$L_{\mathrm{X}}=10^{32}$ erg s-1, and rescale $\zeta_{\mathrm{X}}(r)$ to the
value at a similar radius in the IRAS 2A model. We compare the rates of
reactions of this test calculation with those of the standard IRAS 2A model.

In this test calculation, at $t=10^{5}$ years, the fractional abundance and
absolute number density of water are are $6.9\times 10^{-8}$ and $1.5\times
10^{2}$ cm-3, respectively, and the same for HCO+ are $4.2\times 10^{-9}$ and
$9.4$ cm-3, respectively. On the basis of these values, the rate coefficient
of the ion-molecule reaction with H2O+HCO+$\rightarrow$CO+H3O+, $k_{6}$, is
$\sim 3.5\times 10^{-9}$ cm3 s-1 (Adams et al., 1978), and the reaction rate,
$R(6)=$$k_{6}$$n_{\mathrm{H}_{2}\mathrm{O}}$$n_{\mathrm{HCO}^{+}}$, is $\sim
2.2\times 10^{-5}$ cm-3 s-1 at $t=10^{5}$ years. In contrast, the rate
coefficient of X-ray-induced photodissociation leading to H+OH, $k_{7}$, is
$\sim 8.6\times 10^{-11}$ s-1 (Gredel et al., 1989), and the reaction rate,
$R(7)=$$k_{7}$$n_{\mathrm{H}_{2}\mathrm{O}}$, is $\sim 1.3\times 10^{-8}$ cm-3
s-1 at $t=10^{5}$ years.

Comparing these reaction rates with those of the standard IRAS 2A model (see
Section 3.1), the differences of the reaction rates are larger in the former
ion-molecule reaction ($R(6)/R(1)$$\sim 25$) than the latter X-ray-induced
photodissociation ($R(7)/R(2)$$\sim 2.5$). It is because the former reaction
is the“second-order” process and the latter reaction is the “first-order”
process. Thus, as the gas densities become larger, the“second-order” processes
including ion-molecule reactions become much more dominant compared with
the“first-order” processes including X-ray-induced photodissociation.

##  Appendix B Sub-grid calculations for the IRAS 4A envelope models

Figure 13:  The radial profiles of gaseous fractional abundances of of H2O,
O2, O, OH, HCO+, and CH3OH in the NGC 1333-IRAS 4A envelope models, with X-ray
luminosities between $L_{\mathrm{X}}=$$10^{30}$ and $10^{31}$ erg s-1. The
line colors are gradually change from yellow to orange, red, and brown as the
values of $L_{\mathrm{X}}$ increase. In the top left panel, the observational
best-fit H2O gas abundance profile obtained in van Dishoeck et al. (2021) is
over-plotted, as we plot in Figure 10. In the top right panel, the three model
O2 gas abundance profiles obtained in Yıldız et al. (2013) are over-plotted,
as we plot in Figure 10.

Figure 13 shows the radial profiles of H2O, O2, O, OH, HCO+, and CH3OH gas
fractional abundances in the IRAS 4A envelope models, with X-ray luminosities
between $L_{\mathrm{X}}=$$10^{30}$ and $10^{31}$ erg s-1. We plot these sub-
grid model profiles since there is a large jump in abundances in this X-ray
luminosity range (see Figures 3-7). For the abundance profiles of H2O gas,
between $10^{30}$ and $2\times 10^{30}$ erg s-1 seems to be the clear
boundary, and they decrease from $\sim 10^{-4}$ to $<10^{-7}$ at $r\lesssim
10^{2}$ au. For the abundance profiles of HCO+ and CH3OH gas, between
$10^{30}$ and $2\times 10^{30}$ erg s-1 also seems to be the clear boundary.
Compared to them, the abundance profiles of O2 and O gas gradually increase in
the inner region as the values of $L_{\mathrm{X}}$ increase from $10^{30}$ to
$\sim 6\times 10^{30}$ erg s-1.

##  Appendix C CO2 and CO fractional abundances

Figure 14:  The radial profiles of CO2 gas and ice fractional abundances
$n_{\mathrm{CO}_{2}}$/$n_{\mathrm{H}}$ (top panels) and
$n_{\mathrm{CO}_{2},\mathrm{ice}}$/$n_{\mathrm{H}}$ (bottom panels) in NGC
1333-IRAS 2A (left panels) and NGC 1333-IRAS 4A (right panels) envelope
models.

