EVIDENCE FOR DCO⁺ AS A PROBE OF IONIZATION IN THE WARM DISK SURFACE

In this study, a two-dimensional and azimuthally symmetric disk physical structure that represents a T Tauri disk has been adopted (i.e., structure of the TW Hya T Tauri system; see Cleeves et al. 2013; Schwarz & Bergin 2014 and references therein). Being the same settled disk structure as the one adopted by Schwarz & Bergin (2014), we simply refer to this paper for a complete description of the density/temperature structure and grain distribution.

We use the same deuterated chemical network as in Aikawa et al. (2012), who worked on star-forming cores, except for the following updates and modifications needed for disk chemistry. (i) The energy barriers of the endothermic reactions involving the CH₂D⁺ ion are updated following Roueff et al. (2013). (ii) The X-ray ionization of H₂ and He along with UV photolysis induced by X-rays are included (Fogel et al. 2011). (iii) Lyα photodesorption radiation on dust grains is taken into account (see Bethell & Bergin 2011; Fogel et al. 2011 for further details). (iv) CO, H₂, HD, and D₂ self-shielding are included in a time-dependent way (see Fogel et al. 2011). (v) Finally, grain surface reactions are limited to the formation of H₂, OH, and H₂O since gas-phase chemistry prevails in the DCO⁺ formation.

The network contains a total of 1565 species and 43,353 reactions.⁶ Among the reactions listed above, the model also includes grain surface recombination reactions, adsorption, photodesorption, two body reactions (including ion, molecule, negative ion, and neutral), cosmic-ray ionization (ζ = 1.3 × 10⁻¹⁷ s⁻¹), cosmic-ray-induced photodissociation of ice, photolysis, thermal desorption, and non-thermal desorption (i.e., cosmic-ray evaporation), gas phase, and grain surface photodissociation (see Hasegawa & Herbst 1993; Garrod et al. 2008; Fogel et al. 2011; Aikawa et al. 2012 for further details). Incidentally, in our analysis, following Garrod & Herbst (2006), we assume a CO binding energy set to 1150 K (which corresponds to a desorption temperature of about ∼21–25 K; see Supplementary Materials of Cleeves et al. 2014). Therefore, the CO snow line from our model is shifted by several AU in comparison with Schwarz & Bergin (2014). Although, the chemical evolution of the disk is run independently (i.e., a 1D vertical model), the code was run for a given range of radii resulting in a pseudo two-dimensional result as described by Schwarz & Bergin (2014) and Fogel et al. (2011). The gas-grain chemical model is run for 3 × 10⁶ yr (typical disk age) with 45 vertical zones and 22 radial zones.

In Figure 1, we illustrate where the CO snow line is in our model by showing the relative abundance to molecular hydrogen for CO, CO_ice, and N₂H⁺. The latter ion has been reported to be a good tracer of the CO snow line since it is destroyed by gas-phase CO through Reaction (6) (i.e., Hersant et al. 2009; Qi et al. 2013; Schwarz & Bergin 2014):

$$\begin{eqnarray}&&{{{\rm N}}_{2}}{{{\rm H}}^{+}}+{\rm CO}\to {\rm HC}{{{\rm O}}^{+}}+{{{\rm N}}_{2}}.\end{eqnarray} \tag{ 6 }$$

Our model is consistent with this interpretation.

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In Figure 1, we also show the relative abundance to molecular hydrogen for DCO⁺ along with the one of its two potential key precursors, CH₂D⁺ and H₂D⁺ (see Reactions (2) and (3)). It is immediately apparent that H₂D⁺ probes the CO snow line as expected from Reaction (2). Indeed, the H₂D⁺ distribution is clearly anticorrelated with the one of CO since H₂D⁺ is located beyond the CO snow line (i.e., where CO is adsorbed on ice grain mantles) and in the upper disk layers where the CO is photodissociated. As for CH₂D⁺, it is more abundant in the upper disk layers where ionization supplied by X-rays is higher. Regarding the overall distribution of the DCO⁺ abundance, it is more or less correlated with that of CO, with one important exception: there is a greater concentration in the surface of the inner disk. More specifically, the DCO⁺ distribution is not restricted to the CO snow line but rather spreads up to the disk surface with a maximal abundance reached in the inner warmer (T ∼ 50–100 K) surface layers (see Figure 1).

