P Cacciani

P Čermák

J Vander Auwera

A Campargue
email: alain.campargue@univ-grenoble-alpes.fr

The ammonia absorption spectrum between 4700 and 5650 cm -1

 46, 140, and 304 Pa). Additionally, we use an existing Kitt Peak spectrum to extend the analysis up to 5650 cm -1 . In total, 9110 absorption lines with intensity ranging from 1 × 10 -25 to 1.6 × 10 -20 cm/molecule were retrieved, for the two principal isotopologues. Another Kitt Peak spectrum was used to identify 505 15 NH 3 transitions within the experimental line list. The rovibrational assignments of the 14 NH 3 lines relied on the position and intensity agreement with the C2018 theoretical line list (Coles et al. JQSRT 2018;219 199-212) and were validated by the systematic use of Lower State Combination Difference (LSCD) relations. In the process, a number of intensity transfer between nearby transitions were identified. Finally, 6562 transitions were assigned to 61 vibrational bands of the main isotopologue, 14 NH 3 , representing over 99.8% of the C2018 integrated absorption at room temperature in the region. The upper state empirical energy of a total of 2215 rovibrational levels of 14 NH 3 were derived. Most of them are newly reported. The comparison with the current HITRAN2020 list is discussed. A recommended line list for ammonia in natural isotopic abundance is provided for the studied region.

Introduction

Ammonia is an essential component in various astrophysical and terrestrial objects, including the Earth's atmosphere. Therefore, understanding its infrared absorption spectra is a prerequisite for accurate monitoring of these environments [START_REF] Čermák | Accurate 14 NH 3 line-list for the 2.3 µm spectral region[END_REF][START_REF] Serjeant | The future of astronomy with small satellites[END_REF]. This task is made difficult by numerous interactions between its six vibrational modes and the internal inversion motion.

The current work is part of the analysis of the ammonia high resolution spectrum recorded by Fourier Transform Spectroscopy (FTS) in the 3900-5600 cm -1 range. The low energy part of the range, from 3900 to 4700 cm -1 , was covered in our previous contribution [START_REF] Cacciani | The ammonia absorption spectrum between 3900 and 4700 cm -1[END_REF], while the remainder of the data set, up to 5600 cm -1 , is analyzed in the current work. The present FTS data are complemented with an existing Kitt Peak FTS spectrum in the weak absorbing 5600-5650 cm -1 interval, in order to fill the gap up to our previous analysis of the 5650-6350 cm -1 range [START_REF] Cacciani | The absorption spectrum of ammonia between 5650 and 6350 cm -1[END_REF].

The HITRAN line list [START_REF] Gordon | The HITRAN2020 molecular spectroscopic database[END_REF] in the considered range is based on the study of a FTS spectrum recorded at Kitt Peak with a 0.011 cm -1 spectral resolution [START_REF] Brown | Empirical line parameters of NH 3 from 4791 to 5294 cm -1[END_REF]. The spectrum is dominated by the ν 1 + ν 4 and ν 3 + ν 4 bands centered at 4956 cm -1 and 5050 cm -1 , respectively. The upgrade of the HITRAN database from 2016 [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] to 2020 [START_REF] Gordon | The HITRAN2020 molecular spectroscopic database[END_REF] has increased the number of 14 NH 3 transitions from 1875 to 2493 while the 15 NH 3 dataset in the region has remained unchanged.

The overview of HITRAN2020 list is presented in the upper panel of Fig. 1. About 620 new transitions of 14 NH 3 included in HITRAN2020 were not observed but transferred from the hybrid CoYuTe list created by adjusting the line positions predicted from the C2018 potential energy surface [START_REF] Coles | ExoMol molecular line lists -XXXV. A rotation-vibration line list for hot ammonia[END_REF] according to empirical energy levels determined using the MARVEL algorithm [START_REF] Furtenbacher | Empirical rovibrational energy levels of ammonia up to 7500 cm -1[END_REF]. For the HITRAN2020 edition [START_REF] Gordon | The HITRAN2020 molecular spectroscopic database[END_REF], it was decided to add to the HITRAN2016 dataset [START_REF] Gordon | The HITRAN2016 molecular spectroscopic database[END_REF] only the CoYuTe transitions for which both the lower and upper levels have empirical energies and their calculated line intensities are larger than 1×10 -25 cm/molecule. In our region, the added transitions include several hot band transitions for which the upper levels were determined from ground state transitions, thus at higher energy [START_REF] Down | Re-analysis of ammonia spectra: Updating the HITRAN 14 NH 3 database[END_REF].

Their intensities are generally less than 3 × 10 -24 cm/molecule which was the intensity cut-off of the HITRAN2016 list. Among the 14 NH 3 transitions, 1255 are given with full assignment of the lower and upper states, whereas no or incomplete assignment is given for 1201 transitions. Experimental intensities have been kept for the transitions transferred from HITRAN2016, whereas C2018 calculated intensity values [START_REF] Coles | Improved potential energy surface and spectral assignments for ammonia in the near-infrared region[END_REF] are given for the added transitions.

Regarding the previous experimental studies in our region, in addition to Ref. [START_REF] Brown | Empirical line parameters of NH 3 from 4791 to 5294 cm -1[END_REF], it is worth mentioning the recent work of Beale et al. [START_REF] Beale | Infrared transmission spectra of hot ammonia in the 4800-9000 cm -1 region[END_REF]. These authors reported an analysis of ammonia FTS spectra recorded at different temperatures from 295 to 973 K with a 0.01 cm -1 spectral resolution. Due to its lower accuracy, this study was used neither for the HITRAN2020 update nor for the derivation of new MARVEL energy levels [START_REF] Coles | Improved potential energy surface and spectral assignments for ammonia in the near-infrared region[END_REF]. Nevertheless, it is a very useful source for the application of Lower State Combination Differences (LSCD) relations used for validation of our quantum assignments [START_REF] Cacciani | The absorption spectrum of ammonia between 5650 and 6350 cm -1[END_REF].

As the experimental setup, conditions of the recordings, fitting process and construction of the line list were detailed in Ref. [START_REF] Cacciani | The ammonia absorption spectrum between 3900 and 4700 cm -1[END_REF], they are briefly recalled in the two next sections. Section 4 describes some aspects of the assignment process before discussing the results in particular the occurrence of intensity transfers between resonant lines.

Experimental details

Four room temperature FTS absorption spectra of ammonia were recorded at ULB with a Bruker IFS 120 (upgraded to 125) in the 3900-5600 cm -1 range (Fig. 2). The experimental conditions of the measurements are summarized in Table 1.

In the 5600-5650 cm -1 interval where the ammonia absorption is very weak, an existing Kitt Peak spectrum with reference 900308R019 (KP1) was analyzed. Also, a second Kitt Peak spectrum (Ref. 930826R016, KP2 in Table 1) recorded with a 15 NH 3 enriched sample was treated to identify the 15 NH 3 transitions. Notes: For the four spectra studied in this work (TW1-TW4), p is the average pressure (the numbers between parentheses are the uncertainties of measurement, provided in the units of the last digit quoted, L is the interaction pathlength and R is the spectral resolution used for the recording. c15 N is the estimated value of the 15 NH 3 relative abundance (the natural value is 0.37%).

Line list construction

Line positions and line intensities were retrieved using a multi-line fit of the spectra. The fit was performed assuming a simple Voigt function as line profile, thus, including in an effective way the Instrument Line Shape (ILS).

The Lorentzian and Gaussian components of the Voigt profile were assumed to be identical for all the lines and adjusted in the fit. The fitted value of the Gaussian width was found slightly above the calculated value of the 14 NH 3 Doppler broadening (FWHM 0.015 cm -1 ), confirming a small contribution of ILS. Constraining the line widths helped to disentangle blended lines.

In Ref. [START_REF] Cacciani | The ammonia absorption spectrum between 3900 and 4700 cm -1[END_REF], it was demonstrated that our data treatment neglecting the ILS leads to underestimated line intensities in case of strong absorbance, and the correction of this bias was presented. The same process was applied in the current range. As a test of the correction and consistency of the intensity values in this new range, Fig. 3 plots the ratio of intensities retrieved from different sources. The intensities from the 140.4 Pa spectrum are compared to those retrieved from of the 13.2 Pa spectrum. For the KP1 data in the 5550-5600 cm -1 interval, the intensity ratio between the 304 Pa and the KP1 spectra is presented for a few lines. Isolated lines were preferred for the comparison (minimum position separation of 0.03 cm -1 ). The oscillator strength spans over two decades between 1.2 × 10 -23 and 1.2 × 10 -21 cm/molecule (in order to correspond to absorbances not too small at 13.2 Pa spectrum and not too large at 140.4 Pa).

On average, a small overestimation of 1.5% is noted between 1.2 × 10 -22 and 1.2 × 10 -21 cm/molecule for the 140.4 Pa spectrum and the root mean square deviation less than 5% in the whole range. This confirms the efficiency of the applied correction and allows for using either spectrum. To construct the global line list, we selected at least two spectra for each spectral interval, according to the absorption amplitude (see Fig. 2): the 13.2 Pa spectrum was used from 4850 to 5250 cm -1 , the 46 Pa spectrum in 4700-4850 cm -1 and 5200-5300 cm -1 regions, the 140.4 Pa in the 4700-5500 cm -1 range, the 304 Pa spectrum from 5260 to 5600 cm -1 and, the KP1 spectrum in the 5550-5650 cm -1 range. The comparison between the 304 Pa and the KP1 spectra in the range 5550-5600 cm -1 was used to calibrate in intensity the latter (Fig. 3).

Several water vapor lines (present as an impurity) were also observed in the spectra, accidentally hiding some ammonia lines above 5200 cm -1 . They were removed manually or subtracted from the spectrum by comparison with the HITRAN2020 line list [START_REF] Gordon | The HITRAN2020 molecular spectroscopic database[END_REF]. Finally, the resulting ammonia list includes 9110 lines with intensity ranging between 1 × 10 -25 and 1.3 × 10 -20 cm/molecule including 505 15 NH 3 transitions (see lower panel of Fig. 1). In case of superposition of a 14 NH 3 line and a 15 NH 3 line (or a water line), the intensity of the interfering line was carefully estimated and subtracted in order to minimise its impact on the retrieval of the 14 NH 3 line intensity.

