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Observation and interpretation of the Cygnus X-1 system Ninkov, Zoran 1985

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OBSERVATION AND INTERPRETATION OF THE CYGNUS X-1 SYSTEM by ZORAN NINKOV M.Sc., Monash University, 1981 B.Sc.(Honours), University of Western Australia, 1978 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Department of Geophysics and Astronomy We accept t h i s thesis as conforming to the req^r^o" standard THE UNIVERSITY OF BRITISH COLUMBIA July 1985 £ © Zoran Ninkov, 1985 In presenting t h i s thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the The University of B r i t i s h Columbia, I agree that the Library s h a l l make i t fre e l y 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 or her representatives. It 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 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date: July 1985 ABSTRACT The results of a long term monitoring program on the massive X-ray binary Cygnus X-1, whose constituents are believed to consist of a normal 0 star primary and a black hole companion, are presented. Spectra of t h i s system were c o l l e c t e d between 1980 and 1984 using a Reticon detector. The resulting absorption l i n e r a d i a l v e l o c i t y (RV) curve i s c h a r a c t e r i s t i c of a single l i n e spectroscopic binary. These v e l o c i t i e s were combined with those avai l a b l e in the l i t e r a t u r e to determine an o r b i t a l period of 5.59977 ± 0.00001 days. A P/P =* 10"5 day" 1 was found from analysis of a l l available v e l o c i t y measures. This change in the period i s larger than that expected as a result of mass loss from the primary or from- models of the system in which large mass transfer rates occur between the components. A f i t of the o r b i t a l motion of the primary to the RV curve gives a K = 75.0 ± 1 km/s and no s i g n i f i c a n t e c c e n t r i c i t y . The v s i n i of the primary was found, using the fourier transform technique, to be 94.3 km/sec. This i s substantially smaller than the l i t e r a t u r e value of v s i n i = 140 km/sec. The value of the K and v s i n i allow the r a t i o m /m to be determined as p x * 2.0 . The equivalent width of H7 allows the absolute magnitude - o l the primary to be estimated at -6.5 ± 0.2 . A comparison of the spectrum of the primary to those of an array of standards allows the spectral type to be given as between 09.5 and 09.7 I . This spectral type i s consistent with the absolute magnitude obtained and i t i s thus l i k e l y that the primary i s a normal star of mass « 20 M Q . The mass of the secondary i s therefore 10 ± 3 MQ. Measurement of the i n t e r s t e l l a r l i n e s to obtain an independent E(B-V) reveals that the i n t e r s t e l l a r l i n e strength per unit E(B-V) i s lower than in any other d i r e c t i o n in the sky. Stars for which v e l o c i t y - e x c i t a t i o n slopes and mass loss estimates, from UV line p r o f i l e modeling and/or radio free-free emission measures, are available in the l i t e r a t u r e were c o l l a t e d . An empirical f i t to t h i s material allowed the mass loss rate for HDE 226868 (the primary of Cygnus X-1) to be estimated at 5.7 ± 2 x 10~6 M/year. The He II X4686 and Ha lines are found in emission. After removal of the contribution to the l i n e p r o f i l e from the primary the r a d i a l v e l o c i t y curve of the residual He II X4686 l i n e i s found to have small scatter from a smooth f i t ( ± 10 km/sec ) with no s i g n i f i c a n t e c c e n t r i c i t y . No sizeable variation in the K amplitude at d i f f e r e n t epochs was found contrary to a previous investigation and the or i g i n of the emission i s thus apparently fixed and stable. A phase lag of 130° i s measured between the absorption and emission v e l o c i t y curves and thus the simple interpretation of the emmision o r i g i n a t i n g near the secondary can not be correct. The He II emission equivalent width, corrected for the underlying primary absorption, shows strong modulation (30%) over the 5.6 day o r b i t a l period. This variation is probably the result of the p r o f i l e of the primary varying with which face of the star i s directed towards the observer. During two separate observing sessions in 1982 the He II equivalent widths were found to be 40% and 15% larger than the mean of a l l other observations while s t i l l showing the same variation with o r b i t a l phase. Such a change has been seen once before and may be associated with tr a n s i t i o n s to the X-ray high state. The H7 and H/3 l i n e s show a 20% variation on the 294 day X-ray period in the sense of largest equvalent widths at X-ray minimum ( 0 phase ). The Balmer li n e s are a composite of an absorption component from the primary and a weak emission component. This i s best explained by variations in the outflow from the star, which i s the source of both the emission component and the X-ray flux v i a accretion. Such variations may be the result of pulsation of the primary. The Ha l i n e p r o f i l e has been decomposed into three components; the absorption component from the primary, emission from a s h e l l with an inner radius 1.4 times that of the primary, arid a component with properties similar to the He II X4686 l i n e . The great width of the Ha l i n e , previously explained as being the result of rotation of the disc, is instead shown to be the res u l t of superposition of these components. The o r i g i n of the He II X4686 emission i s explained by assuming that a s t e l l a r wind enhanced in the di r e c t i o n of the . secondary i s completely ionized within a volume surrounding the secondary. The He II between the edge of t h i s volume and the surface of the primary is enhanced as a result of X-ray heating and i o n i z a t i o n . Model p r o f i l e s appear in reasonable agreement with high dispersion spectra. The obvious explanation for the o r b i t a l v a r i a t i o n in the He II l i n e i s that X-ray heating of the side of the primary facing the secondary produces a change in the e f f e c t i v e temperature. Calculation of the size of t h i s e f f e c t reveals that i t i s too small to explain the changes observed. X-ray observations made with EXOSAT with excellent time resolution allowed timing of the X-ray absorption features seen near o r b i t a l phase zero. Simultaneous X-ray spectra allowed an estimate of their column density as 2.0 x 10 2 3 cm"2. Two scale lengths of dips were found of 10s and 10 1 1 cm. These values are in good agreement with t h e o r e t i c a l predictions for the sizes of inhomogeneties in high mass loss s t e l l a r winds. The location of the material producing the absorption dips was calculated as being * 4-8 R @ from the X-ray source. v Table of Contents Abstract i i Table of Contents vi L i s t of Tables v i i i L i s t of Figures x Acknowledgements xiv 1 . Introduction 1 1.1 Early History of X-ray Binaries 1 1.2 History of Cygnus X-1 6 2. Data Collection and Analysis 11 2.1 The Observations 11 2.2 The Reticon Detector 12 2.3 The Data Reduction 16 2.4 Problems with Darks ". 19 2.5 Cosmic Ray Events 23 2.6 The Data 36 2.7 D i g i t a l Subtraction 36 3. The Absorption Line Spectrum 48 3.1 Rationale for the Study 48 3.2 The Spectrum I t s e l f 50 3.3 Equivalent Width Determination 58 3.4 The Spectral Type 64 3.5 The Rotational Velocity 80 3.6 The Radial V e l o c i t y Curve 92 3.7 Masses of the Components 131 3.8 E(B-V) and the I n t e r s t e l l a r Lines 136 3.9 Mass Loss Rate 138 v i 3.10 Equivalent Width Variations 146 3.11 Line Halfwidth Variations 160 4. The Emission Line Spectrum 165 4.1 Rationale for the Study 165 4.2 Analysis of the He II 74686 Data 166 4.2.1 Finding a Good Reference Star 166 4.2.2 Correction of the He II P r o f i l e s 172 4.2.3 The CFHT He II 74686 P r o f i l e s 181 4.3 The He II Emission Radial Velocity Curve 181 4.4 Equivalent Width Measures 192 4.5 The Ha Data 199 4.6 The Ha P r o f i l e of the Primary 206 4.7 The Hydrogen Absorption Lines 216 5. Emission Mechanisms ..222 5.1 X-Ray heating of the Primary 222 5.2 Overflow onto the Secondary 223 5.3 T r a i l i n g Shock Model 231 5.4 Emission from the Disc 233 5.5 Enhanced S t e l l a r Wind 234 5.6 The Model 238 5.7 Variation of He II Absorption Line 255 6. X-Ray Observations 266 7. Conclusions 281 Bibliography 285 Appendix A 30.2 v i i L i s t of Tables 1.01 Type I vs Type II X-ray System Charact e r i s t i c s 5 1.02 Observed Properties of the Cygnus X-1 System 8 2.01 Ret icon Systems 16 2.02 De t a i l s of occurrence of spikes 32 2.03 D e t a i l s of observations of Cygnus X-1 37 2.04 De t a i l s of observations of Comparison Stars 40 3.01a Line L i s t for Early Type Stars (blue) 56 3.01b Line L i s t for Early Type Stars (Red) ....57 3.02 Standard Star C h a r a c t e r i s t i c s 67 3.03 Standard Star Ratios of Spectrally Sensitive Lines 78 3.04 Line weights for least squares f i t t i n g r a d i a l v e l o c i t y curve and ex c i t a t i o n potential' for li n e groups 97 3.05 Calculated v e l o c i t i e s for spectra of HDE 226868 ....98 3.06 F i t t e d ?T? at di f f e r e n t epochs ...123 3.07 Weights for least squares f i t t i n g r a d i a l v e l o c i t y curve by year 130 3.08 Orbit Solution for Cygnus X-1 130 3.09 E(B-V) as determined from the I n t e r s t e l l a r l i n e s ..137 3.10 Mass loss rates from d i f f e r e n t techniques ...142 3.11 Normalized equivalent width variations with phase .158 3.12 Normalized phase variations of He I halfwidth 162 4.01 Line L i s t for CFHT 169 4.02 Equivalent Widths for l i n e s from CFHT Data 174 v i i i 4.03 He II X4686 emission r a d i a l v e l o c i t i e s and equivalent widths ..187 4.04 Orbit parameters for He II X4686 emission r a d i a l v e l o c i t y curve 191 4.05 He II X4686 equivalent widths and halfwidths as function of o r b i t a l phase 194 4.06 Equivalent Widths Binned on the 294 day Period ....217 5.01 Assumed Basic Parameters of Cygnus X-1 253 5.02 Parameters for Her X-1 and Cygnus X-1 259 6.01 Journal of EXOSAT observations 267 ix L i s t of Figures 2.01 Fourier Transform of Cygnus X-1 Spectrum in figure 2.02 20 2.02 CFHT Spectrum of Cygnus X-1 25 2.03 Histogram of Bad Pixels for CFHT Data 28 2.04 D i s t r i b u t i o n of sizes of spikes from CFHT Data 30 2.05 The spectrum of X Per and a Ori .-...43 2.06 The difference spectrum of X Per ; 45 3.01 Spectrum of HDE 226868 and 19 Cep 52 3.02 Equivalent Width here vs Equivalent Width Others, for 19 Cep 60 3.03 Line depth vs equivalent width 62 3.04 Ratio of S i l V 74116 /Hel 74121 for standards 70 3.05 Ratio of S i l l l 74552 /Hel 74387 for standards 72 3.06 Ratio of S i l l l 74552 /Hel 74541 for standards 74 3.07 Ratio of S i l V 74089 /Hel 74121 for standards 76 3.08 Spectral Mosaic for wavelength range centered on X4686 81 3.09 v s i n i derived from FT Technique vs that used by Stoeckly and Mihalas 87 3.10 Fourier Transform of He I X4713 p r o f i l e for HDE 226868 and 19 Cep 90 3.11 Observed and Theoretical He I X4713 for HDE 226868 93 3.12a Mean He I l i n e r a d i a l v e l o c i t y curve for HDE 226868 101 3.12b He I ra d i a l v e l o c i t y residuals for HDE 226868 103 x 3.13a Mean Hell absorption l i n e r a d i a l v e l o c i t y curve for HDE 226868 105 3.13b Hell absorption l i n e r a d i a l v e l o c i t y residuals for HDE 226868 107 3.14a Mean Balmer l i n e r a d i a l v e l o c i t y curve for HDE 226868 109 3.14b Balmer l i n e r a d i a l v e l o c i t y residuals for HDE 226868 111 3.15a Mean Metal l i n e r a d i a l v e l o c i t y curve for HDE 226868 1 13 3.15b Metal l i n e r a d i a l velocity residuals for HDE 226868 1 15 3.16 Power spectrum for a l l HDE 226868 v e l o c i t i e s (1939 to 1984) 121 3.17 Change in T? with epoch 125 3.18 Zero ve l o c i t y vs excitation energy for l i n e s from HDE226868 139 3.19 Mass loss rates vs v e l o c i t y excitation slopes 144 3.20 Phase variations of hydrogen li n e s equivalent widths in Cygnus X-1 148 3.21 Phase var i a t i o n of mean He I l i n e equivalent width in Cygnus X-1 150 3.22 Phase var i a t i o n of He II (absorption lines ) equivalent width in Cygnus X-1 152 3.23 Phase var i a t i o n of mean metal l i n e equivalent width in Cygnus X-1 154 xi 3.24 Phase variation of i n t e r s t e l l a r l i n e s equivalent width in Cygnus X-1 156 3.25 Normalized phase va r i a t i o n s of He I halfwidth 163 4.01 Standard stars taken at CFHT 167 4.02 Broadened p r o f i l e s of standards 170 4.03 He II X4686 p r o f i l e before correction for absorption from primary 175 4.04 He II X4686 p r o f i l e a f t e r correction for absorption from primary 178 4.05 Spectrum of HDE 226868 and HD 167264 (from CFHT) ..182 4.06 He II X4686 after correction for absorption from primary(CFHT data) 184 4.07 He II X4686 ra d i a l velocuty curve vs Orbi t a l Phase 189 4.08 He II 74686 equivalent widths vs o r b i t a l phase ....195 4.09 He II 74686 halfwidths vs o r b i t a l phase 197 4.10 Standard star spectra (red region) 200 4.11 Ha P r o f i l e s shifted to rest frame of primary 202 4.12 Ha p r o f i l e f i r s t stage correction 204 4.13 Corrected He II and Ha emission p r o f i l e 207 4.14 Components of Ha in HDE 226868 ...209 4.15 Derived Ha P Cygni p r o f i l e and the o r e t i c a l p r o f i l e 214 4.16 Equivalent Widths of HDE 226868 binned on 294 day period 218 5.01 Schematic of Lubow and Shu Model 225 x i i 5.02 Flux Spectra of accretion discs and the primary in the Cygnus X-1 system 228 5.03 Mass Loss Rate for Cygnus X-1 vs Angle from Axis of Binary 235 5.04 Schematic of Enhanced S t e l l a r Wind Model for Cygnus X-1 239 5.05 X-ray Spectrum of Cygnus X-1 244 5.06 Variation of temperature and ionization with ? ....247 5.07 Model and Observed Hell X4686 p r o f i l e s in Cygnus X-1 251 5.08 X-ray Spectrum of Cygnus X-1 and Her X-1 257 5.09 X-ray Heating of primary of Her X-1 and Cygnus X-1 263 6.01 EXOSAT observations on the 07,08,09 July 1984 268 xi i i Acknowledgements I would l i k e to acknowledge the assistance I have received from a number of people during my time here at U.B.C. " F i r s t l y I would l i k e to thank my friend and supervisor Gordon Walker for his considerable help during my graduate studies. His candour and enthusiasm was much appreciated as well as his considerable assistance in keeping Ottawa at bay. My good friend and colleague Stephenson Yang has been invaluable at a l l lev e l s of t h i s project from observing through to discussion of r e s u l t s . I thank him h e a r t i l y for a l l his help in making t h i s thesis come about. I also acknowledge . him for . introducing me to the most hallowed i n s t i t u t i o n of the hockey pool and for allowing me to make the best bet of my l i f e . Many others in the department have also contributed. Numerous fellow students have helped in observing and discussions including P h i l Bennett, Daniel Thibault, Garry J o s l i n , Katherine Moyles, Chris Millward, John Amor, Grant H i l l and Denis Crabtree. John Amor was instrumental in getting Reticent up and running on the departmental VAX and Gerry Grieve answered many annoying questions on VAX usage. John Nico l also provided considerable computer assistance on the AMDAHL machine and caused my complete inebriation on more times than I care to (or can) remember. I would also thank Greg Fahlman, Paul Hickson, Jason Auman and David Vogt for assistance in various ways at various times. Michael xiv Ovendon provided many enjoyable and informative conversations. Ron Johnson ensured that the detector mostly worked well and was always available for questioning on i t s performance. I would l i k e to thank the staff of the Dominion Astrophysical Observatory, where most of the observations in this thesis were made, for both a l l o c a t i n g the time and providing assistance. In p a r t i c u l a r I would mention Murry Fletcher for his extensive help over the years. Observing t r i p s were made available courtesy of NSERC operating grants. During the course of my graduate study I held a Commonwealth Scholarship and Fellowship Plan Award and I am grateful to them for the f i n a n c i a l assistance but not their' bureaucracy. A number of friends have made my stay in Canada more enjoyable. In particular I would thank Frank Orfino and his family. I would also l i k e to thank my parents and brothers for providing me with the upbringing to allow me to go 'per adra ad astra' . F i n a l l y but most importantly I would l i k e to thank my wife Marie Boudreau from whom I learnt the most important things of a l l during my time in Canada. She suffered in the hardships of graduate school with me, assisted on observations and helped make the good times better and the bad times not as bleak. For a l l this and for teaching me xv that the p r i o r i t y in l i f e should not always be with learning more but with using what you know, I dedicate th i s thesis to her. xvi To Marie Andree Boudreau xvi i / that is gold does not glitter Not all who wander are lost. —J.R.R. Tolkien Lor d of t he Ri ngs xvi i i Chapter 1 INTRODUCTION 1.1 EARLY HISTORY OF X-RAY BINARIES The f i r s t ever detection of e x t r a t e r r e s t r i a l X-rays occurred on the 5th August 1948 when a V2 rocket equipped with photographic f i l m detected the sun (Burnright [1949]). The finding was not unexpected as a hot plasma in the corona had been postulated to explain the strong 5007A 01II feature seen in the sun. Studies of the sun, using rockets and balloons, continued but i t was not u n t i l the 18th June 1962 that an extrasolar source, Sco X-1, was detected (Giacconi et a l [1962]). This discovery was accidental as the intended purpose of the • rocket f l i g h t was to measure secondary fluorescence X-ray emission from the moon. By 1967 there were already about 50 detected X-ray sources. The i d e n t i f i c a t i o n of o p t i c a l counterparts moved along slowly due to the poor s p a t i a l resolution of the early X-ray telescopes. The f i r s t o p t i c a l i d e n t i f i c a t i o n of an X-ray source was of the Tau X-1 (Bowyer et a l [1964]) which was conveniently occulted by the moon and therefore allowed an accurate position for i t to be determined. This proved to be coincident with the position of the Crab Nebula. Later synchronism between the X-ray, radio and o p t i c a l pulsations confirmed the pulsar as the X-ray source. The large brightness changes in the v i s i b l e bought attention to.the o p t i c a l counterpart of Sco X-1(Sandage et a l [1966]). 1 2 Cyg X-2 was i d e n t i f i e d serendipitously due to i t s large blue excess, noticed while the authors were searching for the o p t i c a l counterpart to Cygnus X-1 (Giacconi et a l [1967]). Despite considerable e f f o r t , in 1970 these were the only three sources for which o p t i c a l i d e n t i f i c a t i o n s were considered certain (Hiltner and Mook [1970]). The spectrum of Sco X-1 (Sandage et a l [1966]) was found to have s i m i l a r i t i e s to spectra of old novae. It i s well known that such objects are close binaries in which mass i s l o s t from one member to a white dwarf companion ( Kraft [1964] ). Burbidge at a l [1967] reported evidence for the binary nature of Cyg X-2 and these observations therefore suggested two classes of X-ray sources; the supernovae remnants ( l i k e the Crab) and the (binary) Sco X-1 type. If a binary hypothesis for the X-ray sources was correct, simple physics indicated that a suitable model for these systems would involve mass loss from the primary star accreting onto the companion releasing g r a v i t a t i o n a l potential energy in the process. A simple estimate for the g r a v i t a t i o n a l energy released would be GM /R where the secondary has mass M and a radius R. For a mass accretion rate M the luminosity from the secondary would be t . <L£ X8 - , 0».r 9/..c &) {§•} 1 „ . . » , } © © J The temperature produced by thermalization of the flow i s on the order of 3 T ~ SSpJM* _ a 10 7(|X} {§©} °K © where mp i s the proton rest mass. k i s the Boltzmann constant a i s the efficency factor = 0.1 for adiabatic shock heating = 10~5 to 10"6 for viscous heating in a disk Since the temperatures derived from the X-ray observations for the sources were of the order 10 8°K , then & } {|©} ~ £ 100 © a For main sequence stars the M/R parameter has values 0.5 to 10. The only objects for which t h i s parameter i s s u f f i c e n t l y large are collapsed objects supported by degenerate electron or nucleon pressure or black holes. For degenerate dwarfs the M/R r a t i o i s about 100 so temperatures on the order 10 8°K can be produced by shock wave heating but not v i s c o s i t y heating. For neutron stars and black holes the mass radius r a t i o i s about 10 s, so high temperatures can be produced by viscous heating. From equation (1) i t can be seen that for degenerate dwarfs a mass accretion rate of 1 0" 7Mg)year"1 can produce luminosity of the order 1 0 3 6 erg sec" 1 while for neutron stars and black holes an accretion rate of 10"BMQ year" 1 w i l l give 10 3 8 ergs s e c " 1 . 4 In fact Shklovski [1962] had already suggested accretion into a potential well as a p o s s i b i l i t y for powering the extragalactic radio sources. Guseinov and Zeldovich [1966] used similar arguments to suggest searching for the presence of emission l i n e s from unseen companions in binary systems. The late 1960s saw many models of t h i s vein presented (see Burbidge [1972] or Blumenthal and Tucker [1974] for reviews). However further observation of Sco X-1 and Cyg X-2 at that time f a i l e d to show d e f i n i t e evidence for binary motions. Consequently, for a time, binary models f e l l from favour and 'Crab' analogous models, using the rotational energy of the neutron star as the energy source, became accepted. The launching of the X-ray s a t e l l i t e UHURU answered many of the questions of that time. Observations in 1971 with UHURU discovered two p e r i o d i c a l l y pulsating sources, Cen X-1 with a period 4.8 sees (Schreier et a l [1972]), and Her X-1 of period 1.2 sees (Tananbaum et a l [1972]). The detections of eclipses and of doppler variations in the pulsations conclusively established the binary nature of some sources. As a result of continued radio, o p t i c a l and X-ray observations a f a i r l y convincing case can now be made that a l l s t e l l a r X-ray sources not in a supernova remnant are mass transfer binaries that contain a collapsed companion. The recent review of Bradt and McClintock [1983] l i s t s 115 sources that have been detected at energies >> 1 keV with a flux density >> 1 vJy with accurate positions determined. Of 5 t h e s e 75 a r e i d e n t i f i e d and 40 have as y e t no o p t i c a l c o u n t e r p a r t . Of t h e o p t i c a l l y i d e n t i f i e d s o u r c e s the m a j o r i t y f a l l i n two w e l l r e s o l v e d groups commonly r e f e r r e d t o as Type I and Type I I X-ray systems. The major i d e n t i f y i n g c h a r a c t e r i s t i c s a r e g i v e n i n t a b l e 1.01 . table 1.01 Type I vs Type II Type I Hard X - r a y S p e c t r a T > 10 8K Of t e n p u l s a t i n g Luminous e a r l y type (0 4 B) o p t i c a l c o u n t e r p a r t s °' 0 1 * L x / L o p t * 1 0 In t h e g a l a c t i c p l a n e l i k e P o p u l a t i o n I X-ray System C h a r a c t e r i s t i c s Type I I S o f t e r S p e c t r a T < 10 8K Not P u l s a t i n g O p t i c a l l y f a i n t b l u e e x c e s s o b j e c t s ( F t o M ). 1 0 * V L o p t * 1 0 4 C o n c e n t r a t e d toward g a l a c t i c c e n t r e l i k e o l d d i s c p o p u l a t i o n 6 The type I systems have proved to be the more intensely studied as they are brighter. The evolutionary history of these systems i s also believed to be well understood ( van den Heuvel [1983,1981] ). The system seen now i s the result of the more evolved ( i n i t i a l l y more massive ) star in an early type binary becoming a supernova and transfering mass onto the less evolved companion. The system eventually passes through a phase where the mass loss from the now more massive system ( through the Roche Lobe or via winds ) accretes onto the now secondary ; this i s the phase we label as Type I X-ray bin a r i e s . From li f e t i m e estimates and re l a t i v e numbers i t can be deduced that t h i s must be an r e l a t i v e l y normal occurrence amongst the massive binaries. Eventually the i n t i a l l y less massive component becomes a supernova, and a binary compact star system or two runaways i s generated. 1.2 HISTORY OF CYGNUS X-1 Although the existence of the strong X-ray source Cygnus X-1 was known from the e a r l i e s t days of X-ray Astronomy i t s i d e n t i f i c a t i o n was a mystery t i l l the early seventies. The combined results by UHURU ( Tananbaum et a l 1971] ), an MIT rocket f l i g h t ( Rappaport et a l [1971] ) and Japanese balloon f l i g h t s ( Miyamoto et a l [1971] ) gave an accurate location for the source. This determined location led to the discovery of a radio source by Braes and Miley [1971] and Hjellming and Wade [1971]. This radio source was observed to 7 have a sudden increase in its radio flux in March 1971 which coincided with a change in the X-ray luminosity ( Tananbaum et a l [1972] ). The error box determined for the radio source ( ^  1" ) contained the star HDE 226868 which was soon found to be a 5.6 day spectroscopic binary ( Webster and Murdin [1972], Bolton [l972a,b] ). The X-ray source was identified as being in the binary system by the observation of a weak 5.6 day modulation in the X-ray flux ( Sanford et al [1974], Holt et al [1976,1979] ). Assuming a reasonable mass of the primary given i t s spectral type of 09.7Iabp ( Walborn [1973] ) and a distance of £ 2kpc ( Margon et al [1973] ), gives a mass for the secondary much larger than the maximum for a neutron star ( 1.4 M-. ). There are arguments that any ' compact bodies of ' mass >> 3M@ are inevitably black holes ( Rhoades and Ruffini [1974] ). Sensitive searches for a main sequence companion to HDE 226868 have not been successful ( Shafter et al [1980] ) and thus the Cygnus X-1 system is now widely accepted as consisting of a normal supergiant plus a black hole. Recently Cowley et al [1983] have reported a second example of a system of this type, LMC X-3. A summary of the basic observables of the Cygnus X-1 system are given in table 1.02 One fact about Cygnus X-1 missed by the western literature is that there are historic records of a supernova occurring close to the present day position of the X-ray source. The paper of Li Qi-Bin [1979] reports on 8 t a b l e 1.02 Observed P r o p e r t i e s of Cygnus X-1 System I d e n t i f i c a t i o n HDE 226868 SAO 69181 BD +34 3815 V1357 Cyg AG 1910 Co-ordinates Right Ascension 19 56 28.843 Declination +35 03 54.51 RA proper motion (s/yr) -0.0016 Dec proper motion C/yr) -0.018 1(11) = 71 20 05 b(II) = 3 4 1 Magnitude U = 9.50 B = 9.74 V = 8.89 J = 7.01 H = 6.74 K = 6.54 L = 6.45 M = 6.34 N = 6.25 ( Be a l l et a l [1984] ) Orbital B change = 0.045 mag ( Walker and Q u i n t a n i l l a [1978] ) 294 day B change = 0.0049 mag ( Kemp et a l [1983] ) X-ray Luminosity 4 to 6 x 1 (rergs/sec ( Liang and Nolan [1984] ) Radio Luminosity ( long term ) = 0.015 Jy ( Tananbaum et a l [1972] ) ( peak ) = 0.033 Jy ( Gibson and Hjellming [1974] ) Nearest Cluster NGC 6871 RA = 20 04.0 Dec = +35 38 m - M = 12.68 B-V = -0.25 ( Janes and Adler [1982] ) Orbital Period = 5.6 days observations from various Chinese sources on a bright new star, much brighter than Vega but not as bright as Venus appearing on September 10, 1408 close to the location of Cygnus X-1. This object i s the same as the supernova of 1404 reported by Clark and Stephenson [1977] who used an incorrectly translated ancient record according to L i Qi-Bin [1979]. The star was s t i l l almost as bright 44 days la t e r 9 and t h i s gives confidence in the supernova interpretation. L i Qi-Bin [1979], from the records, estimates that at maximum the star must have been brighter than -3 m. From the present day reddening and distance estimates for Cygnus X-1 th i s gives an absolute magnitude for the event of brighter than -I8.5 m. Barbon et a l [1973] give an average type I supernova maximum brightness of -18.6 ± 0.15m, while Barbon et a l [1979] f i n d for type II supernovae a maximum brightness of -16.45 ± 0.6m. Thus the observed brightness points to Cygnus X-1 being the result of a type I supernova. This i s in disagreement with Maza and van den Bergh [1976] who claim that type I supernovae are not associated with the young s p i r a l arm population, and in agreement with Johnson and MacLeod 11963] who state the opposite. The range of progenitors for Type I supernova i s s t i l l uncertain ( Trimble [1984] ). The concern of thi s thesis i s a another look at a system in which the secondary i s a good candidate for being a black hole. Chapter Two deals with explaining the use and problems of a Reticon detector, which was used in thi s study. Chapter Three deals with what has been learnt from the examination of the absorption l i n e s found in the spectrum. Chapter Four deals with the problems of properly interpreting what i s seen in the two prominent emission l i n e s He II X4686 and Ha. Chapter Five deals with an explanation for the or i g i n of the emission l i n e s . Chapter Six describes what has been learnt from EXOSAT X-ray 10 observations ( simultaneous with the July 1984 o p t i c a l observations ). Chapter Seven summarizes the conclusions of t h i s thesis. An a t l a s of spectra for stars with spectral type between 08 and B1 i s found in Appendix A. A l l the l i t e r a t u r e v e l o c i t y measures for HDE 226868 are tabulated in Appendix B. Chapter 2 DATA COLLECTION AND ANALYSIS 2.1 THE OBSERVATIONS The o p t i c a l data used in t h i s thesis was collected using three telescopes. The majority of the spectra were collected at the Dominion Astrophysical Observatory (DAO) using the 48" telescope. The McKellar Coude Spectrograph ( Richardson [1968] ) 32" ( short ) camera was used together with the 300 line/mm grating giving a dispersion of 40.9 Amm"1 ( 3231 configuration ). The IS32B image s l i c e r gave a projected s l i t width of 18 jxm. The red spectra were obtained with the DAO 72" telescope using the cassegrain spectrograph in the 2161 configuration, where the 600 line/mm grating together with the IS32B image s l i c e r gives a dispersion of 31.1 Amm"1 with a projected s l i t width of 22/um . The high dispersion blue data was obtained with the Canada-France-Hawaii Telescope 3.6m (CFHT) coude spectrograph with the 830 line/mm grating in second order which gives a dispersion of 2.4 Amm"1 and an image s l i c e r giving a projected s l i t width of 45^m ( CFHT Observers Manual ). 