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Appendix A: Comments on individual molecules

Eighteen molecular species were detected in our frequency survey between 129.8 GHz and 175.0  GHz in the 2 mm atmospheric window and between 241.0 GHz and 260.0 GHz in the 1.3 mm window. In this appendix, we provide details of the Gaussian profile fitting and blending cases of individual transitions.

For some special cases, we performed synthetic Gaussian fits using the MASSA software, which reads the spectra and the spectroscopic parameters of the selected lines (using the JPL catalog), and then attemps to measure iteratively the column density, excitation temperature, velocity, and FWHM of the lines until it finds a simultaneous, optimal, Gaussian fits for all of them.

For instance, the synthetic Gaussian fit method was applied to the weak molecules NO, NH₂CN, SO, and SO₂. For each species, all the transitions that lie in our survey were included, enabling MASSA to compare the strengths of the lines and ensure that the line identifications are reliable (since all the transitions of the same strength are either identified or not).

In a similar way, synthetic Gaussian fits were applied to molecules with hyperfine structure. In these cases, MASSA fits one Gaussian profile to each component, taking into account the strength of each one. However, since the M 82 lines are quite broad (60−120 km s^-1), the hyperfine structure is not resolved and results in one single Gaussian (see Martín et al. 2010 for details about the C₂H(2 − 1) synthetic fit). This method was also applied to these cases where two or more species are blended (see Fig. A.1 for an example).

The synthetic Gaussian fits do not provide errors in the integrated intensities. However, these errors are required when doing the Boltzmann diagrams if one wishes to obtain appropriate errors associated with the rotational temperatures and column densities. Thus, unless otherwise indicated, in cases where a synthetic Gaussian profile was fitted, we calculated an error in the integrated area using (A.1)where rms is the 1σ noise level of the spectrum that contains the line, and Dv is the spectral resolution in velocity units. All the parameters are in international system units.

• Hydrogen recombination lines. TheH36α, H35α, and H34α were observed at 135.3 GHz, 147.0 GHz, and 160.2 GHz respectively. However, H35α is blended with CS(3 − 2) and H36α is blended with H₂CS (4_1,4 − 3_1,3). We first fitted a Gaussian profile to H34α, which is the only recombination line that does not suffer from contamination by other species. We then assumed that the three lines have similar intensities, and used the same Gaussian profile to subtract H35α and H36α from the blended spectra.

• Cyanoacetylene – HC₃N. We detected five transitions of this linear molecule. The HC₃N (16 − 15) transition at 145.561 GHz is blended with H₂CO (2_0,2 − 1_0,1) (Fig. A.1). For this cyanoacetylene line, we fitted a synthetic Gaussian profile according to the physical parameters derived from all the other detected transitions, and fixed the velocity and the line width to 300 km s^-1 and 100 km s^-1, respectively. We also included the transition HC₃N (24−23) at 218.325 GHz observed by Aladro et al. (2011).

  Fig. A.1 Example of a synthetic Gaussian fit performed with MASSA. In this case, HC3N (16 − 15) (the line on the left) is blended with H2CO (20,2 − 10,1) (the line to the right). The bump at higher frequencies is the emission from the centre of the galaxy picked up by the telescope beam. This bump was originally subtracted before any Gaussian fit, although here we show it as an example of the strength of this emission. See details about the Gaussian fitting in the text.

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• Propyne (methyl acetylene) – CH₃CCH. None of the five detected lines of this symmetric top molecule are blended. Each (J → J − 1) transition consists of a number of K components (being K = 0,...,J − 1) that are not resolved because of the large line widths. Thus, we fitted unique Gaussian profile to each group of transitions. Given the rotational temperature derived from the Boltzmann diagram (T_rot = 31.6 ± 0.1 K), only the K = 0 to 4 components contribute to the line intensity, with the K = 4 component having a contribution of less than 1% to the total T_peak. Therefore, higher values of the K-ladder (i.e., K > 4) were not taken into account. Before fitting the Gaussian, we subtracted a bump in the CH₃CCH (8 − 7) line due to emission from the centre of M 82, that was detected by the beam of the telescope. The CH₃CCH (9 − 8) transition, at 153.817 GHz could be contaminated by the HNCO (7_0,7 − 6_0,6) line, but because no other lines of isocyanic acid with similar spectroscopic parameters are detected, we assume that its contribution is negligible. From Aladro et al. (2011) we gathered data for the CH₃CCH (16 − 15) transition at 273.420 GHz, which lies outside our survey coverage.

