ExoMol molecular line lists – IX. The spectrum of AlO

arXiv:1504.02938v1 [astro-ph.GA] 12 Apr 2015 Mon. Not. R. Astron. Soc. 000, 1–?? (2012) Printed 14 April 2015 (MN L A T EX style file v2.2) ExoMol molecular line lists: IX The spectrum of AlO Andrei T. Patrascu, Sergei N. Yurchenko and Jonathan Tennyson Department of Physics and Astronomy, University College London, London WC1E 6BT, UK Accepted XXXX. Received XXXX; in original form XXXX ABSTRACT Accurate line lists are calculated for aluminium monoxide covering the pure rotation, rotation-vibration and electronic (B – X blue-green and A – X infrared bands) spectrum. Line lists are presented for the main isotopologue, 27Al16O, as well as for 27Al17O, 27Al18O and 26Al16O. These line lists are suitable for high temperatures (up to 8000 K) including those relevant to exoplanetary atmospheres and cool stars. A combination of empirical and ab initio methods is used: the potential energy curves were previously determined to high accuracy by fitting to extensive data from analysis of laboratory spectra; a high quality ab initio dipole moment curve is calculated using quadruple zeta basis set and the multi-reference configuration interaction (MRCI) method. Partition functions plus full line lists of transitions are made available in an electronic form as supplementary data to this article and at www.exomol.com. Key words: molecular data; opacity; astronomical data bases: miscellaneous; planets and satellites: atmospheres; stars: low-mass 1 INTRODUCTION Aluminium monoxide (AlO) is an interesting astronomical species whose spectrum is prominent in a new class of Nova-stars first discovered by Tenenbaum & Ziurys (2009) of which the most prominent examples are probably V838 Mon and V4332 Sgr (Merrill et al. 1962; Bernard & Gravina 1984; Banerjee et al. 2005; Tylenda et al. 2005; Banerjee et al. 2012). These two objects defined a new type of eruptive variables called intermediate luminosity red transients and the observational data showed the intense presence of the near-infrared A – X system of the AlO radical. Indeed this A – X band is also found to be fairly prominent in a variety of cool, oxygen rich stars (Bernard & Gravina 1984; Banerjee et al. 2012): besides the Mira variables discussed above AlO emissions were also observed in the OH/IR stars and two bright infrared sources (Banerjee et al. 2012). Transitions in the blue-green B – X system have been observed in sunspots (Sriramachandran et al. 2013) and the red supergiant VY Canis Majoris (Kaminski et al. 2013), in which millimeter-wave rotational transitions have also been observed (Tenenbaum & Ziurys 2009). Finally, AlO spectra have been used to try and determine abundance of the longlived, radioactive 26Al isotope (Banerjee et al. 2004). Terrestrially AlO emissions arise from rocket exhausts in the atmosphere (Johnson 1965; Knecht et al. 1996). Its spectrum is also extensively used in the laboratory to monitor AlO in plasmas and other applications (Bescos et al. 1995; Naulin & Costes 1999; Glumac et al. 2001; Zhang & Li 2003; Bai et al. 2014; Surmick & Parigger 2014). These applications, combined with technological uses of AlO spectra, have motivated a number of laboratory studies which have produced molecular constants characterising the lowest three states of AlO X2Σ+, A 2Π and B2Σ+. There have also been attempts to produce line lists. Parigger & Hornkohl (2011) constructed a comprehensive line list for the X – B system for temperatures up to 6000 K but did not provide a transition dipole, so all their transition intensities are only relative. Launila & Berg (2011) performed a