OBSERVATION AND INTERPRETATION OF THE 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 this thesis as conforming

to the req^r^o" standard

THE UNIVERSITY OF BRITISH COLUMBIA

July 1985 £

© Zoran Ninkov, 1985 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the The University of

British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my

Department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.

Department of Geophysics and Astronomy

The University of British 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 -1, whose constituents are believed to consist of a normal 0 primary and a black hole companion, are presented. Spectra of this system were collected between 1980 and 1984 using a Reticon detector.

The resulting absorption line radial velocity (RV) curve is characteristic of a single line spectroscopic binary. These velocities were combined with those available in the

literature to determine an of 5.59977 ±

0.00001 days. A P/P =* 10"5 day"1 was found from analysis of all available velocity measures. This change in the period

is 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 fit of the orbital motion of the primary to the RV curve gives a K =

75.0 ± 1 km/s and no significant eccentricity. The vsini of

the primary was found, using the fourier transform

technique, to be 94.3 km/sec. This is substantially smaller

than the literature value of vsini = 140 km/sec. The value

of the K and vsini allow the ratio m /m to be determined as p x

* 2.0 . The equivalent width of H7 allows the absolute magnitude -ol 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 is consistent

with the absolute magnitude obtained and it is thus likely that the primary is a normal star of mass « 20 MQ. The mass

of the secondary is therefore 10 ± 3 MQ. Measurement of the interstellar lines to obtain an independent E(B-V) reveals that the interstellar line strength per unit E(B-V) is lower than in any other direction in the sky.

Stars for which velocity-excitation slopes and mass loss estimates, from UV line profile modeling and/or radio free-free emission measures, are available in the literature were collated. An empirical fit to this 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/.

The He II X4686 and Ha lines are found in emission.

After removal of the contribution to the line profile from the primary the radial velocity curve of the residual He II

X4686 line is found to have small scatter from a smooth fit

( ± 10 km/sec ) with no significant eccentricity. No sizeable variation in the K amplitude at different epochs was found contrary to a previous investigation and the origin of the emission is thus apparently fixed and stable.

A phase lag of 130° is measured between the absorption and emission velocity curves and thus the simple interpretation of the emmision originating 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 orbital period. This variation is probably the result of the profile of the primary varying with which face of the star is 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 all other observations while still showing the same variation with orbital phase. Such a change has been seen once before and may be associated with transitions to the X-ray high state.

The H7 and H/3 lines 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 lines are a composite of an absorption component from the primary and a weak emission component. This is best explained by variations in the outflow from the star, which is the source of both the emission component and the X-ray flux via accretion. Such variations may be the result of pulsation of the primary.

The Ha line profile has been decomposed into three components; the absorption component from the primary, emission from a shell with an inner radius 1.4 times that of the primary, arid a component with properties similar to the

He II X4686 line. The great width of the Ha line, previously explained as being the result of rotation of the disc, is instead shown to be the result of superposition of these components.

The origin of the He II X4686 emission is explained by assuming that a stellar wind enhanced in the direction of the . secondary is completely ionized within a volume surrounding the secondary. The He II between the edge of this volume and the surface of the primary is enhanced as a result of X-ray heating and ionization. Model profiles appear in reasonable agreement with high dispersion spectra.

The obvious explanation for the orbital variation in the He

II line is that X-ray heating of the side of the primary facing the secondary produces a change in the . Calculation of the size of this effect reveals that it is 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 orbital phase zero. Simultaneous X-ray spectra allowed an estimate of their column density as 2.0 x 1023 cm"2. Two scale lengths of dips were found of 10s and 1011 cm. These values are in good agreement with theoretical predictions for the sizes of inhomogeneties in high mass loss stellar 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 ii

Table of Contents vi

List of Tables viii

List 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 Digital Subtraction 36

3. The Absorption Line Spectrum 48

3.1 Rationale for the Study 48

3.2 The Spectrum Itself 50

3.3 Equivalent Width Determination 58

3.4 The Spectral Type 64

3.5 The Rotational Velocity 80

3.6 The Radial Velocity Curve 92

3.7 Masses of the Components 131

3.8 E(B-V) and the Interstellar Lines 136

3.9 Mass Loss Rate 138

vi 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 Profiles 172

4.2.3 The CFHT He II 74686 Profiles 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 Profile 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 Trailing Shock Model 231

