PRICE, Stephan Donald, 1941- QUANTITATIVE INTERPRETATION OF THE INFRARED SPECTRA OF LATE-TYPE .

The Ohio State University, Ph.D., 1970 Astronomy

University Microfilms, A XEROX Company, Ann Arbor, Michigan QUANTITATIVE INTERPRETATION OF THE INFRARED

SPECTRA OF LATE-TYPE STARS

01SSERTATION

Presented in Partial F u lfillm e n t of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State U niversity

By

Stephan Donald Price, A.B., M.Sc.

*****

The Ohio State University 1970

Approved by

Department of Astronomy ACKNOWLEDGMENTS

I would lik e to acknowledge Dr. Robert F. Wing for many valuable discussions and c ritic is m which were essen- tial in defining and detailing this thesis topic. I would also lik e to thank Dr. Russel G. Walker, whose encouragement and assistance made the completion of this thesis possible.

i i VITA

3 August 1941 . Born — Trenton, New Jersey

June, 1963 . ■ > A.B,, University of California, Los Angeles, Los Angeles, California

April 1966 . . . M.Sc., The Ohio State University, Columbus, Ohio

t il TABLE OF CONTENTS

Page ACKNOWLEDGMENTS ii

VITA lii

LIST OF TABLES v

LIST OF FIGURES vi

Chapter

I. INTRODUCTION 1

I I . ANALYSIS AND STATEMENT OF THE PROBLEM 6

111. DETERMINATION OF MOLECULAR ABSORPTION COEFFICIENTS 13

IV. H20 27

V. CO VIBRATION-ROTATION BANDS 32

VI. THE CN RED SYSTEM, A2TTj-X2£ 35

V II. C2 BALL IK-RAMSAY AND PHILLIPS BANDS 1*8

V I I I . TIO AND VO 62

IX. SYNTHETIC SPECTRA AND MOLECULAR BLANKETING 68

X. CONCLUDING REMARKS 112

BIBLIOGRAPHY 118

APPENDIX

A 126

B 136

iv LIST OF TABLES

TABLE Page

1. Wavenumbers of Rjj and Rj ^ Bandheads hi

2. Partition Functions for and C^c'^ 53

3. Wavenumbers of the P h illip s R Bandheads and Bal1ik-Ramsay R^ ^ Bandheads 60

*♦. Parameters of the Representative Stars 66

5. Blanketing in Magnitudes Due to H^O for Various Values of the Equivalent Width of the 1.38 Micron Band 85

6. Blanketing in Magnitudes Due to CO for Various Values of the Equivalent Width of the F irst Overtone 89

7. Blanketing in Magnitudes Due to CN for Various Values of the Depressions in the (0,0) Band 93

8. Blanketing in Magnitudes Due to C 2 for Various Assumed Carbon Abundance Classes 97

9. CalculatedBlanketing in Magnitudes Due to CN and C2 in Carbon Stars 103

10. Colors and Spectral Types for Some Carbon Stars 105

11. Blanketing in the 1 and J Filters Due to TiO+VO 110

V LIST OF FIGURES

FIGURE

1. Log of the Mass Absorption Coefficients for H20 at 1008 and 3360°K

2. Log of the Mass Absorption Coefficients for CO at 1008 and 3360°K

3. Log of the Mass Absorption Coefficients for C120 and C130 at 3360°K

4. Log of the Mass Absorption Coefficients for C12N at 1008 and 3360°K

5. Log of the Mass Absorption Coefficients for C12N and C13N at 3360°K

6. Log of the Mass Absorption Coefficients for c j2 at 1008 and 3360°K

7. Log of the Mass Absorption Coefficients for C]22 and C,2 C13 at 3360°K

8. Calculated Residual Intensities Due to TiO+VO at 1500 and 3000°K and the Normalized Spectral Response of the 1 F ilt e r

9. The Calculated Residual Intensities Due to C2, CN, CO and H^O Plus the Transmission of the tar Atmosphere and the Normalized Response of the Johnson F ilte rs

10. The Observed and Calculated Normalized Energy Distributions for «Tau 11. The Observed and Calculated Normalized Energy Distributions foro-Ori 79

12. The Observed and Calculated Normalized Energy Distributions for^uCep 80

13. The Observed and Calculated Normalized Energy Distributions for R Leo 81

14. The Observed and Calculated Normalized Energy Distributions for o Ceti 82

v ii CHAPTER I. INTRODUCTION

Stars with surface temperatures lower than about

^000°K radiate more than h alf of their flu x in the infrared

at wavelengths longer than one micron. Black-body or grey-

body extrapolation of their infrared fluxes from visual observations was shown by Barnhart and Mitchell (1966) to

lead to very large errors. Therefore, to assure the

accuracy of any calculated quantity related to the flux,

such as or bolometric correction, measurements in the infrared for cool stars must be made.

Since the classic radiometric s te lla r measurements of

P e ttit and Nicholson (1928), equipment and observational

techniques have improved considerably and now the litera­

ture abounds with infrared observations on stars of all

spectral classes. With some notable exceptions, these observations are wide band pass photometry obtained from

the ground. As our atmosphere is completely opaque to

incoming radiation in certain spectral regions, the principal absorbers being water vapor, carbon dioxide and ozone, ground based photometric systems are confined to

the relatively transparent atmospheric "windows" centered at 1.25, 1.65, 2.2, 3.8, 5.0, 10 and 20 microns. The most extensive system currently being used, both in terms of

number of observations and number of colors employed, is

the 10 color photometry defined by Johnson (1965), which

I has five "visual" colors (0.36 to 0.9 microns) plus filters at 1.25, 2.2, 3.8, 5.0 and 10 microns. Barnhart and Mitchell (1966) give an excellent review of other

Infrared photometric and radiometric systems in use prior to 1965.

Johnson's system does not make use of the 1.65 micron window, though model atmosphere calculations by

Gingerich and Kumar (1964) and Gingerich, Latham and

Linsky (1967) predict a flux excess at 1.64 microns for cool stars due to a minimum in the H~ opacity. Walker

(1966) employs a 7 color system (from 0.35 to 2.21 microns) which s p e c ific a lly does include a 1.63 micron f i l t e r to attempt to measure this flux excess. Bahng (1967* 1969 a,b) also measured stars in three colors, 1.21, 1.59 and

2.15 microns, through intermediate band pass filters in looking for the effe cts of the H“ opacity which the models p red ict.

As his photometry covers the spectral regions in which most of the stellar radiation falls, Johnson (1964,

1966) has proposed a revision, based on his measurements, of the effective temperature scale originally set up by

Kuiper (1938). After calibrating his photometry and approximating the stellar energy distribution in the unobserved and unobservable spectral regions, he integrates the observed energy distribution to obtain a total

lrrad lance. By applying this technique to stars whose angular diameters are at least approximately known, he derives effective temperatures and bolometric corrections for these stars. He then finds a which varies smoothly with temperature for his "fundamental11 stars, and assigns a temperature to any which has a measured color index. Originally, Johnson (196*0 used the (R + I)*

(J + K) index, but has since (Johnson, 1966) found that the

(I - L) index is a more sensitive temperature indicator for H stars.

The revised temperature scale assigns higher temper­ ature to the late K and M stars. Johnson's calculations are sensitive to the absolute calibration of the photom­ etry and particularly to the fluxes assigned to the unobserved stellar spectral regions. Johnson (1966) approximates the 1.64 micron flux excess and the depres­ sions due to stellar water vapor by considering the balloon observations on 7 K and M stars obtained by Woolf,

Schwarzschi1d, and Rose (1964). Walker (1966), who included 1.6 micron measurements, obtained temperatures about 100-1 7 5 °K higher for K5 to M3 stars than did

Johnson. Thus, there is some uncertainty in whether or not Johnson's calculations adequately account for all of the stellar flux.

The re la tio n between a given color index and temper­ ature appears not to be unique for all stars. In the case of carbon stars, Yamashlta (1967) found two distinct 4 sequences when he plotted the spectroscopic temperature classes against the color temperatures derived by Mendoza and Johnson (1965) from their (R + l)-(J + K) index.

Mendoza (1967) found that this d uality is not removed if the (I - L) index is used. I t is notable that there is a trend for the sequence of lower temperature to be clas­ s ifie d as being more abundant in C 2 . in fa c t, Solomon and Stein (1966) attribute the depression noted by

Johnson, Mendoza, and Wisniewski (1965) in the J band

(1.25 microns) of some carbon stars to strong electronic transitions of C 2 and CN.

Molecular absorption in stars has long been known to occur. Keenan (1963) uses band strengths of TiO and VO to determine spectral classes for the M stars and the Swan

C2 bands for the carbon stars. Furthermore, molecules which have infrared transitions can have the most profound influence on the physical structure of a cool star and its emergent flux, but only rather recently has it been possible to study these infrared absorptions.

Kuiper (1962, 1963), Sinton (1962), Boyce and SInton

(1965)» Moroz (1966), Slnton (1968), and Woolf,

SchwarzschtId, and Rose (1964) have detected the presence of water vapor and CO In low resolution infrared spectra of stars. Slnton (1968) measured p artia l equivalent widths of the CO first overtone in stars cooler than K4 and studied the variation of it and the 1.9 micron HjO 5

band in the variable stars R Leo and \ Cyg over a cycle.

The balloon spectrometry of Woolf, Schwarzschi1d and

Rose (196*t), above essentially ail of the atmospheric water vapor (~80000 ft), enabled them to measure total equivalent widths of the 1.4 and 1.9 micron H^O bands in

R Leo and . Higher resolution spectra by McCammon,

Munch, and Neugebauer (1967), by Johnson, Coleman,

M itchell and Steinmetz (1968) and Johnson and Mendez (1970), who normalize their observations to 40,000 feet, resolve

the first and second CO overtones into series of vibra­

tional bands. The CO fundamental has been observed by

Gillet, Low and Stein (1968) and Gil let, Stein, and

Low (1969).

In carbon stars, spectra by McCammon, Munch, and

Neugebauer (1967), Johnson, Coleman, M itc h e ll, and

Steinmetz (1968), Thompson, Schnopper, M itchell and

Johnson (1969) and Johnson and Mendez (1970) reveal the very strong absorption feature at 1.77 microns due to the

Ballfk-Ramsay (0,0) transition of Cg. Miller (1953) and

McKellar (1954) noted that CN also attains considerable

strengths at 1.09 microns in carbon stars, while Wing

and Splnrad (1970) and Thompson and Schnopper (1970)

have Identified CN bands at longer wavelengths.

A complete and comprehensive survey of the lite ra tu re ,

prior to 1969, on infrared spectra of stars has been compiled by Spinrad and Wing (1969)* CHAPTER I I . ANALYSIS AND STATEMENT OF THE PROBLEM

Molecules can and do have a profound effect on the energy distributions of the cool stars. To understand the photometry on these stars, an attempt should be made to account for the Influence of these molecules.

By calcu latin g absorption strengths for the impor­ tant molecules and applying them to a simple atmospheric model, an infrared s te lla r energy spectrum can be calculated. From such a spectrum one can determine which spectral regions are relatively free from absorp­ tion and can be used as "continuum11 points and which regions are depressed by each molecule and may be used as indicators of the presence of that molecule in filter photometry.

Also, by applying a calculated spectrum to spectral responses of an established photometric system, the effe cts of molecules on that system may be obtained. I f the calculated results are reasonably in accord with the available observations, then some confidence may be placed in the accuracy of the calculated spectrum in the unobservable regions.

Johnson's 10 color photometric system was chosen to be used in this investigation as his is the most widely used. Other investigators either transform their system to his or, at least, compare their observations to his. Of his colors, five, t (0.9 microns), J (1.25 microns),

K (2.2 microns), L (3.8 microns) and M (5.0 microns), plus the H (1.65 microns) filte r as defined by Walker

(1966), were chosen to be used in the calculations. The molecular absorptions in the shorter wavelength regions have been investigated by Smak (196*0 in cool stars; these regions contribute little to the total flux and are useless in connection with photometric temperature determinations. The longer wavelength filters, N (10 microns) and beyond, are only important for the coldest stars. Also, few observations have been made in them, their calibration is very uncertain, and little is known of the spectral features they contain.

The molecules considered in this study were chosen because of their importance in the infrared spectra of stars. Molecular equilibrium calculations for stellar atmospheric conditions have been carried out with recently determined molecular constants for M stars by

Tsuji (1964), Vardya (1966) and Dolan (1965) and for carbon stars by Tsuji (1964), Vardya (1966) (see also

Spinrad and Wing, 1969), Dolan (1965), and Morris and

Wyller (1969). For la te K and M stars, the most abun­ dant molecules are H^, CO, OH, and SiO. For carbon stars N^, CN and C 2 are the most abundant molecules a fte r H2 and CO. 8

High abundance alone does not ensure that a molecule w ill be an important source of opacity. For example* is the most abundant molecule in most cool stars but has no permitted infrared transition as the Infrared dipole vlbration-rotation bands are strictly forbidden for homonuclear molecules and the quadrapole transitions

(Spinrad 1966) appear only very weakly. Linsky (1969) has calculated that pressure induced dipole radiation of

H2 may be important if the pressure in the is high enough* but it need not be considered except for the coolest dwarf stars. The infrared spectra of Ng is similarly forbidden.

SfO, the most abundant m e tallic oxide, has not been identified with certainty in stellar spectra and can be neglected in this study. The fundamental band at 8.2 microns, a tentative identification of which has been reported by Knacke, Gaustad, G illett, and Stein (1969)* lies outside the wavelength region considered here, while the proposed Id e n tific a tio n of the *v - U, S, and

6 vibration-rotation bands of SiO shortward of 2.5 microns in stellar spectra by Fertel (1970) is very uncertain, according to Wing and Price (1970).

TIO and VO, although of re la tiv e ly low abundance, do display prominent bands throughout the visual and near infrared where they have been used to c la s s ify M stars on low dispersion survey plates (Cameron and Nassau 1955; 9

McCarthy, Treanor, and Ford 1967). Absorptions due to these molecules have not been observed longward of 1.1 microns and thus a ffe c t only the I f i l t e r .

After H 2 » CO is the most abundant molecule because of its very large dissociation energy. The fundamental, first overtone and second overtone do lie in the infrared where they are important absorbers. Indeed, the M band depression in cool stars found by Low and Johnson (1964) was shown by Solomon and Stein (1966) to be due to the

CO fundamental. This molecule has been well studied.

Young (1965) and Kunde (1967* 1968a,b,c, 1969) have calculated spectral absorption coeffeclents for CO.

Kunde (Spinrad and Wing 1969) has also generated detailed

CO spectra which have been used by Spinrad, Kaplan, 12 11 Connes, Connes, and Kunde (1970) to obtain the C /C J ra tio for <7 O ri.

Water vapor, according to equilibrium calculations, attains abundances comparable to CO in very cool M stars and produces deep absorptions in the infrared. However, the importance of water on the structure and spectral energy distribution of warmer stars is in doubt. Auman

(1969) calculates that H^o should begin to have an appreciable effect for stars as warm as T - 3500°K. © Wing and Spinrad (1970) find that H 0 is not as abundant 2 as previously thought for warm stars and suggest an 0/C ratio of 1.05 Instead of the value 1.6 used by Auman 10

in order to explain the absence or great weakness of

the water vapor absorption features for stars in the

range 3000°K to 3500°K. Spectral absorption coeffecients for water vapor at elevated temperatures in the spectral

regions of interest have been calculated by Auman (1967) and Ferriso, Ludwig and Thompson (1966).

For some early M stars OH is the third most abundant molecule and Tsuji (1966) calculated that it should be as Important an infrared absorber as CO.

However, as will be shown later, the rotational lines in

the OH bands are so widely separated that they may contribute very little to the absorption, i.e. they take out very little flux. This may explain why the only observation of OH in stellar spectra, reported by Mertz

(1970), is a slight absorption feature in stars with a

large amount of water vapor.

In carbon stars, the two most important absorbers are CN and C^» because of th e ir large abundances and high transition probabilities. In spite of the importance of these molecules, detailed calculations of the absorption spectra have not previously been carried out even though there now exist sufficient laboratory and theoretical data to permit such calculations. CN may also be

Important In M stars. Wing and Spinrad (1970) have pro­ posed that CN Is the cause of the depressions which Woolf,

Schwarzschi1d and Rose (1964) and Danielson, Woolf and 11

Gausted (1965) a ttrib u te to H^O In the spectra of

Orlonts and /-‘ Cephei.

Thus, because of th eir large abundances and/or strong transition probabilities, TiO, VO, CO, CN, C^ and

H20 were considered in this study. No other molecule has nearly as profound an effect on the infrared spectra of carbon and oxygen stars as these.

As no spectral absorption coefficients were avail­ able for C2 and CN in the infrared, they were calculated

in this study. A 100 cm*1 spectral interval was chosen for computing the average absorption coeffeclents. These were calculated fo r six temperatures, T - 1008, 2016,

2520, 3360, and 4500* (6 - 5, 3. 2.5, 2, 1.5, and 1.14).

The calculations for CN and C^ are thus compatable with the spectral intervals and temperatures used by Kunde (1968a)

in his CO calculations and by Auman (1967) fo r H^O. The interval Is small enough to reproduce the gross spectral features of the molecular absorption spectrum and to give at least 10 points within each of the Johnson filters, it is large enough to permit the representation of the average absorption coeffecient as the sum of all the lines

in the interval, and to permit errors In the calculated line positions on the order of 10 cm*1. The temperatures cover the range of stellar temperatures for which molecular absorptions are important and are taken at enough values to permit accurate Interpolation between temperatures. 12

By applying molecular absorption coefficients to

simple atmospheric models and generating synthetic

spectra the following problems can be investigated at

least qualitatively:

1. Can the depressions observed in the balloon

spectra of nt Or! and v Cep be accounted for by CN absorp­

tion as proposed by Wing and Spinrad (1970)?

2. What are the effects of molecular absorptions on wide band pass photometric measurements on stars, e.g. can

the carbon temperature class-color index duality be explained by molecular absorption?

5. Can bolometric magnitudes be improved by pre­ dicting the stellar energy distributions in unobservable portions of the spectrum?

if. Which stellar spectral regions are relatively free of molecular absorption and what color index is best suited

for temperature determinations for each spectral class?

5* Can indices of the strengths of molecular bands

be obtained from the existing wide band photometry?

6. Can a ground-based photometric system be designed

that would serve more adequately than the standard system

in the determination of temperature and band strengths? CHAPTER III. DETERMINATION OF MOLECULAR ABSORPTION COEFFICIENTS

If the electronic, vibrational, and rotational motions are sufficiently uncoupled, usually a good as­ sumption for diatomic molecules, then the wavenumber of a given rotational line in an electronic transition is given by Herzberg (1950) as

„(cm“ 1 )»(T^-Tji)+(G 1 (v 1) -6" (v ") )+ (F 1 (J 1) - F" ( J")) (1)

where, traditionally, the single prime refers to upper state values and the double prime to the lower.

In equation (1), (Ti ”Te^"v e ls the dlfference in energy, in terms of cm "', between the two electronic states involved in the transition. G(v) is the an- harmonic o s c illa to r energy, In cm"1, of the vibrational motion of the molecule and is given by the series expans I on

G(v) - We(>rt-i)-%xe(v+i)2+^ye(v+i)3+ ... (2)

where u l Is the harmonic oscillator energy, in cm , for the electronic state in question, and <*>eye are the f i r s t and second anharmonic terms, respectively, and v Is the vibrational quantum number of the state.

13 U*

F(J) is the rotational term value, i.e . the energy on the rotational state considered, in cm"', and its exact expression depends on the type of electronic state involved

(the total angular momentum of the electrons, \) , the total electron spin £ of the electronic state and the degree of coupling of the angular momentum of the electrons to the internuclear axis. The expressions for F(J) will be discussed in more detail as each molecular band system is treated.

The total absorption for the transition whose line position is given by equation (I) is

dv - N B heum_(I-exp(-c-v /T)) (3) v m mn mn 2 mn where

m refers to the lower electronic, vibrational and rotational state described by the values of v, and J. n refers to the upper state values.

Bmn Is the Einstein transition probability for the occurance of this particular transition.

hc^mn is the energy of transition and

(1-exp(-c,,y /T)) is the correction factor to account 2 mn for stimulated emission.

If it is assumed that the electronic, vibrational and rotational motions are independant, i.e. accepting the Franck-Condon p rin cip le is v a lid , the total tran sitio n 15 probability may be expressed as the product of the individual vibrational. rotational and electronic prob­ abilities. This is given by Herzberg (1950. p. 382) as

The quanti ty is the electronic M transition probability, the sum being over all sublevels of the upper and lower electro n ic states, and d^ is the degeneracy of the lower electronic state and equals

(2S+l)(2-6 the total spin multiplicity of the elec- o A. tronic state times 1 if the state Is a £ state (A pO) and times 2 If not (VO).

The quantity |RJ,J"|2, designated S|t is called M ij^ii 1 rot 1 J the Hdnl-London factor. The sum is over all magnetic quantum numbers from |M-J| to | M+J| and thus the J**1 level is 2J+1 times degenerate. This degeneracy appears in the denominator tn equation (4). The sum of the S 's J from all the levels of a given J" value, i.e. the sum from all spin multlplet states and \ doublet levels is subject to the normalizing condition (Schadee 1967; Tatum 1967)

ES - (2J“+1)(2S"+1)(2-6 J (5) J o ' 16

The exact expression for S. depends, as does F (J ), J on the type of electronic state involved, the spin multiplet of that state and the coupling strength of the orbital angular momentum to the internuclear axis. For

the transitions studied here, expressions for Sj have been derived by Earls (1935) for the ^n^-2Sred system of CN, by Bud6 (1937) for the ^ £-^fl Bal11k-Ramsay C2 system,

and by Honl and London (1925) fo r the 1H-1 £ Phi 11 ips

system. Schadee (1964) has tabulated the Honl-London

factors fo r these band systems In terms of the lower electronic states normalized to (2J+1). The values of

Schadee, times (2S+1)(2 - 6 ^ ), were used in the present calculations. Recently, Bennett (1970) has determined a higher order solution for the values of Sj for doublet- doublet transitions. However, for CN, Bennett's values 6 d iffe r from those of Earls by one part in 10 . i v 1 v"i 2 The vibrational transition probability, lRvib I •

is called the overlap integral or, more commonly, the

Franck-Condon factor. In terms of the vibrational eigen­ functions K.T'M v X - v v <6 where if) Is the vibrational eigenfunction and the integral

Is over all space. 17

Franck-Condon factors are usually derived using some analytic function to represent the potential energy, the one most commonly used is that due to Morse (1929)* Using the Morse approximation to the potential energy In the wave equation, the equation can be rigorously solved in a closed form convenient for numerical analysis. This solution yields an expression for the vibrational term values which is quadratic in (v+i), i.e. the w y and higher terms

In equation (2) are identically zero. Thus, the smallness of the experimentally determined ra tio a) Y*/a>*x is one C C 0 0 measure of how adequate the use of the Morse potential is in deriving the Franck-Condon factors.

A more exact approximation to the potential energy of an electronic state can be obtained by the Rydberg

(1932, 1933)» Klein (1932) and Rees (19^7), or RKR method.

Here the potential energy function is constructed point for point from the observed values of the molecular constants for each vib ratio nal sta te. For electronic states with appreciable anharmonicity, and especially for perturbed states, the Morse function is a poor represen­ tatio n to the potential energy, and the Franck-Condon factors based on the RKR representation are to be pre­ ferred.

For many molecular transitions, such as the red system of CN and the Swan C2 system, the assumption that the electronic and vibrational transitions are independent 18

Is a poor one. Replacing |R^ for these systems by a value averaged over all vibrational transitions and then assuming this mean to be independant of the vibrational motion leads to systematic and sometimes large errors.

Fraser and Jarmaln (1953) Introduced the concept of the "r-centrold" of a vibrational transition in an attempt to account for the interdependence of the transition probabilities. As the Internuclear distance Is a function of the vibrational motion, the electronic transition is also. The r-centroid of the (v',v") transition is defined by

(7) rviv '1 " J K*

From equation (7) we can see that the r-centroids, lik e the Franck-Condon factors, are derived using the vibrational eigenfunctions and thus, are sensitive to the assumed potential energy function.

Jeucnnehomme (1965) expresses the dependance of the electronic transition probability on the r-centrolds in the following form

(9)

where r , „ and rM are the r-centroids for the (vjv") v 'v oo 19 and (OfO) transitions, respectively, and 4 is an empirically determined constant for the electronic transition in question.

Experimental determination of the strength of a transition is usually expressed as the electronic oscil­ lator strength, f , given by

8irm c , .2 f a - — f - vei lRe(r) I /dm (10) 3 he or by the oscillator strength of a particular transition, e.g. the (0,0) transition, which is related to f by 6

f(0,0) - f v /y q e 00 el oo where v , and v are the wavenumbers of the electronic el oo and (0,0) transitions respectively.