Figure 15:  The radial profiles of CO gas and ice fractional abundances
$n_{\mathrm{CO}}$/$n_{\mathrm{H}}$ (top panels) and
$n_{\mathrm{CO},\mathrm{ice}}$/$n_{\mathrm{H}}$ (bottom panels) in NGC
1333-IRAS 2A (left panels) and NGC 1333-IRAS 4A (right panels) envelope
models.

Figure 14 shows the radial profiles of CO2 gas and ice fractional abundances
$n_{\mathrm{CO}_{2}}$/$n_{\mathrm{H}}$ in IRAS 2A (left panels) and IRAS 4A
(right panels) envelope models, for the various X-ray luminosities. At $r\sim
3\times 10^{2}-4\times 10^{3}$ au (in the IRAS 2A model) and $r\sim 3\times
10^{2}-2\times 10^{3}$ au (in the IRAS 4A model), which are the regions
between CO2 and CO snowlines, CO2 ice abundances are around 10-6 for
$L_{\mathrm{X}}\lesssim 10^{30}$ erg s-1. In contrast, for
$L_{\mathrm{X}}\gtrsim 10^{31}$ erg s-1, CO2 ice abundances increase (up to
10-5) in these regions. On the basis of Drozdovskaya et al. (2016), Eistrup et
al. (2016, 2018), and Bosman et al. (2018b), in the presence of X-ray fluxes,
the X-ray induced photodissociation of H2O ice forms OH radicals within the
ice mantle, which subsequently react with CO on grain surfaces to form CO2 ice
inside the CO snowline.

CO2 gas abundances at $r\lesssim 10^{4}$ au in the IRAS 2A model and at
$r\lesssim 6\times 10^{3}$ au in the IRAS 4A model are affected by strong
X-ray fluxes. For low and moderate X-ray luminosities101010For the definition
of the values of low, moderate, and high X-ray luminosities, please see
Section 3.2., CO2 gas abundances become smaller, and reach $\lesssim 10^{-9}$
at $r\sim 3\times 10^{2}-10^{3}$ au (outside the CO2 snowline). In contrast,
for high X-ray luminosities, CO2 gas abundances become larger, and they reach
around 10-6 (for IRAS 2A) and 10-7 (for IRAS 4A) at these radii for
$L_{\mathrm{X}}\sim 10^{32}$ erg s-1. At $r\lesssim 3\times 10^{2}$ au (inside
CO2 snowline), CO2 abundances are around $10^{-6}-10^{-5}$ for low X-ray
luminosities. In addition, like OH, the CO2 gas abundances increase as the
X-ray fluxes become larger, and they reach $\sim 10^{-5}-10^{-4}$ for moderate
X-ray luminosities, However, they decrease for high X-ray luminosities. At
$L_{\mathrm{X}}\gtrsim 10^{31}$ erg s-1 in the IRAS 2A model and
$L_{\mathrm{X}}\gtrsim 10^{32}$ erg s-1 in the IRAS 4A model, the CO2 gas
abundances are around $3\times 10^{-7}-10^{-6}$.

Outside the CO2 snowline, CO2 gas is supplied by X-ray induced photodesorption
reaction of CO2 ice. In the inner envelope, gas-phase CO2 is mainly formed by
two body reaction of CO$+$OH (Bosman et al., 2017), and destroyed with X-ray
induced photodissociation. Therefore, CO2 abundance profiles strongly depend
on the radial profiles of X-ray fluxes and OH abundances.

The CO2 abundances in the outer envelopes around low-mass protostars can be
probed through the observations CO2 ro-vibrational lines with JWST (see also
Section 4.1), as done for high-mass protostellar envelopes using ISO (van
Dishoeck et al., 1996; Boonman et al., 2003). For low-mass protostellar
envelopes, a hint of gas-phase CO2 lines has been obtained using Spitzer (see
e,g., Poteet et al. 2013). We note that high dust opacities in the near and
mid-infrared wavelengths make it difficult to probing the CO2 gas abundances
directly in the inner envelopes around low-mass protostars.

