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Appendix A: Fit details for individual molecules

¹³CO, C¹⁸O: carbon monoxide was detected in the J = 1−0 transitions of the two isotopic variants ¹³CO and C¹⁸O. The latter is only a tentative detection, the peak flux being only at the two-sigma level. Since we only detected one line per species, we could not fit an excitation temperature to the emission. By fixing the excitation temperature to 70 K, which is the lower limit to the CO J = 2−1 brightness temperature detected by Costagliola et al. (2013), a column density on the order of 10¹⁸ and 10¹⁷ cm^-2 is found for ¹³CO and C¹⁸O, respectively.

CS,¹³CS, C³³S, C³⁴S: we detect the J = 2−1 and J = 6−5 rotational transitions of carbon monosulfide and its ¹³C, ³³S, and ³⁴S isotopic variants. For CS, the population diagram analysis and the LTE fit both find an excitation temperature of ~20 K, and a column density of 6 ± 0.6 × 10¹⁶ cm^-2. In order to calculate isotopic ratios, we fix the excitation temperature of the isotopic variants at 20 K. This implies the emission to be co-spatial and the excitation to be similar for all isotopic variants. Under this assumption, the LTE fit gives column densities on the order of 10¹⁵ cm^-2 for ¹³CS and C³³S, and on the order of 10¹⁶ cm^-2 for C³⁴S. An NLTE fit of CS emission was also performed. We find that the emission is best fit by a model with hydrogen density n(H₂) = 10⁵ cm^-3, kinetic temperature T_kin = 50 K, and column density N = 4 × 10¹⁷ cm^-2. The NLTE values for T_kin and N are significantly higher than the LTE results. This may be due to the high critical density of the J = 6−5 line, which would require n(H₂)> 10⁷ cm^-3 to be efficiently excited by collisions.

CN: we detect the CN multiplet at 3 mm, including nine merged lines spanning from 113.12 to 113.52 GHz in rest frequency. The lines have very similar upper-state energies (~5 K) and do not permit a reliable fit. In order to obtain a lower limit to the molecule’s column density, we performed an LTE fit with a fixed temperature of T_ex = 70 K. The resulting column is N ~ 5×10¹⁷ cm^-2. As discussed for ¹³CO and C¹⁸O, the T_ex value was chosen as the lower limit to the observed CO brightness temperature.

NS: we detect the strongest lines of the J = 11/2–9/2 multiplet of nitric sulfide at rest frequencies 253.57−255.6 GHz. Even if so close in frequency, the detected lines span a wide interval in upper state energies (E_u = 40−360 K). We derive an excitation temperature of T_ex = 350 ± 150 and a column density of N = 8 ± 4×10¹⁶ cm^-2. The large uncertainties on the derived quantities are due to the line blending in band 6.

SO,³⁴SO: emission from sulfur monoxide is heavily blended, the only sure detections being the lines 3₂–2₁ (99.3 GHz), 2₃–1₂ (109.25 GHz), and 6₆–5₅ (258.255). Because of the strong blending, the χ² surface of our LTE fit is not well defined, giving only a lower limit for the excitation temperature of T_ex> 20 K. The fitted value for the column density is relatively well defined, N = 4 ± 3×10¹⁵ cm^-2. We also performed a NLTE fit of the isolated lines, resulting in hydrogen densities between 10⁶ and 10⁷ cm^-3, kinetic temperatures of 50−200 K, and column densities from 2×10¹⁵ to 2×10¹⁶ cm^-2. The isotopic variant ³⁴SO is only tentatively detected as two highly blended lines at 251.4 and 255.1 GHz. The LTE fit with a fixed excitation temperature of 20 K results in a poorly constrained column density of 10¹⁵–10¹⁶ cm^-2.