Reaction (2), involving H₂D⁺, is usually considered as the main source of DCO⁺ in disks at low temperatures (see Mathews et al. 2013). If this is the case, the qualitative distribution of DCO⁺ abundance should resemble that of CO. However, as shown in Figure 1, the bulk of the DCO⁺ abundance is located in a narrow layer near the surface. This finding suggests that Reaction (2) is not the only formation route for DCO⁺ in disks. This is further illustrated in Figure 2, which shows the DCO⁺, HCO⁺, CO_ice, and H₂D⁺ column densities as a function of the radius when Reaction (2) is activated (top panel) and turned off (bottom panel).⁷ The DCO⁺ profile remains almost the same in the inner 60 AU whether or not the H₂D⁺ channel (Reaction (2)) is involved. Further out, Reaction (2) contributes about 40% to the DCO⁺ abundance, the other main contribution being through HCO⁺ (via the reaction ${\rm HC}{{{\rm O}}^{+}}+{\rm D}\to {\rm DC}{{{\rm O}}^{+}}+{\rm H}$; Y. Aikawa et al. 2015, in preparation).

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One notable feature of Figures 3 and 4 is that the formation of DCO⁺ in the inner surface layers inside of 60 AU involves CH₂D⁺ or one of its product that have previously been created by Reaction (3). Indeed, Figure 3 shows the abundance of the DCO⁺ ion for up to 60 AU when Reaction (3) is activated (left panel) and turned off (right panel). It is immediately apparent that Reaction (3), which involves the CH₂D⁺ channel, leads to the observed maximal DCO⁺ abundance in the inner surface layers of the disk. Likewise, a similar result is observed in the abundance profiles of DCN and HDCO (see Figure 3) molecules that can both also be formed through Reaction (3). In addition, in Figure 4, we give the radial distribution of some key ions (such as CH₂D⁺ and CH₄D⁺) that can lead to the formation of DCO⁺ along with the one for H₂D⁺ when Reaction (3) is activated (top panel) and turned off (bottom panel). A decrease in the DCO⁺, CH₂D⁺, CH₃D⁺, and CH₄D⁺ column density is clearly observed when Reaction (3) is not activated in our network. Finally, we find that more than 80% of the DCO⁺ abundance in the inner 60 AU surface layers is due to a DCO⁺ formation through the pathway of Reactions (3)–(5).

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In Figure 5, we show that the use of the new exothermicities leads the warm channel (i.e., Reaction (3)) to dominate the DCO⁺ production. More specifically, Figure 5 illustrates the impact, within the inner disk, of the change of exothermicity on the DCO⁺/HCO⁺ abundance ratio but also on that of other easily observable molecules (e.g., DCN, formaldehyde). One notable feature is that the abundance of DCO⁺, DCN, and HDCO is enhanced in the 20 AU inner radii when the chemical modeling includes the new exothermicities set by Roueff et al. (2013; ΔE of 654 K for Reaction (3)), as opposed to the chemical modeling that includes the previous ones (ΔE = 370 K; see Smith et al. 1982). Furthermore, it is immediately apparent that within the 20 AU inner radii the distribution of the DCO⁺/HCO⁺ abundance ratio is affected by the change of exothermicity: the latter does not increase with increasing radius while using the most recent exothermicities (Roueff et al. 2013), whereas assuming a lower exothermicity (i.e., the one of Smith et al. 1982), the ratio shows a rise with increasing radius in the inner disk.

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Our results are a consequence of the increase in the exothermicity ΔE of Reaction (3), as suggested by Roueff et al. (2013), which favors deuterium fractionation in warm gas, up to temperatures as high as T ≤ 300 K. We note that in the case of DCO⁺ only, which has its main formation route from channel (5), and for an exothermicity of 654 K, a temperature ≥71 K is hot enough to turn off the DCO⁺ enrichment toward the inner disk. Indeed, the activation of the backward reaction is shifted to higher temperatures, enabling efficient deuteration closer to the star. This is a nice illustration of the influence of the energy budget of deuteration reactions. This is similar to the well-known effect of the H₂ ortho/para ratio on deuterium chemistry (see, e.g., Pagani et al. 1992; Flower et al. 2006): at low temperatures, the backward counterpart of Reaction (1) is strongly favored for ortho-H₂ over para-H₂ due to a lower ${\Delta }E$ for the former. However, we did not consider the spin states of H₂ in the present study. As DCO⁺ is mainly produced by Reaction (3), we do not expect this omission to be of crucial importance in the present case (see Section 4.4 for further details).