By substituting equations (10) f (6) and (4) into

(3)* the total absorption for a given rotational transition is f nm2 LSJ Jkydt'- — H f q , |. \ {1-exp(-c.y /T ) t v 1/11V ^ 2 m e v'v"2J+l 2 mn mn el I me

We now need an expression which relates the number of molecules in a given rotational, vibrational and electronic state, N , to the total number of molecules m of that species, i.e . the Boltzmann d is trib u tio n fa c to r. 20

According to Tatum (1967) I f the Hon1-London factor is

normalized according to equation (5)» then the Boltzmann

distribution is given by

N - N2|»(2J+l)exp (-c„(T +G(v)+F(j) )/T)/Q (12) in 4 C

where ^ is a p a rity factor which depends on the symmetry

properties of the molecule and the nuclear spins. It

Is £ for heteronuclear molecules and is a function of the

nuclear spin for homonuclear ones. Q is the total

partition function and is a combination of the electronic, vibrational and rotational partition functions. The factor (2J+1) is the statistical weight of the rotational

level in question.

The electronic states possible to a given molecule depend on the electron configuration and not on the vibrational or rotational motions of the molecule. Thus,

the electronic contribution to the partition function may be separated from the total and Q can be written as

Q - Qef(Qv.Qr) (13)

where Q , according to Tatum (196h), is 6

Qe “ a H ^ -V ^ '^ -V e '1) states 21

The rotational partition function, Qr, is given by Herzberg (1950) as

Qr - ?(2J+l)exp(-c2F(J)/T) (15) J—0

If the temperature is high enough and/or the linear rotator value, B^, is small enough to permit the replacing of the sum by an integral and assuming that the rotation

is linearly harmonic, equation ( 1 5 ) becomes

Q <■ J(2J+l)exp(-BvJ(J+l)c2/T)«- T/c^ (16)

For the temperatures and molecules of interest.

Cl ament1 (I960) determines that expression (16) Is correct L to at least one part in 10 .

Although the total partition function is usually written as the product of the electronic, vibrational and rotational functions, i.e. that these functions are independent, equation (16) clearly shows that the rota­ tional partition function is vibrational 1y dependent.

Clement! (I960) writes the total partition function as

T* V f n A x Q - >],(2-«o/v)(2S+1)«xp(-c2Te/T) I - Z exp(-c2G(v)/T)/Bv states 2 v-0 (17) where the vibrational sum is to be taken from v-0 to 22

the value of v at the dissociation energy. TsujI (1967)

in reviewing his 1964 equilibrium calculation which used an assumption of independence in the individual p a rtitio n functions in calculating Q, found that using equation (17) produced a small, but not insignificant, change in his equilibrium values.

Substituting the value of Q given by (17) into the

Boltzmann d is trib u tio n (12) and then elim inating N from m equation (11) the total absorption coefficient for a given rotational line becomes

Kdv . 24 VvV,SJ V* <-c2(Te+G(v)+F(J)/T>) me el 2

l-exp(-c v /T) X ______2 mn —- _ v max Z ( 2 - & )(2S+I)exp(-c T /T) Vexp(-c G(v)/T)/B a ll oA 2 e * n 2 > states v” ° (18)

Equation (18) gives the total absorption for a given electronic, vibrational and rotational transition per molecule of the absorbing species. By multiplying (18) by Avagadro's number and dividing by the molecular weight of the molecule, the line absorption per gram of absorbing molecule Is obtained.

If the molecular constants and electronic oscillator

strength for a diatomic molecule are known, equation (18) 23 will give a total absorption strength for any rotational line of any band system. As desirable as it would be to generate a synthetic spectrum lin e by lin e , the amount of calculation over the spectral region considered is prohibitive. Therefore, absorption averages over spectral intervals need to be considered.

The following procedure was used in calculating the

CN and averaged absorption coefficients in this study.

Consider a spectral interval much larger than the width of an individual line, i.e. an interval large enough such that the entire absorption line will lie within the spectral interval. We can approximate the average absorption coefficient in the spectral interval by summing the strengths of all the lines occur!ng in the interval and dividing by the Interval width. If represents the strength of the i-th rotational line (S^JkvdV) then the average absorption coefficient is

kAO - X s f& 0 (19)

All lines occuring in with a line strength stronger than a cut off limit are included in the sum. Kunde

(1968a,1968b) found that this approximation, in general, reproduces the absorption coefficient obtained by line by line integration for CO to within 1% but is less accurate in regions where the lin e wings are important 2k

such as in the regions past the band heads.

This method has the advantage that, for a molecule

such as CN or C^, which has well determined molecular

constants, the individual line absorptions may be used

In the averaging and the rotational structure of the

band may be determined in some detail rather than having

to make some approximations to the band structure as the

other methods must.

The method used fo r TiO and VO absorption c o e ffic ie n t

determination is the "just-overlapping" or "smeared line" model. This development assumes that the individual lines

overlap enough or are smeared enough to form a psuedo-

continuum. The spectral absorption coefficient Is

expressed as a d iffe re n tia l o s c illa to r strength across

the band, i.e .

l . -a x u mc

The &f/to> Is selected to match the observations. Tsuji

(1966, 1967) calculated the H^O, OH, and CO absorption

coefficients by this method. The form of this model used fo r TIO and VO in th is study was taken from Penner

and 01fe (1968, pp. k 3 -k k ) and may be w ritte n as

c B" v* kv'v,,eXp(‘ B^f" (Wv'v"'u)/T) e e 25 where

k Is the absorption coefficient at the (v*,v") v'v" bandhead

Wy.. * , yl* „ is the wavenumber of the (v '.v " ) bandhead B1 and B11 are the equilibrium values of the firs t e e rotational constant for the upper and lower states respective! y

co is the wavenumber for which the calculations are carried out, and is constrained to values for which the individual exponents are negative.

The sums are over a ll transitio ns which can contribute to the absorption coefficients at co . A complete treat­ ment of this model as well as related ones may be found

In the first chapter of Penner and 01fe (1968).

A third method is a s ta tis tic a l one. By assuming a statistical distribution in line position and intensity,

It is possible to calculate spectral absorption coeffi­ cients without considering individual lines. The statistical parameters in the line and intensity distri­ butions are determined by applying this model to actual measurements and adjusting the parameters until the calculations agree with the measurements. Once the model parameters are defined, absorption coefficients for any spectral region and temperature may be obtained. Penner

(1959) and Goody (1964) have shown that this model gives a good approximation to the absorption profile and is 26

especially useful for polyatomic molecules whose line

positions are difficult to calculate.

Tsujl (1966) has shown that the "smeared-1ine" model is very sensitive to the degree of overlapping of

the lines. For molecules such as TiO and VO which form

continuous bands, overlapping of lines is quite good.

For 0Hf on the other hand. Tsuji calculates the average

distance between lines to be 50 to 100 times the line

width for stellar temperatures and pressures, and the

overlapping line approximation overestimates the amount

of absorption. For the same reason OH is not an important

source of opacity in cool stars and is neglected in this

study. CHAPTER IV. HO 2

The most recent determinations of water vapor spectral absorption coefficients are those of Ferriso,

Ludwig and Thompson (1966) and Auman (1967). Ferriso et a l. assumed a random band model with an exponential line intensity distribution and determined spectral absorption coefficients for 25 cm * intervals, while

Auman (1967) calculated line strengths and positions for 2.3 x 10^ lines and averaged his calculations over -1 100 cm intervals.

The data used in this study for the spectral region between 1550 cm"* and 10950 cm’ * are those of Ferriso et a l , smoothed to 100 cm”* in te rv als. Auman's data was used between 11050 cm"* and 12450 cm”*. I t was assumed that the tabulated coefficients at temperatures o o o of 1000 , 2000 , and 2500 by Ferriso et a l . were correct for 0*5, 2.5 and 2 (T-1008°f 2016°, and 2520°K). The values fo r 6-3.5 were obtained by interpolating between the tabulated values for T-1500° and 2000°K, and the values for 6-1.5 were obtained by extrapolation. No o absorption coefficient was obtained for T-4500 K. Since, as a first approximation, the absorption coefficient varies inversely as temperature, the interpolations and extrapolations were done In terms of 6 . A ctually, the

27 28 calculations of Ferriso et a I. at T-1500° and 1000°K were done only for 1X 7550 cm \ Rather than extrap­ olating to 6-3 and 5, the absorption coefficients were obtained by multiplying Auman's values at these temper­ atures by the ratio of the values of Ferriso et a l. and

Auman at 6-2.5 .

The values of the absorption coefficients for the region between 11050 and 12450 cm”' are by Auman (1967) for the case which yields straight mean opacities. The corrections suggested by Auman (1967) to account for the more recent experimental determination of band strengths were applied to these values.

Although Auman's calculations were done by a method similar to the one employed in the present study for

CN and In that individual line positions and inten­ sities for J -4 0 were calculated and then averaged over

100 cm"1 spectral intervals. It was felt that his values were not as reliable as those of Ferriso et a l, for several reasons. First, Auman's selection criteria for line strength and quantum number lim it were fncompatable, resulting In the rejection of some lines with J£40 which were stronger than the cutoff strength. Also, he neglected the vibratlon-rotation interaction of the major water vapor bands at 1.9, 2.7 and 6.3 microns.

Then, as Auman (1967) points out, a calculation error affects the values in the spectral region 29

^<2600 cm *. Lastly, although the calculations of line positions are very accurate for low-excitation, well observed bands, errors in lin e position for the higher ex cita tio n transitions can be as much as several hundred cm"** Auman estimates that the mean erro r in his calculated line positions is between 25 and 50 cm"*.

The calculations of Ferriso et a l. (1966) include the more recent measurements of band strengths and account for the vibration-rotatlon interaction of the strong bands. Agreement between th e ir calculations and the published emission and absorption spectra from which they derived distribution parameters is very good. The largest discrepancies between observation and ca lcu la tio n are at band heads where the absorption coefficients vary rapidly with wavenumber, but, as they point out, empirically determined absorption coefficients also show large scatter for these regions. Smoothing the absorp­ tion coefficients from 25 cm"* to 100 cm"* Intervals should reduce this s c a tte r.

More recent! yv calcul at ions by Ludwig and Malkmus

(1967) based on measurements over much longer path lengths agree very well with those of Ferriso et a l .

(1966), except In the region 7800 to 8800 cm"* where they are about 10% smaller. These lower values in this spectral region were adopted in this study. 30

In figure 1 the spectral absorption coefficients used in this investigation for water vapor are plotted

against wavenumber.

o

o

CM

o

o CM

1500 5500 10500

Wavenumber (cm*!)

Fig. 1. Log of the mass absorption coefficient of h^O averaged over 100 cm"' intervals as a function of wavenumber. CHAPTER V. CO VIBRATION-ROTATION BANOS

Kunde (1967* 1968a, 1968b) has calculated individual line positions and strengths for the infrared transitions 12 13 of C 0 and C 0 as well as the absorption coeffi­ cients for C,20*c'*0 averaged over 100 cm*1 spectral intervals weighted by the te r re s tria l abundance.

However, since all these line strength calculations assume 1 a I j terrestrial C J/C ratios, they are not readily applicable to the present study. 12 13 The averaged absorption for C 0 and C 0 were calculated using a modification of Reta Beebe's (1970)

C00PAC program. This program is a generalized form for a diatomic molecule having only a P and R branch, with all the molecular constants being read in on data cards.

The program was modified to include the e ffe c ts of over­ lapping vibrational sequences and to include the vibra­ tional dependance of the rotational partition function.

This latter modification is non-trlvial in that for the warmer temperatures it changes the total band strength by as much as 5%. All of this difference is attributable to the different methods used in calculating the partition function.

The details of the method of line strength calculation are given by Young and Eachus (1966). Briefly, for a line from the v th level to the (v+n)th of the av-n sequence, 32 the line strength is given by

S VT ll^ e x p t- ^ (F(j)+G(v)))(l-exp(!^_)) V 3 he v+n 2 X | m| |R (m)| v where m is the rotational index and is defined con­ ventional 1 y as

m m j * - j+1 R branch

m m - j 1 - 1 « - j P branch

v+n Ry (m) is the matrix element for this transition.

If the dipole moment function can be expressed in a power series, H(r) « 2 Em ( r - r ) , then the m atrix I I 6 element is given by

M j RV+0(m) - . tl(r)(r-r ) f .dr v i i % T v + n ,j1 e ' v ,j

Young and Eachus (1966) find that the integral in the above expression can, to within 1% accuracy, be expressed as a quartic in m . Thus

k . v+n, v r v+n, „ k R (m) ■ £ -a y (i)m k-0

For the present calculation, the electric dipole m atrix elements, , of Young and Eachus (1966), and the 33 v+n expansion elements, a (I), of Beebe (1970), were used. v It was assumed that these values are equally applicable 13 12 to C as for CO .

The molecular constants of Rank, St. Pierre and

Wiggins (1965) were used for the lin e position calculation 1 2 of C O while those of Benedict, Herman, Moore and 13 Silverman (1962) were used for C 0, with the exception of co which Kunde (1968b) points out is incorrect in e this reference. The value of Mills and Thompson (1953) was used. These constants give positions which agree to

• i within 0.05 cm of the observed positions to very high

J values.

All lines up to J" - 200 arising from vibrational levels up to v" - 2k were considered. Lines weaker than 10~^ times the strength of the strongest tran sitio n in a band sequence were rejected. The strengths were averaged over 100 cm”^ intervals for six temperatures,

T-1008, 1680, 2016, 2520, 3360 and 4500 (6 - 5, 3, 2.5,

2, 1.5, 1.12). Figure 2 plots the averaged absorption 1 2 coefficients of C 0 against wavenumber. Figure 3 13 12 shows the isotopic shift of C 0 against C 0 for a temerature of 3360°K. CJ

CJ

o o

15 . 25 .45 . 55 . 55

Log of the mass absorption coefficient for o CO averaged over 100 cm"* Intervals at 1008 and 3360°K.

o o

o o

. 2 55 . 55.

Fig. 3. Log of the averaged mass absorption coeffi cients for C'^0 and C'^0 at 33bO°K showing the isotopic shift. CHAPTER VI. THE CN RED SYSTEM. a V j -X2£

Davis and Phillips (1963) have published an excellent

study of the red CN system out to about 1.1 microns. They

determined rotational structure to fairly high rotational

levels (N ^ 5 0 to 80) for 1** bands, including the (0 .0 )

band. Weinberg. Fishburne and Rao (1987) observed the

*v ■ -1 and -2 band sequences and gave a rotational

analysis for the (0 .1 ) and (1.2) bands. Neither Davis

and Phillips nor Weinberg. Fishburne and Rao attempted to

analyze their data to determine the molecular constants.

Poletto and Rigutti (1965). using the data of Davis 2 and Phillips, derived molecular constants for the A Tf 2 12 1 and X £ states of C N. Besides determining the molecular constants for each vibrational state from

v" ■ 0 to 6 and v1 * 0 to 12. they also derived the

functional values.

To obtain line positions, the expressions for

F"(N") and F '(N ') are needed. Herzberg (1950) gives.

for the ^ state.

F,(N) - 8 N(H+1)-D N2(N+I) ***N 1 v v 2 where B and D are the rotational constants for the v v vth level. If is the spin splitting constant of that level.

35 36

and N is the rotational quantum number for Hund's

case (b). The symbol N is used in accordance with

international convention (see Tatum, 1967)* The sub­

scripts I and 2 refer to the components with J * N+£

and J - N-£, respectively.

For the upper A2^ state Herzberg (1950) gives

F((J) - B^((J+±)-My])-D^J +^(J) ( 22)

F (J) - B'((J+i)-l+±y )-D'(J+l) +d (J) 2 v I v i

where 2 1 (J) - (Y(Y-4)+*f(J+i) )

Y - A/B* v

A is a measure of the strength of the coupling

between the total electron spin and the o rb ita l electron

angular momentum for a given vibrational level. ^ is

an expression which accounts for the A doubling of the

state.

Twelve branches are to be expected in each band of a

system, but only eight are resolvable i f the spin

s p littin g of the lower state is small as in the case of

CN. In each of the four cases of coincident branches,

one of the branches is a s a t e llit e branch which is much weaker than the coincident main branch at a l 1 J values. 37

Also, the in te n s itie s in the s a te llit e branches drop o ff much faster with increasing J than do the main branches.

Therefore, line positions were calculated for the eight S resolvable branches ( R , R , R , Q , Q , P , P , 0 21 22 11 22 11 22 11 and P^) for J values up to 150 in the *v-4, 3, 2,

1, 0, -1, -2, and -3 vibrational sequences for v" up to 12. Line strengths were calculated for all twelve branches, the strengths of the coincident s a te llit e branch being added to the main branch lin es.

Line positions were calculated using equations (1),

(2), (21) and (22) and using the constants of Poletto and

Rigutti for G(v), B, 0, and A expressed as a power series in (v + i). I t was found that the use of the functional expressions leads to large deviations from the measured line positions of Davis and Phillips for moderate to high J values. The descrepancy is especially bad for the perturbed levels, v'*7 and 8. To improve the accuracy of the calculations, the individually derived values of these molecular constants for each level, as determined by Poletto and R ig u tti, were used. In the case of levels for which they did not determine a value of the rotational constants, the functional relationships were used. In addition the term, the next higher constant in the series expansions (21), and (22) calculated from the formula given by Herzberg (1950, p. 104), was also included. The agreement between observed and calculated line positions ts within about 0.5 cm ' for high J values, and is much better for the lower J values. However, the agreement is about ten times worse for the high J values of the bands which involved the perturbed 7th and

8*** levels of the TT state.

Line positions and strengths were also calculated 13 12 for C N using the observed molecular constants of C N and the isotopic relationships given by Herzberg (1950, pp. 142 and 144). Comparing the calculated positions with those observed by Wyller (1966) for the (2,0) and

(3*1) transitions yields discrepancies of up to 2 cm’ 1.

However, th is is s t i l l much smaller than the 100 cm'1 spectral interval over which the lines were averaged and since more extensive observational data are lacking for

C^N, no attempt to refine the calculations was made.

Fay, Harenin and van Citters (1970) have determined molecular constants which give better agreement for high 12 13 J lines of C N and C N than those used In these cal­ culations. However, the present determinations are good enough for the absorption model used in that large errors in lin e position exist only fo r the high J values which have weak line strengths and are overlapped by the stronger low J transitions of the next higher vibrational band. A comparison of the averaged absorption coefficients using the molecular constants employed in this study and 39 those of Fay, Marenin and van CItters has been made by

Johnson, Marenin and Price (1971) and excellent agreement has been found between the two.

The most recent calculations of Franck-Condon factors for the red CN system are those of Nlcholls (1964), who used the Horse potential function and calculated the factors for bands up to vibrational levels of v'«v"*l9, and Spindler (1965), who uses the RKR approximation and determined Franck-Condon factors for both the 2t t , - 2b and 2 TIL.* - 2e. transi tfons for the bands of interest. * For 3/2 the present calculations, the Franck-Condon factors of

Spindler were used. Not only are they based on more accurate approximations, but Nlcholls1 values are errone­ ous due to an incorrect value of the internuclear distance, rv , used for the TT state. The error arises from a © m isprint in the a r tic le by Douglas and Routley (1954), whose values Nlcholls adopts. As Nlcholls (1965b) and

Quercl (1967) point out, calculations of Franck-Condon factors based on the Horse potential are very sensitive to the adopted value of r^ of the states involved in the transi tion.

The r-centrolds of Otxon and Nlcholls (1958), based on the Horse potential, were used. They are the most extensive published, being determined for values up to v'«9 and v"-IO . For higher transition, the r-centroids were extrapolated from the data of Dixon and Nfcholls. ko

Wyller (1958) has calculated both Franck-Condon factors and r-centroids up to v'»vM»8 using a higher order

approximation to the potential energy but, unfortunately, has adopted a dissociation energy 20% too low and his calculations are in error for the higher vibrational

levels. Lambert (1968) has published a few r-centroids

based on the RKR approximation, and these agree with those of Olxon and Nicholls to w ithin 0.3%*

Jeunnehomme (1966) measured the ra d ia tiv e lifetim es of the first nine vibrational levels of the upper ,

state and obtained values for the (0,0) band oscillator

strength, fQ Q , and the dependence of the electronic

transition moment on the r-centroids, * in equation (9)*

Unfortunately, the values he derived were based on

N lc h o lls 1 Franck-Condon fac to rs. With Jeunnehonvne's * radiative lifetimes, Spindler's values for the Franck-

Condon factors and the r-centroids of Dixon and Nicholls values for „ and * were determined in the present 0,0 study and found to be

f - (3.3±0.3)x10‘3 0,0

« - 1.7 5 ± 0 .17

a reduction of about 10% in both values compared to the onesdeterm1ned by Jeunnehomme. Lambert (1968) calculated 41 -3 values of 3.3x10 for the oscillator strength of the

(0f0) band and 1.6 for £■ t using measurements of the solar

CN bands, RKR Franck-Condon factors and a model solar

atmosphere. However, in computing f and cc through 0,0 radiative lifetimes the characteristic wavenumbers of the

transitions must be known. Lambert assumes these to be the

bands origins when, more correctly, they should be taken

as the wavenumbers at which the maximum absorption, or emission, occurs. Taking this into account would raise

Lambert's values somewhat, and the agreement between his value of CL and the one derived in the present study would be b e tte r.

For CN a positive value of CL means that, in general,

the p ositive a v sequences are weakened and the negative ones are enhanced compared to the a v - 0 sequence. Greene

(1969) finds the opposite Is true when he calculates CN

line strengths for the sun and CL Ser. Although

Grevasse (1970) calculates a similar variation of CN for

the sun, the majority of published data to date indicate

that the value of € Is positive.

With these data, namely Spindler's Franck-Condon

factors, the values given above for f and £, 0,0 Schadee's (1964) values of S normalized to J 2Ts - (2J+1)(2S+1)(2-S ), and equation (18), the line J OA strengths were calculated for all the lines whose posi­

tions were determined, for 9-5, 3, 2.5, 2, 1.5, 42 and 1.12. Every line in the 0.7 to 6.45 micron region .c was retained unless the line strength was less than 10 that of the strongest line. These line strengths were averaged over 100 cm"' intervals; no lines whose calculated strength was stronger than the cutoff limit were rejected.

Tentative identifications of the CN vibration- rotatlon bands in stellar spectra have been reported by

Connes, Connes, Bouigue, Q uerci, Chauville and Querci

(1968) and G illett, Low, and Stein (1969). Although no d ire c t laboratory measurements of these tran sitio n s exist an attempt was made to account for these bands in cal­ culating the averaged absorption coefficients. A value o of 0.66 debye/A was adopted for the dipole moment of the fundamental band. This value is an average of the measurements of the stretching of the CiN bond in t r i - atomic molecules (XCN) by Hyde and Hornig (1952) and

Nixon and Cross (1950). Young and Eachus (1966) derive a value five times this for CO. As CN and CO are similar molecules one might expect a similar dipole moment. In lieu of a better value, 0.66 was adopted.

The (1,0) matrix element was calculated using the method detailed by Heaps and Herzberg (1952). To obtain the matrix elements for the (2,0) and (3,0) bands the ratios R2,0/R*'® and R^*°/r', derived by Cashion

(1963), were used. It was further assumed that the molecule is a lin e a r dipole with a Horse potential representation for the ground state, for not too large a value of v, Heaps and Herzberg have shown that the following relation is valid:

lRV+n|2/\Rnl2 - (v+n)J/vJnJ (23) v o

Line positions and strengths were determined for the i o fundamental and first and second overtones of C N and were included in the average absorption coefficients, subject to the same cutoff limits as the electronic bands.

Similar line intensities and average absorption i a coefficients were calculated for C N using the isotopic molecular constants but with the same values of f , oo 12

Condon factors are not identical for the two Isotopes, but that the difference is quite small, amounting to 10% or less. As this is the order of the error of f and oo no attempt was made to allow for the tsotopic differ­ ences in qv iv». .

As noted previously, the accuracy in determining line positions is quite good, especially for the low J values.

For very high J's the calculations are less accurate, but these lines have very little influence upon the absorption because they overlap with much stronger lines from the next band. Mf

In figu re k the calculated averaged absorption i o coefficient for C N Is plotted against wavenumber.

Figure 5 plots the averaged absorption coefficients for

and C^N for a temperature of 3360°K against wave­ number. A total of about 100,000 tines was considered for each temperature in calculating the average absorption coefficient for each isotope of CN. Appendix A contains the tables of the calculated values of these coefficients.

The calculated wavenumbers of and band- heads for some of the more important transitions which are longward of one micron are given in table 1. a a co o o

.20 . l»S f G0 .75 . ,90 1.05 1.20 1.35 1 /A (/<•' » 0.0001 cm" ) Fig. *i. Log of the moss absorption coefficient of C N averaged over 100 cm™^ intervals at 3360°!< and 1003°K as a function of v/avenumber.

-p- Kn o o• * I o < ■ • to

- 1- 1.S0 , -1 -1 (/A. » 0.0001 cm ) 12 Fig. S. ° f t *1e averaged absorption coefficients for C N and C N at 3360 K. showing the isotopic shift as a function of wavenumber.

