Andrei V Nikitin

Xavier Thomas

L Regalia

L Daumont

Pierre Von Der Heyden

Vladimir G Tyuterev

Le Wang

Samir Kassi

Alain Campargue

L Régalia

First assignment of the 5nu4 and nu2+4nu4 band systems of 12CH4

Keywords: methane, spectra, transparency window, Titan, CRDS, long path FTS

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The precise knowledge of the methane absorption in the study of planetary systems, and especially of Titan (Saturn's largest satellite whose atmosphere is mainly composed of nitrogen and methane at temperatures ranging between 70 K and 200 K), is of great importance because it gives access to the determination of the physical properties of these objects [START_REF] Coustenis | Titan 3 m spectral region from ISO High resolution spectroscopy[END_REF][START_REF] Coustenis | Titan trace gaseous composition from CIRS at the end of the Cassini-Huygens prime mission[END_REF][START_REF] Boudon | Methane in Titan's atmosphere: From fundamental spectroscopy to planetology[END_REF]. The full interpretation of the Titan data returned by the ground-based and space observations is severely limited by the lack of precise knowledge of the methane absorption which dominates the spectrum in the near infrared.

Despite many years of experimental and theoretical studies [START_REF] Brown | Methane line parameters in HITRAN[END_REF][START_REF] Brown | Empirical line parameters of methane from 1.1 to 2.1m[END_REF][START_REF] Hippler | High-resolution Fourier transform infrared and cw-diode laser cavity ringdown spectroscopy of the  2 +2 3 band of methane near 7510 cm -1 in slit jet expansions and at room temperature[END_REF][START_REF] Champion | Spectroscopy of the Earth atmosphere and interstellar medium[END_REF][START_REF] Robert | First Assignment and Line Strengths of the 4 4 Band of 12 CH 4 near 1.9 m[END_REF][START_REF] Boursier | Identification of hot band transitions of CH 4 near 3000 cm -1[END_REF][START_REF] Boudon | The vibrational levels of methane obtained from analyses of high-resolution spectra[END_REF][START_REF] Kassi | The near-infrared (1.30-1.70 m) absorption spectrum of methane down to 77[END_REF][START_REF] Gao | Empirical low energy values for methane transitions in the 5852-6181 cm -1 region by absorption spectroscopy at 81 K[END_REF][START_REF] Albert | Global analysis of the high resolution infrared spectrum of methane 12 CH 4 in the region from 0 to 4800 cm -1[END_REF][START_REF] Hilico | Analysis of the interacting octad system of 12 CH 4[END_REF][START_REF] Schwenke | Vibrational energy levels for CH 4 from an ab initio potential[END_REF][START_REF] Wang | A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schroedinger equation in nine dimensions[END_REF][START_REF] Bowman | Variational quantum approaches for computing vibrational energies of polyatomic molecules[END_REF][START_REF] Nikitin | GOSAT-2009 methane spectral linelist in the 5550-6236 cm -1 range[END_REF][START_REF] Boudon | Symmetry-adapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups[END_REF][START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF], the infrared methane spectrum is still insufficiently understood. In particular, the line-by-line analyses based on the expansion of an effective Hamiltonian and dipole moment, were able to provide precise data reductions only up to 4800 cm -1 [START_REF] Boudon | The vibrational levels of methane obtained from analyses of high-resolution spectra[END_REF][START_REF] Albert | Global analysis of the high resolution infrared spectrum of methane 12 CH 4 in the region from 0 to 4800 cm -1[END_REF][START_REF] Hilico | Analysis of the interacting octad system of 12 CH 4[END_REF]. This is because the number of strongly interacting near-degenerate vibration levels increases very rapidly with energy due to the high symmetry of the methane molecule. On the other hand direct variational predictions of methane rovibrational lines using ab initio potential energy and dipole moment surfaces [START_REF] Schwenke | Vibrational energy levels for CH 4 from an ab initio potential[END_REF][START_REF] Wang | A contracted basis-Lanczos calculation of vibrational levels of methane: Solving the Schroedinger equation in nine dimensions[END_REF][START_REF] Bowman | Variational quantum approaches for computing vibrational energies of polyatomic molecules[END_REF] are not at present sufficiently accurate for the assignment of experimental spectra and a calculation of high-J rotational transitions is not yet possible.

Considering the weakness of the absorption of 12 CH 4 and 13 CH 4 , the 6287-6550 cm -1 region studied in this work can be used to detect other planetary species such as CH 3 D and CO. A description of the methane absorbance in transparency windows represents a particular difficulty for the theoretical approach because it requires an extrapolation to high-J transitions and because intensities of these weak transitions are extremely sensitive to numerous resonance interactions which are still poorly defined. As already presented in [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF], the CH 3 D isotopologue contributes significant absorption in the region, complicating any analysis of laboratory spectra using natural methane samples.

Theoretically speaking, in terms of the resonance polyad structure of methane vibration states, the considered spectral range corresponds to the lowest frequency bands of the icosad which are very weak bands in interaction. The complexity of the vibrational structure is illustrated in Fig. 1. This scheme shows the vibrational levels 5v 4 , v 2 +4v 4 , v 1 +3v 4 splitted into 26 vibrational sublevels. The 5 4 vibrational system has eight sublevels of A 1 , E, 3F 1 , 3F 2 symmetry types, the  2 +4 4 system has 14 sublevels (2A 1 , 2A 2 , 4E, 3F 1 , 3F 2 ) and the  1 +3 4 system has 4 sublevels (A 1 , F 1 , 2F 2 ). The symmetry notations correspond to irreducible representations of the T d point group [START_REF] Champion | Spectroscopy of the Earth atmosphere and interstellar medium[END_REF][START_REF] Boudon | Symmetry-adapted tensorial formalism to model rovibrational and rovibronic spectra of molecules pertaining to various point groups[END_REF]. The nv 4 bending overtone levels are the lowest energy levels of the different vibrational polyads of methane and separate progressively from the remaining part of the polyad due to the high anharmonicity in the  4 mode.

Rovibrational transitions from the vibration ground state (GS) to icosad sub-levels form the corresponding absorption band systems. An accurate characterization of these weak absorption features and of their dependence with the temperature is mandatory for the interpretation of various optical measurements at large optical paths. As already stressed, this is particularly important for a remote sounding of the Titan surface [START_REF] Coustenis | Titan 3 m spectral region from ISO High resolution spectroscopy[END_REF][START_REF] Coustenis | Titan trace gaseous composition from CIRS at the end of the Cassini-Huygens prime mission[END_REF][START_REF] Boudon | Methane in Titan's atmosphere: From fundamental spectroscopy to planetology[END_REF].

Until recently, the only line list available in the literature for the considered transparency window was constructed by Brown from spectra recorded at room temperature by Fourier Transform Spectroscopy (FTS) with path lengths up to 97 meters [START_REF] Brown | Empirical line parameters of methane from 1.1 to 2.1m[END_REF]. In absence of theoretical modeling, this FTS list, adopted in the HITRAN 2004 database [START_REF] Rothman | The HITRAN 2008 molecular spectroscopic database[END_REF], was limited to empirical line positions and intensities at room temperature without rovibrational assignments. Another limitation was the lack of sensitivity resulting in relatively high intensity cut off (about 4×10 -26 cm/molecule).

A considerable improvement has been recently achieved by some of us using two spectra recorded by Cavity Ring Down Spectroscopy (CRDS) at room temperature and at 79 K [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF][START_REF] Campargue | Empirical line parameters of methane in the 1.63-1.48 lm transparency window by high sensitivity Cavity Ring Down Spectroscopy[END_REF]. For the 6289-6526 cm -1 region, two lists of 6868 and 4555 transitions with intensities as weak as 1×10 -29 cm/molecule were constructed from the recordings at 297 and 79 K, respectively. The empirical lower state energy and lower state J" values were derived from the variation of their line intensities at 297 and 79 K. Although a complete assignment was not provided, the low-J quantum numbers from Ref. [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] provides the temperature dependence of the line intensities and a considerable help in the line identification. In order to complete the review of the previous observations in our region of interest, the results obtained by Deng et al [START_REF] Deng | Empirical line intensities of methane at 1.51 m[END_REF] in the 6607-6625 cm -1 section should be mentioned. These authors used direct absorption with a tunable diode laser and a White cell with a 973 m path length to detect 288 lines with intensities down to 1.4×10 -27 cm/molecule. The forthcoming analysis is based on the CRDS line lists of Ref. [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] completed with new long path FTS spectra recorded at 290 K in Reims with a 1603 m pathlength and pressures of 1, 7 and 34 mbar. The paper is structured as follows. In Sections 2 and 3 the experimental setup and recordings of long-path FTS and CRDS spectra are outlined. Section 4 is devoted to the assignment, line position and intensity modelling of the 5 4 and  2 +4 4 band systems. We argue about the necessity to consider the coupling with the  1 +3 4 band to correctly reproduce the measured intensities. Section 5 presents the construction of a synthetic 12 CH 4 line list that combines both experimental data and predicted lines. The advantages and shortcomings of the calculated line list as well as possible applications of new data are discussed in the concluding Section 6.

Long path FTS spectra and calibration

Several long path spectra of methane at "natural" abundance were recorded in Reims in the 3800 -8100 cm -1 spectral region. The overview of the spectrum in the investigated region is presented in Fig. 2 for three pressure values. As seen in Fig. 1, the weak absorption features under study are surrounded by the strongly absorbing regions of the tetradecad and icosad.

The prominent 30012-00001 CO 2 band near 6350 cm -1 used for calibration purpose falls in the centre of the transparency window.