As mentioned in Ref. [START_REF] Cacciani | The ammonia absorption spectrum between 3900 and 4700 cm -1[END_REF], the FTS spectra under analysis do not correspond to the ammonia natural isotopic abundance but are enriched in the 15 NH 3 isotopologue due to previous recordings with 15 N enriched gas samples. The 15 NH 3 transitions in the different spectra were identified by comparison with a Kitt Peak spectrum highly enriched in 15 NH 3 (Ref. 930826R016, p = 2.00 Torr, T = 23.8 • C, L = 2.4 m with CO for calibration). The 15 NH 3 relative abundance corresponding of our FTS spectra has been estimated in two ways: using the absolute intensities obtained in Ref. [START_REF] Čermák | Spectroscopy of 14 NH 3 and 15 NH 3 in the 2.3µm spectral range with a new VECSEL laser source[END_REF] already used in Ref. [START_REF] Cacciani | The ammonia absorption spectrum between 3900 and 4700 cm -1[END_REF] or by comparison with the calculated intensity values of Ref. [START_REF] Yurchenko | A theoretical room-temperature line list for 15 NH 3[END_REF]. The two results agree and lead to the relative abundance values included in Table 1. The 15 NH 3 abundance increases from 0.54% (340 Pa) to 0.78% (13.2 Pa) to be compared to a natural value of 0.366% [START_REF] Gordon | The HITRAN2020 molecular spectroscopic database[END_REF]. As the four spectra were recorded successively by decreasing steps of the pressure, the isotopic ratio increased, due to the progressive desorption of

ν 1 , ν 2 , ν 3 , ν 4 , L 3 , L 4 , τ inv , Γ vib , J, K, Γ rot , N B , Γ tot where ν i are the vibrational normal-mode quantum numbers, L i = |l i |
are the corresponding vibrational angular momentum quantum numbers, τ inv = a/s is the inversion symmetry, and Γ vib is the symmetry of the vibrational motion. J is the total angular-momentum quantum number, K = |k| is the projection of the total angular momentum on the molecule-fixed axis z, and Γ rot is the rotational symmetry. Finally, Γ tot stands for the full symmetry of the eigenstate, and N B is the block counting number used during the generation of the C2018 list. Let us recall that only J and Γ tot are exact quantum numbers, the others are approximate ones which describe helpfully the level considering its true wavefunction and how this wavefunction is projected on the basis set.

In each (J, Γ tot ) subspace, the diagonalization process gives the eigenvalues and eigenstates which correspond to the energy levels, ordered by increasing energy and with a rank number N B . In this context, let us mention the work of Huang et al. who have processed the same type of calculations, using a refined potential surface [START_REF] Huang | Rovibrational spectra of ammonia. I. Unprecedented accuracy of a potential energy surface used with nonadiabatic corrections[END_REF][START_REF] Huang | Rovibrational spectra of ammonia. II. Detailed analysis, comparison, and prediction of spectroscopic assignments for 14 NH 3 , 15 NH 3 , and 14 ND 3[END_REF]. The quality of the predicted energy positions is claimed to be improved compared to C2018 but the transition intensities are not provided.

The assignment process has been described in detail in our previous contributions [START_REF] Čermák | Accurate 14 NH 3 line-list for the 2.3 µm spectral region[END_REF][START_REF] Cacciani | The ammonia absorption spectrum between 3900 and 4700 cm -1[END_REF]. Coincidences between the experimental and C2018 lists were searched automatically with the constraints δν = |ν exp. -ν calc. | ≤ 1 cm -1 and 0.5 ≤ S exp. /S calc. ≤ 2. For a given measured line, the C2018 candidates were tested using LSCD relations combined with intensity considerations. It means that the LSCD candidate partners were also subjected to the intensity screening with a similar criterion as for the initial C2018 match. For the search of LSCD relations, different studies extending from 3900 to 6500 cm -1 were considered [START_REF] Cacciani | The ammonia absorption spectrum between 3900 and 4700 cm -1[END_REF][START_REF] Cacciani | The absorption spectrum of ammonia between 5650 and 6350 cm -1[END_REF][START_REF] Gordon | The HITRAN2020 molecular spectroscopic database[END_REF]. The method of branches was used to complement the assignment procedure [START_REF] Cacciani | The ammonia absorption spectrum between 3900 and 4700 cm -1[END_REF]. The (obs.-calc.) wavenumber differences within a given vibrational branch are expected to vary slowly with the rotational quantum numbers. This expected tendency was used to confirm the LSCD assignments and for transitions missing LSCD partners. In some cases, the application of the LSCD relations leads to an assignment of two or more C2018 predicted transitions to a single experimental line. In such a case, the original line was artificially split into the corresponding number of independent transitions with positions shifted by a negligible value of 1×10 -5 cm -1 .

The intensities of these new transitions were obtained by affecting to each transition the fraction of the measured total intensity following the predictions of the C2018 line list.

Overall, 6562 out of 8610 transitions were assigned to 61 14 NH 3 vibrational bands listed in Table 2. In this table, the vibrational bands are defined by the vibrational quantum labels: ν 1,2,3,4 , L 1,2 and Γ vib (the τ inv label has been added). The line assignments are included in the list provided as a Supplementary Material. Considering the C2018

intensities, the assigned transitions represent 98.9 % of the total integrated intensity in the region. f Minimum and maximum values of the rotational quantum numbers of the assigned lines.

ν i (i = 1 -4)
g Sum of the experimental intensities derived from the optical depth, temperature and total pressure of the spectrum for the considered band.

h Ratio of the sum of the C2018 intensities of the transitions identified in the studied spectrum by the total C2018 intensity of the considered band.

i Average value of the (exp.-C2018) position differences of the considered band. (cm -1 ) (cm/molecule) (cm/molecule) (%) (cm -1 ) j Sum of the number of transitions or intensities of the listed bands. Note, that the intensity ratio is calculated with the C2018 intensities. If we compare the sum of experimental intensities (assigned vs. all lines), we obtain a ratio of 99.5 %. k For the experimental list of transitions, "others" correspond to the intensity sum of the unassigned transitions, while for the C2018 line list, it corresponds to the total intensity of the predicted vibrational bands with intensity smaller than the smallest observed band. l Sum of the two above values corresponding to the total C2018 intensity (intensity cut off of 1 × 10 -25 cm/molecule) and all the measured absorption lines. Figure 4 compares the set of unassigned lines to that of the C2018 lines with no experimental counterpart. All unassigned lines have an intensity smaller than 2.5 × 10 -23 cm/molecule. Except for one transition, all the C2018 transitions with intensity above 2.5 × 10 -23 cm/molecule have been found. Overall, the appearance of the two data sets is similar. We nevertheless note that the unpaired C2018 transitions have a larger intensity than the unassigned lines at the high energy edge near 5600 cm -1 while the situation is opposite near the low energy edge around 4800 cm -1 . Extra experimental absorption could be partly due to NH 2 D which has a natural abundance of about 3.4 × 10 -4 which leads to transitions with rough estimated intensity of a few 10 -24 cm/molecule for the stronger lines. Let us recall that the identified 15 NH 3 lines have been removed from the experimental panel.

Continued on next page

Upper state energies of 14 NH 3

By adding the lower state energies [START_REF] Furtenbacher | Empirical rovibrational energy levels of ammonia up to 7500 cm -1[END_REF] to the measured experimental line positions, the upper state empirical energies of 2215 14 NH 3 rovibrational levels were derived from the assigned transitions. The determined upper levels were reached by up to 11 transitions. 560 levels were derived from a single transition, 496 from two transitions and the remaining (1151) from more than two transitions. In the last case, the average value and standard deviation were calculated in two ways, for all the transitions and for a 30% trimmed selection of them. In the last case, the rms of the standard deviation over the determined energies was reduced from (0.9 ± 1.8) × 10 -3 cm -1 to (0.3 ± 0.3) × 10 -3 cm -1 . The list of derived energy levels is given in Supplementary Materials.

The determined 14 NH 3 energy levels have been highlighted on Figure 5 which presents the overall set of C2018 energy values for upper states of transitions predicted in the 4705-5650 cm -1 interval, with intensity larger than 1 × 10 -25 cm/molecule. The average rotational term [9.7J(J + 1) -3.6K 2 ] have been subtracted for the clarity of the plot. Three groups of energy levels are observed as upper levels of transitions located in our region of interest. Their reduced energies belong to the 4500-5500, 5500-6100 and 6100-7000 cm -1 ranges depending if they were determined from cold transitions, hot transitions starting from ν 2 , hot transitions from 2ν 2 and ν 4 , respectively.

Among the 2215 upper state energy levels determined in this work, 1939 are new compared to the MARVEL set of levels of Ref. [START_REF] Furtenbacher | Empirical rovibrational energy levels of ammonia up to 7500 cm -1[END_REF]. Figure 6 presents the differences between upper state energies and the calculated C2018 values, versus the quantity [J + K/(J + 1)]. Except for a few outliers, the agreement with MARVEL values [START_REF] Furtenbacher | Empirical rovibrational energy levels of ammonia up to 7500 cm -1[END_REF] is very good (average and rms values of 2 × 10 -4 and 7 × 10 -4 cm -1 for the (MARVEL-exp.) differences, respectively). A small overestimation of the MARVEL values of 2 × 10 -4 cm -1 is noted (right panel). As concerns the C2018 values [START_REF] Coles | Improved potential energy surface and spectral assignments for ammonia in the near-infrared region[END_REF], the deviations remain in a ±0.6 cm -1 range.

Comparison with the HITRAN line list

The overview comparison of our experimental list to the HITRAN2020 list (Fig. 1) illustrates the significant amount of new information provided by the analysis. Unassigned and assigned 14 NH 3 lines, as well as minor 15 NH 3 isotopologue lines can be distinguished on the plot. Our 14 NH 3 line list includes about four times more lines than the HITRAN2020 list. As for the 3900-4700 cm -1 range [3], the 15 NH 3 transitions contribute to about 0.4% of the absorption in the studied range which is consistent with the natural relative abundance of 0.366% [START_REF] Gordon | The HITRAN2020 molecular spectroscopic database[END_REF]. Note that both our work and HITRAN database do not consider the possible contribution of weak NH 2 D lines.

In Fig. 7, a part of the 140.4 Pa spectrum is compared to a simulation based on the HITRAN2020 list around 5290 cm -1 . Transitions with experimental line parameters transferred from HITRAN2016 are distinguished from the transitions newly added through the MARVEL procedure. In general, the latters show a nice agreement in position and intensity. A number of additional Figure 5: Upper state energies of the 14 NH 3 transitions of the C2018 list in the 4705-5650 cm -1 interval predicted with intensity larger than 1 × 10 -25 cm/molecule (grey dots). The average rotational term [9.7J(J + 1) -3.6K 2 ] has been subtracted for clarity. The experimental values determined in this work are superimposed (orange dots) together with the existing empirical values provided by the MARVEL procedure (green squares) [START_REF] Furtenbacher | Empirical rovibrational energy levels of ammonia up to 7500 cm -1[END_REF]. Some vibrational hot and cold bands from which the energies have been derived are indicated. Note that in some cases, the same upper levels are reached through both hot and cold bands. a 140 assignments were lost from the 2008 to 2016 editions of the HITRAN database with no explanation.

b This number is the sum of the HITRAN2016 transitions (639) and those added using the MARVEL process (616) [START_REF] Furtenbacher | Empirical rovibrational energy levels of ammonia up to 7500 cm -1[END_REF]. 7: FTS spectrum at 140.4 Pa in the 5289-5292 cm -1 range (blue line) compared to HITRAN2020 simulation (red): the two components on the right came from experimentally observed data and were present in HITRAN2016 issue. One of them is a water line at 5291.7064 cm -1 present as an impurity. On the left, a line corresponding to a transition added in HITRAN2020 from MARVEL process [START_REF] Coles | ExoMol molecular line lists -XXXV. A rotation-vibration line list for hot ammonia[END_REF] is visible (indicated by the "+" sign). All the other lines are not present in HITRAN2020. lines are observed in our FTS spectrum illustrating the achieved sensitivity. Note that the water line at 5291.7062 cm -1 is present in the HITRAN ammonia line list.

