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Carbon stars : absolute magnitudes and carbon and nitrogen isotope ratios 1977

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CARBON STARS: ABSOLUTE MAGNITUDES AND CARBON AND NITROGEN ISOTOPE BATIGS by B EH NT INGE MAR OLSON B . S c , Simon Fraser U n i v e r s i t y , 1969 M.Sc. , U n i v e r s i t y of B r i t i s h Columbia, 1971 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOE THE DEGREE OF DOCTO'fi OF PHILOSOPHY THE FACULTY OF GRADUATE STUDIES i n the Department of GEOPHYSICS AND ASTRONOMY We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA August 1977 Bernt Ingemar Olson, 1977 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Geophysics and Astronomy The University of Brit ish Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 D a t e August 19, 1977 i ABSTRACT Carbon stars are r e l a t i v e l y uncommon, luminous, cool stars whose spectra exhibit exceptionally strong bands of carbon-con- taining molecules. This i s d i r e c t evidence of extensive nucleo- synthesis, as w i l l occur i n the la t e stages of s t e l l a r evolu- t i o n . The two aspects investigated here are the i r luminosities and atmospheric carbon and nitrogen isotope r a t i o s . The luminosities are derived through the study of those carbon stars which are members of double star systems. Since the companion star i s apparently normal and thus of known lumi- nosity, the carbon star luminosity i s d i r e c t l y a t t a i nable. Photometry and spectroscopy of suspected binaries y i e l d absolute v i s u a l magnitudes for a dozen stars as bright as - 4 . 7 , and bolo- metric magnitudes primarily in the range - 4 to - 8 . This means they are s l i g h t l y mere luminous than normal giants. The i s o t o p i c r a t i o s have been deduced by a comparison of synthetic spectra with the observed near infrared s t e l l a r spectra. The synthetic spectra were calculated by d i r e c t i n t e - gration of the flux emerging from an appropriate model atmo- sphere, and contain l i n e s primarily of the Bed band system of the CN molecule. A new analysis technique, used i n time series analysis, which i s based on the mutual coherence of the spectra being compared and makes f u l l use of the enti r e spectrum, has been employed. By varying the parameters describing the synthetic spectrum, including the isotopic r a t i o , the coherence can be maximized and the i s o t o p i c r a t i o of the s t e l l a r spectrum deduced. R e s u l t s f o r f i v e c a r b o n s t a r s y i e l d 1^c/i3Q r a t i o s i n the range 2.5 t o 30. A s e a r c h was a l s o made f o r t h e i s o t o p e s l*C and i s j } ; i *c was not found, w h i l e a t e n t a t i v e l y p o s i t i v e r e s u l t i s r e p o r t e d f o r 1 5 N . i i i TABLE OF CONTENTS Introduction «... 1 Part I. Absolute Magnitudes .............................. 9 Carbon Stars i n Clusters 11 S t a t i s t i c a l Studies .................................... 14 Carbon Stars i n Binary Systems ......................... 17 The Observational Data , 19 Discussion of Individual Systems .................... 46 Discussion ......... 54 Part I I . Carbon Isotope Abundance Ratios ................. 61 The Observational Material ............................. 66 Synthetic Spectra - Theory 69 Synthetic S p e c t r a - Practice 73 Molecular Parameters ... • 73 Molecular Equilibrium Calculation 82 Spectrum Parameters .,.... ............,...... ....... . 86 Computational Procedure . , . . 88 Analysis Technique 90 Computational Details ................ ............... ,92 Comments 95 Tests ......... . , ............ . 97 Results ... .... .................. ... 105 The » 2 C / * 3 C Ratios ..................................105 Turbulence ....................... ................... 109 A Note on the Carbon Abundance .,,..............,,.,.111 The Search f o r **C and *»8 ..........................115 i v a Recap of the Coherency Technique 129 Summary . . . .131 References .133 Appendix I. Radial V e l o c i t i e s of Carbon Stars . .138 Appendix I I . Ose of flicrodensitometer and Computer Programs to Measure Radial V e l o c i t i e s . . . , . , . . 1 4 7 Appendix I I I . The Ratio of Total to Selective Absorption .161 Appendix IV. Coherency Tables ...........................,169 Appendix V. Parameters of S p e c i f i c Model Atmospheres . . . , . 1 7 9 V LIST OF TABLES 1. Summary of Data on Carbon Stars i n Clusters 12 2. Summary of S t a t i s t i c a l Absolute Magnitudes ........... 15 3A. Observed Photometric Extinction C o e f f i c i e n t s ......... 21 3B. Photometric Errors for Standard Stars ................ 21 4. Suspected Binary Systems with Observations 24 5. Data on Observed Systems. Part 1 32 6. Data on Observed Systems. Part 2 .................... 35 7. Data on Observed Systems., Part 3 38 8. Data on Observed Systems.. Part 4 ....................41 9. VRI Photometry ....................................... 44 10. Some Uninvestigated Double St ars ........... . , ,, ,. ,,., 45 11. Model Atmosphere Parameters ..........................64 12. High Dispersion Carbon Star Spectra 67 13. Molecular Data for the Red System of CN .............. 76 14. Molecular Data for the P h i l l i p s System of C 2 ......... 77 15A. Known Energy Levels of the CN Molecule 78 15B. Known Energy Levels of the C^ Molecule 78 16. Coherency Peaks for a Test Case 98 17. Summary of Derived Spectral Parameters 106 18. Coherency f o r 1 CVn vs i 2 C i s N a n d » 3 c » s N ...........122 19. Stars with n A H - q u a l i t y V e l o c i t i e s Used to Establish Standard Wavelengths i n the Infrared ................. 141 20. Standard Wavelengths and Accuracies of Features Defining the Radial Velocity System 142 v i 21. Acceptance c r i t e r i a for Wavelength Standards ......... 1̂ 3 22.., C o e f f i c i e n t s of Polynomials To Determine H from E(B-V) and (B-V)0 ...........................,168 v i i LIST OF FIGURES 1. Prominent Features of Carton Star Spectra ............ 4 2. Hv {Carbon Star) vs Mv {Companion) 57 3. H(bol) {Carbon Star) vs M (bol) (Companion) 58 4., Bolometric Correction vs V-R 59 5. H{bol) V S (V-R)0 • , , , »••;» • 60 6. Rotational Energy Level Structure for the Red System of CN 79 7. Rotational Energy Level Structure for the P h i l l i p s System of C a ................................ 81 8. Pretreatment of Spectra 94 9. Calculated and Observed Spectra of 19 Psc .102 10. C^ Features i n the Spectrum of 19 Psc ................113 11. Coherency Curves for the **C Test Cases ..............118 12. Coherency Curves f o r Stars vs **C abundance ........ 120 13. Coherency Curves f o r Stars vs * SN Abundance ........121 14. "*SN Features" and the Spectrum of Y CVn 126 15. I d e n t i f i c a t i o n of Wavelength Features for Near Infrared Radial Velocity System 144 16. R vs £{B-V) f o r various types of stars .....166 17. R [S E{B-V)=0] vs (B-V)Q .......................... 167 v i i i ACKNOWLEDGEHENTS I would l i k e to express my appreciation to my supervisor, Dr. Harvey Richer, for his continued aid, encouragement and enthusiasm throughout t h i s project. Special thanks go to Dr. Hans Fast for providing the computer programs f o r spec- trogram reduction, and to Dr. Jason Auman for many invaluable discussions and suggestions dealing with the model atmospheres and molecular c a l c u l a t i o n s . I am also indebted to Dr. H o l l i s Johnson, without whose model atmospheres t h i s thesis would not have been possible i n the present form, and especially to Dr. Tad Olrych, for introducing me to the coherence spectrum technique. The f r i e n d l y assistance of the s t a f f at K i t t Peak made my v i s i t there very enjoyable, while numerous friends have considerably enhanced the enjoyment of doing t h i s thesis., F i n a l l y the U.B.C. Computing Centre was invaluable in the production of the physical copy, while a l l typing, diagrams and layout were done by myself. 1 INTRODUCTION A two dimensional system of s t e l l a r c l a s s i f i c a t i o n based on a star's luminosity and temperature does not f u l l y characterize the nature of that star. This i s most readily apparent among the late-type giants where abundance differences r e s u l t i n many dif f e r e n t classes of stars showing widely d i s s i m i l a r spectra.. This thesis is about some aspects of one of these classes of stars: the carbon stars. The generic name "carbon s t a r " refers to many di f f e r e n t kinds of stars, a l l of which have one thing i n common: their spectra show the presence of carbon-con- taining molecules in greater strength than i n normal stars of simi l a r temperature and luminosity. The classes of carbon stars are: 1. R stars - these stars correspond to the normal K stars, showing spectra with a comparable set of atomic l i n e s plus bands of C^ and enhanced CN and CH. 2. N stars - generally cooler than the fl sta r s ; exhibit extre- mely heavy blanketing by the bands of C £ and CN. Most N stars are long period variables. Every carbon star i s eithe r of type R or N. This, the o r i g i n a l c l a s s i f i c a t i o n system, depends on the r e l a t i v e v i s i b i l i t y of the blue spectral region, with N stars being more heavily blanketed there. 3. J stars - R or N stars with exceptionally strong 1 3 C l 4 N bands (especially at 6168 A) and usually also with strong neutral l i t h i u m . 2 4. CH stars - show an abnormally strong G band and other bands of CH, and generally weak metals. These are a l l high v e l o c i t y stars and hence belong to population I I . , 5. Ba II stars - exhibit strong l i n e s of Ba, Sr and other heavy metals, plus enhanced CH. 6 . Hrl stars - the hydrogen deficient stars, show strong C 2 but weak CH bands. Host Hd stars are also variables of the E CrB type. The CH, Ba II and Hd stars are subgroups of the R stars. 7. CS (or SC) stars - show conspicuous CN bands, enhanced atomic l i n e s {Ba I I , etc.) but very weak bands of ZrO or C 2 , making i t d i f f i c u l t to decide at low dispersion whether they are C or S stars. Other chemically peculiar cool stars are the ju s t mentioned S stars which show oxide bands {especially ZrO, plus LaO, YO) and MS stars which are intermediate between S stars and the normal cool M s t a r s , which are characterized by bands of TiO., The primary factor producing this variety i s the C/a r a t i o ; because of the great s t a b i l i t y of the CO molecule v i r t u a l l y a l l the C or 0 i s t i e d up i n the form of CO, so that stars with an excess of carbon form carbon stars while those with excess oxygen form M or S stars. The CS stars are presumably stars with a C/0 r a t i o of almost exactly unity so that small amounts of both C and 0 are avail a b l e to.form other molecules. C l e a r l y other factors are also important, to produce such d i f f e r e n t types as the CH and Hd stars; these include the population type 3 (metal abundance) , mass and age to name but the most obvious. The t h i n g I want t o emphasize i s t h a t the carbon s t a r s as a whole a r e a very d i v e r s e group indeed. although each subgroup i s a more co h e s i v e s e t , there i s s t i l l no a p r i o r i reason to assume t h a t the N s t a r s ( f o r example) are s u f f i c i e n t l y c l o s e l y r e l a t e d t h a t they can be described by the same b a s i c parameters. In f a c t I s h a l l show t h a t t h e i r l u m i n o s i t i e s ( i n p a r t i c u l a r ) cover q u i t e a wide range. The p h y s i c a l p r o p e r t i e s of carbon s t a r s have r e c e n t l y been reviewed by W a l l e r s t e i n (1973). as a guide t o carbon s t a r s p e c t r a . F i g . 1 i l l u s t r a t e s many of the more prominent and p e c u l i a r f e a t u r e s t h a t may be present i n the v i s u a l and near i n f r a r e d r e g ion of c o o l carbon s t a r s . C a i s r e p r e s e n t e d by the Swan and P h i l l i p s band systems, degrading towards the bl u e and r e d , r e s p e c t i v e l y . CH bands from both the V i o l e t and Red systems are present, a l s o degrading i n o p p o s i t e d i r e c t i o n s ; the Red bands show three separate bandheads r e s u l t i n g from d i f f e r e n t branches of the band. The i s o t o p i c bands (not shown) o f t 2 c * 3 c are o f f s e t from the main bands by approximately +8 A per u n i t v i b r a t i o n a l quantum number change ( A T ) f o r the Swan bands while f o r the red bands of C 2 and CM the o f f s e t i s on t h e order of +40 A. CH i s present as the G band and s e v e r a l o t h e r bands i n the 3900 - 4400 A r e g i o n ; the M e r r i l l - S a n f o r d bands near 4900 A are almost c e r t a i n l y due to S i C ^ ; CaCl bands are o c c a s i o n a l l y seen i n some s t a r s . [The two redward bands of CaCl shown belong t o the Red system and a r e degraded to the blue; the 593 4 A band belongs to the Orange atomic rt U II n O 1 a CO 1 X 1 m z I 8 X '_! 1 1 misc. X CJ 1 o CO r CN o to l> h y ° u o r 11 CN 1 o 1 o" 1 V i o l e t R e d rfT rif* *1 "» *» » f" rfT rfT rfT C 2 ©_ •m •ml «- O Til rrrl i-> «•# o" S w a n I I [ I 4000 I I I I i i > 1 > 5000 i i i i i — r 1 I 1 1 6000 1 1 | 1 1 at m. CN O o z /\ CN O o CN X atomic 1 1 C a  II  C a  II - rfT- H f fir nf- o rfT art e rfT &2 P h i l l i p s r r — N M r © r 1 i i i ' i i i i 7000 i i i i •"• i i — ' 1 ' 8000 1 ' "' T '"—1 I 1 i r i i i i 9000 i i i i i Figure 1. Prominent Features of Carbon Star Spectra 5 system. According to Pearse and Gaydon (1941) t h i s band i s degraded t o the red whereas the spectra of Hybski (1973) appa- r e n t l y show the band extending to the blue i n t o the Na D l i n e s . ] Polyatomic molecules have a l s o been detected i n carbon s t a r s : a C 5 band has been de t e c t e d at 4 050 A while HCN and C^H^ l i n e s have been i d e n t i f i e d i n the 1^ r e g i o n . Bands of CO do not appear i n the v i s u a l r e g i o n , the c l o s e s t being the A V = 3 sequence at 1.6^.. The atomic l i n e s i n d i c a t e d are not by any means exhaustive but merely show some of the s t r o n g e r and/or i n t e r e s t i n g f e a t u r e s . T h i s t h e s i s i s d i v i d e d i n t o two p r i n c i p a l p a r t s . Part I deals with an i n v e s t i g a t i o n i n t o the a b s o l u t e magnitudes of carbon s t a r s . , P a r t I I presents a new technique f o r determining carbon i s o t o p e r a t i o s from molecular bands and c a r r i e s out t h a t a n a l y s i s f o r f i v e carbon s t a r s . The remainder of t h i s i n t r o - d u c t i o n d e a l s with the o r i g i n of the carbon s t a r s . Although the o r i g i n o f carbon s t a r s i s o u t s i d e the scope of t h i s t h e s i s i t i s worthwhile t o b r i e f l y c o n s i d e r the mechanisms which have been proposed to c r e a t e carbon s t a r s from the normal oxygen s t a r s . S i n c e carbon s t a r s have C/0 > 1 i t i s c l e a r t h a t some n u c l e a r p r o c e s s i n g must have occurred; t h i s means e i t h e r hydrogen-burning by the CNO c y c l e or 3-alpha helium-burning. A means of t r a n s p o r t i n g the processed m a t e r i a l t o the s u r f a c e , where we can see i t , must a l s o be provided. As i t now appears l i k e l y t h a t the observed s u r f a c e abundances of carbon and n i t r o - 6 gen are only with d i f f i c u l t y compatible with CNO p r o c e s s i n g {e. g. K i l s t o n 1975, summary by Irgens-Jensen 1976), a process i n v o l v i n g helium-burning r e a c t i o n s , at l e a s t i n p a r t , must be considered, producing lower N/C r a t i o s . The e v o l u t i o n a r y stage t h a t seems best a b l e to p r o v i d e f o r both the p r o c e s s i n g and t r a n s p o r t a t i o n requirements occurs during the helium s h e l l - f l a s h phase. During t h i s e v o l u t i o n a r y phase the s t r u c t u r e of the s t a r i s as f o l l o w s : there i s an i n e r t core c o n s i s t i n g of the products of helium-burning, C and 0, above t h i s i s a t h i c k helium-burning s h e l l , f o l l o w e d by an i n e r t helium r e g i o n , a t h i n hydrogen-burning s h e l l and a deep convec- t i v e envelope extending to the s u r f a c e . As the s t a r e v o l v e s the helium-burning s h e l l g r a d u a l l y narrows u n t i l a thermal i n s t a - b i l i t y develops: the energy r e l e a s e d by the helium-burning r e a c t i o n s i s not a b l e t o escape due to a combination o f t h e high heat c a p a c i t y o f the s h e l l and the pressure i n the s h e l l not i n c r e a s i n g p r o p o r t i o n a l l y t o the d e n s i t y change ( c f : Sackmann 1977) . S i n c e the helium-burning r e a c t i o n s are very temperature s e n s i t i v e a helium f l a s h o c c u r s . A c o n v e c t i v e zone then deve- l o p s , extending almost up to the hydrogen-burning s h e l l . A f t e r a while the f l a s h i s quenched {Sackmann 1977) and the c o n v e c t i v e zone decreases and d i s a p p e a r s ; quiescent helium-burning then continues' u n t i l the next f l a s h s t a r t s . Se thus have an e v o l u - t i o n a r y stage where carbon i s produced { v i o l e n t l y ) and t r a n s - ported upwards; s i n c e the c o n v e c t i v e zone was, however, contained i n the i n t e r i o r i t i s not yet c l e a r how the carbon reaches the s u r f a c e . 7 Three basic approaches have been proposed to overcome t h i s d i f f i c u l t y . 1. The deep envelope {DE) model {Sackmann, Smith and Despain 1974) makes the ad hoc assumption that the i n t e r i o r convective zone actually does physically merge with the convec- tive envelope. Though there i s nothing impossible about this scheme {e.g. by convective overshooting) the fact remains that no model star yet calculated has exhibited such a continuous convective region. 2. The plume model {Scalo and Olri c h 197 3) supposes that, at the maximum extent of the i n t e r i o r convective zone, protons can tunnel through the th i n inert helium zone into the convective s h e l l . They would there react with the carbon, setting up convective plumes l i n k i n g the convective s h e l l with the envelope, thus acting as conduits for the processed material into the envelope. The disadvantages of t h i s scheme are that the plume properties can not be calculated from f i r s t p r i n c i - ples, and that just the right number of protons need to enter the convective s h e l l to produce the observed d i s t r i b u t i o n of s-process elements. 3. Iben's {1975) scheme, which i s a dire c t result of the evolutionary sequence of s t e l l a r model cal c u l a t i o n s , sees the convective envelope dip down int o the helium-burning residue. During the f l a s h the regions within and above the helium-burning s h e l l are pushed outward, and the helium-burning products are distributed throughout the region occupied by the convective s h e l l , which does not quite extend as fa r as the hydrogen-burning s h e l l . a f t e r the flash has stopped the envelope again descends, continuing past i t s previous 8 position (in mass) u n t i l i t encompasses the top part of the residue l e f t behind by the convective s h e l l . This material w i l l then be convected to the surface., Successive flashes w i l l bring more and more processed material into the envelope. Each of these models w i l l enhance the envelope carbon abun- dance more than the nitrogen, since nitrogen i s not produced during helium-burning. They a l l also suffer from the d i f f i c u l t y that the just produced carbon w i l l be processed through the CNO reactions as i t passes through the hydrogen-burning region and also during the i n t e r - f l a s h periods. An envelope base tempe- rature cool enough to prevent 1 2 C destruction also hinders the production of 1 3C. Iben's scheme at least has the feature that the luminosity due to hydrogen-burning i s considerably reduced during the time that the envelope i s actually dipping into the helium-burning residue; the other two schemes necessarily t r e a t the structure as constant during the mixing phase, while Iben's mixing i s caused by the s t r u c t u r a l changes. On the whole, Iben's model i s to be preferred at present, primarily because i t s e s s e n t i a l features are d i r e c t l y calculable and involve no additional hypotheses. 9 Part I. ABSOLUTE MAG NIT ODES The p o s i t i o n of carbon stars in the evolutionary sequence i s not well understood. I t i s not clear, for example, whether most stars become carbon stars or i f only some do, whether the carbon star phenomenon i s recurrent or occurs only once, or how the core products of nucleosynthesis are transported to the surface., Moreover, as has been mentioned, carbon stars are not a homogeneous group; some are found in globular c l u s t e r s while others (N stars) are strongly concentrated toward the g a l a c t i c plane. The problem i s compounded by the fact that many of the basic observational data are imprecise, making comparison with t h e o r e t i c a l studies d i f f i c u l t . In p a r t i c u l a r , carbon star temperatures and luminosities are not accurately determined. I s h a l l here address myself to the absolute magnitude problem. Most previous studies of this question have employed s t a t i s t i c a l methods to derive mean absolute magnitudes fo r large groups of s t a r s ; t h i s approach does, however, tend to obscure the range of luminosities that actually e x i s t s . The only way to reveal t h i s range i s to determine the absolute magnitude of as many i n d i v i d u a l carbon stars as possible. Since t h i s requires a knowledge of the distance to the star t h i s can only be done f o r carbon stars which are members of clusters or binary systems. This part of the thesis begins with a b r i e f summary of work dealing with carbon stars in c l u s t e r s and s t a t i s t i c a l studies.. This i s followed by a description of the photometric and 10 spectroscopic data available pertaining to carbon stars which are members of binary systems and a discussion of the pertinent points of each i n d i v i d u a l system, plus a general discussion of the derived magnitudes. [Much of the material discussed in t h i s part has already been published (Olson and Richer 1975).] 