• Carbon monosulfide – CS. Two transitions of CS fall within our frequency survey. The line CS (3 − 2) at 146.969 GHz is blended with H35α. We first subtracted the estimated contribution of the hydrogen recombination line, and then fitted a Gaussian profile to the residual feature. The CS (5 − 4) at 244.936 GHz does not show any special characteristics. To estimate the physical parameters of CS, we also used the detections reported by Bayet et al. (2009b) and Aladro et al. (2011). This is the only molecule in the survey that haves two components in the Boltzmann diagram, with rotational temperatures of 5.8 ± 0.1 K and 15.1 ± 0.9 K (Aladro et al. 2011).

• Methyl cyanide – CH₃CN. Three transitions of methyl cyanide were clearly detected at 147.174 GHz, 165.565 GHz, and 257.483 GHz, none of which are blended. In a similar way to propyne, CH₃CN is a symmetric top molecule whose lines contain a number of unresolved K components (K = 0,...,J − 1). As a first approximation, the Boltzmann diagram gave us T_rot ~ 30 K. For this temperature only the K = 0,...,4 components contribute to the total line intensities, the K > 4 components contributing less than 1%. Taking into account only these first K-ladder components, we finally obtain a T_rot = 32.9 ± 1.6 K. On the other hand, as mentioned in Sect. 5 this molecule probably arises from the cores of the molecular clouds. This is consistent with the narrow FWHM of its lines, about 80 km s^-1 for CH₃CN (8_K − 7_K) and CH₃CN (9_K − 8_K), and especially for the  ~ 60 km s^-1 of the CH₃CN (14_K − 13_K) transition.

• Hydrogen cyanide – H¹³ CN. The group of transitions of H¹³CN (2_K − 1_K) were detected at 172.678 GHz. We fitted a synthetic Gaussian profile using the same line width and position for the five hyperfine components of the line. We then assumed T_rot = 20 ± 10K in the Boltzmann diagram. The large error in the column density reflects the error in the integrated areas found using the formula in Eq. (A1). Following the lower limit to the carbon isotopic ratio in M 82, ¹²C/¹³C > 138 by Martín et al. (2010), we can estimate the column density of HCN as N_HCN > 2.3 × 10¹⁴ cm^-2, in agreement with the results of Seaquist & Frayer (2000).

• Formaldehyde – H₂CO. We detected three transitions of this molecule, the H₂CO (2_1,2 − 1_1,1) line at 140.840 GHz being the only that is not blended. Thus, the width and position of the Gaussian fit of this line were used to fix the Gaussian fitting to the other two lines. The transition H₂CO (2_0,2 − 1_0,1) at 145.603 GHz is blended with HC₃N (16 − 15), and is also contaminated by the emission from the centre of the galaxy detected by the telescope beam (Fig. A.1). We first subtracted the contributions of both cyanoacetylene and the emission from the centre of the galaxy, and then fitted a Gaussian profile to the residuals. Likewise, H₂CO (2_1,1 − 1_1,1) at 150.498 GHz is blended with c-C₃H₂(2_2,0 − 1_1,1) and NO (3/2 − 1/2)Π ⁻ . In this case, we first fitted a Gaussian profile to the formaldehyde feature. All the fits are synthetic.