combined analysis of the A –X and B – X band systems involving 21 500 lines; we compare with some of their results below. There is, however, no single line list that combines a comprehensive set of transition frequencies with an accurate model for the transition intensities. It is this that we aim to do here as part of the ExoMol project. ExoMol aims to provide line lists of spectroscopic transitions for key molecular species which are likely to be important in the atmospheres of extrasolar planets and cool stars; its aims, scope and methodology have been summarised by Tennyson & Yurchenko (2012). Line lists for 2Σ+XH molecules, X = Be, Mg, Ca, have already been published (Yadin et al. 2012), as well as for a number of closed-shell diatomics (Barton et al. 2013, 2014; Yorke et al. 2014). In the present paper, we present rotation-vibration transition lists and associated spectra for AlO. These line lists are particulary comprehensive and should be valid for temperatures up to 8000 K. c 2012 RAS 2A.T. Patrascu, S.N. Yurchenko and J. Tennyson 2 METHOD Rotation-vibration line lists for the three lower electronic states of AlO were obtained by direct solution of the nuclear motion Schr¨odinger equation using program Duo (Yurchenko et al. 2015). The calculations require both a potential energy curve (PEC) for each of the three states considered and also couplings between these curves. These curves were taken from our previous study (Patrascu et al. 2014), which computed ab initio potential energies, spinorbit and electronic angular momenta couplings, and refined them using available experimental data. Nuclear motion calculations using these refined curves showed that the observed transition frequencies and energy levels could be reproduced with root mean square error of only 0.07 cm−1. In order to cover all vibrational excitations below 35,000 cm−1, we have increased the sizes of the vibrational basis set to 90 for each of the X, A, and B states from those used by Patrascu et al. (2014). The ranges of rotational excitations are listed in Table 2. 2.1 Dipole moments There appears to be no experimental measurements of any AlO transition dipoles. For this reason we constructed new dipole moment curves (DMC) using high level ab initio calculations. These are compared to previous, highlevel ab initio determinations (Zenouda et al. 1999) below. The ab initio calculations were performed using MOLPRO (Werner et al. 2010); we used multi-reference configuration interaction (MRCI) methods with different choices of basis sets. Our optimal basis choice was aug-cc-pVQZ; the active space used in MOLPRO representation was (9,4,4). Electronic dipole moments as function of bondlength, R, were computed as the expectation value µ(R) = ehΨM|X i ri|ΨNi,(1) where the integral and the summation run over the electron coordinates, denoted by ri, and eis the charge of the electron. For permanent dipole moments, the electronic wavefunctions in the bra and ket are the same, ie M=N, and the dipole moment, which is denoted µ(M) below, also contains a term due to permanent nuclear charge. For transition dipole moments, M6=N, and the dipole is denoted is µ(M−N) below. For transition dipole moments, care must be taken to ensure the that the dipole phases are consistent as a function of R(Tennyson 2014; Patrascu et al. 2014). Our calculations produce the values for the dipole at equilibrium given in Table 1 which compare well to the previous results obtained by Zenouda et al. (1999). Our ground state value of the dipole and that of Zenouda et al. (1999) are both slightly smaller than the value 4.60 D used in the JPL database (Pickett et al. 1998) which was taken from the earlier calculations of Lengsfield & Liu (1982). Figures 1 and 2 compare our calculated diagonal and off-diagonal DMCs, respectively, with those of Zenouda et al. (1999). The agreement is good. Our calculations suggest that the µ(B-A) DMC is small at all geometries meaning that the B – A band will be very weak; a similar conclusion was reached by Partridge et al. (1983). Table 1. Ab initio electric dipole and transition dipole moments in Debye at R= 1.76 ˚ A. Transition moments This Work Zenouda et al. (1999)a X2Σ+−4.39 −4.24 A2Π−1.30 −1.40 B2Σ+−2.18 −2.27 X2Σ+–B 2Σ+1.85 1.66 X2Σ+–A 2Π 0.61 0.61 B2Σ+–A 2Π−0.046 aThe signs of the diagonal dipoles have been changed to conform to the convention used by MOLPRO. 1.4 1.6 1.8 2 2.2 2.4 2.6 R [Å] -6 -4 -2 0 µ [Debye] µ(A) µ(B) µ(X) µ(A) µ(B) µ(X) Figure 1. Ab initio permanent dipole moment curves for AlO for the lowest three electronic states. The previous calculations by Zenouda et al. (1999) are represented by crosses. The ab initio DMC grid points were used directly in Duo to produce a line list for AlO. There is a lack of experimental data on AlO transition dipoles or transition intensities. Table 2 therefore compares the lifetime for the B 2Σ+state with experimental data available from Johnson et al. (1972); Dagdigian et al. (1975) and two ab initio estimates from Partridge et al. (1983). For Partridge et al. (1983) we have taken their figures which include the small contribution from the weak B – A decay channel since this contribution is also included in our estimate. Our lifetimes were computed by summing over all decays from a given B 2Σ+(v, J). Our results in Table 2 are for J= 0.5; calculations for J= 24.5, which lies in the region of the band head, give lifetimes about 0.5 % longer. We conclude that the lifetimes are not strongly Jdependent. In common with the other studies we find that the lifetime grows slowly with v. Our results are intermediate between the two predictions of Partridge et al. (1983) and slightly shorter than, but marginally consistent with, the measurements of Dagdigian et al. (1975). The measurements of Johnson et al. (1972) give longer lifetimes than all studies and we suggest these are too long. c 2012 RAS, MNRAS 000, 1–?? ExoMol: IX The spectrum of AlO 3 Table 2. Radiative lifetimes (nsec) for B 2Σ+state of AlO, compared to the measurements of Johnson et al. (1972) and Dagdigian et al. (1975), and the two separate calculations of Partridge et al. (1983). Vibrational Level This work Partridge et al. (1983) I Partridge et al. (1983) II Johnson et al. (1972) Dagdigian et al. (1975) 0 92.4 88.1 109.9 128 ±6 100 ±7 1 94.5 90.5 112.6 125 ±3 102 ±7 2 96.7 93.0 115.2 130 ±7 102 ±4 1.4 1.6 1.8 2 2.2 2.4 2.6 R [Å] -1 0 1 2 µ [Debye] µ(B-A) µ(X-A) µ(B-X) µ(B-X) µ(X-A) Figure 2. Ab initio transition dipole moment curves for AlO linking the lowest three electronic states. The previous calculations by Zenouda et al. (1999) are represented by crosses. 0 10 20 30 40 50 60 70 80 0 1x10 -19 2x10 -19 3x10 -19 4x10 -19 Intensity, cm/molecule wavenumber, cm -1 T =298 K 900 920 940 960 980 1000 0.0 5.0x10 -22 1.0x10 -21 1.5x10 -21 2.0x10 -21 Intensity, cm/molecule wavenumber, cm -1 T =298 K Figure 3. Computed spectra of 27Al16O at T=298 K given as sticks with the intensity (cm molecule−1) represented by their height. Upper panel: rotational region; lower panel: vibrational fundamental. 