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Journal of Quantitative Spectroscopy &Radiative Transfer

Journal of Quantitative Spectroscopy & Radiative Transfer 116 (2013) 101–109

0022-40

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journal homepage: www.elsevier.com/locate/jqsrt

New assignments in the 2 mm transparency windowof the 12CH4 Octad band system

L. Daumont a,n, A.V. Nikitin a,b, X. Thomas a, L. Regalia a, P. Von der Heyden a,Vl.G. Tyuterev a, M Rey a, V. Boudon c, Ch. Wenger c, M. Loete c, L.R. Brown d

a Groupe de Spectrometrie Moleculaire et Atmospherique, UMR CNRS 6089, Universite de Reims, U.F.R. Sciences Exactes et Naturelles,

B.P. 1039, 51687 Reims Cedex 2, Franceb Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, SB RAS, 1, Academician Zuev Square, 634021 Tomsk, Russiac Laboratoire Interdisciplinaire Carnot de Bourgogne, UMR 5209, CNRS—Universite de Bourgogne, 9, Avenue Alain Savary, BP 47870,

F-21078 Dijon Cedex, Franced Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA

a r t i c l e i n f o

Article history:

Received 22 March 2012

Received in revised form

23 August 2012

Accepted 24 August 2012Available online 31 August 2012

Keywords:

Methane

Intensities

Spectra

Transparency window

Titan

Long path FTS

Octad

73/$ - see front matter & 2012 Elsevier Ltd. A

x.doi.org/10.1016/j.jqsrt.2012.08.025

esponding author. Tel./fax: þ33 3 26 91 33

ail address: ludovic.daumont@univ-reims.fr (

a b s t r a c t

This paper reports new assignments of rovibrational transitions of 12CH4 bands in the

range 4600–4887 cm�1 which is usually referred to as a part of the 2 mm methane

transparency window. Several experimental data sources for methane line positions

and intensities were combined for this analysis. Three long path Fourier transform

spectra newly recorded in Reims with 1603 m absorption path length and pressures of

1, 7 and 34 hPa for samples of natural abundance CH4 provided new measurements of12CH4 lines. Older spectra for 13CH4 (90% purity) from JPL with 73 m absorption path

length were used to identify the corresponding lines. Most of the lines in this region

belong to the Octad system of 12CH4. The new spectra allowed us to assign 1014 new

line positions and to measure 1095 line intensities in the cold bands of the Octad. These

new line positions and intensities were added to the global fit of Hamiltonian and

dipole moment parameters of the Ground State, Dyad, Pentad and Octad systems.

This leads to a noticeable improvement of the theoretical description in this methane

transparency window and a better global prediction of the methane spectrum.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Methane is abundant in the atmospheres of the Earth, theouter planets of our own Solar System [1], in exoplanetsaround other stars [2], sub-stellar objects (Brown dwarfs [1])and in a few moons (such as Titan [3]). In planetary atmo-spheres, methane plays a similar role to that of H2O and CO2

in the terrestrial atmosphere in that its bands frequentlydominate the infrared spectra and mask the spectral con-tributions from other important molecules. This makes theintervals between strong absorption bands (the

ll rights reserved.

33.

L. Daumont).

‘‘transparency windows’’) especially important for deter-mining chemical species and physical properties of astro-nomical bodies via remote sensing [4–7]. Thus reliableknowledge of methane spectroscopy over a wide range ofwavelengths is crucial [6,7]. Generally speaking, the above-cited astronomical objects can have temperatures rangingfrom 50 K to over 2500 K. As a result, the theoreticalmodels for methane must provide complete and accuratepredictions for both low and high quantum numbers oftransitions arising from both the ground state and lowerpolyad states.

