N2-broadening coefficients of CH3CN rovibrational lines and their temperature dependence for the Earth and Titan atmospheres

Icarus 256 (2015) 30–36

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N2-broadening coefficients of CH3CN rovibrational lines and their temperature dependence for the Earth and Titan atmospheres A.S. Dudaryonok a,b,c,⇑, N.N. Lavrentieva b,c, J.V. Buldyreva a a

Institute UTINAM, UMR CNRS 6213, University of Franche-Comte, 16 Gray Road, 25030 Besancon cedex, France V.E. Zuev Institute of Atmospheric Optics, Siberian Branch of the Russian Academy of Sciences, 1 Akademishian Zuev square, 634021 Tomsk, Russia c National Research Tomsk State University, 36 Lenina Avenue, 634050 Tomsk, Russia b

a r t i c l e

i n f o

Article history: Received 4 January 2015 Revised 9 April 2015 Accepted 14 April 2015 Available online 18 April 2015 Keywords: Earth Titan, atmosphere Spectroscopy

a b s t r a c t Theoretical nitrogen-broadening coefficients and their temperature exponents for methyl cyanide lines in parallel (DK = 0) bands are calculated by a semi-empirical approach suitable for CH3X-type absorbers with large dipole moments. Together with the standard four-parameter correction factor determined from fitting on experimental line widths for each fixed K and requiring an extrapolation for higher K inaccessible experimentally, a new form accounting explicitly for the K-dependence and reducing the number of required parameters is proposed and successfully tested. Extensive (0 6 J 6 70, 0 6 K 6 20) R- and P-line lists are provided for the Earth and Titan atmosphere temperature ranges, which could be useful for atmospheric/astrophysical applications and spectroscopic databases. Ó 2015 Elsevier Inc. All rights reserved.

1. Introduction Methyl cyanide (acetonitrile) CH3CN, produced by biomass burning and industrial processes (Singh et al., 2003; Li et al., 2003), is known as one of long-living pollutants in the Earth’s atmosphere. A precise knowledge of its spectroscopic parameters (line positions, intensities, pressure-induced widths and shifts as well as their temperature dependence) constitutes therefore an important condition for reliable atmosphere monitoring, radiative transfer modeling and climate evolution simulations. In addition, these parameters are of interest for astrophysical applications since this molecule has been also detected in interstellar medium (Remijan et al., 2005), in comets (Remijan et al., 2006) and in planetary atmospheres, namely in that of Saturn and its moon Titan (Lara et al., 1996; Bezard et al., 1993). One of the key parameters for atmospheric studies is the pressure-induced isolated-line width, whose value is influenced by the collision partner and the temperature of the medium. In a previous work (Dudaryonok et al., 2015) we applied the theoretical semi-empirical (SE) method (Bykov et al., 2004) to obtain extensive lists of CH3CN self-broadening coefficients and their temperaturedependence parameters (temperature exponents) for parallel-band lines with wide ranges of rotational quantum numbers (0 6 J 6 70, ⇑ Corresponding author at: Institute UTINAM, UMR CNRS 6213, University of Franche-Comte, 16 Gray Road, 25030 Besancon cedex, France. Fax: +7 3 822492086. E-mail address: [email protected] (A.S. Dudaryonok). http://dx.doi.org/10.1016/j.icarus.2015.04.025 0019-1035/Ó 2015 Elsevier Inc. All rights reserved.