11 12 2.2 THE RETICON DETECTOR The data was co l l e c t e d over the period from 1980 to 1984 at these three observatories and the detector used for a l l observations was an 1872 element refrigerated Reticon. The choice of a Reticon, besides i t s a v a i l a b i l i t y at UBC, comes from the desire to obtain as high a signal-to-noise spectra as possible. This requires the accumulation of a large number of photons to minimise the Poisson photon noise, and consequentially the detector needs a large dynamic range. Photographic plates were not used for a number of reasons including, limited dynamic range ( optimum detection occurs only over a limited range of detected photons ), re c i p r o c i t y f a i l u r e and the low Detective Quantum Efficency. Photographic plates t y p i c a l l y give a maximum signal to noise of =* 60 ( Hoag [ 1976], Walker [ 1985] ) which i s too low for the study of l i n e p r o f i l e v a r i a t i o n s . A Reticon i s an almost ideal detector for t h i s program ( and spectroscopy in general ) for a number of reasons. The DQE i s ~ 40% in the blue compared to = 2% for photographic plates ( Walker [1985] ). The detector i s l i n e a r ( Campbell [1977], Vogt [1981] ) with a saturation l e v e l of £ 2 x 107 equivalent photons ( Timothy [1983] ). This gives a dynamic range that can be as high as 10* with proper reduction. There i s no dead space between the detector elements 13 ( Timothy [1983] ). The detector i s mounted to be quite stable and to have good absolute position over the duration of an observing run. The shape of the diodes ( 15 x 750 /um ) allows a reasonable area for c o l l e c t i o n of photons and matched resolution to the image s l i c e r . The data i s aquired in d i g i t a l form. A Reticon i s a monolithic s i l i c o n diode array manufactured by the EG & G Reticon Corporation. The array consists of a series of bars of p-doped s i l i c o n 2 Mm thick formed at regular intervals along an n-doped s i l i c o n substrate ( 300 u thick ) on a gold substrate acting as an anode. The surface of the chip i s covered by a 3/um layer of S i 0 2 to reduce r e f l e c t i o n from the array. A reverse bias ( 5 Volts ) applied to the junction between the two s i l i c o n regions w i l l create a region at the interface depleted of free charge c a r r i e r s and that has low current leakage and high c a r r i e r mobility. Electron/hole pairs produced by absorption of photons, or thermally, w i l l accumulate in a thin layer along the interface. This slowly discharges the diode u n t i l some set integration time i s reached, at which time the diode i s reset to i t s o r i g i n a l voltage. The amount 14 of charge required to rebias the diode gives a measure of the accumalated signal and dark current. The rebiasing of the diodes ( the readout ) i s done sequentially using a s h i f t register clocked to connect each diode to the appropriate video l i n e . This signal i s amplified and d i g i t i s e d and then stored on magnetic tape. The readout technique described above has been improved in the most recent Reticon systems using Correlated Double Sampling which eliminates extra capacitance introduced by the video l i n e Walker et a l [1983]. A Reticon Array operating at room temperature would require < 10 seconds ( Vogt [1981] ) to saturate due to thermally generated free charges. This dark signal i s not linear with exposure time ( Percival and Nordsieck [1980] )] For this reason the array i s normally cooled to near l i q u i d nitrogen temperatures. Temperature s t a b i l i t y ( to compensate for atmospheric temperature changes ) i s maintained to ± 0.2°C at 160°K using a heater in a temperature sensor loop ( Campbell et a l [1981] ). For the presently available generation of UBC b u i l t Reticon there i s negligible dark current at these temperatures ( Campbell [1977] ), however e a r l i e r Reticons with which some of the data in thi s thesis was obtained occasionally needed some correction for t h i s effect ( pre 1982 ). This was done by using equivalent length dark exposures to f i n d the l e v e l of the thermal contribut ion. 15 The noise in a Reticon i s dominated by the reset noise of the bias voltage due to Johnson noise in the s h i f t register switch resistance. The RMS v a r i a t i o n in successive bias charges i s ( Geary [1979] ) A = 2.5 x 109 A T C where A i s the number of equivalent electrons C i s the diode capacitance in pF k i s the Boltzmann Constant T i s the temperature in Kelvin The best attainable figure i s expected to be A= 300 electrons ( Walker et a l [1983] ). This value i s close to being achieved in the most recent UBC Reticons. The readout noise i s normally monitored by measuring the variance in short dark exposures which i s t y p i c a l l y * 2-3 ADC units. As an example of what t h i s means to the observer, using a figure of 185 e" per ADC unit ( Walker et a l [1983] ) an exposure of 1000 ADC units ( a 3 hour exposure of a 9th magnitude star at 40 A/mm on the DAO 48" ) would have a signal to noise of ^ 280 . Unfortunately a number of problems exist in achieving the figure for the signal to noise given above. Table 2.01 l i s t s some c h a r a c t e r i s t i c s of the Reticon Systems used in t h i s thesis. 1 6 T a b l e 2.01 R e t i c o n Systems Reticon # Prototype 1 DAO 2 UBC 3 CFHT 4 e"/ADC(hi) high/low r a t i o 400 5 185 5 150 3.5 250 3.5 2.3 THE DATA REDUCTION To properly reduce the data, appropriate material must be col l e c t e d during the observing run at the telescope. The output spectra a l l contain an output additive fixed pattern which i s due to coupling of the clock pulses to the video output l i n e s . This fixed pattern i s a large amplitude saw-tooth waveform that has a repeat cycle of multiples of the number of video l i n e s ( i . e . of 4 ). The pattern i s f a i r l y stable with time i f the clock pulses are stable and the temperature of the Reticon i s constant. A normal technique for removal of t h i s pattern i s to numerically subtract a second (short) exposure taken immediately after the i n i t i a l readout of the data frame ( Walker [1977] ). This frame should have i d e n t i c a l fixed pattern and the d i g i t a l subtraction should be good. The next step in the procedure i s to correct for any small scale changes in s e n s i t i v i t y across the array. These changes may be inherent in the array or the result of foreign material ( e.g. dust at CFHT ) on the detector. For 17 the best correction a f l a t spectrum from a distant source should be used, as the l i g h t path followed by the star's and the f l a t f i e l d ' s photons would then be i d e n t i c a l . This would remove small errors due to differences in po l a r i z a t i o n of the incoming l i g h t and in d i f f e r i n g illumination of the exit p u p i l . Unfortunately no bright s t e l l a r f l a t spectrum sources exist and instead an incandescent lamp i s used. The best corrections were found taking f l a t f i e l d exposures produced when the lamps were positioned at the top of the telescope and made to illuminate the inside of the dome. However the time for signal levels comparable to s t e l l a r exposures to be achieved was excessive. The technique f i n a l l y adopted was to position the lamp in the s l i t room just before the l a s t element in the coude t r a i n . The telescope exit pupil was defined using a c i r c u l a r stop so as to ensure the illumination of lamp and s t e l l a r spectra was the same. For best re s u l t s i t was necessary to adjust the i r i s diaphragm, used as a stop, for each star observed. This i s thought due to a s l i g h t mis-collimation of the coude mirrors. The average of many lamp exposures ( t y p i c a l l y 100 x 50 sec exposures ) i s used in the f i n a l d i v i s i o n to correct the s t e l l a r spectrum. As lamps of s u f f i c e n t l y high temperature to produce a f l a t spectrum in the blue are not av a i l a b l e , the lamp spectrum i s divided by a low order polynomial f i t t e d to the spectrum to correct for the lamp blackbody curvature, 18 The gains of the d i f f e r e n t output amplifiers attached to each l i n e are only possible to adjust to within a few percent. Thus to c a l i b r a t e their r e l a t i v e gains continuous spectra from an incandescent c a l i b r a t i o n lamp were exposed to d i f f e r e n t signal l e v e l s . Normally a f i l t e r was used which when combined with the blackbody curve from the lamp produced a region of a few hundred pixels which had a constant exposure (ADC) l e v e l . T y p i c a l l y f i f t e e n d i f f e r e n t exposure leve l s ( each with 20 to 50 exposures ) between zero and saturation l e v e l were taken. Corrections to each l i n e in order to move them to the mean of a l l the data were obtained and this was then f i t t e d by a ( f i r s t order ) polynomial to give a correction according to gain l e v e l which was then applied to a l l spectra on that night. The change in gain i s * 5 x 10"8/ADCU for the high gain mode of operation. After a l l these corrections i t may be possible that a small four l i n e pattern remained. A small additive correction was then applied to the lines to set a l l the l i n e s means' equal. Thus to properly reduce Reticon data involves dealing with on the order of 600 recorded spectra per night or for the t o t a l data set used here ^ 36000 spectra. 19 2.4 PROBLEMS WITH DARKS The technique described above works well on high signal to noise spectra of bright stars ( i . e . short exposures < 2000 seconds). The data obtained for t h i s thesis on standard stars was well reduced in t h i s way. The exposure time, at a l l telescopes, to obtain spectra on Cygnus X-1 was, on average, approximately two to four hours. It was found during reduction that there was a problem with proper dark subtraction of these long exposures in order to remove the fixed pattern. Figure 2.01 i s the Fourier Transform of the spectra shown in figure 2.02 . The horizontal scale is given in percent of the Nyquist Frequency so that 50% corresponds to a p e r i o d i c i t y in the spectrum with a s p a t i a l frequency of 4 p i x e l s . The gradual r i s e in power towards low frequency i s due to transforming spectral features and the presence of negative spikes i s caused by noise and does not repeat on other spectra. In the case shown, and on some other occasions, a pattern of eight ( 25% ) was p a r t i c u l a r i l y evident. This i s believed the resu l t of a s i g n i f i c a n t warming of the array between the beginning and end of an exposure. For data obtained with the prototype Reticon system there were almost c e r t a i n l y problems associated with the l i q u i d nitrogen cooling system. On occasions blockage in the f i l l i n g system would cause only p a r t i a l f i l l i n g of the storage dewar and leaks in the vacuum insulation system resulted in poor insul a t i o n and fro s t i n g problems. This l a t t e r problem was e a s i l y detected as the lamps rather than 20 Figure 2.01 Fourier Transform of spectrum of Cygnus X-1 in f igure 2.02 . X N y q u i s t F r e q u e n c y 22 being smooth were extremely 'ropey'. The new Reticon system is more random in i t s properties. Sometimes the baseline exposure taken immediately following the s t e l l a r exposure resulted in excellent removal of the fixed pattern whereas at other times only an exposure of equal duration proved s a t i s f a c t o r y . At other times no dark of either, short, long or intermediate exposure time was found to be suitable. A possible explanation for t h i s problem i s that the heater in the dewar moves out of range of the temperature sensor loop on occasion and a constant temperature can not be maintained. If t h i s were the case the dark current contribution may vary. The temperature near the chip inside the dewar was in fact monitored on occasion and no changes were seen. However u n t i l an on chip temperature sensor i s available the real chip temperature variation w i l l not be known. Another p o s s i b i l i t y for the lack of sati s f a c t o r y darks i s self heating of the array. Normally the time between readouts is less than an hour. Each readout induces some heating in the array due to current flow to reset the diodes. After a three hour lag the array w i l l be at a temperature below that found immediately after a readout and thus the current flow to reset the diodes w i l l need to be higher. Thus a three hour dark w i l l be di f f e r e n t from a ten second exposure and th i s may be why a short dark exposure may not correct the fixed pattern of a long s t e l l a r exposure. The reason for the long darks not working well on long s t e l l a r exposures i s probably due to long term d r i f t s . 23 If consecutive long darks are taken i t i s found that the mean l e v e l changes randomly by =*10-15 ADC units for a three hour exposure. Shorter length darks ( <1000 sec ) while being more stable on a series of exposures seem to d r i f t by a few ADC units between l i q u i d nitrogen r e f i l l s and nights. One way of correcting for these long term zero d r i f t s was by reading out 52 dummy diodes before and 76 af t e r , each read out of the 1872 elements. That i s a normal intergration cycle i s ca r r i e d out with the switch opening and clos i n g but without a c t i v a t i n g the s h i f t register to address the individual diodes. Thus, in p r i n c i p l e , 32 zero point samples per video l i n e were available to be averaged and applied as a correction to the actual p i x e l s . This correction was only available for our most recent data and could not be used in a l l cases due to electronic problems with these dummy p i x e l s . The extra p i x e l s in lamp exposures were found to be unuseable presumably because of the heating e f f e c t of the many lamp photons on the video l i n e s . 2.5 COSMIC RAY EVENTS It had been noticed from the e a r l i e s t Reticon observations that on occasion large spikes were seen in the data. At f i r s t these were attributed to noise in the detector but as the system performance improved i t was clear that i t was something else. A clear indication of how these events l i m i t the usefulness of long exposures is seen in figure 2.02 where two CFHT spectra ( which have a dark subtracted ) are 24 shown. The spectra are of a less than two hours duration and the s t e l l a r features are i d e n t i f i e d . Clearly seen i s the range in energy of the spikes and t h e i r effect on the observations. The lower spectrum shows a massive event of =*500,000 electrons while the upper spectrum shows the more serious effect of the many lower energy events including quite broad features which can seriously af f e c t l i n e p r o f i l e s ( for example the He I X4713 l i n e ) and thus r a d i a l v e l o c i t y determination. These events have also been noticed by other users of Reticon detectors ( Vogt [1981] ) and ascribed to cosmic rays s t r i k i n g the array. As the rate of these events seemed to vary for the four d i f f e r e n t Reticon chips used in t h i s thesis and because of the importance of knowing the l i m i t s of long exposure time, high signal to noise spectroscopy, these events were investigated futher. The ideal time for intensive study of t h i s problem occurred during a campaign of observations on Cygnus X-1. This consisted of observations from the CFHT and the DAO which are at considerably di f f e r e n t a l t i t u d e s . The difference in the rate of events between observatories should depend on the known absorption of the atmosphere. There were f i f t e e n individual spectra of Cygnus X-1 obtained at CFHT over f i v e nights, a l l of approximately two hours duration ( see table 2.02 for d e t a i l s ). These spectra were inspected for a l l scales ( 1 to 20 pixels ) of non-stellar features. Such affected pixels or groups of pixels were corrected by replacing their ADC l e v e l with a value obtained 25 Figure 2.02 CFHT Spectra of Cygnus X-1 with basline removed. 6500 600  500 500  45000 40000' 4000 h 3000 2000 h 1000 30  60  90  120  Pixel U 150  180  900 1200 1500 tRnn 27 by polynomial interpolation of the ADC values of 'clean' pixels around them. The histogram in figure 2.03 shows the frequency with which spikes occurred on individual diodes. Notice that no p i x e l showed spikes on more than six of the f i f t e e n spectra. The He II X4686 emission l i n e in Cygnus X-1 f e l l in the region between pi x e l s 300 to 700. Only the most obvious spikes were modified in t h i s region which probably accounts for the low number of events. The frequency of occurrences away from t h i s region looks quite random which rules out any breakdown on c e r t a i n p i x e l s . The histogram in figure 2.04 displays the d i s t r i b u t i o n of sizes ( how many pixels were affected by a spike ) of recorded events on a l l the spectra. Clearly the narrowest events ( <3 p i x e l ) are the most common. One futher piece of evidence against the p o s s i b i l i t y of problems in the e l e c t r o n i c s , due to the long exposure time, producing the spikes was that the spike number was linear with time ( i . e . the number of spikes found in 360x10 second darks was the same as that found in one 3600 second exposure ). The rate of events found at the d i f f e r e n t observatories i s shown in table 2.02 along with t h e o r e t i c a l estimates from published cosmic ray fluxes. These predicted numbers are based on values using information from the 'Particle Properties Data Booklet' ( Aguilar-Benitez et a l [1984] ). Cosmic Ray muons are highly penetrating and suffer l i t t l e attenuation from the material of the observatory building. A l l k o f f e r [1975] and Aguilar-Benitez et a l [1984] give the 28 Figure 2.03 Histogram of bad pi x e l s for CFHT Data taken 08-12 July 1984. 30 Figure 2.04 D i s t r i b u t i o n of sizes of spikes as determined from a l l CFHT 08-12 July 1984 spectra. 31 D i s t r i b u t i o n o f UJ i d t h s o f s p i k e s W i d t h o f E u e n t ( i n p i x e l s ) 32 Table 2.02 Deta i l s of Ocurrence of Spikes (normalised to a Reticon Area = 21 mm2) Observatory DAO CFHT CFHT (CCD) K i t t Peak Altitude m 229 4200 4200 2100 Measured counts/hr 1 1 19 18 58 Expected counts/hr 10 20 18 flux of muons at 4300 metres as =*0.03 muons/cm2/sec and that at sea l e v e l as .014 muons/cm2/sec. Variations from t h i s rate due to the latitude ( =5% ) and longitude ( ^5% ) difference or the diurnal variation ( < 0.1% ) are i n s i g n i f i c a n t ( Allkofer [1975] ). Therefore for a Reticon array of area 21 mm2 the expected number of cosmic events in a one hour exposure i s 20 for the CFHT and 10 for the DAO. As can be seen in table 2.01 these values seem to agree with the measured rates and also with a value found for CFHT CCD observations ( Walker et a l [1985] ). The value found by Leach and Gursky [1979] for CCD frames obtained at K i t t Peak i s 0.08 cm~ 2sec" 1 or 58 events/hour per Reticon area. This i s much higher than our observations f i n d and probably indicates either an extraneous source of spikes in th e i r data or possibly solar a c t i v i t y which can produce large changes in the muon flux ( A l l k o f e r [1975] ). The expected effect of a muon passing through a diode can also be roughly evaluated. The peak of the muon energy 33 spectrum i s at about 400 MeV. According to Aguilar-Benitez et a l [1984] these muons w i l l lose on average 1.1 MeV/gm/cm2 when passing through carbon. Assuming a similar figure for s i l i c o n and a 30#um depth for the depletion region ( Livingston et a l [1976] ) gives an average loss of 0.006 x 1.1 MeV / 400MeV muon = 7 x 103 eV, where 0.006 gm/cm2 i s the area density of s i l i c o n in the depletion region. The excitation energy for the production of electrons in the depletion region i s 3.6 eV/electron. Hence the energy loss by a muon passing through a diode could produce = 2000 electrons, which i s approximately that found for the average spike value in the Reticon data. Thus the fact that the events occur randomly across the array, are t y p i c a l l y narrow and the - agreement of the frequency, variation of frequency with a l t i t u d e and amplitude of the observed spikes with those predicted from the known properties of cosmic ray muons strongly suggests that t h i s indeed i s the source of the spikes. The penetration depth of these p a r t i c l e s i s so large that shielding i s not fe a s i b l e . For the current generation of detectors they seem to be a fundamental l i m i t a t i o n to precise spectrophotometry. Future detectors u t i l i s i n g small detecting elements and/or shorter- exposure times may reduce the significance of these events. The very large spikes seen at a rate 1 per (1 to 2 ni g h t s ) " 1 probably have a d i f f e r e n t o r i g i n . They are much rarer and the energies involved ( >500,000 e" ) are much 34 larger than for the average spike. Together with the observation that one of the Reticon chips suffered a much higher rate of these spikes than the others, suggested the p o s s i b i l i t y of radioactive contamination of the Reticon chip i t s e l f . To investigate t h i s further the two chips available at UBC ( #1 and #3) were taken to the TRIUMF f a c i l i t y where their 7-ray spectrum was measured. 7-rays have the advantage that they suffer l i t t l e attenuation in most materials and allow bulk properties to be measured. Unfortunately the 7 spectrometer was designed for much higher levels of a c t i v i t y than found in these chips and the actual fluxes are somewhat unreliable ( ±30% ). The 7 peaks that did stand out above the background were i d e n t i f i e d as those from the decay of R a 2 2 6 , Bi 2 1» and Pb 2 1• with a c t i v i t i e s of «* 0.5, 0.1 and 0.3 Bequerels. The presence of these t r a n s i t i o n s implies the decay sequence of U 2 3 8 ( Walker, Kirouac and Rourke [1977] ) is being seen. The Uranium (4n+2) series produces 8 a p a r t i c l e s whose energies range between 5 and 9 MeV. The penetration depth for such a p a r t i c l e s i s = 70vm ( Yaney et a l [1979] ) although there i s evidence for much longer penetrations ( Kirkpatrick [1979] ). The electrons produced by j3 decay have energies of a few MeV, the i r t y p i c a l pathlengths are =* 1-2 cm ( Aguilar-Benitez [1984] ) and they are u n l i k e l y to interact in the s i l i c o n ( May and Woods [1979] ). . The location of t h i s radioactive material is not determined from the 7-ray measurements but i t could come 35 from the ceramic packaging or the quartz window material or even the gold substrate. A l l these materials are known to contain contain uranium from the work of May and Wood [1979] who investigated a p a r t i c l e induced soft errors in dynamic memory. Taking the observed rate of decay in this sequence as 0.5 Bequerels ( decays/sec ) and knowing the half l i f e of U 2 3 8 as 4.5 x 109 years gives the number of U 2 3 8 atoms as = 10 1 7. Taking the chip volume as 0.9"x0.288"x0.1" (EG & G spe c i f i c a t i o n s ) and the density t y p i c a l of a s i l i c a t e of =* 2 g/cc ( Handbook of Chemistry and Physics ), gives a fr a c t i o n of U 2 3 8 as = 10 ppm. This i s similar to the l e v e l s found by May and Woods (1979) in semiconductor packaging material. U n t i l the exact location of the decaying material i s known the expected number of spikes can not be well estimated. An observed rate of a c t i v i t y of =*0.2 Bequerels gives an a p a r t i c l e flux of 10" hour" 1. Although this rate i s much higher than the observed spike rate the effects of c o l l e c t i o n s o l i d angle and attenuation by the s i l i c o n below the depletion region w i l l reduce the figure considerably. Notice that a t y p i c a l a p a r t i c l e of 5 MeV, i f completely stopped in a single diode, w i l l produce a hole-electron pair for each 3.6eV of ionizing p a r t i c l e energy ( Kirkpatrick [1979] ) or *10 6e". This i s on the order of the energy of the largest spike events seen in the Reticon detectors (see figure 2.01). 36 2.6 THE DATA A summary of a l l the observations of Cygnus X-1 used in t h i s thesis are given in table 2.03 . In fact there are a number of lower signal to noise spectra available, but when examined were found to be too poor to be used in t h i s study. On each night that a spectrum of Cygnus X-1 was taken a spectrum of the designated comparison star ( 19 Cepheus ) was also obtained. The exceptions to t h i s rule were the night of June 25, 1982 when clouds moved in extremely rapidly, and the observations at the CFHT where 19 Cepheus spectra were only taken on the nights of July 08 and 11, 1984. The spectra of the standard were always of much higher signal to noise. Vega ( a Lyr ) spectra were also obtained on each night to check that the alignment of the spectrograph was optimum. This data on Vega has been published elsewhere ( Walker et a l [1984] ) and displays well the long term s t a b i l i t y and consistency of the Reticon detector. In order to study how HDE 226868 compares to stars of similar spectral type, many standards were observed. A summary of these observations i s given in table 2.04. 2.7 DIGITAL SUBTRACTION To those accustomed to photographic plates the idea of d i g i t a l l y subtracting two aligned spectra may seem a l i t t l e dangerous. One of the advantages of a Reticon type detector is that the number of ADC units recorded i s related to the number of electrons produced by s t e l l a r signal photons by a Table 2.03 De t a i l s of Observations of Cygnus X-1 D a t e BJD Te1escope D1! D/M/Y 2440000+ A/l 0 1 / 1 0 / 8 0 4513 . 770 DAO 48" 40 0 2 / 1 0 / 8 0 4514 .691 DAO 48" 40 0 3 / 1 0 / 8 0 4515 .698 DAO 48" 40 0 4 / 1 0 / 8 0 4516 .680 DAO 48" 40 07/09/81 4854 . 722 DAO 48" 40 08/09/81 4855 .822 DAO 48" 40 09/09/81 4856 .838 DAO 48" 40 10/09/81 4857 .818 DAO 48" 40 11/09/81 4858 .810 DAO 48" 40 13/09/81 4860 .853 DAO 48" 40 09/05/82 5098 .705 DAO 48" 40 10/05/82 5099 .716 DAO 48" 40 22/06/82 5142 .843 DAO 48" 40 23/06/82 5143 .852 DAO 48" 40 24/06/82 5144 .839 DAO 48" 40 25/06/82 5145 .855 DAO 48" 40 05/08/82 5186 . 793 DAO 4 8 " 40 06/08/82 5187 .828 DAO 48" 40 07/08/82 5188 .767 DAO 48" 40 07/08/82 5188 .869 DAO 48" 40 07/08/82 5188. .953 DAO 48" 40 08/08/82 5189 . 793 DAO 48" 40 09/08/82 5190. .762 DAO 48" 40 09/08/82 5190. .901 DAO 48" 40 29/09/82 5241 .707 DAO 48" 40 30/09/82 5242 . .669 DAO 48" 40 30/09/82 5242. , 767 DAO 48" 40 01/10/82 5243. .697 DAO 48" 40 20/10/82 5262. .657 DAO 4 8 " 40 27/06/83 5512 . . 799 DAO 48" 40 28/06/83 5 5 1 3 . 822 DAO 4 8 " 40 30/06/83 5515 . 875 DAO 48" 40 29/07/83 5544 . 773 DAO 48" 40 29/07/83 5544 . 907 DAO 48" 40 V r e g i o n Exposure B a r y c e n t r 1 c A i r Re A T i m e ( s e c s ) RV(km/sec) Mass & ( 4686 10800 14 . 55 1 . 22 1H 4686 10000 14.61 1 .05 1H 4686 10800 14 . 79 1 .06 1H 4686 10000 14.93 1 .05 1H 4686 10000 9 . 16 1 .03 1L. 4686 7200 9 . 5 8 1 . 18 1L 4686 10000 9 .86 1 . 24 1L 4686 7200 10 .08 1 . 18 11 4686 7200 10.31 1 . 17 1L 4686 8000 10 .85 1 . 36 1L 4686 10000 - 1 7 . 3 9 6 .79 2H 4686 10000 - 1 7 . 3 8 5 .41 2H 4686 15000 - 1 1 . 8 1 1 . 1 1 2H 4686 15000 - 1 1 . 5 7 1 .09 2H 4686 15000 - 1 1 . 3 7 1 . 1 1 2H 4686 10600 - 1 1 . 1 2 1 .07 2H 4686 12900 - 0 . 14 1 .03 2H 4686 12500 0 . 2 2 1 .03 2H 4686 10000 0 . 4 0 1 .04 2H 4686 7700 0 . 5 9 1 .08 2H 4686 6700 0 . 7 2 1 . 34 2H 4686 12000 0 . 7 5 1 .03 2H 4686 12000 0 . 9 8 1 .04 2H 4686 12000 1 .23 1 . 16 2H 4686 15000 14.01 1 .06 2H 4686 8000 14.13 1 .03 2H 4686 10000 14 . 28 1 . 19 2H 4686 14200 14 . 35 1 .05 2H 4686 13000 1 6 . 9 0 1 .07 2H 4686 13700 - 1 0 . 8 1 1 . 19 2H 4686 15000 - 1 0 . 5 4 1 . . 12 2H 4686 13500 - 9 .98 1 . .04 2H 4686 10200 - 2 . 3 1 1 , ,06 2H 4686 13000 - 2 .06 1 . . 10 2H 3 0 / 0 7 / 8 3 5 5 4 5 . 7 2 4 DAO 4 8 " 4 0 4 6 8 6 3 0 ^ 0 7 / 8 3 5 5 4 5 . 8 8 6 DAO 4 8 " 4 0 4 6 8 6 3 1 / 0 7 / 8 3 5 5 4 G . 7 7 4 DAO 4 8 " 4 0 4 6 8 6 3 1 / 0 7 / 8 3 5 5 4 6 . 9 1 4 DAO 4 8 " 4 0 4 6 8 6 0 1 / 0 8 / 8 3 5 5 4 7 . 8 5 6 DAO 4 8 " 4 0 4 6 8 6 2 9 / 1 1 / 8 3 5 6 6 7 . 6 3 5 DAO 7 2 " 31 4 6 8 6 3 0 / 1 1 / 8 3 5 6 6 8 . 6 2 4 DAO 7 2 " 31 4 6 8 6 0 1 / 1 2 / 8 3 5 6 6 9 . 6 3 5 DAO 7 2 " 3 1 4 6 8 6 0 2 / 1 2 / 8 3 5 6 7 0 . . 6 1 5 DAO 7 2 " 31 4 6 8 6 1 9 / 1 2 / 8 3 5 6 8 7 . 6 2 7 DAO 7 2 " 31 4 6 8 6 0 7 / 0 7 / 8 4 5 8 8 8 . 7 8 2 DAO 4 8 " 4 0 4 6 8 6 0 7 / 0 7 / 8 4 5 8 8 8 . 8 9 1 DAO 4 8 " 4 0 4 6 8 6 0 8 / 0 7 / 8 4 5 8 8 9 . 8 0 7 DAO 4 8 " 4 0 4 6 8 6 0 8 / 0 7 / 8 4 5 8 8 9 . . 9 0 4 DAO 4 8 " 4 0 4 6 8 6 0 9 / 0 7 / 8 4 5 8 9 0 . 7 9 4 DAO 4 8 " 4 0 4 6 8 6 0 9 / 0 7 / 8 4 5 8 9 0 . 8 9 5 DAO 4 8 " 4 0 4 6 8 6 1 0 / 0 7 / 8 4 5 8 9 1 , . 7 9 9 DAO 4 8 " 4 0 4 6 8 6 1 0 / 0 7 / 8 4 5 8 9 1 . . 8 9 7 DAO 4 8 " 4 0 4 6 8 6 1 1 / 0 7 / 8 4 5 8 9 2 . . 8 0 0 DAO 4 8 " 4 0 4 6 8 6 1 1 / 0 7 / 8 4 5 8 9 2 . . 8 9 7 DAO 4 8 " 4 0 4 6 8 6 1 2 / 0 7 / 8 4 5 8 9 3 , , 8 7 8 DAO 4 8 " 4 0 4 6 8 6 1 3 / 0 7 / 8 4 5 8 9 4 . . 7 9 5 DAO 4 8 " 4 0 4 6 8 6 1 3 / 0 7 / 8 4 5 8 9 4 . . 8 5 5 DAO 4 8 " 4 0 4 6 8 6 0 6 / 0 7 / 8 4 5 8 8 7 . . 8 0 7 DAO 7 2 " 31 Ha 0 7 / 0 7 / 8 4 5 8 8 8 . , 8 0 0 DAO 7 2 " 31 Ha 0 7 / 0 7 / 8 4 5 8 8 8 . . 8 9 3 DAO 7 2 " 31 Ha 0 8 / 0 7 / 8 4 5 8 8 9 . . 8 9 4 DAO 7 2 " 31 Ha 0 9 / 0 7 / 8 4 5 8 9 0 . 8 0 5 DAO 7 2 " 31 Ha 0 9 / 0 7 / 8 4 5 8 9 0 . 8 9 5 DAO 7 2 " 3 1 Ha 1 0 / 0 7 / 8 4 5 8 9 1 . 7 9 7 DAO 7 2 " 31 Ha 1 0 / 0 7 / 8 4 5 8 9 1 . . 8 9 1 DAO 7 2 " 31 Ha 1 1 / 0 7 / 8 4 5 8 9 2 . 7 8 9 DAO 7 2 " 31 Ha 1 1 / 0 7 / 8 4 5 8 9 2 . 8 9 5 DAO 7 2 " 31 Ha 1 2 / 0 7 / 8 4 5 8 9 3 . 8 1 0 DAO 7 2 " 31 Ha 1 3 / 0 7 / 8 4 5 8 9 4 . 8 0 2 DAO 7 2 " 31 Ha 1 3 / 0 7 / 8 4 5 8 9 4 . 8 9 2 DAO 7 2 " 31 Ha 1 4 / 0 7 / 8 4 5 8 9 5 . 7 9 1 DAO 7 2 " 31 Ha 1 4 / 0 7 / 8 4 5 8 9 5 . . 8 9 5 DAO 7 2 " 31 Ha 1 0 0 0 0 - 2 . 10 1 . 15 2H 1 0 8 0 0 - 1 . 8 1 1 . 0 7 2H 1 0 8 0 0 - 1 . 72 1 . 0 5 2H 1 3 5 0 0 - 1 . 4 7 1 . 13 2H 1 8 0 0 0 - 1 . 28 1 . 0 4 2H 1 0 0 0 0 16 . 4 0 1 . 3 3 2L 1 1 0 0 0 16 . 27 1 . 2 9 2 L 1 3 3 0 6 16 . 16 1 . 3 6 2L 1 1 1 2 0 16 . 0 1 1 . 2 8 2 L 1 3 1 0 0 13 . 0 8 1 . 6 4 2H 7 2 0 0 - 8 . 19 1 . 16 3H 9 0 0 0 - 8 . 0 1 1 . 0 3 3H 8 5 1 1 - 7 . 9 0 1 . 0 9 3H 8 1 0 0 - 7 . 7 2 1 . 0 3 3H 8 0 0 0 - 7 . 6 5 1 . 1 1 3H 1 0 0 0 0 - 7 . 4 7 1 . 0 3 3 H 7 6 0 0 - 7 . 38 1 . 10 3H 9 3 0 0 - 7 . 2 0 1 . 0 3 3H 7 5 0 0 - 7 . 1 1 1 . 0 9 3H 9 0 0 0 - 6 . 94 1 . 0 3 3H 1 0 4 3 1 - 6 . 7 1 1 . 0 3 3H 8 199 - 6 . 59 1 . 0 9 3H 8 0 2 0 - 6 . 48 1 . 0 3 2 H 1 3 0 0 0 - 8 . 3 5 1 . 0 5 2H 7 2 0 0 - 8 . 17 1 . 1 1 2H 9 0 0 0 - 8 . 0 0 1 . 0 3 2H 8 7 O 0 - 7 . 74 1 . 0 3 2H 7 4 0 8 - 7 . 6 4 1 . 0 9 2H 8 2 2 4 - 7 . 47 1 . 0 3 2H 6 6 0 0 - 7 . 38 1 . 10 2H 9 5 0 0 - 7 . 22 1 . 0 3 2H 7 7 5 0 - 7 . 13 1 . 