gregory j. harris, oleg l. polyansky and jonathan tennyson- opacity data for hcn and hnc from a new...

8/3/2019 Gregory J. Harris, Oleg L. Polyansky and Jonathan Tennyson- Opacity Data for HCN and HNC From a New Ab Initio Line List

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OPACITY DATA FOR HCN AND HNC FROM A NEW AB INITIO LINE LISTGregory J. Harris, Oleg L. Polyansky, 1 and Jonathan Tennyson 2

Department of Physics and Astronomy, University College, London WC1E6BT, UKReceived 2002 May7; accepted 2002 June 13

ABSTRACTA new extensive ab initio rotation-vibration HCN/HNC line list is presented. The line list contains rota-

tion-vibration energy levels, line frequencies, and line strengths for transitions between states with energy lessthan 18,000 cm À1 and with J 60. This line list greatly improves the quality and range of HCN/HNC dataavailable. It is presently the most extensive and most accurate ab initio HCN/HNC line list in existence. It ishoped that this data set will be used in models of C star atmospheres and elsewhere.Subject headings: line: identication — molecular data

1. INTRODUCTION

HCN and HNC are important molecules throughoutastronomy; for example, HCN has been observed in comets(Huebner, Snyder, & Buhl 1974; Irvine et al. 1996), plane-

tary atmospheres (Hidayat et al. 1997), molecular clouds(Hatchell, Millar, & Rodgers 1998; Hirota et al. 1998), car-bon star atmospheres (Aoki, Tsuji, & Ohnaka 1998, 1999;Bieging, Shaked, & Gensheimer 2000), and circumstellarmasers (Bieging 2001). In fact, prior to its detection in theinterstellar medium in 1971 by the radio astronomersSnyder & Buhl (1971, 1972), HNC had been observed in thelaboratory only by means of matrix isolation spectroscopy.

Of particular interest to us is the role of HCN in C staratmospheres. Calculationsby Eriksson et al. (1984) and Jør-gensen et al. (1985) suggest that the proper detailed treat-ment of the vibration-rotation spectrum of HCN can haveprofound effect on the structure of the C star model atmos-pheres. Jørgensen et al. (1985) found that including HCN

opacity in their model atmospheres caused the atmosphereto expand by a factor of 5 and lowered the gas pressure of the surface layers by 1 or 2 orders of magnitude.

Several sets of HCN opacity data have been used inmodel C star atmospheres. These include the ab initio opac-ity data of Jørgensen et al. (1985), the empirical data of Jør-gensen (1990), and the recent line list of Aoki et al. (1998).The ab initio opacity data of Jørgensen et al. (1985) havebeen recently used by Loidl et al. (1999) in their model C staratmospheres. They contain band frequencies and intensitiesfor transitions between states with energy less than 10,000cmÀ1. The data of Jørgensen (1990) use the experimentaldata of Smith et al. (1987, 1989) with empirical estimates of the intensities of the hot bands. These data include high-fre-

quency bands such as the (4000) C-H stretch overtone.Finally, the data of Aoki et al. (1998) are based on experi-

mental data that have become available since the work of Jørgensen (1990). They cover a limited number of bands,the (0110), (0200), (100), (0111), and (100)–(0110) transitionsand their hot bands up to v2 ¼ 4.

All data sets cover the most intense HCN transitions,which are primarily the C-H stretch and bend fundamentalsand some of their hot bands. The effects of these two modes

at 3 and 14 l m are well known. However, all these data setshave their weaknesses. The data of Jørgensen (1990) are rel-atively inaccurate for the hot bands and cover a limitednumber of bands. The data of Aoki et al. (1998) also coveronly a limited number of bands and their hot bands up tov2 ¼ 4. The ab initio data of Jørgensen et al. (1985) cover alltransitions involving states less than 10,000 cm À1 above thezero point energy but are inaccurate by today’s standards.Furthermore, HCN is believed to be an important opacitysource in C stars up to T eff $ 2800 K (Eriksson et al. 1984).At these high temperatures, states with energy greater than10,000 cmÀ1 may contribute signicantly to the overallopacity. Finally, HNC has been neglected by all workers todate. In thermodynamic equilibrium, the HNC/HCN ratiofor T ¼ 2000–4000 K is between 0.05 and 0.34 (Barber,Harris, & Tennyson 2002). The transition dipoles of HNCare considerably stronger than comparable transitions of HCN, which increases the likelihood that HNC will have asignicant effect on opacity.

