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Development of LLTV techniques for detection/analysis of spectra with application top cephei stars and… Goldberg, Bruce Arthur 1973

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n n c DEVELOPMENT OF LLTV TECHNIQUES FOR DETECTION/ANALYSIS OF SPECTRA WITH APPLICATION TO 3 CEPHEI STARS AND OTHER OBJECTS by BRUCE ARTHUR GOLDBERG B.S. Engr. (Hons), Case I n s t i t u t e of Technology, 1967 M.S., Case Western Reserve Un i v e r s i t y , 1969 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Geophysics and Astronomy We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA July 1973 In presenting t h i s thesis i n p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t freely available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Geophysics and Astronomy The University of B r i t i s h Columbia Vancouver 8, Canada Date n J u l y 1973 ABSTRACT New techniques f or the detection and analysis of astronomical spectra have been developed and applied s u c c e s s f u l l y i n a study of the s p e c t r a l v a r i a t i o n s of 6 Cephei s t a r s and other objects of a s t r o p h y s i c a l i n t e r e s t . The method involves the replacement of the photographic p l a t e as the detection and recording medium by a t e l e v i s i o n camera and an associated data a c q u i s i t i o n system, with r e s u l t i n g improvements i n s e n s i t i v i t y , p r e c i -s i o n , and f a c i l i t y of data reduction. The system l i m i t a t i o n s have been set p r i m a r i l y by the p a r t i c u l a r t e l e v i s i o n camera s e l e c t e d , with important de-f i c i e n c i e s being degraded r e s o l u t i o n and a.lim i t e d i n t e g r a t i o n c a p a b i l i t y . This paper f o l l o w s , from one viewpoint, development of the system hardware, assessment of.the system p o t e n t i a l and i t s subsequent a p p l i c a t i o n to a s t r o p h y s i c a l problems, development of the software package for optimal data r e t r i e v a l , and i n t e r p r e t a t i o n of the r e s u l t s w i t h i n the framework of current theory. The r e s u l t s and contributions are discussed under two headings: ( i ) Engineering Development and ( i i ) System A p p l i c a t i o n s . (i) Engineering Development The operation of many detectors used i n astronomy b e n e f i t s from an environment of reduced and s t a b i l i z e d temperature. Such i s the case f o r the t e l e v i s i o n detectors used i n th i s program. As a consequence, a cooling system was developed f or an Image Isocon tube, the prime detector employed. This system c i r c u l a t e s cold a i r through the yoke of the t e l e v i s i o n camera i n a closed c i r c u i t and cools the tube uniformly by forced convection. I t i i s a t i s f i e s the requirements f o r s u c c e s s f u l operation of the Isocon and has general value i n demonstrating (a) the f e a s i b i l i t y of an a i r - c o o l i n g approach i n s i t u a t i o n s of awkward geometry or unusual heat d i s s i p a t i o n and (b) that the hardware associated d i r e c t l y with a detector can be simple, compact, and inexpensive. (ii) System Applications The c a p a b i l i t y of the detection system for improved time r e s o l u -t i o n spectroscopy was of p a r t i c u l a r b e n e f i t i n examining the short-term s p e c t r a l changes i n the g Cephei s t a r s , a group distinguished by t h e i r regular v a r i a t i o n i n l i g h t and r a d i a l v e l o c i t y . The stars a V i r g i n i s ( S p i c a ) , 8 Cephei, and BW Vulpeculae, representing some of the extremes i n v a r i a b i l i t y within the group, were observed i n 1971 and 1972. The observa-tions of S p i c a , the f i r s t of the program, served to demonstrate the value of the new instrumentation f o r t h i s a p p l i c a t i o n . Marked gains were made i n the case of BW Vul where, f o r the f i r s t time, s u f f i c i e n t time and s p e c t r a l r e s o l u t i o n were attained to resolve the very rapid s p e c t r a l v a r i a t i o n s occurring at c e r t a i n phases of i t s p u l s a t i o n c y c l e . The observations made poss i b l e a more accurate determination of the dynamic properties of i t s atmosphere and c r i t i c a l t e s t s of 'models' attempt-ing to explain i t s v a r i a t i o n . A r e f i n e d p i c t u r e i s presented of t h i s v a r i -a t i o n , taking as i t s basis the shock wave 'model' of Odgers (1956). The long-term v a r i a t i o n i n BW Vul's period and i n the amplitudes of i t s l i g h t and v e l o c i t y curves were also considered. The present data, viewed i n context with that obtained over the past f i f t y years, demonstrate the existence of a pseudo-sinusoidal v a r i a t i o n i n the p u l s a t i o n p e r i o d , super-i i i imposed on a mean rate of increase of +3.7 sec/century, plus a s e c u l a r l y i n c r e a s i n g v e l o c i t y amplitude. Thus the pulsation amplitude i s also i n c r e a s i n g and the s t a r may be i n a rapid phase of e v o l u t i o n . For B Cep, the f i r s t d e f i n i t i v e record of a v a r i a t i o n i n l i n e p r o f i l e c o r r e l a t e d with i t s v a r i a t i o n i n l i g h t and r a d i a l v e l o c i t y was obtained. The r e s u l t i s c r i t i c a l to an understanding of i t s p u l s a t i o n . In summary, the main astronomical program has provided information important i n understanding the p h y s i c a l processes occurring i n the 6 Cephei stars and has demonstrated the value of a new type of instrumentation f o r studies of rapid spectrum v a r i a b l e s . iv TABLE OF CONTENTS ABSTRACT TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES ACKNOWLEDGMENTS CHAPTER 1. INTRODUCTION 1.1 INTRODUCTORY REMARKS 1.2 DEVELOPMENT OF THE DETECTION SYSTEM 1.3 COOLING THE DETECTOR 1.4 APPLICATION OF THE DETECTION SYSTEM CHAPTER 2. INSTRUMENTATION 2.1 THE DETECTION SYSTEM: A GENERAL DESCRIPTION 2.2 THE COOLING SYSTEM Design Constraints The Feasibility Study The Camera Hardware • The Cold Air 'System' Operation of the System System Control System Performance CHAPTER 3. THE ASTRONOMICAL PROGRAMS 3.1 SELECTING THE PROGRAM V 3.2 THE PROGRAM 16 3.3 OBSERVATIONAL GOALS 20 CHAPTER 4. OBSERVATION AND ANALYSIS 4.1 INTRODUCTION 21 4.2 THE 8 CEPHEI OBSERVATIONS 24 A General Description 24 The Preliminary Observations . 24 The Primary Observations 26 4.3 DATA REDUCTION AND ANALYSIS 27 Introduction 27 27ze Preliminary Data Check 27 27ze Preliminary Data Analysis 27 TTze Refinement Process 28 27ze Quantitative Analysis 28 Techniques for Resolution Enhancement and Improved Signal Extraction 32 Summary 32 CHAPTER 5. RESULTS AND DISCUSSION: THE INDIVIDUAL STARS BW VULPECULAE 5.1 INTRODUCTION 34 5.2 THE OBSERVATIONS 35 5.3 THE RADIAL VELOCITY VARIATION 35 The Velocity Curve 35 The Accuracy of the Velocities 38 The 'Van Hoof Effect' 38 The Repeatability of Successive Cycles 39 The 1971 Data , 39 v i 5.4 THE LINE PROFILE VARIATION 42 5.5 THE LIGHT VARIATION 51 5.6 THE VARIATIONS IN RADIUS AND ACCELERATION 54 5.7 DISCUSSION 59 Introduction 59 Previous Interpretations 60 The Role of Shock Waves 61 A Refined Interpretation 67 The Line Doubling Phase Preceding Stillstand 71 5.8 THE LONG-TERM VARIATIONS 72 Introduction 72 Variation in the Period 72 Amplitude Variations in the Light and Radial Velocity Curves 73 Summary 76 5.9 FUTURE WORK 77 g CEPtfEI 5.50 INTRODUCTION _ 78 5.15 TtfE NEW DATA 80 5.22 Tffi? LONG-TERM VARIATION 81 5.53 FUTURE WORK 85 CHAPTER 6. ' SUMMARY AND CONCLUSIONS 86 BIBLIOGRAPHY 92 v i i APPENDIX A. EXPERIMENTAL ANALYSIS OF THE COOLING SYSTEM 97 B. DESCRIPTION OF THE COOLING SYSTEM HARDWARE 98 C. THE RECTIFICATION PROGRAM 101 D. THE VARIATION IN EFFECTIVE DISPERSION ACROSS THE SCANNING RASTER 105 E. SHOCK WAVE COMPUTATIONS FOR BW VUL 106 v i i i LIST OF TABLES Table 4.1 Observed p h y s i c a l properties of the program s t a r s 22 a V i r g i n i s , BW Vulpeculae, and 8 Cephei Table 4.II General features of the 8 Cephei observations 25 Table 5.1 Observations of BW Vul 36 Table 5.II Observations of 8 Cep 82 ix LIST OF FIGURES F i g . 2.1 Geometry of the Isocon and camera yoke plus the 6 method of read-out. The target i s scanned s e q u e n t i a l l y perpendicular to the d i r e c t i o n of d i s p e r s i o n . Two spectra may be accommodated. For the present program, a target background l e v e l i s obtained at the p o s i t i o n of the second spectrum. F i g . 2.2 Schematic of the c o o l i n g system. 12 F i g . 4.1 A sample a p p l i c a t i o n of the data processing techniques. 33 A l l spectra shown are centered on the same epoch. They are: (A) a s i n g l e frame normalized; (B) the mean of 8 frames normalized (a one-minute e f f e c t i v e exposure); (C) the mean of 24 frames normalized; (D) the mean of 24 frames r e c t i f i e d and low-pass f i l t e r e d ; (E) the mean of 24 frames r e c t i f i e d , low-pass f i l t e r e d , and deconvolved. The h o r i z o n t a l s c a l e has al s o been expanded i n the case of (D) and ( E ) . F i g . 5.1 Radial v e l o c i t i e s f o r BW Vul on 9 August 1972 UT: 1.1 37 cycl e of the p u l s a t i o n . A hollow c i r c l e i n d i c a t e s the v e l o c i t y of the weaker component of a s p e c t r a l l i n e where two components are present. A bar over the c i r c l e i n d i -cates that the r e s u l t i s u n c e r t a i n . F i g . 5.2 Radial v e l o c i t i e s f o r BW Vul on 9 August 1972 UT: 40 the phases of r a p i d v a r i a t i o n preceding s t i l l s t a n d . Successive cycles are shown. F i g . 5.3 Radial v e l o c i t i e s f o r BW Vul on 8 August 1971 UT: 41 the phases of rap i d v a r i a t i o n preceding s t i l l s t a n d . F i g . 5.4 Radial v e l o c i t i e s f o r BW Vul on 9 August 1971 UT: 41 the phases of rapid v a r i a t i o n preceding s t i l l s t a n d . F i g . 5.5 Line p r o f i l e s f o r BW Vul on 9 August 1972 UT: 43 the v a r i a t i o n over approximately one c y c l e . F i g . 5.6 Line p r o f i l e s f o r BW Vul on 9 August 1972 UT: 44 a demonstration of the extremes i n v a r i a b i l i t y over one c y c l e . F i g . 5.7 The v a r i a t i o n i n l i n e depth over 1.1 c y c l e f o r BW Vul 45 on 9 August 1972 UT. X F i g . 5.8 Line p r o f i l e s f o r BW Vul on 9 August 1972 UT: 47 the phases of rapid v a r i a t i o n preceding s t i l l s t a n d f o r the f i r s t c y c l e . F i g . 5.9 Line p r o f i l e s f o r BW Vul on 9 August 1972 UT: 48 the phases of rapid v a r i a t i o n preceding s t i l l s t a n d f o r the second c y c l e . F i g . 5.10 Deconvolved l i n e p r o f i l e s f o r BW Vul on 9 August 1972 49 UT: the phases of rapid v a r i a t i o n preceding s t i l l s t a n d f o r the f i r s t c y c l e . F i g . 5.11 Line p r o f i l e s f o r BW Vul on 9 August 1971 UT: 50 the phases of rapid v a r i a t i o n preceding s t i l l s t a n d . F i g . 5.12 In t e n s i t y r a t i o s of the l i n e components.for the phases 52 of rapid v a r i a t i o n preceding s t i l l s t a n d f o r BW Vul on 9 August 1972 UT. F i g . 5.13 Equivalent widths f o r the phases of rapid v a r i a t i o n 53 preceding s t i l l s t a n d f o r BW Vul on 9 August 1972 UT. F i g . 5.14 In d i v i d u a l observations of the brightness v; and of 55 the Stromgren indices (u-u) , (v-b), and (b-y) f o r B W V u l . Taken from Kubiak (1972, p. 23). F i g . 5.15 In d i v i d u a l observations of the Stromgren [C-^l index. 55 The broken curve i s the adopted mean. Taken from Kubiak (1972, p. 27). F i g . 5.16 The displacement curve f or BW Vul on 9 August 1972 56 UT: 1.1 cycle of the p u l s a t i o n . A hollow c i r c l e i n d i c a t e s the displacement obtained from the weaker component of a s p e c t r a l l i n e when two components are present. A bar over the c i r c l e i ndicates that the r e s u l t i s uncertain. F i g . 5.17 The a c c e l e r a t i o n curve f o r BW Vul on 9 August 1972 UT: 57 1.1 cycle of the p u l s a t i o n . A hollow c i r c l e i n d i c a t e s the a c c e l e r a t i o n obtained from the weaker component of a s p e c t r a l l i n e when two components are present. F i g . 5.18 T h e o r e t i c a l p r o f i l e s f o r a star undergoing non-radial 62 o s c i l l a t i o n s i n Ledoux's (1951) mode. The abscissa i s AA/AA (or V/V s i n i ) , where AA i s the r o t a t i o n a l R e K width defined as AA R = A(Ve s i n i / c ) ; V e denotes the equa t o r i a l r o t a t i o n a l v e l o c i t y , i the i n c l i n a t i o n of i t s equator to the c e l e s t i a l plane (90° f o r t h i s case), and c the v e l o c i t y of l i g h t . The ordinate uses an a r b i t r a r y scale and $ i s the phase. A ' t y p i c a l ' r e s u l t from Osaki (1971, p. 488). XX F i g . 5.19 The r a d i a l v e l o c i t y curve corresponding to the l i n e 62 p r o f i l e s given i n F i g . 5.18. Taken from Osaki (1971, p. 489). F i g . 5.20 T h e o r e t i c a l r a d i a l v e l o c i t y curves; A and B r e s p e c t i v e l y 66 represent the cases f o r a = 0 and a = 0.2, where a i s the r a t i o of r a d i a t i o n pressure to the gas pressure. The observations of Odgers (1956) during the c y c l e begin-ning J.D. 2435009.760 are represented by s o l i d dots. Taken from Bhatnagar et a l . (1971, p. 136). F i g . 5.21 The same as F i g . 5.20 but with the e f f e c t s of a 2.1 66 Gauss magnetic f i e l d included. Taken from Bhatnagar et a l . (1971, p. 136). F i g . 5.22 A summary of the observed features of the v a r i a t i o n 69 of BW V u l . F i g . 5.23 The v a r i a t i o n i n the period of BW Vul as indicated 74 by the phase of V^-crossing, p l o t t e d against the square of the time elapsed since J.D. 2428000. The l i n e represents the r e l a t i o n found by P e t r i e (1954) to f i t the observations of 1924-1952; the data are based on observations made since 1952 (the hollow c i r -c l e s are from the present program). The Figure i s taken from Percy (1971). F i g . 5.24 The v a r i a t i o n i n the r a d i a l v e l o c i t y amplitude (2K) 75 f o r BW V u l . The v e r t i c a l bars i n d i c a t e the range i n the observed amplitude i n a s i n g l e year i f there were more than one observation; the dots are the mean. Observations through 1952 are from P e t r i e (1954); from 1953 to 1954 from Odgers (1956), from 1966 from Kubiak (1972), and from 1971 to 1972 from the present program. F i g . 5.25 Line p r o f i l e s f or B Cep on 16 October 1972 UT. Only 83 a p o r t i o n of the observations are shown. F i g . 5.26 Measures of the r a d i a l v e l o c i t y , l i n e asymmetry, and l i n e 84 depth f o r 6 Cephei. The asymmetries of the l i n e s are in d i c a t e d by the d i f f e r e n c e between the angle of a s t r a i g h t l i n e f i t t e d through the red side of the pro-f i l e and one through the blue. x i i ACKNOWLEDGMENTS I am g r a t e f u l to my supervisor (and the project d i r e c t o r ) Dr. G.A.H. Walker, f or the opportunity to work with the instrumentation and f o r providing me with f i n a n c i a l support (through a National Research Council of Canada grant) throughout the program. His many h e l p f u l and stimulating discussions were g r e a t l y appreciated. P a r t i c u l a r thanks go to Dr. Z. Rotem of the Department of Mechanical Engineering f o r h i s help and guidance at v i r t u a l l y every stage of the program, and to Drs. G.J. Odgers and K.O. Wright of the Dominion As t r o p h y s i c a l Observatory f o r t h e i r encouragement and i n t e r e s t during the astronomical phases. I would also l i k e to thank Dr. Wright f o r h i s gen-erous c o n t r i b u t i o n of observing time on the D.A.O. telescopes. During the instrumental design stages, Dr. Rotem and Dr. A.C. Pinchak of Case Western Reserve U n i v e r s i t y provided many h e l p f u l sugges-t i o n s . During the construction phases, K.D. Schreiber, B.C. Isherwood, and V. Buchholz of the Department of Geophysics and Astronomy gave w i l l i n g and valuable a s s i s t a n c e . I am pleased to thank Dr. G. H i l l of the D.A.O. f o r h i s valuable advice concerning the astronomical program ( p a r t i c u l a r l y during i t s early s t a g e s ) , to Drs. M.W. Ovenden and J.R. Auman, J r . , f o r t h e i r many h e l p -f u l suggestions, to Dr. J . Glaspey f o r h i s p a r t i c i p a t i o n i n obtaining the observations, and to Drs. T.J. Ulrych and H. Fast f o r t h e i r assistance i n the data processing. Mrs. R. Rumley and Miss J . Bercov deserve c r e d i t f o r t h e i r e f f o r t s i n typing t h i s paper, as does Mr. S. Mochnacki f o r h i s help with the preparation of the tables and f i g u r e s . A program of th i s type i s i n several respects a team e f f o r t . I am indebted to many others f o r t h e i r contributions to i t s success. 1 CHAPTER 1. INTRODUCTION 1.1 INTRODUCTORY REMARKS One of the goals of astronomy has been to obtain a detector that could respond i n a completely p r e d i c t a b l e fashion to all electromagnetic r a d i a t i o n i n c i d e n t upon i t i n a desired s p e c t r a l region and provide an out-put s u i t a b l e f o r analysis and i n t e r p r e t a t i o n . In the v i s i b l e region of the spectrum, the photographic p l a t e i s the mainstay of astronomical detectors; representing a tremendous improve-ment i n most a p p l i c a t i o n s over i t s predecessor, the human eye. I t s strength l i e s i n i t s i n t e g r a t i o n c a p a b i l i t y and i t s huge storage capacity; i t s weak-ness i n i t s poor quantum e f f i c i e n c y (about one p e r c e n t ) , i t s l i m i t e d dynamic range, and i t s somewhat unpredictable and d i f f i c u l t to c a l i b r a t e response. In a d d i t i o n , considerable e f f o r t i s frequently required to recover i t s store of information. Advances i n detectors and detection systems have followed three avenues: ( i ) attempts at improving the photographic p l a t e ; ( i i ) attempts at developing instrumentation to complement i t ; and ( i i i ) attempts at r e -p l a c i n g i t e n t i r e l y . Better emulsions and processing techniques f a l l i nto the f i r s t category, image i n t e n s i f i e r s i n t o the second, and photomultipliers in t o the l a s t ; while t e l e v i s i o n and electronographic techniques may come under more than one. These e f f o r t s , have generally resulted i n moderate gains with few r e s t r i c t i o n s (as with improved emulsions), or large gains with s u b s t a n t i a l r e s t r i c t i o n s (as with image i n t e n s i f i e r s ) . I f the i d e a l i s to be approached, the photographic plate as we know i t must be supplanted. No s i n g l e detector 2 or system yet devised has the necessary f l e x i b i l i t y to do so. The most promising candidates are the re c e n t l y developed l o w - l i g h t - l e v e l t e l e v i s i o n detectors and the electronographic techniques, with current trends i n t e c h -nology favoring the t e l e v i s i o n approach ( L i v i n g s t o n , 1973; Carruthers, 1971). Indeed, some of the t e l e v i s i o n detectors now being developed ( p a r t i c u l a r l y those employing photoemissive devices) may come close to achieving t h i s goal. I t i s c l e a r that the development of t e l e v i s i o n detectors and t h e i r associated systems represents an important phase i n the development of a s t r o -nomical instrumentation. This paper follows one such system from the i n i t i a l design stages through i t s successful a p p l i c a t i o n to a s t r o p h y s i c a l problems. The disc u s s i o n ranges from the i n i t i a l engineering contributions through the i n t e r p r e t a t i o n of the astronomical data obtained from the working system. Emphasis i s placed on the development of one major po r t i o n of the i n s t r u -mentation, on the b a s i c problems encountered i n applying the system and the methods of t h e i r s o l u t i o n , on the astronomical r e s u l t s , and on the avenues f o r future work i n using the instrumentation and i n t e r p r e t i n g the r e s u l t s . 