The spectra were recorded with the Connes' type FTS built in the GSMA laboratory as described in Refs. [START_REF] Connes | Astronomical Fourier Spectrometer[END_REF][START_REF] Plateaux | Reims high resolution Fourier transform spectrometer. Data reduction for ozone[END_REF][START_REF] White | Long Optical Paths of Large Aperture[END_REF][START_REF] Lux | Réalisation d'une cellule d'absorption réflexions multiples de grande dimension (longueur : 50 m)[END_REF][START_REF] Régalia-Jarlot | Line intensities of the:  3 , 4 2 ,  1 + 3 , 3 1 and 2 1 +2 2 bands of 16 O 12 C 32 S molecule[END_REF]. This spectrometer has been used to perform several high resolution spectroscopic studies of various molecules [START_REF] Régalia-Jarlot | A complete study of the line intensities of four bands of CO 2 around 1.6 and 2.0 m: A comparison between Fourier transform and diode laser measurements[END_REF][START_REF] Lyulin | Line positions and intensities of acetylene in the 2.2 m region[END_REF][START_REF] Mandin | Line intensities of acetylene at 3 m[END_REF][START_REF] Jenouvrier | Fourier transform measurements of water vapor line parameters in the 4200-6600 cm -1 region[END_REF][START_REF] Lamouroux | Measurements of line intensities and determination of transition moment parameters from experimental data for the  1 and  3 bands of D 2 32 S[END_REF][START_REF] Mikhailenko | Update of line parameters of ozone in the 2550-2900 cm -1 region[END_REF]. The maximum optical path difference of 3 meters corresponds to a non-apodized resolution of 0.0017 cm -1 . With the recent fitting of this spectrometer to the 50-meter base long White type cell [START_REF] White | Long Optical Paths of Large Aperture[END_REF], spectra with an absorption path length of 1.6 km can be recorded [START_REF] Régalia | FTS improvements and connection with a long White cell. Application: H 2 16 O intensity measurements around 1200 cm -1[END_REF]. The methane spectra were recorded at 1.34, 6.66 and 33.13 mbar (referred to as spectra (a), (b) and (c) respectively in Fig. 2) with a temperature of 290 K. The iris diameter at the entrance of the spectrometer was 3.5 mm.

The pressures were measured with a MKS Baratron capacitance manometer with an uncertainty of 0.01 %. The temperatures were obtained and controlled continuously during the recordings by platinum-resistance thermometers with an uncertainty of 1K. All the spectra were recorded with the following optical setup: a SiO 2 beam splitter, two InGaAs detectors with lenses and windows in BaF 2 . The whole path between the long 50-m White cell and our spectrometer was maintained under vacuum.

For the wavenumber calibration of the spectra (a) and (b), we introduced in the optical path before the entry of the interferometer a cell with a small pressure of CO 2 . The CO 2 pressure was about 1.5 and 20 mbar for the (a) and (b) spectra, respectively. The wavenumber calibration was carried out in two steps. First, the low pressure spectrum (a) was calibrated using 56 lines of CO 2 by Miller and Brown [START_REF] Miller | Near infrared spectroscopy of carbon dioxide I. 16 O 12 C 16 O line positions[END_REF] with a standard deviation of 2.18×10 -4 сm -1 .

Then medium and high pressure spectra (b) and (c) were calibrated using 22 relatively strong isolated methane transitions of (a) in the region 6300-6700cm -1 with corresponding standard deviations of 2.08×10 -4 сm -1 and 2.55×10 -4 сm -1 .

Note that the positions in the HITRAN2008 line list [START_REF] Brown | Empirical line parameters of methane from 1.1 to 2.1m[END_REF][START_REF] Rothman | The HITRAN 2008 molecular spectroscopic database[END_REF] for 20 of 22 CH 4 transitions used at this step of the calibration are lower than ours by 5×10 -4 сm -1 . On the contrary the line positions in the recent CRDS line list [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] are in average higher than ours by 6.5×10 -4 сm -1 for this calibration sample. This comparison was only carried out in the 6400-6507 сm -1 range where lines were strong enough and mostly free of CH 3 D lines. It was found that the intensities from FTS was 10% lower than CRDS intensities. So the FTS intensities were adjusted by a factor of 1.1.

Cavity Ring Down Spectroscopy.

Spectra at room temperature

As presented in Ref. [START_REF] Liu | High sensitivity CW-cavity ring down spectroscopy of CH 4 in the 1.55 m transparency window[END_REF], the CW-CRDS spectra at room temperature (RT) were recorded over the whole methane transparency window (6165-6750 cm -1 ) with the fibered distributed feedback diodes (DFB) laser CW-CRDS spectrometer developed in Grenoble. The present analysis considers only the 6275-6525 cm -1 section of the recordings. The reader is referred to Refs. [START_REF] Liu | High sensitivity CW-cavity ring down spectroscopy of CH 4 in the 1.55 m transparency window[END_REF][START_REF] Morville | Two schemes for trace detection using cavity ringdown spectroscopy[END_REF][START_REF] Perevalov | CW-cavity ringdown spectroscopy of carbon dioxide isotopologues near 1.5 m[END_REF] for the description of the experimental apparatus. The 6275-6525 cm -1 region was continuously covered with the help of 10 fibered DFB lasers and about 60 minutes were needed to complete a temperature scan of one DFB laser. The corresponding noise equivalent absorption is on the order of 5×10 -10 cm -1 [START_REF] Liu | High sensitivity CW-cavity ring down spectroscopy of CH 4 in the 1.55 m transparency window[END_REF].

Spectra at 80 K

The cryogenic cell specifically developed for CW-CRDS at low temperature has been described in Refs. [START_REF] Kassi | The near-infrared (1.30-1.70 m) absorption spectrum of methane down to 77[END_REF][START_REF] Gao | Empirical low energy values for methane transitions in the 5852-6181 cm -1 region by absorption spectroscopy at 81 K[END_REF][START_REF] Kassi | Mode by Mode CW-CRDS at 80 K: Application to the 1.58 m transparency window of CH 4[END_REF]. It is based on an original design (see Fig. 1 of Ref. [START_REF] Kassi | Mode by Mode CW-CRDS at 80 K: Application to the 1.58 m transparency window of CH 4[END_REF]) which dispenses with an external vacuum jacket by exploiting the fact that a low pressure sample constitutes itself a good thermal insulation. A Mode by Mode CRDS acquisition scheme was preferred instead of the usual piezoelectric actuator that modulates the optical cavity length in standard CW-CRDS [START_REF] Kassi | Mode by Mode CW-CRDS at 80 K: Application to the 1.58 m transparency window of CH 4[END_REF]. Using mirrors with 99.992% reflectivity, a noise equivalent absorption of 3×10 -10 cm -1 was obtained.

The gas temperature in the cryogenic cell was calculated to be 82.6 K from the Doppler profile of several dozen lines [START_REF] Kassi | Mode by Mode CW-CRDS at 80 K: Application to the 1.58 m transparency window of CH 4[END_REF], in good agreement with the rotational temperature (79.3 K) evaluated from the intensity distribution of the 3 2 band of CH 3 D [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF]. During the scanning, the pressure, measured by a capacitance gauge and the ringdown cell temperature were monitored. The room temperature value was 297±2 K and most of the RT spectra were recorded at 3.3 and 13 mbar, as presented in Ref. [START_REF] Liu | High sensitivity CW-cavity ring down spectroscopy of CH 4 in the 1.55 m transparency window[END_REF]. The LNT spectra were recorded at 1.3, 6.5 and 13 mbar.

Each 35 cm -1 wide RT spectrum recorded with one DFB laser was calibrated independently on the basis of the wavelength values provided by the Michelson-type wavemeter. The wavemeter accuracy being limited to 3×10 -3 cm -1 , the absolute calibration was obtained by using reference line positions of methane obtained either from the HITRAN database [START_REF] Rothman | The HITRAN 2008 molecular spectroscopic database[END_REF] or from the FTS spectrum. The precision of the obtained wavenumber calibration estimated from the dispersion of the wavenumber differences is 1×10 -3 cm -1 . Each 80 K spectrum was then calibrated by statistically matching the line positions to those of the corresponding RT spectrum. Fig. 3 shows a comparison of the CW-CRDS spectra at RT and 80 K near 6494 cm -1 .

The achieved sensitivity reveals the considerable spectral congestion of the spectra and the dramatic change induced by cooling. The multiline fitting procedure used to derive the line intensities and the construction of the line lists at RT and 80 K have been described in Refs. [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF][START_REF] Campargue | Empirical line parameters of methane in the 1.63-1.48 lm transparency window by high sensitivity Cavity Ring Down Spectroscopy[END_REF].

Line position and line intensity modelling

The theoretical analysis was performed within the global effective Hamiltonian approach using the polyad vibration extrapolation scheme reviewed in [START_REF] Champion | Spectroscopy of the Earth atmosphere and interstellar medium[END_REF]. The formalism of irreducible tensor operators developed in a series of works by the Dijon group and collaborators [7, 19 and references therein] allows fully account for molecular symmetry properties. The major advantage of this method is that all the terms and corresponding constants obtained in the previous analyses of the lower polyads (GS in microwave and THz regions, dyad in the 1100-1800 cm -1 region, pentad in the 2300-3300cm -1 region, octad in the 3500-4700 cm -1 region, tetradecad in the 4800-6200 cm -1 region) are directly involved in the icosad calculations. The version of the rovibrational tensors coupling corresponds to that defined in our previous work [START_REF] Nikitin | Improved Algorithms for the Modeling of Vibrational Polyads o Polyatomic Molecules: Application to Td , Oh , and C3v Molecules[END_REF] and the line positions and intensities analyses were performed using the MIRS software described in [START_REF] Nikitin | The MIRS computer package for modeling the rovibrational spectra of polyatomic molecules[END_REF].

The polyad structure of the methane molecule is essentially governed by the quasi coincidence of the stretching fundamental frequencies with the first overtones of the bending

frequencies  1 (A 1 )≈  3 (F 2 ) ≈2 2 (E)≈ 2 4 (F 2 )
. The polyads P n are defined by an integer n expressed in terms of the principal vibrational quantum numbers as n=2(v 1 +v 3 )+ v 2 +v 4 .

Reduced vibrational energy diagram of the methane molecule is plotted in

} cos { } { } { } { } { } { ad I Tetradecad Octad Pentad Dyad GS             
where the subsequent terms correspond to the successive polyads with increasing vibrational energies. Each group contains a series of terms identified by rotational, vibrational and symmetry indices [START_REF] Champion | Spectroscopy of the Earth atmosphere and interstellar medium[END_REF] according to the general nomeclature ) , ( ) , (

4 3 2 1 4 3 2 1 4 3 2 1 4 3 2 1 kC K m m m m n n n n kC K m m m m n n n n r r T t  
, where T designated a tensor operator and t the corresponding adjustable parameters.