0 6 K 6 20) requested by spectroscopic databases. In the present work we focus our attention on the CH3CN line broadening by nitrogen pressure. This buffer gas is of prime importance for both Earth and Titan atmospheres due to its very high abundances (78.1% and 98.4%, respectively), while only scare values for one band are listed in the HITRAN database for the air-broadened CH3CN line widths and a constant value is adopted for the temperature exponents. To get CH3CN-N2 line-broadening coefficients we use the same SE approach. Indeed, for the polyatomic active molecule CH3CN even interacting with the diatom N2, the standard intermolecular potential model (electrostatic plus pairwise atom–atom interactions) employed in semi-classical formalisms contains many terms whereas the values of the atom–atom parameters and the hypothesis of the additivity of the atom–atom contributions itself are questionable. In these circumstances it seems reasonable to make use of few empirically adjustable parameters in the semi-classical expressions (the key idea of the SE method), as it has already been successfully done for massive computations of collisional line widths for similar polyatomic molecular systems CH3Cl–CH3Cl (Dudaryonok et al., 2013), CH3Cl–CO2 (Dudaryonok et al., 2014) and CH3CN–CH3CN (Dudaryonok et al., 2015). Most reported in the literatures studies of CH3CN-N2 line widths referred to the pure rotational absorption band (Srivastava et al., 1973; Derozier and Rohart, 1990; Fabian et al., 1998; Colmont et al., 2006). The early work (Srivastava et al., 1973) communicated only the experimental width of the rotational line JK = 20 10 at room temperature. Two rotational transitions JK = 52 42 and

31

A.S. Dudaryonok et al. / Icarus 256 (2015) 30–36 Table 1 SE-model fitting parameters (for K-independent correction factor) deduced from experimental values of N2-broadening coefficients of R-branch CH3CN lines (Rinsland et al., 2008). K

c1

c2

c3

c4

0 1 2 3 4 5 6 7 8 9 10

0.436(19) 0.410(18) 0.390(14) 0.370(11) 0.352(12) 0.335(13) 0.319(12) 0.311(14) 0.292(23) 0.279(19) 0.266(19)

0.060(3) 0.072(4) 0.081(4) 0.090(3) 0.098(5) 0.108(6) 0.119(6) 0.130(5) 0.141(5) 0.149(6) 0.160(6)

0.0010(1) 0.0025(2) 0.0040(1) 0.0055(1) 0.0070(2) 0.0085(2) 0.0100(1) 0.0115(2) 0.0130(3) 0.0145(2) 0.0160(2)

8(2) 9(2) 10(1) 11(1) 12(2) 13(2) 14(1) 15(2) 16(2) 17(1) 18(2)

53 43 at 150–300 K were investigated in the paper (Derozier and Rohart, 1990) from both experimental and theoretical [Anderson– Tsao–Curnutte theory (Anderson, 1949; Tsao and Curnutte, 1961)] points of view, providing the reference-temperature line widths and the associated temperature exponents. Room-temperature broadening coefficients for two other groups of lines J = 6 5, 5 4 (with all possible K-values) were measured by Fabian et al. (1998). Colmont et al. (2006) extracted the experimental K-dependence of collisional line widths for the rotational transition J = 12 11 at 303 K and employed Birnbaum (Birnbaum, 1967) and Robert–Bonamy (Robert and Bonamy, 1979) formalisms to get its theoretical estimate; their analysis of the K = 3 component in the temperature range 235–340 K yielded additionally the temperature exponent value. The most complete from the viewpoint of CH3CN-N2 line-broadening parameters is the work of (Rinsland et al., 2008) dedicated to the (parallel) m4 band: the authors reported experimental results for over 700 mid-infrared transitions (J 6 48, K 6 10) in both P- and R-branches. These experimental data appear as the most appropriate for fitting the SE model parameters and are used in our study. The remainder of the paper is organized as follows. The main features of the semi-empirical method and details of its application to the case of N2-broadened CH3CN lines are resumed in the next section. The room-temperature line widths and their temperature exponents for the temperature ranges of Earth and Titan atmospheres are presented and discussed in Section 3. The concluding section summarizes the main results of the present work.