From past experimental and theoretical studies of CH4

[8–24] using effective Hamiltonian and dipole momentexpansions, line-by-line predictions are available up to6300 cm�1 [14,25,26]. However these are insufficient for

4000

4400 21

3ν2

ν2+ν3ν1+ν22ν2+ν4ν3+ν4ν1+ν4

ν2 +2ν4

Term

val

ues

/ cm

-1

All A1 A2 E F1 F2

3ν4

0

2000

4000

6000

GS (P0)

Dyad (P1)

Pentad (P2)

Octad (P3)

Tetradecad (P4)

Fig. 1. Scheme of vibrational level patterns of methane polyads (upper panel) and of vibration sublevels of the Octad (lower panel). In each case, the left

part contains all the sublevels which are separated in the right part according to the Td irreducible representation they belong to.

L. Daumont et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 116 (2013) 101–109102

astronomical applications. The complexity of the spec-trum increases very rapidly with energy so that theshorter wavelengths become intractable to interpretation.Intensities of the huge number of transitions in excitedpolyads are extremely sensitive to numerous resonanceinteractions that are still poorly defined. Even the use ofab initio potential energy and dipole moment surfaces[27] do not permit the multitude of existing experimentaldata [28] to be understood to a sufficient degree.

The present analysis is undertaken to support inter-pretation of Cassini spectral observations of Titan [29],Saturn’s largest satellite whose atmosphere is dominatedby N2, CH4 and C2H6 at temperatures ranging between80 K and 180 K. The 4600–4887 cm�1 region is specifi-cally studied because it comprises the lower half of the2 mm methane transparency window. This corresponds toa gap between the Octad and Tetradecad polyads (seeFig. 1) containing high J transitions. The contributions ofthe 13CH4 isotopologue and of 12CH4 hot bands are alsoimportant.

The complex vibrational structure of methane is illu-strated in Fig. 1. The Octad energy levels (n1þn2, n1þn4,n2þn3, n3þn4, 3n2, 2n2þn4, n2þ2n4 and 3n4) possessmultiple components leading to a total of 24 vibrationalsublevels (shown in Fig. 1 according to the vibrationalsymmetries). Rovibrational transitions from the vibra-tional ground state (GS) to all these sub-levels form thecorresponding absorption band system. An accurate char-acterization of these weak absorption features and of theirdependence with the temperature is mandatory forproper interpretation of various optical measurements atlarge optical paths and high astronomical opacities.

The methane line list in the HITRAN 2008 database[30] for the 2 mm transparency window was constructedfor Earth applications by L. Brown based on the analysesof spectra at room temperature recorded with a Fouriertransform spectrometer (FTS) and absorption path lengths

up to 433 m [12,14,25,26,31]. Below 4800 cm�1 the listwas composed of a theoretical prediction [25] withselected positions and intensities replaced by measuredvalues for stronger transitions. Above 4800 cm�1, the listwas formed using only measured positions and intensitiesgreater than 4�10�26 cm/molecule with very few quan-tum assignments [12] (required to compute the tempera-ture dependence of the intensities). For outer planets andTitan, transitions weaker by two or more orders ofmagnitude are needed. The present study was undertakento improve this situation and to obtain a better modelingof the Octad region, especially in its high energy end. Theprogram SpectraPlot [32] was used for assignment andpartly for line positions/intensities retrievals.

2. Long path FTS spectra from Reims

Several long path spectra of ‘‘natural’’ abundance methanewere recorded in Reims in the 3800–8100 cm�1 spectralregion. An overview of the spectra in the investigated regionis presented in Fig. 2 for three pressure values. The absorptionfeatures under study are surrounded by the strongly absorb-ing regions of the Octad and Tetradecad. The CO2 bands usedfor calibration purpose are located in the most transparentpart of the transparency window.

The spectra were recorded with the Connes’ type Four-ier transform spectrometer built in the GSMA laboratory asdescribed in Refs. [16,33]. The 50-m base long White typecell [34–37] was used to record spectra with an absorptionpath length of 1.603 km. The methane spectra wererecorded at 1.37, 6.73 and 33.7 hPa (referred to as spectra(a), (b) and (c), respectively, in Fig. 2) with a temperature of290 K. The iris diameter at the entrance of the spectro-meter was 3.5 mm and the maximal optical path differencewas set to 65 cm leading to a resolution of 0.008 cm�1.

The pressures were measured with a MKS Baratroncapacitance manometer having an uncertainty of 0.01%.