As a preliminary approach, the 5 4 band system and the lower sub bands of  2 +4 4 can be considered "separately" from all the other icosad bands, except for   +3 4 . This is because the ratio of the specific polyad interaction terms to the energy gap between n 4 and other states gradually decreases with the polyad number [START_REF] Champion | Spectroscopy of the Earth atmosphere and interstellar medium[END_REF]. This approximation does not mean that the corresponding upper vibration states are treated as isolated ones: within the polyad extrapolation scheme, the {5 4 , ( 2 +4 4 )} coupling comes from operators specific to the dyad and the {5 4 , ( 2 +4 4 ), ( 1 +3 4 )} couplings come from the operators specific to the pentad.

Note that we were able to achieve a satisfactory fit of the line positions in our spectral range without including higher-order resonance terms specific to the icosad part of the Hamiltonian.

Although the vibration extrapolation scheme provides a systematic way to expand the effective Hamiltonian and dipole moment, it is well-known that the accuracy of extrapolations from lower to higher polyads is not sufficient for a direct assignment of complicated rovibrational methane spectra. Moreover, despite considerable progress in previous methane analyses [START_REF] Brown | Methane line parameters in HITRAN[END_REF][START_REF] Champion | Spectroscopy of the Earth atmosphere and interstellar medium[END_REF][START_REF] Robert | First Assignment and Line Strengths of the 4 4 Band of 12 CH 4 near 1.9 m[END_REF][START_REF] Boursier | Identification of hot band transitions of CH 4 near 3000 cm -1[END_REF][START_REF] Albert | Global analysis of the high resolution infrared spectrum of methane 12 CH 4 in the region from 0 to 4800 cm -1[END_REF][START_REF] Hilico | Analysis of the interacting octad system of 12 CH 4[END_REF]] not all coupling parameters of lower polyads are well determined. In particular, the assignments and parameter determinations of the tetradecad are not yet fully completed. For this reason in the present work, we used a limited model dedicated to the assignment of the lowest states of the icosad. As an initial iteration, the octad 12 CH 4 model of [START_REF] Albert | Global analysis of the high resolution infrared spectrum of methane 12 CH 4 in the region from 0 to 4800 cm -1[END_REF] was used, with an addition of 132 parameters [START_REF] Nikitin | GOSAT-2009 methane spectral linelist in the 5550-6236 cm -1 range[END_REF] specific to the tetradecad. Finally only four new diagonal vibration operators specific to the  1 +3 4 system of the icosad were included in our model. We have proceeded then by successive iterations including rovibrational extrapolations to 5 4 ,  2 +4 4 and  1 +3 4 bands, combination differences determination for observed lines and parameter fitting involving low J values. The simultaneous use of cold (T= 80K) and room temperature spectra as well as the descrimination of CH 3 D transitions from the line list of [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] have considerably facilitated the assignment which however proved to be very laborious. We were able finally to assign and include in the fit 1955 lines up to J = 15.

In order to stabilize the lower order parameter optimization, the experimentally known energy levels [START_REF] Albert | Global analysis of the high resolution infrared spectrum of methane 12 CH 4 in the region from 0 to 4800 cm -1[END_REF] of the dyad up to J=19, of the pentad up to J=16 and of the octad up to J=12 were also included in the fit. This limited model is not suitable for the description of the tetradecad, especially for its middle part between 5475 and 5750 cm -1 . In spite of this imperfection, our model describes satisfactorily the lowest 5 4 and  2 +4 4 icosad band systems and permitted us to make reliable assignments to most of the relatively intense 12 CH 4 transitions in the 6287-6550 cm -1 region.

Detailed statistics of the fit of line positions and intensities are given in Tables 1 and2 for the 5 4 and  2 +4 4 band systems, respectively, ranked by upper state vibration sub-levels.

The maximum upper-state rotational quantum number included in the fit of line positions and line intensities is J = 15.

The 5v 4 vibration sublevels included in Table 1 are the first accurate experimental determination of 12 CH 4 levels with a total vibrational excitation V=5. Note that the theoretical predictions of these sub-levels from the best published ab initio potential function [START_REF] Bowman | Variational quantum approaches for computing vibrational energies of polyatomic molecules[END_REF] lead to up to 20 cm -1 discrepancies compared to our J=0 values. These new information can be useful for a further improvement of potential energy surfaces and theoretical models.

Among the limitations of our analysis, we mention that some higher J values could be perturbed by other icosad states lying above 6800 сm -1 not considered in this work. In addition, the experimental room temperature spectrum could include hot bands which are completely unknown in this range.

Even if the 5 4 / 2 +4 4 and 5 4 / 1 +3 4 resonance couplings are relatively small, the resulting intensity borrowings are sufficient to greatly perturb the intensities of the 5 4 system because the 5v 4 band is much weaker than the nearby  2 +4 4 and  1 +3 4 bands. The   +3 4 band system being the strongest in the 6300-6800 cm -1 region, it was necessary to fit selected line intensities of this band as well, though it is beyond the range of our calculated line list described in the next section. We have thus taken these couplings into account for a realistic intensity modelling of 5 4 and  2 +4 4 . The fitted values of the vibrational effective dipole transition moment parameters of the {5 4 ,  2 +4 4 ,  1 +3 4 } interacting system are listed in Table 3. These values was defined from simulatious least-square fit of 9 vibrational and 18 (from 22) rotational R1(1,F 1 ) dipole moment parameters of the {5 4 ,  2 +4 4 ,  1 +3 4 } interacting system.

Methane line list between 6287 and 6550 cm -1

A major difficulty of the analysis results from the very high density of rovibrational transitions. The superposition of five-quanta excited bands of a five atom tetrahedral molecule leads to a very high density of lines (about 25 lines/cm -1 in the CRDS spectrum at room temperature [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF][START_REF] Campargue | Empirical line parameters of methane in the 1.63-1.48 lm transparency window by high sensitivity Cavity Ring Down Spectroscopy[END_REF]). The spectral resolution of nearly coincident transitions is frequently hampered by the Doppler broadening leading to some uncertainties in purely empirical line parameter determination. The theoretical calculations described above are particularly valuable in those situations as they may allow identifying the various components contributing to a blended line. This is the case when the number of nearby calculated lines is higher than the number of components obtained from the empirical line list (see Fig. 4 for instance). Thanks to this additional theoretical information we re-determined experimental line parameters at about 30 blended absorption features using a profile fitting routine. The primary aim of such modification was not a systematic improvement of the empirical line list [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] but to extend the assignments. According to the improved calibration we also lowered all empirically determined line positions of Ref. [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] by 0.00065 cm -1 . We shall refer to the obtained modified line list as the "corrected" empirical CRDS list.

The experimental methane spectrum in the 6287-6550 cm -1 region contains contributions of the 12 CH 4 , CH 3 D and 13 CH 4 isotopologues. A detailed theoretical analyses of the CH 3 D [43, add 3v2] and 13 CH 4 [44, add Lulin] isotopologues is not complete in the region and a rigorous extrapolation is not yet possible. The determination of the CH 3 D lines in the CRDS list of methane was performed in Ref. [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] on the basis of a FTS spectrum of CH 3 D recorded separately. CH 3 D has been found to contribute to the total absorbance by as much as 25 % in some spectral intervals of the room temperature spectrum [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF][START_REF] Campargue | Empirical line parameters of methane in the 1.63-1.48 lm transparency window by high sensitivity Cavity Ring Down Spectroscopy[END_REF]. A rough estimation for the 13 CH 4 spectrum can be obtained by shifting the 12 CH 4 line positions down to 37 сm -1 for 5  and 29 cm -1 for  2 +4 4 [START_REF] Nikitin | Isotopic substitution shifts in methane and vibrational band assignment in the 5560-6200 cm -1 region[END_REF] and by scaling the absorbance according to the 13 C/ 12 C abundance ratio (1.1 %).

Both pure empirical and theoretical line lists have their own advantages. For some applications, the knowledge of fully assigned upper state transition is preferable (see Conclusion). The theoretical list provides this assignment and helps resolving some ambiguities for closely lying transitions, but it is limited to the 12 CH 4 main isotopologue and does not account for hot bands and very high J transitions.

The positions in the calculated line list are less precise and the accuracy of calculations is not "homogeneous". As the coupling with other icosad bands is not fully implemented in the model, the error of calculations increases with rotation quantum numbers. We considered various cut-off in J for the line list generation. For T = 80 K, our calculations are in a very good agreement with the observed CRDS data and the J = 10 cut-off is sufficient to characterise more than 99% of the observed 12 CH 4 absorbance at room temperature. For the room temperature spectra, the integrated intensity of all predicted lines in the 6350-6500 cm -1 region is 1.2×10 -23 cm/molecule, while integrated intensities of transitions with J upper =15 and 16 are 8.7×10 -26 and 4.4×10 -26 , respectively. Then, the total intensity contribution of J =15 and J = 16 lines is 0.7% and 0.3%, correspondingly. For this reason, a J upper =15 cut-off was chosen for the calculated line list at room temperature. Though the RMS deviation for the total of 1955 transitions included in the fit was 0.003 cm -1 , the predicted positions of some  2 +4 4 lines with J > 12 and intensities less than 4×10 -27 could be shifted by up to 0.1 cm -1 compared to the observations [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF].

Depending on the spectral interval, various bands and isotopologues can provide major contributions at different temperatures. The 6287-6550 cm -1 region was divided in four sections (L1-L4) limited as indicated in Fig. 5: (a) List L1: 6287-6350 cm -1 .

In this spectral interval, there are many lines which do not belong to the 5 4 ,  2 +4 4 band systems. Moreover, the contribution of CH 3 D is strong [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF][START_REF] Campargue | Empirical line parameters of methane in the 1.63-1.48 lm transparency window by high sensitivity Cavity Ring Down Spectroscopy[END_REF] in this region that considerably complicates the assignment and theoretical modeling of 12 CH 4 lines. This is why we prefer the experimental CRDS list at room temperature [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] with the corrections described above and some identifications added.

