJ, 468, 269,doi: 10.1086/177689Federman, S. R., Glassgold, A. E., & Kwan, J. 1979, ApJ,227, 466, doi: 10.1086/156753Flower, D. R., & Roueff, E. 1998, Journal of Physics BAtomic Molecular Physics, 31, 2935,doi: 10.1088/0953-4075/31/13/012Flower, D. R., Roueff, E., & Zeippen, C. J. 1998, Journal ofPhysics B Atomic Molecular Physics, 31, 1105,doi: 10.1088/0953-4075/31/5/017France, K., Schindhelm, E., Bergin, E. A., Roueff, E., &Abgrall, H. 2014, ApJ, 784, 127,doi: 10.1088/0004-637X/784/2/127Gerlich, D. 1990, JChPh, 92, 2377, doi: 10.1063/1.457980Gerlich, D., Disch, R., & Scherbarth, S. 1987, JChPh, 87,350, doi: 10.1063/1.453580Gredel, R., & Dalgarno, A. 1995, ApJ, 446, 852,doi: 10.1086/175843Heays, A. N., Bosman, A. D., & van Dishoeck, E. F. 2017,A&A, 602, A105, doi: 10.1051/0004-6361/201628742Kamp, I., Thi, W. F., Woitke, P., et al. 2017, A&A, 607,A41, doi: 10.1051/0004-6361/201730388Krijt, S., Bosman, A. D., Zhang, K., et al. 2020, ApJ, 899,134, doi: 10.3847/1538-4357/aba75d Krijt, S., Schwarz, K. R., Bergin, E. A., & Ciesla, F. J.2018, ApJ, 864, 78, doi: 10.3847/1538-4357/aad69bLe Bourlot, J. 2000, A&A, 360, 656Le Bourlot, J., Pineau des Forˆets, G., & Flower, D. R. 1999,MNRAS, 305, 802, doi: 10.1046/j.1365-8711.1999.02497.xLe Petit, F., Nehm´e, C., Le Bourlot, J., & Roueff, E. 2006,ApJS, 164, 506, doi: 10.1086/503252Matar, E., Bergeron, H., Dulieu, F., et al. 2010, JChPh,133, 104507, doi: 10.1063/1.3484867Miotello, A., Facchini, S., van Dishoeck, E. F., et al. 2019,arXiv e-prints, arXiv:1909.04477.https://arxiv.org/abs/1909.04477Nagy, Z., Van der Tak, F. F. S., Ossenkopf, V., et al. 2013,A&A, 550, A96, doi: 10.1051/0004-6361/201220519Nomura, H., Aikawa, Y., Tsujimoto, M., Nakagawa, Y., &Millar, T. J. 2007, ApJ, 661, 334, doi: 10.1086/513419Pascual, R. Z., Schatz, G. C., Lendvay, G., & Troya, D.2002, Journal of Physical Chemistry A, 106, 4125,doi: 10.1021/jp0133079Ruaud, M., & Gorti, U. 2019, ApJ, 885, 146,doi: 10.3847/1538-4357/ab4996Semenov, D., & Wiebe, D. 2011, ApJS, 196, 25,doi: 10.1088/0067-0049/196/2/25Sternberg, A., & Dalgarno, A. 1989, ApJ, 338, 197,doi: 10.1086/167193Sultanov, R. A., & Balakrishnan, N. 2005, ApJ, 629, 305,doi: 10.1086/431356Tielens, A. G. G. M., & Hollenbach, D. 1985, ApJ, 291,722, doi: 10.1086/163111Tin´e, S., Lepp, S., Gredel, R., & Dalgarno, A. 1997, ApJ,481, 282, doi: 10.1086/304048van Dishoeck, E. F., & Black, J. H. 1986, ApJS, 62, 109,doi: 10.1086/191135Visser, R., Bruderer, S., Cazzoletti, P., et al. 2018, A&A,615, A75, doi: 10.1051/0004-6361/201731898Wakelam, V., Loison, J. C., Herbst, E., et al. 2015, ApJS,217, 20, doi: 10.1088/0067-0049/217/2/20Walsh, C., Millar, T. J., Nomura, H., et al. 2014, A&A,563, A33, doi: 10.1051/0004-6361/201322446Wolniewicz, L., Simbotin, I., & Dalgarno, A. 1998, ApJS,115, 293, doi: 10.1086/313091Wrathmall, S. A., & Flower, D. R. 2007, Journal of PhysicsB Atomic Molecular Physics, 40, 3221,doi: 10.1088/0953-4075/40/16/003Zanchet, A., Ag´undez, M., Herrero, V. J., Aguado, A., &Roncero, O. 2013a, AJ, 146, 125,doi: 10.1088/0004-6256/146/5/125Zanchet, A., Godard, B., Bulut, N., et al. 2013b, ApJ, 766,80, doi: 10.1088/0004-637X/766/2/80 hemistry of ro-vibrationally excited H in disks13