We have performed a systematic comparison of our assignments to those attached to the HITRAN2020 transitions. Among the 1275 transitions present in HITRAN2020 in our region, only 756 can be found within a 0.005 cm -1 interval around the measured position value. Indeed, a significant number of HITRAN transitions missing in our list corresponds to newly added transitions with MARVEL line positions and C2018 intensities which are too weak to be detected in our spectra (see Fig. 1). 70 of the transitions with coincident positions show a large intensity disagreement. Part of these intensity mismatches might be due to accidental position coincidence between a weak HITRAN transitions with MARVEL origin and a strong measured line. Among the 686 remaining transitions in common, the assignment fully coincides for 362, is incompatible for 53 as J value differs and, for the remaining part (271), some differences are observed. For example, J and K are correct but the vibrational assignment is different, mainly interchanged between ν 1 + ν 4 and ν 3 + ν 4 above J = 7.

Intensity considerations

As the assignment process is supported by the intensity matching between the experimental spectrum and the C2018 calculations, it is important to discuss their level of agreement. The corresponding intensity ratios are plotted in Fig. 8 where the values relative to the main vibrational bands -ν 3 + ν 4 (E), ν 1 + ν 4 (E) and ν 3 + ν 4 (A)) -are highlighted. These bands represent 63.5 % of the total number of assigned transitions but bring 95.4 % of the total intensity. Overall, the agreement between the experimental and calculated values is excellent. The increase of the dispersion for small line intensities is a usual phenomenon partly due to the larger relative uncertainty of the small experimental intensity values. However, there are some cases of strong transitions showing a large disagreement as for example, the transition measured at 4967.3479 cm -1 with intensity of 7.09 × 10 -22 cm/molecule, (orange square on Fig. 8) which is predicted to have a ten times smaller C2018 intensity. This particular example is analyzed in details just below.

Remember that the first step of the assignment process is to associate C2018 and experimental lines with similar intensities and close line centers. Obviously, in the considered example, the intensity mismatch prevented the association to the C2018 transition with closest position. Nevertheless, loosening the intensity criterion, the LSCD search gives a reasonable agreement for the C2018 transition at 4967.2327 cm -1 with a smaller intensity of 7.3 × 10 -23 cm/molecule. This transition belonging to the ν 1 + 2ν 2 vibrational band starts from J = 7, K = 6 s level and reaches J = 6, K = 3 s upper level with an energy of 5389.6889 cm -1 .

The systematic search for the LSCD partners revealed three hot band transitions assigned in our previous study at lower energy [START_REF] Cacciani | The ammonia absorption spectrum between 3900 and 4700 cm -1[END_REF] and four matches in the interval presently studied, thus confirming the assignment in spite of a strong underestimation of the C2018 intensity. While the hot transitions show an almost perfect intensity agreement, the FTS/C2018 intensity ratio for the five ν 1 + 2ν 2 band transitions vary from 1.09 up to 9.7 (Fig. 9).

Let us recall that the only two good quantum numbers for 14 NH 3 are J and Γ tot . The other labels given in C2018 list are only approximate. In fact, each wavefunction is found through the diagonalization of the Hamiltonian inside J, Γ tot blocks and is expressed as a linear combination of basis wavefunctions characterized by (J, Γ tot ) and completed by quantum labels ν 1 , ν 2 , ν 3 , ν 4 , The situation observed for the N B = 80 and 81 pair of levels is not isolated and many other cases of intensity transfer were found during the assignment process. This is also the case in other spectral regions. For instance, some examples can be found in our preceding study in the 5650-6300 cm -1 range [1] and, Huang et al. [START_REF] Huang | A collaborative 14 NH 3 IR spectroscopic analysis at 6000 cm -1[END_REF] pointed out two similar occurrences in their re-analysis of the ammonia spectrum in this region.

L 3 , L 4 , τ inv , K, Γ vib , Γ rot
Let us now try to select systematically the states with possible interaction with their nearby states in our range of interest.

In the 4705-5650 cm -1 interval, 1061 doublets of transitions with intensity above 1 × 10 -25 cm/molecule have been found in the C2018 list with upper energy levels separated by less than 2 cm -1 (in identical blocks). In addition, 115 triplets, 16 quadruplets and 2 quintuplets fulfill this criterion. Loosening the transition cut-off, the number of possibly interacting transitions groups rises The intensity ratios corresponding to the ν 3 + ν 4 (E), ν 1 + ν 4 (E) and ν 3 + ν 4 (A) strong bands are distinguished (red, blue and green, respectively). The highlighted outlier corresponding to a strongly underestimated C2018 intensity is discussed in the text as an example of intensity transfer. Table 4: An example of C018 intensity transfer between the transitions arriving into two close upper states of the same J , Γ tot subspace.

Upper state up to 1724 from previously mentioned 1194 ones. Comparing this list to our dataset we have found all experimental counterparts for 266 cases (250 doublets, 13 triplets and 3 quadruplets).

J = 6, Γ tot = A 2 , N B = 80 J = 6, Γ tot =A 2 , N B = 81 Lower State E C2018 = 5389.6889 cm -1 E C2018 = 5389.9834 cm -1 Sums and ratio E emp = 5389.80603 cm -1 E emp = 5390.03104 cm -1 J τ inv N B E C2018 ν T W S T W S 2018 r T W/C2018 ν T W S T W S C2018 r T W/C2018 Σ C2018 Σ T W r Σ (cm -1 ) (cm -
To test possible intensity transfer within the identified multiplets, we present in the upper panel of Fig. 10 the exp./C2018 intensity ratios with different symbols for the transitions reaching the resonant multiplets and the isolated levels. The first observation is that most of the large deviations correspond to resonant levels. In the lower panel of Fig. 10, we plotted the ratios for the intensity sum of the resonant transitions. The obtained result is impressive: while a significant fraction of the individual components show important disagreement between the experimental and C2018 intensities, their intensity sums coincide very well. We believe that the sensitivity of the wavefunctions to small inaccuracies of the potential energy surface could explain the phenomenon: a small variation of the energy separation of the interacting upper levels leads to a large intensity change for the weak component of the resonant doublets but the resulting intensity transfer does not affect the intensity sum of the involved transitions. Note that at higher energy the number of resonances within blocks increases sharply leading to more frequent intensity transfers and might degrade the agreement with C2018 intensity calculations. Let us hope that the results presently obtained will help to improve future theoretical predictions of line intensities at higher energy.

Conclusion

New high resolution and low-pressure FTS recordings have allowed an in depth analysis of the room temperature ammonia spectrum from 4703 to 5650.3 cm -1 range. Among the 9110 measured lines, 505 are identified as due to 15 NH 3 minor isotopologue, and a rovibrational assignment is proposed for 6562 14 NH 3 lines. This is a significant improvement compared to the HITRAN2020 list [START_REF] Gordon | The HITRAN2020 molecular spectroscopic database[END_REF], which provides 2493 14 NH 3 transitions (with 1255 assignments), 626 of them predicted by theory and not experimentally observed. Overall, our assigned transitions belong to 35 cold and 26 hot bands and bring over 98.8% of the integrated absorption in the region. 2215 upper energies were derived with accuracy better than 0.001 cm -1 . Among them 1939 are new, compared to those derived in Ref. [START_REF] Furtenbacher | Empirical rovibrational energy levels of ammonia up to 7500 cm -1[END_REF] using the MARVEL procedure. A recommended list of 9110 transitions for ammonia in natural isotopic abundance is provided as Supplementary Material. The 14 NH 3 line positions were calculated using our best empirical determination of the upper energy levels (estimated accuracy on the order of 5 × 10 -4 cm -1 ). Despite the quality of ab initio calculations to accurately predict position and intensity of the 14 NH 3 transitions [START_REF] Coles | Improved potential energy surface and spectral assignments for ammonia in the near-infrared region[END_REF] and the power of the Lower State Combination Difference technique to assign them, a number of important disagreements between the measured and C2018 intensities was evidenced. Most of the intensity mismatches concern weak transitions reaching an upper level with a close lying neighbour level reached by a stronger transition. As the intensity sum of the two interacting transitions coincides with the C2018 predictions, we conclude that the problematic situations result from intensity transfer between interacting multiplets. In those situations, line intensities provide a sensitive tool to reveal small inaccuracies of the potential energy surface used to generate the C2018 list [START_REF] Coles | Improved potential energy surface and spectral assignments for ammonia in the near-infrared region[END_REF]. As a result, the intensity agreement with C2018 calculations which is in general highly valuable for rovibrational assignment, should be used with caution, in particular at higher energy where the level density increases rapidly making resonance interactions more and more probable. In particular, the rovibrational assignments of the ammonia spectrum in the 1.5 µm range (6300-7000 cm -1 ) already studied in Refs. [START_REF] Cacciani | Spectroscopy of ammonia in the range 6626-6805 cm -1 : using temperature dependence towards a complete list of lower state energy transitions[END_REF][START_REF] Sung | Extended line positions, intensities, empirical lower state energies and quantum assignments of NH 3 from 6300 to 7000 cm -1[END_REF] might be extended by a careful consideration of possible intensity transfers. /S C2018 intensity ratios for the 14 NH 3 transitions assigned in the 4705-5650 cm -1 region. According to the energy separation of the upper energy level in a given (J , Γ tot ) subspace, a different symbol is used: black circles and cyan points when the energy separation from the neighbour level is more or less than 2 cm -1 , respectively. Lower panel: Intensity ratios for cases when all the possibly interacting components in a given group (belonging to the same J , Γ tot with ∆E < 2 cm -1 and sharing the same lower state) were identified experimentally, individual ratio (cyan dots) and ratio of corresponding intensity sums (red /yellow dots).

Figure 1 :

 1 Figure 1: Upper panel: Overview of the HITRAN2020 transitions of 14 NH 3 (green and orange) and 15 NH 3 (cyan) in the studied region. 14 NH 3 transitions were added using MARVEL algorithm (orange). Lower panel: Ammonia transitions measured in the present work: 14 NH 3 and 15 NH 3 (green and cyan circles, respectively), and unassigned (yellow circles).

Figure 2 :

 2 Figure 2: Overview of the Fourier transform absorption spectra of ammonia recorded in the present work with the resolution of 0.003 cm -1 .The arrows mark the spectral intervals of the spectra used in the analysis. In the 5600-5650 cm -1 interval, the Kitt Peak spectrum (KP1) with Ref. 900308R019 was used.