Table 2 RMS-deviations (cm1 atm1) of SE broadening coefficients calculated with the K-dependent correction factor from experimental data (Rinsland et al., 2008). K

R-branch

P-branch

0 1 2 3 4 5 6 7 8 9 10

0.0028 0.0042 0.0021 0.0016 0.0021 0.0021 0.0029 0.0029 0.0043 0.0046 0.0065

0.0036 0.0035 0.0016 0.0017 0.0015 0.0012 0.0019 0.0016 0.0030 0.0018 0.0059

transitions (including electrostatic, induction, dispersion and orientation interactions). Since the efficiency functions (determined in particular by the interaction potential) have no well established analytical forms, they are modeled as products of the analytical Anderson–Tsao–Curnutte functions PATC ðxjj0 Þ and the empirical corl rection factors C l ðxjj0 Þ:

Pl ðxjj0 Þ ¼ PATC ðxjj0 ÞC l ðxjj0 Þ: l

ð2Þ

The choice of explicit mathematical expression for the correction factor depends on the features of the experimentally observed J- and K-line width dependences (i.e. on the considered molecular system). For example, H2O line widths are very well modeled by a simple two-parameter correction factor (Bykov et al., 2004; Lavrentieva et al., 2008) whereas the CH3Cl case requires a more general four-parameter form (Dudaryonok et al., 2013). The parameters’ values are determined from fits of a few calculated line widths to the corresponding experimental results. Numerical analyses for different molecular systems [see, e.g. Bykov et al. (2004) and other abovementioned references to the SE-method applications] show that the correction factor introduces only a small (less than 5%) correction to the efficiency functions of the Anderson– Tsao–Curnutte theory. 2.2. Choice of the correction factor and determination of the fitting parameters

2. Theoretical background and details of calculations

To keep the analogy with our previous SE-computations for the CH3CN self-broadening case1 (Dudaryonok et al., 2015), we first employed the identical four-parameter form for the correction factor assumed to be the same for both dipole and quadrupole transitions

2.1. Semi-empirical method

C l ðxjj0 Þ ¼

According to the SE method (Bykov et al., 2004), the halfwidth

cif associated with the radiative transition i ? f and calculated up to the second-order term in the perturbation expansion of the scattering matrix is defined by

cif ¼

Z 1 X nX qðrÞ tFðtÞb20 ðt; r; i; f Þdt þ D2 ðii0 jlÞPl ðxii0 Þ c r 0 i0 l X 2 0 þ D ðff jlÞPl ðxff 0 Þ;

ð1Þ

f 0l

where n and q(r) are the density and r-level rotational populations of the perturbing molecules, F(t) is the Maxwell–Boltzmann distribution over relative molecular velocities t, b0(t, r, i, f) is the cut-off 0 parameter, Dðjj jlÞ is the reduced matrix element and Pl ðxjj0 Þ is the ‘‘efficiency function’’ corresponding to the scattering channel j j0 in the active molecule for the dipole (l = 1), quadrupole (l = 2), etc.

c2

c 1 pffiffiffi1    J j þ 1 c 3 J j  c4 2 þ 1

ð3Þ

and fitted the model parameters c1–c4 on measured R-branch line widths (Rinsland et al., 2008) for each experimentally accessible K-value (the data for the R-branch are more complete and our previous study of the self-broadening case show that the parameters c1–c4 are not branch-sensitive). The bulk of SE parameters with their uncertainties obtained for K 6 10 is collected in Table 1. Uncertainties of parameters c1–c4 were determined from the fit to experimental data. Because of the smooth K-dependences of experimental line widths, these c1–c4 parameters vary relatively slowly with increasing K. Therefore, as the next step we attempted to incorporate the K-dependence in the correction factor of Eq. (3) and to reduce the total number of parameters. 1 The molecular parameters and multipole moments used in calculations are those of Dudaryonok et al. (2015) for methyl cyanide and those of Reuter et al. (1986) and Harries (1979) for nitrogen.