5.4 Emission from the Disc 233

5.5 Enhanced Stellar 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

vii List of Tables

1.01 Type I vs Type II X-ray System Characteristics 5

1.02 Observed Properties of the Cygnus X-1 System 8

2.01 Ret icon Systems 16

2.02 Details of occurrence of spikes 32

2.03 Details of observations of Cygnus X-1 37

2.04 Details of observations of Comparison 40

3.01a Line List for Early Type Stars (blue) 56

3.01b Line List for Early Type Stars (Red) ....57

3.02 Standard Star Characteristics 67

3.03 Standard Star Ratios of Spectrally Sensitive

Lines 78

3.04 Line weights for least squares fitting radial

velocity curve and excitation potential' for line

groups 97

3.05 Calculated velocities for spectra of HDE 226868 ....98

3.06 Fitted ?T? at different epochs ...123

3.07 Weights for least squares fitting radial velocity

curve by year 130

3.08 Solution for Cygnus X-1 130

3.09 E(B-V) as determined from the Interstellar lines ..137

3.10 Mass loss rates from different techniques ...142

3.11 Normalized equivalent width variations with phase .158

3.12 Normalized phase variations of He I halfwidth 162

4.01 Line List for CFHT 169

4.02 Equivalent Widths for lines from CFHT Data 174

vi i i 4.03 He II X4686 emission radial velocities and

equivalent widths ..187

4.04 Orbit parameters for He II X4686 emission radial

velocity curve 191

4.05 He II X4686 equivalent widths and halfwidths as

function of orbital 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 List 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 Distribution 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 SilV 74116 /Hel 74121 for standards 70

3.05 Ratio of Silll 74552 /Hel 74387 for standards 72

3.06 Ratio of Silll 74552 /Hel 74541 for standards 74

3.07 Ratio of SilV 74089 /Hel 74121 for standards 76

3.08 Spectral Mosaic for wavelength range centered on

X4686 81

3.09 vsini derived from FT Technique vs that used by

Stoeckly and Mihalas 87

3.10 Fourier Transform of He I X4713 profile for HDE

226868 and 19 Cep 90

3.11 Observed and Theoretical He I X4713 for HDE

226868 93

3.12a Mean He I line radial velocity curve for HDE

226868 101

3.12b He I radial velocity residuals for HDE 226868 103

x 3.13a Mean Hell absorption line radial velocity curve

for HDE 226868 105

3.13b Hell absorption line radial velocity residuals

for HDE 226868 107

3.14a Mean Balmer line radial velocity curve for HDE

226868 109

3.14b Balmer line radial velocity residuals for HDE

226868 111

3.15a Mean Metal line radial velocity curve for HDE

226868 1 13

3.15b Metal line radial velocity residuals for HDE

226868 1 15

3.16 Power spectrum for all HDE 226868 velocities

(1939 to 1984) 121

3.17 Change in T? with 125

3.18 Zero velocity vs excitation energy for lines from

HDE226868 139

3.19 Mass loss rates vs velocity excitation slopes 144

3.20 Phase variations of hydrogen lines equivalent

widths in Cygnus X-1 148

3.21 Phase variation of mean He I line equivalent

width in Cygnus X-1 150

3.22 Phase variation of He II (absorption lines)

equivalent width in Cygnus X-1 152

3.23 Phase variation of mean metal line equivalent

width in Cygnus X-1 154

xi 3.24 Phase variation of interstellar lines equivalent

width in Cygnus X-1 156

3.25 Normalized phase variations of He I halfwidth 163

4.01 Standard stars taken at CFHT 167

4.02 Broadened profiles of standards 170

4.03 He II X4686 profile before correction for

absorption from primary 175

4.04 He II X4686 profile after 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 radial velocuty curve vs Orbital

Phase 189

4.08 He II 74686 equivalent widths vs orbital phase ....195

4.09 He II 74686 halfwidths vs orbital phase 197

4.10 Standard star spectra (red region) 200

4.11 Ha Profiles shifted to rest frame of primary 202

4.12 Ha profile first stage correction 204

4.13 Corrected He II and Ha emission profile 207

4.14 Components of Ha in HDE 226868 ...209

4.15 Derived Ha profile and theoretical

profile 214

4.16 Equivalent Widths of HDE 226868 binned on 294 day

period 218

5.01 Schematic of Lubow and Shu Model 225

xii 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 Stellar 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 profiles 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 ii Acknowledgements