1.2 DEVELOPMENT OF THE DETECTION SYSTEM The present system i s comprised of a l o w - l i g h t - l e v e l t e l e v i s i o n camera and i t s associated instrumentation: the camera c o n t r o l u n i t , the camera cooling system, and the data a c q u i s i t i o n system. The prime detector has been an English E l e c t r i c P850 Image Isocon tube i n a modified Marconi TF1709 camera. Major hardware development has followed the d i v i s i o n s j u s t i n d i -cated. The camera c o n t r o l unit has been discussed by Buchholz (1972), the data a c q u i s i t i o n system by Isherwood (1971), and the camera cooling system 3 Goldberg et a l . (1973b). The system i s discussed further i n Chapter 2, with the cooling system as a separate t o p i c . 1.3 COOLING THE DETECTOR Cooling of the Isocon was necessary f o r i t s intended a p p l i c a t i o n to problems of s t e l l a r spectroscopy. The design r e s t r i c t i o n s , coupled with the awkward geometries of the Isocon and i t s associated t e l e v i s i o n camera, made development of a s u i t a b l e cooling system d i f f i c u l t . The adopted system represents a novel approach to cooling detectors of t h i s type. 1.4 APPLICATION OF THE DETECTION SYSTEM The observational program was selected on the basi s of astrophys-i c a l merit and the perceived advantages and l i m i t a t i o n s of the instrumenta-t i o n . The system showed promise of o f f e r i n g s u b s t a n t i a l gains i n the area of h i g h - d i s p e r s i o n , high-time-resolution spectroscopy; and thus appeared w e l l s u i t e d f o r studies of rapid spectrum v a r i a b l e s . On t h i s b a s i s , a study of the s p e c t r a l v a r i a t i o n s of the 8 Cephei stars (and a d d i t i o n a l objects as circumstance would permit) was i n i t i a t e d , with the i n t e n t i o n of f i l l i n g the gaps l e f t by t r a d i t i o n a l observational techniques. A general discussion of the program i s given i n Chapter 3, the observational r e s u l t s and t h e i r i n t e r p r e t a t i o n are presented i n Chapters A and 5. 4 CHAPTER 2. INSTRUMENTATION 2.1 THE DETECTION SYSTEM: A GENERAL DESCRIPTION The detection system has been discussed i n d e t a i l by Walker et a l . (1971, 1972), the operation of the Image Isocon by Nelson (1969), and the Modulation Transfer Function (MTF) of the system by Buchholz (1972). The Isocon has an S-20 photocathode with a peak quantum e f f i -o ciency of about 10 percent, a t y p i c a l r e s o l u t i o n of 0.2 mm (about 0.5 A o at a d i s p e r s i o n of 2.4 A/mm) over a usable target length ( i . e . , i t s diameter) of ^70 mm, and a l i n e a r dynamic range of ^100:1.* With cooling to 0°C i n order to reduce noise l e v e l s and maintain r e s o l u t i o n , i n t e g r a t i o n f o r p e r i -ods of up to four minutes i s p o s s i b l e . Spectra are imaged on the photocathode, from which photoelectrons are emitted to form a r e l a t e d charge pattern on a t h i n glass t a r g e t . A f t e r an exposure time s u f f i c i e n t f o r adequate charge accumulation(the i n t e g r a t i o n p e r i o d ) , the target i s scanned s e q u e n t i a l l y normal to the d i r e c t i o n of s p e c t r a l d i s p e r s i o n by an e l e c t r o n beam. The p o r t i o n of the beam that i s 'scattered' from the target** i s amplified i n a dynode chain and c o n s t i t u t e s the tube output, which i s sampled and d i g i t i z e d at each passage of the reading beam across the [charge] spectrum. For purposes of c a l i b r a t i o n , a measure of the target 'background' i s also obtained i n t h i s fashion. Effective exposure times are determined on the basis of the number of i n d i -v i d u a l read-outs (or frames) that must be averaged point by point to achieve *The effective dynamic range is based on a lower bound set by the onset of non-linearities at low l i g h t levels and an upper bound fixed by target s a t u r a t i o n . The working range i s roughly half the effective range. **The remainder of the beam i s e i t h e r n e u t r a l i z e d by the p o s i t i v e charge on the target or specularly r e f l e c t e d and subsequently screened out. 5 an acceptable signal-to-noise r a t i o . The geometry of the Isocon and the camera yoke plus the method of read-out are i n d i c a t e d i n Figure 2.1. Hie output of the system i s a uni-dimensional d i g i t a l representa-t i o n of the l i g h t i n t e n s i t y d i s t r i b u t i o n on the photocathode of the Isocon which Is stored on 9-track, IBM 360 compatible magnetic tape v i a an Inter-data Model Four mini computer. The number of data points (or channels) representing a spectrum and the effective dispersion i n points per angstrom are dependent on both the c o n f i g u r a t i o n of the scanning r a s t e r and the spectrograph d i s p e r s i o n . For the observations discussed here, the number of channels was between 680 and 900, and the spectrograph d i s p e r s i o n between 0.5 A/mm* and 2.4 A/mm. Further information concerning the system output i s given i n Section 4.3. A s i l i c o n - t a r g e t (S-T) v i d i c o n (RCA No. 4532A) was also used f o r some of the observations. The v i d i c o n has e x c e l l e n t red s e n s i t i v i t y (the peak i n responsivity being at ~7000 A) , much higher r e s o l u t i o n than the Isocon ('vSOu) , but a smaller ' c o l l e c t i n g ' area ('v.62-inch diameter). Neither the tube nor the observational r e s u l t s obtained with i t (which were of a preliminary nature) w i l l be discussed i n any d e t a i l . The method of read-out i s s i m i l a r to that of the Isocon. 2.2 THE COOLING SYSTEM Design Constraints The p r i n c i p a l reasons f o r cooling the Isocon were twofold: ( i ) to increase the target r e s i s t i v i t y i n order to prevent charge d i f f u s i o n *0btained with a 5X t r a n s f e r lens developed by E.H. Richardson of the D.A.O. 6 Focus i ng Co iI Target Mesh DefIect1ng CoiIs Photocathode Dynode Cha i n Anode >/////////////////////////777Z\ Spectra / 1 1 1 1 ; 1 / / 1 1 1 1 1 l / / 1 1 1 1 1 1 1 1 1 i 1 1 I I 1 1 i l i 1 I / / 1 1 1 1 1 1 i l f 1 1 l 1 i l Scanning Raster F i g . 2.1 Geometry of the Isocon and camera yoke plus the method of read-out. The target i s scanned s e q u e n t i a l l y perpendicular to the d i r e c t i o n of d i s p e r s i o n . Two spectra may be accommodated. For the present program, a target background l e v e l i s obtained at the p o s i t i o n of the second spectrum. 7 during extended i n t e g r a t i o n times (which r e s u l t s i n a serious d e t e r i o r a t i o n of the MTF) and ( i i ) to reduce thermal background noise which i s due to random e l e c t r o n emission at the photocathode, the scanning beam gun, and the dynode chain. A d i s c u s s i o n of the e f f e c t s of cooling on a t h i n glass t a r -get such as that found i n the Isocon has been given by L i v i n g s t o n (1963). An operating temperature of +10°C i s suggested f o r achieving optimum r e s o l u t i o n under 'normal' c o n d i t i o n s , with a lower operating l i m i t of about - 5 0° C . I f the target i s operated at too low a temperature, the problem of remnant images ('sticking') occurs. Its s e v e r i t y increases with the t o t a l charge i n v o l v e d . However, i t can be reduced by exposing the tube to a souce of r e l a t i v e l y high i l l u m i n a t i o n f o r brief time I n t e r v a l s . The optimum operating temperature i s c l e a r l y dependent on the a p p l i c a t i o n . For the case i n p o i n t , the b a s i c cooling requirements were to achieve an optimum target temperature for the periods of astronomical observation, and to keep the remainder of the tube at a s u f f i c i e n t l y low temperature to reduce the thermal background noise to n e g l i g i b l e l e v e l s . I n i t i a l l y i t was thought to be about 0°C but l a t e r found to be somewhat lower. A d d i t i o n a l considerations were the cool-down time, the temper-ature s t a b i l i t y , and the constraints on the s i z e and weight of the camera, d i c t a t e d by i t s p o t e n t i a l use at the Cassegrain focus of a telescope. A maximum cool-down time of approximately one hour was set by considerations of convenience and a minimum cool-down time by considerations of st r e s s (namely that the maximum temperature d i f f e r e n t i a l between any two points on the tube surface not exceed 11°C) . Temperature s t a b i l i t y to b e t t e r than 3°C at the operating temperature was required. Some of the improve-8 ments r e a l i z e d i n cooling the Isocon have been considered i n the ana l y s i s of the system MTF mentioned p r e v i o u s l y . I t was further required that the e n t i r e system be p o r t a b l e , economical, operable under normal observatory c o n d i t i o n s , and that the coolant be r e a d i l y obtainable. The Feasibility Study A f e a s i b i l i t y study was undertaken i n i t i a l l y to determine the most reasonable cooling approach.* The design constraints eliminated the p o s s i b i l i t y of using 'conventional' methods such as a cold box. In a d d i t i o n , the close tolerance between camera yoke and tube plus the sub-s t a n t i a l heat generation i n the yoke made l i q u i d c o oling i m p r a c t i c a l w i t h -out major modifications to the camera. A forced-convection system using a i r or a s i m i l a r gas as coolant c i r c u l a t e d between yoke and tube appeared to o f f e r the best a l t e r n a t i v e . Three coolants were considered: ( i ) l i q u i d nitrogen vapor; ( i i ) freon which had undergone expansion c o o l i n g ; ( i i i ) a i r which had passed through a heat exchanger containing a c o o l i n g f l u i d . The f i r s t two were eliminated because of expense and/or t h e i r l i m i t e d a v a i l a b i l i t y . A model tube was constructed by J . Lees of the U.B.C. Physics Department ( l a t e r to be replaced by a r e a l , substandard tube), instrumented with copper-constantan thermocouples and in s e r t e d i n t o the camera. The camera was sealed and l i q u i d nitrogen vapor pumped through i t . Flow rates were measured using a DISA hot-wire anemometer ( c a l i b r a t e d i n the large *The o r i g i n a l camera had no s p e c i a l p r o v i s i o n f o r cooling other than a small t h e r m o s t a t i c a l l y - c o n t r o l l e d fan to prevent over-heating (the standard operating temperature was ^ 7 5 ° F ) . **Type 55D50. subsonic wind tunnel of the U.B.C. Mechanical Engineering Department), temperatures and temperature d i f f e r e n t i a l s were determined from thermo-couple outputs, and flow patterns charted by smoke tracers observed through a window over the photocathode. Temperatures were measured as a function of time f o r a v a r i e t y of flow rates and hardware c o n f i g u r a t i o n s . In p a r t i c -u l a r , close a t t e n t i o n was given to the v a r i a t i o n i n temperature over the photocathode as a function of the separation between i t and the adjacent imaging o p t i c s . A schematic of the test instrumentation and r e s u l t s of the i n i t i a l measures are given i n Appendix A. The experimental work during t h i s stage was supplemented by a t h e o r e t i c a l a nalysis of heat tra n s -f e r r a t e s , flow r a t e s , and flow patterns, aimed at providing the q u a n t i -t a t i v e information necessary f o r s e l e c t i n g the system components and optimizing the hardware c o n f i g u r a t i o n s . Emphasis was placed on understand-ing the heat loading w i t h i n the system, the pressure losses i n the airstream and the flow patterns needed for uniform cooling of the Isocon. The f e a s i b i l i t y study indicated that the a i r - c o o l i n g approach could s a t i s f y the operational requirements wi t h i n the framework of the design c o n s t r a i n t s . The next stage was to f i n a l i z e the hardware c o n f i g u r -ations associated with the camera and to develop the equipment necessary f o r the r e q u i s i t e production of cold a i r . The system components and t h i s part of the development are described i n the following s e c t i o n s . The Camera Hardware The cooling system components associated d i r e c t l y with the camera were designed to f i t w i t h i n i t s o r i g i n a l housing. These consisted of i n l e t and o u t l e t flow manifolds, flow chambers, c o n t r o l valves and s e a l i n g devices 10 mounts f o r the imaging o p t i c s (integrated with one of the o u t l e t flow chambers) and temperature and pressure sensors. M a t e r i a l s e l e c t i o n was based on requirements f o r low thermal c o n d u c t i v i t y , a low c o e f f i c i e n t of thermal expansion, dimensional s t a b i l i t y , m a c h i n a b i l i t y , and c o m p a t i b i l i t y with other system hardware. A cotton cloth-phenolic laminate ( T a y l o r i t e , Grade CE) was found to s a t i s f y these requirements, as w e l l as the r e q u i r e -ment of a v a i l a b i l i t y . Most camera s e a l i n g was based on the use of rubber 0-rings, sometimes applied i n a non-standard f a s h i o n . Working drawings of some of the components are given i n Appendix B. The Cold-Air 'System' In p r i n c i p l e , t h i s p o r t i o n of the system need only include a pump for c i r c u l a t i n g a i r and a heat exchanger f o r c o o l i n g i t . The p r a c t i c a l demand f o r a smooth, dry, clean flow of a i r at s u f f i c i e n t head to overcome the pressure losses through the e n t i r e system d i c t a t e d the use of several a d d i t i o n a l components. The s p e c i f i c flow requirement at the pump was 8 CFM @ 5 PSIG. Se l e c t i n g an a i r pump represented the major d i f f i c u l t y . A survey was made of the a v a i l a b l e u n i t s , and experimental tests of a vortex (Ranque-Hils c h ) tube, c e n t r i f u g a l blower, and an assortment of fans were c a r r i e d out. A r o t a r y , graphite-vane compressor (Gast Model 1550) was f i n a l l y chosen, being an o f f - t h e - s h e l f item and meeting the general project requirements. The compressor had the unpleasant side e f f e c t s of i n j e c t i n g graphite par-t i c l e s i n t o the airstream, introducing s u b s t a n t i a l flow p u l s a t i o n s , and r a i s i n g the a i r temperature s i g n i f i c a n t l y (an unavoidable consequence of a i r compression).* To counteract these problems i t was necessary to i n t r o -*The adiabatic temperature r i s e f or a i r i s ^ 9 ° F per PSI during compression. 11 duce a vibration-damper, an a f t e r c o o l e r (a water-cooled heat exchanger at the compressor o u t l e t ) , and f i l t e r s into the system. For primary cooling of the airstream, a heat exchanger using a copper c o i l (made of 1-inch diameter copper tubing) submersed i n a bath of methanol cooled by s o l i d CC^ was constructed. When the ambient temperature was below about 7 5°F , the e x i t temperature of the a i r was s u f f i c i e n t l y low to accommodate the temperature r i s e through the system between heat ex-changer and camera. Water condensing or f r e e z i n g out of the airstream due to cooling e i t h e r remained i n the c o i l of the primary heat exchanger (as ice) or was removed by two vortex t r a p s , one following each of the two heat exchangers. This p o r t i o n of the system was constructed as a s i n g l e u n i t ; a l l components mounted on a Dexion frame with the compressor and motor i s o -l a t e d by v i b r a t i o n dampers. Operation of the System A schematic of the cooling system i s shown i n Figure 2.2. An o u t l i n e of the operation of the system following that given by Goldberg et a l (1973b) i s now given. The system c i r c u l a t e s c o l d , f i l t e r e d a i r i n an e s s e n t i a l l y closed c i r c u i t . From the po r t i o n of the system described i n the previous s e c t i o n , the a i r i s ducted to the camera by heavily i n s u l a t e d , low-temperature Tygon tubing (length V>0 feet) and i s i n j e c t e d i n t o the t o r o i d a l air-space between camera yoke and tube near the target. The flow i s drawn o f f tan-g e n t i a l l y from both front and rear ends of the camera through t o r o i d a l e x i t chambers and returns to the compressor. The aerodynamic properties of the t e l e v i s i o n camera are u t i l i z e d to reduce temperature d i f f e r e n t i a l s across the 12 O U T L E T F I L T E R , P U L S A T I O N DAMPER A I R COMPRESSOR I N L E T F I L T E R 3 C WATER-COOLEt HEAT EXCHANGER ' F I L T E R -S E P A R A T O R T E M P . READOUT P R E S S U R E READOUT DRY I C E -ALCOHOL HEAT EXCHANGER P R O P O R T I O N A L T E M P E R A T U R E C O N T R O L L E R F I L T E R -S E P A R A T O R CONTROL R E H E A T E R : H E A T I N G T A P E O U T L E T MAN I FOLD I S O C O N T E L E V I S I ON CAMERA I N L E T MAN I FOLD Fig. 2.2 Cooling system schematic. 13 tube and to counteract the e f f e c t s of heat generation i n the camera yoke. Uniform l o n g i t u d i n a l c o o l i n g i s ensured by the a x i a l symmetry of the flow pattern and the r e l a t i v e l y high flow rate through the camera body. Cooling of the photocathode i s accomplished by a secondary convective flow induced by the e x i t i n g vortex flow at the photocathode edge. The i n v e s t i g a t i o n of the flow pattern and heat t r a n s f e r rate there showed the ef f e c t i v e n e s s of t h i s convective flow to be dependent upon the separation between photo-cathode and imaging o p t i c s , with the optimum about 5 mm. A safe cooling rate allows e q u i l i b r i u m to be reached i n les s than one hour, with temper-ature d i f f e r e n t i a l s across the tube not exceeding 5°C . Thermocouples set i n the camera i n l e t and o u t l e t and a pressure transducer at the i n l e t ( E d c l i f f e Model 4-105-5D) allow checks of system performance. System Control Close temperature s t a b i l i t y can be maintained by a c o n t r o l re-heater c o n s i s t i n g of a heating tape switched by a proportional-type temper-ature c o n t r o l l e r (Howe et a l . , 1969). The c o n t r o l l e r i s a c t i v a t e d from a platinum res i s t a n c e sensor i n the i n l e t manifold. An i n d i c a t i o n of the thermal t r a n s f e r function (see, e.g., Kutz, 1968) of the system was obtained experimentally by t e s t i n g i t s s t a b i l i t y against various temperature changes. The system as a whole, as w e l l as the tube i t s e l f , has a s u b s t a n t i a l thermal i n e r t i a . This i s a s i t u a t i o n of inherent s t a b i l i t y but one where prec i s e temperature c o n t r o l can be d i f f i c u l t i f there i s a sudden change of temperature. In t h i s case, the ambient temperature generally changes by only a small amount over r e l a t i v e -l y long periods of time and the heat exchanger can be operated at nearly constant temperature; making the system so stable under most circumstances 14 that active temperature c o n t r o l i s unnecessary. When i t i s re q u i r e d , the arrangement described proves s a t i s f a c t o r y . The response of the co n t r o l system i s r a p i d and there i s l i t t l e overshoot. The temperature probe mon-i t o r s the airstream as i t enters the camera and temperature adjustment i s made by heating the a i r at an upstream point not so f a r removed that there i s s i g n i f i c a n t thermal l a g . Temperature c o n t r o l of the airstream entering the camera ensures a stable tube temperature. The control system is not the limiting factor in the system stability. System Performance E s s e n t i a l l y a l l the design requirements were met and the system has performed i n a generally s a t i s f a c t o r y fashion f o r more than two years. I t has at present a few important flaws due to unforeseen problems: on occasion the ambient temperature has exceeded 75°F preventing cooling to desired l e v e l s ; and under conditions of extreme humidity icing-up w i t h i n the primary heat exchanger has occurred due to incomplete system s e a l i n g , with consequent losses i n pressure. The present system must, however, be considered a prototype, and i t would be r e l a t i v e l y simple to a l l e v i a t e the problems. The required improvements would be a lar g e r c o i l i n the primary heat exchanger, more complete system s e a l i n g , and more e f f i c i e n t vapor t r a p s . Besides serving i t s function i n cooling the Isocon, the cooling system has demonstrated that the a i r - c o o l i n g approach can o f f e r an a t t r a c -t i v e s o l u t i o n i n s i t u a t i o n s of awkward geometry or unusual heat d i s s i p a t i o n . I t d i f f e r s from most other cooling apparatus used for astronomical detectors by separating most of the usually bulky cooling system hardware from the detector i t s e l f - a more f l e x i b l e and convenient arrangement. 