Impact of an Active Sgr A* on the Synthesis of Water and Organic Molecules throughout the Milky Way

To calculate the X-ray flux during the AGN phase of Sgr A*, we use a numerical model that is described in detail in Liu et al. (2016). This model computes the SED of an accretion disk based on three parameters, the Eddington ratio defined as $\eta := L/{L}_{\mathrm{Edd}}$, where L is the bolometric luminosity of the disk, the X-ray spectral index α, and the magnetic parameter β which characterizes the relative importance between the sum of the gas and radiative pressure and the magnetic pressure. In this model, hard X-rays are produced by a hot corona screening the disk. The solid curves in Figure 1 show the output SED as a function of the Eddington ratio. In the calculation we assume that α = 0.1, β = 100, and the BH mass is 4 × 10⁶ M_⊙. We find that when η ≳ 1, the X-ray flux above 2 keV is more or less constant, at a level of a few times ${10}^{-3}\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$. This result from numerical simulation is consistent with our analytical estimation in Paper I. When η ≲ 0.5, we find that the luminosity of hard X-ray falls linearly with decreasing Eddington ratio.

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Soft photons are subject to extinction as they propagate in the Galactic plane. To quantify it, we adopt the empirical density profile of the atomic hydrogen ${\rho }_{{\rm{H}}}(R)$ and molecular hydrogen ${\rho }_{{{\rm{H}}}_{2}}(R)$ in the MW (McMillan 2017), and we use the software Xspec⁵ to calculate the extinction. Because most molecular clouds are inside the Galactic plane, we only consider the horizontal (in-plane) gas distribution. The corresponding column density at a Galactic distance of R is

$$\begin{eqnarray}&&{\rm{\Sigma }}(R)={\int }_{0}^{R}\left[{\rho }_{{\rm{H}}}(x)+{\rho }_{{{\rm{H}}}_{2}}(x)\right]{dx}.\end{eqnarray} \tag{ 1 }$$

The residual SEDs at R = 8 kpc, for example, are shown in Figure 1 as the dotted–dashed curves. We can see that the optical and UV radiation is completely absorbed. For this reason, in our chemistry model we focus on the effects induced by X-rays.

It is mainly through ionization that X-ray irradiation could affect the chemistry inside a molecular cloud (Maloney et al. 1996). Other effects, such as Coulomb heating, are less important in an environment where the ionization fraction x_e is relatively low. In our model we consider two types of ionization.

Primary ionization, also known as direct photoionization, is caused by an X-ray photon striking an atom (e.g., Latif et al. 2015). The primary ionization rate for a given species i can be calculated with

$$\begin{eqnarray}&&{\zeta }_{p}^{i}={\int }_{{E}_{\min }}^{{E}_{\max }}\displaystyle \frac{F(E)}{E}{e}^{-\tau (E)}{\sigma }^{i}(E){dE},\end{eqnarray} \tag{ 2 }$$

where F(E) is the monochromatic X-ray flux incident on the surface of a molecular cloud, ${\sigma }^{i}(E)$ is the photoionization cross section given a photon energy of E (Verner et al. 1996), τ is the optical depth defined as

$$\begin{eqnarray}&&\tau (E)=\displaystyle \sum _{i={\rm{H}},\mathrm{He}}{N}_{i}{\sigma }^{i}(E),\end{eqnarray} \tag{ 3 }$$

and N_i is the column density of a species. In calculating the optical depth, we have taken into account the fact that H (mostly in molecular hydrogen) and He contribute to most of the opacity.