Boonman et al. (2003) and Bosman et al. (2018a) noted the disagreements of CO2
gas abundances within the CO2 snowline between models ($\sim 10^{-5}$) and
observations ($\sim 10^{-7}$), both for high-mass protostar envelopes and
Class II disks. Bosman et al. (2018a) discussed that the CO2 should be
destroyed within $10^{4}$ years after the sublimation of CO2 ice. X-ray
induced destruction reactions discussed in this paper would help to destroy
CO2 molecules within the above timescale, assuming that CO2 chemistry is
similar among these type of sources.

Figure 15 shows the radial profiles of CO gas and ice fractional abundances
$n_{\mathrm{CO}}$/$n_{\mathrm{H}}$ in IRAS 2A (left panels) and IRAS 4A (right
panels) envelope models, for the various X-ray luminosities. Unlike other
dominant oxygen-bearing molecules (e.g., H2O, O2, O, CO2), both of CO gas and
ice abundances do not depend on X-ray fluxes. CO gas fractional abundances are
around 10-4 at $r\lesssim 3\times 10^{3}$ au at IRAS 2A and $r\lesssim 10^{3}$
au at IRAS 4A (within the CO snowline), and CO ice fractional abundances are
around 10-4 at $r\gtrsim 4\times 10^{3}$ au at IRAS 2A and $r\gtrsim 10^{3}$
au at IRAS 4A (outside the CO snowline).

With an ISM level cosmic-ray ionisation rate of
$\xi_{\mathrm{CR}}(r)=$$1.0\times 10^{-17}$ s-1, longer timescale ($>10^{6}$
years, which is a typical age of Class II disks) than that in our modeling
($10^{5}$ years, which is a typical age of Class 0 protostars) is required to
achieve a CO depletion by a factor of 10 and more (Bosman et al., 2018b;
Eistrup et al., 2018; Schwarz et al., 2018). Moreover, in the inner envelopes
where $\xi_{\mathrm{X}}(r)$$>\xi_{\mathrm{CR}}(r)$, efficient X-ray induced
destruction reactions of other dominant molecules, especially H2O, consider to
supply more atomic oxygen, and it reacts with C+ to returning to CO. According
to previous studies of chemical modeling with a timescale of $>10^{6}$ years,
CO is chemically processed and the carbon is sequestered into less volatile
species such as CH3OH, CH4, and CO2 (e.g., Furuya & Aikawa 2014; Yu et al.
2016; Bosman et al. 2018b; Schwarz et al. 2018, 2019; Krijt et al. 2020).

According to recent observations with e.g., ALMA, CO gas abundances in the
Class 0-I disks with $<10^{6}$ years are consistent with the ISM abundance
($\sim 10^{-4}$) within a factor of 2 (Harsono et al., 2014; van’t Hoff et
al., 2020; Zhang et al., 2020), nearly one order of magnitude higher than the
average value in $10^{6}-10^{7}$ years Class II disks (e.g., Ansdell et al.
2016; Long et al. 2017; Zhang et al. 2019; Bergner et al. 2020).

##  Appendix D CH4, HCN, and C2H fractional abundances

Figure 16:  [Top panels]: The radial profiles of CH4 fractional abundances
$n_{\mathrm{CH}_{4}}$/$n_{\mathrm{H}}$ in NGC 1333-IRAS 2A (left panel) and
NGC 1333-IRAS 4A (right panel) envelope models. [Middle panels]: The radial
profiles of HCN gas fractional abundances $n_{\mathrm{HCN}}$/$n_{\mathrm{H}}$
in the IRAS 2A (left panel) and IRAS 4A (right panel) envelope models. [Bottom
panels]: The radial profiles of C2H gas fractional abundances
$n_{\mathrm{C}_{2}\mathrm{H}}$/$n_{\mathrm{H}}$ in the IRAS 2A (left panel)
and IRAS 4A (right panel) envelope models.

Top panels of Figure 16 show the radial profiles of CH4 gas fractional
abundances $n_{\mathrm{CH}_{4}}$/$n_{\mathrm{H}}$ in IRAS 2A (left panel) and
IRAS 4A (right panel) envelope models, for the various X-ray luminosities. For
$L_{\mathrm{X}}\lesssim 10^{28}$ erg s-1, the CH4 gas abundances are around
$(3-8)\times 10^{-6}$ at $r\lesssim 10^{3}$ au in the IRAS 2A model and at
$r\lesssim 6\times 10^{2}$ au in the IRAS 4A model (within the CH4 snowline).
As the X-ray flux becomes large, the CH4 gas abundances in these radii
decrease. For $L_{\mathrm{X}}\gtrsim 10^{31}$ erg s-1, the CH4 gas abundances
are around $10^{-9}-10^{-8}$ at $r\lesssim 10^{2}$ au.

