The Molecular Composition of Shadowed Proto-solar Disk Midplanes Beyond the Water Snowline

The disk midplane temperature is potentially affected by the dust traps/rings. The dust depletion beyond the water snowline will cast a shadow. In this study, we adopt a detailed gas-grain chemical reaction network, and investigate the radial gas and ice abundance distributions of dominant carbon-, oxygen-, and nitrogen-bearing molecules in disks with shadow structures beyond the water snowline around a proto-solar-like star. In shadowed disks, the dust grains at r ∼ 3–8 au are predicted to have more than ∼5–10 times the amount of ices of organic molecules such as H2CO, CH3OH, and NH2CHO, saturated hydrocarbon ices such as CH4 and C2H6, in addition to H2O, CO, CO2, NH3, N2, and HCN ices, compared with those in non-shadowed disks. In the shadowed regions, we find that hydrogenation (especially of CO ice) is the dominant formation mechanism of complex organic molecules. The gas-phase N/O ratios show much larger spatial variations than the gas-phase C/O ratios; thus, the N/O ratio is predicted to be a useful tracer of the shadowed region. N2H+ line emission is a potential tracer of the shadowed region. We conclude that a shadowed region allows for the recondensation of key volatiles onto dust grains, provides a region of chemical enrichment of ices that is much closer to the star than within a non-shadowed disk, and may explain to some degree the trapping of O2 ice in dust grains that formed comet 67P/Churyumov-Gerasimenko. We discuss that, if formed in a shadowed disk, Jupiter does not need to have migrated vast distances.

The disk thermal structure plays a predominant role in controlling the disk chemical structure. The midplane temperature T(r) in protoplanetary disks is determined by heating due to viscous dissipation (only in the innermost region) and the stellar irradiation grazing the disk surface (e.g., Oka et al. 2011;Mori et al. 2021). Since the amount of heating per unit volume from both of these sources decreases with increasing disk radius r, in a smooth (non-shadowed) disk, the temperature monotonically decreases as the disk radius increases (Kusaka et al. 1970;Kenyon & Hartmann 1987;Chiang & Goldreich 1997;Oka et al. 2011). Inside the water snowline, H 2 O ice evaporates from the dust grain surfaces into the gas phase, whereas outside it is frozen out onto the dust grain surfaces (Hayashi 1981). In addition, the cold outer disk is needed for the formation of various complex organic molecules, since the sequential hydrogenation of CO on the cold (T(r) ∼ 10-30 K) dust grain surfaces leads to the formation of H 2 CO and CH 3 OH, which are key feedstock molecules that produce more complex organic molecules (e.g., Tielens & Hagen 1982;Watanabe & Kouchi 2002;Cuppen et al. 2009;Fuchs et al. 2009;Drozdovskaya et al. 2014;Furuya & Aikawa 2014;Walsh et al. 2014Walsh et al. , 2016Chuang et al. 2016;Bosman et al. 2018;Aikawa et al. 2020).
Under the assumption of classical monotonically decreasing disk temperature profiles, previous studies have discussed the disk radial locations of formation of planets. Here we introduce the example of Jupiter in the solar system. Recent extensive observations toward Jupiter's atmosphere (by the Galileo probe, Cassini, and Juno spacecraft) have revealed uniform enrichment patterns of the elemental abundances from protosolar abundances by a factor of two to four, (see, e.g., Atreya Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Li et al. 2020). The heavy element enrichment has been proposed to originate from planetesimals and/or pebbles dissolved in the atmospheres (e.g., Pollack et al. 1986;Iaroslavitz & Podolak 2007;Hori & Ikoma 2011;Venturini et al. 2016;Shibata & Helled 2022) and/or core erosion (e.g., Moll et al. 2017). It has been noted that the abundances of highly volatile elements, such as N and noble gas elements, are comparable to the other elemental abundances. Owen et al. (1999) suggested that this uniform enrichment originates from planetesimals formed in extremely cold (T(r) < 30 K) environments, where nitrogen and noble gases can freeze. Öberg & Wordsworth (2019) and Bosman et al. (2019) suggested that such uniform enrichment could be explained if the Jovian core had formed at r > 30 au, where the disk temperature is extremely cold (T(r) < 30 K, outside the N 2 snowline) under the classical monotonically decreasing disk temperature profile. However, according to theoretical studies on core formation and migration (Bitsch et al. 2019), the occurrence rate of the migration of a core from r > 30 au to 5 au is extremely low, and the core migration timescale is of the order of a few megayears even if such a migration occurs. Kruijer et al. (2017Kruijer et al. ( , 2020 discussed that Jupiter's core may be formed within 1 Myr to demarcate the inner and outer solar system, on the basis of the isotope analyses of meteorites. However, the disk temperature profile may not have a monotonically decreasing distribution if a disk has substructures, as found in recent observations of radial gas and dust distributions on many disks (e.g., Andrews 2020;. Several previous studies have suggested that a shadowed region where the direct stellar light does not reach is potentially generated, depending on the inner disk density structure. A puffed inner disk rim can block the radiation from the central star and cast a shadow, so-called self-shadowing (e.g., Dullemond et al. 2001;Dullemond & Dominik 2004;Dullemond & Monnier 2010;Flock et al. 2016;Ueda et al. 2017). Ueda et al. (2019) showed that a dust pileup at the inner edge of the magnetorotational instability dead-zone casts a shadow behind it, producing cold regions of T(r) ∼ 50 K at r ∼ 2-7 au around Herbig Ae/Be stars. Jang-Condell & Turner (2012), Turner et al. (2012), Isella & Turner (2018), and Okuzumi et al. (2022) described that the outer wall of the gap produced by a giant planet receives extra starlight heating and puffs up, throwing a shadow across the disk beyond. Isella & Turner (2018) showed that the surface brightness contrast between the outer wall and shadow for the 1000 M ⊕ (∼3.1 M Jupiter ) planet is an order of magnitude greater than a model neglecting the temperature disturbances. In addition, Ueda et al. (2021) and Okuzumi et al. (2022) discussed that a small puffedup rim and outer shadowed region will result in the formation of ring and gap structures in disks by thermal wave instabilities. Recently, Ohashi et al. (2022) found a steep temperature decrease outside the dust clumps at r ∼ 20 au in the disk around Class 0/I protostar L1527 IRS. They suggest that the dust clumps create a shadowed region outside, resulting in the sudden drop in temperature.
A dust pileup at the water snowline may also cast a shadow behind it. The dust surface density just inside the water snowline can be enhanced by orders of magnitude. This is because efficient fragmentation slows the radial drift of silicate grains, leading to enhanced production of small grains within the water snowline (e.g., Birnstiel et al. 2010;Banzatti et al. 2015;Cieza et al. 2016;Pinilla et al. 2017;Müller et al. 2021).
Such fragmented dust, with higher surface density and scale height, will cast a shadow behind the water snowline and provide cold environments where volatile materials can freeze (Ueda et al. 2019;Ohno & Ueda 2021).
These disk shadow structures may have a significant effect on the atmospheric composition of planets forming within. Ohno & Ueda (2021) computed the temperature structure of a proto-solar (T Tauri) disk that has a shadowed region beyond the water snowline, and investigated the radial volatile distributions. They found that the vicinity of the current orbit of Jupiter (r ∼ 5 au) could be T(r) < 30 K if the small dust surface density decreases by a factor of 30 across the water snowline. They discussed that the shadow can cause the condensation of most volatile substances, namely N 2 and noble gases, and that the dissolution of shadowed solids can explain the elemental abundance patterns of the Jovian atmosphere even if Jupiter formed near the current orbit. However, Ohno & Ueda (2021) included limited carbon-, nitrogen-, and oxygenbearing molecules (H 2 O, CO, CO 2 , C 2 H 6 , N 2 , and NH 3 only; see also Öberg & Wordsworth 2019). In addition, they fixed the total (gas+ice) abundances of each volatile and calculated the balance between thermal desorption and freeze-out onto dust grains within each molecular species only. In order to investigate the effects of the shadow beyond the water snowline on disk chemical evolution including H 2 CO, CH 3 OH, and more complex organic molecules (such as, e.g., NH 2 CHO and HCOOCH 3 ), more detailed gas-grain chemical modeling is needed (e.g., Walsh et al. 2014Walsh et al. , 2015Eistrup et al. 2016Eistrup et al. , 2018Bosman et al. 2018;Notsu et al. 2021).
In this study, we calculate the chemical structure of a shadowed disk midplane around a T Tauri star (a proto-solarlike star), using a detailed gas-grain chemical reaction network. We investigate the radial abundance distributions of dominant carbon-, oxygen-, and nitrogen-bearing molecules and the radial distributions of elemental abundance ratios (C/O and N/O ratios) in the gas and ice of disks with shadow structures. We also investigate the dependence of the disk chemical structures on ionization rates and initial abundances. We discuss the effects of disk shadowing on chemical evolution of complex organic molecules and forming planetary atmospheres. We also discuss the implications of our results for the chemical composition of comets and asteroids in the solar system. The outline of our model calculations are explained in Section 2. The results and discussion of our calculations are described in Sections 3 and 4, respectively. The conclusions are presented in Section 5.

The Physical Model of the Protoplanetary Disk Midplane
We adopt the physical model of a steady, axisymmetric Keplerian disk around a T Tauri star (a proto-solar-like star) with mass M * = 1.0 M e , radius R * = 2.6 R e , and effective temperature T * = 4300K. For the disk density structure, we adopted the same parameterized disk model as Ohno & Ueda (2021) in which the dust surface density steeply varies around the water snowline. The radial surface density profiles are described by the following equations: where r is the disk radius from the central star, Σ gas is the gas surface density, Σ dust is the surface density of the small dust (0.1-100 μm) that contributes to the dust opacity, and R SL (H 2 O) = 1.3 au is the assumed radial position of the water snowline. In protoplanetary disks, the maximum grain size is expected to be larger than that of the typical ISM dust due to significant dust growth. However, large grains (  100μm) have little impact on the disk temperature structure because they have small opacity and are depleted at the disk surface where stellar irradiation is absorbed. The power index of the radial gas surface density profile (= −3/5) is calculated under the assumption of a disk with steady accretion and viscous heating (e.g., Nakamoto & Nakagawa 1994;Oka et al. 2011). We adopted various values of the parameter f (= 1.0 to 0.3, 0.03, and 0.003) to investigate the effects of the magnitude of shadowing on the disk thermal and chemical structures. The actual values of the parameter f depend on the efficiency of fragmentation of silicate and icy grains, which is controlled by the turbulence viscosity strength and stickiness of the dust grains (e.g., Birnstiel et al. 2010;Banzatti et al. 2015;Pinilla et al. 2017). Banzatti et al. (2015) reported dust surface density variations of f ∼ 0.1, 0.001, and 0.01 around the water snowline for turbulence viscosity strengths of α t 7 = 10 −2 , 10 −3 , and 10 −4 , respectively.
The disk midplane temperature profiles were extracted from the results of the 2D thermal model calculation in Ohno & Ueda (2021; see also Section 2 in Ueda et al. 2019). In this calculation, the above radial density profiles (see Equations (1) and (2)) are adopted, and the Monte Carlo radiative-transfer code RADMC-3D (Dullemond et al. 2012) is used. Scattering is assumed to be isotropic because full-scattering treatment is computationally expensive. We expect that the temperature structure is not significantly modified even if we consider the full scattering because the temperature at the shadowed region seems to be insensitive to the presence of scattering (Ueda et al. 2019). The vertical dust density distribution and the temperature structure are mutually dependent; thus, the radiative-transfer calculations were iteratively performed to obtain a self-consistent disk structure (for more details, see Ueda et al. 2019). The calculations also include the internal radiative flux produced by viscous accretion, q acc , determined by the following equation (Lynden-Bell & Pringle 1974;Pringle 1981;Nomura & Millar 2005): , 3 acc t gas s 2 K where α t is set to be 3 × 10 −4 , ρ gas is the gas mass density, c s is the sound speed, and Ω K is the Keplerian frequency. The surface density coefficient (Σ 0 = 670 g cm −2 ) and α t in Equation (1) are adjusted so that the water snowline position is outside the current Earth orbit (= 1.3 au) in the calculation of the temperature profiles. We note that we have adopted the same dust surface density within the water snowline in all models so that the position of the water snowline is fixed. This is because in this study, we focus on the effects of shadowing on disk chemical structures beyond the water snowline. Eistrup et al. (2016) adopted a lower surface density model (Σ gas (5.2 au) = 16 g cm −2 ) than our adopted model (Σ gas (5.2 au) = 249 g cm −2 ), and the water snowline position in their model is around 0.7 au. We assume the same dust and gas temperatures (T dust = T gas = T), which is a valid assumption in the dense molecular regions of the disk. The radial profile of the midplane gas mass density ρ 0, gas (r) is given by the following equation: , 4 0, gas gas gas where h gas = c s /Ω K is the gas scale height. We adopted the DSHARP dust opacity model ; see also, e.g., Henning & Stognienko 1996;Draine 2003;Warren & Brandt 2008), and assumed a dust-sized distribution that follows a power law with an index of −3.5, similar to the Mathis, Rumpl, & Nordsieck (MRN) distribution (Mathis et al. 1977), with minimum and maximum dust radii of 0.1 and 100 μm, respectively. We assume that larger grains have been removed from the disk atmosphere by settling and radial drift. The bulk densities of dust grains ρ internal are set to be 3.0 g cm −3 for the region where the icy component is evaporated (T > 160 K) and 1.4 g cm −3 elsewhere. We note that icy grains can efficiently coagulate into larger ( ?1 mm) dust particles and centimeter-sized pebbles outside the water snowline (e.g., Ros & Johansen 2013;Sato et al. 2016;Dráżkowska & Alibert 2017;Pinilla et al. 2017), but such large dust particles and pebbles have negligible contribution to the opacity compared with that of smaller dust particles (Miyake & Nakagawa 1993), and they are confined to the disk midplane. Thus, Σ dust is not necessarily the same as the total surface density of all solid components (dust grains and pebbles), for example, outside the water snowline (Banzatti et al. 2015). We note that in our disk chemical modeling (see Section 2.2), we use the dust density profile in the disk midplane calculated from this small dust (0.1-100 μm) surface density profile Σ dust . The left panel of Figure 1 shows Σ gas (r) and Σ dust (r) for different values of the parameter f (= 1.0, 0.3, 0.03, and 0.003). The right panel of Figure 1 shows the radial profiles of the gas number density n gas (r) and temperature T(r) in the disk midplane for different values of the parameter f. n gas (r) is calculated by dividing ρ 0, gas (r) by the mean particle mass (= 2.33 amu). The values of n gas are largest in the innermost region (10 14 cm −3 at r  1.4 au), and decrease as the value of r increases (10 12 cm −3 at r  17 au). The value of T within the water snowline is independent of f, and is primarily controlled by viscous heating, yielding the radial dependence of ∝ r −9/10 (Oka et al. 2011).
As demonstrated in Ohno & Ueda (2021), the depletion of small dust grains outside the water snowline casts a shadow, changing the disk midplane temperature significantly. In the cases of smaller values of f, the decrease of dust surface density outside the water snowline results in reduced dust opacity, which reduces the amount of stellar radiation received per unit volume and cools the outer region compared with the case of the non-shadowed disk ( f = 1.0). The values of T at r ∼ 1.3-17 au decrease with decreasing f, as the shadow extends farther out. Even in the case of a small variation in the dust density profile with f = 0.3, T is around 20 K lower than that in the non-shadowed disk with f = 1.0. For f 0.03, T is <30 K at r ∼ 3-8 au, and <25 K at around the current orbit of Jupiter (∼5 au). In contrast, the values of T at r > 20 au increase with decreasing f, although the degree of increase is small and T is <35 K even for f = 0.003. We interpret that reduced dust surface density beyond the water snowline allows the reprocessed stellar radiation to enter the outer disk midplane from the upper disk surface (Cleeves 2016). At the outer disk midplane (r > 20 au), the heating effect by such radiation overcomes the cooling effect, which reduces as r increases. The disk temperature is expected to be higher in the outer disk (beyond r > 20 au) if we assume lower surface densities than we initially chose. The values of disk masses are determined by the density profile in the outer region of the disk. We note that we have adopted the surface densities following a single power-law profile for the sake of simplicity (see Equations (1) and 2). The disk gas mass within 20 au and 40 au is ∼2.2 × 10 −2 M e and ∼5.8 × 10 −2 M e , respectively. Eistrup et al. (2016) adopted a disk surface density profile with an outer exponential cutoff radius of r c = 20 au. If we include such an outer exponential cutoff with r c ∼20 au in the disk surface density profile, the total disk mass within 40 au will be around half of the value without cutoff. Recently, Trapman et al. (2022) estimated from HD and C 18 O line observations that the disk masses for some typical Class II T Tauri disks (such as TW Hya) are around a few ×10 −2 M e .
We assumed that the water snowline position as 1.3 au, but it might be outside the current orbit of Mars (1.52 au). Hansen (2009) discussed that Mars forms from a protoplanet that has moved by scattering from near the current orbit of Earth.
In our calculations, the far-UV (FUV) and X-ray radiation from both the central T Tauri star and interstellar radiation fields are neglected, since the disk has a high surface density (Σ gas (r) ∼10 2 − 10 3 g cm −3 ) and the disk midplane is effectively shielded (e.g., Nomura & Millar 2005;Nomura et al. 2007;Walsh et al. 2015). Cleeves et al. (2014b), Eistrup et al. (2016Eistrup et al. ( , 2018, and Schwarz et al. (2018Schwarz et al. ( , 2019 discussed that disk chemical evolution (such as chemical processing of CO) is affected by the degree of (cosmic-ray) ionization. In order to investigate the effects of ionization on chemistry in the shadowed disk, we adopt two values of radially constant ionization rates ξ CR (r) = 1.0 × 10 −17 [s −1 ] and 1.0 × 10 −18 [s −1 ] (e.g., Cleeves et al. 2014b;Eistrup et al. 2016Eistrup et al. , 2018. The former high ionization value includes contributions from the decay products of short-lived radionuclides (SLRs; Cleeves et al. 2013aCleeves et al. , 2013b and from cosmic-rays, originating externally to the disk (e.g., Umebayashi & Nakano 2009;Padovani et al. 2018), whereas the latter low ionization value considers contribution from the decay products of SLRs only. We note that, in reality, the ionization rate has radial dependence, since the contribution from SLRs decreases as r increases (Cleeves et al. 2013b) and that from cosmic-rays increases as r increases (e.g., Umebayashi & Nakano 2009;Padovani et al. 2018;Aikawa et al. 2021;Seifert et al. 2021;Fujii & Kimura 2022). Using Equation (30) of Cleeves et al. (2013b) and our assumed Σ gas (r) profile, the ionization rates for the contribution from SLRs are estimated to be ∼5 × 10 −19 [s −1 ] at r ∼5 au and ∼7 × 10 −19 [s −1 ] at r ∼1 au. Nonetheless, we assume a constant value of the ionization rate at all radii to clarify its impacts on the disk chemical evolution.

