© ESO, 2014

1. Introduction

Intermediate-mass young stellar objects (IMs) are the precursors of stars in the 2−8 M_⊙ mass range (Herbig Ae/Be stars). They share some characteristics with massive young stellar objects (clustering, photodissociation regions), but they are more common than the more massive stars and therefore they can be found closer to the Sun (d< 1 kpc), which allows determination of the physical and chemical structure of their envelopes at similar spatial scales as can be done for low-mass protostars. From a chemical point of view, IMs are interesting because they constitute the link between the low-mass and high-mass ranges, covering an intermediate range of luminosities, densities, and temperatures.

Hot molecular cores are compact (<0.05 pc) objects with high temperatures (>100 K) and densities (n(H₂) >  10⁶ cm^-3) and they are characterized by a very rich chemistry of complex organic molecules (COMs). The typical massive hot core is the one associated with Orion KL; it hosts one of the richest molecular chemistries observed in the interstellar medium (Blake et al. 1987; Beuther et al. 2005, 2006; Tercero et al. 2010, 2011, 2013; Motiyenko et al. 2012; Cernicharo et al. 2013); COMs have also been detected coming from the inner regions of a few low-mass protostars, the so-called hot corinos (IRAS 16293-2422: Cazaux et al. 2003; Bottinelli et al. 2004a; Pineda et al. 2012; NGC 1333 IRAS 2A: Jørgensen et al. 2005, 2007; NGC1333-IRAS 4AB: Bottinelli et al. 2004b, 2007). These regions have smaller sizes (~150 AU) and lower temperatures (~100 K). Although high sensitivity interferometric data on hot cores and corinos are still scarce and the comparison is difficult, there is some general consensus that hot corinos are richer in O-bearing molecules like CH₃OCHO, CH₃CHO, CH₃OCH₃, or HCOOH, and poorer in N-bearing compounds. Furthermore, large abundances of deuterated molecules and large deuterium fractions are only associated with hot corinos (Vastel et al. 2003; Parise et al. 2004; Demyk et al. 2010).

A handful of well studied hot cores exist in the IM range: NGC 7129 FIRS 2 (Fuente et al. 2005a, hereafter FU05), IC 1396 N (Neri et al. 2007; Fuente et al. 2009), IRAS 22198+6336 (Sánchez-Monge et al. 2010; Palau et al. 2011), and AFGL 5142 (Palau et al. 2011). The sizes of these IM hot cores range from ~130 AU (IRAS 22198) to ~900 AU (NGC 7129) and their chemistries present some differences. Fuente et al. (2005a,b) proposed that IM hot cores, like hot corinos, are richer in H₂CO and HCOOH relative to CH₃OH than massive hot cores, and they did not find any variation in the CH₃CN/CH₃OH abundance ratio across the stellar range. Palau et al. (2011) studied the chemistry of IRAS 22198+6336 and AFGL 5142 and concluded that these IM hot cores are richer in oxygenated molecules with two or more CH_2/3 groups than hot corinos, but poorer in N-bearing molecules than massive hot cores. As yet, the number of studied objects is very low and the derived column densities have large uncertainties.

In this paper, we present a 4 GHz interferometric frequency survey towards the hot core NGC 7129 FIRS 2 (hereafter, FIRS 2) that, with a luminosity of ~500 L_⊙, lies near the middle of the IM luminosity range. FIRS 2 is a prototypical young IM protostar; it is associated with energetic outflows (Fuente et al. 2001) and presents clear signs of CO depletion and enhanced deuterium fractionation when observed with single-dish telescopes (scales of ~10 000 AU; Fuente et al. 2005b; Alonso-Albi et al. 2010). It is located at a distance of 1250 ± 50 pc from the Sun (Shevchenko & Yakubov Shevchenko1989) and FU05 detected a compact hot core at its center. FIRS 2 was observed with Herschel within the Water In Star-forming regions (WISH) key program (van Dishoeck et al. 2011) and it is one of the best known IM protostars with a huge set of data at both millimeter and far-IR wavelengths (Johnstone et al. 2010; Fich et al. 2010; Fuente et al. 2012). This source and IRAS 22198+6336 are the only hot cores without clear signs of clustering which suggests that their luminosity could come from a single binary system (Palau et al. 2013).

2. Observations

The interferometric observations were carried out with the Plateau de Bure Interferometer (PdBI) in its CD configuration during August and November 2012. This configuration provided an angular resolution of 1.43″ × 1.26″ PA 144° (~1870 AU  ×  1647 AU at the distance of FIRS 2) at the central frequency. The 1 mm receivers were tuned at 219.360 GHz which allowed the simultaneous imaging of the C¹⁸O 2 → 1 and ¹³CO 2 → 1 lines, both within the ~4 GHz receiver’s band. The narrow 40 MHz correlator units were used to sample the C¹⁸O and ¹³CO lines at the high spectral resolution of 40 kHz. The wideband correlator WideX sampled the whole 4 GHz bandwidth with a spectral resolution of ~2 MHz. MWC 349 was used as flux calibrator (1.92 Jy) and the rms in each WideX channel, 4−6 mJy/beam (~0.058–0.087 K).

The interferometric observations were complemented with single-dish observations using the 30 m telescope and the same frequency setup. These observations were done in December 2012 and the achieved rms () was ~0.012 K (0.09 Jy) in a channel of ~1.953 MHz. Therefore, the 30 m observations are ~15 times less sensitive than the PdB images. The telescope was pointed towards the phase center of the interferometric observations: , (J2000). Forward and main beam efficiencies are 0.92 and 0.63, respectively. The selected intensity scale is main beam temperature.

This paper is dedicated to the analysis of the chemical complexity revealed by the WideX data towards the mm continuum source.

3. Results

3.1. Continuum maps

The high density of lines detected made it impossible to accurately measure the continuum flux from the low spectral resolution WideX data. Instead, we used the empty emission channels around the C¹⁸O and ¹³CO lines measured at higher spectral resolution using the 40 MHz correlator units to determine the continuum flux. As expected, the continuum flux was slightly different at 219.560 GHz and 220.398 GHz. We derived two continuum maps at 219.560 GHz and 220.299 GHz. Fitting the visibilities we obtained the position of the compact source: , , i.e., offset by −0.17″ in right ascension from our phase center. The measured fluxes are 0.37(0.01) Jy at 219.560 GHz and 0.38(0.01) at 220.398 GHz, respectively. In FU05, we determined a mm emission spectral index of 2.56 based on the continuum images at 86 GHz and 230 GHz. The new fluxes at 219.6 GHz and 220.4 GHz are consistent with these results taking into account the uncertainty of 10% in the absolute flux calibration.

3.2. Molecular lines

In Fig. A.1 we show the WideX spectra towards the continuum peak. The continuum image at 219.560 GHz was subtracted from the spectral maps before the cleaning process. This subtraction is not perfect since the continuum presents a smooth slope across the observed bandwidth, but it is good enough for our current detection goals.

The spectrum towards the compact source is crowded with lines, typical of those found in massive hot cores. In order to estimate the flux that the interferometer is missing, we compared the PdBI spectrum with that obtained with the 30 m telescope. In Table 1 we show the list of all the lines detected with both telescopes and the fraction of flux recovered using the PdBI. We note that only the H₂CO, CH₃OH, SO, C¹⁸O, and ¹³CO lines are missing a significant fraction of their fluxes when observed with the PdBI. The emission of OCS, HNCO, CH₃CN, and HC₃N comes mainly from the hot core although 20% of the flux of the lowest energy HNCO line is missing. This is also consistent with the spatial distribution as observed with the PdBI. In Fig. 1, we show the integrated intensity images of some of the more intense lines. Only ¹³CO, C¹⁸O, and SO present large-scale structure. In all the other molecules the emission is point-like at the angular resolution of our observations.

