© L. A. Busch et al. 2022

1 Introduction

To date, more than 270 molecules have been detected in space¹ and the detection rate is speeding up thanks, in particular, to the perpetual advancement of broad-band receivers on single-dish telescopes such as the Yebes 40 m, IRAM 30 m telescopes, or the Green Bank Telescope allowing for observations of sensitive spectral-line surveys that cover a wide range of frequencies (McGuire 2022). Observations of molecules help us understand the structure and evolution of the interstellar medium (ISM) and shed light on the various phases of the star-formation process from diffuse clouds (n_H ~ 10²–10³ cm⁻³), to dense clouds and cores with densities beyond 10⁸ cm⁻³, and to protostellar and protoplanetary disks (for a recent review see Jørgensen et al. 2020). Amongst these, observations of complex organic molecules (COMs), which are carbon-bearing molecules that consist, per definition, of at least six atoms (Herbst & van Dishoeck 2009), are of special interest as they are potential precursors of even more complex and possibly prebiotic species. Therefore, they may play a role in the build-up of the complex organic and prebiotic inventory seen in meteorites and comets in the Solar System and, going one step further, in the emergence of life on Earth.

Many COMs have first been detected in the close vicinity of high- and low-mass protostars. These regions are referred to as hot cores and hot corinos, respectively. The spatial extent of these regions is usually associated with a gas temperature of ~100K (Jørgensen et al. 2020). The characteristic temperature of ~ 100 K denotes the point when water desorbs from the dust grain surfaces, along with many other species, perhaps including the COMs themselves. At the end of the cold collapse phase of a dense cloud core, an ice mantle consisting of mostly water (with traces of, e.g. CO, CO₂, and NH₃, Boogert et al. 2015) covers the grain. A widely accepted paradigm for the production of COMs was the photodissociation of molecules in this ice mantle, notably methanol, producing radicals that would become mobile, and thus reactive, during the gradual warm-up of dust grains that occurs once a protostar is born and starts heating up its collapsing envelope (Garrod & Herbst 2006). At high enough temperatures, both the simple and complex molecules would thermally desorb from the grains into the gas phase. The release of the simple species in particular could also induce gas-phase chemistry. Recent models by Garrod et al. (2022), which include non-diffusive surface and bulk-ice chemistry, indicate that significant COM production on dust grains may actually occur at low temperatures when the simple ices themselves are beginning to form, which is in agreement with recent experimental findings involving the co-deposition of atomic H and simple molecules such as CO (e.g. Fedoseev et al. 2015).

Assuming that COMs are indeed formed on the dust grains (which does not rule out complementary gas-phase formation in some cases), their temperature-dependent desorption behaviour will be important to the observed spatial morphologies of their emission regions. The desorption of COMs from the grains has been studied in the laboratory using interstellar ice analogues (e.g. Collings et al. 2004; Martín-Doménech et al. 2014), but the precise temperature dependence is complex. In particular, for a COM more volatile than water, the desorption of that molecule from a water ice mixture may partially occur at a relatively low temperature, corresponding to direct thermal desorption, perhaps mediated by some diffusive transport of molecules through surface-pore structures. Another component would be trapped within the water-ice structure, eventually co-desorbing with the water, and therefore, exhibiting a similar desorption temperature as water itself.

Astrochemical models have typically used simple treatments for the desorption of COMs; so-called two-phase models (e.g. Garrod 2008), which consider the grain-surface ices to be a single physical phase, and three-phase models (e.g. Garrod 2013), which distinguish the bulk ice from the ice-mantle surface, usually allow molecules to desorb according to their own binding energies, meaning that there is no trapping of any kind. The more recent three-phase model of Garrod et al. (2022) adopts the other extreme; material in the bulk ice is trapped beneath the upper layer, meaning that only a small fraction of COMs in the bulk is able to desorb until water rapidly begins to desorb at its own characteristic desorption temperature (Viti et al. 2004, used an empirical treatment to model temperature-dependent molecular desorption, but did not include actual grain-surface chemistry, only desorption). There has so far been no direct observational confirmation of the co-desorption of COMs with water, mainly because the angular resolution of observations has been insufficient to resolve the temperature gradient as traced by the COM emission, which is needed to pinpoint their desorption temperatures. The alternative picture, in which COMs do not desorb alongside water but according to their own independent binding energies, would lead to the appearance of COMs at different temperatures even below 100 K. This dependence on binding energy has neither been confirmed nor refuted observationally, either, again due to observational limitations.

Moreover, observations of COMs in the absence of protostars in cold (T ≲ 20 K) regions, for example the dark cloud TMC-1 (e.g. Agúndez et al. 2021, and references therein) or prestellar cores (Bacmann et al. 2012; Jiménez-Serra et al. 2016, 2021; Scibelli & Shirley 2020), but also in protostellar outflows such as L1157 (Codella et al. 2015, 2017) and, for example the shocked region (while quiescent in star formation) G+0.693–0.027 located in the Galactic centre region (e.g. Requena-Torres et al. 2006; Zeng et al. 2018), point to additional or purely non-thermal desorption processes. These processes may include grain-sputtering and subsequent release of COMs into the gas phase due to shock passing induced by outflows, accretion shocks (e.g. Csengeri et al. 2019), or cloud interactions, desorption after interaction of molecules on dust grain surfaces with cosmic rays (Shingledecker et al. 2018; Paulive et al. 2021), or other diffusive and non-diffusive reactions taking place on the dust surface that lead to the chemical desorption of COMs (e.g, Ruaud et al. 2015; Jin & Garrod 2020).

The investigation of COMs and the many possible ways for them to arrive in the gas phase is one of the objectives of the ReMoCA (Re-exploring Molecular Complexity with ALMA) survey (Belloche et al. 2019), an imaging spectral line survey performed at 3 mm with the Atacama Large Millimetre/submillimetre Array (ALMA) towards the giant molecular cloud Sagittarius B2 (hereafter Sgr B2), which is located at a distance of 8.2kpc from the sun (Reid et al. 2019) in the Galactic centre region. Sgr B2 hosts two sites of active high-mass star formation. Amongst them, Sagittarius B2 North (hereafter Sgr B2 (N)) has a high record of first detections of interstellar molecules turning it into an excellent target to look out for COMs. Observations towards this region revealed several highmass protostars with hot cores (Bonfand et al. 2017), HII regions (Gaume et al. 1995; De Pree et al. 2015), filaments through which accretion probably happens (Schwörer et al. 2019), and outflows (Higuchi et al. 2015; Bonfand et al. 2017). Therefore, it fulfils the requirements to study all thermal and non-thermal desorption processes mentioned above.

Before ReMoCA, its predecessor, the EMoCA survey (Exploring Molecular Complexity with ALMA, Belloche et al. 2016), which itself succeeded a spectral line survey of Sgr B2 (N) and (M) with the IRAM30m single-dish telescope (Belloche et al. 2013), already allowed to study Sgr B2 (N) in the 3 mm spectral window at a high angular resolution of 1.6″. Insights that were obtained from the data of this survey included first detections of new COMs such as i-C₃H₇CN (Belloche et al. 2014) and CH₃NHCHO (Belloche et al. 2017, 2019), a detailed study on the complex chemistry in translucent clouds along the line of sight (Thiel et al. 2017), the discovery of three new hot cores and their outflows, if present (Bonfand et al. 2017), and an inventory of COMs in the hot cores Sgr B2 (N2–N5) (Bonfand et al. 2019). The latter analysis does not include the main and most massive hot core Sgr B2 (N1) because the observed line forest at the confusion limit, spectral lines that have full width at half maximum (FWHM) of ~7 km s⁻¹ and additional line wings, and the high column density and optical depth of the dust continuum made it challenging to probe the inner part of this hot core at this wavelength. Now, with the ReMoCA survey and its sub-arcsecond angular resolution and four-times better sensitivity, it becomes possible to resolve the COM emission in Sgr B2 (N1).

In this work, we aim to shed light on the thermal desorption process, in particular on the question whether COMs co-desorb with water or rather depending on their binding energies. To do so, we studied the morphology of the emission of 16 organic molecules and chose ten of them, all COMs, for further analysis. The spectra of these ten COMs (including one isotopologue) were modelled under the assumption of local thermodynamic equilibrium (LTE) and population diagrams were derived. Based on this analysis, we derived resolved profiles of rotation temperature and COM abundance starting from ~0.5″ distance from the continuum peak and proceeding to the point of non-detection for each COM. By comparing these profiles with results from state-of-the-art astrochemical models, we want to trace (back) each species’ evolution in the solid and gas phases, and the transition from one phase to the other in order to answer the question above. The article is structured as follows: Sect. 2 provides details on the used data and the LTE modelling of the spectra. In Sect. 3 we present our results including an analysis of the continuum data, a description of the morphology of the COM emission, and the path towards derivation of the COM abundance profiles. The discussion on the results is done in Sect. 4 including the comparison to chemical models and a conclusion is provided in Sect. 5.

2 Observations and method of analysis

2.1 The ReMoCA survey

The observations of the ReMoCA line survey were conducted with the ALMA interferometre and cover the complete frequency range from 84.1 to 114.4 GHz. The phase centre is located at (α,δ)_J2000 = (17^h47^m19^ṣ87, −28°22′16″.00) halfway between Sgr B2 (N1) and (N2). The survey is split into five observational setups, called S1 to S5, each of which delivers four spectral windows. The observations were performed with different antenna configurations, which yield mean synthesised beam sizes that vary from ~0.75″ in setup 1 to 0.3″ in setup 5. The detailed list of covered frequency ranges, beam sizes, and average rms noise levels for all spectral windows can be found in Table 2 of Belloche et al. (2019). We refer to the latter article for more details on the observations and the data reduction. The FWHM of the primary beam varies between 69″ at 84 GHz and 51″ at 114 GHz (ALMA Partnership 2016). The reduced spectra have a spectral resolution of 488 kHz, which translates to 1.7–1.3 km s⁻¹.

2.2 1.3 mm ALMA data

Sánchez-Monge et al. (2017) observed Sgr B2 (N) and (M) with ALMA using an extended configuration. The continuum map used here was obtained at 242GHz with a synthesised beam of 0.4″. The average rms noise level in the map is 12.7 mK. The phase centre is located at (α,δ)_J2000 = (17^h47^m195887, −28°22′15″.76) but was shifted to the phase centre of the ReMoCA data in this work. More details on these observations are presented in Sánchez-Monge et al. (2017).

2.3 LTE modelling

To analyse the spectral line data, we performed radiative transfer modelling under conditions of LTE, which is appropriate given the high densities found towards Sgr B2 (N) (~10⁷ cm⁻³, Bonfand et al. 2017). The spectral line emission has already been split from the continuum emission as reported by Belloche et al. (2019) (see their paper for details), who performed a preliminary baseline subtraction, which has been improved subsequently (Melosso et al. 2020). Another subtraction was performed in this work, when residual baseline issues were identified, however, only for spectra at distances larger than 2″ from Sgr B2 (N1) because of the difficulty of distinguishing between the continuum and the pervasive line emission.

The line identification and modelling of the spectra were done with Weeds (Maret et al. 2011), which is an extension of the GILDAS/CLASS software². To produce a synthetic spectrum, Weeds requires five input parameters, which are: total column density, rotational temperature, source size, velocity offset with respect to the systemic velocity of the source, and line width (FWHM). We performed 1D Gaussian fits to optically thin and unblended transitions, from which we obtained the velocity offset and the line width. Column density and rotational temperature were determined in an iterative way. From a first model, in which these parameters were selected by eye, we derived population diagrams (see Sect. 3.4), which also yield column density and rotational temperature. The Weeds parameters were adjusted until the model and the results of the population diagram were in good agreement. The molecular emission is assumed to follow a 2D Gaussian distribution in Weeds. Because the COM emissions show extended but also small-scale structures, the determination of the source size is challenging and is discussed in more detail in Sect. 3.2.

A species is identified when the synthetic spectrum correctly predicts each observed transition. Models of all analysed species were subsequently combined to a complete synthetic spectrum, in which blending of lines is treated by adding up the model predictions of individual species. More details on the modelling procedure can be found in Belloche et al. (2016).

The spectroscopic calculations used to create the models are based on the CDMS (Cologne Database for Molecular Spectroscopy, Endres et al. 2016) or JPL (Jet Propulsion Laboratory, Pearson et al. 2010) catalogues in most instances. We provide details on the laboratory background and on the vibrational spectroscopy in Appendix A. The former is necessary to give credit to at least the most important contributors who often carried out the respective measurements to support the radio astronomical community. The latter is important to account for the molecules in excited vibrational states which are populated at excited temperatures such as in our work but may be characterised too little or not at all or may be too weak to be detected securely.

3 Astronomical results

3.1 Continuum emission at 1.3 and 3 mm

Figure 1 shows the continuum map at 1.3 mm (242 GHz, Sánchez-Monge et al. 2017) in colour scale and a ReMoCA continuum map at 3 mm (99.2 GHz) with contours. The continuum at 1.3 mm is dominated by dust emission and peaks towards the two main hot cores N1 and N2. We show continuum peak positions of Sgr B2 (N1) derived by various authors along with the position determined by us in the following way: using continuum maps obtained from setup 5, which is the ReMoCA setup of highest angular resolution, and computing the peak position by intensity-weighting the four brightest pixels, we located the 3 mm continuum peak at (0.02 ± 0.03,−2.47 ± 0.04)″ from the phase centre (see the white cross in Fig. 1).

In addition to N1 and N2, hot core N3 is indicated, which has only been discovered recently (together with N4 and N5, which are located outside the field shown in Fig. 1, Bonfand et al. 2017). Further continuum sources at 1.3 mm have been identified by Sánchez-Monge et al. (2017), those of which located within the shown field are indicated with orange crosses in Fig. 1. Each of these sources has a counterpart in the 3 mm continuum map as can be seen from the contours suggesting that a substantial part of the continuum emission traces dust. One exception is HII region K1 which is seen at both wavelengths but whose emission seems to be dominated by free-free emission even at 1.3 mm (see Fig. 2 and Sánchez-Monge et al. 2017). Moreover, there are features that are not seen at 1.3 mm, for example the large-scale structure to the north-east. It resembles the one reported by Gaume et al. (1995), who performed observations of the continuum towards Sgr B2 (N) at 1.3 cm with the VLA. At this wavelength, free-free emission originating from HII regions dominates over dust. Therefore, the continuum at 3 mm is not exclusively tracing dust but also free-free emission to a substantial extent. The positions of the HII regions reported by Gaume et al. (1995) and De Pree et al. (2015) are indicated with pink crosses in Fig. 1, and all (except K9.69) are associated with intensity peaks in the 3 mm continuum map.

