Linking ice and gas in the $\lambda$ Orionis Barnard 35A cloud

The sample of sources was observed on September 19, 2018 with the Submillimeter Array (SMA; Ho et al. 2004). The array was in its subcompact configuration with 7 operating antennas. The targeted region was covered by two overlapping pointings; the first pointing was centered on B35A$-$3 (i.e., IRAS 05417+0907) and the second was offset by one half primary beam to the south-east. Their exact coordinates are $\alpha_{J2000}=05^{\mathrm{h}}44^{\mathrm{m}}30^{\mathrm{s}}.00$, $\delta_{J2000}=+09^{\circ}08\arcmin 57\aas@@fstack{\prime\prime}3$ and $\alpha_{J2000}=05^{\mathrm{h}}44^{\mathrm{m}}30^{\mathrm{s}}.58$, $\delta_{J2000}=+09^{\circ}08\arcmin 33\aas@@fstack{\prime\prime}8$, respectively.

The SMA observations probed frequencies spanning from 214.3 to 245.6 GHz with a spectral resolution of 0.1 MHz (0.135 km s^-1). Among other species this frequency range covers the CH₃OH $J_{K}$ = 5${}_{K}-$4_K branch at 241.791 GHz, ¹³CO $J$ = 2$-$1 at 220.398 GHz and C¹⁸O $J$ = 2$-$1 at 219.560 GHz (Table 2). The observational setup consisted of a first long integration on the bandpass calibrator, the strong quasar 3c84, followed by alternated integrations on the source and on the gain calibrator, the quasar J0510+180. The absolute flux scale was obtained through observations of Uranus. The SMA data set was both calibrated and imaged using CASA²²2http://casa.nrao.edu/ (McMullin et al., 2007). At these frequencies, the typical SMA beam-sizes were 7$\aas@@fstack{\prime\prime}$3 $\times$ 2$\aas@@fstack{\prime\prime}$4 with a position angle of -32.2^∘ for CH₃OH, and 7$\aas@@fstack{\prime\prime}$9 $\times$ 2$\aas@@fstack{\prime\prime}$6 with a position angle of -31.2^∘ for ¹³CO and C¹⁸O.

To trace the more extended structures in the region, the SMA data were complemented by maps obtained using the Atacama Pathfinder EXperiment (APEX; Güsten et al. 2006) on August 20$-$22, 2018. The single-dish observations covered frequencies between 236$-$243.8 GHz, matching the SMA 240 GHz receiver upper side band. The spectral resolution of the APEX observations was 0.061 MHz (0.076 km s^-1). The APEX map size was 100${}^{\prime\prime}\leavevmode\nobreak\ \times$ 125^′′ and it extended over both SMA primary beams. The coordinates of the APEX pointing are $\alpha_{J2000}=05^{\mathrm{h}}44^{\mathrm{m}}30^{\mathrm{s}}.00$, $\delta_{J2000}=+09^{\circ}08\arcmin 57\aas@@fstack{\prime\prime}3$. The APEX beam size was 27$\aas@@fstack{\prime\prime}$4 for the CH₃OH $J_{K}$ = 5${}_{K}-$4_K lines emission. The APEX data set was reduced using the GILDAS package CLASS³³3http://www.iram.fr/IRAMFR/GILDAS. At a later stage, the reduced APEX data cube was imported to CASA and combined with the interferometric data using the feathering technique. A description of the combination procedure is given in Appendix A.1.

Ancillary data to the SMA and APEX observations were adopted in this study. To construct H₂ column density maps of B35A, we used submillimeter continuum maps at 850 $\mu$m obtained with the SCUBA$-$2 camera at the James Clerk Maxwell Telescope (JCMT) by Reipurth & Friberg (2021), visual extinction values from the $Spitzer$ c2d catalog⁴⁴4https://irsa.ipac.caltech.edu/data/SPITZER/C2D/cores.html and 2MASS and $Spitzer$ IRAC photometric data (Skrutskie et al., 2006; Evans et al., 2014). Institut de RadioAstronomie Millimétrique (IRAM) 30 m telescope observations (Craigon, 2015) were used to trace the extended emission for ¹³CO and C¹⁸O $J$ = 2$-$1. Finally, to produce gas-ice maps of B35A we made use of the ice column densities determined by Suutarinen (2015), from AKARI satellite observations.