Fig. 2. Overview of the FTS Reims spectra at three methane pressures

(L¼1603 m, T¼290 K). From top to bottom: (a) 1.37 hPa (b) 6.73 hPa (c)

33.7 hPa. The 20013-00001 and 20011-00001 bands of CO2 – located

near 4853 and 5099 cm�1, respectively – was used for wavenumber

calibration. The resolution is 0.008 cm�1 and the rms signal-to-noise

ratio is around 3500.

L. Daumont et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 116 (2013) 101–109 103

The temperatures were obtained and controlled continu-ously during the recordings by platinum-resistance ther-mometers with an uncertainty of 1 K. All the spectra wererecorded with the following optical setup: a SiO2 beamsplitter, two InSb detectors with lenses and windows inBaF2. The whole path between the long 50-m White celland our spectrometer was maintained under vacuum.

The wavenumber calibration described in our previouspaper [18] is repeated here for the reader’s convenience: ‘‘Toestablish the wavenumber calibration, we introduced aknown pressure of CO2 in a 8.5-m optical path between the50-m White cell and the entrance of the interferometer.Spectra (a) and (b) were recorded with stable CO2 pressuresof �1.5 and 2 hPa, respectively. The CO2 transitions of the(20013)-GS band at 4853 cm�1 and (20011)-GS band at5099 cm�1 are readily seen in Fig. 2. The calibration proce-dure was first applied using as reference standards 41 CO2

lines from Miller and Brown [38] in the (20013)-GS and(20011)-GS bands for spectra (a) and 23 lines for spectra (b).In two cases the standard deviation was 0.00023 cm�1 and0.000056 cm�1, respectively. Then the highest pressuremethane spectrum (c) was calibrated using 32 well-isolatedCH4 lines that could be reliably measured in both spectra.The corresponding standard deviation is 0.00013 cm�1.The results were later checked using residual H2O featuresnear 5000 cm�1 by comparing to the five line centers listedin [30]. For example, measured H2O positions from spectrum(a): 5081.209629, 5096.600150, 5109.184895, 5119.416199,5119.455055 cm�1 differ from [30] by �0.000071, 0.000690,0.000025, �0.000081, �0.000155 cm�1, respectively. TheseH2O lines had been calibrated by Toth [39] using the 2–0band of CO [40], the same reference standard used by Millerand Brown for the two CO2 bands.’’

3. FTS spectra from JPL

One spectrum of enriched sample 13CH4 recorded in1999 at 0.0109 cm�1 resolution with the Fourier trans-form spectrometer located on Kitt Peak Mountain in

Arizona was used to identify this isotopologue’s lines inthe Reims long path spectra. The characteristics of thespectrum was already described in [18,41] and are sum-marized here. The signal from a Quartz halogen lamppassed through a stainless steel multipass cell (6.01 mbase length), through a CaF2 beam splitter and fell ontotwo InSb detectors. The absorption cell was set to anoptical path length of 73 m and held an enriched sampleof 13CH4 (nominally 90%). Temperatures were monitoredusing thermistors in contact with the exterior wall of thecell. This same spectrum was used recently for an empiri-cal study of lower state energies of 13CH4 in the 2n3 regionfrom 5850 to 6150 cm�1 [41]. The line positions andrelative intensities were retrieved using non-linear leastsquares [42]. The line positions were calibrated using H2Olines at 1.9 mm [43] which had been calibrated using the2–0 band of CO [40]. As described in Lyulin et al. [41] theretrieved line intensities had to be adjusted by 20%, butthe line positions were considered sufficient enough toidentify the isotopic features in the Reims spectraobtained with normal abundance of methane. In addition,another Kitt Peak enriched sample spectrum was used toconfirm that our new linelist contained no CH3D lines.

Three near infrared spectra of the enriched 12CH4

isotopologue were also used in the analysis (although nomeasurements from them are being reported in thepresent paper). One spectrum with a sample pressure of9.92 Torr at 291 K [25] covered the 2800–9316 cm�1

range. Two others spanned the 3030–7273 cm�1 inter-val; their gas conditions were 10.42 Torr at 193 K and0.738 Torr at 206 K. All three were obtained using amultiplass cell set to an absorption path length of 12.4 m.

