ExoMol molecular line lists -- XXXVII: spectra of acetylene
MMNRAS , 1–16 (0000) Preprint 15 January 2020 Compiled using MNRAS L A TEX style file v3.0
ExoMol molecular line lists - XXXVII: spectra of acetylene
Katy L. Chubb, , (cid:63) Jonathan Tennyson, † Sergey N. Yurchenko ‡ Department of Physics and Astronomy, University College London, London, WC1E 6BT, UK SRON Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA, Utrecht, Netherlands
15 January 2020
ABSTRACT
A new ro-vibrational line list for the ground electronic state of the main isotopologueof acetylene, C H , is computed as part of the ExoMol project. The aCeTY line listcovers the transition wavenumbers up to 10 000 cm − ( λ > µ m), with lower andupper energy levels up to 12 000 cm − and 22 000 cm − considered, respectively. Thecalculations are performed up to a maximum value for the vibrational angular momen-tum, K max = L max = 16, and maximum rotational angular momentum, J = 99. Highervalues of J were not within the specified wavenumber window. The aCeTY line list isconsidered to be complete up to 2200 K, making it suitable for use in characterisinghigh-temperature exoplanet or cool stellar atmospheres. Einstein-A coefficients, whichcan directly be used to calculate intensities at a particular temperature, are computedfor 4.3 billion (4 347 381 911) transitions between 5 million (5 160 803) energy levels.We make comparisons against other available data for C H , and demonstrate thisto be the most complete line list available. The line list is available in electronic formfrom the online CDS and ExoMol databases. Key words: C H - acetylene - line list - exoplanet - atmosphere - ExoMol In its electronic ground state, acetylene, HCCH, is a lin-ear tetratomic unsaturated hydrocarbon whose spectra isimportant in a large range of environments. On Earth,these range from the hot, monitoring of oxy-acetylene flameswhich are widely used for welding and related activities(Gaydon 2012; Schmidt et al. 2010), to the temperate, mon-itoring of acetylene in breath, giving insights into the na-ture of exhaled smoke (Mets¨al¨a et al. 2010), vehicle exhausts(Schmidt et al. 2010), and other air-born pollutants (Hughes& Gorden 1959). Acetylene is also important in the produc-tion of synthetic diamonds using carbon-rich plasma (Kellyet al. 2012).Further out in our solar system, acetylene is found inthe atmospheres of cold gas giants Saturn (Moses et al.2000; de Graauw et al. 1997), Uranus (Encrenaz et al. 1986)and Jupiter (Ridgway 1974; Drossart et al. 1986), the hy-drothermal plumes of Enceladus (Waite et al. 2006; Milleret al. 2014), and in the remarkably early-earth-like atmo-sphere of Titan (H¨orst 2017; Oremland & Voytek 2008;Singh et al. 2016; Dinelli et al. 2019), where there has evenbeen some speculation as to acetylene’s role in potential non- (cid:63)
E-mail: [email protected], [email protected] † E-mail: [email protected] ‡ E-mail: [email protected] earth-like life (McKay & Smith 2005; Lovett 2011; Orem-land & Voytek 2008; Belay & Daniels 1987; Bains 2004;Seager et al. 2013) and reactions involving molecules ofpre-biotic interest (H¨orst 2017; Lovett 2011; Oremland &Voytek 2008). It has been detected on comets such as Hyako-take (Brooke et al. 1996), Halley, and 67P/Churyumov-Gerasimenko (Le Roy et al. 2015). Even further into thegalactic neighbourhood, acetylene appears in star formingregions (Ridgway et al. 1976; van Dishoeck et al. 1998;Rangwala et al. 2018), is speculated to be an importantconstituent of clouds in the upper atmospheres of browndwarfs and exoplanets (Tennyson & Yurchenko 2017, 2016;Bilger et al. 2013; Madhusudhan et al. 2016; Oppenheimeret al. 2013; Shabram et al. 2011), and is thought to playan important role in dust formation (Dhanoa & Rawlings2014) and AGB star evolution and atmospheric composi-tion (Jørgensen et al. 2000; Cernicharo 2004; Gautschy-Loidlet al. 2004; Loidl et al. 1999; Aringer et al. 2009), provid-ing a major source of opacity in cool carbon stars (Rinslandet al. 1982; Gautschy-Loidl et al. 2004). For example, C H was detected in the carbon star Y CVn by Goebel et al.(1978) and in the low-mass young stellar object IRS 46 byLahuis et al. (2005). The first analysis of the atmosphereof a “super-Earth” exoplanet, 55 Cancri e by Tsiaras et al.(2016), speculates that acetylene could be present in its at-mosphere; however the spectral data available at the timedid not allow for an accurate verification of its presence c (cid:13) a r X i v : . [ a s t r o - ph . S R ] J a n Katy L. Chubb et al. in such a high temperature environment. A similar conclu-sion was found for the “hot Jupiter” extrasolar planet HD189733b (de Kok et al. 2014) and for carbon-rich stars inthe Large Magellanic Cloud (Matsuura et al. 2006; Lederer,M. T. & Aringer, B. 2009; Marigo, P. & Aringer, B. 2009).The infra-red spectrum of acetylene has been well stud-ied in the lab, see Amyay et al. (2016); Lyulin & Campargue(2017) for example; a complete, up to 2017, compilation oflaboratory studies can be found in Chubb et al. (2018c).More recent studies include those of Lyulin & Campargue(2018); Cassady et al. (2018); Lyulin et al. (2019, 2018).At the temperatures of many exoplanets and cool stars(up to around 3000 – 4000 K (Tanaka et al. 2007; Gaudi et al.2017)), molecules are expected in abundance (Tsuji 1986).An essential component in the analysis of such astrophys-ical atmospheres is therefore accurate and comprehensivespectroscopic data for all molecules of astrophysical impor-tance, for a variety of pressures and temperatures. While alarge amount of highly accurate data have been determinedexperimentally for a number of such molecules, they havelargely been measured at room-temperature and are thusnot well suited to the modelling