SiO,²⁹SiO, ³⁰SiO: strong silicon monoxide emission is detected in band 3 (J = 2−1) and band 6 (J = 5−4). The two rotational lines are free of blending and well identified. Our LTE fit gives an excitation temperature of 10 ± 5 K and a column density of 3 ± 1×10¹⁵ cm^-2, comparable with those found with the population diagram analysis. The NLTE fit results in an hydrogen density lower than 10⁶ cm^-3, a kinetic temperature greater than 20 K, and a column density greater than 10¹⁶ cm^-2. We also detect the isotopic variants ²⁹SiO and ³⁰SiO. The emission lines from these two species are strongly blended, but still clearly identified. In our LTE fit we fix their excitation temperature to that of SiO, i.e., T_ex = 10 K. The resulting column density estimation is on the order of 10¹⁵ cm^-2, with large uncertainties (>50%) due to the line blending.

HCN, H¹³CN: hydrogen cyanide is detected in its J = 1−0 and J = 3−2 transitions. The J = 3−2 line is the strongest molecular line detected in our scan, with an integrated flux density of 50 ± 5 Jy km s^-1, and a peak brightness temperature of 35 K. Both emission lines have FWHM> 140 km s^-1, broader than than the average 120 km s^-1 assumed in our fit. The derived properties are thus representative only of the line core. The LTE fit gives T_ex = 7 ± 1 K and N = 2 ± 1×10¹⁶ cm^-2, while the NLTE analysis results in a hydrogen density lower than 10⁶ cm^-3, T_kin> 100, and N> 10¹⁶ cm^-2. The large discrepancy in excitation temperature between the two fitting methods is most likely due to a limitation of the LTE fit, which gives unreliable results for high opacities. An excitation temperature of 8 K seems too low when compared with the CO brightness temperature of >70 K reported by Sakamoto et al. (2013) and Costagliola et al. (2013), and may be an indication of sub-thermal excitation of HCN. The brightness temperature for a source size of 0.̋4 is ~35 K and ~65 K for the two lines respectively (see Table 2). This sets a lower limit for the excitation temperature of the molecule, and thus to the kinetic temperature of the gas, of at least 65 K. For these reasons, we will assume the NLTE fit to best represent the HCN emission in NGC 4418.

The H¹³CN J = 1−0 line was also detected. A column density estimate of 2 ± 1×10¹⁵ cm^-2 was obtained by fixing the excitation temperature at 7 K. If we assume an extragalactic ¹²C/¹³C ratio between 40 and 100 (Henkel et al. 2014), this correspond to a column densities of HCN of (0.8–2) × 10¹⁷ cm^-2.

HNC, HN¹³C: we detect the J = 1−0 and J = 3−2 rotational transitions of hydrogen isocyanide. Both the population diagram analysis and the LTE fit of the total spectrum result in an excitation temperature of 8−9 K, and column densities in the range 3−8×10¹⁵ cm^-2. An NLTE fit of the emission was also performed, resulting in an hydrogen density <10⁶ cm^-3, a kinetic temperature greater than 100 K, and a column density >10¹⁶ cm^-2. The results of the LTE and NLTE fitting of HCN and HNC are very similar, including the discrepancy of the fitted excitation temperatures for the two methods. The LTE fit results in very low T_ex , lower than the brightness temperature of the two detected lines of HNC (T_b = 45 K and 30 K for the J = 1−0 and J = 3−2 transitions, respectively). The NLTE fit results in T_ex≃ 40 K, which is consistent with the brightness temperature of the lines for the assumed source size of 0.̋4. The J = 1−0 transition of HN¹³C is also detected. The LTE fit with a fixed excitation temperature of 8 K results in a column density of 1.5 ± 0.5×10¹⁵ cm^-2.

HCN, v2 = 1, HNC, v2 = 1: vibrationally excited HCN and HNC are tentatively detected in our scan. For each molecule we only detect the J = 3−2, v2 = 1f transitions, therefore we cannot produce a reliable fit to the rotational temperature. However, we can derive the vibrational temperature by comparing the intensity of the J = 3−2 transitions of both the v2 = 1 and v = 0 states. We find that the relative population of the v2 = 1 and v = 0 states is well described by a vibrational temperature of ~350 K for HCN and 450 K for HNC. When assuming these temperatures to be also the rotational excitation temperatures of the v2 = 1 emission, we obtain line intensities which are consistent with the observed spectrum.