(b) List L2: 6350-6500 cm -1 .

As most of the lines of in this spectral interval belong to the 5 4 and  2 +4 4 band systems of 12 CH 4 , theoretical predictions are rather complete and we provide the results of our calculations. An advantage of predicted transitions is related to very high density of 5 4 lines, thus one observed absorption feature could result of a superposition of several calculated lines with different assignments. This is important for correct extrapolations to other temperature and pressure conditions. Rare calculated high-J transitions of  1 +3 4 falling in this interval with a total intensity contribution of 2.3×10 -25 cm/molecule were removed because the assignment of the corresponding experimental lines is not yet available, being beyond the scope of the present paper. For completeness we added about 67 unassigned experimental lines from Ref. [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] with total intensity contribution 2.9×10 -25 which probably belong to high-J transitions of  1 +3 4 band of 12 CH 4 or to 13 Similarly to L1, we provide a corrected experimental CRDS list [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] with some identifications added. In this range and in the following L4 range, a large fraction of lines doesn't belong to 5 4 and  2 +4 4 and could not be assigned.

(d) List L4: 6525-6550 cm -1 .

The upper limit of the line list attached to Ref. 20, being 6525 cm -1 , we used the FTS line list from Reims measurements with a 2×10 -28 cm/molecule intensity cut-off. The line intensities were obtained by a line profile fitting Spectro-Plot routine. This range could also contain some CH 3 D and 13 CH 4 lines which are not yet assigned.

As for L1, the two last intervals based on experimental determinations contain also high-J lines which are perturbed by resonance interactions with upper icosad bands and are difficult to predict precisely.

The global 12 CH 4 line list in the 6287-6550 cm -1 region is given in Electronic Supplementary Materials: Appendix A. Table 4 gives a sample of the line list.

As complementary information, we also give in Appendices B and C some experimental FTS transitions in the 6256-6287 and 6550-6788 cm -1 regions, respectively, used for the construction of our theoretical model. These complementary lists B and C (in the same format as Appendix A) are not complete: they contain only 179 assigned lines used to stabilize the determination of model interaction parameters; the upper range includes also some  1 +3 4 lines. Though this band is beyond the scope of the present work, this was necessary to describe an intensity borrowing for the 5 4 ,  2 +4 4 band systems under study (see above). In the 6717-6788 cm -1 region, for the assignments of these lines, we used the empirical low J values determined in Ref. [START_REF] Campargue | Temperature dependence of the absorption spectrum of CH 4 by high resolution spectroscopy at 81 K: (II) The Icosad region (1.49-1.30 m[END_REF]. These auxiliary line lists are separated from the principal one (A) because they only contain needed selected lines and a systematic measurements of all lines in these ranges were not a purpose of this work. All the line intensities are given at 296 K since the 6 K difference between the different experimental spectra leads to intensity corrections that are below the experimental accuracy of the FTS measurements.

The isotopic number given in the first column of the line list may be wrong because some experimental lines could be blended or belong to isotopologues of methane (see notes of Table 4 for more details).

The good agreement between the experimental spectra and the calculations is illustrated in Figs. 678. Fig. 6 shows a comparison with the FTS spectrum while Fig. 7 and8 show a comparison with the CRDS spectrum and line list at 80 K and 296 K, respectively.

Conclusion

The major aim of this study was the first assignment of the 5 4 and  2 +4 4 band systems and a contribution to the construction of a 12 CH 4 line list in the 1.6 m methane transparency window for astrophysical and planetary applications. This task was very challenging as it represents the first rather complete high-resolution analysis and modeling of 5-quanta band systems in 12 CH 4 . We were able to assign 1955 rovibrational transitions belonging to 26 subbands of 12 CH 4 corresponding to the 5 4 ,  2 +4 4 and  1 +3 4 band systems. All these line positions and 1462 line intensities were included in the fit using the model described above with RMS standard deviations of 0.003 cm -1 and 13.4%, respectively. This resulted in a predicted line list (L2) for the 6350-6500 cm -1 region that contained more than 5000 transitions up to J = 15. The use of low temperature CRDS spectra at T=79 K was very useful for the assignment and modeling as this allowed much easier identification of low-J transitions at the first step of the analysis. In Ref. [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF], the so called "two temperature method" was used to determine the empirical values of the lower state rotational number from the ratio of the line intensities measured at room temperature and at 80 K. In Fig. 9, we present the histogram of the differences between the approximate empirical determinations of low-J values attached to the room temperature line list of Ref. [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] and the J values theoretically determined in this study. This comparison was obtained from an automatic association of the lines whose calculated and measured centers coincide within 5×10 -3 cm -1 . About 87 % of the rounded empirical J values of the lower state are found to coincide with their theoretical values, illustrating the reliability of the two temperature method.

The use of new long-path FTS spectra provided complementary information particularly for the calibration and for lines beyond the interval reported in Ref. [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF]. This information helped for the theoretical determination of the intensity borrowing due to the resonance coupling with higher lying icosad bands.

The line list given in the Electronic Appendix A in the 6287-6500 cm -1 region contains predicted transitions for 5 4 / 2 +4 4 band systems completed with experimental CRDS transitions from [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] (see Fig. 5) which were not assignable to these bands. It contains (obs.calc.) values for positions and intensities for all cases where experimental line parameters were possible to extract from observations. The reason for such mixed format of our line list is the following. On the one hand it would be desirable for applications that the list would be as complete as possible and contain all available information. On the other hand a full assignment when available would be useful in the future to include pressure broadening and shift parameters as well. The m quantum number appearing in the upper state assignment is involved in various models for the broadening coefficient interpolation [START_REF] Lyulin | Measurements of N 2 -and O 2 -broadening and shifting parameters of methane spectral lines in the 5550-6236 cm -1 region[END_REF][START_REF] Predoi-Cross | Multispectrum analysis of 12 CH 4 from 4100 to 4635 cm -1 : I. Self-broadening coefficients (widths and shifts)[END_REF][START_REF] Predoi-Cross | Multispectrum analysis of 12 CH 4 from 4100 to 4635 cm -1 . Part II. Air-broadening coefficients (widths and shifts)[END_REF][START_REF] Mondelain | Measurement of the temperature dependence of line mixing and pressure broadening parameters between 296 and 90 K in the  3 band of 12 CH 4 and their influence on atmospheric methane retrievals[END_REF][START_REF] Mondelain | Line profile study by diode laser spectroscopy in the 12 CH 4  2 +  4 band[END_REF][START_REF] Pine | Multispectrum fits for line mixing in the  3 band Q branch of methane[END_REF][START_REF] Pine | Self-broadening, N 2 -broadening, O 2 -broadening, H 2 -broadening, Arbroadening and He-broadening in  3 band Q-branch of CH 4[END_REF]. Though the N 2 , O 2 and self broadening coefficients were not yet measured for the 5 4 /  2 +4 4 bands one could use for their modelling in a first approximation the results of [START_REF] Lyulin | Measurements of N 2 -and O 2 -broadening and shifting parameters of methane spectral lines in the 5550-6236 cm -1 region[END_REF][START_REF] Predoi-Cross | Multispectrum analysis of 12 CH 4 from 4100 to 4635 cm -1 : I. Self-broadening coefficients (widths and shifts)[END_REF][START_REF] Predoi-Cross | Multispectrum analysis of 12 CH 4 from 4100 to 4635 cm -1 . Part II. Air-broadening coefficients (widths and shifts)[END_REF][START_REF] Mondelain | Measurement of the temperature dependence of line mixing and pressure broadening parameters between 296 and 90 K in the  3 band of 12 CH 4 and their influence on atmospheric methane retrievals[END_REF][START_REF] Mondelain | Line profile study by diode laser spectroscopy in the 12 CH 4  2 +  4 band[END_REF][START_REF] Pine | Multispectrum fits for line mixing in the  3 band Q branch of methane[END_REF][START_REF] Pine | Self-broadening, N 2 -broadening, O 2 -broadening, H 2 -broadening, Arbroadening and He-broadening in  3 band Q-branch of CH 4[END_REF] relative to the lower polyads. Suitability for using the empirical line list [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] or our combined line list given in Appendix A depends on required applications. The predicted line list is not recommended for applications which are very sensitive to line position precisions at relatively high temperatures, where high J transitions and also hot bands are involved. On the contrary for low resolution and/or low temperature applications, for example in typical measurements conditions in Titan atmosphere, our synthetic 12 CH 4 line list in the 6350-6500 cm -1 region could be preferable because it contains more information on upper state assignments that can be useful for line shift and broadening models. It should be completed by isotopic lines from other sources when available. For example, CH 3 D lines can be taken from Refs. [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF][START_REF] Campargue | Empirical line parameters of methane in the 1.63-1.48 lm transparency window by high sensitivity Cavity Ring Down Spectroscopy[END_REF]. This work allowed a first accurate determination from experimental spectra of 8 vibrational sublevels given in Table 2 that can be used for a validation and improvement of the methane potential function. The effective Hamiltonian model employed in this work was designed to partly describe the lower edge bands 5 4 /  2 +4 4 of the 12 CH 4 icosad in the 6287-6550 cm -1 range. This "pragmatic" model is undoubtedly an approximation because we did not have all needed information on a huge bulk of remaining assigned isocad levels extending to higher energies up to 7600 cm -1 . We thus do not claim that this model could serve for a global modelling of all lower polyads (particularly of all octad and tetradecad transitions). In order to build a global effective Hamiltonian model relying on successive vibration polyad extrapolations [START_REF] Champion | Spectroscopy of the Earth atmosphere and interstellar medium[END_REF], one should first considerably improve the tetradecad analysis [START_REF] Robert | First Assignment and Line Strengths of the 4 4 Band of 12 CH 4 near 1.9 m[END_REF] which is far from being completed. One of "weak points" of our limited model is a poor description of the  1 +3 4 subbands, which are in fact beyond the scope of this study, but are just above the studied 5 4 /  2 +4 4 band systems. The higher-J v 2 +4v 4 levels which are close to the v 1 +3v 4 levels can be perturbed by resonance interactions; the v 1 +3v 4 levels are in turn perturbed by other higher energy icosad states and so on. For a realistic description of these successive bands a full rovibrational assignment and analysis of the entire icosad system would be necessary. We hope that the present study constitutes a first step towards this extremely challenging goal.