The photoelectrons released in primary ionization could further collide with other atoms and cause secondary ionization (Maloney et al. 1996; Stäuber et al. 2005). In principle, the secondary ionization rate can be calculated with

$$\begin{eqnarray}&&{\zeta }_{\sec }^{i}={\int }_{{E}_{\min }}^{{E}_{\max }}\displaystyle \frac{F(E)}{E}{e}^{-\tau (E)}{N}_{\sec }(E,{x}_{e}){\sigma }^{i}(E){dE},\end{eqnarray} \tag{ 4 }$$

where N_sec(E, x_e) is the number of secondary ionization events produced by each photoelectron in average. If the energy of the photoelectron is E, this number can be calculated with

$$\begin{eqnarray}&&{N}_{\sec }(E,{x}_{e})=\displaystyle \frac{{\eta }_{\mathrm{ion}}({x}_{e})E-{E}_{\mathrm{th}}}{W(E)},\end{eqnarray} \tag{ 5 }$$

where ${\eta }_{\mathrm{ion}}$ is the fraction of the photoelectron's energy that goes into secondary ionization, E_th is the ionization threshold of an atom, and W is the mean energy needed to produce an ion–electron pair. In practice, we simplify the calculation by adopting the ionization rates presented in Shull & van Steenberg (1985). These rates are derived from a Monte Carlo simulation of the secondary ionization of H and He atoms over a wide range of electron fractions (0.0001 < x_e < 1) and photoelectron energies (from 100 eV to several keV).

Although we have two types of ionization in our model, the secondary ionization rate predominates. For example, if we consider a typical value of ${x}_{e}\leqslant 1 \%$ for a cold (T ∼ 10 K) molecular cloud, approximately 40% of the energy of primary photoelectrons goes into secondary ionization. Because the ground state of neutral H has an ionization threshold ${E}_{\mathrm{th}}=13.6\ \mathrm{eV}$, using η_ion = 40% and W(E) = E_th, we find that for a typical primary photoelectron with E = 1 keV, the number of secondary ionization events it will cause is ${N}_{\sec }(E,{x}_{e})\approx 30$.

For H₂, H, and He, we consider both primary and secondary ionization. For heavy elements (C, N, O, etc.) and molecules (CO, CO₂, etc.), we consider only the secondary ionization for simplicity. We assume that the ionizing electrons are mainly from the three most abundant neutral species, i.e., H₂, H, and He. Then, the ionization rate of heavy elements and molecules can be derived from

$$\begin{eqnarray}&&{\zeta }^{m}=\displaystyle \frac{\left.{\sigma }_{{\rm{ei}},m}(E\right)}{\left.{\sigma }_{{\rm{ei}},{\rm{H}}}(E\right)}{\zeta }_{\sec }^{{\rm{H}}},\end{eqnarray} \tag{ 6 }$$

where σ_ei(E) is the electron-impact cross section at energy E (Maloney et al. 1996; Ádámkovics et al. 2011). We note that heavy elements are usually bound in molecules, but the current derivation of ${\sigma }_{\mathrm{ei}}(E)$ assumes that the cross section is unaffected by the molecular binding energy. Moreover, we notice that the ratio of the cross sections, which appears in the last equation, is insensitive to E (Maloney et al. 1996). For this reason, we use the cross sections at $E=50\,\mathrm{eV}$, which is the typical energy of the secondary electrons.

For completeness, we also consider the destruction of H₂ and several other molecules caused by photoionization. For example, photoionization of H₂ can have two possible outcomes, pure ionization and dissociation, which can be expressed as

$$\begin{eqnarray*}\begin{array}{c}\begin{array}{rcl}{{\rm{H}}}_{2} & \to & {{\rm{H}}}_{2}{}^{+}+{{\rm{e}}}^{-},\\ {{\rm{H}}}_{2} & \to & {{\rm{H}}}^{+}+{\rm{H}}+{{\rm{e}}}^{-}.\end{array}\end{array}\end{eqnarray*}$$

We take the branching ratio suggested by Krolik & Kallman (1983), that the fraction of pure ionization is approximately 80% and that for dissociation is 20%. For other atomic and molecular reactants, we adopt the same products from the OSU chemical database osu_01_2007,⁶ as well as the corresponding branching ratios for cosmic-ray ionization and dissociation. We choose this database because it was used by Wakelam & Herbst (2008) to explain the molecular abundances observed in the cold dense cores in the MW. These cores represent the initial conditions of the molecular clouds of our own interest. To be able to reproduce the results in Wakelam & Herbst (2008), we did not choose the latest chemical database provided by the OSU group. The later updates included more anions, which are more important for the formation of long carbon chains (Herbst & van Dishoeck 2009).