Figure 3 :

 3 Figure 3: Ratios of the intensities derived from the 140.4 Pa spectrum to those of the 13.2 Pa spectrum (orange dots) for isolated transitions in the 1.2 × 10 -23 -1.2 × 10 -21 cm/molecule range.15 NH 3 transitions were removed from the comparison. Intensity ratios between the KP1 Kitt Peak spectrum and the 304 Pa spectrum are plotted for a few weak lines below 5600 cm -1 (cyan dots). They are used for the intensity calibration of the 5600-5650 cm -1 interval.

  are the vibrational normal modes corresponding to the ν 1 symmetric stretch, ν 2 symmetric bend, ν 3 the antisymmetric stretch and ν 4 antisymmetric bend, respectively. L 3 = |l 3 | and L 4 = |l 4 | are the vibrational angular momentum quantum numbers of the ν 3 and ν 4 modes, respectively. b Energy of the lowest level of the upper vibrational state (corresponding generally to J = K = 0 as calculated in the C2018 list. In the case of the hot bands, the J = K = 0 value of the lowest state was subtracted. c Number of lines of the corresponding band with C2018 intensity larger than 1 × 10 -25 cm/molecule. d Sum of the C2018 intensities of given band, larger than 1 × 10 -25 cm/molecule. Note that the C2018 intensities are calculated for pure 14 NH 3 . e Number of lines of the corresponding band assigned in the studied spectrum.

Figure 6 :

 6 Figure 6: Differences between the C2018 [11] (grey) and MARVEL (green) [9] energies of the upper levels of 14 NH 3 and the corresponding values derived in the present work. The values corresponding to upper levels derived from four vibrational bands are highlighted.

Figure

  Figure7: FTS spectrum at 140.4 Pa in the 5289-5292 cm -1 range (blue line) compared to HITRAN2020 simulation (red): the two components on the right came from experimentally observed data and were present in HITRAN2016 issue. One of them is a water line at 5291.7064 cm -1 present as an impurity. On the left, a line corresponding to a transition added in HITRAN2020 from MARVEL process[START_REF] Coles | ExoMol molecular line lists -XXXV. A rotation-vibration line list for hot ammonia[END_REF] is visible (indicated by the "+" sign). All the other lines are not present in HITRAN2020.

  . The labeling is completed by the rank in the block, N B , which unambiguously designates the N th B level of the (J, Γ tot ) block ordered by increasing value of the energy. The upper state involved in the discussed example corresponds to N B = 80 in the (6, A 2 ) block and has an experimental energy of 5389.80603 cm -1 . The experimental value of the energy separation from the next N B = 81 level is only 0.225 cm -1 . The N B = 81 upper state is the upper state of strong transitions and we interpret the large intensity of the ν 1 + 2ν 2 transitions reaching the N B = 80 level as due to an intensity borrowing from those involving the N B = 81 levels. It is interesting to note that the energy separation of the N B = 80 and N B = 81 levels is significantly smaller than its C2018 value of 0.2945 cm -1 . This closer energetic resonance might explain the fact that the resulting intensity transfer is much larger than predicted by theory. Table4presents the experimental and calculated energies and intensities of the five LSCD pairs of the ν 1 + 2ν 2 band together with the corresponding intensity ratios. If we sum the experimental intensities of the doublets of transitions reaching the N B = 80 and 81 levels (last set of columns in Tab. 4), and compare them to the corresponding C2018 sums, an agreement within the experimental error bar (5%) is obtained.

Figure 8 :

 8 Figure 8: Ratios of the 14 NH 3 line intensities measured in this work in the 4705-5650 cm -1 spectral region to the corresponding C2018 values[START_REF] Coles | Improved potential energy surface and spectral assignments for ammonia in the near-infrared region[END_REF]. The intensity ratios corresponding to the ν 3 + ν 4 (E), ν 1 + ν 4 (E) and ν 3 + ν 4 (A) strong bands are distinguished (red, blue and green, respectively). The highlighted outlier corresponding to a strongly underestimated C2018 intensity is discussed in the text as an example of intensity transfer.

Figure 9 :

 9 Figure 9: Calculated [11] and experimental transitions reaching the N B = 80 upper level of the block (J = 6, Γ tot = A 2 at 5389.6889 cm -1 ). The experimental transitions of the ν 1 + 2ν 2 -ν 2 band were reported in Ref. [1] while the ν 1 + 2ν 2 cold band transitions are observed in the present work. The transition under study is the one at 4967.3479 cm -1 with a C2018 intensity underestimated by a factor of 9.68. The C2018 values are plotted with different symbols (open squares and open triangles) according to the inversion symmetry (a or s, respectively) of the lower state. The corresponding exp./C2018 intensity ratios are indicated for each transition. The experimental counterparts (orange circles) were found in this work and in Ref. [3].

Figure 10 :

 10 Figure 10: Upper panel: S exp./S C2018 intensity ratios for the 14 NH 3 transitions assigned in the 4705-5650 cm -1 region. According to the energy separation of the upper energy level in a given (J , Γ tot ) subspace, a different symbol is used: black circles and cyan points when the energy separation from the neighbour level is more or less than 2 cm -1 , respectively. Lower panel: Intensity ratios for cases when all the possibly interacting components in a given group (belonging to the same J , Γ tot with ∆E < 2 cm -1 and sharing the same lower state) were identified experimentally, individual ratio (cyan dots) and ratio of corresponding intensity sums (red /yellow dots).

Table 1 :

 1 Experimental parameters of the four FTS spectra used in this work.

	p	c15 N	L	R

Table 2 :

 2 Statistics and integrated absorption of the various vibrational bands contributing to the 14 NH 3 spectrum between 4705 and 5650.3 cm -1 . The bands are ordered according to their C2018 integrated intensities.

				C2018		This work
	Vibrational	E 0	b	Nb c Band Int. d	Nb e	J min /J max	f	Band Int. g	Int. ratio h < δ > i
	band a	(cm -1 )	(cm/molecule)				(cm/molecule) (%)	(cm -1 )
	ν 1 3 + ν 1 4 (E ) s	5052.6	1508 3.15E-19	911	0/17 3.16E-19	99.8	0.03
	ν 1 3 + ν 1 4 (E ) a	5053.2	1480 3.07E-19	909	0/17 3.08E-19	99.8	0.02
	ν 1 + ν 1 4 (E ) s	4955.8	1063 2.15E-20	564	0/14 2.18E-20	97.9	0.01
	ν 1 + ν 1 4 (E ) a	4956.9	1021 2.08E-20	525	0/15 2.11E-20	97.9	0.06
	ν 1 3 + ν 1 4 (A 1 ) s	5067.8	552 1.56E-20	337	1/13 1.60E-20	98.8	0.04
	ν 1 3 + ν 1 4 (A 2 ) a	5067.7	546 1.32E-20	324	0/13 1.33E-20	98.3	0.06
	ν 1 3 + ν 1 4 (A 2 ) s	5052.0	577 6.62E-21	297	2/12 6.45E-21	96.2	0.01
	ν 1 3 + ν 1 4 (A 1 ) a	5052.7	585 6.21E-21	299	2/13 6.12E-21	96.3	0.00
	4ν 2 + ν 1 4 (E ) s	5104.9	638 5.86E-21	161	4/11 5.42E-21	92.9	0.20
	2ν 2 + 2ν 0 4 (A 2 ) a	5093.6	402 5.03E-21	109	3/13 6.20E-21	96.0	0.17
	ν 2 + ν 1 3 + ν 1 4 (E ) s ← ν 2	5080.4	485 4.28E-21	257	0/14 4.20E-21	96.2	-0.05
	ν 2 + ν 1 3 + ν 1 4 (E ) a ← ν 2	5104.1	467 3.25E-21	241	0/14 3.20E-21	95.6	-0.10
	2ν 2 + ν 1 3 (E ) s	5144.9	706 2.89E-21	279	1/14 2.96E-21	86.3	0.21
	ν 1 + 2ν 2 (A 1 ) s	5000.2	448 2.47E-21	186	1/12 3.32E-21	92.0	0.19
	2ν 2 + 2ν 2 4 (E ) a	5113.3	314 1.25E-21	58	4/15 1.06E-21	86.6	0.35
	2ν 2 + ν 1 3 (E ) a	5353.0	651 1.08E-21	368	0/12 9.92E-22	89.8	0.15
	3ν 1 4 (E ) s	4799.2	496 9.91E-22	42	4/16 4.02E-22	38.8	0.15
	3ν 1 4 (E ) a	4801.4	452 5.48E-22	13	3/16 7.24E-23	14.4	-0.09
	3ν 3 4 (A 2 ) s	4840.9	262 4.95E-22	52	2/10 3.46E-22	60.9	0.19
	3ν 3 4 (A 1 ) s	4841.6	245 4.94E-22	46	1/13 4.16E-22	57.9	0.12
	3ν 3 4 (A 2 ) a	4843.4	204 4.23E-22	30	0/12 4.08E-22	57.6	0.16
	3ν 3 4 (A 1 ) a	4843.0	251 3.95E-22	27	6/11 1.51E-22	54.3	0.10
	3ν 2 + ν 1 3 (E ) s ← ν 2	4923.6	266 3.86E-22	121	1/11 3.11E-22	74.2	0.15
	ν 1 + 2ν 2 (A 2 ) a	5233.8	207 3.12E-22	58	0/12 1.94E-22	73.7	0.28
	2ν 2 + 2ν 0 4 (A 1 ) s	4756.9	163 1.80E-22	20	1/10 9.07E-23	48.0	0.16
	2ν 2 + 2ν 2 4 (E ) s	4773.8	294 1.71E-22	4	5/9 6.60E-24	3.0	0.16
	2ν 2 + ν 1 3 + ν 1 4 (E ) s ← 2ν 2	5119.8	179 1.67E-22	23	2/8 6.51E-23	38.7	-0.20
	ν 2 + ν 1 3 + ν 1 4 (A 2 ) a ← ν 2	5117.2	159 1.56E-22	31	2/10 1.04E-22	59.6	-0.22
	ν 2 + ν 1 3 + ν 1 4 (A 1 ) s ← ν 2	5091.8	159 1.50E-22	38	3/9 1.02E-22	63.8	-0.29
	ν 2 + ν 1 3 + ν 1 4 (A 1 ) a ← ν 2	5101.2	156 1.39E-22	33	2/9 7.75E-23	43.7	-0.20
	ν 2 + ν 1 3 + ν 1 4 (A 2 ) s ← ν 2	5075.6	113 1.20E-22	22	4/8 9.06E-23	63.6	-0.22
	ν 1 + ν 2 + ν 1 4 (E ) a ← ν 2	4998.4	206 1.14E-22	25	1/9 4.55E-23	28.7	-0.33
	ν 1 + ν 1 3 (E ) s ← ν 4	4982.5	267 1.09E-22	5	4/7 6.42E-24	5.8	0.02
	ν 1 + ν 2 + ν 1 4 (E ) s ← ν 2	4965.4	196 9.84E-23	15	2/10 2.37E-23	23.3	-0.36
	ν 1 3 + 2ν 2 4 (A 2 ) a ← ν 4	5025.8	103 8.53E-23	1	6/6 1.58E-24	1.6	0.17
	ν 1 3 + 2ν 2 4 (A 1 ) a ← ν 4	5025.4	81 5.67E-23	1	4/4 1.96E-24	2.5	0.10
	ν 1 + 3ν 2 (A 1 ) s ← ν 2	4805.4	73 3.89E-23	33	1/8 2.98E-23	67.1	0.33
	2ν 2 + ν 1 3 + ν 1 4 (E ) a ← 2ν 2 5355.5	105 3.44E-23	2	5/7 1.92E-24	3.6	-0.10
									Continued on next page