11 CARBON STARS IN CLUSTERS The data on carbon stars in the l i n e of sight to c l u s t e r s has been summarized by Gordon (1968). Assuming that the carbon stars a c t u a l l y are cluster members she finds absolute v i s u a l magnitudes ranging from •0.5 to -3.5. Unfortunately the suppor- ting observational data i s rather sketchy and the absolute magnitudes hence somewhat uncertain. Since that time several other cases have been discovered and more data gathered on other suspected cl u s t e r members. Table 1 summarizes the current status of carbon stars i n c l u s t e r s . The carbon star near NGC 2477 i s approximately two c l u s t e r r a d i i from the cl u s t e r center. , I t s r a d i a l v e l o c i t y of +5.5 ± 3 km/s agrees well, however, with that of an early M-star (+7 ± 3) which i s a cluster member on the basis of i t s proper motion; furthermore the galac t i c f i e l d v e l o c i t y at the distance of the cluster i s *27 km/s, making t h i s star a probable member. The magnitude range shown i s caused by nonuniform reddening across the c l u s t e r . Hartwick and Hesser (1973) f i n d that i f the carbon star which i s 2* from the center of NGC 2660 i s a cluster member i t s Mv = -2.0 and i t has a mass of about 1.8 MS. The r a d i a l velocity of MSB 75 (-46 ± 3 km/s) makes i t a probable member of the very old cluster NGC 7789 (-45 ± 7 km/s) when compared with the f i e l d v e locity (-25 km/s). walker (1972) has found another very red star {(B-V) = TABLE 1. SUMMARY OF DATA ON CARBON STARS IN CLUSTERS l "" - • - i Cluster T ' T- J Star 1 V 1 B-V l 1 1 Clus. E (B-V) - r - T- 1 (ni-M) 1 1 app ] Cluster Type Age • T J MV • i -" I Ref J NGC 2477 j 1 10-7 J 2. 9 1 1 1 1 0. 20 0.40 I 11-2 J l 11-8 J Open 10» I -0-5 J -1-1 1 U 2 I NGC 2660 j j 11. 53 ! 4. 26 1 J J 0.38 J 13.55 1 Open 10« J -2-0 3 3 1 NGC 7789 J MSB 75 ] (10.2) | 1 1 1 0. 26 i 12.1 | Open 10 9-10 J -1.9 J 4,8 i SMC-NGC 419 ] Anon 1 | 16-3 1 1 J I 19.4 J Glob 109 1 -3. 1 1 5 1 SMC-Kron 3 I #24 | 16-48 j 2- 37 1 1 J J 19.4 I Glob 10 9-10 I -2-9 J 5 i SMC-NGC 121 I V8 ] <16.4> <1- 9> 1 I ] J 19.4 J Glob 10io J -3.0 1 5 i u> Cen ] RGO 5 5 | | RGO 70 | i anon J 11. 56 11.61 12. 16 i 1. 1. 1. 55 80 50 i I 1 1 I ] 14.28 J Glob 10io 3 -2-72 | -2.67 1 -2.12 3 7,9 1 10,6 1 1 1 i LMC 1 many 1 15.7 i 1 1 j . 1 - J 18.7 f 1 -3 1 12 L .1 - JL i - ! .i „ Refs: 1. Catchpole and Feast (1973) 7- Harding (1962) 2. Hartwick et a l . (1 972) 8. Haqen (1970) 3. Hartwick and Hesser (1973) 9- Arp (1965) 4. Gaustaa and Conti (1971) 10- Dickens (1972) 5. Feast and Lloyd Evans (1973) 11- Bond (1975) 6. Cannon and Stobie (1973) 12. Hesterlund (1964) 13 +4.2, Mv = -1.9) i n NGC 419 i n t h e Small Magellanic Cloud, although no s p e c t r a o f t h i s s t a r e x i s t , i t seems probable t h a t i t i s a carbon s t a r . The t h r e e SMC s t a r s i n T a b l e 1 are a l l l o c a t e d r i g h t at the t i p of the r e d - g i a n t branch {Feast and Ll o y d Evans 1973), as are the three known CH s t a r s i n to Cen {Smith and Wing 1973; Bond 1975). A l l carbon s t a r s so f a r found i n g l o b u l a r c l u s t e r s have been l o c a t e d at the t i p of the g i a n t branch. The approximately 400 carbon s t a r s found by Besterlund (1964) i n the LMC have a mean estimated v i s u a l magnitude o f 15.7 with a spread of about h a l f a magnitude, i n d i c a t i n g an a b s o l u t e v i s u a l magnitude of about -3., Because of the s c a r c i t y of C- s t a r s near c l u s t e r s and the d i f f i c u l t y i n e s t a b l i s h i n g whether a s t a r i s a c l u s t e r member i n our galaxy, the l a r g e numbers of carbon s t a r s i n the Large Magellanic Cloud hold great promise i n regard t o absolute magni- tude s t u d i e s . Recently a s m a l l sample o f these have been s t u d i e d by C r a b t r e e , R i c h e r and Westerlund (1976) ; they range i n apparent magnitude from 13.9 to t h e i r i n s t r u m e n t a l l i m i t of 16.8, r e s u l t i n g i n a b s o l u t e v i s u a l magnitudes as b r i g h t as -4.6 {using m-M = 18.5} . 14 STATISTICAL STUDIES Since most carbon stars are f i e l d stars, t h e i r absolute magnitudes can only be calculated on a s t a t i s t i c a l basis using the observed r a d i a l v e l o c i t i e s and/or proper motions i n con- junction with the apparent magnitudes. Sanford (1944) found <Hv> = -0.4 ± 0.4 for 62 S-stars and -2.3 ± 0.2 for 171 N-stars. The E-stars were further subdivided by Vandervort (1958) who derived <Mv> = + 0.44 ± 0,29 from 43 RO and R2 stars, and -1.10 ± 0.49 from 42 R5 and B8 star s . Richer (1971) calculated <Mv> = -2.7 ± 0.7 for 33 sta r s c l a s s i f i e d C3 to C7 on h i s i n f r a r e d c l a s s i f i c a t i o n system; these stars were mostly of type N. Baumert (1972) has calculated near infrared 1.04 micron narrowband absolute magnitudes <M(104)> of -1.7 ± 0.5 and -4.3 + 0.6 for R and N-stars, respectively. To convert these numbers to vis u a l magnitudes the colour index (V-I(104)) was formed f o r a sample of stars in common with the l i s t s of Richer (1971) and of Mendoza and Johnson (1965). This resulted i n <V-I(104)> = + 2.4 ± 0.9 (st. devn) for the R-stars and +3.9 ± 0.7 for the S-stars. The average (B-?) i n d i c e s for the samples were +1.67 and +3. 13, as compared to the more complete sample values of • 1.67 f o r Vandervort's R-stars and +3.10 for Richer's N-stars, in d i c a t i n g that the samples used are representative of the general population. The re s u l t i n g Mv*s are +0.7 and -0.4, s i g n i f i c a n t l y f a i n t e r than the previous r e s u l t s . 15 r J 1. Author • T I Type Hv N "T I Type i _ _ t _ H V N i i i I I 1 T" — r - i Sanford (1944) i H ) -0.4 ± 0.4 | 62 1 N ] -2.3 ± 0.2 | 171 Vandervort (1958) 1 RO J . 82 | •0.44 ± 0.29 | 43 | j i | R5 J 1 R8 | -1. 10 ± 0.49 | \ j 42 | i ! Richer (1971) i j 1 C3 | 1 C7 j -2.7 ± 0.7 | 33 Baumert (1974) 1 R 1 M(104) = | -1.7 ± 0.5 | Hv = ••0.7 # | 115 1 N | H (104) = -4.3 ± 0.6 Hv = -0.4 # | 202 i . . . i 1,, , L . •j i... —x., .,„ . j # See text., T A B L E 2., SUMMARY OF S T A T I S T I C A L A B S O L U T E M A G N I T U D E S OF CARBON S T A R S 16 Peery (1975), assuming that most of the dispersion i n colour of Bau inert* s photometric data i s due to i n t e r s t e l l a r reddening, has deduced boloraetric magnitudes for a saaple of N i r r e g u l a r variables i n the range -4 to -6, again considerably brighter than Baumert*s value for a s i m i l a r group. Baumert (1975) subsequently revised his value for this group of stars by -1.5 magnitudes by deleting a single star from his sample. Thus i s seems plausible' that s i m i l a r errors may be responsible for a large part of the above mentioned discrepancy. 17 CAfiEON STARS IN BINARY SYSTEMS The other major approach to determining absolute magnitudes of i n d i v i d u a l carbon stars makes use of binary systems with one member a carbon star. This method i s e s s e n t i a l l y i d e n t i c a l to that used for carbon stars in c l u s t e r s ; namely, determine the distance modulus to the system (cluster) and use the apparent magnitude to ca l c u l a t e the absolute magnitude. To do this one must: a) establish the r e a l i t y of the physical proximity of the C-star and i t s suspected companion (or the cluster) , and b) calculate the distance modulus of the companion (cluster)., The distance modulus of a cl u s t e r i s f a r easier to derive accurately than that of a single star, however, since i n that case we have access to a l l the cl u s t e r members. Comparison of the observed colour-magnitude diagram with the zero age main sequence yie l d s the distance modulus and reddening as well as the age of the clus t e r and the mass of the carbon s t a r , though t h i s i s more strongly dependent on the evolutionary model sequence used., A cluster distance modulus i s obtainable to an accuracy of a few tenths of a magnitude. In contrast to t h i s the modulus of a single star must be computed from a knowledge of i t s absolute magnitude, which, i n turn, must be in f e r r e d from some observational parameter that has been calibrated i n terms of absolute magnitude. In practice t h i s would normally e n t a i l HK spectral c l a s s i f i c a t i o n , photometry for B-stars, or H/s plus uvby photometry f o r A and F-stars.. Whereas the absolute magnitude c a l i b r a t i o n s for si n g l e stars of early type may be 18 comparable i n accuracy to the cluster moduli, l a t e r types can often not be placed to better than a magnitude. In t h i s inves- t i g a t i o n the f i r s t two methods have been employed., The most conclusive ways of proving the r e a l i t y of a suspected binary system would be to observe eith e r an o r b i t or one star e c l i p s i n g the other. No such cases are known among carbon stars although a few do show composite spectra, indicating a very close companion. , That these are the resu l t of a chance superposition i s highly unlikely. As the angular separation of the two stars increases there i s an increasing need for corroborating evidence of their physical association. Agreement of t h e i r r a d i a l v e l o c i t i e s , or common proper motion, would strongly support this conclusion, as would the presence of the same set of i n t e r s t e l l a r absorption l i n e s i n both stars, although t h i s would be d i f f i c u l t to apply to carbon stars because of the complexity of their spectra. F i n a l l y , the absolute magnitude derived for the carbon star ought to be "reasonably* 1 close to the range indicated by the s t a t i s t i c a l studies and those carbon stars which are members of c l u s t e r s (see previous sections). 19 The Observational Data The l i s t of candidate carbon stars which may be members of binary systems has been compiled from several sources. The i n i t i a l l i s t was prepared by Dr. H. B. Richer during h i s obser- ving run at Cerro Tololo i n 1969, when, while taking spectra of the C-stars, he noticed that several stars had f a i r l y close companions. Three systems were added when his photometry indicated that the (U-B) indices of the supposedly single carbon stars were much too blue compared to (B-V). The results f o r these systems have already been published (Richer 1972). A secondary l i s t was kindly supplied by Dr. H. E. C r u l l , J r . , (1972) of the U.S. Naval Observatory at Washington, D.C., while a few systems were chosen from the A.A.V.S.O. charts and some were gleaned from the l i t e r a t u r e . Kith the aid of the Palomar Sky Survey prints and v i s u a l observations of the candidates through the department*s 30-cm (12-inch) telescope, t h i s p r e l i - minary l i s t was narrowed down to those systems with companions thought bright enough to be feasibly investigated further. Photometric and spectroscopic observations of some of these systems were obtained at the K l t t Peak National Observatory near Tucson, Arizona, during the periods Sept., 10-12 (photometry) and Sept. 18-24 (spectroscopy) of 1972, by the author. In addition, Dr. Richer has obtained some VRI photometry from Cerro Tololo during the periods Oct. 12-14, 1971 and June 5-7, 1974. UBV and photometry was obtained of 17 suspected systems using the K i t t Peak #2 36-inch (91-cm) telescope and the 20 reductions were done by a computer program written by the author using standard reduction methods; taking into account the red leak of the U f i l t e r . The red leak f i l t e r i s a standard 0 f i l t e r with the U bandpass region blocked, allowing a d i r e c t measure of the leak in the red region. Ose of t h i s f i l t e r i s necessary for the C-stars because of t h e i r extremely red colours., The photometer deflections through the u l t r a v i o l e t , blue, visual and red leak f i l t e r s are denoted by u, b, y and r l , r e - spectively, and the raw colours are Cy = -2.5 log (b/y) Cu = -2.5 log (u\/b) ( 1) where u* = u - r l . These are related to the magnitude and colors above the atmosphere via y (Q) = y - km * sec z Cy(0) = Cy - ky * sec z (2) Cu (0) = Cu - ku * sec z where ky = k1 • k2 * Cy{0), and sec z i s the a i r mass of the observation* The calculated extinction c o e f f i c i e n t s f o r each of the three photometric nights are tabulated i n Table 3A, along with standard K i t t Peak values (Barnes 1974). F i n a l l y OBV colours are calculated from V = c l + c2 * (B-V) + y (0) B-V = c3 «• c4 * Cy (0) (3) U-B = c5 • c6 * Cu (0) 1 Date (1972) 1- k1 k2 l ku km Sept. 10/11 Sept. 11/12 Sept. 12/13 0.107 0.087 0.088 -0. 006 -0. 029 -0.025 0.234 0. 136 0.269 0.117 0.101 0.145 Average; S t . Devn: 0.094 ±0.011 -0.020 ±0.012 0.213 ±0.069 0. 121 ±0.022 Std. KPNO values 0.100 -0. 020 0.340 0. 150 TABLE 3A. OBSERVED PHOTOMETRIC EXTINCTION COEFFICIENTS i 1 r i 1 \ Colour | V | B-V | U-B | , j. 4 I I I I ] | S t . Devn | 0.019 | 0.016 \ 0.023 | I 1 I 1 I t 1 1 1 i TABLE 3B.„ PHOTOMETRIC ERRORS FOR STANDARD STARS 22 where the " c n c o e f f i c i e n t s are calculated from observations of standard s t a r s . The expected uncertainties are given in Table 3S. Since the magnitudes of the very red carbon stars are calculated, in part, from an extrapolation of the r e l a t i o n defined by the (bluer) standards, one would expect the uncer- t a i n t i e s of the C-star magnitudes to be somewhat greater than those of bluer stars, and may be systematically i n error. No attempt has been made to t r y to combat t h i s problem. The VHI reductions were c a r r i e d out in a s i m i l a r manner. Blue plates of 127 A/mm dispersion at were secured of the companions i n 10 systems, as well as several MK and v e l o c i t y standards. Spectral c l a s s i f i c a t i o n was done r e l a t i v e to the known standards using the c r i t e r i a outlined i n the K i t t Peak Spectral Atlas (Abt et a l . 1968). The r a d i a l v e l o c i t i e s were measured on the Grant oscilloscope measuring engine i n t h i s u n i v e r s i t y ^ Physics Department. The i n t e r n a l errors r e s u l t i n g from the measurement of (typ i c a l l y ) a dozen l i n e s were about 16 km/s (st. devn), whereas a comparison of measured and standard v e l o c i t i e s gave standard deviations of 15.2 and 11.8 km/s for B, A and F-stars and f o r G and K-stars, respectively, i n d i c a t i n g that there were no systematic errors present. Several a d d i t i o n a l spectra have also been obtained at the Dominion Astrophysical Observatory, V i c t o r i a . These were obtained with the 183-cm (72-inch) telescope at a dispersion of 78 A/mm. The i n t e r n a l accuracy of these plates i s about 10 km/s (st. devn) from a half dozen l i n e s . Also a v a i l a b l e ware 200 23 A/ran bl u e p l a t e s of many o f the suspected companions obtained by Dr. Richer at Cerr o T o l o l o i n September 1971. U n f o r t u n a t e l y these p l a t e s turned out t o be unusable f o r r a d i a l v e l o c i t y measurements as there were l a r g e random unexplained systematic s h i f t s between the s t e l l a r s p e c t r a and the comparison a r c s , amounting i n some cases t o e q u i v a l e n t v e l o c i t i e s of s e v e r a l hundred km/s. A l i s t o f suspected carbon s t a r b i n a r y systems f o r which o b s e r v a t i o n s e x i s t i s given i n T a b l e 4, along with two suspected systems c o n t a i n i n g S - s t a r s . Columns 1, 2 and 3 gi v e the name and e q u a t o r i a l and g a l a c t i c c o o r d i n a t e s of the C - s t a r . Column 4 r e f e r s to the EN s p e c t r a l type, the Keenan-Morgan C-type as d e f i n e d on the Okayama system (Yamashita 1972), and R i c h e r ' s (1971). i n f r a r e d C-type. Column 5 give s the companion's name, while column 6 g i v e s the angular s e p a r a t i o n of the two s t a r s i n seconds of a r c and the p o s i t i o n angle of the v e c t o r from the C-st a r to the companion, measured c o u n t e r c l o c k w i s e from the north p o i n t ( i . e . N-E-S-W). The o b s e r v a t i o n a l data t h a t a r e r e l e v a n t t o determining the r e a l i t y o f the systems and the C- s t a r s * a b s o l u t e magnitudes are given i n T a b l e s 5 through 8. The l a s t column of Table 4 g i v e s which of these f o u r t a b l e s con- t a i n s the ob s e r v a t i o n s f o r t h a t system. The s t a r s have been d i v i d e d i n t o four groups depending on the p r o b a b i l i t y t h a t the systems are r e a l and the s t a t u s of the o b s e r v a t i o n a l data. Those systems which have s e v e r a l items of sup p o r t i n g evidence and no neg a t i v e ones are con s i d e r e d to be 24 Name HD DM R.A. Dec. (1900) 1 b RN KM Rh Comp. Sep. , P. A. X Cas 01 49.8 • 58 46 13-1.2 -2.6 Ne C5,4e 60 70 0 Cam 22611 +62 596 03 33.2 +62 19 141.2 6.0 +62 594 C5 , 4 208 349 30710 +15 691 04 44.9 • 15 37 183.8 -17.9 N C5,3 C4 34467 +35 1046 05 12.5 • 35 41 171.2 -0.9 N C6,3 C4 24 44 UV Aur 34842 +32 957 05 15.3 + 32 24 174.2 -2.4 Ne C8,1Je C9 ADS 3934B 3 4 TO Tau 38218 •24 943 05 39.1 • 24 23 183.8 -2.4 N C5,4 C5 TABLE 4. SUSPECTED BINARY SYSTEMS WITH OBSERVATIONS 1 — r " - T — — — - r - • ~T T I Name I R.A. , I 1 I RN l Comp. I Sep. I Th J | HD | Dec. | b i KM | | P.A. I No j | DM (1900) 1 I Rh _ J I . J T j ] ] | MSB 22 ! 06 20.5 -27 01 j 234.9 - 17.5 I N | C4,4 | i 5 i | -26 2983 ! ! I C6 . . . . 1 i i i , ' 1 • T i 1 BY Mon 1 07 02 . 1 -07 24 221.1* -0.0 I H I C5,5 ! | 28 1 6 j | - 7 1742 j | | C6 j i j j j T J i W CMa 1 07 03.4 1 225.4 | N J -11 1801 I 158 i 5 | J 54361 ! -11 46 1 -1.8 I C6,3 j I i | | -11 1805 j • i i C5 I i 1 3 i * j I T —1 \ MSB 31 j 07 45.0 -00 38 j | R8 j i 4 J 119 1 5 J i i j j ~l 1 08 42.4 1 252.6 | R8 i HD 75022 J 110 | 5 ( I 75021 I -29 21 I I | 1 ! j | -29 6735 i j | . J ! ! I r i J T • * I V Hya 1 10 46.8 1 i | 46 i 5 i | ^20 3283 1 -20 4 3 1 I ! | 186 i ! 1 - X - j J. a. . j . . . J TABLE 4., (Cont.) 26 Name HD DM R . a., Dec. (1900) 1 b RN K15 Rh 1 1 I Comp. | Sep. P. A. SZ Sgr 161208 •18 4634 17 39.1 -18 37 8.7 5.5 N C7,3 C5 2 215 T Dra +58 1772a 17 54.9 • 58 14 86.8 29.9 Ne UY Dra 15 225 HK Lyr 173291 +36 3243 MSB 64 + 5 3950 18 39.4 + 36 51 66.1 17.5 N C7,4 C 5 18 42.6 + 05 20 37.3 3.4 C6 28 S Set 174325 8 4726 18 44.9 -08 01 2 5.8 -3.4 N C6 ,4 C 5 UV Aql 176200 +14 3729 18 54.0 + 14 14 46.6 5.0 C 6 20 . J t TABLE 4. (Cont.) 27 I X I Name | 1 HD | { DM | R. A. Dec. C1900) - T 1 \ b | RN KM Rh i I Comp. - i - i Sep. P. A. ~~i i 1 Tb 1 1 No \ j J j ] - +- i I X Sge | 20 00.7 I 59.7 | N I 6 1 6 | | 190606 I + 20 22 I -5 .9 | ! [ j j | +20 4417 I ! C6 i ! 1 i | Sv Cyg J 20 06.4 ! 83.2 | N3 | +47 3032 i 145 1 5 J i 191738 | +47 33 ! 8.0 | C7,4 ! ! 140 ! ! I + 47 3031 I ! ! i ! i | RS Cyg j 20 09.8 ! 75.9 | Ne | +38 3956 ! 132 | 7 J | 192443 | + 38 26 i 2.4 j C8,2e ! J 355 i 1 | +38 3957 | J j C5 J +38 3960 56 106 | ! I « Cyg | 20 16.5 ! 84.2 | Ne | +47 3078 ', 64 1 7 i I 193680 f •47 3 5 I 6.6 J C8,2 I ! 51 I ! ] +47 3077 j .4 i C em j ( ! ! T : 1 J * | MSB 41 1 20 45.2 + 32 51 J 75.8 | -6.7 | N 1 cp. 1 J 10 I 6 | | +32 3954 | I i I cp. 2 i 18 ! j v ._ _. . 1, -J. _ J~ _ _ j — X 1 TABLE 4. (Cont.) 28 r - i Name HD DM T i R.A. 1 Dec. | (1900) -T T " 1 1 1 1 b ] " T _ RN J KM | Rh | i Comp. T- _ J _ Sep. P. A. | Tb J I No | i ' j i T i i H V Agr | 21 00.7 | -00 36 1 49.6 | I -29.6J He | C em | j ! 8 | | 21 59.5 1 94.? ) N | ! 9 1 6 1 209596 | +45 05 1 -7.9 | ! _ J • i J | J i~ t —1 | 21 59.7 | 78.6 | R3 J ! 1 8 j 209621 ] +20 34 1 -27.1 | C2,2CH | J i ! +20 5071 ! i j C2 | ! I .„ 1 } j . J • 1 1 BZ Peg I 22 01.5 J 87.6 | Ne j 15 I 6 1 209890 | +33 02 | -17.8 | C9,1e J I 1 ! +32 4335 ! ! C em j i i i MSB 73 J 22 40.7 | +48 57 1 10 2.8 ] I -8.4 ] N | | 6 325 •+*"• i 1 6 1 •48 3827 J i ! i j i SO And \ 23 59.4 | 114.0 J N 1 ! 15 1 5 | 225217 | +43 00 I -18.5 1 C6,4 | 1 1 1 •42 4827 I 1 1 C5 1 } ! i i i , _. i — j . ,. j. -J... I TABLE 4. (Cont.) 29 Name HD DM 8 Cyg 185456 +49 3064 S Cyg 3 +57 2134 R. A. Dec. (190 0) 19 34.1 + 49 58 20 03.4 +57 42 1 b 82.7 13.8 91.8 13.7 RN KM Sh S4 ,9 S5,2e T T 1 Comp. | Sep. P. A. +49 3065 91 14 31 TABLE 4. (Concl. ) 30 r e a l (Table 5) , while the systems with strongly discordant data are considered to be not real (Table 7). Systems with few supportive (or mildly conflicting) data are considered i n Table 6; these systems frequently lack some v i t a l observation and cannot be decided one way or the other on the basis of the present observational data. F i n a l l y there are those systems (Table 8) for which so l i t t l e data i s available that i t would be meaningless to claim t h e i r r e a l i t y or otherwise. The Tables 5 to 8 have, because of space l i m i t a t i o n s , been divided i n t o three parts each (A, B and C) . The photometry of parts A refe r s to the carbon stars {columns 2 - 4) and the i r companions (columns 5 - 7) . for the years indicated [ 1969 = Sept./Oct. 1969 (Richer 1971); 1971 = Sept. 1971 from Cerro Tololo (by Dr. Richer, mostly unpublished); 1972 = Sept. 1972, author's data from K i t t Peak]., A l l the H/s photometry was done in 1972. The carbon star V magnitudes at maximum ( c o l . B. 2) are derived from the present photometry (p) unless otherwise i n d i - cated. The colour excesses (col. A.7) and absolute magnitudes (col. B.5) of the companions are based on the c a l i b r a t i o n s of Johnson (1966) and Blaauw (1963), respectively. Column C.4 gives the r a d i a l velocity of the g a l a c t i c f i e l d at the distance of the companion, calculated from the Oort g a l a c t i c rotation formula and corrected for the standard solar motion. Columns C. 5 and C.6 give the dereddened colour index (cf. Appendix III) and the calculated brightest absolute v i s u a l magnitude of the carbon sta r . F i n a l l y , column C.7 gives the author's confidence l e v e l , on a scale from 0 to 10, in these derived absolute magni- 31 tudes., This i s a combination of the confidence l e v e l of a physical connection between the component stars and the r e l i a - b i l i t y of the companion's luminosity c l a s s . The l e t t e r s also appearing i n some of the columns of parts B and C refer to the sources of the data. These are; A - A.A.V.S.O. magnitude estimates (Barnes 1974), E - Eggen (1972) , F - Franz and White (1973), G - Gordon (1968) , ft - Mendoza and Johnson (1965), W - Wilson (1953) , p - brightest V magnitude from part A of Table 5, a,b,c,d,e - Sanford's (1944) probable error of velocity: a=±1, b=±2-3, c=±4-5, d=+6-8, e=±> 10 (km/s) . VI - V i c t o r i a - 7 8 A/mm spectra. KP - Ki t t Peak - 128 A/mm spectra. CT - Cerro Tololo - 200 A/mm spectra - companions. - 124 A/mm IH spectra - C-stars. The carbon star r a d i a l v e l o c i t i e s mentioned on the previous l i n e have been measured on a system developed here and described in Appendix I. The VBI photometry i s presented i n Table 9, while a few additional double stars from Crull»s (1972) l i s t which have not been investigated a t a l l are given i n Table 10. These companions* magnitudes are guesses from the Palomar Sky Survey p r i n t s . 