HCO⁺, H¹³CO⁺, HC¹⁸O⁺: the J = 1−0 and J = 3−2 transitions of HCO⁺ (formylium) are detected in band 3 and band 6, respectively. The population diagram analysis and the LTE model fit result in an excitation temperature of 6−8 K and a column density of 1−6×10¹⁵ cm^-2. The RADEX models that best fits the emission have n(H₂)<6 × 10⁵ cm^-3, T_kin> 100 K, and N> 10¹⁶ cm^-2. For HCO⁺ we find the same discrepancy between the LTE and NLTE fitted excitation temperatures that we discuss in the HCN and HNC case. The NLTE fit provides more physically reasonable results, consistent with an observed brightness temperature of the lines of >20 K (see Table 2).

We also detect the J = 1−0 emission line of H¹³CO⁺. By fixing the excitation temperature of the molecule at 6 K, we obtain an LTE estimate of the column density of N(H¹³CO⁺) = 7 ± 4×10¹⁴ cm^-2. If we assume an extragalactic ¹²C/¹³C ratio between 40 and 100 (Henkel et al. 2014), this corresponds to a column density of HCO⁺ of (0.8–2) × 10¹⁷ cm^-2.

The HC¹⁸O⁺, J = 3−2 transition is tentatively detected in band 6, with heavy blending. The LTE fit is highly degenerate, and only results in an upper limit of 20 K for the excitation temperature and a lower limit to the column density of 10¹⁴ cm^-2.

H₂S: at least 6 transitions of hydrogen sulfide are included in the scan, but only one transition (2_(2,0)–2_(1,1) at 216.71 GHz) is free of blending and clearly identified. By fixing the excitation temperature of H₂S at 70 K, the LTE fit results in a column density of 1 ± 0.5×10¹⁷ cm^-2.

CCH: we detect the N = 1−0 multiplet of ethynyl at rest frequencies between 87.28 and 87.45 GHz (sky frequency ~86.76 GHz). The 6 lines have very similar upper state energies (~4 K) and thus do not allow an accurate fit of the excitation temperature. By fixing T_ex = 70 K we obtain an LTE estimate of the column density of 2 ± 1×10¹⁷ cm^-2.

HCS⁺: the J = 2−1 and J = 6−5 rotational transitions of HCS⁺ (thioformylium) are detected in band 3 and band 6, respectively. The 1 mm line is heavily blended with emission from vibrationally excited HC₃N, while the 3 mm line is free of blending. The emission can be reproduced by our LTE model with T_ex = 20 ± 10 K and N = 8 ± 4×10¹⁵.

CCS: we detect 6 emission lines of thioxoethenylidene, with upper energy levels ranging from 20 to 110 K. The emission is free of blending and is well fit by our LTE model. The best fit values are T_ex = 20 ± 10 K and N = 1.5 ± 0.5×10¹⁶ cm^-2.

N₂H⁺: we detect the J = 1−0 triplet at 93.17 GHz and the J = 3−2 line of N₂H⁺ (diazenylium). The triplet emission is totally blended, but free of contamination from other species. The LTE and NLTE fit procedures give very similar results (see Table 4) with T_ex~ 30 K and N ~ 5×10¹⁵ cm^-2. The best fit hydrogen density in our NLTE analysis is 10⁷ cm^-3, which is higher than the critical density of the detected transitions (n_c ~ 10⁵–10⁶ cm^-3), and the T_kin and T_ex coincide for both lines. We conclude that the RADEX best fit represents an LTE excitation of the molecule.