To increase the amount of HCN and HNC data availableand to ll in the gaps in the existing data, we have calculateda new extensive HCN/HNC line list. This line list containsrotation-vibration energy levels, line frequencies, and linestrengths for transitions involving states with energy lessthan 18,000 cm À1 and with values of the rotational quantumnumber, J , of J 60.

In x 2, the calculation of the line list is discussed, and inx 3 the results of the calculation are presented. Finally, inx 5 we discuss the results and conclude.

2. CALCULATION

Querci & Querci (1970) claimed to detect the (400

0) HCNstretching overtone at 791 nm in the atmosphere of the Cstar UU Aur. Later, Giguere (1973) tentatively identiedthe (3000) HCN stretching overtone at 1 l m in the same star.However, using a new line list based on experimental data,Jørgensen (1990) disputed that any bands beyond 1.5 l mcould be observed in C star atmospheres. Therefore, the aimof this work is to compute the HCN and HNC transitions,including hot bands contributing signicantly, longward of 1.5 l m. To give an accurate value for the band intensity andthe distribution of the intensity across the band, the datamust extend to a high value of J , such that for a given band,transitions to and from the highest value of J have only afraction of the peak line intensity of band. As a result, we

1 Permanent address: Institute of Applied Physics, Russian Academy of Science, Uljanov Street 46, Nizhnii Novgorod, Russia 603024.

2 Corresponding author; [email protected].

The Astrophysical Journal , 578:657–663, 2002October10# 2002.The American AstronomicalSociety.All rights reserved. Printed in U.S.A.

657



have extended our line list to J 60. At T ¼ 3000 K withenergy levels less than 18,000 cmÀ1 and J 60, the rota-tional-vibrational partition function is calculated to be35,653. This is 93% of the rotationally converged value of 38,405, reported in a forthcoming paper (Barber et al.2002). This gives an indication that the line list reported hereaccounts for approximately 93% of the opacity of HCN/HNC at T ¼ 3000 K.

The accuracy of the nuclear motion calculation dependson the accuracy of the potential energy surface (PES) anddipole moment surface (DMS) used in the calculation.Therefore, it is desirable to use the most accurate PES andDMS available. There are currently three ab initio semiglo-bal HCN/HNC PES available: the ANO/CCSD(T) PES of Bowman et al. (1993), the PES of Varandas & Rodrigues(1997), and the VQZANO+ PES covered in our earlierpaper (van Mourik et al. 2001). Of these surfaces, theVQZANO+ surface uses the largest electronic basis set. Asa result, in general, the band origins and intensities calcu-lated with the VQZANO+ surface reproduce more closelythe laboratory data than do those calculated with either of the other two semiglobal PES (see van Mourik et al. 2001).This surface is also capable of reproducing quite subtleeffects observed in laboratory experiments; see Harris, Poly-ansky, & Tennyson (2002). Thus, for the calculations per-formed here we use the VQZANO+ PES.

The ab initio VQZANO+ PES simultaneously ts 1527ANO/CCSD(T) points calculated by Bowman et al. (1993)with 242 points calculated at the higher cc-pCVQZ/CCSD(T) level. The surface is morphed with 17 aug-cc-pCVQZ/CCSD(T) points calculated in the HNC region of the PES, to improve the representation of the HNC part of the surface. To improve the rotational representation, theVQZANO+ surface is also adjusted to coincide with threecc-pCV5Z/CCSD(T) points calculated at the critical pointsof the HCN/HNC system. The VQZANO+ PES includesrelativistic and adiabatic corrections, which are oftenneglected when constructing an ab initio PES.