The surface of a dust particle (grain) is an important place for the synthesis of complex molecules. A grain accretes many molecular species to its surface from the surrounding gas, where these molecules can interact more frequently and the chemical reactions such as hydrogenation can proceed more efficiently. Because we are interested in the synthesis of H₂O, CH₃OH, and H₂CO (see Section 1), we include in our model the surface reactions containing the species made of H, C, N, and O. Only those species with no more than two C atoms are selected as we do not study long-carbon-chain species in this work. Table A1 in Appendix A shows the relevant reactions, which are selected from the network presented in Hasegawa et al. (1992). The last column shows the activation energies for those reactions with high energy barriers. This network is sufficient to simulate the species we are interested in. The reaction parameters in this network are still frequently used today, although there are works that extend the reaction mechanisms so that the desorption energy may depend on the fraction of surface coverage by molecules (Garrod & Pauly 2011) and that the molecules in ice mantle could react with each other (Chang & Herbst 2014). More recent grain-surface chemical networks (e.g., Garrod et al. 2008) are usually concerned with the formation of more complex organic molecules, which is not the focus of the current work. On one hand, the abundances of those very complex molecules are usually low, so that including them in our network should have a negligible effect on the species studied in this paper. On the other hand, it may be interesting to ask to what extent those more complex molecules are affected by the mechanisms discussed in the current paper, which may be a topic for future investigation.

We calculate the accretion rate of molecules onto dust grains following the method developed in Hasegawa et al. (1992). We consider accretion, via weak van der Waals forces (physisorption), onto "classic" dust grains, which have a fixed radius ${r}_{d}=1000\ \mathring{\rm A}$, a density of ρ = 3 g cm⁻³, and N_s = 10⁶ sites for adsorption (the number of molecules that can be absorbed to and held on a dust grain). The dust temperature T_d is assumed to be the same as the gas temperature T ∼ 10 K, following the assumption in Hasegawa et al. (1992). This is a reasonable approximation for the clouds at ≳2 kpc but may be too crude for those at 1 kpc. This is because, within 1 kpc from the AGN, the X-ray flux significantly exceeds $0.1\,\mathrm{erg}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-1}$ so that heating due to ionization cannot be ignored given our cloud density of 10⁴ cm⁻³ (Meijerink et al. 2007). Moreover, we did not consider the difference between the gas and dust temperatures because the difference is small due to the efficient gas–dust coupling at a high density of ${10}^{4}\,{\mathrm{cm}}^{-3}$ (Goldsmith 2001). Moreover, the reaction rates are insensitive to small temperature changes (at least in the range of temperature of our interest). For the gas-to-dust ratio in mass, we adopt the standard value of 100. We assume that the velocities of the gas species obey the Maxwell distribution. For any species that strikes a dust grain, a sticking probability of 1 is assumed.

For the desorption of molecules, we consider three channels, namely, thermal desorption, cosmic-ray desorption, and photodesorption. (i) Given the adsorption energy E_D and dust temperature T_d, the thermal evaporation rate can be calculated with ${R}_{\mathrm{evap}}\propto {E}_{D}^{1/2}\exp [-{E}_{D}/{{kT}}_{d}]$ (Hasegawa et al. 1992), where k is the Boltzmann constant. The value of E_D for each species is from Allen & Robinson (1977) and Hasegawa & Herbst (1993). We note that although thermal evaporation is common, the rate is negligible for any species heavier than He because of the low temperature in our molecular clouds. (ii) The cosmic-ray-induced desorption rates are calculated as in Hasegawa & Herbst (1993). Every time a cosmic-ray particle strikes a dust grain, the dust temperature is assumed to rise to 70 K immediately and then drop via thermal desorption. (iii) Photodesorption can be induced by either UV or X-ray photons. For UV-induced desorption, we assume a rate of 10⁻³ molecules per grain per incident UV photon for any species in our grain-surface network (also see Visser et al. 2011). Because UV-induced desorption depends strongly on the visual extinction, which is a function of the optical depths of a molecular cloud, we will study in Section 4.3 the dependence of the rate on the column density of the molecular cloud. The X-ray desorption processes are more complex (see Jiménez-Escobar et al. 2018 for a brief review) and not as well understood both in theory and in experiment. However, X-ray photons are more penetrative than UV photons, so that the interaction happens deeper inside the bulk of a grain and hence does not as often lead to desorption. Therefore, the X-ray desorption is less significant compared to UV photodesorption, and we ignore it in our model.