We created a spectral index map using the 1.3 and 3 mm continuum maps and show the result in Fig. 2. The spectral index α is computed by (1)

where S₂₄₂ and S_99.2 are the flux densities measured at each position in the continuum map of the respective frequency. We smoothed the 3 mm data to the resolution of the 1.3 mm data for a more precise analysis. The spectral index was only computed above a flux density threshold of 1σ, where σ is the average noise level in the respective continuum map. For most parts in Fig. 2, the spectral index has values ranging from 2.5 to ≳4 suggesting prevalence of optically thin dust emission. In some regions the spectral index is smaller than 2–2.5 including the HII regions K1, K3, and K7 (Gaume et al. 1995), but also AN 20 (Sánchez-Monge et al. 2017), whose nature is not certainly known. Besides at 99.2 GHz and 242 GHz, the latter source was detected at 40GHz (Rolffs et al. 2011; Sánchez-Monge et al. 2017) suggesting a possible contribution of free-free emission to the observed flux. K1 even shows values <1, which is most likely the result of a mixture of dust and free-free emission (see also Sánchez-Monge et al. 2017).

We also expect a contribution of free-free emission originating from K2 to the continuum at the position of Sgr B2 (N1) as they are nearly co-located. Because we want to derive H₂ column densities from the 3 mm dust emission at positions close to Sgr B2 (N1) it is important to disentangle the contributions of free-free and dust emission, particularly at this position. De Pree et al. (2015) reported a flux density of 80 mJy for K2 at 44.2 GHz for a size of the emitting region of 0.22″ × 0.1″. Given a total peak continuum flux of 190 mJy beam⁻¹ at the position of Sgr B2 (N1) at 99.2 GHz for a beam size of 0.4″, free-free emission contributes ~40% to this flux assuming that the free-free emission is optically thin (α_ff,thin = −0.1) above 44.2GHz.

An advantage of the 3 mm continuum is that dust opacities are smaller at this wavelength than at 1.3 mm. To confirm this, we estimated the optical depth t at the position of Sgr B2 (N1) and the position N1S (0.00, −3.48)″ (see Fig. 3), which was used for analysis in Belloche et al. (2019). The flux density at the position of Sgr B2 (N1) was corrected for the contribution of free-free emission as derived above, while for N1S the contribution is negligible. We used the equation presented in Bonfand et al. (2017), which is (2)

where is the beam solid angle, the peak flux density, and B_ν(T_d) the Planck function of the dust emission evaluated for the dust temperature T_d. Because the optical depth is sensitive to the dust temperature we assumed two values: T_d = 200 K and 250 K. We used the smoothed map for a direct comparison of the 1.3 and 3 mm continuum and therefore, a beam size of HPBW_min = HPBW_maj = 0.4″. The results are summarised in Table 1 and show that opacities are lower for the observations at 3 mm at both positions. We have a closer look at the optical depth in Sect. 3.5 when we derive H₂ column densities.

An effect biasing the comparison between the continuum levels may be spatial filtering by the ALMA interferometre, which occurs as a consequence of limited (u,v) coverage at shortest baselines. This leads to a lower sensitivity to larger-scale emission, in other words, emission that is extended beyond a certain spatial scale might be filtered out, which eventually leads to a decrease of the observed flux density. This maximum recoverable scale depends on the length of the shortest baseline (ALMA Partnership 2016). For the observations at 1.3 mm, 34–36 antennae were used covering baselines from 30 m to 650 m and hence, ensuring sensitivity to structures on scales of 0.45″ at an angular resolution of 0.4″ (Sánchez-Monge et al. 2017). The ReMoCA survey has been observed with different configurations using 36–6 antennae that cover baselines from 15 m to 3600 m (cf. Table 2 in Belloche et al. 2019). Therefore, maximum scales that can be recovered at 100 GHz are between ~3″ and ~8″ for the highest and lowest angular resolutions, respectively (see able 7.1 in ALMA Partnership 2016). Because the two datasets have a similar maximum recoverable scale the spectral index map in Fig. 2 should be reliable for the scales traced by both.

3.2 Spatial distribution of COMs

To explore the morphology of the COM emission we created Line-width- and Velocity-corrected INtegrated Emission maps (LVINE). The LVINE method is an extension of the VINE method, which was introduced by Calcutt et al. (2018), and takes into account gradients of velocity and spectral line width in the observed region. The LVINE method is explained in more detail in Appendix B.

Figure 3 shows the 1.3 mm continuum map in colour scale, which is overlaid by contours of an LVINE map of a C₂H₅OH transition at 97.139 GHz (E_u = 264 K). The continuum exhibits a lot of structure that was associated with filaments by Schwörer et al. (2019), who described the continuum emission at 1.3 mm in detail. The authors reported on the differences in the morphology of O- and S-bearing COM emission that follows the structured continuum emission, which can also be seen for C₂H₅OH in Fig. 3, and N-bearing species, which reveal a more spherical morphology. In order to investigate these reported differences, we show LVINE maps of emission from various COMs in Fig. 4.

Similarly to C₂H₅OH, the emissions of CH₃OH, its ¹³C isotopologue, CH₃OCH₃, and CH₃OCHO, all of which are O-bearing COMs, closely follow the morphology of the continuum. The distribution of CH₃CHO emission is slightly different, however, it shows the tendency of the morphology seen for the other O-bearing COMs. The emissions of the N-bearing COMs such as ¹³CH₃CN, C₂H₅CN, C₂H₃CN, and HC¹³CCN share a similar morphology that is less structured and more compact around the central region of Sgr B2 (N1), with the latter two showing the smallest spatial extent. The morphology of HNCO emission is similar to the N-bearing COMs. The spatial distributions of CH₃NCO, NH₂CHO, and NH₂CH₂CN emissions are similar, with the latter being more compact, and follow a slightly different morphology as it shows the compactness of the N-bearing COMs with a pattern similar to what is seen for the O-bearing COMs. i-C₃H₇CN and n-C₃H₇CN emissions are extremely compact and weak and cannot be compared to the other COMs. In summary, we observe a spatial segregation of species, approximately between O- and N-bearing COMs. Moreover, there may even be indications of a third group.

The determination of the physical size of the emission region is challenging because the morphology for all COMs does not simply follow a 2D Gaussian profile as assumed by Weeds, instead it shows extended emission as well as structures on smaller scales. In the following we assume that we always resolve the emission region. In the Weeds model we set the size (FWHM) of the emission region to 2″, which yields a beam filling factor of approximately 1 and thus, satisfies the requirement.

In the region closest to Sgr B2 (N1) we found that the continuum becomes optically thick and obscures the COM emission. Therefore, the true intensity of the COM emission is unknown and this inner region is masked in the maps shown in Figs. 3 and 4. The determination of the mask size is explained in Appendix C. It varies between the observational setups and spectral windows because the opacity effect on the continuum is higher for higher frequency and higher angular resolution.

3.3 Line and position selection

We focussed our analysis on commonly abundant O- and N-bearing COMs, that show numerous strong lines and have enough lines that are not optically thick. This selection comprises CH₃OH (methanol), C₂H₅OH (ethanol), CH₃OCH₃ (dimethyl ether), CH₃OCHO (methyl formate), CH₃CHO (acetaldehyde), CH₃NCO (methyl isocyanate), C₂H₅CN (ethyl cyanide), C₂H₃CN (vinyl cyanide), and NH₂CHO (formamide).

As discussed above, optical depth of the continuum at its peak, and therefore obscuration of the COM emission, prevents us from starting our analysis at this position. Therefore, Belloche et al. (2019) selected a position that is 1″ to the south of Sgr B2 (N1) for their analysis and called it N1S. Spectral lines at this position suffer less from masking by the continuum. Moreover, they have moderate average line widths of ~5 km s⁻¹ and do not show wings, which would be indicative of emission originating from the outflow of Sgr B2 (N1) (Higuchi et al. 2015). Based on this reasoning, we decided to start from this position and go further south in order to determine the COM rotational temperature and column density profiles along this direction. The positions were chosen so that they are approximately one beam size apart (0.5″). The transition to source AN 20 was analysed with an additional position (N1S6). The analysis was continued up to the distance where none of the selected COMs is detected any longer. This maximum distance varies for different COMs and can either result from the limited sensitivity of the observations or is due to the prevailing chemical or physical conditions. The used positions to the south are indicated with maroon star symbols in Fig. 3 and listed in Table E.1, where we adopt the naming from Belloche et al. (2019) and term positions N1Si (i = 1,2, …) with increasing distance starting from N1S. Additionally, we studied the position N1S-1, which is at a distance of 0.6″ from Sgr B2 (N1). During the analysis we found that this position is already affected by the high continuum optical depth, severely in spectral windows 2 and 3 of observational setup 5, which cover the highest frequencies and have the highest angular resolution. Therefore, transitions covered by these spectral windows at N1S-1 were not used in the following (see also Appendix C).

The results obtained southwards are compared to another direction. Because in this study we focussed on the COMs’ behaviour under the influence of heating by the protostar, that is the process of thermal desorption, we did not use directions towards the south-east and north-west as they correspond to the axis of the Sgr B2 (N1) outflow (Higuchi et al. 2015). The outflow induces shocks in the ambient gas, which may trigger non-thermal desorption of COMs. The impact of the outflow on the COM emission will be topic of a forthcoming paper. To the north, there are multiple continuum sources that may bias the results of COM abundances and to the north-east, we face uncertain contributions of free-free emission (see Fig. 1) to the continuum. Therefore, these directions were not used, instead, we decided to go west as indicated with maroon symbols in Fig. 3. The positions are listed in TableE.1. Because the molecular emission seemed slightly less spatially extended than to the south (cf. Fig. 4), the positions where the emission is more intense are chosen in a somewhat smaller distance from each other. Similar to N1S, we refer the distance at 1″ from Sgr B2 (N1) to as N1W and then increase numbers with increasing distance. Additionally, we looked at position N1W-1 which is at a distance of 0.5″ from Sgr B2 (N1). Positions closer to Sgr B2 (N1) in either direction were not used because the continuum becomes optically thick.

In Appendix E we provide the parameters used for the LTE modelling of the selected COMs at each position. Additionally, we show observed spectra for each COM at position N1S (or N1S1 for CH₃OCH₃) together with the synthetic spectra in Appendix F. These figures only show transitions that have been used to create the respective population diagram (see Sect. 3.4).

3.4 COM rotational temperature and column density profiles

At each position selected in the previous section we derived population diagrams in order to determine the rotational temperature T_rot and column density N_col profiles for each COM. In the population diagrams we plot the natural logarithm of the upper level column density N_u divided by the level degeneracy g_u against the upper level energy E_u (Mangum & Shirley 2015) as they are related by (3)

where k_B is the Boltzmann constant, c the speed of light, h the Planck constant, the beam filling factor, A_ul the Einstein A coefficient, N_tot the total column density, and Q the partition function. Intensities in brightness temperature scale J(T_B) are integrated over a manually selected velocity range d_v.

In Fig. 5 the population diagram for CH₃OH towards N1S is shown as an example including data points for the observed as well as the modelled transitions. We used the vibrational ground state v = 0 and the first and second torsionally excited states v = (1,2) of CH₃OH, all of which were modelled with the same Weeds input parameters. We considered setups 1–3 and 4–5 separately and used different input parameters for both, if necessary, because of their different angular resolutions that can vary by more than a factor of 2 (see Fig. C.1 of Motiyenko et al. 2020 for another version of this population diagram of methanol that includes all setups). Without this separation, we might introduce larger scatter in the population diagram because different beams may see different portions of the gas. Because rotational temperatures derived from the population diagrams for either setups 1–3 or 4–5 differ by at most 3σ, where σ is the error on the linear fit, and in roughly two thirds of the cases the difference is even ≲1σ we only used the higher-resolution setups 4–5 to determine the temperature and column density profiles in the following. Except for ¹³CH₃OH and NH₂CHO, for which we had to use setups 1–3, there are enough transitions of each COM detected in setups 4–5 to make reliable linear fits to the data in the population diagrams. Population diagrams for all analysed COMs and for all possible positions can be found in Appendix G. All vibrational states of a COM that were used during the analyses are indicated in these population diagrams and are summarised in Table G.1.

We applied two corrections to the data points, which are only considered in the right panels of Fig. 5 and Figs. G.1–G.21. First, although we selected only transitions that are not too contaminated some contamination is inevitable due to high spectral line intensity. Therefore, we created a complete Weeds model that includes all transitions of all species used for the analysis. Based on this model, the contamination of neighbouring transitions of at least other identified species was estimated and subtracted from the integrated intensities.

Second, to consider possible effects of line optical depth we multiplied the integrated intensities of both the observed and modelled transitions with a correction factor (see Goldsmith & Langer 1999; Mangum & Shirley 2015), where we used the opacities obtained from our Weeds model for the respective transition. Depending on the species, the upper level energy of a transition, and the distance to Sgr B2 (N1), opacities can be extremely high, which cannot be properly accounted for in our simple Weeds model. Hence, the correction factor might not be able to counteract the effect on the intensity. This may be seen for the lowest upper-level energy transitions of CH₃OH from setups 4–5 in Fig. 5, for which we obtained an optical depth of ~3 from the model. When corrected for it, the data points (red) remain slightly below the fitted line, while the model (grey) overestimates the observation for these two transitions. Therefore, we only considered transitions in the population diagram that have opacities of ≲2–3 for all molecules.

After applying these two corrections, deviations between the observed and synthesised data points are generally small indicating that our chosen input parameters for the Weeds modelling are reliable. However, scatter amongst the observed data points can still occur due to a remaining contamination by unidentified lines, line opacity effects, or inaccurate baseline subtraction due to line confusion. Furthermore, the Weeds model was produced by taking into account the background continuum temperature, which is given by the baseline level initially subtracted from the spectra. Due to the different angular resolutions of the observational setups, the continuum level varies, which can introduce scatter amongst both the observed and synthesised data points. Moreover, at positions close to Sgr B2 (N1), we face the problem that the continuum starts becoming optically thick and therefore, hiding the line emission from our view. Because in Weeds the continuum is only considered as another background source, the model does not perform properly in this situation. Accordingly, intensities of some transitions may be overestimated by the model resulting in larger scatter in the population diagrams of observed data points. This is indeed evident in population diagrams at position N1S-1, where the continuum can be expected to become optically thick. Because transitions covered by spectral windows 2 and 3 of observational setup 5 suffer most from this effect they were not included for the analysis at this position as mentioned in Sect. 3.3.