I would like to acknowledge the assistance I have

received from a number of people during my time here at

U.B.C. " Firstly I would like 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 all levels of this project from observing

through to discussion of results. I thank him heartily for

all his help in making this thesis come about. I also

acknowledge . him for . introducing me to the most hallowed

institution of the hockey pool and for allowing me to make

the best bet of my life.

Many others in the department have also contributed.

Numerous fellow students have helped in observing and

discussions including Phil Bennett, Daniel Thibault, Garry

Joslin, Katherine Moyles, Chris Millward, John Amor, Grant

Hill 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 Nicol 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 its performance.

I would like to thank the staff of the Dominion

Astrophysical Observatory, where most of the observations in this thesis were made, for both allocating the time and providing assistance. In particular I would mention Murry

Fletcher for his extensive help over the . Observing trips 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 financial 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 like to thank my parents and brothers for providing me with the upbringing to allow me to go 'per adra ad astra' .

Finally but most importantly I would like to thank my wife Marie Boudreau from whom I learnt the most important things of all 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 all this and for teaching me

xv that the priority in life should not always be with learning more but with using what you know, I dedicate this 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 first ever detection of extraterrestrial X-rays occurred on the 5th August 1948 when a V2 rocket equipped with photographic film 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 it was not until the 18th June 1962 that an extrasolar source, Sco X-1, was detected (Giacconi et al [1962]). This discovery was accidental as the intended purpose of the • rocket flight was to measure secondary fluorescence X-ray emission from the moon.

By 1967 there were already about 50 detected X-ray sources. The identification of optical counterparts moved along slowly due to the poor spatial resolution of the early

X-ray telescopes. The first optical identification of an

X-ray source was of the Tau X-1 (Bowyer et al [1964]) which was conveniently occulted by the moon and therefore allowed an accurate position for it to be determined. This proved to be coincident with the position of the Crab . Later synchronism between the X-ray, radio and optical pulsations confirmed the pulsar as the X-ray source. The large brightness changes in the visible bought attention to.the optical counterpart of Sco X-1(Sandage et al [1966]).

1 2

Cyg X-2 was identified serendipitously due to its large blue excess, noticed while the authors were searching for the optical counterpart to Cygnus X-1 (Giacconi et al [1967]).

Despite considerable effort, in 1970 these were the only three sources for which optical identifications were considered certain (Hiltner and Mook [1970]).

The spectrum of Sco X-1 (Sandage et al [1966]) was

found to have similarities to spectra of old novae. It is well known that such objects are close binaries in which mass is lost from one member to a white dwarf companion

( Kraft [1964] ). Burbidge at al [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 (like 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 gravitational potential energy in the process. A simple estimate for the

gravitational 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 .

The temperature produced by thermalization of the flow is on

the order of 3

7 T ~ SSpJM* _a 10 (|X} {§©} °K ©

where mp is the proton rest mass.

k is the Boltzmann constant

a is 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 108°K , then

&} {|©} ~ £ 100 © a

For stars the M/R parameter has values 0.5 to

10. The only objects for which this parameter is sufficently large are collapsed objects supported by degenerate electron or nucleon pressure or black holes. For degenerate dwarfs the M/R ratio is about 100 so temperatures on the order

108°K can be produced by shock wave heating but not viscosity heating. For neutron stars and black holes the mass radius ratio is about 10s, so high temperatures can be produced by viscous heating. From equation (1) it can be seen that for degenerate dwarfs a mass accretion rate of

7 1 3 6 1 0" Mg)year" can produce luminosity of the order 1 0 erg sec"1 while for neutron stars and black holes an accretion