Table 2 -

 2 Continued from previous page

				C2018		This work
	Vibrational	E 0	b	Nb c Band Int. d	Nb e	J min /J max	f	Band Int. g	Int. ratio h < δ > i
	band a	(cm -1 )	(cm/molecule)				(cm/molecule)	(%)	(cm -1 )
	ν 1 + 2ν 0 4 (A 2 ) a ← ν 4	4978.4	74 2.73E-23	1	3/3 1.15E-24	3.5	0.09
	ν 2 + ν 1 3 (E ) a	4435.4	33 2.72E-23	13	11/14 2.05E-23	79.6	0.04
	ν 1 + 3ν 2 (A 1 ) s	5737.9	35 2.59E-23	21	4/8 2.79E-23	89.2	0.42
	6ν 2 (A 1 ) s ← ν 2	5110.9	22 2.48E-23	4	8/9 1.87E-23	63.0	0.00
	3ν 2 + 2ν 2 4 (E ) s	5622.6	61 2.30E-23	3	1/5 3.16E-24	11.9	0.87
	4ν 2 + ν 1 4 (E ) a	5708.3	51 1.81E-23	1	7/7 2.52E-25	1.3	0.12
	2ν 2 + ν 1 3 + ν 1 4 (E ) s ← ν 4	5091.0	84 1.77E-23	1	6/6 6.06E-25	0.6	-0.35
	3ν 2 + ν 1 3 (E ) a ← ν 2	5398.9	79 1.72E-23	9	2/7 4.00E-24	21.6	0.11
	ν 2 + ν 1 3 (E ) s	4416.9	25 1.54E-23	16	12/15 1.39E-23	90.9	0.12
	3ν 2 + ν 1 3 (E ) s	5856.1	35 1.21E-23	5	7/9 5.37E-24	37.6	0.22
	ν 1 3 + 2ν 2 4 (A 2 ) a ← 2ν 2	5054.6	43 9.89E-24	1	6/6 8.00E-25	7.8	0.18
	3ν 2 + 2ν 0 4 (A 2 ) a ← ν 2	5201.1	17 9.56E-24	2	9/9 6.11E-24	40.2	0.27
	ν 1 + 3ν 2 (A 2 ) a ← ν 2	5297.9	35 6.86E-24	2	4/6 8.34E-25	8.7	0.57
	ν 1 + 2ν 2 + ν 1 4 (E ) s ← ν 4	4955.9	32 5.71E-24	1	6/6 5.03E-25	9.3	-0.30
	2ν 2 + ν 1 3 + ν 1 4 (E ) s ← ν 2	5784.8	19 4.87E-24	1	6/6 4.80E-25	4.2	-0.35
	ν 1 + ν 2 (A 1 ) s	4294.5	5 2.41E-24	3	12/13 2.10E-24	85.8	0.10
	ν 2 + 3ν 3 4 (A 1 ) s	5718.7	3 2.26E-24	1	4/4 1.35E-24	43.0	0.50
	ν 1 + ν 2 (A 2 ) a	4320.0	8 2.02E-24	4	12/14 1.40E-24	64.5	0.02
	ν 2 + 2ν 2 4 (E ) s	4135.8	5 1.89E-24	1	13/13 8.83E-25	40.5	0.42
	ν 2 + 2ν 2 4 (E ) a	4192.9	4 1.62E-24	2	11/13 1.10E-24	78.9	0.29
	ν 2 + 3ν 3 4 (A 1 ) s ← ν 2	4786.3	4 1.54E-24	1	4/4 5.74E-25	32.2	0.49
	ν 1 + 3ν 2 (A 2 ) a ← 2ν 2	4632.8	4 4.66E-25	1	6/6 1.15E-25	26.8	0.57
	ν 2 + 2ν 0 4 (A 2 ) a	4173.1	1 4.13E-25	1	12/12 2.88E-25	100.0	-0.11
	Sum j			16759 7.38E-19	6562			7.39E-19	98.93
	Others k			1182 0.01E-19	2048			0.03E-19
	Total l			17941 7.39E-19	8610			7.43E-19
	Notes:

a Vibrational band labeling:

Table 2 -

 2 Continued from previous page

				C2018		This work
	Vibrational	E 0	b	Nb c Band Int. d	Nb e	J min /J max	f	Band Int. g	Int. ratio h < δ > i
	band a

Table 3 :

 3 Statistics and integrated absorption in various databases for ammonia in the 4703-5650.3 cm -1 spectral range (intensity cut-off of 1 × 10 -25 cm/molecule at 296 K).

	HITRAN2008 a	HITRAN2016	HITRAN2020	This work	C2018
	14 NH 3	15 NH 3	14 NH 3	15 NH 3	14 NH 3	15 NH 3	14 NH 3	15 NH 3	14 NH 3
	Transitions 2001	129	1875	126	2493	126	8632	465	17941
	Assignments 771	129	639	126	1255 b 126	6562	0	17941
	Intensity sum 7.66 (×10 -19 cm/molecule)	0.0146 7.65	0.0146 7.66	0.0146 7.42	0.034	7.39
	Notes:

NH 3 adsorbed on the walls of the cell and exchanges with ammonia in natural isotopic abundance initially injected in the cell. Note that the estimated value of the 15 NH 3 abundance in the various analyzed spectra was used to scale the[START_REF] Huang | Rovibrational spectra of ammonia. I. Unprecedented accuracy of a potential energy surface used with nonadiabatic corrections[END_REF] NH 3 line intensities accordingly, and the reported intensity values correspond to the natural abundance.4. Rovibrational assignmentsFollowing our recent analysis[START_REF] Čermák | Accurate 14 NH 3 line-list for the 2.3 µm spectral region[END_REF][START_REF] Cacciani | The ammonia absorption spectrum between 3900 and 4700 cm -1[END_REF][START_REF] Cacciani | The absorption spectrum of ammonia between 5650 and 6350 cm -1[END_REF], the C2018 variational list of 14 NH 3[START_REF] Coles | Improved potential energy surface and spectral assignments for ammonia in the near-infrared region[END_REF] was used as a primary source for the rovibrational assignment of the experimental line list. The C2018 rovibrational labeling uses 13 quantum numbers:

Acknowledgments

This research was supported by the joint Slovak-Czech-French Danube Region project (DS-FR-19-0050), and by the Slovak Research and Development Agency (contract number APVV-19-0386). This work was also a contribution of the CPER research project CLIMIBIO. The authors thank the French Ministère de l'Enseignement Supérieur et de la Recherche, the Hauts de France Region and the European Funds for Regional Economic Development for their financial support to this project. This work was performed in the frame of the ANR project e PYTHEAS (ANR-16-CE31-00 5).

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

CRediT authorship contribution statement P. Cacciani: Investigation. P. Čermák: Investigation. J. Vander Auwera: Investigation. A. Campargue: Investigation.


Jessy Elias

Alessandro Faccinetto

Sebastien Batut

Olivier Carrivain

Mariano Sirignano

Andrea D'anna

Xavier Mercier

Thermocouple-based thermometry for laminar sooting flames: Implementation of a fast and simple methodology

Keywords: Thermometric Sensors, Flame temperature, Thermocouple methodology, Extrapolation method, Radiative loss correction

Introduction

Temperature measurements are crucial in the context of laboratory flame studies for the development and validation of detailed kinetic models [START_REF] Shaddix | Correcting thermocouple measurements for radiation loss: A critical review[END_REF] . These measurements are usually performed by optical methods or thermocouple thermometry. Optical methods have the great advantage of being non-intrusive, thus allowing local measurements without disturbance of the flame [START_REF] Eckbreth | Laser Diagnostics for Combustion Temperature and Species[END_REF] . In that context, methods such the line-of-sight attenuation (LOSA) [START_REF] Snelling | Spectrally Resolved Measurement of Flame Radiation to Determine Soot Temperature and Concentration[END_REF][START_REF] Yon | Revealing soot maturity based on multi-wavelength absorption/emission measurements in laminar axisymmetric coflow ethylene diffusion flames[END_REF] and spectral soot emission (SSE) [START_REF] Kholghy | Comparison of multiple diagnostic techniques to study soot formation and morphology in a diffusion flame[END_REF] are relatively easy to implement and give access to integrated temperature measurements requiring nevertheless complex inversion procedures to recover the temperature mapping of the flame. Moreover, these methods are dependent on the presence of soot particles, being therefore only applicable to sooting flames and providing temperature information restricted to the region where soot are formed. Laser-induced fluorescence (LIF) and coherent anti-stokes Raman scattering (CARS) are certainly the most commonly used methods for the determination of temperatures in flames [START_REF] Eckbreth | Laser Diagnostics for Combustion Temperature and Species[END_REF] .

LIF is based on the excitation of species, usually radicals, formed in the flame (e.g. OH or NO) and the recording of their rovibronic excitation spectra over a certain collection wavelength range [START_REF] Bessler | Quantitative multi-line NO-LIF temperature imaging[END_REF][START_REF] Rensberger | Laser-induced fluorescence determination of temperatures in low pressure flames[END_REF][START_REF] Hartlieb | Temperature measurement in fuel-rich non-sooting low-pressure hydrocarbon flames[END_REF][START_REF] Rahinov | Absorption spectroscopy diagnostics of amidogen in ammonia-doped methane/air flames[END_REF] . Being the intensity of the lines proportional to the Boltzmann factor, the temperature of the flame can be obtained by comparison with simulated spectra. LIF, which is widely used in laboratory flames [START_REF] Foo | The accuracy and precision of multi-line NO-LIF thermometry in a wide range of pressures and temperatures[END_REF] , with satisfying accuracy (less than 100 K uncertainty). CARS is probably the optical method offering the highest accuracy (less than 50 K uncertainty) [START_REF] Hancock | Nitrogen and hydrogen CARS temperature measurements in a hydrogen/air flame using a near-adiabatic flat-flame burner[END_REF] for flame temperature measurements. However, this method relies on complex non-linear optics and requires a delicate experimental implementation, in particular the crossing of several laser beams at the temperature measurement point which noticeably limit the spatial resolution of this technique.

Compared to optical techniques, thermocouple-based temperature measurements require much less expensive equipment and appear much simpler to implement. A thermocouple consists of two different metal alloy wires, joined at one end. When the junction of the two metals is heated, a voltage is produced at open ends that can be correlated back to the junction temperature. Unlike optical measurements, the use of thermocouples necessarily results in a disturbance of the investigated medium as the junction needs to be physically located at the temperature measurement point. In addition, thermocouple-based measurements in combustion environments require some corrections to retrieve the flame temperature that include the effect of losses by heat conduction, convection and thermal radiation [START_REF] Shaddix | Correcting thermocouple measurements for radiation loss: A critical review[END_REF] . Thermocouple measurements can also be biased by catalytic oxidation processes likely to occur at the surface of the alloys, in particular under the action of H or OH radicals in flames [START_REF] Heitor | Thermocouples and sample probes for combustion studies[END_REF] . Many works have been searching methods for mitigation of the impact of all these phenomena on temperature measurements [START_REF] Shaddix | Correcting thermocouple measurements for radiation loss: A critical review[END_REF][START_REF] Kholghy | Comparison of multiple diagnostic techniques to study soot formation and morphology in a diffusion flame[END_REF][START_REF] Bradley | Measurement of High Gas Temperatures with Fine Wire Thermocouples[END_REF][START_REF] Hindasageri | Thermocouple error correction for measuring the flame temperature with determination of emissivity and heat transfer coefficient[END_REF][START_REF] Lemaire | Assessment of radiation correction methods for bare bead thermocouples in a combustion environment[END_REF] . It is notably recommended to allow single temperature measurements that the Biot number characterizing the heating uniformity of the junction should be well below 0.1 [START_REF] Shaddix | Correcting thermocouple measurements for radiation loss: A critical review[END_REF] . Measurement biases related to conduction can also be greatly reduced by selecting thermocouples having a wire length/diameter ratio greater than 200 [START_REF] Heitor | Thermocouples and sample probes for combustion studies[END_REF][START_REF] Bradley | Measurement of High Gas Temperatures with Fine Wire Thermocouples[END_REF] . Finally, surface coatings with beryllium or yttrium oxide are known to limit catalytic oxidation [START_REF] Kent | A Noncatalytic Coating for Platinum-Rhodium Thermcouples[END_REF][START_REF] Peterson | The emittance of yttrium-beryllium oxide thermocouple coating[END_REF] .