32 Star v B-V U-B 1969 C-star V B-V D-B 1971 h V B-V U-B 1972 Companion V V H beta B-V B-V E(B-V) U-B U-B 1971 1972 +- I UV aur | I * • 1 j 9.59 | 1.42 | -0.26 | 9.39 || 1.67: H -0.13 I] | 10.96 | | 0.21 | | -0.30 | 2.679 0.20 I -26 2983 | 1 % 1 8.58 | 3.47 | 1.00 | 8.56 j 3.26 | 1.35 I j j (12.8) ! | 0.0 I SZ Sgr | i % 1 8.44 | 2.31 | 1.72 j | j (11.8) I | 0.21 I TO Tau | 1 % 1 8.42 | 2.95 | 8.29 | 2.72 j 1.36 | 8.45 || 2.73 || 1.1)9 || (11-7) I i 0.44 1 H CMa | 6.77 | 2.53 | 4.68 | 6.55 | 2.38 | 4. 24 j 7.48 || 2.50 || <*-32 J | 8.76 0.00 -0. 69 I 8.82 | j -0.01 | 1 -0.69 | ; 2.642 0.24 | SU and | 8.22 | 2.58 | 4. 13 | 8. 19 | 2.45 ] 4. 85 | 12.77 0. 38 0.01 | j 0.07 | SV Cyg | j 8.55 || 3.19 || 5. 2 : | | | 9.75 | | 1.21 | 1 1-24 | 0.11 1 MSB 64 | j 9.60 | 3.79 | 9.51 | | 3. 46 | | 11.81 0.73 0.49 | 11.85 | I 0.72 | | 0.48 | 2.818 0.58 | HD 75021 | 7.08 J 1.94 | 3. 17 j j j 7.58 1. 45 1.60 i . . _ — . . i „,. 0.35 ; J j 11 " I i | MSB 31 | I # | 9.0 | ! I I 10. 8 0. 2 | | I V Hya | i * i 6.7 1 ! i ! 11. 58 i I i * i t J... X, — X- - J - A — J _ . . . . . JL % C-star photometry includes companion. # See text. TABLE 5.a DATft ON OBSERVED SYSTEMS - PROBABLY REAL PHOTOMETRY 33 r - - — -T— • T — ' " " 1 I Star | V (max) | C-star | AV C-star i Spectrum Co m p ! Comp j V max,C* | -V(cp) j 1 i i 1 l j T T I OV Aur | 7.4 F | 3.2 F I B9 V KP ! -0. 1 j -3.5 j ] -26 2983 1 8.55 p I | A5 V CT | + 1.8 j -4.25 j I SZ Sgr J 8.4 p | 1 A7 V CT ! +2.0 | -3.4 | ] TO Tau | 8.3 p | 0.2 p | A2 I I I : CT KP ! -0.6 | # I -3.4 1 I » CMa | 6.55 p | 0.9 p | 32 V KP CT j -2.5 { -2.2 j | SO And | 8.2 p | | FO V: VI •2.4 | -4.6 I J SV Cyg | 8.4 A | 0.5 A | K1 III KP +0.8 | -1.4 ] | MSB 64 ] 9.4 p | i A6 IV: CT VI 1 • 1.5 J -2.4 | | HD 75021 } 7.1 p I 0. 1 H | K1 III G, E CT j +0.8 | -0.5 ) • I MSB 31 | 9.0 | | A6 III-V: G | • 1.9 | * 1 ... _ —+ -1.8 | I V Hya | 6.7 J | KO I I I : G +0.8 | - 4.3 ] i _*,,„ J - t . j — _ i- 1 # See text. TABLE 5.B DATA OH OBSEfiVED SYSTEMS - PROBABLY REAL HAGHITODES AND SPECTRA 34 T T T 1 Star Radial Velocity I 1 C-star Comp Gal | | C-star | C-star | 1 1 i i J 1 1 J T 1 J • I OV Aar | - 1 0 a | - 1 7 KP j • 6 | | 3 . 0 | - 3 . 6 | 10 | - 2 6 2 9 8 3 | • 2 3 e | - 6 CT J ! + 3 8 | | 4 . 1 1 - 2 . 4 | 1 0 | SZ Sgr | • 19 b | j - 1 0 | | 2 . 4 | - 1 . * I 1 0 I TO* Tau | - 2 4 c J - 1 9 CT | ! • 1 5 | | 2 . 8 | - 3 . 9 | 8 | W CMa | • 2 1 d | • 1 9 G | + 3 7 J | 2 . 2 | - 4 . 7 | * I 7 | SU And | - 6 b | - 1 1 CT | - 6 VI ] - 2 0 | | 2 . 4 | - 2 . 2 | 9 | SV Cyg 1 - 8 c | - 1 5 KP | - 1 4 | | 3 . 1 | - 0 . 5 | 6 | MSB 6 4 | - 1 7 c | •4 CT | + 1 VI { - 1 0 || 3 . 0 | - 0 . 8 | 7 | HD 7 5 0 2 1 ) • 1 1 a J # _ _ i + 18 | | 1 . 6 | • 0 . 3 | 8 l I j f i i * | MSB 3 1 | •4 J j j j j + 0 . 1 i I V Hya | i - , ;..., . J - 8 ] I _ — j . . — .... i. - _ J. - 3 . 5 | . i . (B-V)o Mv See text. TABLE 5.C DATA ON OBSERVED SYSTEMS - PROBABLY REAL VELOCITIES AND DERIVED MAGNITUDES 35 * • •' — . - - J — ' — i ] 1 C-star 11 Companion 1 1 V V V If V V H beta j I Star J B-V B-V B-V M B-V B-V E(B-V) J | I D-B U-B U-B J | U-B U-B 1 1 1969 1971 1972 | J 1971 1972 i i . i... i • * i i i i t t J j 1 t | RY Hon j 8.10 j 7.91 J II 1 12.29 J —— 1 1 i 4. 15 | 4.03 | | | | 0.49 1 0 . 1 - 1 . | 1 ! —— • ~ I II 1 0.01 J 1 RZ Peg J 9.25 j 12.31 J | — 1 I | | 3.93 | | | 0. 57 | | 0.0 J 1 1 1 2.66 j i l 0. 13 1 1 | OV Aql | ! 8.39 | j j 12. 05 J J —— 1 I | | 3.55 J 11 1.53 ] | 0.88 J • > • — 1 H 1. 50 I I | HD 34467 J 9.20 j 9.20 H 1 12.90 J 2.826 J | | 2.75 | ] 2.78 | J I 0.53 | — 1 — • I 4. 28 J | I 0.30 J | MSB 41 | J 9.61 | 9.52 I) 10. 72 I 10.81 1 — i | | | 4. 14 | 4.36 H 0.89 | 0.88 J 0.0 i j I — J N 0.44 1 0.44 J J cp.2 | j j J j 11.94 | 12.00 I —— 1 I I | | j | 1.08 1 U10 I 0.0 i I I 1 II 0.80 I 0.86 I I X Sge | 8.36 8.53 | 13. 18 | J —— 1 1 1 3.29 ] 3. 35 | t) 0.77 | ] 0.41 | 1 1 —— > — i 1 I 0. 16 1 1 | HD209596 1 J j 10.18 H 1 12.96 J 2.608 J | | | | 2.40 11 1 0.85 | — j 1 1 1 1 4.05 H 1 0.39 1 I MSB 73 | J j 10.29 H 1 12.74 J 2.615 1 1 1 | 1 2.30 I | 1 0.74 | 0.29 1 | | \ 1 3.44: | l 1 0.08 J 1 1 -4. 1 1 1 ;l I i j . T 1 j • i i i i R Cyg | J 1 6.80 || 1 9.88 1 2.899 j I | 1 j 1.91 H } 0.09 | 0.0 1 1 1 1 1 2. 18 | J 1 0 .11 J 1 S Cyg | 1 J 11.24: H i 9.17 I — 1 1 1 i 1 2.01 || | 1.00 | 0.0 1 1 1 3 1 1.00 I I I 0.80 I t. ... j... . 1 . 11 _ j . — i _ 1 TABLE 6.1 DATA ON OBSERVED SYSTEMS - POSSIBLY REAL PHOTOMETRY 36 i i ....... . _.j.- St ar | — - • r 7 (max) | C-star | C- A 7 star Spectrum Comp ~T~ Mv Comp — i 7 max,C* i -V (cp) | t ] ! i • i * j" T ! HY Mon [ 7.9 p J 1. 5 A i F3 1 7 CT i • 2. ! -4.4 | j fi.2 Peg | 8.2 A | 4. 0 A F9 7 CT | *4.2 | -4.1 J J U7 Agl { 8.4 p j G4 7 : CT j +1.8 * ! -3.7 J J HD 34467 | 9.2 p | j •2. 1 j -3.7 j i MSB 41 | 9.5 p | G6 III G I +0.4 -1.3 } j c p . 2 J I K 71 1 -2.5 ] X Sge | 8.4 p | F2 7 71 j +2.8 I -4 .7 I I HD209596 | 10.2 p | j F8 I I I - 7 G 7 1 + 1.0 or +4.0 1 -2.8 | j MSB 73 | 10.3 p | i F6 I I I - 7 G + 1.0 or •3.5 -2.4 | i * * 1 1 1 8 Cyg J 6.8 A | 7. 1 A ! A5 7 KP • 1.8 -3.1 { i S Cyg j 9.5 A | 5. 7 A I K0 III KP i +0.8 I -0.2 | J. i„ . . X , - X - J # See te x t . TABLE 6.B DATA ON OBSEE7ED SYSTEMS - POSSIBLY REAL MAGNITUDES AND SPECTBA 37 T "3 Star Radial Velocity C-star Comp Gal -H- (B-V)o C-star Mv C-star RY Mon RZ Peg UV kql HD 34467 MSB 41 cp.2 X Sge HD 20 9 5 96 MSB 73 R Cyg S Cyg • 2 c +4 CT -27 d -21 CT + 21 b + 15 d -11 e • 32 -15 -17 + 9 +21 VI G -9 + 26 e + 32 CT -18 c -13 b + 1 VI + 3: VI + 1 VI -10 4.0 3.9 2.9 2.5: 4. 1 3.1 -30 H -15 KP -2 3 KP +2 1.9 2. 0 -2. 4 • 0. 1 -1.9 -1.6 -0.9 •1.8 -1.8 or + 1. 2 -1.4 or • 1. 1 -1.3 • 0.6 TABLE 6.C DATA ON OBSERVED SYSTEMS - POSSIBLY REAL VELOCITIES AND DERIVED MAGNITUDES r - i — — r r { i C-star 11 Companion 1 | V V V | | V V H beta J Star | B-V B-V B-V B-V B-V E(B-V) j | U-B U-B U-B | | U-B U-B I 1 1969 1971 1972 | ] 1971 1972 • i i . • ! I T I T Dra J | j 12 .48 || J 1 0 . 9 9 j J \ | i 5.6 : | | I 1.16 | ! j } •mm mm i 1 . 15 j | n Cam | i j 7 .55 |j I 9 . 6 3 | 2 . 816 1 1 i 4. 29 ) J I 0 . 21 | 0 . 3 0 ! I j j 4 . 49 J S | - 0 . 0 5 i 1 0 Cyg ] j I 10 .08 I I I 7 . 8 7 | | | i i 5. 18 11 | 0 . 8 0 I 0 . 0 | J I ! I I I 0 . 51 | | BS Cyg J 7 . 4 8 | j 8.32 jj | 7 . 0 9 J 2.561 1 1 2 . 8 6 | i 3.45 11 | 0 . 5 0 J 0 . 7 5 1 1 3 . 9 0 | 3.61 N 1 " 0 . 4 5 | J cp . 2 J 1 II | 9 . 24 | — I 1 | i I j J 1.93 J 0.31 1 1 • II 1 2 . 2 4 1 t _ _ _ j _ J — *.. l L J J ~ TABLE 7.A DATA ON OBSERVED SYSTEMS - NOT REAL PHOTOMETRY r - r~ • T T - " - - T - j Star J V (max) C-star | AV | C-star l Spectrum Comp I Comp | V max,C* -V(cp) I i * 1 r • 1 T Dra J 9.6 A | 2.5 A ] K2 III-IV KP | + 1. | -1.2 | 0 Cam J 7.2 A | 0.6 A j B8 V KP j 0. , I -2.4 J U Cyg J 7.1 A I 3.5 A i G2 III KP j •0.4 | -0.8 | RS Cyg \ 7.2 A | 0.7 A i BO.5 l b KP j -6.1 | • 0.1 1 cp.2 J I * j K7 II KP -2 | -2.0 i • , ,. J ,.. .3 - _ - X - . — . X - # See t e x t . TABLE 7.B DATA ON OBSERVED SYSTEMS - NOT REAL MAGNITUDES AND SPECTRA 1 — _ T _ _._ _ - r r - r - T" ! Star 1 Radial Velocity | C-star Comp Gal j i (B-V) o i C-star | Hv | C-star | Wt i 1 I i i i . j | r 1 I 1 t t j J j T Dra I -23 a | -84: KP | !! ! -0.2 | 0 j 0 Cam | -3 c | -35 KP | -10 i i 4.1 \ -2.4 I 0 ! U Cyg I +13 a | -25 KP | -15 i i . 5.2 j -0.4 | 0 RS Cyg I -50 a | -14 I 1 - 2 KP | -7 W j || J -6 j 0 j cp. 2 1 1 -18 KP J -9 i i j -4 j i _ —I ._ .. . X. . . J — .. . , . J.. _ —X- TABLE 7.C DATA ON OBSERVED SYSTEMS - NOT REAL VELOCITIES AND DERIVED MAGNITUDES 41 r T - - r r - •—8 ) 1 C-star | | Companion I | V V V i 1 v V H beta | 1 Star | B-v B-V B-V i | B-V B-V E{B-V) | | ) U-B U-B U-B II U-B U-B 1 1 1969 1971 1972 II 1971 1972 % i i i j J i i I i l I i i * • T | X Cas | j j 11.01 || I 11.15 | 2.665 | ! | | ) 4.99 11 | 0.53 | — I J I { J •mm mm | j \ 0.02 | | HD 30710 | 9.43 | 9.17 { |j 14.04 j J | | 2.75 | 2.58 J II 1.39 | | j j 4.27 | 3.44 | J I 0.97 | J I HK Lyr | 7.97 | H 14.26 J J I t | 3. 24 J || 0.84 | | | | || 0.01 j J I S Set | 6.70 1 j 6. 87 j j | ^ dm * mm Z j | | 2.93 | 2.91 j | 1 1.9: | j J " 1 j 5. 48 J J I 2.1: | j EV Aqr | s 9.20 | || 14.92 J J | | 1 4.56 | || 1.22 I | j J I I l l 0.20 j J ] HD209621 } j 8.82 | II 13.10 5 | ] ) 1 1.42 | || 1.43 i i I I 1 1.13 | || 1.23 J i i .,, i . .- X i _x_ -j-i. J - . . . _ X. . , . J TABLE 8.A DATA ON OBSERVED SYSTEMS - INADEQUATE DATA PHOTOMETRY 42 t T I Star J V (max) C-star T - - - r | AV J J C-star | Spectrum Comp - r — i — I M v | | Comp | i i V max,C* -V(cp) ! . I T I X Cas | 9.6 A ! 2.3 A | -1.6 | HD 30710 | 9.2 p ! ! | j -4.8 | HK Lyr | 8.0 p | i | -6.3 I S Set i 6.7 p | 0.7 A ) -5.5 | RV Agr | 9.2 p | j I -5.7 3 HD209621 | 8.8 p j J G (?) VI I j - 4 . 3 I , 1 — 1 J L I I TABLE 8.B DATA OH OBSERVED SYSTEMS - INADEQUATE DATA MAGNITUDES AND SPECTRA 13 1 - . — 1 " I Star I i i Radial C-star - " r r T T -a Velocity {| (B-V)o | Mv 1 St J Comp Gal j j C-star | C-star | j t i I I! I I X Cas | -55 a | ! I I ! ! I | HD 30710 | + 38 c | i i i i i i | HK Lyr | -5 a 1 II | j j | S Set | 0 a | i i i i i i I EV Agr | -1 b j ! i l J 1 J ! l -4 CT } ! !! I ! I | HD209621 I -381 a ) ! 11 i S ! 1 J - - x. .. i t~i L a J TABLE 8.C DATA ON OBSERVED SYSTEHS - INADEQUATE DATA VELOCITIES AND DERIVED MAGNITUDES *_" T J Star | V V-B V-I — i — i 1 Year | | UV Aur | 10.01 2.43 4.26 | 71 | J -26 2983 | 8.72 2.15 3.56 1 71 | J SZ Sgr | 8. 74 1.99 3.45 | 74 | | 8 CMa | 6.59 1.74 3.02 | 71 | 1 1 6.65 1.78 3. 20 I 74 \ | MSB 64 | 9.40 2.41 4.Q5 \ 74 J ] HD 75021 | 7.26 1.51 2.88 | 71 | I V Hya | 8.36 3.03 4.69 i 74 | | BY flon J 8.26 2.47 4.06 I 71 ) I BZ Peg | 8-42 1 .92 3.34 ] 74 | i DV Agl | 9.05 2.46 3.93 I 74 | | X Sge | 8.58 2.20 3.59 | 74 | 1,- . „ ...1 j _ _ J TABLE 9. FBI PHOTOMETRY 45 i : r HA Dec 1900 Star Spec Sep +- V cp V Cnc 08 16.0 + 17 36 S2,9e 7. 1 10 >13 HD 76115 08 49.1 + 75 50 SO 8. 0 31 14 —1 BT Cap 20 11.3 -21 38 ] I 1_ C5,3 8.6 26 15 ADS 13616 TABLE 10. SOME UNINVESTIGATED DOUBLE STABS 46 Discussion of Individual Systems UV Aur The spectral type of the 3.4" distant companion i s B9 V, i n excellent agree- ment with Gordon's (1968) type of BB.5 V; the photometric data may, however, have been contaminated by the brighter carbon star. Franz and White (1973) have measured V = 10.92 and B-V = 0.12 f o r the companion; t h i s agrees well with the present V value but i s bluer by 0.09 mag. The Q index [Q = (0-B) 0.72 (B-V) ] corresponding to the B9 spectral type points to the star being above the main seguence, while the Ĥa value indicates an absolute magnitude of -1.5 (Stromgren 1966). As these data could also have been contaminated an absolute magnitude of -0.1 has been adopted; t h i s corresponds to a point barely above the main sequence at B9. Recently Garrison (1977) has expressed the opinion that t h i s star i s brighter than luminosity c l a s s V, possibly as bright as c l a s s I I I . This agrees quite well with the assigned absolute magnitude. A normal star of t h i s spectral type i s expected to have a mass of 3.5 to 4 m (Allen 1973}, and Iben (1967) indicates that such a star would be -1 - 1.5 x 10 s years old. Since the post main sequence evolution of the companion carbon star i s much fas t e r than t h i s we can assign i t a main sequence mass of *t4'H»; as i t may subsequently have suffered mass l o s s , however, t h i s i s only an upper l i m i t to i t s present mass. Since the v e l o c i t i e s agree reasonably well and are s i g n i f i c a n t l y d i f f e r e n t from the expected g a l a c t i c f i e l d velocity there i s no reason to suppose that these stars do not form a physical pair. The carbon star absolute magnitude i s variable between -3.6 and -0.4. The period of t h i s v a r i a b i l i t y i s approximately 390 days. -26° 2983 These stars with composite spectra have SZ Sgr been discussed by Richer (1972), and no further observations have been obtained. He derives absolute magnitudes of -2.4 and -1.4, respectively, under the assumptions that the U magnitudes are influenced only by the early-type companion and that the reddening can be obtained from the nearby f i e l d stars. As there i s no reason to doubt the v a l i d i t y of these assumptions, these magnitudes w i l l be adopted, TO Tau This system was also discussed by Richer, who derived a carbon star absolute magnitude of -3.9 based on the same assumptions as above and using a spectral type f o r the companion of A2 I I I . One a d d i t i o n a l spectrum has been obtained of t h i s s t a r . Onfortunately i t i s rather weak and does not permit either v e r i - f i c a t i o n or disproval of Richer*s assigned luminosity c l a s s . The only features d e f i n i t e l y present between H-gamma and H-delta are 4315 (Fe I ) , G-band (CH) , 4260 (?) and 4226 (Ca I ) ; a l l attributable to the carbon star. Even i f the luminosity sensi- t i v e blend 4173-8 i s weakly present i t would be more d i f f i c u l t to detect on the weak plate because of the higher dispersion used (128 vs 200 A/mm). I t i s interesting to note, however, that SZ Sgr, wherein the carbon star i s r e l a t i v e l y brighter i n the bluei region than TO Tau, also shows (in Richer*s F i g . 1) a 48 l i n e at the same position, i n d i c a t i n g that t h i s feature may be from the carbon star spectrum. I f t h i s i s the case the companion's absolute magnitude must be decreased by 1.8 mag to +1.2, corresponding to a main sequence s t a r . Because of the small separation (zero) there i s l i t t l e room fo r doubt as to the physical r e a l i t y of t h i s system, even though corroborating r a d i a l velocity data i s lacking. Thus the absolute magnitude of TO Tau i s either -3.9 or -2.1. W CHa Despite the large separation of the two stars (158") there are several reasons for supposing t h e i r physical proximity., Primary i s the obser- vation that W CMa illuminates a r e f l e c t i o n nebula which i s probably part of the CMa 0B1/CMa fi1 complex (Herbst, Racine and Richer 1977). The spectral type of the companion i s B2 V, given by several spectra and confirmed by the Q-value (-0.69) as well as the luminosity indicated by the YLp index, and not B5 as given by Gordon (1968). The g a l a c t i c f i e l d r a d i a l velocity at the distance,of t h i s star i s +37 km/s, s i g n i f i c a n t l y d i f f e r e n t from both the B-star i t s e l f (+19 km/s) and the C-star (+21 km/s) which agree quite well., Since the solar motion component i n t h i s d i r e c t i o n contributes +18 km/s to these v e l o c i t i e s i t i s clear that the B-star motion d i f f e r s greatly from the g a l a c t i c f i e l d . Furthermore the declination components of the proper motions agree very well {+0.0 23" and +0.019" ± 0.020" (st. devn)) although the r i g h t ascension components are somewhat discordant (-0.036" and +0.017" ± 0.027") (SAO Catalog 1966). I t should be noted, however, that the C-star v e l o c i t y (though of 49 poor quality) does not d i f f e r greatly from the LSE v e l o c i t y and hence i s not inconsistent with a much fa i n t e r absolute magnitude., SU And The FQ spectral type i s based on two medium well to weakly exposed spectra. As these make i t rather d i f f i c u l t to determine the luminosity, class V has been assumed because of the width of the Balmer l i n e s . Because of the excellent agreement of the v e l o c i t i e s t h i s system seems to be on a s o l i d basis. SV Cyg The r a d i a l velocity data f o r these stars can't be used to v e r i f y the r e a l i t y of t h i s system as both of the v e l o c i t i e s agree well with the galac- t i c f i e l d v e l o c i t y and the system i s i n a d i r e c t i o n (^=83°) where the velocity i s rather i n s e n s i t i v e to distance. Since the derived C-star absolute magnitude i s i n the r i g h t ballpark, however, and there i s no contradictory data t h i s system cannot be ruled out as r e a l . MSB 64 The luminosity c l a s s i f i c a t i o n of the companion i s based on the width of the Balmer l i n e s ; i f the star i s on the main sequence the absolute magnitude w i l l be f a i n t e r by 0.4 magnitudes.. The V i c t o r i a r a d i a l v e l o c i t y agrees well with the infrared C-star v e l o c i t y but not with Sanford's " ^ ' - q u a l i t y { ± 5 km/s according to Sanford) blue velocity. Better r a d i a l v e l o c i t i e s are obviously needed to s e t t l e t h i s question. 50 HD 75021 Most of the data on these stars have MSB 31 been taken from Gordon {1968). New pho- tometry of HD 75021 has yielded improved colours, and the sp e c t r a l type i s a compromise of Gordon, Eggen {1972) and a low dispersion spectrum. Proper motion data for t h i s double agrees in declination (-0.010" and -0.0 08" + 0.0 13 (st. devn)) but not in right ascension (-0.028" and +0.00 2" ± 0.013) (SAO 1966) . Gordon says the r a d i a l v e l o c i t i e s agree to within the measurement errors but the ga l a c t i c v e l o c i t y gradient i n this d i r e c t i o n i s very small and hence t h i s datum does not carry much posit i v e weight. The magnitude data for the compa- nion to MSB 31 i s based on a photographic magnitude by Sanford (1940) of 11.0 and Gordon's spectral type. Although she cannot distinguish between luminosity classes I I I and V, the main sequence class has been assumed i n Table 5. The small separation of t h i s pair lends c r e d i b i l i t y to the r e a l i t y of t h i s system. V Hya VBI photometry of t h i s double gives (V-E, V-I) colours for the companion of (0.81, 1.56), consistent with a spectral type of K1 or K2 I I I , or K0 I I I : , the sp e c t r a l type given by Gordon (1968). I f t h i s system i s r e a l , V Hya i s both the reddest and i n t r i n s i c a l l y brightest star investigated here.. 51 R¥ Hon This star lacks s u f f i c i e n t data to be either accepted or rejected as a r e a l system. The photometry i s consistent with an unreddened F6 V star, considerably l a t e r than i s indicated by the available spectrum, which has been given the greater weight. , Should t h i s system be r e a l the photometric spectral type would set a f a i n t l i m i t to the C-star absolute magnitude of -0.9. RZ Peg This star also lacks data. Here, however, at least the spectral type i s not open to question as both the photometry and the spectrum agree. a r a d i a l velocity for the companion would be most int e r - esting here as the suggested C-star absolute magnitude would be among the f a i n t e s t known fo r N-stars i f the system i s r e a l . I t i s i n t e r e s t i n g to note that the carbon star shows emission i n the infrared Ca I I t r i p l e t (Richer 1971). 0? Aql This double lacks both a r a d i a l v e l o c i t y and r e l i a b l e spectral c l a s s i f i c a t i o n . The spectral type i s based on a rather weak spectrum; hence the uncertain luminosity c l a s s . The photometry i s consistent with a K2 giant and supergiant but only marginally acceptable as a main sequence star and then as a late K dwarf. This double i s best l e f t u n t i l more data i s available. HD 34467 This double i s severely lacking i n data. The OBV photometry i s consistent with spectral types B9 V, A8 V and gF, while the Ĥs value i s compat- i b l e with the B9 V and A8 V types only.. I f the a8 V type i s 52 assumed (this requires the least reddening and sets the f a i n t l i m i t to the C-star) the carbon star would have an absolute magnitude of -1.6 i f the system i s r e a l . MSB 41 The C-star velocity does not agree well with either of the companions but i t s poor quality makes thi s of l i t t l e s i g n i f i c a n c e . X Sge The photometry i s ind i c a t i v e of a s l i g h t l y l a t e r spectral type f o r this companion than i s given by the spectrum. The weakness of the Ca I 4226 l i n e and the 6—band i s strongly supportive of the e a r l i e r type however; perhaps the star i s metal poor. Sanford's C-star v e l o c i t y i s confirmed by the presently measured infrared v e l o c i t y , while the companion's v e l o c i t y seems to be s i g n i - f i c a n t l y d i f f e r e n t although t h i s i s based on only three wide l i n e s and thus i s of low weight. This system does not seem to be r e a l . HD 209596 The C-star absolute magnitudes for these MSB 73 doubles are based on Gordon's (196 8) spectral types for the companions and the present improved photometry. The v e l o c i t y f o r HD 209596 's companion i s based on but four broad l i n e s on a weak plate; these do agree f a i r l y well however. 