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A.S. Dudaryonok et al. / Icarus 256 (2015) 30–36

Table 3 Example of SE-calculated N2-broadening coefficients c (in cm1 atm1) of methyl cyanide QR-branch lines for K = 0, 5 and J 6 35 at the reference temperature of 296 K and corresponding temperature exponents N for the Earth’s and Titan’s temperature intervals. The quoted uncertainties correspond to one standard deviation. J

K

c(296)

%u

NEarth

NTitan

J

K

c(296)

%u

NEarth

NTitan

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0.1748 0.1765 0.1779 0.1787 0.1787 0.1784 0.1775 0.1761 0.1744 0.1724 0.1702 0.1679 0.1655 0.1631 0.1607 0.1583 0.1559 0.1536 0.1514 0.1493 0.1473 0.1454 0.1435 0.1418 0.1401 0.1385 0.1369 0.1354 0.1340 0.1325 0.1311 0.1299 0.1288 0.1279

0.5 2.8 3.4 0.4 1.7 2.8 2.2 0.3 0.2 0.1 0.1 1.8 1.2 1.2 3.7 1.9 1.9 1.3 0.7 0.2 2.7 3.4 3.5 1.4 0.7 0.4 0.1 0.1 0.6 2.3 3.8 0.8 0.8 1.6

0.838(1) 0.839(1) 0.836(1) 0.828(1) 0.815(2) 0.800(3) 0.783(4) 0.764(4) 0.746(5) 0.728(6) 0.710(6) 0.694(6) 0.678(7) 0.664(7) 0.651(6) 0.639(6) 0.628(6) 0.619(6) 0.611(6) 0.604(5) 0.600(5) 0.596(4) 0.593(3) 0.592(3) 0.591(2) 0.592(1) 0.592(1) 0.593(1) 0.594(1) 0.595(2) 0.595(2) 0.596(3) 0.599(3) 0.605(4)

0.844(1) 0.840(1) 0.828(4) 0.809(7) 0.786(9) 0.76(1) 0.73(1) 0.71(1) 0.69(2) 0.67(2) 0.65(2) 0.63(2) 0.61(2) 0.60(1) 0.59(1) 0.58(1) 0.57(1) 0.570(9) 0.567(7) 0.568(5) 0.571(3) 0.576(1) 0.583(3) 0.591(5) 0.601(8) 0.61(1) 0.63(1) 0.64(2) 0.65(2) 0.66(2) 0.67(2) 0.67(2) 0.68(2) 0.69(2)

34 35 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

0 0 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

0.1271 0.1264 0.1537 0.1568 0.1592 0.1608 0.1616 0.1616 0.1607 0.1590 0.1570 0.1549 0.1528 0.1507 0.1487 0.1467 0.1449 0.1430 0.1413 0.1397 0.1381 0.1365 0.1351 0.1336 0.1323 0.1309 0.1296 0.1284 0.1272 0.1262 0.1254 0.1247 0.1240

0.1 3.2 1.2 2.3 2.3 0.9 0.2 0.2 1.4 1.0 0.4 0.6 0.2 0.6 0.4 0.1 0.2 1.4 0.9 0.7 0.6 2.0 2.3 3.1 1.4 1.8 1.0 0.1 0.2 0.3 1.1 0.6 1.3

0.611(5) 0.617(5) 0.806(2) 0.790(3) 0.772(4) 0.753(5) 0.734(5) 0.716(6) 0.699(6) 0.684(6) 0.669(6) 0.657(6) 0.644(6) 0.634(6) 0.624(6) 0.616(6) 0.609(5) 0.604(4) 0.600(4) 0.597(3) 0.596(3) 0.594(2) 0.594(1) 0.595(1) 0.595(1) 0.596(1) 0.596(2) 0.596(2) 0.597(3) 0.600(3) 0.606(4) 0.612(4) 0.618(5)

0.70(2) 0.70(2) 0.77(1) 0.75(1) 0.72(1) 0.70(2) 0.67(2) 0.65(2) 0.64(2) 0.62(2) 0.61(1) 0.60(1) 0.59(1) 0.58(1) 0.575(9) 0.572(7) 0.572(5) 0.575(2) 0.579(1) 0.586(3) 0.594(6) 0.603(9) 0.61(1) 0.63(2) 0.64(2) 0.65(2) 0.66(2) 0.67(3) 0.67(3) 0.68(3) 0.69(3) 0.70(3) 0.70(3)

Notes: % u values are the uncertainties of the adjacent broadening coefficients in percent.