1 1 2H 9 6 0 0 - 6 . 9 4 1 . 0 3 2H 1 0 5 7 0 - 6 . 8 3 1 . 0 7 2H 7 1 0 0 - 6 . 57 1 . 0 8 2H 8 2 4 3 - 6 . 4 1 1 . 0 3 2H 8 0 0 0 - 6 . 32 1 . 0 9 2H 9 5 0 0 - 6 . 13 1 . 0 4 1H co oo 08/07/84 5889. .854 CFH 3. . 6m 2 . 4 4686 5704 - 8 . .01 1 .31 4H 08/07/84 5889 .983 CFH 3 . 6m 2 . 4 4686 6001 - 7 . 7 1 1 .04 4H 08/07/84 5890 .072 CFH 3 . 6m 2 . 4 4686 6002 - 7 .50 1 . 23 4H 09/07/84 5890 .857 CFH 3 . 6m 2 . 4 4686 7202 - 7 . 74 1 .27 4H 09/07/84 5890 .959 CFH 3 . 6m 2 . 4 4686 7203 - 7 . 50 1 .04 4H 09/07/84 5891 . .051 CFH 3 . 6m 2 . 4 4686 4602 - 7 . . 28 1 . 16 4H 10/07/84 5891 .938 CFH 3 . 6m 2 . 4 4686 6000 - 7 . . 29 1 .05 4H 10/07/84 5892. .023 CFH 3 .6m 2. .4 4686 6000 - 7 .08 1 .09 4H 10/07/84 5892 . 105 CFH 3 . 6m 2 .4 4686 5306 - 6 .91 1 .46 4H 11/07/84 5892 .854 CFH 3 . 6m 2 .4 4686 6501 - 7 .21 1 . 26 4H 11/07/84 5892 .940 CFH 3 . 6m 2 . 4 4686 5502 - 7 .02 1 .05 4H 11/07/84 5893 .078 CFH 3 . 6m 2 . 4 4686 8002 - 6 .69 1 . 3 0 4H 12/07/84 5893 .824 CFH 3 . 6m 2 . 4 4686 7001 - 7 .00 1 .43 4H 12/07/84 5893 .947 CFH 3 . 6m 2 . 4 4686 6002 - 6 . 73 1 .04 4H 12/07/84 5894 .059 CFH 3 . 6m 2 . 4 4686 7001 - 6 . 46 1 . 22 4H TabTe 2.04 Details of observations of Comparison Stars S t a r Date T e l e s c o p e D i s p e r s i o n V re( D/M/Y A/mm A x o n 15/11/80 DAO 48" 40 4686 HD 40111 15/11/80 DAO 48" 40 4686 t Per 07/09/81 DAO 48" 40 4686 £ Per 07/09/81 DAO 48" 40 4686 40 Per 08/09/81 DAO 48" 40 4686 AE Aur 08/09/81 DAO 48" 40 4686 HD 195592 10/09/81 DAO 48" 40 4686 it Or t 10/09/81 DAO 48" 40 4686 HD 199579 11/09/81 DAO 48" 40 4686 HD 199216 11/09/81 DAO 48" 40 4686 HD 217086 13/09/81 DAO 48" 40 4686 I o n 22/10/81 DAO 48" 40 4686 a o n 22/10/81 DAO 48" 40 4686 « o n 22/10/81 DAO 48" 40 4686 HD 36822 22/10/81 DAO 48" 40 4686 i/ o n 22/10/81 DAO 48" 40 4686 HD 36960 22/10/81 DAO 48" 40 4686 n o n 22/10/81 DAO 48" 40 4686 42 o n 22/10/81 DAO 48" 40 4686 0' o n c 05/03/82 DAO 48" 40 4686 15 Mon 06/03/82 DAO 48" 40 4686 A Leo 24/06/82 DAO 48" 40 4686 15 Sgr 07/08/82 DAO 48" 40 4686 9 Sge 07/08/82 DAO 48" 40 4686 HD 207198 08/08/82 DAO 48" 40 4686 HD 218915 08/08/82 DAO 48" 40 4686 S o n 30/09/82 DAO 48" 40 4686 HD 225146 30/09/82 DAO 48" 40 4686 6 o n 01/10/82 DAO 48" 40 4686 HD 47432 01/10/82 DAO 48" 40 4686 HD 194280 01/10/82 DAO 48" 40 4686 HD 13745 01/10/82 DAO 48" 40 4686 HD 204 172 20/10/82 DAO 48" 40 4686 y Cas 28/06/83 DAO 48" 40 4686 Exposure Magn i tude Time ( see s ) ( V ) Ret 1 con & G a m 750 3 .66 1H 3200 4 .82 1H 200 2 .89 1L 200 2 .85 1L 500 4 .97 1L 500 5 .96 11 1500 7 .08 1L 250 2 .06 1L 500 5 .96 1L 1000 7 . 1 1L 2000 7 .64 11 500 2 . 77 1H 200 3. .81 IH 100 1 .70 1H 200 4 .41 1H 500 4 . 42 1H 500 4 .78 1H 200 3 . 36 1H 200 4 , 59 1H 1000 5 . 13 2H 500 4 . 66 2H 500 3 . 85 2H 900 5 . 38 2H 890 6 . 23 2H 1500 5. 95 2H 3600 7 . 18 2H 50 2 . 05 2H 5000 8 . 60 2H 400 2 . 23 2H 2000 6 . 2 1 2H 7200 8 . 39 2H 4 200 7 . 88 2H 1000 5. 94 2H 100 2 . 47 2H a Cam 29/07/83 DAO 48" 40 4686 400 4 .29 2H X Per 17/12/83 DAO 48" 40 4686 1600 6 . 16 2H HD 188209 09/07/84 DAO 48" 40 4686 500 5 .62 3H HD 193322 10/07/84 DAO 48" 40 4686 750 5 .84 3H 14 Cep 11/07/84 DAO 48" 40 4686 775 5 . 56 3H HD 206267 11/07/84 DAO 48" 40 4686 600 5. .62 3H HD 199579 11/07/84 DAO 48" 40 4686 400 5 . 96 3H 68 Cyg 11/07/84 DAO 48" 40 4686 300 5 .00 3H 10 Lac 11/07/84 DAO 48" 40 4686 300 4 . 88 3H X Cep 11/07/84 DAO 48" 40 4686 300 5 .04 3H K Cas 11/07/84 DAO 48" 40 4686 300 4 . 16 3H 9 Sge 11/07/84 OAO 72" 31 Ha 600 6 . 23 2H HD 204 172 10/07/84 DAO 72" 31 Ha 1200 5 . 94 2H HD 188209 11/07/84 DAO 72" 31 Ha 900 5 62 2H 67 Oph 12/07/84 DAO 72" 31 Ha 1 15 7 08 2H a Ly r 12/07/84 DAO 72" 31 Ha 35 0 03 2H HD 188209 08/07/84 CFH 3. 6m 2.4 4686 750 5 62 2H Nor 09/07/84 CFH 3. 6m 2.4 4686 1000 4 . 94 2H 15 Sgr 11/07/84 CFH 3. 6m 2 . 4 4686 1800 5 . 38 2H HD 195592 11/07/84 CFH 3. 6m 2.4 4686 2001 7 . 08 2H 19 Cep 12/07/84 CFH 3. 6m 2.4 4686 750 5. 1 1 2H 42 constant which i s the same for a l l spectra ( i . e . the detector i s linear ). Coupled with the large dynamic range of the Reticon, t h i s enables the normalised spectra of two id e n t i c a l stars of very d i f f e r e n t exposure l e v e l to be subtracted d i r e c t l y from one another with very l i t t l e residual spectrum in the difference. This i s without the elaborate precautions required with photographic spectra to allow for reciprocity f a i l u r e . To i l l u s t r a t e how well d i g i t a l subtraction can work an example of a much observed star i s shown. X Per ( HR 1209 ) has been i d e n t i f i e d as a X-ray source ( Bradt and McClintock [1983] ). Its spectrum has been detailed by Cowley et a l [1972] and Hutchings et a l [1975] and a spectral type of 09.5Ve has been assigned. Its spectrum, obtained as part of the c o l l e c t i o n of standards, shows emission in the Balmer li n e s as expected for an 'e' star but also a considerable weakening of the He I t r i p l e t l i n e s r e l a t i v e to the He I singlet l i n e s . This may be due to a contribution from a surrounding nebula, as detailed in Osterbrock [1974]. A t y p i c a l 09.5V star spectrum ( o Ori ) afte r suitable s h i f t i n g , was subtracted from the spectrum of X Per. The input spectra and the resultant difference are plotted in figure 2.05 and 2.06. Clearly the underlying absorption lines are removed and the residual spectrum contains the emission lines from a nebula surrounding the star. Any errors in this technique would c l e a r l y evidence themselves in the process above. Notice the lower signal to noise and 43 Figure 2.05 Spectrum of X Per (upper) and a Ori (lower) 45 Figure 2.06 The difference spectrum of X Per 4200 4400 4600 N a u e l e n g t h ( A n g t s r o m ) 4800 5000 47 the problem of f i t t i n g a good continuum at the blue end of the spectrum. Further tests were also conducted subtracting d i f f e r e n t length exposures ( i . e . d i f f e r e n t ADCU l e v e l ) of standard stars from each other. In a l l cases the subtraction resulted in very small residuals thus giving confidence that the difference technique works well. Chapter 3 THE ABSORPTION LINE SPECTRUM 3.1 RATIONALE FOR THE STUDY As outlined in Chapter 1, Cygnus X-1 was an object of considerable attention in the mid nineteen seventies. There seemed to be a number of compelling reasons to believe the time was right for a detailed re-examination of t h i s system. These arguments included ; unfortunately p r a c t i c a l l y a l l the o p t i c a l observations available in the l i t e r a t u r e were obtained before the advent of the current generation of low noise s i l i c o n detectors. Most of the published spectra were therefore of low signal to noise or the average of spectra taken over many di f f e r e n t o r b i t a l cycles. Any variations from cycle to cycle or within a revolution were conseguentialy d i f f i c u l t to detect. Claims of observed changes in the spectral type as a function of phase ( Smith et a l [1973] ) and in the equivalent widths at certain epochs ( Walker, Yang and Glaspey [1978]) needed to be investigated c a r e f u l l y . long term monitoring at high precision of the v e l o c i t y curve might uncover new periods and features that would shed new l i g h t on the system. Models of the system that do not involve a black hole require a t h i r d body in the 48 49 system ( Bahcall et a l [1974], Abt et a l [1977], Bahcall [1980] ). Bahcall [1980] makes two s p e c i f i c predictions for his distant t r i p l e model for Cygnus X-1 in which two heavier stars form a close binary with a l i g h t e r X-ray source moving in an extended orbit about the close pair ( a l a X Tauri ). F i r s t l y , the centre of mass vel o c i t y of the two massive stars should vary by a few kmsec"1 with a period of the order of a month. Secondly the o r b i t a l period should change by the order of (d/dt) ln( period ) =* 10"*'5 year" 1. For an observed period of 5.6 days t h i s would imply a change in the period of about half an hour in fiv e years. The f i r s t e f f ect i s due to an assumed 1 X-ray source perturbing the v e l o c i t y of the centre of mass of the inner binary. The second ef f e c t i s due to the necessary mass loss from the inner binary to power the X-ray source. Both these ef f e c t s should be measurable, i f present, with available instrumentation. Wilson and Fox [1981] in fact reported evidence for a 4.5 year period from their photometric measures of Cygnus X-1, which they interpret as being due to a t h i r d body. There are other p o s s i b i l i t i e s for longer period changes ( > o r b i t a l period ) in t h i s system. A suggested explanation for the long period changes seen in a number of low and high mass systems i s that either a postulated disc about the secondary precesses, or the primary star precesses or both. The recently discovered 294 day 50 period in Cygnus X-1 might be att r i b u t a b l e to t h i s effect ( Priedhorsky et a l [1983] ). Apsidal motion may also be present and using the expression from Boyle and Henrichs [1984] one finds an apsidal period of order 14 years for parameters appropriate to Cygnus X-1. High qua l i t y spectra of both HDE 226868 and stars of similar spectral type to determine i f there are abundance anomolies as would be expected from, stars involved in s i g n i f i c a n t mass loss ( Dearborn [1977], Deaborn and Eggelton [1977] ) or i f the primary were a low mass, low gravity B star such as HZ 22 ( Trimble et a l [1973] ). Such high q u a l i t y spectra might also reveal any weak l i n e s a t t r i b u t a b l e to -a BV companion star to HDE226868 as i s required by t r i p l e star models of the system. Variations in the spectrum of the primary due to X-ray heating ( Milgrom [1977] ) or e l l i p t i c a l d i s t o r t i o n by the secondary ( Hutchings [1977], Guinan et a l [1979] ) could be expected at observable l e v e l s . 3.2 THE SPECTRUM ITSELF With these goals in mind t h i s study was concentrated on the blue region of the spectrum. There were a number of good reasons for t h i s choice; the blue region is free of t e l l u r i c l i n e s the Reticon detector works well in t h i s region early type stars are bright in the blue and contain 51 spectral lines with a range of excitation energies the mysterious emission lin e of He II at X4686, an as yet unexplained feature, could be monitored red optics were unavailable on the DAO telescope A second emphasis was to obtain most spectra in as few o r b i t a l cycles as possible. This was expected to show c l e a r l y the effects of variations between di f f e r e n t epochs. Shown in figure 3.01 i s the spectrum of HDE 226868 and of the primary standard used in the ensuing analysis, 19 Cepheus. The blue spectrum shown was obtained on the night of 07 August 1982 on the DAO 48" Telescope and the red region was obtained on the 09 July 1984 on the DAO 72" Telescope. They represent an example of our higher signal to noise data. Futher information on the d e t a i l s of data c o l l e c t i o n can be found in Chapter 2. The i d e n t i f i c a t i o n of features in figure 3.01 i s l i s t e d in Table 3.01. Wavelengths for s t e l l a r l i n es are from Moore [1959], for night sky lines from Meinel et a l [1975] and for i n t e r s t e l l a r l i n e s from Herbig [1975] and Scholz [1972], There are a number of l i n e s not previously i d e n t i f i e d in the l i t e r a t u r e . The weak i n t e r s t e l l a r feature seen at X4963 stands out in spectra of HDE 226868 as i t does not share in the large velocity variations associated with binary motion. This l i n e i s also c l e a r l y seen in spectra obtained of other well reddened early type stars such as HD 206267 and HD 207198. There are also two unidentified emission l i n e s at X6667 and X6700 in the spectrum of 19 Cepheus reminiscent of the l i n e pair at 52 Figure 3.01 The Spectrum of HDE 226868 (upper) and 19 Cep (lower). T ic marks indicate l i n e s i d e n t i f i e d in table 3.01. M i v f l t n g t h (Angstrom) Table 3.01a Line l i s t for ear ly type stars (b lue) . N 2 (Aurora) 3914.4 A He I 4471.477 A 0 II 3919.29 Mg II 4481.228 He II 3923.48 ? 4485.7 He I 3926.530 ? (IS) 4501.8 Ca l l (IS) 3933.64 4503.7 0 II 3954.370 N III 4510.92 0 II 3961.59 N III 4514.89 He I 3964.727 He II 4541.59 Cal l (IS) 3968.470 Si III 4552.654 He 3970.074 Si III 4567.872 0 II 3982.72 Si III 4574.777 N III 3998.69 O II 4590.971 N III 4003.64 O II 4596.17 He I 4009.270 N II 4613.87 He I 4026. 189 N II 4630.537 N II 4035.087 N II 4634.16 Hg I (NS) 4047. O II 4638.85 0 II 4069.897 N III 4640.64 0 II 4075.86 C III 4647.40 Si IV 4088.863 C III 4650.74 N III 4097.31 Si IV 4654.32 H6 4101.737 0 II 4661.635 Si IV 4116.104 O II 4673.75 He I 4120.812 0 II 4676.234 0 II 4132.81 • He II 4685.682 He I 4143.759 O i l 4699.21 0 II 4153.30 o n 4705.355 Blend 4156.7 He I 4713.143 C III 4162.86 ? (IS) 4726. He I 4168.97 ? (IS) 4763.0 0 II 4185.456 ? (IS) 4779.7 N III 4195.70 m 4861.332 He II 4199.83 ? (IS) 4882. S III 4211.68 He I 4921.929 Ne II 4219.76 ? (IS) 4963. CH+ IS 4232.6 He I 5015.675 N II 4241.787 He I 5047.736 0 II 4253.74 C II 4267.02 C II 4267.27 0 II 4276.21 Si III 4284.99 CH IS --43O0..6-o n 4319.93 H7 4340.468 o n 4349.426 Hgl (Nightsky) 4358.3 0 II 4366.896 N III 4379.09 He I 4387.928 o n 4414.909 ? (is) 4428. Table 3.01b Line l i s t for early type stars (red). He I I 6406.3 He I I 6527.3 Ha 6562.817 ? IS 6613.63 ? IS 6660.71 ? 6667.0 He I 6678.149 ? 6700.0 He I I 6683.2 58 X4486 a n d X4504. 3.3 EQUIVALENT WIDTH DETERMINATION To i n v e s t i g a t e p r o p e r l y t h e s p e c t r a t h a t h a v e b e e n c o l l e c t e d , t h e e q u i v a l e n t w i d t h s o f t h e l i n e s n e e d t o be m e a s u r e d . F o r s p e c t r a o f l o w e r d i s p e r s i o n t h i s c a n p r o v e d i f f i c u l t t o do due t o b l e n d i n g o f l i n e s . C o n v e n t i o n a l l y one d e t e r m i n e s t h e e q u i v a l e n t w i d t h by f i r s t f i n d i n g t h e l i m i t s o f t h e l i n e w i n g s by v i s u a l i n s p e c t i o n , a n d t h e n i n t e g r a t i n g t h e a r e a b e t w e e n t h e c o n t i n u u m a n d t h e l i n e p r o f i l e , u s i n g t h e s e l i m i t s , e i t h e r d i g i t a l l y o r w i t h a p l a n i m e t e r . I n o u r o b s e r v a t i o n s t h e m a j o r c o n t r i b u t o r t o t h e w i d t h o f t h e l i n e s o b s e r v e d i s t h e i n s t r u m e n t a l p r o f i l e . F r o m a r c l i n e s we f i n d t h a t t y p i c a l h a l f w i d t h s a r e on t h e o r d e r o f 2.5 p i x e l o r a b o u t 1.5 A. The b r o a d e n i n g due t o r o t a t i o n i s n o t more t h a t 90 km/sec o r a b o u t 1 A. The l i n e we s e e i s t h e c o n v o l u t i o n o f t h e n a t u r a l l y b r o a d e n e d l i n e c o n v o l v e d w i t h t h e r o t a t i o n a l b r o a d e n i n g a n d t h e i n s t r u m e n t a l p r o f i l e . As t h e b r o a d e n i n g t e r m s a r e e s s e n t i a l l y t h e same f o r a l l l i n e s , t h e e q u i v a l e n t w i d t h w i l l be a f u n c t i o n o f t h e c e n t r a l d e p t h o f t h e l i n e . T h e r e f o r e one m e r e l y n e e d s t o f i n d t h e c o n s t a n t t e r m r e l a t i n g t h e d e p t h t o t h e e q u i v a l e n t w i d t h t o d e t e r m i n e a l l t h e e q u i v a l e n t w i d t h s i n a s p e c t r u m . T h i s t e c h n i q u e t h u s a l l o w s t h e e q u i v a l e n t w i d t h s o f b l e n d e d l i n e s t o be d e t e r m i n e d . I n o r d e r t o c h e c k on how w e l l t h e a b o v e t e c h n i q u e w o r k e d , t h e o b s e r v a t i o n s o f 19 C e p h e u s f r o m J u l y 1984 were 59 inspected and l i n e s were selected with a range of central depths for which the l i m i t s of the l i n e wings could be well determined. The equivalent widths, using the v i s u a l l y selected l i n e l i m i t s , were evaluated using a numerical Simpson's Rule integrating routine while the l i n e depths were found f i t t i n g a Gaussian to the six points straddling the l i n e minimum. Shown in figure 3.02 are the equivalent widths, from a single spectrum, determined from the above integration versus those obtained for 19 Cepheus by Conti and Alschuler [1971], Conti [1973], Conti [1974] and Takada [1977]. The agreement i s quite good. Figure 3.03 shows a plot of the l i n e depth and corresponding equivalent width as determined by the technique descibed above. It i s clear that the two are approximately related by merely a constant over the entire range of l i n e strengths. The deviations from linear due to l i n e saturation e f f e c t s do not s i g n i f i c a n t l y a f f e c t the r e s u l t s . Thus on any spectrum a l l that i s needed i s to determine the equivalent width and l i n e strength for one l i n e and a l l the remaining lines can then have their l i n e depth determined and scaled to give the equivalent width. For heavily blended l i n e s this method may not give the absolute equivalent width but in this work the primary concern i s with r e l a t i v e values where the technique i s adequate. 60 Figure 3.02 Equivalent Width here Vs . Equivalent Width from work of others (in mA) for 19 Cepheus. Stars are from Takada [ 1 9 7 7 ] , c i r c l e s from Cont i ' s ser ies of papers (see t ex t ) . 61 5 0 0 E Ul (mi 1 1 iAngstrom) 1 0 0 0 others 62 Figure 3.03 Line depth, as f rac t ion of continuum, vs. equivalent width (mA) determined using l i n e l i m i t method. Central depth 64 3.4 THE SPECTRAL TYPE There are two important reasons for wanting to know how well HDE 226868 can be classed by spectral type with other stars. F i r s t l y such a cataloging allows us an estimate of the star's absolute magnitude and thereby a distance and hence minimum mass for the unseen companion. Secondly once a reasonable estimate of i t s spectral class has been made, differences from the mean s t e l l a r spectrum for t h i s class due to the primary's history or current configuration can be looked for. The ultimate aim of spectral c l a s s i f i c a t i o n i s to place p a r t i c u l a r stars in homogeneous spectral type and luminosity bins by using spectral l i n e s , blends and bands for the c l a s s i f i c a t i o n c r i t e r i a . There has been a long history of improvements in t h i s area beginning with the work of Secchi [1868] who divided stars into four groups with colours white, yellow, orange and red and according to strength of certain l i n e s . This was followed by the monumental Henry Draper Catalogue ( Cannon and Pickering [1918-1924] ). The widely accepted c r i t e r i o n today i s the Morgan-Keenan System ( Morgan et a l [1943], Morgan and Keenan [1973] ) which i s defined by a basis set of standard stars located on a two dimensional spectral type vs luminosity class plane. The process of c l a s s i f i c a t i o n i s a d i f f e r e n t i a l comparison to these standards. Such a system forces stars to f i t into a f i n i t e array of c e l l s when in fact that r e a l l y form a continuum of p o s s i b i l i t i e s . The s i m p l i c i t y of arranging t h i s 65 system in terms of two simple parameters, temperature and luminosity, however makes the system extremely a t t r a c t i v e . A word of caution should however be noted for c l a s s i f i c a t i o n of early type stars under such a system. If spectral type i s to be correlated monotonically with e f f e c t i v e temperature then the e f f e c t i v e temperature must be the parameter which most stongly determines what the conditions in the photosphere are l i k e . Underhill [1983] has shown that for 03,04,05 stars t h i s assumption breaks down completely and in Underhill [1984] i t i s shown that mechanisms other than the underlying radiation f i e l d can a f f e c t the l i n e forming region in spectral types 04 to 09. We s h a l l proceed with t h i s caution in mind. Over small ranges of spectral type i t i s possible to quantitatively define variation of spectral type. In the MK system the variation of the r a t i o of Hel X4471 to Hell X4541 i s the primary c l a s s i f i c a t i o n c r i t e r i a for 0 type stars. In 09 stars the former i s strongest but the r a t i o changes slowly so that by 05 the l a t t e r predominates. Conti and Aschuler [1971] and Walborn [1971a] attempted to improve on the o r i g i n a l MK c l a s s i f i c a t i o n by c a r e f u l l y looking at a large number of 0 stars and attempting to c l a s s i f y them uniformly. They found the most consistent system resulted when the variation of ra t i o s of cert a i n Hel, Hell and ionized s i l i c o n l i n e s was used. Unfortunately neither paper gave quantitative values for these rat i o s and unless one i s an expert in c l a s s i f i c a t i o n i t can be d i f f i c u l t to determine 66 the exact spectral type. For t h i s reason, and to be able to c a r e f u l l y compare HDE 226868 to stars of similar spectral type, high signal to noise spectra of a number of l i k e stars was obtained. The stars of primary interest were confined to those with spectral type 08 to B1 as t h i s might have been the maximum expected region of v a r i a b i l i t y of HDE 226868 with phase due to the presence of the compact secondary. Listed in Table 3.02 are a l l comparison stars between 08 and B1 for which spectra were obtained. Column 3 gives the spectral type, whenever available, taken from one of Walborn's series of papers (Walborn [1971 a],[1971b],[1972],[ 1976]) on c l a s s i f i c a t i o n of early type stars. This i s the most consistent set of spectral types available as they were determined by the same person using objective c r i t e r i a . Column 4 has the spectral type from the Bright Star Catalog ( Hoff e i t and Jaschek [1982] ) for a l l stars s u f f i c e n t l y bright. Column 5 has the e f f e c t i v e temperature expected for that MK spectral type type from Bohm-Vitense [1981 ] while column 6 contains the values of the temperature found by Underhill et a l [1979] from f i t t i n g the u l t r a v i o l e t continuum. The equivalent widths of a l l s i g n i f i c a n t l i n e s in the spectra of the standards were evaluated using the technique described previously. The ratios of a number of l i n e s which appeared sensitive to spectral type(S) and/or luminosity(L) were evaluated. The most sensitive r a t i o s were found to be Table 3.02 Standard Star C h a r a c t e r i s t i c s Name HD Walborn type BS type TMK TU V on 368G1 08 . 5Iab 08 34 100 35046 139 Tau 401 1 1 BOIb 25700 t . 24760 B0.5V 27300 £ Per 24398 B1 lb B1 lb 20600 19867 40 Per 22951 B0.5V 22900 AE Aur 34078 09 . 5V 09 . 5V 31600 195592 09 . 71a 29000 »t on 38771 B0.5lav 22900 19921G B 111 26500 217086 07,OVn 07 .OVn 37500 l on 37043 09111 09III 33600 a Ori 37468 09.5V 09.5V 31600 31556 8 on 37128 BOIa BOIa 25700 25091 36822 BOIV 31000 i/ Or 1 36512 BOV 29500 34347 36960 BO. 5V BOVp 27300 n Ori 3541 1 B0.5V 27300 42 on 37018 B 1V 25000 S' on c 37027 07 .OV 06p 37500 S Mon 47839 08.011 If 07 35600 35427 p Leo 91316 B1Iab B1 lb 20600 15 Sgr 167264 09.7Iab BOIa 29000 9 Sge 188001 08Iaf 08 If 35200 34527 207198 09Ib-II 09III 33600 218915 09.5Iab 09.5 29000 S on 37742 09.71b 09.51b 29000 27583 225146 09.71b 09 . 71b 29000 6 on 36486 09.511 09.511 32400 31082 47432 09.71b 09.511 29000 194280 0C9.7Iab 29000 13745 09.7IK (n) ) 32400 G9 Cyg 204 172 BOIb BOIb 25700 y Cas 5394 BOIV?e 31000 a Cam 306 14 09.51a 09 .51a 2 9 OOO 24999 X Per 24534 (BOV) Ope 29500 CTi - J 188209 09.5 l a b 1993322 0 8 . 5 1 1 1 14 Cep 209481 09V 206267 06 5V(<f)) 199579 0 6 . 5 1 1 1 68 Cyg 203064 08 . OV 10 Lac 214680 08.0111 V. Cep 210839 06.0I(n) FP K Cas 2905 BC 0.7 l a 19 Cep 209975 0 9 . 5 1 b 09.5111 290CX) 3^078 09V/ 34700 3 4 ° 7 5 08. 5111 33200 06f 39000 06Ve 39000 0 8 35600 0 9 V 35600 35401 o s i f 3 8 7 0 0 3 7 7 2 1 B1I3 2 2 9 0 0 09.51b 2 9 ° 0 0 69 those of; Si IV X4116 / He I X4121(S,L), Si III X4552 / He I X4387(L), Si III X4552 / He II X454KS) and Si IV X4089 / He I X4121(S,L). Table 3.03 contains a tabulation of these ratios for a l l the standards and figures 3.04 to 3.07 give a graphical representation of t h i s data. In these figures the dashed li n e represents the r a t i o to be found for HDE 226868, the star symbols that for supergiant standards, the squares for class I l l s and the hourglass symbols for class Vs. It can be seen there i s considerable scatter in using any one set of l i n e s as a c r i t e r i o n of spectral type for a p a r t i c u l a r star. The f i r s t determination of spectral type for HDE 226868 was made by Seyfert and Popper [1941 ] who gave BO. Subsequently Morgan at a l [1955] found BOIb, Murdin and Webster [1971] also gave BOIb, Smith et a l [1973] quoted 'between 09.5 and BO1 and then Walborn specified i t as 09.7lab (p-var) where the p-var indicates the presence of Hell X4686 having variable emission. From figures 3.04 to 3.07 i t can be seen that the primary of Cygnus X-1 does indeed f a l l in the part of each graph that gives a consistent spectral type of between 09.5 and 09.7. No p e c u l i a r i t i e s are noted. In order to more c l e a r l y show how HDE 226868 compares in spectral type to the comparison stars obtained, selected segments of the spectrum were plotted for each star on a grid of spectral type versus luminosity c l a s s . Figure 3.08 70 Figure 3.04 Ratio of Si IV X4116 / He I X4121 for a l l ava i lab le standards in table 3.2. Dashed l i n e indicates r a t i o measured HDE 226868. OJ \ CD o OJ z • • • X Z z E Z z X •* L 06 07 08 09 09.7 S p e c t r a l T y p e B0.5 B1 72 Figure 3.05 Ratio of Si III X4552 / He I X4387 for a l l ava i lab le standards in table 3.2. Dashed l i n e indicates r a t i o measured for HDE 226868. 73 ID 06 07 08 0 9 09.7 ' B0.5 S p e c t r a l T y p e B1 74 Figure 3.06 Ratio of Si III X4552 / He II X4541 for a l l ava i lab le standards in table 3.2. Dashed l i n e indicates r a t i o measured for HDE 226868. 75 \ OJ tn in S p e c t r a l T y p e 76 Figure 3.07 Ratio of S i IV X4089 / He I X4121 for a l l ava i lab le standards in table 3.2. Dashed l i n e indicates r a t i o measured for HDE 226868. Ra t i o 4089/4121 • 1 2 3 4 o 'l r 1 i | 1 1— 1 T 1— "I * T 1 1 9 - M [BJ M -- -T J <0 8- • M • * -o c* - • • * -J o CD • * -H N N * * * CC O T J CO * _ ID H N -8 MM M * ro -i i i i 1 i i , . i , • 1 . . Table 3.03 Standard Star Ratios of Spectrally Sensitive Lines. Name HD 4116/4121 X O r i 36861 1.33 139 Tau 40111 0.694 « 24760 0.43 5 Per 24398 0.44 40 Per 22951 0.42 AE Aur 34078 0.67 195592 K. Or i 2004 1.12 199216 0.41 217086 1.05 l O r i 37043 a O r i 37468 0.84 l O r i 37128 1.63 36822 0.72 v O r i 36512 0.72 36960 0.50 n O r i 3541 1 0.73 42 O r i 37018 0.39 0' O r i C 37027 0.66 S Mon 47839 0.83 p Leo 91316 0.49 15 Sgr 167264 1.62 9 Sge 188001 1.69 207198 1.58 218915 1.69 5 O r i 37742 1.69 225146 1.39 6 O r i 36486 1.40 47432 1.65 194280 1.57 13745 1.41 69 Cyg 204172 1.37 T Cas 5394 0.79 a Cam 30614 2.57 X Per 24534 0.97 4552/4387 4552/4541 4089/4121 0 . 14 1 .07 2 . 37 1 .09 5 . 57 1 .08 0 .50 9 .46 0 . 77 0 . 74 >> 0 .724 0 . 32 12 . 93 0 . 76 0 .09 >> 0 .82 1 . 2 1 0 .86 4 .54 1 .71 0 .88 8 . 18 0 . 75 0 . 54 0 . 35 1 .60 0 . 35 0 . 16 1 . 27 0 . 34 0. 76 1 .04 0 .87 2 . 79 2 . 18 0 .63 3 . 39 1 . 10 0. . 34 0. 97 1 . . 12 0 54 4 . 34 0 8 1 0 . 35 >> 0 . 94 0 . 32 4 . 76 0. 64 0. . 35 0. 16 1. . 25 0. 19 0. 08 1. 35 0 99 3 . 15 0. 76 0. 73 1 . 79 2 . 25 0. 26 0. 10 3 . 85 0. 28 0. 25 2 . 24 0. 42 0. 56 1 . 81 0. 46 0. 61 2 . 66 0. 63 1 . 45 1 . 85 0. 48 0. 59 1 . 95 0. 46 0. 77 2 . 18 0. 76 1 . 75 2 . 00 0. 54 , o. 78 1 . 91 0. 79 3 . 06 1 . 94 0. 47 1 . 16 1 . OO 0. 44 0. 46 3 . 68 0. 50 0. 86 0. 38 188209 2. ,02 0. 46 0.64 2 .67 1993322 0. ,92 0, , 28 0. 33 1 . 47 14 Cep 209481 1 . , 38 0. 47 0.65 2 .08 206267 0. ,90 0. 27 << 2 .00 199579 0. ,71 0. 31 0.76 1 . 99 68 Cyg 203064 0. 80 0. 27 << 1 . 47 10 Lac 214680 1 . ,08 0. 28 0. 33 1 .61 V Cep << 1 . 19 ix Cas 2905 0. ,81 1. 06 >> 1 . 19 80 i s such a plot for the supergiants centered on X4686. Similar diagrams for the giants and dwarfs, and for spectral regions centered on X4550 and X4100 are to be found in Appendix A of thi s thesis. The p e c u l i a r i t y of He II X4686 emission at spectral type 09.7lab of HDE 226868 i s c l e a r l y seen in the diagram. No s i g n i f i c a n t difference i s seen in the strength of the metal l i n e s ( of N, C and 0 ) as might be the case i f s i g n i f i c a n t mass loss from the primary affected abundances ( Dearborn and Eggleton [1977] ). 3.5 THE ROTATIONAL VELOCITY It i s of considerable interest to determine accurately the rotational v e l o c i t y of the primary in this system for two reasons. It has been stated by Hutchings [1982] that v r o t / vsync n a s v a ^ - u e n«5, meaning that the secondary i s o r b i t i n g much faster than the primary i s rotating. Current o r b i t a l solutions show that there i s no s i g n i f i c a n t e c c e n t r i c i t y . Hence i t appears we have a system in which o r b i t a l c i r c u l a r i z a t i o n has had time to occur but synchronization has not. If true t h i s could have repercussions on the structure of the primary and estimates for the time scales of evolution of X-ray primaries ( see van den Heuvel [1983], Savonije [1982,1983] for discussion ). Secondly the r a t i o of the o r b i t a l v e l o c i t y to the rotational v e l o c i t y , i f synchronization i s assumed, can give an estimate for the mass of the unseen secondary. gure 3 .08 Spectra l Mosaic for Wavelength Range centered on X4686 . A Cep 9 Sge a C a m 061 081a A Ori 09.51a 19 Cep 08.5lab 09.5lab HD188209 09.5lab HD218915 09.5!ab HD207198 09lb-ll 6 Ori 09.511 HD195592 e Ori K Ori 09.71a BOIa B0.5la K Cas B0.7la Cyg X-1 09.7lab 15 Sgr 09.7lab HD194280 09.7lab C Ori 09.71b 69 Cyg BOIb HD225146 09.71b HD47432 09.71b HD13745 09.711 <; Per Bllb HD 40111 Bllb p Leo Bllb HD199216 B i l l 0 0 83 84 The estimation of rotational v e l o c i t i e s began with the simple idea that the observed widths of l i n e s of stars are too broad to be due to natural l i n e broadening processes and that the measured width could be due to the range of v e l o c i t i e s produced between the receding and forward moving edges of a rotating s t e l l a r surface. C a r r o l l and Ingram [1933] were the f i r s t to developed the technique of using the position of the zeros of the fourier transform of a spectral l i n e to estimate ro t a t i o n a l v e l o c i t i e s . Gray [1973,1976] has used the shape of the entire transform p r o f i l e to estimate v s i n i for a variety of stars. Ebbets [1979] has used t h i s technique to estimate both ro t a t i o n a l broadening and macroturbulence in the 0 type stars. Many d i f f e r e n t mechanisms exist for the broadening of a s t e l l a r l i n e and their e f f e c t can be thought of as a convolution with some i n t r i n s i c p r o f i l e . Assume a spherical star rotating as a r i g i d body whose i n t r i n s i c p r o f i l e i s the same over the entire s t e l l a r surface. Taking O(AX) as the observed p r o f i l e , P(AX) as the i n t r i n s i c p r o f i l e , R(AX) as the rotation p r o f i l e , M(AX) as the macroturbulence broadening function, and I(AX) as the instrumental p r o f i l e , then , O(AX) = P(AX) * R(AX) * M(AX) * I(AX) which in the fourier transform domain becomes, o(s) = p(s) x r(s) x m(s) x i ( s ) The interesting property of t h i s transform i s that the f i r s t zero crossing i s determined by the rotation p r o f i l e alone. 