B 1 38 1 rate of 10" MQ year" will give 10 ergs sec" . 4

In fact Shklovski [1962] had already suggested accretion into a potential well as a possibility for powering the extragalactic radio sources. Guseinov and

Zeldovich [1966] used similar arguments to suggest searching for the presence of emission lines from unseen companions in binary systems. The late 1960s saw many models of this 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 failed to show definite evidence for binary motions. Consequently, for a time, binary models fell 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 satellite UHURU answered many of the questions of that time. Observations in

1971 with UHURU discovered two periodically pulsating sources, Cen X-1 with a period 4.8 sees (Schreier et al

[1972]), and Her X-1 of period 1.2 sees (Tananbaum et al

[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, optical and X-ray observations a fairly convincing case can now be made that all stellar X-ray sources not in a are mass transfer binaries that contain a collapsed companion.

The recent review of Bradt and McClintock [1983] lists 115 sources that have been detected at energies >> 1 keV with a flux density >> 1 vJy with accurate positions determined. Of 5 these 75 are identified and 40 have as yet no optical counterpart.

Of the optically identified sources the majority fall in two well resolved groups commonly referred to as Type I and Type II X-ray systems. The major identifying characteristics are given in table 1.01 .

table 1.01 Type I vs Type II X-ray System Characteristics

Type I Type II

Hard X-ray Spectra Softer Spectra

T > 108K T < 108K

Often pulsating Not Pulsating

Luminous early type Optically faint blue

(0 4 B) optical counterparts excess objects ( F to M ).

10 L 104 °'01 * Lx/Lopt * 10 * V opt *

In the galactic plane Concentrated toward galactic centre like Population I like old disc population 6

The type I systems have proved to be the more intensely studied as they are brighter. The evolutionary history of these systems is also believed to be well understood ( van den Heuvel [1983,1981] ). The system seen now is the result of the more evolved ( initially 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 is the phase we label

as Type I X-ray binaries. From lifetime estimates and

relative numbers it can be deduced that this must be an

relatively normal occurrence amongst the massive binaries.

Eventually the intially less massive component becomes a

supernova, and a binary compact or two runaways

is generated.

1.2 HISTORY OF CYGNUS X-1

Although the existence of the strong X-ray source Cygnus X-1

was known from the earliest days of X-ray Astronomy its

identification was a mystery till the early seventies. The

combined results by UHURU ( Tananbaum et al 1971] ), an MIT

rocket flight ( Rappaport et al [1971] ) and Japanese

balloon flights ( Miyamoto et al [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 al [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 its 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 table 1.02 Observed Properties of Cygnus X-1 System

Identification

HDE 226868 SAO 69181 BD +34 3815 V1357 Cyg AG 1910

Co-ordinates Right Ascension 19 56 28.843 +35 03 54.51 RA (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 ( Beall et al [1984] )

Orbital B change = 0.045 mag ( Walker and Quintanilla [1978] ) 294 day B change = 0.0049 mag ( Kemp et al [1983] ) X-ray Luminosity 4 to 6 x 1 (rergs/sec ( Liang and Nolan [1984] ) Radio Luminosity ( long term )= 0.015 Jy ( Tananbaum et al [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 is the same as the supernova of 1404 reported by Clark and Stephenson [1977] who used an

incorrectly translated ancient record according to Li Qi-Bin

[1979]. The star was still almost as bright 44 days later 9 and this gives confidence in the supernova interpretation.

Li Qi-Bin [1979], from the records, estimates that at maximum the star must have been brighter than -3m. From the

present day reddening and distance estimates for Cygnus X-1

this gives an absolute magnitude for the event of brighter

than -I8.5m. Barbon et al [1973] give an average type I

supernova maximum brightness of -18.6 ± 0.15m, while Barbon

et al [1979] find 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 is in disagreement with Maza and van den Bergh [1976]

who claim that type I supernovae are not associated with the

young spiral arm population, and in agreement with Johnson

and MacLeod 11963] who state the opposite. The range of

progenitors for Type I supernova is still uncertain (

Trimble [1984] ).