Namely, each SE parameter ck (k = 1, 2, 3, 4) was assumed to be a linear function of K:

ck ¼ c0k þ c1k K:

ð4Þ

To test the validity of such modeling we adjusted the eight new parameters on experimental R-branch data (Rinsland et al., 2008) for K = 1 and K = 7 only (c01 ¼ 0:4265, c11 ¼ 0:0165, c02 ¼ 0:06, c12 ¼ 0:01, c03 ¼ 0:001, c13 ¼ 0:0015, c04 ¼ 8, c14 ¼ 1) and compared the recalculated halfwidths with the previous theoretical values for all experimentally available K (K = 0–10). Typically, the differences were less than 0.3%, whereas the number of parameters was reduced from 44 to 8. With this new K-dependent correction factor we also evaluated the root-mean-square (RMS) deviations of new theoretical results from experimental values (Rinsland et al., 2008) in both R- and P-branches (Table 2). Except for the K = 0 case, the deviations for the P-branch are even smaller than the deviations for the R-branch which was used for fitting. It means that similar to the self-broadening case the SE parameters deduced from R-branch values can be safely used to calculate the P-branch ones. We kept this 8-parameter correction factor for further massive computations of CH3CN-N2 line broadening coefficients. 2.3. Temperature dependence of line widths An analysis of variables entering the right-hand side of Eq. (1) shows that the temperature dependence of line broadening comes mainly from the first term: n / T1, t / T1/2, q / exp(Erot/kT), etc. Since the standard expression for the temperature dependence of the collisional halfwidth



cðTÞ ¼ c T ref

   T N T ref

ð5Þ

is valid for limited temperature ranges (about 100 K around the reference temperature Tref = 296 K) and since the SE parameters are generally temperature-independent [see Dudaryonok et al. (2015) and references cited therein], we performed SE-calculations of line widths for two sets of temperatures: 250, 280, 310, 340 K for the terrestrial atmosphere [characterized by the temperature range 200–310 K (Keckhut et al., 2012)] and 90, 130, 170 K for Titan’s atmosphere [featured by the interval 94–170 K (Fulchignoni et al., 2005)]. After that, by the use of Eq. (5) we extracted two associated sets of temperature exponents N and their uncertainties deduced from linear least-squares fits. 3. Results and discussion 3.1. N2-broadening coefficients at room temperature N2-broadening coefficients of methyl cyanide QP- and QR-branch lines calculated for the reference temperature 296 K and the rotational quantum numbers 0 6 J 6 70, K 6 20 are collected in Supplementary material. Examples for QR-lines with K = 0, 5 and J 6 35 can be found in Table 3. Uncertainties of line widths were determined from uncertainties of fitting parameters. The J- and K-dependences of QR-branch broadening coefficients are visualized in Fig. 1 (upper and lower panels, respectively). The main features of calculated curves (decreasing of broadening with increasing J, position of J-dependence maxima, initially slow and

33

A.S. Dudaryonok et al. / Icarus 256 (2015) 30–36

3.2. Temperature exponents The bulk of SE temperature exponents deduced for the Earth and Titan temperature ranges is given in Supplementary material. The results obtained for the QR-lines are additionally plotted in Fig. 4 as functions of the rotational quantum number J for fixed K-values. From the experimental point of view, only few measurements are available from the rotational-band studies (Derozier and 2

The uncertainties of SE values are shown for P-branch only. Higher SE P-branch results but with larger R–P differences have already been obtained for small J and K values in the case of CH3CN self-broadening (Dudaryonok et al., 2015). 3