The X-ray induced photodissociation and ion-molecule reactions (with He+,
H${}_{3}^{+}$ etc.) are considered to be dominant destruction processes of CH4
in the inner envelopes (e.g., Aikawa et al. 1999; Eistrup et al. 2016). We
note that ion-molecule reactions of gas-phase CH4 with e.g., C+ within the CH4
snowline are important to form unsaturated carbon chain molecules, such as
C2H, C3H2, and C4H (WCCC, e.g., Hassel et al. 2008; Sakai et al. 2008; Sakai &
Yamamoto 2013; Aikawa et al. 2012, 2020).

Middle panels of Figure 16 show the radial profiles of HCN gas fractional
abundances $n_{\mathrm{HCN}}$/$n_{\mathrm{H}}$ in IRAS 2A (left panel) and
IRAS 4A (right panel) envelope models, for the various X-ray luminosities. The
binding energy of HCN is somewhat smaller than that of H2O and similar to that
of CH3OH ($E_{\mathrm{des}}$(HCN)=3610 K, $E_{\mathrm{des}}$(H2O)=4880 K,
$E_{\mathrm{des}}$(CH3OH)=3820 K, see Table 2), and the HCN snowline position
($\sim 2\times 10^{2}$ au) exists outside the water snowline ($\sim 10^{2}$
au). For low X-ray luminosities, the HCN gas abundances are around $\sim
10^{-6}-10^{-5}$ within the HCN snowline. As the X-ray flux becomes large, the
HCN gas abundances in these radii decrease. For high X-ray luminosities, the
HCN gas abundances are $\lesssim 10^{-9}$ within the HCN snowline. The X-ray
induced photodissociation and ion-molecule reactions (with He+, H${}_{3}^{+}$
etc.) are considered to be dominant destruction processes of HCN in the inner
envelopes (e.g., Huntress 1977; van Dishoeck et al. 2006; Walsh et al. 2015).

Bottom panels of Figure 16 show the radial profiles of C2H gas fractional
abundances $n_{\mathrm{C}_{2}\mathrm{H}}$/$n_{\mathrm{H}}$ in IRAS 2A (left
panel) and IRAS 4A (right panel) envelope models, for the various X-ray
luminosities. The C2H gas fractional abundances are around $10^{-10}-10^{-8}$
at $r\gtrsim 10^{3}$ au, and decrease at the inner radii. Within $10^{2}$ au,
they are $\sim 10^{-16}-10^{-13}$ at IRAS 2A and $\sim 10^{-17}-10^{-14}$ at
IRAS 2A. The dependance of X-ray fluxes are smaller (within two orders of
magnitude) than other dominant carbon-bearing molecules such as CH3OH, HCN,
and CH4. C2H is the representative products of WCCC in star-forming cores
(e.g., Sakai & Yamamoto 2013; Higuchi et al. 2018; Aikawa et al. 2020, see
also Section 4.6), and it is mainly produced by the ion-molecule reaction of
CH4 gas with C+ and the subsequent electron recombination reaction (Aikawa et
al., 2012). C2H also reacts with C+, which links to the formation of longer
carbon chain molecules. Henning et al. (2010) discussed that in the
atmospheres of Class II disks, the C2H abundance is larger around Herbig Ae
stars with stronger X-rays, than that in T Tauri stars.

##  Appendix E NH3 and N2 fractional abundances

Figure 17:  [Top panels]: The radial profiles of NH3 fractional abundances
$n_{\mathrm{NH}_{3}}$/$n_{\mathrm{H}}$ in NGC 1333-IRAS 2A (left panel) and
NGC 1333-IRAS 4A (right panel) envelope models. [Bottom panels]: The radial
profiles of N2 gas fractional abundances $n_{\mathrm{N}_{2}}$/$n_{\mathrm{H}}$
in the IRAS 2A (left panel) and IRAS 4A (right panel) envelope models.