The spectral line data of the detected molecular transitions are listed in Table 2. Figures 2–4 display moment 0 maps of the ¹³CO and C¹⁸O $J$=2$-$1 lines and CH₃OH $J$=5${}_{0}-4_{0}$ A⁺ line, using SMA, IRAM 30 m and APEX data. Moment 0 maps of the CH₃OH $J$=5${}_{0}-4_{0}$ A⁺ line are presented in this section as this transition is the brightest of the CH₃OH $J$=5${}_{K}-4_{K}$ branch at 241.791 GHz. The maps show that the SMA observations filter out spatially extended emission related to the B35A cloud. The SMA data only recover $\approx$10% of the extended emission detected in the single-dish data. Thus, consequently we need to combine the interferometric data with the single-dish maps in order not to underestimate the column densities severely.

Panels (a) of Figures 2–3 show that the interferometric emission is predominantly compact and the peak intensity is seen, for both CO isotopologues, at the location of B35A$-$2. The emission observed in the IRAM 30 m data sets (panels (b) of Figures 2–3) is extended and mostly concentrated around B35A$-$2, B35A$-$3 and B35A$-$5. In the combined SMA + IRAM 30 m maps (panels (c) of Fig. 2–3) the peak emission is also located in the region where B35A$-$2, B35A$-$3 and B35A$-$5 are present.

In contrast, the observed CH₃OH peak intensity is exclusively localized at the B35A$-$5 position in the SMA data (panel (a) of Fig.4). B35A$-$5 lies along the eastern lobe of the giant bipolar molecular outflow emanated from IRAS 05417+0907 (i.e., B35A$-$3) and terminating at the location of the Herbig-Haro object HH 175 (Craigon, 2015). The CH₃OH emission is extended in the APEX data (panel (b) of Fig.4) and hence not resolved at one particular source position. The emission in the SMA + APEX moment 0 map (panel (c) of Fig.4) is compact and concentrated in one ridge in the proximity of B35A$-$5. The channel maps (Figures 14$-$14) and the spectra (Figure 10) extracted from the combined interferometric and single-dish data sets show predominantly blue-shifted components (Appendix A.3). Blue- and red-shifted components are seen for the CO isotopologues, which were previously observed by De Vries et al. (2002), Craigon (2015) and Reipurth & Friberg (2021) and attributed to outflowing gas.

The ¹³CO emission is optically thick towards the B35A sources, therefore the ¹³CO column densities are underestimated towards the targeted region (Appendix A.2). Consequently, the optically thin C¹⁸O emission is adopted to estimate the column density of ¹²CO in B35A. First, C¹⁸O column densities towards the protostellar system members are obtained from the integrated line intensities of the combined SMA + IRAM 30 m maps (panels (c) of Figure 3), assuming optically thin emission and a kinetic temperature for the YSO region equal to 25 K (Craigon, 2015). The formalism adopted in the column density calculation is presented in Appendix A.4, whereas the calculated C¹⁸O column densities and their uncertainties are listed in Table 3. The C¹⁸O column densities are converted to ¹²CO column densities assuming a ¹⁶O/¹⁸O isotope ratio of 557 $\pm$ 30 (Wilson, 1999). The resulting ¹²CO column densities (Table 3) are in good agreement with the values reported in Craigon (2015).

The CH₃OH column density towards B35A$-$5 is estimated from the integrated line intensities of the combined SMA + APEX maps for the five CH₃OH lines (Table 6), assuming optically thin CH₃OH emission, a kinetic temperature of 25 K (Craigon, 2015) and local thermodynamic equilibrium (LTE) conditions. The CH₃OH column density and its uncertainty is reported in Table 3. For all the gas-phase species, the uncertainty on the column densities is estimated based on the spectral rms noise and on the $\sim$20% calibration uncertainty.