4. Line position and line intensity modeling

The theoretical analysis was performed using theglobal effective Hamiltonian approach and the polyadvibrational extrapolation scheme reviewed in [44]. Theformalism of irreducible tensor operators developed in aseries of works by the Dijon group and collaborators[8,44,45] and references therein permits molecular sym-metry properties to be fully considered. The major advan-tage of this method is that all the terms andcorresponding constants obtained in the previous ana-lyses of the lower polyads (Ground State in microwaveand THz regions, Dyad in the 1100–1800 cm�1 region,Pentad in the 2300–3300 cm�1 region) are directlyinvolved in the Octad region (3500–4700 cm�1) calcula-tions. Line positions and intensities analyses were per-formed using two different software. The first one, calledMIRS, uses the version of the rovibrational tensors cou-pling defined in a previous work [46] and is described in[47]. MIRS was used for line assignments and fits.The second software is STDS [8], now part of the XTDSsystem [48]. It implements the rovibrational tensorscoupling scheme of Refs. [44,45] that differs from Ref.[46]. STDS was used to perform an independent fit of thesame assignments and to provide a Hamiltonian anddipole moment parameter list in the same format as inRef. [26]. As we will see below, these two independent fitsof this complex region lead to similar fit statistics and

L. Daumont et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 116 (2013) 101–109104

identical spectrum simulations, which comforts theresults. In both cases, we performed a global fit of allassigned transitions in the 0–4900 cm�1 region, but theline intensity fit was obtained only for Octad–GroundState transitions.

The polyad structure of the methane molecule is essen-tially governed by the quasi coincidence of the stretchingfundamental frequencies with the first overtones of thebending frequencies, say n1(A1)En3(F2)E2n2(E)E2n4(F2).The polyads Pn are defined by an integer n expressed interms of the principal vibrational quantum numbers asn¼2(v1þv3)þv2þv4. Polyad P0 corresponds to the vibra-tional ground state, P1 to the Dyad, P2 to the Pentad, and soon. The reduced vibrational energy diagram of the methanemolecule is plotted in Fig. 1. The effective ro-vibrationalHamiltonian adapted to the polyad structure of the CH4

molecule is expressed as: H¼HfGSg þHfDyadg þHfPentadg þ

HfOctadg, where the subsequent terms of this expansiongather operators that are specific to the successive polyads.Each group contains a series of terms identified by rota-tional, vibrational and symmetry indices [44] according to

the general nomenclature tOrðK ,kCÞn1n2n3n4m1m2m3m4

TOrðK ,kCÞn1n2n3n4m1m2m3m4

,

where T designates a tensor operator and t the correspond-ing adjustable parameters. The upper indices indicate therotational characteristics of the considered term: Or is therotational power with respect to the angular momentumcomponents; K is the tensor rank in the full rotation group;C is the rotational symmetry coinciding with the vibrationalsymmetry to satisfy the invariance condition under themolecular point group operations. The lower indices ni andmi (i¼1, y, 4) are, respectively, the powers of creation andannihilation vibrational operators associated with the fournormal modes of the molecule. Effective dipole momentexpansion is represented in a similar manner as that of theHamiltonian but the full symmetry type under the opera-tions of Td group is different: it is A1 for the Hamiltonianterms and F2 for the dipole moment terms in the molecule-fixed frame and A2 in the space-fixed frame [44].

The main objective of this work is the improvement ofthe description of the Octad–Ground State band system inthe 2 mm methane transparency window. We started withthe previous set of assignments reported in [25,26]. Withthese Octad assignments, the Octad positions and Octad–GSintensities could be reproduced with precisions of3.5�10�3 cm�1 and 8.1%, respectively. The global analysisapproach [26] describes not only the Octad band system butall known methane lines in the 0–4800 cm�1 region. Onthe other hand, in Ref. [25] only 604 Octad positions up toJ¼17 (highest position 4746.6232 cm�1) and 432 Octad–GSintensities up to J¼15 (highest line with measured intensityat 4723.796 cm�1) were included in a fit of the 4600–4850cm�1 region. New assignments obtained in the presentwork contain 1570 positions and 693 Octad–GS intensitiesup to J¼21 (highest line with measured intensity at4868.698 cm�1). In the work [25] only 17 lines withJ415 could be assigned between 4600 and 4850 cm�1