(Russia) and CAS (China) is acknowledged. We acknowledge the support from IDRIS computer centre of CNRS France and of the computer centre Reims-Champagne-Ardenne. Note:

The different columns are: the vibrational sub-level / symmetry type, the corresponding band origin (J=0), the number of fitted rovibrational line positions, the corresponding RMS standard deviation, the number of fitted intensities and the corresponding RMS standard deviation. Note:

The different columns are: the vibrational sub-level / symmetry type, the corresponding band origin (J=0), the number of fitted rovibrational line positions, the corresponding RMS standard deviation, the number of fitted intensities and the corresponding RMS standard deviation. Lower rovibrational assignment are given by the vibrational polyad number P, the rotational quantum number J, the rovibrational symmetry type S (Td irreducible representation) and the ranking vibration sublevel number α. 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 appear for assigned lines only. 8. Io-Ic % is the relative difference between observed and calculated intensities included in the fit. These values appear for assigned lines if their intensity was included in the fit. 9. The vibrational band assignment: contains the principal vibrational quanta (v 1 ,v 2 ,v 3 ,v 4 ) and vibrational symmetry type Sv (Td irreducible representation).

E" = E_low : lower energy value when available [in cm-1]. a

In case where only J_lower is given, this is determined empirically from a Boltzman populations at two temperatures [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] Comparison of the spectrum of methane at 296 K near 6440 cm -1 : Upper panel: CRDS spectrum (P= 13 mbar) Middle panel: CRDS line list of Ref. [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] Lower panel: calculated line list of 12 CH 4 Fig. 9 Histogram of the differences between the J values and the corresponding empirical values obtained in Ref. [START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] from the temperature dependence of their line intensities. The comparison applies to the 836 lines whose calculated and measured line centres coincide within 5×10 -3 cm -1 .

Figure Captions

Fig. 1 .

 1 The partially transformed ro-vibrational hamiltonian adapted to the polyad structure of the CH 4 molecule is expressed as:

  CH 4 . (c) List L3: 6500-6525 cm -1 .

Fig. 1

 1 Fig. 1Scheme of vibrational level patterns of methane polyads (a), and of vibration sublevels of the lower icosad edge (b) corresponding to rovibrational bands analyzed in this work. At the right hand side panel, the principal vibration quantum numbers, symmetry types ( T d irreps) of vibration sublevels and vibrational ranking numbers within the icosad are given.

Fig. 2

 2 Fig. 2 Overview of the FTS Reims spectra ( L=1603 m , T = 289.6 K ) at three methane pressures (a) 1 mbar (b) 7 mbar (c) 34 mbar. The CO 2 band near 6350 cm -1 was used for calibration purpose.

Fig. 3

 3 Fig. 3Comparison of the CW-CRDS spectrum of methane recorded at room temperature (upper panel) and 80 K (lower panel) near 6494 cm -1 . The sample pressure was 1.3 mbar. Note the considerable change of the line intensities depending on the low energy value of the transition.

Fig. 4

 4 Fig. 4Examples explaining corrections required to improve the experimental CRDS line list accounting for our assignments. (a) calculated line list of12 CH 4, (b): CRDS line list of Ref.[START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF], (c) CRDS spectrum T=296K, (d) CRDS spectrum T=80K One CH 3 D transition is marked with a star (*) on the panel (b). Assignment notation: Lower rovibrational assignment are given by the vibrational polyad number P(GS=0), the rotational quantum number J, the rovibrational symmetry type S (Td irreducible representation) and the ranking vibration sublevel number α. Upper rovibrational assignment in the same format but vibrational polyad number P(Icosad=5).

Fig. 5 .

 5 Fig. 5. Overview of the line lists provided as Supplementary Material. The line list is divided in four sections which were constructed differently: L1 and L3 are based on the room temperature line list of Ref. 20, L2 is the calculated line list obtained in this work from the theoretical model and L4 is based of the present FTS measurements.

Fig. 6

 6 Fig. 6Comparison of the spectrum of methane at 296 K near 6460 cm -1 : Upper panel: calculated line list of12 CH 4 Lower panel: FTS spectrum 33mbar The CH 3 D transitions with intensities larger than 1×10 -26 cm/molecule are marked with a star

Fig. 7

 7 Fig. 7Comparison of the spectrum of methane at 80 K near 6400 cm -1 : Upper panel: CRDS spectrum (P= 1.3 mbar) Middle panel: CRDS line list of Ref.[START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] Lower panel: calculated line list of12 CH 4 The CH 3 D transitions with intensities larger than 1×10-26 cm/molecule are marked with a star (*) on the two upper panels.

Fig. 8

 8 Fig. 8Comparison of the spectrum of methane at 296 K near 6440 cm -1 : Upper panel: CRDS spectrum (P= 13 mbar) Middle panel: CRDS line list of Ref.[START_REF] Wang | High sensitivity absorption spectroscopy of methane at 80 K in the 1.58 m transparency window: Temperature dependence and importance of the CH 3 D contribution[END_REF] Lower panel: calculated line list of12 CH 4

Table 1 : Detailed fit statistics for the 5ν 4 band system.

 1

	Vibrational sublevels and ranking number	Calculated Vibration Energy	Number of fitted line positions	St.Dev (10 -3 cm -1 )	Number of fitted line intensities	St.Dev (%)
	F 2 1	6377.526	192	2.59	144	13.0
	A 1 1	6405.965	76	2.50	54	14.1
	F 1 1	6429.239	213	2.35	161	13.2
	F 2 2	6450.059	270	2.39	207	12.7
	E 1	6507.389	113	2.27	85	13.4
	F 2 3	6507.553	182	2.13	129	13.7
	F 1 2	6529.777	181	2.42	137	13.5
	F 2 4	6539.180	204	2.61	158	13.6
		Total	1441	2.40	1075	13.4

Table 2 : Detailed fit statistics for the ν 2 +4ν 4 band system

 2

	Vibrational sublevel and	Number of	St. Dev	Number of	St. Dev
	ranking number	fitted line	(10 -3 cm -1 )	fitted line	(%)
	for J=0 in the icosad	positions		intensities
	E 2	27	4.4	20	13.7
	A 1 2	18	3.9	14	14.4
	F 1 5	28	4.0	20	13.6
	F 1 3	67	4.0	50	13.7
	E 5	42	4.1	30	13.7
	A 1 3	12	4.0	8	13.4
	F 1 4	45	3.7	33	13.5
	A 2 1	10	3.8	7	13.7
	E 3	30	4.3	23	14.2
	F 2 7	54	3.7	40	12.7
	F 2 5	44	4.5	33	14.1
	A 2 2	21	3.6	16	13.4
	E 4	34	3.9	25	13.7
	F 2 6	69	3.9	53	12.7
	Total	501	4.0	372	13.6

Table 3 . Principal dipole transition moment parameters for the {5v 4 /v 2 +4v 4 /v 1 +3v 4 } interacting band system

 3

	Vibrational Dipole Transition Moment	Value (in 10 -6
	Parameters	Debye)
	v 1 +3v 4 (F 2 9)	280
	v 1 +3v 4 (F 2 8)	30
	v 2 +4v 4 (F 2 7)	-48
	v 2 +4v 4 (F 2 5)	27
	v 2 +4v 4 (F 2 6)	97
	5v 4 (F 2 2)	-8.8
	5v 4 (F 2 1)	27
	5v 4 (F 2 4)	12
	5v 4 (F 2 3)	6.3

Table 4 : Sample extracted from the line list attached as Electronic Supplementary data Calculated and observed methane transitions in the 6287-6550 cm -1 region.

 4

	Iso Sc	  cm -1	S°(296K) cm/molec	Rotational assignment Lower state Upper state	Obs-calc 10 -3 cm -1	S°o bs -S°c al %	Vibrational assignment Upper	E" cm -1
	61	6349.43005 4.43e-29
	61	6349.53345 9.00e-28	9 a
	61	6349.56265 2.89e-26 0 9 A 2 1 5 8 A 1 8	0.77 -5.5	0005 F 2	470.872
	60	6349.58485 5.88e-28
	60	6349.61845 2.47e-28
	61	6349.64025 7.61e-28
	61	6349.66795 2.64e-27 0 8 F 1 2	5 7 F 2 18 -0.56 -3.4	0005 F 2	376.804
	61	6349.73955 9.67e-27 0 8 F 1 1	5 7 F 2 18 -1.10 -7.3	0005 F 2	376.733
	60	6349.77865 8.98e-28
	61	6349.81595 3.20e-28
	61	6349.89725 6.61e-28
	61	6349.92855 8.34e-28
	61	6349.96545 2.21e-28
	61 PR 6350.07866 2.24e-26 0 6 F 2 2	5 5 F 1 10 -1.59 -0.0	0005 F 2	219.936
	61 PR 6350.10037 1.96e-27 0 6 F 2 1	5 5 F 1 10 -1.17 26.3	0005 F 2	219.915
	61 PR 6350.12762 1.15e-28 0 14 F 1 1 5 13 F 2 61			0005 F 1 1095.632
	61 PR 6350.18216 2.04e-28 0 11 F 2 2 5 12 F 1 5			0005 F 2	689.876
	Notes: in this table, the columns are:
	1. ISO: isotopologues: 61 for 12 CH 4 and 60 might be 12 CH 4 , CH 3 D or 13 CH 4 . In the L1,
	L3 and L4 ranges, the lines marked with ISO = 61 could include some contributions
	from blended lines of other isotopologues (except for CH 3 D in case of L1,L3).
	2. Sc: means type of source: PR means predictions, R means Reims FTS origin, blank
	corresponds to the CRDS data of Ref. [20].
	3.   : line positions; except for PR type calculated lines, these are experimental data.
	4. S°(296K) line intensities; except for PR type calculated lines, these are experimental
	data.
	5.