The radiative losses, which are inherent to the heating of the thermocouple and thus cannot be completely avoided, can lead to underestimation of the flame temperature by several hundreds of degrees in high temperature media [START_REF] Kholghy | Comparison of multiple diagnostic techniques to study soot formation and morphology in a diffusion flame[END_REF] . Also, if present, soot can deposit on the junction, significantly changing its diameter and emissivity. Even though thermocouples can be used to estimate the soot amount in flame by thermophoretic particle densitometry (TPD) [START_REF] Mcenally | Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples[END_REF][START_REF] De Falco | Experimental and numerical study of soot formation and evolution in coflow laminar partially premixed flames[END_REF][START_REF] De Falco | The evolution of soot particles in premixed and diffusion flames by thermophoretic particle densitometry[END_REF] , reliable temperature measurements in sooting flames are still challenging. In a recent paper, Lemaire et al. [START_REF] Lemaire | Assessment of radiation correction methods for bare bead thermocouples in a combustion environment[END_REF] proposed a comparative study of 4 different thermocouple methods relying on different corrections processes, namely the electrical compensation (EC), the reduced radiative error (RRE), the multi-element methods (MET) and the extrapolation method. In this work, the authors have made a detailed study relating the implementation of the methods along with a comparison of their sensitivity and accuracy relative to each other. The EC method consists of heating the thermocouple in a vacuum by imposing a high frequency alternating current and measuring the DC electromotive force at the terminals of the thermocouple. In vacuum, since there is no external energy input through gases, the electrical energy supplied per unit length to the thermocouple is equal to the heat loss by radiation. Hence, a first calibration curve is obtained in vacuum condition characterizing the temperature reached by the thermocouple according to the applied current. The thermocouple is then placed at different heights in the flame and by applying the same procedure as in vacuum, it is possible to deduce by comparison with the initial calibration curve the losses by radiation as a function of the measured temperature. Hence, the EC method, although very accurate, requires expensive equipment (ultra-high vacuum cell to determine the radiation losses) and a relatively long and complex implementation which can represent a limitation to its use for flame studies. The RRE method [START_REF] Lemaire | Assessment of radiation correction methods for bare bead thermocouples in a combustion environment[END_REF] which aims to evaluate by calculation the radiative losses requires knowledge or estimates of the parameters of the studied medium (viscosity, density, flow velocity, gas environment....) which can be difficult to determine and thus might also appear to a limitation for the use of this method. The MET method, which is based on the use of a simple analytical expression to find the true temperature using two or three thermocouples of different diameters, has been shown to often give inconsistent results, as also noted elsewhere [START_REF] Hindasageri | Thermocouple error correction for measuring the flame temperature with determination of emissivity and heat transfer coefficient[END_REF][START_REF] Lemaire | Assessment of radiation correction methods for bare bead thermocouples in a combustion environment[END_REF] . The reason might be related to the terms in T 4 in the used expression, being too sensitive to temperature variations. Finally, the extrapolation method, assuming the radiative losses to be proportional to the diameter of the thermocouple [START_REF] Bradley | Measurement of High Gas Temperatures with Fine Wire Thermocouples[END_REF][START_REF] Daniels | Measurement of Gas Temperature and the Radiation Compensating Thermocouple[END_REF][START_REF] Nichols | On the Temperature of the Acetylene Flame[END_REF] , requires only simple equipment and no a priori knowledge on the combustion medium to retrieve flame temperature. Thus, by making measurements with thermocouples of different diameters, the flame temperature can be deduced by extrapolation to the zero diameter. Besides, the use of thermocouple with two different bead sizes can also be judiciously used to determine the radiation correction for the gas temperature in a steady flames by solving a simple energy balance equation [START_REF] Seshadri | Optical methods and results of dew point and deposition rate measurements in salt/ash-containing combustion gases-B2O3(I) deposition rates by interference methods and comparisons with theory[END_REF][START_REF] Ren | Temperature measurement of a turbulent buoyant ethylene diffusion flame using a dual-thermocouple technique[END_REF] . In the paper of Lemaire [START_REF] Lemaire | Assessment of radiation correction methods for bare bead thermocouples in a combustion environment[END_REF] , the result of the extrapolation method implemented with only two measurement points corresponding to two thermocouples of different diameters is compared with the three other methods (EC, RRE and MET). The good agreement obtained by linear extrapolation with the results of the EC and RRE methods appears to be satisfactory. These preliminary results suggest that the use of the extrapolation method with more measurement points could therefore allow obtaining temperature measurements corrected for radiative losses with a high degree of accuracy. However, despite being one of the oldest documented methods in modern combustion science [START_REF] Mcenally | Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples[END_REF] , systematic studies aiming to validate the use of this simple-to-implement and inexpensive method for the measurement of temperature profiles in flames are scarce in the literature [START_REF] Bradley | Measurement of High Gas Temperatures with Fine Wire Thermocouples[END_REF][START_REF] Hindasageri | Thermocouple error correction for measuring the flame temperature with determination of emissivity and heat transfer coefficient[END_REF][START_REF] Daniels | Measurement of Gas Temperature and the Radiation Compensating Thermocouple[END_REF][START_REF] Nichols | On the Temperature of the Acetylene Flame[END_REF]25 . Moreover, there exist some discrepancies between the published works on the analytical treatment of the data to recover flame temperature. To address this lack of consistency, we propose herein to test the possibilities and limitations offered by the extrapolation method for the measurement of temperature profiles corrected from radiation losses in sooting flames. This work is carried out in a well-characterized laminar diffusion flame [START_REF] Faccinetto | Evidence on the formation of dimers of polycyclic aromatic hydrocarbons in a laminar diffusion flame[END_REF][START_REF] Mercier | Dimers of polycyclic aromatic hydrocarbons: the missing pieces in the soot formation process[END_REF] and explains in details the principle and the methodology to implement the extrapolation method to sooting flames. A validation of the method is proposed based on the comparison with temperature measurements performed by laser based techniques like OH and NO LIF thermometry and numerical simulations. Finally, a discussion on the measurement biases potentially occurring due to the presence of soot is proposed.

Experimental Setup

Burner and flame apparatus

Measurements were performed along the axis of a 120 mm height, non-smoking, laminar diffusion flame (0.52 L min -1 CH 4 , 87 L min -1 air) stabilized at atmospheric pressure on a modified McKenna burner with a central injector tube (10.25 mm diameter) and an outer air flow tube (88 mm diameter) producing a homogenous air shield. This flame has already been characterized in previous works [START_REF] Faccinetto | Evidence on the formation of dimers of polycyclic aromatic hydrocarbons in a laminar diffusion flame[END_REF][START_REF] Mercier | Dimers of polycyclic aromatic hydrocarbons: the missing pieces in the soot formation process[END_REF] . In particular, laser induced incandescence (LII) measurements showed that soot particles along the vertical central axis of the flame are located between 55 and 100 mm height above the burner (HAB), with a peak volume fraction at 80 mm HAB.

LIF thermometry

OH and NO LIF thermometry are well-established experimental optical techniques that were used as reference methods for validating the temperature profile measurement. The flame was not doped, so the temperature measurements were limited to the HABs providing a sufficient concentration of OH and NO radicals for the recording of the excitation spectra. Hence, NO LIF thermometry was preferentially used for the lowest HABs up to 40 mm, while OH LIF thermometry could only be used above 80 mm HAB, in the oxidation zone of the flame.

OH and NO LIF thermometry measurements were carried out with a Nd:YAG laser (Quanta-ray, Spectra Physics), generating laser pulses at 1064, 532 and 355 nm (6 ns pulse width, 10 Hz) mixed and used to pump an OPO (premiScan-ULD/240, GWU-Lasertechnik) with tunable wavelengths in a large spectral range from the UV to the IR. Two different optical schemes were used according to the excited species. In both cases, the laser beam was focused on the flame axis using a spherical UV lens (1000 mm focal length).

The laser beam diameter at the probed volume was estimated to be around 500 m. The laser fluence was kept below 20 mJ cm -2 with an optical attenuator to be in the linear regime of fluorescence.

NO LIF experiments were carried out by exciting NO lines in the A-X (0-0) band system around 226 nm.

The emitted fluorescence was collected at a right angle in the (0-2) band around 245 nm with two spherical lenses (50 mm diameter, 100 and 75 mm focal length, respectively) and imaged into a bundle of optical fibers (1.25 mm diameter) connected to a spectrometer (IHR320, Jobin Yvon) coupled to a photomultiplier tube (XP2020Q, Photonics). With this spectroscopic scheme, no spectral interference or overlap with aromatic hydrocarbons fluorescence was reported. Finally, the spectral comparison between experimental and simulated spectra did not consider quenching variations as the fluorescence quenching of NO has been demonstrated to be insensitive to the rotational quantum number [START_REF] Mcdermid | Radiative lifetimes and electronic quenching rate constants for single-photon-excited rotational levels of no (A2Σ+, ν′ = 0)[END_REF][START_REF] Nutt | Measurement of electronic quenching rates in nitric oxide using two-photon spectroscopy[END_REF][START_REF] Zacharias | Two-photon excitation of NO(A2Σ+; ν′ = 0,1,2) and radiation lifetime and quenching measurements[END_REF] , making these species highly recommended for temperature profile determination in flames.