0.19

K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 K=10

0.17

-1

Broadening coefficient, cm atm

-1

0.18

0.16 0.15 0.14

K=11 K=12 K=13 K=14 K=15 K=16 K=17 K=18 K=19 K=20

0.13 0.12 0.11 0.10

0

10

20

30

40

50

60

70

J J=3 J=6 J=11 J=16 J=21 J=26 J=31 J=40 J=50 J=60 J=70

0.19

-1

0.18 0.17

-1

Broadening coefficient, cm atm

then rapid decrease of line width with growing K) are very similar to those of air-broadened lines of another strongly polar symmetric top CH3Cl, and the theoretical interpretations given for the latter (Buldyreva, 2013) apply to the former. It can be stated from Fig. 1 that for high J-values the K-dependence become very weak; the apparent slight increase of broadening between J  60 and J  70 (upper panel) has not however been verified experimentally. We have calculated the broadening using Eq. (1) without empirical correction factors, in this case the ‘‘slight increase’’ of the broadening at high J takes the place as well. Comparisons between SE-calculated QR broadening coefficients and experimental data reported for the pure rotational (Fabian et al., 1998; Colmont et al., 2006) and the m4 (Rinsland et al., 2008) bands can be seen in Fig. 2 for K = 1–10 (the case K = 0 is analyzed in detail below). We underline that for the sake of coherence only the rotational-band data obtained with Voigt profile are retained. Moreover, the theoretical values obtained by Colmont et al. (2006) for J = 11 with the use of Birnbaum and Robert– Bonamy formalisms are shown for completeness. In general, the semi-empirical results provide smooth rotational dependences well consistent with the observations, as expected from the SE-parameters fits, and predict nearly constant values for very high J not accessed experimentally. With respect to the theoretical data of Colmont et al. (2006), our calculations eliminate the line-broadening overestimation for K 6 7 and keep a very good agreement with measurements for all probed K. Because of a very limited number of measurements in the rotational band no definite conclusion can be drawn on the vibrational dependence of CH3CN-N2 line widths. It seems nevertheless that the most recent experimental points of Colmont et al. (2006) argue in favor of its negligible character. Fig. 3 plotted for K = 0 gives an example of detailed analysis of CH3CN-N2 line broadening in the QR- and QP-branches.2 In the upper part of this figure the semi-empirical broadening coefficients computed separately for P- and R-lines are compared to the corresponding experimental data of the m4 (Rinsland et al., 2008). For the simultaneous representation of results for both branches the broadening coefficients are put as functions of the absolute value of the quantum number m (m = J + 1 for the R-branch and m = J for the P-branch). Our computations show slightly higher values for the P-branch lines3 at very small J but this difference can be hardly considered as meaningful given the fitting aspect of our theoretical approach and the use of R-branch-adjusted parameters for both branches. For |m| greater than 7 the SE curves are strictly identical for P-and R-lines, perfectly verifying the well-known empirical relation cP(J, K)  cR(J  1, K). As a result, the branchdependence of CH3CN-N2 line-broadening coefficients can be considered as negligible and the theoretical values computed for the R-branch lines can be easily and safely used for the P-branch lines just by replacing J with J + 1. The absence of any systematic deviation in the (cR – cP) differences (shown at the bottom of Fig. 3) for both calculations and measurements corroborates this conclusion.

0.16 0.15 0.14 0.13 0.12 0.11 0.10 0

2

4

6

8

10

12

14

16

18

20

K Fig. 1. Semi-empirically calculated room-temperature N2-broadening coefficients of CH3CN QR-branch lines as functions of the rotational quantum numbers J (upper panel) and K (lower panel). On the lower panel, for the sake of clarity, only some typical values of J are selected.