• Cyclopropenylidene – c-C₃H₂. A total of eight transitions of this molecule were detected in the survey. Six of them are blended with other lines, and two are tentative. The transitions c-C₃H₂(3_1,2 − 2_2,2) at 145.090 GHz and c-C₃H₂(2_2,0 − 1_1,1) at 150.436 GHz are blended with CH₃OH (3 − 2)A+ and H₂CO (2_1,1 − 1_1,1), respectively. Both Gaussian profile fits are synthetic. The pair of lines at 150.8 GHz is spectrally unresolved. The same holds for the pair at 151.3 GHz. In all these cases, the width and the velocity of the cyclopropenylidene Gaussian profiles were fixed to 100.0 km s^-1 and 300 km s^-1, respectively. The fixed velocity is supported by the results of the two non-blended lines, at 305.1 and 307.6 km s^-1. However, only the c-C₃H₂(3_2,1 − 2_1,2) line at 244.222 GHz has a non-fixed line width, which is a bit narrower than 100 km s^-1 (~85 km s^-1). Some molecules occasionally have narrower features at higher frequency transitions (e.g. CS, Bayet et al. 2009b), hence the assumption of a line width of 100 km s^-1 may be a good guess for the lower transitions. The tentative detections are the two at 151.3 GHz, with line intensities of  ~ 1 and  ~ 2 mK.

• Methanol – CH₃OH. Six lines or groups of lines of methanol were identified at 145.103, 157.179, 157.271, 165.050, 170.060, and 241.791 GHz. A synthetic Gaussian profile was fitted to all of them since, except for the lines at 170.060 GHz and 241.791 GHz, all the transitions are tentative, having an intensity lower than two times the noise level of the corresponding spectrum. In addition, the CH₃OH (3 − 2)A+ line at 145.103 GHz is blended with c-C₃H₂(3_1,2 − 2_2,2), whose contribution had been previously subtracted. The group of CH₃OH (J_1,K − 1 − J_0,K)E lines at 165.050 GHz is also blended with the faint feature of SO₂(5_2,4 − 5_1,5). In this case, we first estimated the contribution of the methanol lines using their spectroscopic parameters and helping us with the other non-blended transitions. From the Boltzmann diagram, we obtain N_CH3OH = (1.2 ± 1.1) × 10¹⁴ cm^-2 and T_rot = 26.2 ± 11.7 K. The large errors are related to the low intensity of the lines because the baselines of the spectra have a strong influence on the results of the rotational parameters.

• Nitric oxide – NO. Four transitions of nitric oxide were tentatively detected at 150.176, 150,546, 250.437, and 250.796 GHz. Although they are clearly seen (in particular the two at 2 mm wavelengths), their intensities do not reach a S/N of 2. The line at 150.546 GHz is blended with H₂CO (2_1,1 − 1_1,1), whose contribution was firstly subtracted as explained for formaldehyde. We fitted synthetic Gaussian profiles to the 2 mm and 1.3 mm hyperfine lines separately. Since we had two groups of lines at different frequencies, we were able to calculate the rotational temperature. However, this value is not very precise because the dynamic range in energies is quite low (ΔE = 5cm^-1). Thus, we associated a 50% error to the derived rotational temperature. The low T_rot ~ 9 K and the high column density (N ~ 10¹⁵cm^-2) indicate that nitric oxide arises from the external cold layers of the molecular clouds.

• Thioformaldehyde – H₂CS. Only one transition of thioformaldehyde was detected at 135.297 GHz, which is blended with H36α. We first subtracted the contribution of the recombination line and then fitted a Gaussian profile to the residuals. Since we only detected one transition of this species in the whole survey, we fixed the rotational temperature to 20 ± 10 K to calculate its column density.

  	Fig. A.2 Boltzmann diagrams of the molecules observed in the survey for which we detected more than one transition. The resulting rotational temperatures are indicated.
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  Table A.1

  Gaussian parameters for the fit performed to the observed spectral features.