15 CHAPTER 3. THE ASTRONOMICAL PROGRAM 3.1 SELECTING THE PROGRAM At the time the astronomical program was chosen, the general operating c h a r a c t e r i s t i c s of the detection system and the s e n s i t i v i t y and r e s o l u t i o n of the Isocon were 'known' from p r i n t e d s p e c i f i c a t i o n s and i n i t i a l t e s t runs (some at the D.A.O. 48-Inch, the telescope to be used f or the prospective program) . I t was c l e a r that a c e r t a i n degree of photometric p r e c i s i o n could be achieved, the pr e c i s e degree dependent on c e r t a i n e l u s i v e q u a n t i t i e s such as the instrumental s t a b i l i t y and s c a t t e r i n g e f f e c t s w i t h i n the Isocon. I t was not at a l l c l e a r what the ultimate i n t e g r a t i o n c a p a b i l -i t i e s would be. This information - or lack of i t - made a p p l i c a t i o n s r e q u i r i n g long i n t e g r a t i o n s or prec i s e q u a n t i t a t i v e spectroscopy u n c e r t a i n . I t did ind i c a t e that use of the detection system could b r i n g about a considerable reduction i n exposure time r e l a t i v e to the photographic p l a t e or spectrum scanner. In l i g h t of the burgeoning i n the study of rapid l i g h t v a r i a t i o n s of many kinds of objects and the knowledge that many of these objects d i s -play (or should display) spectrum v a r i a t i o n s as w e l l , i t appeared that the new system could make a r e a l c o n t r i b u t i o n i n the f i e l d of high-time-resolu-t i o n spectroscopy. In a d d i t i o n , t h i s a p p l i c a t i o n would lend i t s e l f to d i f f e r e n t i a l measurement techniques, e x p l o i t i n g the data handling c a p a b i l -i t i e s of the system while subjugating i t s possible (and probable) s h o r t -comings . 16 3.2 THE PROGRAM I t was f e l t that the new instrumentation could be used to advan-tage i n a study of the 6 Cephei (or 8 Canis Majoris) s t a r s ; a small group of e a r l y B stars thought to be p u l s a t i o n a l l y unstable and characterized by short-period v a r i a t i o n s i n l i g h t and v e l o c i t y . In the H-R diagram, they are located i n a s t r i p p a r a l l e l to and about one magnitude above the main sequence, extending from = -3 to above = -5.5. The group can be broken i n t o two major d i v i s i o n s : those having a known v e l o c i t y v a r i a t i o n (the ' c l a s s i c a l 8 Cephei stars') and those having a known l i g h t v a r i a t i o n . The former are slow rotators which follow a f a i r l y well-defined p e r i o d -luminosity r e l a t i o n ; the l a t t e r , f o r the most part discovered by H i l l (1966, 1967), are rapid rotators which apparently do not. The i d e n t i f i c a t i o n of several members of t h i s l a t t e r group as 8 Cephei stars i s somewhat unc e r t a i n . The 8 Cephei stars are b r i g h t , many being 'naked-eye' s t a r s . Their general c h a r a c t e r i s t i c s have been reviewed by Struve (1955a), U n d e r h i l l (1966), Percy (1967), and van Hoof (1970), among others. Within the class as presently defined, there e x i s t many large d i f f e r e n c e s . Projected r o t a t i o n a l v e l o c i t i e s vary from near 0 to more than 250 km/sec, p u l s a t i o n a l v e l o c i t y amplitudes from near 0 to more than 200 km/sec, l i g h t v a r i a t i o n s from a few hundredths to several tenths of a h h magnitude, and 'pulsation' period from l e s s than 4 to more than 7 . The range i n luminosity c l a s s i s lb to V; i n temperature cla s s i t i s from 09.5 to B3. Some of these stars are s i n g l y p e r i o d i c , some m u l t i - p e r i o d i c , and some display a beat phenomenon. The actual l i m i t s of these c h a r a c t e r i s t i c s w i t h i n the group are not known, and the correct i n t e r p r e t a t i o n of some of 17 them uncertain.* The dif f e r e n c e s may be the r e s u l t of a number of f a c t o r s - v a r i a t i o n s i n mass and composition, evolutionary s t a t e , mode of p u l s a t i o n , aspect e f f e c t s , e t c . L i s t s of the 6 Cephei stars and t h e i r i n d i v i d u a l features have been given by H i l l (1967), Watson (1972), and Lesh (1973). A fundamental d i f f i c u l t y i s the lack of understanding of the i n s t a b i l i t y mechanism a f f e c t i n g these s t a r s . One key to s o l v i n g t h i s problem i s knowledge of t h e i r state of e v o l u t i o n . Watson (1972) and Lesh (1973) have shown that the 6 Cephei ' i n s t a b i l i t y s t r i p ' corresponds roughly with the S-bend region of evolutionary tracks i n the H-R diagram, encompas-sing phases of core hydrogen-burning, secondary contraction following depletion of hydrogen i n the core, and s h e l l hydrogen-burning. I t i s presently impossible to determine which of these phases describes the g Cephei s t a r s . Lesh suggests that normal B stars found i n t h i s same region of the H-R diagram are near the end of the core hydrogen-burning phase, while the 6 Cephei sta r s are i n the secondary contraction or s h e l l hydrogen-burning phase. This idea i s based on the assumption that the i n s t a b i l i t y i s t r iggered i n some fashion by s t r u c t u r a l changes wit h i n the s t a r s , a s s o c i -ated with t r a n s i t i o n s between the evolutionary phases. Watson c i t e s s t a t i s t i c a l evidence which contradicts t h i s view, i n d i c a t i n g that the majority of 6 Cephei s t a r s are i n the core hydrogen-burning phase. An understanding of the p h y s i c a l processes associated with t r a n s i t i o n s between these phases should o f f e r clues to the p u l s a t i o n - t r i g g e r i n g mechanism. Stothers and Simon (1969) have proposed the 'y-Mechanism Theory' to explain the i n s t a b i l i t y : *For example, l i n e broadening i n t e r p r e t e d as Doppler broadening due to r o t a t i o n may i n f a c t be due to other types of v e l o c i t y f i e l d s (Le Contel, 1970). 18 In a close binary system, the o r i g i n a l primary s t a r , being more massive than the secondary, w i l l evolve f i r s t , expanding i t s radius during hydrogen burning u n t i l i t reaches i t s Roche lob e . Thereupon i t w i l l quickly lose mass to the secondary, which accretes f i r s t the outer zero-age envelope of the primary s t a r and then, on top of tha t , the helium enriched outer portions of the primary's core. I f s u f f i c i e n t helium i s accreted and the t o t a l mass exceeds 6 Mg, the compression of the secondary's envelope by the weight of the helium (u mechanism) has been found to r a i s e the e f f e c t i v e temperature and to permit the development of r a d i a l pulsations which are strongly energized by the hydrogen-burning reactions i n the core. C r i t e r i a f o r the discovery of 8 Cephei stars on t h i s b a s i s have also been set f o r t h (Stothers and Simon, 1971). At l e a s t two major aspects of the theory are contradicted by the observations: the requirement that a l l 8 Cephei stars be b i n a r i e s and the suggestion of anomalous abundances (Watson, 1971). Pu l s a t i o n models have been proposed by several people (e.g., Ledoux, 1951; Chandrasekhar and Le b o v i t z , 1962; Clement, 1965, 1966, 1967; Osaki, 1971). Some of the observational features - spectrum v a r i a t i o n s , v e l o c i t y v a r i a t i o n s , and multiple p e r i o d i c i t i e s , f o r example - can be accounted for by these models. Some can be explained i n terms of simple r a d i a l p u l s a t i o n s , others seem to require non-radial pulsations or i n t e r -actions between more than one p u l s a t i o n mode. There i s evidence to suggest that a sta r ' s p u l s a t i o n mode may be unstable and change i n the course of a few years (Shobbrook et a l . , 1972). The p u l s a t i o n mode(s) may be a c r i t i c a l f a c t o r i n the basic i n s t a b i l i t y . Analyses have been made of the p u l s a t i o n a l s t a b i l i t y of e v o l u t i o n -ary models to various types of o s c i l l a t i o n . Davey (1973) considered the p u l s a t i o n a l s t a b i l i t y toward r a d i a l o s c i l l a t i o n of models passing through those portions of the H-R diagram occupied by the 8 Cephei stars at several 19 stages of e v o l u t i o n . A l l were found to be stable i n several modes of o s c i l l a t i o n , making i t impossible to determine the evolutionary state of the 8 Cephei stars on t h i s b a s i s . The longer-term v a r i a t i o n s i n these s t a r s ; p a r t i c u l a r l y important from an evolutionary standpoint, have also been s t u d i e d . Included are the changes i n p e r i o d , v e l o c i t y amplitude, l i g h t amplitude, and p u l s a t i o n mode as noted above. In s e v e r a l cases, the observations extend over i n t e r v a l s of more than f i f t y y e a rs, but with r e s u l t s that are f a r from c o n c l u s i v e . The long-term v a r i a t i o n s of BW Vulpeculae and g Cephei are discussed i n Sections 5.8 and 5.12 r e s p e c t i v e l y . I t i s obvious that the b a s i c problems of understanding the i n s t a b i l i t y mechanism i n these s t a r s and of reconciling the great v a r i e t y of observational c h a r a c t e r i s t i c s w i t h i n the framework of the group can be approached i n a number of ways. One i s to improve the observational data. An important gap i n t h i s area has r e s u l t e d from an i n a b i l i t y to resolve c e r t a i n aspects of the s p e c t r a l v a r i a t i o n s due to l i m i t a t i o n s set by exposure times and spectrographic r e s o l u t i o n . I t appeared that the new instrumentation could help f i l l t h i s observational gap. The brightness of these s t a r s would put them w e l l w i t h i n reach of the detection system at coude" d i s p e r s i o n s , t h e i r short periods would make po s s i b l e the a c q u i s i t i o n of a meaningful quantity of data within a l i m i t e d time of observation, and the c y c l i c a l nature of t h e i r v a r i a t i o n would be an asset i n d i s t i n g u i s h i n g r e a l from instrumentally-induced changes. I t was hoped that the new data would serve as a basis f o r t e s t i n g more c r i t i c a l l y the current models and provide the information needed for the s o l u t i o n of some of the major problems j u s t discussed. 20 3.3 OBSERVATIONAL GOALS The primary goal f o r t h i s phase of the program was to obtain data f o r s t a r s representing the widest p o s s i b l e range of c h a r a c t e r i s t i c s of the 3 Cephei group and were, at the same time, i n d i v i d u a l l y i n t e r e s t i n g . The search f o r new 3 Cephei stars was not a part of the present program. The secondary goal was to observe a d d i t i o n a l stars of i n t e r e s t f o r which observations of a s i m i l a r nature could be of b e n e f i t . 21 CHAPTER 4. OBSERVATION AND ANALYSIS 4.1 INTRODUCTION The 8 Cephei stars a V i r g i n i s ( S p ica, HD 116658), 8 Cephei (HD 205021), and BW Vulpeculae (HD 199140) were observed i n the course of t h i s program. Two of these, 8 Cep and BW V u l , are c l a s s i c a l 8 Cephei s t a r s , while a V i r was c l a s s i f i e d as a 8 Cephei s t a r only r e c e n t l y (Shobbrook et a l . , 1969). A l l have an extensive observational h i s t o r y . Spica i s a known binary and 8 Cep i s a suspected one. The extremes i n p u l s a t i o n a l v e l o c i t y amplitude, projected r o t a t i o n a l v e l o c i t y , and l i g h t v a r i a t i o n f o r the group are represented by these s t a r s . Their c h a r a c t e r i s t i c s are sum-marized i n Table 4.1. The 8 Cephei s t a r 12 Lacertae was also monitored with the present instrumentation by G. H i l l of the D.A.O. These observations cover approx-imately two cycles of the p u l s a t i o n . They w i l l not be considered here i n d e t a i l . A d d i t i o n a l programs using the instrumentation were c a r r i e d out i n a s s o c i a t i o n with K.O. Wright and G.C.L. Aikman of the D.A.O. With Dr. Wright, observation of 32 Cygni (HD 192909/10, K5I + B3V) were made near e c l i p s e i n an attempt to detect short-term changes (on the order of minutes) i n the H and K l i n e s of C a l l . Changes i n the p r o f i l e s of these l i n e s might be expected as a r e s u l t of chromospheric e f f e c t s (Wright, 1952; Wellmann, 1957). The emission features usually found i n t h e i r centers might also change as a r e s u l t of causes not associated with the e c l i p s e ( L i l l e r , 1968). From observations covering the ecl i p s e s of 1949 and 1952-53, Wellmann found that the chromospheric e f f e c t s i n the K l i n e were v i s i b l e up to 70 days Table 4.1. Observed p h y s i c a l properties of program stars a V i r g i n i s , BW Vulpeculae, and 6 Cephei Symbol BW Vul Ref. a V i r Ref. 3 Cep Ref. MK Spectral Type - B 2III 1,2,3 B 1 IV B 1 V 2 3 B 2 III B 1 III 1,3 2 Visual Magnitude V 6.44 6.29 1 6 0.97 5 3.32 1 Color Index B-V -0.130 1 • -0.23 1,5 -0.22 1 Ultra-Violet Color Index U-B -0.870 1 -0.94 -0.93 1 5 -0.94 1 Ultra-Violet Reddening Excess E(U-B) 0.11 1 0.05 1 0.02 1 Absolute Magnitude M V -4.42 -3.57 -4.10 1 2 3 -3.83 -4.05 2 3 -4.26 -3.83 -4.00 1 2 3 E f f e c t i v e Temperature Parameter = 5040 T°K e eft 0.207 2 0.214 2 0.207 2 Log of Gravity log g 3.81 3 3.85 3 3.88 3 Log of Period (days) log P -0.697 1 -0.760(var. ) 6 -0.719 1 Apparent Rotational Broadening v s i n I e 26 38(narrow) 60(broad) 1 3 3 155 • 3 43 25 1 4 Amplitude of Light Curve (passband given). Am 0.200(D) 0.260(u) 7 8 6.014-0.03(y) 6 0.034(blue) 7 Radial Velocity Range 2K 150 7 16(var.) 6 23 7 (Kin./sec.) 190 References: 1. H i l l (1967) 2. Lesh & Aizenman (1973) 3. Watson (1972). 4. McNaraara & Hansen (1961) 5. Shobbrook et a l . (1969) 6. Shobbrook et a l ^ (1972) 7. Percy (1967) 8. Kubiak (1972) 23 from the beginning or end of t o t a l i t y . Mid-eclipse (which was not to t a l ) was estimated to be J.D. 2441256.96 (Saito et a l , 1972). Saito and Sato (1972) concluded that at mid-eclipse about h a l f the disc of the B-type component was ec l i p s e d by the photosphere of the K s t a r . The p a r t i a l phases l a s t e d f o r seventeen days. Observations were made with the Isocon on J.D. 2441210, 11, 12, o and 48 at a di s p e r s i o n of 2.4 A/mni using the D.A.O. 48-inch telescope. The longest s i n g l e period of observation was about one hour. The r e s o l u t i o n was not s u f f i c i e n t to show whether the c e n t r a l emissions were present. The r e s u l t s were consequently i n c o n c l u s i v e . With Mr. Aikman, an attempt was made to detect the secondary 2 component of the spectroscopic binary 0 Orionis (HD 37041, 09k) by u t i l i z i n g the increased* dynamic range of the t e l e v i s i o n system. The observations were made with the Isocon i n October 1971 at a di s p e r s i o n of 2.4 A/mm. O Three s p e c t r a l regions (centered on V3860, 4026, and 4860 A) were covered. A preliminary data analysis produced no d e f i n i t e evidence of the secondary. 2 Interest was revived i n the program when 0 O r i was found to l i e i n the error box of the X-ray source 2U0525-06 (Barbon et a l . , 1972). I t was the only binary to do so which had an unseen secondary component s u f -f i c i e n t l y massive to be a black h o l e . Since the existence of X-ray sources i n binary systems with non-luminous massive companions i s the most convinc-ing evidence of black holes (Barbon et a l . ) , the coincidence i s s i g n i f i c a n t . Furthermore, the co-existence of a highly evolved black hole i n a binary system with a very young 0-star would be extraordinary! *Relative to the photographic plate 24 Further processing of the t e l e v i s i o n data has been c a r r i e d out and Mr. Aikman i s presently reducing p l a t e m a t e r i a l which he has obtained of the ob j e c t . 4.2 THE 6 CEPHEI OBSERVATIONS A General Description V i r t u a l l y a l l observations were made between May 1971 and October 1972 using e i t h e r the Image Isocon or s i l i c o n v i d i c o n t e l e v i s i o n cameras as detectors at the coude focus of theD.A.0.48-inch telescope. Only the best of these are discussed i n depth. The main features of the observations have been summarized by Goldberg et a l . (1973a) and are repeated i n Table 4.II. Further information Is provided i n Tables 5.1 and 5.II. The Preliminary Observations The s t a r a V i r was the f i r s t of the program s t a r s . I t s v a r i a b l e v e l o c i t y was found from observations begun i n 1876, i t has been known to be a spectroscopic binary since 1890 (Vogel, 1890), and i t s l i g h t v a r i a b i l -i t y was discovered by Stebbins (1914). I t was c l a s s i f i e d as a 3 Cephei s t a r on the basis of a 4.17-hour period i n i t s l i g h t v a r i a t i o n . A thorough a n a l y s i s of the c h a r a c t e r i s t i c s of t h i s system has been made by Evans et a l . (1971). The observed l i g h t curve i s the superposition of the 4.17-hour v a r i a t i o n and a 4-day v a r i a t i o n due to aspect changes i n the t i d a l l y d i s -torted primary (Shobbrook et a l . , 1969). The p u l s a t i o n a l v a r i a t i o n i s e s s e n t i a l l y s i n u s o i d a l with an amplitude of '^0.016 mag. i n V, while the o r b i t a l v a r i a t i o n has an amplitude of ^ 0.03 mag. The short period v a r i a t i o n i n v e l o c i t y was f i r s t reported by Table 4.II. General features of the B Cephei observations Spectral S p e c t r a l Region Dispersion ~ t - M a x i m u m Time c ^ ^ ^ r . ^ , ^ * * Star Detector ( & ) ( £ / m m ) Resolution R e s o l u t i o n * ( M i n > ) Spectrograph** (A) a V i r Isocon 4000 - 4160 2.4 0.5 0.3 9682M BW Vul Isocon Isocon 4460 - 4590 6540 - 6585 2.4 4.8 0.5 1.0 1 3 9682M 9681M 8 Cep Isocon Vidicon 4548 - 4572 6490 - 6630 0.5 10.1 0.1 0.3 2 9 9682M + T.L. 32121 12 Lac Isocon 4548 - 4572 0.5 0.1 9682M + T.L. *An estimate based on the minimum acceptable signal-to-noise r a t i o . **Code: f o c a l length of camera i n inches; hundreds of grooves per mm of grating; order of d i f f r a c t i o n ; M = mosaic g r a t i n g ; T.L. = tr a n s f e r lens (Richardson, E.H. , J.R.A.S. Canada 62, No. 6.) 