of high-temperature en-vironments; theoretical data are required for this purpose.The ExoMol project (Tennyson & Yurchenko 2012; Ten-nyson et al. 2016) was set up for this reason, to producea database of computed line lists appropriate for modellingexoplanet, brown dwarf or cool stellar atmospheres. As aresult, high quality variational line lists which are appro-priate up to high temperatures have been computed for ahost of molecules as part of the ExoMol project, includ-ing CH (Yurchenko & Tennyson 2014; Yurchenko et al.2014, 2017b), HCN/HNC (Barber et al. 2014), NH (Coleset al. 2019), PH (Sousa-Silva et al. 2015), H O (Al-Refaieet al. 2016), SO (Underwood et al. 2016a), H S (Azzamet al. 2016), SO (Underwood et al. 2016b), VO (McKem-mish et al. 2016), CO (Zak et al. 2017), SiH (Owens et al.2017), H O (Polyansky et al. 2017), C H (Mant et al. 2018),and, as presented in this work, C H (see also Chubb et al.(2018b)). Other molecular spectroscopic databases includeHITRAN (Rothman et al. 2010a), HITEMP (Rothman et al.2010b), CDMS (Endres et al. 2016), GEISA (Jacquinet-Husson et al. 2016), TheoReTS (Rey et al. 2016), SPEC-TRA (Mikhailenko et al. 2005), PNNL (Sharpe et al. 2004),MeCaSDA and ECaSDa (Ba et al. 2013); however none ofthese provide line lists for hot acetylene. The ASD-1000database of Lyulin & Perevalov (2017) provides data onacetylene transitions which is designed to be valid for tem-peratures up to 1000 K; we compare with this database be-low. Acetylene is a four-atomic (tetratomic) molecule whichis linear in its equilibrium configuration. The rotation-vibration spectrum of a polyatomic molecule of this size,at the temperatures of exoplanets and cool stars, typicallyspans the infra-red region of the electromagnetic spectrum.In this region, only transitions between rotation-vibration(ro-vibrational) levels are important; electronic transitionsare of too high energy to be of interest. Such ro-vibrationalcalculations essentially require a solution to the nuclear-motion Schr¨odinger equation, with some approximations re-quired to enable feasible computational treatment. The chal-lenge with acetylene comes with its linear geometry at equi-librium structure; linear molecules require special consid- eration for calculations of ro-vibrational energies. This wasdemonstrated by Watson (1968) and very recently by Chubbet al. (2018b); these two approaches differ in their choice ofinternal coordinates used to represent the vibrational Hamil-tonian.This paper is structured as follows. In Section 2 weoutline the details of the calculations used to produce theaCeTY line list. This Section includes details on the basisset in Section 2.1, the potential energy surface (PES) in Sec-tion 2.2, the refinement of this surface to empirical energylevels in Section 2.3, empirical band centre replacement inSection 2.4, and details of the dipole moment surface (DMS)and its subsequent scaling in Sections 2.5 and 2.6, respec-tively. The results of the line list calculations are given inSection 3, with comparisons of the resulting spectra madeagainst previous works in Section 4. In Section 5, we demon-strate the differences in applying different line list data toexoplanet atmosphere modelling. We give our summary inSection 6. The (3 N −
5) model for treating a four-atomic linearmolecule such as HCCH has been fully implemented in thevariational nuclear motion program
TROVE (TheoreticalROVibrational Energies) (Yurchenko et al. 2007; Yachmenev& Yurchenko 2015; Yurchenko et al. 2017a), as detailed inChubb et al. (2018b). Here, we outline only the main cal-culation steps towards computing the extensive aCeTY ro-vibrational line list for C H in its ground electronic state. The polyad number used to control the size of the primitiveand contracted basis sets is given by: P = 2 n + n + n + n + n + n + n ≤ P max . (1)Here, the vibrational quantum numbers follows the TROVE basis set selection, with n corresponding to the excitation ofthe C–C stretching mode, n and n representing the C–H and C–H stretching modes and n , n , n and n represent-ing the bending modes (see Table 1). This local mode nota-tion deviates from the standard normal mode quantum num-bers used for C H , most notedly for the bending modes:the TROVE bending quantum umbers n , n , n , n rep-resent excitations along the ∆ x , ∆ y , ∆ x , ∆ y , while thecorresponding normal mode quantum numbers correspondto symmetric ( υ ) and asymmetric ( υ
5) modes as well as tothe corresponding vibrational angular momenta ( (cid:96) and (cid:96) ),see Table 1 and also Section 3.For a linear molecule such as HCCH, another condi-tion has been introduced in TROVE to control the basisset size; a maximum value for the total vibrational angu-lar momentum, L max , which is equal to the z -projectionof the rotational angular momentum, K max . This is linkedto the total number of bending mode quanta (i.e. n bend = n + n + n + n ) in each vibrational band. Therefore wehave a condition that: L max = K max ≤ n bend(max) , (2)which is linked to the polyad number of Eq. (1). The aCeTY MNRAS000
5) modes as well as tothe corresponding vibrational angular momenta ( (cid:96) and (cid:96) ),see Table 1 and also Section 3.For a linear molecule such as HCCH, another condi-tion has been introduced in TROVE to control the basisset size; a maximum value for the total vibrational angu-lar momentum, L max , which is equal to the z -projectionof the rotational angular momentum, K max . This is linkedto the total number of bending mode quanta (i.e. n bend = n + n + n + n ) in each vibrational band. Therefore wehave a condition that: L max = K max ≤ n bend(max) , (2)which is linked to the polyad number of Eq. (1). The aCeTY MNRAS000 , 1–16 (0000) xoMol line lists - XXXVII: C H Table 1.