The ice column densities of H₂O, CO and CH₃OH made use of in this paper were originally derived by Suutarinen (2015) from the AKARI (2.5$-$5 $\mu$m) NIR spectra of the targeted B35A sources. Suutarinen (2015) adopted a non-heuristic approach, employing ice laboratory data and analytical functions to concurrently account for the contribution of a number of molecules to the observed ice band features. A detailed description of the AKARI observations is given in Noble et al. (2013) and the methodology adopted to derive the column densities of the major ice species can be found in Suutarinen (2015).

The total ice column densities from Suutarinen (2015) are listed in Table 3. Among the three molecules, H₂O ice is the most abundant in the ices of B35A, with column densities up to 3.35 $\times$ 10¹⁸ cm^-2, followed by CO and CH₃OH (Table 3). The column densities of the latter two molecules are comparatively one order of magnitude less abundant than H₂O ice. Upper limits are given for the CO and CH₃OH column densities towards B35A$-$5 because of difficulties in distinguishing the absorption features in the spectrum of this YSO (Noble et al., 2013; Suutarinen, 2015). A trend is observed for the CO and CH₃OH values: the column densities towards B35A$-$2 are the highest reported, followed by B35A$-$3, B35A$-$4 and B35A$-$5. The CO and CH₃OH ice column densities appear to follow the visual extinction with B35A$-$2 and B35A$-$3 being the most extincted sources and showing the highest CO and CH₃OH column densities (Tables 1 & 3). In this regard, it is important to recall that B35A$-$2 is not detected in the J, H and K bands, making the determination of its visual extinction uncertain (Section 3.3 and Appendix B).

An important factor to consider when combining ice- and gas-mapping techniques is that ice absorption and dust and gas emissions may probe different spatial scales (Noble et al., 2017). As a matter of fact, the targeted sources may be embedded to different depths in the B35A cloud and consequently, the gas and ice observations may not be tracing the same columns of material. Therefore, the search for gas-ice correlations towards B35A has to be performed by comparing gas and ice abundances relative to H₂, following the approach adopted in Perotti et al. (2020).

To keep the gas and ice observations in their own reference frame, two H₂ column density maps are produced: one to derive gas abundances and one to determine ice abundances (Figure 5). For the gas observations, estimates of the H₂ column density are made using submillimeter continuum maps of B35A at 850$\mu$m (SCUBA$-$2; Reipurth & Friberg 2021), under the assumption that the continuum emission is originated from optically thin thermal dust radiation (Kauffmann et al., 2008). In this regime, the strength of the submillimeter radiation is dependent on the column density ($N$), the opacity ($\kappa_{\nu}$) and the dust temperature ($T$). The adopted value for the opacity per unit dust+gas mass at 850 $\mu$m is 0.0182 cm² g^-1 (”OH5 dust”; Ossenkopf & Henning 1994). The temperature of B35A has been estimated by Morgan et al. (2008) and Craigon (2015). Both studies found two distinct regimes within the cloud: a cold region ($T_{\mathrm{gas}}=$ 10 – 20 K, $T_{\mathrm{dust}}=$ 18 K) in the shielded cloud interior to the east of the YSOs and a warm region ($T_{\mathrm{gas}}=$ 20 – 30 K) to the west of the YSOs. Since the region where the YSOs are located lies close to the warm cloud western edge, a $T_{\mathrm{dust}}=$ 25 K is adopted to estimate the H₂ column density map illustrated in Figure 5 (a) based on Craigon (2015) and Reipurth & Friberg (2021). The H₂ column density towards the B35A sources is reported in Table 3. The error on the H₂ column density was estimated according to the 5% flux calibration uncertainty (Dempsey et al., 2013). It does not include the errors on $T_{\mathrm{dust}}$ due to the uncertainties on the upper and lower limits for $T_{\mathrm{dust}}$ in the YSOs region.

Increasing the dust temperature to 30 K would lower the H₂ column density by 22% and consequently increase the abundance of the gas-phase species by the same amount – while lowering the dust temperature to 18 K would increase the H₂ column density by 61% and consequently lowering the gas abundance likewise. The above estimates assume an excitation temperature equal to 25 K for CO and CH₃OH. Increasing both the excitation temperature and the dust temperature to 30 K would result in gas abundances increasing by 24%. Conversely, lowering both temperatures to 18 K, would lower the abundances by 33%. A comprehensive description of the production of the H₂ column density map from SCUBA$-$2 measurements is given in Appendix C of Perotti et al. (2020).