26 Shobbrook et a l . (1972). The amplitude i s ^15 km/sec. The e a r l i e r v e l o c -i t i e s i ndicated the presence of at l e a s t three more p e r i o d i c i t i e s , i n c l u d i n g one of about 6 hours. I t appeared that the mode of p u l s a t i o n had changed a number of times since 1908. V a r i a b i l i t y i n the l i n e p r o f i l e s has been reported i n a number of papers. Struve (1948) found that some of the l i n e s were o c c a s i o n a l l y double (or a l t e r n a t i v e l y had emission cores) and i n a l a t e r paper (Struve et a l . , 1958) noted that the l i n e s t r u c t u r e sometimes v a r i e d on a time scale of hours. The v a r i a b i l i t y i s associated with the o r b i t a l motion, the times of change coincident with the conjunctions. Dukes (1973) found a p o s s i b l e v a r i a t i o n of from 2 to 5 percent i n scans of Hel A4471, with a very t e n t a -t i v e frequency of 4.10 cycles per day (very close to the frequency he 'obtained from h i s r a d i a l v e l o c i t y data). An attempt was made i n May 1971 to detect a p u l s a t i o n - c o r r e l a t e d v a r i a t i o n i n the l i n e p r o f i l e s by using the Isocon (see Table 4.II). Nearly two cycles were covered at o r b i t a l phases intermediate between the conjunc-tions and the times of maximum v e l o c i t y separation. A preliminary analysis i n d i c a t e d no s i g n i f i c a n t change i n the p r o f i l e s . However, the ease with which the instrumentation could be applied to programs of t h i s type (as w e l l as the advantages of obtaining the data i n d i g i t a l form) was demonstrated. The analysis i s presently being continued by using some of the techniques described i n Section 4 . 3 . Further observations of t h i s type, but at a higher d i s p e r s i o n and probably i n a d i f f e r e n t s p e c t r a l region, may be required to define the p u l s a t i o n a l l i n e p r o f i l e v a r i a t i o n i f one e x i s t s . The Primary Observations The observations of BW Vul and 8 Cep w i l l be discussed i n d e t a i l i n Chapter 5. 27 4.3 DATA REDUCTION AND ANALYSIS Introduction Data reduction and an a l y s i s takes place i n f i v e stages: ( i ) a preliminary data check during the time of data a c q u i s i t i o n ; ( i i ) a p r e l i m -inary a n a l y s i s designed to provide a measure of the s i g n a l l e v e l during the course of observations and an i n d i c a t i o n of the nature and degree of processing required i n the o v e r a l l a n a l y s i s ; ( i i i ) a refinement process designed to put the spectra i n a form s u i t a b l e for q u a n t i t a t i v e study; (iv) q u a n t i t a t i v e a n a l y s i s ; (v) a p p l i c a t i o n of techniques f o r r e s o l u t i o n enhancement and improved s i g n a l e x t r a c t i o n . The Preliminary Data Check A preliminary data check i s accomplished on line with the use of an Interdata Model Four mini computer. Checks are made f o r the a c c e p t a b i l -i t y of the s i g n a l l e v e l , f o r errors associated with the d i g i t i z a t i o n p r o -cess, and f o r accuracy of the data t r a n s f e r to magnetic tape (Walker et a l . , 1972). The Preliminary Data Analysis A preliminary data a n a l y s i s , based on a program developed by A.C. Gower of the U.B.C. Department of Geophysics and Astronomy involves the computation of normalized means of s p e c i f i e d numbers of s i n g l e frames. Normalization i s accomplished by eq u a l i z i n g the areas under each mean spectrum between s p e c i f i e d wavelength l i m i t s . The s i g n a l l e v e l i s ind i c a t e d by the normalization f a c t o r . A background l e v e l recorded during each read-out of the tube and a dark l e v e l obtained at the end of each 'run' on a 28 source are generally subtracted from the s i g n a l before normalization. The Refinement Process Included i n the refinement process are noise reduction and r e c t i -f i c a t i o n procedures; the former to enhance the si g n a l - t o - n o i s e r a t i o , the l a t t e r to remove the instrumental response c h a r a c t e r i s t i c s and restore the proper i n t e n s i t i e s . The spectra are r e c t i f i e d to a continuum defined by a l e a s t squares f i t of third-order orthogonal polynomials to points selected from tho se s p e c t r a l regions representing r e a l continuum. This s e l e c t i o n i s c a r r i e d out automatically once the continuum boundaries are defined (the process i s described i n Appendix C ) . The accuracy of the process i s depen-dent on the q u a l i t y of f i t ; and the s t a b i l i t y , l i n e a r i t y , and response c h a r a c t e r i s t i c s of the system. The assumption of a l i n e a r response i s im-p l i c i t i n t h i s approach. The work by Buchholz (1972) plus the general experience gained i n using the instrumentation has shown t h i s assumption to be correct to at l e a s t a f i r s t order. A new continuum f i t i s made f o r each mean spectrum to compensate f o r p o s s i b l e f l u c t u a t i o n s i n the system response. A background and a dark l e v e l are subtracted from the s i g n a l before r e c t i f i c a t i o n i n a fashion s i m i l a r to that used i n the normalization process. At present, the computed means are based on equal time i n t e r v a l s . Noise reduction i s accomplished by two methods: ( i ) averaging s i n g l e frames h to give an N improvement i n the signa l - t o - n o i s e r a t i o , where N i s the num-ber of frames; and ( i i ) by l i n e a r smoothing or use of a low-pass f i l t e r . Use of an optimum f i l t e r was found to be an unnecessary refinement. The Quantitative Analysis The q u a n t i t a t i v e analysis involves the computation of r a d i a l 29 v e l o c i t i e s , l i n e depths, equivalent widths, and s i m i l a r parameters from the r e c t i f i e d and f i l t e r e d (or smoothed) spec t r a . Radial v e l o c i t i e s are determined numerically by two methods: ( i ) by the p o s i t i o n s of l i n e minima (Method I), and ( i i ) by the p o s i t i o n s found from b i s e c t i n g the area between continuum and l i n e (Method II). Measurements of multiple component p r o f i l e s are made manually when the p o s i t i o n of other than the strongest component i s required. Method II provides a weighted mean of the p o s i t i o n s of a l l components wit h i n set wavelength l i m i t s and i s quite s e n s i t i v e to v a r i a t i o n s i n the l i n e p r o f i l e s . I t requires an accurate knowledge of the extent of the s p e c t r a l l i n e s * and a p r e c i s e continuum f i t . Method I gives only the v e l o c i t y of the deepest component of a l i n e . A good signal-to-noise r a t i o i s required i f acceptable r e s u l t s are to be obtained. A technique proposed by Hutchison (1971) would probably be more e f f e c t i v e than the present methods i n s i t u a t i o n s where the l i n e p r o f i l e s do not change r a p i d l y or have a complex s t r u c t u r e . I t involves a l e a s t -squares f i t of a polynomial to the f i r s t d e r i v a t i v e of a l i n e p r o f i l e , with the p o s i t i o n of l i n e minimum determined by the zero cro s s i n g of the p o l y -nomial. The primary l i m i t a t i o n s on the accuracy of the r a d i a l v e l o c i t i e s were set by the s t a b i l i t y of the instrumentation ( i n a s s o c i a t i o n with the c a l i b r a t i o n procedures employed) and the techniques of data reduction ( i n a s s o c i a t i o n with the s i g n a l - t o - n o i s e r a t i o s , which frequently had to be compromised f o r the sake of be t t e r time r e s o l u t i o n ) . In a l l numerical r a d i a l v e l o c i t y computations, l i n e p o s i t i o n s *Determined on the basis of the l i n e p r o f i l e s given by Wilson (1956), B u t l e r and Seddon (1958), and Wright et a l . (1964). 30 were determined only to the nearest instrumental channel, r e s u l t i n g i n quantized values l i m i t e d i n accuracy by the s i z e of the quantum jump (which can be i n f e r r e d from the e f f e c t i v e d i s p e r s i o n ) . In a d d i t i o n , corrections f o r v a r i a t i o n s i n the e f f e c t i v e d i s p e r s i o n across the spectrum (due to n o n - l i n e a r i t i e s associated with the scanning r a s t e r and the imaging process) have not been applied because of i n s u f f i c i e n t c a l i b r a t i o n proce-dures. However, t h i s c o r r e c t i o n should be r e l a t i v e l y small (see Appendix D). The instrumentation generally proved stable i n the wavelength regime ( i . e . , the p o s i t i o n of the scanning r a s t e r remained nearly f i x e d ) . This was demonstrated by the s t a b i l i t y i n the p o s i t i o n s of two f i d u c i a l marks located on the photocathode during some of the observations, as w e l l as by some of the longer sets of observations on a s i n g l e source. One example of the s t a b i l i t y r e a l i z e d during s a t i s f a c t o r y operation of the system i s given by the observing run of 9 August 1972 UT on BW Vul; during which a f a i r l y uniform d r i f t of 1 channel (VL8 km/sec) occurred. O c c a s i o n a l l y , large non-linear s h i f t s occurred over periods of minutes. These were r e a d i l y i d e n t i f i a b l e as being instrumental i n o r i g i n even i n the absence of the f i d u c i a l marks. Hardware improvements over the past year have helped eradicate t h i s problem. Guiding errors also have an e f f e c t on the accuracy of the r a d i a l v e l o c i t i e s . The maximum poss i b l e error corresponds to the projected s l i t width; t y p i c a l l y ^25 km/sec f o r the present observations. Errors of t h i s type did not appear to manifest themselves. Radial v e l o c i t y standards were taken during most observing ses-s i o n s , but have not yet been used i n the present a n a l y s i s . A l l v e l o c i t y 31 computations have so f a r been d i f f e r e n t i a l ; not a serious d e f i c i e n c y as the primary concern has been motion w i t h i n the frame of the s t a r . A general error a n a l y s i s i s not p a r t i c u l a r l y meaningful because of the wide v a r i a t i o n s encountered i n the operation of the instrumentation. Quantitative assessments of the accuracy must be made on the basis of i n d i v i d u a l sets of observations. They are therefore relegated to the i n d i v i d u a l discussions of the star s observed. The epochs given are based on an i n t e r p o l a t i o n between the recorded s t a r t i n g and ending times f o r a s i n g l e set of observations. The 'frame time' i s used as the i n t e r p o l a t i o n f a c t o r . The absolute accuracy i s on the order of f i v e minutes, the r e l a t i v e accuracy consider-ably higher. Line depths are given by the differences between the continuum, and the i n t e n s i t y values at the p o s i t i o n s of l i n e minima. Their accuracy i s most strongly influenced by the q u a l i t y of the r e c t i f i c a t i o n , but a p p l i -c a t i o n of a f i l t e r with a cu t - o f f at too low a frequency can lead to erroneously shallow l i n e s , e s p e c i a l l y when the l i n e s are sharp. Poor r e s -o l u t i o n has a s i m i l a r e f f e c t . Equivalent widths may be computed on the basis of the areas determined during the r a d i a l v e l o c i t y computations by Method I I . This program option has not yet been exercised. The program can be expanded without d i f f i c u l t y to accommodate computations of a d d i t i o n a l spectrum parameters (such as half-widths of l i n e s , l i n e asymmetries, e t c . ) . 32 Techniques for Resolution Enhancement and Improved Signal Extraction A d d i t i o n a l information may be obtained from the data under c e r t a i n circumstances by a p p l i c a t i o n of the techniques described below. The deconvolution techniques developed by Ulrych (1972) are used f o r r e s o l u t i o n enhancement. In p a r t i c u l a r , they provide a r e l a t i v e l y good i n d i c a t i o n of the true separations between blended l i n e s or components. The basic procedure i s to ( i ) examine the power spectrum of the data; ( i i ) construct an appropriate low-pass f i l t e r to reduce the high frequency noise content to very low l e v e l s ; and ( i i i ) deconvolve the f i l t e r e d s p e c t r a . The optimum r e s u l t i s achieved by a t r i a l and error process. The com-ponent separations derived i n t h i s fashion are not p a r t i c u l a r l y dependent on the assumptions made i n choosing the deconvolution parameters. The prime requirement f o r s a t i s f a c t o r y a p p l i c a t i o n of the technique i s a good signal - t o - n o i s e r a t i o . Taking r a t i o s or d i f f e r e n c e s of spectra i s p a r t i c u l a r l y u s e f u l i n i s o l a t i n g small changes i n the continuum or i n the s t r u c t u r e of a l i n e . The spectra of d i f f e r e n t s t a r s may be compared i n t h i s fashion as w e l l . Ratios or d i f f e r e n c e s are taken of the normalized s p e c t r a . Summary Some of the processing techniques j u s t discussed are demonstrated on spectra of the 3 Cephei s t a r BW Vul i n Figure 4.1. C e r t a i n aspects of the data processing are discussed i n more d e t a i l under the headings of the i n d i v i d u a l s t a r s . Relevant discussions of data processing techniques have been given by Bonsack (1971), Brault and White (1971), Biraud (1969), and Lorre (1973). Si Ml 4 57 5 Silll 4 5 6 8 S i lit 4 553 M g l ! 4 4 8 l H e l 4 4 7 l F i g . 4.1 A sample a p p l i c a t i o n of the data processing techniques. A H s p e c t r a shown are centered on the same epoch. They are: (A) a s i n g l e frame normalized; (B) the mean of 8 frames normalized (a one-minute e f f e c -t i v e exposure); (C) the mean of 24 frames normalized; (D) the mean of 24 frames r e c t i f i e d and low-pass f i l t e r e d ; (E) the mean of 24 frames r e c t i f i e d , low-pass f i l t e r e d , a n d deconvolved. The h o r i z o n t a l s c a l e ; has a l s o been expanded i n the case of (D)- and CE). 34 CHAPTER 5. RESULTS AND DISCUSSION: THE INDIVIDUAL STARS BW VULPECULAE 5.1 INTRODUCTION The s t a r BW Vulpeculae i s perhaps one of the most i n t e r e s t i n g p e r i o d i c v a r i a b l e s known ( i t s c h a r a c t e r i s t i c s are given i n Table 4.1). I t displays the l a r g e s t r a d i a l v e l o c i t y , l i g h t , and l i n e p r o f i l e v a r i a t i o n s of the known 8 Cephei s t a r s , and has undergone what appear to be s i g n i f i c a n t changes i n i t s period and i t s r a d i a l v e l o c i t y amplitude during the past several decades. The s t a r ' s v a r i a b l e v e l o c i t y was discovered by H i l l (1930), i t s short period by P e t r i e (1937) , and i t s l i g h t v a r i a t i o n by Huffer (1938). The spectroscopic observations were begun i n 1924. Extensive spectroscopic studies have been made by P e t r i e (1954), Struve (1955a), McNamara and Williams (1955), McNamara et a l . (1955), and Odgers (1956). Photometric i n v e s t i g a t i o n s have been c a r r i e d out by Huffer (1938), Eggen (1948), Nikonov and Nikonova (1952) , Kraft (1953) , Walker (1954), Lynds (1954), and Percy (1971). A j o i n t spectroscopic and photo-metric study has recently been completed by Kubiak (1972). • In contrast to t h i s extensive observational a s s a u l t , there have been few serious attempts at explaining the observed phenomena. The primary d i f f i c u l t i e s have been the complexity of the v a r i a t i o n , the lack of under-standing of the basic i n s t a b i l i t y mechanism, and the i n a b i l i t y of t r a d i t i o n -a l observational techniques to resolve the s p e c t r a l v a r i a t i o n s during the phases of the rapid change. 35 5.2 THE OBSERVATIONS The general f e a t u r e s of the observations are given i n Table 4.II and the d e t a i l s i n Table 5.1. 5.3 THE RADIAL VELOCITY VARIATION The Velocity Curve The r a d i a l v e l o c i t i e s obtained w i t h the Isocon i n 1971 and 1972 from the l i n e s of Hel A4471, M g l l A4481, and S i l l l AA4553, 4568, 4575 are presented here. They are not l i s t e d i n the customary t a b u l a r form f o r two reasons: ( i ) because the d i s c r e t e values obtained are dependent on the method of a n a l y s i s ( i n p a r t i c u l a r on the time increments chosen* and the treatment of multiple-component p r o f i l e s ) and ( i i ) because they are p r e s e n t l y d i f f e r e n t i a l * * . The v e l o c i t y curve obtained by Method I on 9 August 1972 UT i s given i n F i g u r e 5.1. Approximately 1.1 c y c l e was covered. The data were reduced to produce three-minute means at three-minute i n t e r v a l s w i t h a r e s u l t i n g s i g n a l - t o - n o i s e r a t i o of —25:1. The outstanding f e a t u r e s of the v e l o c i t y curve are i t s extreme amplitude, the ' d i s c o n t i n u i t y ' a t phase M).4, the s t i l l s t a n d from phases M).4 to 0.55, and the extreme b l u e - s h i f t immediately f o l l o w i n g s t i l l s t a n d . A l s o notable are the s m a l l r e d - s h i f t near the end of s t i l l s t a n d , the 'hump' i n the curve a t phase M).65, the i n c r e a s e i n the v e l o c i t y g r a d i e n t a t phase M)..2, and the s c a t t e r i n v e l o c i t i e s at phase M).25. The r e a l i t y of these f e a t u r e s has been v e r i f i e d by a comparison of the present r e s u l t s w i t h pre-*The e f f e c t i v e exposure time and the overlap between the e f f e c t i v e exposures. **The s t i l l s t a n d v e l o c i t y was taken as the zero l e v e l on the b a s i s of previous photographic r e s u l t s . D i f f i c u l t y i s encountered i n determining the r a d i a l v e l o c i t y o f , t h e center of mass. Table 5.1. Observations of BW Vulpeculae UT Date H e l i o c e n t r i c J u l i a n Date 2441000 + H.A. @ Sta r t Frame Time (Minutes) E f f e c t i v e Exposure Time* (Minutes) Mean E f f e c t i v e Dispersion** (points/A) Phases Covered Quality FactorV 8 Aug. 71 171.776-.981 1:32E 0.375 3.8 0.97-1.0-0.60 2-3 9 Aug. 71 172.838-.917 0:01E 0.333 3.5 3.8 0.23-0.55 2-3 9 Aug. 72 538.751-.985 2:00E 0.125 3.5 0.37-1.0-0.50 *The 'best' compromise between time r e s o l u t i o n and the signal-to-noise r a t i o (the average over the time i n t e r v a l ) . **The average over the region of i n t e r e s t . VAn estimate of the q u a l i t y of the data (1 = excellent to 4 = poor). Notes: (1) Only the data discussed i n t h i s paper i s l i s t e d here. The remainder are ei t h e r of lower q u a l i t y or require further a n a l y s i s (as i n the case of the data obtained i n the region of Ha). (2) The primary l i n e s observed were those of He I X4471, Mg II X4481, and S i I I I XX4553, 4568, 4575. (3) The 1971 data was obtained before the ad d i t i o n of new high reflectance coatings to the coude spectrograph of the D.A.O. 48-inch telescope. B W VUL 9 Aug 1972 UT S i l 4533.4568.4575 150 • y- 0 T " r * » - - i tut." u O Ui > to < ec - i 5 0 -PHASE 0.4 U T I 0.5 0.6 0.7 0.8 0.9 0.0 0.I _l_ . 0.2 _J 0.3 0.4 JL 0.5 6:00 7:00 8:00 9:00 10:00 II; 00 F i g . 5.1 Rad i a l v e l o c i t i e s f or BW Vul on 9 August 1972 UT: 1.1 cycle of the p u l s a t i o n . A hollow c i r c l e i n d i c a t e s the v e l o c i t y of the weaker component of a s p e c t r a l l i n e where two components are present. A bar over the c i r c l e i ndicates that the r e s u l t i s uncertain. 38 vious photographic data - particularly that of Kubiak (1972) and Odgers (1956) . The Accuracy of the Velocities The relative accuracy of the individual velocities can be i n -ferred from the scatter, which is about 10 km/sec. Where the velocity gradient i s small (phases ^ 0.8 to 0.2), the quantization effect discussed in Section 4.3 is more apparent. The scatter may be reduced by increasing the effective exposure time and thus the signal-to-noise r a t i o . Corrections for instrumental d r i f t (see Section 4.3) have been applied. The 'Van Hoof Effect ' Evidence of the 'Van Hoof Effect' (van Hoof and Struve, 1953); a systematic time lag in the radial velocities derived from the hydrogen lines relative to the other st e l l a r l i n e s , has been found for a number of 8 Cephei stars (Laskarides, 1971). An effect that may be interpreted in this vein has been seen in BW Vul. McNamara et a l . (1955) found a large positive residual in the difference (V, , -V .,..) during the phases immediately hydrogen a l l o r preceding and immediately following the s t i l l s t a n d , and Odgers (1956) noted a difference in the strength of the redward component of Hy. relative to the redward components of the S i l l l lines during the phases of doubling.