There are three semiglobal dipole moment surfaces(DMSs) available; these are the TZP/AQCC DMS of Jaku-betz & Lan (1997), the aug-cc-pCVTZ/CCSD(T) DMS of Bowman et al. (2001), and the cc-pCVQZ/CCSD(T) DMSof van Mourik et al. (2001). The DMS of Jakubetz & Lan(1997) was calculated with the smallest basis of these threeDMSs; the intensities calculated with it compare with labo-ratory data far less favorably than do calculations with theDMS of van Mourik et al. (2001; see Harris et al. 2002). TheDMS of Bowman et al. (2001) uses fewer points and asmaller basis than the van Mourik et al. (2001) DMS. Thevan Mourik et al. (2001) DMS, as a result, is the best avail-able DMS and the one that is employed here.

To allow the calculation of HCN and HNC energy levelssimultaneously, the calculation was performed in Jacobicoordinates. The coordinate r was chosen to represent theC-N distance, and the R coordinate was chosen to be the Hto C-N center of mass distance. Finally, the angular coordi-nate is the angle between the R and r coordinates; theHCN minimum is located at ¼ 0, and the HNC minimumisat ¼ .

Our vibrational, rotational, and transition dipole calcula-tions were performed with the DVR3D program suite (Ten-nyson, Henderson, & Fulton 1995), which uses an exactkinetic energy (EKE) operator and a discrete variable repre-sentation (DVR) for the vibrational motions. Jacobi coordi-

nates were used with Legendre polynomials to give theangular grid points and Morse oscillator-like functions forthe radial grids. Thirty-ve grid points were used for the Rcoordinate, 21 for the r coordinate, and 50 for the angularcoordinate. This basis was optimized to obtain a balancebetween the level of convergence and theavailable computerresources. This basis is large enough to converge all calcula-tions reported here and is the same as used in our previouscalculation (Harris et al. 2002). The parameters for theMorse oscillator-like basis in the r coordinate are re ¼ 2:3a0,D eðrÞ ¼ 29:0E h , and ! eðrÞ ¼0:0105E h . The parameters forthe Morse oscillator-like basis in the R coordinate areR e ¼ 3:2a0, D eðRÞ ¼5:0E h, and ! eðRÞ ¼0:004E h. Where reis the equilibrium distance, D e is the dissociation energy and! e is the harmonic frequency (see Tennyson et al. 1995).

The huge number of lines that were calculated required alarge amount of processing power. This made it necessaryto parallelize the processor-intensive routines of theDVR3D codes. The openMP FORTRAN API multiproc-essing directives (openMP Consortium 2002) 3 with theMIPSpro 7 FORTRAN 90 compiler (MIPSpro, SiliconGraphics Inc. 2002) 4 on the ‘‘ Miracle ’’ 24 processor SGIOrigin 2000 computer were used to perform the paralleliza-tion. The most processor-intensive module of the DVR3Dsuite is DIPOLE3, which calculates dipole transitionstrengths between states that are not rigorously dipole for-bidden. One loop of this module calls a rank 1 matrixupdate subroutine and consumes 95% of the run time. Byparallelizing this loop, we were able to reduce the run timeby up to a factor of about 5 when running on eight process-ors, depending on computer load.

3. RESULTS

The line list contains all HCN/HNC transitions involving

rotational-vibrational energy levels below 18,000 cm À1 andwith J 60. There are just under 400 million lines and over168,000 energy levels in the full data set. This is a vastamount of data that requires a lot of storage space. To fullydescribe each of the 400 million records requires approxi-mately 20 Gbytes. This size of le is not easily manipulatedor ported from machine to machine. Ideally, we would liketo reduce the overall size of the le and split it into smallerblocks of data that cover specic frequency ranges. The fol-lowing discussion covers the compact format that has beenchosen to store the data.

Each rotational-vibrational state is often described by aset of quantum numbers, some of which are good quantumnumbers and some of which are approximate quantumnumbers. The good quantum numbers are the rotationalquantum number J , the rotational parity, and n, the statenumber within the J -parity symmetry block. The approxi-mate quantum numbers are the vibrational quantum num-bers v1, v2, and v3, and the vibrational angular momentum l .The good quantum numbers are output from the calcula-tion in conjunction with the energy levels and the wave func-tions, whereas the approximate quantum numbers areassigned after the calculation.

3 See http://www.openmp.org.4 See http://www.sgi.com/developers/devtools/languages/

mipspro.html.