53 S Cyg This star i s a member of the t r i p l e star ADS 13385 . The K-star i s the A-com- ponent while the S-star i s a binary with 0.6" separation (BC) . No data i s available f o r the C-component because of i t s close proximity and the faintness of the system (BC) as a whole. T Dra The large velocity differences between 0 Cam the carbon stars and the suspected com- U Cyg panions r u l e out these doubles as r e a l BS Cyg systems. According to the A.A.V.S.O. data the v i s u a l magnitude variation of RS Cyg has been ste a d i l y decreasing from at least the early 60's. The amplitude has changed from about 1.i| mag to the present 0.5 magnitude. S Set This star i s i n a very r i c h region of the Milky Way and has several f a i r l y close companions. The photometry reported here r e f e r s to the brightest of these. Because of the crowded f i e l d t h i s star i s not worth investigating further., 54 Discussion The r e l a t i o n between the absolute vis u a l magnitudes of the C stars and t h e i r companions i s shown in Figure 2. The f a i n t l i m i t s shown i n t h i s f i g u r e are at least p a r t i a l l y affected by observational se l e c t i o n . , Nonetheless, there seems to be some indicatio n of a trend in the sense that the early A and B type companions are associated with the brightest C s t a r s , and the higher weighted late-type giants are associated with f a i n t e r C stars. Use of the bolometric absolute magnitudes (see below), instead of the v i s u a l magnitudes, s t i l l shows t h i s trend (Figure 3) : carbon stars with B type companions tend to be more luminous than those with A and K type companions. Since the early-type stars are expected to be younger (on the average) and t h e i r evolved companions therefore more massive ( i n i t i a l l y at least) t h i s may be taken as a mild indication f o r a mass - luminosity r e l a t i o n f o r carbon stars. , If the stars for which only Gordons (1968) absolute magni- tudes are available as well as the S stars are deleted, and i f we apply the weights indicated in the l a s t column of Tables 5 and 6 the group properties can be derived. The average absolute v i s u a l magnitude of the remaining 13 N stars i s -2.3 ± 1.1 (st. .devn).. , Since the average i n t r i n s i c (B-V) colour of these stars i s *3.0 (cf. the " S t a t i s t i c a l Studies" section), and there i s nothing obviously peculiar about them other than having companions, they can be taken to be a t y p i c a l sample of N s t a r s . Since most of the energy from carbon stars i s radiated in 55 the i n f r a r e d , t h e i r v i s u a l absolute magnitudes are not as ph y s i c a l l y meaningful as t h e i r bolometric absolute magnitudes. To properly c a l c u l a t e the bolometric corrections, however, one needs photometric information extending far into the infrared, and such data e x i s t for but a few dozen stars (Mendoza and Johnson 1965). Fortunately, their data show that there exists a good co r r e l a t i o n between the calculated bolometric corrections and the V-R colour index f o r both R and N s t a r s . These r e l a - tions are shown i n Figure 4., Since one would expect the stars in Figure 4 to be reddened by different amounts, i t i s s u r p r i - sing at f i r s t that the c o r r e l a t i o n i s as t i g h t as i s indicated. The e f f e c t of i n t e r s t e l l a r reddening i s , however, not only to make the observed colours redder, but also to increase the r a t i o of the nonvisual to v i s u a l flux (since most of the f l u x i s i n the i n f r a r e d ) , thus causing an overestimate of the bolometric corrections based on the reddened colours. Hence reddening w i l l cause a star to move more or l e s s along the l i n e s of Figure 4, rather than across them, retaining the tightness of the r e l a t i o n . To derive bolometric corrections the observed (V-R) colours, where available (Table 9; Mendoza and Johnson 1965) were corrected f o r the reddening shown by the companions according to E(V-R) =0.75 E(B-V). The bolometric corrections were then read o f f from Figure 4. These are expected, i n most cases, to be good to a few tenths of a magnitude. The r e s u l t i n g bolometric absolute magnitudes have been plotted i n Figure 5 versus the deduced i n t r i n s i c (V-R) colours. For reference the 56 normal giant and supergiant branches from MO to M6 are also included (Blaauw 1963; Jchnson 1966). I t i s thus apparent that the late-type carbon stars are not confined to a narrow lumi- nosity range, but i n fact populate a wide band (about H magni- tudes wide) corresponding to the region between the normal giant branch and the supergiants. KO III A 2 III B9 V 58 + F9 V + F3 IV + K O III B9 V AS V F2 V n o A7 V K 1 »• a A6 IV J L a K l III 1 B2 v| 0 -2 -4 M o o . ( C P) Figure 3 . M (bol) (Carbon star) vs M(bol) (Companion! 59 o/ • / Figure U. Bolometric Correction vs V-R 60 Figure 5 . M (bol) vs (V-R) 61 Part I I . CARBON ISOTOPE ABUNDANCE RATIOS Carbon exists i n nature i n only two stable isotopic forms {viz. **C S * 3 C ) . The t e r r e s t r i a l » 2C/*3C r a t i o i s approx- imately 90, while reported r e s u l t s for carbon stars range from a low of 2 to highs of greater than 100. For normal late-type stars (mostly K giants) r a t i o s have recently been reported primarily i n the 10 to 30 range (Tomkin, Luck and Lambert 1976; Dearborn and Eggleton 1976). A knowledge of the *zc / » 3 C r a t i o s i n carbon stars i s important because of the constraints i t places on the models of C stars, which should t e l l us something about t h e i r evolutionary state, nucleosynthesis reactions {to produce the isotopes) and structure {convection zones to transport them to the surface). In carbon stars we can observe carbon primarily in three forms: the molecules CO, CN and C 2; the observational problems involved i n determining the abundance r a t i o s d i f f e r depending on which molecule and spectral region i s to be studied. The CO vibrati o n - r o t a t i o n bands are a l l i n the infrared (from 5^ to 1..6p. f o r AV = 1 and 3, resp.) and thus are not accessible using conventional methods; the CN and C 2 bands in the blue and visual regions are a l l very crowded, resulting in great problems with l i n e blending* The Red system of CN i n the near infrared avoids both these problems: the spectral region i s readily available using both photographic N-type emulsions and the newer s o l i d state detectors, and the r o t a t i o n a l band structure i s s u f f i - 62 c i e n t l y open that i n d i v i d u a l r o t a t i o n a l l i n e s are frequently resolved, even at moderate dispersions. Past values of the 1 2 C / l 3 C r a t i o i n carbon stars have been derived using three main techniques. Most quoted values have been obtained using some variant of the standard curve-of-growth method. Line blending i s often severe, r e s u l t i n g i n r e l a t i v e l y few usable l i n e s ; i n the extreme, Byl l e r (1966) based his results on only 2 l i n e s . Even more serious i s the question of locating the continuum, in a strong-CN star l i k e Y CVn the spectrum hardly ever approaches anything that can be c a l l e d a continuum l e v e l . In t h e i r analysis of UD Sur Querci and Querci (1970) determined th e i r continuum through an i t e r a t i v e procedure based on the temperature and l i n e s that should be on the f l a t part of the curve of growth. The i s o - i n t e n s i t y method of F u j i t a (1970) avoids the problem of the continuum by using the central depths of the l i n e s and a pseudo-curve-of-growth analysis. This method i s , however, very s e n s i t i v e to the ex c i t a t i o n temperature adopted. The t h i r d method (Climenhaga 1960) uses calculated synthetic spectra which are then matched to the observed spectrum. His synthetic spectra were calculated using the empirical Minnaert formula and the matching was done v i s u a l l y . The present investigation i s a greatly improved version of Climenhaga's basic approach.. Since i t i s well known that carbon stars are at least giants and probably somewhat brighter [see Part I of t h i s t h e s i s ] t h e i r atmospheres must be quite extended, 63 and one would not expect methods which are based on a uniform s l a b model of t h a t atmosphere t o n e c e s s a r i l y produce r e l i a b l e r e s u l t s . Thus I decided t o c a l c u l a t e s y n t h e t i c s p e c t r a by d i r e c t l y i n t e g r a t i n g the f l u x through an a p p r o p r i a t e model atmo- sphere. I t would a l s o be d e s i r a b l e t o have an a n a l y s i s t e c h - nigue that was independent of the p r e j u d i c e s o f the observer. I d e a l l y such a technique should make use of the e n t i r e i n f o r m a t i o n content of the spectrum, r a t h e r than j u s t c e r t a i n s e l e c t e d p i e c e s , i t should a l s o be r e l a t i v e l y i n s e n s i t i v e to those s p e c t r a l f e a t u r e s t h a t one i s not i n t e r e s t e d i n (e. g. t e l l u r i c l i n e s ) . For s p e c t r a such as these of molecular bands i n carbon s t a r s , where the vast m a j o r i t y of s p e c t r a l f e a t u r e s a re i n f a c t due to the molecule (s) being s t u d i e d , I b e l i e v e t h a t the method based on the coherence spectrum (to be d e s c r i b e d l a t e r ) s a t i s f i e s the above c o n d i t i o n s . I t a l s o has the f u r t h e r advantage of being i n s e n s i t i v e to the assumed continuum l e v e l . The o n l y model atmospheres a p p r o p r i a t e t o the c o o l carbon s t a r s i n v e s t i g a t e d here t h a t I have been ab l e t o o b t a i n a re those of Johnson (197 4). These were c a l c u l a t e d on a l o o s e g r i d of parameters t o ex p l o r e the e f f e c t s of temperature, s u r f a c e g r a v i t y , composition and o p a c i t i e s . , The model parameters a r e o u t l i n e d i n Table 11; most of the models are arranged i n sequences with one or two of the parameters v a r i a b l e . The number of p o s s i b l y u s e f u l models i s 17. The models were c a l c u l a t e d under the u s u a l assumptions of a plane p a r a l l e l atmo- sphere, LTE and using s t r a i g h t mean o p a c i t i e s . I n s p i t e o f 1 i Parameter T — ~ — r 1 Range J " "" "•' i p r i n c i p a l l y J J C/0 1 [ 1 , 5 0 ] | 2,5 | I T (ef f } (°K) j [2000,3500] | 3 500 | 1 C/H | [ 0 . 1 , 1 0 0 ] (C/H)« | i l o g g i [ 0 , + V ] | 0 (giants) j | N/H ] [ 1 , 1 2 0 ] (N/H)« | t _ _ _ _J _ „. _ i _ _ J TABLE 1 1 . MODEL ATMOSPHERE PARAMETERS 65 these l i m i t a t i o n s they are s t i l l b e t t e r than the uniform s l a b model. T h i s p a r t of the t h e s i s opens with a b r i e f d e s c r i p t i o n of the o b s e r v a t i o n a l m a t e r i a l used here. T h i s i s fo l l o w e d by a d e s c r i p t i o n of how to c a l c u l a t e s y n t h e t i c s t e l l a r s p e c t r a , both a t h e o r e t i c a l summary and the p r a c t i c a l d e t a i l s a p p r o p r i a t e to molecular band s p e c t r a . The a n a l y s i s t echnique i s then presented, along with some comments on i t s advantages and a few t e s t s i l l u s t r a t i n g i t s a p p l i c a b i l i t y . Next the r e s u l t s of the carbon i s o t o p e r a t i o a n a l y s i s are shown, i n c l u d i n g remarks on the microturbulence and carbon content o f the carbon s t a r s , as w e l l as a se a r c h f o r the **C and 1 5 N i s o t o p e s . A resume of the pros and cons of the a n a l y s i s technique concludes t h i s p a r t . 66 The Observational Material The basic observational material f o r t h i s part of the study consists of near infrared photographic spectra of f i v e carbon stars (Table 12). The spectra were obtained by Dr. H. B. Richer at the 122-cm (48 inch) telescope of the Dominion Astroph y s i c a l Observatory i n V i c t o r i a during the period Nov.,21, 1970 to Dec. 18, 197G. The plates are at a dispersion of 13 a/mm on IN hypersensitized emulsions covering the wavelength region 7500 - 8800 A. The region of the spectra from 780 0 a to 8300 A was d i g i t i z e d with the department's automated Joyce-Loebl Micro- densitometer and reduced to an intensity versus wavelength array using computer programs developed by H. Fast (1973), as follows. D i g i t i z i n g scans were made along the s t e l l a r spectrum as well as across the c a l i b r a t i o n s t r i p s and the spectrum i t s e l f at several d i f f e r e n t wavelengths. Grain noise was then reduced by the application of a d i g i t a l f i l t e r to remove s p a t i a l frequencies greater than 1/3 of the Nyguist frequency. Next an equal-wave- length-interval array of log (intensity) was generated; the wave- length scale was defined using "unblended" s t e l l a r (CN) l i n e s of known wavelength while the i n t e n s i t y scale was determined from int e r p o l a t i o n between the several c a l i b r a t i o n curves. , Note that the photographic density of each spectrum point was f i r s t corrected to compensate for the non-uniform exposure (streaks) caused by the image s l i c e r of the spectrograph. F i n a l l y the highest points were selected as representing the continuum and 67 r 1 • — T T —i | Star | Plate # | Date I 00 Aur | 6485 | Nov. 21, 70 \ I X cue | 6486 j Nov. 21 , 70 ] | I cvn | 6487 j Nov. 21, 70 | | 19 Psc | 6542 | Dec. 18, 70 J | Z Psc j 6543 I Dec. ,18, 70 | i i ..in j TABLE 12., HIGH DISPERSION CARBON STAR SPECTRA 6 8 the array transformed to a normalized in t e n s i t y array. Indicative of the extremely heavy l i n e blanketing i s the f a c t that t y p i c a l l y there were no more than a half dozen such "continuum" peaks throughout the entire 400 A region of i n t e r e s t . This r e l a t i v e l y poorly determined continuum l e v e l has no effect on the subsequent analysis however; t h i s w i l l be dealt with more f u l l y i n a l a t e r section. The one additional parameter to be derived from the spectra was the instrumental broadening; i t was assumed that the i n s t r u - mental p r o f i l e was a Gaussian with a half-width to be deter- mined. To t h i s end the Argon comparison arc l i n e s of a sample plate were d i g i t i z e d and converted to i n t e n s i t y . Not a l l the l i n e s could be used, however, as the arc l i n e s were more heavily exposed near the i n s i d e edge and were frequently saturated there. This resulted i n an under-estimation of the true l i n e strength and thus an overestimation of the width at the deduced h a l f - i n t e n s i t y l e v e l . Using nineteen l i n e s which were d e f i - n i t e l y not saturated resulted in an average half-width of 0.56 A ± 0.09 (st. devn). 69 SYNTHETIC SPECTRA - THEORY Following Mihalas (1970) the flux radiating from a s t e l l a r atmosphere i s given by = 2 f°° S „ ( T J E 2{^} d r , (4) J a where F v i s the flux per unit frequency i n t e r v a l , Bz i s the second exponential i n t e g r a l defined by E 2{x) = exp(-xt)/t2 dt (5) i and S v i s the source function, here, for pure absorption l i n e s , approximated fey the Planck black body function B„<T) = C 2 h ^ / c 2 J [ 1/<exp{hVkT)-1) ] (6) to conform to the LTE assumption of the model atmospheres. The o p t i c a l depth scale i s given by T*> = / [ k(ccnt) * l ^ ] / k (std) d-r(std) (7) where r(std) i s the standard o p t i c a l depth as given by the model atmosphere, k (std) i s the model opacity at a standard wave- length, k{cont) i s the continuous opacity and l u i s the opacity contribution of the l i n e s lv = £ °V(sp) N(sp) (8) S P for a l l species (sp). N i s the number density of the appro- priate species and ocv i s the absorption cross-section of one atom (molecule) of that species at frequency •» under the 7 0 conditions at that point i n the atmosphere. The absorption cross-section per atom (molecule) at f r e - quency -2-> i s CrreVmc)- f 4\, [»(i)/n (T) ] (9) where f i s the o s c i l l a t o r strength of the appropriate t r a n s i t i o n , i s the absorption line p r o f i l e normalized to unit area, and n(i)/n(T) i s the fr a c t i o n of the t o t a l number of atoms (molecules) that are i n the lower state of the t r a n s i t i o n . For a Gaussian l i n e p r o f i l e <K, = U / f f ^ ) exp[-[(»-];.)/^} (10) where i s the l i n e width and D 0 i s the c e n t r a l frequency. The l i n e width A D b i s the Doppler width qiven by ^ = \ ^ i i / c £2kT/M* t t 2 l */ 2 (11) For a single r o t a t i o n a l l i n e of a diatomic molecule the o s c i l l a t o r strength i s given by (Carbon 1973) f.. = f o ~±L -11 - — S(HL) (12) l ' 9oo Z : t S e < r O 0 ) l 2 (2J«+1) where; f o o = (0,0) -band o s c i l l a t o r strength, v.. , v o o = wavenumbers of t r a n s i t i o n ( i , j ) and the (0,0) band o r i g i n , q v V, = Franck-Condon factor for the (v*,v M)-band, ^31 Rc (f v V,) J 2 = sum of squares of the e l e c t r o n i c t r a n s i t i o n moments, 71 (2S*1) = m u l t i p l i c i t y of the electronic t r a n s i t i o n . (2-6^,,) = 1 f o r 52 states, = 2 for any other loser state, (2J"+1) = r o t a t i o n a l degeneracy of the lower state, S(HL) = Honl-London factor, normalized to J^S(HL) (J'»-»J») = 2J"+1. J" (13) The Honl-London factor i s a measure of the l i n e strength. Extensive formulae for t r a n s i t i o n s between various types of el e c t r o n i c states are given by Schadee (1964). I t should be noted, however, that his formulae for 2 TT - 2 XI t r a n s i t i o n s (the CN red system) must be multiplied by 2 to s a t i s f y the above normalization c r i t e r i o n . (N.B. In the notation used here a single prime refers to the upper l e v e l of a t r a n s i t i o n , a double prime r e f e r s to the lower level.) The f r a c t i o n a l number of molecules in the lower state of t r a n s i t i o n ( i j ) i s given by (Tatum 1967) This eguation applies to Hund*s coupling case (b) which i s appropriate here since both the CN and C^ t r a n s i t i o n s of i n t e r e s t come from a lower "T - -state. , In t h i s eguation 4> = 1/2 for a heteronuclear molecule, whereas for a homonuclear molecule 0 i s a function of the nuclear spin; the energy of the lower l e v e l [T(el) *G(v") *-F(Jn) ] i s separated i n t o three terms repre- senting the e l e c t r o n i c term value, the v i b r a t i o n a l energy and the r o t a t i o n a l energy; the denominator £Q(T) ] i s the t o t a l M i ) 2<f> (2J" + 1) exp{-[ hc/kT][T{el) *G (v")+F{J") J} OH) n (T) Q(el) Q(vib) Q(rot) 72 i n t e r n a l p a r t i t i o n function, again separated into e l e c t r o n i c , v i b r a t i o n a l and r o t a t i o n a l contributions. , These are given by Q(el) =2^9(el) exp{-(hc/kT)T{el)} (1.5) i l l states where g(el) i s the degeneracy of the e l e c t r o n i c state g(el) = (2 -5 0 | A ) (2S + 1), (16) v Q(vib) exp{-(hc/kT)G(v)}, (17) v = o and Q(rot) = kT/hcB(v"). (18) C o l l e c t i n g these terms and e x p l i c i t l y putting i n a Gaussian l i n e p r o f i l e we arrive at the f i n a l expression ° ^ = ) 2cbf O G --± 1— (2S*1)(2-X ) S(HL) • (19) exp£-{hc/kT) X . ] • * e x p[-(D - u . ) V A V 3 Q(T) A l ^ where the energy of the lower l e v e l has now been denoted by X ; . The f i r s t group of terms i s a constant for each i n d i v i d u a l l i n e , the second group contains terms depending on the atmospheric l e v e l (temperature) whereas the l a s t term depends primarily on the frequency. 73 SYNTHETIC SPECTRA - PRACTICE Molecular Parameters The relevant molecular data for CN and C 2 have been summarized i n Tables 13 and 14. The energy lev e l s (3c* •) and frequencies {V\'.) of the i n d i v i d u a l r o t a t i o n a l l i n e s have been computed for CN from the formulae of Fay, Marenin and van C i t t e r s (1971) and for C 2 from Marenin and Johnson (1970). For the bands used here the errors i n these c a l c u l a t i o n s are usually less than 0.1 cm-* for **C*«N and »2C»zc and 0.2 c*-» for i 3 C * * N up to N values of at least 60, the maximum used here; these equal 0.06 and 0.13 A. Thus one would expect the errors f o r the other i s o t o p i c bands to be l e s s than 0.25 A, since the atomic masses are approximately equally accurate. To ensure that the wavelengths of the l i n e s are as accurate as possible the computed wavelengths have been replaced by actual observed wave- lengths wherever these are available. Observed wavelengths f o r the l i n e s from the (2,0), (3,1), (7,4) and (8,5) bands of the Red system of 1 2C 1*N have been taken from the extensive tabu- l a t i o n of Davis and P h i l l i p s (1963); a few of the branches (P and R 2 ) i n particular) have been extrapolated somewhat past the tabular cutoffs, with the aid of the computed wavelengths, as the observed c u t o f f s were caused by the r e l a t i v e l y cooler source temperatures they used. Observed wavelengths f o r the corre- sponding bands of 1 3C**N are from Wyller (1966), and f o r the P h i l l i p s system of » 2 C l 2 C from B a l l i k and Ramsay (1963). In a very few instances missing r o t a t i o n a l l i n e s have been i n t e r - polated; i n general missing l i n e s have not been added, since i t 74 i s assumed that the f a c t that they are missing indicates that no l i n e was i n f a c t observed at the expected wavelength, probably caused by perturbations of the energy l e v e l s . Note that the above l i n e s are the only l i n e s included in the synthetic spectra. This s p e c i f i c a l l y excludes a l l atomic l i n e s , l i n e s of i 2 C 1 3 C , and a l l t e l l u r i c l i n e s , even though the l a t t e r may be r e l a t i v e l y numerous i n some portions of the spectra. The p a r t i t i o n functions were calculated, as a function of temperature, fo r CN and C^ using the energy l e v e l s i n Tables 15A and 15B, and the above calculated v i b r a t i o n a l [G(v)] and rota- t i o n a l £8{v") ] parameters of the lower l e v e l f o r each molecule. Schematic layouts of the r o t a t i o n a l structure of the appropriate states of CN and C^ are presented i n Figures 6 and 7, with the t r a n s i t i o n s giving r i s e to the f i r s t few r o t a t i o n a l l i n e s of each branch l a b e l l e d . Note that the drawn f i n e structure separations of the l e v e l s are not to scale. The stan- dard nomenclature i s used to label the l e v e l s according to their parity (+,-) , symmetry (s,a) , r o t a t i o n a l quantum number (N) and angular momentum (J) (for the Cz s i n g l e t states J=N) . The various branches are known as P, Q or S branches depending on whether AJ = -1, 0 or +1, respectively, and the i n d i v i d u a l rota- t i o n a l l i n e s are l a b e l l e d by the N value of t h e i r lower l e v e l s . The CN bands consist of 6 primary branches (AN=AJ) and 6 s a t e l l i t e branches (4N#AJ) with 4 of the s a t e l l i t e branches being i n t e r n a l {overlapping primary branches) and 2 {P(a and 75 S ) 2) external; the i n t e n s i t i e s of most of the s a t e l l i t e l i n e s are much les s than the primary l i n e s . Because 1 2 C l 2 C i s a homo- nuclear molecule with zero nuclear spin the anti-symmetric level s are forbidden, hence tr a n s i t i o n s can arise only from alternate l e v e l s . f o e = 2.19 x 10 -3 £ 0 O = 9117.37 cm-* g o o = 0.50015 g a o = 0. 