Quantum numbers used to classify the energy states ofacetylene, C H .Label DescriptionConventional (normal mode) quantum numbers υ CH symmetric stretch (Σ + g ) υ CC symmetric stretch (Σ + g ) υ CH antisymmetric stretch (Σ + u ) υ Symmetric (trans) bend (Π g ) (cid:96) Vibrational angular momentum associated with υ υ Antisymmetric (cis) bend (Π u ) (cid:96) Vibrational angular momentum associated with υ L = | l | Total vibrational angular momentum, | (cid:96) + (cid:96) | K = | k | Rotational quantum number; z -projection of J J QN associated with rotational angular momentum, J . e/f Rotationless parity of the ro-vibrational state ortho / para Nuclear spin state, see Chubb et al. (2018a)
TROVE local mode quantum numbers n CC symmetric stretch n CH stretch n CH stretch n x bend n y bend n x bend n y bend L = | l | Total vibrational angular momentum L = K Γ str Symmetry of the vibrational component ( D n h , n = 34) K = | k | Rotational quantum number; z -projection of J Γ rot Symmetry of the rotational component ( D n h , n = 34) J QN associated with rotational angular momentum, J .Γ tot Symmetry of the rotational component ( D n h , n = 34) line list is relatively small in comparison to other polyatomicmolecules of this size, largely due to the fact that the K = L condition limits the number of allowed rotational sub-states in a vibrational band. As vibrational states go upquickly in energy with increasing n bend , their energy willalso rise quickly with increasing values of L . We thereforedo not expect high values of L to contribute until muchhigher energies. TROVE uses a multi-step contraction scheme. At step1, the stretching primitive basis functions φ n ( ξ ), φ n ( ξ )and φ n ( ξ ) are generated using the Numerov-Cooley ap-proach (Yurchenko et al. 2007; Noumerov 1924; Cooley1961) as eigenfunctions of the corresponding 1D reducedstretching Hamiltonian operators ˆ H (1D) i , obtained by freez-ing all other degrees of freedom at their equilibrium val-ues in the J = 0 Hamiltonian. For the bending basis func-tions, φ n ( ξ ) , . . . , φ n ( ξ ), 1D harmonic oscillators are used.These seven 1D basis sets are then combined into three sub-groups φ (1D) n ( ξ ) = φ n ( ξ ) , (3) φ (2D) n n ( ξ , ξ ) = φ n ( ξ ) φ n ( ξ ) , (4) φ (4D) n n n n ( ξ , ξ , ξ , ξ ) = φ n ( ξ ) φ n ( ξ ) φ n ( ξ ) φ n ( ξ ) (5)and used to solve eigenvalue problems for the three corre-sponding reduced Hamiltonian operators: stretching ˆ H (1D) and ˆ H (2D) , and bending ˆ H (4D) . The reduced Hamiltonians ˆ H ( N D) ( N = 1 , ,
4) are constructed by averaging the to-tal vibrational Hamiltonian operator ˆ H ( J =0) over the otherground vibrational basis functions (Chubb et al. 2018a,b).The eigenfunctions of the three reduced problems ψ (1D) λ , ψ (2D) λ and ψ (4D) λ are contracted and classified according withthe D n h (M) symmetry using the symmetrisation procedureby Yurchenko et al. (2017a) to form a symmetry-adapted 7Dvibrational basis set as a product ψ (1D) λ ψ (2D) λ ψ (4D) λ . At step2, the ( J = 0) eigenproblem is solved using this contractedbasis. The eigenfunctions of the latter are then contractedagain and used to form the symmetry-adapted ro-vibrationalbasis set, together with the spherical harmonics representingthe rotational part.For the current work, the polyad number in Eq. (1) waschosen as P max =18 for the primitive basis set and reduced to16 after the 1st contraction. Energy cutoffs of 60 000 cm − ,50 000 cm − and 22 000 cm − were used for the primitive,contracted and ( J = 0)-contracted basis functions, respec-tively. The ro-vibrational basis set was formed using theenergy cutoff of 22 000 cm − . The energies computed usingthese cutoff values are better converged than those of the ab initio room-temperature line list of Chubb et al. (2018b).The vibrational and rotational states are classified with the D n h representations ( n = 34) and the projections of thevibrational and rotational angular momenta, L and K , re-spectively, with the constraint K = L . The maximum valuefor the total vibrational angular momentum, K max = L max ,used to build the multidimensional basis sets, see Eq. (2),is 16. The ro-vibrational states can only span the four ir-reducible representations of D ; A g , A g , A u and A u .For the vibrational basis set used ( L max = 16), the symme-try group D is equivalent to D ∞ h . The following selectionrules apply to the electric dipole transitions of C H : J (cid:48) + J (cid:48)(cid:48) > J (cid:48) ↔ J (cid:48)(cid:48) ± , (6) A g ↔ A u and A g ↔ A u . (7)The corresponding nuclear statistical weights g ns are 1 and3 for the A g , A u and A g , A u pairs of states, respectively.The kinetic energy and potential energy expansions are trun-cated at 2 nd and 8 th order, respectively (the kinetic energyterms of higher than 2 nd order appear to contribute very lit-tle to the calculated ro-vibrational energies, with expansionto higher orders becoming more computationally demand-ing). The equilibrium bond lengths are set to 1.20498127 ˚Aand 1.06295428 ˚A for the C-C and C-H bonds, respectively.Nuclear masses were used. Calculations were performed upto a high value of J = 99, which was determined by themaximum values of lower and upper energies used in theline list calculations; these have an effect on the tempera-ture dependence of the line list, as discussed in Section 3. TROVE represents all components of the Hamiltonian op-erator using a Taylor expansion about the equilibrium struc-ture in terms of the linearised coordinates ξ λ , λ = 1 . . . V ( ξ ), is represented in terms of user-chosen curvi-linear coordinates; TROVE uses a quadruple-precision nu-
MNRAS , 1–16 (0000)
Katy L. Chubb et al. merical finite difference method to re-expand V ( ξ ) in termsof the TROVE -coordinates ξ = { ξ λ } . As detailed in Chubbet al. (2018b), the TROVE linearised coordinates for C H are selected as ξ = ∆ R lin , ξ = ∆ r lin1 , ξ = ∆ r lin2 ,ξ = ∆ x , ξ = ∆ y , ξ = ∆ x , ξ = ∆ y . where R lin , r lin1 and r lin2 are based on the curvilinear, bond-length coordinates R ≡ r CC , r ≡ r CH and r ≡ r CH ; x , y , x and y are Cartesian coordinates of the hydrogenatoms along the x and y axes. The displacements are takenfrom the equilibrium values of R , r and r , respectively.The equilibrium values (at the linear configuration) of x i and y i ( i = 1 ,
2) are zero.Here we use the potential energy function of C H re-ported recently by Chubb et al. (2018b). It is represented interms of the linelarised coordinates as follows: V ( χ ) = (cid:88) i,j,k,... f i,j,k,... χ i χ j χ k . . . , (8)where χ λ are given by: χ = 1 − exp (cid:16) − a ∆ R lin (cid:17) , (9) χ = 1 − exp (cid:16) − b ∆ r lin1 (cid:17) ,χ = 1 − exp (cid:16) − b ∆ r lin2 (cid:17) ,χ = ∆ x ,χ = ∆ y ,χ = ∆ x ,χ = ∆ y . Here a and b are two Morse parameters.The ab initio PES of Chubb et al. (2018b) was com-puted using MOLPRO (Werner et al. 2012) at the VQZ-F12/CCSD(T)-F12c level of theory (Peterson et al. 2008) ona grid of 66 000 points spanning the 6D nuclear-geometrycoordinate space up to 50 000 cm − . A least squares fit wasused to determine the coefficients f i,j,k,... in Eq. (8) to the ab initio energies, using a grid of 46 986 ab initio pointscovering up to 14 000 cm − , with a weighted root-mean-square ( rms ) error of 3.98 cm − and an un-weighted rms of 15.65 cm − , using 358 symmetrised parameters expandedup to 8 th order.To improve the accuracy of the variational calculations,here we refine the ab initio PES of C H by fitting the ex-pansion potential parameters f i,j,k,... to experimental data,as outlined below. The refinement procedure is carried out under the assump-tion that the ab initio