In our fiducial model, the Eddington ratio of the AGN is $\eta =1$. The molecular cloud is at a Galactic distance of 4 kpc and has a column density of ${N}_{{\rm{H}}}={10}^{22.5}$ cm⁻² (A_V = 16.8). The results for the chemical evolution are shown in Figures 2 and 3. In general, the abundances of molecules on the dust grain surface are several orders of magnitude higher than their gas-phase counterparts. This is mainly because at low temperatures (∼10 K) molecules stay on the surface of dust grains, and the grain surface acts as a reaction container and a catalyst leading to much more efficient formation of H₂O, CH₃OH, etc.

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For H₂O (Figure 2), on the grain surface (lower panels), even without X-rays (the black dotted–dashed curves) the abundance keeps growing during the first ${10}^{5}\mbox{--}{10}^{6}$ yr and afterward saturates. The increase is caused mainly by two surface reactions, (i) H₂ + OH → H₂O + H and (ii) H + OH → H₂O. The first reaction usually predominates because of the high abundance of H₂, even though the activation energy is high (Hasegawa et al. 1992). The second one has a much lower energy barrier but the rate is limited by the low concentration of atomic H at the grain surface. The saturation of the water surface abundance in the late stage is due to a balance between the photoevaporation and the formation processes.

If we start X-ray irradiation at the very beginning (green solid curves), the H₂O surface abundance increases faster and in the end, slightly exceeds that in the case without X-ray. We find that the first reaction is not significantly affected by the X-ray irradiation, because the H₂ surface abundance only slightly decreases. On the contrary, the second reaction becomes faster because the atomic hydrogen abundance increases significantly due to the X-ray dissociation of H₂. After we remove the X-ray irradiation at the end of 10⁶ yr (green dashed curve), the surface abundance of H₂O stays more or less constant. The value is slightly lower than that in the case of X-ray irradiation because atomic H quickly recombines to form H₂, and thus the rate of the second reaction drops.

For the gas phase (the upper panels of Figure 2), when there is no X-ray, the abundance of H₂O first increases until a plateau is reached around the time of ${10}^{4}\mbox{--}{10}^{5}$ yr. During this period, ionization leads to the formation of H₃⁺, which is a highly reactive species that can quickly produce OH⁺, H₂O⁺, and H₃O⁺ (Krolik & Kallman 1983). Gaseous water is synthesized mainly by the recombination of H₃O⁺ with electrons. Around the time of 10⁶ yr, the abundance of gas H₂O starts to decrease because materials such as OH⁺, H₂O⁺, and H₃O⁺ run out following the exhaustion of O, so that the formation of H₂O slows down. The final gaseous abundance is limited mainly by the interaction with atomic cations, such as Si⁺ through the ion–neutral reaction Si⁺ + H₂O → HSiO⁺ + H.

When X-ray irradiation is turned on, the behavior of the water abundance in the gas phase in similar to that on the grain surface. However, both the rise and fall of the H₂O abundance are more prominent, which leads to a higher plateau around 3 × 10⁵ yr and a lower abundance at about ≳10⁶ yr. The sharper evolution is caused by the higher cation density during the X-ray ionization, such as H₃⁺, OH⁺, and H₂O⁺, during the early formation stage of H₂O, as well as the higher abundance of Si⁺ during the later stage of H₂O destruction. After we remove the X-rays, the abundance of H₂O first decreases but within about 10⁵ yr recovers the value which is seen in the case of no X-ray irradiation. The recovery is caused by the dissociative recombination, H₃O⁺ + e⁻ → H₂O + H, as well as the photoevaporation from the grain surface.