658 HARRIS, POLYANSKY, & TENNYSON Vol. 578



The six integers required to describe the transition are thegood quantum numbers of the upper and lower states. Thefour oating point variables required to describe the transi-tion are the energies of the upper and lower states ( E 0, E 00),the transition frequency ( ), and the Einstein A-coefficient(Aij ). There are two facts that allow us to store the data in amore compact format. These are:

1. can be calculated from E 0and E 00.

2. The energy and quantum numbers of each rotational-vibrational state are repeated throughout the data le.

Consequently, the full transition le can be split into anenergy level le and a transition le. The good quantumnumbers and energies of each level are stored in the energylevel le. Where approximate quantum numbers have beenassigned, they are also given. An integer ag that identiesthe state as HCN, HNC, a delocalized state, or unassignedis also given. Finally, each level is given a unique index inte-ger. The index numbers of the upper and lower state and theline strength are stored in the transition le. This is a moreefficient way of storing the line list, resulting in nearly a fac-tor of 3 reduction in le size. Short extracts from the energylevel le and the transition le are given in Tables 1 and 2.

It is often the case that only a small portion of the spec-trum is of interest. It was therefore decided that the le besplit into smaller les, each with a specic frequency range,thereby allowing only the spectral regions of interest to bedownloaded. Further to this, the data also have been sortedinto frequency order. For the Einstein A-coefficient, thedata beyond the sixth signicant gure are meaningless;consequently, data are given only to the sixth signicant g-ure. For reasons of compatibility, the data have been con-verted to text format andgzipped.

The Einstein Aif -coefficient, in sÀ1, is related to the inte-grated line absorption intensity, I i , in units of cmÀ2 atm À1,by

I i ¼ 3:507293 Â 10À6 Â ð2J 0 þ 1ÞQvr 2

273:15T exp ÀE 00

kT Â 1 À exp

Àhc kT Aif ; ð1Þ

where is the wavenumber in cm À1 of the line, h is Planck’sconstant, c is the speed of light, k is Boltzmann’s constant,E 00is the energy of the lower rotational-vibrational energy

level, T is the temperature, and Qvr is the rotational-vibra-tional partition function. 5

To generate some simple absorption spectra, one needs toobtain k , the absorption coefficient or opacity function atfrequency or wavenumber . The absorption coefficient of the spectrum is given by

k ¼ Xi I i f i ð À 0;i Þ; ð2Þ

where f i ð À 0;i Þis the line prole and 0;i is the line centerof line i . Once k has been obtained, the Lambert-Beer lawcan be used to generate spectra. The Lambert-Beer law givesthe intensity of a beam of radiation passing through a gas of pure HCN, with path length l and pressure p:

I ¼ I ð0ÞexpðÀk pl Þ; ð3Þ

where I ð0Þis the initial intensity of the beam and k is theabsorption coefficient or opacity function. The integratedabsorption, I i , of line i is found from the absorption coeffi-cient of the line, k ; i , by

I i ¼ Z þ1

À1k ; i d : ð4Þ

The integrated absorption for the complete spectrum is thus

I ¼ Xi I i : ð5Þ

Here I is of limited use. Clearly, to calculate k , one wouldneed to know the line prole of each line and be able to sumover all lines. However, equations (2) and (4) suggest that k for the spectrum in the interval to þ D can be foundmore simply. This we do by summing I i for all lines in thefrequency interval À þ D and dividing by D . This fre-quency binning method gives an approximate average valuefor k in the region to þ D . It also has the effect of reducing the resolution of the full spectrum to = D . Fre-quency-binned opacity data have been presented by, forexample, Schryber, Miller, & Tennyson (1995) and Neale,Miller, & Tennyson (1996). This method is adequate to illus-trate the usefulness of the line list and obtain some simple

5 Both the energy level le and the frequency-ordered transition les canbe retrieved by (1) anonymous ftp to ftp://ftp.tampa.phys.ucl.ac.uk;change to the directory/pub/astrodata/HCN, or (2) via the TAMPAgroup Web page http://www.tampa.phys.ucl.ac.uk; follow the links for‘‘ Astrodata and Molecular Data,’’ then ‘‘ Astrodata,’’ then ‘‘ HCN.’’ Adecompaction code is provided, which is described in the accompanying‘‘ readme’’ le.