Top panels of Figure 17 show the radial profiles of NH3 gas fractional
abundances $n_{\mathrm{NH}_{3}}$/$n_{\mathrm{H}}$ in IRAS 2A (left panel) and
IRAS 4A (right panel) envelope models, for the various X-ray luminosities. The
binding energy of NH3 is smaller than that of H2O and HCN, and larger than
that of CO2 ($E_{\mathrm{des}}$(NH3)$=$2715 K, $E_{\mathrm{des}}$(HCN)$=$3610
K, $E_{\mathrm{des}}$(CO2)$=$2267 K, and $E_{\mathrm{des}}$(H2O)$=$4880 K, see
Table 2), and the NH3 snowline position exists outside the water snowline and
the HCN snowline ($>2\times 10^{2}$ au) and inside the CO2 snowline ($<3\times
10^{2}$ au). Zhang et al. (2018) discussed the possibility to observe the NH3
line emission (the 23GHz 1,1 and 2,2 lines) with ngVLA as a proxy of the water
snowline in disks.

According to Figure 17, for $L_{\mathrm{X}}\gtrsim 10^{31}$ erg s-1, NH3 gas
abundances become higher (up to $\sim 10^{-8}-10^{-7}$) outside the NH3
snowline, compared with the values ($\sim 10^{-9}-10^{-8}$ in IRAS 2A and
$\sim 10^{-10}-10^{-9}$ in IRAS 4A) for $L_{\mathrm{X}}\lesssim 10^{30}$ erg
s-1. The X-ray induced photodesorption is considered to be important in this
region. Inside the NH3 snowline, for low X-ray luminosities, the NH3 snowline
gas abundances are around $\sim 10^{-5}$. As the X-ray fluxes increase, the
NH3 snowline gas abundances in these radii decrease. For
$L_{\mathrm{X}}\gtrsim 10^{30}$ erg s-1, the NH3 gas abundances are $\lesssim
10^{-8}-10^{-7}$ within the NH3 snowline. The X-ray induced photodissociation
and ion-molecule reactions are considered to be dominant destruction processes
of NH3 in the inner envelopes (e.g., Gredel et al. 1989; Walsh et al. 2015;
Eistrup et al. 2016). Thus, with strong X-ray field, the NH3 abundance is no
longer dominant nitrogen carrier. In addition, it cannot be used as the tracer
of the water snowline position, since NH3 gas abundances are similar within
and outside the NH3 snowline.

The NH3 line emission (e.g., the 23GHz (1,1), (2,2), and (3,3) lines) have
been observed toward protostar disks and envelopes using VLA (e.g., Choi et
al. 2007, 2010). However, the spatial resolutions of such VLA observations
($\sim 1.0"$) were not sufficient to resolve the inner structures around the
protostars at a few hundred pc. Future ngVLA observations of these NH3 lines
with much higher resolutions ($\lesssim 0.3"$ at around 23 GHz) will resolve
the NH3 gas emission within its snowline towards many protostars, and can also
constrain the impact of X-rays on NH3 gas abundances. In addition, such
observations will be important to trace the chemical history of nitrogen
bearing molecules.

Bottom panels of Figure 17 show the radial profiles of N2 gas fractional
abundances $n_{\mathrm{N}_{2}}$/$n_{\mathrm{H}}$ in IRAS 2A (left panel) and
IRAS 4A (right panel) envelope models, for the various X-ray luminosities.
Like CO, N2 gas abundances do not depend on X-ray fluxes.

##  Appendix F The fractional abundances and percentage contributions of major
oxygen bearing molecules

Table 3 shows the fractional abundances of major oxygen bearing molecules at
$r=60$ au ($T_{\mathrm{gas}}\sim$150 K, inside the water snowline) in the IRAS
2A and IRAS 4A envelope models for the various X-ray luminosities, and their
percentage contributions (see also Figures 8 and 9 in Section 4.1). The cut-
off threshold is 0.01% for the contributions.