4r O' 47

TABLE 1

12 -1 Wave numbers of RAI and Ft C N Bandheads (cm ) 21 22______

( v1,v") R R (v',v") R R 21 22 21 22

(0,0) 9195.8 9150.3 (0,1) 7159.1 7108.7 CM) 8939.6 8895.4 (1.2) 6928.2 6880.0 (2,2) 8682.if 8639.5 (2,3) 6703.3 6657.8

(3.4) 6476.3 6425.4

(4,5) 6247.7 6199.8

(5,6) 6011.1 5963.5

(0,2) 5150.3 5093.7 (0,3) 3169.83 3105.3

(1,3) 4946.5 4891.3 (1,4) 2992.3 2929.3

(2,4) 4744.3 4689.1

(3.5) 4543.3 4489.4 CHAPTER VII. C BALL IK-RAMSAY AND PHILLIPS 8ANDS 2

C2 has two infrared transitions, the Phillips b V f-x 'c ^ and the B al1ik-Ramsay A1 X ' systems.

The (0,0) Ballfk-Ramsay band at 5656 cm*' is quite prominent in the spectra of carbon stars published by

McCammon, Hunch and Neugebauer (1967). Johnson, Coleman,

M itchell and Steinmetz (1968), and Thompson, Schnopper,

Mitchell and Johnson (1969). Hunaerts (1967) first identified this absorption feature.

Calculations of line positions and strengths were done for both band systems and for the equivalent systems of C,3C12. The vibration-rotation bands were omitted 2 since the most important species, C ^ * is homonuclear and thus those transitio ns are forbidden. Since the 12 13 nuclear spins for C and C are 0 and ±, respectively, 2 every other line Is missing for C^ while all lines are present for C^2C^ (see Herzberg, 1950, pp. 130 to 140).

Line positions for the &v - 4,3»2,1,0,-1,-2, and -3 sequences of the P h illip s system were calculated up to v"-13 and J-132. The rotational term values for both states are given by Herzberg (1950) as

F(J) - BvJ(J+1)-DvJ2(J+l)2 (24)

48 49

The molecular constants derived by Marenin and

Johnson (1970) were used to calculate the line positions for lines up to J ■ 132 for the P, Q and R branches of the bands of this system. If listed, the individual constants for each band were used, otherwise the func­ tional values were employed. Also used was the functional form, given by Marenin and Johnson, of the correction to be applied to equation (24) to account for the A doubling of the TT state which appears In the Q branch lin e s . Agreement between the observed and calculated line positions is excellent, the discrepancies are less than 0.1 cm~\ for all J values.

For the A^ZT* state, Ballik and Ramsay (1963a) give the rotational term values as

F,(N) - BvN(N+))t (2N+3 ) ^ ; ^ (2N+3)2B2+ ^ ^

3 V (25)

+ tfN(N+l)-DvN2(N *l)2+HvN3( ^ l ) 3

F (N) - B N(N+1)-0 N2(N+I)2+H N3(N+1)3 2 v v v

The subscripts 1, 2, and 3 refer to states with J values of H+l, N and N-l . In the first expression, the upper signs are for subscript 1, the lower for subscript 3; the ^ and / are spin splitting constants. 50

The lower state of the Bal1 Ik-Ramsay tra n s itio n , a the X'^TT state, is also as the lower state of the Swan u system. For th is state Herzberg (1950) gives the term values as

F,(J) - B (J(J+1 )tYT -2Z )-D (Jr* ) (26) 1 V + 1 2 v +3/2 3

F (J) - B (JCJ+D+W (J))-D (J+i)2 Z V Z V where

ZjCJ) - Y(Y+if)+it/3+^J(J+l)

Z2(J) - (Y(Y-l)-if/9-2J(J+l))/3Z1(J)

The observed values of Phillips and Oavis (1968) for the lower state were used. These authors tabulate not only By and 0y but also the values of Y(Y+*f)+V3 and Y(Y-1)-V9 , and Include the A doubling effects of the state. For the upper state, the functional values derived by BalIlk and Ramsay were used.

Herzberg (1950) predicts that a -^TT transition w ill have 27 branches, 9 main ones and 18 s a te llite s .

Since B a llik and Ramsay found an indeterminate value of

V In equation (25) and a constant value of many of the satellite branches will be either coincident with the main ones or a distance of 3 («0.6 cm*1) away from them. 51

If the coincident, or very nearly coincident, lines are combined with the main lines then there should only be

15 discernible branches, the P, Q, and R branches for each multiplet state plus six satellite branches. The line positions and in te n s itie s for each lin e up to J m 132 for each of the 15 branches in the Av ■ 4, 3, 2, 1, 0,

-1, -2, and -3 sequences, up to v" - 7, were calculated.

In the line strength calculations, the line strengths of the coincident s a t e llit e branch lin e were added to the strength of the main branch line to give a total effective lin e strength. The agreement between observed and calculated line positions is quite good, being within

1.5 cm~^ out to the limits of observation.

It may be noted that the line strengths, through equation (18), depend inversely on the partition function, given by equation (17)* As noted previously, most inves­ tigators, e.g. Tsuji (196*0, Include only the two or three lowest electronic states in determining the electronic partition function. This is fine for molecules such as

CN, the third lowest state of which is 25,800 cm"1 above the ground state. However, the calculations of Fougere and Nesbit (1966) and observations of Bailtk and Ramsay

(1963b) show that Cj has a number of low-lying electronic states. Clement! (I960) demonstrates that the neglect of many of these states in the partition function calculations can lead to large errors in the abundance determinations 52 of C2 derived from absorption strengths. Bal11k and

Ramsay empirically reordered the energy structure of the observed C2 electronic states and l i s t the molecular constants pertinent to each state. Fougere and Nesbit

(1966) list values of T and co for the predicted e e states; the other molecular constants for these states are either listed by Clementi (I960) or derived by the formulae given by him. inclusion of the predicted states

Is demanded by the theory of partition functions in molecules whether their existence is observationaly confirmed or not.

Altogether, nine states were considered in the calculations, six of which have been observed. These states include all energy levels lying below 30,000 cm-1; contributions from higher states will be less than g one part in 10 for the temperatures considered here.

It was necessary to use all the molecular constants in calculating the partition function as some state, e.g. a the upper TT state of the Swan system, are highly perturbed, in table 2 the calculated partition functions 12 13 of C_ and C C are tabulated as a function of 2 temperature.

There does not exist any reliable published data on observationally derived oscillator strengths for eith er the P h illip s or the Bal1ik-Ramsay system. There­

fore, the electronic oscillator strength, fe , used in 53

Table 2

Parti tlon Functions for c’ 2 and C,2 C13

>erature (°K) Q

1008 434.18 453.66

1680 1935.65 2030.97

2016 3140.14 3299.48

2520 5567.87 5859.79

3360 11523.57 12149.44

4500 24152.24 25501.87

this study are those derived by Clement! (I960) for both systems. He calculates a value of f - 0.0027 fo r the P h illip s system and 0.0066 for the Sal 1ik-Ramsay transition. Since there are no observational data to

Indicate otherwise, |Re| Is assumed constant for the vibrational transitions of both systems.

For the P h illip s bands, the Franck-Condon factors determined by Spindler (1965) were used. Spindler's calculations are based on the RKR approximation, and extend up to v1 - v" - 9, farther than the array of

Nlcholls (1965a). However, i t was found that for the warmer temperatures used in this study levels higher

than v" - 9 could contribute appreciably to the

absorption. I t was discovered that the Franck-Condon 54 factors determined for the B^TT transition of a by 8ensh, Vanderslice, Tilford and Wtlkenson (1966) agreed well with those of Spindler for the Phillips

System. This Is not unexpected as the molecular constants on the two states involved in both transitions are almost the same, especially the difference in the Internuclear distance* The qv(vii's determined by Bensch, et a l. were adopted fo r the higher vibrational transitions of the

P h illip s system in preference to neglecting them or trying to extrapolate Spindler*s values.

For the Bal1ik-Ramsay tra n s itio n s , the Franck-

Condon factors determined by Nicholls (1965a), based on the Morse p o te n tia l, were used. Unfortunately,

Nicholls' values are tabulated only up to vH * 5, and higher v" levels will contribute very significantly to the absorption coefficient. The average of the values of Bensch et al. (1965) for the alTT -a* 27,. and g u u"* J7g transitions of N^ were adopted for the higher vibrational transitions using the interpolation scheme of Nicholls (1965b). The molecular constants of the states involved in these transitions correspond well with those of the Bal11k-Ramsay states. The qv iyn for the two N2 systems bracket nicely those calculated 55

by Nicholls for the Bal1(k-Ramsay bands as fa r as comparisons could be made.

Individual line strengths for both systems of were calculated by equation (18) and the appropriate

Sj values of Schadee (1964) were normalized to

« (2J+1) for the P h illip s system and to 6(2J+1) J J for the Bal1ik-Ramsay system. All lines stronger than

10“5 times the strength of the strongest line were

averaged over 100 cm"* spectral intervals to obtain the

spectral averaged absorption coefficients. Approximately

100,000 lines for C*2 and 150,000 lines for C13C12 were calculated for each temperature. I t 12 The C •'C calculations were done using the isotopic molecular constants obtained by applying the appropriate

isotoplc shift formulae given by Herzberg (1950). The 12 same values of f and q , „ used fo r the C- caicu- e v v & It 12 tat ions were used for C ■’C . Although Halman and

Lauchlet (1968) find an isotopic dependance of qyivn

for Cj, such effects are small, especially in comparison

to the errors In determination of the oscillator strengths,

and were neglected. It should be noted that every line it 12 of C C had to be calculated since it is not homonuclear, 12 12 whereas every other line is missing in C C . The

vibratIon-rotation bands of the isotoplc molecule were

neglected. These bands have not been observed and they

are expected to be weak because of the near symmetry of 56

the molecule. Figure 6 plots the spectral absorption

- 1 12 coefficients averaged over 100 cm intervals for

against wavenumber for several temperatures. Figure 7 12 compares the averaged absorption coefficients of C2 and g12gl3 fQr a temperature of 3360°K.

For all three infrared electronic transitions of

CN and the calculations excluded reversed bands.

These are bands involving a transition from a low

vibrational level of the upper electronic state to a more

energetic vibrational level of the lower state, e.g. the av ■ -k sequence for the Bal11k-Ramsay system. Such

transitions, in general, are about 1000 times weaker than

those due to the main band sequences just considering the

Franck-Condon factors of the tran sitio n s. Also, the

reversed bands are further greatly weakened by the

Boltzmann facto r. Therefore, the strengths of the re­

versed bands are so small as to fall outside of the

adopted cutoff limits.

The line strength and position calculations of all

the transitions depend on the assumption that there is

no vibration-rotation interaction. Indeed for low to

intermediate values of J this is an excellent assumption

as the vibrational motion is much faster than the rota­

tional. However, for the high J values, the rotation

becomes s ig n ific a n t compared to the vib ratio n and the two

motions interact, and calculations which are based on 57 non-interaction deviate systematically from the true values. This, and the fact that some of the vibrational and rotational levels are perturbed, accounts for the discrepancies between observed and calculated lin e positions. Where the positions disagree the line strengths should also. However, the disagreement is only severe for very high J values, where the line strengths are weak and the lines are overlapped by much stronger low

J transitions of the next bands in the sequence.

Table 3 lists the positions of the heads of various bands of the P h illip s and Bal11k-Ramsay systems. I t can be noted that the tv - k, 3 and 2 Bal1ik-Ramsay sequences overlap the ■ 2, 1 and 0 Phillips sequences. From figure 6 I t can be seen than the Bal11k-

Ramsay transitions are much stronger than the Phillips bands. This could explsin why the Phillips bands are difficult to observe in stellar spectra.

The averaged absorption coefficients calculated in this study for both Cj2 and are lis ted in Appendix

B for various temperatures. f l

'.IS .IS .60 .15 .90 1.05 1.20 1.35 1.50

1& {jjl* « 0.0001 cm*1)

Fig. 6. Log of the mass absorption coefficients of C 2 averaged over 100 cm"' spectral intervals for temperatures of 3360°K and o 1008 K as a function of wavenumber. log kg 5 | \ i. * o o te vrgd bopin ofiins o and for coefficients absorption averaged the of Log 7* Fig. f wavenumber. of hwn te stpc f a 36° a a function a as 3360°K at ift h s isotopic the showing / (*’) 2 , ) (I*'’ 1/A .60.75* 9 l.5 12 13 l.SO 1.35 1.20 ' l'.05 .90

I V 60

Table 3

Wavenumbers of the Phi 11ips R Bandheads (cm-1 )

tv '.v " ') R (v '.v " ) R ( V . v") R

(1.0 ) 9865.* (0,0) 8282.6 (0.1) 6*56.5

(2,1 ) 9597.6 (1.1 ) 8039.0 (1.2) 62*1.2

(3,2 ) 9333.8 (2,2) 7799.5 (2,3) 6030.9

(*.3 ) 907*.9 (3,3) 756*.9 (3 ,* ) 5826.6

(5 ,* ) 8821.8 < *.*) 7336.3 (*.5) 5629.3

(6,5 ) 8575.5 (5,5) 711**5 (5,6 ) 5*39.7

(7,6) 8336.8 (6,6) 6900.* (6,7) 5258.9

(0,2) *658.7 (0.3) 2890.9

(1.3) **72.7 (1 .* ) 2735.1

(2 .*) *292.7 (2,5) 2586.5

(3,5 ) *119.8 (3,6) 2**5 .8

(* ,6 ) 395*.7 (*,7) 231*.0

(5,7) 3798.* (5,8) 2192.1 Table 3 (Continued)

Wavenumbers of the Bal11k-Ramsay Bandheads (cm*1)

(v '.v " ) R ( v ', v“ ) < v \v " ) R 11 R11 11

(3,0) 9930.5 (2,0) 8527.4 (1,0) 7102.5

(4,1) 9694.2 ( 3 . 0 8313.0 (2,1) 6904.5

(5,2 ) 9459.5 (4,2) 8100.1 (3,2) 6719.1

(6.3 ) 9226.3 (5,3 ) 7888.6 (4,3) 6529.5

<7,*0 8994.9 (6,4 ) 7678.7 (5,4 ) 6341.3

(8,5) 8765.4 (7,5) 7470.6 (6.5) 6154.8

(9,6) 8537,8 (8,6) 7264.4 (7,6) 5970.0

(0,0) 5656.2 (0,1 ) 4039.7

( 1 , 0 5485.7 0 , 2 ) 3892.8

(2,2 ) 5316.7 (2,3) 3747.1

(3,3 ) 5149.0 (3 ,4 ) 3602.9

(4,4 ) 4982.6 (4 ,5 ) 3459.6

(5,5 ) 4817.8 (5 .6 ) 3318.1

(6,6 ) 4654.6 (6 ,7 ) 3178.1 CHAPTER Vt M . TiO AND VO

Although a number of near infrared stellar bands are identified as belonging to these molecules, analysis of the electronic states involved in these transitions is incomplete. To date there is no oscillator strength determination for these bands, either theoretically or em pirically; and, indeed some of the bands do not have structural analyses. Low dispersion spectra of very late stars taken by McCarthy, Treanor and Ford (1967) show strong bands with heads at AA 7054, 7589* 8344, 8432,

8859* 9205 and 1 1032, attrib u ted to TiO, and at A A 781*9,

7440, 7447, and 10465 due to VO. All these bands degrade to longer wavelengths. Bobrovnlkoff (1933) first inves­ tigated the stellar bands sequences which give rise to the AA 7054, 7589, and 8344 bands. These bands are of the a v » 0, -1 and -2 sequences of the / system of

TiO which Phillips (1969) has reclassified as an

A^$-X^A tra n s itio n . The A A 8859 and 11032 are the (0,0 ) bands of the and transitions, respectively

(Spinrad and Wing, 1969)* Additionally, Lockwood (1969) and Spinrad and Wing (1969) report stellar observation on faint bands due to the higher transitions of the av* 0 and the av - -I sequences of the tran sitio n and the av * +1 sequence of the sequence. The 63 strong bands at A A 8*f32 and 9205 as well as the fa in te r bands at 9230 and 92*f8, Id e n tifie d with TiO, remain unclassified.

The VO bands at AX 7Mt0 and 7900 are id e n tifie d by

Keenan and Schroeder (1952) as due to a (1,0) and (0,0 ) tra n s itio n . The A 10465 band is ac tu a lly a complex of seven or more bands with the deepest depression occurtng around 1.06 microns. Both systems involve transitions to the ground state, which Carlson and Moser (1966) i*— _ designate as probably a 2J state.

As there are no available oscillator strengths for the near infrared bands of either molecule, an empirical approach was used to calculate their absorption coeffi­ cients. If the absorption can be represented by a smeared lin e model* then the absorption c o e ffic ie n t at wave- number cO Is given by equation (20), which may be rewritten as

kw-E H C 1(/U exp (-DCO/T) (27) y l y l l V V

The constant, c v i v *i * involves the molecular constants of the states involved, the temperature, and the product of the Franck-Condon factors and the oscillator strength.

D is the coefficient of co/T in equation (20) and the sum is over all the vibrational transitions which can contribute to the absorption coefficient at , 64

If a simple Schuster-Schwarzschl1d model Is assumed to represent the absorption of these molecules In cool stellar atmospheres, then the total number of molecules of the absorbing species, N , which contribute to the absorption is assumed to lie in a layer in the stellar atmosphere which has a ch a rac teris tic temperature T .

In this model, the absorption at CO is given by

ro>- l/O+Nk^) (28)

If the temperature of the specified layer in the star and the Franck-Condon factors and molecular constants for the transitions of interest are known, then a measure of ru at some point in the band system will give a value for the product of the oscillator strength and the number of molecules, Nf . Excluding saturation effects, this value of Nf0 may be used fo r the rest of the band system to calculate the residual intensities by means of equation (28).

The absorptions due to av « 1, 0 and -1 sequences of the H i-1 A and bands and the av - 0 and -1 sequences of the ^ system of TiO were treated in this manner. The molecular constants for the 'TT and ^ states are those of Pettersson and Lindgren (1962), while the values of Phillips (1950) for the 'A state and Herzberg (1950) for the states involved in the 65

system were adopted. The Franck-Condon factors for the / system, determined by Fraser. Jarmain and Nicholls (195*0 were used for a ll three systems. The molecular constants for the V-^A and V-^27 transitions, particularly the change In Internuclear distance. &r . are similar to

those of the t system, so applying the t system's

Franck-Condon factors to the other bands introduces

relatively little error, as pointed out in Chapter VII.

The scanner measurements of Wing (1967) on M stars, chosen to be representative for effective temperatures of 3500. 3000. 2500. 2000. and 1500°K, were used to provide the r

sions at A7812 for the (2 .1 ) band of the ^ system.

A^8880 and 9820 for the (0 .0 ) and (1 .2 ) bands, respec­

tiv e ly . of the H r-1 A system and ^ 10154 fo r the (2,1)

band of the transitions. The unclassified band

at X 8432 was accounted for by using the measurements of Wing at ^ 8712 and assuming that the molecular constants of the system were applicable.

For V0, the measurements at M 7564. 8116 and 10564

by Wing were used for the XA 7440. 7849 and 10465 bands.

Molecular constants of Herzberg (1950) and Keenan and

Schroeder (1952) for the only analysed near infrared

bands of V0 were used. The Franck-Condon factors of

Nicholls (1962) for the visual bands were assumed to hold

for the two infrared systems. 66

Table **■ lists the stars assumed to represent the effective temperatures of Interest

Table k Parameters of the Representative Stars Sp.T. Te Star

3500 M2 ir Leo, X Peg

3000 ta V ir

2500 M6 EU Del

2000 M8 RX Boo

1500 Ml 0 TX Cam (a t minimum)

The values of r^ for a star with T^ - 1500 and

3000°K due to TiO+VO , calculated by the above described method, Is shown in figure 8 along with the normalized spectral response of the I f i l t e r . Filter Response Residual Intensity 0.5 8500 i. . h cluae rsda itniis u t TOV in TiO+VO to due intensities residual calculated The 8. Fig. n v i V TO TiO TiO VO TiO omlzd pcrl epne f h 1 . r e t l i f 1 the of response spectral normalized tr o 10 ad 00K fetv tmeaue n the and temperature effective 3000°K and 1500 of stars 10000 Wavenumber i TOTOV TO VO TiO VO TiO TiO TiO ( cit ) * T 12000

TiO CHAPTER IX. SYNTHETIC SPECTRA ANO MOLECULAR BLANKETING

Synthetic spectra were calculated using the averaged absorption coefficients generated ortin the case of H^O, adopted in this study. Saturation effects on the individual molecular lines were neglected and it was assumed that the depression of the continuum produced by the absorbing molecule is given by the Milne-

Eddington approximation derived by Munch (1958)

D - RcNkv (1+Nky) (29)

where N is the number of absorbers which have an absorption coefficient kv at wave number x> . Rc is the residual intensity for infinite absorption in the spectral region and is assumed to be given by

D G(Te)-B(Tc)

c - where G(T ) is the continuum energy d is trib u tio n calculated by Chandrasekhar(1950. p. 67) three point quadrature formula for the emergent flu x of a grey body.

The solar T-f distribution derived by Krisha Swamy

(1967) scaled to the effective temperature T , was used to derive the temperature inputs to the quadrature

68 69 formula. ®(^Q) is the black body flux at the surface of the star which is at a temperature IQ . The surface temperatures from the model atmospheres of cool stars calculated by Auman (1969) were used. The absorption layer In the star was taken to be at a temperature

T ■ 0.89 T0 which corresponds to a value of V~o.2 in

Krisha Swamy's 1 - X distribution. This is the value of

X that Schadee (1968) found as the typical optical depth of formation for stars of effective temperature

4000 to 3500°K and is consistant with the value adopted by Splnrad and Vardya (1966) for cooler stars.

The normalized system response for the I, J, K, L and M filters defined by Johnson (1965) and the 1.63 micron filte r, H, defined by Walker (1966), as well as the atmospheric transmission and a calculated spectrum for each molecule is shown in figure 9. The absorption coefficients used in the calculations for C^, CN and CO were for a temperature of 2670°K, which is assumed to be representative of the absorbing layer for a star of

3000°K effective temperature. The H^O calculations are for a temperature of 2250°K which is believed represent­ ative for a star with an effective temperature of 2500°K.

The absorption strengths for and CN are typical for a carbon star, while the CO value Is typical for an M4 s ta r. The H^0 abundance derived by Auman and Goon (1970) fo r a model atmosphere of 2500°K e ffe c tiv e temperature Figure 9

The calculated residual intensities of C^, CN, CO and 1^0 plus the transmission of the earth 's atmosphere and the normalized filte r response of the Johnson (1965) filters and the H (I . 6 3 micron) filter are plotted against l/Jl (yuT1) •

70 71

90 V* V* g o

X

LA

O CM O CM U O O o oo oo o o oo oo o 72 was used. The atmospheric transmission is taken from

the charts of McClatchey et a l. (1970) for mid-latitude winter conditiom from an altitude of 2 km. Under these conditions there is about 2 mm precipi table water in

a one a ir mass v e r tic le column. Kuiper (1970) determines

that this is an optimum value for K itt Peak.

The K, L, and M f i l t e r s , as well as the 1.63 micron

band, more than cover the atmospheric windows. The 1.38 micron te rre s tria l water vapor band severely depresses

the response of the J f i l t e r at wavelengths longer than

about 1.34 microns. The window at 5 microns is a rather

poor one, as can be seen from figure 9. There is a small

amount of absorption in the I filte r due to H^O at 0.8

and 0.92 microns and due to 0^ at 0.75 microns.

The filters are influenced by absorptions due to

each of the molecules considered in this study in the

follow ing manner:

I f i l t e r - depressed by TiO+VO as well as

the positive av sequences of CN, the av - 3,

4, 5 and 6 B al11k-Ramsay bands and a v ■ 2, 3 and

4 Phillips bands. H^0 and CO absorptions are weak

or absent.

J f i l t e r - the a v - 0 and -1 P h illip s and CN

sequences lie within this filte r as well as the +2

bands of the Bal11k-Ramsay system. The and CN

absorption at 1.4 microns is probably masked by the 73

1.38 micron terrestrial water vapor band. CO is absent but, if abundant, H^O will absorb slightly in this band.

H filter - absorptions on both sides of the filter may slightly influence it as may the higher order Av - -1 CN transitions. The second overtone of CO does lie in this filter. However, it is calculated, and observed, e.g. by Johnson and

Mendez (1970), to have a very small a ffe c t on the stellar spectrum. The H 2 O absorption effects on this filter are calculated to be slight. In general, this band is calculated to be relatively free of molecular absorption.

K f i l t e r - the av ■ -2 band of CN and the higher transitions of the a v * 0 sequences of the

Bal11k-Ramsay bands influence the short wavelength side of the filte r, while the CO first overtone depresses the long wavelength side. Depressions due to H^O occur on both sides of the filte r.

L filter - although the av - -3 CN and Av - -2

Bal1ik-Ramsay sequences occur In the middle of this filter, their absorption effects are calculated to be very weak. I f abundant, H^O absorbs throughout the filter, but If not, this filter is calculated to be relatively free from molecular absorption. 7*4

M filte r - the strong CO fundamental falls in

the middle of this band, and the 6 . 3 micron water

vaporfundamental greatly influences this band if

HgO is abundant.