* ....When the lines are double the redward component of Hy remains more intense than the component at the stationary position for about seven minutes after the redward components of S i l l l , X4552, X4568 have become less intense than the components at the stationary position. No significant difference i n either phase or amplitude was ob-*With reference to a set of observations obtained by A.J. Deutsch at Mount Palomar on 15 October 1954 covering the phase of 'discontinuity' preceding s t i l l s t a n d . 39 served f o r the He, Mg, and S i l i n e s . A p r e c i s e c o r r e l a t i o n i n phase of the Hex data obtained with the Isocon and the observations ju s t discussed was not p o s s i b l e . The Repeatability of Successive Cycles A comparison of the c y c l e - t o - c y c l e change i n the character of the ' d i s c o n t i n u i t y ' preceding s t i l l s t a n d was used as one t e s t of the r e p e a t a b i l -i t y of successive c y c l e s . * The relevant portions of the v e l o c i t y curve shown i n Figure 5.1 are displayed with much greater time r e s o l u t i o n i n Figure 5.2. Three-minute means computed at one-minute i n t e r v a l s by Method II are given. The curves thus show the s h i f t i n the 'center-of-gravity' of the e n t i r e l i n e p r o f i l e s . No s i g n i f i c a n t c y c l e - t o - c y c l e d i f f e r e n c e s are apparent i n t h i s case. There have been previous i n d i c a t i o n s , however, that they may occur. Odgers (1956) noted a lack of r e p e a t a b i l i t y between successive cycles i n one instance, but attached no great s i g n i f i c a n c e to i t because of inaccuracies i n the data. The data obtained with the Isocon i n September 1971 also gave some evidence of a d i f f e r e n c e (Goldberg et a l . , 1972), but the r e s u l t was clouded by instrumental problems. The 1971 Data Some of the v e l o c i t i e s obtained with the Isocon i n 1971 are shown i n Figures 5.3 and 5.4. Only portions of c y c l e s , with emphasis on the phase of the ' d i s c o n t i n u i t y ' preceding s t i l l s t a n d , were recorded. The 1971 data are of lower q u a l i t y than those obtained i n 1972 for several reasons: ( i ) the t e l e v i s i o n system was not functioning as w e l l ; ( i i ) the observations •Further comparisons are made i n Section 5.4 on the b a s i s of the l i n e p r o f i l e s . 40 < £ 150 >-t 8 too T 9 AUG -1972 UT He I & Silll Average 5 50 a CE 2 o 2 • • • • +±+ PHASE 0.35 0.40 0.45 0.50 0.55 U.T. 6:00 6:10 6:20 6:30 6:4 0 6:50 7:00 1 1 9 AUG 1972 UT He I 8 S i l l l Average u €> I ISO o O 100 _1 > < 50 O < z < 0 ui 2 •• •••• xrtr PHASE 0.35 0.40 0.45 0.5 0 U.T. I 10:50 I I |!0 0 II: 10 I 11:20 I 11:30 I 11:40 Fig. 5.2 Radial velocities for BW Vul on 9 August 1972 UT: the phases of rapid variation preceding stillstand. Successive cycles are shown. 41 ~ 150 o o ijSioo < 50 oc z < 111 -2 0 T ; — i — - — 8 AUG 1971 UT S l l l l A v e r a g e -» w-U T 8:10 • 8 2 0 8-30 8=40 8 :50 9=00 Fig. 5.3 Radial v e l o c i t i e s f o r BW Vul on 8 August 1971 UT: the phases of ra p i d v a r i a t i o n preceding s t i l l s t a n d . •130 u 100 3 Id > 50 < < Ut 2 9 AUG 1971 UT S l l l l A v e r a g e JL , « ' . * t _L U T 8=20 8 - 3 0 8=40 8-50 9-00 9 •• 10 Fig. 5.4 Ra d i a l v e l o c i t i e s f o r BW Vul on 9 August 1971 UT: the phases,of rapid v a r i a t i o n preceding s t i l l s t a n d . 42 preceded the adoption of more e f f i c i e n t coatings on the coude" o p t i c s ; and ( i i i ) observing conditions were generally not as good. The magnitude of these differences may be i n f e r r e d from Table 5.1. The oharaotev of the ' d i s c o n t i n u i t y ' preceding s t i l l s t a n d i s v i r t u a l l y unchanged from 1971 to 1972. The amplitude of the v e l o c i t y curve has decreased s l i g h t l y , but not by enough to i n d i c a t e a meaningful trend. The changes i n the amplitude of the v e l o c i t y curve are discussed further i n Section 5.8. 5.4 THE LINE PROFILE VARIATION The character of the s p e c t r a l l i n e s changes s i g n i f i c a n t l y through-out the pul s a t i o n c y c l e . The changes i n l i n e p r o f i l e are d i r e c t l y c o r -r e l a t e d with the changes i n r a d i a l v e l o c i t y and have the same period of v a r i a t i o n . The pattern of the p r o f i l e v a r i a t i o n i s ind i c a t e d i n Figures 5.5 and 5.6. The v a r i a t i o n i n l i n e depth i s p l o t t e d i n Figure 5.7. Cert a i n d e f i c i e n c i e s i n the present data,* which at times a f f e c t e d the accuracy of the continuum l e v e l , made pr e c i s e determinations of equivalent widths d i f f i c u l t . For t h i s reason, the equivalent widths and some of the other l i n e parameters given by Kubiak (1972) are used as an a i d i n i n t e r p r e t i n g the present data. The pattern of v a r i a t i o n f o r the l i n e s of He, Mg, and S i that were observed i s as fo l l o w s . At the V Q - c r o s s i n g on the ascending branch of the v e l o c i t y curve the l i n e s are sharpest and deepest and e s s e n t i a l l y *Probably due to an intermittent l i g h t leak. t 43 S i III 4 5 7 5 S i III 4 5 6 8 SUM 4 5 5 3 M g l l 4 4 8 l H e l 4 4 7 l F i g . 5.5 Line p r o f i l e s f o r BW Vul on 9 August 1972 UT: the v a r i a t i o n over approximately one c y c l e . P hose = 0.40 Phase = 0.0 Phase = 0.36 B W VUL 9 AUG 1972 UT Si III 4575 Silll 4568 Sill 4553 I l Mg II 4481 He| 4471 F i g . 5.6 L i n e p r o f i l e s f o r BW V u l on 9 August 1972 UT: a demonstration of the extremes i n v a r i a b i l i t y over one c y c l e . i [ 3 => Z o 0.80 o Ui > £ 0.70 _i bJ ce o 4 CC >-Z UI I : I r- 1— B W V U L 9 Aug 1972 U T He I 44 71 • . \ •. •• V ... . • . V • ..... - • • .... . ... ... 0.60 UI ce o u 0.50 0.40 PHASE U T • _ ... .. . . • • • . ...... • • .  ... . . . _L _L JL 0.4 0.5 0.6 0.7 0.8 0.9 0.0 0.1 0.2 0.3 0.4 0.5 -I 1 1 I [ I I I I I I I 6:00 7:00 8«00 9.00 10-00 11:00 F i g . 5.7 The v a r i a t i o n i n l i n e depth over 1.1 c y c l e f o r BW V u l on 9 August 1972 UT. 46 symmetric. As the c y c l e progresses, the l i n e s became shallower, broader, and somewhat asymmetric. The change i n the asymmetry appears to be c o r -r e l a t e d with the change i n the slope of the v e l o c i t y curve ( i . e . , with the a c c e l e r a t i o n ) . At phase ^0.35 the l i n e s begin to double as a component develops at approximately the V q v e l o c i t y . This component strengthens while the o r i g i n a l r e d - s h i f t e d component weakens and eventually fades away (while i t s r e d - s h i f t continues to i n c r e a s e ) . During s t i l l s t a n d the l i n e s become sharper and deeper again, but l e s s so than during the V Q - c r o s s i n g at phase 0.0. During the b l u e - s h i f t following s t i l l s t a n d , the l i n e s became highly asymmetric, and there i s some evidence to suggest that two components may e x i s t for a short time (Odgers, 1956). As the magnitude of the v e l o c i t y decreases, the l i n e s become sharper, deeper, and more symmetric. The c y c l e then begins anew. A more extensive analysis has been made of the p r o f i l e v a r i a -tions during the phases of l i n e doubling preceding s t i l l s t a n d . P r o f i l e s obtained on 9 August 1972 for these phases are given i n Figures 5.8, 5.9, and 5.10; and those obtained on 9 August 1971 i n Figure 5.11. The p r o f i l e s i n d i c a t e the close r e p e t i t i o n of successive c y c l e s , as did the v e l o c i t y curves discussed i n Section 5.3. In comparing the two sets of p r o f i l e s , d i f f e r e n c e s i n the sign a l - t o - n o i s e r a t i o should be noted. Accurate comparisons of the 1971 and 1972 p r o f i l e s are d i f f i c u l t because of the s u b s t a n t i a l d i f f e r e n c e s i n the q u a l i t y of the data. The gross v a r i a t i o n s are c l e a r l y s i m i l a r for the two years. F i g . 5 .8 L i n e p r o f i l e s f o r BW V u l on 9 August 1972 UT: the phases of r a p i d v a r i a t i o n preceding s t i l l s t a n d f o r the f i r s t c y c l e . 48 S i l l l 4 5 7 5 Silll 4 5 6 8 SMII 4 5 5 3 Mg II 4 4 8 1 H e l 4 4 7 1 F i g . 5.9 L i n e p r o f i l e s f o r BW V u l on 9 August 1972 UT: the phases of r a p i d v a r i a t i o n preceding s t i l l s t a n d f o r the second c y c l e . T T — n r r T r r D E C O N V O L V E D 4^  U U I I S i UI 4573 S I I 4 5 6 9 S > l « 5 3 3 U L_J M 4 I I 4401 Ht 1 4471 F i g . 5.10 Deconvolved l i n e p r o f i l e s f or BW Vul on 9 August 1972 UT: the phases of rapid v a r i a t i o n preceding s t i l l s t a n d f o r the f i r s t c y c l e . o < 3 > m 8 : 4 5 : 0 0 8 : 4 6 : 4 0 8 : 4 8 : 2 0 8 : 5 0 : 0 0 8 : 51:40 8 : 5 3 : 2 0 8 : 5 5 : 0 0 8 : 5 6 : 4 0 8 : 5 8 : 2 0 9:00:00 9:01:40 9:0 3 : 2 0 50 1 r siin sim 4 5 7 5 4 5 6 8 si in 4 5 5 3 M 0II Hel 4481 4471 F i g . 5.11 L i n e p r o f i l e s f o r BW V u l on 9 August 1971 UT: the phases of r a p i d v a r i a t i o n preceding s t i l l s t a n d . 51 Intensity ratios and equivalent widths have been computed from the profiles of the f i r s t 'discontinuity* of 9 August 1972 (the latter from planimeter measures). These are given in Figures 5.12 and 5.13 respectively. The total equivalent width remains essentially unchanged during the doubling process, and both the development and weakening of components appear to occur i n a smooth and regular fashion. 5.5 THE LIGHT VARIATION Although further observations of the light variation have not been a part of the present investigation, measurements of this type are considered here because of their fundamental importance. Kubiak (1972) presents a set of observations made i n a system closely matching the Stromgren u,v,b,y system*. These data are given in Figure 5.14. As noted by Walker (1954), there is a variation in the amplitude as a function of wavelength, which agrees f a i r l y well with the variation expected for a black body at the appropriate temperature. There i s no detectable shift with wavelength of the times of maximum and minimum lig h t . The star i s bluest at maximum light (temperature class B 1.5) and coolest at minimum light (temperature class B 2.5). The amplitude can generally be accounted for by changes i n the radius obtained by integration of the velocity curve, but attempts at applying semi-emperical tests of pulsation (such as Wesselink's method of points of equal color) to simultaneous observations of light and velocity have not been successful (Walker, 1954). Kubiak obtains a relation between the Stromgren [Cj] index, [CJ = (u-v) - (v-b) - 0.2 (b-y) , *Stromgren (1963). r B W V U L 9 Aug 1972 U T P h a s e s - 0 . 3 7 - 0 .48 Si l l l 4 5 5 3 , 4 5 6 8 J_ 10 20 3 0 T I M E ( M i n u t e s ) Fig. 5.12 Intensity ratios of the line components for the phases of rapid variation preceding stillstand for BW Vul on 9 August 1972 UT. , 1 i ; r r i B W V U L 9 Aug 1972 U T • Phases -0.37 - 0.48 0.4 o s • SilSI 4 5 5 3 • • . 0 • • 0.3 _ • • • • 0 A Q A A »- 0.2 A A -z UJ A ^ _ J < > /•"» A A A UJ A A 0.1-A A A • STRONGER COMPONENT 1 1 1 1 * WEAKER COMPONENT 1 1 0 10 20 30 T I M E (Minutes ) F i g . 5.13 Equivalent widths f o r the phases of rapid v a r i a t i o n preceding s t i l l s t a n d f o r BW Vul on 9 August 1972 UT. 54 and the e f f e c t i v e temperature: G e = 0.305 [C x] + 0.188, eg = 5040/Te . He j u s t i f i e s i t s a p p l i c a b i l i t y to BW Vul on the assumption of q u a s i - s t a t i c e q u i l i b r i u m . A p l o t of the [C^] index i s given i n Figure 5.15. The i n t e r e s t i n g (and d i f f i c u l t to explain) features of the l i g h t curve are the s t i l l s t a n d on the ascending branch at phases ^0.3 to 0.4 and the r i s e during v e l o c i t y s t i l l s t a n d (during which there appears to be no s i g n i f i c a n t change i n r a d i u s ) . 5.6 THE VARIATIONS IN RADIUS AND ACCELERATION The displacement and a c c e l e r a t i o n of the atmosphere of BW Vul have been derived from the v e l o c i t y curve of Figure 5.1 by graphical i n t e g r a t i o n and d i f f e r e n t i a t i o n r e s p e c t i v e l y . The c o r r e c t i o n f o r center-to-limb e f f e c t s (Parsons, 1972) has been applied to obtain the a c t u a l p u l s a t i o n a l amplitudes. The displacement curve i s given i n Figure 5.16; the accel e r a t i o n s i n Figure 5.17. The radius of BW Vul i s ^6.8 R or about 5.0 x 10 6 km (Watson, 1972) . The maximum displacement of the s t e l l a r atmosphere thus corresponds to a change i n radius of about 10 percent. The general slope of the d i s -placement curve resembles the t r a j e c t o r y of a p r o j e c t i l e . The c o n f i g u r a t i o n of the curve f o r the phase of l i n e doubling preceding s t i l l s t a n d i s , to some degree, 'model-dependent'; since the V q component appears i n a d i s -continuous fashion, making a determination of i t s l o c a t i o n ( i . e . , of the material from which i t o r i g i n a t e s ) impossible by simple i n t e g r a t i o n t e c h -niques. Since the errors i n the displacement curve are cumulative, the Av -.04 .00 .04 .08 .12 .16 i r 55 1 i r i i i i r • v • •• v-fc .00 .01 .02 .03 • • o • ••••\ .. y * *. i * • • . ... • . .00 .04 .08 .12 .16 r- # J L • » • • • , [ ~ 0 . J 5 ] J ! L L -.02 .00 +.02 P H A S E 5 . 6 7 . g 9 0 , 2 5 4 5 6 F i g . 5.14 Ind i v i d u a l observations of the brightness v; and of the Stromgren indices (u-v), (v-b) , and (b-y) f o r BW V u l . Taken from Kubiak (1972, p. 23). [Ql .00 02 04 06 D8 J O .12 .14 i r i .o.' i i i i r ^ o v. [~0.5] J _ J I I -i PHASE 6 .7 .8 .9 .0 .1 .2 .3 4 .5 • a si F i g . 5.15 Individual observations of the Stromgren [Cj] index. The broken curve i s the adopted mean. Taken from Kubiak (1972, p. 27). ( x I0 5) 4 0 3-0 •1 2 ' ° z UI 2 1-0 ui o < a. V) o 0 - 68 0 Bo »»» O N - I • 0 -2-0 PHASE U T r« [/vdt] 1.31 v * r a d i a l ve loc i ty est. error (3) cycle end JL 0.4 0.5 0.6 0.7 0.8 1 I I i 0.9 0.0 0.1 0.2 0.3 0.4 J 0.5 J 6-00 7'00 8>00 9'00 10-00 11-00 F i g . 5.16 The displacement curve f o r BW V u l on 9 August 1972 UT: 1.1 c y c l e of the p u l s a t i o n . A hollow c i r c l e i n d i c a t e s the displacement obtained from the weaker component of a s p e c t r a l l i n e when two components are present. A bar over the c i r c l e i n d i c a t e s that the r e s u l t i s u n c e r t a i n . - ISO -1 1 1 1 ! 1 •" r _ , 1 1 ; 1 i : r—— — -100 u • < -E z - 5 0 o »-< tr • • • -'' ACCEL • • • • • + 100 • + 150 • a *(dv/dt)l.3l v« radial velocity_ PHASE I i t i i i 1 i i i i 0.4 0.5 0.6 0.7 0.8 0.9 0.0 0.1 0.2 0.3 0.4 0.5 U T i i i i i 1 1 I I i i 6'00 7'00 8'00 9'00 10-00 ll'OO F i g . 5.17 The a c c e l e r a t i o n curve f o r BW Vul on 9 August 1972 UT: 1.1 cycle of the p u l s a t i o n . A hollow c i r c l e i n d i c a t e s the acceleration obtained from the weaker component of a s p e c t r a l l i n e when two components are present. 58 r e s u l t s at successively l a t e r phases are l e s s accurate. An estimate of the probable error near the end of the cyc l e i s given i n Figure 5.16. The a c c e l e r a t i o n curve emphasizes the subtle changes i n the v e l o c i t y v a r i a t i o n that are both r e a l and error-induced, and thus should be viewed with caution. The improved time r e s o l u t i o n and the i n t e r n a l con-sistency of the new data are p a r t i c u l a r l y valuable i n i t s determination. Noteworthy features are the extreme accele r a t i o n s following s t i l l s t a n d , the i n t e r v a l of nearly constant dece l e r a t i o n from phases M).7 to 0.2, and the rapid increase i n de c e l e r a t i o n at phase M).2. During the line-do u b l i n g phase preceding s t i l l s t a n d , the decele r a t i o n i s , i n a sense, indeterminate. Odgers (1956) noted that the deceleration computed from the slope at the V o ~ c r o s s i n g on the ascending branch of the v e l o c i t y curve was con-side r a b l y l e s s than the g r a v i t a t i o n a l value c a l c u l a t e d from the star ' s mass and ra d i u s . A value of log g = 3.81 or -65 m/sec2 (correspond-2 ing to 11 MQ and 6.76 EQ f o r the mass and radius i n the r e l a t i o n G = GM/R ) i s given by Watson (1972). For the values of 12 Mg and 7.7 RQ (min.) given 2 by Kubiak (1972), the r e s u l t i s 8 S £ C= ~55 m/sec . In comparison, the values 2 obtained from the a c c e l e r a t i o n curve are ^ 2 4 m/sec at the V - c r o s s i n g , o 2 ^ 6 3 m/sec at phase M).3 j u s t preceding the onset of l i n e doubling (the 2 maximum d e c e l e r a t i o n ) , and ^ +160 m/sec following s t i l l s t a n d (the maxi-mum a c c e l e r a t i o n ) . The maximum inward a c c e l e r a t i o n i s the same order as 8 S £ C ' During the phases of nearly constant deceleration the re s u l t a n t of forces on the gas must be p r i m a r i l y composed of the g r a v i t a t i o n a l force p a r t l y balanced by ihe gas and r a d i a t i o n pressure f o r c e s . 