4. Line identification and rotational diagrams

For line identification we used José Cernicharo’s personal catalogue which is included in the radiative transfer and molecular excitation code MADEX (Cernicharo 2012), the JPL (Pickett 1991, 1998), and the CDMS (Müller et al. 2001, 2005) catalogues. Our procedure can be summarized as follows. We started with the identification of the lines of the most common species. The rotation temperatures, molecular column densities, and source sizes were estimated by fitting the line intensities of the whole family of molecules (all isotopologues) within the program MADEX. In these calculations, we assumed local thermodynamic equilibrium, v_LSR = −10 km s^-1, a linewidth of 8 km s^-1 and a face-on disk as the source morphology. In the case of a good fit, we created a synthesized spectrum using the derived parameters and subtracted it from the observations. Then, we went on with line identification in the residual spectrum. Sometimes, especially for the weak lines, the fit was not good enough. In these cases, we did not subtract the synthesized spectrum in order to avoid spurious features and just went on identifying the features in the original spectrum.

The number of parameters that can be determined for each species depends on the number of lines detected. For example, the source size can only be determined when the lines of the main isotopologue are optically thick. In the optically thick case, T_B ≈ η_ff × J_ν(T_rot), where η_ff is the beam filling factor, and J_ν(T_rot) = hν/kT_rot × (1 − exp(hν/kT_rot))^-1 with T_rot the rotation temperature. Provided that we know T_rot, we can estimate the effective size of the emitting region from the line intensities. The emission sizes cannot be constrained if the main isotopologue lines are optically thin.

For the less abundant molecules, the number of detected lines was too low or the line intensities were too uncertain to estimate the rotation temperature. In these cases, a rotation temperature of ~200 K was assumed and only the molecular column densities are calculated using MADEX. In Sects. 4.1 to 4.19, we give a more detailed description of the fitting for each species and the results of these calculations are shown in Tables 2 and 3.

Frequencies and line identifications are shown in Table A.1. We compare our synthesized spectrum including all species with observations in Fig. A.1.

4.1. Methyl cyanide: CH₃CN, CH₃NC

Methyl cyanide (CH₃CN) is one of the best thermometers in hot cores. The symmetric rotor presents a K-ladder structure with transitions that are easily thermalized at the densities prevailing in hot cores. In addition, it is well known that this molecule is especially abundant in these regions. We have detected the whole 12_K → 11_K ladder, from K = 0 to K = 11 in the ν = 0 ground vibrational state and in the ν₈ = 1 vibrational level at E_vib = 525.17 K (see Table A.4). The high number of detected lines would allow us to determine the rotation and vibrational temperature of this molecule providing that the emission is optically thin (see Fig. 2). As discussed below, this is not the case of the ν = 0 lines. Instead, we used the ν₈ = 1 lines to estimate the rotation temperature. Unfortunately, most of the lines are blended or partially blended. This is the cause of the large uncertainties in the integrated intensities shown in Table A.4. All the lines have T_b> 3σ, but the uncertainty in the linewidth is large for partially blended lines. As a first step we plotted all the detected lines in a rotational diagram and visually checked if any of them were clearly above or below the straight line defined by the other points. We removed the line at 221 265 MHz that was clearly above the fit and derived K using the rest of the points (the parameters of this fit are shown in Table 2). The fit was good (R = 0.81) suggesting that the contribution of other species to the measured line integrated intensities were within the errors. To corroborate this assumption, as a second step, we removed the lines that were severely blended (difference in frequency less than 4 MHz) and kept only those that were isolated or partially blended. In the end we had only eight transitions and derived K. The higher rotation temperature was due to the suppression of the lines at 221 199, 221 394, 221 403, and 221 422 MHz. The obtained value was still in agreement with our previous fit within the errors. We were worried because the velocity integrated line intensities of the transitions with E_rot> 400 K (221 059, 221 210 MHz) present large uncertainties. In order to check the robustness of our temperature estimate, we make a new least squares fitting without these lines. This fit provided a lower limit to the rotation temperature of K. Again the value obtained for the rotation temperature is in agreement with that shown in Table 2 within the errors. Therefore, we decided to keep the estimate shown in Table 2 as a good value for the average rotation temperature, although we are aware that, more likely, we have strong temperature gradients across the hot core with temperatures varying between ~250 K and ~600 K.

The results from the CH₃CN ν = 0 rotational diagram are shown in Table 2. We obtained a higher rotational temperature in ν = 0 than in ν₈ = 1. One could think that the high temperature in the ground vibrational state was an artifact due to the missing flux in the low K components of the CH₃CN 12_K → 11_K ladder. However, comparison of the interferometric PdBI and single-dish 30 m observations showed that the spatial filtering is not important and therefore this possibility was discarded. An alternative explanation is that the ground state vibrational lines are optically thick. The opacity can be derived by comparing the CH₃CN and CH₃¹³CN lines (the lines of the other ¹³C isotopologue ¹³CH₃CN are outside the observed frequency range). Unfortunately, the CH₃¹³CN 12₀ → 11₀ and 12₁ → 11₁ lines are blended with those of the main isotopologue. The lowest K transition without any obvious contamination is K = 4 (220 571 MHz) where we have a feature with T_b ~ 0.39 K (with an uncertainty of 25% because of partial blending with other lines). Comparing with the main isotopologue, we have I(CH₃CN 12₄→ 11₄)/I(CH₃¹³CN 12₄ → 11₄) ~ 7, which implies opacities of ~10 in the main isotopologue line. Since the line opacities are very high, the rotational diagram analysis is not valid and the resulting rotation temperature in the ground state is severely over-estimated. Instead, we derived the CH₃CN column density assuming T_rot = 405 K (the same as in the ν₈ = 1 vibrational level) and an opacity of ~10 for the CH₃CN 12₄ → 11₄ line and obtained N(E-CH₃CN) = N(A-CH₃CN) = 2.6 × 10¹⁸ cm^-2, i.e., a total (A+E) CH₃CN column density of 5.2 × 10¹⁸ cm^-2. With these parameters, we fit the high energy rotational lines with a source size of ≈0.07″ (125 AU). The uncertainty in the source size comes from the assumed rotation temperature. By varying the rotation temperature between 250 K and 600 K we would obtain sizes of 100−160 AU. We note that these sizes are quite small, similar to typical scales of circumstellar disks.

This compact source model successfully predicted the intensities of the high excitation lines, but the intensities of the low-energy transitions were severely underestimated. The only way to fit the whole spectrum was to consider a two-component model: (i) the compact component described above; and (ii) a more extended second component that is filling the beam. We fit the K< 4 lines with N(E-CH₃CN) = N(A-CH₃CN) = 2.5 × 10¹⁴ cm^-2 and T_rot = 350 K for this extended component. We tried with a temperature of 250 K obtained from the fitting of the E_rot< 400 K ν₈ = 1 lines, but this lower temperature would overestimate the K = 0 and K = 1 lines. Furthermore, the assumed value is within the uncertaintly of this fit (=250 K).

Our estimate of the total methyl cyanide column density relies on the ¹³C isotopologue line. Of course there is also the possibility that the CH₃¹³CN 12₄ → 11₄ line is contaminated by another line and its real intensity is lower. We did not find any good candidates at this frequency. One line of EA-(CH₃)₂CO is very close in frequency, but the emission of this line is very weak (see also Sect. 4.7). Furthermore, the small sizes derived for other species (see following sections) prompted us to consider the two-component model as the most likely one. We would also like to point out that we refer to a beam filling component at the spatial resolution of our observations (~1900 AU) as “extended component”. This component would not encompass the entire envelope.