The calculations indicate that the H and L filters are most free from molecular absorptions and may be used as a measure of the continuum. However, for some cool stars there is a strong absorption due to an unidentified molecule at 3.15 microns which will influence the L measurements.

The calculated spectra in figure 9 also show that much of the infrared absorption due to CN and C^ occur in spectral regions obscured from the ground by te rre s ­ trial atmospheric absorptions. The 1ong-wavelength edge of the l.*t micron water band partially obscures the av ■ -1 CNand P h illip s band and the 4 v - +1 B a llik -

Ramsay sequence. The 1.87 and 2.7 micron water vapor bands mask the av ■ 0 and - 1 Bal1ik-Ramsay sequences.

All of these transitions are strong for carbon stars.

Thus, effective temperature or bolometric correction determinations for carbon stars which ignore these regions, e.g. Mendoza and Johnson (1965) and Mendoza

( 1 9 6 7 ), are systematically in error.

It should be noted that the abundance of these molecules, N In equation (29), adopted in order to calculate synthetic spectra and molecular blanketing are 75 obtained from quantities measured in specific spectral regions in real stars. These abundance parameters are derived as follows:

HjO - from the equivalent width of the 1 .if micron

band

CO - from the equivalent width of the first overtone

CN - from a narrow band photometric determination of

the depression in the (0,0) band

C2 - from the calculated strength of the (0,0) Swan

band.

Thus, by neglecting the effects of saturation, it may not be possible to accurately predict the size of the depressions due to the molecular absorptions in spectral regions far from the ones used In abundance determination.

In order to determine how well the calculations are able to predict the gross spectral features found in cool stars, calculated spectra were compared to the measured spectra of

Woolf et al. (196*0 and Danielson et al. (1965). These spectra were chosen for the comparison as they are the only spectra taken at a high enough altitude to eliminate much of the telluric absorption; the only evident telluric spectral feature is the COj band at 2.7 microns. These data also are the only calibrated infrared scans of medium resolution for which the actual numerical values have been published. The Stratoscope spectra were divided 76 by a blackbody energy distribution of an appropriate

Infrared color temperature for each star and then normalized to the resulting peak value In order to reduce the flux scale.

The residual intensities for each spectral region in each star were calculated by means of equation (29). The

CO abundance parameter fo r

(1968) on the first overtone in these stars. The o Cett

CO abundance was assumed to be equal to that found for

R Leo. The HjO abundance for ^ Ori and ^ Cep was assumed to be n eg lig ib ly small while for R Leo and o Ceti the HjO abundances are calculated from the equivalent width of the l.*f micron band measured by Woolf et al . The CN and

TiO+VO indices of Wing (1967) for the five stars were taken as abundance indicators for these molecules.

The flu x d is trib u tio n s from model atmosphere calcu­ lations by Gingerich (1969) for giant stars of effective temperatures of 3750° and 3500°K were taken to represent the continuum energy d istrib u tio n s of <£- Tau and Ori respectively. The flux distribution for the 35O0°K model was also adopted fo r jul Cep. These models assume contin­ uous opacity sources only. Although the models are for 77 giant stars and ^ Ori and p * Cep are super giants,

Auman's (1969) calculations show that the flux d istri­ butions calculated for these two luminosity classes differ little at these temperatures. The calculated residual in ten sities for Tau, a. Ori and j i Cep were applied to the appropriate continua. The resulting energy distributions were divided by blackbodies of effective temperatures appropriate for each of these three stars in order to directly compare them with the normalized observation. These values were then adjusted by a scaling constant until a "best" fit to the observed data was obtained. A similar procedure was used for R Leo and o Cetl except that a greybody energy distribution was assumed for the continua in these two stars.

The normalized observed spectra for a Tau, ot Ori,

Cep, R Leo and o Ceti are compared to th eir calculated spectra in figures 10, 11, 12, 13 and l*t, respectively.

The points are the observed values for detectors A and B while the line is a plot of the calculated values. As can be seen from these p lo ts, the agreement between the c a l­ culated values Is fair. There appears to be more observed flu x in the 3200 to 3800 cm** spectral region than calcu­ lated fo r d Tau, A Ori and ji. Cep. However, the data reduc­ tion technique used by Woolf et a l.(196*0 on these stars is >2 92 19 M 1.12 1.22 UflVENUMBER '(MU-1)

Fig. 10. The observed and calculated normalized energy distributions for<£Tau. The crosses and boxes are the values obtained from detectors A and B, respectively, of Woolf et al (196b); -si the line Is the calculated values. 00 CD ♦ x CD X X r> *1

o

.32 ,52 .52 .72 .92 ’ .02 UflVENUMBER tMU-1I Fig. 11, The observed and calculated normalized energy distributions f o r * O ri. The meaning of the symbols is the same as for fig . 10. NORMALIZED FLUX/BB o o .0.00 .20 .40 .50 .50 32 Ft 9 v' !* 1. h osre ad acltd omlzd nry distribution energy normalized calculated and observed The 12. . .42 ofCep, eetr A n B rsetvl, f ailo e a (1965); al et Danielson of respectively, B, and A detectors h lne s h cluae values. calculated the Is e lin the h coss n bxs r vle otie from obtained values are boxes and crosses The .52 xx' fVNME (MU-13 UflVENUMBER .72 .32 .52 ). 02 1 .! 2

o

o ;

O .32 .72 .92 UflVENUMSER (MU-1) Fig. 13. The observed and calculated normalized energy distributions for R Leo. The meaning of the symbols Is the same as fig . 10. Note the deep Ho depressions at 0.36# 0.52 and 0.7 CD CD

X o L t i M a:~-{ s z ' . ar -5 o £ z " «f

o

32 32 WRVENUMBER IM U - l) Fig, 14, Same as figure 13 except the values are for o Cetl.

CD K> 83 most sensitive to calibration errors in this spectra)

region. Also, as Woolf (196*0 point out, the spectra may have some wavelength dependent error. The greatest disagreement is for yu.Cep, the star with the largest observational scatters. This star is reddened and this could explain the wavelength dependent discrepancy be­

tween the calculated and observed points.

The calculated CN depressions at 10850, 9050, 6850 and

MJ80 cm"^ match rather well the features Woolf et a l . ( 196*0

a ttrib u te to H^O in 4 Ori and y u - Cep, thus lending quanti­

tative support to the conclusion of Wing and Spinrad (1970)

that CN is the major infrared absorber for these stars.

The agreement between the observations and calcu la­

tions is especially good for the two very cool stars,

R Leo and o Ceti. The discrepancies are largest at the

short wavelength end of the spectra where the signal to

noise ratios of the observations are small for these two

stars. Also, the spectral resolution of the observations

In these regions is from 5 to 9 times less than that of

the calculations and this will tend to fill in the

calculated depressions.

The agreement between these observed data and c a l­

culations lends confidence in the ability of the present

method of calculating synthetic spectra to predict the

gross spectral features found in cool stars and quanti­

tatively to determine the molecular blanketing on them. The blanketing effe c t of H^O, C0r CN, C^ and TiofVO were calculated for each of the filters by convolving the system response with the synthetic spectra for each molecule calculated by means of equation (29). The atmospheric transmission, which is variable, was not

Included in these calculations. The effects of the blanketing in the filters were calculated for three assumed continuum energy d is trib u tio n s ; case I assumes an equal energy continuum; a Rayleigh-Jeans energy distribution, 2 FCV , is assumed in case II; and case III adopts a

Wien energy d is trib u tio n , F* V^e"c2 ^ ^ , for the continuum. Case II is the lim itin g case fo r a high

temperature and/or long wavelength regions. The true

continuum distribution should lie somewhere between case tI and case III.

The blanketing due to HjO, in magnitudes, for stars of effective temperatures T - 3000, 2500, 2000, and

1500°K Is given in table 5, fo r four values of the

equivalent width of the 1.4 micron band: 40, 120, 400

and 600 cm"*. The 400 and 600 cm"^ values were found

for R Leo and o Cetl by Woolf, SchwarzschiId and Rose

(1964). o Cetf was near minimum lig h t (and maximum H^O

band strength) at the time of observation. The top entry

for a given filte r and temperature in table 5 is for

continuum case 1, the middle is for case I I , and the

bottom Is for case III. Note that the M filter, which Table 5

Blanketing in Magnitudes Due to H^O for Various Values of

the Eouivalent Width of the 1.38 Micron Band ■1 40 cm"1 120 cm'

F IIte r/T . 3000° 2500° 2000° 1500° 3000° 2500° 2000° 1500°

0.001 0.001 0.001 0.001 0.002 0.002 0.002 0.002 i 0.000 0.000 0.000 0.001 0.001 0.001 0.001 0.002 0.001 0.001 0.001 0.001 0.002 0.003 0.003 0.003

0.012 0.013 0.013 0.014 0.037 0.038 0.038 0.039 J 0.010 0.011 0.010 0.011 0.031 0.031 0.031 0.032 0.013 0.015 0.017 0.022 0.040 0.044 0.049 0.060

0.016 0.014 0.011 0.009 0.050 0.042 0.032 0.025 H 0.016 0.015 0.010 0.009 0.051 0.043 0.032 0.025 0.016 0.014 0.011 0.009 0.050 0.042 0.032 0.025

0.043 0.046 0.044 0.046 0.126 0.124 0.123 0.118 K 0.042 0.047 0.045 0.046 0.127 0.126 0.125 0.120 0.042 0.046 0.044 0.046 0.126 0.124 0.122 0.116

0*076 0.077 0.060 0.045 0.202 0.187 0.156 0.118 L 0.085 0.084 0.066 0.050 0.224 0.204 0.172 0.130 0.084 0.081 0.062 0.045 0.220 0.198 0.163 0.118

0.092 0.109 0.112 0.131 0.229 0.247 0.258 0.281 M 0.084 0.099 0.102 0.114 0.212 0.224 0.233 0.249 0.084 0.100 0.103 0.122 0.212 0.226 0.238 0.264 T a b le 5 (Continued)

400 cm"1 600 cm"*

3000° 2500° 2000° 1J00° 3000° 2500° 2000° 1500°

0.008 0.008 0.008 0.009 0.015 0.015 0.016 0.018 1 0.006 0.006 0.006 0.007 0.012 0.012 0.013 0 . 0 1 s 0.016 0.011 0.013 0.017 0.019 0.021 0.025 0.032

0.435 0.134 0.133 0.139 0.226 0.220 0.216 0.223 J 0.115 0.113 0.111 0.115 0.195 0.189 0.182 0.187 0.144 0.153 0.170 0.210 0.239 0.249 0.270 0.326

0.191 0.161 0.127 0.140 0.329 0.281 0.220 0.188 H 0.194 0.164 0.129 0.104 0.334 0.286 0.228 0.190 0.191 0.161 0.125 0.104 0.329 0.279 0.221 0.187

0.390 0.382 0.380 0.372 0.584 0.575 0.575 0.570 K 0.398 0.392 0.394 0.388 0.597 0.595 0.597 0.596 0.392 0.382 0.377 0.361 0.588 0.576 0.570 0.552

0.499 0.477 0.430 0.379 0.673 0.650 0.614 0.583 L 0.538 0.507 0.464 0.412 0.698 0.683 0.653 0.625 0.530 0.497 0.445 0.381 0.693 0.672 0.631 0.585

0.492 0.522 0.533 0.615 0.617 0.654 0.701 0.794 M 0.471 0,494 0.517 0.566 0.598 0.630 0.667 0.747 0.47 0.497 0.525 0.530 0.598 0.632 0.675 0.770

CD o* 87 is strongly influenced by the 6.3 micron fundamental, has the largest blanketing of the filters considered, and this blanketing increases with decreasing temperature.

The blanketing in J is nearly independent of temperature since this filte r is affected by the 1 .*♦ micron band which Is being used as an abundance ind icato r. The blanketing In the remaining filters decreases with decreasing temperature. The 6.3 micron band Is a funda­ mental for and arises from low lying energy levels whereas bands which influence the other filters arise from more energetic states. This means that these absorption bands become narrower more rapidly than the

6.3 micron band with decreasing temperatures. The calculated blanketing using cases II and til for the continuum agree, for the most part, to within 0.02 magnitudes of the values for case I. There is a trend for the blanketing in the L filter for case II and for the warmer values for case III to be 0.03 to 0.0*f magnitudes more than the equal energy case, while the

M filte r blanketing is up to 0.05 magnitudes less.

These extremes are fo r the most abundant H^O values.

The distributions in cases II and III, for the temper­ atures mentioned, weight more heavily the short wave­ length end of these two filters. From figure 9 it can be seen that most of the absorption in the L filte r is on the short wavelength side, while the opposite is true 8 8 for the M f I 1 ter.

i 5 The blanketing for C O Is given In table 6 for stars of effective temperature T « 4000, 3500, 3000,

2500, 2000, and 1500°K and for equivalent widths of the first overtone of 30, 50, 70 and 100 cm"^. Woolf,

Schwarzschi1d and Rose (1964) measured equivalent widths for

Sinton (1968) measured the partial equivalent width of the first overtone of CO for ju . Cep as being 1.4 times

that of tfrOri. If this ratio holds for the entire band, then its total equivalent width is about 100 cm”*. As 12 C 0 has no absorption In the I, J and L filters, these were not included in table 6. From table 6 it can be seen that the M filte r is strongly depressed by CO.

Cases II and III for the continuum distribution, the middle and bottom entry In the table fo r each f i l t e r , again weight the short wavelength side of the filte r.

As this is where the maximum absorption occurs, the

blanketing fo r these two cases is s lig h tly greater than

for the equal energy case.

Ideally, we should now compare the calculated values of the CO blanketing in the M filte r with the observed

depressions. However, the measured values of flu x and

M magnitudes for the brighter stars are not as accurate

as the literature claims. Low, et al. (1970) state that

the previous H band photometry is systematically in error 89 Table 6

Blanketing in MagnitudeiDue to CO for Various Values

of the Equivalent Widths of the F irs t Overtone

30 cm*' 1* F iIte r 4000° 3500° 3000° 2500° 2000° 1500°

0.001 0.001 0.001 H 0.001 0.001 0.001 *** ------0.001 0.001 0.001

0.025 0.025 0.025 0.025 0.025 0.025 K 0.020 0.020 0.020 0.020 0.021 0.021 0.022 0.020 0.023 0.024 0.026 0.028

0.566 0.576 0.596 0.615 0.643 0.701 M 0.596 0.602 0.627 0.654 0.694 0.771 0.586 0.605 0.628 0.653 0.685 0.743

50 cm'1

0.002 0.001 0.001 0.001 0.001 0.001 H 0.002 0.001 0.001 0.001 0.001 0.001 0.002 0.001 0.001 0.001 0.001 0.001

0.01(2 0.01(2 0.01(2 0.042 0.042 0.042 K 0.034 0.03l( 0.031( 0.034 0.034 0.035 0.036 0.037 0.039 0.040 0.043 0.047

0.633 0.61(3 0.666 0.684 0.712 0.778 H 0.651 0.667 0.696 0.724 0.764 0.818 0.653 0.669 0.697 0.722 0.755 0,819

70 cm-1

0.002 0.002 0.002 0.001 0.001 0.001 H 0.002 0.002 0.002 0.001 0.001 0.001 0.002 0.002 0.002 0.001 0.001 0.001

0.059 0.059 0.059 0.059 0.059 0.059 K 0.049 0.01(8 0.048 0.048 0.048 0.049 0.051 0.052 0.054 0.054 0.057 0.067

0.672 0.683 0.709 0.728 0.757 0.826 H 0.688 0.706 0.737 0.767 0.809 0.897 0.690 0.708 0.738 0.765 0.800 0.868 90 Table 6 (Continued)

1 100 cm" T F ilt e r 4000° 3500° 3000° 2 5 0 0 ° 2000° 1500°

O.OOU 0.003 0.003 0.002 0.002 0.001 H 0.004 0.003 0.003 0.002 0.002 0.001 0.004 0.003 0.003 0.002 0.002 0.001

0.085 0.085 0.085 0.085 0.085 0.086 K 0.069 0.069 0.069 0.069 0.069 0.070 0.074 0 . 0 6 8 0.078 0.082 0.089 0.092

0.709 0.723 0.752 0.774 0.757 0.881 M 0.723 0.743 0.772 0.811 0.857 0.951 0.724 0.734 0.779 0.809 0.848 0.929 by 0.1 magnitudes. But when the M magnitude they lis t

for Or! Is compared to previous values, e.g. Johnson

(1967)* the difference Is 0.5. Thus for * Ori, the M

depression goes from a 1967 value of about 0.6 magnitudes, compared to 0.68 calculated and listed In table 6, to a value around 0.1 magnitudes. Although d Or! is variab le

and the M magnitude may change due to changes In the CO

opacity as well as true continuum changes, the L magni­

tudes in both references are the same.

It must be noted that these calculation neglect the

affects of atmospheric transmission. To account accu­

rately for the total band response, the transmission of

the atmosphere must be convolved with the system response.

For the conditions depicted in figure 9, the atmospheric

transmission would halve the effective system response.

This means that for the M filte r the measured blanketing

Is really some value less than what is listed in table 6.

How much less depends on the atmospheric transmission and

how the photometry is reduced. However, some general

comments may be made. The affects of increasing the

p rec ip ltab le water vapor in the atmosphere is to close

in the long wavelength side of the window. The e ffe c t

of increasing CO absorption is to deepen the depression

at the band head and widen the “wings" of the band. This

widening takes place more rapidly with increasing CO

abundance than does the deepening of the bandhead 92 depression. Since the atmosphere may absorb In the regions where the higher vibrational transitions of the CO funda­ mental are important, this could explain some of the discrepancy between the observed and calculated blanket­

ing values given above.

In any event, for an idealized situation, with little or no atmospheric effects on the system, the present calculations give a quantitative estimate how much CO absorption affects this band.

The first overtone of CO will depress the K filte r by as much as 0.1 magnitudes. As this absorption feature

lies on the long wavelength side of the filte r the blanketing values derived for case II and the warmer

temperatures for case 111 will be smaller than those for

the equal energy continuum. Since the first overtone was chosen as an abundance ind icato r, the blanketing in

K remains f a i r l y constant for a given value of the equivalent width.

In table 7 the amount of blanketing due to CN is

listed for temperatures of ffOOO, 3500, 3000, 2500, 2000

and 1500°K and for the three continuum distributions.

The blanketing calculations were done for three values

for depressions in the (0,0) band of 0.1, 0.3 and 0.8 magnitudes as measured by Wing (1967), who used a 30 A

bandpass centered at 10976A. The values of 0.1 and 0.3

magnitudes cover the range Wing found for giant and 93 Table 7

Blanketing in Magnitudes Due to CN for Various Values

______of the Depressions in the (0.0) Band ______

0.1 magnitude

Ft 1 ter 4000° 3500° 3000° 2500° 2000° 1500°

0.011 0.008 0.008 0.006 0.005 0.004 1 0.010 0.008 0.007 0.005 0.004 0.003 0.011 0.008 0.008 0.007 0.006 0.005

0.012 0.010 0.010 0.008 0.007 0.006 J 0.013 0.011 0.011 0.009 0.008 0.007 0.012 0.010 0.009 0.007 0.005 0.003

0.002 0.001 0.001 H 0.002 0.001 0.001 ------... 0.002 0.001 0.001

0.001 0.001 0.001 K 0.001 0.001 0.001 ------0.001 0.001 0.001

0. 3 magnitude

0.035 0.027 0.024 0.019 0.016 0.012 1 0.032 0.025 0.022 0.018 0.014 0.011 0.035 0 . 0 2 8 0.026 0.021 0.018 0.016

0.039 0.032 0.030 0.026 0.022 0.018 J 0.042 0.035 0.033 0.028 0.025 0.020 0.038 0.031 0.028 0.022 0.017 0.011 O O O O O O O O O

0.008 0.004 . . . 0.001 H 0.008 0.004 0.001 ------0.008 0.004 0.001

0.004 0.002 0.002 0.001 K 0.004 0.002 0.002 0.001 ... ------0.004 0.002 0.002 0.001 9*+ Table 7 (Continued)

0.8 magni tude

T F i1 ter 4000° 3500° 3000° 2500° 2000° 1500°

0.120 0.090 0.079 0.061 0.049 0.038 1 0.111 0.083 0.073 0.056 0.049 0.034 0.120 0.091 0.083 0.067 0.056 0.047

0.121 0.098 0.090 0.074 0.063 0.050 J 0.130 0.106 0.098 0.082 0.070 0.058 0.119 0.093 0.083 0.064 0.049 0.031

0.029 0.014 0.010 0.002 0.001 H 0.030 0.015 0.011 0.002 0.001 O O OOOO O O O 0.029 0.014 0.010 • . . 0.001 0.001

0.017 0.009 0.007 0.003 0.001 0.001 K 0.017 0.009 0.007 0.003 0.001 0.001 0.017 0.009 0.007 0.003 0.001 0.001 super giant M stars, while the 0.8 value is typical of carbon stars. The (0,0) depression measurements of

Wing are roughly related to the violet CN Index of

G r iffin and Redman (I960) by

ON . - - 1.9+0.32 m(0,0)u. violet Wing for giant stars earlier than Kit; for later stars the violet index is smaller than that given by this relation

ship. As a CN abundance indicator Wing's index is to be preferred over that of G r iffin and Redman because it is d ire c t measurement of the CN red system and, because i t

is an Infrared measurement, i t is less contaminated by atomic lines and Is not subject to the large violet continuous absorption found in many carbon stars.

The abundance parameter for CN was calculated by determining the amount of molecular absorption per molecule of CN expected tn the spectral bandpass of

Wing's 1.09 micron measurement and solving equation (29) fo r N,

From table 7 we see that the I and J filters are most affected by CN absorption, being depressed by 0.05

to 0.13 magnitudes for carbon stars and 0.01 to 0.0*t magnitudes for M stars. In all continuum cases, the calculated depressions for the L and H filters are

in sig n ifican t and thus these f i l t e r s were omitted from 96 the table. As shown fn figure 9 most of the CN absorption occurs between the f i l t e r s .

Table 8 lists the blanketing due to at 3500, 3000,

2500, 2000 and 1500°K fo r carbon stars of low, moderate and high carbon abundance. The carbon abundance c la s s i­ fication, defined by Shane (1928) and modified by Keenan and Morgan (1941, 1950), is based on eye estimates of the

intensity of one of the Swan bands, usually the (1,0) band, and is difficult to Interpret quantitatively.

Schadee (1968) defines the band intensity as

WQ/S0 In the expression

Wj /S j - W0/SQ exp(-F(J) c 2/T)

where S. is the HCnl-London factor and W, is the ° th equivalent width, in mA, of the J transition. If a

single layer atmosphere is assumed and saturation effects are neglected, then for the (0,0) transition

2 c-(T e+G (v))c2/T - It4 f 2(2-S 2 oo Ob me Q (30) M n - ' W T x (1.0-e 4 )

which Is obtained by sunvning equation (18) over all J

transitions and noting that the total band intensity Is 97 Table 8

Blanketing fn Magnitudes Oue to C2 for Various Assumed

______Carbon Abundance Classes ______

Class 1

F ilt e r ?5 0 0 ° 3000° 2500° 2000° 1500°

0.017 0.016 0.012 0.010 0.003 1 0.016 0.015 0.011 0.009 0.002 0.018 0.018 0.014 0.012 0.004

0.053 0.051 0.040 0.032 0.009 J 0.050 0.048 0.037 0.030 0.008 0.053 0.052 0.042 0.036 0.010

0.035 0.032 0.021 0.014 0.006 H 0.036 0.033 0.022 0.014 0.006 0.035 0.032 0.021 0.014 0.006

0.016 0.015 0.010 0.006 0.002 K 0.019 0.017 0.011 0.007 0.003 0.018 0.016 0.010 0.006 0.002

0.002 0.001 L 0.002 0.001 ------0.002 0.001

0.001 0.001 M 0.001 0.001 --- ... --- 0.001 0.001 v

98 Table 8 (Continued)

Class 3

Fi1 ter 3500° 3000° 2500° 2000° 1500°

0.111 0.106 0.082 0.065 0.019 1 0.1 04 0.098 0.076 0.062 0.018 0.119 0.116 0.093 0.079 0.026

0.279 0.269 0.213 0 . 1 7 4 0.063 J 0.270 0.260 0.203 0 . 16*» 0.059 0.280 0.273 0.221 0.188 0.071

0.200 0.185 0.123 0.080 0.041 H 0.206 0.191 0.126 0.082 0.041 0.201 0.185 0.121 0.079 0.042

0.094 0.087 0.058 0.038 0.018 K 0.106 0.098 0.066 0.043 0.019 0.100 0.090 0.059 0.037 0.017 O O O O O O O O O 0.012 0.009 » • • 0.001 0.004 L 0.013 0.010 0.001 0.003 0.013 0.010 0.001 0.003 O O O O O O O O O 0.011 . . . 0.005 0.002 0.002 M 0.11 0.005 0.002 0.002 0.11 0.005 0.002 0.002 99 Table 8 (Continued)

Class 5

F11 ter 3500° 3000° 2500° 2000° 1500°

0.524 0.499 0.389 0.307 0.123 I 0.499 0.475 0.369 0.291 0.114 0.546 0.531 0.426 0.348 0.163

0.910 0.893 0.714 0.510 0.344 J 0.905 0.885 0.702 0.554 0.329 0.911 0.896 0.725 0.593 0.380

0.721 0.699 0.513 0.354 0.242 H 0.739 0.718 0.582 0.366 0.245 0.725 0.699 0.508 0.344 0.239

0.355 0.237 0.164 0.116 K 0.385 0.262 0.181 0.123 .p-0\Uj OOO 0.370 ... 0.239 0.159 0.111

0.079 0.060 0.023 0.007 0.024 L 0.086 0.066 0.026 0.008 0.026 0.085 0.065 0.025 0.007 0.024

0.069 0.060 0.033 0.018 0.014 H 0.072 0.064 0.035 0.018 0.014 0.073 0.064 0.035 0.011 0.014 100

Table 8 (Continued!