59 5.7 DISCUSSION Introduction The problem of understanding the v a r i a t i o n of BW Vul can be approached on s e v e r a l l e v e l s . A f i r s t - o r d e r a n a l y s i s w i l l y i e l d some knowledge of the general character of the v a r i a t i o n and the most important p h y s i c a l processes involved. Further, a f u l l envelope c a l c u l a t i o n ( i . e . , a q u a n t i t a t i v e modeling of the e n t i r e atmosphere) i s required to obtain a c l e a r and d e t a i l e d p i c t u r e of the r e l a t i o n between the envelope p u l s a t i o n and r a d i a t i v e and hydrodynamic phenomena. Such atmospheric models can i n c i d e n t a l l y be of b e n e f i t i n a determination of the structure of the s t a r as a whole since the parameters describing the atmosphere serve as the outer boundary conditions i n c e r t a i n s t e l l a r model computations. F i n a l l y , the i n t e r r e l a t i o n between all relevant analyses; whether they concern the i n d i v i d u a l B Cephei s t a r s , the c l a s s as a whole, or other types of s t a r s , must be considered. The direct analysis of BW Vul has so f a r proceeded only at the f i r s t l e v e l . There has been no d e t a i l e d q u a n t i t a t i v e model capable of explaining the atmospheric v a r i a t i o n over the e n t i r e c y c l e . Progress has p r i m a r i l y been made by ( i ) obtaining improved observational data; ( i i ) making d e t a i l e d studies of c e r t a i n c r i t i c a l aspects of the v a r i a t i o n ; and ( i i i ) formulating general semi-quantitative 'models'. Odgers (1956) and Osaki (1971) have made contributions under one or more of these categories. Their work w i l l be discussed i n t h i s s e c t i o n . In a d d i t i o n , s e v e r a l papers have attempted to i n t e r p r e t one aspect of the v e l o c i t y v a r i a t i o n i n terms of d e t a i l e d q u a n t i t a t i v e shock wave models. These w i l l also be considered i n t h i s section i n context with more general (but relevant) hydrodynamic 60 analyses. The f i n a l part of the d i s c u s s i o n w i l l deal with a r e f i n e d p i c t u r e of the o v e r a l l v a r i a t i o n , incorporating r e s u l t s obtained from the new ob-s e r v a t i o n a l data. Previous Interpretations Odgers (1956) has developed a semi-quantitative model to explain the p r i n c i p a l features of the v a r i a t i o n . His i n t e r p r e t a t i o n i s based on the following p i c t u r e . ... I t i s supposed that an atmosphere i s ejected with high v e l o c i t y which a f t e r t r a v e l l i n g outwards f o r a time then f a l l s back i n t o the general s t e l l a r photosphere at high speed. For a time at the s t i l l s t a n d phase the s t e l l a r surface proper i s v i s i b l e and then another atmosphere i s e j e c t e d . M a t e r i a l i s ejected at phase ^0.55 by a r e l a t i v e l y high Mach number shock wave to form an 'atmosphere' or envelope ( e s s e n t i a l l y a density maximum) separated from the o r i g i n a l photospheric l a y e r s . The recession of t h i s envelope through the r e l a t i v e l y s t a t i o n a r y photosphere i s assumed to be the cause of the l i n e doubling preceding s t i l l s t a n d . The developing V component a r i s e s from the photospheric l a y e r s , the fading r e d - s h i f t e d component from the envelope. The r i s e i n l i g h t during s t i l l s t a n d i s a t t r i -buted to heating from i n t e r a c t i o n of the l a y e r s . It i s implied that the o s c i l l a t i o n i s purely r a d i a l and s p h e r i c a l l y symmetric i n nature. Osaki (1971) gives a d e t a i l e d d i s c u s s i o n of a p a r t i c u l a r type of p u l s a t i o n model and concludes that the existence of non-radial o s c i l l a t i o n s by themselves can explain most of the fundamental properties of the 6 Canis Majoris s t a r s . He attempts to show that the l i n e p r o f i l e s and the v e l o c i t y curve r e s u l t i n g from a wave t r a v e l l i n g i n the same d i r e c t i o n as the r o t a -t i o n , which i s symmetric, with respect to the equator; i . e . , Ledoux's (1951) 61 -mode also considered by C h r i s t y (1966), are s i m i l a r to those seen i n BW V u l . A t y p i c a l r e s u l t f o r the l i n e p r o f i l e s and the corresponding v e l o c i t y curve i s given i n Figures 5.18 and 5.19. The l i n e p r o f i l e s and v e l o c i t y curve determined by Osaki bear general resemblance to those of BW V u l , but the time of l i n e doubling i s much longer. Furthermore, the model does not demonstrate some of the major s t r u c t u r a l features of BW Vul's v e l o c i t y curve. For example, the model curve displays none of the r e l a t i v e l y sudden changes i n slope nor does i t show the non-symmetry with respect to V . The la c k of agreement may be due i n part (as noted by Osaki) to c e r t a i n s i m p l i f y i n g assumptions made i n d e r i v i n g the model. Therefore a c a r e f u l assessment of these s i m p l i f y i n g assumptions i s i n order. The method by which the v e l o c i t y curve i s obtained ( p a r t i c u l a r l y when more than one component i s present) must also be considered c a r e f u l l y while making comparisons. Nevertheless the agreement between Osaki's model and the v a r i a -t i o n seen i n some of the other 3 Cephei sta r s (such as 12 Lac) i s quite remarkable. However, i n the case of BW Vul i t would c e r t a i n l y be more convincing i f the time scale of l i n e doubling i n the model were more com-p a t i b l e with that observed. Based on the present state of knowledge of BW V u l , Odgers' p i c t u r e of the v a r i a t i o n appears more p l a u s i b l e . The propa-gation of shock waves i n BW Vul's atmosphere, an important part of t h i s p i c t u r e , i s discussed below. The Role of Shock Waves Theories concerned with the propagation of shock waves have been applied to explain a number of a s t r o p h y s i c a l phenomena. As a r e s u l t , there have been numerous discussions of the t o p i c , some relevant to the case i n p o i n t . A good general background i s provided by Shapiro (1954), Zel'dovich 62 1 1 1" - r 1— — " i ' - ••• \ / V/ 4> = o.io 4> = 0.60 \ J cf> = 0.70 \ / <J> = 0.75 4>«Q80 t i i <{> = 0.9C i i i Wto* -1.0 0 1.0 -1.0 0 1.0 F i g . 5.18 T h e o r e t i c a l p r o f i l e s f o r a st a r undergoing non-radial o s c i l l a t i o n s i n Ledoux's (1951) P22 mode. The abscissa i s AA/AAR (or V/Ve s i n i ) , where AA R i s the r o t a t i o n a l width defined as AA R = A (Ve s i n i / c ) ; V e denotes the equ a t o r i a l r o t a t i o n a l v e l o c i t y , i the i n c l i n a t i o n of i t s equator to the c e l e s t i a l plane (90° f o r t h i s case), and c the v e l o c i t y of l i g h t . The ordinate uses an a r b i t r a r y s cale and $ i s the phase. A ' t y p i c a l ' r e s u l t from Osaki (1971, p. 488). LO • / / / 1 J / / 1 0 (Phase) 0 0.5 I0_ F i g . 5.19 The r a d i a l v e l o c i t y curve corresponding to the l i n e p r o f i l e s given i n F i g . 5.18. Taken from Osaki (1971, p. 489). 63 and Raizer (1966, 1967), and Thompson (1972), and a comprehensive discussion of the r e l a t e d a s t r o p h y s i c a l problems by Thomas (1967). Evidence of shock waves has been found i n several types of s t a r s . Perhaps the most convincing i s the emission i n the Balmer l i n e s and doubling of the metal l i n e s i n Population I I v a r i a b l e s (e.g., Castor, 1972). In BW V u l , the large accelerations and v e l o c i t i e s ( i n context with the general pattern of v a r i a t i o n ) provide the primary evidence. There i s also direct evidence for the existence of shock waves i n the sun. The s i t u a t i o n i s h i g h l y complex even f o r such a 'normal' stable s t a r (e.g., Wentzel and Tidman, 1969). A few of the analyses have been reasonably thorough i n attempting to define the r e l a t i o n s h i p between the atmospheric o s c i l l a t i o n and the associated shock wave structures [e.g., H i l l (1972) and Keeley (1970) for R.R. Lyrae and long-period v a r i a b l e s r e s p e c t i v e l y and H i l l e n d a h l (1969, 1970a, b) f o r c l a s s i c a l Cepheids]. H i l l e n d a h l constructed a s e r i e s of radiative-hydrodynamic models which included an extensive atmosphere. A mechanism was i d e n t i f i e d whereby material was accelerated outward by a s e r i e s of outward-moving shock waves, each followed by an inward-moving r a r e f a c t i o n wave. This shock wave-rarefaction -process (hereafter termed the Hillendahl Mechanism) may have importance i n the BW Vul v a r i a t i o n . ' Most studies of shock wave phenomena i n sta r s have been based on a s i m i l a r set of r e s t r i c t i v e assumptions. The pattern has been to consider p l a n a r , hydrodynamic, isothermal shocks of a s e l f - s i m i l a r character propa-gating through an atmosphere which obeys a c e r t a i n density law (see, e.g., Carrus et a l . , 1951; Laurobach and P r o b s t e i n , 1971; Sachdev and Ashraf, 1971). In general, the 'strong shock' approximation i s adopted and the 64 gas assumed to be collision-dominated. Turbulent, magnetic, and viscous stresses are ignored, as w e l l as precursor e f f e c t s ; the r a t i o of s p e c i f i c heats i s assumed to remain constant (although comparisons are made for d i f f e r e n t adopted v a l u e s ) ; the flow behind the shock i s taken as isothermal ( j u s t i f i e d on the basis of the high rate of r a d i a t i v e t r a n s f e r i n the o p t i c a l l y t h i n gas); and the p h y s i c a l conditions for the undisturbed gas are generally obtained from static s t e l l a r atmospheres when such models are required. Despite these many assumptions and r e s t r i c t i o n s , u s e f u l r e s u l t s are sometimes obtained. A few shock wave studies have been aimed d i r e c t l y at BW Vul (Odgers and Kushwaha, 1959; Bhatnagar and Kushwaha, 1961a, b, 1963; Bhatnagar et a l . , 1971). A l l stem from Odgers' (1956) attempt to explain the v e l o c i t i e s seen after the rapid b l u e - s h i f t following s t i l l s t a n d , from phases ^0.6 to 0.9, by the decay of a shock wave of r e l a t i v e l y high Mach number (about 6 ) . A l l are s i m i l a r i n t h e i r approach, but each i n succession o f f e r s refinements by incor p o r a t i n g the e f f e c t s of r a d i a t i o n and mag-n e t i c f i e l d s . The problem as treated here i s e s s e n t i a l l y that of b l a s t wave propagation i n a s t a r (see, e.g., Sakurai, 1965; Korobeinikov et a l . , 1961; Kochina and Mel'nikova, 1958, 1960). The existence of the shock i s assumed a priori and the highest observed gas v e l o c i t y taken as an i n i t i a l condition - e s s e n t i a l l y the v e l o c i t y of the gas seen through the transparent shock front when i t f i r s t becomes v i s i b l e . From that time, i t i s postulated that the shock front decays, with i t s energy u l t i m a t e l y being t r a n s f e r r e d to the gas.* A r e l a -*The r a d i a t i v e f l u x leaving the s t a r as a r e s u l t of the process i s not considered. 6 5 t i o n between the r e l a x a t i o n time of the shock and the v e l o c i t y of the gas i s derived and good agreement with the observed v e l o c i t i e s obtained. The best agreement between the t h e o r e t i c a l and the observed v e l o c i t y curves i s achieved by considering the decay of an isothermal shock i n the presence of a weak magnetic f i e l d (about 2.1 Gauss) with a r a t i o of r a d i a t i o n to gas-pressure of ^ 0.2 (Bhatnagar et a l . , 1971). The r e s u l t s are shown i n Figures 5.20 and 5.21. On t h i s b a s i s , i t i s concluded that ( i ) the observed humps i n the v e l o c i t y curve at these phases can best be accounted f o r by the decay of a shock i n the presence of a weak magnetic f i e l d ; and ( i i ) that magnetic f i e l d s are important i n the i n t e r p r e t a t i o n of the r a d i a l v e l o c i t y v a r i a t i o n i n 3 Cephei s t a r s . These conclusions are i n t e r e s t i n g , but prob-ably not p a r t i c u l a r l y s i g n i f i c a n t i n l i g h t of the s c a t t e r i n the observa-t i o n a l data, the s u b s t a n t i a l v a r i a t i o n i n the appearance of the f i t t e d features between c y c l e s , and the f a c t that s i m i l a r features are seen i n the v e l o c i t y curves of other 8 Cephei sta r s (e.g., 8 Cep and v A r i ) where the pu l s a t i o n amplitude i s such that shock waves may be unimportant. I t should also be noted that there i s no observational evidence f o r the existence of A magnetic f i e l d s i n any of the 8 Cephei s t a r s . An a d d i t i o n a l explanation of the humped appearance of the v e l o c i t y curve i s given by Bhatnagar and Kushwaha (1963) i n terms of the i n t e r a c t i o n of incoming and outflowing m a t e r i a l , and by the present paper. The general r e s u l t s of these analyses are important i n that they lend strength to the shock wave hypothesis. The v e l o c i t y changes and time scales are of the correct order of magnitude. An a l t e r n a t i v e way of looking at the problem i s to consider the e f f e c t s that a shock wave would have on the c h a r a c t e r i s t i c s of the gas ( p a r t i c u l a r l y i t s v e l o c i t y ) when passing with undiminished strength through * The e f f e c t s of such a small field,however, would be v i r t u a l l y impossible to detect by present observational methods. 0 •01 -02 -03 - 0 4 - 0 5 -06 F R A C T I O N O F A DAY — F i g . 5.20 T h e o r e t i c a l r a d i a l v e l o c i t y curves; A and B r e s p e c t i v e l y represent the cases f o r a = 0 and a = 0.2, where a i s the r a t i o of r a d i a t i o n pres-sure to the gas pressure. The observations of Odgers (1956) dur-ing the cycle beginning J.D. 2435009.760 are represented by s o l i d dots. Taken from Bhatnagar et a l . (1971, p. 136). 0 F i g . 5.21 The same as F i g . 5.20 but with the e f f e c t s of a 2.1 Gauss magnetic f i e l d included. Taken from Bhat-nagar et a l . (1971, p. 136). 67 the region of the s t e l l a r atmosphere i n which the s p e c t r a l l i n e s are pro-duced. An approximate c a l c u l a t i o n of the shock conditions i n t h i s circum-stance have been made using the model atmosphere grids of Gingerich (1969) and Van C i t t e r s and Morton (1970) and adopting the a n a l y t i c a l procedures o u t l i n e d by Sachdev and Ashraf (1971). The computations are given i n Appendix E. Results obtained i n t h i s fashion are also compatible with the shock wave hypothesis. The analyses are too coarse to recommend a d e f i n i t e model. The important problem of determining the behavior of a shock wave at the surface of a st a r where the density goes to zero has been considered by Zel'dovich and Raizer (1966), Gandel'man and Frank-Kamenetskii (1956), and Sakurai (1960). - _ . A Refined Interpretation A r e f i n e d p i c t u r e , which attempts to go somewhat further i n ex-p l a i n i n g the more d e t a i l e d aspects of the v a r i a t i o n over the e n t i r e cycle and i s compatible with most of the a v a i l a b l e observational data, i s pr e -sented here i n q u a l i t a t i v e terms. I t e s s e n t i a l l y stems from the basic idea proposed by Odgers (1956) and i s based on the following assumptions: (1) The discontinuous nature of BW Vul's v e l o c i t y v a r i a t i o n i s e s s e n t i a l l y an amplitude e f f e c t - the amplitude of the basic v a r i a t i o n s u f f i c i e n t i n t h i s circumstance to promote the development of shock waves, which i n turn are responsible f o r the e j e c t i o n of an "envelope"* and the extreme accele r a t i o n s observed. (2) The v e l o c i t y v a r i a t i o n can thus be explained on the basis of two 'mechanisms': a. Shock-induced mass motions • E s s e n t i a l l y a density maximum separated from the general photospheric l a y e r s . 68 b. Motion of the envelope and i n t e r a c t i o n between i t and the underlying l a y e r s . (3) Beneath the o p t i c a l l y t hick (only i n the l i n e ) envelope, the s t a r i s undergoing an e s s e n t i a l l y s i n u s o i d a l o s c i l l a t i o n , s i m i l a r to that displayed by s t a r s such as 6 Cephei. (4) The o s c i l l a t i o n of the general photosphere (and not that of the ejected envelope) i s most d e c i s i v e i n the l i g h t v a r i a t i o n . A summary of the observed v a r i a t i o n [from Kubiak (1972) and the present program] and a d e s c r i p t i o n of the proposed underlying o s c i l l a t i o n i s presented i n Figures 5.1, 5.16 and 5.22 f o r general Comparisons only. One cycle w i l l be considered on the b a s i s of t h i s information. At phase 0.55, the approximate epoch of maximum l i g h t and minimum r a d i u s , and the r e -fore the time of maximum compression of the gases, a compression wave i s •formed i n the s t e l l a r atmosphere i n the v i c i n i t y of the photosphere. The wave propagates outward with i n c r e a s i n g amplitude and becomes a shock wave. The e f f e c t s of t h i s shock (plus the r a r e f a c t i o n wave that may succeed i t a f t e r i t s a r r i v a l at the s t e l l a r 'surface' as per the H i l l e n d a h l Mechanism) are observed as the extreme a c c e l e r a t i o n of the gas from phases 0.55 to 0.6. The v e l o c i t y of the accelerated material increases r a p i d l y and an envelope i s formed above the o r i g i n a l photospheric l a y e r s . Concur-r e n t l y , the underlying layers begin t h e i r outward expansion, but are l e f t behind by the r a p i d l y a c c e l e r a t i n g envelope. The drop i n temperature during t h i s process takes place smoothly and i s associated p r i m a r i l y with the underlying o s c i l l a t i o n . From phases 0.6 to 0.75, the v e l o c i t y curve has the p e c u l i a r humped appearance described i n Section 5.3. This e f f e c t i s associated with the formation of a r a r e f i e d region behind the envelope as i t separates furthe r from the general photosphere. As t h i s occurs, the gas pressure F i g . 5.22 A summary of the observed features of the v a r i a t i o n of BW Vul. 70 from the underlying layers decreases. The pressure forces increase s i g -n i f i c a n t l y again at phase 0.74, when the underlying layers 'catch up'. A s l i g h t increase i n the outward v e l o c i t y at t h i s time i s ind i c a t e d by some of the previous data. The motions of the envelope and i t s underlying layers are essen-t i a l l y p a r a l l e l u n t i l phase "Ml.2. Throughout t h i s i n t e r v a l , the dec e l e r a -t i o n of the envelope i s nearly constant, but s u b s t a n t i a l l y l e s s than the g r a v i t a t i o n a l value; due to the modifying e f f e c t s of gas and r a d i a t i o n pressure. The envelope reaches i t s maximum a l t i t u d e i n t h i s i n t e r v a l and the v a r i a t i o n i n temperature continues i n a smooth f a s h i o n . Near phase 0.2, the underlying layers begin to recede from the envelope, again producing a r a r e f i e d zone with an associated reduction i n the force of gas pressure on the envelope. The decele r a t i o n of the enve-lope increases u n t i l i t approaches the f r e e - f a l l value (8 f c ) a t phase 0.3 at which i t remains f o r about 0.05 c y c l e . At nearly the same time as the f r e e - f a l l a c c e l e r a t i o n i s a t t a i n e d , the l i n e s become double, with the appearance of a weak component at the V Q v e l o c i t y . The outward features of t h i s process have been discussed i n Sections 5.3 and 5.4. An explanation of i t s p h y s i c a l s i g n i f i c a n c e w i l l be deferred to the following s e c t i o n . The l i n e doubling terminates at phase 0.45 with the disappearance of the o r i g i n a l component, now highly red-s h i f t e d . During the phases of l i n e doubling, the envelope r e j o i n s the general photospheric l a y e r s . A s t i l l s t a n d i n temperature i s observed over much of this, i n t e r v a l . During the l a t t e r part of s t i l l s t a n d (phases 0.45 to 0.55) con-71 t r a c t i o n of the st a r continues u n t i l minimum radius and maximum temperatures are again reached. A part of the temperature r i s e that takes place during t h i s i n t e r v a l i s probably due to factors other than the simple c o n t r a c t i o n of the photosphere. The Line Doubling Phase Preceding Stillstand The l i n e doubling preceding s t i l l s t a n d appears to be a complex process with no simple explanation. The displacement curve i n d i c a t e s that i t may begin due to the onset of transparency i n the envelope and may end with the passage of the envelope i n t o the general photospheric l a y e r s , the hi g h l y r e d - s h i f t e d component o r i g i n a t i n g from inc r e a s i n g o p t i c a l depths. P r e c i s e l y how the transparency i n the envelope may occur, why the new components develop at the V v e l o c i t y and remain there, why the components remain so sharp and d i s t i n c t , why the t o t a l equivalent width remains nearly constant, why there i s a l a g i n the hydrogen l i n e v e l o c i t i e s , and why the s t i l l s t a n d i n l i g h t occurs, are some of the questions that may be answered by a d e t a i l e d q u a n t i t a t i v e a n a l y s i s . Some of the po s s i b l e 'mechanisms' are: (1) Onset of transparency i n the f a l l i n g envelope (the r e d - s h i f t e d component a r i s i n g from the envelope, the V Q component from the photospheric layers below i t ) . (2) P h y s i c a l i n t e r a c t i o n between the f a l l i n g envelope and the pho-tosphere (the r e d - s h i f t e d component a r i s i n g from the envelope, the V D component from the photospheric layers above i t ) . (3) Shock wave (or shock wave-rarefaction) e j e c t i o n of mat e r i a l to a l o c a t i o n above the envelope (the r e d - s h i f t e d component a r i s i n g from the envelope, the V Q component from the ejected material above i t ) . (4) Non-radial p u l s a t i o n s . (5) The movement of 'spots' ( l o c a l i z e d regions having p a r t i c u l a r c h a r a c t e r i s t i c s ) along the s t e l l a r equator, as suggested by Struve (1950) as a po s s i b l e explanation f o r the s p e c t r a l changes i n 12 Lac. 72 Considered i n d i v i d u a l l y , a l l of these s u f f e r from c e r t a i n fundamental d e f i c i e n c i e s . Perhaps several i n combination may provide the bas i s f o r a s a t i s f a c t o r y explanation. On the other hand, perhaps none of them holds a c l u e . 