Calculation of the Disk Chemical Structure
We calculated the chemical evolution of the shadowed disk midplane around a T Tauri star (a proto-solar-like star) using a detailed gas-grain chemical reaction network. The chemical reaction network adopted in this work is basically similar to that in Notsu et al. (2021). The detailed background theories and procedures are also discussed in our previous works (e.g., Walsh et al. 2010, Heinzeller et al. 2011Eistrup et al. 2016Eistrup et al. , 2018Eistrup & Walsh 2019, Notsu et al. 2016, 2019, although there are some differences between the models in these studies and our adopted model, which we explain in this Section. Our model calculates the time-dependent chemical evolution at the disk midplane of each radial distance and does not include physical mass transport in the radial direction by viscous accretion and in the vertical direction by diffusive turbulent mixing and disk winds (Heinzeller et al. 2011).

Gas-phase Reactions
Our gas-phase chemistry includes the complete network from the release of the UMIST Database for Astrochemistry, called RATE12, and is publicly available 8 (McElroy et al. 2013). RATE12 includes gas-phase two-body reactions, photoionization and photodissociation, direct cosmic-ray ionization, and cosmic-ray-induced photoionization and photodissociation. Since the FUV radiation fields from the central T Tauri star and interstellar FUV fields are neglected in our calculations (see also Section 2.1), the photodissociation and photoionization by FUV radiation are effectively zero. In the cosmic-ray-induced photoreactions, UV photons are generated internally via the interaction of secondary electrons produced by cosmic-rays with H 2 molecules (Gredel et al. 1987(Gredel et al. , 1989. As in Walsh et al. (2015), we also added a set of three-body reactions and "hot" H 2 chemistry, although they are not expected to be important around the water snowline (∼100-200 K). Moreover, the gas-phase chemical network is supplemented with reactions for important species, for example the CH 3 O radical, which are not included in RATE12. The gasphase formation and destruction reactions for these species are from the Ohio State University (OSU) network (Garrod et al. 2008).

Gas-grain Interactions
As in Notsu et al. (2021), we include the freeze-out of gasphase molecules on dust grains, and the thermal and nonthermal desorption of molecules from dust grains (Hasegawa et al. 1992;Walsh et al. 2010Walsh et al. , 2012Notsu et al. 2016). As nonthermal desorption mechanisms, cosmic-ray-induced photodesorption, reactive desorption (see Section 2.2.3), and direct cosmic-ray-induced (thermal) desorption (Leger et al. 1985;Hasegawa & Herbst 1993;Hollenbach et al. 2009) are adopted. We note that the direct cosmic-ray-induced (thermal) desorption has no significant impact on chemistry, since its reaction timescale is typically much longer (?10 7 yr) than the age of a Class II disk (Hollenbach et al. 2009). We adopt the value for the integrated cosmic-ray-induced UV photon flux as 10 4 photons cm −2 s −1 (Prasad & Tarafdar 1983;Walsh et al. 2014). We scale the internal UV photon flux by the cosmic-ray ionization rate. On the basis of the adopted dust-sized distribution (see Section 2.1), we assume compact spherical grains with an average radius a of 0.1 μm. We note that the total dust surface area is mainly dominated by the smallest dust grains, under the MRN distribution. The values of photodesorption yields adopted in this work, Y des ( j), are the same as those adopted in Notsu et al. (2021). We use experimentally determined photodesorption yields, where available (e.g., Öberg et al. 2007, 2009a, 2009bFillion et al. 2014;Bertin et al. 2016;Cuppen et al. 2017, see Table 1 of Notsu et al. 2021). For all species without experimentally determined photodesorption yields, a value of 10 −3 molecules photon −1 is used. As in Notsu et al. (2021), we include the fragmentation pathways for photodesorption of water and methanol molecules (e.g., Öberg et al. 2009b;Arasa et al. 2010Arasa et al. , 2015Bertin et al. 2016;Cruz-Diaz et al. 2016).
The sticking coefficient is assumed to be 1 for all species, except for H, which leads to H 2 formation (for more details, see Appendix B.2 of Bosman et al. 2018). We adopt the same values of the binding (desorption) energies E des ( j) for all molecules as used in Notsu et al. (2021). In Table 1, E des ( j) for several dominant molecules and their estimated snowline positions R SL ( j) in the non-shadowed disk ( f = 1.0) are listed (see also Section 3). We defined the snowline positions as the radii where the gas and ice abundances of each molecule are the same because of the balance between thermal desorption and freeze-out. We note that the binding energies of molecules depend on the chemical compositions and physical structures (e.g., crystal or amorphous) of the ice mantles on the dust grains (e.g., Cuppen et al. 2017;Penteado et al. 2017;Kouchi et al. 2021, see also Section 4.2). For CO and N 2 , we assume the values of pure CO and N 2 ices, respectively (Öberg et al. 2005).

Grain-surface Reactions
For the grain-surface reactions, we adopt the same reaction network as Notsu et al. (2021) used. Those reactions are mostly based on the OSU network (Garrod et al. 2008), with including some extended network for some molecules (such as CH 3 OH and NH 2 CHO; see Section 2.2.3 of Notsu et al. 2021and, e.g., Noble et al. 2015Chuang et al. 2016). In addition to grainsurface two-body reactions (Hasegawa et al. 1992) and reactive desorption, grain-surface cosmic-ray-induced photodissociation is also included in our calculations (Garrod et al. 2008;Walsh et al. 2014Walsh et al. , 2015. Only the top two monolayers of the ice mantle are chemically active. We assume that the size of the barrier to surface diffusion is 0.3 × E des ( j) . For the lightest reactants, H and H 2 , we adopt either the classical diffusion rate or the quantum tunneling rate depending on which is fastest (Hasegawa et al. 1992;Bosman et al. 2018). For the quantum tunneling rates, we adopt a rectangular barrier of width 1.0 Å (Hasegawa et al. 1992;Bosman et al. 2018).

Initial Abundances
As Eistrup et al. (2016Eistrup et al. ( , 2018 conducted, the disk chemical evolution is calculated with two different sets of initial abundances: molecular species and atomic species. All abundances in our calculations of this paper are with respect to the total number density of H nuclei. For both sets of initial abundances (molecular and atomic), the elemental ratios are consistent. The choice of these initial abundances is motivated by the following two extreme scenarios about the history of the disk midplane material (Öberg & Bergin 2021;). The use of molecular initial abundances assumes that the disk material is wholly inherited from the molecular cloud and the pre-stellar core from which the central star formed, implying a more quiescent mode of disk formation. The enhanced deuterium fractionation of water and organic molecules in disks is considered to be a probe of pre-stellar inheritance, since efficient deuteration of water and organic molecular ices is only possible in cold and embedded prestellar cloud cores where UV radiation is almost completely attenuated and CO is frozen out onto dust grains (e.g., Cleeves et al. 2014a;Furuya et al. 2016Furuya et al. , 2017Drozdovskaya et al. 2019;Jensen et al. 2021). Drozdovskaya et al. (2019) described that the relative abundances of volatile organic molecules (with respect to, e.g., methanol) correlate, with some scatter, between Atacama Large Millimeter/submillimeter Array (ALMA) data toward the protostar IRAS 16293-2422 B and Rosetta's in situ monitoring data of comet 67P/Churyumov-Gerasimenko. This result implies that the volatile composition of solar system comets may be partially inherited from the pre-stellar and protostellar phases. In contrast, the use of atomic initial abundances implies that full chemical reset has occurred during disk formation. Throughout disk formation, infalling material is subject to radiation from the central star and accretion shocks, which may alter the chemical composition of material (e.g., Visser et al. 2009;Drozdovskaya et al. 2016;Miura et al. 2017;Notsu et al. 2021). Öberg & Bergin (2021) and  discussed that neither a complete inheritance nor a complete reset scenario can explain the results of recent disk observations (by, e.g., ALMA) and the full solar system record. They described that both must have played an important role during disk formation.
As Walsh et al. (2015) and Notsu et al. (2021) adopted, the values of volatile elemental abundances for He, O, C, N, and S are, respectively, 9.75 × 10 −2 , 3.20 × 10 −4 , 1.40 × 10 −4 , 7.50 × 10 −5 , and 8.00 × 10 −8 relative to total hydrogen nuclei density. For other elements, we use the low-metallicity elemental abundances from Graedel et al. (1982). In the reset scenario, we use the above elemental abundances as initial abundances of our disk chemical calculations, except hydrogen. We assume that the abundances for H 2 and H are, respectively, 5.0 × 10 −1 and 5.0 × 10 −5 . Table 2 shows the gas and ice fractional molecular abundances with respect to total hydrogen nuclei density, which are used as molecular initial abundances in the inheritance scenario. In this Table 2, we include dominant species and molecules that are important in disk chemical evolution. We adopt the same molecular abundances as Notsu et al. (2021) used for the initial abundances in their chemical modeling. Previous chemical calculations (e.g., Walsh et al. 2015;Eistrup et al. 2016Eistrup et al. , 2018Drozdovskaya et al. 2016) adopted a similar water-rich molecular abundances as initial conditions.

Results
In Sections 3.1-3.2, we investigate the results for our standard model (assuming molecular initial abundances and ξ CR (r) = 1.0 × 10 −17 [s −1 ]), and describe the effects of a disk shadow on the radial molecular abundance distributions. In Appendix A, we also study the disk chemical structures for different disk ionization rates and for atomic initial abundances (see also Section 3.3). In addition, in Sections 3.1-3.2 we show the chemical abundance distributions at t = 10 6 yr, which is the typical age of Class II disks and consistent with previous studies (e.g., Eistrup et al. 2016). In Appendix B, we also investigate the time evolution of radial molecular abundance distributions (see also Section 3.4).
In the non-shadowed disk, the dominant carbon carriers at r = 5.3 au are CO 2 ice (∼36%) and CO gas (∼40%). In the shadowed disk, CO freezes out onto the dust grain surface, and the amounts of CO 2 ice (∼30%), CO ice (∼25%), and ices of unsaturated hydrocarbon molecules (such as C 3 H 4 ) decrease, whereas those of H 2 CO ice (∼19%), CH 4 ice (∼6%), C 2 H 6 ice (∼5%), HCN ice (∼4%), NH 2 CHO ice (∼4%), and CH 3 OH ice (∼3%) increase. The enhanced abundances of these organic molecules in the shadowed disks are owing to the reaction pathways in which the sequential hydrogenation of CO on the dust grain surfaces and cosmic-ray-induced photodissociation of CH 3 OH are the key reactions, as we explain in Sections 3.2.2 and 3.2.3.
In the non-shadowed disk, the dominant nitrogen carriers at r = 5.3 au are N 2 gas (∼76%) and NH 3 ice (∼17%). In the shadowed disk, N 2 mostly freezes out onto the dust grain surface, and the amount of N 2 gas (∼5%) decreases, whereas that of NH 3 ice is almost similar (∼20%), and those of N 2 ice (∼51%) and other nitrogen-bearing molecules such as NH 2 OH, NH 2 CHO, and HCN ices (∼7%-8% each) increase. The enhanced abundances of NH 2 OH, NH 2 CHO, and HCN in the shadowed disks are due to hydrogenation reactions on the dust grain surfaces (see Section 3.2.3).
According to these results, in shadowed disks the dust grains at around the current orbit of Jupiter (r ∼5.3 au) are expected to have significant amounts of saturated hydrocarbon ices such as CH 4 and C 2 H 6 , ices of organic molecules such as H 2 CO, NH 2 CHO, and CH 3 OH, in addition to H 2 O, CO, CO 2 , NH 3 , N 2 , HCN, and NH 2 OH ices, compared with those in the non-shadowed disks (mostly ices of H 2 O, CO 2 , NH 3 , and unsaturated hydrocarbon molecules). These abundant saturated hydrocarbons and various organic molecules such as H 2 CO, NH 2 CHO, and CH 3 OH were not reported by Ohno & Ueda (2021), since they approximated various organic molecules by considering C 2 H 6 alone. In addition, our results provide intriguing implications for the compositions of small bodies (such as comets and asteroids) formed at around the current orbit of Jupiter, as we discuss in Section 4.2.