while in the present work, there are 189 ones. In the globalfit, these assigned lines with J415 were critical in obtaininga reliable prediction of Octad–GS transitions in this side ofthe transparency window. Detailed fit statistics (using MIRS

and STDS) of line positions and intensities for Octad–GS andOctad–Dyad transitions sorted by upper state vibrationsublevel are given in Table 1.

We should note that both fits, although they give verysimilar root mean square deviations, show quite differentnumbers of lines for each upper sublevel. This is notsurprising since the sublevels labelling relies on the mainprojection on the initial basis set. Due to extremely strongcouplings between the different bands, many rovibrationallevels are so mixed that such an labelling becomes veryambiguous. Thus, in particular, the use of two differentcoupling schemes can lead to different labelling.

The total number of line positions and line intensitiesinvolved in the fit of the Octad–GS region is 10626 and3503 lines, respectively. Although these numbers arebigger than the number of positions (7911) and thenumber of intensities (2408) involved in the fit for theOctad–GS system in [25], the principal part of new linesbelong to the upper part of the Octad. That is why in thiswork we report only predictions between 4600 and4878 cm�1. Moreover, the STDS fit uses slightly less lines,since some duplicates found in the assignments of Ref.[26] have been corrected. The STDS result will be used toupdate the calculated line database to be made availablethrough the VAMDC European Network [49].

The good agreement between the experimental spec-tra and the calculations is illustrated in Fig. 3. Fig. 4displays the fit residuals for line positions for the differenttransitions involved in the global fit. Fig. 5 displaysexperimental line intensities and fit residuals for Octad–GS transitions. Figs. 4 and 5 can be compared to thecorresponding ones in Ref. [26]. In particular, Fig. 5 clearlyshows the new weak assignments in the high wavenum-ber end of the Octad region. A major difficulty of theanalysis results from the high density of rovibrationaltransitions. In the 4600–4850 cm�1 region, besidesOctad–GS transitions, there are many hot band transitionsarising between the upper polyad (Tetradecad) and thedyad (v2,v4). These cannot be assigned and studied untilthose upper state levels are analyzed. Some 4v4–GStransitions with high J values also contribute to theabsorption in this transparency window [9], as do 13CH4

transitions. Detailed theoretical analyses of all thesetransitions remain to be done. In order to build a globaleffective Hamiltonian model relying on successive vibra-tional polyad extrapolations [44], a complete analysis ofthe Tetradecad [14] is particularly important.

5. Methane line list between 4600 and 4850 cm�1

In this spectral interval, all the lines could not bemeasured, so we decided to produce a line list based onthe predictions from the Hamiltonian and dipole momentparameters that could be fitted. When available, experimen-tal data from either Reims (source ‘‘R’’) or JPL (source ‘‘B’’)spectra is given in the form of an Fo�Fc difference betweenthe observed and calculated line positions, and of an Io� Icrelative difference between the observed and calculated lineintensities. Only the 12CH4 isotopologue is taken into account.In determining the effective parameters and assignment of

Fig. 3. Observed spectrum and simulation. This comparison shows the

methane spectrum at 290 K near 4734 cm�1 (spectrum c), two simula-

tions under the same physical conditions (from the paper of Albert et al.

[26] and from this work) and the HITRAN 2008 line list (intensity scale

sticks) of 12CH4. Eleven transitions between 4734.0 and 4735.5 cm�1 are

given in Table 2.

Table 1Detailed fit statistics for the Octad band system.