The concern of this thesis is a another look at a

system in which the secondary is 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 this

study. Chapter Three deals with what has been learnt from

the examination of the absorption lines found in the

spectrum. Chapter Four deals with the problems of properly

interpreting what is seen in the two prominent emission

lines He II X4686 and Ha. Chapter Five deals with an

explanation for the origin of the emission lines. Chapter

Six describes what has been learnt from EXOSAT X-ray 10 observations ( simultaneous with the July 1984 optical observations ). Chapter Seven summarizes the conclusions of this thesis. An atlas of spectra for stars with spectral type between 08 and B1 is found in Appendix A. All the literature velocity measures for HDE 226868 are tabulated in

Appendix B. Chapter 2

DATA COLLECTION AND ANALYSIS

2.1 THE OBSERVATIONS

The optical data used in this 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 slicer gave a projected slit 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 slicer gives a dispersion of

31.1 Amm"1 with a projected slit 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 slicer giving a projected slit width of 45^m ( CFHT Observers

Manual ).

11 12

2.2 THE RETICON DETECTOR

The data was collected over the period from 1980 to 1984 at these three observatories and the detector used for all observations was an 1872 element refrigerated Reticon. The choice of a Reticon, besides its availability 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 ), reciprocity failure and the low Detective Quantum Efficency.

Photographic plates typically give a maximum signal to noise of =* 60 ( Hoag [ 1976], Walker [ 1985] ) which is too low for the study of line profile variations.

A Reticon is an almost ideal detector for this program

( and spectroscopy in general ) for a number of reasons.

The DQE is ~ 40% in the blue compared to = 2% for

photographic plates ( Walker [1985] ).

The detector is linear ( Campbell [1977], Vogt [1981] )

with a saturation level of £ 2 x 107 equivalent photons

( Timothy [1983] ). This gives a dynamic range that can

be as high as 10* with proper reduction.

There is no dead space between the detector elements 13

( Timothy [1983] ).

The detector is 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 collection of photons and matched

resolution to the image slicer.

The data is aquired in digital form.

A Reticon is a monolithic silicon diode array manufactured by the EG & G Reticon Corporation. The array consists of a series of bars of p-doped silicon 2 Mm thick

formed at regular intervals along an n-doped silicon

substrate ( 300 u thick ) on a gold substrate acting as an

anode. The surface of the chip is covered by a 3/um layer of

Si02 to reduce reflection from the array. A reverse bias ( 5

Volts ) applied to the junction between the two silicon

regions will create a region at the interface depleted of

free charge carriers and that has low current leakage and

high carrier mobility. Electron/hole pairs produced by

absorption of photons, or thermally, will accumulate in a

thin layer along the interface. This slowly discharges the

diode until some set integration time is reached, at which

time the diode is reset to its original 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 ) is done sequentially using a shift register clocked to connect each diode to the appropriate video line. This signal is amplified and digitised 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 line Walker et al [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 is not linear with exposure time ( Percival and Nordsieck [1980] )]

For this reason the array is normally cooled to near liquid nitrogen temperatures. Temperature stability ( to compensate

for atmospheric temperature changes ) is maintained to ±

0.2°C at 160°K using a heater in a temperature sensor loop

( Campbell et al [1981] ). For the presently available generation of UBC built Reticon there is negligible dark current at these temperatures ( Campbell [1977] ), however earlier Reticons with which some of the data in this thesis was obtained occasionally needed some correction for this effect ( pre 1982 ). This was done by using equivalent

length dark exposures to find the level of the thermal contribut ion. 15

The noise in a Reticon is dominated by the reset noise of the bias voltage due to Johnson noise in the shift register switch resistance. The RMS variation in successive bias charges is ( Geary [1979] )

A = 2.5 x 109 ATC where

A is the number of equivalent electrons

C is the diode capacitance in pF k is the Boltzmann Constant

T is the temperature in

The best attainable figure is expected to be A= 300 electrons ( Walker et al [1983] ). This value is close to being achieved in the most recent UBC Reticons. The readout noise is normally monitored by measuring the variance in short dark exposures which is typically * 2-3 ADC units. As an example of what this means to the observer, using a figure of 185 e" per ADC unit ( Walker et al [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 lists some characteristics of the Reticon Systems used in this thesis. 16