2.2 Partition function Partition functions for AlO were calculated by summing all the calculated energy levels below using Duo (Yurchenko et al. 2015). When summing these levels it is necessary to multiply by the appropriate degeneracy factors. Since we follow HITRAN (Fischer et al. 2003) and use the full nuclear spin degeneracy, the degeneracy factor, g, is given by (2J+ 1)(2IAl + 1)(2IO+ 1) where Jis the total angular momentum quantum number obtained by adding the rotational and spin angular momenta. IAl and IOare the nuclear spins of the isotopes of Al and O in the given isotopologue. Explicit inclusion of these nuclear spin factors accounts for hyperfine effects which we make no attempt to resolve. These factors are 11, 6, 1, 6 and 1 for 26Al, 27Al, 16O, 17O and 18O, respectively. Table 3 compares our results for 27Al16O with those of Sauval & Tatum (1984). We have multiplied the results of Sauval & Tatum (1984) by the appropriate nuclear spin factors to bring their results into line with our convention outlined above. Table 3 shows good agreement between our 27Al16O partition function and that given by (Sauval & Tatum 1984) at temperatures above 1000 K for which their results are valid. At lower temperatures we also agree well with the partition function given by JPL (Pickett et al. 1998) who, for example, give Q(300) = 3926.45 which is slightly lower than our value of 3966.90, probably due to neglect of the contribution of excited vibrational states. As we use all ro-vibrational energy levels there are no issues with convergence of this sum. We follow Vidler & Tennyson (2000) and represent our partition function using the following functional form log10 Q(T) = 8 X n=0 an[log10 T]n(2) where the fitting parameters anare given in Table 4. These fits reproduce the partition functions for the entire region below 9000 K with a relative root-mean-square (rms) errors of better than 1.6 %. 2.3 Line list calculations Line lists were calculated for the four isotopologues 27Al16O, 27Al18O, 27Al17O, and 26Al16O. All rotation-vibration states were considered and transitions satisfying the dipole selection rule ∆J= 0,±1. These line lists span frequencies up to 35 000 cm−1(λ > 0.286 µm). The procedure described above was used to produce line lists, i.e. catalogues of transition frequencies ˜νij and Einstein coefficients Aij , for four Aluminium oxide isotopologues 27Al16O, 27Al18O, 27Al17O, c 2012 RAS, MNRAS 000, 1–?? 4A.T. Patrascu, S.N. Yurchenko and J. Tennyson Table 4. Partition function parameters for various isotopologues, see Eq. (2) 27Al16O27Al18O26Al16O27Al17O a0-1.04093681038 -1.59727184392 -0.677569296333 -0.541673874468 a19.64080670554 11.9848644854 9.21909668136 10.8157290731 a2-14.3512337912 -18.2945471026 -13.6457740234 -16.3230021925 a313.0627960677 16.7055086746 12.4154930773 14.8789580623 a4-7.20103828655 -9.21814194734 -6.84559240132 -8.20306751046 a52.49431683028 3.17902318889 2.37492955521 2.83289571369 a6-0.538890191754 -0.677958762340 -0.514966111414 -0.607255974396 a70.0673568508718 0.0828183310157 0.0647424233238 0.0749009373167 a8-0.00372906050126 -0.004450320873 -0.00360977781061 -0.00407761291349 Table 5. Summary of our AlO linelists. 27Al16O27Al18O26Al16O27Al17O X2Σ+ Maximum v66 69 66 68 Maximum J300.5 300.5 300.5 300.5 A2Π Maximum v63 65 62 64 Maximum J300.5 300.5 300.5 300.5 B2Σ+ Maximum v40 41 39 40 Maximum J232.5 241.5 230.5 237.5 Number of lines 4 945 580 5 365 592 4 866 540 5 148 996 Table 3. Partition function, Q(T), for 27Al16O, as a function of temperature. T / K Q(T) T Q(T) Sauval & Tatum (1984) 10 134.73 1000 17595.69 17693.4 20 265.35 2000 57302.56 57060.6 30 396.01 3000 138649.47 135168 40 526.68 4000 283031.72 274740 50 657.37 5000 508066.61 487708 60 788.07 6000 828224.93 793980 70 918.78 7000 1254881.70 1216536 80 1049.50 8000 1795616.84 1781718 100 1310.96 200 2621.45 300 3966.90 400 5407.40 500 6988.27 600 8734.58 750 11692.87 and 26Al16O. The full line list for each of the studied isotopologues are summarised in Table 5. 