We also looked for the deuterated compounds in our spectrum. The most abundant species CH₂DCN and CHD₂CN have no intense lines in the observed frequency range. Only CD₃CN has three intense transitions at 219.965, 219.983, and 219.993 GHz. We have detected the three lines but need a very low rotation temperature, T_rot = 40 K, to fit them. Because of this surprisingly low rotation temperature, we consider that a misidentification is possible and keep the derived column density as an upper value to the real one. Several weak lines of CH₃NC were identified, a molecule so far only detected towards Sgr B2 (Cernicharo et al. 1988). Unfortunately, most of them are blended or partially blended. Assuming that CH₃NC is coming from the CH₃CN compact core, we calculated a CH₃NC column density of 1.5 × 10¹⁶ cm^-2, i.e., about 350 times lower than that of CH₃CN. Since we have only one unblended line, we keep this detection as tentative.

4.2. Isocyanic acid: HNCO, HN¹³CO

The HNCO lines are well fitted with K and N(HNCO) = 1.6 × 10¹⁵ cm^-2 (see Fig. 2 and Table 2). In our frequency range, most of the lines of HN¹³CO are blended with those of the main isotopologue and so we cannot estimate the line opacities. Comparing this with the 30 m spectrum, we calculated that the interferometer is missing about 20% of the flux of the low energy lines, showing that there is an extended component. For this reason, we adopt the beam filling solution. We looked for the isomer HCNO and the deuterated compound DNCO, but unfortunately they do not have intense transitions in the sampled frequency range.

4.3. Methyl formate: A-CH₃OCHO, E-CH₃OCHO

We detected more than sixty lines of A-CH₃OCHO and E-CH₃OCHO in our spectrum, both in the v_t = 0,1 vibrational states, the latter at E_vib = 188.40 K. We tried to fit a rotational diagram to each vibrational state separately in order to measure the rotation and vibrational temperatures independently, but this was not possible. The dynamical range of E_u within each vibrational level is very small and the uncertainties in the integrated intensities are too large to obtain a good fit. However, we could get a reasonable fit by considering the two vibrational levels together (see Table 2). We measured K, slightly lower than that of CH₃CN, but still in good agreement taking into account the associated uncertainties. We fixed the temperature and varied the source size to fit the lines. The best fit was obtained with a size of ~0.1″. Even with this small size, the opacities of the CH₃OCHO ν = 0 lines are always ≤1.3 suggesting that our estimate of the rotation temperature is reliable. Unfortunately, the lines of the ¹³C isotopologues are blended with other species and it was not possible to have an estimate of their column densities. We used a weak feature at 128.952 GHz to derive an upper limit to the total column density of ¹³CH₃OCHO of <3.0 × 10¹⁷ cm^-2 in the ~0.1″ core, which would imply an upper limit to the total (A- +E-) main isotopologue column density of <2.0 × 10¹⁹ cm^-2 assuming ¹²C/¹³C = 65. This allows us to say that the methyl formate column density is accurate within a factor of 4. When considering deuteration, we have three detected lines at 219 242 MHz, 218 730 MHz, and 219 132 MHz that would correspond to CH₃OCDO and CH₂DOCHO. The first two lines are blended with lines of EE-(CH₃)₂CO which makes the derived deuterium fraction more uncertain. Taking into account the contribution of acetone, we fitted the intensities of the three lines assuming a deuterium fraction of ~0.06.

4.4. Ethyl cyanide: CH₃CH₂CN

The detection of eight lines of CH₃CH₂CN strongly confirms the identification of this species. Although three of them are heavily blended, the other five lines are sufficient to identify this species. The lines belong to the ground state and to the lowest energy vibrational states at E_vib = 297.12 K (Daly et al. 2013). We tried to fit the rotational diagram, but unfortunately the points did not follow a clear pattern and we could not determine the rotation temperature. Hence, we fixed the rotation temperature to a value of 200 K (a reasonable value from the rotational temperatures measured with the other species; see Table 2) and fitted the column density. A beam averaged column density value of 5.2 × 10¹⁴ cm^-2 was derived from the intensity of the most intense lines. The fit improved assuming that the emission comes from a compact source with a diameter of ~0.1″, because some lines become optically thick. This is the solution we finally adopted (see Table 3). We searched for the lines of the ¹³C isotopologues and the deuterated species, but the lines were too weak to obtain a significant upper limit to their column densities.

4.5. Methanol: A- and E-CH₃OH, A- and E- ¹³CH₃OH, CH₂DOH

Only five lines of methanol (including the A- and E- species and their vibrational states) were detected and their intensities were not consistent with LTE. This is not unexpected since the emission of the low energy lines is optically thick and extended (see Table 1). We searched for the lines of ¹³CH₃OH and the deuterated species CH₂DOH. Ten lines of CH₂DOH were detected. We removed from our fit the lines that could be blended with other more intense lines and we still kept four clean lines that allowed us to derive the results shown in Fig. 2 and Table 2. The rotation temperature of CH₂DOH, ~157 K is lower than that of CH₃CN, suggesting that it arises from a different region within the hot core. Based on the different spatial distribution of the high excitation and low excitation lines of methanol, FU05 proposed the existence of two components: a hot component towards the hot core and a colder component that extends along the outflow direction. Although the two components are expected to contribute to the total CH₂DOH emission, its low rotation temperature suggests that it is dominated by the extended one.

For ¹³CH₃OH, we detected two lines of the ν_t = 0 vibrational state (220 323 and 221 282 MHz) and one (221 424 MHz) of the ν_t = 1 state. Although the emissions of the low energy lines of the main isotopologue are extended (see Table 1), we considered that the emissions of the 13-methanol lines come mainly from the compact source. The line at 220 323 MHz is heavily blended and cannot be used to estimate the 13-methanol column density. Using the other two lines we fitted a vibrational/rotation temperature of ~238 K and a total ¹³CH₃OH ν_t = 0,1 column density of 5.3 × 10¹⁸ cm^-2. In order to estimate the uncertainty in our estimate of the 13-methanol column density, we repeated the fit by fixing the rotation temperature to 200 K and 400 K. The derived column densities are 3.0 × 10¹⁸ cm^-2 and 6.1 × 10¹⁸ cm^-2, respectively, which suggests that our estimate of the ¹³C-methanol column density is accurate within a factor of 2.

Since the CH₃OH lines are optically thick, we derived the methanol column density from ¹³CH₃OH assuming that all the ¹³CH₃OH emission comes from the compact component and ¹²C/¹³C = 65. Then we added an extended component to fit the rest of lines. The value obtained for the CH₃OH column density in the extended component is not reliable because the intensities of the main isotopologue lines are affected by spatial filtering and opacity effects. Moreover, the separation of the methanol emission in these two components is model-dependent since we fixed the size of the compact core in our calculations. The beam average CH₃OH column density derived from ¹³CH₃OH is, however, reliable as long as the ¹³C-isotopologue is optically thin regardless of the detailed spatial distribution of methanol within the observational beam. For this reason, we used this value to calculate the deuterium fraction, [CH₂DOH]/[CH₃OH] = 0.02. This is an average value within the hot core.