Class 7

F i 1 te r 3500° 3000° 2500° 2000° 1?00°

1.502 1.474 1.181 0.908 0.581 1 1.469 1.437 1.146 0.880 0.551 1.531 1.521 1.241 0.975 0.714

1.743 1.847 1.639 1.300 1.230 J 1.758 1.858 1.642 1.292 1.203 1.740 1.840 1.637 1.311 1.294

1.384 1.474 1.334 1.106 0.996 M 1.398 1.493 1.363 1.101 1.011 1.387 1.474 1.326 1.041 0.978

0.855 0.852 0.667 0.477 0.543 K 0.892 0.896 0.714 0.518 0.567 0.874 0.867 0.672 0.467 0.526

0.336 0.262 0.135 0.047 0.155 L 0.358 0.304 0.149 0.053 0.167 0.356 0.299 0.144 0.050 0.156

0.324 0.301 0.191 0.103 0.096 M 0.336 0.314 0.201 0.113 0.099 0.337 0.314 0.203 0.111 0.097 101

W. . - 2 w - W /S (2S"+1)Q band j J o o rot

Actually, Schadee performs hfs calculations fn terms of the logarithm of W0/$ 0 normalized to the solar value, i.e. log (W0/SQ)c-log (W0/SQ)0-jWQ/sJ . This definition of the band intensity was adopted in as much as eye estimates of intensity, such as used for deter* mining the carbon abundance c la s s ific a tio n , tend to be logarithmic in scale.

As a test of the ability of equation (30) to predict the abundance, it was used to calculate the number of

Cj molecules per square centimeter above the solar . Arnolds's (1968) value of 0.035 for f and Schadee's value of -0.19 for log (w0/s0)# f°r the

(0,0) Swan band, were substituted Into equation (30) and a value of ~lo'® was obtained. This is close to the value found by Stanger, see A lter (196*0, from molecular equilibrium calculation for the sun.

Schadee also derives a value of CW0/ S01 ■ 1.69 for a star classified as C1,l. This value was adopted as a starting point and it was assumed that each successive carbon abundance class represents an e-fold increase in molecular abundance.

As might be expected, the J filte r has the largest calculated blanketing of the filters listed In table 8. 1 0 2

For a star with a spectral temperature class of 5 to 6,

corresponding to effective temperatures between 3000° and

2500°K according to Keenan (1963), and a carbon class

of 5, the J filte r is depressed by about 0.3 magnitudes

more than the I f i l t e r . Johnson, Mendoza and Wisniewski

(1965) have observed depressions on this order of magni­

tude for the J filter for T Lyr (C6,5) and T One (C5,5).

However, detailed q uantitative comparisons are d if f ic u lt

to make in that the calculations of the values in table 8

were done by folding the system response of the Johnson

filters with the calculated spectra, ignoring the effects

of atmospheric transmission. Also absorption due to CN

will further depress this filter.

Figure 9 shows that the earth 's atmosphere w ill

diminish the importance of the absorptions of the

Av ■ -1 bands of the P h illip s system and the Av - +1

sequence of the Bal1ik-Ramsay system. Thus, the blanket­

ing values calculated for the J f i l t e r w ill be too

large, by an amount depending on the atmospheric trans-

mi ssion.

Table 9 shows the calculated depressions in the

filters due to CN, CO and Cj for stars of carbon class 3 and 5. The calculations indicate that the L filter is

relatively free from molecular absorption for carbon

stars but the I, J and K filters are strongly depressed

for the stars of high carbon abundance. Thus, the use 103

Table 9

Calculated Blanketing In Magnitudes Due to CN t

CO and C2 in Carbon Stars

Class 3

T F ilte r 3 5 0 0 ° 3000° 2 5 0 0 ° 2 0 0 0 ° IJOO1

1 .275 .199 .132 .09** . 0 7 0

J . 2 8 0 .215 , 1 ** 6 . 0 1 0 .068

H .09** . 0 6 2 .032 . 0 1 8 . 0 1 2

K . 1 8 0 . 1 5 6 .133 . 1 2 ** .125

L .005 .003 . 0 0 1 . 0 0 0 . 0 0 0 00 00 00 r- r\ c M . .825 .859 . .976

AT 3 6 0 1 6 0 6 0 0 0 Class 5

1 .687 .616 .**81 . 3 8 8 ,336

J 1 . 0 ** .98** . 7 8 6 .629 .536

H .753 .70** .**9** .321 .203 00 -a-

K .530 9 .365 .277 . 2 2 2

L . 1 1 0 . 0 8 1 .029 . 0 0 8 . 0 0 0

M .788 . 8 2 6 .860 .900 .978

AT 690 M»0 220 110 50 1C* of the (l-L) index by Mendoza (1967) and the (R+L)-(J+K)

index by Mendoza and Johnson (1965) to represent the effective temperatures for carbon stars will yield values system atically too low for stars of high carbon abundance.

The AT's lis ted in table 9 for each temperature and carbon class are the amounts which the temperature derived from

the (l-L) indices for these carbon stars will be under­ estimated due to blanketing in the I filter. It should be noted, though, that the spectra of Gausted, G illett,

Knacke and Stein (1969) and Johnson and Mendez (1970) do show a deep depression at 3.19 microns in some cool M and carbon stars, which will influence the short wave­

length side of the L filter.

In table 10, the stars which have (l-L ) measurements and a C classification are listed. The first column gives the designation of the star, the second, third and

fourth l i s t the measured ( l- L ) , (B-V) and (U-V) indices,

the fifth gives the C classification of the star and the

last column lists the type of variability. The measured

indices are from Mendoza and Johnson (1965), Mendoza

(1967). Wing (1967), Neugebauer (1970) and Woolf (1970).

The C c la s s ific a tio n s are taken from Keenan and Morgan

(19^1). Yamashita (1967) and Kukarkin et a l. (1967).

The variable types are from Kukarkin et al. The stars,

which are listed in the table in the order of decreasing Table 10 105

Colors and Spectral Types for some Carbon Stars

Spectral Variable Pes ignation I-L B-V U-V Type Type

V Cyg 7.44 5.0-6.5 C6,4-C7,4 M

S Cep 6.89 5.6 C5,4-C7,4 H

V Hya 5.70 5.70 C6.3 SR

V Oph 5.36 C6,3e M

V CrB *♦.50 *♦.*♦1 12.7 C6,2e-C6.5.3 M

U Cyg *♦.*♦9 *♦.16 7.83 C7»2-C9»2 M

R Lep 4.44 5.00 10. C6.5-C7.6 M

T Lyr *♦.06 5.53 14.5 C5,3-C6,5 LP

T Cnc 3.97 5.30 13.3 C4.5-C5.5 SR

RX Set 3 . 8 0 2.86 7.97 C4,8 LP

SV Cyg 3.80 3.27 9.77 C5,5 LP

LW Cyg 3.60 *♦.16 13.2 C4,2-C4,4 LP

RY Ora 3.50 3.26 12.16 C3,4-C4,4 SR

HD 168227 3.43 1.89 3.89 C4,4

Y CVn 3.26 2.54 9. C5.4 SR

V I942 Sgr 3.12 2.34 6.67 C4,6 LP

V460 Cyg 3.11 2.52 7.82 C6,3-06,5 LP

VY UMa 3.06 2.41 7.18 C6,3 LP

RS Cyg 3.01 2. 6.76 C8,2e SR Table 10 (Continued) 106

Spectral Variable Designation l-L B-V U-V Type Type

WZ Cas 3.01 2.86 7.13 C9.1 SR

HD 133332 2.85 1.42 2.70

U Hya 7.83 2.72 7.85 C7»3 SR

TX Psc 2.71 2.61 6.11 C6,2

HO 113801 2.30 1.17 2.22 Cl ,1

TT CVn 2.05 1.83 3.67 C3,3CH LP

HD 156074 1.34 2.06 2.06 Cl ,2

HD 182040 0.44 1.72 1.72 Cl ,2

M - Hi ra Variable

SR - Semi-Regular Variable

LP « Slowly Varying Irregular Variable (l-L) Index, divide into three groups. One group, composed of Mira variables, has a large (l-L) index /• hi (>4.4), a relatively^carbon abundance class (2 to 4) and cool spectral temperatures. Another group has a high carbon abundance class (4 to 8) and an (l-L ) index between 3.4 to 4.0 which is correlated with the spectral temperature class in the sense that as the spectral tem­ perature decreases as the (t-L) index increases. There

is a third group of stars which have an (l-L ) index between 2.7 and 3.3 which is not correlated with spectral temperature class and is composed of stars classified as having relatively low carbon abundance classes (2 or 3).

These la tte r two groups of stars are composed of semi- regular or irregular variables. Indices other than

(l-L) were investigated in an attempt to obtain a correlation between the Index and the spectral temperature class but no such correlation was found.

For a temperature of 3000°K, the calculated blanket­

ing from table 9 wl 11 increase the ( l-L ) index by 0.2 and 0.54 magnitudes for abundance classes 3 and 5, respectively. The difference between the group of carbon stars at ( l-L ) of about 3*0 and the rest of the stars is

0.8 to 4.0 magnitudes, or 3 to 10 times more than the calculations predict. However, the method of assigning abundance class In the calculations is somewhat arbitrary. 108

I f what is assumed as abundance class 7 is ac tu a lly representative of 5, then from table 8 the (l-L ) index is increased by 1.19 magnitudes, which is sufficient to explain the discrepancy for most stars.

Thus, the calculations indicate that some of the duality in the (l-L) index versus spectral temperature class for carbon stars can be explained by molecular blanketing in the I f i l t e r . However, i f the visual and ultraviolet spectral regions are also heavily blanketed, as well they may be as indicated by the large (B-V) and

(U-V) values for most of the stars in table 10, and especially for the Mira variables, the redistribution of the energy caused by the blanketing w ill enhance the emergent flu x in spectral regions with l i t t l e or no blanketing, e.g. the L filter. This will tend to increase the ( l- L ) index for carbon stars.

To determine how the energy redistribution due molecular blanketing affects the emergent flux, detailed model atmospheres must be calculated which is beyond the scope of the present study. However, the profound affects of CN and in carbon star spectra indicate that they must be included in any model calculations and i t is hoped that the molecular absorption coefficients derived 109

in the present study may eventually be used to carry out

these calculations.

The synthetic spectra for the models at « 3000°K

in table 9 for carbon classes 3 and 5 were integrated to obtain the total flux in the 0.7 to 6.3 micron spectral region. The calculated blanketing in the Johnson filters for the same two cases were applied to the assumed continuum flux at the effective wavelengths of the filters to get the energy distributions which the filte r photometry would predict. These distributions were then numerically integrated by lin e a rly interpolating between the calculated points and compared to the flu x computed from the synthetic spectra. For carbon class 3 the two are in good agreement. For carbon class 5 the calculated

total flux is about 15% less than the filte r photometry would predict, indicating that the bolometric corrections

that Johnson and Mendoza (1965) derive may be systemati­ cally too large for stars of high carbon class.

Table 11 lists the blanketing in the I and J bands due to TiO+VO for stars of 3000°K, 2500°K, 2000°K and

1500°K effective temperature. The depressions for these calculations were obtained by the method detailed in

Chapter 8 using the measured depressions of Wing (1967) 110

Table 11

Blanketing In the I and J Filters Due to TiO+VO

F i 1 ter 3000° 2500° 2000° 1500°

0.183 0.353 0.423 0.500 1 0.213 0.410 0.491 0.577 0 . 1 * 1 6 0.257 0.268 0.271

0.004 0.003 0.026 0.074 J 0.005 0.004 0.033 0.093 0.003 0.002 0.018 0.036

due to these two molecules for the representative stars

In table 4. The entries in table 11 are for the three adopted continuum cases. As these calculations are for stars of effective temperatures of 3000°K or less, the equal energy and Rayleigh-Jeans approximations to the continuum (cases I and II) are probably not accurate representations of the true situation. These two distributions weight the short wavelength side of the 1 and J f i lt e r s more than does case 111. As much of the absorption due to these two molecules occur in this region the calculated blanketing for the first two cases will be too large.

For M stars molecular equilibrium calculations predict that as the temperature decreases water vapor should form and the blanketing In L due to H^O should compensate the TiO+VO blanketing In I. The calculations of Auman and Goon (1970) predict HjO number abundances

in giant stars with Te of 3500, 3000, 2500 and 2000°K which roughly correspond to the ones determined in the blanketing calculation presented in table 5 for values of the equivalent width of the 1.4 micron H2o band of

40, 120, 400 and 600 cm"^ at these respective temperatures.

However, the spectra of Johnson and Mendez (1970) show

little or no HjO absorption for cool giants, not even for EU Del which is taken as the standard in table 4 used

to calculate the TiO+VO blanketing for a 2500°K star.

The calculated HjO blanketing for this star, according to abundance calculations, should be as great as for o Ceti.

This raises serious doubt as to advisability of adopting a solar 0/C ratio for giant M stars. In any event, it is apparent that HjO blanketing in the L filter will not compensate for the TiO+VO blanketing in the I f i l t e r , at

least for stars 2500°K and warmer. The blanketing in I

ts, at most, 0.27 magnitudes and this value is approached

for stars 2500 ° k and cooler where Johnson (1965) finds

the (l-L) Index is relatively sensitive to a temperature change. As the L f i l t e r is predicted to be free of molecular absorption, the (l-L) index for M stars Is a good one. CHAPTER 10. CONCLUDING REMARKS

The averaged absorption coefficients have been calculated fo r CO, CN and C^. These c o e ffic ie n ts , along with HjO values calculated from the data given by Ferriso,

Ludwig and Thompson (1966), were used to calculate synthetic spectra representative of cool, late type stars.

Agreement between the calculated spectra and the ones observed by Woolf, SchwarzschiId and Rose was found to be good, lending confidence in the ability of the calcula­ tions to describe the gross spectral distributions of late type stars.

The blanketing effects of these molecules were calcu­ lated for the Johnson filters. The (l-L) index was found to be a good temperature indicator for M stars, as the calculated blanketing in 1 and L filters are significant only for the very cool stars where the (l-L ) index is relatively sensitive to temperature change. The blanketing due to Cj and CN in the I filter for carbon stars, which is variable, make this index unreliable for this group of stars. The M f i l t e r was found to be strongly influenced by CO and, if abundant, H 2 O. The I and, especially, the J filte r are depressed by CN and

C2 absorption. Unfortunately, it does not seem possible to separate indices of CN and Cj in carbon stars from the

112 113

Johnson photometry.

Apparently, Johnson's choice of f i lt e r s and band­ passes was dictated by the atmospheric transmission and system s e n s itiv ity constraints. The f i l t e r s were chosen as wide as possible, consistent with the window, presum­ ably in order to maximize the energy on the detector.

The spectral resolutions of the J, K, L and M filters,

to 0.25* are wide enough to be influenced strongly by the atmospheric absorption bands. This complicates considerably the interpretation of the photometric measurements. As previously discussed this is especially true for the M and J filters; but, as can be seen from fig u re 9, both the L and K system responses are depressed on the short wavelength sides of the filters.

On the basis of the present calculations a new set of infrared f i lt e r s may now be chosen in order to maximize the amount of information about a star that can be obtained from wide bandpass photometry. Oetector sensitivity and instrumental techniques have improved enough since

Johnson established his system, that restricting the f i l t e r bandpass to a a * /a of about 0.1 will not limit the usefulness of the system. The calculations show that such bandwidths aie the maximum consistent with the atmospheric transmission and the spectral absorption features in the stars. The following set of filters is reconvnended: m

1. An I filte r centered at 1.0^+ microns (9600 cm"') with a bandpass from 0.98 to 1.09 microns (10200 to 9150 cm"'). This is a good spectral region to represent the

s te lla r continuum. For M stars, the only prominent

absorption feature in this band is V0 (see figure 8) and,

according to Wing (1967), it is strong only for stars

later than M7. This conclusion is further supported by

the fact that the I filter in the six color system of

Stebbins and Kron (196^), which extends from 1.1 to 0.9 microns, was found by Smak (1961+) to have li t t l e or no

blanketing. For carbon stars this region is somewhat

influenced by the ta il of the a v - 1 sequence of CN and

also by the P h illip s Av * 1 and the Bal1ik-Ramsay

Av * 3 sequences of C^.

2. A filter at 1.63 microns (6130 cm"') extending

from 1.52 to 1.76 microns (6550 to 571^ cm"'). This is

very similar to the H filter adopted for this study. The

present calculations show that this is a good region in

which to measure the stellar continuum, being strongly

depressed only for carbon stars of very high carbon

abundance. Also, this f i l t e r would provide a measure of

the affects of the H" opacity minimum for late G and

early K stars.

3. A f i l t e r narrower than the Johnson's K in order

to minimize the atmospheric absorption affects on the

short wavelength side of the present filter and the 115 stellar CO first overtone on the long wavelength side.

The new band would be centered at 2.21 microns (*+525 cm*') and would have a bandpass from 2.1 to 2.31 microns

(4750 to 4350 cm'1).

4. A filter centered at 3.6 microns (2750 cm"1) and w ith a bandpass from 3.2 to 4.15 microns (3125 to 2400 cm*1). This f i l t e r would avoid the atmospheric absorp­ tion to which the L filter is subject. It would also avoid the 3.15 micron absorption which appears to be strong in some cool stars, although it is doubtful that the present L filte r is influenced much by this absorption feature, as the transmission of the earth 's atmosphere is down quite a bit at this wavelength. Usually, the long wavelength cu to ff of this band is determined by the r o llo f f In the detector s e n s itiv ity . However, lead sulfide detectors can be selected which are responsive out to 4.2 microns; Johnson's o rigin al L f i l t e r system response consisted of such a filte r and cell combination.

5. Finally, a 5 micron filter centered at 4.8 microns (2100 cm"1) extending from 4.5 to 5.1 microns

(2200 to 1060 cm-1). This would avoid some of the problems of interpreting the M measurements, as pointed out earlier, by avoiding as much of the atmospheric absorption as possible. 116

It should be noted that the first three of the proposed filters are very similar to the W, Y and Z filters of Walker (1966, 1969). His photometric data indicates that the general conclusions arrived at by the present study are correct: the 1.0** and 1,63 micron f i l t e r s (his W and Y bands) are good continuum measures.

The present calculations indicate that there is no spectral region, relatively free of terrestrial atmospheric absorption, wide enough to be able to indicate unambiguously the quantitative presence of one of the molecules in this study by means of wide band-pass photometry. The X filte r of Walker (1966, 1969), which is centered on the 1.16 micron water vapor band, does indicate the presence of CN in stars. However, the terrestrial water vapor absorption in this region make the quantitive interpretation of the photometry very difficult. The molecular abundance indicators will have to be derived from actual spectra or narrow band photom­ etry, e.g. Wing's (1967) scanner photometry which was used in this study as abundance indicators fo r CN, TiO and VO.

Thus, the synthetic spectra can explain quantita­ tively the affects of molecular absorption in cool stars on the existing wide bandpass photometry and offers a method by which the photometry may be analyzed. With the proposed filters and the synthetic spectra generated with the molecular constants calculated In this study,

i t should be possible to predict q u a n titative ly the gross spectral features found in late type stars. 118

BIb1ioqraphy

A lte r, L. H ., 1963, "The Atmospheres of the Sun and Stars". 2nd e d ., Ronald Press.

Arnold, J. 0 ., 1968, J.Q .R .S .T ., 8, 1781.

Auman, J. R ., Jr ., 1967, Ap. J. Supp., U*, 171 (No. 127).

...... , 1969, Ap. J ., H Z . 799.

Auman, J. R ,,Jr ., and Goon, G. , 1970, Ap. J. , 161 . 533 .

Bahng, J., 1967, "Colloquium on Late Type Stars", ed. M. Hack, T rieste, p. 225.

...... , 1969a, M.N.R.A.S., Jj*2, 73.

...... , 1969b, Publ. A .S .P ., 81, 861.

8allfk, E. A., and Ramsay, 0. A., 1958, J. Chem. Phys., 22, 1M 8.

— ------, 1963a, Ap. J., 137. 61.

...... , 1963b, Ap. J ., 122, 8*f.

Barnhart, P. E.,and Mitchell, W. M., Jr., 1966, Contr. from the Perkins Obs., Series II., No. 16.

Beebe, R., 1970, private communication.

Benedict, W. S., Herman, R ., Moore, G. E ., and Silverman, S., 1962, Ap. J., 135. 277.

Benesch, W., Vandersllce, J. T., Tilford, S. G., and Wilkinson, P. G., 1965, Ap. J., V*2, 1227.

------, 1966, Ap. J., 1 kk, ^08.

Bennett, R. J. M., 1970, M.N.R.A.S., U*Z» 35.

Bobrovnikoff, N, T., 1933, Ap. J., 2§» 211.

Boyce, P. B ., and Sinton, W. M ., 1965, Sky and Telescope, M , 78.

Bud6, A., 1937, Z. Phys., 102, 579. 119

Cameron, D. M., and Nassau, J. J ., 1955, Ap. J . , 122. 177.

Cashion, K., 1963, J. Molec. Spec., J_0, 182.

Carlson, K. 0., and Moser, C., 1966, J. Chem. Phys.. 44, 3259.

Chandrasekhar, S., 1950, "Radiative Transfer11. Oxford Univ. Press. dementi, E., i960, Ap. J., 132. 8 9 8 .

...... , 1960, Ap. J ., i i i ,303.

Connes, P ., Connes, J ., Bouigue, R., Querci, M., Chauville, J ., and Querci, F . , 1968, Ann. Ap., <2J_, **85.

Danielson, R. E., Woolf, N. J ., and Gausted, J. E., 1965, 141. 116.

Oavls, S. P., and Phillips, J. G., 1963, "The Red System (A^t t -X^a ) of the CN Molecule". Univ. of California Press, Berkeley and Los Angeles.

Dixon, R. N., and Nicholls, R. W., 1958, Can. J. Phys., 2 6 , 1 2 7 .

Dolan, J. F ., 1965, Ap. J ., J42, 1621.

Douglas, A. E., and Routley, P. M., 1954, Ap. J. Supp., J., 295 (No. 9).

Earls, L. T., 1935, Phys. Rev., 48, 423.

Fay, T., Marenin, I., and van Citters, W., 1971, in preparation.

Ferriso, C. C., Ludwig, C. B., and Thompson, A. L ., 1966, J.Q.S.R.T., 6, 24*

Fertel, J. H., 1970, Ap. J., L7.

Fishburne, E. S., Weinberg, R., Edse, R., and Rao, K. N., 1964, J.O.S.A., 5 4 , 1288.

Fishburne, E. S., Rao, K. N., and Weinberg, J. M., 1965, Combustion and Flame, £ , 425.

Fougere, P. F., and Nesbit, R. K., 1966, J. Chem. Phys., 44, 285. Fraser, P. A ., and Jarmain, W. R. , 1953, Proc. Phys. Soc., A66, 1153.

Fraser, P. A., Jarmain, W. R., and Ntcholls, R. W., 1954, Ap. J ., J_L2, 285.

Gausted, J. E., Glllett, F, C., Knacke, R. F ., and Stetn, W. A., 1969, Ap. J., 158, 613.

G llle t t , F. C., Low, F. J ., and Stein, W. A ., 1968, Ap. J . , 15V. 677.

Gingerich, 0. J . , and Kumar, S. S., 1964, A. J . , 62, 139.

Gingerlch, 0. J . , Latham, 0. W., Linsky, J . , and Kumar, S. S., 1967, "Colloquium on Late Type Stars11, ed. M. Hack, p7"T5T*T

Golden, S. A ., 1967, J.Q .S .R .T ., 2, 225.

Goody, R. M., 1964, "Atmospheric Radiation". Oxford Press, London.

Greene, T. F„, 1969, Ap. J ., 157. 737.

Grevesse, N ,, 1970, private communication.

Griffin, R. F., and Redman, R. 0., I960, M.N.R.A.S., 120. 287.

Halmann, M., and Laulicht, 1., 1966, Ap, J. Supp., 12. 307 (No. 110).

Heaps, H. S ., and Herzberg, G ., 1952, Z. Phys., 133. 48.

Herzberg, G ., 1950, "Spectra of 01 atomic Molecules11. 2nd ed., 0. van Norstrand Co., Princeton, N.J.

Honl, H., and London, F., 1925, Z. Phys., 21» 803.