3 RESULTS The line lists contain about 5 million transitions each and, therefore, for compactness and ease of use, are divided into separate energy level and transitions file. This is done using standard ExoMol format (Tennyson et al. 2013) which is based on a method originally developed for the BT2 line list (Barber et al. 2006). Extracts for the start of the 26Al16O files are given in Tables 6 and 7. The full line list for each of these isotopologues can be downloaded from the CDS, via ftp://cdsarc.u-strasbg.fr/pub/cats/J/MNRAS/xxx/yy, or http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/MNRAS//xxx/yy. The line lists and partition function together with auxiliary data including the potential parameters and dipole moment functions, as well as the absorption spectrum given in cross section format (Hill et al. 2013), can all be obtained from there as well as at www.exomol.com. Figure 3 shows the rotational component, and the Pand weaker R-branches of the vibrational fundamental (v= 0−1) obtained at T=298 K. As has been noted before (Lengsfield & Liu 1982), the X-state dipole is very flat in the equilibrium region. As the strength of a ∆v= 1 vibrationrotation transition depends on the slope of the dipole in this region, this causes the vibrational fundamental to be particularly weak. Therefore this feature, which lies between 10 and 11 µm, is unlikely to be astronomically important. Our calculations suggest that the overtones (∆v > 1) are also weak so the entire AlO vibration-rotation spectrum is unlikely to feature strongly in astronomical objects. Much more significant at infrared wavelengths is the A – X electronic band. Figure 4 shows an overview of the A – X and B – X electronic transitions which are presented as absorption spectra generated at T= 2000 K. Our spectra are compared to available experimental data (Launila & Jonsson 1994; Saksena et al. 2008): we note that these measurements do not give absolute intensities, so have been scaled by us. A more detailed comparison of a portion of the A – X spectrum with the experimental results of Launila & Berg (2011) is presented in Fig. 5. Figure 6 compares the theoretical spectrum obtained here with an astronomical spectrum of Kaminski et al. (2013). The agreement is remarkable. The calculation performed using the vic 2012 RAS, MNRAS 000, 1–?? ExoMol: IX The spectrum of AlO 5 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56 0.58 0.6 10 -19 10 -18 10 -17 10 -16 10 -15 10 -14 10 -13 Saksena et al. (2008) erg cm /(s molecule sr) wavelength, m ExoMol B-X 0.8 1 2 3 4 5 6 10 -16 10 -15 10 -14 10 -13 10 -12 A-X erg cm /(s molecule sr) wavelength, m ExoMol Launila & Jonsson (1994) Figure 4. Overview of the theoretical (ExoMol) and experimental (Launila & Jonsson 1994; Saksena et al. 2008) spectra of 27Al16O. The theoretical spectra were obtained as cross sections convolved with a Gaussian line profile of width 1 cm−1assuming the local thermal equilibrium at T= 2000 K. The experimental A – X and B – X spectra were scaled by 1×10−17 and 5×10−18, respectively. brational Tvib and rotational Trot temperatures of 2200 K and 700 K, respectively as suggested by Kaminski et al. (2013). We use a gaussian convolution with the half-width at half-maximum derived of 0.3 cm−1to match the spectrum by Kaminski et al. (2013). Also shown (in red) is the simulation of their observed spectrum by Kaminski et al. (2013); for this they generated their own line