At larger distances, where the COM emission becomes weak, scatter amongst the observed data points may be introduced when the larger beams of setup 4 capture material closer to the protostar that is no longer seen with the smaller beams of setup 5. For COMs and positions for which this effect is severe, we used spectra from setup 5 that are smoothed with a 2D Gaussian kernel to the angular resolution of spectral window 3 of setup 4.

For CH₃OCHO, and to a lesser extent for CH₃NCO, we noticed a systematic deviation of observed points from setups 4 and 5. We do not know the reason for this for sure. This is not caused by the different angular resolutions of the setups as smoothing the spectra of setup 5 to the resolution of setup 4 does not yield improvement. A possible explanation may however be filtering of extended emission by ALMA (see Sect. 3.1) which would affect setup 5 more than setup 4 due to the average shortest baselines that are longer for setup 5 (see Table 1 in Belloche et al. 2019). Data points observed with setup 5 would be expected to lie below those of setup 4 if emission was filtered, which is what we see in the population diagrams of these two molecules. However, this effect cannot be confirmed quantitatively and its impact remains questionable as it is not clear why the two mentioned COMs should be more affected than others.

Many of the above-mentioned uncertainties cannot be meaningfully quantified. Therefore, the error bars shown in the population diagrams only reflect the standard deviation from fitting and an additional factor of 1σ, where σ is the median noise level measured in channel maps of the continuum-removed data cubes taken from Table 2 in Belloche et al. (2019), to account for the uncertainty in the continuum level. However, the fit was performed by not weighting the data points by the errors in order to avoid giving too much weight to extremely strong lines and contaminated lines.

The data points in all population diagrams follow a linear trend meaning a single temperature can explain the level distribution for each molecule at each position. Therefore, we fitted a straight line to the observed data points in all cases and obtained the desired temperature profiles for each COM. We performed the fit only as far as positions N1S4 and N1W4, respectively, for reasons explained below. The profiles are shown as solid lines in Fig. 6 and the slopes of the linear fits to these profiles are summarised in Table 2. The errors on the data points correspond to values obtained from the population diagrams and determine the uncertainty on the temperature profiles. Few profiles seem to deviate from a straight line at shorter distances to Sgr B2 (N1). Therefore, we applied an additional fit to the data that includes only those positions at larger distances from Sgr B2 (N1) that seemingly lie on a straight line (dashed lines in Fig. 6). The second fit is kept only when the slopes of both fits differ by more than 15%.

To the south, CH₃OH, CH₃OCH₃, and CH₃OCHO are the COMs detected farthest from Sgr B2 (N1) with a reliable temperature determination beyond a distance of 3.5. Especially for CH₃OH and CH₃OCH₃, it is evident in Fig. 6 that the rotational temperatures beyond this distance (corresponding to positions N1S5–N1S7) lie above the fit. These slightly higher temperatures can possibly be associated with the continuum source AN 20 (see Figs. 1 and 3) that heats the gas in addition to Sgr B2 (N1). Therefore, we excluded these positions from the fit of the temperature profiles. To the west, there seems to be a drop in temperature at positions N1W4 and N1W5 for CH₃OCHO and less pronounced for C₂H₅CN and a subsequent rise to ≳100 K at larger distances. Therefore, position N1W4 was not included in the fit for these two molecules. A same trend may be expected for CH₃OCH₃ and C₂H₃CN, however, these molecules are not detected at these two positions. They reappear at larger distances. Remarkably, there is a change in velocity and line width starting from N1W5. Up to this position, spectral lines are detected at v_lsr ~ 65 km s⁻¹ with FWHM ~ 5 km s⁻¹. This component is undetected at larger distances, instead the line appears at v_lsr ~ 69 km s⁻¹ and is extremely narrow with fwhm ~ 2–3 km s⁻¹ (indicated with crosses in all figures where necessary). This is also evident in the peak-velocity map in Fig. B.2. We did not include these positions to the fit of the temperature profile.

The slopes of the southbound profiles for the O-bearing COMs vary in a range from −0.6 to −0.8 when including all positions up to N1S4, except CH₃OCHO, whose profile is slightly steeper. However, given the apparent separation of data points from setups 4 and 5 at some positions for this molecule, we may expect a greater overall uncertainty for its profile. The westbound profiles of CH₃OH, its ¹³C isotopologue, C₂H₅OH, and CH₃CHO show similar slopes as their southbound counterparts. The westbound profile of CH₃OCH₃ has a much steeper slope of −1, while that of CH₃OCHO has a much shallower slope (approximtely −0.5) than to the south. When including only points farther away from Sgr B2 (N1), CH₃OH shows a slightly steeper slope of −0.81, which is still in the above-mentioned range. Also, CH₃CHO has a steeper slope of −1.15.

The slopes of the N-bearing COMs, except NH₂CHO, are slightly shallower (−0.4 to −0.6, NH₂CHO: −0.3) than those of the O-bearing COMs when including all points. Only when the closest positions to Sgr B2 (N1) are excluded, C₂H₅CN and NH₂CHO show steeper slopes that are comparable to those of the O-bearing COMs. The slopes of the westbound profiles of the N-bearing COMs are similar to the southbound ones. When considering only larger distances, the slopes of C₂H₅CN and CH₃NCO again become similar to those of the O-bearing COMs. The slope of NH₂CHO remains shallow. Up to now, it is unclear what may cause a deviation from a linear fit with all points included and the difference between the COMs. Aside from an underestimation of uncertainties, possible reasons may be presented in an underestimation of line optical depth or the absence of a species in the closest vicinity of Sgr B2 (N1). In the latter case, we may then observe a cloud layer where this species is still abundant and which has a lower temperature. In the case of NH₂CHO (also ¹³CH₃OH) the larger beams of setups 1–3 may influence the result, especially to the west, since the distances between positions are smaller than the average beam size and hence, adjacent positions are not independent of each other.

The temperature profile (T ∝ D^γ) is derived from the diffusion equation (e.g. Kenyon et al. 1993). The slope γ varies depending on whether the dust emission is optically thin or thick , where β is the dust emissivity spectral index, which likely varies in a range from 0.5 to 2 at 3 mm in dense cores (e.g. Kwon et al. 2009; Li et al. 2017), and n is the density power law index, which typically is n = −1.5 for a free-falling envelope (Shu 1977). Assuming these values the slope γ varies from ~[−0.3, −0.4] for optically thin and ~[−0.7,−1.3] for optically thick dust emission. Therefore, the slopes derived above that include all positions generally lie in between these ranges with the tendency towards the range for optically thick continuum.

Total column density profiles for each COM were obtained from the linear fit performed in the population diagrams and are shown in Fig. 7, where the errors on the data points again correspond to those obtained from the population diagrams. In addition, column densities used for the modelling with Weeds are shown as dotted lines. Usually, the difference is less than a factor 2, except for CH₃CHO and CH₃NCO, for which the difference can be up to a factor 3–4 for some positions. This is mainly caused by the fact that the Weeds model considers the background continuum, while it is ignored (and cannot be properly accounted for) when fitting the population diagram. For this reason, we only use column densities from Weeds in the following. To all values we applied a vibrational correction factor that accounts for contributions to the column density by vibrational states, in the cases where the partition function provided by the various databases does not include this contribution that cannot be neglected at the high temperatures measured here. Southbound profiles of almost all O-bearing species resemble a plateau between 0.5″ and 2.5″ and then start to decrease at larger distances from Sgr B2 (N1), with those of CH₃OH and C₂H₅OH dropping more abruptly than CH₃OCH₃ and CH₃OCHO. The column density of CH₃CHO rather continuously decreases with increasing distance. To the south, column densities of N-bearing COMs decrease similarly to CH₃CHO, with C₂H₃CN and NH₂CHO showing a steeper decrease of column density with increasing distance from Sgr B2 (N1).

At close distances, the westbound profiles of all COMs, except CH₃OCH₃, behave similarly to their southbound counterparts with values that are equal or slightly smaller. The column density of CH₃OCH₃ decreases towards Sgr B2 (N1) such that at N1S-1, we were not able to derive a population diagram and hence, only an upper limit from the Weeds model was determined by extrapolating its temperature profile. At large distances the west- and southbound profiles start deviating from each other. On the one hand, C₂H₅OH, CH₃CHO, and CH₃NCO are only detected to shorter westward distances than to the south, while on the other hand, CH₃OH and CH₃OCHO show a cavity to the west, where column densities drop by up to two orders of magnitude reaching a minimum at N1W4-N1W5 only to increase again beyond these distances. This coincides with the drop in temperature seen in Fig. 6. This cavity is also observed for CH₃OCH₃, C₂H₃CN, and C₂H₅CN, because although they are not even detected at positions N1W4 and, for the former two, N1W5, their column densities can be determined at the larger distances. For ¹³CH₃OH, this drop in column density is less pronounced if evident at all. This may be because it has been smeared out due to the larger beam sizes of setups 1–3 that are used for this COM. NH₂CHO is detected up to position N1W5, however only upper limits (see below) could be determined. According to these, NH₂CHO may show a trend similar ¹³CH₃ OH concerning the cavity.

At some position at farther distance from Sgr B2 (N1) some COMs may still be detected, however, the linear fit in the population diagram did not yield a reliable result. In theses cases we fixed the rotational temperature by extrapolating the derived temperature profile of the respective species shown in Fig. 6 in order to determine column densities. Vertical lines in Fig. 7 indicate the largest projected distance from Sgr B2 (N1) up to which the COM is still detected and its column density can be derived. Accordingly, the COMs disappearing southwards first are C₂H₃CN and CH₃NCO, followed by CH₃CHO and C₂H₅OH, NH₂CHO, C₂H₅CN, and at last CH₃OH, CH₃OCHO, andCH₃OCH₃. Due to the cavity in column density, such astatement is difficult to make to the west. However, all COMs that are detected farthest from Sgr B2 (N1) to the south are also the ones detected at largest distances to the west, which is also seen in Fig. D.2, where these maximum distances are summarised. At distances beyond the shown vertical lines and at positions of the cavity, if necessary, upper limits for the column densities were determined, where the rotational temperature was again obtained from extrapolating the respective temperature profile. These upper limits were computed assuming an average velocity offset and line width determined from detected molecules at a specific position and making sure that the Weeds model for the undetected species did not overestimate the intensity over a 3σ threshold, where σ was taken from Table 2 in Belloche et al. (2019).

3.5 H₂ column densities from dust

Assuming that LTE conditions apply to the COMs, the rotational temperatures derived in Sect. 3.4 correspond to the kinetic temperature of the gas. Moreover, assuming that the gas is well coupled to the dust, the kinetic temperature of the gas also corresponds to that of the dust. Based on this, we computed again optical depth using Eq. (2), however, this time, we made use of the rotational temperatures derived in Sect. 3.4 and determined optical depth as a function of distance from Sgr B2 (N1) for both the continua at 1.3 and 3 mm. The profiles are shown in Fig. 8a. We used the temperature profile of C₂H₅OH because its population diagrams together with the temperature profile seem to be the most reliable amongst the COMs analysed here. The error bars correspond to an uncertainty that allows the dust temperature to differ by 20% from the gas temperature, which dominates over other uncertainties.

Based on the contribution of free-free emission to the 3 mm continuum at the position of Sgr B2 (N1) derived in Sect. 3.1, we estimated the remaining contribution at closest distance to Sgr B2 (N1) considered here (~0.2″, which is roughly half the average beam size of spectral window 0 of setup 5) to be ~16% and negligible at larger distances. The continuum at 1.3 mm has no significant contribution of free-free emission.

The results shown in Fig. 8a demonstrate again that the 3 mm continuum is less optically thick than the 1.3 mm continuum. Opacities are generally lower and the difference between the two continua is more pronounced to the west. The maximum distance from Sgr B2 (N1) denotes where the continuum is detected above 2σ. At positions N1S4 and N1S5, the continuum at 242 GHz drops below 1 σ, hence, we used an upper limit of 2σ at these positions in the following. At distances beyond 3.5″ (corresponding to positions N1S5-N1S7), the optical depth increases again, which can be associated with continuum source AN 20 (see Figs. 1 and 3), whose location coincides with these positions.

To the south, the profile for both frequencies slightly decreases at shorter distance to Sgr B2 (N1) between 0.6″ and 0.2″, which may be the result of an underestimation of the continuum level. The continuum at both frequencies corresponds to the baseline, which is subtracted from the spectra. At these short distances, line emission is detected in almost every channel making the identification of the true baseline level more difficult. We checked the already baseline-subtracted spectra (done by Belloche et al. 2019) at the closest distance to Sgr B2 (N1) and estimated a possibly remaining continuum level of at most 20 K that would lead to an increase of the current level by about 10%. Therefore, missing continuum emission cannot fully account for the lower optical depth at short distances at least at 99.2 GHz. Though we accounted for a possible difference between gas and dust temperature in the error bars, we may still underestimate the optical depth, hence the dust temperature, that is assumed to be the gas temperature, may be overestimated. The underestimation of optical depth would in turn lead to an underestimation of H₂ column densities to an unknown extent. Therefore, southbound distances to Sgr B2 (N1) smaller than 0.6″ are not considered in the following.

From the optical depth H₂ column densities N(H₂) can be derived using (4)

where is the mean molecular weight per hydrogen molecule, m_H the mass of an hydrogen atom, and κ_ν the dust mass opacity. The latter follows a power law given by: (5)

where χ = 100 is the standard gas-to-dust ratio and κ₀ is the dust mass absorption coefficient at frequency ν₀.

Assuming that H₂ column densities derived from the 1.3 mm and the 3 mm continuum yield the same result, the dust emissivity spectral index can be derived using the formalism introduced by Bonfand et al. (2017), which in our case leads up to (6)

where τ_99.2 and τ₂₄₂ are continuum optical depths at the respecive frequency. We show β as a function of distance from Sgr B2 (N1) to the south and west in Fig. 8b. The points at largest distance to the south corresponding to N1S5–N1S7 are not reliable as these positions are attributed to AN 20 and the contribution of free-free emission there is unknown. To the south, β has a value 0.4 at closest distances to Sgr B2 (N1) and increases to 1.3 at larger distances while to the west, β increases from roughly 0 up to a value of ~2.5. Based on these profiles, it is, therefore, difficult to assign a single β value that is able to describe the dust in both directions. Furthermore, β as well as k rely on the dust properties, which are generally highly uncertain. Therefore, we decided to follow the approach described in Bonfand et al. (2019), who derived κ as a function of wavelength for β = 1.2 (see their Fig. F.1) and compared their results to models by Ossenkopf & Henning (1994). Ultimately, they used β = 1.3, which fits best the model that includes no ice mantles and assumes a gas density of 10⁶ cm⁻³. Accordingly, they used κ₀ = 1.99 cm² g⁻¹ at V0 = 230 GHz (i.e. λ₀ = 1.3 mm). In the following we adopt these values for κ₀ and β and assume an uncertainty of ∆β = 0.5.