Level Sublevel Wave-number

(cm�1)

Positions MIRS Positions STDS Intensities MIRS Intensities STDS

Nb. data dRMS

(10�3 cm�1)

Nb. data dRMS

(10�3 cm�1)

Nb. data dRMS (%) Nb. data dRMS (%)

3v4 F1 3870.485 600 2.4 630 2.1 224 8.7 220 9.0

A1 3909.200 202 2.4 15 1.3 70 8.6 8 4.9

F2 1a 3920.510 626 2.4 794 2.3 245 8.7 345 8.5

F2 2a 3930.924 662 2.2 707 2.7 277 8.4 283 11.5

v2þ2v4 E 1b 4101.393 327 3.6 271 3.3 76 12.3 10 5.9

F1 4128.764 378 3.2 372 3.1 107 15.4 92 15.1

A1 4132.871 166 3.5 0 – 49 11.9 0 –

F2 4142.864 530 3.2 590 2.6 176 11.2 197 11.7

E 2b 4151.204 255 3 168 2.2 71 12.5 63 11.7

A2 4161.839 139 3 62 2.4 44 13.2 19 14.2

v1þv4 F2 4223.462 507 3.5 751 4.0 179 9.0 218 6.8

v3þv4 F2 4319.208 775 3.9 474 3.3 252 9.7 177 6.4

E 4322.179 504 4.1 179 4.4 142 9.8 34 18.8

F1 4322.591 843 3.7 1444 4.3 260 9.3 405 8.4

A1 4322.703 226 3.9 60 4.3 64 10.0 20 7.9

2v2þv4 F2 1c 4348.713 403 4.1 361 5.6 116 15.3 57 17.2

F1 4363.609 473 3.8 172 5.7 137 13.4 21 16.1

F2 2c 4378.946 391 4.4 316 5.4 104 14.1 44 19.8

v1þv2 E 4435.115 259 3.6 431 5.0 70 17.8 130 8.9

v2þv3 F1 4537.549 845 3.4 1025 2.8 268 10.0 336 11.0

F2 4543.761 915 3.2 1139 2.9 345 10.0 474 11.8

3v2 E 4592.032 275 3.2 369 1.9 100 19.0 138 17.6

A2 4595.275 155 2.8 159 2.4 66 16.0 77 16.2

A1 4595.511 170 3.3 132 2.0 61 15.3 44 15.9

Total 10,626 3.39 10,621 3.50 3503 11.3 3411 10.4

a Labels of levels 3v4 F2 1 and F2 2 in [26] are 9P3 21S and 9P3 24S, respectively.b Labels of levels v2þ2v4 E 1 and E 2 in [26] are 9P3 15S and 9P3 18S, respectively.c Labels of levels 2v2þv4 F2 1 and F2 2 in [26] are 9P3 12S and 9P3 14S, respectively.

L. Daumont et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 116 (2013) 101–109 105

the lines, careful attention was paid to the presence of 13CH4

lines which were observed in the JPL spectra. The choiceof spectra used to measure the 12CH4 lines was also

made to avoid saturation effects. This gives an intensitythreshold around 10�26 cm/molecule (at 296 K) whichin turns gives the limit at which the lines are saturatedin the Reims spectra. A sample of data contained in thelinelist is shown in Table 2 with the usual fields(Isotopologue number Iso being the same as HITRAN[30] one). Here only ‘‘61’’ the principal isotopologue isgiven since this is a predicted line list for this isotopo-logue. In the case where the 13CH4 spectrum indicatedan absorption line, the line was simply not measured.The field Sc points the origin of the observed value whenavailable (either from Reims spectra if the tag is ‘‘R’’, orfrom the JPL spectra if the tag is ‘‘B’’). ‘‘Nu’’ is thecalculated line position in cm�1. ‘‘I’’ is the calculatedline intensity in cm/molecule at 296 K. ‘‘P J C N’’ is theformat for the rovibrational assignment of the upper andlower levels, with P the polyad number, J the rotationalquantum number, C the symmetry species (irreduciblerepresentation of the Td point group), and N the rankingnumber in order of increasing energy of the vibrationalsublevel. Fo�Fc is the difference between the observed(when available) and calculated line positions in10�3 cm�1. In the full list, ‘‘Io� Ic%’’ is the relativedifference between the observed and calculated lineintensities at 296 K (however, only one intensity in this

Fig. 4. Fit residuals for the global fit of line positions using STDS. This can be compared to Fig. 3 of Ref. [26]. Here were use the polyad numbering P0 for

ground state, P1 for dyad, P2 for pentad and P3 for Octad.