Radial Molecular Abundance Distributions for Our Standard Model
In this Section, we describe the effects of disk shadowing on the radial molecular abundance distributions. The radial profiles of fractional abundances with respect to total hydrogen nuclei densities n X /n H at t = 10 6 yr for dominant carbon-, oxygen-, and nitrogen-bearing molecules are shown in Figures 3-5 in Sections 3.2.1-3.2.3, with separate panels for each molecule, for different values of the parameter f (=1.0, 0.3, 0.03, and 0.003), respectively. In Figures 6-8 in Section 3.2.4, the radial fractional abundance distributions at t = 10 6 yr of other major carbon-, nitrogen-, and oxygenbearing molecules, mainly complex organic molecules, are shown. In Figure 9 in Section 3.2.5, the radial profiles of fractional abundances with respect to total hydrogen nuclei densities at t = 10 6 yr for sums of larger (complex) organic molecules are shown. We show this to demonstrate the efficiency of conversion from more simple to more complex Figure 6. Same as Figure 3, but for C 2 H 2 (n C H 2 2 /n H , top-left panel), C 2 H 4 (n C H 2 4 /n H , top-right panel), C 3 H 2 (n C H 3 2 /n H , middle-left panel), CH 3 CCH (n CH CCH 3 /n H , middle-right panel), CH 2 CCH 2 (n CH CCH 2 2 /n H , bottom-left panel), and CH 3 CHCH 2 (n CH CHCH 3 2 /n H , bottom-right panel). molecules for different dust depletion factors. The panels in these Figures 3-9 show the results for the radially constant cosmic-ray ionization rate of ξ CR (r) = 1.0 × 10 −17 [s −1 ] with assuming molecular initial abundances (the "inheritance" scenario).
Since previous studies (e.g., Eistrup et al. 2016Eistrup et al. , 2018 have discussed the chemical structure of the non-shadowed disk ( f = 1.0) in detail, in this paper we mainly focus on the effects of shadowing on disk chemical structures. We note that the results of our calculations for the non-shadowed disk are largely consistent with those in Eistrup et al. (2016Eistrup et al. ( , 2018 with some exceptions, such as HCN (see Section 3.2.3 of this paper).  CO (carbon monoxide), CO 2 (carbon dioxide), and O 2 (molecular oxygen). The water snowline position (∼1.3 au, T(r) ∼140 K) and the H 2 O gas abundances (∼2 × 10 −4 ) within the water snowline do not change for various values of f, since the disk midplane temperature is significantly changed only beyond the water snowline. We note that the gas abundances of other molecules are also unchanged within the water snowline.
Outside the water snowline, H atoms are supplied onto the dust grain surface from the gas or produced in situ within the grain mantles. We note that in the gas phase, H atoms are mainly produced by cosmic-ray-induced photodissociation of H 2 . Since the fractional abundances of H 2 with respect to total H nuclei (∼5 × 10 −1 ) are much larger than those of other molecules, the gas-phase production is dominant. Thus, if we conduct disk chemical modeling with atomic initial abundances (see Appendix A), H 2 O ice is efficiently formed outside the water snowline via the following reaction (Eistrup et al. 2016), However, because we have adopted abundant initial water ice abundances (=1.984 × 10 −4 , see Table 1), further water ice formation in the outer disk midplane does not proceed efficiently. Thus, the H 2 O ice abundances beyond the water snowline are relatively constant (∼(1-2) × 10 −4 ) for various values of f. We note that the H 2 O ice abundances increase (from ∼1.5 × 10 −4 to ∼2 × 10 −4 ) in the coldest regions with T (r)  20 K (at r ∼3-8 au for f = 0.003 and at r  25 au for f = 1.0), where the formation of CO 2 ice does not proceed efficiently (see below).
As introduced later, the chemical conversion of CO plays vital roles in producing other carbon-bearing molecules. CO molecules accreting onto the dust grain surfaces can react with OH radicals produced on the ice by cosmic-ray-induced photodissociation of H 2 O ice (e.g., Drozdovskaya et al. 2016;Eistrup et al. 2016Eistrup et al. , 2018Schwarz et al. 2018Schwarz et al. , 2019. This produces CO 2 ice via the following grain-surface reaction: In addition, for the ISM level ionization rate (ξ CR (r) =10 −17 [s −1 ]), the following destruction pathway of gas-phase CO by He + is also efficient:  Nomura et al. 2016Nomura et al. , 2021Schwarz et al. 2016;Krijt et al. 2018Krijt et al. , 2020Bergner et al. 2020;Zhang et al. 2020Zhang et al. , 2021.
In the shadowed disk ( f 0.03), CO freezes out onto dust grains at around the current orbit of Jupiter (r ∼3-8 au, T(r)  25 K), and CO ice abundances are ∼(3-6) × 10 −5 . In addition, CO returns to the gas phase at r > 8 au. At r > 20 au, CO (re-)freezes out onto dust grains, and the adsorption front moves outward with decreasing f, since the values of T(r) at r > 20 au increase (35 K at the maximum) with decreasing f (see also Section 2.1). This CO abundance profile is consistent with the results reported in Ohno & Ueda (2021). We suggest that reducing the dust surface density beyond the water snowline allows the reprocessed stellar radiation to enter the outer disk midplane from the disk upper layers, and that the penetration of such radiation causes the temperature to rise in the outer disk (r > 20 au).
In the non-shadowed disk ( f = 1.0), the CO 2 snowline position is r ∼3.3 au (T(r) ∼75 K). CO 2 ice abundances are ∼5 × 10 −5 between the CO 2 and the CO snowlines, and decrease (<10 −6 ) beyond the CO snowline. The CO 2 snowline position moves inward with decreasing f. In the shadowed disk ( f 0.03), CO 2 ice abundances decrease at r ∼3 − 8 au (from ∼5 × 10 −5 to <10 −5 ) with decreasing f, whereas H 2 O ice abundances at such radii slightly increase (from ∼1.5 × 10 −4 to ∼2 × 10 −4 ). Eistrup et al. (2016) discussed that at the coldest conditions (T(r)  20 K), formation of H 2 O ice (Equation (5)) is faster than that of CO 2 ice (Equation (6)). This is because at the coldest conditions (T(r)  20 K), the mobility of H is higher than those of CO and OH, and because the adsorption rate of atomic hydrogen onto dust grains at T(r)  20 K becomes larger than that at T(r) > 20 K (E des (H) = 650 K).
In our standard disk model, O 2 abundances are much smaller (10 −6 for gas and 10 −9 for ice) than those of H 2 O, CO, and CO 2 . O 2 is formed in the gas phase via the following reaction Eistrup et al. 2016;Notsu et al. 2021): Figure 9. Same as Figure 3, but for the total reservoir of larger (complex) organic molecules. The left panel ("All") shows the sums of all of larger organic molecules for which we show the results in Section 3.2 (Figures 4-8). The right panel ("Reduced") shows the sums of all of larger organic molecules after we subtract dominant unsaturated hydrocarbon molecules for which we show the results in Figure 6.
Since O 2 is very volatile (the binding energy E des (O 2 ) =898 K; Noble et al. 2012), it remains in the gas phase at r  20 au in the non-shadowed disk ( f = 1.0). The O 2 gas abundances between the water and O 2 snowlines are ∼10 −7 − 10 −6 . In the shadowed disk ( f 0.03), O 2 freezes out onto dust grains at r ∼2-10 au, and returns to the gas phase at r > 10 au. Outside the O 2 snowline, O 2 ice is formed via the following grain-surface reaction (Taquet et al. 2016;Eistrup & Walsh 2019): In our standard disk model, the initial atomic oxygen is zero (see Table 2). In addition, the gas-phase production route of atomic oxygen from CO by the reaction of Equation (7) is not efficient outside the O 2 snowline since the binding energies of CO and O 2 are almost similar (see Table 1). Thus, in our standard disk model, O 2 ice abundances are low (= 10 −9 ) both in the shadowed and non-shadowed disks. We note that our calculations also yield higher O 2 ice abundances (∼10 −5 − 10 −4 ) for atomic initial abundances and low ionization rates. Such larger abundances are consistent with the measured cometary abundances (Bieler et al. 2015;Rubin et al. 2015b, see also Section 4.2 of this paper). Moreover, we find that in the shadowed disk, such an O 2 abundant region is located in the inner region (r ∼2-10 au) compared with that in the non-shadowed disk (r  20 au), as detailed in Section 4.2 and Appendix A.1. Figure 4 shows the radial profiles of fractional abundances for other dominant carbon-bearing molecules (CH 4 , C 2 H 6 , H 2 CO, and CH 3 OH). We note that CH 4 (methane) and C 2 H 6 (ethane) are dominant acyclic saturated hydrocarbon molecules (alkanes). In the non-shadowed disk ( f = 1.0), the CH 4 snowline position is r ∼15 au (T(r) ∼38 K), and the CH 4 gas abundances between the CO 2 and CH 4 snowlines are ∼10 −7 . These values are much smaller than those in the disk with a lower ionization rate (=10 −18 [s −1 ]; see Appendix A) and that for the initial CH 4 gas abundance (=1.120 × 10 −6 ). Outside the CH 4 snowline, CH 4 ice abundances are slightly enhanced (∼10 −5 ) compared with the initial CH 4 ice abundances (=7.384 × 10 −6 ).

Other Dominant Carbon-bearing Molecules
Here we describe the dominant formation and destruction routes of CH 4 both in the gas phase and icy phase. The destruction of gas-phase CO by He + (see Section 3.2.1) produces C + , and a sequence of reactions with, e.g., H 2 transform C + to, e.g., CH 2 + /CH 3 + /CH 5 + , which lead to CH 4 gas and ice (e.g., Aikawa et al. 1999;Furuya & Aikawa 2014;Bosman et al. 2018, see Section 3.2.1). In addition, Bosman et al. (2018) and Eistrup et al. (2018) discussed that CH 4 ice is also produced both inside/outside the CO snowline through the hydrogenation of CH 3 ice, which is formed by cosmic-rayinduced photodissociation of CH 3 OH (see also below). Inside the CH 4 snowline, CH 4 gas is destroyed by cosmic-ray-induced photodissociation and ion-molecule reactions (such as CH 4 + C + ), and the carbon is thus converted from CH 4 gas to CO 2 , H 2 CO, and hydrocarbons such as, e.g., C 2 H 2 , C 2 H 4 , and C 3 H 4 (Aikawa et al. 1999;Eistrup et al. 2016Eistrup et al. , 2018Yu et al. 2016, see also Section 3.2.4).
The CH 4 snowline positions moves inward with decreasing f. In the shadowed disk ( f 0.03), CH 4 snowline positions are r  2 au, and CH 4 ice abundances at r ∼2-15 au are around ∼10 −5 . This result indicates that the CH 4 ice abundances are comparable in both CO sublimation and frozen regions. Thus, we interpret that the above reaction pathway starting from cosmic-ray-induced photodissociation of CH 3 OH is efficient for CH 4 ice formation in this region.
Previous modeling studies suggested that unsaturated hydrocarbon molecules (such as C 2 H 2 , C 3 H 2 , and C 3 H 4 ) are efficiently produced with the chemical reaction pathways starting from CH 4 + C + , where C + is formed by CO + He + (e.g., Aikawa et al. 1999;Furuya & Aikawa 2014;Eistrup et al. 2016Eistrup et al. , 2018Yu et al. 2016;Bosman et al. 2018, see Section 3.2.1). In addition, such unsaturated hydrocarbon molecules are also supplied by the cosmic-ray-induced photodissociation of CH 4 and subsequent gas-phase combination reactions of CH x radicals (e.g., Aikawa et al. 1999;Eistrup et al. 2016;Yu et al. 2016). These reaction pathways are efficient in the inner warm disk, at least within the CH 4 snowline (see also Section 3.2.4). The saturated hydrocarbons including C 2 H 6 are formed on the grain surfaces by the hydrogenation of such unsaturated hydrocarbon ices (e.g., Aikawa et al. 1999;Bosman et al. 2018). In addition, Bosman et al. (2018) and Eistrup et al. (2018) discussed that C 2 H 6 ice is also produced both inside/outside the CO snowline by CH 3ice + CH 3ice , where CH 3 ice is formed by cosmic-ray-induced photodissociation of CH 3 OH ice. Thus, we conclude that grainsurface reactions are needed to form icy-phase saturated hydrocarbon molecules, including C 2 H 6 .
In the shadowed disk ( f 0.03), C 2 H 6 snowline positions are r < 2 au, and C 2 H 6 ice abundances at r ∼2-10 au significantly increase (∼5 × 10 −6 ) compared with the values in the non-shadowed disk. We interpret that the reaction pathway starting from CH 3 OH ice destruction becomes more important at these radii of the shadowed disk, since the abundances of unsaturated hydrocarbon ices (such as C 2 H 2 , C 3 H 2 , and C 3 H 4 ) decrease in the shadowed disk (see Section 3.2.4 for details).
In the non-shadowed disk ( f =1.0), the H 2 CO (formaldehyde) and CH 3 OH (methanol) snowline positions are r ∼1.8 au (T(r) ∼100 K) and ∼1.5 au (T(r) ∼120 K), respectively, and they are just outside the water snowline (r =1.3 au). The H 2 CO and CH 3 OH ice abundances outside their snowlines increase with increasing r. The H 2 CO ice abundances between the H 2 CO and CO snowlines are ∼8 × 10 −6 at most, which is similar to the initial H 2 CO ice abundance (=8.437 × 10 −6 ). The CH 3 OH ice abundances between the CH 3 OH and CO snowlines are ∼2 × 10 −7 , which is smaller than the initial CH 3 OH ice abundance (=6.027 × 10 −7 ). We suggest that the differences in the CH 3 OH and H 2 CO abundances with respect to the initial abundances inside the CO snowline are also related to whether or not gas-phase formation pathways are present (e.g., Fockenberg & Preses 2002;Atkinson et al. 2006;Loomis et al. 2015;Walsh et al. 2016;Pegues et al. 2020). Both H 2 CO and CH 3 OH ice abundances increase outside the CO snowline (∼(2-5) × 10 −5 for H 2 CO ice and ∼(2-9) × 10 −6 for CH 3 OH ice).
The freeze-out of CO onto dust grains plays a central role in producing organic molecules, such as H 2 CO and CH 3 OH. According to previous studies (e.g., Tielens & Hagen 1982;Watanabe & Kouchi 2002;Cuppen et al. 2009;Fuchs et al. 2009;Drozdovskaya et al. 2014;Furuya & Aikawa 2014;Walsh et al. 2014Walsh et al. , 2016Chuang et al. 2016;Bosman et al. 2018;Aikawa et al. 2020; see also Appendix A.2), the following sequential hydrogenation of CO on the dust grain surfaces leads to the formation of H 2 CO and CH 3 OH ices: This grain-surface reaction pathway produces a large amount of H 2 CO and CH 3 OH ices in the cold regions where CO freezes out onto dust grains. The cosmic-ray-induced photodissociation of CH 3 OH ice produces many radicals such as CH 3 O, CH 3 , and CH 2 OH ices, and radical-radical reactions on the warmer grains also create more complex organic molecules, in addition to atom addition reactions on the colder grains . We note that our chemical reaction network includes both hydrogenation and abstraction pathways along the methanol formation route (Chuang et al. 2016), and CH 2 OH ice is the dominant methanol H-atom abstraction product.
In the shadowed disk ( f 0.03), the H 2 CO and CH 3 OH ice abundances at r ∼2-10 au significantly increase (∼(1-5) × 10 −5 for H 2 CO ice and ∼(2-9) × 10 −6 for CH 3 OH ice) compared with the values in the non-shadowed disk, since the temperature is low (T(r)  30 K) and the sequential hydrogenation of CO ice (Equations (10) and (11)) proceeds efficiently. In contrast, their ice abundances at r  20 au become a bit smaller (∼10 −5 for H 2 CO ice and ∼(1-3) × 10 −6 for CH 3 OH ice), since the CO adsorption front moves outward with decreasing f. Figure 5 shows the radial profiles of fractional abundances for dominant nitrogen-bearing molecules (N 2 , NH 3 , HCN, and NH 2 CHO). In the non-shadowed disk ( f =1.0), the N 2 (molecular nitrogen) snowline position is r ∼24 au (T(r) ∼23 K), which is slightly outside the CO snowline. For the atomic initial abundances, atomic N quickly forms N 2 gas and it freezes out onto dust grains outside its snowline (Schwarz & Bergin 2014;Eistrup et al. 2016). In addition, for the molecular initial abundances, the initial atomic N abundance (=2.1 × 10 −5 ; see Table 1) is similar to the initial N 2 gas + ice abundance (=1.5 × 10 −5 ; see Table 1), and this atomic N is also quickly converted to N 2 in the disk. Thus, the N 2 gas + ice abundances are relatively constant (∼(2-3) × 10 −5 ) throughout the disk for various values of f and various initial conditions (see also Appendix A.3).