list based on the line positions of Saksena et al. (2008), transition moments of Zenouda et al. (1999), Franck-Condon factors of Coxon & Naxakis (1985) and rotational line-strength factors which they computed themselves. We note that our line list provides all these data within a single framework and without making any underlying assumptions about the Franck-Condon approximation or rotational form factors. Figure 7 compares the B – X emission spectrum obtained in this work with accurate experimental results of Saksena et al. (2008). Again the agreement is very good. Finally, Fig. 8 compares our calculated spectra B – X for the two isotopologues 26Al 16O and 27Al 16O. The shift in the band head feature should be observable astronomically at even moderate resolution. 4 CONCLUSIONS We present comprehensive line lists for the four most important isotopologues of AlO. These are based on the direct solution of the nuclear motion Schr¨odinger equation using a potential energy curves and couplings obtained by fitting to extensive dataset of measured transitions. These data are reproduced to near experimental accuracy resulting in high 1.658 1.660 1.662 1.664 1.666 1.668 2000 1800 1600 1400 1200 1000 800 600 400 arbitrary units wavelength, m 1x10 -14 2x10 -14 3x10 -14 4x10 -14 erg/(s molecule sr) Launila & Jonsson (1994) ExoMol Figure 5. A – X emission spectrum of 27Al 16O, comparison with experiments of Launila & Jonsson (1994) at T=3200 K. The theoretical spectrum was obtained as cross sections convolved with a Doppler line profile assuming the local thermal equilibrium at T= 3200 K. VY Canis Majoris 4840 4850 4860 4870 4880 4890 4900 1x10-14 8x10-15 6x10-15 4x10-15 2x10-15 0 erg/(s molecule sr) wavelength, Å ExoMol 0.5 1.0 1.5 2.0 2.5 3.0 Normalized flux Kaminski et al. (2013) Figure 6. B – X ∆v= 0 emission spectrum at Trot=700 K and Tvib=2200 K compared with an astronomical spectrum obtained by Kaminski et al. (2013) for VY Canis Majoris (Trot and Tvib in (Kaminski et al. 2013)). Cross sections (lower part) were obtained by convolving with a Gaussian profile of width 0.3 cm−1. accuracy line positions. A new ab initio dipole moment is computed. This dipole is used to compute Einstein A coefficients for all possible dipole-allowed transitions within each AlO isotopologue. The result is a comprehensive line list for each species. The line lists can be downloaded from the CDS, via ftp://cdsarc.u-strasbg.fr/pub/cats/J/MNRAS/, or http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/MNRAS/, or from www.exomol.com. ACKNOWLEDGEMENTS This work is supported by ERC Advanced Investigator Project 267219. REFERENCES Bai X., Motto-Ros V., Lei W., Zheng L., Yu J., 2014, Spectra Chimica Acta B, 99, 193 c 2012 RAS, MNRAS 000, 1–?? 6A.T. Patrascu, S.N. Yurchenko and J. Tennyson Table 6. Extract from the state file for 27Al16O. Full tables are available from http://cdsarc.u-strasbg.fr/cgi-bin/VizieR?-source=J/MNRAS/xxx/yy. n˜ E g J +/−e/f State v|Λ| |Σ| |Ω| 1 0.000000 12 0.5 + e X2SIGMA+ 0 0 0.5 0.5 2 965.435497 12 0.5 + e X2SIGMA+ 1 0 0.5 0.5 3 1916.845371 12 0.5 + e X2SIGMA+ 2 0 0.5 0.5 4 2854.206196 12 0.5 + e X2SIGMA+ 3 0 0.5 0.5 5 3777.503929 12 0.5 + e X2SIGMA+ 4 0 0.5 0.5 6 4686.660386 12 0.5 + e X2SIGMA+ 5 0 0.5 0.5 7 5346.116382 12 0.5 + e A2PI 0 1 0.5 0.5 8 5581.906844 12 0.5 + e X2SIGMA+ 6 0 0.5 0.5 9 6066.934830 12 0.5 + e A2PI 1 1 0.5 0.5 10 6463.039443 12 0.5 + e X2SIGMA+ 7 0 0.5 0.5 11 6778.997803 12 0.5 + e A2PI 2 1 0.5 0.5 12 7329.427637 12 0.5 + e X2SIGMA+ 8 0 0.5 0.5 13 7483.145675 12 0.5 + e A2PI 3 1 0.5 0.5 14 8159.170405 12 0.5 + e A2PI 4 1 0.5 0.5 15 8201.467744 12 0.5 + e X2SIGMA+ 