12685 q i ( = 0.19400 q 7 4 = 0. 12095 g 8 5 = 0.08440 4> - 1/2 for a l l l e v e l s ZZ |'He | 2 = constant B(v=0) = 1.890658 cm -J (2S+1) = 2 <2~VJ = 1 Arnold and Nicholls 1972 Arnold and Nicholls 1972 « n n ti Tatum 1967 Carbon 1973 TABLE 13. , SUMMARY OF RELEVANT MOLECULAR DATA FOR THE RED SYSTEM OF CN (A 2 TT- " X 2 £ * ) 77 3.76 x 10-3 Cooper and Nicholls ^ oo — 8268.33 cm-i 91 O O 0.4157 Spindler 1965 0.0589 41 *4» = 0. 1216 tt 0.1429 tt 0.0602 tt 0.0962 tf «73 = 0. 1.135 n * 8 * = 0.1085 it 4> = 1 for s l e v e l s Tatum 1967 cp = 0 for a l e v e l s |B el 2 = 0.36 f o r AV=0 Cooper and Nicholls = 0.42 AV=3 (extrapolation) = 0.44 AV=4 _ ii _ B(v=2) • •=; 1.774422 (2S+1) = 1 (2-6 ) = 1 TABLE 14. SUMMARY OF RELEVANT MOLECULAR DATA PHILLIPS SYSTEM OF 78 i " T - - T 1 ] State I _ T(el) (cm-*) I 9 (el) 1 * T j • 1 B «r. ! 25,751.8 i 2 | I A 2 TT I 9,117.37 i 4 1 1 X 2 I 0.0 1 2 | _x , I TABLE 15A. KNOWN ENERGY LEVELS OF THE CN MOLECULE r T ~ - r " - ~~i | State I T(el) <cm-i) 1 g(el) 1 I E | 55,034.6 1 1 1 I D | 43,240.23 1 1 1 I e | 40,7 96.65 1 6 | I C *TT, | 34,261.9 1 2 | I d | 20,022.50 1 6 | i y * | 16,000 1 1 J I c M. | 13,312. I 3 | | 10,000 I 2 ] i & 1 1 1 < ] 8,391.00 I 2 | I b | 6,434.27 I 3 | I a 3 T T U | 716.24 I 6 | l x | 0.0 i 1 i i . . _ i , .. _ j. j TABLE 15B. KNOWN ENERGY LEVELS OF THE C,, MOLECULE M tin S + . 1 ( / £ a  + S 40/9 C i 1 e /o a - " a i 1 / ' 0 j «» s+ O tto 8 + - . — • t- "i- a - + 1 11/2 5 1 1/2 1 + N J + S ft / 0 A a 9/2 4 - a 0 2 T T i n v ( w + s 0 ± § "i !•> 9 a a !>/' £ a T • o o CC CM CO CM 0. CM CM a CO CM cc CM CO CM CM a. CO r r CM O CM CO CM CC CM CO T- CM a. CM CO o CM O *— o CM CC CM * | 3/2 1 •+ s 9/2 J 1 0 c m ' 1 * s 7 > 2 4 _ a 7/2 0 a 5 / 2 O c 5 / ? ~ 2 r - + 3/2 * a 1/0 . Z - n - a 1 / 2 1 J N Figure 6a. Rotational Energy Level Structure for the Red System of CM (lower levels) 9 A 9 9 l / o i • -,. . J N 2 TT i n >) 9 9. 9 9 1A Z4 '/2 24 '/£ __ 9 1 1/. 9 1 22 21 1/2 — — - /2 ^« 9 9 V* 9 9 21 20 1/2 " 1% zz N .1 — ^ ~ 9 1 1/ 9 1 0 cc C M a C J a C J CC a. C M O C M DC C M a. C M O C M CC Zl / 2 21 2 4 ! / 2 9 . 1 100 cm"1 23 1/2 2 4 23 1/2 22 1/2 " . 22 V2 „„ 21 1/2 " 21 Vz 9 1 20 y 2 Figure 6b. Rotational Energy Level Structure for the Red Systea of CN (upper levels) 6 a + A 71 u c a + •J s — a + 3 2 + 1 N s — a + a + s — X 2L» g 5 a - 10 cm 4 s + 3 a - 2 s + 1 a - 0 s + CM 0-1 CM o CM 1 ^ Figure 7. Rotational Energy l e v e l Structure f o r the P h i l l i p s System of Cz 82 Molecular Equj.libriurn Calculation In order to calculate the l i n e and continuous opacities throughout the model atmosphere the densities of CH, C 2, H and H 2 are required i n addition to the electron density, which i s given d i r e c t l y i n the model. To this end the equations of molecular equilibrium were solved for a l l the same species used in the models by Johnson. The computer program used f o r the solution b a s i c a l l y follows the procedure used by Vardya {1965), although i t has been modified to force the t o t a l pressure to equal the known pressure of the model. The basic program was kindly supplied by Dr. J . R. Auaan. The abundances used were the same as those used by Johnson; i . e . for H, He, C, N and 0 as spec i f i e d for each model and the other elements from the solar composition as deduced by Lambert and his co-workers (Lambert 1968; Lambert and Earner 1968a, b, c; Warner 1968; Lambert and Mallia 1968). Dissociation constants were taken from polynomial f i t s to the data from the JANAF theraochemical tables (I960) or from the c o e f f i c i e n t s of Vardya (1965) or Morris and Hyller (1967), again as spec i f i e d by Johnson. Since the JANAF di s s o c i a t i o n constants are of a d i f f e r e n t form from those required by Vardya's (1965) procedure i t w i l l be useful to consider the necessary conversion technique. The JANAF tables refer to e q u i l i b r i a of the kind n, A • n z B ==̂  n^ AB 83 where A and B represent the reactants i n the i r reference states, AB represents the product and n,, n 2 and n 3 are the number of molecules of each kind. The tabulated equilibrium constants (K') are then defined as K« (AB) = — (21) where [A] = the p a r t i a l pressure of reactant A i n atmospheres.. Note that the units of the K* s are defined by the number of reactant molecules for each par t i c u l a r reaction and are of the form (atm 3 1 ) . As an example consider the s p e c i f i c case of the molecule NH: 1/2 H-j, 1/2 H a ^ 1 NH (22) since the reference states of N and H are N 2 and H 2. Thus [ N H ] K* (NH) = , (23) [H,,]*/ 2 [ N 2 ] t / 2 also, e.g. K«(H) = [H ] / [H.,]*/2 for 1/2 Ez =?= 1 H. The type of equilibrium constant (K) used by Vardya i s defined as K (AB) = p(AB) / p(A) p(B) (24) where p(A) - the p a r t i a l pressure of reactant A i n dynes cm - 2. 84 Hence we derive [ NH] K» (NH) K (NH) = = . (2 5) [N ] [ H] K» (N) K» (H) F i n a l l y , to convert to cgs units divide by (in t h i s case) 1.013250 x 10* dy c r * / atm. To check that the calculated number density d i s t r i b u t i o n of CN (in particular) corresponded to that of the actual model atmospheres two t e s t s were performed. Using CN opacities from Johnson, Harenin and Price (1972), hydrogenic (H, H~, Ha) continuous opacity as given i n "Theory and Observation of Normal S t e l l a r atmospheres" (1969, ed. Gingerich), and Mutschlecner- Keller (1970, 1972) atomic l i n e blanketing as modified by Johnson (1974) the output fluxes were computed as a function of frequency for several different models; these flux curves compared very well with Johnson* s calculated fluxes. Secondly the CN density d i s t r i b u t i o n was calculated from the tabulated values of the volume absorption c o e f f i c i e n t at 1^ and the (interpolated) value of the CN mass absorption c o e f f i c i e n t at 1̂*. (Johnson, Harenin and Price 1972). For this purpose i t was assumed that the only opacity sources were CN and the hydrogenic species; although the models also incorporate CO and HgO opacity t h i s should be a good approximation f o r the 1^ wavelength used here, atomic l i n e blanketing was not included as i t i s not clear how Johnson calculated i t at the 1^ standard wavelength, where he has a discontinuity i n applying the blanketing. The r e s u l t i n g CN density was then compared with that from the 85 equilibrium c a l c u l a t i o n s . The general agreement i s quite good over the entire depth of the atmospheres, a range of several orders of magnitude, although in places the disagreement can r i s e to as much as a factor of 2.5., In view of the excep- t i o n a l l y large uncertainty in the dissociation energy of the CN molecule t h i s i s s t i l l thought to be quite acceptable agreement (Johnson 1975) . 8 6 Spectrum Parameters The main f a c t o r i n f l u e n c i n g the appearance of the s y n t h e t i c spectrum i s the amount of CN i n the atmosphere. S i n c e the a v a i l a b l e s e t of model atmospheres was c a l c u l a t e d on a r a t h e r coarse g r i d of parameters [C/0, T ( e f f ) , C/H, l o g g] there i s need f o r a f i n e r g r a d a t i o n i n the amount of CN to permit a b e t t e r match to the observed spectrum., I t was decided to do t h i s by a l t e r i n g the metal [C, N, OJ abundance by some f a c t o r [X(CNO)], thus p r o v i d i n g f o r i n t e r p o l a t i o n i n model sequences with v a r y i n q C/H r a t i o while keeping the C/O r a t i o the same. Since most of the C and 0 w i l l form CO and o n l y the l e f t o v e r C can be used f o r CN and C 2 the CN abundance should s c a l e as X(CNG ) 3 / 2 and C a as X{CNO) 2; th a t t h i s i s i n f a c t the case, to a good approximation, has been v e r i f i e d by r e c a l c u l a t i n g the mole- c u l a r e q u i l i b r i u m u s i n g the s c a l e d abundances. ; Furthermore, s p e c t r a o f neighbouring models along a C/H-varying sequence can be reproduced from each other q u i t e w e l l by t h i s method. Heedless t o say, by tampering i n t h i s way we no longer have a proper model atmosphere, and t h a t the more we have t o change the X{CNO) f a c t o r the matchup becomes l e s s s a t i s f a c t o r y . . , Since we are not p r i m a r i l y i n t e r e s t e d i n the s t r u c t u r e of the atmosphere, however, but r a t h e r i n the r e s u l t i n g spectrum, I f e e l t h a t t h i s i s an a c c e p t a b l e procedure and w i l l produce q u i t e s a t i s f a c t o r y i n t e r p o l a t i o n s as long as X (CNO) i s "not too f a r " from u n i t y . 87 Real s p e c t r a l l i n e s have Voigt p r o f i l e s rather than Gaussian. This has been handled by using a Gaussian p r o f i l e i n the l i n e core, and (2 7) i n the wings. This i s a good approximation for small values of a. Thus the synthetic spectrum depends on f i v e parameters. These are: 1. the model atmosphere used, 2. the CNO scaling factor [X(CNO)J, 3. ,• the microturbulence [ J, 4. the l i n e p r o f i l e wing strength [ a ] , 5. the isotope abundance r a t i o s . 88 Computational Procedure The computer program used to calc u l a t e the emergent fl u x consists of a short main program and a few opacity subroutines written i n Fortran, plus a longer section to handle the actual integration through the atmosphere and a few subroutines to do simple interpolations written i n IBM Assembly Language. By using Assembly Language for the more intensive part of the program the execution time has been reduced by a factor of approximately 2.5. , Following i s a schematized description of the program layout. ; 1. P a r t i t i o n functions [Q(T) ] and exponential i n t e g r a l s [ E 2 ( r s + d )] were calculated separately and e x p l i c i t l y put into the program. 2. Read i n spectrum parameters: wavelength l i m i t s , micro- turbulence (%t) * X (CNO) factor, l i n e p r o f i l e parameter (a) , i s o t o p i c abundance r a t i o s . 3. Calculate the wavelength i n t e r v a l £A>; ] about the current wavelength within which a l l s p e c t ral l i n e s must be used; A ^ T = f (£ t,a). 4.., For each l e v e l of the atmosphere: a. Read i n model parameters: T{std), T, n(e), K, f, 8(H), H<H2), N(CH), N(C 2). {Note that the N»s have been calculated by the molecular equilibrium program.) b. Calculate: B{T), k(cont)[N (H), N(H £), n{e)], k(std) [ = *,/] 89 c. Calculate normalization factors f o r the various isotopes of CN and for C a, scaled by the X (CNO) factor [ = const x N (Isotope)/<a^ D • Q ]. , 5. Integrate continuous opacity - gives continuum flux at ends of region to be synthesized. 6. a. Increment wavelength counter b. Read i n more s p e c t r a l l i n e parameters u n t i l we have a l l l i n e s within A ) ^ of the current wavelength 7. For each atmospheric l e v e l : a. Sum opacity contributions of a l l l i n e s (within A / \ J ) using the appropriate p r o f i l e and number density b. Add on continuous opacity c. Integrate - gives output flux d* Normalize to continuum 8. Go to 6. When finished - broaden output spectrum by convolving with a Gaussian instrumental p r o f i l e . (This i s a separate program.) The integration routine: 1. Normalize given k values: k (v, l e v e l ) / k (1|u, std, level) . 2. F i t a (smooth) spline curve to the points. 3. Integrate along curve: — > T{*J, l e v e l ) . 4. Calculate: B V[T (level) ] • E ££r(^, l e v e l ) ] , (E 2 values interpolated i n the precalculated table.) 5. Integrate by summation under the B » E £ curve: —> Flux. 90 ANALYSIS TBCHNIQDE The method of analysis selected to compare the observed s t e l l a r spectra with the calculated synthetic spectra makes use of the coherence spectrum of the two traces to be compared. This method has been borrowed from the f i e l d of time series analysis and i s there used to detect s i m i l a r i t i e s between two time s e r i e s . I t i s especially suitable when both time series contain noise; since neither the observed s t e l l a r spectrum {with i t s photographic noise) nor the synthetic spectrum (lacking atomic and t e l l u r i c lines) i s i n fac t an accurate representation of the actual s t e l l a r spectrum t h i s s i t u a t i o n c e r t a i n l y exists here. [Note that the word "spectrum" w i l l be used with two dif f e r e n t meanings: 1) the o r i g i n a l astronomical meaning of an intensity vs wavelength representation, and 2) the time series meaning of (something) vs frequency representation.. An astro- nomical spectrum i s i d e n t i c a l with a time s e r i e s . The p a r t i - cular meaning intended must be found from the context.] The technique involves c a l c u l a t i n g the auto- and cross-covariance functions of the two input time series, and their power spectra by Fourier-transforming these into the frequency domain and then normalizing the cross-spectrum by the auto-spectra, res u l t i n g i n the coherence spectrum., The coherence plays the r o l e of a c o r r e l a t i o n c o e f f i c i e n t at each frequency. As a f i n a l step, to reduce the information i n the entire coherence spectrum to a manageable quantity, the average coherence was calculated f o r a l l frequencies at which the 91 auto-power s p e c t r a l density of the s t e l l a r spectrum was above some cutoff f r a c t i o n of the peak power. This thus re s u l t s i n one number characterizing the goodness of f i t between the two inputs., I s h a l l c a l l t h i s number the coherency. 92 Computational Details Let the two input time series be denoted by x*(t) and y* i t ) , t=1,N. The data are f i r s t reduced to give a zero mean value and detrended by subtracting a s t r a i g h t l i n e f i t t e d to the points. Next the time series are tapered by multiplying 10% from each end by a cosine-squared b e l l function. The series are then detrended again, extended with zeroes to give a length fl, where B i s a power of 2 (for reasons of computational economy), and f i n a l l y extended again to a length of 2fl (so as to eliminate a l i a s i n g i n the power spectra), giving x and y (see Figure 8). In the next step we calculate auto- and cross-covariance functions Rx, By and Bxy,. These are defined as 8 x(r) = r: x(n) x (n+r) r=0,H-1 (28) and B ^ ( r ) = - £2 x (n) y(n+r) r=0,M-1 (29) and are most economically computed by the roundabout method of Fourier transforming the time series via the fast-Fourier-trans- form (FFT) technique to give X (k) and Y(k) f o r k=0 to H-1, then computing the raw auto- and cross-spectral estimates G x(k) = X (k) • X*(k), (30) Gxy{k) = |X*(k) • Y(k)|, k=0,M-1 and computing the inverse FFT of these to y i e l d 8^ and Bxy,. The covariance functions are now multiplied by an appropriate "window function"; t h i s has the e f f e c t of smoothing 9 3 the spectra i n frequency space. The window used here i s the Parzen weighting function WP(r) = 1-6 (r/m)z*6 (r/m)3, r=0,m/2 = 2(1-(r/m) «) 3 , r=m/2*1,m (31) = 0, r>m where m i s the length of the non-zero part; the shorter t h i s e f f e c t i v e length, the greater the frequency smoothing. The use of the Parzen window ensures that the res u l t i n g coherence function stays between i t s t h e o r e t i c a l l i m i t s of ±1. Smoothed auto- and cross-spectral power densities are then computed from the windowed covariances by applying a forward FFT and calcu l a t i n g the power densities as i n equations (30). The squared coherence function i s then calculated as C(k) = - — ^ l - - , k=0,H-1 (32) G x(k) G y(k) where the ~*s represent the smoothed spectra. F i n a l l y , to exclude spurious coherence values, the average coherence i s calculated only for those frequencies at which the signal-to-noise r a t i o of the s t e l l a r auto-power spectrum i s high, i . e . where the power i s at least some s p e c i f i e d f r a c t i o n of the peak. 94 I n i t i a l time s e r i e s : (t) , 7» (t) , t=1,N. Detrended: (t) , y" (t) , t=1,N. 1 i N 10 9N N 10 T a p e r i n g f u n c t i o n : T ( t ) 0 M F i n a l s e r i e s : 2M x ( t ) = x M (t) «T (t) , t=1,2H. M= 2m such t h a t K/2<N<H. Figure 8. Pretreatment of Spectra 95 Comments This analysis technique i s b a s i c a l l y an extension of the cross-correlation concept, k simple cross-correlation y i e l d s a sequence of values [ H x y ( r ) 3 f o r t l i e various lags (r), with, i f t h e c o r r e l a t i o n i s good, a peak near the zero-lag point; the amplitude of t h i s peak i s then an i n d i c a t i o n of the "goodness of f i t " . Such an approach, however, makes no use whatsoever of the remainder of the c o r r e l a t i o n function, which has most of the information content of the o r i g i n a l inputs. The coherence function i s the transform of the correlation function and as such s t i l l contains a l l the information while changing i t into a form we can use more e a s i l y . The zero-mean condition on the o r i g i n a l time seri e s i s a requirement f o r t h i s technique to be applicable at a l l , the slope removal i s not required but serves to minimize low frequency power that may s p o i l the power spectra (and coherence) quite spuriously., Because of t h i s and the necessary norma- l i z a t i o n , the coherence i s independent of both the mean l e v e l of the ( s t e l l a r and synthetic) spectra and the amplitude of the features. This means that an error in the drawn continuum l e v e l i s of no consequence, which i s a big plus for carbon s t a r spectra where the continuum i s determined by only a few points. Mote also that the smoothing of the power spectra (by the window function) i s a required part of the procedure; otherwise the computed coherence w i l l equal unity for a l l frequencies. The above description has been drawn la r g e l y from the very 96 good explanation of Bendat and P i e r s o l (1971); much relevant material may also be found i n Jenkins and Satts (1968). 97 Tests As an example and to test the accuracy of the method, a short (20 A) sample spectrum was generated with a l l f i v e parameters [model, X (CHO) factor, ? , a, *3C/* 2C] chosen randomly from a set known to produce plausible looking spectra. Parameter s e l e c t i o n and program execution were done in such a manner that the p a r t i c u l a r parameters chosen was not known at the time. Random noise with peak amplitude 10% of the continuum was then added and the res u l t smoothed, thus simulating a t r u l y unknown spectrum. Various synthetic spectra were then produced and the parameter space was searched u n t i l the maximum coherency location was found. ~ Since i t was soon apparent that the a (line wing shape) value was quite small, a l l spectra were calculated with a=0 as t h i s considerably reduced the computation time required., When the coherency peak had been located, i t s parameters were compared to that of the "unknown" spectrum. Several d i f f e r e n t sets of random noise with 10% and 20% peak-to-peak amplitudes were then added to the unknown and the analysis repeated for each such new unknown. The derived parameter values are summarized in Table 16. The actual value of a was 0.01, only s l i g h t l y d i f f e r e n t from zero; a s i g n i f i c a n t l y larger value (say 0.03) produced spectra which were re a d i l y d i s t i n - guishable since the i n t e r - l i n e i n t e n s i t y i n several c r i t i c a l places was systematically depressed by the p r o f i l e wings. Several things are worth noting: the deduced 1 3C/ 1 2C r a t i o 98 1 "T " T - - —I Noise I Coherency Peak | Mea n l i Nr Amplitude i Model X (CNO) 1 3 C / 1 2 C 1 Level J I 1 10% . i K 1 5 j 1 - 8 5 | 2.83 | 0.083 1 0.219 | I — ti — K16 | 1.20 I 2.86 | 0.091 I 0.215 | 1 •— fi 5 K24 1 0.63 | 2.93 | 0.091 1 0.212 J 1 2 10% ! " 1 0.?2 I 2.80 | 0.080 | 0.210 1 | 3 10% I " I 0.65 | 2.94 | 0.079 1 0.214 | i *» 10% i II I 0.73 | 2.88 | 0.092 | 0. 198 ] 1 5 10% I " 1 0.74 I 2 . 8 9 I 0.084 I 0.202 | i 6 20% I n | 0.85 I 2.97 | 0.080 | 0. 185 | 1 7 20% l II | 0 . 7 7 | 2.81 | 0.084 | 0. 205 | 1 * ' J | i 1 | J 1 1 | actual unknown ! K24 | 0.80 I 2.90 J 0.080 i 0.207 J | Mean K24 values i ! 0 . 7 3 I 2 . 8 9 \ 0.084 1 0.204 | 1 ± std. devn. ! ! 0.07 I 0.06 | 0.005 1 0.010 | i . ;. „ _ A - . j a -j. _. _ , „ j TABLE 16. COHERENCY PEAKS FOR A TEST CASE 99 i s i n no case very f a r from the actual value; neither the deduced 1 3 C / 1 2 C r a t i o nor the microturbulence depends strongly on the model atmosphere assumed, in s p i t e of the d i f f e r i n g X{CNO) values required; the mean levels of the spectra agree quite well with the unknown, again i n d i c a t i n g that the scaling by the X (CHO) factor works. Visual inspection of the various unknowns frequently showed systematic differences s u f f i c i e n t to assign s i g n i f i c a n t l y d i f f e r e n t * 3C/* 2C r a t i o s ; that the coherency method was not s i m i l a r l y affected shows the advantage of employing an analysis technique that uses the e n t i r e spectrum rather than just selected features. I t i s also important that appropriate values be used in the coherency analysis; the two variables are the cutoff point of the window function (eqn 31) and the cutoff l e v e l f o r the power spectrum to determine which coherence points are to be included in the f i n a l average. The window function has here been termi- nated at the l i m i t of the covariance function [ i . e . m (eqn 31) = M-1 (eqn 28) ] i n order to get maximum frequency smoothing while also not completely discarding any part of the covariance. The power cutoff must be selected at a high enough le v e l that most of the high frequency noise points are eliminated, yet not so high that a l l the weaker " r e a l " s p e c tral features are also discarded. To explore t h i s , various cutoffs from 2% to 20% were used i n the analysis of UU Aur. , The parameter values of the coherency peaks for the several cutoffs are summarized below. For low cutoffs the peak coherency r i s e s quite sharply up to about the 5% point; [The 1% point (whose peak was not located) 1 00 i s also part of t h i s trend.] after t h i s the increase i s much slower., This indicates that at the 5% l e v e l most of the I Cutoff 1* » 3 C / 1 2 C Coherency 20 % 10 % 7.5 5 % 3 % 2 % I . 