The H₂ column density map calculated from the SCUBA$-$2 measurements supplies an accurate estimate of the total beam-averaged amount of gas towards B35A, and therefore provides a useful reference for the optically thin gas-phase tracers. However, the derived H₂ column density map can not directly be related to the AKARI data that supply (pencil-beam) measurements of the column densities towards the infrared sources that may or may not be embedded within the B35A cloud.

For the ice observations, the H₂ column density map is therefore obtained by performing a linear interpolation of the tabulated visual extinction ($A_{V}$) values for B35A taken from the $Spitzer$ c2d catalog⁵⁵5https://irsa.ipac.caltech.edu/data/SPITZER/C2D/cores.html (see Appendix B). Since no calculated $A_{V}$ values are reported for B35A$-$2 and B35A$-$3, the $A_{V}$ for B35A$-$3 is acquired by de-reddening the spectral energy distribution (SED) at the 2MASS J, H, K photometric points to fit a blackbody and using a second blackbody to model the infrared excess at longer wavelengths. A detailed description of the fitting procedure adopted for B35A$-$3 is given in Appendix B. Following Evans et al. (2009) and Chapman et al. (2009) we adopt an extinction law for dense interstellar medium gas with $R_{V}=$ 5.5 from Weingartner & Draine (2001) to calculate $A_{V}$. The visual extinction for B35A$-$2 could not be estimated through a similar procedure due to the lack of near-IR photometry data available for this object, thus the $A_{V}$ for this source is obtained through the interpolation of the available visual extinction measurements for B35A. The final $A_{V}$ values of the four sources are listed in Table 1. Finally, the visual extinction is converted to $H_{2}$ column density using the relation: $N_{\mathrm{H_{2}}}=1.37\times 10^{21}$ cm^-2 ($A_{V}$/mag) established for dense interstellar medium gas (Evans et al., 2009). The H₂ column density calculated from the $A_{V}$ map is shown in Figure 5 (b).

The H₂ column densities calculated from both methods are of the same order of magnitude, 10²² cm^-2 (Table 3). The column densities differ by approximately a factor of 4 possibly due to variations in the exact column densities traced by SCUBA$-$2 and $A_{V}$ measurements and assumptions on the dust temperature. In both H₂ column density maps (Fig. 5 a and b), it is seen that the four sources lie in the densest region of the cloud, confirming the results previously presented in Craigon (2015) and Reipurth & Friberg (2021). Although the two maps were calculated using two different methods, they reproduce the same trend: B35A$-$2 and B35A$-$3 are located where the H₂ column density peaks, whereas B35A$-$4 and B35A$-$5 are situated in less dense regions. However, in the H₂ column density map calculated from the visual extinction (Fig. 5 b), lower $N_{\mathrm{H_{2}}}$ values are reported for B35A$-$5 with respect to the other YSOs, whereas this is not the case in the H₂ column density map calculated from the SCUBA$-$2 map (Fig. 5 a) where lower $N_{\mathrm{H_{2}}}$ values are observed for B35A$-$4. This difference can be explained by recalling that B35A$-$5 is the less extincted YSO ($A_{V}$ = 19.5 mag) and it is located along the trajectory of the giant outflow launched by B35A$-$3. Consequently, the SCUBA$-$2 observations (14.6$\arcsec$ beam) are likely tracing the more extended structure of the dust emission in the region and not resolving the more compact emission towards each individual objects. It is worth observing that embedded protostars and Herbig-Haro objects can substantially affect the dust emission morphology (Chandler & Carlstrom, 1996), hence, the $N_{\mathrm{H_{2}}}$ enhancement seen in Figure 5 (a) likely reflects dust heating by the embedded protostars and by HH175 resulting in an increase of the submillimeter continuum flux, rather than in an higher column density.