TABLE 1Extract from the Full Energy Level File

Index J p a nE

b

(cmÀ1 ) i c v1 v2 l v3

1.......... 0 1 1 0.000000 0 0 0 0 02.......... 0 1 2 1414.915929 0 0 2 0 03.......... 0 1 3 2100.582377 0 0 0 0 14.......... 0 1 4 2801.459102 0 0 4 0 05.......... 0 1 5 3307.745835 0 1 0 0 06.......... 0 1 6 3510.991764 0 0 2 0 1

a If p ¼ 1,thisis an e state; if p ¼ 0,this isan f state.b This is the energy of the level relative to the HCN ground state. The

zero-point energy is 3481.5053 cm À1.c This ag denotes the structure of the molecule in this state. Here i ¼ 0

denotes HCN, i ¼ 1 denotes HNC, i ¼ 2 denotes a delocalized state, andi ¼ 3 denotes an unassigned state.

TABLE 2Extract from the Transition File

Index i Index j Aij

a

(sÀ1)

6530... .. .. .. .. . 9178 0.328590D À21157848 ........ 158599 0.354054DÀ1519118 .......... 15561 0.151754D À1640575 .......... 44648 0.918852D À1832589 .......... 30544 0.113946D À13

a This is the Einstein A-coefficient of thetransition between state i (upper) and state j (lower). The A-coefficient is presented inFORTRAN syntax, in which ‘‘D ’’ denotesan exponent in a fashion identicalto ‘‘ E.’’

No. 1, 2002 NEW HCN/HNC LINE LIST 659



absorption spectra. There are more sophisticated methodsfor opacity sampling that are beyond the scope of this work.

4. DISCUSSION

To demonstrate the usefulness of our line list, we nowcompare our opacity data with observed stellar spectra. Theresolving power of the Infrared Space Observatory (ISO )short-wavelength spectrometer (SWS) in its low-resolutionmode (SWS01) is about 200 ( ISO Data Centre 2002). 6 Thisis the resolution at which Aoki et al. (1998) have observed Cstar spectra. So for spectra of comparable resolution, inte-

grated absorption intensities have been put into bins of 3cmÀ1. Figures 1 and 2 show the resulting absorption coeffi-cient (k ) in the spectral region of 300–1100 and 1100–3900cmÀ1 at temperatures of 1500, 2000, 2500, and 3000 K. Inthe 300–1100 cmÀ1 interval, there are over 73 million lines;the main features are a result of D v2 ¼ 1 HCN and HNCbending fundamentals and hot bands, centered on 715 and465 cmÀ1, respectively. In the 1100–3900 cm À1 frequencyinterval, there are over 165 million lines and several strongabsorption features. These are the HCN D v2 ¼ 2 overtoneand its hot bands at $ 1400 cmÀ1, the HNC CN stretch fun-damental and hot bands at $ 2000 cmÀ1, the HCN (10 00)–

(011

0) band and its hot bands at $ 2600 cmÀ1

, the HCN HCstretch fundamental and hot bands at $ 3300 cmÀ1, and theHNC HN stretch fundamental and hot bands at $ 3660

0.0001

0.001

0.01

0.1

1

10

100

300 400 500 600 700 800 900 1000 1100

A b s o r b a n c e c m

- 1 a

t m - 1

Wavenumber cm -1

HNC ∆v 2 =1

HCN ∆v 2 =1

HNC ∆v 2 =2

3000 K2500 K2000 K1500 K

Fig. 1. —Absorption coefficient at T ¼ 1500,2000, 2500, and 3000 K at STP, in theregion of theHCN andHNC bend fundamentals

0.001

0.01

0.1

1

1500 2000 2500 3000 3500

A b s o r b a n c e

c m - 1

a t m - 1

Wavenumber cm -1

HCN ∆v 2 =2

HNC ∆v 3 =1

HCN ∆v 1 =1, ∆v 2 =-1

HCN ∆v 2 =1, ∆v 3 =1

HCN ∆v 1 =1

HNC ∆v 1 =1

3000 K2500 K2000 K1500 K

Fig. 2. —Absorption coefficient at T ¼ 1500, 2000,2500, and3000K at STP, in theregion of theHCN andHNC stretch fundamentals