Dominant Nitrogen-bearing Molecules
In the shadowed disk ( f 0.03), like CO, N 2 freezes out onto dust grains at around the current orbit of Jupiter (r ∼3-8 au), and N 2 ice abundances are ∼2 × 10 −5 . In addition, N 2 returns to the gas phase at r > 8 au. At r > 20 au, N 2 (re-)freezes out onto dust grains, and the adsorption front moves outward with decreasing f, since T(r) at r > 20 au increases (35 K at the maximum) with decreasing f (see also Section 2.1). This N 2 abundance profile is consistent with the results reported in Ohno & Ueda (2021).
In the non-shadowed disk ( f =1.0), the NH 3 (ammonia) snowline position is r ∼2.3 au, which is slightly outside the water snowline (r =1.3 au). NH 3 ice abundances just outside the NH 3 snowline (r ∼2-4 au) are =10 −6 , and those at r > 5 au are ∼1 × 10 −5 , which is similar to the initial NH 3 ice abundance (=1.327 × 10 −5 ). We suggest that on the warm grain surfaces at r ∼2-4 au, NH 3 ice is converted to NH 2 CHO ice via the following grain-surface reaction route (Jones et al. 2011;Walsh et al. 2014;López-Sepulcre et al. 2015): where NH 2 ice is formed by the cosmic-ray-induced photodissociation of NH 3 ice.
In the shadowed disk ( f 0.03), NH 3 snowline positions are r 2 au. NH 3 ice abundances at r ∼2-5 au are significantly enhanced, since the disk temperature decreases, and the above destruction route of NH 3 ice (see Equation (12)) becomes inefficient.
Formamide (NH 2 CHO) has been proposed as a key precursor of various (pre)metabolic and (pre)genetic molecules such as pyruvic acid and adenine (Saladino et al. 2012). Gasphase NH 2 CHO has been detected in pre-stellar cores and protostar envelopes (e.g., Kahane et al. 2013;López-Sepulcre et al. 2015;Okoda et al. 2021) and comets (e.g., Bockelée-Morvan et al. 2000), but has not yet been detected in Class II disks. The NH 2 CHO snowline position (r ∼1.2 au, T(r) ∼150 K) is slightly inside the water snowline (E des (NH 2 CHO) =5560 K, E des (H 2 O) =4880 K); thus, the NH 2 CHO snowline position does not move in our chemical modeling.
In the non-shadowed disk ( f =1.0), the NH 2 CHO ice abundances are 10 −6 in the outer cold disk (around the CO/N 2 snowlines, r ∼14-33 au), and <10 −7 at r 10 au. In addition, NH 2 CHO is efficiently formed (10 −6 ) just outside its snowline (r ∼1.2-4 au). We interpret that just outside its snowline, the above radical-radical formation route on the warm dust grains is efficient (see Equation (12)).
In the shadowed disk ( f 0.03), NH 2 CHO ice abundances at around the current orbit of Jupiter (r ∼3-8 au) are enhanced (10 −6 ). We propose that the following hydrogenation routes become efficient in this region. Garrod et al. (2008), and López-Sepulcre et al. (2015 discussed that grain-surface NH 2 CHO can form via the atom addition reactions in the cold region, such as the following reaction routes: where OCN ice is formed via the grain-surface reactions (CN ice +O ice and ON ice +C ice ) or gas-phase radical-radical reactions. We note that our chemical reaction network includes a competing hydrogenation abstraction pathway during hydrogenation from HNCO to NH 2 CHO, on the basis of the experimental results in Noble et al. (2015). HCN (hydrogen cyanide) and CN (cyanide) are the simplest molecules containing both C and N atoms, and reactions including HCN lead to the formation of more complex cyanides (such as CH 3 CN and aminoacetonitrile H 2 NCH 2 CN; Öberg et al. 2011;Noble et al. 2013). In the non-shadowed disk ( f =1.0), the HCN snowline position is r ∼1.5 au (T(r) ∼120 K), which is just outside the water snowline (r =1.3 au). HCN ice abundances are ∼(1-3) × 10 −6 at r ∼3-20 au and ∼4 × 10 −6 at r  20 au, which are slightly smaller/larger than the initial HCN ice abundance (=2.772 × 10 −6 ). Eistrup et al. (2016) showed much lower HCN ice abundances (=10 −7 outside the HCN snowline) for their model calculations with molecular initial abundances, since they set the initial HCN ice abundance to zero.
In the shadowed disk ( f 0.03), the HCN ice abundances at around the current orbit of Jupiter (r ∼3-8 au) are slightly enhanced (∼5 × 10 −6 ). According to Aikawa et al. (1999) and Eistrup et al. (2016), HCN is formed through the gas-phase reaction of HCO with an N atom, with subsequent freeze-out onto dust grains. HCO gas is efficiently formed by hydrogenation of CO on the cold dust grain surface and cosmic-rayinduced desorption of HCO ice (see also Sections 3.2.1 and 3.2.2). Schwarz & Bergin (2014) and Eistrup et al. (2018) showed that HCN ice becomes abundant in the outer cold region of the disk where CO freezes out onto dust grains, although it is efficiently produced within a few megayears. Our calculations for both non-shadowed and shadowed disks also show that HCN ice is efficiently formed at the cold regions where CO freezes out onto dust grains. Thus we confirm that the above HCN formation route, which starts from hydrogenation of CO, is dominant in the disks.
As we describe in Section 3.2.2 (see also, e.g., Aikawa et al. 1999;Furuya & Aikawa 2014;Eistrup et al. 2016Eistrup et al. , 2018Yu et al. 2016;Bosman et al. 2018), the formation pathways of these unsaturated hydrocarbon molecules are efficient within the CH 4 snowline, since the gas-phase chemical reaction pathways starting from CH 4 + C + , and the cosmic-ray-induced photodissociation of CH 4 and subsequent gas-phase combination reactions of CH x radicals are active. In the shadowed disks ( f 0.03), the CH 4 snowline positions are r 2 au, and such gas-phase formation reactions do not proceed efficiently at r  2 au. Thus, the unsaturated hydrocarbon ices are deficient at r ∼3-15 au (including the current orbit of Jupiter), in contrast to saturated hydrocarbons such as CH 4 and C 2 H 6 . Figure 7 shows the radial profiles of fractional abundances for CH 3 NH 2 (methylamine), CH 2 NH (methylene imine), CH 3 CN (acetonitrile), HC 3 N (cyanoacetylene), NH 2 OH (hydroxylamine), and HNCO (isocyanic acid). Figure 8 shows the radial profiles of fractional abundances for CH 3 CHO (acetaldehyde), CH 3 OCH 3 (dimethyl ether), HCOOH (formic acid), HCOOCH 3 (methyl formate), CH 3 COOH (acetic acid), and C 2 H 5 OH (ethanol). The ice abundances of CH 3 NH 2 and NH 2 OH at r ∼3-8 au (around the Jupiter orbit) are smaller in the non-shadowed disk (∼10 −8 and ∼2 × 10 −6 for f =1.0, respectively) than those in the shadowed disk (∼(2-7) × 10 −6 and ∼(3-8) × 10 −6 for f 0.03, respectively). These are saturated molecules. In contrast, the ice abundances of CH 2 NH, HC 3 N, HCOOH, HCOOCH 3 , CH 3 COOH, and HNCO at r ∼3-8 au are larger in the non-shadowed disk (e.g., ∼10 −7 − 10 −6 for HCOOH and f =1.0) than those in the shadowed disk (e.g., 10 −8 for HCOOH and f 0.03). Moreover, the ice abundances of CH 3 CN, CH 3 CHO, CH 3 OCH 3 , and C 2 H 5 OH at r ∼3-8 au are larger for f =0.03 (e.g., ∼10 −7 − 10 −6 for CH 3 CN) than those for f =1.0, 0.3, and 0.003 (e.g., <10 −7 for CH 3 CN). Walsh et al. (2014) discussed that CH 3 NH 2 is formed via the sequential hydrogenations of CH 2 NH ice, where CH 2 NH ice is originated from atom addition to small hydrocarbon radicals (CH 3 , CH 2 ) on the dust grain surfaces. In addition, Garrod et al. (2008) and Walsh et al. (2014) described that on the warm dust grain surfaces, the association of the methyl and amine radicals (CH 3ice + NH 2ice ) is also dominant. Such small hydrocarbon radicals are efficiently formed both in the warm and cold grain surfaces by cosmic-ray-induced photodissociation of CH 3 OH ice, which is efficiently produced by Equations (10) and (11) (see Section 3.2.2 and Eistrup et al. 2018). Thus, we find that the former atom addition reaction route is efficient in the shadowed region (T(r) < 30 K). Garrod et al. (2008) explained that NH 2 OH is formed initially by NH + OH addition on grains, followed by hydrogenation. Also, the addition reaction of OH+NH 2 becomes dominant on the warm dust grains (see also, e.g., Molyarova et al. 2018). We propose that the former reaction route is efficient in the shadowed region.
We find that the dependence of CH 3 CN and HC 3 N ice abundances on the values of f are determined by the combination of the following reaction routes. Walsh et al. (2014) described that similar to H 2 CO, both CH 3 CN and HC 3 N can form in the gas phase through multiple pathways. On the cold dust grain surfaces (T(r) ∼10-30 K), CH 3 CN ice is formed via the sequential hydrogenations of C 2 N ice, and C 2 N can form via C ice + CN ice and N ice + C 2ice , or freeze out from the gas phase . In warmer regions, CH 3 CN ice can also form via the following radical-radical reaction with no reaction barrier, CN ice + CH 3ice . In addition, on the cold dust grain surface (T(r) ∼10-30 K), HC 3 N ice is formed via the hydrogenation of C 3 N ice. Garrod et al. (2008), Walsh et al. (2014), and López-Sepulcre et al. (2015) described that HNCO is formed on the cold dust grain surfaces by hydrogenation of OCN, but is further hydrogenated to NH 2 CHO (see Equations (13) and (14) in Section 3.2.3).
For other organic molecules, grain-surface association of large radical-radical reactions in the warm regions (T(r) ∼50 K) is needed for their formation (e.g., Garrod Walsh et al. 2014). In addition, the dependence of ice abundances on the values of f is determined by the combination of the following radical-radical reactions and radical formation reactions from CO and/or CH 3 OH on the dust grain surfaces. CH 3 CHO, CH 3 OCH 3 , HCOOCH 3 , and C 2 H 5 OH ices can form via the following radical-radical reactions with no reaction barriers on the dust grain surfaces, respectively (Garrod et al. 2008;Walsh et al. 2014 The radicals of HCO, CH 3 , CH 3 O, and CH 2 OH are produced during the sequential hydrogenation of CO to form CH 3 OH and/or the cosmic-ray-induced photodissociation of CH 3 OH ice. The abundance of CH 3 OH ice at r ∼3-8 au is larger in the shadowed disk than that in the non-shadowed disk (see Section 3.2.2), whereas the shadowed disks with lower values of f (=0.003) exhibit lower ice abundances for CH 3 CHO, CH 3 OCH 3 , HCOOCH 3 , and C 2 H 5 OH. This trend is owing to the temperature dependence of the radical-radical reaction efficiency: the mobility of such radicals is lower than that of hydrogen and light atoms, especially on the cold dust grain surfaces (T(r) ∼10-30 K). HCOOH and CH 3 COOH ices can also form via the radialradical reaction routes on the warm dust grain surfaces. However, CH 3 CO, the precursor of CH 3 COOH and CH 3 CHO (the hydrogenation route), cannot form on the cold dust grain surfaces, since the reaction barrier of CH 3ice + CO ice is large (=3460 K; Walsh et al. 2014). Moreover, COOH, the precursor of CH 3 COOH and HCOOH, cannot form on the cold dust grain surfaces, since the reaction barrier of OH ice + CO ice is large (=3000 K; Walsh et al. 2014). We suggest that HCOOH ice can be formed via OH ice +HCO ice , although the mobility of both ices is low on the cold dust grain surfaces (Garrod et al. 2008). Figure 9 shows the radial profiles of sums of fractional abundances with respect to total hydrogen nuclei densities at t =10 6 yr for larger (complex) organic molecules. In the left ("All") panel of Figure 9, we show the sums of all larger (complex) organic molecules introduced in Section 3.2 (Figures 4-8); C 2 H 6 , H 2 CO, CH 3 OH, NH 2 CHO, C 2 H 2 , C 2 H 4 , C 3 H 2 , CH 3 CCH, CH 2 CCH 2 , CH 3 CHCH 2 , HC 3 N, CH 3 CN, CH 3 CHO, CH 3 OCH 3 , CH 3 NH 2 , HCOOH, HCOOCH 3 , CH 3 COOH, CH 2 NH, HNCO, and C 2 H 5 OH. We note that CO, H 2 O, O 2 , CH 4 , N 2 , NH 3 , HCN, and NH 2 OH are not included in this Figure, since they are smaller molecules and/or inorganic molecules.