85 The r o t a t i o n a l b r o a d e n i n g f u n c t i o n h a s b e e n d e t e r m i n e d p r e v i o u s l y i n Huang a n d S t r u v e [1953] a n d G r a y [1976] a n d f r o m E b b e t s [1979] R ( x ) = a [ 2 * ( 1 - x 2 ) ° " 5 A + 0.5 * /J * ( 1 - x 2 ) ] where x = AX / A X R A X R = V s i n i X / c a = 3 / ( 3 + 2/3 ) |3 = l i m b d a r k e n i n g p a r a m e t e r ( 0 ^  0 £ 1.5 ) and r ( s ) = [ a / * ] * J,(2T T S) - [ 2a/3 / (2 T T S ) 2 ] C O S ( 2 J T S ) + [ 2a/3 / (2T T S) 3 ] sin(27rs) / (2 T T S) 3 ] sin(2irs) I f t h e z e r o s o f t h i s t r a n s f o r m f u n c t i o n a r e t h e n o b s e r v e d a t f r e q u e n c i e s z^ ( m e a s u r e d i n u n i t s o f c y c l e s / a n g s t r o m ) , t h e v s i n i i s g i v e n by v s i n i = s. c / z. . 1 1 A where s, = 0.665 , s 2 = 1.162 , s 3 = 1.663 , . . . The i n s t r u m e n t a l f u n c t i o n w i l l be t h e r e s u l t o f a c o n v o l u t i o n o f a L o r e n t z i a n ( t h e p r o j e c t e d s l i t ) a n d t h e f i l t e r i n g f u n c t i o n u s e d on t h e d a t a ( G a u s s i a n ) . F o r t h e CFHT d a t a we ha v e a d i s p e r s i o n g i v i n g a p p r o x i m a t e l y 0 . 0 3 6 A/pixel. On a v e r a g e t h e w i d t h o f t h e a r c l i n e s o b s e r v e d i s 2 p i x e l s a n d t h i s r e s u l t s i n t h e t r a n s f o r m d r o p p i n g t o h a l f t h e v a l u e o f t h a t a t t h e z e r o f r e q u e n c y a t a f r e q u e n c y o f 14 c y c l e s / A . The i n t r i n s i c p r o f i l e c a n be o b t a i n e d f r o m 86 s u i t a b l e m o d e l s o f e a r l y t y p e s t a r s s u c h t h o s e f o u n d i n A u e r a n d M i h a l a s [ 1 9 7 2 ] . T h e i r NLTE m o d e l f o r a T = 3 0 0 0 0 ° K a n d l o g g = 3.3 s t a r ( t y p i c a l o f HDE 226868 a n d 19 C e p ) g i v e s p r o f i l e s o f t h e He I l i n e s t h a t d r o p t o h a l f t h e i r v a l u e i n l e s s t h a n 0.5A, a n d t h e i r t r a n s f o r m d r o p s t o h a l f i t s v a l u e by a b o u t 2 c y c l e s / A . T h u s b o t h t h e s e b r o a d e n i n g t e r m s r e s u l t i n z e r o s t h a t w o u l d o c c u r a t much h i g h e r f r e q u e n c i e s t h a n t h a t e x p e c t e d f r o m r o t a t i o n a l b r o a d e n i n g i n t h e e a r l y t y p e s t a r s b e i n g l o o k e d a t . I n o r d e r t o t e s t t h a t t h i s m e t h o d w o r k s , t h e r o t a t i o n a l l y b r o a d e n e d NLTE t h e o r e t i c a l p r o f i l e s o f S t o e c k l y a n d M i h a l a s [ 1 9 7 3 ] were F o u r i e r t r a n s f o r m e d i n o r d e r t o t e s t how w e l l t h e v s i n i t h e y u s e d t o g e n e r a t e t h e p r o f i l e s c o u l d be r e c o v e r e d . T h e i r p r o f i l e s a l l o w e d f o r t h e f u l l l i m b - d i s t a n c e v a r i a t i o n o f b o t h c o n t i n u u m i n t e n s i t y a n d l i n e s h a p e , a n d h e n c e a l s o a l l o w u s t o s e e how s e r i o u s l y t h e a s s u m p t i o n o f a c o n s t a n t p r o f i l e o v e r t h e e n t i r e s u r f a c e a f f e c t s t h e F o u r i e r t r a n s f o r m t e c h n i q u e . F i g u r e 3.09 shows t h e v s i n i d e r i v e d by d e t e r m i n i n g t h e v s i n i u s i n g t h e f i r s t z e r o o f t h e f o u r i e r t r a n s f o r m o f t h e H e l X 4713 l i n e . I t i s c l e a r t h a t f o r v a l u e s o f v s i n i l e s s t h a n 100 k m s e c " 1 t h e t e c h n i q u e w o r k s w e l l i n r e c o v e r i n g t h e v s i n i . A b o v e 100 k m s e c " 1 t h e r e i s a p r o g r e s s i v e l y g r e a t e r d i f f e r e n c e b e t w e e n m e a s u r e d a n d a c t u a l v e l o c i t i e s . T h i s i s due t o t h e S t o e c k l y a n d M i h a l a s [ 1 9 7 3 ] p a p e r o n l y p r o v i d i n g v a l u e s f o r t h e p r o f i l e s w i t h i n 2A o f t h e l i n e c e n t r e . F o r t h e more r a p i d l y r o t a t i n g s t a r s t h i s r e s u l t s i n most o f t h e l i n e i n f o r m a t i o n 87 Figure 3.09 v s i n i derived from FT Technique versus v s i n i used to generate p r o f i l e s by Stoeckley and Mihalas [1973]. 88 89 being lost and the consequentially poor re s u l t s . The July 1984 CFHT data i s of suitable dispersion to be able to c a r e f u l l y measure the v s i n i of HDE 226868. A disperion of 2.4 Amm"1 corresponds to 0.036 A p i x e l " 1 which in turn gives a nyquist frequency of 25 cycle/A" 1. The data co l l e c t e d at the DAO i s of dispersion 40 Amm"1 which gives 0.6 A p i x e l " 1 and therefore a nyquist freqency of 1.7 cyclesA" 1, c l e a r l y unsuitable for any fourier transform work. Figure 3.10 shows the fourier transform of the mean HDE 226868 and 19 Cep Hel X4713 p r o f i l e from the CFHT July 1984 data. The straight l i n e in th i s figure i s an estimate of the noise l e v e l as derived from the expression given in Smith and Gray [1976] and Smith [1976] which i s S f = SXAX/N where S^  i s the transform noise to signal r a t i o S^ i s the noise to signal r a t i o in the data AX i s the wavelength i n t e r v a l between data points N i s the number of real p r o f i l e data points From the f i r s t zero in figure 3.10 one can derive a value of the v s i n i for 19 Cep of 75.1 kmsec"1 which i s in good ageement with Ebbets [1979] value of 72 kmsec"1 derived using the same fourier transform technique. The value obtained for the HDE 226868 v s i n i i s 94.3 ±5 kmsec"1 which is quite d i f f e r e n t from the value of 140 kmsec"1 given by Bolton [1975], The error in the v s i n i i s estimated from the 90 Figure 3.10 Fourier Transform of mean CFHT He I X4713 p r o f i l e for 19 Cep (upper) and HDE 226868 (lower). 91 Ql T J 3 £ <E £ o c T J Ql in CCS £ o 1 1 1 1 r JL ' v ; • i_ _ + 4-° 0 - 5 1 1 . 5 F r e q u e n c y ( c y c 1 e s / A n g s t r o m ) 92 scatter in the individual v s i n i measures from the five nights observing at CFHT. Ebbets [1979] has f i t t e d p r o f i l e s to the fourier transform to extract a value for a macroturbulence parameter which i s postulated to characterise large scale v e l o c i t y f i e l d s on the s t e l l a r surface. Mihalas [1979] has severely c r i t i c i z e d this technique on the grounds that the assumption of a constant l i n e p r o f i l e over the s t e l l a r disc i s 'simply i n v a l i d ' . Note that the technique used above for estimating the v s i n i of HDE 226868 whilst using this assumption as a basis to proceed, c a l i b r a t e s against stars with theore t i c a l r o t a t i o n a l v e l o c i t i e s and can in that way be considered an empirical technique. Figure 3.11 shows the He I X4713 line p r o f i l e for HDE 226868, used in the fourier transform, plotted with theore t i c a l p r o f i l e s from Stoeckly and Mihalas [1973] over a range of input v s i n i . As can be seen any small systematic errors ( 2% ) in placing the continuum w i l l not aff e c t the determined v s i n i s i g n i f i c a n t l y . 3.6 THE RADIAL VELOCITY CURVE Even though the data obtained at the DAO over the years 1980-84 was of low dispersion ( 40 Amm-1 ) the fact that i t is in d i g i t a l —f-orm—from a Reticon makes i t possible to obtain r e l a t i v e l y good v e l o c i t y estimates. After reduction of the raw data as outlined in Chapter 2 a l l l i n e s l i s t e d in table 3.04 had their doppler ve l o c i t y s h i f t determined. The position of each l i n e was found using a centre of weight 93 Figure 3.11 Actual HDE 226868 He I X4713 p r o f i l e together with p r o f i l e s from Stoeckly and Mihalas [1973] for the range of v s i n i labeled (in km/sec). Uavelength (Angstrom) KD 95 c r i t e r i o n in which P =( I. I• p. ) / ( I. I.) where P = the estimated l i n e position p^ is the position of each pi x e l in the l i n e p r o f i l e 1^ i s the associated absolute intensity r e l a t i v e to the continuum at each pixel position The summation i s performed over some consistent estimate of the l i n e l i m i t s . These l i m i t s are, i f possible, the positions where the l i n e merges into the continuum but, as th i s i s usually not possible due to blending, some other appropriate l e v e l ( half intensity ) can be used. Other position estimators were compared to the above method. Fahlman and Glaspey [1973] and Fahlman [1984] have outlined a cross-correlation technique in which two similar spectra may have the s h i f t between them determined by taking one of the spectra, applying small s h i f t s in the fourier domain and then creating a difference function, summed over a l l points on the l i n e p r o f i l e at each shifted p o s i t i o n . After a l l the s h i f t s are performed a high order polynomial i s f i t t e d to the difference function values and the position of the minimum gives the s h i f t in position between the two li n e s (Yang [1985]). This technique gave good results when tested on some of t h i s data but the increased cost in terms of computing time did not allow i t s use. Listed in table 3.05 and shown in figures 3.12 to 3.15 ( folded on the o r b i t a l period found from figure 3,16 ) are 96 the r a d i a l v e l o c i t i e s found using the centre of gravity method on the l i n e s in HDE 226868 and the corresponding date of observation. These v e l o c i t i e s are corrected to the solar system barycentre ( corrections given in table 2.2 ) using the parameters from Stumpff [1979], The v e l o c i t i e s presented are given in four groups; the 'H' v e l o c i t i e s are the mean hydrogen l i n e v e l o c i t i e s , the 'He I' v e l o c i t i e s are those of neutral helium, the 'He II' are from singly ionized helium and the metal l i n e s are from a l l others combined ( i . e . a l l C, N, O, Si l i n e s ). The l i n e s used in each group and the weight assigned each l i n e in c a l c u l a t i n g a mean group v e l o c i t y for each night i s given in table 3.04. The weights were assigned subjectively depending on the strength of the l i n e , and i t s location in the spectrum. Note that for the 1984 DAO 72" red data only the He I X6678 l i n e was available to determine an absorption l i n e v e l o c i t y . There are a number of sources of error in determining v e l o c i t i e s from the spectra obtained on the DAO 48" telescope at 40Amm"1. The technique of f i t t i n g a centre of gravity to a p r o f i l e w i l l y i e l d d i f f e r e n t values depending on how many points are available in the p r o f i l e , t h i s is a form of d i g i t i z a t i o n error. Also blends with weak li n e s w i l l perturb the shape of the l i n e of interest and cause error. Various experiments have been conducted to test for these e f f e c t s using multiple spectra of bright standard stars. It is found that these errors occur at a l e v e l of * 0.1 pixel or = 4 kmsec"1 in these spectra. Another, and unexpected, Table 3.04 Line weights for least squares f i t t i n g r a d i a l v e l o c i t y curve and exc i ta t ion po tent ia l for l i n e groups. Line Hydrogen Lines 4101.737 4340.468 4861 .332 He I Lines 4009.270 4026.189 4120.812 4143.759 4387.928 4471 .477 4713.143 4921.929 5015.675 5047.736 He II Lines 4199.83 4541.598 4685.685 Metal Lines 4069.897 4075.86 4088.863 4097.31 4116.104 4349.426 4366.896 4379.09 4481.228 4510.92 4514.89 4552.654 4567.872 4574.777 4630.537 4634.16 4640.64 4647.40 4650.74 Excitation Weight Potential (eV) ="1 0 0.5 1 .0 0.8 ="21 0.1 0.8 0.4 0.8 0.8' 1 .0 1 .0 0.8 0.8 0.5 ="75 0.4 0.4 1 .0 ="50 0.2 0.1 1 .0 0.4 0.8 0.1 0.1 0.8 0.6 0.5 0.5 0.5 0.5 0.1 0.1 0.2 0.5 0.2 0.2 Table 3.05 Calculated V e l o c i t i e s f o r Spectra of HDE 226868 JO 240000+ 1980 48" DAO 4513.76806 4514.68889 4515.69653 4516.67778 1981 48" DAO 4854.71944 4855.81944 4856.83542 4857.81528 4858.80764 4860.85069 1982 48" DAO 5098.70486 5099.71528 5142.84028 5143.84931 5144 .83681 5145.85278 5186.78958 5187.82431 5188.76319 5188.86597 5188.94931 5189.78958 5190.75903 5190.89792 5241.70486 5242.66736 5242.76458 B i n a r y X-ray H He I Phase Phase 0.282 0.447 0.627 0.802 0. 322 0.325 0.329 0. 332 61.72 10. 14 -52.80 -92.65 64.85 5.89 -65.01 -89.63 0. 169 0. 366 0.547 O. 722 0.899 0.264 0.482 0. 486 0.489 0.493 0.496 0.503 128.08 42 .69 - 17.94 -98.33 -93.43 53.84 122.09 47 . 38 -22.49 -96. 12 -60.87 67 . 50 0.740 0.921 0.622 0.802 0.978 0. 160 0.470 0.655 0.823 0.841 0.856 0.006 0. 179 0.204 O. 277 O. 449 0.466 0.312 0.315 0.462 0.465 0.469 0.472 0.612 0.615 0.618 0.619 0.619 0.622 0.625 0.626 0.798 0.802 0.802 -81.43 -43.10 -47 . 47 -85.83 -29.33 55 . 10 7 .65 -70.62 -66.81 -64.83 -63.09 -7 . 25 52 .94 69 . 72 70. 25 14 . 32 -20.91 -77.29 -30.07 -39. 14 -72.22 -26.06 54 . 50 12 .98 -59.97 -74.25 -70.47 -65.28 - 10. 14 56.52 66 .04 74 . 78 10.48 -2.92 He II Meta 1 75 .06 39.23 -26.45 -82.67 87 .05 20. 55 -56.67 -91.38 137.94 55.09 -28.59 -71.91 -69.23 93.85 132.98 65 . 27 -8 .95 -94.79 -67.55 71 .86 -50.26 -26.57 -47.32 -70.09 - 13.34 74 . 29 1 1 .35 -66.74 -55.90 -55. 1 1 -55.34 11.18 52.91 75. 16 83.71 26.71 18.84 -70.71 -28.94 -41.82 -70.46 -22.67 70.53 21 .85 -61 .85 -60.97 -61.07 -54 . 18 4 .02 47 . 87 67 . 89 62.91 1 1 4 4 vo - 1 . 75 CO 5243.69514 5262.65625 0.632 0.019 0.805 0.870 -80.50 0. 27 -78.69 -3 .02 1983 DAO 5512.79653 5512.93819 5513.81944 5515.87222 5544.76944 5544.90347 5545.72083 5545.88264 5546.77014 5546.91042 5547.85278 5667.63681 5668.62500 5669.63681 5670.61667 5687.62917 0.689 0.714 0.871 0.238 O. 398 0.422 0.568 0. 597 0.756 0.781 0.949 0. 340 0.516 0.697 0.872 0.910 0.720 0. 721 0.724 0. 731 0.829 0.830 0.832 0.833 0.836 0.836 0.840 0. 247 0.250 0.254 0. 257 0.315 -79 . 18 -77.45 -66.41 76 . 34 28 . 22 26 .43 -41 .58 -45.99 -90.54 -92.09 -37.78 49 . 70 -27.64 -99.58 -60.58 -60.82 - 77.98 -86.05 -65.96 70. 94 37 . 19 31 .54 -30.91 -36.51 -75.88 -82.44 -42.77 70. 58 -9.31 -80.16 -53.31 -55.71 1984 48" Data 5888.77847 5888.88819 5889.80347 5889.90139 5890.79097 5890.89236 5891.79583 5891.89444 5892.79653 5892.89375 5893.87431 5894.79236 0.831 0.851 0.014 0.032 O. 191 0.209 0.370 0. 388 0.549 0.566 0.741 0.905 0.999 0.000 0.003 0.003 0.006 0.006 0.010 0.010 0.013 0.013 0.017 0.020 -84.51 -64.92 - 11 .58 -1.13 7 1 . 54 73.51 47 . 52 59 . 18 -24.63 -26.57 -86.91 -6 1.72 -74.56 -65 .89 -5 . 70 5.72 68 . 70 68 .58 55 . 32 50.61 -23.69 -31.59 -85 . 12 -52.39 -94.02 7.59 -73.89 2 .03 -61.77 -53.54 -46.62 79.04 50.08 47.40 -31 .72 -35 . 19 -76.07 -80.40 -42 .79 108.16 12 .77 -55.55 -31.06 -48 . 22 -62.89 -61 .50 -56.96 80. 49 45 .26 40. 16 -24 .68 -37 . 24 -68.62 -75.72 -35.66 76 . 97 6 .45 -73.38 -61 .96 -49.23 -72 .63 -67.59 7 .05 14.19 76 .93 69 . 1 1 67 .06 66 .52 -14.65 -20.28 -67.78 -48.20 -7 1.47 -61.69 -2 . 75 6 .44 64 . 7 1 76 . 32 61 .58 ' 55 .97 -8 . 52 -19.77 -74 . 10 -47.31 1984 72" DAO 5887.83889 5888.79653 5888.89028 5889.89792 5890.80208 5890.89167 5891 . 79444 5891 .88750 5892.786 1 1 5892.89167 5893.80694 5894.7993 1 5895.78750 5895.89167 1984 CFHT 5889.85069 5889.97986 5890.06875 5890.85417 5890.95625 5891.04792 5891.93542 5892.01944 5892.10139 5892.85069 5892.93681 5893.07500 5893.82083 5893.94375 5894.05625 0.663 0.834 0.851 0.031 O. 193 0.209 0. 370 0. 386 0. 547 0.565 0. 729 0.906 0.083 0. 102 0.023 0.046 0.062 0.202 0.220 0. 237 0.395 0.410 0.425 0.558 0.574 O. 599 0.732 O. 754 0.774 0.996 0.999 0.000 0.003 0.006 0.006 0.010 0.010 0.013 0.013 0.016 0.020 0.023 0.023 0.003 0.003 0.004 0.006 0.007 0.007 0.010 0.010 0.011 0.013 0.013 0.014 0.016 0.017 0.017 -61 .59 -66.80 -60.21 -6 . 38 63 .90 64 .89 56 .80 47 .82 -33.36 -34.24 -78.40 52 .03 19.23 28.22 2 . 35 16.26 24.23 61.18 71 .60 71 .80 49.59 49.90 38.65 -24 . 11 -29.60 -41.50 -73.74 -75.42 -73.43 101 Figure 3.12a Mean He I l i n e r a d i a l v e l o c i t y curve for for HDE 226868. Crosses denote data from the D A O , c i r c l e s indicate CFHT data, dotted curve is best o r b i t a l so lut ion to the data . U e l o c i t y (km/sec) 100 • 100 o ~0 ro 201 103 Figure 3.12b Residuals for best f i t o r b i t a l so lut ion to He I r a d i a l v e l o c i t y curve of HDE 226868. Crosses denote data from the DAO, c i r c l e s indicate CFHT data . vol 105 Figure 3.13a Mean H e l l r a d i a l v e l o c i t y curve for HDE 226868 using data from the DAO. Dotted l i n e is best o r b i t a l so lut ion to the data . o -J cr ZT Ul ro U g l o c i t y (km/sec) 100 • 100 i — • — • — • — • 90 L 107 Figure 3.13b Residuals for best f i t o r b i t a l so lut ion to H e l l absorption r a d i a l v e l o c i t y curve for HDE 226868 using data from the DAO. o -I "0 3* ro 801 109 Figure 3.14a Mean Balmer l i n e r a d i a l v e l o c i t y curve for HDE 226868 using data from the DAO. Dotted l i n e i s best o r b i t a l so lut ion to the data. Uelocity (km/sec) 100 • 100 i . . . . ^  • o cr ro OU 111 Figure 3.14b Residuals for best f i t o r b i t a l so lut ion to Balmer l i n e r a d i a l ve loc i ty curve for HDE 226868 using data from the DAO. o ZT "0 3" ro Z l I 113 Figure 3.15a Mean Metal l i n e r a d i a l v e l o c i t y curve for HDE 226868 using data from the DAO. Dotted l i n e is best o r b i t a l so lut ion to the data . U e l o c i t y (km/sec ) -100 • 100 o cr TJ zr in ID Ul 115 Figure 3.15b Residuals for best f i t o r b i t a l so lut ion to Metal l i n e r a d i a l v e l o c i t y curve for HDE 226868 using data from the DAO. o ro 9L I 117 error was of small random s h i f t s in the spectra. Comparing standard stars taken on the same night or a series of arcs taken over many hours small s h i f t s in the position of the l i n e s can be measured. These s h i f t s are of order 0.2 p i x e l or roughly lOkmsec" 1. Yang et a l [1982] have noticed such s h i f t s in the similar design spectrograph at the coude of the CFHT. One suggestion to explain the s h i f t s i s that are due to guiding errors, however t h i s i s unlikely as an image s l i c e r was used, and exposures were t y p i c a l l y of three hours duration, factors that would minimise th i s e f f e c t . Fletcher [1983] has also ruled out image motion due to a i r currents in the coude room by d i r e c t observation of images. Flexure in the Reticon mounting i s possible but i t i s d i f f i c u l t to then understand why the s h i f t s change direction at random. As these s h i f t s are seen both at CFHT and DAO i t may be that they are integral to the readout of the Reticon system. These s h i f t s are quite small and would only cause problems i f attempting to measure accurate r a d i a l v e l o c i t i e s at low dispersion. This means that such measurements are not detector (signal to noise) l i m i t e d but l i m i t e d by the s t a b i l i t y of the system. One method of eliminating these s h i f t s i s to use the i n t e r s t e l l a r l i n e s d i s t r i b u t e d across the spectrum as a set of f i d u c i a l s . In practise however most of the l i n e s are weak and/or blended, thus estimating t h e i r position accurately i s not possible. The strong l i n e at X4428 i s heavily blended and unuseable. The C a l l H and K l i n e s were not available on 118 a l l t h e s p e c t r a a n d when a v a i l a b l e f e l l n e a r t h e edge o f t h e a r r a y where r e m o v a l o f t h e f i x e d p a t t e r n i s n o t a s w e l l e x e c u t e d a s a t t h e c e n t r e ( s e e C h a p t e r 2 ) . T h i s a f f e c t s d e t e r m i n i n g t h e l i n e p o s i t i o n a c c u r a t e l y a n d t h u s f i n d i n g t h e s m a l l random s h i f t . The e r r o r s i n v e l o c i t y d e t e r m i n a t i o n f o r t h e DAO 72" r e d d a t a were s m a l l e r . T h i s was b e c a u s e o f t h e p r e s e n c e o f t e l l u r i c l i n e s o f H 2 0 i n t h e s p e c t r u m w h i c h c a n be u s e d t o a c c u r a t e l y remove a n y s h i f t s ( G r i f f i n a n d G r i f f i n [ 1 9 7 3 ] ) . C a m p b e l l [ 1 9 8 3 ] g i v e s i n h i s r e v i e w t h a t t h e v a r i a t i o n i n t h e t e l l u r i c l i n e s f r o m n a t u r a l s o u r c e s u c h a s u p p e r a t m o s p h e r i c w i n d s a n d t o p o c e n t r i c v a r i a t i o n i s i n t h e r a n g e 10-50 m s e c " 1 . A t a d i s p e r s i o n o f 3lAmm" 1 t h i s i s more t h a n a d e q u a t e f o r a f i d u c i a l s y s t e m a s t h e l i n e f i t t i n g r o u t i n e s h a v e an a c c u r a c y o f =*0.1 p i x e l o r 3 k m s e c " 1 . S h i f t s o f t h e k i n d n o t e d i n t h e a b o v e c h a p t e r were m a s k e d by l a r g e r s h i f t s t h a t o c c u r r e d w i t h m o t i o n o f t h e t e l e s c o p e . The most s i g n i f i c a n t e r r o r i n t h e CFHT 2.4Amm"1 d a t a was f r o m b r o a d c o s m i c r a y e v e n t s d i s t o r t i n g t h e l i n e s h a p e a n d p r o d u c i n g s h i f t s i n t h e c e n t r e o f w e i g h t . Q u a n t i f y i n g t h e m a g n i t u d e o f t h i s e f f e c t i s d i f f i c u l t b u t t h e f a c t t h a t t h e CFHT v e l o c i t i e s f o r He I X 4713 f a l l w i t h i n t h e r a n g e o f s c a t t e r o f t h e DAO He I v e l o c i t y c u r v e ( s e e f i g u r e 3.-4-2 j — makes i t r e a s o n a b l e t o assume i t i s s m a l l . A l l o t h e r s o u r c e s o f e r r o r f o r t h e CFHT d a t a a r e m i n i m a l a s a r e s u l t o f t h e v e l o c i t y r e s o l u t i o n (2 k m s e c " 1 ) . 119 As a check on our errors and on any absolute o f f s e t , the v e l o c i t y of 19 Cepheus for a l l nights i t was observed (1980 to 1984) was measured. The mean ve l o c i t y so obtained was -14.5 ± 1.5 kmsec"1, close to the value of -14.3 ± 1-2 kmsec"1 by Conti et a l [1977], -10.7 ± 3 kmsec"1 by Garmany et a l [1980] and -13 kmsec"1 by H o f f l e i t and Jaschek [1982]. No long term change was measured in the v e l o c i t y of t h i s star over the four years of observations and no spectroscopic variations were noted, thus i t seems l i k e l y that 19 Cepheus i s a bona fide single O-star. The f i r s t step in determing o r b i t a l parameters for Cygnus X-1 i s to determine the period of the binary. Moreby [1978,1985] has outlined a period searching routine for unequally spaced data and this technique has been applied, with some small modification, to the r a d i a l v e l o c i t y data obtained. The method e s s e n t i a l l y e n t a i l s folding data on a series of t r i a l periods and then searching for s i g n i f i c a n t upgoing followed by downgoing modulation. The longest period that could be detected i s set by the timespan of the observations, here being 4 years and the phase error of individual points ( ±1 hour ) sets the accuracy. When applied to t h i s data set a period of 5.60172 ± 0.00003 days i s found to be the most s i g n i f i c a n t peak in the pseudo power spectrum. No s i g n i f i c a n t peak i s found at 294 days, which i s the period found for the long timescale X-ray variations ( Priedhorsky et a l [1983] ).. 120 In order to better search for any long period variation in t h i s system and to see i f there has been any long term change in the o r b i t a l period, a l l h i s t o r i c v e l o c i t y measures were compiled and combined with the data from t h i s work to form a data set spanning 45 years. The h i s t o r i c data set included data from Seyfert and Popper [1941], Webster and Murdin [1972], Brucato and K r i s t i a n [1973], Smith et a l [1973], Brucato and Zappala [1974], Mason et a l [1974], Abt et a l [1977], and Gies and Bolton [1982] ( includes a l l of Bolton's e a r l i e r data ). The most s i g n i f i c a n t period found was at 5.59964 ± 0.00001 days, shown in f i g 3.16, somewhat shorter than found for our data set alone and close to the figure Gies and Bolton [1982] found from analysis of their data set alone. The difference between the period determined from recent ahd h i s t o r i c data would imply a P/P =* 10"7 day" 1, over the time of observation of the system. In order to further test this p o s s i b i l i t y a l l h i s t o r i c and new observations with two or more vel o c i t y measures at similar epochs were f i t t e d to a ve l o c i t y sinusoid. The procedure used the best estimates for the period from above and o r b i t a l parameters determined l a t t e r in t h i s section, and l e f t the T 0 parameter (epoch of zero phase) to be f i t t e d . The results are given in table 3.6 and shown in figure 3.17 where the v e r t i c a l axis i s the change in T 0 found for a best f i t and the horizontal axis is the Ju l i a n . Date of observation using 2445513.770 as a zero (my f i r s t observation of Cygnus X-1). A linear least squares f i t ( 1 2 1 Figure 3.16 Pseudo power spectrum of a l l HDE226868 v e l o c i t y measures (1939 to 1984). Table 3.06 F i t t e d 6To values f o r a l l v e l o c i t y data on Cygnus X- 1 . Mean epoch of Number of J T o Source of o b s e r v a t i o n (JD) o b s e r v a t i o n s (days) Data 2429664 2200 2 -0 .968 S e y f e r t and Popper [194 1] 2441207 4305 4 -0 . 235 Webster and Murdin [1972] 2441233 6543 7 -0 . 137 Webster and Murdin [1972] 2441215 0783 3 -o . 127 B r u c a t o and K r i s t i a n [1973] 2441476 8595 4 -0 003 B r u c a t o and K r i s t i a n [1973] 2441495 8498 5 -0 023 Smith e t a l [ 1973] 2441587 7885 2 +0 067 Smith e t a l [ 1973] 244 1859 7022 1 3 +0 007 B r u c a t o and Zappala [1974] 2441919 7360 3 +0 002 B r u c a t o and Zappala [1974] 2441269 7975 2 -0 079 Mason et a l [ 1974 ] 2441400 3493 3 -0 037 Mason et a l [ 1974 ] 2441424 1528 4 . +0 061 Mason et a l [ 1974 ] 2441453 5910 2 -0 343 Mason et a l [ 1974 ] 2441525 4365 2 -0 698 Mason et a l [ 1974 ] 2441935 0195 2 +0 092 Mason et a l [1974] 2442205 854 5 +0 038 Abt et a l [ 1977 ] 2442229 4679 18 +0 086 Abt et a l [1977] 2442257 7712 4 -0 006 Abt e t a l [1977] 2442266 3144 7 -0 052 Abt e t a l [1977] 2442286 8819 35 +0 033 Abt et a l [ 1977] 2442680 3177 6 +0 087 Abt et a l [ 1977] 2442909 6020 6 +0 053 Abt et a l [1977] 2441225 1380 2 -0 216 Gies and B o l t o n [1982] 2441257 8820 3 -0 161 G i e s and B o l t o n [1982] 2441464 7885 4 -0 010 Gies and B o l t o n [1982] 2441535 1965 2 -0 071 G i e s and B o l t o n [1982] 2441893 1980 6 -0 065 Gies and B o l t o n [1982] 2441929 9543 3 -0 032 Gies and B o l t o n [1982] 2442306 1300 2 -0 129 G i e s and B o l t o n [1982] 2442542 7823 3 -0 045 G i e s and B o l t o n [1982] 2443342 7575 2 +0. 029 Gies and B o l t o n [1982] 00 2443373 .6688 4 +0. 111 2444058 . 3552 13 +0. 088 2444795 .0557 3 +0. 131 2444514 .7178 3 -0. 057 2444858 .0783 4 +0 . 120 2445099 .2101 2 -0. 007 2445144 . 3448 4 +0. 103 2445189 .0799 8 +0. 224 2445243 .0424 3 -0. 125 2445513 . 3080 2 +0 145 2445545 .9832 6 +0. 183 2445669 . 6208 2 +0. 145 2445891 . 2030 1 1 +0. 231 2445891 .9116 15 +0. 230 2445892 . 1 149 13 +0. 188 G1es and B o l t o n [1982] Gies and B o l t o n [1982] Gie s and B o l t o n [1982] t h i s work t h i s work t h i s work t h i s work t h i s work t h i s work t h i s work t h i s work t h i s work t h i s work t h i s work t h i s work 125 Figure 3.17 Change in T 0 with epoch of observations for a l l v e l o c i t y measures (1939 to 1984). Crosses and c i r c l e s indicate two and greater than two observations at that p a r t i c u l a r epoch re spec t ive ly . © . . .© ©+ + © o © © ^' © ^ + $ + + i ^ • j • 1 1 i •15000 -13000 -4000 -2000 • 2000 E p o c h ( - 2 4 4 4 5 1 3 . 7 7 0 J D ) 127 Bevington [1969] ) to these observations using the h i s t o r i c measures from 1939/40 ( at -14850 days in figure 3.17) y i e l d s 6T 0 = 0.13(08) + 6.3(3.1) x 10"S T Not including these e a r l i e s t observations gives a best f i t of 5T 0 = 0.12(08) + 5.7(3.7) x 10"5 T where T i s the days from Julian day 2444513.770. In either case a P/P =* 10"5 day" 1 i s implied. This i s larger than the value found from period folding previously but this may be because for the period folding a l l points were of equal weight while in the f i t t i n g of the TO values points were weighted by number of data points at that epoch. Kundt [1979] has modeled Cygnus X-1 as consisting of a unseen secondary with a massive d i s c . The period change predicted due to mass transfer from the primary into t h i s disc i s given by P/P = - 10"* y r " 1 [ - M/10"3 M @yr" 1 ] The estimated present mass loss rate i s 5.7 x 10"6 M^yr" 1, which y i e l d s an expected P/P * 2 x 10"9 day" 1 which i s far too small to explain the observed change. If the system were in a period of disc f i l l i n g the estimated mass loss ( 10"3 M 0yr" 1, Kundt [1979] ) would give a P/P =* 3 x 10"7 day " 1, s t i l l less than that found above. The reason for the probable large period change i s therefore unknown. More data at longer time baseline are needed to confirm the r e a l i t y of the period change. 