In Figure 6, the distributions of gas-phase ¹³CO 2$-$1 (panel a) and C¹⁸O 2$-$1 (panel b) emissions are compared to CO ice abundances. Both CO isotopologue emissions are concentrated at the B35A$-$2, B35A$-$3, B35A$-$5 source positions. The emission towards these three sources is of comparable intensity but it drops in the surroundings of B35A$-$4 and especially towards the southern edge of the cloud. The CO ice abundances with respect to H₂ are not characterized by large variations, instead, they are quite uniform and consistent within the uncertainties (Table 4). Only an upper limit could be determined for the CO ice column density towards B35A$-$5, due to the uncertainty in distinguishing the absorption feature at 3.53 $\mu$m in the spectrum of this object.

In Figure 6 (c), the distribution of gas-phase CH₃OH 5${}_{0}-$4₀ A⁺ emission is compared to CH₃OH ice abundances. As described in Section 3.1, the CH₃OH emission is concentrated solely in one ridge, located in proximity of the B35A$-$5 position. At this location only an upper limit on the CH₃OH ice abundance could be determined. The morphology of the CH₃OH emission suggests that while B35A$-$5 is situated in a shocked region, sitting along the trajectory of the giant outflow, B35A$-$4 lies in a more quiescent area, less influenced by high-velocity flows of matter. The CH₃OH ice abundances with respect to H₂ are characterized by slightly larger variations compared to CO ice (Table 4).

Finally, in Figure 6 (d), the distribution of gas-phase CH₃OH 5${}_{0}-$4₀ A⁺ emission is compared to H₂O ice abundances. The H₂O ice abundances are approximately one order of magnitude higher than the CO and CH₃OH ice abundances (Table 4). The lowest H₂O ice abundance is reported towards B35A$-$5 where the CH₃OH peak emission is observed. In contrast, the highest H₂O ice abundance is obtained towards B35A$-$4, where CH₃OH emission is not detected.

In Figure 7, the search for gas-ice correlations towards B35A is addressed by analysing gas and ice abundances relative to H₂ (Table 4). The y-axes of all three panels display CO gas abundances, which are compared to abundances of CO ice (panel a), CH₃OH ice (panel b) and H₂O ice (panel c). To maintain gas and ice observations in their own reference frame, the CO gas abundances have been estimated using $N_{\mathrm{H_{2}}}$ calculated from SCUBA$-$2 850 $\mu$m maps, whereas the ice abundances have been calculated using $N_{\mathrm{H_{2}}}$ obtained from the visual extinction map (see Section 3.3 and Appendix B). The formalism adopted to propagate the uncertainty from the column densities to the abundances is reported in Appendix A.4.

It can be immediately noted that none of the ice species exhibits a predictable trend in ice abundance with gas abundance. Panels (a) and (b) show a similar behaviour since they are comparing molecules chemically linked - CO gas versus CO ice and CO gas vs CH₃OH ice being CO the precursor of CH₃OH. At the same time, panel (c) does not display the same relationships seen in the previous two panels. The latter observation is not surprising since there are no reasons for CO and H₂O to be directly linked from a purely chemical perspective.

In both panels (a) and (b) of Figure 7, B35A$-$4 displays the highest CO gas and the lowest CO and CH₃OH ice abundances. When the uncertainties are taken into account, the CO ice abundances towards B35A$-$2, B35A$-$3 and B35A$-$4 are alike (Table 4). For the CH₃OH ice abundances, B35A$-$3 and B35A$-$4 are consistent within the error bars, only towards B35A$-$2 a significant difference is found. Both CO and CH₃OH ice abundances towards B35A$-$5 are upper limits (Table 4). The similarity between CO and CH₃OH ice trends and the fact that the CH₃OH/CO ice ratios are $>$ 0.3 indicates an efficient CH₃OH formation through CO hydrogenation (Watanabe & Kouchi, 2002) on the grain surfaces of B35A. The CO gas abundances towards B35A$-$2, B35A$-$3 and B35A$-$5 are in agreement within the uncertainties (Table 4).