Hunaerts, J ., 1967, Ap. J., 149. L31.

Hyde, G. E ., and Hornig, 0. F ., 1952, J. Chem. Phys., 20, 647.

Jeunnehonvne, M., 1965, J. Chem. Phys., 42, 4086.

Johnson, H. L ., 1964, B oll. Tont. y Tac. Obs., 2 , 303. Johnson, H. L ,, 1966, Ann. Rev, of Astro, and Astro- 121 phys.. 4, p. 193.” Palo A1 to, ITal . , Ann Reviews, Inc.

...... , 1967, Ap. J ., U+2, 345.

Johnson, H. L ., Coleman, I . , M itch ell, R. I . , and Steinmetz, D. L., 1968, Comm. L. P. L., ]_t 83.

Johnson, H. L . f and Mendez, M. E ., 1970, A. J. , 25., 785.

Johnson, H. L ., Mendoza, V ., E. E., and Wisniewski, W. Z . , 1965, Ap. J ., J42, 12^9-

Johnson, H. R., Marenin, 1., and Price, S. D. , 1971, in preparat ion.

Keenan, P. C ., 1963, “ Basic Astronomical Data11, ed. K. Aa, Strand., Univ"! of Chicago Press, CK7 8.

Keenan, P. C ., and Morgan, W. W., 1941, Ap. J. , 501.

------, 1951, " Astrophvsics11. ed. J, A. Hynek, McGraw H ill Co.

Keenan, P. C ., and Schroeder, L. W., 1952, Ap. J . , I I S . 82.

Klein, 0 ., 1932, Z. Phys., JS, 226.

Knacke, R. F ., Cudaback, D. 0., and Gausted, J. E ., 1969, Ap. J ., J£8, 151.

Krishna Swamy, K. S., 1967, Ap. J. , JJ>0, 1161.

Kuiper, G. P., 1938, Ap. J. , 88, 429.

------( 1962, Comm. L. P. L .,

...... , 1963, Comm. L. P. L . , J_, 179.

------, 1964, Mem. Soc. Roy. Sci. Liege, 365.

----- , 1970, Comm. L. P. L., 8, 121.

Kukarkin, B. V., Kholopov, P. N., Efremov, Yu. N., Kudarkina, N. P ., Kurochkin, N. E ., Medvedeva, G. I . , Perova, N. B., Fedorovich, V. P., and Frolov, M. S., 1969, “General Catalogue of Variable S tars". 3rd. ed.

Kunde, V. G ., 1967, NASA Tech Note X-622-67-248.

...... 1968a, Ap. J ., I l l , 436.

, 1968b, NASA Tech Note, TND-4798. Kunde, V. G., 1968c, NASA Tech Note X-622-68-452.

...... , 1969, Ap. J., 158, 1167.

Lambert, D. L., 1968, J.Q.S.R.T., 8, 1265.

Linsky, J. L., 1969, Ap. J,. ig6, 9 8 9 .

Lockwood, G. W., 1968, A, J ., 139. 1130.

Low, F, J ., 1970, AFCRL Semi-Annual Tech. Report 70-0179.

Low, F. J ., and Johnson, H. L ., 1964, Ap. J ., 139. 1130.

Low, F. J ., Johnson, H. L ., Kleinmann, D. E., Latham, A. S and Geisel, S. L ., 1970, Ap. J ., .160, 531.

Ludwig, C. B ., and Malkmus, W., 1967, NASA Tech Note TH- X-53711 .

HeGammon, 0 ., Hunch, G., and Neugebauer, G., 1967, Ap. J . , 147. 525.

HcCarthy, H. F., Treanor, P. J., and Ford, W. K., 1967, 11 Colloquium on Late Type Stars1*, ed. H. Hack, T rieste p. 100.

HcClatchey, R. A ., Fenn, R. W., Selby, J. E. A ., Garing, J. S., and Volz, F. E., 1970, Environmental Research Papers No. 331. AFCRL-70-0527.

HcKellar, A., 1954, Publ. A. S. P., 66, 312.

Hendoza, V., E. E ., 1967, Bol. Tont. y Tac. Obs., 6, 114.

Hendoza, V., E. E., and Johnson, H. L ., 1965, Ap. J . , 141. 161.

Hertz, L., 1970, private communication.

Hiller, F. D., 1953, Ap. J., JJ_8, 572.

Hills, I. H,, and Thompson, H. W., 1953, Trans. Faraday. Soc., 42, 224.

Horoz, V. 1., 1966, Astr. Tsirk (Sternberg Institute), No. 368, 4, April 1966.

...... 9 1 9 6 6 , Astron Z h ., 42, 63, (Eng. Trans., Sov. Astron.-A.J.. 10. 47). 123

Morris, S., and Wyller, A., 1967, Ap. J., 150. 877.

Morse, P. M ., 1929* Phys. Rev,, 2k* 57.

Munch, G., 1958, Ap. J ., \2 l, 642.

Neugebauer, G ., 1970, p riva te communication.

Nlchol1s, R. W., 1962, J. Res. N.B.S., 66*. 227.

...... , 1964, J. Res. N .B .S ., 68A, 75.

...... , 1965a, J. Res. N.B.S., 69A, 397.

, 1965b, J .Q .S .R .T ., 2, 647.

Nixon, E. R., and Cross, P. C., 1950, J. Chem. Phys., 19. 1316 . Penner, S. S., 1959, "Q uantitative Molecular Spectroscopy and Gas Emlssivities". Addison-WesYev. Reading, Mass.

Penner, S. S., and 01fe , D. M ., 1968, ''Radiation and Re­ entry11 . Addison-Wesley, Reading, Hass.

Pettersson, A. V., and Lindgren, B., 1962, Ark. Fys., 22, 491.

Pettit, E., and Nicholson, S. 0., 1928, Ap. J,, 68, 279.

P h illip s , J. G., 1950, Ap. J ., J_n, 314.

...... , 1969, Ap. J., 449.

Phillips, J. G,, and Davis, S. P., 1967, "The Swan System of the Molecule", Univ. of Calif. Press, Berkeley and Los Angeles.

Poletto, G*, and R lg u ttl, M., 1965, Nuovo Cimento, 22.* 516.

Querci, M., 1967, Ann. Ap., ^0, 677.

Rank, D. H., St. Pierre, A. G., and Wiggins, T. A., 1965, J. Molec. Spec., J[8, 418.

Rees, A. L, G ., 1947, Proc. Phys. Soc. London, 52* 99®*

Rydberg, R ., 1932, Z. Phys., 2 2 * 376.

. » 1933, Z. Phys., 80. 514. 12*+

Schadee, A., 196*+, B.A.N., \J_, 311.

...... , 1967, J.Q.S.R.T., 2. 169*

...... , 1968, Ap. J. , 151 , 239.

Shane, C. D ., 1928, Lick Obs. B u ll., H , 123.

Sinton, W. M. , 1962, App. Opt., J_» 1®5.

------( 1968, “ Infrared Astronomy11, ed. P. J, Brancazio and A. G. W. Cameron, 75or8on and Breach Publ., p. 55.

Smak, J ., 196*+, Ap. J. Supp. , Series 2* No* 89.

Solomon, P., and Stein, W. A., 1966, Ap. J. , 1 *+*+. 825.

Spindler, J., 1965, J.Q.S.R.T,, 165.

Sp inrad, H ., 1966, Ap. J ., l*+5. 195.

Spinrad, H ., Kaplan, L. D ., Connes, P., Connes, J . , and Kunde, V. E ., 1970, paper read at the Conference on Late-Type Stars, (Tucson; October 1970).

Spinrad, H., and Vardya, M. S., 1966, Ap. J., 1 *+6. 399.

Spfnrad, H ., and Wing, R. F , , 1969, "Ann. Rev, of Astro, and Astrophvs.". 2» 2lf9.

Stebbins, J . , and Kron, G, E, , 196*+, Ap. J ., 139. *+2*+.

Tatum, J. B. , 1967. Ap. J, Supp., V±, No. 12*+, 21.

Thompson, R. I . , and Schnopper, H. W., 1970, Ap. J . , 158, L55.

Thompson, R. 1., Schnopper, H. W,, M itc h e ll, R. 1., and Johnson, H, L ., Ap. J . , 158. L55.

T su ji, T ., 196*+, Ann. Tokyo Obs., 2* '•

------1 1966, Publ, Ast. Soc. of Japan, Jji, 127.

.... -----. . p 1 9 6 7 , "Colloquium on Late Type Stars", ed. M. Hack, T rieste, p. 266.

Vardya, M. S., 1966, M.N.R.A.S., !£*♦, 3**7. 125

Walker, R. G., 1966, Ph. D. dissertation, Harvard,

...... t 1 9 6 9 , Phil, Trans, of the Roy. Soc. of London, 264. 209.

Weinberg, J. M., Fishburne, E, S., and Rao, K. N., 1967, J. Molec. Spec., 22, 406.

Wing, R. F., 1967, Ph. D. dissertation, Univ. of Calif., Berkeley.

Wing, R. F ., and Spinrad, H ., 1970, Ap. J . , 159. 973.

Wing, R. F ,, and Price, S. D ., 1970, Ap. J . , 162, L73.

Woolf, N. J., Schwarzschi1d, M., and Rose, W. K., 1964, Ap. J., J44, 833.

Woolf, N. J ., 1971, to be published.

W yller, A., 1958, Ap. J ., _!_2Z. 763.

. , 1966, Ap. J ., 143. 828,

Yamashita, Y., 1967, Publ. Dom. Astrophys. Obs., H , 67.

Young, L. E ., 1967, J.Q .S .R .T ., 8, 693.

Young, L. E., and Eachus, W. J ., 1966, J. Chem. Phys., 44, 4195. 126

APPENDIX A

The mass absorption coefficients averaged over

- 1 19 100 cm spectral intervals calculated for C N and

C^N by the method detailed in Chapter VI are listed as in this appendix. The first column gives the wave- number, in cm"*, at the midpoint of the 100 cm"* interval over which the summing of the line strengths was taken.

Columns two through six list the mass absorption coefficients, in cm^/gm determined in this study for the spectral Interval at temperatures of 1008, 1680, 2016,

2520, 3360 and k$QQ°K (9 « 5, 3, 2.5, 2, 1.5 and 1.12) respectively. A value of 5.810E-01 is to be interpreted as 5.810x10"*. 12 MASS ABSORPTION COEFFICIENTS FOR C N WAVENO* /T 1008 1680 2016 2520 3360 4500

1550 0. 0 0 0 5 810E-01 4 018E 00 1650 0. 0 0 0 1 216E 00 6 954E 00 1750 0. 0 0 1 061E-02 2 331E 00 1 122E 01 1650 0. 0 0 3 293E-01 4 365E 00 1 817E 01 1950 0. 0 0 9 821E-01 8 359E 00 3 042 E 01 2050 0. 0 0 2 250E 00 1 544E 01 4 927E 01 2150 0. 0 2 557E-01 4 710E 00 2 665E 01 7 590E 01 2250 0. 0 1 002E 00 7 108E 00 3 455E 01 8 851E 01 2350 0. 4 977E-02 2 258E 00 1 247E 01 5 093E 01 1 163E 02 2450 0. 6 687E-01 4 052E 00 1 752E 01 6 087E 01 1 236E 02 2550 0. 1 460E 00 U 979E 00 2 568E 01 7 779E 01 1 430E 02 2650 0* 3 273E 00 1 149E 01 3 561E 01 9 118E 01 1 487E 02 2750 0. 4 928E 00 1 495E 01 4 042E 01 9 118E 01 1 362E 02 2850 0. 9 036E 00 2 304E 01 5 287E 01 1 012E 02 1 35 6E 02 2950 0.031E-O2 8 506E 00 1 882E 01 3 773E 01 6 421E 01 8 426E 01 3050 3.518E-01 1 190E 01 2 286E 01 3 955E 01 5 892E 01 7 605E 01 3150 5.405E-0' 1 576E 00 2 914E 00 4 830E 00 1 053E 01 3 344E 01 3250 0. 0 0 2 567E-01 7 195E 00 4 179E 01 3350 0. 0 0 8 215E-01 1 253E 01 6 472E 01 3450 0. 0 0 1 705E 00 1 947E 01 8 969E 01 3550 0. 0 7 005E-02 3 495E 00 3 294E 01 1 347E 02 3650 0. 0 4 635E-01 6 646E 00 5 297E 01 1 948E 02 3750 0* 0 1 426E 00 1 273E 01 8 303E 01 2 751E 02 3650 0. 1 432E-01 2 994E 00 2 294E 01 1 301E 02 3 869E 02 3950 0. 8 210E-01 6 795E 00 4 015E 01 1 9S3E 02 5 318E 02 4050 0. 2 154E 00 1 400E 01 7 133E 01 3 067E 02 7 390E 02 4150 0, 5 267E 00 2 592E 01 1 147E 02 4 296E 02 9 333E 02 4250 0. 1 212E 01 5 122E 01 1 982E 02 6 487E 02 1 268E 03 *350 0. 2 453E 01 8 954E 01 3 003E 02 8 538E 02 1 502E 02 4450 1*129E-01 5 127E 01 1 649E 02 4 873E 02 1 217E 03 1 933E 03 4550 1.06?E 00 9 585E 01 2 661E 02 6 800E 02 1 470E 03 2 099 E 03 4650 3»602E 00 1 882E 02 4 630E 02 1 045E 03 1 990E 03 2 571E 03 MASS ABSORPTION COEFFICIENTS FOR C 1 *N WAVENO. /T 1008 1680 2016 2520 3360 4500

4750 1 oetE 01 2 968E 02 6 251E 02 1 210E 03 1 9B1E 03 2 294E 03 4850 2 89-tE 01 5 215E 02 9 877E 02 1 711E 03 2 495E 03 2 640E 03 4950 6 128E 01 5 759E 02 9 256E 02 1 364E 03 1 704E 03 1 626E 03 5050 1 24?E 02 8 431E 02 1 234E 03 1 644E 03 1 845E 03 1 628E 03 5150 4 022E 00 2 716E 01 3 982E 01 5 523E 01 8 103E 01 1 490E 02 5250 0 0 9 262E-02 3 420E 00 3 151E 01 1 305E 02 5350 0 0 2 905E-01 5 631E 00 4 368E 01 1 661E 02 5450 0 0 9 646E-01 1 006E 01 6 667E 01 2 276E 02 5350 0 1 227E-01 1 861E 00 1 424E 01 8 590E 01 2 750E 02 5650 0 3 757E-01 4 125E 00 2 597E 01 1 366E 02 3 952E 02 5750 0 1 150E 00 7 359E 00 4 005E 01 1 861E 02 4 890E 02 5850 0 2 584E 00 1 366E 01 6 456E 01 2 665E 02 6 405E 02 5950 0 6 985E 00 3 116E 01 1 274E 02 4 537E 02 9 728E 02 6030 0 1 570E 01 6 067E 01 2 163E 02 6 841E 02 1 330E 03 6150 1 164E-01 3 779E 01 1 271E 02 3 991E 02 1 089E 03 1 898E 03 6250 6 92J1E-01 8 595E 01 2 536E 02 7 005E 02 1 676E 03 2 636E 03 6350 3 03-E 00 1 923E 02 5 010E 02 1 219E 03 2 562E 03 3 643E 03 6450 1 138E 01 4 128E 02 9 503E 02 2 038E 03 3 770E 03 4 858E 03 6550 4 148E 01 9 231E 02 1 874E 03 3 533E 03 5 718E 03 6 641E 03 6650 1 241E 02 1 705E 03 3 067E 03 5 122E 03 7 344E 03 7 779E 03 6750 4 434E 02 3 689E 03 A 82 IE 03 8 497E 03 1 062E 04 1 012E 04 6850 1 109E 03 6 005E 03 0 487E 03 1 109E 04 1 237E 04 1 081E 04 6950 3 012E 03 9 451E 03 * 163E 04 1 319E 04 1 281E 04 1 011E 04 7050 6 913E 03 1 529E 04 1 702E 04 1 739E 04 1 513E 04 1 096E 04 7150 1 152E 03 2 207E 03 2 358E 03 2 317E 03 1 995E 03 1 613E 03 "7250 0 2 986E-01 3 897E 00 2 557E 01 1 420E 02 4 335E 02 7330 0 9 1B5E-01 6 846E 00 3 957E 01 1 959E 02 5 462E 02 7450 0 2 083E 00 1 196E 01 6 031E 01 2 662E 02 6 815E 02 7550 0 4 534E 00 2 239E 01 1 014E 02 3 985E 02 9 308E 02 7650 0 6 195E 00 3 565E 01 1 436E 02 5 076E 02 1 095E 03 7750 0_ 1 714E 01 6 533E 01 2 328E 02 7 26 2 E 02 1 422 E 03 7850 79LE- •02 2 917E 01 1 002E 02 3 2 18E 02 9 056E 02 1 640E 03 129

CO CO CO CO CO CO CO 4 4 4 4 4 4 IN IN IN fO IO fO IO IO to CO IO 4 4 4 4 4 4 *H*o io o o o o o o o o O O O O O O O o o O O O o o OO O O O O O o a o o

UI UJ UI UI UJ UI UJ UI UI UJ UJ UI UJUI UI 111 I I I I I I 111 I I I UJ UI UI LU UJ UJ UI UJ UJ UJ U J U I UJ O CO IN 0 IN m CO o 4 N O CO O ' r - ao i n O ' mom i n a m«—* m 0 o rH r - v—1n « o o N o n # r t o IN H O 4 4 m O 0 O O 0 O ( N N ■—i ao OINNO r - CD f - rH c n 4 «n o o i n cd i n 4 N* o t o as 4 IN 4 IN N N - «—1 0 IN N CO O 0 ® O CO r - m 0 rH mo i n m 4 IN IN IN CO 4 m r- rH i- * i—i IN CO H sO P- O' rH i—1IN IN CO m 0 ao —i H rH rH rH IN 0 H H

CO CO IO IO IO CO CO 4 4 4 4 4 4 IN IN ININ IN t o IO CO IO IO IO 4 4 4 4 4 4 4 IN IN o O O O o o o O OOO O O O O O O O O O o o O o OOO O O O a o o

UI UJ U I UJUJ UJUIUJ UIUJUI UJ UJ UJ UJ UJ UJ UJ U i U i U I UJ U I U i UJ UIUI U i U I UJ U I U I U I IN IN 4 m1-1 O' IN H 0 O' o o 4 i n vO 0 IN o O CD O' 0 O ' m i n 0 0 r - N O' O * CO 0 O IO O H as 0 O CO 1-1 *—1 O' o rH 4 o 4 O ' O ' O H r—•—i r - ao i n CO ao ao IO: 0 mi m a 0 IN N - O f - O' o CD f—1 r - m N» 4 4 i n 4 r - o rH 4 O ' CO IN O' r - h m IN rH m 4 a o m M m n rH • - I IN IN CO m r - H •H IN CO in IN IN CO 4 0 O ' rH rH IN 4 m ao rH rH IN IN IN IO rH i n vO a: o Ii. rsi IN IN co in n io 4 4 4 4 4 4 f—I *—1ININININ IN COm coCO CO4 4 4 4 4 4 IN IN O O o O o o o o o o o O o o o o O O O o o OO O o o O O O O O O O VI* A »- UI UJ UJUI UJ UJui UI LUUJUJUJUJUI UJUI UJUJ UJUJ UI UIUI UI UI UI UJ UJ UJ UI UJUI UI z m o to IN l~- r- i—i IN 1- r-

O u oiNNCMnmmn444ir-|HHHrtC\jNN(Mm

i j 11| | i i i i» 11. i i i i 1.1 iii i iii iii it j ii H ‘1 1,1 N| 1,1 1,1 ‘i1 1,1 1,1 1,1111 lu u j u j u j biU JU J u i LU Ui co rH 0 HH(M»ffm4,A(nNn«»

t o H IN ININ IN IO IO to 4 4 4 m 4 a O rH rH m o o O OO o o o o o O o o o o o o X U I U I U I UI UI ui ui UI U i UI UJ U I U I UJ U i LU UJ iii iii iii iiiiii 1.1 iii iii iii iii iiiii11.1 <0 IN 4 f- 4 rH r* O' rH 4 r- IN 0 0 4 O' IN o IN 0 m CD4 m i n 4 r- 0 r- IS m rH CO O IN CO 4 O r- 4 r- IN CO r- IN 0 4 rH i n m o o r~ 4 i-H m rH rH IO 0 rH i n m rH IN m rH D I N O H r i m r - rH IO 4 rH IN i n O' IN IN 4 1 - IN rH rH

rH O O rH rH IN IN CO IO 4 4 m 4 IN rH rH O rH rH IN IN IN t o co 4 4 m 4 ' 0 o o o O O O O o o o o o O O O O o o o O o o o O o o O 1 1 1 1 UJ UJ Ui UI UI Ui LU UI 111 l l 1 I I I 111 I I I Ui Ui Ui UJ UJ LU UJ UJ UI UJ UI UI UJ UI Ui 0 1 ~ c . tZ 4 4 tY 4 IN CD O ' CP C1 N r l h O rH 4 f - IO i n t o I IN H CO 0 IN CD 4

2 , rH IO rH rH IN H IO rH CO rH 4 rH 4 rH ^ H ff. O 0, 0. IN O ' IO CO CO IN ao rH 4 *-t 4 jO O

O 0 0 O 0 0 0 O 0 0 0 O 0 0 0 O 0 0 0 0 0 0 0 O O 0 0 O O z m m m m mm «n m m i n m • n m m mm m m m i n m i n i n m m m m m UJ O ' 0 rH IN CO 4 m 0 h a j O ' 0 rH IN CO 4 m 0 r - 0 O' 0 rH IN CO 4 i n 0 > r- 0 0 0 0 0 a 4 0 0 o>O ' O ' O' O ' O ' O' o> O'O' 0 O 0 0 0 O O < rH rH 1—I rH rH rH rH 12 MASS ABSORPTION COEFFICIENTS FOR C N WAVENO. /T 1008 1680 2016 2520 3360 4500

11250 8.67TE-02 3 492E 01 1.126E 02 3 410E 02 9 108E 02 1 604E 03 11350 5«04wE-dl 6 9596 01 2*024E 02 5 528E 02 1 328E 03 2 153E 03 11450 1.663E 00 1 235E 02 3.262E 02 8 072E 02 1 751E 03 2 629E 03 11550 5 .U 9 E 00 2 206E 02 5.282E 02 1 182E 03 2 319E 03 3 224E 03 11650 1.524E 01 4 261E 02 9.138E 02 1 830E 03 3 210E 03 4 093E 03 11750 3.66QE 01 7 221E 02 1*418E 03 2 597E 03 4 159E 03 4 946E 03 11650 8.80OE 01 1 153E 03 *1.045E 03 3 385E 03 4 902E 03 5 415E 03 11950 2.639E 02 2 308E 03 •P.681E 03 5 467E 03 7 087E 03 7 174E 03 12C50 5.574E 02 3 447E 03 5.026E 03 6 815E 03 8 056E 03 7 621E 03 12150 1.1C8E 03 4 592E 03 6.077E 03 7 487E 03 8 072E 03 7 164E 03 12250 3.255E 03 8 969E 03 1.066E 04 1 178E 04 1 135E 04 9 251E 03 12350 6.610E *3 1 325E 04 1.447E 04 1 465E 04 1 293E 04 9 877E 03 12450 8.779E 03 1 133E 04 1.116E 04 1 025E 04 6 318E 03 6 138E 03 12550 2.498E 04 2 168E 04 1.925E 04 1 587E 04 1 15 IE 04 7 774E 03 12650 4.765E 04 3 063E 04 2.504E 04 1 897E 04 1 268E 04 8 144E 03 12750 1.69?E 03 1 093E 03 9.385E 02 8 682E 02 1 041E 03 1 411E 03 12650 l*72*.,E-02 2 802E 01 9*056E 01 2 743E 02 7 328E 02 1 299E 03 12950 3.74‘>E-■01 5 431E 01 1.593E 02 4 376E 02 1 056E 03 1 726E 03 13050 9*97«E- ■01 8 928E 01 2.397E 02 6 015E 02 1 323E 03 2 015E 03 13150 2.35*1E 00 1 213E 02 2.989E 02 6 887E 02 1 395E 03 2 006E 03 13250 6.395E 00 2 203E 02 4.951E 02 1 038E 03 1 914E 03 2 561E 03 13350 1.696E 01 3 971E 02 8«077E 02 1 530E 03 2 536E 03 3 122E 03 13450 2.673E 01 4 672E 02 8.856E 02 1 565E 03 2 434E 03 2 872E 03 13550 6.108E 01 7 221E 02 1.241E 03 1 987E 03 2 805E 03 3 089E 03 13650 l*71AE 02 1 390E 03 2.166E 03 3 137E 03 3 989E 03 4 040E 03 13750 2,81-E 02 1 698E 03 2.453E 03 3 296E 03 3 893E 03 3 751E 03 13850 4.701E 02 1 924E 03 2.534E 03 3 116E 03 3 404E 03 3 149E 03 13950 U203E 03 3 376E 03 4.Q27E 03 4 473E 03 4 406E 03 3 762E 03 14050 2.597E 03 5 364E 03 5*897E 03 6 026E 03 5 426E 03 4 296E 03 14130 2.164E 03 3 121E 03 3.169E 03 3 025E 03 2 643E 03 2 183E 03 14250 5.503E 03 5 365E 03 4.943E 03 4 264E 03 3 18 7E 03 2 63 BE 03 14350 1.468E 04 1 012E 04 8.415E 03 6 538E 03 4 590E 03 3 175E 03 l