PES can be used to initially determinea set of energy levels and eigenfunctions. In this case, a cor-rection is added to the ab initio
PES in terms of a set ofinternal coordinates ξ (Yurchenko et al. 2011a):∆ V = (cid:88) ijk... ∆ f ijk... χ i χ j χ k . . . , (10)where ∆ f ijk... are the refined parameters, given as cor-rection terms to the expansion coefficients of the original PES in Eq. (8), with the symmetry of the molecule takeninto account in the same way as for the original ab initio PES. The eigenfunctions of the “unperturbed”, ab initio
Hamiltonian are used as basis functions when solving thenew ro-vibrational eigenproblems with the correction ∆ V to the PES included. This process is performed iterativelyin TROVE , with the fitting procedure making use of em-pirical energy levels which should be added in gradually, ac-cording to the level of confidence placed in them. For detailsof the
TROVE refinement procedure the reader is referredto Yurchenko et al. (2011a).Highly accurate experimentally determined data pro-vide an essential component in the calculation of a high-quality line list, for both effective Hamiltonian and the ma-jority of variational approaches. Fortunately for C H ,a wealth of experimental ro-vibrational spectral data hasbeen recorded over the decades (see, for example, Lyulin& Campargue (2017); Amyay et al. (2016); Herman (2007);Didriche & Herman (2010); Herman (2011)). Chubb et al.(2018c) gathered, collated and analysed all such experimen-tal data from the literature for C H . They used the Marvel (measured active vibration-rotation energy level)procedure (Furtenbacher et al. 2007) to provide a set ofempirically-derived energy levels. We use these
Marvel en-ergies for the PES refinement procedure, with level weightedaccording to the level of confidence in their experimental as-signment. The ab initio energies which were used to fit theinitial PES (see above) are also included in the refinementprocedure in order to constrain the shape of the refined PESto the ab initio
PES (see Yurchenko et al. (2003)).Good quantum numbers for acetylene states are the ro-tational angular momentum quantum number J and overallsymmetry Γ. These are therefore the primary criteria used tomatch energy levels from the energy levels in the supplemen-tary data of Chubb et al. (2018c) to those computed using TROVE . An important parameter in the
Marvel energylevel output of Chubb et al. (2018c) is NumTrans, whichgives the number of transitions linking a particular state toother energy levels. The higher the number of linking tran-sitions, the higher the confidence which should be given tothat empirical energy level. States with NumTrans=1 weredeemed unreliable and were therefore not included into thefit. A few states with NumTrans=2 and large residuals werealso omitted. The fact that vibrational states which includesome quanta of C-H stretch are more likely to be observedin experiment than those without was used to inform ourjudgement when matching theoretical
TROVE energy levelswith their experimentally determined counterpart. Table 2 isa summary of the fit, for which only experimental energieswith J ≤ rms errors between the exper-imental ( Marvel ) and calculated (refined) ro-vibrationalenergies are shown for a set of vibrational bands in the col-umn rms-I. The full Table is included as part of the supple-mentary information to this work. The vibrational quantumnumbers used for labelling the states of C H in Table 2are detailed in Table 1 together with the rotational quantumnumbers used typically (see Chubb et al. (2018c)).The refined potential energy function is available as sup-plementary data to this article and from exomol.com . MNRAS000
TROVE energy levelswith their experimentally determined counterpart. Table 2 isa summary of the fit, for which only experimental energieswith J ≤ rms errors between the exper-imental ( Marvel ) and calculated (refined) ro-vibrationalenergies are shown for a set of vibrational bands in the col-umn rms-I. The full Table is included as part of the supple-mentary information to this work. The vibrational quantumnumbers used for labelling the states of C H in Table 2are detailed in Table 1 together with the rotational quantumnumbers used typically (see Chubb et al. (2018c)).The refined potential energy function is available as sup-plementary data to this article and from exomol.com . MNRAS000 , 1–16 (0000) xoMol line lists - XXXVII: C H Table 2.
An extract of the Obs.-Calc. residuals for C H . The root-mean-square errors between the experimental and calculated(refined) ro-vibrational energies for different vibrational bands (classified by their symmetry Γ, quantum numbers υ , υ , υ , υ , l , υ , l , k and energy E i /hc ), before (rms-I) and after (rms-II) the band-centre shifts. The full table is given as part of the supplementary informationto this paper. E i /hc is the TROVE energy after the band centre shift.Γ υ υ υ υ l υ l k E i /hc rms-I rms-IIΣ + g g u + g g + u − u u + g g g u u + g g g g u + u g − u + g − g g u + u + g g + u + u − u u + g u u + g g g g u u As mentioned previously,
TROVE uses a double layer con-traction scheme with vibrational basis functions obtained asthe solution of the J = 0 problem. This J = 0-representationhas a more compact vibrational basis set and also facili-tates the matrix elements calculations. Indeed, the vibra-tional part of the ro-vibrational Hamiltonian is diagonal onthis basis with the matrix elements given by the correspond-ing vibrational ( J = 0) band centres E (vib) i . An indirectadvantage of this representation is a direct access to the J = 0 energies used in the consecutive ro-vibrational cal-culations allowing us to empirically modify the band cen-tres (Yurchenko et al. 2011b). This is a necessary proce-dure if the line list is to be used in any high-temperature,high-resolution Doppler-shift studies (see, for example Brogi et al. (2017); de Kok et al. (2014)), where the line posi-tions in a line list need to be as accurate as possible. Inthis work, 128 calculated band-centres were shifted to min-imise the difference with the ro-vibrational Marvel termvalues (Chubb et al. 2018c). Again, we only used
Marvel energies with J ≤ MNRAS , 1–16 (0000)
Katy L. Chubb et al. referenced as EBSC. To improve the accuracy of our linepositions, we “MARVELise” the data: the energy levels inthe ExoMol states file are replaced by the