The Total Complex Organic Reservoir
In the non-shadowed disks, the total icy fractional abundances of the listed organic molecules is ∼3 × 10 −6 just outside the water snowline (r ∼1.5 au), and gradually increases with increasing r. It is (1-2) × 10 −5 at r ∼3-8 au, around the current orbit of Jupiter, and is (4-6) × 10 −5 outside the CO snowline. In the shadowed disk, it is (3-5) × 10 −5 at r ∼3-8 au, and 2 × 10 −5 at r  10 au. Thus in the shadowed disk, our model predicts that the dust grains at r ∼3-8 au contain ∼2-5 times the amount of larger (saturated+unsaturated) organic molecules in total compared with those in the non-shadowed disks.
In the right ("Reduced") panel of Figure 9, we show the sums of all larger (complex) organic molecules but exclude the dominant unsaturated hydrocarbon molecules shown in Figure 6: C 2 H 2 , C 2 H 4 , C 3 H 2 , CH 3 CCH, CH 2 CCH 2 , and CH 3 CHCH 2 . In the non-shadowed disks, at r ∼3-8 au, the icy abundances of sums of these "Reduced" organic molecules are smaller (∼(3-9) × 10 −6 ) than those of "All" organic molecules ((1-2) × 10 −5 ). In contrast, in the shadowed disks, the icy abundances of sums of organic molecules are similar ((3-5) × 10 −5 ) between these two cases. This is because such dominant unsaturated hydrocarbon molecules are frozen onto the dust grains at r ∼3-8 au, and their ice abundances significantly decrease with decreasing f (see Figure 6). This result demonstrates that the shadowed region promotes the synthesis of saturated organic molecules rather than unsaturated hydrocarbons. Thus in the shadowed disk, the dust grains at r ∼3-8 au are predicted to have around 5-10 times the amount of larger saturated organic molecules in total compared with those in the non-shadowed disks.

The Dependence of the Disk Chemical Structure on Ionization Rate and Initial Abundances
In this subsection, we briefly summarize key results of disk chemical evolution for atomic initial compositions and different ionization rates, which are detailed in Appendix A. Figures 14-16 in Appendix A show the radial profiles of fractional abundances at t =10 6 yr for dominant oxygen-, carbon-, and nitrogen-bearing molecules (H 2 O, CO, CO 2 , O 2 , CH 4 , C 2 H 6 , H 2 CO, CH 3 OH, N 2 , NH 3 , HCN, and NH 2 CHO) in the shadowed and non-shadowed disk midplane ( f =1.0 and f =0.03, respectively). In these Figures, we assume either molecular or atomic initial abundances and either low or high ionization rates (ξ CR (r) =10 −18 , 10 −17 [s −1 ]). We note that Figures 3-5 in Section 3.2 show the radial abundance profiles for the same molecules with molecular initial abundances and ξ CR (r) =10 −17 [s −1 ].
In Appendix A, we show these results and explain the dependence of the disk chemical evolution on disk ionization rates and initial abundances in detail. According to our calculations, CO/CO 2 abundances become smaller/larger with increasing ionization rates, respectively. CH 4 and C 2 H 6 gas abundances within their snowline become smaller as the ionization rates become larger. In addition, abundances of H 2 O and organic molecules are larger for molecular initial abundances than those for atomic initial abundances. It is worth noting that O 2 ice abundances are ∼10 −5 − 10 −4 (consistent with the measured cometary abundances; see also Section 4.2) only for atomic initial abundances and the low ionization rates.

Time Evolution of Molecular Abundances
In this subsection, we briefly summarize some key results for the time evolution of molecular abundances, which are detailed in Appendix B. Figures 17-19 in Appendix B show the time evolution of the radial profiles of fractional abundances for dominant oxygen-, carbon-, and nitrogen-bearing molecules (H 2 O, CO, CO 2 , O 2 , CH 4 , C 2 H 6 , H 2 CO, CH 3 OH, N 2 , NH 3 , HCN, and NH 2 CHO) in the shadowed and non-shadowed disk midplane ( f =1.0 and 0.03), when assuming molecular initial abundances and high ionization rates (ξ CR (r) =10 −17 [s −1 ]). These initial conditions are similar to those in Sections 3.1 and 3.2.
In Appendix B, we describe these results and explain the time evolution of molecular abundances in detail. According to our calculations, in the shadowed region (r ∼3-8 au), the icy abundances of CO 2 and organic molecules such as H 2 CO, CH 3 OH, and NH 2 CHO become larger with time. Thus, we find that if the shadowed region is maintained for a relatively long time (t ∼10 6 yr), chemical evolution may produce dust grains and solid objects with large amounts of CO 2 and organic molecular ices (see also Section 4.2). In addition, the ice abundances of these molecules can be a clue in constraining the formation age of solid bodies in the shadowed region.

The C/O and N/O Ratios and Implication for Planetary Atmospheres
The carbon-to-oxygen (C/O) ratios of exoplanetary atmospheres have been proposed to be a possible tool to link gasgiant exoplanets to their formation sites in the natal protoplanetary disk (e.g., Öberg Mollière et al. 2022). This is because the radial-dependent positions of snowlines of abundant oxygen-and carbon-bearing molecules result in systematic radial variations in the C/O ratios in the gas and ice. However, disk chemistry can affect the C/O ratios in the gas and ice, thus potentially erasing the chemical fingerprint of snowlines in atmospheres (Eistrup et al. 2016(Eistrup et al. , 2018Notsu et al. 2020). Notsu et al. (2020) discussed that hot Jupiters with C/O > 1 can only form between the CO 2 and CH 4 snowlines in the non-shadowed disk, which has fully inherited interstellar abundances, and where negligible chemistry has occurred because of a low ionization rate. They also discussed that carbon-rich planets are likely rare unless efficient transport of hydrocarbon-rich ices via pebble drift to within the CH 4 snowline (Booth et al. 2017;Booth & Ilee 2019) is a common phenomenon. We note that disk chemistry significantly affects the C/O ratios, through the change of abundances of hydrocarbons and O 2 gas abundances (e.g., Helling et al. 2014;Eistrup et al. 2016Eistrup et al. , 2018Notsu et al. 2020;Ohno & Ueda 2021).
The left panels of Figures 10 and 11 show the radial profiles of C/O ratios at t =10 6 yr. Different color lines show the profiles for different values of the parameter f (=1.0, 0.3, 0.03, and 0.003), respectively. As shown in our previous studies (Eistrup et al. 2016(Eistrup et al. , 2018Notsu et al. 2020), the inclusion of chemistry has a significant impact on the disk elemental abundance ratios of both gas and ice. The ices remain, on the whole, dominated by oxygen (i.e., C/O < 0.5). In the nonshadowed disk ( f =1.0), between the H 2 O and CH 4 snowlines, the gas is carbon rich relative to the initial elemental value (=0.44) for molecular initial abundances, whereas gas-phase C/O ratios are 0.44 for atomic initial abundances. For molecular initial abundances, the gas-phase C/O ratios in these regions are ∼1.0-1.1 for the low ionization rate and ∼0.7-1.0 for the high ionization rate.
In the shadowed disk ( f 0.03), however, the gas-phase C/ O ratios in the shadowed region (r ∼2-10 au) are almost unity for the high ionization rate and/or molecular initial abundances (as suggested by Ohno & Ueda 2021) and 0.8 for the low ionization rate and atomic initial abundances. This is because CO carries most of the gas-phase C and O there. In addition, the icy-phase C/O ratios reach the initial elemental value (=0.44 in our model) since almost all C and O reservoirs freeze out onto dust grains in the shadowed region (r ∼3-8 au). Thus, if planets acquire their atmospheres from the gas in the disk shadowed region, the atmospheres will have substellar metallicities and larger C/O ratios than the initial elemental value (=0.44 in our model) regardless of disk initial abundances and ionization rates. In addition, the C/O ratios are unity unless the disk has fully atomized initial abundances and negligible chemistry has occurred because of the low ionization rate. We note that the atmospheres can be polluted by dissolution of accreting oxygen-rich icy planetesimals/ pebbles (e.g., Hori & Ikoma 2011;Mordasini et al. 2016) and erosion of cores (e.g., Moll et al. 2017), potentially lowering C/O ratios in planetary atmospheres.
In the bottom-left panel of Figure 11 (the case for low ionization and atomic initial abundances), the icy-phase C/O ratios just outside the water snowline are larger than the initial elemental value, and they exceed 1.0 for f 0.3. The peak position shifts inside with decreasing f. In this region, H 2 O ice abundances are much smaller (∼10 −6 ) than those in other models (>10 −5 ). In addition, this region is between the HCN and CO 2 snowline, and the HCN ice abundance is larger than those of other molecules (such as H 2 O and H 2 CO) in this region (see Appendix A). We note that the presence or otherwise of this large peak depends on the relative binding energies of HCN and CO 2 assumed in the model (see also Eistrup et al. 2016).
Since previous studies suggested that atmospheric N/O ratio is also a useful tracer of planet formation locations (Piso et al. 2016;Cridland et al. 2020b;Turrini et al. 2021;Ohno & Ueda 2021), we also study the radial distributions of N/O ratios in our disk models. The right panels of Figures 10 and 11 show the radial profiles of N/O ratios at t =10 6 yr. The ices remain, on the whole, dominated by oxygen (i.e., N/O < 0.23). In the non-shadowed disk ( f =1.0) and for molecular initial abundances, the gas-phase N/O ratios increase (>0.4) outside the water snowline; they gradually increase (∼0.4-0.5 and ∼1.0 outside the H 2 O and CO 2 snowlines, respectively) for the high ionization rate, whereas they are ∼0.5 for the low ionization rate. This is because of the significant enhancement of CO 2 abundances in the disk with a high ionization rate (see Appendix A.1). In the non-shadowed disk ( f =1.0) and for atomic initial abundances, the gas-phase N/O ratios do not increase outside the water snowline, since gas-phase abundances of NH 3 , HCN, and NH 2 CHO are at least around an order of magnitude smaller than those for molecular initial abundances (see Appendix A.3). For the high ionization rate, they reach around unity outside the CO 2 snowline. This is because CO/CO 2 abundance ratios are smaller in the high ionization rate case than those in the low ionization rate case (see Appendix A.1). In addition, the gas-phase N/O ratios exceed unity and reach around 10 just outside the CO snowline in all models, because the binding energy of N 2 is lower than that of CO (see Table 1), leading to the higher N 2 gas abundances around these radii (see also, e.g., Turrini et al. 2021).
In the shadowed disk, the radial profiles of the gas-phase N/ O ratios show spatial variations that are much larger than those of the C/O ratios, and thus the N/O ratio would be a useful tracer of the shadowed region in the disks. For molecular initial abundances, the gas-phase N/O ratios are much larger than unity in the shadowed region (r ∼3-8 au), and they are ∼6-9 for the low ionization rate and ∼10-20 for the high ionization rate. This is because of the difference in the binding energies between N 2 and CO, similar to the situation outside the snowline of the non-shadowed disk ( f =1.0). In addition, the icy-phase N/O ratios reach the initial elemental value (=0.23 in our model) since almost all N and O reservoirs freeze out onto dust grains in the shadowed region (r ∼3-8 au). For atomic initial abundances, the overall pictures are similar, and around the shadowed region, the gas-phase N/O ratios are 10 and icy-phase N/O ratios reach 0.23. We note that in our results, the icy-phase elemental carbon, oxygen, and nitrogen abundances at r =5.3 au are ∼1.4 × 10 −5 , ∼3.2 × 10 −4 , and ∼(6.5-7.1) × 10 −5 , respectively, which are similar to the initial elemental abundances.
The results for molecular initial abundances and the low ionization rate are consistent with those in Ohno & Ueda (2021), although the gas-phase N/O ratios in the shadowed region are much larger (>100) than that in our disk model (∼10). This is likely because they used larger literature values of binding energies of CO and N 2 (E des (CO) =1180 K and E des (N 2 ) =1051 K) than ours, as the gas-phase N/O ratio is sensitive to those values when both CO and N 2 are frozen. In addition, Ohno & Ueda (2021) included several dominant molecules only (i.e., N 2 and NH 3 only) and did not include the effects of disk chemical evolution. Moreover, they assumed slightly larger N 2 abundances (=3.50 × 10 −5 ) and smaller NH 3 abundances (=7.78 × 10 −6 ) than those in our calculations (see Figure 16). Our calculations also investigate the dependence on initial disk conditions. Therefore, if planets acquire their atmospheres from the gas in the shadowed region (r ∼3-8 au in our disk model), they are expected to have the super-stellar N/O ratios of ?1 and substellar metallicities. On the other hand, they are expected to have the stellar N/O ratios and super-solar metallicities if the planetary atmospheres are efficiently polluted by solid components (including the case of Jupiter; see Ohno & Ueda 2021).
As discussed in Ohno & Ueda (2021), Saturn, in contrast to Jupiter, may not have the uniform enrichment in the elemental abundances of their atmospheres, if formed in their vicinity of the current orbits. This is because the current Saturn orbit is outside the shadowed region (r ∼3-8 au), and N 2 has sublimated into the gas phase. In the shadowed disk, the icyphase N/O ratios at around the current orbit of Saturn (r ∼10 au) are 0.1 for all models, whereas they reach the initial elemental value (=0.23 in our model) at around the current orbit of Jupiter. In addition, regardless of the initial abundances and ionization rates, the icy-phase N/O ratios at r ∼10-40 au are 0.1 in the shadowed disk, whereas in the non-shadowed disk, they reach the initial elemental value at r > 24 au (outside the N 2 snowline). Future observations and entry probe missions on Saturn and also outer icy planets (Uranus and Neptune) would help to distinguish the shadow formation scenario proposed in Ohno & Ueda (2021) from other scenarios, since the elemental abundances such as N in such planets are still uncertain (see, e.g., Atreya et al. 2018;Mandt et al. 2020).
Nitrogen abundances within the atmospheres of exoplanets (such as hot Jupiters) can be constrained by the observations of HCN and NH 3 (e.g., MacDonald & Madhusudhan 2017;Hawker et al. 2018;Giacobbe et al. 2021), which are the major nitrogen-bearing species in hot gas-giant atmospheres along with N 2 (e.g., Moses et al. 2011Moses et al. , 2013. Through upcoming observations with the James Webb Space Telescope (JWST) and observations with next-generation facilities (such as ARIEL and ground-based telescopes), it is anticipated that the elemental composition of carbon, oxygen, and nitrogen, and the ratios between them will be determined with much higher precision than currently possible for the atmospheres of many exoplanets such as hot Jupiters (see, e.g., Tinetti et al. 2018;Madhusudhan 2019;Changeat et al. 2020;Turrini et al. 2022).
We note that in addition to C/O ratios, the C/H ratios (carbon elemental abundances) of exoplanetary atmospheres have also been proposed to be a possible tool to link gas-giant exoplanets to their formation sites in the protoplanetary disk (e.g., Öberg et al. 2011;Madhusudhan et al. 2014;Pontoppidan et al. 2014;Line et al. 2021;Pelletier et al. 2021). Recently, super-solar and Jupiter-like C/H ratios (10 −3 ) have been confirmed for some hot Jupiters (e.g., Brogi & Line 2019;Gandhi et al. 2019;Pelletier et al. 2021). Pelletier et al. (2021) analyzed thermal emission spectra of a nontransiting hot Jupiter τ Boo b with high spectral resolutions (R =λ/Δλ =70000) and reported that the planet's atmosphere has a super-solar C/H ratio and possibly super-solar C/O ratio. We suggest that the super-solar C/H and C/O ratios might be explained if the atmosphere was formed near the inner edge of the shadowed region and polluted by solid components, since the solid C/O ratio exceeds unity there when disk chemistry starts from the atomized initial abundances and the cosmic-ray ionization rate is low (see Figure 11; see also Eistrup et al. 2016). Figures 20,21,and 22 in Appendix C show, respectively, the radial profiles of C/H, O/H, and N/H ratios at t =10 6 yr. In the shadowed disk ( f 0.03), at r ∼3-8 au (around the current orbit of Jupiter), the gas-phase N/H ratios (∼10 −7 − 10 −5 ) are Figure 11. Same as Figure 10, but for atomic initial abundances ("reset" scenario).