H₂CO: we detect eight transitions of formaldehyde, four from para-H₂CO and four from ortho-H₂CO. The LTE fit for both species results in an excitation temperature of 350 ± 100 K and column a column density of 5−8×10¹⁶ cm^-2. The NLTE analysis results in an hydrogen density of 10⁵ cm^-3, a kinetic temperature greater than 300 K and a column density of 7×10¹⁵–10¹⁶ cm^-2. In our NLTE fit we only obtain a lower limit to the kinetic temperature because the LAMBDA database does not contain collision coefficients for temperatures greater than 300 K.

c-HCCCH: we detect 15 emission lines of cyclopropenylidene at the 3σ level across ALMA bands 3 and 6. The detected lines have upper state energies ranging from 40 to 500 K. The LTE model well fits the emission, resulting in an excitation temperature of 180 ± 100 K and a column density of 1 ± 0.5×10¹⁷ cm^-2. The large uncertainties are mostly due to the blending in band 6.

H₂CS, HCS: three isolated emission lines of thioformaldehyde are detected at sky frequencies 103.89, 268.66, and 276.95 GHz. Three more lines from HCS are tentatively detected (~ 2σ) in band 3. The detected transitions of H₂CS have upper state energies ranging from 20 to 70 K. The LTE fit results in an excitation temperature of 35 ± 10 K and a column density of 1 ± 0.5×10¹⁶ cm^-2. By fixing the excitation temperature at 35 K we derive an upper limit for the column density of HCS of 5 ± 2×10¹⁵ cm^-2.

HC₃N, H¹³CCCN, HCC¹³CN: we detect bright cyanoacetylene emission in all three ALMA bands. Nine isolated lines are detected, with upper state angular momentum ranging from 10 to 32, and upper state energies from 24 to 230 K (see Table 2). The population diagram analysis and the LTE fit of the whole spectrum give an excitation temperature of ~70 K and column densities in the range 2−9×10¹⁶ cm^-2 (see Tables 2, 4). The H¹³CCCN and HCC¹³CN isotopomers are also detected in all three bands, for a total of nine isolated emission lines with upper state energies ranging from 20 to 240 K. We performed an LTE fit of both species, assuming the same excitation temperature of 70 K as HC₃N. The fitted column densities are very similar, in the range of 1−2×10¹⁵ cm^-2, with uncertainties on the order of 50%.

Vibrationally excited HC₃N: emission from vibrationally excited HC₃N dominates the mm-wave spectrum of NGC 4418. We detect rotational transitions from the four vibrationally excited states HC₃N, v6 = 1, HC₃N, v7 = 1, HC₃N, v6 = 1, v7 = 1, and HC₃N, v7 = 2, for a total of 25 transitions. The upper state energies of such vibrationally excited lines are very high, ranging from 300 to 900 K. The emission from all four species is well fitted by our LTE model and by the rotational diagram analysis. We find similar excitation temperatures, in the range 70−100 K, and column densities ranging from 10¹⁵−10¹⁶ cm^-2. From the relative population of the vibrational levels it is possible to derive the vibrational temperature of the molecule via a population diagram analysis. The results are reported in Fig. 4. We are able to derive the vibrational temperature of three different angular momentum states (J = 10, 11, 12) for which emission of more than two vibrational states was detected. The three fits give remarkably similar results, with vibrational temperatures ranging from 330 to 400 K.

CH₂NH: we identify three spectral features as emission from methanimine at rest frequencies 105.79, 257.11, and 266.27 GHz, with upper state energies ranging from 30 to 60 K. The LTE fit of the spectrum results in an excitation temperature of 45 ± 30 K and a column density of 1.5 ± 0.5×10¹⁷ cm^-2.

NH₂CN: emission from cyanamide is tentatively detected in NGC 4418. Only one isolated line at sky frequency 98.62 GHz is unambiguously identified as the NH₂CN J = 5−4 transition, while most emission across the observed ALMA bands is heavily blended. Our LTE fit results in an excitation temperature of 30 ± 20 K and a column density of 5 ± 2×10¹⁵ cm^-2. However, the derived parameters are highly uncertain because of the blending of the lines at 1 mm.