Acknowledgements

This work is part of the ANR project "CH4@Titan" (ref: BLAN08-2_321467). The support of the Groupement de Recherche International SAMIA between CNRS (France), RFBR


MD, PhD Cédric Lemogne
email: cedric.lemogne@egp.aphp.fr

MD, PhD Philippe Fossati

MD, PhD Frédéric Limosin

PhD Hermann Nabi

Gaelle Encrenaz

MSc Sébastien Bonenfant

MD, PhD a,b . Silla M Consoli

PhD Gaëlle Encrenaz

Cognitive hostility and suicide

Keywords: Epidemiology, Hostility, Personality, Risk, Suicide

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Over one million people die by suicide worldwide each year [START_REF]World report on violence and health[END_REF]. This huge yet preventable public health burden urges to better understand its risk factors. Although depression is one of the most important risk factor for suicide attempts [START_REF] Cavanagh | Psychological autopsy studies of suicide: a systematic review[END_REF], most depressed individuals never attempt suicide. Besides environmental factors, other psychological factors may play a role in attempted and completed suicide. State factors, including some specific depressive dimensions such as pessimism or hopelessness, as well as trait factors, including personality traits such as impulsivity or hostility, have been associated with an increased risk of suicide attempts [START_REF] Hawton | Suicide[END_REF].

Many studies addressed the association between hostility and suicidal behaviour. Some of these studies were based on non-clinical samples or targeted the wider phenomenon of deliberate self-harm and thus yielded only indirect evidence [START_REF] Daigle | Cultural traits and immigration: hostility and suicidality in Chinese Canadian students[END_REF][START_REF] Brittlebank Ad | Hostility, hopelessness and deliberate self-harm: a prospective follow-up study[END_REF]. Most of the studies that found direct evidence linking hostility with completed suicide were indeed retrospective, comparing suicide attempters with either healthy subjects (see ref. [START_REF] Farmer R | Hostility and Deliberate Self-Poisoning: The Role of Depression[END_REF] for a review of these early studies) or non-suicidal psychiatric patients [START_REF] Crook | Factors associated with attempted suicide among hospitalized depressed patients[END_REF][START_REF] Keilp Jg | Aggressiveness, not impulsiveness or hostility, distinguishes suicide attempters with major depression[END_REF][START_REF] Castrogiovanni | Suicidality and aggressive behaviour[END_REF], or suicide completers with accident victims [START_REF] Conner Kr | Violence, Alcohol, and Completed Suicide: A Case-Control Study[END_REF]. Some prospective studies were carried out on relatively small sample of depressed patients [START_REF] Paykel | Suicide attempts following acute depression[END_REF][START_REF] Oquendo | Prospective study of clinical predictors of suicidal acts after a major depressive episode in patients with major depressive disorder or bipolar disorder[END_REF], and then focused on suicide attempts, being underpowered to examine completed suicides. To our knowledge, only one large-scale cohort study found hostility to predict suicide [START_REF] Romanov K | Self-Reported Hostility and Suicidal Acts, Accidents, and Accidental Deaths: A Prospective Study of 21,443 Adults Aged 25 to 59[END_REF]. However, completed suicides and suicide attempts were not analyzed separately but merged into one single dependent variable. Additionally, this study considered hostility as being a single psychological construct, leaving unanswered the question of a specific association between suicide and one component of hostility. For instance, hostility scales generally discriminate at least between a behavioural (or overt) and a cognitive (or covert) component. More importantly, this study did not control for depressive mood, which is associated with both hostility and suicide and thus may account for their statistical association [START_REF] Farmer R | Hostility and Deliberate Self-Poisoning: The Role of Depression[END_REF].

Aims of the study

The aim of this prospective study was to refine our understanding of the association between hostility and completed suicide. We took advantage of the large-scale French "GAZ et ELectricité" (GAZEL) cohort to determine whether the association between hostility and completed suicide, henceforth referred to as "suicide", is explained by a specific component of hostility (i.e. cognitive or behavioural), controlling for depressive mood.

Material and methods

Participants

Details of the GAZEL cohort study are available elsewhere [START_REF] Goldberg | Cohort profile: the GAZEL Cohort Study[END_REF]. The target population consisted of 44,992 employees of the French national gas and electricity company [START_REF] Hardy | Cynical hostility and vulnerability to disease: social support, life stress, and physiological response to conflict[END_REF]411 men aged 40-50 and 13,511 women aged 35-50). The study protocol was approved by the French authority for data confidentiality ("Commission Nationale Informatique et Liberté") and by the Ethics Evaluation Committee of the "Institut National de la Santé et de la Recherche Médicale" (INSERM) (IRB0000388, FWA00005831). In 1989, 20,625 employees (45.8%) (15,011 men and 5,614 women) gave written informed consent to participate in the GAZEL cohort study. In 1993, questionnaires were mailed to the 20,488 remaining members of the GAZEL cohort to assess depressive mood and hostility [START_REF] Consoli Sm | Validation of a personality questionnaire designed for defining subgroups at risk for ischemic cardiopathy or cancer in the GAZEL cohort[END_REF].

Depressive mood

Depressive mood was assessed with the French version of the 20-item Center of Epidemiologic Studies Depression Scale (CESD), which has been designed for use in community studies with a high internal consistency ranging from α=0.8 to α=0.9 across samples and a moderate 2-week test-retest reliability (r=0.51) [START_REF] Radloff | The CES-D Scale: a self-report depression scale for research in the general population[END_REF][START_REF] Fuhrer R | The French version of the Center for Epidemiologic Studies-Depression Scale[END_REF]. The CESD asks participants how often they have experienced specific symptoms during the previous week (e.g. "I felt depressed", "I felt everything I did was an effort", "My sleep was restless.").

Responses range from 0 ("hardly ever") to 3 ("most of the time"). Based on the validation of the French version, a global score ≥ 17 among men and ≥ 23 among women may signal clinically significant depression according to the International Classification of Diseases (ICD) or the Diagnosis and Statistical Manual of Mental Disorders [START_REF] Radloff | The CES-D Scale: a self-report depression scale for research in the general population[END_REF].

Hostility

Hostility was assessed with the Buss and Durkee Hostility Inventory (BDHI). The BDHI was previously validated in French on 408 randomly selected participants of the GAZEL cohort study [START_REF] Consoli Sm | Validation of a personality questionnaire designed for defining subgroups at risk for ischemic cardiopathy or cancer in the GAZEL cohort[END_REF]. The BDHI is composed of 75 items with "true-false" answers [START_REF] Buss Ah | An inventory for assessing different kinds of hostility[END_REF].

It has eight subscales, seven of which are designed to measure different components of hostility: assault, verbal aggression, indirect hostility, irritability, negativism, resentment, and suspicion. The sum of these seven sub-scales leads to a "total hostility" score with a high 3month test-retest reliability (r=0.87) [START_REF] Consoli Sm | Validation of a personality questionnaire designed for defining subgroups at risk for ischemic cardiopathy or cancer in the GAZEL cohort[END_REF]. Several factor analyses identified two overarching factors, namely "behavioural" (i.e. hostile behaviours) and "cognitive" hostility (i.e. hostile thoughts), formed by the first three sub-scales (i.e. assault, verbal aggression, indirect hostility) and the last two sub-scales (i.e. resentment, suspicion), respectively [START_REF] Suarez Ec | The relationships between dimensions of hostility and cardiovascular reactivity as a function of task characteristics[END_REF]. In the present study, the internal consistency was high for total, behavioural and cognitive hostility scores (α=0.87, 0.78 and 0.77, respectively).

Mortality

Vital status and date of death were obtained annually for all participants from the French national gas and electricity company itself as it pays out retirement benefits. Dates and causes of death were available from baseline (i.e. 1 January 1993) to 31 December 2008.

Causes of death were coded by the French national cause-of-death registry (CépiDc, INSERM) using the ICD, 10th Revision [START_REF] Pavillon | The 10th revision of the International Classification of Diseases[END_REF]. Completed suicides correspond to the codes X60 to X84.

Covariates

Age, sex, education level (primary, lower secondary, higher secondary or tertiary), and occupation grade (unskilled workers, skilled workers, managers) were obtained from employer"s human resources files at baseline. Marital status (living in couple or not), income (<1600€, 1600-2592€, >2592€), alcohol consumption, and smoking were self-reported in 1993. Alcohol consumption, as drinks per week, was categorized as non-drinkers, occasional drinkers (1-13 for men, 1-6 for women), moderate drinkers (14-27 for men, 7-20 for women) or heavy drinkers (≥28 for men, ≥21 for women). Smoking in the same period was categorized as non-smoker and as smoker of 1-10, 11-20 or ≥21 cigarettes per day.

Statistical analyses

All statistical analyses were computed with SPSS 16.0.1 software (SPSS Inc.).

The association between discrete variables and suicide was estimated with the Hazard Ratio computed in Cox regressions. Discrete variables with more than 2 classes were considered as nominal covariates and, if necessary, classes were merged to obtain at least 4 events (i.e. completed suicide) by class. Coefficients of correlation were computed to examine the relation between depressive mood and hostility scores (i.e. total, cognitive, and behavioural hostility). The association between continuous variables and suicide was modelled using the Relative Index of Inequality (RII) computed through Cox regression [START_REF] Sergeant | Relative index of inequality: definition, estimation and inference[END_REF].

The RII is computed by ranking the predictor on a scale from 0 to 1. For a given predictor, each score covers a range on this scale that is proportional to the number of participants who have that score and is given a value on the scale corresponding to the cumulative midpoint of its range. The RII resembles relative risk in that it compares suicide occurrence at the extremes of the predictor but it is estimated using the data on all scores and is weighted to account for the distribution of the personality scores. An RII of 2 indicates a doubling of the risk of suicide for individuals at the extremes of the predictor.