Rohart, 1990; Colmont et al., 2006); the same authors report the corresponding theoretical estimates obtained with the Anderson– Tsao–Curnutte and Robert–Bonamy formalisms, respectively. The measurements of (Derozier and Rohart, 1990) for K = 2, 3 are lower than the SE-values but the one-standard-deviation uncertainties given by these authors and shown in the figure might be underestimated. The most recent experimental datum of Colmont et al. (2006) for K = 3 confirms our calculation for the terrestrial atmosphere temperatures. As for the previous semi-classical calculations, the results obtained in both works (Derozier and Rohart, 1990; Colmont et al., 2006) are much farther from the measurements than our semi-empirical values. Looking at the behavior of the SE-curves, it can be stated that, similar to the CH3CN selfbroadening case (Dudaryonok et al., 2015), the fits on different temperature intervals lead to different temperature exponents, so that the use of an appropriate N-set appears to be crucial for reliable modeling of temperature-dependent CH3CN line-broadening. Moreover, the K-dependence is most pronounced for J around 20 whereas it is practically negligible for small J and J > 25. The qualitative theoretical interpretation of J-dependences of temperature exponents has been already given in Buldyreva (2013) for CH3Cl perturbed by air, and it remains valid for CN3CN-N2. It is just noteworthy that the different temperature intervals used to extract the N-values influence in a different manner the collision strength (i.e. the positive or negative kinetic term contributing to N) and the resonance effects between the active and perturbing molecules (i.e. the negative resonance contribution to N), so that the

34

A.S. Dudaryonok et al. / Icarus 256 (2015) 30–36 0.19

0.19

K =1

0.18

-1

0.15

-1

-1

Expt 2008 (v 4 )

0.17

0.16

γ, cm atm

-1

0.17

γ, cm atm

K =2

0.18

0.14

0.15 0.14

0.13

0.13

0.12

0.12

0.11

Expt 2006 (rot) Expt 1998 (rot) Calc. 2006 (B) Calc. 2006 (RB) Calc. SE

0.16

0.11

0

10

20

30

40

50

60

70

0

10

20

30

J 0.19

-1 -1

γ, cm atm

-1 -1

γ, cm atm

0.16 0.15 0.14

0.13

0.13

0.12

0.12 0.11

0

10

20

30

40

50

60

70

0

10

20

30

40

J 0.19

K =5

0.18

-1 -1

0.15

γ, cm atm

-1 -1

γ, cm atm

0.16

0.14

0.13

0.13

0.12

0.12

0.11

0.11

0

10

20

30

40

50

60

70

0

10

20

30

J

-1

0.16

-1

0.15

γ, cm atm

-1 -1

γ, cm atm

70

0.17

0.14

0.14

0.13

0.13

0.12

0.12

0.11

0.11

0

10

20

30

40

50

60

70

0

10

20

J

30

40

50

60

70

J

0.19

0.19

K =9

0.18

K =10

0.18

0.17 -1

0.17

0.16

γ, cm atm

0.15

-1

-1

60

K =8

0.18

0.17

-1

50

0.19

K=7

0.18

γ, cm atm

40

J

0.19

0.15

70

0.17

0.14

0.16

60

K =6

0.18

0.17

0.15

50

J

0.19

0.16

70

0.17

0.14

0.11

60

K =4

0.18

0.17

0.15

50

0.19

K =3

0.18

0.16

40

J

0.14

0.16 0.15 0.14

0.13

0.13

0.12

0.12

0.11

0.11

0

10

20

30

40

J

50

60

70

0

10

20

30

40

50

60

70

J

Fig. 2. Comparison of semi-empirical room-temperature CH3CN-N2 QR line-broadening coefficients with the measurements in the m4 (Rinsland et al., 2008) and the rotational (Fabian et al., 1998; Colmont et al., 2006) bands; calculations with the Birnbaum (B) and Robert–Bonamy (RB) formalisms previously reported by Colmont et al. (2006) are also shown.

A.S. Dudaryonok et al. / Icarus 256 (2015) 30–36 0.20

0.16

-1

Broadening coefficient, cm atm

-1

K=0

0.12

0.08

P-branch Expt 2008 (v4)

0.04

R-branch Expt 2008 (v4)

Calc. SE

Differences: Expt 2008 (v4)

Calc. SE

35

N-minima positions and details of evolution with increasing J differ for the Earth and Titan sets. As a final test of our temperature exponents, we employed Eq. (5) to calculate the CH3CN-N2 broadening coefficient for the line JK = 123 113 studied experimentally and theoretically by Colmont et al. (2006) at 236, 273, 303 and 347 K. The comparison is shown in Fig. 5. It can be seen that the semi-classical calculations of the authors systematically overestimate the line broadening whereas our SE values reproduce quite well the temperature dependence observed experimentally.