1 28 Again no s i g n i f i c a n t power was found at the 294 day period in t h i s longer time span data set. This i s in agreement with the findings of Gies and Bolton [1984] who, however, used a much shorter data base in t h e i r period search. Kemp et a l [1978] have claimed to have detected a 39/78 day e f f e c t in the U band flux, the X-ray flux and their p o l a r i z a t i o n data. No s i g n i f i c a n t power was found at this p e r i o d i c i t y in the data compiled here. A n u l l result was also found for the 91 day possible p e r i o d i c i t y suggested by Walker and Quintanilla [1978]. The v e l o c i t i e s measured were f i t t e d to a v e l o c i t y curve from which orbit parameters could be derived. Herbison-Evans and Lomb [1971] outline t h i s physical problem well and the technique for solution (• a more accessible summary i s by Petrie [1962] ). The v e l o c i t y expected for a single l i n e binary i s v = r + K [ e cos OJ + cos( u + v) ] where T i s the mean ve l o c i t y K i s the amplitude of the o r b i t a l v e l o c i t y curve e i s the e c c e n t r i c i t y of the o r b i t CJ = C J 0 + 2ir( t - T 0) / P a a CJ is the longitude -of-periastron CJ 0 i s the longitude of periastron at epoch T 0 t i s the epoch of observation P Q i s the period of the apsides v i s the true anomly 129 where tan( v/2 ) = tan( E/2 ) • [ (e+1) / (1-e) ] and E i s the eccentric anomaly which i s derived from Kepler's Equation E - e sin E = M where M = 2JT ( t - T ) / Pfa and is the o r b i t a l period. The above was put into a subroutine function which could then be c a l l e d by a routine to optimise the parameters to the data. The values quoted used the BMDP [1981] software which was available through the UBC Computing Centre. BMDP is a s t a t i s t i c a l software package which optimises the parameters using a least squares approach. The v e l o c i t i e s were weighted according to the quality of the spectra which was mainly a function of which year the data was co l l e c t e d ( i . e . of which Reticon System was used). These weights are l i s t e d in table 3.07. The best estimates of the orbit parameters for the H, He I, Hell and metal absorption l i n e s are to be found in Table 3.08. The best solution for a l l the lin e s was found with an e c c e n t r i c i t y of e s s e n t i a l l y zero ( < 0.03 ). Lucy and Sweeny [1971] have outlined a test for objectively deciding i f a derived e c c e n t r i c i t y i s s i g n i f i c a n t . In a l l cases here the significance of the ec c e n t r i c i t y was < 5% according to their c r i t e r i a . Thus no si g n i f i c a n t e c c e n t r i c i t y was found in t h i s data as opposed to Bolton's [1975] analysis, and in agreement with Gies and 130 r Table 3.07 Weights for least squares f i t t i n g r a d i a l v e l o c i t y curve by year. Year Weight 1980 DAO 48" 0.4 1981 DAO 48" 0.4 1982 DAO 48" 1.0 1983 DAO 48" 1.0 1983 DAO 72" 0.7 1984 DAO 48" 1.0 1984 DAO 72" 1.0 1984 CFHT 3.6m 1.5 Table 3.08 Orbi t Solutions for Cygnus X-1 Element H He I He II Period (days) TO (2440000+) V0 (kmsec" 1) K (kmsec" 1) e a f i t (kmsec" 1) held held -9.15(70) 78.1(16) 0.0 6.5 5.6017(1) held 1869.17(1) held -4.44(50) 6.27(70) 75.0(10) 75.4(20) 0.0 6.2 0.0 9.5 Metal held held 0.10(70) 75.9(15) 0.0 5.6 131 Bolton [1982]. This result of a c i r c u l a r o r b i t disagrees with interpretation of the photometric observations by Hutchings [1978] and Guinan et a l [1979] who found that to explain the l i g h t curve an e c c e n t r i c i t y between 0.015 and 0.04 i s required. 3.7 MASSES OF THE COMPONENTS It i s normally accepted that the components in a t i d a l l y linked binary after a suitable time are in c i r c u l a r , synchronous o r b i t s . Press et a l [1975] give expressions for the c i r c u l a r i z a t i o n and synchronization timescales due to di s s i p a t i v e tides and using parameters appropriate to the Cygnus X-1 system one finds the values are 10s years and 10" years respectively. However Cygnus X-1 has a c i r c u l a r orbit (shown e a r l i e r in thi s chapter) and i f indeed i t was only formed 400 years ago as suggested by h i s t o r i c Chinese records ( L i Qi-Bin [1979] ) then i t would seem that the supernova that created the compact companion did not seriously perturb the o r i g i n a l binary system. A l t e r n a t i v e l y Savonije and Papaloizou [1983] have suggested that c i r c u l a r i z a t i o n could occur on a much shorter timescale (^100 years) i f the system passed through a resonance between the orbit and a s t e l l a r pulsation mode. Unfortunately without an independent estimate for the in c l i n a t i o n of the system i t is not possible to know for certain whether synchronization has occurred. Let us proceed however with t h i s normal assumption that the angular 132 rotational v e l o c i t y of the star i s the same as i t s o r b i t a l angular v e l o c i t y , hence v s i n i / K = R / R . cm ' star where R c m i s the distance from the star's centre to the system centre of mass R s t a r * s t n e ° ^ s t a n c e between the surface and centre of the star As we believe that the star i s close to f i l l i n g i t s Roche Lobe in t h i s system ( denote F as the f r a c t i o n f i l l e d ) we can use the expression from Kopal [1959] and more recently Plavec [1968], Paczynski [1971] which gives R s t a r " Rsep * [ ° ' 3 8 + °' 2 l o 9 ( » p / mx } ] to f ind v s i n i / K = F * [ ( m + m ) / m ] * p X X [ 0.38 + 0.2 log( m / m ) ] P x where v s i n i = 94.3 kmsec"1 K = 75.0 kmsec"1 F = 0.95 ( from Conti [1978] ) This gives a m_/m r a t i o of 2.0 ( a v s i n i = 140 km/sec gives P x a r a t i o of * 3 ). Taking an assumed mass for the primary of 25 M@, t y p i c a l of an 09.7Iab ( Schmidt-Kaler [1982] ), gives a mass estimate for the secondary of 12 M@. Underhill 133 [1983a] c o l l a t e s mass estimates for the 0 stars and concludes that most have masses between 20 and 40 M-,. Even using an estimate for the primary as low as 20 gives a mass for the secondary of 10 M@. Note that t h i s estimate i s independent of the system i n c l i n a t i o n and only assumes that the axis of the primary i s the same as that of the binary. Hutchings et a l [1979a] suggested that the mass of a l l primaries in X-ray binaries was too low for the observed luminosity. More recent work by Rappaport and Joss [1983] using more precisely determined masses and better evolutionary tracks shows that this i s c e r t a i n only in the case of Cen X-3. In fact HD 77581 (the primary in Vela X-1), which has very similar spectral type (B0.5Ib) to HDE 226868, has mass e n t i r e l y normal for i t s MK spectral type. Thus a minimum mass for the primary bf 20 MQ appears reasonable. Thus The mass r a t i o for a single l i n e spectroscopic binary i s given by Bachall [1977] as f(m p fm x,i) = m x ( s i n i ) 3 [ mx / ( mx + mp) ] 2 = [ 4 *r2/G ] * [ ( a, s i n i ) 3 / P 2 ] Knowing the masses for the two components from above and setting a , s i n i = P * K / 2* gives a derived i n c l i n a t i o n for the system of 40°. This i s in agreement with the independent UV l i n e modeling estimate of i £ 40° ( Davis and Hartman [1983] ) and in the range 25° 134 < i < 40° as determined from X-ray p o l a r i z a t i o n measures ( Long et a l [1980] ). An independent lower l i m i t for the mass of the secondary can be made using the method of Paczynski [1974] and Bachall [1978] i f an estimate for the distance can be made. This technique r e l i e s only on the geometrical constraint implied by lack of observed ec l i p s e s . A value for the distance of HDE 226868 can be calculated using the equivalent width of H 7 . Using early type supergiants in h and x Per Walker and Millward [1984] have recently produced a c a l i b r a t i o n of H 7 equivalent width vs absolute magnitude which they give as Mv = -9.456 + ( 2 - 0.0942s) * W( H 7 ) where s i s the number of spectral sub-classes from BO. The measured H 7 equivalent width i s 1.5 ± 0.1A, when the same c r i t e r i a as that of Walker and Millward [1984] are used in avoiding the e f f e c t of blends. This gives an absolute magnitude for HDE 226868 of -6.46 ± 0.2 using the above r e l a t i o n . Using the standard value of E(B-V) = 1.12 from the work of Bregman et a l [1973], a value of R of 3.2 ( Seaton [1979] ) and the observed V magnitude of 8.81 (Kemp et a l [1981] ) gives a distance modulus of 11.68 or a distance of 2170 pc. It has been noted that HDE 226868 l i e s about one degree from the centre of NGC 6871 which i s the nuclear centre of the Cyg OB3 Association. Janes and Adler [1982] give a distance modulus for the c l u s t e r of 12.68 ± 0.55 and an E(B-V) of 0.46 which gives a corrected distance modulus 135 of 11.2 or a distance of 1740 pc. Remembering the uncertanties present i t seems HDE 226868 can be considered a c l u s t e r member. The magnitude expected for normal stars of spectral type 09.7lab in the MK system i s -6.4 ( Schmidt-Kaler [1982] ), in good agreement with the value obtained above. Now that we have a value for the distance of the system, Bachall's [1978] estimate for the minimum mass of the secondary of Mx > 3.4 d 2 , where d i s the distance in units of 2 kpc, can be used. For a distance estimate of 2.17 kpc, a minimum mass for the secondary of 4.0 M @ i s found. In passing we mention that we checked that the H 7 equivalent width c a l i b r a t i o n of Walker and Millward [1984] could be used on O supergiants and X-ray binaries by looking at the case of HD 153919. This system consists of an 07Iaf primary with a neutron star companion of o r b i t a l period 3.4 days ( Jones et a l [1973] ). It i s a member of the cluster NGC 6231, the core of the Scorpius , OB1 association, which has a distance modulus of 11.7 and a R = 3.2 ( Garrison and Schild [1979] ). From Feinstein and Forte [1974] HD153919 has V = 6.51 and B-V = 0.27 while from Schmidt-Kaler [1982] a normal star of t h i s type has B-V = -0.31. This therefore gives for HD153919 a My = -7.05. Conti and Cowley [1975] find log[ W(mA { H 7 } ) ] = 3.00 which using the above c a l i b r a t i o n gives My = -7.17 . The absolute magnitudes derived from the two di f f e r e n t estimates are in excellent agreement. 136 3.8 E(B-V) AND THE INTERSTELLAR LINES The standard E(B-V) can be checked using the spectra available from t h i s study by measuring the equivalent widths of the i n t e r s t e l l a r features seen towards Cygnus X-1. The best l i n e for t h i s purpose i s at X6613 which i s narrow, strong and unblended. The feature at X4430 although strong is blended with s t e l l a r l i n e s and may have a circumstellar contribution ( Tug and Schmidt-Kaler [1981] ). The Ca II K li n e could also be used but i t i s more prone to measurement errors as i t i s close to the edge of the spectrum in a l l cases. As well Bromage and Nandy [1973] find that t h i s l i n e i s not well correlated with E(B-V) in the Cygnus d i r e c t i o n . A l l the the other i n t e r s t e l l a r l i n e s in the available spectra are too weak to be useful. The cor r e l a t i o n of equivalent widths of the i n t e r s t e l l a r l i nes with E(B-V) has been investigated by Herbig [1975] and by Bromage and Nandy [1973]. They both find that the li n e s in stars between 1^75° and 82° are 30% weaker per unit E(B-V) than the average of a l l other areas on the sky. Table 3.09 shows the E(B-V) as determined for Cygnus X-1 from the X6613 l i n e for both the Cygnus and non-Cygnus d i r e c t i o n s . If HDE 226868 i s indeed a normal 0 supergiant ( therefore {B-V}0 - -0.25 ) then i t s measured B-V colour of 0.85 gives an E(B-V) = 1.10, which i s the accepted value in the l i t e r a t u r e . T h i s value however is higher than the independent estimate of E(B-V) to be found in table 3.09. 137 T able 3.09 E(B-V) as d e t e r m i n e d from the I n t e r s t e l l a r l i n e s u s i n g the c a l i b r a t i o n of H e r b i g [1975] f o r the whole sky and j u s t t h e d i r e c t i o n of Cygnus. l i n e EW E(B-V) E(B-V) A mA a l l Cygnus 6613 0.16(2) 0.56 0.76 4430 1.5(3) 0.56 0.79 Note t h a t t h i s lower v a l u e makes no assumption a t a l l about the Cygnus X-1 p r i m a r y as i t r e l i e s o n l y on the i n t e r s t e l l a r l i n e s t r e n g t h s . A v a l u e of the E(B-V) of 0.95 was deduced from the UV o b s e r v a t i o n s o f Wu e t a l [1982]. T h i s s m a l l e r E(B-V) can be e x p l a i n e d i n two ways ; HDE 226868 does not have t h e normal c o l o u r s f o r an O s u p e r g i a n t . The change i n i n t r i n s i c c o l o u r r e q u i r e d t o agree w i t h the measured (B-V) would move the ( B - V ) 0 c o l o u r t o t h a t e x p e c t e d from a l a t e B s u p e r g i a n t . As the spectrum i s o b v i o u s l y t h a t of an O s u p e r g i a n t t h i s would i m p l y t h e p r i m a r y i s p e r c u l i a r . However the f a c t t h a t the H7 e q u i v a l e n t w i d t h i s i n such good agreement w i t h t h a t found f o r s t a r s of i t s type makes t h i s u n l i k e l y . The i n t e r s t e l l a r e x t i n c t i o n law i s unique i n the d i r e c t i o n of Cygnus X-1. As the i n t e r s t e l l a r l i n e s are a l r e a d y weakest per E(B-V) towards Cygnus ( compared t o any o t h e r d i r e c t i o n i n t h e sky ) t h i s would mean an even 1 38 weaker dependence in the pa r t i c u l a r d i r e c t i o n of Cygnus X-1. This could be checked by observation of other distant stars around the same position on the sky. 3.9 MASS LOSS RATE Hutchings [1970,1979] l i s t s seven d i f f e r e n t mass loss indicators in early type stars. One of these indicators is p a r t i c u l a r i l y useful as i t can be used to quantitively estimate the mass loss rate without detailed modelling. As l i n e s in a star are formed at di f f e r e n t depths due to varying excitation energies, in the expanding atmosphere of an early type star lower energy l i n e s are systematically blue shifted r e l a t i v e to those of higher energy ( Karp [1978] ). The amount of i n i t i a l energy provided to drive the wind i s related to th i s v e l o c i t y gradient and to the t o t a l mass los s . Suitable c a l i b r a t i o n of the mass loss vs vel o c i t y gradient r e l a t i o n allows i t s use to determine mass loss rates for individual stars. Table 3.08 l i s t s the r e l a t i v e zero v e l o c i t i e s of li n e s of d i f f e r e n t excitatation energy in HDE 226868 ; namely H, He I, He II and Metal l i n e s having excitation energys 10, 21, 75 and 50 eV ( Hutchings [1976] ). Figure 3.18 shows these quantities plotted together with the best least squares f i t ( dotted l i n e ) given by Velocity(km/sec) = 0.224(20)(km/sec/eV)* Energy(eV) -10.4(9) (km/sec) 139 Figure 3.18 Zero v e l o c i t y vs exc i ta t ion energy for l ines from HDE 226868. 1 4 0 o OJ in \ £ o o Q l 100 E x c i t a t i o n E n e r g y ( e U ) 141 The value obtained for the gradient is higher than the 0.13 km sec" 1eV- Hutchings [1976] l i s t s for HDE 226868. A mass loss rate for HDE 226868 can now be obtained by comparing t h i s value of the v e l o c i t y e xcitation gradient to that of stars with known mass loss rate and vel o c i t y e x c i t a t i o n gradients. The only such compilation comes from Hutchings [1976]. However t h i s work is t i e d to only seven stars whose mass loss rates were believed well known at the time from modelling of o p t i c a l P-Cygni p r o f i l e s . Subsequently new techniques have been developed for measuring mass loss rates, namely measurement of the free-free radio and infrared emission, and modeling of the UV resonance l i n e s . Table 3.10 i s a compilation of those stars for which a v e l o c i t y gradient i s known from Hutchings [1976] and for which there are independent recent estimates for the mass loss rate. The older (too large) mass loss rates from Hutchings and Morton are include to show the basis stars from which Hutchings [1976] estimated rates for other stars. The infrared determinations l i s t e d in table 3.10 have been c r i t i c i s e d by Castor and Simon [1983] and Abbott et a l [1984] as they require the assumption of the form of the v e l o c i t y law in order to extract information about the mass loss rate. Figure 3.19 shows the mass loss rates as determined using UV or radio techniques plotted against the velocity e x c i t a t i o n gradient. The least squares f i t to the data below a gradient of 20 eV/kmsec"1 i s Table 3.10 Mass loss rates ( 10" sM Qyear- 1 )from d i f f e r e n t techniques S t a r HD 108 14947 24398 3G486 37128 37742 46150 46223 47839 48099 6681 1 91316 93129 101190 151804 152236 Name £ Per 6 O r l t Or1 s o n 5 Mon £ Pup p Leo S p e c t r a l Type 06- 7f 05-6If B1Ib 09.511 BOIa 09.51b 05- 6f 04-5Vf 07- 8Vf 07V 04If B1 l b 03 06- 7V 09f B1Ia G r a d i e n t 2eV/kmsec Radio 20 >40 10 >40 15 >40 >40 >40 9 15 10 34 9.3 4 4.0' 3. r 2.3 s 3.5 s 6. UV IR Opt i ca1 8.5" 50' 10' 2.4" 29 s 0. 45' 0.5" 1.3' 3.5' 0.5" 2.2' 0.8' 2.5' 0.15' 0.85' 0.6' 3.5' 4.1' 1.4' 1.4' 1.0' 7.9' 9.1'° 8 1 1.2' 1 .0" 3.5' 1 ' ' 1.7': 3.2'° 1.2' 8 ' ' 9 ' 21 1 16.6'"- 1 0 " 10' 152408 08f 3 152424 091 >40 188001 9 Sge 08If 7 193237 P Cyg B1p 1.4 210839 V. Cep OGIf 12 1 = Garmany e t a l [1981] ' = G a t h l e r e t a l [1981] 3 = Garmany and C o n t i [1984] ' = O l s o n and C a s t o r [1981] 5 = Abbott et a l [1980] 8 = Abbott et a l [ 1981 ] ' = Morton and Wright [1978] • = Barlow and Cohen [1977] ' = P e r s e i et a l [1983] 1 0 = K l e i n and C a s t o r [1978] ' 1 = C a s s i n e l 1 i et a l [1978] 1 ! = Morton [ 1967 ] ' 1 = C o n t i and F r o s t [1977] '• = H u t c h i n g s [ 1968] 1 ' = H u t c h i n g s [1970] 1 5 = Peppel [ 1984] 10' 2 1 . 4 1 0 100 1 0.8 1 5 . 2 1 0 6.3' 1 1 ' 13" 4.8 7.8 s 350' 4.0' 6 . 5 1 4 4 F i g u r e 3.19 Mass l o s s r a t e s , d e t e r m i n e d by d i f f e r e n t methods vs v e l o c i t y e x c i t a t i o n g r a d i e n t . S t a r s a r e UV d e t e r m i n a t i o n s , open c i r c l e s from r a d i o measure and f i l l e d c i r c l e t h a t p r e d i c t e d f o r Cygnus X-1. 2 0 >40 S l o p e 2 ( e U / [ k m/s e c ] ) 146 Mass loss (lO" 6M/year) = 11.61 - 0.661 * VE (2eV/kmsec-1) The gradient determined previously for HDE 226868 then gives a mass loss rate of 5.7±2 x 10~6 M^year" 1 for the primary of Cygnus X-1. This is higher than the IR value of 3.5 x 10"6 found by Persi et a l [1980]. Garmany et a l [1981] fi n d that the mass loss and the s t e l l a r luminosity for many stars can be related by log[ M ] = -7.15(10) + 1.73(16) log [ L / 10 5 L @ ] For the mass loss found above th i s gives a luminosity for HDE 226868 of 1.3 ± 0.5 x 106 L Q . Schmidt-Kaler [1982] gives a t y p i c a l value for a 09.7 supergiant of between 2.6 and 5.3 x 105 L Q . A S the luminosity of the primary found e a r l i e r from the H7 c a l i b r a t i o n was e n t i r e l y normal, the larger luminosity found using the above expression implies that non-radiative effects in the wind may be considerable. 3.10 EQUIVALENT WIDTH VARIATIONS Using the same technique as outlined e a r l i e r in t h i s chapter a l l l i n e s , except the Balmer series, of s u f f i c e n t strength had their equivalent widths determined. These values were then placed in o r b i t a l phase bins of width 0.1 and normalised to the average. The Balmer s e r i e s l i n e s are much broader than other l i n e s due to stark broadening, 147 consequentially their equivalent widths were determined by numerical intergration between the l i n e l i m i t s . A l l the equivalent width measures are l i s t e d in table 3.11 and plotted in figure 3.20 to 3.23 . The i n t e r s t e l l a r l i n e at 4726.OA provides a useful check on the consistency of our methods. The scatter found in that l i n e i s about 10%, which i s similar to the maximum difference found between equivalent width measures from spectra of the same star taken on the same night. The cause of t h i s scatter in the i n t e r s t e l l a r l i n e may be because the l i n e i s f a i r l y weak and not s t r i c t l y Gaussian as can be seen in figure 4.1. As the equivalent width measurement technique r e l i e s on the p r o f i l e being approximately Gaussian, measurement of t h i s l i n e i s d i f f i c u l t . It i s l i k e l y that an error of 10% in the equivalent width can be considered as t y p i c a l for a single l i n e measurement. As can be seen from the plots no s i g n i f i c a n t phase va r i a t i o n is seen in the equivalent widths ( as opposed to the claim by Smith et a l [1973] ) except possibly in the hydrogen l i n e s which w i l l be discussed further in the next chapter. The magnitude of the var i a t i o n expected from the eff e c t of the e l l i p s o i d a l d i s t o r t i o n of the primary has been modeled by Hutchings [1977]. He predicts a 10% v a r i a t i o n in the equivalent widths in the case of HDE 226868 in the sense of largest values at phase zero. This would be near the detection l i m i t here but no such variation i s apparent. As the photometric l i g h t curve observed i s that c h a r a c t e r i s t i c 148 Figure 3.20 Phase v a r i a t i o n of hydrogen l i n e s equivalent width in Cygnus X-1 . C i r c l e s are from H7, s tars from H/3. N o r m a l i s e d E q u i v a l e n t W i d t h 0 . 9 1 1 . 1 -i 1 1 1 1 1 1 1 1 1 r * 0 1 . 2 ro o o to -rj ro CT) a M s s \ \ 0 * / / / I 6. * a oo : I : I ':» / / / 6 * 1 150 Figure 3.21 Phase va r i a t i o n of mean He I l i n e equivalent width in Cygnus X-1. ro o o "0 • OJ • m N o r m a 1 i s e d E q u i w a l e n t U l i d t h 0 . 9 1 1 . 1 1 . 1 1 l • 1 1 1 • I 1 1 1 1 (J / / / M 1 » i - i -i • \ \ m i i m j j • - \_ -* \ ' • • * / • ' ' I \ • • 1 • 1 1 1 - L 1 1 1 1 1 1 1 1 1 1 1 1 191 152 Figure 3.22 Phase v a r i a t i o n of He II (absorption l ines ) equivalent width in Cygnus X-1. C i r c l e s are X4200, s tars are X4542. N o r m a l i s e d E q u i v a l e n t W i d t h 0 . 9 1 1.1 1 t T 1 1 1 I 1 1 1 r t T 1 r a ro o o a- ^ O 3K 0 s y Q "0 3" Ul ro a N. a • oo _i i i_ / / X © -i i I i i_ -i i i i _ £91 154 Figure 3.23 Phase variation of mean metal l i n e equivalent width in Cygnus X-1. N o r m a l i s e d E q u i v a l e n t W i d t h 0.9 1 1.1 1.2 -i 1 1 r T r t ro o a a- j> so ro ro CT) P O 00 J I L. J • 1_ SSI 156 Figure 3.24 Phase v a r i a t i o n of i n t e r s t e l l a r l i n e s equivalent width in Cygnus X-1. Squares are X4726, c i r c l e s are Ca II K, s tars are X4763. N o r m a l i s e d E q u i v a l e n t U l i d t h 0.9 1 1.1 1 ro o o "TJ ZT $" ID a cn o 00 ~i 1 1 r a T 1 r t s. ¥ .* ,K \ \ w * -. A # © p / /• \ \ y A ' . / \\ V* ^ . . I \ >. \ ; \ " V v '. / v / v / • T 1 r _i i L. Z.SI Table 3 . 1 1 Normalized Equivalent Width Variations with Orbital Phase L i n e Mean EW 0 .0- 0 . 1 - 0 . 2- 0 . 3- 0 . 4 0 .5-A . (mi) 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 .6 Hydrogen 4340. 468 1744.99 1 . 135 1 .052 0 .966 1 .093 0 .931 0 .922 4861 . 332 1232.04 1 .013 0 .977 1 .018 1 .030 '0 .946 0 .957 He I 4026 . 189 547 .45 1 .056 0 .997 0 .995 0 . 957 0 .990 1 .035 4120. 812 233 . 15 1 .017 1 . 1 10 0 .909 0 .918 0 .968 1 .029 4143 . 759 236 . 83 1 .032 1 .036 0 . 959 0 . 94 1 1 .009 1 .017 4387 . 928 318 .20 1 .087 0 .958 0 .966 1 .022 1 .020 0 .989 447 1 . 477 645 . 23 1 .032 0 .979 0 .959 0 .985 1 .003 1 .009 4713 . 143 273 .06 1 .068 0 .976 0 .96 1 1 .003 1 .005 1 .005 4921 . 929 406 .43 1 .053 0 .989 0 .980 0 .932 1 .071 0 .964 5015 . 675 292 . 23 1 .061 0 .979 1 .031 0 .983 1 .042 0 .965 He II 4199 . 83 193 .90 1 .025 1 . .068 0 . 993 0 . 943 1 . 001 0 .968 454 1 . 598 190 .54 0 .947 1 . 030 0 .934 1 .047 1 . 072 1. .010 Metal 4069 . 897 243 .06 1 .053 1 . 012 0. 88 1 1. .046 1 . 050 0. 886 4075 . 86 163 . 73 0 .973 1 . 099 1. 005 0. .886 0. 960 1. 022 4088 . 863 598 .71 0 .986 0. 959 1. 008 1. 010 0. 992 1. 019 4097 . 31 628 .56 1 .026 1. 003 0. 997 0. 935 1. 003 0. 97 1 41 16. 104 434 . 36 1 .045 1. 015 0. 897 0. 938 0. 976 1. 037 4379 . 09 148 .53 1. . 100 1. 094 0. 897 1. 104 1. 049 0. 956 4481 . 228 91 . 13 0. .957 0. 996 0. 907 0. 998 1. 014 1. 102 4510. 92 142 .43 0. .940 0. 927 0. 907 1. 068 0. 964 1. 013 4514 . 89 175 .91 0. 963 0. 894 0. 878 1. 047 1. 024 1. 04 1 4552 . 654 164 . 39 1. 061 0. 982 0. 977 0. 980 0. 993 0. 957 4630. 537 129 .66 1. 018 1. 01 1 0. 986 0. 955 0. 992 1. 002 4634 . 16 132 .26 0. 978 1. 092 1. 017 0. 944 1. 001 0. 931 4640. 64 238 . 34 1. 087 1. OOO 0. 964 0. 993 0. 964 0. 977 4647 . 40 4 17 .98 1. 076 0. 970 0. 954 1. 000 1. 000 0. 973 0 .6- 0 . 7- 0 . 8- 0 . 9-0 . 7 0 . 8 0 . 9 1 .0 0 .911 1 .010 1 .022 0 .997 0 .932 1 .027 1 .021 0 .978 0 .970 1 .038 0 .988 0 . 975 0 .977 1 . 108 0 .965 0 .999 1 .020 1 .016 0 . 934 1 .038 0 .960 1 .040 1 .006 0 .952 0 .990 1 .028 1 .006 1 .01 1 0 .985 1 .032 0 .983 0 . 981 0 .964 1 .074 0 .984 0 . 991 0 .961 1 .045 0 . 940 0 .994 1 .067 0 .983 1 .045 1 .024 0 .925 1 .089 0 .955 0. . 990 0. .984 1 .083 0. .993 1. 031 1. 031 0. .973 0. 918 1. 102 0. 968 1. .066 1. 029 0. 964 0. 980 1. 088 0. 997 1. 001 0. 983 1. 117 0. 979 1. 010 0. 876 1. 011 0. 972 0. 963 1. 041 0. 983 0. 983 1. 018 1. 057 1. 045 1. 048 1. 032 0. 978 1. 109 1. 032 1. 035 1. 002 1. 087 0. 903 1. 059 0. 991 1. 103 1. 047 1. 013 0. 902 1 . 046 1. 140 0. 950 1. 002 1 . 067 1. 05 1 1. 07 1 0. 946 1. 002 1. 038 1. 041 CO 4650.74 446.59 1.039 1.062 0.999 0.936 1.030 0.964 0.993 0.983 1.010 0.984 IS 3933.64 572.44 1.035 1.020 0.932 0.977 0.984 1.019 0.976 0.945 1.089 1.025 4726.0 132.87 1.064 0.985 0.993 0.997 0.971 1.015 1.034 0.986 0.982 1.000 4763.0 105.71 0.963 0.987 1.011 0.963 1.012 0.961 1.077 0.989 1.048 1.000 160 of e l l i p s o i d a l variables, i t seems l i k e l y therefore that the prediction for the size of the e l l i p s o i d a l e f f e c t on the absorption l i n e s is in error. 3.11 LINE HALFWIDTH VARIATIONS Priedhorsky et a l [1983] have suggested that the most satisfactory way in which to explain the observed 294 day period in the X-ray flux i s in terms of a slaved disc scenario as suggested by Roberts [ 1974.]. Precession of the primary produces a forced disc precession which modulates the X-ray flux by changing the angle between l i n e of sight and the outer disc plane. Sokolov and Tsymbal [1984] have explained the long period l i g h t variations in t h i s way and find that the primary's rotation axis i s varying in orientation by =* 16° on a period 39 days. Kopylov and Sokolov [1984] support t h i s interpretation with spectroscopic data. A change in the i n c l i n a t i o n of the primary of ±8° would produce a change in the v s i n i of ± 15%. To search for such a variation the halfwidths of the He I X4471 and X4713 were measured. These li n e s were chosen as they are r e l a t i v e l y insensitive to temperature fluctuations, have no emission component, are r e l a t i v e l y unblended and are quite deep. In order to ensure that instrumental changes were not affecting the r e s u l t s , the halfwidths of the He I l i n e s in the 19 Cepheus spectrum taken on the same night were also measured. The HDE 226868 measurements were divided by the 19 Cepheus 161 widths. These values were then binned using the o r b i t a l phases and the results are tabulated in table 3.12 and i l l u s t r a t e d in figure 3.24. There i s no s i g n i f i c a n t v a r i a t i o n connected with the 5.6 day period. The period searching technique described previously was applied to t h i s data and no periodic variations were found in the range 1 to 350 days. It i s unlikely that a v a r i a t i o n with an amplitude as large as predicted would have been missed. 162 Table 3.12 Normalized phase variations of He I halfwidth phase bin Hel Cyg X4713 X -1/19 Cep He I X4471 Cyg X-1/19 Cep 0.0-0, 0.1-0, 0.2-0, 0.3-0, 0.4-0, 0.5-0, 0.6-0, 0.7-0.8 0.8-0.9 0.9-1 .0 , 1 ,2 ,3 ,4 ,5 6 ,7 13 13 10 12 14 15 1 2 17 16 12 .15 .16 . 1 1 .12 .09 .13 .10 .16 .15 .15 163 Figure 3.25 Normalized phase variation of He I halfwidth with phase. i ' 1 • 1 1 r Ol U CO \ I X o> Z P s: 3 © • •©, • . © • 5* ©. V > ' / '© —5K •••o-^ v © s 0 0.2 0 .4 0.6 Or b i t a 1 P h a s e • . 8 Chapter 4 THE EMISSION LINE SPECTRUM 4.1 RATIONALE FOR THE STUDY The i d e n t i f i c a t i o n of Cygnus X-1 with HDE 226868 came conclusively in papers in 1972. Wade and Hjellming [1972] found an accurate interferometric position coincidence between the radio source and HDE 226868. Bolton [1972a, 1972b] reported that He II X4686 was in emission, which was not expected for the primary's spectral type, and that the emission appeared to move in antiphase to that of the primary. This sparked considerable interest in the study of the emission lines as i t was thought that i t might give insight into conditions in the postulated d i s c . It was however Hutchings et a l [1973] who r e a l i s e d that in order to study the He II emission l i n e properly the absorption l i n e contribution from the primary had to be accounted for. Walker et a l [1978] went into the d e t a i l s of this subtraction process and produced corrected p r o f i l e s which, unfortunately, were of poor signal to noise. The Ha l i n e has also been the subject of study using similar techniques by Hutchings et a l [1974, 1979b] and Brucato and Zappala [1974]. A l l this data however lacked sufficent d e t a i l to give good information on the emission l i n e s and to answer the p r i n c i p a l question of where do they originate. 165 4.2 ANALYSIS OF THE HE II X4686 DATA 166 4.2.1 FINDING A GOOD REFERENCE STAR The observed He II emission l i n e i s the result of some unknown emission p r o f i l e coming from an unidentified region in the binary system combined with the absorption p r o f i l e from the primary. As the primary moves in orbit i t s absorption p r o f i l e i s doppler s h i f t e d . In order to correct the observed p r o f i l e for thi s e f f e c t the i n t r i n s i c p r o f i l e of the He II X4686 from the primary must be known. This can be done by finding a comparison star of s i m i l a r spectral type that would have He II l i n e s of similar strength. The He II li n e at the spectral type of HDE 226868 ( 09.7Iab as determined in Chapter 2 ) i s p a r t i c u l a r i l y sensitive to changes in e f f e c t i v e temperature and the match in spectral type must be very close. The observations at CFHT included observations of a number of stars of similar spectral type to HDE 226868. These are shown in figure 4.01 with the lines i d e n t i f i e d in order l e f t to right in table 4.01 . The two stars with spectral type closest to HDE 226868 had l i n e s of He I X4713 that were too deep and narrow. This stems from HDE226868 rotating synchronously in orbit with the secondary while HD 149038 and HD 167264 are presumably single stars (or wide binaries) and not forced to rotate as quickly. In order therefore to see how well the 167 Figure 4.01 Standard stars taken at CFHT for comparison with HDE 226868. T i c marks indicate l i n e s i d e n t i f i e d in table 4.01 . 19 Cep /09.51b HD188209/09.5Iab HD149038/O9.7Iab HD167264/09.7Iab HD195592/09.7Ia 19 Cep /09.51b 4665 4675 4685 4695 4705 4715 4725 Wauelntgtlj (Angstrom) cn CO 169 Table 4 .01 Line l i s t for CFHT data. Line Wavelength (A) O II 0 II Oil He I Oil ? IS on on N i l He II 4673.75 4676.234 4677.93 4685.682 4699.21 4705.355 4710.04 4713.143 4713.373 4726.0 spectra of these stars could be made to match that of HDE 226868 they needed to be broadened to the same v s i n i . The broadening was done by convolving the observed p r o f i l e with a function that simulates the ef f e c t of rotational broadening ( Huang and Struve [1953], Gray [1976] ). This function has the the form G(AX) = C,[ 1 - x 2 ] 0 > 5 + C 2 [ 1 - x 2 ] where x = AX / AX L AX_ = X v s i n i / c JLi C, = 2( 1 - e ) / ( T T A X l ( 1 - e/3 ) C 2 = ire / [ 2?rAXL ( 1 - e/3 ) e i s the limb darkening parameter =* 0.6 ( Gray [ 1976] ) Figure 4.02 shows the result of convolving t h i s function with the X4713 l i n e p r o f i l e of the standards. The s o l i d l i n e in each case i s the HDE 226868 X4713 p r o f i l e , the dashed l i n e is the p r o f i l e of the standard and the 170 Figure 4 .02 Broadened P r o f i l e s of Standards S o l i d l i n e = HDE226868 He I X4713 p r o f i l e Dashed l i n e = indicated standard's p r o f i l e Dot-Dash l i n e = broadened standard's p r o f i l e 171 Wavelength (Angstrom) 172 dashed dot l i n e i s the p r o f i l e resulting from a convolution to 94 kmsec"1, the v s i n i of HDE 226868 (see Chapter 3 for d e t a i l s ) . The p r o f i l e s look as i f they f i t those of HDE 226868 approximately. For the subsequent analysis HD 167264 broadened to a v s i n i of 94 kmsec"1 was considered a close match to the spectrum of HDE 226868. 