6 See http://isowww.estec.esa.nl.




cmÀ1. The HCN CN fundamental, its hot bands, theD v2 ¼ 3 overtone, and hot bands at $ 2100 cmÀ1 are just dis-cernible, as is the Q-branch of the (01 11)–(000) band at$ 2800 cmÀ1. In both spectral ranges, HNCfeatures contrib-ute signicantly to the opacity and lie in regions where thereis little HCN absorption. We have used HCN/HNC parti-tion functions of 3523.9, 8731, 19,288, and 38,405 atT ¼ 1500, 2000, 2500, and 3000 K, respectively. These arerotationally converged values and will be reported in aforthcoming paper (Barber et al. 2002).

The effect of temperature on opacity is evident in Figures1 and2. In general, with increasing temperature, the absorp-tion features resulting from strong HCN bands broaden,while their peak absorption decreases. This is a result of theexcited HCN states becoming more populated, while thepopulation of the HCN ground state decreases. Conse-quently and not surprisingly, the hot bands become respon-sible for more absorption as temperature increases. ForHNC, as temperature increases, the strong HNC featuresbroaden and their peak absorption increases. This is pri-marily a result of the population of HNC increasing withrespect to HCN as temperature increases. The ratio of theintensity of the HCN HC stretch fundamental to the HNCHN stretch fundamental may prove to be a useful tool forobtaining temperature estimates. The temperature depend-ence of the HNC/HCN ratio will be discussed in detail inBarber et al. (2002).

To generate some simple absorption spectra, we use theLambert-Beer law (eq. [3]). This allows a determination of the transmittance [ I =I ð0Þ] of the beam, from . Figure 3shows the spectrum generated with our HCN/HNC opacityfunction, over the wavelength range 2.6–8 l m. This range iscomparable to the range over which Aoki et al. (1998) mea-sured the spectra of six C stars. Most of the main features inthe HCN/HNC spectra (Fig. 3) appear to correlate wellwith the stellar spectra. For example, the 3.2, 4, and 7–8 l mfeatures are present in both HCN/HNC and the stellarspectra of Aoki et al. (1998). The $ 5 l m HNC CN stretch

features present in the HCN/HNC spectrum may bepresent in the stellar spectra. However, this is difficult toconrm; in the case of the HNC CN stretch feature, there isabsorption from other molecular species, possibly C 3 (Aokiet al. 1998).

Aoki et al. (1998) have also taken higher resolution spec-tra of TX-Psc and WZ Cas in the 2.75–4.2 l m region. Theyused ISO ’s SWS06 spectrometer, which has a resolution of around 1500. For comparison with these stellar spectra, wehave calculated an HCN/HNC spectrum in the same region(see Fig. 4). To aid the reader, we have also plotted the spec-trum of WZ Cas taken by Aoki et al. (1998) in Figure 4; thestellar spectrum has not been normalized. The two majorfeatures, at 3.2 and 4 l m of the spectrum of WZ Cas, arepresent in the HCN/HNC spectra. The 4 l m feature isattributable to the (10 00)–(0110) band and its hot bands.The $ 2.8 l m HNC HN stretch feature present in the HCN/HNC spectrum may also be present in the stellar spectrum.A more detailed comparison, which could include a propertemperature determination, must await a full stellar modelbased on our new data.

The C star synthetic spectra calculated by Aoki et al.(1998) indicate that the predicted strength of the 4 l mabsorption feature is particularly sensitive to the amount of hot band data used. The HCN opacity data used by Aoki etal. (1998) are based upon experimental data; they includetransitions with bend excitations up to v2 ¼ 4. The limitednature of these data resulted in a considerable discrepancybetween the synthetic and observed spectra of Aoki et al.(1998). In an attempt to better model this feature, Aoki etal. (1998) used an empirical extension to their data to extendit up to hot bands containing v2 ¼ 9. The synthetic spectracalculated with the extended HCN data compare consider-ably better with the observed spectra. The data used byAoki et al. (1998) are considerably less extensive than thedata presented here. Our data will not suffer from this lackof hot band data. Aoki et al. (1998) identied the Q-branchof the (0111)–(0000) overtone in the spectrum of WZ Cas.