Marvel ener-gies of Chubb et al. (2018c). The MARVEL uncertaintiesare kept as part of the line list. In doing this we take advan-tage of the ExoMol data format; see Tennyson et al. (2013)for details. It should be noted that the
Marvel analysis wasperformed in 2017, and a periodic update will be undertakenat some point in the future in order to include experimentaldata which has been published since then. We also provideindicative estimates of the uncertainties of all
TROVE en-ergies. This is done using the following approximation. 1)For all states which were replaced with
Marvel energies,we take the associated
Marvel uncertainty. 2) Where wehave applied band centre shifting, we take the root-mean-square error for a particular band, before band shifting (i.e.rms-I in Table 2). 3) For all other bands which have notbeen “MARVELised” or had a band centre shift applied, weuse an approximate method to determine the shift, basedon how the rms-I for each shifted band correlates with thenumber of quanta associated with the C-C stretch ( n in thelocal mode, TROVE notation), the C-H stretches ( n + n )and the bending modes ( n + n + n + n ):0 . n + 0 . n + n ) + 0 . n + n ) + 0 . n + n ) . (11)These uncertainities are then rounded to the nearest inte-ger, with those under 0.5cm − rounded up to 0.5cm − . Westress that the estimation of these uncertainties in this wayis very approximate, and the main aim is to distinguish be-tween those states considered reliable and those states whichshould not be considered reliable when comparing to high-resolution observations. Here we use the ab initio dipole moment surface (DMS) com-puted by Chubb et al. (2018b) with the finite field method inMOLPRO at the CCSD(T)/aug-cc-PVQZ level of theory ona grid of 66 000 points covering energies up to 50 000 cm − .The electric dipole moment components, µ α ( α = x, y, z ),were represented using the same set of seven linearised co-ordinates as for the 3 N − µ x ( ζ ) = (cid:88) i F xi,j,k,... ζ i ζ j ζ k . . . , (12) µ y ( ζ ) = (cid:88) i F yi,j,k,... ζ i ζ j ζ k . . . , (13) µ z ( ζ ) = (cid:88) i F zi,j,k,... ζ i ζ j ζ k . . . . (14)where ζ λ are given by: ζ = ∆ R lin , ζ = ∆ r lin1 , ζ = ∆ r lin2 ,ζ = ∆ x , ζ = ∆ y , ζ = ∆ x , ζ = ∆ y . Use was made of discrete symmetries (see Chubb et al.(2018a)), and the three components of the dipole were ex-panded up to 7 th order and symmetrised according to theoperations of D . The value of n here in D n h is determinedby the order up to which the function (dipole moment or po-tential energy) is expanded. See, for example Chubb (2018).The three Cartesian components of the dipole moment, µ x , µ y , µ z , transform differently to one another ( µ x and µ y as E u and µ z as A u for D nh ( M ) (Bunker & Jensen 2006)): the µ x and µ y components share the corresponding expansionparameters, while that the parameters for the µ z componentare independent. This dipole moment function is provided assupplementary material to this work as a Fortran program. In order to improve the quality of the line intensities, atleast for the vibrational bands known experimentally fromHITRAN, we have applied scalings to the corresponding vi-brational transition dipole moments. This is a new approachimplemented in
TROVE which takes advantage of the J = 0representation of the basis set. Since the rovibrational lineintensities are computed using vibrational matrix elementsof the electronically averaged dipole moment components¯ µ x , ¯ µ y and ¯ µ z , modifying these vibrational moments by ascaling factor specific for a given band will propagate thisscaling to all rotational lines within this band in a consistentmanner. A band scaling factor was obtained as a geometricaverage of n matched individual line intensities within eachvibrational band:¯ S = (cid:34) n (cid:89) i =1 I HITRAN i I TROVE i (cid:35) n , (15)which leads to a √ ¯ S scaling factor on the dipole moment.To this end, we have correlated the HITRAN transition T = 296 K intensities to the corresponding intensities com-puted with TROVE using the methodology described above(after the band centre shifts).Figure 1 shows an example of the dipole scaling pro-cedure applied to the (000110) Σ + u band. The unscaledTROVE (shown in green) intensities are ∼ / √ . z dipolemoment component of the corresponding vibrational matrixelement (cid:104) | µ z | (cid:105) , with the result shown in Fig-ure 1 in blue. We have thus applied scaling factors to 216bands, listed in the supplementary information to this work.Extracts are given in Tables 5–7. The aCeTY line list has been computed using the varia-tional calculations outlined above. Figure 2 illustrates thetemperature-dependence of the acetylene spectra computedusing the aCeTY line list, with cross-sections computed us-ing ExoCross (Yurchenko et al. 2018) at a variety of tem-peratures between 296–2000 K. The cross-sections are cal-culated at a low-resolution of 1 cm − for demonstration pur-poses.The TROVE assignment is based on the largest basisset contribution to the eigenfunction.
TROVE uses the localmode quantum numbers (QNs) to assign vibrational state,collected in Table 1. This selection of the quantum numbersis based on the choice of the vibrational basis set in Eqs. (3–5). There is no direct correlation between the local mode andnormal mode assignment. For an approximation correlation,
MNRAS000
MNRAS000 , 1–16 (0000) xoMol line lists - XXXVII: C H Figure 1.
Comparison of aCeTY (this work) stick spectra, before(green) and after (blue) dipole moment scaling by a factor of0.856, against HITRAN for the vibrational band (000110) Σ + u ofacetylene at T = 296 K. -28 -26 -24 -22 -20 -18 T=2000 K T=1500 K T=1000 K T=500 K T=300K c r o ss s e c t i on s , c m / m o l e c u l e wavenumber, cm -1 wavelength, mm Figure 2.
Variation of aCeTY line list spectra with tempera-ture: low-resolution (1 cm − ) cross-sections computed using Ex-oCross (Yurchenko et al. 2018). The spectrum becomes flatterwith increasing temperature. the following rules apply: υ + υ = n + n , (16) υ = n , (17) υ + υ = n + n + n + n . (18)The number density of a particular molecular state as afraction of the total number density of the molecular speciesis given by the Boltzmann law. The total internal partitionfunction, Q , is a sum over all molecular states, weightingeach by their probability of occupation at a given tempera-ture, and therefore offers an indication of the completenessof a calculated line list at a particular temperature: Q = N (cid:88) i =1 g ns ( i ) (2 J i + 1) exp (cid:18) − c ˜ E i T (cid:19) . (19)Here, c = hck is the second radiative constant, ˜ E i is the en-ergy term value of each i molecular state (relative to theground ro-vibronic state), T is the temperature, g ns ( i ) is thenuclear statistical weight of each i molecular state, and thesum is over all molecular states. The partition function caneasily be computed from the ExoMol states file (Tennyson P a r t i t i on f un c t i on T, K TIPS Irwin x 4 ASD-1000 ExoMol
Figure 3.