For CH₃OH, the evolution of the abundance after the first 10⁶ yr is shown in the two upper panels of Figure 3. We do not show the evolution in the first 10⁶ yr because it is a monotonic increase. Also, we are more interested in the molecular abundances millions of years after the AGN turns off. At the grain surface (right panel), when there is no X-ray irradiation, the abundance is almost constant over 10⁷ yr of evolution. The dominant synthesis process is hydrogenation, via CO → HOC → CHOH → CH₂OH → CH₃OH. When X-ray irradiation is turned on, the abundance of CH₃OH becomes more than two orders of magnitude higher. The increase is caused by a faster hydrogenation process, as the result of a larger atomic hydrogen abundance due to the X-ray disassociation. Even after we remove the X-ray, the CH₃OH surface abundance stays nearly the same. This is because in our model there is no chemical reaction at the grain surface for CH₃OH destruction (also see Hasegawa et al. 1992) and also the photoevaporation of CH₃OH is inefficient.

In the gas phase (upper-left panel), without X-ray irradiation, the abundance of CH₃OH stays constant for about 10⁶ yr and afterward slightly decreases. Gaseous CH₃OH mainly comes from the grain surface, and the later decrease is caused by the reactions with cations, e.g., CH₃OH + He⁺ → OH⁺ + CH₃ + He/OH + CH₃⁺ + He. With X-rays and for the particular Galactic distance of our choice, i.e., 4 kpc, the abundance of CH₃OH increases by about one order of magnitude relative to that in the case without X-rays. The increase is closely related to the enhancement of the CH₃OH abundance on dust grains. After we remove the X-rays, the abundance increases even more because cations recombine and the destruction of CH₃OH slows down.

For H₂CO, the results are shown in the lower two panels of Figure 3. Unlike CH₃OH which forms only at the grain surface, H₂CO can form both on the surface of grains, mainly through hydrogenation CO → HCO → H₂CO, and in the gas phase, via CH₃ + O → H₂CO + H. Moreover, there is also one pathway for H₂CO on the grain surface to dissociate, H₂CO + H → HCO + H₂. The O atom can then be transferred to species like CO₂ through reaction O + HCO → CO₂ + H. Although the activation energy of this dissociation is high, the reaction rate is still orders of magnitude higher than photoevaporation.

With these differences in mind, we can understand the behavior of H₂CO at the grain surface (lower-right panel). During the X-ray irradiation, the formation rate is first enhanced due to a higher hydrogenation rate. In the last several million years of our simulation, the abundance of H₂CO significantly decreases, because the disassociation process becomes important and O atoms are slowly transferred to species like CO₂. After we remove the X-ray irradiation, the decrease of the surface abundance of H₂CO becomes slower because the surface abundance of H falls substantially. Because the formation (hydrogenation) of H₂CO is also proportional to the surface abundance of H, we do not see an increase of H₂CO after we remove the X-ray irradiation.

In the gas (lower-left panel), even without X-rays, the abundance of H₂CO drops by almost four orders of magnitude by the end of 10⁶–10⁷ yr of evolution. The drop is mainly caused by the exhaustion of CH₃ and O, so that the rate of the reaction CH₃ + O → H₂CO + H significantly decreases by the end of our simulation. With X-rays, the abundance decreases relative to that in the case without X-ray irradiation, by a factor of a few. The drop is due to the higher abundance of cations. In this case, the destructive reactions, such as H₂CO + S⁺ → HCO⁺ + HS, become more efficient. When we remove the X-rays, the H₂CO abundance first recovers the value in the case of no X-ray irradiation, and in about 10⁶ yr significantly decreases due to the exhaustion of CH₃. Finally, the abundance balances at a value that is higher than that in the no-X-ray case, because more CH₃ has been produced during the episode of X-ray irradiation.

For completeness, we show in Appendix B the evolution of the other species that are often detected in molecular clouds. In general, we also find that their abundances with and without X-rays are different.

Because the X-ray flux decreases with increasing distance from the Galactic Center, we also explore the chemical evolution at different Galactic distances. The results are shown in Figure 4, where the column density of each cloud is still set to ${N}_{{\rm{H}}}={10}^{22.5}$ cm⁻².