4.6. Trans- and gauche-ethanol: T- and G-CH₃CH₂OH

We detected six ethanol lines which includes four from T-CH₃CH₂OH and two from the G conformer that is at 60 K above the T state. However, only three lines are clearly detected (at 218 554, 218 655, and 220 155 MHz) since the other are significantly blended with transitions from other species or U lines. Because of this, we could not apply the rotational diagram technique. Instead, we assumed a rotation temperature of T_rot = 200 K, and derived the column densities using the most intense lines. We assumed a size of ~0.1″ to more accurately fit the data published by FU05 (see Sect. 5). The results are shown in Table 3.

4.7. Acetone: AA-(CH₃)₂CO, AE-(CH₃)₂CO, EA-(CH₃)₂CO, EE-(CH₃)₂CO

Several lines of acetone were detected in our spectrum (218 773, 219 076, 219 220, 219 242, 219 264, 220 355, 220 466, 220 764, 220 962 MHz), the most intense being at 219 220, 219 242, and 219 264 MHz. Because many of them are blended, it is not possible to determine an accurate rotation temperature. We assumed T_rot = 200 K and obtained a total (AA+EA+AE+EE) beam average column density of 1.0 × 10¹⁵ cm^-2.

4.8. Formaldehyde: H₂CO

Three lines of p-H₂CO and one of o-H₂¹³CO were detected in the PdBI spectrum. The lines of the main isotopologue are optically thick and most of their emission has been filtered by the interferometer (see Table 1). Because of the large fraction (85%) of missing flux in the main isotopologue line, we are surely missing an extended component. As can be seen in Fig. 1, the emission of the o-H₂¹³CO is unresolved by our observations. In addition, FU05 derived a size of 0.58 ± 0.24′′× 0.40 ± 0.24′′ for the D₂CO emission. Based on these results, we were able to fit all the lines of this work and FU05 with an (ortho+para)-H₂¹³CO column density of 1.1 × 10¹⁶ cm^-2 and (ortho+para)- D₂CO column density of 5.9 × 10¹⁵ cm^-2, and a source with a diameter of 0.34″ (~426 AU ). We assume T_rot = 200 K and an ortho-to-para ratio of 3.

There are no H₂C¹⁸O and HDCO lines in the frequency range of our observations that we could use to further constrain our model.

4.9. Carbonyl sulfide: OCS, O¹³CS

The J = 19 → 18 rotational lines of the ground vibrational states of OCS and O¹³CS lie in the range of wavelengths covered by our observations. We measured T_b[OCS 19 → 18]/ T_b[O¹³CS 19 → 18 ] ~ 5. Comparing the 30 m and PdB spectra, we discarded the possibility that this low intensity ratio is a consequence of the spatial filtering. The opacity of the OCS 19 → 18 line must be very high, τ ~ 12. Assuming T_rot = 200 K, we derived a OCS column density of ~ 2 × 10¹⁸ cm^-2 and a source size of ≈0.32″ (400 AU), four times that derived for the compact component of CH₃CN. In our spectrum, we also detected two lines of the OCS ν₂ = 1 vibrational state at E_vib = 748.8 K (see Table A.1). Assuming the same source size, the intensities of these lines imply a vibrational temperature, T_vib = 170 K, in agreement with the rotational temperature we assumed. The same assumptions are used to fit the OC³³S J = 19 → 18 line in FU05.

4.10. Sulfur monoxide: SO, S¹⁸O

Only the intense line of SO at 219 949 MHz was detected. From its intensity and assuming T_rot = 200 K, we derived a beam averaged SO column density of 2.4 × 10¹⁵ cm^-2. The emission of this line is extended (see Table 1 and Fig. 1) and, most likely, optically thick. There are no lines of ³⁴SO, ³³SO, and/or S¹⁸O in the spectrum that could be used to determine the line opacity. As commented in Sect. 5 a possible detection of S¹⁸O in the spectrum published by FU05 suggests that the column density could be as much as a factor of ~600 higher (see Sect. 5 and Table 3). Unfortunately, this line is blended with other intense lines and this makes the estimate uncertain. We consider our fitted value as a lower limit to the real one.

4.11. Sulfur dioxide: SO₂, ³⁴SO₂

One SO₂ line at 219 276 MHz and two ³⁴SO₂ lines at 219 355 and 221 115 MHz, respectively were detected. These lines are reasonably fitted using T_rot = 200 K, a beam averaged SO₂ column density of 6 × 10¹⁵ cm^-2 and ³²S/³⁴S = 22. The SO₂ line is optically thin providing a good estimate of the total number of SO₂ molecules within our beam. On the other hand, we could not estimate an accurate value of the opacity that would allow us to constrain the size of the emitting region; however, we checked that the SO₂ line would be optically thin even if all the emission arises from the 0.1″ compact core.

4.12. Cyanoacetylene: HCCCN,HCCCN ν₇ = 1, DCCCN, HCCNC

We detected one HC₃N line at 218 325 MHz and two lines of the vibrational state ν₇ = 1 at 218 861 MHz and 219 174 MHz, respectively, although the one at 219 174 MHz is blended with an intense ethanol line. In addition, we tentatively detected the H¹³CCCN 25 → 24 line. Unfortunately, the frequency of the H¹³CCCN line is close to that of the ¹³CO 2 → 1 line and could have some contribution from its wing. Assuming that the isotopologue line is not blended with ¹³CO, we fit this line with T_rot = 200 K and N(H¹³CCCN) = 8.8 × 10¹⁴ cm^-2 and a source size of ~0.20″ which implies an upper limit to the HC₃N column density of <5.7 × 10¹⁶ cm^-2. This value, however, overestimates the intensity of the lines of the main isotopologue, which are better fitted with N(HCCCN) = 2.0 × 10¹⁶ cm^-2. We adopt this latter solution and conclude that our column density is accurate within a factor of 3. There is a weak feature at 219 490 MHz that could correspond to DCCCN J = 26 → 25. Since this line is very weak and there is no other DCCCN line in the spectrum that could confirm the detection, we will consider it as a tentative detection and use its intensity to derive an upper limit to the DCCCN column density of N(DCCCN)/N(HCCCN) < 0.016. We might have detected one line of HCCNC at 218 558 MHz, but it is blended with an intense ethanol line. Therefore, we can only derive a lower limit to the N(HCCCN)/N(HCCNC) column density ratio of >13.

4.13. Acetaldehyde: CH₃CHO

Very few intense lines of CH₃CHO are found in the observed wavelength range and some of them are blended with others from abundant species. We detected without blending the 220 446 MHz line of E-CH₃CHO, and marginally the 221 222 MHz line of A-CH₃CHO ν_t = 1, the 219 780 MHz line of A-CH₃CHO ν_t = 2, and the 221 216 MHz line of E-CH₃CHO ν_t = 2. All these lines were fitted assuming T_vib = 100 K. Making the additional assumption that T_rot = T_vib, we derived a total beam averaged A+E CH₃CHO column density of 4 × 10¹⁵ cm^-2 in the ν = 0 ground state. In this case, the lines of the ¹³C isotopologue were not detected. As for other oxygenated molecules, we assumed that the source is extended relative to our beam. Although the firm detections in the 218–221 GHz frequency range are only a few, this model is fully confirmed by the good match to the data published by FU05 (see Sect. 5).