5.8 THE LONG-TERM* VARIATIONS Introduction The long-term v a r i a t i o n s i n the p e r i o d , and i n the l i g h t and r a d i a l v e l o c i t y amplitudes, are of p a r t i c u l a r importance from considerations of s t e l l a r e volution and s t a b i l i t y . Studies of some of these parameters over time i n t e r v a l s of tens of years have been made for a few of the w e l l -known 8 Cephei st a r s (e.g., 8 Cep and BW V u l ) . I n t e r p r e t a t i o n of the r e s u l t s has generally been d i f f i c u l t because of the small magnitude of the changes and the problems of instrumental and observational nonuniformities. Variation in the Period P e t r i e (1954) noted that an increasing period was required to explain the advancing phase with time of any part of the r a d i a l v e l o c i t y curve. He found that the phase of V^-crossing, on the ascending branch of the v e l o c i t y curve, could be represented by the r e l a t i o n * = 40.24 - 1.56xl0"5(t-2,425,405) + 0.30xl0- 8(t-2,425,405)2 between 1924 and 1952. The mean rate of change i n the period over t h i s i n t e r v a l was +3.7 seconds per century. The study was continued by Odgers (1956), and by Percy (1971). Approximate phases were computed from the •Relative to the p u l s a t i o n p e r i o d . 73 data obtained with the Isocon i n 1971 and 1972. The r e s u l t s were compatible with those obtained p r e v i o u s l y . The character of the v a r i a t i o n i s shown i n Figure 5.23. The observed period changes appear to be s i g n i f i c a n t . I t i s not c l e a r whether they are continuous, or are the r e s u l t of a number of essen-t i a l l y discontinuous changes. Furthermore, an ambiguity e x i s t s because of the p o s s i b i l i t y of a 'missing' cycle between successive measures. The mean rate of change i s greater than that predicted by s t e l l a r e v o l u t i o n (Percy, 1971). I f the observed changes represent a true secular v a r i a t i o n , Lesh's hypothesis (Section 3.2) i s strengthened. There appears to be a pseudo-sinusoidal o s c i l l a t i o n superimposed on the mean rate of in c r e a s e . The p h y s i c a l s i g n i f i c a n c e of t h i s o s c i l l a -t i o n i s not c l e a r . I t i s reminiscent of the changes seen i n the periods of close binary systems, which are also a mystery. The e f f e c t may be s t a t i s -t i c a l i n o r i g i n , or i t may be connected with the b a s i c v a r i a t i o n of the s t a r . Amplitude Variations in the Light and Radial Velocity Curves P e t r i e (1954) found that BW Vul's r a d i a l v e l o c i t y amplitude v a r i e d i n an i r r e g u l a r fashion over short i n t e r v a l s and also appeared to be i n -creasing with time. The increase i n semi-amplitude amounted to VL6 km/sec over the period extending from 1928 to 1952, the rate of increase being 0.7 km/sec/yr. I f both the period and the v e l o c i t y amplitude are i n c r e a s i n g , the amplitude of the pulsation must be increasing as w e l l . Further increases i n the v e l o c i t y amplitude have been demonstrated by Odgers (1956), by Kubiak (1972), and by the present i n v e s t i g a t i o n . The data are shown i n Figure 5.24. Part of th i s increase must be a t t r i b u t e d to ( F i g . 5.23 The v a r i a t i o n i n the period of BW Vul as indicated by the phase of V 0 - c r o s s i n g , p l o t t e d against the square of the time elapsed since J.D. 2428000. The l i n e represents the r e l a t i o n found by P e t r i e (1954) to f i t the observations of 1924-1952; the data are based on observations made since 1952 (the hollow c i r c l e s from the present program). The Figure i s taken from Percy (1971). 300-200 ~ o " V . 6 o e > <3 100 1930 19 40 1950 I960 1970 Y E A R F i g . 5.24 The v a r i a t i o n i n the r a d i a l v e l o c i t y amplitude (2K) for BW V u l . The v e r t i c a l bars i n d i c a t e the range i n the observed amplitude i n a s i n g l e year i f there were more than one observation; the dots are the mean. Observations through 1952 are from P e t r i e (1954); from 1953 to 1954 from Odgers (1956), from 1966 from Kubiak (1972), and from 1971 to 1972 from the present program. ) 76 continuing improvements i n the instrumentation, p a r t i c u l a r l y since the recorded v e l o c i t y amplitude i s c r i t i c a l l y dependent, on the time and spec-t r a l r e s o l u t i o n r e a l i z e d during the phases of rapid v a r i a t i o n . The sudden increase i n amplitude observed i n 1954 may have been due i n part to improve-ments i n the data. I f the true v a r i a t i o n i s to be determined, a l l data must be compared on a uniform b a s i s . I f the r a d i a l v e l o c i t y amplitude has a c t u a l l y increased, an increase i n the amplitude of the l i g h t v a r i a t i o n might also be expected. Unfortunately, the photometric data are f a r l e s s extensive than the spec-troscopic and are quite nonuniform. There are some tenuous i n d i c a t i o n s of an increase i n the amplitude since 1938. There i s also a considerable amount of s c a t t e r i n the data. Huffer (1938) obtained a value of ^0.18 mag. Kraft (1953) found that the amplitude increased from 0.19 to 0.23 mag. i n the 'blue' during the period August 22-26, 1952. Eggen (1948) recorded a f l a r i n g of the s t a r of an unknown amplitude. The most recent observations (Kubiak, 1972) provide amplitudes nearly the same as those obtained i n the 1950's. Summary The trend of an i n c r e a s i n g amplitude i n the p u l s a t i o n of BW Vul as i n d i c a t e d by the i n c r e a s i n g period and r a d i a l v e l o c i t y amplitude seems to be r e a l . However, the extent of t h i s increase i s not c l e a r . 77 5.9 FUTURE WORK The most immediate need is for an extension of the theoretical analysis, which has obviously lagged behind the observational study. Analysis of the present set of observations continues, with emphasis on obtaining better radial velocities through improved analysis techniques and deriving useful information from the rather limited set of observa-tions made at Ha with the Isocon. A continuing program of surveillance of the long-term changes in the period and radial velocity amplitude would be of considerable interest and value. 78 3 CEPHEI 5.10 INTRODUCTION The s t a r 8 Cephei has been l a b e l l e d as the prototype of i t s c l a s s , having a 4.6-hour period of v a r i a t i o n i n l i g h t and r a d i a l v e l o c i t y ( i t s c h a r a c t e r i s t i c s are given i n Table 4.1). I t s v a r i a b l e v e l o c i t y was d i s -covered by Frost (1902) and i t has since been the subject of numerous spectroscopic s t u d i e s , many of which have been summarized by Struve et a l . (1953). The photometric observations have been r e l a t i v e l y sparse, beginning with those of Guthnick and Prager (1914) and extending to those of Gray (1970) at widely-spaced i n t e r v a l s . Observations of 8 Cep i n the UV have recently been made with 0A0-2 ( F i s c h e l and Sparks, 1972). The r a d i a l v e l o c i t y v a r i a t i o n of 8 Cep i s approximately s i n u s o i d a l . The recorded range i n amplitude i s 18-46 km/sec, with small changes (of at most a few km/sec) between successive c y c l e s . The y - v e l o c i t y also varies from c y c l e to c y c l e . F i t c h (1969) c a r r i e d out a periodogram a n a l y s i s using the v e l o c i t y data obtained by Struve et a l . (1953), and found a systematic v a r i a t i o n i n the y - v e l o c i t y which he int e r p r e t e d as an o r b i t a l period of 10^893. He also found a c o r r e l a t i o n between the p u l s a t i o n a l v e l o c i t y amplitude and the phase of the adopted o r b i t a l p e r i o d . On t h i s b a s i s , minimum p u l s a t i o n amplitude would occur at (or near) maximum t i d a l compression and maximum amplitude at minimum compression. Osaki (1971) noted, however, that the v a r i a t i o n i n the y - v e l o c i t y claimed as ' o r b i t a l ' by F i t c h could w e l l be ' p h y s i c a l ' , r e s u l t i n g from a long-period modulation due to a superposition of two o s c i l -l a t i o n s . * i 79 The l i g h t v a r i a t i o n also appears to be s i n u s o i d a l , but has a m i n i -mum about 25% wider than the maximum (Gray, 1970). I t i s somewhat i r r e g u l a r and s i g n i f i c a n t changes i n amplitude between successive cycles have been noted. Stebbins and Kron (1954) have made s i x - c o l o r observations of B Cep i n the UVBGRI system. A t y p i c a l range i n amplitude for one cycle was 0.057 mag. i n U, decreasing to 0.011 mag. i n I. The differences could e s s e n t i a l l y be explained i n terms of a black-body r a d i a t i o n curve. The r a d i a t i o n curves were found to agree i n phase. The color change was s m a l l , amounting to 0.007 mag. f o r V-G. The star was bluest at (or very near) maximum l i g h t i n the usual pattern of the 6 Cephei s t a r s . However, i t was smallest P P P at 0.04 before r a d i a t i o n maximum, compared with 0.08 - 0.12 f o r t h i s d i f f e r -ence i n several c l a s s i c a l Cepheids. Stebbins and Kron also t r i e d to derive a radius f o r 8 Cep on the basis of the a v a i l a b l e l i g h t and r a d i a l v e l o c i t y measures. On the condit i o n that the r a t i o of amplitudes i n short and long wavelengths agree with the computed r a t i o f or small v a r i a t i o n s i n the temperature of a B l s t a r at 23000°K, a value of 9.0 R@ (with a large probable error) was obtained. It was obvious that simultaneous l i g h t and r a d i a l v e l o c i t y measures were r e -quired i f a reasonable accuracy was to be r e a l i z e d - p r i m a r i l y because of the s i g n i f i c a n t cycle to cycle v a r i a t i o n . Popov (1971) obtained a radius of 8.0 RQ using Wesselink's method (Wesselink, 1946). Conclusive evidence f o r a systematic l i n e p r o f i l e v a r i a t i o n i n 8 Cep has been long i n coming. Observations of Ha by Greaves et al.(1955), which were b r i e f l y discussed by Wilson (1956), i n d i c a t e d a s u b s t a n t i a l v a r i a t i o n i n the Ha p r o f i l e r e l a t i v e to Hel X6678 as a r e s u l t of i n c i p i e n t emission. I t was thought that t h i s v a r i a t i o n was of a long-term nature and 80 thus probably not corr e l a t e d with the p u l s a t i o n c y c l e . Struve (1955b) did not share t h i s view. He f ound that the emission feature was strongest h a l f -way on the ascending branch of the v e l o c i t y curve ( i n agreement with s i m i -l a r e f f e c t s seen i n other 8 Cephei stars) and noted f u r t h e r that some of the other hydrogen l i n e s might also have been influenced by emission - as suggested by Karpov (1933). Further evidence f o r a systematic l i n e p r o f i l e v a r i a t i o n has come from the observations of OAC—2 ( F i s c h e l and Sparks, 1972). A t o t a l of 64 scans over 76 days covering 400 cycles of the p u l s a t i o n were obtained of the region centered on the S i l V X1400 and CIV X1550 resonance l i n e s . I t was found that the strength of the CIV l i n e (as determined from measurements of the f l u x at i t s c e n t r a l wavelength) followed the p u l s a t i o n c y c l e , and that i t a lso varied with a period of about 6 days - a v a r i a t i o n shared neither by the continuum nor the S i l V l i n e ! The p o s s i b i l i t y that t i d a l e f f e c t s r e l a t e d to F i t c h ' s o r b i t a l motion were responsible f o r t h i s v a r i a t i o n was termed most probable. I t should be noted that the CIV l i n e i s very lumin-o s i t y s e n s i t i v e while S i l V i s not. 5 . 2 2 THE NEW DATA Observations covering ^0.8 cycle of the p u l s a t i o n period were made on October 16, 1972 UT. The Isocon plus the 5X t r a n s f e r lens developed by E.H. Richardson of the D.A.O. was used to observe the S i l l l XX4553 and 4568 l i n e s . Observations were also made of the region centered on Ha on September 2, 1972 UT with the s i l i c o n v i d i c o n . Approximately one cycle was covered. The general features of these observations are given i n Table 4.II 81 and the d e t a i l s i n Table 5.II. The data obtained with the Isocon provided the first definitive record of a variation in line profile correlated with the variations in light and radial velocity. The p r o f i l e s are given i n Figure 5.25 and measures of the r a d i a l v e l o c i t y , l i n e depth, and l i n e - p r o f i l e asymmetry i n Figure 5.26. The basic pattern of v a r i a t i o n i n the l i n e p r o f i l e s i s as fo l l o w s . When the r a d i a l v e l o c i t i e s are p o s i t i v e , the l i n e s have a more pronounced absorption wing on the blueward s i d e ; when the v e l o c i t y i s zero, the l i n e s are symmetric; and when the v e l o c i t y i s negative, the l i n e s have a more pronounced absorption wing on the redward s i d e . This r e s u l t represents a s i g n i f i c a n t step toward d e f i n i n g the v a r i a t i o n of 8 Cep. The change i n the asymmetries of the p r o f i l e s i n d i c a t e s that d i f f e r e n t i a l motion takes place i n the atmosphere as a r e s u l t of the p u l s a t i o n . A comparison of t h e o r e t i c a l and observed p r o f i l e s should provide a c r i t i c a l t e s t of the nature of t h i s p u l s a t i o n (which appears to be r a d i a l and s p h e r i c a l l y symmetric) as w e l l as an i n d i c a t i o n of the limb darkening and the magnitude of the turbulent v e l o c i t i e s (van Hoof and Deurink, 1952). In more general terms, furth e r weight i s given to the notion that l i n e p r o f i l e v a r i a t i o n s are fundamental to the 8 Cephei phenomenon. Thus some degree of v a r i a t i o n i n the s p e c t r a l l i n e s , and the atmospheric motions that produce them, should be present i n a l l of the 8 Cephei s t a r s . 5.12 THE LONG-TERM VARIATION Struve et a l . (1953) found a secular change i n the p u l s a t i o n period which he expressed as P = 0.1904844 + 5.8880 x 10"1 1 n + 9.8013 x 1 0- 1 7 n2 , Table 5.II.. Observations of 6 Cephei Detector UT Date J u l i a n Date 2441000+ H . A . @ S t a r t Frame Time (Minutes) E f f e c t i v e Exposure Time* (Minutes) Mean E f f e c t i v e Dispersion** (points/X) Quality FactorV Vidicon 2 Sept. 72 562.674-.689 2:50E 8.5 17 Isocon 16 Oct. 72 606.926-.965 606.968-.999 607.000-.083 6:08W 0.129 0.098 0.129 6 6 10 20 20 20 1 1 2-3 *The 'best' compromise between time r e s o l u t i o n and the signal-to-noise r a t i o (the average over the time i n t e r v a l ) **The average over the region of i n t e r e s t . VAn estimate of the q u a l i t y of the data (1 = excellent to 4 = poor). _ 1 1 LINE O E P T H lNon-Dlm«nsionoO • Sllll 4 5 5 3 • SIM 4 5 6 8 Max. I n c r e a s e ~ 30% + 0 o o 9 o • • o • • » o . » • e o o o + 6 + 10 UJ u or o P R O F I L E V A R I A T I O N (R-B) * Silll 4 5 5 3 "Sim 4 5 6 8 o - • 5 e 8 o r -10 + 2 0 -R A D I A L V E L O C I T Y from Silll 4 5 5 3 , 4 5 6 8 Oct 16 ,1972 U T > - - 2 0 • o + 2 0 -i > from H< Sept 2 , 1 9 7 2 U T -20 P « 4 h 3 6 M 0.4 0.5 0.6 0.7 0.8 P H A S E 0.9 0.1 0.2 0.3 F i g . 5.26 Measures of the r a d i a l v e l o c i t y , l i n e asymmetry, and l i n e depth for 3 Cephei. The asymmetries of the l i n e s are i n d i c a t e d by the d i f f e r e n c e between the angle of a s t r a i g h t l i n e f i t t e d through the red side of the p r o f i l e and one through the b l u e . 85 where n i s the number of cycles since J.D. 2422203.790. He noted that an e r r a t i c jump i n the period had occurred between 1914 and 1919. On the other hand, Gray (1970) concludes (on the basis of both the v e l o c i t y and l i g h t measures) that there are no secular changes i n the period of 8 Cep but instead one or more e s s e n t i a l l y discontinuous changes exemplified by the e a r l i e r change. 5.13 FUTURE WORK The s t a r 8 Cep i s an exc e l l e n t subject f o r a d e t a i l e d p u l s a t i o n a l a n a l y s i s ( i ) because of the r e l a t i v e l y large amplitude and r e l a t i v e l y simple pattern of i t s v a r i a t i o n ; ( i i ) because of the s u b s t a n t i a l l i g h t and v e l o c i t y 'data already a v a i l a b l e ; and ( i i i ) because of the r e l a t i v e ease with which new observations can be obtained. Computation of t h e o r e t i c a l p r o f i l e s and a d d i t i o n a l observations aimed at r e s o l v i n g the p r o f i l e v a r i a t i o n should be given high p r i o r i t y . 86 CHAPTER 6. SUMMARY AND CONCLUSIONS The new detection system has proved to be w e l l - s u i t e d to the study of the s p e c t r a l v a r i a t i o n s i n the $ Cephei ($CMa) stars and other r e l a t i v e l y bright objects. Continuing use of the Image Isocon f o r these types of programs i s c e r t a i n l y warranted. The more recently developed detectors (such as the s i l i c o n v i d i c o n and Reticon*) hold promise of even furthe r gains, but perhaps of a d i f f e r e n t nature. The portion of the instrumentation developed as part of the present project - the cooling system f or the Image Isocon - has been an important and r e l i a b l e part of t h i s detection system. I t represents an unusual and v e r s a t i l e approach to the cooling of astronomical detectors and provides a p r a c t i c a l s o l u t i o n to one of the most important problems i n the f a b r i c a t i o n of detection systems of t h i s type. The compactness and s i m p l i c i t y of the hardware associated d i r e c t l y with the detector, the inherent system s t a b i l i t y , and the ease of system c o n t r o l are some of the more noteworthy features. The software package developed f o r handling the s u b s t a n t i a l data output from the detection system has also proved s a t i s f a c t o r y . The processing can be c a r r i e d out r a p i d l y and e f f i c i e n t l y , the instrumental e f f e c t s reduced to n e g l i g i b l e l e v e l s , and the required q u a n t i t a t i v e a n a l y s i s e a s i l y completed. Refinements are c o n t i n u a l l y being incorporated i n t o t h i s package. * A self-scanned array of s i l i c o n diodes (see, e.g., T u l l , R.G. and Nather, R.E. 1973, Astronomical Observations with Television-Type Sensors, (Symposium held at the U n i v e r s i t y of B r i t i s h Columbia 15-17 May 1973). 