The C H partition function up to 3000 K; compar-ing the states from the aCeTY line list (this work) against thatcomputed using TIPS (Gamache et al. 2017), the coefficients of Ir-win (1981), and using energies extracted from ASD-1000 (Lyulin& Perevalov 2017). et al. 2016) using ExoCross (Yurchenko et al. 2018). A com-parison of the partition function for C H computed usingthe aCeTY states file against the partition function com-puted using TIPS (Gamache et al. 2017), the coefficients byIrwin (1981) and the energies extracted from the ASD-1000database of Lyulin & Perevalov (2017) is given in Figure 3.All these partition functions, with the exception of the onedue to (Irwin 1981), use the “physicists” convention whichweights ortho and para states of C H − , and a maximumupper energy of 22 000 cm − , which gives a line list that iscomplete up to 10 000 cm − (i.e. λ > µ m), i.e. the max-imum upper energy is 10 000 cm − above the maximumlower energy level value. The completeness as a function oftemperature of such a line list can be estimated by calcu-lating the partition function up to the lower energy levelcut-off as a percentage of the total partition function whichincludes all states involved in a line list calculation. Figure 5gives these values at a variety of temperatures. A line listis generally considered to be “complete” if the ratio of thepartition function of the lower energy states to the partitionfunction of all energy states involved in a line list calculationis > K max = L max in Eq. (2). As discussed, however, wedo not expect the states below 22 000 cm − which are beingused for the line list to have high values of L max ; the bendingstates which correspond to a high value of L are expectedat very high energies, and therefore temperatures. Figure 4shows the contributions from transitions with upper stateswith different values of K (= L ) to a line list computedup to K max = L max = 16. It can be seen that states with MNRAS , 1–16 (0000)
Katy L. Chubb et al.
Wavenumber (cm −1 ) −27 −25 −23 −21 −19 c r o ss s e c t i o n ( c m / m o l e c u l e ) All up to K=16K=0K=2K=6K=10K=12K=14
Figure 4.
Contribution from transitions with upper states ofdifferent K (cid:48) to the aCeTY opacity at T = 2000 K. Note that the K (cid:48) = 16 transitions do not appear on this scale. Figure 5.
The completeness of the aCeTY line list as a functionof temperature, up to 3400 K. higher values of K contribute a vanishingly small amountto the overall opacity. We therefore do not expect increas-ing the value of K max = L max in a calculation to have asignificant effect on the opacity of a acetylene even at hightemperatures.A complete description of the ExoMol data structurealong with examples was reported by Tennyson et al. (2016).The ExoMol .states file contains all computed ro-vibrationalenergies (in cm − ) relative to the ground state. Each en-ergy level is assigned a unique state ID with symmetry andquantum number labelling; an extract for C H is shownin Table 3. The .trans files, which are split into frequencywindows for ease of use, contain all computed transitionswith upper and lower state ID labels, and Einstein A coeffi-cients. An example from a .trans file for the aCeTY line listis given in Table 4. Figure 6.
Comparison of the aCeTY stick spectrum with theHITRAN data for the range up to 10 000 cm − at 296 K. Figure 6 shows an overview of an absorption spectrumof C H computed using aCeTY (this work) to thatproduced using HITRAN-2016 (Gordon et al. 2017) at T = 296 K for the wavenumber range from 0 to 10 000 cm − .Apart from some missing weak bands in HITRAN, it showsa generally good agreement. Figures 7 and 8 give more de-tailed comparisons of the main bands of C H in the range0–10 000 cm − with the data from HITRAN-2016 (Gor-don et al. 2017), again in the form of stick spectra (absorp-tion coefficients) at room-temperature. The overall agree-ment of the line positions and intensities is good, exceptseveral weaker bands of C H , overestimated by aCeTY, aswell as bands not present in HITRAN. Table 2 gives a sum-mary of the accuracy of the line positions for J ≤ Marvel and used in the refinement and band-centre corrections. The full table is given as supplementaryinformation to this work.Figure 9 shows the hot spectrum (cross-sections) of the3 µ m band of C H at T = 1355 K compared to the ex-perimental data by Amyay et al. (2009) demonstrating thegenerally good agreement also at high temperatures.The ASD-1000 database of Lyulin & Perevalov (2017)is a calculated acetylene line list which covers transitionsup 10 000 cm − and J =100, based on the use of an ef-fective Hamiltonian fit to experimental data and extrap-olated to higher energies. The energies and intensities atroom-temperature agree reasonably well with those in theHITRAN-2016 (Gordon et al. 2017) database (see Lyulin& Perevalov (2017) and Lyulin & Campargue (2017) for de-tailed comparisons), and ASD-1000 has been used to updatethe 2016 HITRAN release in the low energy region (Gordonet al. 2017; Jacquemart et al. 2017). Figure 10 gives a com-parison of cross-sections computed using the aCeTY andASD-1000 line lists at T = 1000 K. The results are signifi-cantly different and it would appear that ASD-1000 fails toadequately account for the many hot bands which becomeimportant at higher temperatures.A comparison with PNNL is given in Figure 11, for T = 50 ◦ . MNRAS000
Comparison of the aCeTY stick spectrum with theHITRAN data for the range up to 10 000 cm − at 296 K. Figure 6 shows an overview of an absorption spectrumof C H computed using aCeTY (this work) to thatproduced using HITRAN-2016 (Gordon et al. 2017) at T = 296 K for the wavenumber range from 0 to 10 000 cm − .Apart from some missing weak bands in HITRAN, it showsa generally good agreement. Figures 7 and 8 give more de-tailed comparisons of the main bands of C H in the range0–10 000 cm − with the data from HITRAN-2016 (Gor-don et al. 2017), again in the form of stick spectra (absorp-tion coefficients) at room-temperature. The overall agree-ment of the line positions and intensities is good, exceptseveral weaker bands of C H , overestimated by aCeTY, aswell as bands not present in HITRAN. Table 2 gives a sum-mary of the accuracy of the line positions for J ≤ Marvel and used in the refinement and band-centre corrections. The full table is given as supplementaryinformation to this work.Figure 9 shows the hot spectrum (cross-sections) of the3 µ m band of C H at T = 1355 K compared to the ex-perimental data by Amyay et al. (2009) demonstrating thegenerally good agreement also at high temperatures.The ASD-1000 database of Lyulin & Perevalov (2017)is a calculated acetylene line list which covers transitionsup 10 000 cm − and J =100, based on the use of an ef-fective Hamiltonian fit to experimental data and extrap-olated to higher energies. The energies and intensities atroom-temperature agree reasonably well with those in theHITRAN-2016 (Gordon et al. 2017) database (see Lyulin& Perevalov (2017) and Lyulin & Campargue (2017) for de-tailed comparisons), and ASD-1000 has been used to updatethe 2016 HITRAN release in the low energy region (Gordonet al. 2017; Jacquemart et al. 2017). Figure 10 gives a com-parison of cross-sections computed using the aCeTY andASD-1000 line lists at T = 1000 K. The results are signifi-cantly different and it would appear that ASD-1000 fails toadequately account for the many hot bands which becomeimportant at higher temperatures.A comparison with PNNL is given in Figure 11, for T = 50 ◦ . MNRAS000 , 1–16 (0000) xoMol line lists - XXXVII: C H Figure 7.