0.9

0.92

0.94

0.96

0.98

1

3 4 5 6 7 8

T r a n

s m

i t t a n c e

Wavelength ( µm)

HNC ∆v 1 =1

HCN ∆v 1 =1

HCN ∆v 2 =1, ∆v 3 =1

HCN ∆v 1 =1, ∆v 2 =-1

HCN ∆v 2 =3 and HCN ∆v 3 =1

HNC ∆v 3 =1HCN ∆v 2 =2

Fig. 3. —Transmittance I =I 0ð Þusing a path length of 2 cm at 1 atm at T ¼ 3000 K (solid line ) and T ¼ 2500 K (dashed line ). The size of the bins is$ 0.01 l m.




The Q-branch of this band is visible in the HCN/HNC spec-trum at $ 3.55 l m but is much less pronounced than in themodel atmosphere spectra of Aoki et al. (1998). The $ 2.85 l m HNC HN stretch feature present in the HCN/HNCspectrum is perhaps visible in the spectrum of WZ Cas. Thisis another and possibly the most promising region in whichHNC could be looked for in C stars. If detected, the ratio of the peak intensity of the HNC D v1 ¼ 1 bands to the HCND v1 ¼ 1 bands may prove a useful tool with which to esti-

mate temperature.

5. CONCLUSION

The main HCN features in the ab initio HCN/HNC spec-tra presented here are in good qualitative agreement withthe HCN features in the C star spectra observed by Aoki etal. (1998). This shows the usefulness of this new HCN/HNC line list. The data presented here indicate that if HCNand HNC are in thermodynamic equilibrium, HNC willplay a signicant role in the opacity of HCN containing Cstars. Possible regions in which HNC might be detected in Cstars have been identied as the regions of the HNC funda-mentals at $ 2.8, $ 5, and $ 20 l m. The $ 2.8 l m feature

looks like the most promising region in which to observe

HNC. If observed, the ratio of the peak intensity of theHNC D v1 ¼ 1 ($ 2.8 l m) absorption feature to the HCND v1 ¼ 1 ($ 3.1 l m) absorption feature may be a useful toolfor obtaining temperature estimates.

In conclusion, the line list presented here is the mostextensive HCN/HNC data set in existence. The line list ismore accurate and more extensive than the ab initio HCNopacity data of Jørgensen et al. (1985), which is used in therecent model C star atmospheres of Loidl et al. (1999). It is

considerably more extensive than the data of Aoki et al.(1998), which are based upon experimental data. Therefore,the use of the line list in a full stellar model should result inimportant effects. This line list is publicly available for usein stellar atmosphere models andotherwise.

We thank Callum Wright for the great deal of help heprovided with computer system issues. We thank HughJones for extracting the spectrum of WZ Cas from the ISOpublic archives. We thank the UK Particle Physics andAstronomy Research Council (PPARC) for Ph.D. student-ship funding. The calculations reported in this work werecarried out on the Miracle 24-processor Origin 2000 super-computer at the HiPerSPACE computing center, UCL,

which is partly funded by PPARC.

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0

0.2

0.4

0.6

0.8

1

2.8 3 3.2 3.4 3.6 3.8 4 4.2

T r a n s m

i t t a n c e

Wavelength ( µm)

HNC ∆v 1 =1

HCN ∆v 1 =1

HCN ∆v 2 =1, ∆v 3 =1

HCN ∆v 1 =1, ∆v 2 =-1

WZCAS

Fig. 4. —Transmittance I =I 0ð Þusing a pathlength of20 cmat 1 atm at T ¼ 3000K (solidline ) and T ¼ 2500K(dashed line ). The wavenumber range selectedis in the region of the HCN and HNC stretching fundamentals and the D v2 ¼ 2 overtone. The size of the bins is $ 0.002 l m. The lower spectrum is the unnor-malized spectrum of theC star WZ Castakenby Aoki et al.(1998).The stellar spectrum is on an arbitrary linearscalewith a constant subtracted to stagger thespectra.




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gregory j. harris, oleg l. polyansky and jonathan tennyson- opacity data for hcn and hnc from a new...

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