87 Data have been obtained with the detection system of the 3 Cephei star s BW Vul and 3 Cep which have contributed s i g n i f i c a n t l y to an under-standing of t h e i r p u l s a t i o n a l c h a r a c t e r i s t i c s and have provided further i n s i g h t s into the 3 Cephei phenomenon. An extensive amount of data has been obtained of BW Vul over the past 50 years; providing a f a i r l y d e t a i l e d p i c t u r e of i t s short-term l i g h t , r a d i a l v e l o c i t y , and l i n e p r o f i l e v a r i a t i o n s as w e l l as an i n d i c a -t i o n of the long-term changes i n i t s period and r a d i a l v e l o c i t y amplitude. The new observations represent the best e f f o r t so f a r at reducing the degrading e f f e c t s of l i m i t e d time and s p e c t r a l r e s o l u t i o n . As a r e s u l t , the l i n e p r o f i l e changes occuring during c e r t a i n c r i t i c a l phases of the pu l s a t i o n have been resolved f o r the f i r s t time, and a more accurate determination of the atmospheric motions throughout the p u l s a t i o n c y c l e (e.g., the displacement and acceleration) has been made p o s s i b l e . In a d d i t i o n , c e r t a i n features appearing i n the photographic data which were previously ascribed to chance e f f e c t s or to noise are now seen to represent r e a l a s t r o p h y s i c a l occurrences. This data can now provide further u s e f u l information i f subject to a d d i t i o n a l a n a l y s i s . The data gives the following p i c t u r e of the st a r ' s v a r i a t i o n . At the approximate epoch of minimum radius a v i o l e n t e j e c t i o n of the s t e l l a r 2 atmosphere takes place with a maximum a c c e l e r a t i o n i n excess of 150 m/sec and a maximum outward v e l o c i t y ( i n the frame of the star) of more than 100 km/sec. The time scale f o r the process i s about 15 minutes. The material then appears to undergo p r o j e c t i l e motion f or about one-half of the p u l s a t i o n c y c l e . The dec e l e r a t i o n during t h i s i n t e r v a l i s nearly 2 constant at ^ 25 m/sec (less than one-half the value of g ) and the sic maximum displacement V5 x 10"* km (or about 10% of the s t e l l a r r a d i u s ) . A short time before the return of the ejected m a t e r i a l to the general 88 s t e l l a r surface the d e c e l e r a t i o n increases r a p i d l y and approaches the value of 8 g £ c ' At roughly t h i s time the s p e c t r a l l i n e s become double as a new component develops and strengthens at the V q p o s i t i o n . The o r i g i n a l component ( o r i g i n a t i n g from the ejected material) disappears i n a time sc a l e of about 30 minutes leaving only the V q component. For approximately the next 30 minutes the s t e l l a r surface appears to remain nearly s t a t i o n -ary. The process then begins anew. The data were examined f o r phase e f f e c t s i n the r a d i a l v e l o c i t i e s and i n the p r o f i l e v a r i a t i o n s of the s p e c t r a l l i n e s , f o r d i f f e r e n c e s b e t -ween cycles ( p a r t i c u l a r l y successive ones), and for evidence of binary e f f e c t s and m u l t i p l e p e r i o d i c i t i e s . Phase di f f e r e n c e s i n the v a r i a t i o n s of d i f f e r e n t s p e c t r a l l i n e s (or i n the r a d i a l v e l o c i t i e s derived from them) are i n d i c a t i v e of dynamic s t r a t i f i c a t i o n s i n the atmosphere. The 'Van Hoof E f f e c t ' , discussed i n Section 5.3, i s one of the most obvious manifestations of such a s t r a t i f i -c a t i o n . Evidence of t h i s e f f e c t has previously been found f o r BW Vul but simultaneous observation of the hydrogen l i n e s and those other elements were not c a r r i e d out i n the present program. The p r i n c i p a l l i n e s that were observed simultaneously (those of H e l , Mg I I , and S i I I I i n the o region ^4450 to 4590 A) appeared to vary i n a synchronous fashion through-out the e n t i r e c y c l e , i n d i c a t i n g that the motion of the atmosphere i n the zone of t h e i r formation was e s s e n t i a l l y uniform. I t should be noted that these l i n e s are a l l formed under s i m i l a r c onditions. The r e p r o d u c i b i l i t y of successive cycles serves as one c r i t e r i o n f o r determining the coupling between the observed atmospheric motion and the basic o s c i l l a t i o n of the s t a r , and f o r obtaining some idea of the nature of the basic i n s t a b i l i t y . Some evidence of a c y c l e - t o - c y c l e v a r i a -89 t i o n i n the p u l s a t i o n amplitude was given both by the previous photographic data and by the observations obtained i n 1971 with the Isocon. The r e s u l t s are uncertain because of the low q u a l i t y of t h i s data. Higher q u a l i t y observations obtained with the Isocon i n 1972 covering ^1.1 c y c l e of the p u l s a t i o n demonstrated no such v a r i a t i o n . Binary e f f e c t s and m u l t i p l e p e r i o d i c i t i e s (with t h e i r associated beat e f f e c t s ) can strongly influence the observational c h a r a c t e r i s t i c s of the B Cephei s t a r s . They are also of importance from s t a b i l i t y considera-t i o n s . There i s l i t t l e evidence to suggest that BW Vul i s a binary or that i t displays more than one p e r i o d . The complexity of the v a r i a t i o n of t h i s star has discouraged theor-e t i c a l a n a l y s i s . The e x i s t i n g studies are discussed i n t h i s paper and the avenues f o r extending them i n d i c a t e d . I t appears that the extreme changes i n the r a d i a l v e l o c i t i e s are an atmospheric e f f e c t , to a c e r t a i n degree unrelated to the basic o s c i l l a t i o n of the s t a r . The e f f e c t s of large scale shock wave propagation i n the atmosphere are probably responsible f o r much of the v a r i a t i o n i n the r a d i a l v e l o c i t i e s and l i n e p r o f i l e s . The l i g h t v a r i a t i o n , which occurs i n a r e l a t i v e l y smooth fa s h i o n , i s more c l o s e l y t i e d to the basic o s c i l l a t i o n . A r e f i n e d p i c t u r e i s presented which attempts to explain many features of the v a r i a t i o n i n terms of the i n t e r a c t i o n between two r e l a t i v e l y d i s t i n c t layers - an envelope ejected by a high Mach number shock wave and the general photospheric l a y e r . The assumption of a r a d i a l , s p h e r i c a l l y symmetric o s c i l l a t i o n i s i m p l i c i t i n t h i s approach. The l i n e doubling preceding s t i l l s t a n d i s perhaps due to two mechanisms: ( i ) the onset 90 of transparency i n the receding envelope and ( i i ) the i n t e r a c t i o n of t h i s envelope with the general photospheric l a y e r . The present program has also provided furt h e r information con-cerning the long-term changes i n the period and the r a d i a l v e l o c i t y amplitude. Both appear to be i n c r e a s i n g , providing evidence for an increase i n the pulsation amplitude as w e l l . The s t a r may be i n a phase of rapid e v o l u t i o n . For 3 Cep, the f i r s t d e f i n i t i v e record of a v a r i a t i o n i n l i n e p r o f i l e c o r r e l a t e d with the v a r i a t i o n s i n l i g h t and r a d i a l v e l o c i t y was obtained. The change i n the asymmetries of the l i n e p r o f i l e s i n d i c a t e s that d i f f e r e n t i a l motion takes place i n i t s atmosphere as a r e s u l t of the p u l s a t i o n . The im p l i c a t i o n s are discussed i n Section 5.11. The new data represents an important observational gain r e l a t i v e to the previous spectroscopic studies of these s t a r s . The r e s u l t has been a s i g n i f i c a n t l y c l e a r e r p i c t u r e of t h e i r i n d i v i d u a l v a r i a t i o n s . The t o t a l value of these r e s u l t s to the understanding of the 3 Cephei phenomenon i s at present unclear. A continuing record of the changes i n p e r i o d , r a d i a l v e l o c i t y , and other fundamental features of the v a r i a t i o n are important from evolutionary considerations. D e t a i l e d p i c t u r e s of the atmospheric behavior should provide some i n s i g h t into the cause and nature of the i n s t a b i l i t y and serve as c r i t i c a l t e s t s of theoret-i c a l models. 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Watson, R.D. 1971, Ap.J. 169_, 343. Watson, R.D. 1972, Ap.J. Supple. 2h_, 167. Wellmann, P. 1957, Ap.J. 126, 30. Wentzel, D.G., Tidman, D.A. 1969, Plasma Instabilities in Astrophysics (Gordon and Breach). Wesselink, A.J. 1946, B.A.N. 10, 91. Wilson, R. 1956, Publ. Royal Obs. Edinburgh 2, No. 1 Wright, K.0. 1952, Publ. D.A.O. 9^ , No. 5, 189. Wright, K.0. 1964, Publ. D.A.O. 12, No. 7, 173. Zel'dovich, Y.B., Raizer, Y.B. 1966, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena 1 (New York and London: Academic P r e s s ) . Zel'dovich, Y.B.,' Rai z e r , Y.B. 1967, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena 2_ (New York and London: Academic P r e s s ) . 97 APPENDIX A. EXPERIMENTAL ANALYSIS OF THE COOLING SYSTEM Carrying out temperature measurements of the Isocon was one of the most important parts of the f e a s i b i l i t y a n a l y s i s . Temperature and temperature d i f f e r e n t i a l s were measured by using copper-constantan thermo-couples located at s t r a t e g i c points on the tube surface. One test setup i s shown here as w e l l as the r e s u l t of one t e s t run. The performance of the ' f i n a l ' system i s considerably b e t t e r than Indicated by these r e s u l t s . Focus ing CoiI Target Mesh DefIect ing CoiIs Photocathode '//;////;//////////////////777* Anode © Outlet Manifold © I n l e t M a n i f o l d 2 0 -o < 1.0 3 as o 0 - QO A • o o ONE OF THE INITIAL TEMPERATURE TEST RUNS Numbers indicate thermocouple locations on tube surface A A 4i • Photocathode (1 ) • Rear of tube U ) A Outlet manifold (2 ) A Target opposite inlet ( 3 O Inlet manifold (5 ) 60 120 TIME (MINUTES) 180 98 APPENDIX B. DESCRIPTION OF THE COOLING SYSTEM HARDWARE Drawings of some of the more important components are given. FLOW MANIFOLD (ENTRANCE) FLOW MANIFOLD (EXIT) 101 APPENDIX C. TEE RECTIFICATION PROGRAM Rectification of the spectra with the consequent removal of the instrumental response characteristic i s of central importance. The spectra must be re c t i f i e d before most quantitative analyses can be carried out. The r e c t i f i c a t i o n portion of the program is presented here. The primary inputs to this program are: (1) The normalized spectra (which may or may not be f i l t e r e d ) ; (2) The regions of continuum (in terms of channel numbers); (3) The extents of the spectral lines; ( 4 ) Various scaling factors. The continuum regions are subdivided into small segments from which individual values are computed (representing the noise-corrected average or maximum in the segment). These continuum values are then f i t t e d by orthogonal polynomials of a specified order (usually third). The data are scaled to the values that the polynomials take in each channel. The program follows. . 12 6.? C SET SORTING VALUES FOR NEW LARGE I NT CALC 126 . 201 Nl = l 126.?1 1220 CONTINUE 126.2? NCSS=0 126.23 .C 126. 3 X SET STARTING VALUES FOR MEW SMALL I NT CALC 12 6.31 1230 NCSS = NC?-S + NrS 126.32 IF ((NLA(Ml)+NCSS-NCS). G E . NL A(N1+1 ) ) GO TO 12 50 126.33 AVE=0. 12 6 .34 DEV=0. 126.35 YMS=0. 12 6.3 6 YMSN^O. 126.37 SUM 1=0. 126.38 SUMSQU=0 . 126.39 LS=raA(Nl) MNCSS-NCS) 12 6.4 LF=LS+NCS 12 6.5 C DETERMINE MAX VALUE IN ONE SMALL INT 126.51 OH 1240 1=1 ^,LF .12 6.5? SU U = SUM1+570(1) 102 126.53 S'JM SQU = S IP-IS 01 i + S I G (I ) **2. 126 .54 IF ( AR S ( YM S ) . GT . A BS ( S IG( I ) ) ) GOTO 1239 126.55 YMS=SIG(I) 126.56 NCYMS=I 126.565 12 39 CONTINUE 126.57 1240 CONTINUE 126.58 AV== SUM!/(NCS + 1) 126.59 PEV = S'.m ( ( SUMSQU/ (NCS + 1 ) )-AVE**2 ) 126.6 YMSN=YVS-DEV 126.601 NCEN T=(L S + 3 ) 126.61 Y7{J)=AVE+DEV 126.611 IF(MAXSI.EO.O) GOTO 7097 126.612 Y7( .J ) = YM$ 126.613 7097 CONTINUE 126.62 X7( J)=FLOAT(NCENT) 126.63 J = J + 1 126.64 c pane EED TO NEXT SMALL I NT 126.65 GOTO 12^0 126.66 C PR0CEE0 TO NEXT LARGE I NT 126.67 12 50 I«= (NLA<Nl+1).GE.NLAJNL2)) GOTO 1300 12 6.68 N1=N 1+2 126. 69 GOTO 122 0 126. 7 1300 CONTINUE 126.701 J = J-1 126.702 WRITE(6,615 ) 126.71 WRITE(6,61?) ( X 7 ( K ) , K = l , J ) 12 6.711 WRITE(6,61b) 126.72 WRITE(6,613) (Y7(K) ,K = 1,J) 126.73 613 FOR M A T (1 OE 1 2 . 5 ) 126.74 614 FORM AT( 1 0 E 1 2 . 5 ) 126.75 615 F O R M A T d X , • X CHOSEN VALUES FOR CONTINUUM') 126.76 616 F0RMAT(1X,«Y CHOSEN VALUES FOP. CONTINUUM') 126.769 JCNT=n 126.771 NL02=NL01+1 126.772 NLQ3=J 126.776 00 8021 I = l t N L Q l 126.777 X ( I )=X7( I ) 126.778 Y( I )=Y7( I ) 126.779 8021 CONTINUE 126.78 M=NL01 126.781 IF (JCNT.EO.O) GO TO 8029 126 .782 802 4 CONTINUF 126.783 00 8022 I=1,NLQ1 126.784 X( I ) =0. 126.785 Y(I )=0 . 126.786 8022 CONT INUE 12 6.78 7 JST=1 12 6.78 8 00 8023 I=NL02,NL03 126.789 X ( J S T ) = X 7 ( I ) 126.79 Y( JST )=Y7( I ) 126.791 JST=JST+1 126.79? 8023 CONTINUE 126.793 "*.= (NLQ3-NLQ1) 126.794 8029 CONTINUE 1Q3 1 2 6 . q C SET STARTING VALUES FOR OLQF FOR SINGLE AVE CALC 126.801 K = 4 126.802 KSAVE=4 126. 82 DO 1301 1=1tM 126.33 Y F ( I J = 0 . 126.84 126.85 126.86 1301 Y0( I ) =0. .._„ . CONTINUE 00 1302 1-1 ,K 126.87 SIGf-1A( I ) =0. 126.88 A ( I ) = 0 . 126.89 B ( I ) = 0 . 126.9 1302 CONTINUE 126.9C9 K1=K+1 126.91 00 1303 1=1,K1 126.92 S ( I ) = 0 . 126.93 p m = o . 126.94 1303 CONTINUE 126.95 127 C OETFRMINE POLYNOMIAL FIT 127.01 CALL OLQF(K,M,x,Y ,YF,YO,WT,NWT,S,SIGMA, A, R, S S , LK, P" 127.02 C PRINT TRIG DEG,FINAL OFG.COEFF OF POLY,AMD SUM OF SO. 127.03 WRITE(6,1310) K S A V E f K , ( P ( L ) , L = 1 , K ) 127.04 WRITE(6, 131 I ) SS 127.05 1310 FORM A T ( I X , I 5,10X, 15,{4F]5.5) ) .12 7.06 1311 FOR 'A AT ( ' SUM OF SQUARES I S » , E 1 5 . 5 ) 127.07 C CALCULATE CONTINUUM FOR ALL CHANNELS 127.071 IF ( JCMT .EQ.1 ) GOTO 8025 127.C8 00 1361 1=1,NCUT1 127.09 XX1=FL0AT(I) 127.1 CM.L C I T T E R ( K » X X 1 , Y Y 1 , A , B , S ) 127.11 CONK I ) = YY1 127.12 1361 C 1NTINUF 127 .13 7081 CON T I M l J E 127.131 7083 CONTINUE 12 7.132 C WRITE CONTINUUM ON F I L E IF F 1 LE = FILENAME 127.133 W R I T E ( l ) CONT 127.134 C READ IN C1NTINUUM IF MC0NSF=1 127.135 IF (MCONSF.FO.O) GOTO 7082 127.136 P, E A n ( 2 ) CONT 127. 137 7082 CONTINUE 127.15 C NORMALIZE TO CONTINUUM AND SCALE 127.16 DO 1370 I=1 ?MCUT1 127.17 CNO R M ( I) = ( S I G ( I ) / CO NT ( I ) ) 127.18 1370 CONTINUE 127.181 IF (MCCNSF.FO.l) GOTO 7084 127.182 IF < I AN.EO. 1) GOTO 7C85 12 7.18 3 IF (MCONS.EO.l) GOTO 7086 127.184 7C35 CONTINUF 127. 19 JCNT=JCNT+1 127.191 IF (NCUTl.EO.NCH) GOTO 8028 127. 192 GOTO 8 02 4 127.2 8025 CONTINUE 127.201 iNCUT2 = NCUTl 4-1 127.21" 00 8026 I=NCUT2,NCH 104 1 2 7 . 2 2 X X I = FLOA T ( I ) 1 2 7 . 2 3 C U I . F I T T E R f K , X X 1 , Y Y 1 , A , B , S ) 1 2 7 . 2 4 _ C 0 N T ( I ) = Y Y 1 _ 1 2 7 . 2 5 3 3 2 6 CTNTTNTIEI 1 2 7 . 2 6 C N O R M A L I Z E T O C O N T I N U U M A N D S C A L E 1 2 7 . 2 6 1 7 3 3 6 C O N T I N U E 1 2 7 . 2 6 2 7 0 3 4 C O N T 1 N U F 1 2 7 . 2 6 3 N C U T 2 = N C U T 1 + 1 12 7.? 7 DO J? 0 2 7 I _ = N C U T2_,_NCH_ 12 7. 28 " CNO rtM'Tl I = ( S I G (I ) 7 CO N T*{ I )~) 1 2 7 . 2 9 3 0 2 7 C O N T I N U E 20.0 6 o X ' e o 10.0 o z < 1 0 D 0.0 - i — i — r — i — | — r i i i i i i — i — i — | — i — i — i — i — i — i — i — r — i — I — i — r 1 — i — i — r - j — i — i — i — i — i — i — i — i — i — | — i — r From a plot of the spectrum of BW Vul obta ined May 27, 1971 UT. Spec t rogra phic d i s p e r s i o n — 10.1 A/mm _J • ' ' I l_ _L _J I I I I I I I L I I I -I I I I l_ J i i i i i t i i i L 4300 4400 4500 W A V E L E N G T H ( & ) 4600 4700 I b to *-3 5c fcj fe! S 3 to <3 b fe; b fe! • ^ C l b fe! 5^ 1 I O The figure indicates that the effective dispersion i s f a i r l y constant across the raster for this set of observations. Some of the scatter may be attributed to inaccuracies associated with the measurement of the positions of the spectral features on the computer plot. 106 APPENDIX E. SHOCK WAVE COMPUTATIONS FOB BW VUL Introduction The following i s based on the paper by Sachdev and Ashraf (1971). The undisturbed density p ahead of the shock i s assumed to be where b and 6 are constants such that p = 0 on the s t e l l a r 'surface'. The time t i s taken to be negative before the shock reaches the surf a c e , and t = 0 i s the time of shock emergence at the surface. The shock p o s i t i o n i s assumed to be X = A ( - t )a, where X i s the distance of the shock from the s t e l l a r surface as measured from that s u r f a c e , t i s the time (which i s negative) before the shock reaches the s u r f a c e , and A and a are constants. I t i s assumed that the heat f l u x across the o p t i c a l l y t h i n shock front i s continuous so that the c l a s s i c a l shock conditions h o l d . The strong shock approximation can be a p p l i e d . The boundary conditions at the shock (expressed as dimensionless values) are then U g = ( 1 _ p ) x P s = p o/ 3 P s - d-3) P GX 2, where U , p , and P are r e s p e c t i v e l y the v e l o c i t y , d e n s i t y , and pressure s s s of the f l u i d immediately behind the shock; 3 Is the density r a t i o across the shock [3 = (y-1)/(y+1)]> and x i s the v e l o c i t y of the shock. 107 For the case of a s p a t i a l l y isothermal flow behind the shock, the values of Y = -| and 6 = 3.25 (noted as being p a r t i c u l a r l y relevant to s t e l l a r envelopes i n r a d i a t i v e equilibrium) are used. The corresponding value f o r the exponent a i s 0.3136. Thus B = — and U = fX p = 4p P = 7p X2 s 4 s o s 4 o Application to BW Vul The non-isentropic sound speed (corresponding to the isothermal de r i v a t i v e ) i s given by a = (-) where P = pressure and p = d e n s i t y . For comparison, the i s e n t r o p i c sound speed (as noted by Ahlborn, 1966) i s vs = [OP/3p)]% = (YgP/p)1'5 where y i s the r a t i o of s p e c i f i c heats. The isothermal sound speed i s appl i c a b l e to the problem at hand (since a strong shock i s n o n - i s e n t r o p i c ) . The approximate value for the sound speed under conditions s i m i l a r to those found i n the atmosphere of BW Vul (as obtained using the grids of model atmospheres of Gingerich (1969) and Van C i t t e r s and Morton (1970) i s 20 km/sec. It i s r e l a t i v e l y i n s e n s i t i v e to changes i n o p t i c a l depth. The primary region of s p e c t r a l l i n e formation i s i n the range of P - 10 2 to 103 dynes/cm2. Interpolating i n the atmospheric grids j u s t noted, a value of Ar 'v 15000 km i s obtained. This contrasts with the displacement of ^ 5 x 105 km obtained by i n t e g r a t i n g the BW Vul r a d i a l v e l o c i t y data. 108 The shook velocity The maximum v e l o c i t y of the gas i s observed to be 'v 100 km/sec (with the c o r r e c t i o n f o r p r o j e c t i o n e f f e c t s a p p l i e d ) . The shock v e l o c i t y i s then X = (4/3) U = 140 km/sec and the Mach number about 7. The time s scale f o r the passage of the shock through the region of l i n e formation i s approximately Ar/X = 1.5 minutes. Formation of the shock For the isothermal case, the shock v e l o c i t y i s X = B X -( 1 _ a ) / a, where B i s a constant. Using the value a = 0.3136, and applying the condition that X = 140 at x = 10,000, the r e l a t i o n X = BX~2 i s obtained, where B = 1.4 x 1 01 0. Therefore, X = (B/X)^ [1.4 x l O1 0) / ^ Taking X = 20, the approximate distance from the s t e l l a r surface of the formation of the shock i s 26000 km. Summary This analysis demonstrates that the order of magnitude of the dist a n c e s , v e l o c i t i e s , and time scales i s correct i n the shock wave i n t e r -p r e t a t i o n of BW V u l . It should be emphasized that the approximations are rather crude and that i t i s impossible at t h i s stage to d i s t i n g u i s h between 109 the various shock wave models. The o b s e r v a b i l i t y of the atmospheric changes associated with the passage of the shock fron t i s one of the most important considerations. Further considerations If the p o s s i b i l i t y of the outward a c c e l e r a t i o n of material i n a r a r e f a c t i o n wave ( i . e . , by H i l l e n d a h l Mechanism) i s accepted, then the shock v e l o c i t y may be considerably lower since a part of the gas v e l o c i t y i s derived from the r a r e f a c t i o n wave. The terminal v e l o c i t y achieved by ac c e l e r a t i o n i n a r a r e f a c t i o n wave may be estimated by equating the o r i g i n a l thermal energy of the gas to i t s terminal k i n e t i c energy. U = U 2 + 2 V z Y 2 = 1 + P 2 / P 2 E 2 Y 2 - I The parameters ahead of the r a r e f a c t i o n fron ( i . e . , behind the o r i g i n a l shock front) are U 2 = v e l o c i t y v 2 = sound speed P 2 = pressure p 2 = density E 2 = i n t e r n a l energy where U 2 represents the a c c e l e r a t i o n i n the shock fron t and 2 C 2 / Y 2 - 1 the ac c e l e r a t i o n i n the r e f r a c t i o n wave. 5 Taking y = — and v2 - 20 km/sec: 2v2 - 60 km/sec. •Y-l Therefore U 2 - 40 km/sec, and X - 90 km/sec. The Mach number i s ^  4 . 5 . 110 Some -problems In general, r e a l i s t i c boundary conditions are d i f f i c u l t to obta (e.g., what i s the surface of a s t a r ? ) , and some of the more important approximations (such as an isothermal flow) require more rigorous j u s t i -f i c a t i o n . 

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