L. Daumont et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 116 (2013) 101–109106

example was directly measured). The upper vibrationalassignment gives the ‘‘(v1, v2, v3, v4)Sv’’ assignmentof the upper state vibration based on the principalcomponent of the wavefunction over the harmonic

decomposition together with the vibrational symmetrytype Sv (an irreducible representation of the point groupTd). Then the lower energy value ‘‘E’’ is given to permittemperature conversion of the line intensities.

Fig. 5. Plot of intensities and intensity fit residuals for the assigned lines in the Octad band. The colors correspond to the eight different bands.

The present study has permitted hundreds of new features to be included at 2 mm to support planetary remote sensing. We note that similar intensity

measurements are needed at the center of the Octad in order to provide the complete interpretation of this polyad.

Table 2Sample extracted from the line list attached as electronic supplementary data.

Iso Src(obs)

Nucalc(cm�1)

I (cm/molecule)

Rotational assignment Fo�Fc

(10�3 cm�1)Io� Ic

(%)

Vibrationalassignment

E00

(cm�1)

Lowerstate

Upperstate

Upper

61 B 4734.06801 3.48�10�25 0 16 F2 3 3 17 F1 215 �0.33 0110 F2 1417.753110

61 4734.07061 7.52�10�27 0 17 F2 2 3 18 F1 218 0110 F1 1593.562049

61 4734.10745 8.73�10�27 0 17 F1 3 3 18 F2 220 0110 F1 1593.523301

61 4734.13920 4.31�10�27 0 18 F2 4 3 19 F1 228 0110 F2 1780.312383

61 4734.17344 4.33�10�27 0 18 E 3 3 19 E 150 0110 F2 1780.269507

61 B 4734.34293 3.52�10�25 0 16 F1 3 3 17 F2 213 �0.40 0110 F1 1417.807376

61 B 4734.75800 6.95�10�25 0 16 A1 2 3 17 A2 73 0.08 0110 F2 1417.865248

61 R 4734.87033 7.70�10�27 0 10 F2 2 3 11 F1 152 0.85 0300 A2 575.170076

61 4734.96051 4.57�10�27 0 20 A2 1 3 21 A1 77 0201 F2 2181.851181

61 R 4734.98775 5.24�10�27 0 10 F2 1 3 11 F1 152 0.91 0300 A2 575.052656

61 4735.45004 5.11�10�27 0 19 A2 2 3 20 A1 79 0102 A1 1976.717999

61 R 4741.04156 4.87�10�27 0 16 E 3 3 17 E 146 �5.37 10.2 0011 F1 1418.118763

Notes: In this table, the columns are:

1. ISO: isotopologues, 61 for 12CH4.

2. Src obs: means type of source of the observed data. All the data are predicted values, for observed lines, ‘‘R’’ means Reims (290 K) FTS origin, ‘‘B’’

corresponds to the JPL (296 K) data.

3. Nu: is so, the calculated line position.

4. I: is S1(296 K), the calculated line intensity at 296 K (HITRAN units: cm/molecule).

5. Lower rovibrational assignment are given by the vibrational polyad number P, the rotational quantum number J, the rovibrational symmetry type C

(Td irreducible representation) and the ranking vibration sublevel number N.

6. Upper rovibrational assignment in the same format.

7. Fo�Fc is the difference between observed and calculated line position included in the fit in 10�3 cm�1 units. These values allow retrieving the

observed positions.

8. Io� Ic% is the relative difference between observed and calculated intensities included in the fit. These values permit the retrieval of the observed

intensities.

9. The vibrational band assignment: contains the principal vibrational quanta (v1, v2, v3, v4) and vibrational symmetry type Sv (Td irreducible

representation).