Comparison of the aCeTY stick spectra (with scaling of the dipole moment applied) against HITRAN for different vibrationalbands of acetylene at 296 K (in the range 0-5000 cm − ). The vibrational assignment of the strongest bands is shown.MNRAS , 1–16 (0000) Katy L. Chubb et al.
Table 3.
Extract from the .states file for the aCeTY line list. The theoretical energies were replaced with MARVEL where available (seetext). N ˜ E g tot J Unc. Γ tot n n n n n n n Γ vib K τ rot Γ rot ˜ E TROVE N : State ID;˜ E : Term value (in cm − ); g tot : Total degeneracy; J : Total angular momentum;Γ tot : Total symmetry in D ∞ h (M) n - n : TROVE vibrational quantum numbers (QN) (see Eq. (16));Γ vib : Symmetry of vibrational component of state in D ∞ h (M); K : Projection of J on molecule-fixed z -axis ( K = L ); τ rot : Rotational parity (0 or 1);Γ rot : Symmetry of rotational component of state in D ∞ h (M);˜ E TROVE : TROVE term value, if replaced with MARVEL (in cm − );Unc.: Uncertainty (cm − ). Table 4.
Extract from a .trans file for the aCeTY line list. f i A fi f : Upper state ID; i : Lower state ID; A fi : Einstein A coefficient (in s − ). Figure 12 gives the transmission spectra of a hypotheti-cal planetary atmosphere of a Jupiter-size planet arounda solar-like star, with an atmosphere of pure C H ,at 1000 K, computed using TauREx (Waldmann et al.2015). A comparison of such an atmosphere using theaCeTY line list is made against one using HITRAN cross-section data (both are computed at a resolving power ofR= λ/ ∆ λ =10 000). It can be seen that a large amount of opacity would be lost if one used HITRAN data at high-temperatures. This is further demonstrated by an atmo-sphere of a planet with the same mass and temperature,which contains H O (Polyansky et al. 2018), CO (Roth-man et al. 2010a), CH (Yurchenko et al. 2017b), CO (Liet al. 2015), HCN (Barber et al. 2014), H S (Azzam et al.2016) and C H at approximately equilibrium abundances.Figure 13 shows the differences between using aCeTY andHITRAN data as input into the transmission spectrum com-putation for C H . Low resolution (R= λ/ ∆ λ =300) k-tablesare used here. All other molecules and parameters remainthe same between the two spectra. The cross-sections andk-tables (the latter are produced using a method of opacitysampling which enables low resolution computations whilestill taking strong opacity fluctuations at high resolution intoaccount; see, for example, Min (2017)) used in these modelwill shortly be made publicly available (Chubb et al. 2019). In this work we present a new ro-vibrational line list for theground electronic state of the main isotopologue of acety-lene, C H ; the aCeTY line list. This line list was com-puted as part of the ExoMol project (Tennyson & Yurchenko2012; Tennyson et al. 2016), for characterising exoplanet MNRAS000
Extract from a .trans file for the aCeTY line list. f i A fi f : Upper state ID; i : Lower state ID; A fi : Einstein A coefficient (in s − ). Figure 12 gives the transmission spectra of a hypotheti-cal planetary atmosphere of a Jupiter-size planet arounda solar-like star, with an atmosphere of pure C H ,at 1000 K, computed using TauREx (Waldmann et al.2015). A comparison of such an atmosphere using theaCeTY line list is made against one using HITRAN cross-section data (both are computed at a resolving power ofR= λ/ ∆ λ =10 000). It can be seen that a large amount of opacity would be lost if one used HITRAN data at high-temperatures. This is further demonstrated by an atmo-sphere of a planet with the same mass and temperature,which contains H O (Polyansky et al. 2018), CO (Roth-man et al. 2010a), CH (Yurchenko et al. 2017b), CO (Liet al. 2015), HCN (Barber et al. 2014), H S (Azzam et al.2016) and C H at approximately equilibrium abundances.Figure 13 shows the differences between using aCeTY andHITRAN data as input into the transmission spectrum com-putation for C H . Low resolution (R= λ/ ∆ λ =300) k-tablesare used here. All other molecules and parameters remainthe same between the two spectra. The cross-sections andk-tables (the latter are produced using a method of opacitysampling which enables low resolution computations whilestill taking strong opacity fluctuations at high resolution intoaccount; see, for example, Min (2017)) used in these modelwill shortly be made publicly available (Chubb et al. 2019). In this work we present a new ro-vibrational line list for theground electronic state of the main isotopologue of acety-lene, C H ; the aCeTY line list. This line list was com-puted as part of the ExoMol project (Tennyson & Yurchenko2012; Tennyson et al. 2016), for characterising exoplanet MNRAS000 , 1–16 (0000) xoMol line lists - XXXVII: C H Figure 8.
Comparison of the aCeTY stick spectra against HITRAN (with scaling of the dipole moment applied) against HITRAN fordifferent vibrational bands of acetylene at 296 K (in the range 5000-10 000 cm − ). and cool stellar atmospheres. It is considered complete upto 2200 K, with transitions computed up to 10 000 cm − (down to 1 µ m), with lower and upper energy levels upto 12 000 cm − and 22 000 cm − considered, respectively.The calculations were performed up to a maximum valuefor the vibrational angular momentum, K max = L max = 16,and maximum rotational angular momentum, J = 99. TheaCeTY line list is based on ab initio electronic structure cal-culations for the potential energy and dipole moment sur-faces, but with improvements on the accuracy of both the line positions and the dipole moments made using the wealthof experimental data available from the literature.Comparisons against other available line list datademonstrate that the aCeTY line list is the most completeand accurate available line list for acetylene to date. It istherefore recommended for use in characterising exoplanetand cool stellar atmospheres. Computing cross-section andk-table opacity data for C H , at a range of temperaturesand pressures suitable for use in exoplanet atmospheres, foruse in retrieval codes such as Tau-REx (Waldmann et al. MNRAS , 1–16 (0000) Katy L. Chubb et al.