Calc. SE

4. Conclusions and perspectives 0.00 0

10

20

30

40

50

60

70

ImI Fig. 3. Analysis of branch-dependence for CH3CN-N2 line-broadening coefficients: SE values computed for QP- and QR-lines (solid curves) are practically identical, in agreement with the experimental data of Rinsland et al. (2008) in the m4 band (full circles and full triangles, respectively). The differences between R- and P-values are explicitly shown at the bottom of the figure for both computations and measurements.

0.90

250-340 K

Temperature exponent

0.85 0.80 0.75

K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 K=10

K=11 K=12 K=13 K=14 K=15 K=16 K=17 K=18 K=19 K=20

90-170 K K=0 K=1 K=2 K=3 K=4 K=5 K=6 K=7 K=8 K=9 K=10

0.70 0.65 0.60 0.55

Expt 2006 (rot): K=3 Expt 1990 (rot): K=2,3

Calc. 2006 (RB): K=3 Calc. 1990 (A): K=2,3

K=11 K=12 K=13 K=14 K=15 K=16 K=17 K=18 K=19 K=20

0.50 0

10

20

30

40

50

60

70

J Fig. 4. ‘‘Earth’’ and ‘‘Titan’’ sets of SE-calculated temperature-dependence exponents for nitrogen-broadened methyl cyanide lines as functions of rotational quantum number J for 0 6 K 6 20 and values of Derozier and Rohart (1990) and Colmont et al. (2006).

0.22

Expt 2006 (rot) Calc. 2006 (RB) Calc. SE

-1

Broadening coefficient, cm atm

-1

0.21 0.20 0.19 0.18

The present work completes the previously reported QP- and QRline lists for CH3CN self-broadening coefficients and associated temperature exponents determined separately for the temperature ranges of Earth and Titan atmospheres. Besides the standard choice of the semi-empirical correction factor with a parametric dependence on K (which requires an extrapolation procedure to get the model parameters sets for high K-values non available experimentally), the nitrogen-broadening line widths and their temperature dependences are obtained, in addition, with a new form of the SE correction factor which contains explicitly the K-dependence and enables computations for any K with the set of only eight adjusted model parameters. These eight parameters deduced from room-temperature experimental data for K = 1 and 7 in the parallel m4 band ensure reliable reproducing of all measured line widths for the other experimentally probed K. Moreover, the predicted broadening coefficients are very close to recent room-temperature measurements in the pure rotational band, which means that the vibrational dependence of CH3CN-N2 line widths is rather negligible. The temperature exponents extracted from SE-computations assuming the temperature-independence of the fitting parameters are found to be in a very reasonable agreement with rotationalband experimental data. In addition, they yield a correct prediction of the temperature-dependent rotational 123 113-line widths in the range 236–347 K. This latter fact argues in favor of the validity of our temperature exponents for the Earth atmosphere. For the low temperatures characteristic of Titan atmosphere, no measurements are currently available, so that our NTitan values should be considered as possible estimates. Acknowledgments A.S.D. and N.N.L. thank the University of Franche-Comte for financial support of their stay in Besancon as post-doctoral fellow and Invited Professor. This work has been also supported by RAS Program ‘‘Fundamental Optical Spectroscopy and Its Applications’’ and by the LIA SAMIA (Laboratoire International Associé ‘‘Spectroscopie d’Absorption de Molécules d’Intérêt Atmosphérique et planétologique: de l’innovation instrumentale à la modélisation globale et aux bases de données’’).

0.17

Appendix A. Supplementary material

0.16

Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.icarus.2015.04. 025.

0.15 0.14 240

260

280

300

320

340

References

Temperature, K Fig. 5. Semi-empirical N2-broadening coefficients calculated for the CH3CN transition J = 12 11, K = 3 in the temperature interval 236–347 K in comparison with the experimental and theoretical values of (Colmont et al., 2006).

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