Implications for the Small Bodies in the Solar System
On the basis of our calculations, in the shadowed region, the snowline positions of molecules with smaller E des than that of H 2 O move inward, and even the most volatile species CO and N 2 freeze out onto dust grains at around the current orbit of Jupiter (r ∼3-8 au), as found in Ohno & Ueda (2021). In the shadowed region, the dust grains at r ∼3-8 au are expected to have significant (more than ∼5-10 times) amounts of saturated hydrocarbon ices such as CH 4 and C 2 H 6 , ices of organic molecules (which are mostly saturated) such as H 2 CO, NH 2 CHO, CH 3 OH, and CH 3 NH 2 , in addition to H 2 O, CO, CO 2 , NH 3 , N 2 , HCN, and NH 2 OH ices, compared with those in the non-shadowed disks (mostly ices of H 2 O, CO 2 , NH 3 , and unsaturated hydrocarbon molecules). In addition, the icy abundances of unsaturated hydrocarbons and other organic molecules in the shadowed disks are much smaller than those in the non-shadowed disks.
Here it is worth discussing whether the presence of the shadowed region influences the chemical composition of small objects, such as primitive comets in the solar system. If primitive comets formed from the icy dust grains in the shadowed region of the disks (such as r ∼3-8 au for f 0.03), they are expected to include more saturated hydrocarbons and complex organic molecules such as H 2 CO, NH 2 CHO, and CH 3 OH, and less unsaturated organic molecules than those formed in the non-shadowed disks.
Reactions of radicals, which are mainly formed by cosmicray-induced photodissociation of CH 3 OH ice, are needed to form complex organic molecules in disks (see Sections 3.2.2 and 3.2.4), assuming that they are not already formed in the molecular cloud phases. In addition, Garrod et al. (2008) discussed that (CH 2 OH) 2 (ethylene glycol) is formed on the dust grains around the water snowline from its precursor radical CH 2 OH, which becomes mobile just as water and other species are beginning to desorb. Moreover, icy grains can efficiently coagulate into larger (?1 mm) dust particles and centimetersized pebbles outside the water snowline (see Section 2.1 and, e.g., Ros & Johansen 2013;Sato et al. 2016;Dráżkowska & Alibert 2017;Pinilla et al. 2017). If CH 3 OH-rich large dust grains and/or pebbles migrate to inside the shadowed region (such as around the water snowline), and/or if the shadowed region disappears due to the disk evolution, the ice abundances of various complex organic molecules in such dust grains and pebbles are also expected to increase (see also Section 4.4). This is because the temperature of such dust grains and pebbles increases (>30 K) and radical-radical reactions can proceed efficiently in such warm conditions. Thus in the shadowed disk, both efficient CH 3 OH ice formation and the formation of ices of further complex organic molecules such as (CH 2 OH) 2 may be realized due to the dissipation of shadowed structures and/ or migration inside the shadowed region, and they can be realized without dust grains and/or pebbles migrating vast distances, compared with the non-shadowed disk. We suggest that in shadowed disks, complex organic molecules can be formed in situ rather than being fully inherited from molecular clouds.
To date, various complex organic molecules have been detected in comets (such as Hale-Bopp and 67P/Churyumov-Gerasimenko). Several studies discussed that the molecular abundances in comets are determined by the combination of chemical evolution in the proto-solar disk and inheritance from molecular clouds (e.g., Mumma & Charnley 2011;Caselli & Ceccarelli 2012;Walsh et al. 2014;Eistrup et al. 2016Eistrup et al. , 2018Altwegg et al. 2017Altwegg et al. , 2019Drozdovskaya et al. 2019;Öberg & Bergin 2021). Walsh et al. (2014) discussed that grain-surface fractional abundances (relative to water ice) for the outer region of the non-shadowed disk (T < 50 K) are consistent with abundances derived for comets, suggesting a grain-surface route to the formation of complex organic molecules observed in cometary comae.
Recently, the abundances of various volatiles and organic molecules (including hydrocarbons) toward comet 67P/Churyumov-Gerasimenko were reported by, e.g., Le Roy et al. (2015), Rubin et al. (2015aRubin et al. ( , 2015bRubin et al. ( , 2019Rubin et al. ( , 2020, Altwegg et al. (2017Altwegg et al. ( , 2019, and Schuhmann et al. (2019). They reported that the relative abundances of CO, CO 2 , and C 2 H 6 with respect to H 2 O are larger than those of other Jupiter-family comets, which might suggest the formation of cometary grains at lowertemperature regions (such as below 30 K). In addition, Rubin et al. (2015a) reported the first cometary detection of N 2 toward comet 67P, and discussed that the lower N 2 /CO abundance ratio (∼3 × 10 −2 based on Rubin et al. 2019Rubin et al. , 2020 compared with the protostar value (∼10 −1 ) suggested the cometary grains of 67P are formed in cold regions with ∼24-30 K. Schuhmann et al. (2019) also reported the existence of unsaturated hydrocarbons in the coma of comet 67P. We note that gasphase reactions within the CH 4 snowline are needed to efficiently form unsaturated hydrocarbons (see Sections 3.2.2 and 3.2.4).
In Figure 12, we compare the molecular ice abundances (with respect to water ice) of the coma of comet 67P (Rubin et al. , 2020 and our standard disk model calculations (see Sections 3.1 and 3.2). On the basis of Figure 12, the ice abundances of CO, CH 4 , and N 2 in the coma of comet 67P cannot be explained by the icy grains within the CH 4 snowline in non-shadowed disks. In addition, as for results in the cold regions where both CO and N 2 are frozen onto dust grains (both in the shadowed and non-shadowed disks), the CO ice abundances are closer to the value of comet 67P than the N 2 ice abundances. These results also suggest that the icy grains of comet 67P were formed between the CO and N 2 snowlines (see above and Rubin et al. 2015aRubin et al. , 2019Rubin et al. , 2020. Such cold regions, where the icy grains of comet 67P are formed, can be located at r ∼a few astronomical unit for the shadowed disks, whereas they are located at r > 20 au for the non-shadowed disk. In the results of our standard disk model calculations, the CO 2 ice abundances at r ∼5.3 au in the shadowed disk are around two orders of magnitude larger than those at r ∼30 au in the non-shadowed disk, although the differences in other molecular ice abundances between the two cases are within around one order of magnitude. This is because CO 2 ice formation on the dust grains is not efficient in the coldest regions with T(r) 20 K (see Section 3.2.1). Thus, the CO 2 ice abundances can be used to distinguish these two regions (the inner cold region (r ∼3-8 au, T(r) ∼20-30 K) in the shadowed disk and outermost coldest region (r ∼30 au, T(r) 20 K) in the non-shadowed disk) as formation sites of icy dust grains. The CO 2 ice abundance at r ∼30 au in the non-shadowed disk is around one order of magnitude smaller than that in comet 67P, whereas that at r ∼5.3 au in the shadowed disk is four to seven times larger than that in comet 67P. Thus, for explaining the CO 2 ice abundance in comet 67P, the formation of CO 2 ice at r ∼5.3 au in the shadowed disk may be more suitable than that at r ∼30 au in the non-shadowed disk. In addition, if we also include the above discussion about the CO and N 2 abundances, we suggest that the icy grains of comet 67P may have been formed at the region with T(r) ∼25 K, such as the shadowed region.
For the model results in the shadowed region (see Figure 12), the abundances of ices such as H 2 CO and CH 3 OH are around one to two orders of magnitude larger than those of comet 67P, whereas those of C 2 H 5 OH and CH 3 COOH are more than one and three orders of magnitude smaller, respectively. We suggest that if the cometary grains of 67P are originally from the shadowed region, a temperature rise (due to the inward migration and/or dissipation of the shadowed region) after CH 3 OH ice formation in the shadowed region may be needed to trigger radical-radical reactions (see also above) to produce more complex molecules such as C 2 H 5 OH and CH 3 COOH. Future detailed chemical modeling including such physical evolutions may be needed to construct the formation scenario that explains the ice abundances of all molecules in comet 67P simultaneously. Bieler et al. (2015) and Rubin et al. (2015b) reported that O 2 ice is abundant in comet 67P and the ratio of O 2 /H 2 O is a few percent (see also Luspay-Kuti et al. 2022). On the basis of Figure 12, our standard disk model is unable to explain the cometary O 2 ice abundances (see Sections 3.1 and 3.2). According to previous studies (e.g., Eistrup et al. 2016Eistrup et al. , 2018Taquet et al. 2016) and our calculations, such higher O 2 ice abundances are possible in disks only if chemical starting conditions were purely atomized and the disk ionization level was low (see Appendix A.1). In addition, O 2 is very volatile and freezes out onto dust grains at r ∼2 − 10 au only in the shadowed disk ( f 0.03, see Appendix A.1). We note that Taquet et al. (2016) suggested that O 2 trapping in H 2 O ice at earlier evolutionary stages (such as in the molecular clouds) may also be an explanation.
Other small objects such as asteroids will have similar abundances (such as CO 2 and CH 3 OH rich), if they are formed from the dust grains in the shadowed region. Yada et al. (2021) reported the results of preliminary analyses of the Hayabusa2 samples returned from C-type asteroid Ryugu, and showed the infrared spectral profile with weak absorptions at 2.7 and 3.4 μm that imply a carbonaceous composition with indigenous aqueous alteration. Kurokawa et al. (2022) compared the infrared spectra (including 3.1 μm absorption features of ammoniated phyllosilicate) of main belt asteroids collected by the AKARI space telescope and their models of water-rock reactions, and suggested that multiple large main belt asteroids formed beyond the NH 3 and CO 2 snowlines and have been transported to their current locations. Fujiya et al. (2019) inferred from the measurements of CO 2 and H 2 O abundances and carbon isotope ratios of carbonate minerals in the Tagish Lake meteorite (an carbonaceous chondrite) that at least some D-type asteroids were formed beyond the CO 2 snowline. We note that D-type asteroids are discovered mainly at the outer edge of the main asteroid belt and in the Jupiter Trojan regions (DeMeo & Carry 2014). Tsuchiyama et al. (2021) reported the discovery of primitive CO 2 -bearing fluids in an aqueously altered carbonaceous chondrite (one of the primitive meteorites), and discussed that its parent body was formed outside the CO 2 snowline and later transported to the inner solar system. Since the CO 2 snowline position moves inward in the shadowed disk, the supply of dust grains and small objects with significant amounts of CO 2 and complex organic molecules to the inner region may be relatively easier than that in the non-shadowed disk. We note that if the shadowed region is maintained for a relatively long time (t ∼10 6 yr), chemical evolution may produce dust grains and solid objects with large amounts of CO 2 ice and ices of complex organic molecules such as H 2 CO and CH 3 OH.
The solid bodies formed at the Kuiper Belt may be CO 2 rich if we consider the disk shadowing effect. This is because at r > 20 au, the CO 2 ice abundance in the shadowed disk is around one order of magnitude larger than that in the nonshadowed disk (see Section 3.2.1 and Figure 3).
We note that the CO 2 snowline position will be important both for chemistry and dust grain growth in the disk. Recent laboratory experiments showed that CO 2 ice is less sticky compared to H 2 O ice (Musiolik et al. 2016a(Musiolik et al. , 2016bFritscher & Teiser 2021). Thus, efficient grain growth is only expected between the H 2 O and CO 2 snowlines (Okuzumi & Tazaki 2019;Arakawa & Krijt 2021). If the disk has a shadowed region beyond the water snowline, the region where efficient grain growth can take place might become narrower. Dartois et al. (2013Dartois et al. ( , 2018 found that ultracarbonaceous Antarctic micrometeorites (UCAMMs) have higher C/Si abundance ratios (10 2 ) and N/C abundance ratios (∼0.05-0.12) in organic compounds than those in other primitive meteorites and the local interplanetary dust particles. They discussed that UCAMMs might be formed in a cold nitrogen-rich environment, such as outside the N 2 snowline. We suggest that if the disk has a shadowed region beyond the water snowline, the formation sites of UCAMMs may be located in the inner region of the disk, such as r ∼3-8 au.