With optical depth and the dust mass opacity at hand, H₂ column densities can be derived using Eq. (4). The results are shown in Fig. 8c. H₂ column densities are listed in TableE.24, ogether with the continuum intensity and optical depth. In both directions we determined a maximum H₂ column density of ~10²⁵ cm⁻², which agrees well with the value of (1.3 ± 0.2) × 10²⁵ cm⁻² derived by Bonfand et al. (2017) for Sgr B2 (N1), based on the data of the EMoCA survey, and a minimum value of −2 × 10²³ cm⁻². However, the westbound profile decreases faster and at already shorter distances than the southbound one. At positions where H₂ column densities were determined along both directions, the westbound values are lower than the southbound ones by a factor of a few or even by roughly one order of magnitude. If free-free emission was indeed contributing to the continuum emission of AN20, H₂ column densities would be lower. Therefore, we consider the values at positions N1S5–N1S7 as upper limits. To the west, we added upper limits of 2σ.

3.6 H₂ column densities from C¹⁸O

Additionally, H₂ column densities were derived from CO, where we used the j = 1–0 rotational transition of its isotopologue ¹²C¹⁸O. Upper level column densities of this isotopologue were converted to those of the main one ¹²C¹⁶O by multiplying with the C¹⁶O/C¹⁸O isotopic ratio of 250 ± 30 (Henkel et al. 1994) and subsequently, to H₂ column densities by multiplying with 10⁴ (Rodríguez-Fernández et al. 2001). We used the opacity-corrected column densities of the Weeds model, for which we fixed the temperature and the velocity offset to that of ethanol. The resulting H₂ column density profiles are shown in Fig. 8c. Column densities of H₂ and C¹⁸O, and Weeds parameters are summarised in Table E.24. At distances of ≤1″, only upper limits were determined to the west as the line is too contaminated by emission from other species at the two closest positions³. However, at these positions, the baseline subtraction may be overestimated due to spectral confusion, such that the upper limit could well be higher. Therefore we also show lower limits. At positions N1S-1 and N1S column densities could not be computed because there is an absorption component absorbing the emission at the respective velocity. Between distances of 1.5″ and 3″ the southbound profiles of H₂ column densities derived from dust and C¹⁸O follow the same trend, with values from C¹⁸O being only slightly smaller. The westbound profiles show greater difference. The value estimated at N1W-1 is in agreement with the one derived from dust while at N1W, the H₂ column density estimated from C¹⁸O may be larger. At even larger distances from Sgr B2 (N1) the column densities derived from the dust are surprisingly smaller than the column densities derived from C¹⁸O by a factor 4–5 or even more, which cannot be explained by contamination alone. In both directions, we are able to go to farther distances with the profile from C¹⁸O emission.

3.7 COM abundances as a function of distance and temperature

Figure 9 shows COM abundances relative to CH₃OH as a function of distance from Sgr B2 (N1) to the south (panels a–b) and to the west (panels c–d). Figures 10a–d and 11 a–d show COM abundances relative to H₂ derived from dust and C¹⁸O 1–0 emissions, respectively, as a function of distance from Sgr B2 (N1) in both directions. For a better comparison, the abundance profiles are normalised to the respective value at 1.5″ distance to Sgr B2 (N1) as is shown in panels e–h, respectively. Given the resemblance of the H₂ column density profiles to the south, also the abundance profiles are similar, where possible to compare. Abundance profiles that were derived from dust continuum emission cover a distance range from 0.6″ to 3″ to the south (we refer to these profiles as S_D hereafter) and 0.5″ to ~2″ to the west (W_D hereafter). The range is shorter for W_D because of the lack of H₂ column density at farther distances. In contrast, abundance profiles that were derived by using C¹⁸O reach farther out to maximum distances of 4.5 to the south (SCO hereafter) and 3.5″ to the west (W_CO hereafter). However, at distances ≤1″, there are only lower and upper limits for W_CO or no values at all for S_CO. Moreover, with the cavity observed for W_CO, peak abundances for the COMs are more difficult to locate.

Figure 12 also shows COM abundances relative to H₂ derived from dust (panels a–e) and C¹⁸O 1–0 emissions (panels f–j), but as a function of rotation temperature using the temperatures derived in Sect. 3.4. The temperatures covered by the abundance profiles are in a range of ~100–300 K for S_D, well-above 100 K for Wd, and between ~80 and 170–200 K for S_CO and W_CO. Therefore, with the additional positions at larger distances for S_CO and W_CO, also abundances at lower temperatures can be analysed.

3.7.1 Methanol CH₃OH

Methanol abundances increase steeply at around 100K, that is between 3″ and 4″ distance from Sgr B2 (N1), to peak at 100–130 K corresponding to ~1.5″ and 3″. Then, the profiles decrease steadily towards higher temperatures and shorter distances for directions S_D, W_D, and S_CO. For W_CO, the profile remains constant or possibly shows a slight increase towards higher temperatures with a peak that could be above 150 K given the limits on abundance. With little variation, most probably due to the different observational setups used for the analysis, that is different angular resolution, ¹³CH₃OH follows the same trend as the main isotopologue.

3.7.2 Ethanol C₂H₅OH

Ethanol and methanol show similar behaviours as can be seen from Fig. 9, where the ethanol abundance profile relative to methanol is relatively flat. However, there is a slight decrease with increasing distance to the south, which is also indicated to the west. This reflects the fact that the abundance of ethanol relative to H₂ stays approximately constant with increasing temperature, while that of methanol decreases, as can be seen in Fig. 12. Abundances with respect to H₂ peak at 120–150 K for all directions (except for W_CO), which corresponds to distances of 1.5–2″ for S_D and W_D and 2.3″ for S_CO, which is closer to Sgr B2 (N1) and at slightly higher temperatures on average than for methanol. Abundances start decreasing at shorter distances from Sgr B2 (N1) and at higher temperatures than for CH₃OH.

3.7.3 Dimethyl ether CH₃OCH₃

The observed abundance profile as function of both distance and temperature shows similar behaviour compared to ethanol and methanol including a steep increase of abundance at 3–4″ distance to Sgr B2 (N1), corresponding to temperatures of ~100 K, followed by an abundance peak at 110–130 K, and a subsequent decrease with increasing temperature or shorter distance. However, while the increase of abundance at ~ 100 K is slightly less steep than for methanol, as can be seen in the profiles for S_CO and W_CO, the decrease towards higher temperatures along the west direction is steeper (cf. Fig. 9). The COM is not detected in the cavity of W_CO, however, it reappears at larger distances from Sgr B2 (N1).

3.7.4 Methyl formate CH₃OCHO

The abundance profile of CH₃OCHO closely resembles that of CH₃ OCH₃, maybe slightly shifted by about +10K. Abundances increase to peak at temperatures between 110 and 160 K corresponding to distances of 2.5–3″ for all, but WCO, for which it is ~1.5″. Similar to all other O-bearing COMs, abundance profiles then decrease towards higher temperatures.

3.7.5 Acetaldehyde CH₃CHO

In contrast to the other O-bearing COMs discussed above, the observed abundance profile of CH₃CHO shows a different behaviour as it continuously increases to a peak just below 300 K, which is the maximum temperature measured at closest distance to Sgr B2 (N1) for S_D, W_D, and W_CO (cf. Figs. 10–12). For S_CO, the maximum temperature is only 170 K due to missing data at positions closest to Sgr B2 (N1). We do not trace temperatures lower than 100 K, therefore, a conclusion on a possibly steeper increase similar to other O-bearing COMs cannot be drawn from the current data.

3.7.6 Vinyl cyanide C₂H₃CN

The observed abundance profile of C₂H₃CN shows an increasing behaviour towards shorter distance and higher temperature, similar to CH₃CHO, but steeper. Moreover, a difference is evident between the southbound and westbound profiles because to the south, the profile increases continuously while to the west, the increase is steeper between ~120–170 K or 1–2″ and flattens for higher temperatures and shorter distances. The location of the abundance peak shows some variance but may well be at highest temperatures and closest to Sgr B2 (N1) for all cases when considering all uncertainties. The different behaviours of the profiles could possibly be explained by an under- and overestimation of the line opacity to the west and south, respectively, since more transitions throughout all vibrational states, used to derive the population diagram of C₂H₃CN, are optically thick at closest distances to Sgr B2 (N1) compared to the other COMs, which can have an influence on the results of the population diagram. Similar to CH₃CHO, the abundance profiles only reliably go down to temperatures of > 100 K and, therefore, we are not able to observe a possible steep increase at these temperatures. And, similar to CH₃OCH₃, vinyl cyanide is not detected in the cavity of W_CO, however, it is observed at one more position at a larger distance.

3.7.7 Ethyl cyanide C₂H₅CN

The abundance profiles of C₂H₅CN show a similarly steep increase as the aforementioned O-bearing COMs at distances of 3–4″ from Sgr B2 (N1), which, for S_D and S_CO, corresponds to a temperature of around 100 K. For W_D and W_CO, the lack of H₂ column density and the cavity, respectively, prevent us from making a statement on the temperature to the west. Abundances then keep gently increasing to a peak at 150–170 K (1.5–2″ distance). Towards higher temperatures and shorter distances, the profile for W_D slightly decreases, while, for the others, the profiles seem to remain flat or to slightly increase. With this behaviour, C₂H₅CN is placed somewhere in between the results seen for C₂H₃CN and CH₃CHO and the other O-bearing COMs.

3.7.8 Methyl isocyanate CH₃NCO

Similar to CH₃CHO, we do not observe a steep increase of abundance for CH₃NCO because the COM is not detected at distances where the increase for other molecules is identified. The profiles do show a continuous increase to a peak at closest distances to Sgr B2 (N1). The same trend is indicated in the profile as function of temperature, however, the error bars on the measured temperatures are large. The temperature of the abundance peak is located at ~110–150 K.

3.7.9 Formamide NH₂CHO

Abundance profiles of NH₂CHO show a similarly steep increase as methanol, however, starting only at a distance of 2.5″ to Sgr B2 (N1), that is at much shorter distances than for other COMs. The temperature of this increase is uncertain, however, it seems to be above 100 K. The southbound abundance profiles of formamide show a plateau at the largest distances that is at roughly 100 K. The profiles peak at 120–140 K or ~1.5″ for S_D, S_CO, and W_D, and show a subsequent plateau or slight decrease.

4 Discussion

4.1 H₂ column densities

H₂ column densities were derived in two ways: from dust emission as well as from C¹⁸O 1–0 emission. While the H₂ column density profiles derived from both show only small differences to the south, the westbound profiles show larger differences at least at distances >1″, where H₂ column densities derived from dust are smaller by factors of a few than those from C¹⁸O. In Sect. 3.6 we concluded that contamination of the C¹⁸O intensity by other species cannot fully explain this difference. The conversion factors from CO to H₂ may have some greater uncertainties than considered here. Chemical models by Garrod et al. (2022) (hereafter G22) show that the typical CO abundance with respect to H₂ of 10⁻⁴ is only reached at temperatures of 100–150 K as the molecule co-desorbs with water from dust grain surfaces. Therefore, we may be underestimating this conversion factor at lower temperatures. However, this does not explain the discrepancy of the profiles to the west because temperatures lower than 100 K are reached in only a few cases and the discrepancy is only seen at temperatures >100K. CO abundances may be further enhanced at higher temperatures when more complex species are destroyed and leave behind CO as one of the final products.

Probably even higher uncertainties exist for the conversion from dust to H₂ due to the unknown dust properties. In Fig. 8b we show the dust emissivity spectral index β, which is directly linked to the dust properties and varies significantly between the south and west directions, but also along one direction. It is rather unlikely that the dust properties vary by this much in one source. Whether β is a constant, however, as is assumed in Fig. 8c, is not certain, either. Whether these uncertainties can explain the differences seen in the H₂ column density profiles to the west or whether environmental differences (e.g. outflow, accretion through filaments) may play a role remains unclear to now.

4.2 Segregation of O- and N-bearing COMs

The morphology of COM emission shown in Fig. 4 suggests a separation of COMs into two, maybe even three groups. Emissions of the O-bearing COMs CH₃OH, C₂H₅OH, CH₃OCHO, CH₃OCH₃, and, to some extent, CH₃CHO are extended and structured following the (dust) continuum emission, while those of the N-bearing COMs C₂H₅CN and C₂H₃CN are more compact and less structured. Morphologies of NH₂CHO and CH₃NCO are in between as these are compact, however, with some structure.

Many observations revealed segregation of O- and N-bearing COMs in other star-forming regions with a variety of explanations. Bisschop et al. (2007) found a segregation of COMs in terms of rotational temperature on the basis of unresolved single-dish observations of seven high-mass young stellar objects. They classified the COMs as either ‘hot’ or ‘cold’ species. In their classification, CH₃CHO (amongst others) is a cold species that traces maximum temperatures of <100K, while CH₃OH, C₂H₅OH, CH₃OCHO, NH₂CHO, C₂H₅CN, and HNCO are hot species because they trace temperatures of >100K. Although primarily, this is not a segregation of O- and N-bearing COMs, all species of the latter type are classified as hot species by Bisschop et al. (2007). This separation was similarly observed in Orion KL (Crockett et al. 2015) and, with a slightly deviating classification, in the hot corino around the low-mass protostar IRAS 16293-2422B (Jørgensen et al. 2018), where the latter study did only investigate O-bearing COMs. In these last two studies, differences between COMs were also observed in the morphology of the COM emission. This classification into hot and cold species was proposed to primarily arise from differences in the binding energy of the molecules. Cold species have low binding energies. Therefore, they can already thermally desorb at lower temperatures and their emissions are more widespread. Hot species desorb at higher temperatures due to higher binding energies and their emitting area is more compact around the protostar. Although this theory is supported by results of chemical models (Garrod 2013) it is not really confirmed observationally because the true desorption temperatures of COMs in interstellar environments are not known.

Deviations from this classification have been observed, for example in IRAS 16293–2422A (Manigand et al. 2020), where CH₃OH and CH₃OCHO, although being hot species, trace a more extended region. Moreover, most recent observations towards CygX-N30 do not reveal a significant difference in temperature between various COMs in general (van der Walt et al. 2021). Such a classification that depends on binding energies is not straightforward as their values are uncertain and vary depending on the dust composition. We discuss the role of binding energies in more detail in Sect. 4.7.