OH LIF spectra were obtained by using a tunable excitation wavelength in the A-X (0-0) band from 309 to 312 nm and by collecting the fluorescence signal in the (0-0) band in the spectral range 305-308 nm corresponding to the R bands. The anti-Stokes collection scheme was necessary to minimize potential spectral interferences with the intense fluorescence of polycyclic aromatic hydrocarbons (PAHs) above 300 nm [START_REF] Mercier | Dimers of polycyclic aromatic hydrocarbons: the missing pieces in the soot formation process[END_REF] . Except the selected fluorescence spectral range, the whole collection system (optics and detectors) was identical to the one used for the NO LIF experiments. Again, based on previous works on OH LIF thermometry [START_REF] Rensberger | Laser-induced fluorescence determination of temperatures in low pressure flames[END_REF][START_REF] Kohse-Höinghaus | Laser techniques for the quantitative detection of reactive intermediates in combustion systems[END_REF][START_REF] Mercier | NO reburning study based on species quantification obtained by coupling LIF and cavity ring-down spectroscopy[END_REF][START_REF] Goldman | Intracavity laser absorption spectroscopy of sooting acetylene/air flames[END_REF] , no quenching variations were considered here. Measurements were obtained promptly after the laser pulse to minimize the effect of quantum yield variations with rotational levels as recommended in the literature, showing that in this case, rotational level-dependences of radiative and quenching rates almost canceled and the error became negligible. The uncertainty reported in the present paper (~160 K at 1750K) corresponds the estimated errors between the fit of the experimental and simulated spectrum [START_REF] Luque | LIFBASE: Database and Spectral Simulation Program (Version 1.5)[END_REF] .

The spectrometer was wavelength-calibrated using the spectral lines of a mercury pen lamp.

Flame temperature simulations

Numerical simulations were performed in order to predict the flame temperature by using a detailed kinetic mechanism for hydrocarbon oxidation and pyrolysis, able to model several premixed and diffusion flames at atmospheric pressure [START_REF] De Falco | Experimental and numerical study of soot formation and evolution in coflow laminar partially premixed flames[END_REF][START_REF] D'anna | A model of particle nucleation in premixed ethylene flames[END_REF][START_REF] Sirignano | Modeling Formation and Oxidation of Soot in Nonpremixed Flames[END_REF][START_REF] Sirignano | Detailed modeling of size distribution functions and hydrogen content in combustion-formed particles[END_REF][START_REF] Sirignano | Experimental and numerical study of a hybrid solar-combustor system for energy efficiency increasing[END_REF] . In the mechanism, benzene formation is a controlling step for PAHs and particle growth and it was modeled considering both propargyl recombination and the C4 route. PAHs formation was modeled by both the hydrogen abstraction acetylene addition (HACA) and the resonantly stabilized free radical (RSFR) mechanisms. The molecular growth of PAHs was followed punctually up to pyrene. The kinetic gas-phase mechanism, as described, consists of 460 reactions involving 120 species.

Particle formation was approached with a multi sectional scheme which considers large molecules, clusters i.e., single particles and aggregates. For each class of particles, a discretization on carbon and hydrogen atoms (31 and 5 sections respectively) and both stable and radical form were considered. All the steps for particle growth and oxidation, including size and temperature dependent coagulation and oxidation induced fragmentation were considered. Extensive details and validation of the model can be found in previous papers [START_REF] D'anna | A model of particle nucleation in premixed ethylene flames[END_REF][START_REF] Sirignano | Detailed modeling of size distribution functions and hydrogen content in combustion-formed particles[END_REF][START_REF] Sirignano | Modeling Formation and Oxidation of Soot in Nonpremixed Flames[END_REF] .

Computations were carried out in a domain that takes into account the geometry of the burner channels.

A typical grid size in the flame region being 0.1 mm radial by 0.5 mm axial was used. Finer grids did not appreciably change the results. All the species equations were solved simultaneously at each spatial location in turn by a modified Newton-Raphson scheme. Velocity and enthalpy employed a tridiagonal matrix form of solution. For a converged solution, the mean absolute residual for a species, normalized by the species maximum value, was typically of the order of 10 -7 , and overall carbon element mass balance error was less than 0.05%. Binary diffusion coefficients of species in nitrogen were used and the gas viscosity was approximated as that for nitrogen at every temperature. Diffusivities of the sectional species were obtained from Stokes friction with Cunningham correction factors based on the Knudsen number. Thermophoretic flux was applied to all the sections. The enthalpies of the sectional species were made the same per unit mass as that for pyrene.

The energy equation was fully solved and temperature was calculated. Radiative transfer was modeled by the discrete transfer method. Radiation heat losses are strongly influenced by the absorption coefficients of all the species. The absorption constant was therefore set to a value previously found for soot species and kept constant in this paper [START_REF] De Falco | Experimental and numerical study of soot formation and evolution in coflow laminar partially premixed flames[END_REF][START_REF] Sirignano | Experimental and numerical study of a hybrid solar-combustor system for energy efficiency increasing[END_REF] . In this particular flame, the amount of soot particles formed (peak and integrated value) was not as high as in other hydrocarbon flames hence the impact of radiation is less important.

Thermocouple measurements

In this work, 4 different type S thermocouples (TC S.A., Pt-Pt/10%Rh) were used (0.20, 0.35, 0.42, 0.50 mm wire diameter given by the manufacturer and 0.62, 1.01, 1.15, 1.27 mm bead diameter measured with a 5 m sensitivity micrometer). These small sized twin bore ceramic probes (the round bead insulation being composed of recrystallized alumina rated to 1700 °C) have been sheathed with Alsint tubes so as to limit conduction issues. To further limit conduction losses, the thermocouples were chosen to have wire length-to-diameter ratio higher than 300 [START_REF] Bradley | Measurement of High Gas Temperatures with Fine Wire Thermocouples[END_REF] . No specific surface treatment was applied to keep the diameter of the junction bead to the minimum size and to minimize the flame perturbation and detection delay.

The thermocouples were inserted radially into the centerline of the flame at different HABs thanks to a motorized remote-controlled system allowing the automatic and reproducible insertion. The difference of electric potential was followed in real time. The thermocouple insertion and permanence in the flame parameters, displayed in table 1, were experimentally adjusted to minimize the flame perturbation during insertion by operating a Labview code specifically written for these experiments.

Angular speed (rpm) 60

Time step (ms) 2

Acquisition time (s) 90

Table 1: Thermocouple fast insertion parameters

Results and Discussion

The extrapolation method correction is based on the principle that the radiation losses are dependent on the emitting surface and therefore, the thinner the thermocouple the lower the radiative losses. By using thermocouples with different diameters d, the flame temperature corrected from the radiation loss can then be deduced from the extrapolation measurements at d=0, as T 0 = T(d → 0) where T is measured at the same position with different thermocouples and d is a typical thermocouple size parameter as discussed below [START_REF] Bradley | Measurement of High Gas Temperatures with Fine Wire Thermocouples[END_REF][START_REF] Daniels | Measurement of Gas Temperature and the Radiation Compensating Thermocouple[END_REF][START_REF] Nichols | On the Temperature of the Acetylene Flame[END_REF] . In addition, the raw temperature measured by each thermocouple is affected by the exposition time to the flame environment T = T(t) and the presence of soot at the insertion point potentially changes the thermal properties of the thermocouple [START_REF] Mcenally | Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples[END_REF][START_REF] De Falco | Exploring Soot Particle Concentration and Emissivity by Transient Thermocouples Measurements in Laminar Partially Premixed Coflow Flames[END_REF] . All the corrections required to retrieve the flame temperature are discussed case by case in the following sections.

Transient regime

Figure 2 shows the time evolution of the recorded temperature T(t) during the insertion of the 0.20 mm thermocouple in the centerline of the flame at 15, 40, 70, 90 and 100 mm HAB, which correspond to very different chemical environments. Below 40 mm HAB, no soot is detected by LII [START_REF] Mercier | Dimers of polycyclic aromatic hydrocarbons: the missing pieces in the soot formation process[END_REF] . In this case, a fast increase of the measured temperature is observed, corresponding to the transient response time of the thermocouple [START_REF] Mcenally | Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples[END_REF] (estimated to be less than 2s in our case), followed by a stable plateau when thermal equilibrium is reached for T(t→∞), defined as when temperature temporal gradient is less than 0.03 K/s. A very similar behavior is observed above 90 mm HAB. Although in this flame region a strong LII signal was detected, the mature and partially oxidized soot does not deposit on the thermocouple surface that remains pristine during the entire data acquisition process [START_REF] De Falco | The evolution of soot particles in premixed and diffusion flames by thermophoretic particle densitometry[END_REF][START_REF] De Falco | Exploring Soot Particle Concentration and Emissivity by Transient Thermocouples Measurements in Laminar Partially Premixed Coflow Flames[END_REF] .

Fig. 2. T(t)

recorded by the 0.20 mm S-type thermocouple at 15, 40, 70, 90 and 100 mm HAB.

Young soot correction

By contrast, in the flame region located between 55-80 mm HAB, soot and high mass hydrocarbons coexist as a high temperature aerosol [START_REF] Mercier | Dimers of polycyclic aromatic hydrocarbons: the missing pieces in the soot formation process[END_REF] and are sufficiently reactive to quickly deposit on the thermocouple surface. This is reflected in the rapid and continuous decrease of T(t) as the deposit builds up. This well-known issue, leading to the underestimation of the flame temperature measured in sooting flames in addition to the radiation losses, has been described by Mc Enally et al. [START_REF] Mcenally | Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples[END_REF] , who notably showed that the errors in rapid insertion gas temperature measurements due to soot deposition depend linearly on the soot volume fraction and more strongly on the gas temperature. From our observations, the soot impact on temperature measurements with thermocouples appears also strongly correlated with its degree of maturity. Deposit of nascent soot emerging in the region 55-80 mm HAB are clearly present onto the thermocouple surface thus affecting temperature measurements. On the contrary mature soot formed upstream in the flame (above 80 mm) -as detected by optical techniquesdoes not remain on the thermocouple. Nascent particles, which are characterized by highest H/C ratio and aliphatic branching than mature soot [START_REF] Kholghy | The core-shell internal nanostructure of soot -A criterion to model soot maturity[END_REF][START_REF] Öktem | Chemical species associated with the early stage of soot growth in a laminar premixed ethylene-oxygen-argon flame[END_REF] making these particles potentially stickier than carbonized and rigid mature soot. Oxidation of soot directly onto the thermocouple in higher regions of the flame, potentially even faster than oxidation occurring in gas phase, can also be responsible for these phenomena. Similar conclusions, were made by De Falco et al. [START_REF] De Falco | Exploring Soot Particle Concentration and Emissivity by Transient Thermocouples Measurements in Laminar Partially Premixed Coflow Flames[END_REF] , who correlated the degree of maturity with the emissivity of the deposit on the thermocouple junction and estimated the soot oxidation onto thermocouple junction.

Mc Enally et al. [START_REF] Mcenally | Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples[END_REF] estimated the error on gas temperature due to soot deposition by extrapolating the gas temperature back to the insertion time. It is to be noted that this method has been validated for relatively mild soot deposition corresponding to soot volume fractions lower than 50 ppm, which is far above the soot mole fraction expected in our flame (less than 300 ppb) [START_REF] Tian | High spatial resolution laser cavity extinction and laser-induced incandescence in low-soot-producing flames[END_REF][START_REF] Tian | Soot measurement in diluted methane diffusion flames by multi-pass extinction and laser-induced incandescence[END_REF] . As illustrated in the inset of fig. 2 for 70 mm HAB, this procedure was also used here to determine the corrected temperature from the soot deposit on the thermocouples in the 55-80 mm HAB range.