DCO⁺ has been proposed to be a good tracer of the CO snow line by Mathews et al. (2013), assuming H₂D⁺ as its parent molecule. However, our study points out that the reaction that involves H₂D⁺ as a parent molecule (see Reaction (2)) is unlikely to be the main formation route that leads to the bulk of the DCO⁺ abundance within the disk. Alternatively, our study shows that reactions involving CH₂D⁺ as a parent molecule of DCO⁺ (see Reactions (3)–(5) as possible pathways for the formation of DCO⁺) are responsible for the observed high abundance of DCO⁺ in the inner surface layers of the disk. This finding leads us to argue that instead of temperature, DCO⁺ is rather tracing ionization. Indeed, the distribution of the DCO⁺ abundance is similar to the one of CO except for its high abundance in the the inner warmer surface layers of the disk where ionization through X-rays is present. In that respect, we predict that DCO⁺ is a tracer of the inner tens of AU of protoplanetary disks surrounding X-ray active T Tauri stars.

Chemical pathways involving the CH₂D₊ channel (Reaction (3)) can sufficiently lead to the formation of different deuterated molecules, such as DCO⁺, DCN, and HDCO in warm conditions (e.g., T ∼ 70–100 K; see Wootten 1987; Öberg et al. 2012). In that context, our study not only shows that the high abundance of DCO⁺ in the inner disk results from pathways involving the CH₂D⁺ ion as a parent molecule, but in addition shows that the DCN and HDCO abundance patterns are also affected by the change of exothermicity (see Figures 3 and 5). Indeed, the DCN and HDCO abundances are enhanced while using the CH₂D⁺ formation route with the most recent exothermicities (ΔE = 654 K; Roueff et al. 2013).

Interestingly enough, from their ALMA observations, Mathews et al. (2013) analyzed the DCO⁺ emission in the disk surrounding HD 163296 as coming from a narrow (confined between 110 and 160 AU) ringlike structure. Although the radial extent of the ring may be subject to revision (C. Qi et al. 2015, in preparation), such a narrow ring, located far from the star, is difficult to reconcile with our modeling.

Likewise, based on SMA observations (Qi et al. 2008) of the TW Hydrae disk and empirical fitting of the data, Öberg et al. (2012) found a central depression and inferred a DCO⁺ abundance profile that increases with abundance with the radius. These suggestions disagree with our results since we find that with higher activation barriers (Roueff et al. 2013), the warm channel (Reaction (3)) dominates, leading to a strong abundance of DCO⁺ in the inner regions of the disk.

One possible caveat could be the ortho:para ratio. Teague et al. (2015) have investigated the effect of the ortho:para ratio on the deuterium fractionation and have found that by a million years, the o:p ratio is low. However, assuming a higher o:p ratio might change our results by reducing the deuterium enhancement. Roueff et al. (2013) show that the exothermicity in Reaction (3) is reduced if there is a significant amount of ortho-H₂ present in the gas (see Table 3 of Roueff et al. 2013). As a result, the backward reaction is actually comparable to the old warm channel rates (Smith et al. 1982). Thus, one way to chemically mimic a hole in the DCO⁺ distribution is to have a gradient in the o:p ratio in the disk that is higher in the inner regions and lower in the outer disk.

Another possible caveat could be the ionization structure. The presence of structure in the inner disk could perhaps prevent the propagation of the X-ray photons in the inner disk and may lead to a reduced production of DCO⁺. However, this effect may not be as important for the more substantially flared outer disk.

Finally, the disk surrounding HD 163296 is much warmer than our TW Hydrae disk model. In this disk, the CO snow line is located around 150 AU (Qi et al. 2011), while it is around 20 AU in our model. Another possibility would thus be that the HD 163296 disk is warm enough (T ≥ 71 K) and/or present a higher o:p ratio to enable endothermic reactions to prevent deuterium fractionation in the inner 100 AU, thereby truncating the DCO⁺ layer. Direct modeling of the DCO⁺ chemistry in the warm disk surrounding HD 163296 would be necessary for further comparisons. In any case, further observations of HD 163296 and TW Hya are required to understand the DCO⁺ distribution in light of our new DCO⁺ formation pathway.