A temperature-dependent segregation of O- and N-bearing COMs can result from carbon-grain sublimation, which was proposed to occur inside the so-called soot line at T ≳ 300 K (van ’t Hoff et al. 2020). This mechanism would lead to an increase in the abundance of nitriles and hydrocarbons that add to the abundances that are already present due to thermal desorption at lower temperatures. Accordingly, this leads to the observation of N-bearing species at higher excitation temperatures with enhanced column densities and with a more compact morphology than O-bearing species. Therefore, when only regarding the morphology, where the emission of N-bearing COMs is more compactly distributed around the protostar, this mechanism may be able to explain the differences between the COMs observed in Sgr B2 (N1).

A segregation of O- and N-bearing COMs was also observed in the hot core of the massive protostar G328.2551–0.5321 (Csengeri et al. 2019). The observed morphologies of the two families of COMs are completely different. O-bearing COMs show two intensity peaks on either side of the protostar, while the emission of N-bearing COMs is more compact and spherically distributed around it. The authors concluded that abundances of O-bearing COMs are enhanced due to a non-thermal desorption process. They interpreted the two observed intensity peaks in the morphology as tracing the location of material falling onto a disk, thereby, inducing accretion shocks, which enhances the abundance of O-bearing COMs. In contrast, the morphology of N-bearing COMs follows the expectations for thermal desorption from dust grains. The morphology of O-bearing COMs in Sgr B2 (N1) does not present such a behaviour as there is no indication of two distinct intensity peaks on opposite sides of the protostar and at opposite velocity offsets from the source velocity that would imply the presence of a disk (cf. Fig. 4 and the peak velocity map in Fig. B.2a).

Results from most recent chemical models by G22 suggest a separation between O- and N-bearing COMs that is caused by their different main formation pathways on dust grains at low temperatures and in the gas phase, respectively. More details are discussed in Sect. 4.4 when these modelled abundance profiles are compared to our observed ones. Based on this comparison and the discussion on the temperature profiles below, we try to identify which of the aforementioned mechanisms may cause the segregation of O- and N-bearing COMs seen around Sgr B2 (N1).

4.3 Temperature profiles

The variation of the slopes of the rotation temperature profiles derived from various COMs is generally small. They span ranges from −0.6 to −0.8 for O-bearing COMs and from −0.4 to −0.6 for N-bearing COMs (except for NH₂CHO). In Sect. 3.4 we have already shown that our derived values lie in between the theoretical slopes expected for central heating through an envelope containing optically thin or thick dust, for which a range of dust emissivity indices β of 0.5–2 was assumed. Assuming β = 1.3, which we used to compute H₂ column densities in Sect. 3.5, the expected power-law indices would be −0.38 or −0.93 for optically thin and thick dust, respectively. Although the values slightly deviate from the observed power-law indices, our results suggest that the COMs in Sgr B2 (N1) along the two analysed directions trace the temperature structure of the collapsing envelope that is heated by the central (proto)star(s).

Temperature profiles have been derived for 22 massive cores as part of the CORE project by Gieser et al. (2021) based on observations of H₂CO and CH₃CN. The slopes span a range from −0.1 to −0.6 with an average value of −(0.4 ± 0.1) excluding three outliers with slopes of −1 to −1.5. With the CORE-extension sample (Gieser et al. 2022), temperature profiles of another ten cores were shown and slopes of −0.1 to −1 reported, where a fit was only applied for those cores whose profiles were resolved and that did not show flat profiles.

An observed temperature profile with a slope of −0.77 was reported for the hot core G31.41+0.31 (Beltrán et al. 2018) and supported by models (Osorio et al. 2009). Models by Nomura & Millar (2004) suggest steeper profiles at similar distances considered here for higher H₂ column densities, which correspond to higher dust optical depths. The modelled temperature profile for Sgr B2 (N2) shows a steepening from far distances to closer distances to the protostar, spanning a range of slopes for the optically thin regime to −0.8 for an optically thicker regime (Bonfand et al. 2019).

Based on this discussion, it seems that, for the scales traced with the ReMoCA survey, the desorption process of COMs in Sgr B2 (N1) is thermally driven, in other words, there is no clear sign in the temperature profiles that would indicate shock chemistry induced by the outflow or accretion shocks, at least not along the two analysed directions. A more detailed discussion on the differentiation between thermal and non-thermal desorption is done in Sect. 4.5, also considering the abundance profiles. In addition to this result, we concluded in Sect. 3.4 that the power-law indices of the temperature profiles are more consistent with expected values for an optically thick dust continuum.

4.4 Abundance profiles

We focussed the discussion on the abundance profiles on a comparison with most recent astrochemical models performed by G22. The chemistry of the G22 models includes new methods for simulating non-diffusive reaction mechanisms, but the general physical and chemical setup is based on earlier works (Garrod 2008, 2013; Garrod et al. 2017). This setup includes two stages: a cold collapse phase (stage 1) and a subsequent warm-up phase (stage 2). In stage 1 the density increases from 3 × 10³ to 2 × 10⁸ cm⁻³ and the dust temperature decreases from ~15 K to 8 K while the gas temperature is kept constant at a value of 10 K on a timescale of ≲10⁶ yr. In stage 2 the final density of stage 1 is adopted and kept constant. Gas and dust temperatures increase simultaneously as it is assumed that they are well coupled during this stage. Three different timescales of this temperature rise are considered separately: 10⁶ yr (slow warm-up), 2 × 10⁵ yr (medium warm-up), and 4 × 10⁴ yr (fast warm-up), which corresponds to the time it takes to reach 200 K, respectively. The models then continue to a maximum temperature of 400 K. In both stages the chemistry takes into account gas-phase, grain/ice-surface, and bulk-ice chemistry, which are all coupled by various thermal and non-thermal processes. Amongst these is the interaction with cosmic rays (CRs) under all conditions, where the ionisation rate is kept constant at the standard value of ζ = 1.3 × 10⁻¹⁷ s⁻¹. The most recent model used in G22, however, does include a number of changes compared to the earlier models. We refer the reader to the article for a detailed description of new adjustments and their influence on the COM abundances. Some of the new implementations will, however, be mentioned in the following as they play a crucial role in explaining our observations.

In general, our results are overall best described by the model of the slow warm-up phase, which was previously also found to best explain the observed abundances in Sgr B2 (N2) (G22). To compare the modelled results to our observations and, based on that, make implications on the main formation and destruction pathways of COMs, we created a diagram similar to Fig. 15 of G22, where they show the ratio of peak COM abundances relative to the peak abundance of CH₃OH. The result is shown with thick bars in Fig. 13, where on the left y axis we plot (7)

where is the peak COM abundance and is the peak abundance of CH₃ OH. The observed peak abundances with respect to H₂ are extracted from Fig. 12. The modelled peak abundance ratios are taken from Table 17 in G22. All values are listed together with the corresponding peak-abundance temperature in Table 3. In addition, we show a comparison of modelled and observed peak abundances ^s without normalising to CH₃OH (thin bars, right y axis). The modelled peak abundances are taken from Table 16 in G22 and multiplied by a factor 2 to convert to abundances with respect to H₂ (from total H).

Besides peak abundances, the behaviours of the profiles were compared to the model predictions. In particular, we used Figs. 12, 20, and 21 from G22 that present results of the cold and subsequent slow warm-up phase. All three show the time evolution of the COM abundances that is also linked to the temperature increase due to the evolution of the protostar. Figure 12 of G22 presents the abundance profile in the solid and gas phase while Figs. 20–21 of G22 (see also their Figs. 13–14 to find responsible chemical reactions) show the rate at which a COM is dominantly formed or destroyed at each point of the evolution.

4.4.1 Methanol CH₃OH

Methanol is the most abundant COM in the observation as well as the model with peak abundances that differ by factors of a few only (cf. Table 3 and thin bars in Fig. 13). According to the model, CH₃OH is predominately formed in the bulk ice before the onset of the warm-up as seen in Fig. 20 of G22. After codesorption with water, starting at ~120 K and finishing at 166 K, the molecule is destroyed in the gas phase, mainly through proton transfer from H₃O⁺. This leads to the drop of gas-phase abundance seen towards higher temperatures right after the peak at 166 K in the model. Except for the value of peak abundance that is underestimated by the model (except for W_CO), however only by factors of a few, and temperature of this peak that is higher in the model by some tens of Kelvin (see Table 3 and Fig. 13), the model is in good agreement with the observations (cf. Sect. 3.7.1). Therefore, the CH₃OH abundance in Sgr B2 (N1) is most likely enhanced in the gas phase due to thermal desorption at ~100 K supported by the increase that seems fairly sudden (see also Sect. 4.5).

The similar behaviour of abundances of the main and ¹³C isotopologues implies that similar formation and destruction mechanisms take place for both species. This also indicates that our model of the CH₃OH emission accounted well for potential optical depth effects. Considering only the abundance plateau, that is distances of ≲ 2″ to Sgr B2 (N1), we find an observed median ¹²C/¹³C isotopic ratio of 22 and 24 to the south and west, respectively, which is consistent with the value of 25 obtained for methanol and ethanol in Sgr B2 (N2) with the EMoCA survey (Müller et al. 2016) and agrees with expected values for the Galactic centre region.

4.4.2 Ethanol C₂H₅OH

The bulk of C₂H₅OH in the model is produced in the cold phase on dust grains and is effectively destroyed after desorption into the gas phase mainly via proton addition by protonated molecules such as H₃O⁺, or HCO⁺, which is followed by electron recombination (cf. Fig. 20 of G22). Similar to methanol, some fraction of the protonated molecule does not recombine with an electron, instead, it transfers the proton to NH₃ and goes back to unprotonated ethanol. The observed slight increase of ethanol abundances relative to methanol beyond the abundance peak (cf. Sect. 3.7.2) suggests that ethanol is less effectively destroyed than methanol after desorption to the gas phase, which is not accounted for by the current model.

Observed and modelled values of peak abundance differ by a factor 2.5 at most, except for W_CO (factor 10). The observed abundance ratios with respect to methanol shown in Fig. 13 are overproduced by the model by factors 3–5 in all cases. The chemical network of G22 may indeed lack several grain-surface reactions that affect the rate of ethanol production; in particular, reactions between atomic H and the set of C₂H_X species generally result in H addition while H abstraction by atomic H to produce H₂ and a less hydrogen-rich hydrocarbon is not included. Jin et al. (in prep.) have made such adjustments to the network, which could result in a moderate reduction in ethanol production efficiency on grain surfaces at low temperatures, for example via C₂H₅ + OH → C₂H₅OH.

4.4.3 Dimethyl ether CH₃OCH₃

In the model the bulk of CH₃OCH₃ is produced on dust grains in the cold collapse phase as well as on the surface during the warm-up phase and co-desorbs with water at T > 120 K. In the gas phase, at temperatures >120K, CH₃OCH₃ is additionally produced via proton transfer from to NH₃. This is an efficient formation pathway because the protonated dimethyl ether is the product of the reaction between two abundant reactants: methanol and protonated methanol. Eventually, this leads to the abundance peak of CH₃OCH₃ at slightly higher temperatures of 200 K and a flat profile as temperature increases (cf. Fig. 12 of G22). With this the modelled profile differs considerably from the observations (cf. Sect. 3.7.3).

Observed and modelled peak abundances differ by factors smaller than 2 for W_CO and up to ~8 for W_D, with S_D and S_CO in between (cf. Table 3). A similar behaviour of peak abundances between observations and model is seen for methanol, therefore, the observed ratio of both COMs is remarkably comparable to the modelled one in all cases, with differences less than a factor 2 (cf. Fig. 13). In summary, while the model succeeds in reproducing the observed peak abundance of dimethyl ether with respect to methanol, it seems that the destruction of this molecule in the gas phase is more efficient in Sgr B2 (N1) than in the model beyond the position of peak abundance at higher temperatures. Whether that indicates a destruction channel missing in the chemical network of the model or whether this is a result of any geometrical or physical conditions not caught by the model remains uncertain. It is likely that the regions closer to the centre of Sgr B2 (N1) have, in addition to higher temperatures, also higher densities, in which case the destruction may be accelerated. Such an effect is not considered by the model as the density is fixed during the warm-up. However, this would reduce the discrepancy between the observations and the model only if the destruction of dimethyl ether would be more accelerated than that of methanol.

4.4.4 Methyl formate CH₃OCHO

Similar to the aforementioned O-bearing COMs, methyl formate is predominantly produced on dust grains in the cold phase as well as during the warm-up in the model and desorbs into the gas phase as soon as uncovered from water at ≲166 K (cf. Fig. 20 of G22). Moreover, CH₃OCHO is efficiently produced in the gas phase at temperatures of water desorption via oxygenation of CH₃OCH₂, which was primarily sourced from CH₃OCH₃. This leads to an abundance peak at a higher temperature than for the other COMs. At T > 200 K, Fig. 20 of G22 suggests some destruction of the molecule, which is only minor and does not lead to a drop in the gas-phase abundance profile. Similar to CH₃OCH₃, the observed values of peak abundance agree well with the model for W_CO and are higher for S_CO, S_D, and W_D by factors 2–4 up to an order of magnitude (cf. Table 3). However, when normalised to methanol the observations and the model agree again more or less within the error bars (cf. Fig. 13). The observed decrease in abundance towards higher temperatures (cf. Sect. 3.7.4), which is similar to the other O-bearing COMs, is not reproduced by the model and may demand a more efficient destruction rate of the molecule. Similar to CH₃OCH₃, higher densities closer to Sgr B2 (N1), not taken into account by the model, may accelerate the destruction process.

4.4.5 Acetaldehyde CH₃CHO

According to the model (cf. Fig. 20 of G22), only a minor fraction of CH₃CHO is produced on dust grains in the cold phase and during the warm-up phase, and co-desorbs into the gas phase with water. A significant amount is formed in the gas phase at temperatures of ≳150 K via the oxygenation of C₂H₅. This leads to a continuously increasing gas-phase abundance profile in the model, which agrees with the observed results for CH₃CHO (cf. Sect. 3.7.5). Peak abundances to the south agree well with the model predictions, while those to the west are overestimated by the model by factors 5 and 10 (cf. Table 3). When normalised to CH₃OH, the model overestimates the abundance ratio by factors 5–10 for all directions (cf. Fig. 13). In the model the acetaldehyde peak abundance and, in turn, the ratio to methanol are sensitive to the warm-up timescale, where the ratio is higher by a factor 6.4 for the slow than for the fast warm-up (cf. Tables 16 and 18 in G22). Therefore, the overestimation of the observed ratio by the model may be an indication that the warm-up in Sgr B2 (N1) proceeds faster than predicted for the slow warm-up model to which we are comparing here. However, for all other COMs, except for C₂H₅OH, the difference between model and observations is slightly larger when assuming the fast warm-up.