4.14. Formic acid: HCOOH

Two lines of HCOOH, one at 218 938 MHz and the other at 220 038 MHz, were detected in our spectrum. However, their line intensities were not consistent with thermalized optically thin emission. Since the two lines have very similar E_u, this discrepancy cannot be due to a wrong rotation temperature. Spatial filtering cannot be the cause of this discrepancy, because such an intense line should have been detected in the 30 m spectrum. However, the Einstein spontaneous emission coefficient, A_ij, of the 220 038 MHz line is ten times lower than that of the 218 938 MHz line which results in a higher opacity of the former for the same physical conditions. We propose that the high opacity of the line at 220 038 MHz causes the anomalous line intensity ratio. The detection of H¹³COOH at 219 341.849 MHz also argues in favor of a high column density of HCOOH in this source. We can reasonably fit both lines of HCOOH and that of H¹³COOH assuming T_rot = 100 K, a total HCOOH column density of 9.5 × 10¹⁸ cm^-2, and a source size of ~0.1″. The profile of the H¹³COOH line is wider than expected (see Fig. A.2), suggesting some contribution from the outflow or partial blending with other line. Because of this possible blending, the integrated intensity of this line is uncertain by a factor of 2. We selected the solution that best fitted the 218 938 MHz line. The fit to the HCOOH line at 220 038 MHz is not perfect, but this is not worrying because our model is not adequate to reproduce the profile of very optically thick lines. The intensity of this line is not sensitive to the HCOOH column density in the range of column densities we are dealing with. Some HCOOH lines were also observed by FU05. As seen in Fig. 5, the lines are reasonably reproduced with our values. We have searched for the DCOOH and HCOOD lines in our spectrum and found one transition of HCOOD at 218 541 MHz from which we derive N(HCOOD)/N(HCOOH) ≈ 0.01 as long as both species come from the same region. Since we have only one line of HCOOD and it is at 4σ, we indicated this detection as tentative in Table 3.

4.15. Dimethyl ether: CH₃OCH₃

We detected four unblended lines of CH₃OCH₃, at 218 492, 219 301, 220 847, and 220 893 MHz. The other lines of this species are blended with intense lines. Assuming that the source is filling the beam, we derived T_rot = 500 K and N(CH₃OCH₃) = 2 × 10¹⁶ cm^-2. We considered that this apparently high rotation temperature was an opacity effect and obtained a better fit assuming T_rot = 200 K, N(CH₃OCH₃) = 4 × 10¹⁸ cm^-2 and a source diameter of 0.1″. These parameters are consistent with the non-detection of the ¹³C isotopologues and we adopted them.

4.16. Ethylene glycol: aGg’-(CH₂OH)₂, gGg’-(CH₂OH)₂

The aGg’ conformer of ethylene glycol, together with methyl formate, is one of those with the highest number of lines in our spectrum. We detected twelve lines, and seven were unblended. We used these seven unblended lines to derive a rotation temperature of 145 K and a beam averaged column density of N(aGg’-(CH₂OH)₂) = 2.3 × 10¹⁵ cm^-2 (see Fig. 2 and Table 2). The line at 218 576 MHz was removed from the final fit since it was very far from the intensity traced by the other lines (see Fig. 2) and is certainly blended with something else. In this case, we did not have information about the transitions of the ¹³C-isotopologues and deuterated species. The emission is compatible with the beam filling assumption, although we cannot discard a smaller size.

We also searched for gGg’-(CH₂OH)₂ in our spectrum. We have a good match with eight lines that can be assigned to this species (218 712, 219 097, 219 389, 219 410, 220 763, 220 448, 220 887, 221 596 MHz). Modeling the spectrum, we obtain that five additional lines are also present in our data but blended with other species. However there are two lines, at 218 144 MHz and 220 249 MHz, that should have been detected and do not appear in the spectrum. These lines have similar energies to the previous ones and their absence cannot be explained with a simple excitation argument. This species has not been detected in any other source thus far. Waiting for confirmation, we do not include it in the model.

4.17. Ketene: H₂CCO

We detected one o-H₂CCO line at 220 177 MHz and one p-H₂CCO at 221 545 MHz with similar intensity. The first transition is at E_u = 62.4 K and the second one E_u = 894.8 K. It is not possible to fit both lines assuming reasonable physical conditions and optically thin emission. One possibility is that the line at 221 545 MHz is not ketene. In this case, we can fit the other line assuming a rotation temperature of T_rot = 200 K and a beam averaged ortho+para H₂CCO column density of 6.7 × 10¹⁴ cm^-2, where we have assumed an ortho-to-para ratio of 3. Another possibility is that the emission is optically thick in both lines. In this case, we need a ketene column density of 4.0 × 10¹⁸ cm^-2 in a compact ~0.1′′ region. There is no line of the ¹³C isotopologue in the observed frequency range that would allow us to determine the opacities. The deuterated compounds have no intense transitions in the observed wavelength range either. We selected the optically thin case adopting a conservative approach. Taking into account the uncertainty in its column density, we do not use this species in our comparison with other sources.

4.18. Glycolaldehyde: CH₂OHCHO, Formamide: NH₂CHO

There are thirteen intense lines of glycolaldehyde in the sampled wavelength range. From these, six are not blended with other features and do not have any other likely identification. Assuming T_rot = 200 K, we estimated a beam averaged column density of 1.0 × 10¹⁵ cm^-2. Only one line of NH₂CHO lies in our spectrum. It is at 218 459 MHz and is blended with a line of T-ethanol. Our fit to T-ethanol failed to predict the high intensity of the observed feature suggesting some contribution from NH₂CHO. The total intensity would be consistent with a beam averaged formamide column density of 3.0 × 10¹⁴ cm^-2.

4.19. Vinyl cyanide: CH₂CHCN

We detected two rotational lines, at 218 675 MHz and 220 345 MHz, that could correspond to CH₂CHCN. The intense line at 220 345 MHz is overlapped with one of CH₃CN. Some features of the ν₁₁ = 1 vibrational state at an energy of 328.4 K could have also been detected but are blended with other more intense lines. Since we could not determine the rotation temperature, we assumed the fixed value of T_rot = 200 K and the same source size as the chemically related species CH₃CN, i.e., a diameter of ~0.1″, but our fit was very bad. The relative intensities of the lines at 220 345 MHz and 218 675 MHz cannot be accounted for by LTE models. We were not able to obtain a better fit by varying the rotation temperature and/or the source size. One possibility is that the intensity of one of the lines is incorrect because of baseline uncertainties or spatial filtering. The second possibility is that our identification is false. Since we do not have a better candidate for the 220 345 MHz line, we derived an upper limit to the vinyl cyanide column density using its line intensity and fixing the rotation temperature to 200 K. This compound is quite abundant in massive hot cores (see López et al. 2014), and this upper limit is interesting for comparison with these objects.

5. The hot core model

Based on the calculations explained in Sect. 4, we propose the hot core model shown in Table 3. This model is not unique and some parameters, especially source sizes, are quite uncertain. However, it cannot be done better. Higher spatial resolution is required to better constrained the spatial structure. Fortunately, the total number of molecules in our beam is well constrained, especially when we have detected the ¹³C isotopologue or the emision is optically thin, which is the case for most species. Our model is self-consistent; i.e., once a molecule is included, its isotopologues and deuterated compounds are also included. For isotopologues, we assume ¹²C/¹³C = 65, ¹⁶O/¹⁸O = 650, ³²S/³⁴S = 22, and ³⁴S/³³S = 6 (Chin et al. 1995; Milam et al. 2005). The column densities of the deuterated species are calculated independently to determine the deuterium fractions. When possible we directly compare the deuterated compound with the ¹³C isotopologue, which is expected to have similar fractional abundance, in order to avoid opacity effects in the derived column density ratio. The obtained values of deuterium fractions are ~0.06 for methyl formate, ~0.02 for methanol, ~0.008 for the doubly deuterated formaldehyde, ~0.01 for DC₃N, and <0.01 for HCOOD (see Table 3). These are average values in the hot core since the hydrogenated and deuterated species could have different spatial distributions. Using MADEX, we have synthesized the total spectrum assuming LTE, the parameters shown in Table 3 and convolving with a circular beam of ~1.4″. The obtained spectrum is compared with observations in Fig. A.1. Our fit is reasonably good taking into account the simplicity of our model. There are, however, two frequency ranges, 218.0–219.12 GHz and 221.46–221.62, where the agreement is poor. One reason is possible observational errors. We note that the second region is at the end of the observed frequency range where the passband calibration is more uncertain, but the existence of intense U lines suggests the existence of a population of COMs that have not been identified yet.