MASS ABSORPTION COEFFICIENTS FOR C N WAVENO. /T 1008 1680 2016 2520 3360 A500 hhhinininin hh h AOHNm ooooooooo ooooooooooooo o o o o o H ^ i H O O O O O O OOIN(N4lf»44iH4r>IN4r'>-l(N4 ID H H O O O H H r l H H H H H N N H r l H O H H H H H N N M O I N N n i n U l U I U J U J U I U J U J U J U J U i U J U J U J U J U i U J U J U I U I U J U i U J U J U J U J U J U J U i U J U l U I UJ UJ I U l U J U i U J U J U J U J U J U J U i U J U I U I U J U J U i U J U J U J U J U i U J U J <-iif>®(MOO'-iiOCD(MinooO'-''C(DHH4o U J r‘ U r^ J i,\o N U I 0 0 U 4 J w n U M J U I r-K U l U U U J J U U Ui J UJ J IU U UJ i U UJ UJ l U UJ UJ UJ UJ I U J U J U J U J U J U J U 4hhhidoo*no«D*-itncofMr''O*cn»ninr-*r-i4cDr''r-i0Dini'-4O*®cMrHiMCMOM»O' J U i U •o4r-cnocnc\j'Ooocn-4r-icnr-OM>cnM> M n c > M O - r n c i - r 4 - n c o o O ' j \ c n c o n c - r 4 o —• j ' C u 0 c 0 4 0 M 0 < 0 o 0 c 0 - ' 0 r 0 o 0 H 0 p 0 n 0 i 0 4 0 D 0 40>Hm<0H(MNmtfi<0iD0>HHoi0NOHiM<<\)ft0»ri0im4^0>HH c 0 \ r 0 i 0 > 0 M 0 0 4cooM>incoot-iinoM>r^cn.-iinaoa'r^fM44inMi4r-if-0'inr'“ 04«-*ocM'OOOfnM»OcM I 1 n 4 N M * < 0 4 0 > 4 ) a N ( i - > 0 0 4 4 D a 4 I I < 4 D M N ( D 1,1 I U I Ii I Ii M I Ii 111 h ( III 111 t I Ii I Ii I i < M Ii I 4 Ii I Ii I Ii 0 iI I I 0 li I Ii I 1110 Ij III 1 Ii I ll l li inocMm«>inr^ri-r-iO'CD<-tinM)MicDmcMomr-cor-iM>cM4cn4 III t j I 111 III I111 I j o h nr^HOOOO^HHHHHHHHH 4 N o m H in . 4i>sO®^-ir-i^-io»otr»r-^o4r-4it>«i3'-«or-4« . in H m o N 4 oooooooooooooooooooooooooooooo I I I I U JU U UJ UJ UJ UJ UJ i U H D t H cm M 4 CM ■—1 pH o oo - f 4 - 1 1 m m UJ CM cn en e'­ cn 0 CM o o o 1 i m M M M M MCM CM CM CM CM CM o o o o oo i - i 4 rH n c - r r-n - r n c ' CM rH O' U I I U in * o o 0 CDO 4 o o O 1 m

- r i m i m h O l r U I I U o - r 4 O 1 m X- ao - X l M a UJ U I UJ U I I U UJ I U UJ CM m ' O ' O 4 i m o o i m H m n c - r o o o ♦ i - t UJ UJ rH - UJ 4 I U UJ — H| H rH fH |H ■—1 H o o o o

i m

Ml o l M o l M M> o o o m n c cn - r cn

8 UJ UJ UJ UJ m N H rl H l r H IN O' O' CM O ' O IN ' O O IN

l D o CD Ml o o o o ' H pH rH O' o o cn o fH H t o CM CMCM h- r-l IM cm n i o o o 1 11 1 1 1 1 1 1

cn t O l M l M O U I I U

p 9 cn ooo o UJ cn cm O'

o H cn Z l M CM cn I U O 4 in r~ c a CM O UJ o •4 <0 cn ao M l l M ao cn <0 4 4

-- cn cn 0 Ml M l M cn 4

-lOi-'f-inKO^inoHHHcjN 4 0 o ) m l M m 4 m n i h o > O D M O < m o o o om o o o o om o o p t r « h O O O O O O O O O U UI JU JUIU U UI U UJ UJ I U UJ UJ UJ I U UJ I U CN c- a co ao - c ' O Ml rH o o o o 4 O O O H H H H N N N I N C M • 1 1 1 1 in •••••• • • • • • • * • • • h- h- m i m i i m i m M 4 CM J J J ill l l i t i l m l l i n i i i i UJ UJ UJ «h (Mn^^OiH i O ^ ^ n M ( h « ' O (NH h m m >o o o> 0 O0 OO O O O O O i m o I 1

m i p r~ ' O O O 4 O O O H H H I N h m i i m u>hino u ' O CD CM ' O o o m m HCOlAH o m oo o o Hp p CM pH pH *H l M II Ml X- HINID 4 Ml M oao 4 l M “* CM ■“ * 4 a m m in l n c t C 4 M O t r CM o o O O l r 4 J IU U UJ 131 - r « H « 41 l M n H n I U UJ O O CM CM <*io> m to cm

MASS ABSORPTION COEFFICIENTS FOR C^N WAVENO. /T 1006 1680 2016 2520 3360 4500

4750 4 783E 00 2 159E 02 5.169E 02 1 136E 03 2 108E 03 2*674E 03 4830 1 42 JE 01 3 531E 02 7.256E 02 1 369E 03 2 183E 03 2*477E 03 4950 3 494E 01 5 641E 02 1.039E 03 1 752E 03 2 489E 03 2.586E 03 5050 8 190E 01 6 923E 02 1.081E 03 1 548E 03 1 877E 03 1 •756E 03 5150 1 184E 02 7 590E 02 1.094E 03 1 434E 03 1 587E 03 1.404E 03 5250 3 644E 00 2 460E 01 3.609E 01 5 092E 01 8 005E 01 1*593E 02 5350 0 0 3.572E-01 4 551E 00 3 715E 01 1.470E 02 3450 0 1 737E-02 8.221E-01 7 667E 00 5 503E 01 2.007E 02 5550 0 1 058E-01 1.717E 00 1 330E 01 6 256E 01 2.694E 02 5650 0 3 493E-01 3.019E 00 1 969E 01 1 099E 02 3.320E 02 5750 0 8 472E-01 5.995E 00 3 421E 01 1 691E 02 4*643E 02 5850 0 1 874E 00 1.024E 01 5 121E 01 2 222E 02 5.538E 02 5950 0 4 490E 00 2.116E 01 9 287E 01 3 565E 02 8 t097E 02 6050 5 805E- 03 1 055E 01 4.317E 01 1 655E 02 5 528E 02 1.127E 03 6150 8 93JE- 02 2 616E 01 9.344E 01 3 126E 02 9 077E 02 1.660E 03 6250 4 521E- 01 5 744E 01 1.802E 02 5 292E 02 1 346E 03 2.224E 03 6350 1 823E 00 1 359E 02 3# 754E 02 9 677E 02 2 154E 03 3.204E 03 6450 6 913E 00 3 084E 02 7.487E 02 1 694E 03 3 301E 03 4.426E 03 6550 2 290E 01 6 308E 02 1.354E 03 2 702E 03 4 636E 03 5.636E 03 6650 8 497E 01 1 444E 03 2.734E 03 4 794E 03 7 210E 03 7.908E 03 6750 2 534E 02 2 566E 03 4.259E 03 6 554E 03 6 641E 03 8.595E 03 6850 8 703E 02 5 667E 03 8.359E 03 1 137E 04 1 323E 04 1.190E 04 6950 1 802E 03 7 026E 03 9.136E 03 1 098E 04 1 130E 04 9.338E 03 7050 6 20CE 03 1 482E 04 1.691E 04 1 777E 04 1 593E 04 1.182E 04 7150 4 18»E 03 8 456E 03 9*159E 03 9 097E 03 7 713E 03 5.590E 03 7250 1 39/E 01 3 349E 01 4.052E 01 6 051E 01 1 600E 02 4.152E 02 7350 0 9 267E-01 6.656E 00 3 822E 01 1 915E 02 5.379E 02 7450 0 1 967E 00 1.122E 01 5 754E 01 2 582E 02 6.656E 02 7550 0 4 347E 00 2.119E 01 9 600E 01 3 809E 02 8.944E 02 7650 0 7 667E 00 3.456E 01 1 412E 02 5 053E 02 1.096E 03 7730 7 569E-03 1 555E 01 6.005E 01 I 16?I_ 02 6 867 E 02. 03 7850 8 T49E-02 3 082E 01 *.066E 0~2 3 445E 02 9 738E 02 1«767E 03 * l-» «-• M *-* »-* H *-* »-*M > I-* o o o o o o o o C'o < o 43 « o vO o < o < o «<> OB o» OB W (9 CD B ®OB m - 4 < H o l OB » V* B UI ru M o sO V-J o* UI B u> IO K» o «o 0» -4O ' m B UI Kl H O l'O m UI U»UI UIUI u* in UI U i u UI m U i u i m U I U I U i U I u i m m u» UI u r m UIUI m UI m m z o 0(0o oo o oo o o o o oooooo o oo o o- o o O o oo o o o o

*-• M l# -* *-•O »-* HUIH BM B»-• BH U l 4 3 ru o O •-» K BM BH U l U l h * U l M U l H • ••••• • • ■ • • • • • • • • • * • • • • • • • • • • • • • • o ru M o >o O BM CD B UI b u i U l a> U l H o U l a> U l IU MBo O' o BU l - 4 o o m O' OB ■4 4 ) U I - 4 O* IU BCD *-• U l o 'O m o <» Ba> • u B OB - j UI ruUI -1 ~4 O 43 r> IU c a o H o 43 r e '­ ■Jl IUB H M B-4 B« ui<0 CD mmnimmmmmmrrimmmmmmTT|en mmmmm m rn m mmmmm I I 11l I o oo oo o ooo oooo o oo Oo oooooo o o o ooo o *-■ru bU i BbbUI U l IUr u M oo i- * IUIU mU l BbUl U l IUIUm m o O M

IU H B - J U l r u IUM O' U l 1—• a> B i- * 'O B r u *-* m U l O' H U l r u t-" vn r u M O' U l m b M O b B W B U l B -u U l M r u u i O ' *-■ o u> o B o 1-1 O ' 1-* u i M U * m r u CD O ' M OB M IB O l 'O OB IU O ' U l « U l r u - I r u - 4 O' u> U l - 4 -4 B43 - 4 U l U l o a> U l ru4 ) I-* -J - 4

31 o» v r u M ao B ru ►-* -4 B M »-• Ul ru H CB B ru ► -IB IU H ru o O JO 00 M B * ru OB CD u i B O' m ai in ~4 OD B Ul r u B B mH O Ul - j B O o o Ul o ru OD Ul I-* T» >1 M U IU o I-* a> O Ul o a> -u B 1-* - 4 O ' ru —4 ru o o o O' - j 43 a t B O' Ul m i-«<41 Ul O * -4 ru Ob -B O' o O' ODru O' U l 4) O' B U>O O' *~* ru vO O ' OD CD 4 ) B IU -4 Ul Ul Ul O' B H O m mim m m m m m mmmmm m m m r n m mm mm mm m m m m m mm m m O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o K * M U l B B B BB U l Ul Ul U l ru r u ru r u h ►-* *-» »-* B Ul B B B Ul U l Ul Ul ru ru IU IU n 6 3 r u i ~>i u i BB r u IU i-* i—• -JB IU I-* 1 l u »-• 43 O' U l ~4 B r u I-* I— U l U l r u I-* 43 - J B r u m n OD a t a> ~4 O O' O' O' H a> O ' OD■4 »-«u> 43 u> O ' -4 o * a> 43 -J -4O' O CD U l U l B ODBB IU*—4 OmUl —44 3 I-* 4 3 a> O ' - 4 o B -1 B O4 3 4 3 o B ~ 4 4 3 43 u> -1 4> o O' B a> O' o m ■ 4 W O « r u B U l r u O' - 4 4 3 B IU BB IU U l U l O r u - j B m -4 m -4 -4CD o O' I-* -4 4 3 z m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m m - 1 V*is i o o o o o o o o o o Oo o o o o o o o o o o o o o o o o o o o o o r u r u t*> BBB BBB UlUl Ul Ul U l l u ru IU IU •-* H B B B B B B u i U l U l U l IU r o r u o JO r> - J U i N i U l r u r u r u I-* »-• 'O O' B U l r u *-» I-* U l r u l u U* U l r u ♦-* -4 BB r u r u 1-* H ui — • 9 W IM OD O ' —4 o 43 H U l -I l u OD o U l M r u B o -4 i —* U l O ' B u> O ' B O' H B a> O O ' o O ' H » z ~ 4 M U -4 o U l CD O m OD B U l U l l u U l r u O' IUIU U l U l O ' O ' U l - 4 U l O' 43 U l ~4 H 43 B o - J u i O ' U l 43 -4 CD K l O ' r u O' OD u i - 4 OD r u B O' U l H O'B U l ao O a t r u a> 43 O U l O ' O ' m m m m m m m m m m m rn m m m m m m m m m m m m m m m m m m m m m

o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o r u r u u i BBB BBB U l U l U l U l U l u> U l r u r u ru IU BBBBBB U l U l U l U l U l U l U l

* - • h M I-* 1-* I-* »-* *-■ I-* 43 -4 U l U l r u i-* H - 4 O' H U l IU I-* l-» •4 U l B U l IU r u i— b B w B i-* Kl CD a> U l -4 B H O ' *-• U l O r u -4 IU O OD U l B r u B -4 Ul O Ul Ul -4 B CD m 4 3 o W M M U O ' o 43 o r u B U i O ' u t B U l B O ' U l I-* r u t u r u U l 43 W U l B K l iO ■4 O' 43 ui o O I U - 4 41 B O' CD B 41 M B 43 I-* * o m - 4 B ao O U l V - 4 -I I-* O *-* 4) O -4 U i B a i - 4 m m m m mm m m m mm mm mm rn m m mm m m mm m m m m rn m m m m o o o o o o o o o o o o o o o O o o o o o o o o o o o o o o o o o U l U l U l B B B B B B U l u> U l U l U l U l U l U l U l IU IU B BBBB B U l u* Ul Ul Ul Ul U l

££I MASS ABSORPTION COEFFICIENTS FOR C ^ WAVENO. /T 1008 1680 2016 2520 3360 4500

11250 4 518E-01 5 246E 01 1 591E 02 4 532E 02 1 134E 03 1 901E 03 11350 1 3l4E 00 9 826E 01 2 696E 02 6 926E 02 1 564E 03 2 415E 03 11450 3 367E 00 1 684E 02 4 191E 02 9 764E 02 1 997E 03 2 867E 03 11550 9 979E 00 3 316E 02 7 436E 02 1 557E 03 2 853E 03 3 757E 03 11650 2 865E 01 6 379E 02 1 288E 03 2 425E 03 3 990E 03 4 B41E 03 11750 5 928E 01 9 128E 02 1 685E 03 2 901E 03 4 369E 03 4 966E 03 11650 1 729E 02 1 751E 03 2 902E 03 4 479E 03 6 041E 03 6 313E 03 11950 4 996E 02 3 409E 03 5 093E 03 7 067E 03 8 544E 03 8 200E 03 12050 8 046E 02 3 846E 03 5 277E 03 6 738E 03 7 533E 03 6 867E 03 12150 2 27*>E 03 7 169E 03 8 826E 03 1 009E 04 1 009E 04 8 446 E 03 12250 6 29..E 03 1 346E 04 1 495E 04 1 5 39E 04 1 381E 04 1 064E 04 12350 7 144E 03 1 08 IE 04 1 109E 04 1 058E 04 e 903E 03 6 708E 03 12450 1 860E 04 1 81 IE 04 1 655E 04 1 406E 04 l 052E 04 7 262E 03 12550 4 7UE 04 3 188E 04 2 643E 04 2 029E 04 l 372E 04 8 805E 03 12650 1 150E 04 6 790E 03 6 456E 03 4 165E 03 3 111E 03 2 598E 03 12750 1 5UE-01 2 681E 01 f> 733E 01 2 668E 02 7 164E 02 1 272E 03 12850 4 552E-■01 4 972E 01 * 473E 02 4 084E 02 9 954E 02 1 641E 03 12950 1 259E 00 6 954E 01 2 404E 02 6 021E 02 1 324E 03 2 013E 03 13050 2 407E 00 1 243E 02 3 086E 02 7 164E 02 1 460E 03 2 106E 03 13150 5 882E jO 2 035E 02 4 588E 02 9 656E 02 1 787E 03 2 399E 03 13250 1 607E 01 3 832E 02 7 836E 02 1 491E 03 2 487E 03 3 073E 03 13350 2 742E 01 4 879E 02 9 272E 02 1 641E 03 2 550E 03 3 002E 03 13450 5 959E 01 7 118E 02 1 226E 03 1 970E 03 2 790E 03 3 084E 03 13550 1 651E 02 1 351E 03 2 109E 03 3 061E 03 3 899E 03 3 952E 03 13650 3 Q7'>E 02 1 642E 03 2 653E 03 3 550E 03 4 172E 03 3 989E 03 13750 4 55«-E 02 1 875E 03 2 4? IE 03 3 039E 03 3 324E 03 3 079E 03 13850 1 273E 03 3 557E 03 4 234E 03 4 695E 03 4 610E 03 3 920E 03 13950 2 549E 03 5 190E 03 5 677E 03 5 769E 03 5 179E 03 4 113E 03 14050 2 37VE 03 3 416E 03 3 45SE 03 3 287E 03 2 852E 03 2 332E 03 14150 5 B51E 03 5 549E 03 5 050E 03 4 320E 03 3 401E 03 2 625E 03 14250 1 446E 04 9 708E 03 8 046E 03 6 236E 03 4 395E 03 3 077£ 03 14350 3 670E 03 2 176E 03 1 774E 03 1 425E 03 1 217E 03 1 162E 03 135

APPENOIX B

The mass absorption coefficients averaged over

100 cm"' spectral intervals calculated for and c ' V 2 by the method detailed in Chapter VIII are listed in this appendix. The first column lists the wavenumber, in cm"', at the midpoint of the 100 cm"' interval over which the summing of the lin e strengths was taken.

Columns two through six list the mass absorption coef­ ficients, in cm^/gm, determined in this study for the spectral interval at temperatures of 1008, 1680, 2016,

2520, 3360 and i*500°K (9-5, 3, 2.5, 2, 1.12) respec­ tively. A value of 1.008E 01 is to be Interpreted as

1.008x10 1. MASS ABSORPTION COEFFICIENTS FOR c j 2 WAVENO. /T 1008 1600 2016 2520 3360 4500

1550 0. 1 008E 01 3.217E 01 9 401E 01 2 373E 02 3 978E 02 1650 9#41^E- 02 2 063E 01 5.581E 01 1 378E 02 2 894E 02 4 164E 02 1750 6.328E- 01 5 059E 01 1.238E 02 2 738E 02 5 088E 02 6 592E 02 1850 1.42^E 00 6 606E 01 1.519E 02 3 182E 02 5 637E 02 7 095E 02 1950 5.142E 00 1 347E 02 2.712E 02 4 942E 02 7 580E 02 8 559E 02 2050 1* 1 l')E 01 2 041E 02 3*78 OE 02 6 345E 02 8 977E 02 9 582E 02 2150 2.946E 01 3 144E 02 5-073E 02 7 423E 02 9 216E 02 9 088E 02 2250 5.685E 01 4 185E 02 6#174E 02 8 276E 02 9 491E 02 9 C13E 02 2350 1* 350E 02 5 706E 02 7.258E 02 8 391E 02 6 457E 02 7 691 E 02 2450 2.017E 01 7 776E 01 1.028E 02 1 395E 02 2 171E 02 3 46 8 E 02 2550 5.592E- 02 9 129E 00 2.615E 01 7 3 31E 01 2 003E 02 3 979E 02 2650 3.087E- 01 1 260E 01 3.312E 01 9 032E 01 I 520E 02 5 123E 02 2750 6*310E- 01 1 849E 01 4.713E 01 1 262E 02 3 498E 02 6 778E 02 2850 1.536E 00 3 234E 01 8.308E 01 2 274E 02 6 005E 02 1 C94E 03 2950 3.054E- 02 2 827E 01 9.267E 01 2 850E 02 7 677E 02 1 36 1 E 03 3050 5.020E- 01 6 439E 01 1.B92E 02 5 192E 02 1 241E 03 2 001E 03 3150 1.96j E 00 1 391E 02 3.670E 02 8 9 48 E 02 1 8 78 E 03 2 716E 03 3250 5.330E 00 2 534E 02 6.179E 02 1 394E 03 2 710E 03 3 694F 03 3350 1.770E 01 5 426E 02 1.176E 03 2 343E 03 3 989E 03 4 8S4E 03 3450 5 *185E 01 1 096E 03 2.152E 03 3 8 69 E 03 5 906E 03 6 621 E 03 3550 1.672E 02 2 197E 03 3.816E 03 6 062E 03 8 171E 03 6 336E 03 3650 5.124E 02 4 393E 03 (*i.824E 03 9 654E 03 1 152E 04 1 06 5 E 04 3750 1.468E 03 7 473E 03 *.017E 04 1 260E 04 1 319E 04 1 107E 04 3850 3.560E 03 1 1B8E 04 1.451E 04 1 610E 04 1 5G7E 04 1 169E 04 3950 9.941E 03 1 906E 04 2.018E 04 1 942E 04 1 5bOE 04 1 109E 04 4050 5.086E 03 8 473E 03 8.575E 03 7 900E 03 6 306E 03 4 6 5 2 E 03 4150 1.497E 00 7 188E 01 1*792E 02 4 2B7E 02 9 405E 02 1 50 8 F 03 4250 5.681E 00 1 613E 02 3.512E 02 7 268E 02 1 368E 03 1 95QE C3 4350 1.504E 01 2 219E 02 4.137E 02 7 502E 02 1 305E 03 1 848E 03 4450 4 . USE 01 4 08 IE 02 6.936E 02 1 157E 03 1 870E 03 2 507E 03 4550 7.65DE 01 4 625E 02 7.443E 02 1 247E 03 2 113E 03 2 915 E 03 4650 1 *251>E 02 5 637E 02 e«478E 02 1 338E 03 2 15 IE 03 2 859E C3 -4 -J -J -4 -4 -4 -4 -4 -J O' O' O' O' O' O' O' O' O' 0 Ui Ui m ui Ul ui mu»u» w p p p : < CD-J o> Ul p ui ru I-* o o ao —J O' Ul p u> IU I-* o MHQtO «M-4 ; ra Ul Ut u> Ul ui UI Ul Ul u»ui Ul mUl Ul Ul UI m u* m ui Ul Ul Ul UI ui m Ul wwui \WU» : z o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o | o o

2 8 Ul I-* UI *—* i-* I-* *-* O' Ul I-* P M o P H ui ►-O' M »-* MM U; h ur ►«*■»* Ml« |D- ! • • • • •• •• •••• ••• m • • • • • • • i• • • • • • i • • • IO 1 ! Ul t“ P U) Ul 41o -J CDi-* CDo « O' -4 m a 4) -4 lo 41 O' o 'Ji’ON t M M ip P W o IU -3 IUIU -J O' CDp O' CDCD 4) * Ul # • -J IU o I V* o <0 MUl O' CDo H* O' u ui C 0»O HIU l> 1 ’ • M > * : h i > o h 1 m rn rn rn mm mmmmnt m m m rn rn m mmfiim ni mm mm m m nf m to m o o o o o o o c o o o o o o o o o o o o o ooo o o oooooo ui ru ru IUH »-■H p Ul p P p Ul Ul Ul Ul Ul N NHH Ul Ul Ul p p W U M l - H O