4.4.6 Vinyl cyanide C₂H₃CN

As can be seen in Fig. 21 of G22, there are two main formation phases of C₂H₃CN in the model. Some formation happens on the dust grains before the warm-up phase, however, the bulk of the molecule is produced in the gas phase at temperatures higher than 160 K, predominantly through the reaction of C₂H₄ and CN. This leads to a continuous increase of abundances in the model and could explain the increase seen in the observations (cf. Sect. 3.7.6). However, the values of observed peak abundance are underestimated by the model by a factor 2 for S_CO up to more than an order of magnitude for W_D with S_CO and W_CO in between (cf. Table 3). This discrepancy is also seen in the abundance ratios with respect to methanol, that is, it is underestimated by factors 6–10 in the model for all but S_CO, for which the ratio is overestimated by a factor 4 (cf. Fig. 13). G22 mention that the model tends to underestimate abundances of N-bearing COMs including C₂H₃CN, which they attribute to a possible overproduction of HC₃N in the model. They propose that this could be counteracted if HC₃N was hydrogenated on grain surfaces at early stages to form C₂H₃CN and C₂H₅CN, eventually.

4.4.7 Ethyl cyanide C₂H₅CN

Ethyl cyanide is exclusively produced on dust grains in the model, partially during the warm-up phase, but mainly in the cold phase (cf. Fig. 21 of G22). As soon as the molecule arrives in the gas phase after co-desorption with water, it is efficiently destroyed via proton transfer from H₃O⁺ leading to a drop in abundance at high temperatures. However, some of the protonated ethyl cyanide goes back to the unprotonated form by transferring the extra proton to NH₃. This behaviour at high temperatures differs significantly from the observations (cf. Sect. 3.7.7).

The observed steeper increase of abundance around 100K may point to thermal desorption, however, peak abundances are only reached at much higher temperatures suggesting an increase of abundance in the gas phase. Although there currently is no efficient gas-phase formation route for C₂H₅CN included in the model, G22 discussed that the reaction of and CH₃CN again leading to C₂H₅CNH⁺ (see also McEwan et al. 1989) could be efficient in increasing the ethyl cyanide abundance at T > 100 K, when the protonated species transfers the extra proton to NH₃.

The observed values of peak abundance are larger than in the model by factors of a few for all cases, except for W_D, for which abundances differ by more than an order of magnitude (cf. Table 3). To the south, the ratio with respect to methanol does, however, agree well with what is expected from the model, while an underestimation by a factor of a few is still evident to the west (cf. Fig. 13). Including the above-mentioned additional gas-phase reaction in the model would probably be able to at least partially counteract the heavy decrease in gas-phase abundance seen in the model and may even somewhat increase the peak abundance to better match the observations. Additionally, there may be another formation channel on dust-grains via multiple hydrogenation of HC₃N as described for C₂H₃CN.

Vinyl and ethyl cyanide are often mentioned together as they share a chemical link. However, there is no such strong link in the new model of G22 compared to former studies (Garrod et al. 2017). Previously, a large fraction of the C₂H₃CN gas-phase abundance was produced from C₂H₅CNH⁺, which, in turn, was sourced from ethyl cyanide, leading to decreasing abundances of C₂H₅CN with increasing temperature in the gas phase. In the new model, the gas-phase reaction mentioned in Sect. 4.4.6 dominates the formation of C₂H₃CN and weakens the gas-phase relationship of the two COMs (G22).

4.4.8 Methyl isocyanate CH₃NCO

According to the model, CH₃NCO is exclusively produced on dust grains mainly during the warm-up phase through the reaction CH₃ +OCN → CH₃NCO (Belloche et al. 2017). Subsequently, a fraction is already destroyed in the grain mantle, where it is hydrogenated to eventually form CH₃NHCHO, a molecule that was recently identified in the interstellar medium (Belloche et al. 2017, 2019). The other fraction desorbs to the gas phase, where it reacts with H₃O⁺ resulting in further decrease in abundance (cf. Fig. D.3). Therefore, we would expect similar behaviour of the abundance profile as, for example for C₂H₅OH, for which abundances peak right after the molecule desorbs and decrease significantly towards higher temperatures. If that were the case, it would disagree with the observed abundance profile of CH₃NCO (cf. Sect. 3.7.8).

Moreover, the model underestimates the observed peak abundances by 2–3 orders of magnitude (cf. Fig. 13), which is also the case for the abundance ratios with respect to methanol. G22 argue that this may partly be explained by uncertainties in the activation barriers of reactions occurring on the grain surface. However, the observed trend of the abundance profile may additionally suggest that CH₃NCO is also produced in the gas phase. Halfen et al. (2015) proposed that the reaction of HNCO with CH₃ would be able to efficiently produce CH₃NCO in the gas phase, which is supported by later studies targeting low-mass protostars (Martín-Doménech et al. 2017; Quénard et al. 2018). However, as Halfen et al. (2015) noted, the CH₃ + HNCO reaction that they proposed could be endothermic, and this seems to be confirmed by the calculations of Majumdar et al. (2018). The latter authors proposed alternative formation mechanisms for the grain-surface production of CH₃NCO. These included a barrierless reaction between atomic N and the CH₃CO radical, and the reaction of H with HCN that is trapped in a van der Waals complex with surface CO. In the latter case, in spite of a barrier to hydrogenation of HCN, the resultant product, H₂CN, would have sufficient energy to overcome the barrier to its own reaction with CO to produce CH₂NCO. This radical would then be hydrogenated to methyl isocyanate. The protostellar chemistry model presented by Majumdar et al. (2018) indicates that their proposed mechanisms can achieve gas-phase abundances of the order of 10⁻⁷ with respect to H₂, following desorption of the ice mantles; these abundances are in line with some of our observed values. It is unclear how the non-diffusive chemistry included in the G22 model might influence the efficiency of mechanisms proposed by Majumdar et al. (2018). Another alternative mechanism for grain-surface production of CH₃NCO, proposed by Vávra et al. (2022), would be a reaction between HNCO and the diradical methylene (CH₂), which is formed during the course of CH₄ production on dust-grain surfaces, and may also be a photoproduct of methane in the bulk ice. Whatever the mechanism, the lack of an efficient gas-phase process to form CH₃NCO would indicate that surface/ice chemistry is at work.

4.4.9 Formamide NH₂CHO

According to the model, NH₂CHO is dominantly produced on dust grains in the cold phase and during the warm-up phase (cf. Fig. 21 of G22). These production mechanisms continue as NH₂CHO starts to co-desorb with water at T ≳ 120 K and moreover, its abundance is enhanced by hydrogenation of NH₂CO when this radical is uncovered as water desorbs. Also, gas-phase reactions start to produce some NH₂CHO at these temperatures. However, gas-phase production through the reaction of NH₂ and H₂CO (Barone et al. 2015) is responsible only for around 9% of total production in the G22 model. Despite the many formation channels of this COM, the model predicts that it is efficiently destroyed via protonation followed by recombination, which is in disagreement with the observed abundance profile (cf. Sect. 3.7.9).

Also for this N(+O)-bearing COM, the observed peak abundance is higher than the modelled one by factors of a few to the west and by more than an order of magnitude to the south (cf. Table 3). Ratios of abundances with respect to methanol are underestimated by the model by factors 3–7. So far, it is uncertain what causes the difference between model and observations. Based on the observed abundance profiles and in comparison with other COMs, we may expect both thermal desorption at ~100 K, which, however, seems to happen at significantly shorter projected distances than for other COMs, and formation in the gas phase at higher temperatures as also predicted by the model. Because there is no indication for a significant drop in the observed abundances with increasing temperature there may exist an additional supply of NH₂CHO or the molecule may be less efficiently destroyed than in the model or both.

4.5 Resolved desorption of COMs in Sgr B2 (N1)

From Sect. 4.3 we concluded that the temperature profiles derived from the COMs reveal the gradient that is expected from heating of an envelope with optically thick dust by a protostar. This is true for all COMs be they predicted to mainly form in the gas phase such as CH₃CHO or in the solid phase (and then desorb) such as CH₃OH. However, the high angular resolution of the ReMoCA survey allowed us to resolve the abundance profiles of the COMs and to reveal their differences. This allows us to draw conclusions on the prevalent desorption process.

4.5.1 Thermal co-desorption with water

In the case of thermal desorption, we expect a sudden rise in column density and abundance of a COM at the location of desorption, which can either happen at the co-desorption temperature of water and COMs or at a specific desorption temperature that depends on the COM's binding energy to the grain surface or to itself. Perhaps the greatest change implemented to the current model used in G22 compared to the earlier studies (Garrod 2013) is that diffusion in the bulk ice as well as from the bulk ice to the surface layers regardless of the temperature is prohibited for all species except H and H₂. This entails that COMs formed in the bulk ice cannot diffuse to the surface from where they could thermally desorb depending on their binding energy. In the new non-diffusive model of G22 the COMs are trapped in the water ice and the bulk of the COMs can only desorb when water does, which happens at 120–170 K in the model. Based on Fig. 12, COMs that present such an abundance profile with a steep increase at a given temperature in SgrB2 (N1) and, thereby, are in agreement with the model are CH₃OH, C₂H₅OH, NH₂CHO, and C₂H₅CN, and tentatively, CH₃OCH₃ and CH₃OCHO. However, instead of a temperature >120K as predicted by the model, abundances of these species already increase at temperatures ~100K. Provided that this behaviour can be associated with their thermal co-desorption with water, then this process seems to start at these low temperatures of about 100 K and to already terminate at ~ 100–150 K, corresponding to the peak-abundance temperature of the above-mentioned species (see Fig. 12). Because the binding energy of water is uncertain as it depends on the precise ice structure, the value in the model could well be lower, leading to a lower desorption temperature of water that would be in better agreement with the observations. Jin et al. (in prep.), who use the model of G22, have in fact recently revised the value downwards and achieved a better agreement between their model and observations of Orion KL.

Though all O-bearing COMs except CH₃CHO present an abundance increase at ~100 K, the column densities of dimethyl ether and methyl formate do not increase as steeply as those of methanol and ethanol (cf. Fig. 7). In the model, gas-phase formation of the two starts as soon as water starts desorbing, which may explain the observed behaviour. Besides, CH₃OCH₃ and CH₃OCHO have lower binding energies than CH₃OH and C₂H₅OH amongst other COMs and water (cf. Table 4), which led to thermal desorption at lower temperatures in earlier models (e.g. Garrod 2013). However, if thermal desorption took place depending on binding energies, we would still expect a steep increase of column density and abundance only at lower temperatures for CH₃OCH₃ and CH₃OCHO, which is not evident in the column density and abundance profiles. However, the observed profiles could also be the result of a two-step thermal desorption process which we elaborate on further in Sects. 4.5.3 and 4.5.4.

The abundance profile of ethyl cyanide increases more steeply around 100 K than at higher temperatures, however, not as steeply as for methanol. This may indicate that only some fraction is released from dust grains at around 100 K, which would be in agreement with desorption either along with water or depending on the binding energy, given its similar values of binding energy as methanol and ethanol (cf. Table 4). Formamide abundances increase steeply, however, only at shorter distances to SgrB2 (N1) than methanol, that is potentially, at higher temperatures.

A steep increase is not observed for CH₃CHO and C₂H₃CN, which is consistent with the expectation of the model, according to which they are mainly formed in the gas phase. Although a fraction is produced on dust grains and released during water desorption in the model of G22, the amount may not be significant enough to be detected in the observed abundance profiles. The same would apply if desorption depended on the binding energy. Temperatures derived from CH₃NCO have higher uncertainties, nonetheless, the abundance profiles of this COM are similar to those of CH₃CHO suggesting a predominant gas-phase formation. Moreover, although the binding energy of CH₃NCO could be as high as 6500 K, thermal desorption at higher temperatures seems unlikely given the only mild increase of abundance with increasing temperatures.

In summary, the behaviour of the observed column density and abundance profiles for COMs that are expected to (partially) form on dust grain surfaces and to desorb subsequently suggests that co-desorption with water is likely to take place. Together with the overall good agreement of the model by G22 with our observations, precisely, because the co-desorption with water was implemented amongst other revisions, this process of thermal co-desorption seems to be the prevalent one in Sgr B2 (N1). Mottram et al. (2020) arrived at a similar conclusion for the hot core W3 IRS 4 based on observations with the Northern Extended Millimeter Array (NOEMA). The authors derived CH₃OH and CH₃CN abundances relative to H₂ as a function of temperature that reveal an increase at 80–100 K. However, the low-temperature regime of their profiles consists of measurements done towards two continuum peaks and an outflow position in the vicinity of the hot core rather than a continuous sampling along a certain direction starting from the hot core. Therefore, the evidence for the desorption process of these COMs is less obvious in this source.

Our interpretation of co-desorption of COMs with water also leads us to exclude that the observed segregation of COMs is based on their binding energies as it was proposed for the classification into hot and cold species as introduced in Sect. 4.2. We observe a small difference between O- and N-bearing COMs in the power law indices of the temperature profiles, where the latter have shallower slopes than the former and, therefore, do not trace as high temperatures on average. Naively, for this situation, we would infer that, when observed along the same line of sight,

N-bearing (or N+O-bearing) COMs show lower temperatures because they are destroyed in the hotter regions that are traced by the O-bearing COMs. This is rather the opposite of what is predicted by the chemical models of G22. However, we cannot exclude this kind of behaviour given that the model does not take into account density changes and neither the model nor the observations consider the three-dimensional (3D) structure of the hot core. There also exists a rough dependence of the power-law indices on the binding energy of the COMs as shown in Fig. 14, where N-bearing (or N+O-bearing) COMs have higher binding energies on average and, thus, can stick to the grain surface until higher temperatures are reached. Why this would lead to N-bearing (or N+O-bearing) COMs tracing lower temperatures is unclear to us.

4.5.2 Transition from non-thermal to thermal desorption

Assuming that the increase in abundance at ~100 K represents the thermal co-desorption of COMs and water into the gas phase, non-zero abundance values at lower temperature, such as the value of 10⁻⁸ at 80 K for CH₃OH or at -55 K for ¹³CH₃OH in Fig. 12f, the value −10⁻⁹ at 55 K for C₂H₅CN in panel (i) of the same figure, and low-temperature values around 10⁻⁹ for NH₂CHO in panel j, would be the consequence of another desorption process. One possibility would be non-thermal desorption, which would be able to enhance COM abundances at temperatures lower than ~100K. The cold-phase chemistry as described in detail by Jin & Garrod (2020) is included in the model of G22, and this includes both chemical desorption and UV-driven desorption of surface molecules. The latter mechanism tends to show only limited ability to desorb molecules at visual extinction values greater than around unity, under the assumption of the standard interstellar radiation field and CR ionisation rate. Chemical desorption (such as desorption induced by the release of chemical energy upon formation of a molecule; see Garrod et al. 2007), on the other hand, is able to drive substantial COM desorption at low temperatures. However, strong desorption occurs during the periods of strongest ice production; at later times in the models, prior to thermal desorption, abundances of COMs relative to H in the gas phase remain below a value of 10⁻¹¹, which is at least two orders of magnitude lower than the observed values that we suspect may indicate non-thermal desorption of COMs.