An important test for our model is to reproduce the interferometric observations published by FU05 with a higher angular resolution of 0.63″ × 0.46″. We synthesized the spectrum assuming the same parameters as in Table 3 but convolving with a smaller beam, ~0.52″, and compared with FU05 observations (see Fig. A.5). We find a remarkably good agreement for most of the species which confirmed that our model was not far from reality.

We identified the line at 231 143 MHz in FU05 as HCS providing an estimate of the H₂CS abundance in the hot core (see Table 3). However, we have only one line of the ¹³C isotopologue and the identification could be wrong. A similar situation occurs for S¹⁸O. We have detected one line at 228 272 MHz, but it is blended with intense CH₃OCHO and CH₃OCOD features. From this line we estimate a S¹⁸O column density of 8 × 10¹⁵ cm^-2 within the ~0.52″ (~650 AU) beam. Because of the blending, this estimate is model-dependent and suffers from larger uncertainty.

An important discrepancy between our model and FU05 observations comes from G+ethanol. There are two predicted G+ethanol lines, 228 491 MHz and 228 560 MHz that do not appear in the FU05 spectrum while all the T−ethanol lines are correctly reproduced. One possibility is that we have a lower kinetic temperature than assumed since the G+ethanol is 60 K higher in energy than T−ethanol. But the temperature would have to be unreasonably low, <50 K, to reproduce the observations.These lines are close to the edge of the spectral band and could suffer from some instrumental effects.

In Table A.2 we give a list with our new identifications of the data published by FU05. In this work we have identified more lines and found some misidentifications. The lines previously identified as c-C₃D are instead carried by CH₃CHO. In fact, CH₃CHO is the carrier of most of the lines in the band centered at 231.3 GHz. We have a handful of lines around the ¹³CS frequency without any plausible identification. One possibility is that we are observing high velocity gas emitting in the ¹³CS 5 → 4 line, but this would imply an outflow with velocities as high as 50 km s^-1. We have not seen such high velocities in the CO single-dish and interferometric spectra (Fuente et al. 2001, FU05). Therefore, we think that there are still some unidentified lines at these frequencies. The intense lines at 228 307 MHz, 228 363 MHz, 228 427 MHz, and 228 467 MHz, although identified, are poorly reproduced by our model. We have not found any simple way to improve the agreement between our model and observations. Either these lines are far from the LTE approximation or we are still missing important species. Additional observations could help to discern their origin.

The observations presented in this paper have significantly contributed to the understanding of the spectra published by FU05 proving that observations in a large range of frequencies are needed for the correct line identification.

6. Discussion

6.1. Physical conditions

It is known that hot cores are heterogenous objects where different species come from different regions with different physical conditions (see, e.g., Beuther et al. 2011; Brouillet et al. 2013; Bell et al. 2014). For this reason, we only compare rotation temperatures measured with the same molecular species.

Methyl cyanide is easily thermalized for the densities prevailing in hot cores and hence a good thermometer of the molecular gas. The rotational diagram shows that the temperature in the FIRS 2 hot core is ≈400 K. This temperature is similar to that measured in massive hot cores. Beuther et al. (2011) proposed the existence of a warm component of 600 ± 200 K in the Orion hot core based on submillimeter CH₃CN lines as observed with the Submillimeter Array (SMA). More recently, Bell et al. (2014) estimated a rotation temperature of ~220 K towards IRc2 and ~400 K in the hot spot located ~14″ NE using data from the 30 m telescope. Lower temperatures, however, are found in hot corinos. Bisschop et al. (2008) derived an upper limit of <390 K in IRAS 16293-2422 A and B based on interferometric SMA data. Fuente et al. (2009) derived a rotation temperature of 97 ± 25 K in the hot core located in the IM protocluster IC 1396 N. A similar rotation temperature, ~100 K, was derived by Sánchez-Monge et al. (2010) in the hot core associated with IRAS 22198+6336. Although the luminosity of FIRS 2 is similar, our observations suggest the existence of a warmer gas component (~400 K) in FIRS 2 than in IC 1396 N and IRAS 22198+6336. IC 1396 N is a protocluster with three young stellar objects (YSOs). Although the total luminosity is similar to that of FIRS 2, the luminosity of each YSO is lower and probably closer to that of an Ae star, i.e., <100 L_⊙. IRAS 22198+6336 is morphologically similar to FIRS 2. Sánchez-Monge et al. (2010) detected only the K lines with E_u = 100 − 300 K, while we used lines with E_u> 600 K in this study. It is possible that a warmer component remains hindered in IRAS 22198+6336 and would require higher sensitivity observations of transitions with higher E_u to be detected. In fact, FU05 determined a gas temperature of 50−100 K in FIRS 2 from lower sensitivity observations of the CH₃CN 5_K → 4_K ladder, from lines with E_u = 13−154 K.

The rotational diagrams of the oxygenated species give lower rotation temperatures than with CH₃CN. We derived rotation temperatures between 100 K and 200 K from the CH₂DOH, CH₃CHO, and aGg’-(CH₃OH)₂ lines and between 200 K and 300 K from CH₃OCHO and HNCO. Palau et al. (2011) derived rotation temperatures of ~100−150 K in the IM hot cores in IRAS 22198+6336 and AFGL 5142 from the ethanol lines. Rotation temperatures of around 100 K are also derived in Orion from CH₃OCH₃, methyl formate, deuterated methanol, and OCS (Tercero et al. 2010; Peng et al. 2012; Brouillet et al. 2013). Therefore, we do not detect significant differences between the rotation temperatures measured with these O-bearing species between IM and massive hot cores. Lower rotation temperatures, ~50 K, are measured with CH₃OCHO in IRAS 16293-2422 (Pineda et al. 2012).

In Table 4, we show a summary of the rotation temperatures derived from different molecules and for different hot cores. The comparison is not totally fair since CH₃CN and the O-bearing molecules could come from different regions. This is the case of IRAS 16293-2422, where CH₃CN comes mainly from the southern component (A) and the O-bearing molecules from the northern one (B) (Bisschop et al. 2008). As commented above, different regions are associated with O- and N-bearing molecules in Orion. Towards the other hot cores, the spatial resolution provided by the existing observations is lower, preventing us from resolving regions with different chemistries. Nevertheless, it seems that there is a weak trend with the maximum gas temperature increasing from low to massive hot cores as measured with CH₃CN. There is no trend for the O-bearing molecules.

This suggests a scenario in which the O-bearing molecules are more abundant in extended regions with temperatures ~100 K in both hot cores and corinos. Instead, CH₃CN probes the hottest region of the core, and its rotation temperature increases with the luminosity. Of course, there is a problem with the spatial scales that are different for low-mass and massive stars, but, taking into account that massive stars are more distant, this would favor the interpretation of higher temperatures in the massive stars. Therefore, within the limitations of our analysis, we can conclude that there is a trend of increasing temperature from hot corinos to massive hot cores. This trend is not so clear between IM and massive stars. As we have already discussed, there is no obvious difference between FIRS 2 and Orion.