Table 2.01 Reticon Systems

Reticon # e"/ADC(hi) high/low ratio

Prototype 1 400 5

DAO 2 185 5

UBC 3 150 3.5

CFHT 4 250 3.5

2.3 THE DATA REDUCTION

To properly reduce the data, appropriate material must be

collected during the observing run at the telescope. The

output spectra all contain an output additive fixed pattern

which is due to coupling of the clock pulses to the video

output lines. This fixed pattern is a large amplitude

saw-tooth waveform that has a repeat cycle of multiples of

the number of video lines ( i.e. of 4 ). The pattern is

fairly stable with time if the clock pulses are stable and

the temperature of the Reticon is constant. A normal

technique for removal of this pattern is to numerically

subtract a second (short) exposure taken immediately after

the initial readout of the data frame ( Walker [1977] ).

This frame should have identical fixed pattern and the

digital subtraction should be good.

The next step in the procedure is to correct for any

small scale changes in sensitivity 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 flat spectrum from a distant source should be used, as the light path followed by the star's and the flat field's photons would then be identical. This would remove small errors due to differences in polarization of the incoming light and in differing illumination of the exit pupil. Unfortunately no bright stellar flat spectrum sources exist and instead an incandescent lamp is used. The best corrections were found taking flat field 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 stellar exposures to be achieved was excessive. The technique finally adopted was to position the lamp in the slit room just before the last element in the coude train. The telescope exit pupil was defined using a circular stop so as to ensure the

illumination of lamp and stellar spectra was the same. For best results it was necessary to adjust the iris diaphragm, used as a stop, for each star observed. This is thought due to a slight mis-collimation of the coude mirrors. The average of many lamp exposures ( typically 100 x 50 sec exposures ) is used in the final division to correct the

stellar spectrum. As lamps of sufficently high temperature

to produce a flat spectrum in the blue are not available,

the lamp spectrum is divided by a low order polynomial

fitted to the spectrum to correct for the lamp blackbody curvature, 18

The gains of the different output amplifiers attached to each line are only possible to adjust to within a few percent. Thus to calibrate their relative gains continuous spectra from an incandescent calibration lamp were exposed to different signal levels. Normally a filter 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) level. Typically fifteen different exposure levels ( each with 20 to 50 exposures ) between zero and saturation level were taken. Corrections to each

line in order to move them to the mean of all the data were obtained and this was then fitted by a ( first order ) polynomial to give a correction according to gain level which was then applied to all spectra on that night. The change in gain is * 5 x 10"8/ADCU for the high gain mode of

operation.

After all these corrections it may be possible that a

small four line pattern remained. A small additive correction was then applied to the lines to set all the

lines means' equal. Thus to properly reduce Reticon data

involves dealing with on the order of 600 recorded spectra

per night or for the total 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 this thesis on standard

stars was well reduced in this way. The exposure time, at

all 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 is 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 periodicity in the spectrum with a spatial frequency of

4 pixels. The gradual rise in power towards low frequency is

due to transforming spectral features and the presence of

negative spikes is 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 particularily

evident. This is believed the result of a significant

warming of the array between the beginning and end of an

exposure. For data obtained with the prototype Reticon

system there were almost certainly problems associated with

the liquid nitrogen cooling system. On occasions blockage in

the filling system would cause only partial filling of the

storage dewar and leaks in the vacuum insulation system

resulted in poor insulation and frosting problems. This

latter problem was easily detected as the lamps rather than 20

Figure 2.01 Fourier Transform of spectrum of Cygnus X-1 in figure 2.02 . X Nyquist Frequency 22 being smooth were extremely 'ropey'. The new Reticon system is more random in its properties. Sometimes the baseline exposure taken immediately following the stellar exposure resulted in excellent removal of the fixed pattern whereas at other times only an exposure of equal duration proved satisfactory. At other times no dark of either, short, long or intermediate exposure time was found to be suitable. A possible explanation for this problem is 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 this 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 until an on chip temperature sensor is available the real chip temperature variation will not be known. Another possibility for the lack of satisfactory darks is 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 will be at a temperature below that found immediately after a readout and thus the current flow to reset the diodes will need to be higher. Thus a three hour dark will be different from a ten second exposure and this may be why a short dark exposure may not correct the fixed pattern of a long stellar exposure. The reason for the long darks not working well on long stellar exposures is probably due to long term drifts. 23

If consecutive long darks are taken it is found that the mean level 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 drift by a few ADC units between liquid nitrogen refills and nights.