4.2.2 CORRECTION OF THE HE II PROFILES There are two data sets of quite d i f f e r e n t dispersion from which the i n t r i n s i c He II X4686 p r o f i l e was recovered. F i r s t l y there i s the fiv e years of 40 Amm"1 data taken mainly (except for four p r o f i l e s ) on the DAO 48" Telescope. For t h i s low dispersion data the p r o f i l e i s e s s e n t i a l l y determined by the projected s l i t width meaning that a l l the absorption l i n e s w i l l e s s e n t i a l l y have the same p r o f i l e and merely vary in central depth. On each night for which a spectrum of Cygnus X-1 was obtained a spectrum of 19 Cepheus was also taken. There were two reasons for t h i s ; It would serve as a check on any long term errors that might creep into the reduction technique i t would provide a p r o f i l e , taken under i d e n t i c a l conditions of a star of similar spectral type, for correction of the e f f e c t of the primary on the He II emission feature. 173 The correction for the primary absorption must be done f a i r l y accurately or i t may affect the resultant v e l o c i t y curve for the He II emission. If the correction i s too large the velocity curve for the emission w i l l be influenced too much by the assumed absorption p r o f i l e and the vel o c i t y curve w i l l tend to r e f l e c t too much t h i s component ( i . e . i t w i l l follow the ve l o c i t y curve of the primary). If too l i t t l e i s subtracted then the l i n e wings w i l l be weighted too heavily and a more extreme range ve l o c i t y curve w i l l r e s u l t . From the CFHT data HD 167264 seems l i k e a close f i t to HDE 226868 in spectral type and the equivalent widths of He II X4686 should therefore be simi l a r . As the p r o f i l e . o f a l i n e in the DAO data i s independent of l i n e depth i t is then possible to use the ra t i o of the equivalent widths for the He II l i n e from the CFHT data for 19 Cep and HD167264 to a l t e r the DAO 19 Cepheus He II X4686 equivalent width to that expected for HDE 226868. The equivalent widths for these l i n e s are l i s t e d in table 4.02 and i t can be seen that the HD 167264 He II X4686 l i n e i s 0.872 that of 19 Cepheus. The procedure then for correcting the He II emission i s as follows. The He I X4713 for both Cygnus X-1 and 19 Cepheus on each night are sh i f t e d and aligned to zero v e l o c i t y ( i.e . they are put in the primary's centre of mass frame ). As has been seen in the previous chapter l i n e s of dif f e r e n t e x c i t a t i o n energy are formed 174 T a b l e 4 .02 E q u i v a l e n t W i d t h s (mA) for s e l e c t e d l i n e s from CFHT d a t a . S t a r He I X4713 He I I X4686 19 C e p 275.1 329.3 HD 167264 316.2 287.1 HDE 226868 319.6 a t d i f f e r e n t d e p t h s i n t h e a t m o s p h e r e ; t h e low e x c i t a t i o n e n e r g y l i n e s a r e f o r m e d h i g h e r a n d h a v e l e s s b l u e s h i f t e d v e l o c i t i e s t h a n t h e h i g h e x c i t a t i o n l i n e s . The v e l o c i t y d i f f e r e n c e b e t w e e n t h e He I l i n e s a n d t h e He I I a b s o r p t i o n l i n e s i s 18.2 k m s e c " 1 f o r 19 C e p h e u s a n d 8.3 k m s e c " 1 f o r HDE 226868. T h u s a f t e r a l i g n m e n t t h e 19 C e p h e u s l i n e i s s h i f t e d b y - 9 . 9 k m s e c " 1 t o e n s u r e t h a t t h e u n d e r l y i n g He I I a b s o r p t i o n l i n e i s a l i g n e d . The 19 C e p h e u s s p e c t r u m i s w e a k e n e d by 13% i n o r d e r t o make t h e l i n e s t r e n g t h s more l i k e t h o s e o f HDE 167264 ( a n d HDE 226868 ) . The two s p e c t r a a r e t h e n s u b t r a c t e d a n d t h e r e s u l t a n t s h i f t e d b a c k i n t o t h e c e n t r e o f mass r e s t f r a m e . F i g u r e 4.03 shows t h e He I I X4686 p r o f i l e s o f C y g n u s X-1 w i t h o u t a n y c o r r e c t i o n ( d a s h e d l i n e s ) t o g e t h e r w i t h t h e p r o f i l e o f 19 C e p h e u s t a k e n on t h e same n i g h t ( s o l i d l i n e ) . F i g u r e 4.4 shows t h e r e s u l t o f t h e s u b t r a c t i o n p r o c e d u r e o u t l i n e d a b o v e . The s u b t r a c t i o n a t t h e He I X4713 i s n o t p e r f e c t b e c a u s e t h e two p r o f i l e s a r e n o t a l i g n e d f o r t h a t l i n e . 175 Figure 4 .03 He II X4686 p r o f i l e s from Cygnus X-1 (dashed l ine ) and from 19 Cep ( so l id l i n e ) . Cyg X-1 : 1980-1984 : He II -^f\/—""V—y—^ Vs  0.006 0.014 0.019 0.032 0.160 0.169 0.179 0.191 0.204 0 . 2 0 9 0 . 2 3 8 0.264 0 . 2 7 7 0 . 2 8 2 0 . 3 4 0 0 . 3 6 6 0 . 3 7 0 4600 4650 4700 4750 Uavelength (Angstrot) Cyg X-1 : 1980-1984 : He II "V ~\T ~^rr~v\j ~~V V" -~v~—v-*" —V^Yy^-t jj* Y" - N C ^ y ^ - y — ^ -vrv\y^ — ^ " V ^ - ^ v ^ -v*— \ r -x/^r*y^—^ "~V~ ~^rr*y\jy~~-—'~yr v— - v ^ ^ ^ <r y-0.568 0.597 - 0.622 0.627 0.632 0.655 0.689 0.597 0.7U 0.722 0.740 0.741 0.756 0.781 0.802 0.802 0.823 0.831 0.9-11 0.851 0.856 0.871 0.872 0.899 0.905 0.910 0.321 0.943 n.97p 4600 4650 4700 4750 Wavelength (Angstroi) 1 78 Figure 4.04 He II X4686 p r o f i l e s af ter correct ion for absorption from primary. Cyg X-1 1980-1984 : He I I 179 181 4.2.3 THE CFHT HE II X4686 PROFILES The technique for removal of the effect of the primary from the He II emission l i n e for the CFHT data is similar to that descibed above. The only difference being that intead of 19 Cepheus for a reference star HD 167264 i s used after broadening i t to 94 kmsec"1 to match the v s i n i of HDE 226868. The two p r o f i l e s superposed are shown in figure 4.05. The result of the subtraction i s shown figure 4.06 and from this i t is clear that the p r o f i l e s exhibit considerable structure at high dispersion not v i s i b l e in the low dispersion DAO data. Chapter fiv e w i l l deal with t h i s structure. 4.3 THE HE II EMISSION RADIAL VELOCITY CURVE The previous data on the r a d i a l v e l o c i t y curve of the He II X4686 l i n e i s quite limited and of variable q u a l i t y . Bolton [1975] c o l l a t e d the available He II v e l o c i t i e s to that time and the data showed great scatter p a r t i a l l y because some of the measurements did not take into account correction • for the primary's absorption. Walker et a l [1978] made a careful analysis of t h e i r He II p r o f i l e s but a l i m i t e d amount of low signal to noise data resulted in no firm conclusions being reached. The centre of gravity position f i t t i n g technique was used on a l l the corrected He II p r o f i l e s ( both DAO and CFHT ) and correction to the solar system barycentre was made. Li s t e d in table 4.03 and shown in figure 4.07 are the 182 Figure 4.05 Spectrum of HDE 226868 near X4686 with inverted spectrum of HD 167264 superposed for Ju ly 1984 CFHT data . 20 -15 -10 -5 0 5 10 15 20 Wavelength (Angstrom) 184 F i g u r e 4.06 He I I X4686 P r o f i l e s a f t e r c o r r e c t i o n f o r a b s o r p t i o n f r o m t h e p r i m a r y f o r J u l y 1984 CFHT d a t a . 185 Wavelength (Angstrom) 186 v e l o c i t i e s for the He II X4686 l i n e in the centre of mass frame of the Cygnus X-1 system. The f i r s t thing to be noted from the plot in figure 4.07 i s that the curve looks quite smooth with l i t t l e of the scatter apparent in previous results ( Bolton [1975] ). It i s also clear that the velocity curve i s approximately 120° phase removed from the vel o c i t y curve of the primary. Emission from the region of the secondary would be shifted 180° in phase, so c l e a r l y t h i s simple explanation i s not the answer. S i m i l a r i l y to what was outlined in the previous chapter, the BMDP software package was used to f i t t h i s r a d i a l v e l o c i t y curve to give 'orbit' parameters. The resultant parameters are l i s t e d in the second column of table 4.04. As in the case of the absorption l i n e curve no s i g n i f i c a n t e c c e n t r i c i t y could be forced to f i t the data. It i s also apparent from figure 4.07 that the best solution to the data does not f i t extremely well. In p a r t i c u l a r the f i t around phase 0.5 ( the X-ray source between the observer and the primary ) and phase 0.0 appears poor. Walker and Q u i n t a n i l l a [1978] find deviations from an e l l i p s o i d a l l i g h t curve, in their f i v e years of photometric data on t h i s system, at these phases also. There i s no straight forward explanation as to where in the system such a v e l o c i t y curve would come from. A simple model would locate the emission on the l i n e of centres between the primary and secondary. A test p a r t i c l e in such a position would have two v e l o c i t y components, one due to or b i t i n g about the centre of mass and the other due to some Table 4.03 He II X46B6 emission r a d i a l v e l o c i t i e s and equivalent widths O r b i t a l He I I X4686 He I I X4686 p h a s e v e l o c i t y e q u i v a l e n t k m s e c " 1 w i d t h (mA) DAO D a t a 0.006 +58.32 533.34 0.014 +57.88 581 .82 0.019 +66.83 538.27 0.032 +56.72 561 .45 0. 160 + 4.52 648.89 0. 169 -18.86 690.69 0. 179 -11.38 622.92 0.191 -31.31 605.41 0.204 -28.98 595.43 0.209 -44.46 648.22 0.238 -41.34 650.18 0.264 -36.10 544.26 0.277 -56.78 500. 13 0.282 -17.86 0.340 -77.38 491.97 0.366 -78.57 460.25 0.370 -68.33 517.94 0.388 -74.96 425.27 0.398 -104.23 460.64 0.422 -87.94 486.38 0.447 -55.57 465.25 0.449 -70.62 409.99 0.466 -65.26 492.31 0.470 -51.77 497.32 0.516 -30.27 0.547 + 2.32 454.47 0.549 452.84 0.566 -8.14 467.24 0.568 -18.89 479.75 0.597 -1 .44 460.90 0.622 +6.67 445.80 0.627 +32.82 487.19 0.632 +13.77 431.95 0.655 +24.75 580. 19 0.689 +31.61 547.47 0.697 0.714 +46.31 546.55 0.722 +53.14 517.74 0.740 +52.33 830.56 0.741 0.756 +60.37 546.59 0.781 +61.40 627.75 0.802 +33.31 580.92 0.802 +69.20 . 557.53 0.823 +70.47 587.48 0.831 +69.59 648.01 0.841 +76.48 615.26 0.851 +80.82 696.16 0.856 +73.39 651.09 0.871 +91.57 593.20 0.872 +56.95 575.33 0.899 +83.95 560.29 0.905 +76.47 597.74 0.910 +64.34 559.83 0.921 +74.70 591.46 0.949 +85.76 571.54 0.978 600.02 CFHT Data 0.046 +47.24 508.15 0.220 -34.15 450.05 0.410 -73.89 296.43 0.570 -3.56 409.29 0.750 +57.35 516.61 189 Figure 4.07 He II X4686 r a d i a l ve loc i ty curve versus o r b i t a l phase. C i r c l e s are from 1980-81 DAO data, stars from 1982-84 DAO data and f i l l e d c i r c l e s from CFHT 1984 data . 061 191 Table 4.04 Orbit parameters from BMDP f i t to He II X46B6 emission r a d i a l v e l o c i t y curve. Elements Orbit Solution Extra Radial Velocity Term Period (days) 5.60172 (held) 5.60172(held) TO (JD 2440000+) 1869.17 (held) 1869.I7(held) V0 ( kmsec"1 ) 0.0 0.0 K ( kmsec"1 ) 76.2(20) 55.2(15) Flow Velocity ( kmsec 1 ) 52.4(15) Flow Angle(°) a f i t 0.0 15.1 89.4(10) 0.0 13.6 streaming velocity from one of a variety of p o s s i b i l i t i e s (e.g. Roche Lobe overflow, s t e l l a r wind, etc ). This can be simply incorporated in the f i t t i n g by including an extra v e l o c i t y term ( v r a , 3 i a i ) * n t n e expression used in the BMDP f i t to the measured rad i a l v e l o c i t i e s . The form of the function to be f i t t e d i s now 192 V f i t = V o r b i t a l + V r a d i a l cos( flow angle + phase*2ir ) The r e s u l t s of such a f i t are shown in the t h i r d column of table 4.04 . They show that a good f i t can be obtained using a v e l o c i t y form such as the one.above. Knowing that the mass ra t i o i s <*2 and that the v e l o c i t y amplitude of the primary centre of the emission region ( assuming co-rotation ) to about half way between the two components. 4.4 EQUIVALENT WIDTH MEASURES It has been suggested numerous times in the l i t e r a t u r e that the He II X4686 l i n e i s subject to large variations ( Bolton [1975] , Walker et a l [1978] ). In order to v e r i f y t h i s the equivalent widths of the corrected p r o f i l e s were measured by determining l i m i t s to the extent of each p r o f i l e and using a Simpson's Rule Integration Routine to calculate the area. When these results were plotted two sets of observations f e l l well off the smooth curve defined by the remainder of the data. The August 1982 observations consist of f i v e nights of observation, while the Spetember 1982 data was of three nights duration. The f i r s t set were corrected by reducing the equivalent widths by 15% and the second had their equivalent widths reduced by 40% . The data then coincided with the rest of the observations. No such variation was seen in the absorption l i n e s in the same i s 75kmsec the V o r b i t a l then fixes the location of the 193 spectra and i t seems these are real changes in the He II emission equivalent width. Walker et a l [1979] reported similar changes in equivalent width between data taken at two d i f f e r e n t epochs ( 1972 and 1975 ). It would of course have been interesting to see i f these increases were associated with tr a n s i t i o n s to the high state. Unfortunately no published X-ray observations of Cygnus X-1 are available for any of the data presented here. The equivalent widths thus derived ( l i s t e d in table 4.03 ) were averaged in bins of 0.1 of the o r b i t a l phase and these values are l i s t e d in table 4.5 . They are plotted in figure 4.08 and i t i s obvious that there i s a previously undetected v a r i a t i o n with o r b i t a l phase. Possible mechanisms for producing t h i s v a r i a t i o n w i l l be discussed in the next chapter. The August and September 1982 equivalent widths had the same o r b i t a l phase variations as the remainder of the data even though the actual values were much larger. The halfwidths of the corrected X4686 l i n e was also measured. In order to guard against instrumental v a r i a t i o n producing changes, each value was divided by the measured halfwidth of the He I X4471 l i n e from the spectrum of 19 Cepheus taken on the same night. 19 Cepheus i s a single star and no variations in the v s i n i are observed. The normalized halfwidths binned on the o r b i t a l phase are l i s t e d in table 4.05 and shown in figure 4.09 . T a b l e 4.05 He I I X4686 e q u i v a l e n t w i d t h s and h a l f w i d t h s as a f u n c t i o n of o r b i t a l phase. Phase A l l DAO Mean EW _[ mA ]_ 547.53 H a l f w i d t h Phase 0.0-0.1 0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0 F r a c t i o n of Mean 1 .000 1 .172 1 .073 0.861 0.859 0.846 0.910 1 .022 1 . 108 1 .067 N o r m a l i z e d 1 .43 1 .38 1 .09 1.12 0.98 1 .47 1 .48 1 .29 1.14 1 .56 195 Figure 4.08 He II X4686 equivalent widths versus o r b i t a l phase. Stars correspond to DAO data. Squares correspond to CFHT data . Connected crosses are for to two runs in 1982 with EW 15% and 40% larger than mean. N o r m a l i z e d E q u i v a l e n t W i d t h 5 1 1 . 5 —I - ' ' • s*>i o '-\ ' ' ' r— ? M \ O Ul o -J ro © * © / / .©* ©; G / • / © © :© / < © *. ©° ©\ \ \ / / / / \ © © '© © © - o V \ \ © © . © / /© : © © M M M ° ©: M :G © : ©J — i 1 : i _ _ Ul 961 1 97 Figure 4.09 He II X4686 halfwidths versus o r b i t a l phase. 1 9 8 -1 - 1 1 - 1 1 - 1 1 i • • ©' ...© •\* • — • 1 6 — i i i i i S ' T T d 9 D 6 T / T - X 6Fi3 H 1 P I m i I B H CO QO OJ in as _E 0_ CO o o nj 199 4.5 THE Ha DATA Simultaneously with the CFHT observations data was obtained on the DAO 72" centered at Ha. Ha has been the subject of previous observations and study ( Brucato and Zappla [1974], Hutchings et a l [1974,1979b] ). The accepted explanation of the p r o f i l e seen i s that i t may be regarded as a single broad emission peak with a variable central absorption due to a wake e f f e c t ( Hutchings [1979] ). Unfortunately again the data was of rather poor quality and futher observations seemed appropriate. The f i r s t stage of analysis of the data i s similar to that for the He II emission l i n e . 19 Cepheus was again selected from the available standards shown in figure 4.10 as being most appropriate to use for correction of the Ha p r o f i l e . Shown in figure 4.11 are the Cygnus X-1 Ha p r o f i l e s , a f t e r a l l preliminary reduction, shifted into the rest frame of the primary. The Ha p r o f i l e for 19 Cep was f i t t e d with a smoothed curve and t h i s p r o f i l e was then subtracted from the Cygnus X-1 Ha p r o f i l e s of figure 4.11 . These f i r s t stage corrected p r o f i l e s are shown in figure 4.12 as the s o l i d l i n e p r o f i l e s . Stars at t h i s spectral type and luminosity class are known to have Ha in emission ( Rosendhal [1973], review of Snow and Morton [1976] ). A good example i s the type I P Cygni Ha p r o f i l e seen in the 09.71b star $ Ori ( Conti and Leep [1974] ). The p r o f i l e s in figure 4.11 and 4.12 show what appears to be a stationary component of emission redward of the centre of the whole emission 200 Figure 4.10 Standard star spectra (red region) . Indicated are two newly noticed emission l i n e s . 2 0 1 188001 ^ — - ^ i ^ ^ ^ Y*^~ • HD 188209 ^ ^ - ^ ^ ^ — r ~ Y * ~ ~ • 19 Cep Cyg n—*^TY^^—"y"^  " 6 7 Oph I I I I u 6 3 8 8 6 4 8 8 6 5 8 8 6 6 8 8 Wavelength (Angstrom) 202 Figure 4.11 Ha P r o f i l e s shifted to primary's rest frame. 203 1 1 1 — : — i 1 1 1 0.663 *~~~~+<ltf(^^ ^ v y ~ v v ~ Q Q 3 4 ^-~*~-«**^^ -Try—- Q Q S ] 0.031 0.193 0.209 0.370 ^lTY^M^^-^l 0.386 ^ ^ i r T r y r T W ^ ^ — H f ~ — 0 . 5 4 7 • ^ W ^ H^^^^T ^ ^ r ^ 0-566 *~* ,*<^^ 0.729 ^ •^^ffY^^^^ 0 , 9 0 6 ^ p ^ ^ <y* 0.083 ^ - ^ y r r ^ —np~~o.io2 6388 6438 6488 6538 6588 6638 6688 6738 Uavelength (flnnsTroa) 204 Figure 4.12 Ha p r o f i l e s corrected with 19 Cep p r o f i l e ( s o l i d curves) and f i t t e d P Cygni p r o f i l e at phase 0.209 (dashed l i n e ) . 205 Wavelength (flngstrot) 206 p r o f i l e . This can be interpreted as the emission peak of a type I P Cygni p r o f i l e ( Beals [1951] ). The p r o f i l e at phase 0.209 was taken as the one showing the clearest contrast between the P Cygni component of the emission and any contribution connected with the motion of the secondary. At t h i s phase any emission associated with the secondary would have the maximum v e l o c i t y blue s h i f t . Figure 4.12 shows thi s f i t t e d P Cygni p r o f i l e plotted as a dashed l i n e over the f i r s t stage corrected p r o f i l e s . The s o l i d l i n e in figure 4.13 shows the net Ha p r o f i l e after the f i r s t stage correction, while the dash curve shows the corrected He II X4686 curve taken at CFHT on the same night. The narrow features observed in the red spectrum are the t e l l u r i c l i n e s found around Ha and their presence makes i t very d i f f i c u l t to measure the f i n a l Ha p r o f i l e l i n e position and thereby compare i t s r a d i a l v e l o c i t y curve to that of ' the He II emission. The two p r o f i l e s however, except for differences in strength, show remarkably similar forms over the cycle observed. It would therefore seem from these p r o f i l e s that the two l i n e s have a common o r i g i n contrary to the suggestion of Hutchings et a l [1974]. 4.6 THE Ha PROFILE OF THE PRIMARY The primary's i n t r i n s i c l i n e p r o f i l e was obtained above through a number of convoluted steps. In figure 4.14 there are three p r o f i l e s v i s i b l e . The dot-dashed absorption l i n e i s the assumed 19 Cep absorption p r o f i l e of Ha, the dotted 207 Figure 4.13 Ha ( so l id l ine ) and He II X4686 (dashed l i n e ) corrected for underlying p r o f i l e of primary for simultaneous observations at DAO(red) and CFHT(blue). 2 0 8 Velocity } km/sec I 209 Figure 4.14 Ha absorption component from f i t to 19 Cepheus p r o f i l e ( dot-dash l i n e ), Ha from f i t to corrected p r o f i l e ( dotted l i n e ) and sum of the two ( s o l i d l i n e ) = HDE 226868 i n t r i n s i c Ha p r o f i l e . 2 1 0 21 1 emission l i n e i s the f i t t e d P Cygni emission p r o f i l e and the s o l i d l i n e i s the sum of these two. This sum i s the net Ha p r o f i l e of HDE 226868. Hearn [1975] has indicated a technique for determining the region from which the Ha emission originates. C a s s i n e l l i et a l [1978] have pointed out a small error in the application of the techique as outlined by Hearn [1975], The method assumes that the p r o f i l e observed is the result of an absorption p r o f i l e originating with the primary and a component due to a spherically symmetric extended envelope (the s h e l l ) . The Ha li n e i s the result of the 3=>2 tr a n s i t i o n in Hydrogen. Assuming that the s h e l l has an inner radius r and a thickness Ar then the absorption component of the p r o f i l e has an equivalent width proportional to the number of absorbers in the l i n e of sight, which i s W = X 2 7 r e 2 f n 2Ar / m c 2 cl 6 where n 2 cm"3 i s the average density of hydrogen atoms in level 2 f i s the absorption o s c i l l a t o r strength for the Ha l i n e 7re 2 / mc i s the intergrated absorption coefficent of a c l a s s i c a l atom X i s the rest wavelength of the Ha l i n e c i s the speed of l i g h t The Ha emission component comes from the region of the s h e l l v i s i b l e to the observer and not on the l i n e of sight to the 212 primary. This intensity i s given by I = n 3A 3 2 ( 4 7 r r 2 - 2 7 r r 0 2 ) Arh?/4ir ergs sec - 1 sterad" 1 where n 3 i s the average density of hydrogen atoms in l e v e l 3 A 3 2 i s the Einstein spontaeous t r a n s i t i o n p r o b a b i l i t y for Ha hv i s the energy of a Ha photon r 0 i s the radius of the primary This intensity i s observed as an equivalent width given by W g = X 2n 3A 3 2 ( 4 7 r r 2 - 2 7 r r 0 2 ) A r hv / c 4 7 r 2 r 0 2 B where B = the Planck function at the Ha frequency for the e f f e c t i v e temperature of the star The r a t i o of W to W gives the r a t i o e a 3 n 3/n 2 = (W / W ) * 0.549 * 1 / ( [ r / r 0 ] 2 - 0.5 ) where the Planck function has been evaluated at a temperature appropriate to the primary of 27500°K. If the populations of the s h e l l are primarily determined by the radiation f i e l d from the primary then n 3/n 2 = (CJ 3/W 2)( A 3 1 / [ A 3 1 + A 3 2 ] )( exp[ " W k T s t a r ]) where co i s the s t a t i s t i c a l weight of the le v e l ( 2n 2 ) For a 27500°K radiation f i e l d t h i s gives a r a t i o of 0.619 This can now put into the e a r l i e r equation for n 3/n 2 to 213 f i n a l l y give r = roV/(W /Wj * 0.887 + 0.5 Figure 4.15 shows as a s o l i d l i n e the derived P Cygni p r o f i l e , while the dashed-dot l i n e i s a NLTE Auer and Mihalas [1972] Ha theore t i c a l p r o f i l e for a log g = 3.3 and T = 30000°K star broadened to 95 kmsec - 1 and the dotted li n e i s a p r o f i l e from C o l l i n s ' [1977] LTE p r o f i l e s with i = 40° and a rotation v e l o c i t y = 0.2 of c r i t i c a l ( t h i s gives the correct v s i n i value ). A number of investigations of 0 stars indicates that neither NLTE or LTE models s a t i s f a c t o r i l y f i t any but a few select l i n e s and are t y p i c a l l y worse for the Balmer lines < Auer and Mihalas [1972], Underhill [1983], Takada [1977] ). Using the NLTE case ( the LTE p r o f i l e i s not very d i f f e r e n t ) as representing the primary's absorption p r o f i l e and assuming the emission p r o f i l e i s symmetric then the horizontal hatched area in figure 4.15 i s the emission equivalent width while the v e r t i c a l hatched area i s the absorption equivalent width. Measuring these areas gives a r a t i o of W /W * 2.5. Hence the inner radius of the Ha s h e l l i s derived as 1.37R*. This i s quite close to the value of 1.3 R* given as the radius of an ionized envelope about the primary from the IR obser-vatlons of Persi et a l [1980]. The X-ray source Wray 977 i s also believed to have a Ha s h e l l beginning at a radius fe 2 R* ( Parkes et a l [1980] ). 214 Figure 4.15 Derived Ha P Cygni p r o f i l e ( so l id l i n e ) , Auer and Mihalas NLTE p r o f i l e (dash-dot l ine ) and C o l l i n s LTE p r o f i l e (dotted l i n e ) . U e l o c i t y ( k m / s Q C ) IT) 216 4.7 THE HYDROGEN ABSORPTION LINES The equivalent widths of the hydrogen absorption l i n e s were measured in the previous chapter and showed no variations when binned according to o r b i t a l phase ( 5.6 days ). Recently Priedhorsky et a l [1983] have found a p e r i o d i c i t y in the long term X-ray monitoring of Cygnus X-1 of 294±4 days. Kemp et a l [1983] post-facto claim to have detected variations in the B photometry and po l a r i z a t i o n with the same period. In order to test whether t h i s variation i s seen in our data the equivalent widths for the He I X4713 and 4471 and the H/3 and Hy was average over each observing run and these values and the appropriate mean X-ray phases are l i s t e d in table 4.06 . The data, with the appropriate errors, are plotted in figure 4.16 a & b. It i s clear from t h i s that the Balmer lines seem to be considerably stronger during X-ray zero phase whereas the He I l i n e s seem to be unchanged. Kemp et a l [1983] f i n d only a change of 0.005 magnitudes in t h e i r B photometry over the 294 day period and t h i s would c e r t a i n l y be well below the detection l i m i t for equivalent width variations. The results shown in figure 4.16b are quite interesting i f i t i s remembered that the Balmer li n e s are the result of an absorption component from the primary plus a weak emission. When binned on o r b i t a l phase the equivalent width variations were weak or non-existent which would indicate no v a r i a t i o n from the primary p r o f i l e i t s e l f . The emission contribution probably has the same o r i g i n as the He II and, 217 T a b l e 4.06 E q u i v a l e n t W i d t h s Binned on t h e 294 day P e r i o d . X-ray He I He I H0 H 7 E r r o i Phase X4471 X4713 + Mean EW mA 645.23 273.06 1232.04 1744.99 N o r m a l i z e d 0.492 0.969 0.939 1 .036 0.977 0.04 0.314 0.979 0.968 0.834 0.958 0.07 0.467 1 .041 1 .074 1 .049 0.999 0.05 0.620 0.968 1 .000 0.968 0.906 0.04 0.802 0.980 0.979 0.942 0.894 0.05 0.724 1.015 1 .034 0.988 0.967 0.05 0.834 1 .005 1 .027 1.012 0.988 0.04 0.252 0.934 1 .004 0.04 0.009 1 .023 1 .041 1 . 166 1.216 0.03 some o f , the Ha e m i s s i o n . As i t has been found u n l i k e l y t h a t X-ray f l u x from the Cygnus X-1 secondary would produce enhanced mass l o s s from t h e p r i m a r y ( London and F l a n n e r y [1982] ) t h e l o g i c a l c o n c l u s i o n seems t o be t h a t what i s seen i s t h e c o u p l i n g between mass l o s s and a c c r e t i o n . For some r e a s o n the mass l o s s from the p r i m a r y i s modulated and as b o t h t h e hydrogen e m i s s i o n component and the X-ray e m i s s i o n s t r e n g t h depend on the amount of mass l o s s , b o th are m o d u l a t e d a l s o . At X-ray minimum l e s s m a t e r i a l i s l o s t from t h e s t a r , hence t h e r e i s l e s s Balmer e m i s s i o n , t h e r e f o r e t h e a b s o r p t i o n l i n e e q u i v a l e n t w i d t h i n c r e a s e s , as seen. T h i s i s f i n a l l y v e r y c l e a r e v i d e n c e f o r the l o n g h e l d 218 Figure 4.16 upper: He I X4471 and 4713 equivalent widths as function of the 294 day X-ray per iod , lower: Ha and H7 equivalent widths as function of the 294 day X-ray p e r i o d . Normal I f id Equivalent Mldth • • 9 1 1.1 1.2 Normal I f id Equiva lent Uldth 0.9 1 1.1 1.2 — 1 — — ». t S to KD 220 belief that mass loss can power an X-ray source. The reason for the primary changing i t s mass loss rate is not c l e a r . One p o s s i b i l i t y i s that a t h i r d body in the system perturbs the g r a v i t a t i o n a l f i e l d between the primary and secondary. No evidence for extra absorption from such a star i s seen in any of our spectra or in the power spectrum of the r a d i a l v e l o c i t y curve. The fact that a 5.6 day p e r i o d i c i t y i s also seen in the X-ray data ( Holt et a l [1976,1979] ) makes the p o s s i b i l i t y of a t h i r d body less l i k e l y . The p o s s i b i l i t y of a precession in the system from either the compact object, the primary or from a t i l t e d accretion disc i s discussed by Priedhorsky et a l [1983]. The l a t t e r two p o s s i b i l i t i e s turn out to have time scales on the order of a year but such calculations are necessarily considerably s i m p l i f i e d . However i t should be kept in mind that there i s no evidence for a disc about the secondary in Cygnus X-1, i t i s d i f f i c u l t to think of a scenario where the rotation axis of the primary i s very d i f f e r e n t from that of the system, and there i s no evidence for the expected associated v a r i a t i o n in the halfwidths of the primary's absorption l i n e s . Our finding that the hydrogen emission varies on the same period as the X-ray flux would tend to support models in which the primary i t s e l f i s variable. Dolan et a l [1979] have already suggested that to explain the X-ray high and low state the primary could be pulsating in an array of g mode o s c i l l a t i o n s which occasionally a l i g n and enhance mass 221 l o s s . In fact photometric o s c i l l a t i o n s have been reported in Cygnus X-1 during a t r a n s i t i o n into the high state ( Natali et a l [1978] ). It may be that one mode of o s c i l l a t i o n or a beat of di f f e r e n t modes re s u l t s in a dominant period of 294 days that induces a modulation in the mass loss and therefore the X-ray output, via accretion. A much more extreme case of a change in the X-ray emission being linked to the outflow from the primary, in fact the changing primary radius, i s the eccentric orbit LMC X-ray source 0535-668 ( Howarth et a l [1984], Hutchings et a l [1985] ). Chapter 5 EMISSION MECHANISMS Although the Hell X4686 and Ha emission has been well known since the e a r l i e s t days of the Cygnus X-1 op t i c a l i d e n t i f i c a t i o n ( Bolton [1972a,b], Smith et a l [1973] ) l i t t l e has been done to explain their o r i g i n . The He II X4686 i s c l e a r l y not a common feature in the spectra of stars at t h i s spectral type as can be seen in Appendix A. The model put forward to explain the emission i s that i t arises from material that has overflowed the Roche Lobe and is f a l l i n g onto the secondary. The resultant heating in th i s process presumably produces the right conditions for the observed emission l i n e s to be produced. This type of model has been variously suggested by Smith et a l [1973], Hutchings et a l [1973], Bolton [1975] and Oda [1977]. There are in the l i t e r a t u r e at present fiv e d i f f e r e n t ( l i k e l y ) mechanisms suggested for the production of the emission observed in massive X-ray binaries. These w i l l be discussed below and the one most l i k e l y applicable to Cygnus X-1 w i l l be futher examined. 