In panels (c) some of the gas-ice variations differ with respect to panels (a) and (b): B35A$-$4 is characterized by the highest H₂O ice abundance, whereas B35A$-$5 shows the lowest H₂O ice abundance. This result corroborates the prediction that the ices of B35A$-$5 are the most depleted of volatile molecules among the B35A sources. The behaviours of B35A$-$2 and B35A$-$3 are similar if the uncertainties are considered (Table 4). The observed ice and gas variations between CO gas, CH₃OH gas and H₂O ice towards B35A$-$4 and B35A$-$5 favour a scenario in which H₂O ice is formed and predominantly resides on the ices of B35A$-$4, likely located in the most ”quiescent” area of the targeted region, whereas in the proximity of a shocked region (B35A$-$5), H₂O ice mantles are partially desorbed. This result is discussed further in Sect. 5.1. Although the gas and ice variations analysed in this Section and in Sect. 4.1 are based on a small sample, they still highlight interesting trends in accordance to what we would expect from our knowledge of the physical structure of the targeted region.

Noble et al. (2017) produced the first gas-ice maps of B35A. They compared AKARI ice abundances from Noble et al. (2013) with single-dish (JCMT/HARP and IRAM 30 m/HERA) gas-phase maps of C¹⁸O (Buckle et al. 2009; Craigon 2015; $J$=3$-$2 and 2$-$1), submillimeter continuum SCUBA maps at 850 $\mu$m, 450 $\mu$m/850 $\mu$m (Di Francesco et al., 2008) and Herschel/SPIRE maps at 250 $\mu$m (Griffin et al., 2010). The H₂ gas-phase map adopted to calculate ice abundances was determined from CO observations (Craigon, 2015).

Noble et al. (2013, 2017) derived their ice column densities without considering the presence of CH₃OH, thus the H₂O ice column densities were routinely higher than those used here from Suutarinen (2015) (Figure 8). Simultaneously, the CO ice column densities were calculated using different laboratory data (e.g., the CO-ice red component was fitted using a CO:H₂O (Fraser & van Dishoeck, 2004) laboratory spectrum as opposite to the CO:CH₃OH mixture (Cuppen et al., 2011), resulting in higher CO-ice column density compared to Suutarinen (2015).

The combination of gas, dust and ice observations proposed in Noble et al. (2017) is characterized by a number of limitations which are taken into account in the presented work. The lower angular resolution of the adopted single-dish observations, the analysis of the chemical behaviours of simple molecules only (e.g., H₂O, CO and CO₂) and the avoidance to consider that the ice and gas observations might probe different depths are some of them. The presented work overcomes these limitations by making use of higher angular resolution interferometric observations, studying the ice and gas variations of both simple (H₂O, CO) and complex molecules (CH₃OH) and lastly, by comparing ice and gas abundances derived using two different H₂ column density maps (to keep the ice and gas observations in their own reference frame).

From the analysis of the gas-ice maps, Noble et al. (2017) inferred that the dust in B35A is mainly localized around B35A$-$2 and B35A$-$3, in agreement with the higher ice column densities of H₂O and CO towards these two sources (Figure 8). However, they observed that the H₂O ice column densities are lower towards B35A$-$5 compared to B35A$-$4, even though the dust emission is higher towards B35A$-$5. The authors concluded that no clear trend is seen between ice, dust and gas in B35A and that more knowledge of the local-scale astrophysical environment is needed to disentangle the exact interplay between ice and gas in the region. The findings of Noble et al. (2017) are in agreement with the observational results and the gas-ice maps of B35A presented here (with the caveat that both CO ice abundances towards B35A$-$5 in Noble et al. (2017) and in this work are upper limits). However, the gas-ice maps produced in this study allow to explain that the lower H₂O ice abundance towards B35A$-$5 compared to B35A$-$4 is plausibly caused by the influence of shocks on the ice chemistry. CH₃OH is a tracer of energetic inputs in the form of outflows (Kristensen et al., 2010; Suutarinen et al., 2014), and it traces the trajectory of the bipolar outflow in B35A. As a result, lower H₂O ice abundances towards B35A$-$5 are likely the result of sputtering effects in the outflow shocks (e.g., Suutarinen et al. 2014 and references therein). Simultaneously, the fact that the submillimeter dust emission towards B35A$-$5 is high where the H₂O ice abundances are lower can also be explained by the presence of the outflow terminating in the HH object 175. In fact, UV radiation generated in the Herbig-Haro object itself may locally heat the dust, enhancing the sub-millimeter continuum flux of the region (Chandler & Carlstrom 1996; Kristensen et al. 2010; Figure 5 a).