Table 3: The fractional abundances of major oxygen bearing molecules at $r=60$ au ($T_{\mathrm{gas}}\sim$150 K, inside the water snowline) in the NGC 1333-IRAS 2A and NGC 1333-IRAS 4A envelope models for the various X-ray luminosities, and their percentage contributions relative to the total elemental oxygen abundance ($3.2\times 10^{-4}$) $L_{\mathrm{X}}$ [erg s-1] | H2O gas | CO gas | O gas | O2 gas
---|---|---|---|---
|  | NGC 1333-IRAS 2A |  |
0 |  $2.0\times 10^{-4}$, 61% |  $1.1\times 10^{-4}$, 34% |  $1.2\times 10^{-9}$, $<$$10^{-2}$% |  $3.7\times 10^{-7}$, $2.3\times 10^{-1}$%
1027 |  $2.0\times 10^{-4}$, 61% |  $1.1\times 10^{-4}$, 33% |  $2.5\times 10^{-10}$, $<$$10^{-2}$% |  $3.0\times 10^{-7}$, $1.9\times 10^{-1}$%
1028 |  $1.9\times 10^{-4}$, 60% |  $1.1\times 10^{-4}$, 33% |  $1.7\times 10^{-10}$, $<$$10^{-2}$% |  $1.9\times 10^{-8}$, $1.2\times 10^{-2}$%
1029 |  $1.5\times 10^{-4}$, 48% |  $8.1\times 10^{-5}$, 25% |  $4.0\times 10^{-8}$, $1.3\times 10^{-2}$% |  $1.5\times 10^{-6}$, $9.2\times 10^{-1}$%
1030 |  $1.9\times 10^{-8}$, $<$$10^{-2}$% |  $1.4\times 10^{-4}$, 43% |  $5.8\times 10^{-5}$, 18% |  $6.0\times 10^{-5}$, 38%
1031 |  $5.3\times 10^{-8}$, $1.6\times 10^{-2}$% |  $1.4\times 10^{-4}$, 44% |  $6.2\times 10^{-5}$, 19% |  $5.9\times 10^{-5}$, 37%
1032 |  $1.4\times 10^{-7}$, $4.5\times 10^{-2}$% |  $1.4\times 10^{-4}$, 44% |  $6.5\times 10^{-5}$, 20% |  $5.8\times 10^{-5}$, 36%
|  | NGC 1333-IRAS 4A |  |
0 |  $2.0\times 10^{-4}$, 62% |  $1.1\times 10^{-4}$, 33% |  $1.1\times 10^{-10}$, $<$$10^{-2}$% |  $1.0\times 10^{-9}$, $<$$10^{-2}$%
1027 |  $2.0\times 10^{-4}$, 62% |  $1.1\times 10^{-4}$, 33% |  $1.1\times 10^{-10}$, $<$$10^{-2}$% |  $1.0\times 10^{-9}$, $<$$10^{-2}$%
1028 |  $2.0\times 10^{-4}$, 62% |  $1.0\times 10^{-4}$, 33% |  $1.2\times 10^{-10}$, $<$$10^{-2}$% |  $1.0\times 10^{-9}$, $<$$10^{-2}$%
1029 |  $1.9\times 10^{-4}$, 60% |  $9.9\times 10^{-5}$, 31% |  $2.6\times 10^{-10}$, $<$$10^{-2}$% |  $1.5\times 10^{-9}$, $<$$10^{-2}$%
1030 |  $7.0\times 10^{-5}$, 22% |  $7.2\times 10^{-5}$, 23% |  $2.0\times 10^{-7}$, $6.3\times 10^{-2}$% |  $2.6\times 10^{-5}$, 16%
1031 |  $1.3\times 10^{-8}$, $<$$10^{-2}$% |  $1.4\times 10^{-4}$, 43% |  $5.3\times 10^{-5}$, 17% |  $6.2\times 10^{-5}$, 39%
1032 |  $3.7\times 10^{-8}$, $1.1\times 10^{-2}$% |  $1.4\times 10^{-4}$, 43% |  $6.2\times 10^{-5}$, 19% |  $5.9\times 10^{-5}$, 37%

##  Appendix G The additional model calculations for X-ray induced
photodesorption rates

Figure 18:  The radial profiles of gaseous fractional abundances of H2O, O2,
and OH, and icy fractional abundances of H2O in the NGC 1333-IRAS 4A envelope
models. The light-green solid lines, the cyan double-dashed dotted lines, and
blue dotted lines show the radial profiles of our standard model calculations,
for values of central star X-ray luminosities $L_{\mathrm{X}}$=1028, 1030, and
1032 erg s-1, respectively (see also Figures 3, 4, 5, 6). The yellow dashed
double-dotted lines, the scarlet dashed dotted lines, and the brown dashed
lines show the radial profiles of our additional model calculations for
$L_{\mathrm{X}}$=1028, 1030, and 1032 erg s-1, respectively. In the additional
model calculations, we include the photodesorption by UV photons generated
internally via the interaction of secondary electrons produced by X-rays with
H2 molecules (see also Figure 19). In the top left panel, the observational
best-fit H2O gas abundance profile obtained in van Dishoeck et al. (2021) is
over-plotted with the black solid line (see also Figure 10). In the bottom
left panel, the three model O2 gas abundance profiles obtained in Yıldız et
al. (2013) are over-plotted (see also Figure 10).