• Ethynyl radical – C₂H. Only the C₂H (2 − 1) transition falls within our frequency coverage. It is the brightest spectral feature and the most abundant molecule of the survey. This line also shows the contribution of emission from the centre of M 82, which was firstly subtracted. After that, we fitted a synthetic Gaussian profile to the unresolved hyperfine structure, taking into account the spectroscopic parameters and line intensities of each component. Since we had only one transition of this molecule, we assumed T_rot = 20 ± 10 K. A study dedicated to this line in M 82 and NGC 253 is presented in Martín et al. (2010).

• Sulphur monoxide – SO. Only the SO (4₃ − 3₂) transition was detected in the survey at 138.179 GHz. Fixing T_rot to 20 ± 10 K, we obtained a column density of N_SO = (3.7 ± 0.5) × 10¹³ cm^-2.

• Sulphur dioxide – SO₂. Only the SO₂(5_2,4 − 5_1,5) transition at 165.145 GHz was detected in the survey. It is blended with a methanol group of lines whose contribution was firstly subtracted as explained before. After fitting a synthetic Gaussian profile to the residuals with a fixed position of 300 km s^-1, the SO₂ line intensity was estimated to be  ~ 1 mK. This value is below the noise level at this frequency so the detection is considered as tentative. Because this line is so faint, the Gaussian parameters are strongly affected by the baseline. As mentioned at the beginning of this section, the synthetic fit does not provide any error in the integrated area of the line. In this case, we did not use Eq. (A1) to calculate the error in the integrated area, since the error is even higher than . Thus, to calculate the column density we assumed a rotational temperature of 20 ± 10 K, and assigned an error of 50% to the resulting N_SO2.

• Oxomethyl – HCO. We detected the HCO (2_0,2 − 1_0,1) transition at 173.377 GHz, which contains seven hyperfine lines with lower level energies of 2.9 K. It is blended with H¹³CO  ⁺ (2 − 1). We first fitted a synthetic Gaussian profile to the hyperfine lines at 173.377 and 173.406 GHz because they are less blended with H¹³CO⁺. We fixed the position and line width to 300 km s^-1 and 100 km s^-1 respectively. In this way, we made sure that the synthetic fit covered oxomethyl and not H¹³CO⁺. We then fitted the rest of the hyperfine lines with the same Gaussian parameters. To calculate the column density, we used a rotational temperature of 20 ± 10 K. As in the case of SO₂, the error in the integrated area from Eq. (A1) is larger than the area itself, thus we did not use any error in the Boltzmann diagram. We note, however, that the resulting error in the column density is quite large.

• Oxomethylium, formyl cation – H¹³CO⁺. The H¹³CO⁺(2 − 1) line at 173.507 GHz is blended with oxomethyl. After fitting a Gaussian profile to the HCO feature, we over-fitted another to the residuals, fixing the position and line width to 300 km s^-1 and 100 km s^-1. Using the carbon isotopic ratio in M 82 given by Martín et al. (2010), ¹²C/¹³C > 138, we estimated a column density of HCO⁺ of N_HCO ⁺  > 1.8 × 10¹⁴ cm^-2. This value is consistent with that derived by Seaquist & Frayer (2000).

• Cyanamide – NH₂CN. Five spectral features of cyanamide were tentatively detected between 158.815 and 158.943 GHz. The line widths and positions in MASSA were fixed to 100.0 and 302.1 km s^-1, respectively, which are the values previously obtained with an approximated non-synthetic Gaussian fit. The line intensities, as calculated with the synthetic Gaussian fitting, are about 2 mK. The resulting Boltzmann diagram gave us T_rot = 80.3 ± 52.9 K and N_NH2CN = 1.2 ± 1.5 × 10¹³ cm^-2. The errors in both parameters, in particular in the column density, reflect the strong effect of the baseline on this weakly emitting species.

• Hydrogen sulfide – H₂S. The H₂S (1_1,0 − 1_0,1) transition was detected at 168.763 GHz. Since there is only one transition of this species, we used a T_rot = 20 ± 10 K in the rotational diagram and derived a column density of N_H2S = (6.1 ± 4.5) × 10¹³ cm^-2.

© ESO, 2011