In Sections 3.1 and 4.1, it is seen that the CH₃OH emission is concentrated almost exclusively in one ridge, which coincides with the B35A$-$5 position. B35A$-$5 sits along the eastern lobe of a large collimated outflow emanated from the binary Class I IRAS 05417+0907 (i.e, B35A$-3$). The eastern lobe has a total extent of 0.6 pc and it terminates into the Herbig-Haro object HH 175 (Craigon, 2015). The total extent of the outflow is 1.65 pc (Reipurth & Friberg, 2021), which places HH 175 among the several dozens HH objects with parsec dimensions (Reipurth & Bally, 2001). Herbig-Haro objects are omnipresent in star-forming regions, but it is still not clear how exactly they are tied into the global star-formation process, e.g., how do they alter the morphology and kinematics of the gas in which they originate. These are highly energetic phenomena which are believed to form when high-velocity protostellar jets collide with the surrounding molecular cloud, inducing shocks. Such shocks compress and heat the gas, generating UV radiation (Neufeld & Dalgarno, 1989). The activity of Herbig-Haro objects can dramatically change the chemical composition of the gas in their vicinity, mutating the chemistry of the region during so-called sputtering processes (Neufeld & Dalgarno, 1989; Hollenbach & McKee, 1989).

Sputtering takes place in shocks when neutral species (e.g., H₂, H or He) collide with the surface of ice-covered dust grains with sufficient kinetic energy to expel ice species (e.g., CH₃OH, NH₃, H₂O) into the gas phase (Jørgensen et al., 2004; Jiménez-Serra et al., 2008; Kristensen et al., 2010; Suutarinen et al., 2014; Allen et al., 2020). During a sputtering event, the ice molecules can desorb intact or be destroyed (e.g., via dissociative desorption) either due to the high kinetic energy or by reactions with H atoms (Blanksby & Ellison, 2003; Dartois et al., 2019, 2020). The fragments of dissociated molecules can then readily recombine in the gas-phase (Suutarinen et al. 2014 and references therein).

The inferred dust temperatures in the B35A region (20$-$30 K) are remarkably lower than the CH₃OH sublimation temperature ($\sim$128 K; Penteado et al. 2017), excluding thermal desorption as potential mechanism triggering the observed CH₃OH emission. This consideration, together with the observation of the CH₃OH emission along the HH 175 flow direction and the anticorrelation between CH₃OH emission and the lower H₂O ice abundances towards B35A$-$5 suggests that ice sputtering in shock waves is a viable mechanism to desorb ice molecules in B35A. Simultaneously, the absence of shocks towards B35A$-$4 likely explains the highest abundance of H₂O ice observed in this more quiescent region (Figure 6 d). Higher angular resolution observations of CH₃OH in the region are required to provide quantitative measurements of the amount of CH₃OH desorbed via sputtering compared to other non-thermal desorption mechanisms. Additional gas-phase observations of H₂O towards the B35A sources are needed to constrain further the processes linking H₂O ice and H₂O gas in this shocked region (e.g., sputtering of H₂O ice mantles versus direct H₂O gas-phase synthesis) and, in a broader context to contribute explaining the high abundances of H₂O observed in molecular outflows (Nisini et al., 2010; Bjerkeli et al., 2012, 2016; Santangelo et al., 2012; Vasta et al., 2012; Dionatos et al., 2013).

Figure 9 displays the CH₃OH (panel a) and CO (panel b) gas-to-ice ratios towards ten sources constituting the SVS 4 cluster located in the Serpens molecular cloud (Perotti et al., 2020) and towards the B35A sources in the Orion molecular cloud. The shaded areas indicate the estimated ranges of gas-to-ice ratios towards both molecular clouds, providing complementary information of the gas-to-ice ratios of both regions compared to the value calculated towards each individual source.