However, with its location in the Galactic centre, SgrB2 (N) resides in a violent environment with enhanced turbulence and enhanced CR fluxes that influence the star-formation process. The enhanced CR flux in Sgr B2 (N) (Bonfand et al. 2019) can work in both directions. CRs and the secondary UV field that they provoke can support formation and non-thermal desorption of some COMs, while they destroy others when upon collision with the dust grains. Non-thermal desorption due to a shock passing and turbulence is most probably the reason for the complex chemistry observed in G+0.693−0.027, a source not far from Sgr B2 (N) without any signposts of active star formation (e.g. Zeng et al. 2018, 2020) although a recent study of this object proposes that it may be on the verge of star formation (Colzi et al. 2022). Shocks are proposed to be induced through a cloud-cloud collision. Multiple studies suggest that these interactions between clouds not only happen in this source but in Sgr B2 in general (Hasegawa et al. 1994; Sato et al. 2000; Armijos-Abendaño et al. 2020; Zeng et al. 2020) and that these may even have triggered the star formation process. Therefore, besides enhanced CR flux, enhanced turbulence could increase the abundance of COMs via non-thermal desorption in the colder gas phase of Sgr B2 (N1). Specifically for this hot core, shocks may also arise from accretion because along the directions analysed here, filaments have been located through which accretion towards Sgr B2 (N1) may happen (Schwörer et al. 2019). However, because we do not see any evidence for accretion shocks in the morphology (as e.g. Csengeri et al. 2019, did in G328.2551−0.5321), we excluded this possibility. Moreover, although we avoided the outflow axes for the analysis in this work, an influence of the outflow of Sgr B2 (N1) can probably not be excluded a priori, especially at shortest distances to the hot core’s centre. In this case, however, we would expect a simultaneous increase of temperature in the shocked gas. Because the temperature profiles do not show any evidence for this, we expect the influence of the outflow to also be minor if existent at all along the directions analysed in this work.

4.5.3 Thermal desorption in two steps

Thermal desorption may also take place in two steps. Figure 8 in G22 shows that, although water is still abundant, CO is the main constituent of the outermost ice layers at the end of the cold collapse phase. Therefore, these outermost ice layers can possibly desorb at much lower temperatures (20–30 K) given the low binding energy of CO. If some COMs are also abundant in these layers, their binding energies will be reduced compared to the value that they have for binding to pure water ice. As a result, these COMs may be able to desorb according to their reduced binding energy at temperatures of <100K. If, after desorption of these CO-rich ice layers, the remaining ice were still mostly CO-related COMs, then the ice would be less polar and binding would presumably be weaker, still allowing for desorption at lower temperatures. Based on Fig. 9 of G22, COMs that seem to be present in these outer ice layers are CH₃OH, C₂H₅OH, CH₃OCH₃, CH₃OCHO, CH₃CHO, but also C₂H₅CN, which is not CO-related. Hence, thermal desorption due to reduced binding energies may not only apply to O-bearing COMs. This process may be able to explain the non-zero abundances at low temperatures for CH₃OH and C₂H₅CN as well as the shallower increase for CH₃OCHO and CH₃OCH₃. The slightly different behaviour shown by methyl formate and dimethyl ether may be due to their somewhat lower binding energies (compared with the other molecules mentioned above), even on water ice. Strong trapping of COMs by H₂O in this picture would then manifest once the upper layers, which are rich in CO, had desorbed along with some COMs. Some COMs would still be present in the more water-rich ice below, to be released at higher temperatures when water desorbs.

4.5.4 Gas-phase production

Gas-phase formation may also present an option to enhance COM abundances at low temperatures. Gas-phase reactions for CH₃OCH₃ and CH₃OCHO may be able to explain their overall shallower increase in abundance at around 100 K. However, it is questionable whether gas-phase formation, for example for NH₂CHO, can explain the non-zero abundance values at low temperatures because, although included in the model, the abundances prior to thermal desorption remain lower than the observed values at low temperatures. This may indicate that gas-phase formation is simply not efficient enough to reproduce the observed abundances or that the reactants are not sufficiently abundant, which is also plausible given the low temperatures, or both. Moreover, for methanol, there is currently no efficient gas-phase formation route that would explain the COM’s non-zero abundances at low temperatures. Eventually, we would exclude gas-phase reactions as the main reason for the non-zero abundances at low temperatures.

4.6 Implications for COM segregation

Taking into account all observational uncertainties and considering the simplicity of the model of G22 in terms of dynamics and geometry, it is striking how well the model can explain the majority of observed results. Moreover, for some of the differences, there may already exist potential explanations that remain to be proven, however. There are plausible reactions that, when added to the chemical network, may already be able to explain differences seen for COMs such as CH₃NCO and C₂H₅CN. Furthermore, although our results are best reproduced under the assumption of a slow warm-up, this may not be the case for Sgr B2 (N1) in reality as perhaps indicated by results from CH₃CHO. According to G22, similar results are possibly obtained for a faster warm-up with enhanced CR flux because the main difference between all three warm-up phases is the exposure time to CRs and their induced secondary UV field, and because CRs present one way of destruction of some COMs on the grain surface as well as in the gas phase. Bonfand et al. (2019) found that a cosmic ray ionisation rate of 50 times that of the standard value best described the COM abundances in the hot cores Sgr B2 (N2-N5) derived on the basis of the lower-angular-resolution survey EMoCA. However, although similar results may be expected for a slow warm-up and a faster warm-up with enhanced CR flux, we can only know for sure if the model is run with these conditions. As already mentioned above, geometry and changes of the density in the warm-up phase are not treated by the current model. On the other hand, our observational results do only consider projected distances and not the underlying 3D structure (e.g. filaments and the outflow).

In Fig. 15a we summarise the three different morphologies of COM emission regions that we identified based on the LVINE maps shown in Fig. 4: (a) extended and structured (dark blue, O-bearing COMs), (b) more compact and uniform (pink, N-bearing COMs, HC₃N, and HNCO), and (c) compact and structured (light blue, CH₃CHO, CH₃NCO, NH₂CHO, NH₂CH₂CN). We also observed differences in the behaviours of the abundance profiles of the various COMs (see Sect. 3.7). Figure 15b shows an overview of the trends seen in the abundance profiles as a function of temperature (taken from Fig. 12). The comparison with model predictions of G22, done for each COM separately in Sect. 4.4, indicates that the observed differences between COM abundance profiles trace back to the COMs’ desorption processes at temperatures around 100 K (thermal co-desorption with H₂O) and at lower temperatures (non-thermal or thermal desorption) and their individual formation and destruction pathways at higher temperatures.

Although the differences seen in the COM abundance profiles do not simply match those seen in the morphology of COM emission, the above reasoning may also be able to explain the morphology to some extent. The extended and structured morphology of the emission regions for the four O-bearing COMs that are mainly formed on dust-grains closely follows the dust continuum emission, suggesting a close relation of the dust and these COMs. Emission from the N-bearing (or N+O-bearing) COMs and CH₃CHO is more compactly distributed around the protostar, where higher temperatures, which are required for the gas-phase reactions to become efficient or to take place at all, are expected and observed. Further differences amongst the latter group may be attributed to a mix of solid- and gas-phase formation with different efficiencies. However, whether the N-bearing (or N+O-bearing) molecules that are not analysed in detail follow this classification cannot be concluded from their morphology alone. For example, CH₃CN and HNCO show a similar morphology as ethyl or vinyl cyanide (cf. Fig. 4) and, according to the chemical model, CH₃CN is indeed efficiently produced in the gas phase, while HNCO seems to rather be formed on dust grains and destroyed when arriving in the gas phase (see Fig. 21 of G22).

Based on our observational results, we do not identify an influence on the COM temperature and abundance profiles due to carbon-grain sublimation (see Sect. 4.2). Although the more compact emission region of N-bearing COMs could have suggested it, the only slightly larger abundance values at highest measured temperatures do not point to a significant enhancement of N-bearing COMs as expected from this process. However, the location of the soot line at ~300 K is only a rough estimate (van't Hoff et al. 2020) and could well be at higher temperatures that is closer to the protostar such that we cannot observe it due to insufficient angular resolution and the high continuum optical depth.

4.7 The role of binding energies

Although, based on our observational results, thermal desorption of the bulk of a COM seems to happen alongside water and does not depend on binding energies as concluded from Sect. 4.5, the latter may still have an influence on the observed profiles. First, the desorption temperature of water and all other molecules depends on their binding energies. Table 4 lists values of binding energies that were either measured in laboratory experiments (Wakelam et al. 2017; Das et al. 2018; Ferrero et al. 2020) or assumed by chemical models (Garrod 2013; Garrod et al. 2022). For those species, for which multiple values are available, it is evident that these can vary greatly. The binding energy depends on a number of parameters, amongst these are the dust surface composition, that is the material the molecule is bound to, and the surface structure, that is depending on the binding site, a COM may stick more strongly to it. The latter can lead to a range of binding energies for a given COM and dust composition as shown by Ferrero et al. (2020). In Sect. 4.5.1 we already mentioned that a lower binding energy in the model is able to better explain not only our results, but also observations in Orion KL (Jin et al, in prep).

We investigated possible correlations of binding energy with various parameters in Fig. 16, where binding energies were taken from the third column in Table 4. In Fig. 16a we look at the correlation of binding energy with the maximum spatial extent of the COM emission, where we used the maximum projected distance to which COM column densities could be determined from Figs. 7 and D.2. We show the average of the values obtained to the west and south and error bars represent the range of possible values. Although we show all analysed COMs, a relation may not be expected for those that are mainly produced in the gas phase, which are CH₃CHO and C₂H₃CN (unfilled symbols), and possibly also C₂H₅CN, CH₃NCO, and NH₂CHO. The former two are, therefore, not considered in the following discussion. There is no obvious trend visible; however, C₂H₅OH and CH₃NCO, which show the smallest spatial extents, have a higher binding energy than water, which could mean that they remain on the grain surface though uncovered from water because even higher temperatures are required for their desorption. All COMs with a smaller binding energy than water co-desorb with it in the model as soon as they are uncovered, which may explain the small variance amongst them in Fig. 16a. However, we cannot exclude a contribution to the abundance by non-thermal desorption processes (Sect. 4.5.2) or thermal desorption due to reduced binding energies (Sect. 4.5.3) at these large distances from Sgr B2 (N1), that is low temperatures, which could introduce a bias to this correlation.

Based on the assumption that C₂H₅OH and CH₃NCO have a higher binding energy than water and that they, therefore, stick longer to the grain surface, we may expect a correlation of the binding energy with the temperature of peak abundance, which is shown in Fig. 16b. Here, we used the median value obtained from S_D, W_D, S_CO, and W_CO extracted from Fig. 12. The error bars indicate the range that is spanned by the four values. No trend is visible, also because the spread in observed temperature values for each COM is large and all COMs could as well peak at the same temperature. Moreover, for most of these species, except for methanol and ethanol, we may expect further enhancement of abundances through gas-phase reactions, either based on the predictions of the model by G22 or based on the observed column density and abundance profiles or both. Additionally, we show the projected distance at which the COM abundances peak in Fig. 16c, where values were taken from Figs. 10 and 11. In this case no correlation is evident at all also because the spread in this parameter for most COMs is large.

Based on the discussion above and in Sect. 4.5, binding energies may not have a great impact on the thermal desorption that is associated with these COMs’ peak abundances in the gas phase and they are not the driving source of segregation between COMs in Sgr B2 (N1). Nonetheless, they may have a minor influence on the power-law indices of the temperature profiles, the temperature of peak abundance, and on the maximum spatial extent of COMs at least for those that are mainly formed on dust grains and despite further enhancement of their abundance in the gas phase and (non-)thermal desorption processes. However, as seen in Fig. 16, not only temperatures and distances show a large spread for each COM, also the values of binding energy do, which makes the discussion let alone final conclusion on the role of binding energies difficult.

5 Conclusion

Thanks to the high-angular resolution of the ReMoCA spectral line survey we were able to resolve the hot core region of the main hub Sgr B2 (N1) located in the star-forming protocluster Sgr B2 (N). Our goal was to shed light on the desorption process that releases COMs from dust-grain surfaces, where most of them are believed to form, into the gas phase. For each of a selected number of COMs, we derived rotation temperature, column density, and abundance profiles going south and west from the continuum peak position of Sgr B2 (N1). The two directions were chosen after an inspection of the morphology of the continuum and COM emission and to avoid the outflow driven by Sgr B2 (N1). Abundances were derived with respect to methanol as well as H₂, where column densities of the latter were derived from the dust continuum emission as well as from C¹⁸O 1–0 emission. Finally, the observational results were compared to state-of-art astrochemical models performed by Garrod et al. (2022). The main results of this article are the following:

1. Based on the morphology of their emissions, the COMs can be classified into two groups. The O-bearing COMs CH₃OH, C₂H₅OH, CH₃OCH₃, and CH₃OCHO show structured emission that closely follows that of the dust continuum emission. In contrast, N-bearing organic molecules such as C₂H₅CN, C₂H₃CN, CH₃CN, and HC₃N have less structured and more compact morphologies. COMs such as CH₃CHO, NH₂CHO, and CH₃NCO reveal morphologies that are somewhere in between.

2. The temperature profiles derived from all COMs have power-law indices that vary from −0.4 to −0.8, which is in agreement with other observations as well as models and which is consistent with a temperature gradient due to protostellar heating of an envelope with optically thick dust.

3. The southbound H₂ column density profiles derived from dust and C¹⁸O emission show similar behaviours with values that agree within the error bars, while the westbound profile from C¹⁸O yields higher values by factors of a few than the one from dust, which is surprising and still demands an explanation.

4. The COM column density and abundance profiles support the segregation of COMs seen in the emission morphology. The comparison with astrochemical models indicates that the gas-phase abundance for the majority of O-bearing COMs is dominantly set by their solid-phase abundance as they are mainly formed on dust-grain surfaces during the cold collapse phase. CH₃CHO and C₂H₃CN rather trace the warmer gas-phase chemistry as this is where they are mainly formed. NH₂CHO seems to be produced in both phases and while, up to now, CH₃NCO and C₂H₅CN are exclusively formed on dust grains in the model, observational results suggest (partial) gas-phase formation for these COMs. There exist reactions, that are not yet included in the model but could be promising candidates for the efficient production of these COMs.