Implication for the Observations of Protoplanetary Disks
Many of the complex (organic) molecules described in Sections 3.2.2-3.2.4 have been observed by previous observations with, e.g., ALMA toward hot cores/corinos in high-/lowmass star-forming regions, respectively (see, e.g., Sakai & Yamamoto 2013;Jørgensen et al. 2020;Yang et al. 2021), and have been detected in the comae of multiple comets (see Section 4.2 and, e.g., Mumma & Charnley 2011;Walsh et al. 2014;Altwegg et al. 2019;Drozdovskaya et al. 2019;Rubin et al. 2020). Lee et al. (2019) reported the detections of CH 3 CHO and CH 3 CN, in addition to CH 3 OH, toward Class I disks around FU Ori-type young star V883 Ori with ALMA. In addition, some of these molecules have been observed toward Class II disks by previous infrared observations (C 2 H 2 ; e.g., Pontoppidan et al. 2010) and ALMA observations, such as H 2 CO and CH 3 OH (see, e.g., Loomis et al. 2015;Walsh et al. 2016Walsh et al. , 2018Booth et al. 2021a;van der Marel et al. 2021;Guzmán et al. 2021), and C 3 H 2 , CH 3 CN, HC 3 N, and HCOOH (see, e.g., Qi et al. 2013;Öberg et al. 2015;Bergner et al. 2018;Favre et al. 2018;Loomis et al. 2018Loomis et al. , 2020Ilee et al. 2021). Booth et al. (2021a) reported the first detection of CH 3 OH in the disk around a Herbig Ae star, HD 100546. They reported that the CH 3 OH to H 2 CO abundance ratio is higher (10) at the inner edge of the dust ring in the disk (∼10-30 au) than those (∼1-2) in the outer disk (>100 au; Carney et al. 2019) and in the TW Hya disk . They discussed that at the inner edge, CH 3 OH is proposed to originate from thermal desorption. van der Marel et al. (2021) and Brunken et al. (2022) reported the detections of CH 3 OH, H 2 CO, and CH 3 OCH 3 line emission in the vicinity of the asymmetric dust trap in the disk around a Herbig Ae star Oph IRS 48 (see also Booth et al. 2021b). They discussed that these molecules are thermally desorbed from icy dust grains and that such dust traps provide huge icy grain reservoirs in the disk midplane.
Recent dust continuum survey observations of protoplanetary disks (with, e.g., ALMA) have shown that disk substructures, most prominently gas-depleted gaps and dustrich rings, are common (e.g., Andrews et al. 2016Andrews et al. , 2018Andrews 2020;Dullemond et al. 2018;Huang et al. 2018;Isella et al. 2016Tsukagoshi et al. 2016). In addition, the recent Molecules with ALMA at Planet-forming Scales 10 survey obtained spatial distributions (with Δr ∼10-50 au) of line emission for CO ) and some other organic molecules (H 2 CO, HCN, CH 3 CN, HC 3 N, and C 3 H 2 ; see Guzmán et al. 2021;Ilee et al. 2021) toward three T Tauri disks (IM Lup, GM Aur, and AS 209) and two Herbig Ae disks (HD 163296 and MWC 480). They found that disk substructures (such as rings and gaps) are also common in molecular gas emission.
Since a shadowed region can be formed in the midplanes beyond such dust rings/traps of these disks by blocking the radiation from the central star, we propose that the effects of shadows need to be taken into account when we discuss chemical evolution of complex organic molecules in disks with such dust rings and asymmetric traps. Alarcón et al. (2020) calculated the temperature and chemical structures of disks with gas-depleted gaps. They showed that the disk midplane temperature in the gap increases, producing local sublimation of key volatiles, while it decreases in the ring, causing a higher volatile deposition onto the dust grain surfaces.  and Okuzumi et al. (2022) described that the outer wall of the gap produced by a giant planet receives extra starlight heating and puffs up, throwing a shadow across the disk beyond. In addition, Ohashi et al. (2022) suggested from their ALMA observations that the dust clumps in the disk around a Class 0/I protostar create the shadowed region outside, resulting in the sudden drop in temperature. We predict that, as well as the shadowed region beyond the water snowline (discussed in this paper), the freeze-out of molecules onto dust grains and efficient formation of organic molecules are also expected to occur in the shadowed region formed by the presence of a giant planet and/or dust clumps.
In this study, we adopt a 1D physical model of the protosolar disk (T Tauri disk) in order to investigate the effects of shadow structures on the chemical evolution of the disk midplane and compare the results with the molecular composition of small objects in the solar system (see also Section 4.2). The influence of disk shadowing is expected to be larger in the disk midplane than in the disk surface, since it is easier for direct stellar light to reach the surface than the midplane (Ueda et al. 2019;Okuzumi et al. 2022). We note that the lines from more rare isotopologues trace deeper regions in the disks, but the disk midplane is obscured if the dust emission is optically thick. In addition to future observations of molecular lines with much higher spatial resolutions toward the disks using, e.g., ALMA and the next-generation Very Large Array (ngVLA), further calculations of disk chemical evolution with 2D physical models of both T Tauri disks and Herbig Ae disks are also important to investigate whether or not the effects of shadows are needed to explain the observed distributions of molecular emission. Since the dust opacities at the frequencies of ngVLA are lower than those of ALMA, observations with ngVLA will be useful to trace the inner molecular gas abundances, such as within 10 au. In addition, ngVLA expects to resolve the dust emission at centimeter wavelengths with Δr 1 au, and thus will be able to confirm the variation in the dust density profile at the water snowline and presence of the shadowed region beyond the water snowline even in disks around T Tauri stars. 11 We note that future calculations of disk chemical evolution with 2D physical models would be also useful to investigate the effects of shadowing on the composition of planetary atmospheres. This is because some recent theoretical studies (e.g., Tanigawa et al. 2012;Morbidelli et al. 2014) and observational studies (e.g., Teague et al. 2019) suggested that the flow of gas into the gap produced by a growing planet is dominated by gas falling vertically from a height of at least one scale height (see, e.g., Cridland et al. 2020a).
N 2 H + is considered to be a useful probe of the CO and N 2 snowlines in disks (e.g., Qi et al. 2013Qi et al. , 2019Aikawa et al. 2015;van't Hoff et al. 2017;Murillo et al. 2022), because it is destroyed by proton transfer to CO, et al. (2015) suggested from their disk modeling that the N 2 H + abundance can have a peak at the temperature slightly below that of CO sublimation, even if the binding energies of CO and N 2 are nearly the same. Figure 13 shows the radial profiles of the N 2 H + abundances for various values of f. The CO freezes out onto dust grains in the shadowed region, and thus N 2 H + abundances at r ∼3-8 au become larger in the shadowed disk (∼10 −15 for f 0.03) than those in the non-shadowed disk (<10 −17 for f =1.0) by several orders of magnitudes. Thus, N 2 H + line emission may potentially trace the shadowed region of the disk beyond the water snowline, although previous observations of N 2 H + lines do not resolve the spatial scales around the water snowline (r ∼1-10 au). We note that the N 2 H + abundances in the disk midplane are lower than those within the disk surface (Aikawa et al. 2015;van't Hoff et al. 2017), because of the high densities and low ionization rates. Further chemical and radiative-transfer modeling in the 2D disk structures with shadow structures are needed to confirm whether N 2 H + line emission can really be used as an observational tracer of such shadowed regions, since the line emission also traces the vertical distributions of CO and N 2 (Qi et al. 2019), and observations of the disk midplane directly are not easy because of the high optical depths at ALMA wavelengths.

Other Model Caveats
In our disk chemical modeling, we implicitly assumed that ices on grains are formed by homogeneous layers regardless of their composition or crystallinity, as most astrochemical models of disks assume. However, recently, Kouchi et al. (2021) suggested from their transmission electron microscopy studies that the macroscopic morphology of icy dust grains are as follows: amorphous H 2 O covered the refractory grain uniformly, CO 2 nano-crystals were embedded in the amorphous H 2 O, and a polyhedral CO crystal is attached to the amorphous H 2 O. Such morphology of dust grains would affect the chemical evolution in the disks, since the binding energies and nonthermal desorption rates depend on the chemical composition of the ice mantles on the dust grains (e.g., Bertin et al. 2016;Cuppen et al. 2017;Penteado et al. 2017). Heinzeller et al. (2011) investigated the effects of physical mass transport phenomena in the radial direction by viscous accretion and in the vertical direction by diffusive turbulent mixing and disk winds. They showed that the gas-phase molecular abundances of such as H 2 O and CH 3 OH are enhanced in the warm surface layer due to the effects of vertical mixing. van der Marel et al. (2021) discussed that this vertical transport may be important to explain the observed abundance of CH 3 OH in the disk around IRS 48, in addition to icy dust concentrations at the dust trap. In addition, we assume that the disk physical structure is steady and that the shadow structure is maintained for 10 6 yr. We note that the inward migration of solids and/or destruction of the shadow structure after the efficient formation of CH 3 OH ice in the shadowed region may increase the abundances of various complex organic molecules in the inner disks around the water snowline (see also Section 4.2). Future observations of organic molecular lines with, e.g., ngVLA and infrared telescopes (such as JWST and GREX-PLUS) are expected to constrain the abundances in such inner warm regions.

Conclusions
In this study, we investigated the radial abundance distributions of dominant carbon-, oxygen-, and nitrogenbearing molecules and the radial distributions of elemental abundance ratios (C/O and N/O ratios) in the gas and ice of disks with shadow structures. We used a detailed gas-grain chemical reaction network and calculated chemical structures in the shadowed disk midplane around a T Tauri star (a protosolar-like star). Gas-phase reactions, thermal and nonthermal gas-grain interactions, and grain-surface reactions were included in our adopted reaction network. We investigated the dependence of the disk chemical structures on ionization rates and initial abundances. We discussed the effects of disk shadowing on chemical evolution of complex organic molecules and forming planetary atmospheres. We also compared the results of our calculations with the molecular composition of small bodies in the solar system (such as Figure 13. The radial profiles of gas-phase fractional abundances with respect to total hydrogen nuclei densities at t =10 6 yr for N 2 H + ( + n N H 2 /n H ). These profiles show the results for ξ CR (r) =1.0 × 10 −17 [s −1 ] and molecular initial abundances (the "inheritance" scenario). The black, red, blue, and green lines show the profiles for different values of the parameter f (=1.0, 0.3, 0.03, and 0.003), respectively. comets and asteroids) and recent observational results of protoplanetary disks. Our findings can be summarized as follows: 1. In the shadowed disks ( f 0.03), the snowline positions of molecules with smaller E des than that of H 2 O move inward, and even the most volatile species, CO and N 2 , freeze out onto dust grains at around the current orbit of Jupiter (r ∼3-8 au). Our detailed calculations confirm the results of Ohno & Ueda (2021) who showed the freezeout of CO and N 2 onto dust grains in the shadowed region with using more simplified calculations. Meanwhile, we newly find that the dust grains within the shadowed regions have significant (more than 5-10 times) amounts of saturated hydrocarbon ices such as CH 4 and C 2 H 6 , ices of organic molecules such as H 2 CO, NH 2 CHO, and CH 3 OH, in addition to H 2 O, CO, CO 2 , NH 3 , N 2 , HCN, and NH 2 OH ices, compared with those in the nonshadowed disks (mostly ices of H 2 O, CO 2 , NH 3 , and unsaturated hydrocarbon molecules). We note that these abundant saturated hydrocarbons and various organic molecules such as H 2 CO, NH 2 CHO, and CH 3 OH were not reported by Ohno & Ueda (2021), since they approximated various organic molecules by considering C 2 H 6 alone. 2. The icy abundances of C 2 H 6 , HCN, NH 2 OH, and complex organic molecules (which are mostly saturated) such as H 2 CO, CH 3 OH, NH 2 OH, NH 2 CHO, and CH 3 NH 2 at r ∼3-8 au in the shadowed disks are enhanced compared with the values in the non-shadowed disk, although the snowline positions of these molecules are r 3 au regardless of the values of f. We concluded that the sequential hydrogenation reactions of (especially) CO on the cold dust grains play a vital role in efficiently forming these molecules, in addition to reaction pathways starting from the cosmic-ray-induced photodissociation of CH 3 OH. We found that if the shadowed region is maintained for a relatively long time (t ∼ 10 6 yr), chemical evolution may produce dust grains and solid objects with large amounts of CO 2 and organic molecular ices (see also Appendix B). 3. The icy abundances of unsaturated hydrocarbons such as C 2 H 2 , C 2 H 4 , C 3 H 2 , C 3 H 4 , C 3 H 6 , and HC 3 N at r ∼3-8 au (just outside their snowlines) are much smaller than those of a non-shadowed disk, since gas-phase chemical reactions especially within the CH 4 snowline (∼15 au for f =1.0 and 2 au for f 0.03) mainly drive the formation of these molecules. Moreover, the icy abundances of unsaturated complex organic molecules such as HCOOCH 3 , HCOOH, and CH 3 COOH outside the snowlines are much smaller than those of a nonshadowed disk, since grain-surface association of large radical-radical reactions in the warm regions (T(r) ∼50 K) is needed for the formation of these molecules. In addition, the icy abundances of other molecules such as CH 3 CN, CH 3 CHO, CH 3 OCH 3 , and C 2 H 5 OH are larger for f =0.03 than those for f =1.0, 0.3, and 0.003, since they are determined by the combinations of radicalradical reactions and gas-phase reactions/radical formation reactions from CO and/or CH 3 OH on the dust grain surfaces. 4. We also studied the impacts of different ionization rates and initial chemical abundances on disk chemical structures in Appendix A. We found that CO/CO 2 abundances become smaller/larger with increasing ionization rates, respectively. In addition, CH 4 and C 2 H 6 gas abundances within their snowline become smaller as the ionization rates become larger. Abundances of H 2 O and organic molecules are larger for molecular initial abundances than those for atomic initial abundances. Moreover, O 2 ice abundances are ∼10 −5 − 10 −4 (consistent with the measured cometary abundances) only for atomic initial abundances and the low ionization rates. O 2 is very volatile and freezes out onto dust grains at r ∼2-10 au only in the shadowed disk. 5. In the shadowed region, the gas-phase C/O ratios are almost unity for the high ionization rate and/or molecular initial abundances and 0.8 for the low ionization rate and atomic initial abundances. In addition, the radial profiles of the gas-phase N/O ratios show spatial variations that are much larger than those of the C/O ratios, and thus the N/O ratio would be a useful tracer of the shadowed regions of disks. For molecular initial abundances, the gas-phase N/O ratios are much larger than unity in the shadowed region, and they are ∼6-9 for the low ionization rate and ∼10-20 for the high ionization rate. The icy-phase C/O and N/O ratios reach the initial elemental values in the shadowed region. Therefore, if the planets acquire their atmospheres from the gas in the shadowed region (r ∼3-8 au in our disk model), they are expected to have super-stellar N/O ratios of ?1, superstellar C/O ratios of around unity in most cases, and substellar metallicities. In contrast, they are expected to have stellar N/O and C/O ratios and super-solar metallicities if the planetary atmospheres are efficiently polluted by solid components (including the case of Jupiter; see Ohno & Ueda 2021). Upcoming and future observations by JWST and ARIEL will constrain such elemental ratios precisely for atmospheres of many exoplanets such as hot Jupiters. 6. We discussed whether the presence of a shadowed region influences the chemical composition of small objects, such as primitive comets and asteroids in the solar system. Recently the abundances of various volatiles and organic molecules toward comet 67P/Churyumov-Gerasimenko were reported, and some of the results (including CO, CO 2 , C 2 H 6 , N 2 , and O 2 abundances) would suggest the formation of cometary grains in lowertemperature regions with T ∼25 K, which can be found in the shadowed region. 7. We propose that CO 2 ice abundances can be used to distinguish the inner cold region (r ∼3-8 au, T (r) ∼20-30 K) in the shadowed disk and the outermost coldest region (r ∼30 au, T(r) 20 K) in the nonshadowed disk as formation sites of icy dust grains. Moreover, if CH 3 OH-rich large dust grains and/or pebbles migrate to inside the shadowed region (such as around the water snowline), and/or if the shadowed region disappears due to the disk evolution, the ice abundances of various complex organic molecules are also expected to increase. This is because radical-radical reactions may be able to proceed efficiently due to the rapid heating. 8. N 2 H + line emission could potentially trace the shadowed region of the protoplanetary disks beyond the water snowline, although further modeling and observations with much higher spatial resolution than currently conducted are needed.
On the basis of our calculations, we conclude that a shadowed region allows the recondensation of key volatiles onto dust grains, and may explain to some degree the trapping of icy molecules such as CO 2 , CO, N 2 , and O 2 in the dust grains that formed comet 67P/Churyumov-Gerasimenko. In addition, in a shadowed disk, Jupiter need not to have migrated vast distances to explain its atmospheric composition. In the shadowed disk, both efficient CH 3 OH ice formation and formation of ices of further complex organic molecules such as (CH 2 OH) 2 driven by rapid heating may be realized without dust grains and/or pebbles migrating vast distances, compared with the non-shadowed disk. Thus, we propose that in the shadowed disks, various complex organic molecules can be formed in situ rather than being fully inherited from molecular clouds. Further chemical modeling (such as using 2D physical models of both T Tauri disks and Herbig Ae disks) and comparison with observations of disks (using, e.g., ALMA and ngVLA), planetary atmospheres, and small objects (comets and asteroids) in the solar system will further constrain the effects of disk shadowing on chemical evolution.
This study was started originally based on the discussion during and after the online workshop in 2021 on planetary system formation for young scientists in Japan, in which S.N. and T.U. were two of organizers of the workshop. We thank the referee for important suggestions and comments. We are grateful to Nami Sakai, Yuri Aikawa, and Satoshi Okuzumi for their useful comments. Our numerical studies were carried out on PC cluster at Center for Computational Astrophysics