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On the grain surface (right panels), when there is X-ray irradiation (solid curves), the abundance of H₂O keeps increasing as the Galactic distance decreases. The increase is caused by the higher abundance of atomic hydrogen as the ionization flux intensifies. For CH₃OH and H₂CO, however, the surface abundance maximizes at a Galactic distance of 4–8 kpc, and further increasing or decreasing the distance would both lead to lower abundance. The location where these two abundances peak is determined by two competing processes. On one hand, an important precursor of both species, CO, can be destroyed by X-rays and hence cannot exist too close to the Galactic Center when the AGN is on. On the other hand, the abundance of H increases toward the AGN due to X-ray disassociation. These two processes balance at about $4\mbox{--}8\,\mathrm{kpc}$ and produce the highest abundance of CH₃OH and H₂CO there.

To understand the behavior of H₂O, CH₃OH, and H₂CO after we turn off the X-ray irradiation (dashed lines), we should first understand the evolution of H₂ and CO. The major difference between the two species is that while the H₂ abundance is lowered by several percents during X-ray irradiation, the abundance of CO could be lowered by orders of magnitude depending on the Galactic distance. Therefore, after we turn off the X-rays, the abundance of H₂ only slightly increases in percentage, due to recombination, and recovers the equilibrium in the case of no X-rays, but the abundance of CO increases more drastically. The difference in the recovery rate causes the different behavior of H₂O versus CH₃OH and H₂CO at the grain surface. We can see that after we turn off X-rays, the surface abundance of H₂O increases slightly, because there is slightly more H₂ for the reaction H₂ + OH → H₂O + H. For CH₃OH and H₂CO, however, there is a lot more CO produced within a short period of time, especially at small Galactic distances. For example, at 1 kpc, the abundances of CH₃OH and H₂CO rise by orders of magnitude after the X-ray irradiation is turned off. One interesting result, which is shared by all three molecular species (H₂O, CH₃OH, and H₂CO ) and at all simulated Galactic distances, is that the final surface abundance after we remove X-rays is higher than the abundance in the case without X-ray irradiation.

In the gas phase (left panels), the behavior of H₂O, CH₃OH, and H₂CO also depends on the Galactic distance. For H₂O, X-ray irradiation in general suppresses the abundance within a timescale of 10⁷ yr, because, as we have explained in Section 4.1, destructive cations form in large amounts but water formation on the grain surface is relatively inefficient. Moreover, the final abundance decreases with decreasing distance, because the X-ray flux is higher at a smaller distance. For CH₃OH and H₂CO, destructive cations also form due to the X-ray irradiation. That is why at small Galactic distances such as 1 and 2 kpc, the abundances of CH₃OH and H₂CO are suppressed when the AGN is on. However, at large distances such as 4 and 8 kpc, the abundances are not significantly suppressed and could even exceed those in the cases without X-rays. The reason is that at these distances the X-ray flux is not as strong so that CH₃OH and H₂CO form very fast on the grain surface, which, through photoevaporation, could also enrich the gas.

After we turn off the X-ray irradiation, the gaseous abundances of H₂O, CH₃OH, and H₂CO all increase within a timescale of 10⁷ yr, regardless of the Galactic distance. The cause is mainly the recombination of cations, which in turn lowers the destruction rate. Photoevaporation also contributes considerably. Even for H₂O, whose gaseous concentration is not as sensitive to the surface abundance, photoevaporation enriches the gas species significantly after ∼5 × 10⁶ yr, when the dissociative recombination has significantly slowed down. We find that at all distances, after we remove the X-rays, the final abundances of gaseous H₂O, CH₃OH, and H₂CO exceed those in the case without an AGN or with a constant AGN.

These results suggest that a relatively short episode (10⁶ yr) of X-ray irradiation could indeed, in the following 10⁷ yr, leave an imprint in the molecular abundances throughout the MW.

To understand the distribution of H₂O, CH₃OH, and H₂CO as a function of the depth inside a molecular cloud, we compute the chemical evolution assuming different column densities (${N}_{{\rm{H}}}$) for the cloud. The results are shown in Figure 5. In these calculations, the Galactic distance of the cloud is fixed at 4 kpc.