Figure 9 (a) shows the CH₃OH gas-to-ice ratios ($N_{\mathrm{CH_{3}OH_{gas}}}$/$N_{\mathrm{CH_{3}OH_{ice}}}$) towards the SVS 4 sources and B35A$-$5. Only an upper limit for the CH₃OH gas-to-ice towards B35A$-$5 is obtained (i.e, 1.1 $\times$ 10^-3) due to the uncertainty on the CH₃OH ice column density determination towards this source (Suutarinen, 2015). Therefore, only limited information is available on the CH₃OH chemistry in B35A. Figure 9 (a) also displays the averaged CH₃OH gas-to-ice ratio towards four low-mass embedded protostars located in nearby star-forming regions from Öberg et al. (2009). A detailed comparison between the CH₃OH gas-to-ice ratios for the SVS 4 cluster members and the value estimated by Öberg et al. (2009) is given in Perotti et al. (2020), and therefore not repeated here.

The observations of B35A address cold quiescent CH₃OH emission ($J$= 5${}_{K}-$4_K transitions at 241.7 GHz and $E_{\mathrm{u}}$ from 34.8 to 60.7 K, see Table 2) and presumably quiescent gas not affected by outflow shocks and/or thermally desorbed in the vicinity of the protostar. The same applies to the observations presented in Öberg et al. (2009) ($J$= 2$-$1 transitions at 96.7 GHz and $E_{\mathrm{u}}$ in the range 14.4$-$35.4 K). However, B35A$-$5 and the SVS 4 sources reporting the highest gas-to-ice ratios are likely affected to some extent by outflow shocks (i.e., B35A$-$5 by the giant outflow terminating in HH 175 and the SVS 4 sources by the outflow notoriously associated to SMM 4). This might justify the mismatch between Öberg et al. (2009) value and the higher values of the gas-to-ice ratios. In the case of the B35A cloud, high-sensitivity infrared observations of B35A are required to constrain further this observation.

CO gas-to-ice ratios ($N_{\mathrm{CO_{gas}}}$/$N_{\mathrm{CO_{ice}}}$) towards the SVS 4 and B35A sources are illustrated in Figure 9 (b). As discussed previously in Perotti et al. (2020), the range of gas-to-ice ratios for SVS 4 extends between 1 and 6 and it is significantly higher than the predicted value ($\sim$4$\times$10^-2; Cazaux et al. 2016). This theoretical prediction is estimated from the three-phase astrochemical model by Cazaux et al. (2016) which includes thermal and non-thermal desorption processes of the species constituting the ice mantles. This comparison with the theoretical prediction has to be taken with care, since the physical model is not specifically tuned to reproduce the structures of the SVS 4 cluster or the B35A cloud. The estimated dust temperature towards the SVS 4 cluster is below 20 K (Kristensen et al., 2010), indicating that CO is likely frozen out on the grain surfaces in this temperature range. We concluded from the high relative CO gas abundances that the gas-mapping is not tracing the densest regions of the SVS 4 cluster but an extended component that is not sensitive to the effect of freeze-out (Figure 8 of Perotti et al. 2020).

High CO gas-to-ice ratios are also observed for B35A, but in this case they are mainly attributable to CO thermally desorbed in the region. The physical conditions of B35A and SVS 4 differ significantly, for example, the western side of B35A is highly influenced by the ionization-shock front driven by the $\lambda$ Orionis OB stars and the dust temperature in the YSOs region of B35A has been estimated to be at least 25$-$30 K (Craigon, 2015; Morgan et al., 2008). Therefore, at these temperatures, above the CO sublimation temperature ($\sim$20 K; Bisschop et al. 2006; Collings et al. 2004; Acharyya et al. 2007), CO is efficiently thermally desorbed from the grain surfaces and it is expected to primarily reside in the gas-phase. According to this result, the observed CH₃OH ice might have formed at earlier stages, prior to the warm-up of the dust grains or alternatively, from CO molecules trapped in porous H₂O matrices, and therefore not sublimated at these temperatures. Additionally, higher abundances of CO might reflect an active CO gas-phase synthesis in the region. Follow-up observations of higher $J$ transitions of CO isotopologues are required to provide a conclusive assessment.