16 | 5 1 .035 | .983 .140 4.7 | .037 | .9582 • 138 4.9 | .039 | .9534 .137 4.8 J .040 | .9497 .125 5.4 1 .057 | .9410 . 105 5.6* | .07 | .9378 spurious coherence caused by "noise" has been eliminated., We also see that f o r cutoffs in the range 58 to 10% the deduced coherency peak locations are v i r t u a l l y i d e n t i c a l , whereas outside t h i s range the peak location deviates from these. For a l l subsequent analysis a coherency cutoff of 5% has been used. Examination of the f i n a l r e s u l t s for the s t e l l a r spectra reveals that the deduced 1 3 C / l 2 C r a t i o i s not a strong function of the micr oturbulence. I t i s somewhat more sensitive to the value of the X(QUO) factor. Thus, of the parameters characteri- zing the synthetic spectra, the coherency peak i s most strongly dependent on the t o t a l amount of CH i n the atmosphere [X(CN0) ] and the isotope r a t i o ; i . e . on the actual amounts of l 2C**N and *3C**N present.„ An examination of the f i n a l synthetic spectrum, which gives 101 the best coherency when compared to the st a r being analyzed (cf. Figures 9 and 13), often reveals that the f i t i s not equally good over the entire region synthesized, i.e..some sections f i t better than others. This i s not very surprising i n view of the extent of the synthesized region. Since the idea i s to get as good a f i t as possible while using only a few parameters, the longer the section synthesized the more the f i t can d r i f t away from perfection. Part of t h i s disagreement i s unquestionably caused by the r e l a t i v e l y poorly determined zero l e v e l of the observed spectrum. This i s especially true here for Y CVn (in Figure 13) which i s very heavily blanketed over a large part of the synthesized region. PEST K26 MODEL a 7900 ^ 7920 7940 Figure 9. Calculated and Observed Spectra of 19 Psc   105 BESOLTS The Batios The detailed set of calculated coherency values i s presented in appendix IV; the deduced parameter values are also summarized i n Table 17. Column 2 of the table gives the mean value of the observed spectrum and the average CN index (Baumert 1972); columns 4 to 8 a l l refer to the parameters of the deduced coherency peak for the model atmosphere i n column 3. The uncer- tainty of the derived »3 c / i 2 c r a t i o s i s estimated to be <20% f o r each i n d i v i d u a l model. This i s based on the deviations shown by the test cases, the curvature of the coherency curves near the peak, and the s l i g h t variations that could be caused by a dif f e r e n t power cutoff l e v e l i n the analysis. a further uncer- tainty i s introduced by the model atmosphere i t s e l f , depending on how c l o s e l y i t approximates the real s t e l l a r atmosphere. This factor i s unknown, but since there i s no obvious dependence on the model chosen [models K12 and K26 are grossly d i f f e r e n t ] we can assign an uncertainty to the average r a t i o of <25%. Note that the accuracy of the K24 model for 19 Psc i s not as good as the others as only a small number of coherency points were calculated to check that the peak was in general agreement with the other two models. ,. Scalo (1977) has summarized previous 1 2 C / 1 3 C ratio deter- minations for 22 carbon stars that were deduced from obser- vations of the CN Bed bands. Comparison with the present 106 1 — 1 J Star T T " — 1 r - _ r — " T " r 1 Sean | \ <CN> I Hodel | X(CSO) ! ?' I » 2 C J Mean _ i Peak Coh *y ! i J | 1 J T" 1 19 Psc J 0.414 J K26 | 0. 10 J 3.?5 1 0.04 J 0.455 ! .94 10 i 77 | K24 J 0. 19 1 3.75 1 G.057 | 0.443 ! .9380 ! I K12 I 0. 80 1 3.5 ! O.05O | 0.491 I .9 369 j Z Psc J 0.411 | K26 | 0.11 1 3.4 ! 0.058 | 0.432 ! .9415 I 79 | K12 | 0.95 i 3.25 i 0.054 | 0.476 ! .9378 I X Cnc | 0.313 | | 89 | K26 | 0. 17 1 3.8 j 0.032 | 0.345 j .9515 ! UU Aur I 0.318 I | 100 | K26 J 0.14 1 4.8 j 0.040 1 0.351 j .94 97 I Y CVn I 0.226 | K26 | 0.20 1 5. 0 ! 0.40 1 0.200 i .9545 i 119 | K12 | 1 .3 1 5.3 ! 0.45 J 0.265 i .9356 i j . .. _ i TABLE 17. S0flflA8Y OF DERIVED SPECT1AL PARAMETEBS 107 r e s u l t s y i e l d the following: r 19 Psc 5 values i n the range 15-25 here 21 2 Psc 1 value of 50 here 18 X Cnc 1 value of 22 here 31 00 Aur 2 values of 20 6 25 here 25 Y CVn 5 values in the range 2-5 here 2.4 J Clearly the r a t i o s for 19 Psc f 00 Aur and Y CVn agree quite well. In view of the very great s i m i l a r i t y of the spectra of 19 Psc and Z Psc, including the l 3 C features, I can not accept such a great difference i n the isotope r a t i o s f or these two stars. Both of the values f o r Z Psc and X Cnc were determined by the i s o - i n t e n s i t y method, which i s quite sensitive to the excitation temperature adopted. Although t h i s method has recently been improved ( F u j i t a and T s u j i 1976) by making use of the s a t e l l i t e l i n e s i n the stronger *2CN bands for comparison with the *3CN l i n e s , thus using l i n e s of more nearly equal strength, t h i s technique was not used for either of these stars. For t h i s reason I do not place great trust i n those values and must prefer those deduced here. With the recent a v a i l a b i l i t y of infrared spectra, isotope r a t i o s have been determined from the av=2 CO bands at 2.2^ for a number of stars, including some carbon stars. These bands are strong f o r both carbon isotopes and the r o t a t i o n a l l i n e s are well separated. The l 2C/ 1 3C r a t i o s deduced from these bands are usually s i g n i f i c a n t l y lower than r a t i o s determined from other 1 08 molecules, such as CN. For the s t a r s s t u d i e d here Johnson and Mendez (1970) give the f o l l o w i n g " e s t i m a t e s " : 19 Psc 8-12, X Cnc 10-12, OU Aur 10-12, I CVn 3-4; though without any d e t a i l s of t h e i r a n a l y s i s . Thompson (1973) has, however, shown that these bands are not s u i t a b l e f o r i s o t o p e r a t i o d e t e r m i n a t i o n s because of t h e i r extreme degree of s a t u r a t i o n , thus making the appear- ance of the spectrum r a t h e r i n s e n s i t i v e to the amount of 1 3 C present., Perhaps more r e l i a b l e r a t i o s c o u l d be determined from the A V=3 bands at 1.6<u, which should s u f f e r l e s s from s a t u - r a t i o n ; t h i s r e g i o n i s , however, more h e a v i l y o v e r l a i d by bands of CN and C 2 ( c f . Qu e r c i and Q u e r c i 1975)., No a n a l y s i s of these bands has yet been done. 109 Turbulence The microturbulence i s one of the more important factors influencing the appearance of the spectrum. The value of the microturbulent v e l o c i t y f o r a " t y p i c a l " carbon star i s , however, not known. For comparison Gustafsson, Kjaergaard and Andersen (1974) found a value of 1.7 km/s with l i t t l e scatter for a sample of G and K giants. Tonkin, Luck and Lambert (1976) derived a mean value of 1.3 km/s f o r giants and 3.0 km/s f o r l b supergiants, while Luck (1977) found 2.4 km/s for supergiants. That t h i s question i s s t i l l open i s indicated by the f a c t that values have been c i t e d for ©cori (M2 la) ranging from 2 to 10 km/s (Gautier et a l . (1976); Hinkle et a l . (1976)). For carbon stars K i l s t o n (1975) derived values for 8 stars i n the range 5 to 7 km/s, including 19 Psc (5.6) and Y CVn (6.3), while F u j i t a and T s u j i ' s (1964) study of Y CVn resulted i n 6.6 km/s. For the stars studied here the microturbulent v e l o c i t y has been l e f t as a free parameter to be determined. The derived values have already been summarized i n Table 17. I t should be remarked r i g h t away that, on the basis of some rather extensive t e s t s , under no conditions i s i t possible to achieve a s a t i s - factory v i s u a l match f o r 19 Psc with a microturbulent v e l o c i t y as high as 6 km/s. This r e s u l t was established p r i o r to the main coherency ca l c u l a t i o n s and i s confirmed by them. Further, note that the derived values are not strongly dependent on the choice of model atmosphere. In view of the apparent trend that higher microturbulence corresponds to a greater depression of 1 10 the mean l e v e l of the observed spectrum, and to a larger CN index, i t i s tempting to speculate that the heavy l i n e blanketing i n some carbon stars i s d i r e c t l y caused by a high value of the microturbulence. The observed change of mean l e v e l with turbulence i s , however, about three times as large as one would expect from the variations of the synthetic spectra. Nonetheless, and in spi t e of using only f i v e s t a r s , at l e a s t part of the observed range i n blanketing and CN strength i s probably caused by the microturbulence. Macroturbulence has not been included i n t h i s analysis. As has been mentioned, non-Gaussian (Voigt) lin e p r o f i l e s were considered, but were not included in the f i n a l analysis f o r several reasons: the high degree of l i n e crowding would terminate the extension of almost a l l p r o f i l e wings, visual inspection of the r e s u l t i n g spectra did not indicate that the p r o f i l e wings were generally important, and the necessary increase in computation time to calcu l a t e the extended wings was thus not deemed worthwhile. Because of the r e l a t i v e l y poor (1/2 A) instrumental resolution i t i s not possible to make a direct measurement of the s t e l l a r l i n e widths. Macroturbulences for normal late-type giants are on the order of 5 km/s (e.g. Luck 1977). 111 A Note on the Carbon Abundance A rough check on the nuclear processing that has occurred i n these s t a r s may be made by comparing the r e l a t i v e strengths of the CN and C 2 features i n their spectra; i n particular I want to examine the r e l a t i v e importance of CNO hydrogen burning and helium burning as revealed by the C, N and 0 content of the stars. In order to form a carbon s t a r by the mixing of nuclear processed material up to the surface, the C/0 ra t i o of the processed material must be greater than unity., I f only hydrogen burning CNO processing has occurred then the maximum producible C/0 r a t i o i s about 7 for a wide range of processing temperatures and the corresponding N/C r a t i o i s about 25. As shown by Irgens-Jensen (1976) mixing t h i s with an unprocessed envelope to give surface C/0 > 1 also produces N/C > 10. One of the model atmospheres (K12) i s a close approximation to t h i s state (C/0=2,N/C-28). For comparison a model with greatly enhanced carbon was also selected (K26) (C/0=50,N/C=0.02) ; such abundances can not have resulted from CNO burning. Computed spectra using these two atmospheres were compared with the observed spectrum of 19 Psc. Because of the r e l a t i v e l y low carbon content the K12 spectrum i s v i r t u a l l y free of C^ li n e s ; the C 2 content of the K26 atmosphere i s higher by a factor of at l e a s t 10 2. In the 140 A section of calculated spectrum, a f t e r adjusting the K26 model to produce a mean l e v e l equal to that of 19 Psc (no adjustment was necessary for K12), 1 12 11 places were found where K26 was s i g n i f i c a n t l y lower than K12.„ A l l of these places correspond to locations of G 2 l i n e s and the differences were roughly proportional to the expected strengths of the C 2 features; thus i t i s safe to state that these addi- t i o n a l features were caused by the C 2 and were not an a r t i f a c t of the (grossly) d i f f e r e n t atmospheric structures. Comparison of these 11 features with the observed spectrum of 19 Psc showed that i n every case the K26 spectrum was a better match than K12 and that i n 9 out of the 11 cases the observed features were even stronger than i n K26. As a control 10 places were found where the K12 spectrum was lower than K26 (opposite of the above); at these locations the comparison with 19 Psc showed that K12 and K26 each matched better 4 times with 2 places equally well matched. Thus i t i s seen that the s t e l l a r features are most l i k e l y r e a l l y caused by C 2 and not by atomic or t e l l u r i c l i n e s , and that these features are stronger than those produced by the K12 model atmosphere (and possibly by K26 a l s o ) . Samples of a few of the observed C^ features are shown in Figure 10. In order to increase the C 2 strength i n the synthetic spectra we must either a) increase the CNO abundances as a whole, fe) increase only the C abundance, or c) decrease the N abundance [decreasing O has the same eff e c t as b)]. , Only a l t e r - native a) i s compatible with r e t a i n i n g the C:S:0 r a t i o s as produced by CNO processing but the required increase (~ x10*) i s so large that the resu l t i n g CNO/H ra t i o i s incompatible with any hydrogen l e f t i n the atmosphere. Hence the only reasonable  1 14 alternative i s to increase the C/N r a t i o ; t h i s can be done most readily by assuming that carbon from the helium burning regions has been admixed with the surface material. Thus i t i s seen that the synthetic spectrum based on a model atmosphere closely resembling the expected res u l t of CNO processing f a i l s to reproduce the observed features. Only additional carbon enhancement (as from helium burning) can reasonably produce s u f f i c i e n t Ĉ, to match these features. Thompson (1977), using the AV=3 sequence CO bands in three carbon stars, has recently also reported s i m i l a r r e s u l t s . It may also be noted here that for those stars where more than one model atmosphere was used i n the determination of the 1 2C/* 3C r a t i o , the resulting peak coherency was always greater for the model containing more carbon. Presumably t h i s r e f l e c t s the f a c t that the a d d i t i o n a l C 2 features produced a better matching synthetic spectrum. 1 15 The Search for »+C and ££N One of the reasons carbon stars are interesting objects i s that they are i n an advanced stage of evolution and often show the evidence for t h i s by the surface enhancement of some elements (e.g. * 3C and Tc). The case of Technetium i s especially i n t e r e s t i n g since i t i s unstable, with a h a l f - l i f e of 2 x10 s years, and i s apparently present only i n s t a r s which are long-period or i r r e g u l a r variables (Peery 1971). Since these elements must have been brought to the surface from the i n t e r i o r regions where they were made i t i s not inappropriate to also search for other elements which have been s i m i l a r l y transported to the surface. I have here made a search for **C and 1 SN, the remaining CN nu c l e i that can be produced during CNO processing. Since **C i s unstable, with a h a l f - l i f e of 5700 years, i t s presence would be proof of very recent mixing i n a st a r . The production of **C has been investigated by Cowan and Rose (1977) who concluded that enrichment i s possible in the i n t e r s h e l l region [between the helium- and hydrogen-burning s h e l l s ] of a star undergoing helium s h e l l flashes i f hydrogen- r i c h material i s injected into t h i s region. Subsequent admix- ture of t h i s material with the envelope could r e s u l t i n a measurable surface abundance of **C, depending on the r e l a t i v e masses of the i n t e r s h e l l region and the envelope. The quanti- t a t i v e aspects of t h i s study have, however, been questioned by Despain (1977), who concluded that the »*c surface enhancement would be n e g l i g i b l e [**C/*2C < 7 x10~*]. Cowan and Rose also 1 16 conclude that s i g n i f i c a n t enhancement of l sH w i l l occur i f " r e l a t i v e l y large aaounts" of matter are rap i d l y mixed in t o the i n t e r s h e l l region. Despain, too, found 1 SN enrichment on a short time scale. The production of 1 SN i s e s p e c i a l l y interesting since the hydrogen burning CNO reactions operating at equilibrium w i l l very guickly (a few years) r e s u l t in an l sN/*»N r a t i o of about 4 x 1 0 _ 5 for any burning temperature, yet the t e r r e s t r i a l r a t i o i s 3 .7 x10~ 3. Either the *SN i s exposed to CHO processing temperatures below and at the base of the envelope f o r only a very short time, or i t s observed abundance i s the resu l t of a different process altogether (e.g. s p a l l a t i o n ) . Querci and Querci (1970) have te n t a t i v e l y i d e n t i f i e d *su i n gg A U r with an **N/lsN abundance r a t i o of a few times 10 3. Wavelengths f o r the (2,0) band of the Bed system of CN were calculated for the various isotopic forms [ t*C l 4N, tzCi^H, » 3C* SNJ and these l i n e s were added to the input l i s t for the synthetic spectrum calculations. Since none of these forms have been observed i n the laboratory, i t was not possible to ensure that the correct wavelengths were used (as was done for » 2 c » 4 N and 13C**N) and the computed wavelengths had to be used uncorrected. As was pointed out by Fay, aarenin and van C i t t e r s (1971) the value of the o r b i t a l e l e c t r o n i c angular momentum (L) used in these c a l c u l a t i o n s can't always be approximated by the L-values of the free-atom or h i t a l s . Changing the L-value by one causes a change in the calculated wavelengths of 0.25 A (for 1 3C 1 SH).• .. Uncertain t i e s caused by errors i n the is o t o p i c masses 1 17 are n e g l i g i b l e . A redetermination of the coherency peak, now a function of four variables [one of l*C and 1 SN added at a time], was deemed impractical. Instead the previously deduced values of X(CNO), ^ and » 3 c / 1 2 C were considered to be f i x e d and various small amounts of **C or l sN were added, thus reducing the problem to but one variable. In view of the expected minor perturbations caused by these species t h i s should be an adequate procedure. In order to check the s e n s i t i v i t y to the amount of added material several tests were done. Synthetic spectra of the f u l l 140 A region were calculated with i*c**N added f o r several values of **C/ 1 2C from 0 to 0.02; several d i f f e r e n t sets of random noise were then added to these spectra and the coherency calculated with respect to the noiseless spectra. Samples of the r e s u l t of these t e s t s are shown i n Figure 11. Coherency curves are shown for eight different combinations of input l*C/ 1 2C r a t i o and noise. Each combination i s represented by three curves, for power cutoff l e v e l s of 10, 5 and 3% {top, middle, bottom) ; the v e r t i c a l placement of a curve i s a r b i t r a r y , only the curve shape i s important. The tests are divided i n t o three groups with input isotope r a t i o s of 0, 0.001 and 0.004, as indicated on the f i g u r e . The noise amplitude was 60% of the continuum for the tests shown; the t h i r d t e s t s for r a t i o s of 0 and 0.004 were done with more slowly varying noise (the noise was interpolated between the random values, which were calcu- lated only every seventh point) i n an attempt to better simulate  1 19 the character of the noise " l i n e s " being added. As can be seen, the peak locations in the coherency curves are usually inde- pendent of the power cutoff l e v e l although i t is, p o s s i b l e to get an occasional discordant curve. C l e a r l y the curves f o r a r a t i o of 0.001 are not always distinguishable from 0; to get a r e l i a b l e non-zero measure the coherency peak should be at a r a t i o > 0.004, and the peak value should be s i g n i f i c a n t l y higher than the zero intercept. The r e s u l t s when the s t e l l a r spectra are analyzed for 1*C and 1 5N are shown i n Figures 12 and 13, respectively. The curves for X Cnc, UO Aur and Y CVn are not distinguishable from the test cases without *»C; the curves for 19 Psc and Z Psc are peculiar i n that the dropoff rate with increasing **C i s much slower than f o r the test cases and the other three stars. Although the reason for t h i s is not known, the p e c u l i a r i t y i s not, however, of such a nature as to indicate the presence of i*C. Thus, f o r a l l f i v e s t a r s , **C was not detected and **c/ 1 2C < 0.004, the d e t e c t a b i l i t y l i m i t . For *SN sim i l a r remarks apply to 19 Psc, Z Psc, X Cnc and 00 Aur. The coherency curves f o r Y Cvn, however, d e f i n i t e l y indicate the presence of *5N. To explore t h i s further synthetic spectra were calculated wherein the amounts of * ZC I SN and l 3 C l 5 N were varied independently. The resulting coherency values are presented i n Table 18; the v e r t i c a l and horizontal scales i n d i - cate the * 5 N / * * N r a t i o used t o ca l c u l a t e the abundances of i 2 C * s u and * 3C 1 SN, respectively; the curve i n Fig. 13 i s given   1 2 2 * I 0 . 0 2 0 • r r " . " - - r - . 9 5 3 96 | r- . 9 5 3 3 1 | - r - , i . 9 4 9 9 9 j I •• 0 . 0 1 0 | J . 9 5 8 8 7 | . 9 5 8 1 6 | . 9 5 6 5 7 T _ i | 0 . 0 0 4 -4 -4- . 9 5 8 8 9 | . 9 5 7 9 5 | . 9 5 6 0 5 I 0 I < . 9 5 4 5 3 | j . 9 5 1 8 2 T l l I J T 1 t . i - J . . 0 ) i _ 0 . 0 0 4 J X 0 . 0 1 0 -A . 0 . 