CH₃CN: bright emission from methyl cyanide is detected as four line forests at sky frequencies 91.3−91.35, 109.56−109.62, 254.87−255.78, 292.11−292.28 GHz. The detected lines have upper state energies ranging from 13 to 500 K, with bright emission from lines with E_up> 200 K. The LTE fit results in a very high excitation temperature of 1000 K, but does not reproduce the intensity of the lines at 3 mm. The NLTE procedure provides a better fit of the emission across all three ALMA bands, resulting in a low hydrogen density of 10⁴ cm^-3, and a high kinetic temperature >500 K, required in order to fit the high energy lines. The critical density of the observed transitions varies between 10⁵ cm^-3 for the lines at 3 mm, and 10⁷ cm^-3 for the lines at 1 mm. It appears that the only way to fit both the 3 mm and the high-energy 1 mm lines is to lower the hydrogen density until the 3 mm lines are not efficiently excited by collisions (n(H₂) <n_c, i.e., they are not at LTE). This could imply that CH₃CN emission is originating from a gas phase that is significantly more diffuse than for the other molecular tracers, or that the low- and high-excitation lines are emerging from different environments.

CH₃CCH: methyl acetylene is tentatively detected in NGC 4418. The emission is heavily bended and no isolated line can be identified. Emission from the molecule is required in order to fit the line forests at sky frequencies 254−254.6, 271.2−271.6, and 288−288.6 GHz. The LTE fit results in an excitation temperature of 350 ± 100 K, and a column density

of 1 ± 0.5×10¹⁶. We advise extreme caution when interpreting these results, since the strong blending makes the fit highly degenerate.

HC₅N: emission from cyanobutadiyne is required in order to explain 11 spectral features across all three ALMA bands, which could not be associated with any other molecule. Nine of the detected lines are isolated lines free of blending with other species. The upper state angular momentum of the detected transitions ranges from 32 to 42, corresponding to energies above ground of 65 to 85 K. The population analysis and the LTE fit of the whole spectrum result in an excitation temperature of 60−70 K, and column densities in the range 0.5−2 × 10¹⁶ cm^-2.

CH₃OH: methanol emission is needed in order to fit the highly blended region between sky frequencies 287.8 and 288.3 GHz. No other transition from the molecule is detected above the 3σ level across the whole observed frequency range. The NLTE fit results in a kinetic temperature of 100 ± 60 K and a column density of 2 ± 1×10¹⁶ cm^-2, for an hydrogen density of 10⁷ cm^-3. The fit is poorly constrained because of line confusion. Non-LTE excitation of methyl acetylene could give a significant contribution to the emission in this region, thus the derived column density of CH₃OH should be considered as an upper limit.

Fig. A.1 The ALMA spectral scan of NGC 4418. The data are shown as a shaded histogram plot, the best fit for each molecule is shown as solid black lines. The total fit to the data is shown as a red solid line. The 1σ level is shown as a dashed green line. The residuals, together with the data rms, are shown below the spectrum as a green histogram plot with error bars. Emission lines above 3σ are labeled.

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Fig. A.2 Comparison of our ALMA data with single-dish spectra of the brightest lines in the scan. The blue line shows the spectrum extracted from the ALMA visibilities by fitting a point source with the CASA routine uvmultifit. The black line shows single dish spectra observed by the authors with the IRAM 30 m telescope. The error bars show the squared sum of the rms of the two datasets. The spectra were interpolated to a common resolution of 28 and 19.5 MHz at 3 and 1 mm, respectively.

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Fig. A.3 Comparison of our ALMA data with SMA observations by Costagliola et al. (2013). The blue line shows the spectrum extracted from the ALMA visibilities by fitting a point source with the CASA routine uvmultifit. The black line shows the flux density measured by the extended configuration of the SMA, with a beam size of 0.̋4 and a maximum recoverable scale of 2′′. The error bars show the squared sum of the rms of the two datasets. The spectra were interpolated to the resolution of the ALMA spectral scan.

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© ESO, 2015