Another important parameter is the total amount of gas in the hot core. One possibility is to calculate it from the dust continuum emission assuming a dust temperature and a dust emissivity value. FU05 adopted a dust temperature of T_dust = 100 K and κ_ν = 0.015 (1300/λ (μm)) cm² g^-1 and derived a total gas+dust mass of 2 M_⊙ in the hot core FIRS 2. More recently, Palau et al. (2013) derived a similar value (1.8 M_⊙) assuming T_dust = 50 K and κ_{1.3 mm} = 0.00899 cm² g^-1. Our results suggest that at least a fraction of the dust must be at T_dust = 400 K. Assuming T_dust = 400 K and κ_{1.3 mm} = 0.01 cm² g^-1, we obtain a lower limit to the gas+dust mass of 0.46 M_⊙. Therefore, the total gas+dust mass of the FIRS 2 hot core is uncertain in a factor of ~4. In Table 5 we show the average molecular abundances in a region of 1.4″ assuming M = 1.8 M_⊙ and 0.46 M_⊙ for the hot core mass, respectively. When detected, we used the ¹³C isotopologue to determine the total average molecular column density which is more reliable. As discussed in Sect. 4, the uncertainties in the molecular column densities would add an error of a factor ≤4−5 to these values.

6.2. Comparison with the Orion hot core

The hot core associated with FIRS 2 is extraordinarily rich in complex molecules. We have detected glycolaldehyde and tentatively formamide; these compounds had only been detected in a few objects thus far. Glycolaldehyde was detected in Sgr B2 (Hollis et al. 2000; Halfen et al. 2006; Requena-Torres et al. 2008), the massive hot core G31.41+0.31 (Beltrán et al. 2009) and more recently towards the hot corino IRAS 16293-2422B (Jorgensen et al. 2012; Zapata et al. 2013). Formamide has been detected in Orion (Motiyenko et al. 2012), Sgr B2 (Belloche et al. 2013), a handful of massive prototypical hot cores (Adande et al. 2013), and IRAS 16293-2422 (Kahane et al. 2013). In Fig. A.1, we compare the FIRS 2 spectrum with that of the Orion hot core as observed with the 30 m telescope (Tercero et al. 2010). Surprisingly, there is a good match between the spectra, in number of lines and relative line intensities, suggesting that both hot cores have similar chemical characteristics. Of course, this is a qualitative comparison and we need to put it on quantitative grounds to establish firm conclusions.

In Table 6 and Fig. 3 we compare the molecular column densities in FIRS 2 and Orion KL. For this comparison, in FIRS 2, we have used the average column densities in a region of 1.4″. The reason is that the sizes of the emitting regions are not determined for most of the species (see Table 3). One needs to know the rotation temperature and the line opacities independently, to be able to determine the source size. In many cases we have not detected the ¹³C isotopologue that would allow us to derive the line opacities. In others, the number of unblended lines is not sufficient to determine the rotation temperature and we had to assume a reasonable value. On the contrary, the number of molecules per beam is a quite well determined parameter as long as the emission is optically thin which is a reasonable assumption for many complex species. When detected, we used the ¹³C isotopologue to determine the total average column density.

Towards Orion KL, the molecular emission is formed of four physically different components: hot core, plateau, compact ridge, and extended ridge. The plateau has a chemistry characteristic of a shocked region and is considered to be associated with the shocks produced by a past eruptive episode. The extended ridge is the parent cloud that hosts the cluster of young stars. The compact ridge is a small (~15″) U-shaped feature that is characterized as being very rich in complex O-bearing molecules. The hot core is a very compact source (6″–10″) particularly rich in complex N-bearing molecules. We cannot resolve different regions within the FIRS 2 hot core; therefore, we consider that the FIRS 2 hot core is comparable to the hot core (HC) and the compact ridge (CR) Orion components together. In Table 6 we show the average column densities of the HC+CR Orion components in a region of 15″. To estimate this value, we have summed up the column densities of the HC and CR weighted by their respective filling factors: 0.44 for HC (assuming a size of 10″) and 1 for the CR. When possible, we used the ¹³C isotopologues to determine the Orion column densities (see Table 6). We assume ¹²C/¹³C = 50 for Orion (Comito et al. 2005; Tercero et al. 2010). Some authors, like Neill et al. (2013) and Comito et al. (2005) used a size of 10″ for the CR. We have multiplied their column densities by 0.44 to account for the different adopted source sizes. For CH₃CHO we have adopted the value of Turner (1991). This author did not distinguish among the different Orion components (hot core, plateau, compact ridge, and extended ridge) and we have taken the total value. For this reason this point is drawn as an empty circle in Fig. 3. In the case of D₂CO, Turner (1990) assumed a source size of 15″ × 25″ that is consistent with ours.

In Fig. 3 we compare the column densities of FIRS 2 and Orion normalized to methanol. Normalization is required if one wants to compare the relative abundances of the different species in the warm gas. Methanol is commonly used to make this kind of normalization in hot cores (Öberg et al. 2011). Instead we could have used methyl cyanide for the normalization but we would have obtained essentially the same trend. As is clearly seen in Table 6, it would simply produce an increase in all the ratios by a factor of 2.

Most of the relative molecular abundances in FIRS 2 agree with those in Orion within a factor of 5, which is quite good taking into account the uncertainty due to the unknown spatial structure of the molecular emission and opacity effects. Only a few molecules have abundances significantly different in both hot cores: CH₃OCHO, CH₃CH₂CN, HNCO, and SO₂ have fractional abundances more than 10 times lower in FIRS 2 than in Orion. In the case of CH₃OCHO, we have not detected the ¹³C isotopologues in FIRS 2 and our column density could be slightly underestimated. As discussed in Sect. 4.3, our estimate is accurate within a factor of 4. Increasing the methyl formate by a factor of 4 would push the methyl formate back to the region within the two black lines in Fig. 3, although still in the lower end. In the case of HNCO, the lines of the main isotologue are blended with those of the ¹³C isotopologue preventing us from a direct estimate of the line opacities. Looking at the top of the figure, there is a group of molecules that are more abundant in FIRS 2 by more than a factor of 4−5. These molecules are CH₂DOH, D₂CO, and CH₃CHO. As commented above, the value of CH₃CHO in Orion is uncertain. However, the differences observed in CH₂DOH and D₂CO could be significant. In the following section, we discuss possible scenarios to explain these differences.

6.3. Sequential formation of complex molecules in hot cores/corinos

Although gas phase reactions can play a role, surface chemistry dominates the formation of COMs. The large sensitivity of surface chemistry on physical parameters, especially the dust temperature, can also explain the observed chemical differentiation within a hot core and among different hot cores. For example, Caselli et al. (1993) found that complex N-bearing species are more easily formed if the dust temperature (T_dust) is about 40 K during the collapse phase. This is primarily due to the higher mobility of carbon and the shortage of hydrogen (H, H₂) on the grain surfaces. A similar argument has been used by Öberg et al. (2011) to explain the over-abundance of CH_2/3-rich molecules in hot cores and corinos compared with molecular ouflows. Öberg et al. (2011) studied a number of cores associated with outflows, low-mass cores observed with single-dish telescopes (tracing envelopes at ~5000 AU spatial scales), low-mass cores observed with interferometers (tracing warmer material at ~500 AU), and an average of high-mass hot molecular cores from Bisschop et al. (2007), and they found that HCO-rich molecules are in general more abundant than CH_3/2-rich molecules in outflows and envelopes of low-mass YSOs, while the situation is reversed for low-mass inner envelopes/disks and high-mass YSOs. They proposed a sequential formation of complex molecules, starting with HCO-rich molecules as long as CO ice is abundant, followed by CH_3/2-rich molecules at higher ice temperatures.