0 2 0 J 1 3 C » S g T A B L E 1 8 . COHERENCY FOR Y C V S VS * * C » s N A N D ISQIS^ 123 by the diagonal e n t r i e s . If * S N i s present the peak coherency should occur along the diagonal, t h i s i s not the case here. The observed peak corresponds to the presence of * 2 C L S N , with * S N / i * H ~ 0.006, but without * 3 C * 5 N . I t should be noted, however, that i t corresponds to a " C I S H / I Z G I + K r a t i o of 0.0025, which i s below the d e t e c t a b i l i t y threshold, so the absence of I 3 C » S N i s not too surp r i s i n g . The observed behaviour may also be interpreted as some sort of contamination from the * 3C 1 4N features, which are displaced from the i 2 c L S N features by only about 5 A, although i t i s not clear how, by e f f e c t i v e l y including a second set of «i3c* • H * * features the coherency could be improved by the amount indicated. An examination of the spectra (Figure 14) reveals 8 features that are s i g n i f i c a n t l y changed by the inc l u s i o n of 1 S N . The observed spectrum of Y CVn i s better represented by the "with isN" spectrum in 5 of these cases, 2 are equally well matched and 1 i s d e f i n i t e l y not compatible with 1 S N . In view of the uncertainties in the wavelengths of the C a sN l i n e s , a new wavelength set calculated with a d i f f e r e n t L-value was substituted and a new set of synthetic spectra calculated. The resultant coherency array had the same feature as before, although the peak was not as high; the spectrum showed a s l i g h t l y d i f f e r e n t set of * S N s e n s i t i v e features, t h i s time none of these was incompatible. The fact remains that there are features i n the spectrum of Y CVn that can not be explained by the constituents of these 124 synthetic spectra, nor by any t e l l u r i c l i n e s or atomic l i n e s that appear i n the Sun or arcturus. E s p e c i a l l y noteworthy i s the feature at 8037.4 A; t h i s i s a continuum point i n 19 Psc, 2 Psc, X Cnc and 00 Aur. The most plausible o r i g i n of these features, without invoking i s tzc* 3C (or even * 3 C l 3 C ) , expecially i n view of the large amount of 1 3 C i n Y CVn. This location i s also depressed i n WZ Cas, which, though not analyzed here, i s reputed to have a high 1 3 C content. To check t h i s p o s s i b i l i t y the wavelengths of the * 2 c* 3C and 1 3 C » 3 C l i n e s were calculated, yielding wavelengths v i r t u a l l y i d e n t i c a l to those used by Querci and Querci (1970). These c a l c u l a t i o n s are probably accurate since t h e i r observed features at these wave- lengths a l l f e l l on the l i n e a r part of the curve of growth and yielded a l 2 C / l 3 C r a t i o about equal to that derived from the CN l i n e s . Though comparison with Y CVn i s d i f f i c u l t because of the heavy CN blanketing, i t does show some indication that there i s absorption caused by 1 2 C 1 3 C . The addition of these species can not, however, explain the observed "*su« features, as most of these avoid the calculated wavelengths., On the other hand there i s also the occasional observed feature which stands up consi- derably higher than the synthetic spectrum. The arguments in favour of the presence of 1 SN are: 1) the existence of the coherency peak, with the c h a r a c t e r i s t i c s we expect to be s i g n i f i c a n t , since the indicated absence of 1 3C* SN i s not s i g n i f i c a n t , and 2) most of the spectral features that would indicate the presence of C 1 5N are i n f a c t observed. Contrary points are: 1) the single observed feature that does 125 not f i t , though the uncertain wavelengths makes t h i s of doubtful value, and 2) the observed matching features may be caused by something else. Since the positive arguments seem to be stronger, we are led to make a tentative i d e n t i f i c a t i o n of l sN in Y CVn with an abundance r a t i o i+H/ l sN ~ 150.    129 A RJCAP OF THE COHERENCY TECHNIQUE Since tbe coherency technique i s a new t o o l for analyzing s t e l l a r spectra i t seems appropriate to make a summary of i t s s a l i e n t features in the l i g h t of what has been learned here. F i r s t : i t s advantages. 1. I t i s an objective method, requiring minimal subjective input by the observer. 2. Errors in the l e v e l of the drawn continuum and i n the scale of the observed spectrum have no e f f e c t whatsoever. 3. The information content of the entire spectrum i s used. This makes i t p a r t i c u l a r l y applicable to molecular spectra where the features of i n t e r e s t are spread over a large range of the spectrum. 4. Particular l i n e s do not need to be selected for a n a l y s i s ; the problem of blends does not enter., This means i t should be applicable to the analysis of lower resolution spectra. 5. weak l i n e s , that are not correlated with the features of i n t e r e s t , ( t e l l u r i c , atomic, etc.) do not a f f e c t the r e s u l t . 6. Isolated extraneous strong features have no e f f e c t . , Second: some possible drawbacks. 1. A l l the major components should be included in the synthetic spectrum to be compared against. 2. This means that the number of s i g n i f i c a n t variables d e s c r i - bing the synthetic spectra can become large. This has not been a problem here because of the nearly complete dominance of the carbon star spectra by the CN molecule. 130 3. Minor components are not accurately measurable. In t h i s context "minor" means features which are of comparable strength to other spectral features ("noise") not included in the synthetic spectra. Even i f some of these minor l i n e s can be resolved, the coherency peak i s l i k e l y to to be s i g n i f i c a n t l y affected by the noise. A l l things considered, i t i s a good way to get an objective measure of the major spectral variables. Though I have no concrete reason for saying so, having used spectra of only one dispersion, I f e e l that better resolution i n the observational data should ease the analysis by making the e f f e c t s of the variables more re a d i l y separable and give the coherency "surface" a stronger curvature near the peak, thus making i t better defined. Some variables (e.g. the microturbulence) may even be d i r e c t l y measured using t r a d i t i o n a l techniques, thus reducing the number of remaining variables. 131 SUMMARY The investigation of carbon stars i n binary systems included most such suspected systems. Nine systems have been judged probably r e a l ; another half-dozen have been assigned lower weights, while for several more there i s i n s u f f i c i e n t e v i - dence to permit even a tentative judgement. Because of t h e i r faintness i t has not been possible to acquire spectra of many of the companions; accurate r a d i a l v e l o c i t i e s i n particular would be valuable to allow one to confirm or r e j e c t the systems as r e a l . The mean absolute v i s u a l magnitude of the carbon stars i s -2.3, while the bolometric magnitudes range between -4 and -8.,, The average carbon star i s thus somewhat more luminous than the normal giants, but the dispersion i n luminosity i s quite large.. There i s also some ind i c a t i o n of a mass - luminosity r e l a t i o n for carbon st a r s . A new, objective method of analyzing spectra, which requires minimal subjective input, has been introduced and demonstrated. I t i s p a r t i c u l a r l y useful for carbon star spectra, which show extensive molecular bands with severe l i n e blending and an uncertain continuum. The f e a s i b i l i t y of calcu- l a t i n g r e a l i s t i c synthetic spectra of carbon stars has also been demonstrated. The * Z C / * 3 C r a t i o s deduced with t h i s technique are i n general agreement with r a t i o s obtained v i a the curve-of- growth method from the same near infrared CN bands. The analysis also revealed an interesting possible c o r r e l a t i o n between the oicroturbulence and the CN index. The presence of 1 32 *5N has been t e n t a t i v e l y i d e n t i f i e d i n I CVn, while **C was not found i n any of the s t a r s analyzed. The presence of * SN i s p o t e n t i a l l y a very important r e s u l t ; t o c o n f i r m i t we need t o i d e n t i f y some s p e c i f i c l i n e s of 1 2 C 1 S N . To t h i s end a thorough l i n e i d e n t i f i c a t i o n study f o r ¥ CVn, using h i g h - d i s p e r s i o n s p e c t r a , would be very v a l u a b l e . There i s s t i l l a gr e a t shortage of r e a l i s t i c model atmo- spheres f o r carbon s t a r s ; i n p a r t i c u l a r t h e r e i s a need f o r models with abundances t h a t r e f l e c t the helium-burning r e a c t i o n s . , Since a CHO-type composition does not r e s u l t i n enough carbon to make adequate amounts of C2# and a carbon- enhanced model y i e l d s too much CN to g i v e r e a s o n a b l e s p e c t r a without g r e a t l y s c a l i n g i t down, i t would appear t h a t some nitr o g e n - p o o r ( s o l a r abundance o r l e s s ) and carbon-enhanced models may be what are needed. 1 33 REFERENCES Abt, H. A., Heinel, A. ,, B . , Morgan, 8. W. and Tapscott, J. a. 1968, An Atlas of Low-Dispersion Grating S t e l l a r Spectra. Allen. C. 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V3, 169. 138 APPENDIX I RADIAL VELOCITIES OF CARBON STARS Radial v e l o c i t i e s for most types of stars are usually measured i n the blue spectral region (3700 - 4600 A) f o r two reasons: v i z . t h i s i s where the photographic plates are most e f f i c i e n t , and there i s a good se l e c t i o n of atomic l i n e s available for a l l s p e c t r a l types. Carbon stars are, however, usually extremely weak i n the blue, and hence long exposures are required to get good blue spectra. The near infrared (7000 9000 A) i s a much more e f f i c i e n t region for taking spectra of carbon stars (using N plates), while s t i l l further i n t o the infrared photographic plates become i n e f f i c i e n t and/or obser- vational methods become more elaborate. This region i s , however, heavily blanketed by bands of CN and C 2, making i t well nigh impossible to f i n d any unblended atomic l i n e s . This problem i s even more severe at low dispersions when almost every spectral feature i s a blend of several l i n e s . , Since several of the carbon stars i n the l i s t of suspected binary systems had poorly determined v e l o c i t i e s (Sanford 194 4) i t was deemed desirable to acguire better data in t h i s regard. Furthermore f u l l y 1/6 of the stars on Sanford's l i s t have v e l o c i t i e s determined from a single c l a s s i f i c a t i o n dispersion spectrum only. I f one could come up with a set of standard wavelengths for use on low dispersion near infrared spectra t h i s s i t u a t i o n could be greatly improved. 1 39 The spectra used for th i s study were obtained by Dr. H. B. Richer at Cerro Tololo in 1969. They are at 124 A/mm dispersion and cover the spectral range 7400 - 8900 A; also used were some high dispersion {13 A/mm) spectra of the same region obtained at the Dominion Astrophysical Observatory, V i c t o r i a . . Tracings of the high dispersion spectra were used to choose a set of l i n e s which were reasonably strong and had no {or few) comparably strong nearby neighbours. These l i n e s were then measured on the low dispersion spectra of the 11 sta r s with " a M - g u a l i t y v e l o c i t i e s {Sanford 1944) l i s t e d in Table 19. A l l these stars are late-type carbon stars except V A r i , which i s a CH star . Since the near in f r a r e d spectra of most carbon stars show very l i t t l e v a r i a t i o n (Richer 1971), t h i s i s not important and the standard wavelengths are applicable to a l l carbon stars showing the CN bands in s u f f i c i e n t strength to make most of the l i n e s measurable. The s t e l l a r spectra were d i g i t i z e d using the department's automated Joyce-Loebl Hicrodensitometer, with a sampling in t e r - val of 5 microns (about 0.6 A), and the l i n e position measure- ments were made by a computer program (see next Appendix) which f i t s s p l i n e functions to the observed points and then calculates both the l i n e center-of-gravity and minimum from the reconstruc- ted spectrum. The wavelengths of both of these were then plotted versus the expected velocity of the star (corrected f o r the earth's o r b i t a l motion) and only those features with the tightest c o r r e l a t i o n retained., 1 40 Seventeen l i n e s were thus chosen to define the r a d i a l velo- c i t y system; these are l i s t e d i n Table 20. The same features are also indicated on the tracing of T Ind i n F i g . 15. Because of the great complexity of carbon star spectra the l i s t e d f e a - tures may not be used unquestioningly, however, but only i f the l i n e shape i s such as to conform to that i n the stars used i n defining the system. These necessary q u a l i f i c a t i o n s are noted in Table 21. A rough idea cf how frequently a feature may be found acceptable can be estimated from the number of l i n e s used to define that rest wavelength (column "NH i n Table 20). Note that features 1 and 4 in the tracing i n F i g . 15 would not be considered acceptable by these c r i t e r i a . This technique was applied to nine of the program stars. An average of 12 l i n e s were measured for each star r e s u l t i n g in an average probable error of the mean of 4 km/s. This i n t e r n a l accuracy i s comparable to Sanford*s H c M - q u a l i t y v e l o c i t i e s , as defined by his error bars. 141 r - . . — r-| Star | T_ Expected ] Velocity | San ford Sp. (1944) — i Type 1 Richer (1971) | : J i ' 1 v Aqi 1 • 65 | N 1 C5 | 1 AQ Sgr | • 42 | N \ C5 | | T Ind | + 24 | N I C5 J j DS Peg j • 19 | N 1 C5 | I HD 173291 | + 10 | N 1 C5 | | TT Tau | -12 \ N i C5 | I HD 180953 j -16 J N \ C5 | I AQ and | -19 | N 1 C6 | | TT cyg I -33 | N 1 C6 | | SS Cyg | -37 | Ne 1 C5 J 1 v A r i | -191 I HO, CH 1 C5 | 1 ,., J _ _ a. „ —i _ _ _ .j TABLE 19.. STARS WITH MAM-QOALTTY VELOCITIES USED TO ESTABLISH STANDARD WAVELENGTHS IN THE INFRARED 112 r~" T" | Feature | 1 No. . | Best Wavelength " X " i Main Contributor _ T _ | St. Devn | (km/s) i N i ! i HK- 1 1 I 7 4 7 9 . 2 8 7 i CN 1 6.1 I 9 I 2 | 7 6 9 2 . 4 7 7 i CN 1 8.5 I 11 I 3 | 7 7 1 4 . 8 0 4 i Ni, Cz I 1 0 . 3 ! 11 I 4 | 7 7 6 5 . 8 4 0 ! C 2, CN I 4 - 0 I 8 I 5 | 7 8 5 1 . 0 3 5 ! CN (bh) | 15 . 5 j 10 | 6 | 7 9 9 5 . 1 4 6 ! CN I 1 o.o I 10 1 7 . • | 7 9 9 9 . 5 9 8 ! CN I 1 3 . 4 ! 11 i 8 | 8 0 2 1 . 0 4 1 I CN I 12 .4 ! 10 1 9 \ 8 1 8 7 . 6 4 4 I CN I 1 3 . ? } 8 | 10 | 8 2 9 7 . 7 0 0 i CN 1 1 1 . 8 ! 8 I 11 | 8 3 3 8 . 2 9 7 ! CN I 7 .9 J 8 1 12 | 8 3 4 3 . 6 2 9 i CN \ 1 0 . 3 | 7 I 13 | 8 4 0 5 . 2 1 1 i CN I 1^.3 J 9 I It I 8426.466 ! CN, Ti | 10 .0 } 9 | 15 | 8 4 8 7 . 9 6 8 ! CN 1 6 .7 j 5 I 16 | 8 4 9 8 . 9 4 1 I Ca I I , CN 1 1 1 . 9 I 10 | 17 | 8 6 6 2 . 2 3 8 ! Ca II I 1 2 . 6 J 7 i ... J - . j . . X - TABLE 20., STANDARD WAVELENGTHS AND ACCOBACIES OF FEAT08ES DEFINING THE RADIAL VELOCITY SYSTEM 1 43 r— : • r- j Feature | 1 No. ) i. i Set on —, 1 I Additional q u a l i f i c a t i o n s J i 1 ! Min I Reasonably symmetrical minimum. j J 2 I CG 1 I 3 I CG i 4 J CG | Ought to have the t y p i c a l width. j | 5 i J3in } Min should be close to steep edge. j I 6 J CG 1 Must resolve 7992 l i n e . j | 7 I CG \ i 8 I CG 1 | 9 I 13 in J Must have sharp min close to steep edge. J I 10 J Min I Must have sharp min close to steep edge. | I. 11 Min \ Must have sharp min 6 very steep edge. j \ 12 Min J Must have sharp min. | 1 13 J Min I Should be f a i r l y deep l i n e . | J 14 CG 1 I 15 i Min I Extremely sharp minimum. | ! 16 i CG+Min 1 | 17 . i CG « I a l l l i n e s to be set on the minimum (Min) should have | \ t h e i r minimum following smoothly from the adjacent { \ maximum without any abrupt changes i n the slope of the | I p r o f i l e . j I Lines to be | be reasonably I t y p i c a l width set on the center-of-gravity (CG) should | symmetrical. These l i n e s generally have a j of 3 to 4 pts (about 2 A). 1 * j TABLE 21, aCCEPTaNCE CRITERIA FOR WaV ELENGTH STANDARDS Figure 15. I d e n t i f i c a t i o n of Wavelength Features for Hear Infrared Badial Velocity System   APPENDIX II USE OF HICBODENSITCHETEB AND C08PU_TEH PEOGEAHS TO 8EASUBE BADIAL VELOCITIES The method of measuring r a d i a l v e l o c i t i e s outlined in the previous Appendix and described i n more d e t a i l here i s , unfor- tunately, rather laborious and time-consuming. Although t h i s University does have a Grant oscilloscope measuring machine, t h i s instrument does not have s u f f i c i e n t s e n s i t i v i t y to permit setting on many of the weak features indicated in F i g . 15, The wavelength standards derived here do not, of course, depend on the measurement technique but only require that the instrument used be s u f f i c i e n t l y s e n s i t i v e with a 5 micron s l i t width to show contrast comparable to that of Fig. 15. For the following i t i s assumed that the reader i s fam i l i a r with the operation of the Joyce-Loebl Autodensidater (see e.g. Olson 1971). The Autodensidater i s used to generate a d i g i t i z e d spectrum punched on paper tape. This spectrum must be: decoded and stored before further processing i s done. The positions of the comparison arc l i n e s are found using the "ARC" program and a dispersion curve i s f i t t e d to those positions. F i n a l l y the HSTELLAB2" program i s used to f i n d the positions of the s t e l l a r features and calculate their wavelengths. Since the comparison arc l i n e s must be recorded at the same time as the s t e l l a r spectrum, a mask has been constructed to f i t immediately i n front of the Autodensidater analyzing s l i t . This 148 permits rapid switching back and fort h between the s t e l l a r and arc spectra. A scan should normally s t a r t near 7450 A and end past 8700 A. The mask should be used to switch over to record the com- parison arc for those l i n e s marked in F i g . 15, except 8654 A which i s too close to the s t e l l a r 8662 A l i n e . To get t h i s l i n e , return past 8521 A and record only the arc; t h i s w i l l allow c a l c u l a t i o n of the o f f s e t to 8654 A. The paper tape should fee started by keying i n the characters " 000*999*" and ended by a "D". The card deck setups for the six applicable programs are given below* Input i s i n either free format of integer, real or l o g i c a l type (I, R, L) or l i t e r a l data in »A» format. The tape i s decoded using the "DENSITY" program: i \ $R0N DENSITY 1=DensityFile I 1. NrPts | SEND NrPts should be a multiple of 2000; max. = 30000. The plate density values should next be printed out using the "PRINTT" program: i~—————————————————————— I | $RUN PRINTT 1=DensityFile I I I i 1 49 The arc l i n e positions are calculated and punched on cards using the "ARC" program. This program requires the point index of the peak of each l i n e as input; t h i s can be gotten from the printed density values. $RUN ARC 1=DensityFile 8=*P0NCH* 1. Line positions Max = 50 (I..,) Repeat card 1 as required. SEND I 1 . ; ; , The dispersion curve c o e f f i c i e n t s are calculated by the "OLQE'* program.. The input i s the same as that required by the OBC l i b r a r y program *OLQF. i — : I $RUN OLQF | 1. Nr of Pts, Order to f i t , *0", "T". j 2. Pos«n, wavelength I Card 2 repeated "Nr of Pts" times. | SEND i ; — i . . This program should be run with judicious deletion of l i n e s u n t i l the f i t i s adequate. (3I,L) (2R) 150 The wavelengths of the s t e l l a r features are calculated using the "STE1LA82*' program: $R0N STELLAR2 1=DensityFile 1. Dispersion curve c o e f f i c i e n t s Max = 5 (58) 2. Line positions Max =100 (I.--) Repeat card 2 as required. SEND The density values near the s t e l l a r l i n e s may be plotted to a s s i s t in judging whether a l i n e p r o f i l e i s acceptable: $R0N PLOTT 1=DensityFile 1. L i t e r a l t i t l e (20A4) 2. Low 6 High pt indices of region to be plotted; Low S High density values to be plotted. (41) Repeat card 2 as desired. $EHD The r a d i a l velocity may now be calculated by the usual method from the measured l i n e wavelengths and the rest wavelengths of Table 20. 151 Appendix II L i s t i n g of Computer Programs C "DENSITY" C INT EG ER*2 IDATA, IDPLT (30000) NC00NT = 0 MISSTP = 0 NCALLS =0 CALL FEE AD (- 2, • ENDFILE • , 1) CALL F8EAD (5,*I:»,NBATA,610) 10 IF (NDATA.LT.1) NDATA=30000 NDATA = (NDATA+1999)/2000*2000 DO 9 J = 1, NDATA NCALLS = NCALLS • 1 CALL JCLBL (IDATA,NCOUNT,NBOGUS,MISSTP,&8) IF (IDATA.EQ.fOOO) GO TO 8 IDPLT (J) = IDATA 9 CONTINUE 8 WRITE <6,4) NCALLS,NCOUNT,MISSTP 4 FORMAT|'NR OF JCLBL CALLS',1 OX,• = •,16,/,'NR OF DATA COUNTS' • * BY JCLBL =',I6,/,»NR OF TAPE ERRO RS » , 1 OX , » =' , 16) ND=((NCALLS+1999)/2000)*2000 DO 1 J = 1,ND,2000 K = J + 1999 WRITE (1) (IDPLT(I), I=J,K) 1 CONTINUE STOP END C SUBROUTINE JCLBL (IDATA,NCOUNT,NBOGUS,MISSTP) INTEGER*2 IDATA,IA(4) NZERO = 0 201 DO 200 N =1,4 CALL PTAPE (1,8210,6210) I = IABS(I) IF (I.GT.128) 1 = 1 - 128 IF (I.EQ.42) GO TO 202 IF (N.EQ.4) GO TO 205 IA(N) • = . 1 - 4 8 IF (IABS (I-53).LE.5) GO TO 200 IF (I.EQ.68) IDATA = 1000 IF (IDATA.EQ.1000) RETURN IF (I.EQ.O) NZERO = NZERO + 1 IF (NZERO.LT.9000) GO TO 201 IF (NZERO.GE.9000) IDATA = 1000 RETURN 200 CONTINUE 202 IF (N.EQ.4) GO TO 204 IF (NCOUHT.EQ.O) GO TO 201 205 MISSTP = MISSTP + 1 DO 206 J = 1,4 CALL PTAPE (1,6210,6210) IF (IABS(I) .GT. 128) I = IABS(I)-128 IF (J.EQ.4. AND.I.EQ.42) WRITE (6,101) NCOUNT IF (J.EQ.4.AND.I.EQ.42) NCOUNT = NCOUNT • 1 152 Appendix II L i s t i n g of Computer Programs IF (I.EQ.42) GO TO 207 206 CONTINUE 207 IDATA = 0 NCOUNT = NCOUNT • 1 WRITE (6,101) NCOUNT 101 FORMAT {« DDE TO TAPE ERROR, DAT A=0 AT POINT =VI6) RETURN 204 IDATA = 100*1 A (1) • 10*IA{2) + IA{3) NCOUNT = NCOUNT • 1 RETURN 210 WRITE (6,152) NCOUNT,NZERO 152 FORMAT {' END OF TAPE AT PT»,15,1QX,•NZERO =',I5) RETURN 1 END C "OLQF" C DIMENSION X(50) ,Y(50) ,YF{50) ,YD{50) , WT (50) ,S (10) ,SG{10), * A (10), B{10) ,P(10) , YL{50) REAL*8 DISP,XO,YO,LAM LOGICAL LK CALL FREAD (—2,* ENBFILE* ,1) 210 LK=.FALSE. , CALL FREAD (5,*3I,Lj*,M,K,NWT,LK,£220) DO 200 I = 1, M CALL FREAD (5 , * 3R: •, X (I) ,Y (I) ,WT (I) ) 200 CONTINUE CALL OLQF (K,M,X,Y,YF,YD,WT,NWT,S,SG,A,B,SS,LK,P) KP = K + 1 KPP = K • 2 WRITE (6,150) K 150 FORMAT < *4 *,T50,* DEGREE OF CHOSEN POLYNOMIAL WAS*,14,//, * T10, 9X«,T26,»Y»,T38,»Y—FITTED RESIDUALS *,5X, * »RESID 1ST ORD*,7X,* SIGMA*,13X,* P*,/) XO = DBLE (X (1) ) YO = DBLE (Y { 1) ) DISP = (DBLE (Y (M) )-YO)/(DBLE (X (M))-XO) DO 230 J = 1, M LAM = DISP * (X(J)-XO) + YO YL(J)=LAH-Y(J) 230 CONTINUE WRITE (6, 151) (X(I),Y{I) , YF (I) , YD (I) , YL (I) , SG (I) , P (I) ,1=1, KP) 151 FORMAT {1X,E16.7,E16.6,E16.6,F12.3,4X,F12.3,4X,2E16.8) WRITE (6,152) (X (I) ,Y (I) ,YF(I) ,YD (I) , YL (I) , I=KPP,H) 152 FORMAT (1X,E16.7,E16.6,E16.6,F12.3,4X,F12.3) GO TO 210 220 WRITE (6, 150) NWT STOP END 153 Appendix II Li s t i n g of Computer Programs C "ABC" C INTEGER*2 18(4000) INTEGER IPOS(50)/50*0/ REAL PP (6),WL (9)/7503. 87,751 4.65,7635. 10 ,7948. 17, 80 1 4. 