Results

Participants and events

Among the GAZEL cohort members who completed the CESD, 14,691 (71.7%) completed the BDHI cognitive subscale, 14,752 (72.0%) completed the BDHI behavioural subscale and 14,595 (71.2%) completed the whole BDHI. In the present study, participants were those who completed the CESD and at least one of the BDHI subscales (i.e. total, cognitive, and behavioural hostility). Compared with non participants, participants (10,819 men, mean age = 49.0 years, standard deviation = 2.9 years, and 3,933 women, mean age = 46.2 years, standard deviation = 4.2 years) were more likely to be male, older, educated, and skilled workers, and less likely to complete suicide (all P<0.05).

During a mean follow-up of 15.7 years, 744 (5.0%) participants had died, including 28 (24 men, 4 women) who completed suicide (0.2%) at a mean age of 54.1 years (standard deviation = 5.7 years). Suicide were completed by firearm discharge (N=11), hanging (N=9), self-poisoning (N=4), using a sharp object (N=1), jumping from high place (N=1) or before a moving object (N=1), and by an unspecified mean (N=1).

Education level, occupational grade and self-reported covariates (i.e. income, marital status, alcohol consumption, and smoking) were available for 12,665 (85.9%) participants.

These participants were more likely to be male, less depressed, and less hostile (all P<0.05).

Because there was no linear association between age and suicide (F=0.00, P=0.993), age was considered as a discrete 3-class nominal covariate (40-46, 47-50, 51-54 years old).

Suicide predictors

Regarding covariates, suicide was predicted by being a non-drinker, being a smoker, and not living in couple (Table 1), but not by age, sex, education level, occupational grade, or income (all P>0.10). Both depressive mood and hostility scores were associated with sex, education level, occupational grade, income, marital status, and alcohol consumption (all P<0.01). Additionally, depressive mood, total and cognitive hostility were associated with age and income (all P<0.05), and hostility scores were associated with smoking (all P<0.01).

Depressive mood was positively correlated with hostility scores (Table 2).

Regarding psychological variables and univariate analyses, suicide was predicted by depressive mood and cognitive hostility, but not by total or behavioural hostility (Table 3).

We subsequently examined the associations of depressive mood and hostility scores with suicide before and after adjustment for each other. In a first set of analyses, all models were adjusted for the covariates that were found to be associated with suicide in univariate analyses with a P value < 0.10 (i.e. marital status, alcohol consumption, and smoking). These covariates were available for 13,433 participants, including 27 who completed suicide (Table 4). Before mutual adjustment, suicide was predicted by depressive mood and cognitive hostility (Table 4).

After adjustment for cognitive hostility, depressive mood was no longer significantly associated with suicide, with a RII reduction of 79.1%. In contrast, cognitive hostility remained significantly associated with suicide, with a RII reduction of only 34.6%. Because each covariate was associated at least with depressive mood or cognitive hostility, all covariates were taken into account in a second set of analyses that included 25 cases of suicide among 11,723 participants and yielded similar results (Table 5). Given the small number of events, we did not perform further subgroup-specific analyses, such as sex-specific analyses.

Discussion

To our knowledge, this is the first prospective study to examine the association between suicide and the behavioural and cognitive components of hostility (i.e. hostile behaviour and hostile thoughts), controlling for depressive mood. First, suicide was predicted by cognitive but not behavioural hostility, even after adjustment for depressive mood and the whole set of covariates. Second, although depressive mood predicted suicide in the GAZEL cohort, this association was dramatically reduced, and indeed disappeared, after adjustment for cognitive hostility. The present lack of association between behavioural hostility and completed suicide does not challenge available evidence for the association between behavioural hostility and suicide attempts (3-13), as we only recorded completed suicides. Although the focus on completed suicides is strength of the study, it does not allow discriminating between factors increasing the lethality of suicide attempts and those increasing the risk of suicide attempts, which may differentially relate to cognitive and behavioural hostility. For instance, cognitive hostility may specifically increase the risk of violent suicide attempts, as suggested by the relatively high rate of suicides by firearm discharge in the present study.

The association between suicide and cognitive hostility could be partially confounded by other suicide risk factors, such as genetic factors, psychosocial adversity, or impulsivity [START_REF] Hawton | Suicide[END_REF][START_REF] Savitz | Trends in Suicidology: Personality as an Endophenotype for Molecular Genetic Investigations[END_REF]. However, although some facets of impulsivity may be associated with an increased risk of suicide attempts [START_REF] Mt | Personality traits as prospective predictors of suicide attempts[END_REF][START_REF] Corruble | Understanding impulsivity in severe depression? A psychometrical contribution[END_REF][START_REF] Swann Ac | Interactions between bipolar disorder and antisocial personality disorder in trait impulsivity and severity of illness[END_REF], evidence linking impulsivity with lethality of suicide is more conflicting [START_REF] Baca-Garcia E | A prospective study of the paradoxical relationship between impulsivity and lethality of suicide attempts[END_REF][START_REF] Swann Ac | Increased Impulsivity Associated With Severity of Suicide Attempt History in Patients With Bipolar Disorder[END_REF], especially outside adolescents and young adults [START_REF] Mcgirr | Impulsive-aggressive behaviours and completed suicide across the life cycle: a predisposition for younger age of suicide[END_REF][START_REF]Severity of personality disorders and suicide attempt[END_REF]. Furthermore, if impulsivity was accounting for the association between hostility and suicide, one should have expected an association with behavioural (i.e. behavioural) rather than cognitive hostility.

Note that impulsivity has also been dichotomized in "cognitive" and "behavioural" factors, which may both relate to the risk of suicide attempts in the context of major depression [START_REF] Corruble | Understanding impulsivity in severe depression? A psychometrical contribution[END_REF]. However, one should not assume that "cognitive" impulsivity (i.e. a lack of cognitive control), is conceptually closer to "cognitive hostility" (i.e. covert feelings of resentment and suspicion) than behavioural impulsivity. Although both cognitive and behavioural impulsivity may contribute to behavioural hostility, they are less likely to contribute to hostile thoughts per se.

Although the naturalistic design of the present study prevents any causal conclusions to be drawn, causal hypotheses should nonetheless be considered as well. First, cognitive hostility may promote suicidal intent. Several motives may precipitate suicide attempt, and eventually suicide, including not only ending one"s own life or escaping from an unbearable state, but also questioning the benevolence of fate, securing the attention of others, or inducing guilt in others. The two last motives suggest that hostile thoughts toward others may play a role in motivating suicide [START_REF] Farmer R | Hostility and Deliberate Self-Poisoning: The Role of Depression[END_REF]. The will to end one"s own life is also consistent with early psychodynamic views of suicide as a hostile act directed inwards on the self [START_REF] Freud | The Standard Edition of the Complete Psychological Works of Sigmund Freud[END_REF].

Second, cognitive hostility may prevent individuals with suicidal intent to seek and find supportive social support and medical help [START_REF] Hardy | Cynical hostility and vulnerability to disease: social support, life stress, and physiological response to conflict[END_REF], resulting in higher risk to actually commit suicide. Third, cognitive hostility may promote access to firearm, which were used in almost half of the cases here [START_REF] Kapusta Nd | Firearm legislation reform in the European Union: impact on firearm availability, firearm suicide and homicide rates in Austria[END_REF].

These results suggest that the association between baseline depressive mood and suicide may be explained by cognitive hostility [START_REF] Mackinnon Dp | The longitudinal effects of social support and hostility on depressive tendencies[END_REF]. For instance, cognitive hostility may independently promote depressive mood (e.g. through an increased risk of interpersonal conflicts) and precipitate suicide, thus confounding their association (34). However, assuming no causal association between depressive mood and suicide is difficult to reconcile with available evidence [START_REF] Cavanagh | Psychological autopsy studies of suicide: a systematic review[END_REF]. Alternatively, depressive mood may promote hostile thoughts through a pessimistic view of others as being at best unhelpful, if not harmful [START_REF] Da | Scientific Foundations of Cognitive Theory and Therapy of Depression[END_REF]. Such hostile thoughts may in turn increase the risk of suicide (i.e. mediate a causal association between depressive mood and suicide). In the absence of a longitudinal assessment of hostility, these two hypotheses are not distinguishable on a statistical ground [START_REF] Mackinnon Dp | The longitudinal effects of social support and hostility on depressive tendencies[END_REF]. Note that both may have the same implications for clinical practice, leading to consider cognitive hostility when assessing the suicide risk associated with depressive mood. Future studies should examine whether resentment and suspicion are associated with an increased risk of suicide in a clinical depression. Some limitations should be considered. First, although the GAZEL cohort covers all regions of France, various neighbourhoods from small villages to large cities and a wide range of socioeconomic status and occupations, it is not representative of the general population as it includes only middle-aged working individuals with employment security and excluded certain categories of the population (e.g. agricultural workers, self-employed, foreigners) [START_REF] Goldberg | Cohort profile: the GAZEL Cohort Study[END_REF]. However, the suicide rate observed in participants of the present study (i.e.

12.1 per 100,000 per year) was roughly similar to the suicide rate observed in France in the late 90"s (i.e. 14.5 per 100,000 per year) [START_REF] Chishti | Suicide mortality in the European Union[END_REF]. Second, the suicide rate was higher in nonparticipants. One can reasonably speculate about a somewhat higher level of cognitive hostility in these survey non-responders. Our results may thus have underestimated the strength of the association between cognitive hostility and suicide. Third, the increased risk of suicide among absolute non-drinkers rather than among moderate and heavy drinkers may seem counterintuitive. A possible explanation is that the lack of alcohol dependence assessment may have blurred the relationship between alcohol consumption and suicide, as absolute non-drinkers were more likely to include participants with a past history of alcohol dependence than occasional drinkers [START_REF] Da | Alcohol consumption, alcohol dependence, and all-cause mortality[END_REF]. Absolute non-drinkers may also include participants presenting with a psychotropic medication or a medical condition preventing alcohol consumption. Fourth, given the relatively small number of events, our study was underpowered to allow subgroup-specific analyses (e.g. sex-specific analyses). The lack of association between behavioural hostility and suicide may have resulted from a lack of statistical power. Using ICD codes to define suicide may have been a bit conservative as coders may have avoided using such codes when alternative options were available. However, although these limitations could explained negative findings (e.g. regarding behavioural hostility), they are less likely to account for the significant association between cognitive hostility and suicide.