OD Ui IU i-< 1—' Ul Ul ►* i-* O' O' ro i-* »—■*-■4>Ul Ul i-« as p *—*-* *-* ODp p -4 O 41O' o O' Ul o Ul Ul UI OD4> o *-* Ui Ul M0"0 -J -0 -4 -4 o *-* ao Ul 41O*4> Ul P Ul Ul MX ru Ul Mcn -J -4 M•4 Ul o o O' Ul CD O' -uiO o H MU>41 -4 Ul »-*O' o O' mO ui M o o o Ul -4 IUH O m m m rn m rn m rn m mm mmm m m mm m rn mm m m m m o o o o o o o o o o o o o o o o o o o o o o o o o o u> Ul Ul U)Ul u>IU IUp Ul p P p P-P P ui Ul Ul Ul M M Ul Ul Ui p p tn > 35 (/» h - j i" u>K> a»at f- im h M v i h O1 M O • •••••••••••••••••••••••••••►a* • O JO HOHHMHO>Oa)(DMt'M>MUO>aiO>Oinf, UlOUlNC»H NUI *-* "O 0'O^lj)li>Ul>JtBa)OW3)\00k0*'0^0DM'>lONMU>Ul'O(BOUl4)M'O O' -T ^ Ul M N O (> H ^w aH O D U Iff'H W ^rJQ O U O t' lO^MluO^^UlHO mmmrnmmmrnmmrnmmmmmmmmrnmmmmmmmmmmrnm oooooooooooooooooooooooooooooooo n O i-'»-■-JUl P ro I—■-4 CD p O' Ul ru »-CD p o O' 00 »-• w >41 u> u» 45 4} - 4 P 4> IU O' o O »-* o ru U»-4 O* P O CD p ■P M 'J o O O' Ul p CDCD H o Ul O' O' ao O' Ul M -4 Ul -4 4> u* Ul P JU O' O' -vl O' ■O' O -J !-■ ~4 'O "4 Ul 4) -4 ru o n> Ui Ui o 4> PP IU m Ul m o M as {m o « ru O' p m m m m m rn rn rn m mrn m mmmmmmmimmmmmmimTOTOTOTOrn !TO ui o o o o o o o o o o o o o o o o o o o o o o o o o o o O OOo O P p Ul Ul Ul Ul Ul Ul p p p p p p p p Ul Ul Ul Ul Ul Ul m Ul p p p P Ul Ul Ul US o ;o rs >—* H M CDO' P Ul O' m Ul m ui Ul ru *—•i—* »-• 45 -4 m Ul Ul O' CD Ul p IU (—«4) Ul p IU Ul *w .% Ul o P CD 41 X Ul Ul O' Ul ru o ru 4) O' ru CD l~* o 4) i—* Ul Ul ~4 »-* O' -4 Ul 4) *-»ao O' -j '41 sO -4 ui p CD O' O' t-> o CDru U OS ao P Ul I-* O' Ul -4 P CD O \Ji O' ►-> Ul P 4) ao o *—• Ul O' M Ul o O' Ul 41 *-■ o CD 00 ru O' o ru IU *—* -4 -4 Ul *-• p ru 414) 4) -4 O' o Ul m m m m m m m mrn m m m m m m m mmm mm rn rn m mmTOTOTO TOmTO o o o o o o o o o o o o o o o o o o o o o o o o o o OO O O o o P P p Ul Ul Ul Ul Ul p p P P p P p P P Ul Ul Ul Ul Ul P P p p P P Ul Ul Ul Ul

t—*H 'O oo O' in O' ui fu Ul ru ru IU »-■ I-* i—*I-1 CDO' UI p Ul Ul Ul Ul ru I-* 41 O' Ul P p Ulm ui P M 4> O' -4 -4 ~4 ru P -4 Ul Ul o ao O' ru o P p Ul ru -4 *-• ao o lu Ul O' 00 Ul o o O' *-* O'O P Ul o »-• CD Ul m 'O P 'O p i—* -4 ~4 -4 ao Kl us O' o P 4) o 41 O 41 IU O' o < o P O' ~4 'O UI Ul Ul vO P ui o P 4) Ul m CDUI ~4 O' t—O' Ul -4 o P Ul ao -4 I- 1 ao p mm mm m m m m m m rn m m m rn m m rn m mmm mmmm TO TOTO TOTOTO o C3 o o oo oo o o n o o o oo oo co o o o o o o O o O O o o PP p Ul Ul Ul Ul Ul p P P P PPP p p P Ul Ul Ul u> PP P p P P Ul Ul Ul Ul i£T MASS mBSORPTICN coefficients FOR 42 WAVENO. /T 1008 1680 2016 2520 336C 4500

7950 7.111E 03 1 642E 04 1 • 969E 04 2 2 38E 04 2 263E 04 1 950E 04 8050 2* 2luE 04 2 9e8E 04 3*118E 04 3 0 92 E 04 2 750E 04 2 174E04 8150 5.09OE 04 4 905E 04 4.482E 04 3 887E 04 3 032E 04 2 187E04 8250 1.368E 05 8 439E 04 7.117E 04 5 664E 04 4 018E 04 2 670E04 8350 1.545E 04 1 755E 04 1.671E 04 1 499E 04 1 242E 04 1 OOOE 04 8450 5.032E 04 3 773E 04 3 • 2 0 4 E 04 2 548E 04 1 862E 04 1 362E04 8550 2.362E 04 1 470E 04 I.201E 04 9 555E 03 7 750E 03 6 853E 03 6650 1.035E 01 3 394E 02 w■09 6E 02 1 806E 03 3 541E 03 4 953E C? 8750 1.937E 01 6 OflOE 02 1•331E 03 2 709E 03 4 819E 03 6 256E03 8850 2.901E 01 7 240E 02 1 a 5 01E 03 2 897E 03 4 899E 03 6 141E 03 8950 7•448 E 01 1 235E 03 2.308E 03 4 016E 03 6 125E 03 7 12CE03 9050 2.009E 02 2 295E 03 3.S89E 03 6 113E 03 8 3 7 ? E 03 8 939E 03 9150 4.073E 02 3 257E 03 5 a 0 70 E 03 r 3 3 2 E 03 9 269 E03 9 341E 03 9250 9.604E 02 5 040E 03 7.061E 03 9 200E 03 1 052E 04 9 B99E 03 9350 2.57HE 03 9 338E 03 la 18 4 E 04 1 390E 04 1 426E 04 1 230E04 9450 5.33VE 03 1 196E 04 1.356E 04 1 426E 04 1 318E 04 1 062E 04 9550 1.477E 04 2 236E 04 2.277E 04 2 149E 04 1 7 7 £ E04 1 310E 04 9650 2.80*E 04 2 842E 04 2.623E 04 2 249E 04 1 70 3 E04 1 196E 04 9750 7.33;iE 04 4 645E 04 3 a 781E 04 2 853E 04 1 9Q5E04 1 228E 04 9850 1*03-E 05 4 946E 04 3.732E 04 2 605E 04 1 6 1 IE 04 9 884E 03 9950 6.468E 03 4 039E 03 3.391E 03 2 906E 03 2 754E 03 2 834E03 10050 7.095E 00 2 139E 02 4a803E 02 1 0 16 E 03 1 914E 03 2 649E 03 10150 7.783E 00 2 35 IE 02 5 a 1 5 4 E 02 1 063E 03 1 954E 03 2 656E 03 10250 1.693E 01 3 710E 02 7.499E 02 1 420E 03 ? 3c OE03 3 00 3 E 03 10350 4# 40I3E 01 6 704E 02 1.229E 03 2 102E 03 3 17&E 03 3 70 IE 03 10450 8*40*»E 01 9 926E 02 1.695E 03 2 696E 03 3 774E 03 4 144E 03 10550 1.549E 02 1 363E 03 2.169E 03 3 219E 03 4 225E 03 4 446E 03 10650 4.1B9E 02 2 456E 03 3a509E 03 4 655E 03 5 425E 03 5 183E 03 10750 8.316E 02 3 701E 03 4.910E 03 6 034E 03 6 496E 03 5 845 E 03 10850 1.641E 03 5 145E 03 6.249E 03 7 0 36 E 03 6 967E 03 5 924E 03 10950 4.196E 03 8 725E 03 9 a 55 7E 03 9 709E 03 B 69 IE 03 6 856E03 11050 6.835E 03 1 321E 04 1.327E 04 1 233E 04 1 C04E04 7 356E 03 11150 1.062E 04 1 145E 04 la065E 04 9 216E 03 7 125E 03 5 176E 03 t 2 MASS ABSORPTION COEFFICIENTS FOR C2 WAVENO. /T 1000 1660 2016 2520 3360 4500

11250 2.246E 04 1 645E 04 1.3B7E 04 1 090E 04 7 702E 03 5.277E 03 11350 5.327E 04 2 722E 04 2.089E 04 1 493E 04 9 612E 03 6.175E 03 11450 2.33'iE 04 9 938E 03 7.344E 03 5 195E 03 3 587E 03 2.691E 03 11530 7.707E 00 1 723E 02 3.547E 02 6 863E 02 1 174E 03 1.496E 03 11650 1.714E 01 2 896E 02 5.563E 02 1 003E 03 1 598E 03 1.926E 03 11750 2.645E 01 3 918E 02 7.207E 02 1 237E 03 1 862E 03 2.136E 03 11850 3.918E 01 4 531E 02 7.780E 02 1 2 42 E 03 1 734E 03 1.381E 03 11950 1.033E 02 8 572E 02 1.356E 03 1 997E 03 2 573E 03 2.627E 03 12050 1.807E 02 1 130E 03 1.657E 03 2 259E 03 2 699E 03 2.618E 03 12150 2.373E 02 1 248E 03 1.742E 03 2 254E 03 2 55 IE 03 2.377E 03 12250 6*419E 02 2 367E 03 3.010E 03 3 5 40E 03 -5 627E 03 3.115E 03 12350 1.001E 03 2 729E 03 3.225E 03 3 534E 03 3 4O0E 03 2.822E 03 12450 1.737E 03 3 592E 03 3.935E 03 3 996E 03 3 563E 03 2.653E 03 12550 4*05uE 03 5 978E 03 5.999E 03 5 573E 03 L 566E 03 3.398E 03 12650 5.499E 03 6 028E 03 5.618E 03 4 86CE 03 3 747E 03 2.712E 03 12750 5.219E 03 4 224E 03 3.672E 03 -a 032E 03 2 393E 03 1.944E 03 12850 1* 502E 04 8 693E 03 6 • 92 7E 03 5 2 3 IE 0 3 3 7 58 E 03 2.830E 03 12950 2.017E 04 8 858E 03 *.565E 03 4 613E 03 3 102E 03 2.256E 03 13050 3.194E 00 1 104E 02 r*« 443 e 02 5 OOOE 02 S 926E 02 1. 169E 03 13150 4.999E 00 1 283E 02 «. • 630E 02 4 974E 02 8 178 E 02 1.003E 03 13250 1.026E 01 1 933E 02 3.657E 02 6 369E 02 9 562E 02 1■09 IE 03 13350 2*4l9E 01 3 210E 02 5.561E 02 8 86CE 02 1 2 1 7 E 03 1.286E 03 1 13450 4.525E 01 4 585E 02 7*403E 02 1 100E 03 * 404E 03 1.400E 03 13550 6.412E 01 4 012E 02 7.231E 02 9 989E 02 1 18 3 E 03 1.122E 03 13650 1.981E 02 1 015E 03 1.381E 03 1 725E 03 1 85 IE 03 1.613E 03 13750 3.649E 02 1 366E 03 1.717E 03 1 979E 03 1 960E 03 1.607E 03 13850 3.50HE 02 9 763E 02 I. 143E 03 1 229E 03 1 136E 03 8.845E 02 13950 8,99nE 02 1 804E 03 1.942E 03 1 920E 03 1 631E 03 1.19CE 03 14050 1.9U E C3 2 802E 03 2 • 780E 03 2 529E 03 1 975E 03 1.350E 03 14150 1.845E 03 2 084E 03 1.936E 03 1 648 E 03 1 203E 03 7.8G7E 02 14250 1.990E 03 1 600E 03 1 * 370E 03 1 077E 03 7 270E 02 4.456E 02 14350 5.72uE 03 3 293E 03 2.586E 03 1 06 IE 03 1 149E 03 6.577E 02 12,13 MASS AFSCRPTION COEFFICIENTS FOR C C /T 1008 1680 2016 2520 3360

0. 1 035E-01 2 399E 00 1 715E 01 7 565E 01 02 0. 9 618E-Q1 6 305E 00 2 S05E 01 9 803E 01 02 0. 3 872E 00 1 622E 01 5 644E 01 1 719E 02 02 0. 1 203E 01 4 032E 01 1 197E 02 2 978E 02 02 5.56^E- 02 3 496E 01 9 751E 01 2 466E 02 5 214E 02 02 1.598E 00 9 342E 01 2 224E 02 4 803E C2 8 649E 02 03 6.940E 00 2 020E 02 4 150E 02 7 736E 02 1 20 IE 03 C 3 2* 554E 01 3 79 IE 02 6 666E 02 1 060E 03 1 40 2 E 03 03 7.770E 01 6 175E 02 9 229E 02 1 245E 03 1 40 OE 03 03 1.40.1E 02 5 853E 02 7 43 2 E 02 8 552E 02 8 387E 02 02 4,85*E 01 1 787E 02 2 201E 02 2 537E 02 2 8 16 E 02 02 5.111E- 03 7 008E 00 1 374E 01 4 920E 01 1 3 2 6E 02 02 2.17PE- 01 8 619E 00 2 085E 01 5 334E 01 1 540E 02 02 5.187E- 01 1 308E 01 3 019E 01 7 842 E 01 2 296E 02 02 1.84VE 00 2 204E 01 4 762E 01 1 263E 02 3 691E 02 02 0. 1 163E 01 4 679E 01 1 74SE 02 5 554E 02 03 6.867E- 02 3 165E 01 1 109E 02 3 560E 02 9 754E 02 03 5.494E- 01 8 172E 01 2 46 1 E 02 6 853E 02 1 62 2 E 03 03 3.215E 00 2 109E 02 5 50 5 E 02 1 3 2 3 E 03 2 689E 03 03 1.424E 01 5 293E 02 1 206E 03 2 526E 03 4 45 8 E 03 03 5.949E 01 1 256E 03 2 471E 03 4 449E 03 fc 738E 03 03 2.211E 02 2 744E 03 4 714E 03 7 4O0E 03 9 747E 03 03 8.480E 02 6 164E 03 9 196E 03 1 2 50E 04 1 420E 04 04 2.733E 03 1 122E 04 1 44 5 E 04 1 6 91E 04 1 654E 04 04 6.48.*E 03 1 598E 04 1 810E 04 1 662 E 04 1 6 06E 04 04 1 •2 1> E i 04 1 999E 04 2 014E 04 1 833 E 04 4. 397E 04 03 2* 222E 02 4 041E 02 4 583E 02 5 623E C2 e 456 E 02 03 1.376E 00 6 183E 01 1 546 E 02 3 806E 02 8 956E 02 03 5.047E 00 1 340E 02 2 918 E 02 6 27SE 02 l 296E 03 03 1.467E 01 2 180E 02 220E 02 8 264E 02 l 590E 03 03 3*647E 01 3 598E 02 U 390E 02 1 161E 03 2 0 78 E 03 03 1.011E 02 5 454E 02 to 737E 02 1 464E 03 2 543E 03 03 MASS ABSORPTION COEFFICIENTS FOR C,2 C ^ WAVENO. /T 1008 1600 2016 2520 3360 4500

4750 9.547E 01 5 335E 02 9 400E 02 1 738E 03 3 057E 03 4 C68E 03 4050 2«229E 01 5 303E 02 1 141E 03 2 306E 03 4 036E 03 5 127E 03 4950 7.663E 01 1 156E 03 2 195E 03 3 906E 03 6 018E 03 6 948E 03 5050 2.915E 02 2 791E 03 h 640E 03 7 178E 03 9 561E 03 9 836E 03 5150 1.172E 03 6 8P0E 03 997E 03 1 346 E 04 1 564E 04 1 444 E 04 5250 4,653E 03 1 690E 04 2 164E 04 2 559E 04 2 585E 04 2 136E 04 5350 1.708E 04 3 829E 04 4 305E 04 4 450E 04 3 915E 04 2 905E 04 5450 6.245E 04 8 774E 04 6 715E 04 7 925E 04 6 098E 04 4 C61E 04 5550 1.994E 05 1 710E 05 1 49 IE 05 1 186E 05 7 967E 04 4 786E 04 5650 2.741E 05 1 770E 05 1 428E 05 1 042E 05 6 407E 04 3 635E 04 5750 2.169E 03 1 730E 03 1 616E 03 1 726E 03 2 409E 03 3 404E 03 5850 4.493E 00 1 90OE 02 4 975E 02 1 216E 03 2 688E 03 4 193E 03 5950 1*66<’iE 01 4 473E 02 9 854E 02 2 116E 03 4 115E 03 5 814E 03 6050 7.14*E 01 9 643E 02 1 834E 03 3 3 99 E 03 5 718 E 03 7 261E 03 6150 2.21-1E 02 1 885E 03 3 23 IE 03 5 412E 03 8 225E 03 9 639E 03 6250 8.453E 02 4 237E 03 6 34fiE 03 9 298E 03 1 240E 04 1 318E 04 6350 l*91*fE 03 6 417E 03 8 918E 03 1 216E 04 1 505E 04 1 503E 04 6450 7.719E 03 1 509E 04 1 820E 04 2 155E 04 2 319E 04 2 0S7E 04 6550 1.751E 03 1 033E 04 1 483E 04 1 967E 04 2 232E 04 2 019E C4 6650 6.093E 03 2 274E 04 2 894E 04 3 389E 04 3 385E 04 2 774E 04 6750 1.524E 04 3 525E 04 3 977E 04 4 129E 04 3 665E 04 2 761E 04 6850 4.51ISE 04 6 849E 04 6 907E 04 6 386E 04 5 035E 04 3 465E 04 o950 8.64uE 04 7 880E 04 7 002 E C4 5 716E 04 4 014E 04 2 583E 04 7050 1.689E 05 1 108E 05 8 971E 04 6 649E 04 4 243E 04 2 566E 04 7150 3.393E 03 2 376E 03 2 157E 03 2 254E 03 3 052E 03 4 176E 03 7250 2.821E 00 2 075E 02 5 614E 02 1 42BE 03 3 166E 03 4 86CE 03 7350 0.66hE 00 3 964E 02 9 732E 02 2 230E 03 4 442E 03 6 269E 03 7450 2.417E 01 7 236E 02 1 595E 03 3 290E 03 5 898E 03 7 679E 03 7550 7.450E 01 1 406E 03 2 765E 03 5 084E 03 8 11BE 03 9 687E 03 7650 1.742E 02 2 355E 03 4 236E 03 7 104E 03 1 034E 04 1 152E 04 7750 5# 703E 02 4 655E 03 7 394E 03 1 095E 04 1 409E 04 1 429E 04 7850 1.349E 03 7 456E 03 1 071E 04 1 4 33 E 04 1 665E 04 1 569E C4 MASS ABSORPTION COEFFICIENTS FOR 1008 1680 2016 2520 3360

4.749E 03 1 4B0E 04 1.849E 04 2 155E 04 2 190E 04 04 1.268E 04 2 420E 04 2.690E 04 2 796E 04 2 545E 04 04 4*563E 04 4 609E 04 4.356E 04 3 8 58 E 04 3 010E 04 04 1.307E 05 7 934E 04 6.587E 04 5 130E 04 3 538E 04 04 3.004E 04 2 632E 04 2.322E 04 1 9 10E 04 1 427E 04 04 S.242E 04 3 372E 04 2.736E 04 2 077E 04 1 46 IE 04 04 7.917E 02 6 823E 02 8.729E 02 1 490E 03 8 510E 02 03 4.869E 00 3 056E 02 7«769E 02 1 8 30 E 03 3 712E 03 03 7.917E 02 6 823E 02 8.729E 02 1 490 E 03 2 95 IE 03 03 4.869E 00 3 056E 02 7.769E 02 1 930E 03 3 712E 03 03 1.09*E 01 4 412E 02 1.018E 03 2 179E 03 4 029E 03 03 3.118E 01 8 450E 02 1.765E 03 3 413E 03 5 692E 03 03 6.612E 01 1 235E 03 2.352E 03 4 143 E 0 3 6 3 lOE 03 03 1.726E 02 2 124E 03 3.634E 03 5 747E 03 7 9 54 E 03 03 4.Q61E 02 3 443E 03 4.354E 03 7 639E 03 9 540E 03 03 9.882E 02 5 2ft7E 03 7.295E 03 9 335E 03 1 036E 04 03 2*479E 03 9 048E 03 *.136E 04 1 315E 04 1 319E 04 04 5* 327E 03 1 190E 04 1.327E 04 1 369E 04 1 233E 04 03 1.404E 04 2 103E 04 2.11CE 04 1 953E 04 1 584E 04 04 2.416E 04 2 316E 04 2.066E 04 1 741E 04 1 285E 04 03 1.404E 04 2 103E 04 2 * 110E 04 1 953E 04 1 574E 04 C 4 2*416E 04 2 316E 04 2.086E 04 1 741E 04 1 285E 04 03 7.561E 04 4 4?6E 04 3.559E 04 2 612E 04 1 685E 04 04 7 * 171E 04 3 21 IE 04 2*377E 04 1 637E 04 1 025E 04 03 3.83^E 00 1 152E 02 2.982E 02 6 7 72 E 02 1 402E 03 03 4* 33yE 00 1 717E 02 3.969E 02 8 597E 02 1 647 E 03 03 1* 204£ 01 3 239E 02 6.79SE 02 1 333E 03 2 3C1E 03 03 1.896E 01 3 767E 02 7.366E 02 1 350E 03 2 195E 03 03 5# 24oE 01 7 088E 02 1.259E 03 2 091E 03 3 064E 03 03 1.112E 02 1 106E 03 1.310E 03 2 760E 03 3 70 2 E 03 03 2.129E 02 1 48 6E 03 2.231E 03 3 129E 03 3 877E 03 03 5.895E 02 2 806E 03 3.809E 03 4 8 13 E 03 5 3 56 E 03 03 1 •124E 03 3 947E 03 4.952E 03 5 776E 03 5 928E 03 03 12 13 MASS ABSORPTION COEFFICIENTS FOR C C WAVENO* n 1008 1680 2016 2520 3360 <►500

10850 2« 532*E 03 5 954E 03 6 763E 03 7 151E 03 6 678E 03 5.479E 03 10950 4.63JE 03 8 197E 03 8 607E 03 8 384E 03 7 20QE 03 5.555E 03 11050 9.150E 03 1 160E 04 1 USE 04 9 992E 03 7 896E 03 5.752E 03 11150 1.123E 04 9 696 E 03 8 557E 03 7 090E 03 5 364E 03 3.956E 03 11250 2.613E 04 1 618E 04 1 303E 04 9 770E 03 6 588E 03 4.388E 03 11350 4.667E 04 2 062E 04 1 525E 04 1 055E 04 6 690E 03 4.366E 03 11450 5.552E 00 1 490E 02 3 136E 02 6 202F 02 1 C77E 03 1.387E 03 11550 1*03^E 01 1 984E 02 3 907E 02 7 230E 02 1 176E 03 1 * 443 E 03 11650 2.547E 01 3 367E 02 6 034E 02 1 016E 03 1 5G3E 03 1.717E 03 11750 3#22**E 01 3 71 IE 02 6 449E 02 1 051E 03 1 505E 03 1.676E 03 11850 7# 541E 01 6 183E 02 9 846E 02 1 467E 03 1 914E 03 1-983E 03 11950 1.63‘JE 02 9 401E 02 1 381E 03 1 384E 03 2 25SE 03 2.204E 03 12050 1.816E 02 9 436E 02 1 336E 03 1 764E 03 2 043E 03 1.948E 03 12150 5*003E 02 1 792E 03 2 295E 03 2 738E 03 2 861E 03 2.521E 03 12250 8.607E 02 2 372E 03 2 826E 03 3 128E 03 3 035E 03 2.54CE 03 12350 9.612E 02 2 12SE t 3 2 397E 03 2 516E 03 2 3 3 8 E 03 1.926E 03 12450 2.864E 03 4 336E 03 4 408E 03 4 161E 03 3 464E 03 2 • 615E 03 12550 4*325E 03 5 20 IE 03 4 945E 03 4 361E 03 3 415E 03 2.493E 03 12650 3*249E 03 3 115E 03 2 816E 03 2 405E 03 1 92 IE 03 1.524E 03 12750 1*01IE 04 6 357E 03 5 144E 03 3 902 E 03 2 721E 03 1 • 912E 03 12850 2.017E 04 8 861E 03 6 534E 03 4 SUE 03 2 8 68 E 03 1.887E 03 12950 2.00AE 00 7 443E 01 1 669E 02 3 4 5 1E 02 6 USE 02 7.839E 02 13050 3*85j E 00 1 063E 02 2 209E 02 4 225E 02 6 937E 02 8.355E 02 13150 6.314E 00 1 308E 02 2 535E 02 4 524E 02 6 927E 02 7.918E 02 13250 1* 771E 01 2 468E 02 4 324E 02 6 973E 02 9 64QE 02 1.019E 03 13350 3* 753E 01 3 794E 02 6 121E 02 9 06 IE 02 1 155E 03 1.145E 03 13450 4.246E 01 3 450E 02 S 274E 02 7 415E 02 8 937E 02 8.509E 02 O 13550 1*22/E 02 A 670E 02 207E 02 1 168E 03 1 268E 03 1.116E 03 13650 3.290E 02 1 219E 03 * 527E 03 1 755E 03 1 729E 03 1 • 41IE 03 13750 2 *166E 02 6 841E 02 8 233E 02 9 094E 02 8 604E 02 6.809E 02 13850 6.079E 02 1 296E 03 1 412E 03 1 4 11 E 03 1 208E 03 6.958E 02 13950 1.880E 03 2 665E 03 2 619E 03 2 3 61E 03 1 822E 03 1.235E 03