10. E00: lower energy value.

L. Daumont et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 116 (2013) 101–109 107

L. Daumont et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 116 (2013) 101–109108

6. Discussion

In the line list, the observed intensities from Reimsspectra are still at 290 K while the calculated and JPLobserved values are at 296 K. This choice was maintainedbecause the temperature conversion for the Reims experi-mental data cannot be reliable without complete knowl-edge of all the cold, hot and of isotopologues features.However, this temperature conversion is limited to 8% inthe worst case because we are dealing with cold bandswith the highest rotational quantum number assigned toJ¼17 (E00 ¼1600 cm�1). Moreover, the greatest errorwould occur for high J weak lines that already have worseprecisions, but the temperature adjustment for the lower Jassignments would not greatly degrade the precision. Thelowest line intensity assigned and included into the fit is3�10�27 cm/molecule at room temperature. The directcomparison to the HITRAN line list is not straightforwardto do line by line because in this region, HITRAN [30]contains calculated values that correspond to extrapola-tions for our new weak lines. However, a global compar-ison of the line lists to the observed spectra as shown inFig. 3 demonstrates the improvement of the line list forboth line positions and line intensities, even for intenselines (notice that only the 12CH4 isotopologue is takeninto account in this region for the two line lists).The experimental values can be retrieved from the linelist given as supplementary material. For the line position,one can use the calculated line position ‘‘Nu calc’’ togetherwith the difference between observed and calculatedvalues ‘‘Fo�Fc’’. For the line intensities, one can use thecalculated intensity at 296 K ‘‘I’’ and the relative differ-ence between the observed and calculated intensity‘‘Io� Ic’’ which is 100� ðIobs�IcalcÞ=Icalc . Determining theobserved intensity this way will lead to the intensity at296 K for the observed data from JPL spectra (‘‘Src’’ is B)and to intensity at 290 K for the observed data from Reimsspectra (‘‘Src’’ is R). For instance, Table 2 gives a sample of11 transitions shown in Fig. 3 between 4734 and4735.5 cm�1 and one transition outside this window thathas observed position and intensity. The positions weremeasured in JPL spectra, for three transitions (B), and 2using Reims spectra (R); the six remaining weakestfeatures are calculated lines. No intensity has been mea-sured for these lines and all values are calculated. Incalculating the line list, a cutoff of 4�10�27 cm/molecule(296 K) was applied to the intensities; it corresponds toone of the lowest intensities that was measured and tolower state J values up to 21. The sum of all the calculatedline intensities is 9.9�10�21 cm/molecule (296 K), whilethe corresponding sum of reported measurements is only7.4�10�21 cm/molecule; this difference occurs becausenot all the lines in the spectra were retrieved (particularlythe obvious blends). In addition, the lines overlapped byother isotopologues were intentionally omitted.

7. Conclusion

This work provides an improved line list for cold bandsof 12CH4 in the upper part of the Octad. To be used forplanetary and astrophysical applications, it should be

completed with 13CH4 data and 12CH4 hot bands. Thespectral range is only a small part of the long path spectrathat were recorded. Other studies concerning the otherregions and isotopologues will be performed in subsequentpapers. The data will be presented for future inclusion intocommonly used databases such as HITRAN [30] or GEISA[50] and through the VAMDC portal [49] and is availableupon request to the authors. Hamiltonian and dipolemoment parameters resulting from the present study arealso included in the MIRS [47] and XTDS [48] softwarepackages, that allow line lists and synthetic spectra to berecalculated. It will also be proposed to simulate Titan’sspectra in that spectral region.

Acknowledgments

This work is part of the ANR project ‘‘CH4@Titan’’(ref: BLAN08-2_321467). The support of the Groupe-ment de Recherche International SAMIA between CNRS(France), RFBR (Russia) and CAS (China) is acknowl-edged. We acknowledge the support from IDRIS compu-ter centre of CNRS France and of the computer centreReims-Champagne-Ardenne. Part of the researchdescribed in this paper was performed at the Jet Propul-sion Laboratory, California Institute of Technology,under contracts with the National Aeronautics andSpace Administration.

Appendix A. Supplementary material

Supplementary data associated with this article can befound in the online version at http://dx.doi.org/10.1016/j.jqsrt.2012.08.025.

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