Appendix A The Dependence of the Disk Chemical Structures on Ionization Rates and Initial Abundances
In this Appendix A, we explain the dependence of the disk chemical evolution on disk ionization rates and initial abundances. Figures 14-16 show the radial profiles of fractional abundances at t =10 6 yr for dominant oxygen-, carbon-, and nitrogen-bearing molecules (H 2 O, CO, CO 2 , O 2 , CH 4 , C 2 H 6 , H 2 CO, CH 3 OH, N 2 , NH 3 , HCN, and NH 2 CHO) in the shadowed and non-shadowed disk midplane ( f =1.0 and f =0.03, respecitively). In these Figures, we assume either molecular or atomic initial abundances and either low or high ionization rates (ξ CR (r) =10 −18 , 10 −17 [s −1 ]). We note that Figures 3-5 in Section 3.2 show the radial abundance profiles for the same molecules with molecular initial abundances and ξ CR (r) =10 −17 [s −1 ].
A.1. H 2 O, CO, CO 2 , and O 2 Figure 14 shows the radial profiles of fractional abundances for dominant oxygen-bearing molecules: H 2 O, CO, CO 2 , and O 2 . For molecular initial abundances, the H 2 O ice abundances outside the water snowline are ∼(1-2) × 10 −4 (see also Section 3.2.1), which are similar to the assumed value of the initial H 2 O ice abundance (=1.984 × 10 −4 ). For atomic initial abundances, they decrease outside the water snowline, and at r ∼2-10 au they are ∼10 −6 − 10 −5 for f =1.0 and ∼(2-5) × 10 −5 for f 0.03. In addition, just outside the H 2 O snowline, the H 2 O ice abundances are about an order of magnitude larger in the high ionization case (∼10 −5 ) than those in the low ionization case (∼10 −6 ). Eistrup et al. (2016) described that in the case of atomic initial abundances, the H 2 O ice is not efficiently produced in the outer disk, and the ion-molecule reactions in the gas phase (Hollenbach et al. 2009) are contributing to the formation of water. Previous studies (e.g., Schmalzl et al. 2014;Notsu et al. 2021;) discussed that it takes more than around 1 Myr of the pre-stellar phase to produce water ice with an abundance of 10 −4 .
For molecular initial abundances, the total CO (gas+ice) abundances outside the water snowline are ∼10 −4 for the low ionization rate and ∼(3-6) × 10 −5 for the high ionization rate. This decrease of CO coincides with the overall enhancement of CO 2 ice outside the CO 2 snowline. Under the high ionization rate, CO destruction pathways of Equations (6) (icy phase) and (7) (gas phase) are efficient (see Section 3.2.1). In the shadowed disk ( f =0.03), CO freezes out onto dust grains at around the current orbit of Jupiter (r ∼3-8 au), and for atomic initial abundances and the high ionization rate, a larger decrease of total CO abundance (10 −5 ) beyond the CO 2 snowline is shown.
CO 2 gas abundances between the H 2 O and CO 2 snowlines and CO 2 ice abundances outside CO 2 snowline are larger for the high ionization rate than those for the low ionization rate. In addition, they are also larger for atomic initial abundances than those for molecular initial abundances. For atomic initial abundances and the high ionization rate, CO 2 ice abundances are larger (10 −4 ) outside the CO 2 snowline, with the decreases of CH 4 gas and total (gas+ice) CO abundances. We note that in the non-shadowed disk ( f =1.0), CO 2 ice abundances at r > 30 au are significantly smaller (<10 −6 ). This is because this region has the coldest conditions (T(r) 20 K), and the formation of H 2 O ice (Equation (5)) is faster than that of CO 2 ice (Equation (6); Eistrup et al. 2016).
The gas-phase O 2 abundances are approximately two orders of magnitude larger for atomic initial abundances than those for molecular initial abundances. The O 2 gas abundances between the water and O 2 snowlines are ∼10 −5 − 10 −4 for atomic initial abundances and <10 −6 for molecular initial abundances. This is because in the gas-phase O 2 is formed from atomic oxygen via Equation (8)   . The radial profiles of fractional abundances with respect to total hydrogen nuclei densities n X /n H at t =10 6 yr for H 2 O (top panels), CO (second-row panels), CO 2 (third-row panels), and O 2 (bottom panels). The left panels show the results for the disk midplane with the monotonically decreasing density and temperature profile ( f =1.0), and the right panels show the results for the shadowed disk midplane ( f =0.03). In each panel, the dashed and solid lines show the profiles for gaseous and icy molecules, respectively. The green and blue lines show the results for molecular initial abundances (the "inheritance" scenario), and the red and black lines show the results for atomic initial abundances (the "reset" scenario). The green and red lines show the results for the higher cosmic-ray ionization rate ξ CR (r) =1.0 × 10 −17 [s −1 ], whereas the blue and black lines show the results for the lower cosmic-ray ionization rate ξ CR (r) =1.0 × 10 −18 [s −1 ]. & Walsh 2019), and the initial atomic oxygen abundance is 3.2 × 10 −4 for atomic initial abundances whereas it is zero for molecular initial abundances. In the shadowed disk ( f 0.03), O 2 freezes out onto dust grains at r ∼2-10 au, and returns to the gas phase at r > 10 au. O 2 ice is mainly formed from atomic oxygen via Equation (10) (Taquet et al. 2016;Eistrup & Walsh 2019). For the high ionization rate, O 2 ice photodissociation becomes efficient and the released oxygen is contained in other major oxygen-bearing molecules (Eistrup et al. 2016;Taquet et al. 2016)). Thus, O 2 ice abundances are low (=10 −9 ) for molecular initial abundances and/or the high ionization rates, and they are ∼10 −5 − 10 −4 only for atomic initial abundances and the low ionization rates, which is consistent with the results of previous studies (e.g., Eistrup et al. 2016;Eistrup & Walsh 2019;Taquet et al. 2016). Such larger abundances are consistent with the measured cometary abundances (Bieler et al. 2015;Rubin et al. 2015b; see also Section 4.2 of this paper).
According to the right-hand panels in Figure 14, both O 2 and H 2 O ice abundances are similar (∼(3-5) × 10 −5 ) in the shadowed region (r ∼2-10 au) in the disk with atomic initial abundances and low ionization rates. As we explain in Section 4.2, the ratio of O 2 /H 2 O in comet 67P is a few percent (Bieler et al. 2015;Rubin et al. 2015b). Thus in reality, the models between our assumed parameters (such as partially inherited initial abundances and/or the ionization rates of ∼5 × 10 −18 ) might well reproduce the observed O 2 and H 2 O ice abundance ratios.

A.2. Other Dominant Carbon-bearing Molecules
For molecular initial abundances, the CH 4 and C 2 H 6 gas abundances within their snowline become smaller as the ionization rate becomes larger. This is because CH 4 and C 2 H 6 gases are not efficiently formed in these regions, and they are destroyed by cosmic-ray-induced photodissociation and ionmolecule reactions (such as CH 4 +C + ). Thus, carbon is converted from CH 4 gas to CO 2 , H 2 CO, and hydrocarbons such as, e.g., C 2 H 2 , C 2 H 4 , C 3 H 2 , and C 3 H 4 (Aikawa et al. 1999;Eistrup et al. 2016Eistrup et al. , 2018Yu et al. 2016; see also Sections 3.2.2 and 3.2.4). In addition, for atomic initial abundances, the CH 4 and C 2 H 6 gas abundances within the CH 4 snowline are much smaller (=10 −8 ) than those for molecular initial abundances. For atomic initial abundances, the CH 4 and C 2 H 6 ice abundances outside their snowlines (<10 −6 for CH 4 ice and <10 −6 for C 2 H 6 ice) are much smaller than those for molecular initial abundances (∼10 −5 for CH 4 ice and 10 −6 for C 2 H 6 ice).
For molecular initial abundances, H 2 CO and CH 3 OH ice abundances between their snowlines and the CO snowline are larger for the low ionization rate (∼2 × 10 −7 for CH 3 OH ice) than those for the high ionization rate (∼5 × 10 −7 for CH 3 OH ice). We note that cosmic-ray photodissociation of these molecules is efficient in these regions and produces many radicals, which creates more complex organic molecules (see Section 3.2.2). In addition, H 2 CO and CH 3 OH ice abundances outside the CO snowline (including the shadowed region) are smaller for the low ionization rate (10 −6 for CH 3 OH ice) than those for the high ionization rate (3 × 10 −6 for CH 3 OH ice). This is because H 2 CO and CH 3 OH ice are mainly formed by the sequential hydrogenation of CO on the grain surfaces (see Equations (10) and (11)), and the atomic hydrogen needed to hydrogenate CO is an end product of H 2 ionization (e.g., Schwarz et al. 2018).
For atomic initial abundances, both H 2 CO and CH 3 OH ice abundances at r ∼2-10 au significantly decrease. The H 2 CO ice abundances at such radii are =10 −7 in the non-shadowed disk ( f =1.0) and ∼(1-6) × 10 −6 in the shadowed disk ( f 0.03). The CH 3 OH ice abundances are =10 −8 in the non-shadowed disk ( f =1.0) and ∼(1-3) × 10 −7 in the shadowed disk ( f 0.03). Schwarz et al. (2018) discussed that the timescales needed to build a reservoir of CH 3 OH ice are longer than those needed for CO 2 , because CO 2 can form directly from CO ice (see Equation (6)) while CH 3 OH ice is formed via a series of hydrogenation reactions.

A.3. Dominant Nitrogen-bearing Molecules
Unlike the case for CO, N 2 gas and ice abundance profiles barely change for different initial abundances and ionization rates.
For molecular initial abundances, NH 3 gas and ice abundances around the NH 3 snowline decrease with increasing the ionization rate. This is because NH 3 is converted into N 2 both through ion-molecule reactions as well as through cosmic-rayinduced photoreactions (Eistrup et al. 2016). In addition, for molecular initial abundances, NH 3 ice abundances at r > 5 au are ∼1 × 10 −5 . In contrast, for atomic initial abundances, NH 3 ice abundances at r > 5 au decrease (∼10 −6 − 10 −5 for the high ionization rate and ∼10 −7 − 10 −6 for the low ionization rate). Schwarz & Bergin (2014) and Eistrup et al. (2016) noted that under atomic initial abundances, atomic N quickly forms N 2 gas.
Between the HCN and CO snowlines, HCN ice abundances are larger for molecular initial abundances (∼10 −6 − 10 −5 ) than those for atomic initial abundances (∼10 −7 − 10 −6 ). In contrast, HCN ice abundances just outside the CO snowline (including the shadowed region) are similar (∼(3-5) × 10 −6 ) both for the atomic and molecular initial abundances. This is because HCN is formed through the gas-phase reaction of HCO with an N atom, with subsequent freeze-out onto dust grains, where HCO is formed by hydrogenation of CO on the dust grain surface (see Section 3.2.3 and, e.g., Aikawa et al. 1999;Eistrup et al. 2016).
Between the NH 2 CHO and CO snowlines, NH 2 CHO ice abundances are larger for molecular initial abundances (∼10 −6 − 10 −5 at r ∼1-5 au) than those for atomic initial abundances (∼10 −9 − 10 −8 at r ∼1-5 au). Just outside the CO snowline (including the shadowed region), NH 2 CHO ice abundances for molecular initial abundances are around 10 −6 − 10 −5 . In addition, NH 2 CHO ice abundances for atomic initial abundances significantly increase with increasing the ionization rate. We find that NH 2 CHO ice can form via the subsequent hydrogenation of OCN in the cold region (see Equation (13) in Section 3.2.3, and Garrod et al. 2008;Walsh et al. 2014;López-Sepulcre et al. 2015), and the atomic hydrogen is an end product of H 2 ionozation. Figures 17-19 show the time evolution of the radial profiles of fractional abundances for dominant oxygen-, carbon-, and nitrogen-bearing molecules (H 2 O, CO, CO 2 , O 2 , CH 4 , C 2 H 6 , H 2 CO, CH 3 OH, N 2 , NH 3 , HCN, and NH 2 CHO) in the Figure 17. The time evolution of the radial profiles of fractional abundances with respect to total hydrogen nuclei densities for H 2 O (top panels), CO (second-row panels), CO 2 (third-row panels), and O 2 (bottom panels). The dashed and solid lines show the profiles for gaseous and icy molecules, respectively. The green, blue, red, and black lines show the profiles for different evolutional stages (t =10 4 , 10 5 , 5 × 10 5 , and 10 6 yr), respectively. These panels show the results when assuming molecular initial abundances (the "inheritance" scenario) and for ξ CR (r) =1.0 × 10 −17 [s −1 ]. The left panels show those for the disk midplane with the monotonically decreasing temperature and density structure ( f =1.0), and the right panels show the results for the shadowed disk midplane ( f =0.03).