9 0 0.5 0.5 16 8857.266385 12 0.5 + e A2PI 5 1 0.5 0.5 17 9029.150380 12 0.5 + e X2SIGMA+ 10 0 0.5 0.5 18 9535.195842 12 0.5 + e A2PI 6 1 0.5 0.5 19 9854.882567 12 0.5 + e X2SIGMA+ 11 0 0.5 0.5 20 10204.019475 12 0.5 + e A2PI 7 1 0.5 0.5 21 10667.668381 12 0.5 + e X2SIGMA+ 12 0 0.5 0.5 22 10864.560220 12 0.5 + e A2PI 8 1 0.5 0.5 23 11464.897083 12 0.5 + e X2SIGMA+ 13 0 0.5 0.5 24 11519.212123 12 0.5 + e A2PI 9 1 0.5 0.5 25 12156.974798 12 0.5 + e A2PI 10 1 0.5 0.5 26 12257.694655 12 0.5 + e X2SIGMA+ 14 0 0.5 0.5 27 12793.671660 12 0.5 + e A2PI 11 1 0.5 0.5 28 13030.412255 12 0.5 + e X2SIGMA+ 15 0 0.5 0.5 29 13421.583651 12 0.5 + e A2PI 12 1 0.5 0.5 30 13790.933964 12 0.5 + e X2SIGMA+ 16 0 0.5 0.5 n: State counting number. ˜ E: State energy in cm−1. J: Total angular momentum quantum number. g: State degeneracy. +/−: Total parity. e/f: Rotationless-parity (Brown et al. 1975). v: State vibrational quantum number. |Λ|: Absolute value of Λ (projection of the electronic angular momentum). |Σ|: Absolute value of Σ (projection of the electronic spin). |Ω|: Absolute value of Ω = Λ + Σ (projection of the total angular momentum). Banerjee D. P. K., Ashok N. M., Launila O., Davis C. J., Varricatt W. P., 2004, ApJ, 610, L29 Banerjee D. P. K., Barber R. J., Ashok N. K., Tennyson J., 2005, ApJ, 627, L141 Banerjee D. P. K., Varricatt W. P., Mathew B., Launila O., Ashok N. M., 2012, Astrophys. J. Lett., 753, L20 Barber R. J., Tennyson J., Harris G. J., Tolchenov R. N., 2006, MNRAS, 368, 1087 Barton E. J., Chiu C., Golpayegani S., Yurchenko S. N., Tennyson J., Frohman D. J., Bernath P. F., 2014, MNRAS, 442, 1821 Barton E. J., Yurchenko S. N., Tennyson J., 2013, MNRAS, 434, 1469 Bernard A., Gravina R., 1984, Z. Naturfors. Sect. A-J. Phys. 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ExoMol: IX The spectrum of AlO 7 0.464 0.466 0.468 0.470 0.472 0.474 0.476 0.478 15000 10000 5000 0 arbitrary units wavelength, m 5x10 -17 1x10 -16 2x10 -16 erg/(s molecule sr) Saksena et al. (20 08) ExoMol 0.484 0.486 0.488 0.490 0.492 0.494 0.496 60000 50000 40000 30000 20000 10000 arbitrary units wavelength, m 1x10 -16 2x10 -16 3x10 -16 4x10 -16 5x10 -16 6x10 -16 erg/(s molecule sr) Saksena et al. (20 08) ExoMol 0.508 0.510 0.512 0.514 0.516 0.518 0.520 20000 10000 arbitrary units wavelength, m 1x10 -16 2x10 -16 erg/(s molecule sr) Saksena et al. (20 08) ExoMol Figure 7. Emission spectra of three sub-bands within the X – B band at 1700 K compared to the experiment of Saksena et al. (2008) (up). Top panel: ∆v= 1, middle panel: ∆v= 0, lower panel: ∆v=−1. The experimental data is in arbitrary units; calculated cross sections were obtained by convolving with a Doppler profile at 1700 K. Merrill P. W., Keenan P. C., Deutsch A. J., 1962, ApJ, 136, 21 Naulin C., Costes M., 1999, Chem. Phys. Lett., 310, 231 Parigger C. G., Hornkohl J. O., 2011, Spectra Chimica Acta A, 81, 404 Partridge H., Langhoff S. R., Lengsfield B. H., Liu B., 1983, J. Quant. Spectrosc. Radiat. Transf., 30, 449 Patrascu A. T., Hill C., Tennyson J., Yurchenko S. N., 2014, J. Chem. Phys., 141, 144312 Pickett H. M., Poynter R. L., Cohen E. A., Delitsky M. L., Pearson J. C., M¨uller H. S. P., 1998, J. Quant. Spectrosc. Radiat. Transf., 60, 883 3x10 -18 2x10 -18 1x10 -18 0 0.507 0.508 0.509 0.510 0.511 0.512 26 Al 16 O wavelength, m intensity, cm/molecule 1x10 -18 2x10 -18 3x10 -18 27 Al 16 O Figure 8. Calculated B – X v′−v′′ = 0−1 absorption spectrum at 1700 K for 26Al16O and 27Al16O obtained by convolving with a Doppler profile at 1700 K. Table 7. Extracts from the transitions file for 27Al16O. 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