5.1 X-RAY HEATING OF THE PRIMARY Milgrom [1977] and London and Flannery [1982] have suggested that emission can come from the secondary facing side of the primary. This emission would be the res u l t of X-ray i r r a d i a t i o n of the surface producing a temperature increase 222 ( e f f e c t i v e l y changing the spectral type for that side of the primary). There are three reasons for not believing t h i s to be the major contributor to the emission seen in Cygnus X-1. F i r s t l y one would expect the equivalent widths of the emission l i n e s to be largest near phase 0.5 where the maximum amount of the affected side of the primary i s seen and minimum near phase 0.0 . This i s not seen, in fact just the opposite behaviour i s seen in the He II X4686 l i n e . Secondly, t h i s mechanism can not produce a large component of ve l o c i t y directed towards the secondary as i s inferred i s neccessary from the observed p r o f i l e s . The major v e l o c i t y component present in t h i s model would be that due to rotation of the primary. Thirdly there i s no evidence for a variation of spectral type, as defined by ra t i o s of sensitive l i n e s , with phase . 5.2 OVERFLOW ONTO THE SECONDARY This has been the most widely suggested mechanism for producing the emission and has been most successful in i t s application to cataclysmic variables. The primary loses mass either due to evolutionary pressure or to decreasing o r b i t a l seperation ( by say g r a v i t a t i o n a l radiation ) and t h i s mass is most—easily lost through the Lagrangian Point L1 , located between the primary and secondary, because of the minimum in the g r a v i t a t i o n a l potential well at t h i s point. Lubow and Shu [1975] have made detailed c a l u l a t i o n s of t h i s mechanism and find that the overflow occurs in a very narrow beam of 224 nearly constant width that terminates in a disc around the secondary for massive X-ray binaries. A schematic diagram for what t h i s model predicts for Cygnus X-1 (taken from t h e i r table 3) i s shown in figure 5.01 . There are two reasons for not believing that t h i s i s the major means of producing the observed emission. Taking the value of the mass r a t i o for Cygnus X-1 as =*0.5 from Chapter 3 and using the values given in table 2 of Lubow and Shu [1975] for a detached binary of that mass r a t i o , the radius for their predicted disc around the secondary i s 0.0683 of the orbit seperation, or 2.8 R^. This value i s somewhat smaller than the accretion disc l i m i t s set by Paczynski's [1977] study of three body orbits about the central object. This i s a quite substantial disc and because of i t s high temperature, due to X-Ray heating, should be observable. The standard 'alpha-disc' models ( after Shakura and Sunyaev [1973] ) predicts that the temperature d i s t r i b u t i o n in the disc follows T(r) = T 0 r ~ 3 / / 4 . Assuming that at a l l r a d i i of interest the disc radiates as a blackbody and knowing the inner disc radius ( r 0 ) and the outer disc l i m i t (r,) then i t i s a simple integration to calc u l a t e the emergent flux from such a model ( Pringle [1981 ] ). One merely integrates the blackbody flux for each increment of disc between the minimum and maximum radius. The maximum extent of the disc determines the low frequency cutoff of the disc. Estimates for the sizes of accretion 225 Figure 5.01 A schematic of the Lubow and Shu [1975] model with mass r a t i o nearest to that estimated for Cygnus X - 1 . 227 discs are available from Paczynski [1977], Lubow and Shu [1975] and Line and Pringle [1976]. They indicate for a mass ra t i o of » 0.5 a radius for the accretion disc of * 3 to 20 R @ ( or 2 x 10s to 8 x 10s Schwarzschild r a d i i {r g} ). The inner bound i s less well determined but Priedhorsky et a l [1979] suggest i t i s greater than 20 r . The'central T 0 can be obtained from Pringle's [1981] estimation for i t of T 0 = [ 3GMM/87TRO 30 ] 0 ' 2 5 where M is the accretion rate M i s the mass of the compact object a i s the Stefan-Boltzmann constant Note that T 0 i s not a physical temperature but merely a parameter. The central region of the disc may in fact be divided into two temperature regions. The very inner part having an electron temperature «* 109K ( Ling et a l [ 1983] ) but not radiating as a blackbody and being the source of the hard X-ray flux seen in Cygnus X-1. Shapiro et a l [1976] estimate that the t r a n s i t i o n to the cooler standard disc would occur at « I00r . Thus estimating r 0 * 100 and r, » 106 and the range of temperature T 0 as 3 x 108 to 6 x 107 °K ( approximate range of uncertainty in the parameters ), then shown in figure 5.02 are the flux spectra expected for such discs ( Beall et al 1984] ) together with that of the primary ( T = 27500°K blackbody ). From figure 5.02 i t can be seen that the maximum contrast between the disc and the s t e l l a r flux 228 Figure 5.02 The Flux Spectra of Accret ion Discs at a distance of 2.5 kpc. Two d i sc models with T 0 indicated ( dotted and dash-dot l i n e s ) and flux expected from HDE 226868 ( s o l i d l i n e ) . 230 occurs at wavelengths in the far u l t r a v i o l e t . In fact at about 1200 A the flux from a disc with temperature of 3 x 108K i s of the same order as that coming from the luminous primary. Pineault [1984] finds similar estimates for the v i s i b i l t y of the disc from his models. Treves et a l [1980] have obtained UV spectra with the IUE of Cygnus X-1 but find that the entire UV flux can be well modeled with a 27000°K blackbody and a E(B-V)=1.05 . This implies that a l l the UV flux comes from the primary. Beall et a l [1984] have searched in the infrared for an excess flux from a disc but they f i n d only that expected from the primary. It must be concluded therfore that i f the temperature structure of the outer parts of accretion discs are understood, the observations indicate that there is no substantial disc around the secondary in Cygnus X-1. The i n f a l l of matter necessary to explain the X-ray emission can be explained by di r e c t accretion of material from the mass loss of the primary ( Shapiro and Lightman [1976], Petterson [1978] ). A second problem with the prediction of the disc model is with the magnitude of the v e l o c i t i e s predicted at the point where the stream s t r i k e s the disc, and from where Hell emission i s expected to originate. For the Cygnus X-1 case t h i s value i s (from Lubow and Shu [1975] table 3 ) =900 km/sec. For our l i n e of sight this would imply a maximum observed r a d i a l v e l o c i t y of 580 km/sec ( i = 40° ) which i s far larger than found from the observed He l l v e l o c i t y curve in Chapter 4. Therefore, although t h i s model seems to well 231 describe the cataclysmic variables where a stream from the low mass companion f a l l s on the white dwarf ( Warner and Peters [1972] ) i t seems unlikely that i t i s appropriate in the case of Cygnus X-1. 5.3 TRAILING SHOCK MODEL Strong absorption components blue shifted r e l a t i v e to the H and He absorption l i n e s from the primary are found in the spectra of some X-ray binaries at phases after the secondary has crossed the l i n e of sight to the observer (i.e phases 0.5 to 0.8 ). The effect can be p a r t i c u l a r i l y strong in the Hel X5876 and i s c l e a r l y seen in the X-ray binaries HD153919 ( Fahlman and Walker [1980] ) and Vela X-1 ( Bessel et a l [1975] ). Fransson and Fabian [1980] propose a model in which the s t e l l a r wind escaping from the primary in the dir e c t i o n of the secondary passes through a region near the X-ray source where the ionizing X-Ray flux i s s u f f i c e n t l y high that the ions which produce the opacity to accelerate the wind by radiation pressure, namely CIV and SilV, are ionized into higher states. This ionized component of the wind therefore ceases to accelerate and coasts on through the ionized volume. As the X-ray source moves on in i t s orbit t h i s material i s l e f t behind and eventually recombines and i s subject to acceleration again. However the wind coming d i r e c t l y from the primary which has been subject to continous acceleration runs up against this material. Hence 232 we have a faster moving, less dense gas c o l l i d i n g with a slower, denser medium. These are the c l a s s i c conditions for a shock front to form. The results of Fransson and Fabian [1980] program to simulate t h i s scenario ( given in their figure 2 and 3 ) show a strong shock region t r a i l i n g the X-ray source in the o r b i t a l plane. The conditions derived ( T~105K , n ^ l O 1 2 cm"2 ) are suitable for Hell l i n e s to be enhanced and the expected v e l o c i t i e s are ^ 0.2 V ) where esc V * 2000 km/sec. The v e l o c i t i e s predicted ( =*400 km/sec ) esc do agree with those measured for the t r a i l i n g absorption feature in Vela X-1 (Bessel [1975], Zuiderwijk [1974]) and HD153919 (Fahlman and Walker [1980]). In Cygnus X-1 these features would be seen in emission due to the lower i n c l i n a t i o n of the system. However the amplitude of the Hell X4686 r a d i a l v e l o c i t y curve for Cygnus X-1 has a much smaller amplitude ( =*75 km/sec ) than would predicted ( 250 km/sec ). As the shock i s produced by the Ram Pressure of the s t e l l a r wind on the slower moving material i t s strength i s dependant on pAv . For comparison the mass loss rate of Cygnus X-1 and HD 153919 are a factor of four d i f f e r e n t (Hutchings [1976]) and the distances of the compact companions from the s t e l l a r surface are 23 R @ ( see Table 5.01 ) and 9RQ ( Fahlman and Walker [1980] ) respectively. Thus the the density of the wind at the distance of the secondary i s a factor of 10 larger in HD153919 than Cyg X-1 and t h i s may explain why ram pressure is appropriate in HD 153919 and not Cyg X-1. 233 5.4 EMISSION FROM THE DISC Hutchings et a l [1974] suggested that the width of the Ha p r o f i l e was best explained by having the emission originate in a rapidly rotating disc about the secondary. The p r o f i l e decomposition in Chapter 4 shows that a more common explanation is just as viable. It may be possible to perturb part of the disc ( by a narrow stream for example ) so as to produce emission with a v e l o c i t y component that would give a phase dependence similar to that seen in figure 4.7. In standard disc models test p a r t i c l e s in orbit about the compact companion move in c i r c u l a r orbits ( Shakura and Sunyaev [1973], Lubow and Shu [1975] ). Thus for a secondary of mass 10 M~ and at a maximum disc radius of » 10 R. ( Paczynski [1977] ) the outer disc v e l o c i t y i s * 450 kmsec"1, or a projected r a d i a l v e l o c i t y of 290 kmsec"1 when viewed from i = 40°. This again i s larger than the observed K amplitude of the He II emission r a d i a l v e l o c i t y curve in Cygnus X-1. Reducing the radius of a disc would increase t h i s rotation v e l o c i t y while reducing the mass of the secondary would decrease i t . However a reduction of more than an order of magnitude in the mass of the secondary would be needed to bring the ve l o c i t y down to the observed K amplitude of 74 km sec" 1 seen. This i s not consistent with other knowledge of the system. 234 5.5 ENHANCED STELLAR WIND In single stars the s t e l l a r wind mass loss i s assumed to be s p h e r i c a l l y symmetric ( Conti [1978], C a s s i n e l l i [1979] ) but in the case of a close binary the presence of a companion d i s t o r t s the potential f i e l d and may result in large enhancements of mass flow towards the secondary. Friend and Castor [1982] have studied the e f f e c t s of a compact companion ( i . e . through gravity and continuum radiation pressure) and the c e n t r i f u g a l force due to o r b i t a l motion on the symmetry of the wind. They find that when these e f f e c t s are included the character of the wind i s a strong function of the size of the primary r e l a t i v e to i t s c r i t i c a l p otential lobe. As the primary comes close to f i l l i n g i t s Roche Lobe the mass loss in the d i r e c t i o n of the secondary becomes enhanced. This idea neatly combines the two popular mechanisms of a s t e l l a r wind and Roche Lobe overflow for providing material to power X-ray sources. The S t e l l a r Wind progressively looks more l i k e what i s normally thought of as Roche lobe overflow as the primary star expands to f i l l i t s Roche Lobe. One of the s p e c i f i c stars that Friend and Castor [1982] model i s Cygnus X-1 and their mass loss rate vs angle from the axis of t h i s binary i s shown in figure 5.03. There were a number of reasons for thinking t h i s might be a good explanation for not only the source of accretion material but also as the o r i g i n of the observed emission l i n e s . The difference between the spectrum of an 09.7lab 235 Figure 5.03 Mass loss rate for Cygnus X-1 vs Angle from Axis of Binary ( Friend and Castor [1980] ) 237 spectrum and an 051f ( see Chapter 5 ) i s primarily in that the H and Hell lines are in emission in the l a t t e r and in absorption in the former. The reason for t h i s i s that the mass loss rate i s much larger in the Of stars and therefore the wind has a higher density, and the central star i s hotter thereby providing a more intense radiation f i e l d . K l ein and Castor [1978] have produced dynamical models of the H and He II l i n e s in the expanding envelopes of Of stars . Using the observed r a t i o of the equivalent widths of Ha to He II X4686 in Cygnus X-1 of =* 2 ( see figure 4.12 ), th e i r models and observation would require a radiation f i e l d of T > 40000°K. Although the primary in Cygnus X-1 could not produce such temperatures, heating by the X-ray source in the region between the primary and the secondary may generate the right conditions. This location for the emission i s also supported by dynamical considerations. The centre of mass for the system l i e s about 0.3 of the binary separation from the primary. Therefore gas in the system located halfway between the primary and secondary would have a v e l o c i t y amplitude about the same as the primary but 180° out of phase. If t h i s gas also had an outflow component this would introduce a phase effect ( i . e . i t would not be exactly out of phase ), as observed in the He II X4686 r a d i a l v e l o c i t y curve. 238 5.6 THE MODEL This l a s t suggested model for the system seemed worthy of further study and so a code was written which attempted to model the l i n e p r o f i l e s expected for an enhanced s t e l l a r wind model of Cygnus X-1. Following Friend and Castor [1982] there i s a region between the secondary and primary through which substantially more mass i s lost than in any other d i r e c t i o n . This region must be quite thin as any material flowing at any distance out of the binary plane w i l l be subject to a g r a v i t a t i o n a l restoring force returning i t to the plane ( Lubow and Shu [1975, 1976] ). This region of the enhanced mass flow and the mass loss vs angle from the binary axis were fixed as that calculated by Friend and Castor [1982] (see figure 5.04) The region was for computational purposes divided into a grid of 50 one degree elements from -25° to +25° from the axis of the binary system and in 100 increments of the radius beginning at the surface of the primary. Each increment of the radius was one f i f t i e t h the binary separation so that the contribution out to twice the binary separation was included. Knowing the mass loss rate at each angle the density along that l i n e could be determined by knowing the variation of velocity with radius. Various v e l o c i t y laws exist in the l i t e r a t u r e ( see review by C a s s i n e l l i [1979] ) but the most appropriate in t h i s case would .seem to be that used by Friend and Castor [1982] and by MacGregor and V i t e l l o [1982]. They both find that in the region between the primary and secondary in a 239 Figure 5.04 A schematic of the Enhanced S t e l l a r Wind Model for Cygnus X-1 as described in text . 241 X-ray binary the v e l o c i t y law i s approximately l i n e a r l y related to the radius. The form of the v e l o c i t y law was then fixed as V(r) = V(D) ( r / r s f c a r - 1 ) where V(D) = v e l o c i t y at the X-ray source r . = radius of star star r = radius from primary's centre The density follows from t h i s p(r) = M/( 47rr 2 V(r) ) where M= mass loss at each angle from axis r= distance from primary centre v(r)= v e l o c i t y of wind at r The v e l o c i t y law assumed i s quite d i f f e r e n t from that conventionally accepted for single stars ( Castor et a l [1975] = CAR ) of v • v i n f 1 " R s t a r ' r > where v^ n£ = terminal v e l o c i t y of the wind R . = radius of the star star r i s the distance from the centre of the star For a v ^ n f * 2000 kmsec"1 the CAR vel o c i t y law gives a ve l o c i t y at the secondary ( 2 R g t a r ) of * 1000 kmsec"1. MacGregor and V i t e l l o [1982] find in their theoretical study that the presence of an X-ray emmitting secondary can change the v e l o c i t y of the wind at the secondary. When they increased the X-ray luminosity from 0 to 10 3"ergs/sec, the v i n f °^ fc^e w * n ^ w a s r educed by a factor of 3 and hence the 242 v e l o c i t y at the secondary was also lower than what CAR gives. Observationally there i s also evidence that the CAR v e l o c i t y i s too high at the distance of the secondary in some X-ray binaries. White and Swank [1984] find that in order to explain the X-ray l i g h t curve of 4U 1223-62 (= WRA 977 = B2Ia + neutron star ) the V\ ^ must be reduced by a factor of 3 from 1500 to 500 kmsec"1. This lowers the v e l o c i t y at 2 R s t a r to 250 kmsec"1. Parkes et a l [1980] from a study of the P-Cygni p r o f i l e s of WRA-977 conclude that the s t e l l a r wind only reaches a v e l o c i t y of 300 kmsec"1 at 3 R s t a r ' Therefore there seem to be reasons for assuming a v e l o c i t y law for the material moving between the primary and secondary in Cygnus X-1 in which the acceleration i s more gradual than for a normal s t e l l a r wind. The next step is to calculate what fraction of t h i s material i s in the correct l e v e l to produce the He II X4686 t r a n s i t i o n . To rigorously determine the temperature and the ionized f r a c t i o n would require solving the l o c a l ionization balance equation and energy equation ( i . e . a balance between X-ray heating and ionization and radiative cooling and recombination). Fortunately given the assumption that the X-ray spectrum does not change due to absorption by intervening gas and that radiation emitted by the gas escapes, both the temperature and ionization fraction can be expressed as functions of a single parameter £ ( McCray et a l [1984] ). where £ = ( L x / n x D 2 ) ( R2 v(R) / { r 2 v(D) } ) 243 and L x = luminosity of the X-ray source n x = density of wind at the X-ray source D = o r b i t a l separation R = distance from the primary r = distance from the X-ray source v(R) = wind v e l o c i t y at R v(D) = wind v e l o c i t y at the X-ray source Buff and McCray [1974] and Tarter et a l [1969] have made calculations and produced results for the variation of the temperature and ionization as a function of i- for a X-ray source imbedded in a s t e l l a r wind. The form of the X-ray spectrum they use i s dL/de - ( L / e m a x ) * exp[ -( e - e ^ / e ^ ] where e m . = 13.6 eV nun £m = v = 1 0 k e V ax The form of the X-ray spectrum of Cygnus X-1 has been the subject of considerable study ( Oda [1977], Ling et a l [1983], Liang and Nolan [1984] ). Shown in figure 5.05 i s the observed spectrum of Cygnus X-1 ( from Oda [1977] ) and the assumed X-ray spectrum as given by Buff and McCray [1974]. The important region of the X-ray spectrum for ionization and heating i s the < 2.5 keV spectrum as thi s i s where many elements' K s h e l l cross-sections are largest and therefore substantial heating i s produced. Unfortunately the 244 Figure 5.05 Observed X-ray Spectrum of Cygnus X-1 from Oda [1977] (dotted)and that assumed by Buff and McCray [1974] (dashed) in the i r work. 245 nj Q-h i i • i • 1 N. S. X S. N. s. \ \ \ 'A \.\ \ -- v.. \ \ \ \ V \ \ V \ V V V \ \ V — V \ V V 1 . . 1 • 2 log [Energy (keU)] 246 distance of Cygnus X-1 ( 2 kpc ) res u l t s in substantial absorption of these soft X-rays by the i n t e r s t e l l a r medium ( Fireman [1974] ). Also there i s considerable v a r i a t i o n in the i n t r i n s i c soft X-ray absorption. This results in both the form and intensity of the soft X-ray flux not being well known and i t w i l l thus be assumed similar to that adopted by Buff and McCray [1974] and which app l i e s to other X-ray systems. Shown in figure 5.06 are the variations of the temperature and io n i z a t i o n with i- assumed in the following work. Knowing the temperature and from that the ionized fr a c t i o n ( using the fraction of He/H = 0.1 from Allen [1976] ) at each g r i d point now allows c a l c u l a t i o n of the populations of the appropriate levels of He. A further e f f e c t to consider i s the re-absorption of the photons emitted in the 4 => 3 He II t r a n s i t i o n . The most s i g n i f i c a n t re-absorption w i l l happen in the v i c i n i t y of where the emission occurs as the gas there i s denser than that out of the plane of the binary and along the l i n e of sight. Also most of the material out of the plane w i l l be ve l o c i t y s h i f t e d out of the doppler width of the l i n e . The equation for reabsorption from Lang (1980) was used, namely ay=( ire2/ mc ) f ( N / Ai>) -( 1 - expt - hv/kT ] ) where e = electron charge m = electron mass f = o s c i l l a t o r strength for the tr a n s i t i o n N = Number of atoms in the lower state A»> = thermal width 247 Figure 5.06 V a r i a t i o n of temperature with £ (upper). V a r i a t i o n of i on iza t ion f rac t ion with £ (lower). From Buff and McCray [1974]. 249 T = temperature of the gas From t h i s one can calculate the o p t i c a l depth as r—a L v where L i s the pathlength through the absorbing material. In t h i s situation the o p t i c a l depth turned out to be less than one through most of the region of interest and thus the gas can be considered to be o p t i c a l l y thin ( as was assumed for the X-ray f l u x ) . The i n c l i n a t i o n of the system ( i » 40°) and the radius of the primary (18 R^) implies that the closest 4 R Q to the primary in the binary plane are obscured by the primary at zero phase. No variation that could be ascribed to obscuration was found in either the Balmer lines or the He II emission l i n e s as a function of o r b i t a l phase. This implies that there i s no s i g n i f i c a n t contribution to the observed emission from the region close to the surface of the primary where the o p t i c a l depths were the highest. Hence the flow path of the code that models the He II X4686 emission begins by assuming the mass loss vs angle from the l i n e of centres form and the ve l o c i t y law and from t h i s obtain a density at each point in a s p a t i a l grid covering the region of enhanced mass loss towards the secondary. A value of £ i s then c a l c u l a t e d — a t a l l grid points and this gives a l o c a l temperature and fractio n of singly ionized helium. The equilibrium in the 4=>3 tr a n s i t i o n i s then calculated following Rybicki and Lightman [1979] and using the expression for a diluted radiation 250 f i e l d f r o m M i h a l a s [ 1 9 7 8 ] , A l l o w a n c e i s t h e n made f o r r e a b s o r p t i o n . F i n a l l y t h e e m i t t e d f l u x f r o m e a c h g r i d p o i n t i s a p p r o p r i a t e l y v e l o c i t y ( f o r t h a t p h a s e ) s h i f t e d , c o r r e c t e d t o p u t i t i n t h e c e n t r e o f mass f r a m e o f t h e s y s t e m a n d summed t o g i v e a r e s u l t a n t p r o f i l e . A summary o f t h e b a s i c s y s t e m p a r a m e t e r s u s e d i n t h i s work i s g i v e n i n T a b l e 5.01 . The p r e d i c t e d p r o f i l e s f r o m s u c h a m o d e l a r e shown i n f i g u r e 5.07 t o g e t h e r w i t h p r o f i l e s o b t a i n e d a t t h e CFHT a t 2.4 A/mm o r 0 . 0 3 7 A / p i x e l . A l t h o u g h t h e p r o f i l e s do h a v e t h e i r d i f f e r e n c e s i t i s p l e a s i n g t o s e e t h a t t h e s t r e n g t h a n d t h e v e l o c i t y s h i f t s a r e o f t h e c o r r e c t o r d e r a t p h a s e s 0.25 a n d 0.75. The d i f f e r e n c e s a t c o n j u n c t i o n p h a s e s a r e s u b s t a n t i o n a l a n d t h i s may be b e c a u s e o f a much more c o m p l e x v e l o c i t y f i e l d a r o u n d t h e s e c o n d a r y t h a n h a s b e e n a s s u m e d h e r e . The p r e s e n c e o f an o f f a x i s e m i s s i o n c o m p o n e n t ( a s i n SMC X-1, H u t c h i n g s e t a l [ 1 9 7 7 ] ) w o u l d a l s o d i s t o r t t h e p r o f i l e . I t s h o u l d a l s o be remembered t h a t t h e a b s o r p t i o n p r o f i l e f r o m t h e p r i m a r y a l s o p r o b a b l y v a r i e s w i t h p h a s e a n d t h i s e f f e c t h a s n o t b e e n a c c o u n t e d f o r i n t h e o b s e r v e d p r o f i l e s . The o n l y p a r a m e t e r s t h a t w e re m a n i p u l a t e d i n t h i s a n a l y s i s were t h e v e l o c i t y a t t h e X - r a y s o u r c e , w h i c h d e f i n e s t h e m a g n i t u d e o f t h e v e l o c i t y l a w , a n d t h e l u m i n o s i t y o f t h e X - r a y s o u r c e . T h e b e s t m a t c h t o t h e o b s e r v e d p r o f i l e s was o b t a i n e d w i t h a v e l o c i t y a t t h e X - r a y s o u r c e o f 350 km/sec a n d a X - r a y l u m i n o s i t y o f 8 x 1 0 3 7 e r g s / s e c . T h i s v e l o c i t y i s a p p r o x i m a t e l y t h e v a l u e f o u n d by 251 F i g u r e 5.07 M o d e l ( s o l i d ) a n d o f He I I X4686 i n p h a s e s i n d i c a t e d . o b s e r v e d p r o f i l e s ( d o t t e d ) C y g n u s X-1 f o r 252 -500 0 500 Velocity j km/sec I 253 Table 5.01 Assinned Basic System Parameters for Cyg X-1, from Davis and Hartmann [1983] ,Friend and Castor [1982] and Liang and Nolan [1984] Radius of Primary = 18 R 0 Separation = 25.2 R Q O r b i t a l Radius of Secondary = 43.2 RQ Luminosity of the X-ray source = 4.2 x 10 3 7 ergs/sec Temperature of Primary = 31000°K Mass of Primary = 21 M Q Mass of Secondary = 13 M @ Inclination = 40° Friend and Castor [1982] which was derived from a complete solution of the CAK wind equations in the dir e c t i o n of the secondary. They did not include the effect of ionization by the X-rays on the wind however. The value i s also similar to the wind v e l o c i t y at the secondary deduced for the very similar X-ray binary WRA 977 ( White and Swank [1984] ). The X-ray luminosity derived i s also higher than the average value of 4x10 3 7 ergs/sec ( Liang and Nolan [1984] ) seen in Cygnus X-1. This may however be a manifestation of the difference between the assumed form of the X-ray spectrum and r e a l i t y . 254 In p r i n c i p l e t h i s t e c h n i q u e can a l s o be used t o dete r m i n e the mass r a t i o of the system. I f the t h e o r e t i c a l model i s c o r r e c t , then a d i f f e r e n t mass r a t i o changes the v e l o c i t y t r a n s f o r m i n t o the c e n t r e of mass system. Model p r o f i l e s u s i n g a range of mass r a t i o s c o u l d be ge n e r a t e d t o f i n d the b e s t f i t t o the o b s e r v e d d a t a . The c u r r e n t models do not j u s t i f y t r y i n g t h i s . A model u s i n g f u l l l o c a l balance e q u a t i o n s , c o u p l i n g the s t e l l a r wind a c c e l e r a t i o n t o l o c a l c o n d i t i o n s and u s i n g NLTE would produce more a c c u r a t e p r o f i l e s and may make such an attempt u s e f u l . One f u r t h e r check on how r e a l i s t i c the enhanced s t e l l a r wind model i s can be made by u s i n g the e s t i m a t e d mass l o s s and wind v e l o c i t y t o det e r m i n e an e x p e c t e d X-ray l u m i n o s i t y from the secondary. T h i s r e q u i r e s e s t i m a t i n g t h e a c c r e t i o n r a t e from a s t e l l a r w ind, a problem d e a l t w i t h most r e c e n t l y by H e n r i c h s [1983] ( and by S h a p i r o and Lightman [1976], Bondi and Hoyle [1944] ) who g i v e s "ac " % * ( V o r b / V w ) a * < 1 / { 1 + tM p/M x]}* ) * < 1 / { 1 + a [ v o r b / v w ] > where V o r k = o r b i t a l v e l o c i t y of the secondary V„ = r a d i a l v e l o c i t y of t h e wind a t the d i s t a n c e of the w •* secondary a - ( 1 - X{ R p / R s e p }')* and X = 1 f o r c o r o t a t i o n . The X-ray l u m i n o s i t y can then be d e t e r m i n e d from 255 x 0 ac where $ is the efficency For the values appropriate to Cygnus X-1 ( table 5.01 and vQrD- 250 kmsec"1, v w* 350 kmsec"1) the X-ray luminosity would be predicted as $ x 2 x 10 3 9 ergs/sec. To produce the observed X-ray flux of =•= 2 x 10 3'ergssec" 1 the value of $=10"2. This is considerably less than the suggested value of 0.1 ( Zel'dovich and Novikov [1971 ] ) but in agreement with the value found for other X-ray binaries by Conti [1978] and Parkes et al [1980]. 