5. Most abundance profiles show a steep increase at ~100 K, and then either a plateau, smooth increase, or drop at higher temperatures. The steep increase can probably be associated with the COMs’ thermal desorption from dust grains and given that it occurs at roughly the same temperature for the respective COMs, we suggest that it represents thermal co-desorption of these COMs with water, rather than thermal desorption depending on binding energies. Co-desorption of COMs and water is in agreement with predictions by the models of Garrod et al. (2022), in which this outcome is a consequence of the deactivation of the ability of COMs to diffuse within the bulk ice mantles. No convincing correlation with binding energies has been found.

6. Non-zero abundance values for some COMs at temperatures below ~100K, that is before the steep increase associated with co-desorption with water, suggest another desorption process at work at these low temperatures. One explanation would be a partial thermal desorption of molecules from the outer, water-poor (and initially CO-rich) layers of the ice mantles, due to weaker binding caused by the lower water content in those layers. CO would desorb at low temperatures (20–30 K), leaving behind COMs that would be bound less strongly to each other than they would be in a water-rich ice, allowing them to desorb at temperatures <100 K. Most of the COMs in the ice would remain trapped in the water-rich layers beneath. Another explanation would be non-thermal desorption, which could include chemical desorption or photo-desorption. In either case, our observations have resolved and revealed for the first time the transition between two regimes of desorption of COMs in a hot core.

Given that our observational results only consider the projected distance from Sgr B2 (N1) and that the model does not take into account any geometrical changes, it is striking how well the two agree. The comparison to the model were focussed on the results for the slow warm-up phase as they best described the observations. However, we may expect similar results from a faster warm-up with enhanced cosmic-ray flux. The latter is confirmed to exist in Sgr B2 (N1) and may be able to still alter the modelled results if taken into account.

Acknowledgements

This paper makes use of the following ALMA data: ADS/JAO. ALMA#2016.1.00074.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. The interferometric data are available in the ALMA archive at https://almascience.eso.org/aq/. Part of this work has been carried out within the Collaborative Research Centre 956, sub-project B3, funded by the Deutsche Forschungsgemeinschaft (DFG) – project ID 184018867. RTG acknowledges funding through the Astronomy & Astrophysics program of the National Science Foundation (grant No. AST 19-06489). The authors would like to thank the developers of the many Python libraries, made available as open-source software, in particular this research has made use of NumPy (Harris et al. 2020), matplotlib (Hunter 2007), and SciPy (Virtanen et al. 2020).

Appendix A Spectroscopic calculations

The CH₃OH data were taken from the CDMS (tag 032504). Version 3 is a recalculation of the original work by Xu et al. (2008). The entry includes transitions up to v_t = 2, and we used data from these three states. Transitions in the range of our survey were contributed by Lees & Baker (1968), Pickett et al. (1981), Sastry et al. (1984), Herbst et al. (1984), Anderson et al. (1990a), Müller et al. (2004), and Xu et al. (2008). This entry resolves intensity issues that prevailed in earlier entries of the CDMS and JPL catalogues. The partition function takes into account energies up to v_t = 3; it should be converged up to ~200 K and should be quite good at 300 K.

We used the ¹³CH₃OH data from the CDMS (tag 033502). Version 2 is a recalculation of Xu & Lovas (1997) with contributions from Haque et al. (1974), Blake et al. (1984), Kuriyama et al. (1986), Anderson et al. (1987), and Anderson et al. (1990b). The intensities were calculated employing scaled partition function values from the main isotopic species. The errors introduced by the scaling are small compared to available alternatives.

The ethanol calculation is from the CDMS catalogue (tag 046524, version 1). It is based on the extensive work by Pearson et al. (2008) with additional data from Pearson et al. (1995, 1996, 1997). The main difference with respect to the JPL catalogue entry are in part very different intensities as shown by Müller et al. (2016). The calculated frequencies are at least nearly identical to those in the JPL catalogue, but no experimental frequencies were merged in the CDMS entry. Vibrational corrections are based on the fundamental frequencies in Durig et al. (2011). We accounted for contributions by overtone and combination states by applying the harmonic oscillator approximation. The errors by this approximation are usually small, especially because the exact energies of low-lying vibrations are frequently not known or, if so, mostly only for the fundamental vibrations.

We employed the CDMS entry for dimethyl ether (tag 046514, version 1). It is based on the analysis of Endres et al. (2009) with additional rest frequencies in the range of our survey from the compilation of Lovas et al. (1979) and from Neustock et al. (1990). We also considered data in the two lowest excited states, v₁₁ = 1 and v₁₅ = 1. These data were provided by C. P. Endres and involve unpublished data. The partition function in the CDMS takes into account vibrational contributions up to 500 cm⁻¹. This is sufficient at 100 K and reasonable around 150 K. In order to account for contributions of higher vibrations, we evaluated the ground state contributions first and corrected them subsequently in the harmonic approximation. Most of the fundamental vibrations were taken from Coudert et al. (2002). We took information on the torsional fundamentals from Fernández et al. (2019) and on the COC bending mode from Kutzer et al. (2016).

We use the JPL entry (tag 060003, version 2) for methyl formate, based on Ilyushin et al. (2009), with additional data from Karakawa et al. (2001). The partition function of methyl formate considers v_t = 1. Its contribution was first subtracted and, subsequently, vibrational corrections added in the harmonic approximation. The torsional band origin was determined in Tudorie et al. (2012), additional low-lying vibrations were mentioned in Kobayashi et al. (2020), higher lying vibrations were summarised by Shimanouchi (1972).

The acetaldehyde data were communicated by R. A. Motiyenko. They are based on Smirnov et al. (2014) with additional data extending beyond v_t = 2. Vibrational contributions were evaluated in the harmonic approximation employing the compilation of Shimanouchi (1972).

We used the CDMS entries (tags 057505 and 057506, version 1 in each case) to identify methyl isocyanate. The entries were generated from the compilation of assignments in Cernicharo et al. (2016). The rotational part of the partition function was determined employing the rigid rotor approximation; this was the best to do given the highly perturbed rotational spectrum. Vibrational corrections were applied in Cernicharo et al. (2016) for states up to 580 K. The errors are small up to ~150 K, but reach the 10% level at 200 K. The vibrational spectrum is unfortunately not known well enough to employ further corrections.

We identified ethyl cyanide employing the CDMS entry (tag 055502, version 2). It is based on Brauer et al. (2009) with frequencies in the range of our survey from Fukuyama et al. (1996). We also used excited state data v₂₀ = 1(A) (tag 055513, version 1) and v₁₂ = 1(A) (tag 055514, version 1), based on Daly et al. (2013), with previously published v₂₀ = 1 data from Fukuyama et al. (1999). The vibrational correction factors are available through the CDMS documentation; they were evaluated using Heise et al. (1981).

The vinyl cyanide data are from the CDMS (tag 053515, version 1). They are based on Müller et al. (2008) with data in the range of our survey mainly from Gerry & Winnewisser (1973), Cazzoli & Kisiel (1988), and Baskakov et al. (1996). Data on the two lowest excited vibrational states, v₁₁ = 1 and v₁₅ = 1, are from unpublished data by one of us (HSPM) and takes also into account published data from Cazzoli & Kisiel (1988). We applied vibrational corrections using low-lying fundamentals of Kisiel et al. (2015) and higher lying fundamentals of Khlifi et al. (1999). The entry needs to be updated, see Kisiel et al. (2015) and references therein with data also on several excited vibrational states, but the current data are sufficient for the purpose of our study.

We used the CDMS entries for formamide in its ground vibrational state (tag 045512, version 2) and in v₁₂ = 1 (tag 045516, version 1). They are based on Motiyenko et al. (2012) and contain data in the range of our survey mostly from Kryvda et al. (2009). We consulted McNaughton et al. (1999) for vibrational correction. We summed up first the contributions of the anharmonic NH₂ out of plane vibration and its overtones and applied further vibrational corrections in the harmonic approximation.

Appendix B LVINE maps

Figures 3 and 4 show Line-width and Velocity-corrected INtegrated Emission (LVINE) maps. The LVINE method is an extension of the VINE method introduced by Calcutt et al. (2018). The authors determined the peak velocity of a bright methanol line at every position in their map in order to integrate intensities of other molecules or transitions of the same molecule over a fixed interval that then was varied around the derived peak velocity. We extended this method by also varying the interval in which intensities are integrated based on the line width at each position.

In order to create maps of peak velocity and line width we looked for a strong line that is neither contaminated nor optically thick. Because it is difficult to find a spectral line that combines all three criteria, we used two lines: an optically thin yet not too strong ethanol transition at 108.44 GHz (E_u = 88 K) for the region closer to Sgr B2 (N1) and a strong methanol transition at 95.91 GHz (E_u = 21K), at far distances from Sgr B2 (N1). The methanol line is optically thick at positions close to Sgr B2 (N1) (τ ~ 3 at N1S), however, at positions used here, its opacity is moderate (τ ~ 0.4 at N1S5). The two transitions are shown in Fig. B.1 at aposition close to Sgr B2 (N1) (N1S), where C₂H₅OH was used, and a position farther away (N1S5), where CH₃OH was used. At each position in the map, that is for each pixel, a 1D Gaussian profile was fitted, from which the peak velocity and line width for the respective map were extracted. If the fitted peak intensity of the ethanol transition at one position dropped below a threshold of 5σ, where σ is the median rms noise level listed in Table 2 in Belloche et al. (2019), then the methanol transition was used instead. The final maps of peak velocity and line width as well as a map that indicates where ethanol, methanol, or neither of the two (None) were used are shown in Fig. B.2 a-c, respectively. When neither the ethanol nor the methanol line had an intensity above the threshold, a fixed value of 64 km s⁻¹ was allocated to the peak velocity and a value of 4 km s⁻¹ to the line width for this pixel.

The Gaussian fitting happened unsupervised for most parts. However, in some regions an adjustment of input parameters or the refinement of the window, in which the fitting was done, or both was necessary, for example due to additional velocity components that lead to contamination and possibly bias the resulting velocity and line width when taken into account during the fitting process. The decision on the true velocity components was made by inspecting neighbouring positions. The decision on when to intervene was also made in the same way. Although we were able to avoid fatal failures of the fitting procedure in that way, some uncertainties remain hidden. However, with our velocity map we trace the major velocity gradients seen in Sgr B2 (N1), that is the lower velocities (< 62 km s⁻¹) seen to the south and the sudden rise in velocity to ~70 km s⁻¹ to the west. Other less pronounced velocity changes, which were associated with filaments (Schwõrer et al. 2019), are evident as well. The line widths for the considered velocity components can be as narrow as 2–3 km s⁻¹ and remain generally below a value of 10 km s⁻¹.

Appendix C Continuum masking

Although for most parts the continuum emission is optically thin (cf. Fig. 2), we identified an increase in optical depth of the continuum at distances ≲0.5″ to Sgr B2 (N1). When the continuum becomes optically thick it obscures the line emission from COMs. Because the Weeds model cannot treat this effect properly an analysis of COM emission in this region is impossible to do. Therefore, we excluded this closest region around Sgr B2 (N1) by creating masks. The definition of the mask size is challenging as the continuum emission depends on angular resolution, hence, on the observational setup and frequency.

To create the masks, we computed the channel-intensity distribution for the continuum-included spectra of each spectral window and determined the intensity at the peak of this distribution T_peak and the maximum intensity T_max. We plot the difference T_max − T_peak normalised by T_max in Fig. C.1. A position in the map was blanked when T_peak < 3σ, where σ is the average noise level in the continuum emission map. In that way, we identified at which distance from Sgr B2 (N1) the emission lines get attenuated due to the increasing continuum optical thickness. As expected, the observational setups of higher angular resolution and higher frequencies are more affected. We decided to use the contour at a value of 0.43 (see red dashed contour in Fig. C.1) to define the mask for each setup. This decision was made based on these maps and also on the comparison to the spectra. It allowed us to keep position N1S in our analysis for all observational setups and N1S-1 for all setups except spectral windows 2 and 3 of setup 5. For these two spectral windows, the Weeds model systematically overestimates intensities at N1S-1 although the model seems to fit otherwise. At this close distance to Sgr B2 (N1) the increasing continuum optical thickness can be expected to attenuate the observed intensity of spectral lines untreated by Weeds. Other reasons may be presented by an overestimation of the source size or filtering of emission by the interferometre.

The approach applied here is not the most accurate because, for example, it does not take into account absorption lines or extremely strong lines from very abundant molecules such as ¹³CO. However, it is sufficient for our purposes. Accordingly, spectral windows 2 and 3 of setup 5 were excluded from the analysis of position N1S-1 and integrated intensities within the mask are blanked in all respective maps. Figure C.1 further suggests to mask emission originating from the HII regions K3 and K1 for some spectral windows. However, inspecting spectra at the continuum peak positions of the two shows that the continuum is still sufficiently optically thin and the spectral lines are simply weak. Therefore, we do not apply any mask to the HII regions.

Appendix D Additional figures

Because the noise level within each LVINE map shown in Fig. 4 is not uniform due to the pixel-dependent integration limits, that is, the number of channels over which the integration was performed is different in each pixel, we show signal-to-noise maps in Fig. D.1 complementary to the LVINE maps. Figure D.2 highlights the maximum distances to the south and west to which emission of a certain COM is still detectable. Figure D.3 shows the same as in Fig. 13 in Garrod et al. (2022), but for CH₃NCO. It illustrates the net rate of change in abundance of the COM starting from the cold phase and assuming a subsequent slow warm-up.

Appendix E Additional tables

Table E.1 lists the positions selected for analysis, which are also indicated in Fig. 3. Tables E.2–E.23 provide the parameters used for the LTE modelling with Weeds of each COM at each position, respectively. Moreover, the results obtained from the population diagrams are shown. Table E.24 lists the H₂ column densities derived from either dust continuum emission or C¹⁸O at each position, respectively, along with the dust continuum flux, continuum optical depth, and the model parameters of C¹⁸O.

Appendix F Additional figures: Spectra at N1S

Figures F.1–F.10 show observed and synthetic spectra of the analysed COMs at position N1S or, in case of CH₃OCH₃, N1S1. Only transitions that are used to create the respective population diagram are shown.

Appendix G Population diagrams

Figures G.1–G.11 show population diagrams of CH₃OH, its ¹³C isotopologue, C₂H₅OH, CH₃OCH₃, CH₃OCHO, CH₃CHO, CH₃NCO, C₂H₅CN, C₂H₃CN, and NH₂CHO for all positions to the south where they are detected. The vibrational states used for each COM are listed in Table G.1. Figures G.12–G.21 show the same for positions to the west.

References

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All Tables

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