Finally, a common caveat of most prospective studies addressing the links between psychosocial variables and mental health relates to the implicit assumption that these variables are stable over time. Although personality is considered to be stable through adulthood [START_REF] Roberts Bw | The rank-order consistency of personality traits from childhood to old age: a quantitative review of longitudinal studies[END_REF], life events may promote high levels of cognitive hostility, as illustrated by the clinical concept of "posttraumatic embitterment disorder" [START_REF] Linden | Posttraumatic embitterment disorder in comparison to other mental disorders[END_REF]. Depressive mood is even more likely to encompass both state and trait components, which may be differentially linked to suicide risk. It is possible that a more proximal measure of depressive mood would have been more directly related to suicide and less prone to be confounded of mediated by baseline cognitive hostility. Furthermore, the CESD is not a diagnosis tool and overlooks the distinction between minor, major and bipolar depression. A more comprehensive and longitudinal assessment of psychological variables associated with suicide, such as depressive mood, impulsivity or hostility is warranted.

In conclusion, this study suggests that cognitive hostility is associated with an increased risk of suicide over time, independently of baseline depressive mood. Further studies should explore the mechanisms linking cognitive hostility and suicide, as potential prevention strategies should address the processes through which cognitive hostility is associated with suicide, rather than cognitive hostility per se.

Table 1 .

 1 Associations between discrete socio-demographic and behavioural variables and suicide in univariate analyses.

				No
		N events / N	Suicide	suicide	Hazard Ratio
		participants	N (%)	N (%)	(95% CI)
	Age	28 / 14,752
	Low (40-46 years)			4,947
			12 (42.9)	(33.6)	1.65 (0.68-4.04)
	Middle (47-50 years)			5,487
			8 (28.6)	(37.3)	Reference
	High (51-54 years)			4,290
			8 (28.6)	(29.1)	1.28 (0.48-3.42)
	Sex	28 / 14,752
	Male			10,795
			24 (85.7)	(73.3)	2.20 (0.76-6.35)
	Female			3,929
			4 (14.3)	(26.7)	Reference
	Education level	27 / 14,131
	Primary & Lower			10,347
	secondary		19 (70.4)	(73.4)	Reference
	Higher secondary &			3,757
	tertiary		8 (29.6)	(26.6)	1.15 (0.51-2.64)
	Occupational grade	28 / 14,698
	Unskilled & skilled			10,128
	workers		23 (82.1)	(69.0)	2.07 (0.79-5.44)
	Managers			4,542
			5 (17.9)	(31.0)	Reference
	Income	28 / 14,281
	<1600€			5,795	1.84 (0.71-4.78)
			14 (50.0)	(40.7)
	1600-2592€			3,923
			8 (28.6)	(27.5)	1.54 (0.54-4.45)
	>2592€			4,535
			6 (21.4)	(31.8)	Reference
	Marital status	27 / 13,705
	Single, separated,			1,628
	divorced, widowed		8 (29.6)	(11.9)	3.15 (1.38-7.18)**
	Living in couple			12,050
			19 (70.4)	(88.1)	Reference
	Alcohol consumption	27 / 13,704
	Non-drinkers			1,653
			7 (26.0)	(12.1)	3.04 (1.16-8.00)*
	Occasional drinkers			7,138
			10 (37.0)	(52.2)	Reference
	Moderate & heavy			4,886
	drinkers		10 (37.0)	(35.7)	1.47 (0.61-3.53)
	Smoking	27 / 13,530
	Non-smokers			10,815
			16 (59.3)	(80.1)	Reference

Table 2 .

 2 Correlations between depressive mood and hostility scores.

		Total	Cognitive	Behavioural
		hostility	hostility	hostility
	Depressive	0.41	0.52	0.15
	mood
	Total		0.71	0.86
	hostility
	Cognitive			0.33
	hostility
	Note. P≤0.01 for all coefficients.

Table 3 .

 3 Associations between psychological variables and suicide in univariate analyses.

			No
		Suicide	suicide
	N events / N	Mean	Mean
	participants	(SD)	(SD)	RII (95% CI)
	Depressive mood	19.20	13.14	8.16 (1.97-
	28 / 14,752	(12.60)	(9.21)	33.85)**
	Total hostility	32.70	29.20	3.68 (0.92-
	26 / 14,595 †	(9.50)	(9.84)	14.73)
	Cognitive hostility	8.32	6.59	10.76 (2.50-
	28 / 14,691	(3.15)	(3.54)	46.42)**
	Behavioural hostility	15.68	14.48
	28 / 14,752	(6.63)	(5.39)	1.37 (0.38-4.97)
	** P≤0.01; † the number of participants who have completed all the BDHI subscales (i.e. a
	conjunction rather than a total); CI: Confidence Interval; SD: Standard Deviation; RII:
	Relative Index of Inequality.

Table 4 .

 4 RII of depressive mood and cognitive hostility in predicting suicide before (models 1 & 2) and after (model 3) mutual adjustment, all models being adjusted for marital status, alcohol consumption, and smoking.

	Predictive variables	Model 1	Model 2	Model 3
	Depressive mood	5.92 (1.41-24.92)*		2.03 (0.41-10.07)
	Cognitive hostility		13.03 (2.75-61.78)** 8.87 (1.52-51.71)*
	Marital status
	Single, separated, divorced, widowed	2.29 (0.98-5.34)	2.37 (1.03-5.48)*	2.23 (0.95-5.21)
	Living in couple	Reference	Reference	Reference
	Alcohol consumption
	Non-drinkers	2.69 (1.02-7.10)*	2.61 (0.99-6.87)	2.56 (0.97-6.75)
	Occasional drinkers	Reference	Reference	Reference
	Moderate & heavy drinkers	1.34 (0.55-3.24)	1.31 (0.54-3.17)	1.32 (0.55-3.20)
	Smoking
	Non-smokers	Reference	Reference	Reference
	Smokers	2.68 (1.23-5.84)*	2.59 (1.19-5.63)*	2.59 (1.19-5.64)*
	* P≤0.05; ** P≤0.01.

Table 5 .

 5 RII of depressive mood and cognitive hostility in predicting suicide before (models 1 & 2) and after (model 3) mutual adjustment, all models being adjusted for age, sex, education level, occupational grade, income, marital status, alcohol consumption and smoking.

	Predictive variables	Model 1	Model 2	Model 3
	Depressive mood	7.94 (1.72-36.63)**		2.73 (0.49-15.18)
	Cognitive hostility		15.22 (2.84-81.49)** 8.68 (1.30-57.72)*
	Age
	Low (40-46 years)	1.64 (0.63-4.24)	1.67 (0.64-4.34)	1.68 (0.65-4.35)
	Middle (47-50 years)	Reference	Reference	Reference
	High (51-54 years)	1.17 (0.42-3.24)	1.20 (0.43-3.31)	1.19 (0.43-3.29)
	Sex
	Male	6.44 (1.76-23.65)**	5.32 (1.46-19.36)*	5.85 (1.59-21.51)**
	Female	Reference	Reference	Reference
	Education level
	Primary & Lower secondary	Reference	Reference	Reference
	Higher secondary & tertiary	2.19 (0.85-5.63)	2.26 (0.88-5.80)	2.25 (0.88-5.78)
	Occupational grade
	Unskilled & skilled workers	3.57 (0.99-12.75)	2.94 (0.83-10.43)	3.03 (0.85-10.83)
	Managers	Reference	Reference	Reference
	Income
	<1600€	0.84 (0.25-2.83)	0.80 (0.24-2.67)	0.79 (0.24-2.65)
	1600-2592€	1.26 (0.38-4.16)	1.25 (0.38-4.11)	1.24 (0.38-4.09)
	>2592€	Reference	Reference	Reference
	Marital status
	Single, separated, divorced, widowed	2.72 (1.07-6.96)*	2.88 (1.14-7.30)*	2.66 (1.04-6.78)*
	Living in couple	Reference	Reference	Reference
	Alcohol consumption
	Non-drinkers	2.85 (1.00-8.12)*	2.77 (0.97-7.89)	2.73 (0.96-7.78)
	Occasional drinkers	Reference	Reference	Reference
	Moderate & heavy drinkers	1.30 (0.52-3.24)	1.31 (0.52-3.25)	1.30 (0.52-3.24)
	Smoking
	Non-smokers	Reference	Reference	Reference
	Smokers	2.62 (1.17-5.85)*	2.60 (1.17-5.79)*	2.59 (1.16-5.76)*
	* P≤0.05; ** P≤0.01.

Acknowledgments

The authors thank the French national gas and electricity company "Electricité de France-Gaz de France" (EDF-GDF), especially the "Service Général de Médecine de Contrôle", and the "Caisse centrale d"action sociale du personnel des industries électrique et gazière". The GAZEL Cohort Study was funded by EDF-GDF and INSERM, and received grants from the "Cohortes Santé TGIR Program", "Agence nationale de la recherché" (ANR)

and "Agence française de sécurité sanitaire de l"environnement et du travail" (AFSSET). The personality data collection was funded by the "Caisse Nationale d"Assurance Maladie" and by the "Ligue Nationale contre le Cancer". We also wish to acknowledge the "Cohortes" team of the Unit INSERM 1018-Versailles St-Quentin University responsible for the GAZEL data base management. Finally, we thank Marie Zins, Marcel Goldberg, Sylvaine Cordier, and Pierre Ducimetière for comments on the manuscript.

Declaration of Interest

None of the authors have conflicts of interest to report. CL has accepted paid speaking engagements in industry-sponsored symposia from Bristol Myers Squibb. PF has accepted paid speaking engagements in industry-sponsored symposia from Euthérapie and Lundbeck, and received a grant from Servier. FL has accepted paid speaking engagements in industrysponsored symposia from Bristol Myers Squibb, Euthérapie, Janssen, and Lundbeck. SMC has accepted paid speaking engagements in industry-sponsored symposia from Astra Zeneca, Boehringer Ingelheim, Euthérapie, Lundbeck, and Pfizer. HN, GE, and SB have no industryrelated interests to report.