79, * 8103.74,826 4.52,8377.61,8521.44/ REAL*8 S,SS LOGICAL PCHHL/.FALSE./ READ (1) (IN (I), 1=1, 2000) READ (1,E8D=200) (IN (I) ,1=2001 ,4000) 200 CALL FREAD (—2,* ENDLINE*,* ST REAM *) CALL .. FREAD (5,M V:»,IPOS) CALL FREAD {-2,* NUMBER*,BP) WRITE (6,152) 152 FORMAT (•1STAR NAME =*,T40,*PLATE NO =*,T80,*ARC POSNS*,//) IF (NP.EQ.15) PCHWL = . TRUE. DO 204 J J = 1, NP P = 0.0 MID = IPOS(JJ) ¥0 = IN (MID-1) Y1 = IN (MID) Y2 = IN(MID+1) B = 2.0*Y1 - 1.5*Y0 - 0.5*Y2 C = 0.5*Y0 - Y1 + 0.5*Y2 IF (C.EQ.0.0) GO TO 317 P = -0.5*B/C + FLOAT(MID—1) 317 DO 300 J = 1, 10 JA = MID-J IF (IN(JA-1) .GT. IN (JA) ) GO TO 301 300 CONTINUE 301 DO 302 J = 1, 10 JB = MID+J IF (IN (JB* 1) . GT. IN (JB) ) GO TO 303 302 CONTINUE 303 IMN = IN(JA) IF (IN (JB) • GT.IMN) IMN = IN(JB) IMX = IN (MID) BT = IMX-IMN DO 305 IL = 3,8 HLV = IMN + 0.1*IL*HT DO 306 J = JA, MID IF (IN {J) . L E. HL V .AND. IN (J* 1) .G T. HLV) GO TO 307 306 CONTINUE 307 PP(IL-2) = J * (HLV-IN(J))/{IN(J+1)-IN(J)) DO 308 J = MID,JB IF (IN(J) .GE. HLV .AND. IN (J+1) . LT. HL V) GO TO 309 308 CONTINUE 309 PP(IL-2) =(J+(HLV-IN(J) ) / (IN (J*1)-IN (J)) *PP (IL-2) ) /2 .0 305 CONTINUE N = 6 314 S = ODO SS .= ODO DO 310 J = 1, N 154 Appendix II L i s t i n g of Computer Programs S = S •• DBLE(PP(J) ) SS = SS •«• DBLE(PP (J) )**2 310 CONTINUE AVG = S/N SD = DSQBT ((SS-S**2/DFLOAT{N))/DFLOAT(N-1)) IF (SD.LE.0.1 .OB. N. LE. 3} GO TO 311 XD =0.0 DO 312 J = 1, N IF { ABS {AVG—PP (J) ) .GT. XD) XD = ABS {A VG-PP (J) ) 312 CONTINUE 8 = 0 DO 313 J = 1, N IF (ABS{AVG-PP{J))«GE* XD) GO TO 313 M = M*1 PP(M) = PP{J) 313 CONTINUE N = M GO TO 314 311 WHITE (6,150) MID,P,AVG,N,3D 150 FOBMAT {'OMIDPT =',I5,10X,'PEAK =*,F10.3,10X,'CENTER = *, + F10.3,10X,I2,« PT ST.DEV =•,F6.3) IF (PCHWL) GO TO 320 IF (JJ.LE. 9) WRITE (8,151) AVG GO TO 204 320 IF (JJ.LE.9) WRITE (8,151) AVG,WL(JJ) 151 FORMAT (F1O.3,*10.2) 204 CONTINUE STOP END C "PRINTT" C INTEGER*2 ID(2000) 200 READ (1,END=201) ID WRITE (6,150) ID 150 FOBMAT (2515) GO TO 200 201 STOP END 155 appendix II L i s t i n g of Computer Programs C "STELLaR2" c DIMENSION X (25) , Y(25) ,IPS (100) ,X0 (100) DIMENSION T (220) ,SS (220) ,SS1 (220) ,SS2 (220) REaL*4 COF(5) INTEGER*2 IN{4000) EPSLN = 1.0E-4 READ (1) (IN(I) ,1=1,2000) READ (1,END=207) (IN (I) , 1=2001,4000) 207 CALL FREAD (5,*R 7; • ,COF) CALL FREAD (-2, * NUMBER* , NCF) CALL FREAD {- 2, ' ENDLINE* ,'STREAM') CALL FREAD (5,'I V:',IPS) CALL FREAD (-2,* NUMBER*,NPOS) WRITE (6, 150) 150 FORMAT (»1STAR = *,T40,* PLATE NO =•,T80,•STELLAR LINES',//) WRITE (6,159) (COF(J), J=1,NCF) 159 FORMAT {* WAVELENGTH COEFFS: »,5G16.7) WRITE (6,161) 161 FORMAT { *0*,T29,'MINIMUM*,T6 0,*CENTER OF GRAVITY',T97, • • DEPTH WIDTH ARE A* ,/,T25, » POSH WAVELENGTH' ,T62, • »POSN WAVELENGTH*,T98, • (DU) (DP) (DD.DP)*) DO 2 50 NT = 1, NPOS MID = IPS (NT) IB = MID - 10 IE = MID +10 DO 251 J = 1, 10 IX = MID - J IF (IN (IX* 1 )-IN{IX).GE.100) GO TO 252 IF (IX.LE.3) GO TO 252 251 CONTINUE GO TO 253 2 52 IB = IX +1 253 DO 254 J = 1, 10 IX = HID + J IF (IN(IX-I)-IN (IX) .GE.100) GO TO 255 254 CONTINUE GO TO 256 255 IE = IX - 1 256 NPTS = IE - IB * 1 IF (NPTS. LE. 10) WRITE (6,155) MID 155 FORMAT (*0NOT ENOUGH PTS FOR SPLINE AROUND MINIMUM AT*,15) IF {NPTS.LE.10) GO TO 250 IX = 0 DO 257 J = IB, IE IX = IX * 1 X (IX) = FLOAT (J) Y (IX) = IN (J) 257 CONTINUE M = 10*NPTS - 9 DO 300 J = 1, M T (J) = IB • 0.1 * (J-1) 300 CONTINUE 156 Appendix II L i s t i n g of Computer Programs CALL SPLINE {NPTS,M,EPSLN,X,Y,T,PBOXIN,SS,SS1,SS2) XM = FLOAT (MID) CALL SPLINV (XM,V,SL,SD) IF (SL.EQ.0.0) GO TO 249 ISP = IFIX (SIGN(1.1,SL)) 260 SLP = SL XMP = XM XM .= XMP - 0.5*ISP CALL SPLINV (XM,V,SL,SD) IF (SL.EQ.0.0) GO TO 249 IS = IFIX (SIGN(1.1,SL)) IF (IS.EQ.ISP) GC TO 260 263 A A = (SL-SLP) /(XM-XMP) BB = SL - AA*XM XMN = -EB/AA CALL SPLINV (XMN,V,SLN,SD) ISN = IFIX(SIGN{1. 1,SLN) ) IF {ISN.NE.ISP) GO TO 261 IF (ABS (XHN-XMP) .LE. 0.0015) GO TO 265 XMP = XM SLP = SL ISP = IS GO TO 262 261 IF (ABS (XMN-XM) .LE.0.0015) GO TO 265 262 XM = XMN SL = SLN IS = ISN GO TO 263 265 XM = XMN 249 DO 301 J = 3, M I F (T(J).GT.XM) GO TO 302 IBOTH = J 301 CONTINUE 302 IBB = J*1 DO 303 I = IBB,M IF (SS(I) .LE.SS ( 1-1) ) GO TO 305 JB = 1 - 1 0 JL = I - 20 IF (JL.LE.IBB) JL = IBB - 1 I B = (JL+I)/2 IF (JH . L T o I H ) JB = IH D = SS (JB) - SS (JL) IF (D.LE.0.0) GO TO 303 XT = (SS(I)-SS (JL))*(JB-JL)/D+JL XT = IB • 0. 1* (XT-1.0) IF (T(I)-XT.LT.0.4) GO TO 303 LRT = (I*JR)/2 GO TO 306 303 CONTINUE 305 LBT = 1-1 306 IBB = IBB - 3 IE = IBB-2 DO 307 IX = 1, IE 157 Appendix II L i s t i n g of Computer Programs I = IBB - IX IF (SS (I) .LE. SS (1*1) ) GO TO 308 JB = I + 20 JL = I • 10 IF {JR. GE.IBB) JB = IBB • 1 IH = (I*JR)/2 IF (JL.GT.IH) JL = IH D .= SS (JR) - SS(JL) IF • (Di.GE.0wQ) GO TO 307 XT = (SS(I)-SS(JL) ) * (JR-JL)/D • JL XT = IB • 0. 1*{XT-1.0) IF (XT-T (I) .LT.0.4) GO TO 307 LLT = (I+JL) /2 GO TO 309 307 CONTINUE 308 LLT = 1+1 309 IF (SS(LLT).GT.SS(LRT)) GO TO 310 VEL = SS (LLT) DO 311 J = IBB, LET IF (SS(J) .GT. VEL) GO TO 312 311 CONTINUE 312 LRT = J-1 GO TO 314 310 VEL = SS (LRT) DO 313 J = LLT, IBB IF (SS (J) . LE. VEL) GO TO 315 313 CONTINUE 315 LLT = J 314 XLEN = (LRT-LLT)/10.0 HHT = VEL - SS (IBOTH) 10 = 1 IF (XLEN.GT.1.0) GO TO 319 AREA = Q.O 10 = 0 XBT =1.0 GO TO 325 319 AH = 0.0 DO 320 J = LLT, LRT AR = AR + (VEL-SS (J) ) 320 CONTINUE AREA = AR/10.0 AR2 = AR/2.0 AR = 0.0 DO 321 J = LLT, LRT AR = AR + (VEL-SS (J) ) IF (AR.GE.AR2) GO TO 322 321 CONTINUE 322 FR = (AR2- (AR- (VEL-SS (J) ) ) ) / (VEL-SS(J)) XWT = J-1+0.5 + FR XHT = IB*0. 1* (XHT-1.0) 325 31 = 0.0 H2 = 0.0 DO 331 J = 1, NCF 158 Appendix II L i s t i n g of Computer Programs W1 .= 81 + CO? (J) *XH** (J-1) W2 = 82 + COF(J) *X»T** (J-1) 331 CONTINUE IF (IO.EQ.O) 82 = 0.0 323 8RITE (6,160) NPTS, HID,XM,131 ,XBT,W2, HHT, XLEN, ABEA 160 FORMAT («0«,I2,* PTS AT»,15,4X,2F11.3,15X,2F11.3,15X, + 2F8.1,F12.3) 250 CONTINUE STOP END C SUBROUTINE SPLINE (N,M,EPSLN,X,Y,T,PROXIN,SS, SS1 ,SS2) C COMPUTES NATURAL CUBIC SPLINE. ALSO GETS INTEGRAL OVER KNOTS. C FINALLY, EVALUATES SPLINE (6S«,S»«) AT VARIOUS ABSCISSAE. C SOURCE: GREVILLE IN <MATH METHODS FOR DIGITAL COMPUTERS> C VOL II RA1STON/HILF INTERPOLATION ON N PAIRS, C (X,Y)-VALUES AT M T-VALUES. INTEGRAL = PROXIN. C SPLINE AND DERIVATIVES IN M SS-,SS1~,SS2-VALUES. C SS2(X) ARE FOUND BY SOR WITH CONVERGENCE PARAMETER EPSLN. REAL X{25) ,Y (25) ,B (25) REAL T{220) ,SS{220) ,SS1 (220) ,SS2 (220) REAL H(25) , DELY (25) , H2 (25) ,DELSQY (25) , S2 (25) ,C (25) , S3(25) N1 = H-1 H(1) = X(2)-X{1) DELY (1) = (Y(2)-Y(1))/H(1) DO 52 I = 2,N1 H(I) = X(I*1)-X(I) H2 (I) = H (I-1)+H (I) B(I) = 0.5*H(I-1)/H2(I) DELY (I) = (Y ( 1 + 1) - Y (I) ) / H(I) DELSQY (I) = (DELY (I)-DELY (I- 1) )/H2 (I) S2(I) = 2.0*DELSQY(I) 52 C(I) = 3.0*DELSQY(I) S2{1) = 0.0 S2(N) = 0.0 OMEGA = 1.071797 5 ETA =0.0 DO 10 1 = 2 , N1 W = (C (I) -B (I) *S2 (I— 1) - (0. 5- B (I) ) *S2 (I* 1) -S2 (I)) *OMEGA IF (ABS(W) .LE.ETA) GO TO 10 ETA = ABS(H) 10 S2 (I) = S2(I) + W IF (ETA.GE. EPSLN) GO TO 5 DO 53 I = 1, N1 53 S3 (I) = (S2 ( 1 + 1)-S2 (2) )/H(I) AR = DELY (N 1) +H (N 1) *S2 (N 1) /6.0 AL = DELY(1)-H{1) *S2 (2)/6.0 PROXIN =0.0 DO 62 I = 1, N1 62 PROXIN = PROXIN*0.5*H(I) *{Y(I) *Y ( 1*1) ) # -H (I) **3*(S2 (I) +S2 (1+1) )/24. IF (M.LE.O) RETURN GO TO 15 159 Appendix II L i s t i n g of Computer Programs ENTRY SPLINV(ARG,SP,SP1,SP2) C COMPOTES SPLINE AND ITS 1ST 2 DERIVS AT *ABG«; RETNS SP,SP1.. M = 1 TCI) = ARG 15 DO 61 J = 1, M I = 1 IF (T(J)-X(1) ) 58,17,55 55 IF (T(J)-X(N) ) 57,59,580 56 IF (T(J)-X(I)) 60,17,57 57 I = 1+1 GO TO 56 58 SS(J) = AL* (T (J)-X (1) ) •¥ (1) SS1(J) = AL SS2(J) = 0.0 GO TO 61 580 SS {J) = AR* <T |J) -X (N) ) +Y (N) SS1 (J) = AR SS2(J) -= 0.0 GO TO 61 59 I = N 60 I = 1-1 17 HT1 .= T{J)-X(I) HT2 = T{J)-X(I+1) PROD = HT1*HT2 SS2(J) = S2(I)+HT1*S3(I) DELSQS = <S2 (I)+S2 (1*1)+SS2(J))/6.0 SS(J) =. Y (I) +HT1 *DELY (I) *PROD*DELSQS SS1(J) = DELY (I) • (HT1 + HT2) *DELSQS+PROD*S3 (I) /6 . 0 61 CONTINUE SP = SS(1) SP1 = SS1 (1) SP2 = SS2(1) RETURN END 160 Appendix II L i s t i n g of Computer Programs C "PLOTT" C R£AL*4 MULT,TITLE(20) INTEGER*2 IN (4000) ,HEX00/ZF0 F0/, NX,NH, * F{9)/» {1«,*H9»,»,I» ,»5,*,« »,* * , * X, * , * 1H • , •*) */ READ (5,1001) TITLE 1001 FORMAT (20A4) CALL FREAD (- 2, * ENDFILE ' , 1) READ (1) (IN (I), 1=1,2000) READ (1,END=2030) (IN (I) ,1=2001, 4000) 2030 CALL FREAD (5,»4I:•,NMIN,NMAX,IBOT,ITOP,£9999) IF (NMAX.LE.NKIN .OR. NMAX.LE.O) GO TO 2030 IF (NMIN.LE.0) NHIN = 1 IF (NMAX.GT.4000) NMAX = 4000 IF (I80T.LT.0 .OR. IBOT.GE.999) IBOT = 0 IF (ITOP.LE.O .OR. ITOP. GT. 999) ITOP = 999 IF (ITOP-IBOT.GE. 124) GO TO 2010 IF (999-IBOT.GE. 124) GO TO 2011 ITOP = 999 IBOT - 875 GO TO 2010 2011 IF (ITOP.GE. 124) GO TO 2012 ITOP = 124 IBOT = 0 GO TO 2010 2012 I HID = (ITOP+IBOT) / 2 ITOP = IMID * 62 IBOT = IMID - 62 2010 MOLT = 124.0 / FLOAT(ITOP-IBOT) ZEE ••= 1.001 - MOLT* I BOT SC = 1.0 / MULT WRITE (6,1051) TITLE,IBOT,ITOP,SC 1051 FORMAT { • 1 * ,20A4 ,//, » BOTTOM VALUE = • ,15 , 10 X, ' TOP VALUE =•, • I5,15X,*SCALE =*,F7.3,« / PRINT POSN*,//) DO 2001 NPT = NMIN, NMAX NX = IN (NPT)*MULT + ZER IF (NX.GE.1 .AND. NX.LE.125) GO TO 2040 IF (NX.LE.O) WRITE (6,226) NPT IF (NX. GT. 125) WRITE (6,227) NPT GO TO 2001 2040 NH = NX/100 F{5) = NH * HEXOO NX = NX-100*NH F{6) = NX/10*256 + NX-NX/10*10 • HEXOO WRITE (6,F) NPT 2001 CONTINUE GO TO 2030 9999 WRITE (6,1052) 10 52 FORMAT ( ,1 i) STOP 226 FORMAT {»9« , 15, • <•) 227 FORMAT (*9',I5,125X,,>*) END 161 APPENDIX III THE RATIO OF TOTAL TO SELECTIVE ABSORPTION I t has long been known that the r a t i o of t o t a l to s e l e c t i v e absorption [R ] for the (OBV) photometric system i s not a constant depending only on the shape of the i n t e r s t e l l a r red- dening curve, but i s also a function of the colour of the star being observed (e.g. Blanco 1956). This a d d i t i o n a l e f f e c t i s caused by the wide bandpass of the (UBV) f i l t e r s , allowing the e f f e c t i v e wavelengths of the f i l t e r s to s h i f t with d i f f e r e n t s t e l l a r i n t e n s i t y gradients. This must be taken in t o account i f we want to derive the i n t r i n s i c colours of the carbon stars or t h e i r distances, since t h e i r colour excesses w i l l not be the same as f o r the bluer companions. Previous studies of t h i s e f f e c t show that the value of R increases toward l a t e r spectral types, but the actual numerical r e s u l t s for very cool stars are not agreed upon. Blanco and Lennon (1961) found an increase from 3.1 for early-type stars to 3.7 for oc Ori (M2 l a , B-V=1.86), the r a t i o being i n s e n s i t i v e to colour excess for the early-type stars but st e a d i l y decreasing with colour excess from about type KO onwards. Schmidt (1956) found R to increase with colour excess for a l l spectral types except N, and found a value of 4.25 for three carbon stars, which was r e l a t i v e l y i n s e n s i t i v e to the excess. S i m i l a r l y , Honeycutt (1972) found R to be r e l a t i v e l y constant at a value of 3.8 f o r two carbon stars with B-V = 2.5. 1 62 In an attempt to eliminate these discrepancies and to define the variation of the B-values with i n t r i n s i c colour and colour excess t h i s problem was re-examined. The r a t i o of t o t a l to s e l e c t i v e absorption i s given by B = A(V) / E(B-V) = A(V) / [A(B)-A(V) ] (33) rCrxa) <(>/<» icA) «") where A (i) = -2.5 log \ — \ . , (3 4) The transmission function of the i ' t h f i l t e r - c e l l combi- nation i s given by <p.(>)r and the star's s p e c t r a l i n t e n s i t y d i s - t r i b u t i o n by I { M # and the transmission function of X units of i n t e r s t e l l a r matter by T"X<» where TO) = 10 ** -f S m ( > ) - S m (oo) 3/2.5 . (35) &m{>) i s the usual ordinate of the i n t e r s t e l l a r reddening curve and S m ( ° o ) i s the value of the i n t e r s t e l l a r absorption extrapo- lated to i n f i n i t e wavelength. The reddening curve has been taken from Ohderhill and Wal- ker (1966) and normalized to give A (V) =0 and E(B-V) = 1: om(>) = 2.23 - 1.83) for \-* •< 2.25 om{» = 1.42 (>-» - 1.59) for A" 1 > 2.25. , (36) The parameter om(«s) i s e s s e n t i a l l y a free parameter and has been 163 set to 3.12 to give a value of R = 3.20 for early-type st a r s . This i s a widely accepted value which seems to hold f o r most regions i n the galaxy. Johnson (1968) concludes that 3.0 i s the minimum possible value and c i t e s several cases of much higher values.. Other authors prefer S values i n the range 3.1 to 3.2 (e.g., Johnson and Borgman 1963, Schmidt-Kaler 1965). The f i l t e r transmission functions have been taken from Matthews and Sandage (1963), while the s t e l l a r i n t e n s i t y d i s t r i - butions are mainly from Willstrop (1965), supplemented by the early-type c a l i b r a t i o n s of Hayes (1970) and of Oke and Schild (1970). S i l l s t r o p * s data cover the wavelength range 4000 A to 6500 A at 25 A i n t e r v a l s for many types of stars, including one S-star, one R-star and two N-stars. The short wavelength range necessitated extrapolation to the f i l t e r l i m i t s of 3600 A and 7200 A. This did not a f f e c t the r e s u l t s , however, since the agreement with Hayes and with Oke and Schild (corrected f o r Bal- mer l i n e absorption) for those stars i n common was guite good. Nor were the late-type stars affected (where the extrapolation was l e s s certain) , as a r e s u l t of the low spectral i n t e n s i t y shortward of 4000 A and the low f i l t e r transmission longward of 6500 Ai The numerical integrations used points at 100 A in t e r - vals after i t had been ascertained that closer spacing affected the r e s u l t s n e g l i g i b l y . The r e s u l t s are presented i n Figures 16 and 17. Note that the r e s u l t for the N-stars (B-V=2.4) i s i n good agreement with that found by Schmidt, while the value for the M-stars (B-V=1.6, 164 B=3.7) compares favourably with the observational r e s u l t of Lee (1970), who found 8 = 3.6 ± 0.3 from i n f r a r e d photometry of (i-stars., The results for blackbodies of various temperatures are also shown i n F i g . 17. These have been used as a guide in extrapolating the observed variation to redder stars. To quantize these r e s u l t s , polynomials were f i t t e d to the reddening curves of Fig. 16; polynomials were again used to define the v a r i a t i o n of the c o e f f i c i e n t s with i n t r i n s i c colour. The c o e f f i c i e n t s of t h i s second set of polynomials are given i n Table 22., During the course of these calculations i t was noticed that the v i s u a l absorption A (?) i s a function of the star*s i n t r i n s i c colour as well as the actual amount of intervening i n t e r s t e l l a r matter (X). Osing the d e f i n i t i o n of X as i n eqn. 35 t h i s r e l a - tion i s given by A{V) = [1.042 - 0. 020* (B-V) Q J X - 0.00385 X* (37) to good accuracy for a l l types of s t a r s . This e f f e c t i s caused by the s h i f t of the e f f e c t i v e wavelength of the V f i l t e r and simply means that the redder stars are absorbed l e s s . This term w i l l produce a d i f f e r e n t i a l change i n A(V) of about 0.1 magni- tude for a colour excess of E (B-V) = 1.0 only i f two stars d i f - fer i n i n t r i n s i c colour by (B-V) > 3.0. Hence t h i s term would usually be quite n e g l i g i b l e . The accuracy of the calculated fi values can be no better than that of the zero point value B = 3.2, which i s generally 165 assigned an uncertainty of ± 0.2 or 0.3 {p.e.). The r e l a t i v e accuracy for comparison of early and late-type s t a r s , however, should be somewhat better than t h i s .   1 i } g ( o , i ) I q d , i ) q (2,i) "T" 1 -+- q (3,i) 0 3- 28067 2. 02458 x10~2 1. 69810 X 1 0-2 -2- 39331 x10- 3 1 2. 47655 x10" I 3. 24753 X 1 0-2 -5. 09329 X 1 0-3 -8. 2 1006 x10~ 4 2 -3. 92830 x10- I 6. 86755 x 10-2 -2. 18495 X 1 0-2 2. 29100 x10- 3 j 3 4. 51732 x10~ l -6. 65211 X 1 0-2 , 7- 44 152 X 1 0 ~ 3 -3. 9 8584 x10- 4 -1. 46818 x10- I 1. 69069 X 10-2 3. 39048 X 1 0-6 -8. 545 19 x10~ S 5 1. 49948 x10- 2 -1. 40081 X 10-3 -1. 34500 x10~* 1. 72167 x10~ s q (m) = II q * (B-V)0 * * i i«0 B[ E (B-V) , (B-V) 0 1 = g g(oi) * E<B-V)**m TABLE 22. COEFFICIENTS OF POLYNOMIALS TO DETERMINE R FROM E{B-V) AND (B-V) c 1 69 APPENDIX IV COHERENCY TABLES This appendix contains, i n tabular form, the computed coherency values for each synthetic spectrum when compared with the various observed s t e l l a r spectra. The tabular entries are the average coherency values calculated with a 5% power cutoff l e v e l . The model parameters for each entry are indicated on the l e f t for the microturbulence and l 3 C / 1 2 C r a t i o [Rj and along the bottom f o r the X (CNO) value. Note that these parameter values are not always i n a uniform sequence; i r r e g u l a r i t i e s are sometimes indicated by double l i n e s separating the columns. Each table i s also marked with the parameter values of the deduced coherency peak and the mean synthetic spectrum l e v e l [ S ] at the peak. The location of the coherency peak was determined by mental interpolation i n the table, with the aid of pencil and graph paper.. An attempt was made to derive the peak location by least-squares f i t t i n g a three-dimensional e l l i p s o i d to the cohe- rency data, but t h i s was not successful as, i n f a c t , an e l l i p - soid i s a poor approximation of the actual functional dependence of the coherency on the three parameters. 170 19 Psc with model K12 Coherency peak at (X,^,B#S) = <0 . 80,3 . 5 , 0 . 050 , 0.491) r — T" T" ~r — — r . " r — - r - — — a I 4.0 i j j j ! ! .07 | J j .93462 j ! I i .05 | 1 .93530 ! .936 23 I .93504 | ! j .03 | i .93258 ] ! J ! I 3.5 J 1 • j ; j ; .10 J | j .92939 | I I 1 .07 | i .934 99 | .93202 | • j .06 1 | i .93633 ] I i g .05 | .93147 | .93579 .93692 | .93573 | .93346 | .9305 3 | .03 | I .93348 | .93527 | 1 1 j j J ! ! j J j • * * I 3.0 ! ! i j J j ! .07 | ' ! ! .93393 | .93132 | | j .05 J I .93491 1 .93601 J .93516 j 1 .9303 6 J .03 | ! ! .93280 | .93490 | ! ! _. L. * j. • t 0.50 0.65 0.80 0.95 1.10 J | 1.25 | i , ,. , i 171 19 Psc with model K24 Coherency peak at (X,|,R,S) = (0. 19,3.75,0.057,0.443) I —:— • 1 — -j T j | T l •**5 ] J 1 1 j || | .05 | J | .93674 J i i i i 4.0 | | .10 | | | .9324 6 J ! II .07 | | J .93680 | I i l ! .05 1 | .93617 | .93779 | | .93299 || | .03 | | J .9349 8 J ! t ! ! 3.5 | | j | i i i i .07 1 | I .93670 | i i i i • 05 | | | .93772 | ! ' I ! .03 | | | .9354 1 I i i i i 3.0 | | j | 1 II 1 .05 J .93041 | | .93628 | .93410 | .93040 || .92263 | 1. ., - J LA. 1 0. 10 0.15 0.20 0.25 0.30 0.40 | 172 19 Psc with model K26 Coherency peak at (X,^,E#S) = (0.10,3.75,0.04,0.455) 1 . T . - (4.0 | ~l T~ 1 I 1 i t _ T" i ! 1 .07 J ; j | .93835 1 j i J .05 | I .94022 | j ! 1 .03 | i i | .93950 I | 3.75 ] j | j \ T 1 i .04 J j j .94034 | .94098 j j ! J 3.5 | I .10 | j j I .93294 i ! ! 1 .07 | ! ! | .93780 | ! ! I .05 | | .93977 J | .94054 | . 9 3 2 4 9 | | 1 .03 | ! ! | .94008 | 1 3.0 | j | ! j j J J .05 | .93322 J j | .93976 J .93176 | .91370 J I— x - _ -L J 1 1_ 1 j 0.05 0.08 0.09 0. 10 0. 15 0.25 | 173 2 Psc with model K12 Coherency peak at (X , £ , 8 , S ) = (0 .95,3.25,0.054,0.476) r - T " " T •"- — r - r- a | 4.0 .07 J J .93629 J | i .05 | .93276 1 .93570 ] .93611 | i I 3.5 .10 I 1 .93427 | ! j j 1 I .07 | .06 | .05 | .93395 I .93745 | | .93776 | | .93717 J .93597 \ .9 3767 | .93667 | .93473 | .9322 7 | ! .03 1 | .93093 | .93453 | ! j I 3.Q j J j j ! .07 | 1 .93691 j .93583 | .93363 { | ! • Q5 | .93360 J .93682 | .93775 | .93705 ] | ! .03 | ! ! .93482 j .93665 J | ft I 2.5 .05 | i i .93536 | | j 1 ! ...„",.• i„ • . 4 „,, ,,, f- J 0.65 0. 80 0.95 1.10 1.25 1 1.40 | 174 Z Psc with model K26 Coherency peak at <Xr^,8,S) = (0. 11,3.4 ,0. 058,0.432) 1 — ' •, - . . — T " ••• ----- j— r r " - i " r r • t 4.0 | j , j j .10 1 • { .93911 | J I I .07 | J .94058 J J l l .06 | | | .94025 | I I .05 | 1 .93911 | 1 i 1 .03 J ! ! .93300 J j !! 3.5 | j j ; j J J .10| j } .93936 | J J J . 07 | j .94081 | .94133 | .94099 | .93992 )| .06 J 1 j .94144 | .05 | .93594 | .9403 6 | .94129 | .94122 || .9378 4 | .03 | ! ! .93427 | ! .93773 J| .9390 3 | 3.0 ] j j j J || . 10 | I I .93784 | | J j .07 | .93819 | ! .94071 J ! .93926 J J .9339 5 | .05 | I J .94035 | ! .94116 I| .9380 0 | .03 | I ! I ! l l .9388 7 J f. t 1 I 0.08 0.09 0. 10 0. 1 1 0. 12 0. 15 | a 1 75 X Cnc with model K26 Coherency peak at (X,^,B,S) = (0. 17,3.8,0.032,0.345) 1 4.5 05 03 T T T T .94883 .94906 .94906 . 94449 4.0 .07 .05 .04 .03 .02 3.5 .05 .03 .02 3.0 .05 ,94531 ,94954 ,95067 ,94565 95092 95134 .95042 .95144 .94881 95072 95001 94759 94887 ,95077 ,94613 9434 8 95132 .95144 ,95058 ,94643 -XX 0. 13 0. 15 0. 16 0.17 0. 19 0.20 ~ J 176 UO Aur w i t h model K26 Coherency peak a t (X,^,B,S) * (0.14,4.8,0.040,0.351) 6.0 .05 5.5 .07 .05 .04 5.0 .07 .05 .04 .03 .94736 .94724 9476 3 ,94753 ,94873 .949 29 .94810 . 94710 . 94891 .94 893 .94944 .94 947 .94809 .94721 4.75 .07 .05 . 04 .03 4.5 .05 .94938 .94739 .94936 .94955 .94825 .94889 .94 966 .94889 94915 .94906 94772 0.10 0.11 0. 1 2 0. 13 0. 14 0. 15 1 77 Y CVn with model K12 Coherency peak at (X,^,R,S) = (1.3,5.3,0.45,0,265) % • 1 1 "i i r n 1 I 6.0 | t | | | || | | .40 i .93475 1 .93482 J .93436 | .93361 | j ( J I j. + , + + + j I 5.5 J | i | | || | | .50 | | | .93556 | | || | | .40 | | .93553 | .9356 1 | .93528 | .93498 || | I .30 | | | .93459 | | || | I 5.0 | I I I I I I I I I I I I I I I I I .50 | I I | | .93487 || | | .40 | | | . 93517 J .93521 | .93495 || . 93436 | | .30 I I I I I .93446 || | I I I I I I I I I I H _ ^ 1 i -I - H 1 I I I I I I I I I I 4.5 I I I I I I I I I I I I I I I I I I I I I I I I I I I .40 | I I I I .93293 || | I I I I I I I I I I I I I I I I I I j. i j i 1 1. i~t ( | 1.00 1.20 1.40 1.60 1.80 2.20 | t 1 178 Y CVn with model K26 Coherency peak at (X,^,R,S) = {0.20,5.0,0.40,0.200) r -j , t , 5.5 5.0 4.0 3.5 .40 | .95368 | .95364 j | | 1 T J ! ! 1 .50 | .95260 | .95401 | .95355 | 1 .40 | I .95453 | .95337 | | .30 | J .95366 1 I 1 .70 | J .95108 | .95226 | \ .50 | | .95350 | .95379 ) .95248 | .40 | j | .95340 | J .30 | | .95276 I .95171 | ] .50 | | .95116 | | .60 J J .94618 | j j .50 | .94395 | .94701 | .94740 | | .40 | | .94690 I 1 1 .30 | | .94503 1 1 1 i . . j . -JL. 1̂  J 0. 15 0 .20 0 .25 0 . 3 0 | C(0.21,4.9,0.41) C{0.22,4. 8,0.42) .95452 .95443 179 APPENDIX V PARAMETERS OF SPECIFIC MODEL ATMOSPHERES r ™' ! - ..--r- T "1 | Model i K12 | K24 ! K26 1 | T(eff) ! 3500 | 3500 I 3500 1 I log g 1 0 1 0 0 1 | He/H 1 • 1 I .1 1 -1 I 1 C/H 1 3. 55 X10-S | 3.55 x10-3 1 3.55 X10-2 | 1 N/H 1 9. 75 x 10- • J 8. 15 X1Q-* I 8.15 X10-* | 1 O/H » 1. 78 X10-5 J 7. 10 x10-» | 7.10 x10~* | 1 c/o I 2 | 5 I 50 | 1 — —i . _..„ i . . L, . . i

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