Table 5.
An extract of vibrational transition dipole moment scaling factors, f µ = √ ¯ S , used to produce the line list for fundamental andovertone bands. √ ¯ S is the band intensity scaling factor. The full table is given as part of the supplementary information to this work.Γ υ υ υ υ l υ l L E i /hc f µ Π u + u u u u u + u u + u + u u u u u + u + u + u + u Table 6.
An extract of the transition dipole moment scaling factors, f µ = √ ¯ S , used to produce the line list for hot bands starting fromthe (000100) Π g state. √ ¯ S is the band intensity scaling factor. The full table is given as part of the supplementary information to thiswork. Γ υ υ υ υ l υ l L E i /hc f µ Π u + u u u u + u u − u u + u u − u u + u + u u u + u − u u Marvel analysis of Chubbet al. (2018c) with new laboratory data, such as Twagirayezuet al. (2018); Di Sarno et al. (2019); N¨urnberg et al. (2019), and then inserting the resulting energy levels in aCeTY;this would ensure that energies and associated transitionwavenumbers are at the current limit of accuracy. The high-accuracy experiments of Tao et al. (2018) and Liu et al.(2013) (which was not included in Chubb et al. (2018c))demonstrates that updates should be made to the ν + 3 ν band included in the Marvel analysis of C H .The new intensity scaling technique presented in thiswork will be useful for future high-precision spectroscopicapplications, especially if combined with the MARVELisa-tion procedure. It has the potential to target the accuracy MNRAS000
An extract of the transition dipole moment scaling factors, f µ = √ ¯ S , used to produce the line list for hot bands starting fromthe (000100) Π g state. √ ¯ S is the band intensity scaling factor. The full table is given as part of the supplementary information to thiswork. Γ υ υ υ υ l υ l L E i /hc f µ Π u + u u u u + u u − u u + u u − u u + u + u u u + u − u u Marvel analysis of Chubbet al. (2018c) with new laboratory data, such as Twagirayezuet al. (2018); Di Sarno et al. (2019); N¨urnberg et al. (2019), and then inserting the resulting energy levels in aCeTY;this would ensure that energies and associated transitionwavenumbers are at the current limit of accuracy. The high-accuracy experiments of Tao et al. (2018) and Liu et al.(2013) (which was not included in Chubb et al. (2018c))demonstrates that updates should be made to the ν + 3 ν band included in the Marvel analysis of C H .The new intensity scaling technique presented in thiswork will be useful for future high-precision spectroscopicapplications, especially if combined with the MARVELisa-tion procedure. It has the potential to target the accuracy MNRAS000 , 1–16 (0000) xoMol line lists - XXXVII: C H Table 7.
Vibrational transition dipole moment scaling factors, f µ = √ ¯ S , used to produce the line list: hot bands starting from the(0000011) Π u state. √ ¯ S is the band intensity scaling factor.Γ υ υ υ υ l υ l L E i /hc f µ Σ + g g + g g + g g g g + g − g g + g g + g g g g + g g Figure 9.
Comparison of the acetylene spectra in the 3 µ m re-gion computed using aCeTY at T = 1355 K with the experimentaldata by Amyay et al. (2009). The aCeTY cross-sections were gen-erated using ExoCross and a Voigt line profile assuming P = 1atm. of experiment when predicting line intensities within a givenvibrational band at different temperatures.The line lists aCeTY can be downloaded fromthe CDS, via ftp://cdsarc.u-strasbg.fr/pub/cats/J/MNRAS/ , or http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/MNRAS/ , or from . ACKNOWLEDGEMENTS
This work was supported by the UK Science and Tech-nology Research Council (STFC) No. ST/R000476/1 andthrough a studentship to KLC. This work made extensive -25 -24 -23 -22 -21 -20 -19 -18 -17 ASD1000 ExoMol c r o ss s e c t i on s , c m / m o l e c u l e wavenumber, cm -1 wavelength, mm T= 1000 K
Figure 10.
Comparison of the aCeTY line list with ASD-1000 (Lyulin & Perevalov 2017); spectra computed up to10 000 cm − at 1000 K. use of UCL’s Legion high performance computing facilityalong with the STFC DiRAC HPC facility supported byBIS National E-infrastructure capital grant ST/J005673/1and STFC grants ST/H008586/1 and ST/K00333X/1. KLCacknowledges funding from the European Union’s Horizon2020 Research and Innovation Programme, under GrantAgreement 776403. REFERENCES
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Figure 11.
Comparison of the aCeTY cross-sections againstPNNL (Sharpe et al. 2004) at T = 50 ◦ . The aCeTY cross-sections were generated using the Gaussian line profile with half-width-at-half-maximum of 0 .
01 cm − . The PNNL data below1 × − cm / molecule are largely due to noise. λ[μm] ( R p / R ⋆ ⋆ aCeTYμEx M lμ300KHITRANμ300KaCeTYμEx M lμ1000KHITRANμ1000K Figure 12.
The transmission spectra of a hypothetical planetaryatmosphere of a Jupiter-size planet around a solar-like star, withan atmosphere of pure C H , at 1000 K, computed using Tau-REx (Waldmann et al. 2015). A comparison is made using aCeTY(this work) against HITRAN line list data as input into the cross-sections used in the transmission spectrum computation.Ba Y. A., et al., 2013, J. Quant. Spectrosc. Radiat. Transf., 130,62Bains W., 2004, Astrobiology, 4, 137Barber R. J., Strange J. K., Hill C., Polyansky O. L., MellauG. C., Yurchenko S. N., Tennyson J., 2014, Mon. Not. R.Astron. Soc., 437, 1828Belay N., Daniels L., 1987, Appl Environ Microbiol., 53, 1604Bilger C., Rimmer P., Helling C., 2013, Mon. Not. R. Astron.Soc., 435, 1888Brogi M., Line M., Bean J., D´esert J.-M., Schwarz H., 2017, As-trophys. J. Lett., 839, L2Brooke T. Y., Tokunaga A. T., Weaver H. A., Crovisier J., Bock-eleeMorvan D., Crisp D., 1996, Nature, 383, 606Bunker P. R., Jensen P., 2006, Molecular Symmetry and Spec- λ[μm] ( R p / R ⋆ ⋆ HITRANaCeTY ExoMol
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