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We find that when the column density is high, i.e., ${N}_{{\rm{H}}}={10}^{23}{\mathrm{cm}}^{-2}$ (or equivalently A_V = 53), the abundances (see the blue curves) are slightly, but systematically lower than those in the fiducial model. This trend can be seen both in the gas phase and on the grain surface. The main cause of this systematic change is the lower UV flux due to higher extinction. The hard-X-ray flux from the AGN is only slightly attenuated inside the molecular cloud, and hence when we turn the AGN on and off, the evolution of the three species is similar to the evolution in our fiducial model.

In low-extinction regions (${N}_{{\rm{H}}}={10}^{22}$ cm⁻², A_V = 5.3, the red curves), the surface abundances (right panels) are more significantly affected by the rise of the UV irradiation. Even when there is no X-ray radiation (dotted curves), the H₂O abundance is lower than that in the fiducial case by one order of magnitude. On the contrary, the surface abundances of H₂CO and CH₃OH are higher than those in the fiducial model. This result is caused by two competing processes. On one hand, surface species evaporate more rapidly in the presence of a higher UV flux. On the other hand, the higher density of H due to UV ionization/dissociation enhances the rate of hydrogenation. Because the synthesis of H₂O uses mainly H₂, not H, a higher UV flux would increase the evaporation rate more than the hydrogenation one, causing the surface abundance of water to decrease. For CH₃OH and H₂CO, the hydrogenation rate is relatively higher than the evaporation rate, so that the surface abundances increase when the UV flux becomes higher.

If we turn on X-rays, the surface abundances of all three species increase (compare the red dotted and the red solid curves), because of enhancement of H density on the grain surface. However, compared to those in the high-extinction regions (blue solid curves), the surface abundances in the low-extinction regions is reduced because of a higher evaporation rate induced by X-rays in the latter case. After we remove the X-ray irradiation, within ∼10⁶ yr the abundances recover the values in the case of no X-rays. The quick recovery is closely correlated with the high reaction and evaporation rate in the low-extinction regions.

In the gas phase of the low-extinction regions (red curves in the left panels), the abundances of H₂O, CH₃OH, and H₂CO without X-rays are much higher than those in the high-extinction ones. After we turn on the X-ray irradiation, the abundances become lower but are still higher than those in the high-extinction regions. The high abundances in the gas are caused mainly by the high photoevaporation rate on the grain surface. After we turn off X-rays, the gas abundances quickly recover the values in the no-X-ray case, and hence the imprint of the X-rays disappears within about 10⁶ yr.

To see the response of a more evolved molecular cloud to the X-rays from the AGN, we run our chemical-reaction network without X-rays for 10⁷ yr and take the resulting chemical abundances as our new initial condition for the later simulations. The other parameters are the same as in the fiducial model. The results are presented in Figure 6. We see that the abundances in the case without X-rays no longer significantly vary with time, both in the gas and on the grain surface, suggesting that the chemical reactions have reached equilibrium on a timescale of 10⁷ yr.

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If we turn on X-ray irradiation after the 10⁷ yr of isolated evolution, on the grain surface (right panels) the abundances of H₂O and CH₃OH will increase, as we have seen in the fiducial model, but the abundance of H₂CO decreases. The decrease is caused by the reaction H₂CO + H → HCO + H₂, which predominates in the current conditions. We notice that the variation of the abundances of CH₃OH and H₂CO after we turn on X-rays is not as prominent as that in a less evolved cloud (see our fiducial model). This difference indicates that a chemically more evolved cloud is more resilient to X-ray irradiation. After we remove the X-rays, the surface abundances return to the values in the case of no X-ray radiation, on a timescale of about 10⁷ yr.

In the gas phase (left panels), the X-ray irradiation significantly lowers the abundances of all three molecules. This behavior is different from that in a less evolved cloud, where the CH₃OH abundance is enhanced by X-rays (see Figure 3). After we remove the X-rays, the abundances rise more quickly than that in a less evolved cloud. As a result of the quick rise, a recovery of the equilibrium state for no X-rays is seen at about ${10}^{4}\mbox{--}{10}^{5}$ yr. After this time, the imprint of an AGN is lost.