5.7 VARIATION OF, HE 11 ABSORPTION LINE As has been seen in the previous chapter the He II X4686 absorption line equivalent width varies with phase. The observed variation can not be due to obscuration by the primary of the emission region between the primary and the secondary as the emission equivalent width is at a minimum at phase 0.5 ( i.e. when the secondary is between the primary and the observer). A possible explanation is that X-ray heating of the surface of the primary may produce variation in the intrinsic absorption profile of the primary. A number of studies have investigated the effect of X-rays from the secondary on the primary. London and Flannery [ 1 982], London et al [1981] and Anderson [1981 ] have looked at the possibility of X-ray induced stellar 256 winds in these binary systems. They a l l concentrated on modeling a system l i k e Her X-1 where the X-ray luminosity at the surface i s much larger than the o p t i c a l f lux and hence the main concern i s with the ef fect of heating high in the atmosphere. Table 5.02 l i s t s a number of the propert ies of Her X-1 and Cygnus X-1 ( from London et a l [1981], Liang and Nolan [1984] ). The Cygnus X-1 system d i f f e r s from the Her X-1 system in two s i g n i f i c a n t ways. The r a t i o of the X-ray to o p t i c a l luminosity i s far larger for Her X-1 than for Cygnus X - 1 . This high value explains the preoccupation of models for Her X-1 with an induced hot corana and the wind associated with i t . Figure 5.08 shows the X-ray spectrum of Cygnus X-1 ( Liang and Nolan [1984] ) and of Her X-1 ( Holt arid McCray [1982] ). C l e a r l y there i s considerably more X-ray energy in the hard X-ray region in Cygnus X-1 than Her X - 1 . As the hard X-ray flux has a much greater penetration depth than the soft f lux th i s may produce e f fec ts deeper in the atmosphere of HDE 226868. The v a r i a t i o n of the equivalent width of He II X4686 l i n e shown in Chapter 4 can be explained conveniently i f the v a r i a t i o n i s a t t r ibuted to change in the strength of the underlying absorption l i n e . Absorption l i n e changes in Her X-1 are seen in coincidence with the o r b i t a l period of the secondary ( Hutchings and Crampton" [1972] ) and they indicate a change in the spectra l type from B1 to B4. Oke [1976] has modelled the changes in the equivalent widths by assuming most of th i s star has a normal s t e l l a r atmosphere 257 Figure 5.08 X-ray Spectrum of Cygnus X-1 (dotted l ine ) and Her X-1 (dash-dot l i n e ) . l o g [ F l u x ( p h o t o n s / c m « ) i E 2 / s e c / l < e U ) ] - 4 - 2 • 2 1 1 1 . o CD m 3 ro CO c . . . -•if .—-' cn CD 259 Table 5.02 X-ray Parameters for Her X-1 and Cygnus X-1 Property Her X-1 Cygnus X-1 Distance (kpc) 5 2.0 Distance between secondary and primary 3X10 1 1 1.8x10*2 surface (cm) X-ray Luminosity (<10 keV) ergs/s 1.5X10 3 7 0.5-4X10 3 7 (>10 keV) ergs/s 1.0X10 3 7 1-3.5X10 3 7 Temperature of Primary 7000 27500 °K Optical Luminosity 1 . 4X1 0 3 5 1 . 1x1 0 3 9 ergs/s Ratio L /L 100 0.03 X o while the region opposite the secondary has a higher 260 temperature atmosphere. The form of the v a r i a t i o n in the H/J line predicted from his simulation (see figure 5 of Oke [1976]) looks very similar to the changes seen in the equivalent width of the He II emission l i n e in Cygnus X-1 (figure 4.8). The f i r s t question to be addressed i s how the heating of the primary in the Cygnus X-1 case compares with that for Her X-1. A code was written to calculate the heating rate that the X-ray flux produces in a s t e l l a r atmosphere. In the soft X-ray region ( > 300 eV ) the primary means of tr a n s f e r r i n g energy from X-rays to the gas i s by K s h e l l ionizations of metal atoms. The cross-sections and ion i z a t i o n energies for t h i s process for the abundant metals has been tabulated by Daltabuit and Cox [1972] and more recently by London et a l [1981]. The energy difference between the incoming X-ray photon and the K s h e l l ionization energy i s assumed to be transferred into electron kinetic energy. For higher X-ray energies ( > 20keV ) the dominant energy loss mechanism becomes Compton Scattering from the thermal electrons in the star ( Guo and Junhan [1985] ). The expression for the cross-section can be found in Lang [1980]. The energy transferred in each c o l l i s i o n i s dependent on the sine of the angle between the outgoing and incoming photons. Jackson [1962] and Pacholczyk [1970] show that for energies much lower than the rest mass of the electron most photons are either forward scattered ( zero energy transfer ) or back scattered ( maximum energy 261 transfer ). For energies near the rest mass of an electron or greater the scattering d i s t r i b u t i o n i s strongly peaked toward forward scattering and only about 10% of the photons are backscattered. To do t h i s c a l c u l a t i o n properly a Monte Carlo simulation would have to be performed in which each photon i s followed through the gas. In the code here an i n i t i a l flux of photons was attenuated in i t s passage through a planar atmosphere by allowing one interaction with the gas ( i. e . no scattering ) The result of t h i s c o l l i s i o n was determined by the p r o b a b i l i t i e s outlined above. The resultant heating rates as a function of depth are shown in figure 5.09 ( as the l i n e s with symbols ) using input parameters appropriate to Her X-1 and Cygnus X-1. The Her X-1 results here are in good agreement with similar calculations by London et a l [1981] for that object. The next step i s to compare this X-ray heating to the energy density of the radiation f i e l d of the star. No tabulation of energy density with depth could be found in the l i t e r a t u r e and thus i t was assumed that the atmosphere was in LTE so that the energy density i s given by the blackbody equivalent at that depth. The run of density and temperature with depth in the atmosphere were obtained from the compilation by Mihalas [1972], Models with T = 30000°K and T = 15000°K , and log g = 3.0 were used to simulate HDE 226868 and the Her X-1 primary respectively. Shown in figure 5.09 as the l i n e s only are the resultant internal radiation 262 f i e l d energy de n s i t i e s . Clearly the secondary in Her X-1 has a much more substantial effect on the primary than i s the case in Cygnus X-1. Note however that t h i s heating is s t i l l present at great depth in Cygnus X-1 ( >1 gem"2 ) due to i t s large hard X-ray fl u x . This c a l c u l a t i o n i s only approximate and a more detailed evaluation would be interesting to see how strong this deep atmosphere heating e f f e c t i s . The question that began t h i s aside was why the He II X4686 shows equivalent width variati o n s with o r b i t a l phase. Underhill [1983b] has shown at what depths in an 0 star the observed lines of He I and He II obtain their maximum contribution. These depths are indicated in figure 5.09 along, the top of the plo t . In Her X-1 the entire l i n e forming region i s strongly affected by the secondary as the X-ray heating i s two orders of magnitude larger than the intern a l radiation f i e l d . This explains the large changes in spectral type observed for t h i s star. For Cygnus X-1 the ef f e c t i s not substantial, always being less than the primary's radiation f i e l d over the entire l i n e forming region. The peak energy deposition in the atmosphere of HDE 226868 occurs at about mass depth 0.1 g/cm2. From figure 5.09 i t can be seen that at t h i s depth the He II ions s t i l l contribute to the l i n e observed from outside the star. At mass fra c t i o n 0.1 g/cm2, log( T ) -1.3 ( Kurucz [ 1979] ) and the non LTE departure coefficents « 1 ( Mihalas [1978] p. 229 ), therefore the atmosphere can be assumed to be in 263 F i g u r e 5.09 Model of X-ray h e a t i n g of p r i m a r y i n Her X-1 (dashed l i n e + symbols) and Cygnus X-1 ( d o t t e d l i n e + symbols ). Energy d e n s i t y i n Her X-1 (dashed l i n e o n l y ) and Cygnus X-1 ( d o t t e d l i n e o n l y ) 264 in * £ o \ o Ql in \ in o> t_ Qt i — i ° O 01 in o o. Ql Q 3> i _ Ql He I 1 1 1 1 ry y Hell I / • i .• / / / / / \ / .• / X /// V / - . - \ L. + - 5 • D e p t h ( 1 o g [ g / c m * * 2 ] ) 2 6 5 LTE. The energy density ( E ) given by E = aT* where a = 4o/c = 7.56 x 10"5 ergs/cm 3/deg" Now i f the eff e c t of the X-ray heating can be treated as a small pertubation on thi s energy density then (T + 6T)« = E/a + 8E /a which expands to give 6T <* 6E /(4T aa) From figure 5.09 the maximum heating i s about 30 ergs/cm 3/sec at depth 0.1 g/cm2.The s t e l l a r temperature i s 24000°K which, using the above expression, implies a temperature increase of only = 70°K. From Auer and Mihalas [1972] study of the change in He II equivalent width with temperature t h i s i s insufficent to produce the observed changes ( need £ 1000°K ). This simple analysis would suggest that X-ray heating can not produce the He II equivalent width modulation observed. Thus some other cause must be sought to explain the change. Chapter 6 X-RAY OBSERVATIONS The previous chapters have discussed mainly the o p t i c a l observations of Cygnus X-1. The IR and UV region have been observed by others in order to detect the postulated disc about the secondary. The only source of UV data i s the IUE Spacecraft which because of i t s aperture can only produce low resolution, poor signal to noise spectra. The radio emission i s quite weak and comes from synchrotron emission in large f l a r e s and from the terminal region of the wind. The X-ray flux comes from near the secondary in the binary system and with the a v a i l a b i l i t y of EXOSAT i t was decided to investigate i t further. The o p t i c a l observations of July 1984 of Cygnus X-1 were obtained almost simultaneously with requested Target of Opportunity Observations by the EXOSAT s a t e l l i t e . The purpose of these observations was to see whether the source was in i t s high or low state. Previous observations ( by the author and Walker et a l [1978] ) indicated large changes in the equivalent widths at various times possibly associated with the X-ray state. Further i t was expected that the op t i c a l spectroscopy could be done with sufficent time and wavelength resolution to enable observation of any changes in the o p t i c a l corresponding to variations in the X-ray. The de t a i l s of those observations are given in table 6.01 . Figure 6.01 shows the X-ray fluxes in the indicated bands 266 267 Table 6.01 Journal of EXOSAT observations of Cygnus X-1. Date 1 984 Day # O r b i t a l ' Phase X-ray Phase 3-13keV Flux 10" sergs/cm 2/sec 07 July 189 0.886 0.000 5.6 ± 0.2 08 July 190 0.990 0.002 5.3 ± 0.2 09 July 191 0.243 0.007 5.6 ± 0.2 during each of the three separate nights of observation. C l e a r l y seen are long dips in the flux in the second nights observations. Cygnus X-1 was one of the f i r s t observed and strongest sources in the X-ray region. It has been studied extensively using a l l available X-ray s a t e l l i t e s ( see Liang and Nolan [1984] for a review). Along with several other X-ray sources, Cygnus X-1 shows irregular intensity dips accompanied by spectral hardening. Previous observers have found that these dips cluster about phase 0.0 ( L i and Clarke [1974], Mason et a l [1974], Parsignault [1976], Murdin [1976], Pravdo et a l [1980], Remillard and Canizares [1984] ). Mason et a l [1974] have suggested that they occur p r i o r to superior conjunction, however using the the new ephemeris for the orbit derived in Chapter 2 on a l l the h i s t o r i c dip observations reveals no such e f f e c t . The dips have timescales ranging from hours to minutes and produce 268 Figure 6.01 EXOSAT X-ray observations on the 07, 08, 09 July 1984. Time i s in units of UT hours. 269 CYG X-1 EXOSRT/ME s.o HflRONESS 0.0 ISO •Verity 5 - 1 3 KEV CJ IU co n V u ' CO o CJ 150 J 1-3 KEV o. 10.00 12.00 OflY NO: 189.0 14.00 16.00 270 CYG X-1 EXOSAT/ME 5.0 o.o 130 J UJ « 0 . CO 3 o 1 2 0 i 0. HARDNESS !1 5-13 KEV 1-3 KEV 0.00 2.00 DAY NO: 190.0 4 .00 6.00 271 CYG X-1 EXOSflT/ME 5 . 0 HARDNESS 0 . 0 130 5 - 1 3 KEV o ^ 0 . CO t— z O (_> 120 1-3 KEV 0. 10.30 12.30 DAY NO: 191 .0 14.30 16.30 272 attentuation of the X-ray flux ranging from a few percent to almost complete absorption. Remillard and Canizares [1984] explain t h e i r data and that of Pravdo et a l [1980] as being due to p a r t i a l l y ionized blobs of gas along the l i n e of sight. Unlike other x-ray binaries that exhibit dip features ( Vela X-1 , Kallman and White [1982], HD 153919, White, Kallman & Swank [1982] ) Cygnus X-1 does not show X-ray or o p t i c a l e c l i p s e s , meaning that the system i n c l i n a t i o n must be less than 62° with the most l i k e l y value of near 40° ( th i s t h esis, Davis and Hartman [1983] ). The high viewing aspect of th i s system makes these dips d i f f i c u l t to explain. They are c e r t a i n l y not formed close to the secondary as the flux of X-rays would produce complete ionization of neutral absorbing material. If the dips are the result of material far from the X-ray source the material i s high out of the plane of the system ( because of the low i n c l i n a t i o n ) and i t s presence must be explained. The fact that the dips are only seen near phase zero indicates that the absorbing region l i e s between the primary and secondary. There are a number of mechanisms suggested in the l i t e r a t u r e to explain a variety of X-ray observations which may pertain to th i s s i t u a t i o n . Lubow and Shu [1976] suggest-that the X-ray absorption dips seen in Her X-1 may be the result of the impact of a stream, associated with Roche Lobe overflow, onto a disc about the secondary. Such an impact would throw material to about three disc scale heights ( 0.15 r-. ) near the edge 273 of the disc ( Lubow and Shu [ 1 9 7 6 ] , table 1 ) . For the size of accretion disc they envisage ( * 3 R Q ) t h i s would not be sufficent to produce the absorption features seen. The stream i t s e l f can not be the source either as i t i s confined e s s e n t i a l l y to the plane of the binary. The height appropriate to hydrostatic equilibrium in the stream is quite small. Any disc that might surround the secondary could be susceptible to i n s t a b i l i t i e s producing an o s c i l l a t i o n in the disc. Such o s c i l l a t i o n s have been reported in some low mass X-ray binaries ( White and Swank [ 1 9 8 2 ] , Walter et a l [ 1 9 8 2 ] ) . The data for 4 U 1 7 5 5 - 3 3 ( Frank and Sztajno [ 1 9 8 4 ] ) i s p a r t i c u l a r l y c l e a r , showing semi-periodic dips between 4 0 0 ' and 7 3 0 seconds. The deeper dips are also longer in duration which the authors interpret as being due to larger excursions in the d i s c . Such an interpretation predicts a c h a r a c t e r i s t i c time scale for such o s c i l l a t i o n s as of the order of the disc thickness divided by the l o c a l sound speed or c h a r a c t e r i s t i c turbulent v e l o c i t y . If the disc thickness is the result of balance between gravity and turbulent pressure the time scale of o s c i l l a t i o n s i s ( Frank and Sztajno [ 1 9 8 4 ] ) where M = the mass for the secondary =* 1 0 MQ for Cygnus X-1 Assuming the o s c i l l a t i o n s are confined to the rim ( as i s believed the case in the low mass systems ) of the disc of 274 radius =* 3 R@, the o s c i l l a t i o n time for a Cygnus X-1 disc is 2600 sees. The data in figure 6.01 does not seem to be periodic however i t i s apparent that the larger flux dips mask the true number of smaller dips. A longer data set i s needed to investigate i f the smaller dips are periodic. The amplitude necessary for such o s c i l l a t i o n s to produce the observed dips ( assuming an i n c l i n a t i o n of 40° ) however would have to be larger ( * 2.5 R @ ) than the disc radius. This i s c l e a r l y not possible. This explanation i s therefore probably not appropriate unless the i n c l i n a t i o n of the system i s in fact near the grazing eclipse l i m i t of 62°. Kemp [1980] has taken standard disc models from Shakura and Sunyaev [1973] and included the effect of illumination of the disc edge by the primary's radiation f i e l d . For his assumed disc radius of 6.6 R~ a disc height of » 1 R_ on the disc edge facing the primary was calculated. This again i s not high enough out of the plane to explain the observed dips for the assumed i n c l i n a t i o n . As well there i s l i t t l e evidence to support the existence of such a substantial d i s c . It has been reported on numerous occasions in the l i t e r a t u r e that the winds of early type stars vary ( e.g. Ebbets [1982] ). These claims are normally j u s t i f i e d with observation of emission l i n e s ( t y p i c a l l y Ha ) in high mass loss s t a r s . One needs to be p a r t i c u l a r i l y c a r e f u l in using such data as the region near Ha i s infested with t e l l u r i c l i n e s which vary independently of the star ( Carlberg 275 [ 1 9 7 8 ] ) a n d b e c a u s e t h e u n d e r l y i n g s p e c t r u m o f e a r l y t y p e s t a r s c a n be v a r y i n g ( N i n k o v e t a l [ 1 9 8 3 ] ) . B e t t e r e v i d e n c e f o r i n h o m o g e n e i t i e s i n t h e w i n d come f r o m t h e f l i c k e r i n g s e e n i n a number o f X - r a y s o u r c e s ( H o l t [ 1 9 8 2 ] ) a n d w h i c h i s a t t r i b u t e d t o a c c r e t i o n o f c l u m p s f r o m t h e s t e l l a r w i n d o n t o t h e s e c o n d a r y . Kahn [ 1 9 8 1 ] h a s shown t h a t i n a r a d i a t i o n d r i v e n w i n d i n h o m o g e n e i t i e s w i l l grow w i t h h e i g h t . f r o m t h e s t a r f o r w i n d s i n w h i c h t h e M s t a r > X/2 w h e r e X i s t h e maximum mass l o s s r a t e a l l o w e d . F o r HDE 226868 t h e f i g u r e i s = 96% o f t h e maximum a n d t h u s i t s w i n d may be q u i t e s u s c e p t i b l e t o c l u m p i n e s s . C a r l b e r g [ 1 9 7 8 , 1 9 8 0 ] h a s m o d e l e d t h e s c a l e s i z e o f i n h o m o g e n e i t i e s t h a t may e x i s t a n d grow i n s t e l l a r w i n d s . The c o n d i t i o n s u s e d i n h i s s t u d y w e re a w i n d t h a t h a d a mass l o s s r a t e 1 x 1 0 ' 6 M @ / y r , a t a d i s t a n c e o f 2R* f r o m t h e s t a r , w i t h a v e l o c i t y o f 1000 k m s e c " 1 . T h e s e c o n d i t i o n s a r e v e r y s i m i l a r t o what w o u l d be f o u n d i n t h e w i n d o f HDE 226868 a t t h e d i s t a n c e o f t h e s e c o n d a r y . The r e s u l t o f h i s l i n e a r i s e d s t a b i l i t y a n a l y s i s i s t h a t t h e r e a r e two d i s t i n c t a b s o l u t e i n s t a b i l i t i e s . T h e f i r s t r e s u l t s f r o m r a d i a t i o n d r i v e n s o u n d waves p r o d u c i n g a R a l e i g h - T a y l o r I n s t a b i l i t y due t o s m a l l p e r t u r b a t i o n s i n t h e v e l o c i t y f i e l d ( a l s o N e l s o n a n d H e a r n [ 1 9 7 8 ] ) . A n y v e l o c i t y p e r t u r b a t i o n i n a d i r e c t i o n away f r o m t h e s t a r w i l l move t h e a b s o r b i n g p r o f i l e f u r t h e r i n t o t h e c o n t i n u u m t h e r e b y i n c r e a s i n g t h e r a d i a t i o n f o r c e . The s e c o n d i s a g a i n a R a l e i g h - T a y l o r i n s t a b i l i t y b u t due t o i n i t i a l f l u c t u a t i o n s i n t h e d e n s i t y o f t h e w i n d . Any 276 pertubation that produces a constant outward v e l o c i t y produces an increase in the density. This density i s subject to an increased radiation force which in turn accelerates the v e r t i c a l flow. These i n s t a b i l i t i e s have c h a r a c t e r i s t i c wavelengths of scale I09cm and lO^cm respectively. Two observations can be made from the data shown in figure 6.01. F i r s t l y dips in the X-ray are seen mainly in the second night's data where the observations are near zero phase as i s the case with previous observations. Secondly there seem to be two classes of dips broad ones, with duration = one hour, seen only near phase zero and with a constant hardness r a t i o , narrow ones with duration of < 5 minutes, with a d i s t r i b u t i o n centered on phase zero but a larger spread in phase and with a highly variable hardness r a t i o . Any inhomogeneities in the s t e l l a r wind when viewed near phase zero have their v e l o c i t y primarily along the l i n e of sight ( r a d i a l ). Thus the ec l i p s e duration i s the time i t takes the background X-ray source to pass through the shadow of a wind inhomogenity in the foreground. From work in chapter three the v e l o c i t y of the secondary is 350 kmsec"1. Therefore a one hour eclipse corresponds to a length of ^ I0 1 1cm and <5 minutes to < 10 1 ocm. These figures correspond well to the theore t i c a l estimates of Carlberg. The c l u s t e r i n g of dips near phase zero imply that the the material producing the dips occupies a region between the orbi t of the secondary and the primary surface. Carlberg 277 [1978] finds that his larger scale disturbances are in fact absolute i n s t a b i l i t i e s ( they can actually generate pertubations ) for temperatures >106K. Thus the region between the primary and secondary where X-ray heating increases the temperature and where there is an enhancement in the density of the wind, would be ideal for t h i s perturbation to grow. Beyond the radius of the secondary the density of the wind drops rapidly and in consequence the more severe e f f e c t s of X-ray ionization ( McCray et a l [1984] ) may destroy the i n s t a b i l i t i e s . The smaller scale i n s t a b i l i t i e s are an amplifying perturbation ( they grow from some i n i t i a l pertubation under the influence of radiative acceleration ). They too are more l i k e l y to grow in the region between the primary and secondary due to the higher d e n s i t i e s . The location of the dips i s possible to estimate in a rough way i f estimates for the ionization parameter £ and the column density of the dip can be made. Pravdo et a l [1980] and Remillard and Canizares [1984] have both found that the spectra of the X-ray source taken during eclipse i s best f i t assuming attenuation by p a r t i a l l y ionized gas. L. S t e l l a at the EXOSAT observatory has made f i t s to the medium energy X-ray spectrum of the long dip on day 190 between times 01:30 and 02:00 UT using opacities for ionized material from Krolik and Kallman [1984]. The best spectral f i t was made with an absorber temperature of 1.7X105 °K and a column density of 2.40±0.05 x 10 2 3 cm"2. From Buff and 278 McCray [1974] t h i s implies that the ionization parameter £ = L/nr 2 > 100 . Rearranging t h i s expression gives r = • L D / N c $ where r = distance from the X-ray source L * 2 to 8 X10 3 7 erg/sec I «* 100 D * 10 1 1cm This gives a value for r, the distance from the absorption region to the X-ray source, as =*4-8 RQ. With an i n c l i n a t i o n for the system of 40°, simple geometry indicates that the absorption region i s positioned =* 3-6 r ^ out of the o r b i t a l plane of the system and at a distance from the primary of 41 R Q or 2 R*. It i s intriguing that this i s also about the distance from the star where the narrow absorption components seen in li n e s in the u l t r a v i o l e t in some early type stars originates. ( Underhill and Fahey [1984] ). Notice that r i s larger than the radius of the sphere in which complete ionization of the gas by X-rays from the secondary occurs. It i s also close, but larger than, the inner radius of the Ha s h e l l found in the previous chapter. The existence and location of these dips i s of relevance to models of O star s t e l l a r winds. C a s s i n e l l i et a l [1981] suggest that the X-ray observations imply that a l l OB supergiants are X-ray sources at a l e v e l >10 3 2 ergs/sec. This l e v e l i s consistent with the Corona and Cool Wind model for s t e l l a r winds ( Waldron [1984] ) and with the shocked 279 inhomogeneties in the wind model ( Lucy and White [1980], Lucy [1982] ). Our studies indicate that there i s a large ionized region around HDE 226868. The X-ray observations indicate the presence of inhomogeneties but only within the radius of the secondary (otherwise dips would be seen at phases other than near 0). If indeed these wind inhomogeneties do form shocks due to their passage through a 'stationary' medium and thus X-rays, then i t may be that these X-rays also ionize the gas in the region within the secondary orbit explaining the lack of Ha emission. The flux of X-rays produced in th i s region would be a number of orders of magnitude smaller than that seen from the secondary ( C a s s i n e l l i and Swank [1983] ) and consequently undetectable. An alt e r n a t i v e explanation for these observations i s due to the presence of magnetic f i e l d s as suggested in Underhill and Fahey [1984] and elaborated by Uchida [1985], It may be possible to produce a hot corona, the dips and the non-thermal radio emission in some 0 stars ( C a s s i n e l l i [1985] ) using a magnetic f i e l d approach. In fact as X-ray luminosity increases monotonically with greater rotational v e l o c i t y , and as th i s i s interpreted as due to a dynamo type mechanism ( Linsky [1985] ), the effect of magnetic mechanisms in Cygnus X-1 may be substantial larger than that found in single stars. Dips are v i s i b l e in a number of other X-ray binaries. Kallman and White [1982] report on dips of several minutes duration in Vela X-1 ( BO.SIb + neutron star ). White et a l 280 [1983] report on a loose c o r r e l a t i o n between X-ray absorption and f l i c k e r i n g X-ray on a 10 minute timescale in HD 153919 ( 06.5f + neutron star ). HD 153919 i s known to suffer variable duration eclipses of the X-ray source by the primary ( Branduardi et a l [1978] ). This v a r i a b i l i t y may be due to the presence of large dips which would be most l i k e l y to produce absorption ( i . e . be along the l i n e of sight) near ingress and egress. SMC X-1 ( BOI + neutron Star ) shows absorption dips of a few hundred seconds following ec l i p s e exit ( Marshall et a l [1983] ) which i s also attributed to inhomogeneities in the wind. In a l l these cases the systems are e c l i p s i n g binaries and thus the dips are produced by material in the plane rather than well out of the plane as in Cygnus X-1. Chapter 7 CONCLUSIONS This thesis describes an ambitious program to maintain long term monitoring of one p a r t i c u l a r i l y interesting X-ray source, namely Cygnus X-1. The project was limited by the developmental state of the Reticon Camera that was used for the program. A number of results can be quoted ; 1. there seems to be a period change in this system corresponding to a P/P =* 10"5 day" 1. A change in the period i s found using the h i s t o r i c data available in the l i t e r a t u r e and applying both a period folding analysis and looking for systematic changes in the T 0 parameter. No periods other than o r b i t a l were detected. 2. the absorption l i n e v e l o c i t y curve i s well defined and the o r b i t a l parameters are determined with great accuracy. 3. the He II emission r a d i a l velocity curve i s quite smooth contrary to the results of previous studies which attributed noise in the i r observations to fluctuations in the system. The emission i s quite stable during the period of the observations reported. 4. the equivalent width of the He II X4686 corrected for the contribution from the primary shows variation with 281 282 o r b i t a l phase, being smallest at phase 0.5 and largest at phase 0.0 . It i s due to change in strength of the He II X4686 absorption l i n e from the primary as seen by the observer. This can not be explained by X-ray heating of the primary. 5. the equivalent width of the hydrogen Balmer lines have a maximum (20% larger) at zero phase of the 294 day X-ray modulation. This i s attributed to a decrease in the emission component in the Balmer lines due to changes in the mass flow from the primary. 6. there are large changes ( £40% ) in the equivalent width of the He II X4686 l i n e on some occasions which may be associated with X-ray tr a n s i t i o n s from low to high states. 7. after removal of the primary contribution the variation of the shape of the Ha and He II X4686 p r o f i l e with o r b i t a l phase looks very similar, contrary to the findings of others. 8. investigation of the Ha l i n e p r o f i l e indicates a region of * 0.4 times the radius of the primary above the primary which does not contribute to the Ha p r o f i l e . 9. modeling of the He II emission l i n e s indicates the 283 o r i g i n of the emission l i n e s i s in the X-ray heated region between the primary and the secondary. A slowly accelerating s t e l l a r wind directed toward the secondary, with a ve l o c i t y at 2RA of only 350 km/sec i s needed to explain the observations. 10. EXOSAT observations reveal dips in the X-ray flux of duration <5 minutes and 1 hour which are interpreted as inhomogeneties in the wind of scale lengths 10 1° and 10 1 1 cm. This i s in agreement with s t a b i l i t y analysis of the wind. The location of the larger dips i s found to be 2 R* from the the primary and outside the complete ionization zone of the secondary. Further study of not just Cygnus X-1 but other X-ray binaries i s needed. Observationally much remains to be done in the o p t i c a l but mainly at s p e c i f i c times. It would be nice to have X-ray monitoring of the X-ray sources that have e r r a t i c long term behaviour so as to know when to make a concerted observing e f f o r t on them. For example the cause of the high and low state in Cygnus X-1 i s not at a l l understood. It would also be productive to continue to observe Cygnus X-1 so as to investigate the possible change in o r b i t a l period of the system. 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A l l spectra are of 110A extent at a d i spers ion of 4OA/nun centered on wavelengths A4686, X4542 and X4100 . 302 A Cep 061 9 Sge 081a a Cam 09.51a A Ori 19 Cep 08.5lab 09.5lab HD188209 09.5lab HD218915 09.5lab HD207198 09lb-ll 6 Ori 09.511 e Ori BOIa « Ori B0.5!a K Cas B0.7la Cyg X-1 09.7lab 15 Sgr 09.7lab HD194280 09.7lab «T Ori 09.71b 69 Cyg BOIb HD225146 09.71b HD47432 09.71b HD13745 09.711 f Per Bllb HD 40111 Bllb p Leo Bllb HD199216 B i l l OJ o OJ CD O HD199579 06.5111 15 Mon 08111 t Ori 09.5111 10 Lac 08111 HD193322 08.5111 HD206269 HD217086 68 Cyg 14 Cep 06.5V 07V 08V 09V 0l Ori C 07V 7 Cas BOIV <j>1 Ori BOIV o Ori v Ori n Ori 42 Ori 09.5V BOV B0.5V B1V AE Aur e Per 09.5V B0.5V X Per HD36960 09.5V B0.5V 40 Per B0.5V A Cep 9 Sge a Cam 061 081a 09.51a A Ori 19 Cep 08.5lab 09.5lab HD188209 09.5lab HD218915 09.5lab HD207198 091b II 8 Ori 09.511 HD195592 e Ori K Ori 09.71a BOIa B0.5la AC Cas B0.7la Cyg X-1 09.7lab 15 Sgr 09.7lab HD194280 09.7lab C Ori 09.71b 69 Cyg BOIb HD225146 09.71b HD47432 09.71b HD13745 09.711 c* Per Bllb HD 40111 Bllb p Leo Bllb HD199216 B i l l o 308 HD199579 06.5111 15 Mon 08111 i Ori 09.5111 10 Lac 08111 HD193322 08.5111 HD206269 HD217086 68 Cyg 14 Cep 06.5V 07V 08V 09V 01 Ori C 07V 7 Cas BOIV <px Ori BOIV a Ori v Ori n Ori 42 Ori 09.5V BOV B0.5V B1V AE Aur e Per 09.5V B0.5V X Per HD36960 09.5V B0.5V 40 Per B0.5V 3 1 0 PQ CD O A Cep 061 9 Sge 081a a Cam 09.51a A Ori 19 Cep 08.5lab 09.5lab HD188209 09.5lab HD218915 09.5lab HD207198 09lb-ll 6 Ori 09.511 e Ori K Ori BOIa B0.5la /c Cas B0.7la 69 Cyg c* Per BOIb Bl lb HD 40111 Bl lb p Leo Bllb HD199216 B i l l 312 HD199579 06.5111 15 Mon 08111 tOri 09.5111 10 Lac 08111 HD193322 08.5111 HD206269 HD217086 68 Cyg 14 Cep 06.5V 07V 08V 09V 61 Ori C 07V 7 Cas BOIV <f Ori BOIV a Ori vOx\ TJ Ori 42 Ori 09.5V BOV B0.5V B1V AE Aur e Per 09.5V B0.5V X Per HD36960 09.5V B0.5V 40 Per B0.5V CD O 

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