In Fig. 4 we present an updated version of the figure by Öberg et al. (2011) complemented with abundances of three intermediate-mass hot cores observed with interferometers (at ~500 AU scales, from this work and Palau et al. 2011), and the new Orion data. In the figure, symbols in warm colors (orange, red) correspond to CH_3/2-rich molecules, while symbols in cold colors (blue/black) correspond to HCO-rich molecules. Our new results for the intermediate-mass hot core FIRS 2 are in line with previous measurements towards IM hot cores at disk-scales (~500 AU). Putting all these data together, we do not find a clear trend for the abundances of the CH_3/2-rich and HCO-rich molecules with the stellar mass. Considering only interferometric observations, the CH₃CHO abundance seems to decrease with the stellar mass. However, the abundance of methyl formate, the only other HCO-rich molecule considered, is larger in Orion than in IM hot cores and hot corinos. Orion is the only source in which we have been able to use the ¹³C isotopologue to derive the methyl formate abundance. If the methyl formate lines were typically optically thick in hot cores/corinos, this would have produced an underestimate of the CH₃OCHO abundance in the rest of objects. Using the upper limit to the emission of the ¹³C isotopologue, we have estimated that the methyl formate abundance in FIRS 2 is accurate within a factor of 4. Even considering an uncertainty of a factor of 4 in the CH₃OCHO abundances towards low-mass and IM YSOs, the [CH₃OCHO]/[CH₃OH] ratio would be larger in Orion than in these objects. In addition, the [CH₃OCHO]/[CH₃OH] ratio seems to increase from the low-mass to the IM sample. We can only compare two HCO-rich molecules in Fig. 4. Therefore we cannot know if methyl formate is a special case (see also Taquet et al. 2012). Further observations in IM and massive hot cores are required to have a deeper insight into the chemistry of this molecule and other HCO-rich species.

We have yet to discuss the deuterium fractions in FIRS 2 and Orion. Deuterated species whose deuteration requires surface chemistry, such as D₂CO, present higher abundances in the warm regions associated with low-mass protostars. Loinard et al. (2003) searched for the doubly deuterated form of formaldehyde (D₂CO) in a large sample of young stellar objects; D₂CO was detected in all low-mass protostars, with [D₂CO]/[H₂CO] ratios of 2−40%. On the other hand, no detection was obtained towards massive protostars (where [D₂CO]/[H₂CO] < 0.5%). This is consistent with the value reported by Turner (1990) in Orion. If the hot cores associated with massive stars are older and/or significantly denser than those surrounding low-mass objects, gas phase chemistry could have had the time to reset the deuterium fractions to values close to the cosmic D/H ratio. The longer time of the evaporated molecules in gas phase would also affect the abundances of the COMs that can be formed in warm gas-phase chemistry (e.g., CH₂CHCN).

An alternative explanation could be that the temperature of the envelope material accreting onto the high-mass protostars is larger than 30 K (Fontani et al. 2002). In this case the deuterium fractionation efficiency in the gas phase is strongly reduced before the hot core phase as the standard H₂D⁺ route (H+HD → H₂D⁺ + H₂) also starts to proceed from left to right. Moreover, at T_dust> 30 K there is no way that deuteration can be enhanced on the grain surfaces. The reason is that H and D are easily evaporated before reacting on the surface (see e.g. Cazaux et al. 2011). The higher temperature during the collapse would also affect the formation of COMs in grain mantles. As CO does not efficiently freeze out at these values of T_dust, the formation of HCO-rich molecules would be strongly diminished too. As commented above, methyl formate could be an exception to this rule.

6.4. Carbon budget

We have used the column densities shown in Table 3 to estimate the carbon gas phase budget in the FIRS 2 hot core. Apart from CO and its isotopologues, most of the carbon is locked in methanol with a total column density of ~3.4 × 10²⁰ cm^-2 in the compact component of the hot core. Taking into account the rest of molecules, the carbon column density reaches to ~4 × 10²⁰ cm^-2 in this small region. One problem in deriving absolute abundances is that we do not know the total column density of gas in the inner R< 0.05″ region. Based on higher angular resolution observations, FU05 derived a size of 0.72″ × 0.52″ for the continuum source that account for 75% of the continuum emission and a point source that contributes to 25% of the flux. Adopting this value for the fraction of continuum flux coming from the compact component of the hot core and a total gas mass of 0.46 M_⊙ (see Sect. 6.1), the total column density of molecular hydrogen would be 2 × 10²⁵ cm^-2 and the fractional abundance of the carbon locked in COMs relative to H nuclei, ~1.0 × 10^-5. This value is 36 times lower than the solar value of the carbon abundance (C/H ~3.6 × 10^-4; Anders & Grevesse 1989) and suggests that methanol and COMs (at least those considered in this paper) are not the main reservoirs of carbon in hot cores.

It is also useful to compare methanol with C¹⁸O. Again we have the problem of the unknown spatial distribution of the C¹⁸O emission within our interferometric beam. We can derive a lower limit to the C¹⁸O abundance assuming that the emission is optically thin and fills the beam. Adopting T_rot = 400 K, we derive N(C¹⁸O) = 1.5 × 10¹⁷ cm^-2 and N(CO) = 9.4 × 10¹⁹ cm^-2. This solution, however, is not compatible with the non-detection of the C¹⁸O 9 → 8 line by Fuente et al. (2012) and we cannot reconcile the PdBI and Herschel results by lowering the temperature down to T_rot = 200 K. The optically thick solution seems more reasonable. Assuming again that the gas temperature is 400 K and that the C¹⁸O emission is optically thick (T_B ≈ T_rot), we derive an effective diameter of 0.15″ for the C¹⁸O emitting region. In this case, our results are compatible with the Herschel upper limit to the C¹⁸O 9 → 8 line and the column density of CO would be >10²² cm^-2 in the compact component of the hot core.

7. Conclusions

The protostar FIRS 2 is probably the youngest IM protostar studied thus far and, as such, is an excellent template on which to base interpretations of other IM and massive star forming regions. The interferometric observations presented in this paper proved that this IM protostar hosts a hot core extraordinarily rich in complex molecules.The gas kinetic temperature as measured with methyl cyanide, is around 400 K, similar to that of the Orion hot core and higher than typical rotation temperatures in hot corinos. A detailed comparison of the chemistry of FIRS 2 with Orion shows that the fractional abundances of most molecules relative to that of CH₃OH agree within a factor of 5, which is reasonable taking into account the uncertainties of our column density estimates. Only CH₃CH₂CN, HNCO, SO₂, CH₂DOH, D₂CO, and CH₃CHO present a significant disagreement; CH₃CH₂CN, HNCO, and SO₂ are more abundant in Orion, and CH₂DOH, D₂CO, and CH₃CHO, in FIRS 2. Since the physical conditions are similar in both hot cores, only different initial conditions (warmer pre-collapse and collapse phase in the case of Orion) and/or different crossing time of the gas in the hot core can explain this behavior. FIRS 2 is a YSO in which most of the accreting envelope still maintains an overall temperature lower than 30 K, allowing deuteration to proceed unhindered, while complex N-bearing molecules like CH₃CH₂CN are not efficiently formed, unlike the Orion hot core.

Acknowledgments

We thank the Spanish MINECO for funding support from grants CSD2009-00038, AYA2009-07304, and AYA2012-32032. D.J. is supported by the National Research Council of Canada and by a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant. A.P. is supported by the Spanish MICINN grant AYA2011-30228-C03-02 (co-funded with FEDER funds), and by the AGAUR grant 2009SGR1172 (Catalonia).

References

Online material

Appendix A

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