Figure 19:  The radial profiles of gaseous fractional abundances of O, HCO+,
and CH3OH, and icy fractional abundances of CH3OH in the NGC 1333-IRAS 4A
envelope models. The line types and color patterns for the radial profiles of
our standard model calculations (see also Figures 5, 6, and 7) and additional
model calculations are same as Figure 18. In the additional model
calculations, we include the secondary (indirect) X-ray induced
photodesorption (see also Figure 18).

Figure 20:  The radial profiles of gaseous fractional abundances of O, HCO+,
and CH3OH, and icy fractional abundances of CH3OH in the NGC 1333-IRAS 4A
envelope models. The profiles are same as Figure 19, except in the additional
model calculations we switch off the direct X-ray induced photodesorption and
include the secondary (indirect) X-ray induced photodesorption only (see also
Figure 11).

In Figure 18 and Figure 11 in Section 4.3, we show the radial profiles of
gaseous fractional abundances of H2O, O2, and OH, and icy fractional
abundances of H2O in the IRAS 4A envelope models, for our standard model
calculations and additional model calculations. In Figures 19 and 20, we show
the radial profiles of gaseous fractional abundances of O, HCO+, and CH3OH,
and icy fractional abundances of CH3OH in the IRAS 4A envelope models, for our
standard model calculations and additional model calculations. For the
additional model calculations in Figures 18 and 19, we include the
photodesorption by UV photons generated internally via the interaction of
secondary electrons produced by X-rays with H2 molecules. For the additional
model calculations in Figure 20 and Figure 11 in Section 4.3, we switch off
the direct X-ray induced photodesorption and include the secondary (indirect)
X-ray induced photodesorption only.

According to Figures 18 and 19, the effects of such additional secondary
(indirect) X-ray induced photodesorption is marginal (the abundances are
changed by ¡1%, see also Section 4.3). For molecules shown in Figure 20, the
differences in abundances between the standard model and the second additional
model are much smaller than those in H2O, OH, and O2 (see Figure 11 in Section
4.3).

##  Appendix H The impacts of the different photodissociation branching ratio
and binding energies on the molecular abundances

Figure 21:  The radial profiles of gaseous fractional abundances of H2O, O2,
O, and OH in NGC 1333-IRAS 4A envelope models. These profiles are obtained
from our test calculations assuming that the product of H2O photodissociation
is 100% atomic oxygen, unlike our fiducial model (100% OH). In the top left
panel, the observational best-fit H2O gas abundance profile obtained in van
Dishoeck et al. (2021) is over-plotted with the black solid line (see also
Figure 10). In the top right panel, the three model O2 gas abundance profiles
obtained in Yıldız et al. (2013) are over-plotted (see also Figure 10).

Figure 22:  The radial profiles of gaseous fractional abundances of H2O, O2,
O, and OH in NGC 1333-IRAS 4A envelope models. These profiles are obtained
from our test calculations assuming the smaller $E_{\mathrm{des}}(j)$ for
atomic oxygen ($=800$ K) than that in our fiducial model (=1660 K). In the top
left panel, the observational best-fit H2O gas abundance profile obtained in
van Dishoeck et al. (2021) is over-plotted with the black solid line (see also
Figures 10 and 21). In the top right panel, the three model O2 gas abundance
profiles obtained in Yıldız et al. (2013) are over-plotted (see also Figure 10
and 21).

Figure 21 shows the gas-phase abundance profiles of H2O, O2, O, and OH, which
are calculated assuming the extreme case that the product of H2O
photodissociation is 100% atomic oxygen (Reaction 15 only both in the gas and
ice). Figure 22 shows the gas-phase abundance profiles of H2O, O2, O, and OH,
which are obtained from our test calculations assuming the smaller
$E_{\mathrm{des}}$(O) ($=800$ K) than that in our fiducial model ($=1660$ K).

We plot these figures in order to investigate the impacts of the different
photodissociation branching ratio of H2O and different binding energies of O
on the abundances of H2O and related molecules. In Section 4.4, we discuss
these impacts in detail (see also Figure 12).

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