Radiative losses

The extrapolation method to correct for the radiative losses was applied to selected HABs at which the soot deposition rate on the thermocouples was verified to be negligible. This point was attested by the fast reaching of a stable temperature plateau as discussed above. T(t→∞, d) was then measured as a function of a characteristic dimension of the junction d. The obtained data for different wire diameters at different HABs in the flame are reported in fig. 3. The wire diameter of the thermocouple was used as the independent variable rather than the bead diameter characterizing the thermocouple junction as sometimes found in the literature. Indeed, bead size correlations tend to be valid for approximately spherical beads much larger than the wire diameter [START_REF] Pitts | Temperature Uncertainties for Bare-Bead and Aspirated Thermocouple Measurements in Fire Environments[END_REF][START_REF] Hayhurst | Heat and mass transfer considerations in the use of electrically heated thermocouples of iridium versus an iridiumrhodium alloy in atmospheric pressure flames[END_REF] . In case of a small bead size relative to the wire diameter as in this work, the wires are rapidly heated by thermal conduction so that the presence of the bead is only a minor perturbation of the local temperature measurement at the junction, and the junction temperature is controlled primarily by heat transfer to the adjacent wires rather than to the junction [START_REF] Hayhurst | Heat and mass transfer considerations in the use of electrically heated thermocouples of iridium versus an iridiumrhodium alloy in atmospheric pressure flames[END_REF] .

Although higher degree polynomial functions are sometimes used [START_REF] Daniels | Measurement of Gas Temperature and the Radiation Compensating Thermocouple[END_REF][START_REF] Nichols | On the Temperature of the Acetylene Flame[END_REF]25 , in this work, linear regressions are found to be the best fitting functions for T(t→∞, d) [START_REF] Hindasageri | Thermocouple error correction for measuring the flame temperature with determination of emissivity and heat transfer coefficient[END_REF][START_REF] Lemaire | Assessment of radiation correction methods for bare bead thermocouples in a combustion environment[END_REF][START_REF] Walker | Thermocouple errors in forest fire research[END_REF] . In fact, at every HAB, T(t→∞, d) increases as the wire diameter decreases, consistently with the reduction of the impact of radiative heat losses on the temperature measurement. The reasons for this behavior are not clear yet, however we note that polynomial functions are often used when an important dispersion of the experimental data is found or in case of long acquisition times to reach a stable reading are needed, potentially indicating additional effects other than radiation losses not considered in the analysis of the data.

Data and correlations reported in Fig. 3 enable to define the calibration curve of each thermocouple, relating the measured raw temperatures to the corrected flame temperature T 0 from the radiation heat loss.

Hence, from the linear extrapolations of the raw temperatures reported in fig. 3 to zero wire diameter, it is possible to determine the value of the temperatures T 0 corresponding to the flame temperature values without radiation for each HAB and for each thermocouple.

Validation of the extrapolation method for flame studies

In order to setup the protocol for the determination of the temperature profiles in sooting flames, analysis of measurements in sooting flame region is reported. Figure 4 shows that, in the absence of soot deposition on the thermocouple surface, the measured temperature at thermal equilibrium corrected for radiation losses

T 0 = T(t→∞, d → 0) is linearly correlated (R 2 >0
.97 ) to the raw output of each thermocouple over the whole range of the flame temperatures.

T(t∞)/ K T 0 / K 12
To finalize the validation of the extrapolation method for flame studies, the raw temperature profile of the flame along the vertical central axis was measured with the thinnest thermocouple (0.2 mm). This thermocouple was preferentially used to limit the impact of the radiative losses and flame perturbation and to maximize the spatial resolution of the measurements.

As discussed above, due to the high deposition rate of soot in the region 55-80 mm HAB, the thermocouples do not reach thermal equilibrium at these HABs. In order to find out the "soot-free" value of the raw temperatures in this case, the procedure proposed by McEnally et al. [START_REF] Mcenally | Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples[END_REF] discussed above was applied.

To give an estimation of the correction provided by the use of the McEnally's method, we report in fig. 4 for the region 55-80 mm HAB the peak temperature values quickly reached after the thermocouple insertion in the flame (corresponding to the peak value around 1s for the case illustrated in the inset of fig. 2). Hence the raw temperature profile reported in fig. 5 correspond to the T(t→∞) temperatures, excepted in the zone 55-80 mm where we reported the measured quickly reached peak temperature values.

The final corrected temperature profile obtained by using to the calibration curve reported in fig. 4 is compared in fig. 5 to the temperature profiles obtained by OH and NO LIF thermometry and to the calculated profile. Uncertainties are estimated in the order of ±50 K for the temperature measurements using the 0.2 mm wire thermocouple over the temperature range from 1100 to 1800K. As shown in fig. 5, the corrected temperature profile T 0 , the LIF thermometry data and the calculated temperature profile are in excellent agreement, therefore validating the use of the extrapolation method for the temperature profile determination corrected from the radiation losses.

Consistently to the theory of radiation losses, the raw thermocouple output clearly appears below the corrected data, the difference gradually increasing with the temperature. The ditch in the raw thermocouple output at 55-80 mm HAB due to the soot deposition on the thermocouple surface almost completely disappears after application of McEnally's correction. The difference between raw and corrected temperature is found in the order of 10-50K depending on the HAB, consistently with the values reported by McEnally in their original work [START_REF] Mcenally | Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples[END_REF] . Taking into account the weak correction allows to get a final perfect match of the experimental data with the reference temperature profiles. However, even in the sooting part of the flame, the dominant bias on the temperature measurement which appears very well corrected by our proposed methodology, clearly remains the radiation losses that lead to underestimations of the temperature in the order of 200K.

Radial profiles were also investigated to test the method with higher temperature gradients. To this aim we determined the radial temperature profiles for two different HABs in the sooting region of the flame and applied the same methodology as described above to obtain the corrected temperature profiles from both radiation losses et soot deposition. The results of these measurements and corresponding simulated temperature profiles are shown in fig. 6. As can be seen, the comparison between the experimental and simulated profiles still highlights a very good agreement. Notably the experimental and simulated peak temperature obtained for each HAB shows an excellent concordance while the shape of the experimental profiles are well reproduced by the simulation.

Our measurements highlight that the spatial resolution of the thermocouple method appears adequate for the determination of temperature profiles with gradients around 500K/mm. Moreover, it can be seen that the experimental measurements might even provide a better description of the radial temperature profile than the model at some locations, enabling for instance to reveal the slight curved shape of the profile between 0 and 2 mm at 70 mm HAB not captured by the model. Finally, a slight drift of the simulated profiles regarded to the experimental one is systematically observed at the edge of the flame for both HABs. These slight discrepancies are likely related to the choice of boundary conditions applied to the model, particularly the heat exchange between the tip of the burner and the flame itself (actually neglected).

Hence, this work demonstrates the capability of this thermocouple method to easily access to accurate temperature measurements in harsh environments characterized by high temperature gradients. The reported work clearly highlights that the impact of the radiation losses appears to be very well corrected by the extrapolation method which allows a fast and accurate determination of the temperature profile all along the flame height including in presence of soot.

Currently, the technique has been demonstrated to be a valuable and simple alternative method for the determination of accurate temperature for the specific case of laminar and potentially sooting flames. We did not check the validity of the method for more complex environments as turbulent flames. One of the main limitation in that context concerns the transient time required by the thermocouple to reach its peak temperature value. Depending on this value, temperature evolutions of turbulent systems might or not be capture by the thermocouple. In our case, the transient time was estimated around 1 s which is definitely too slow to allow the capture of turbulent events. However, Ren et al [START_REF] Ren | Temperature measurement of a turbulent buoyant ethylene diffusion flame using a dual-thermocouple technique[END_REF] succeed to record to record temperature evolutions resolving very short timescales in a turbulent ethylene flame with much thinner thermocouples as we used, letting hope that our methodology implemented with thermocouple characterized by thinner diameter and faster transient times might be envisaged for turbulent applications.

Conclusions

This work reports the implementation and the validation of the extrapolation method for thermocouple temperature measurements corrected from the radiation losses in sooting flames. All the measurements were carried out in a laminar diffusion sooting flame of methane. The method relies on the proportionality of the radiation losses to the size of the thermocouple and thus the flame temperature can be obtained by extrapolation to zero diameter. In this work, the measured raw temperature is shown to be linearly correlated to the wire diameter of the thermocouples. By applying this procedure for selected HABs characterized by different flame temperatures, it is therefore possible to build calibration curves for selected thermocouples that relate the raw measured temperature to the flame temperature corrected from the radiation losses. This linearity has at least one important practical consequence, as in principle only two thermocouples having different diameters are needed for a reliable flame temperature measurement, and could therefore help the development of fast and cheap sensors for either laboratory or large-scale applications.

In terms of accuracy, since the thermocouples located in the sooting region of the flame did not reach thermal equilibrium due to the high soot deposition rate, a specific procedure proposed in the literature [START_REF] Mcenally | Soot volume fraction and temperature measurements in laminar nonpremixed flames using thermocouples[END_REF] had to be applied to determine the "soot-free" value of the raw temperatures. This correction has been found here to be in the order of 10-50K, while the impact of radiative losses has been determined to be as high as to 200K. Finally, the comparison of the determined profile by the extrapolation method with reference temperature profiles obtained by LIF thermometry and numerical simulation show excellent agreements.

These results overall demonstrate that the extrapolation method is an efficient and fast method to determine temperature profiles in flames with high accuracy, even in presence of soot particles. The use of this method, allowing the very fast calibration of thermocouples, appears very simple to implement in comparison to the electrical compensation method or the complex estimation of the radiation loss of the thermocouple.

This proposed methodology could be advantageously used for temperature measurements either for laboratory flames studies or potentially more hostile environments where the radiation losses estimations are quite complex to determine.

Fig. 1

 1 Fig.1 Determination of the temperature by LIF NO (left panel) and LIF OH (right panel) for different HABs.

Fig. 3 .

 3 Fig.3. T(t→∞, d) recorded for each of the 4 thermocouples at 15, 20, 25, 30 and 35 mm HAB and linear fit with extrapolation to obtain the temperature at zero wire diameter T 0 = T(t→∞, d → 0).

Fig. 4 :

 4 Fig.4: Linear fit (calibration) of the measured temperature T(t→∞) against the corrected temperature T 0 in the flame regions characterized by the absence of soot interference with the measurements(15, 20, 25, 30, 35 and 100 mm HAB).

Fig. 4

 4 Fig.4also shows that the radiation losses increase as the flame temperature increases (the thicker the thermocouple, the lower the measured raw temperature), leading to underestimations as high as 200K for a flame temperature in the order of 1600K. These values are in good agreement with previous temperature determinations relying on physical models for the estimation of the thermocouple radiation losses14,15,40 .

Fig. 5 :

 5 Fig. 5: Temperature profiles determined in the methane diffusion flame along the vertical central axis using the thermocouple methodology and compared with the calculated profile and OH / NO LIF thermometry.

Fig. 6 :

 6 Fig. 6: Radial temperature profiles determined in the sooting region of the flame for two different HABs using the thermocouple methodology and compared with the calculated profiles

Acknowledgements

This work was supported by the Agence Nationale de la Recherche through the LABEX CAPPA (ANR-11-LABX-0005), the Région Hauts-de-France, the Ministère de l'Enseignement Supérieur et de la Recherche (CPER Climibio) and the European Fund for Regional Economic Development.