One way of correcting for these long term zero drifts was by reading out 52 dummy diodes before and 76 after, each read out of the 1872 elements. That is a normal intergration cycle is carried out with the switch opening and closing but without activating the shift register to address the individual diodes. Thus, in principle, 32 zero point samples per video line were available to be averaged and applied as a correction to the actual pixels. This correction was only available for our most recent data and could not be used in all cases due to electronic problems with these dummy pixels. The extra pixels in lamp exposures were found to be unuseable presumably because of the heating effect of the many lamp photons on the video lines.

2.5 COSMIC RAY EVENTS

It had been noticed from the earliest Reticon observations that on occasion large spikes were seen in the data. At first these were attributed to noise in the detector but as the system performance improved it was clear that it was something else. A clear indication of how these events limit 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 stellar features are identified. Clearly seen is the range in energy of the spikes and their 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 affect line profiles ( for example the He I X4713 line ) and thus radial velocity determination. These events have also been noticed by other users of Reticon detectors ( Vogt [1981] ) and ascribed to cosmic rays striking the array. As the rate of these events seemed to vary for the four different Reticon chips used in this thesis and because of the importance of knowing the limits of long exposure time, high signal to noise spectroscopy, these events were investigated futher.

The ideal time for intensive study of this 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 different altitudes. The difference in the rate of events between observatories should depend on the known absorption of the atmosphere.

There were fifteen individual spectra of Cygnus X-1 obtained at CFHT over five nights, all of approximately two hours duration ( see table 2.02 for details ). These spectra were inspected for all scales ( 1 to 20 pixels ) of non-stellar features. Such affected pixels or groups of pixels were corrected by replacing their ADC level with a value obtained 25

Figure 2.02 CFHT Spectra of Cygnus X-1 with basline removed. 65000 60000 55000 50000

45000

40000' 600 900 1200 300 Pixel U 1500 1800

400000 h 300000 200000 h 100000

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 pixel showed spikes on more than six of the

fifteen spectra. The He II X4686 emission line in Cygnus X-1

fell in the region between pixels 300 to 700. Only the most obvious spikes were modified in this region which probably accounts for the low number of events. The frequency of occurrences away from this region looks quite random which

rules out any breakdown on certain pixels. The histogram in

figure 2.04 displays the distribution of sizes ( how many pixels were affected by a spike ) of recorded events on all

the spectra. Clearly the narrowest events ( <3 pixel ) are

the most common. One futher piece of evidence against the possibility of problems in the electronics, 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 different observatories

is shown in table 2.02 along with theoretical estimates from published cosmic ray fluxes. These predicted numbers are

based on values using information from the 'Particle

Properties Data Booklet' ( Aguilar-Benitez et al [1984] ).

Cosmic Ray muons are highly penetrating and suffer little

attenuation from the material of the observatory building.

Allkoffer [1975] and Aguilar-Benitez et al [1984] give the 28

Figure 2.03 Histogram of bad pixels for CFHT Data taken 08-12 July 1984.

30

Figure 2.04 Distribution of sizes of spikes as determined from all CFHT 08-12 July 1984 spectra. 31

Distribution of UJ i d t h s of spikes

Width of Euent (in pixels) 32

Table 2.02 Details of Ocurrence of Spikes (normalised to a Reticon Area = 21 mm2)

Observatory Altitude Measured Expected m counts/hr counts/hr

DAO 229 1 1 10

CFHT 4200 19 20

CFHT (CCD) 4200 18 18

Kitt Peak 2100 58

flux of muons at 4300 metres as =*0.03 muons/cm2/sec and that at sea level as .014 muons/cm2/sec. Variations from this rate due to the latitude ( =5% ) and longitude ( ^5% ) difference or the diurnal variation ( < 0.1% ) are insignificant ( Allkofer [1975] ). Therefore for a Reticon array of area 21 mm2 the expected number of cosmic events in a one hour exposure is 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 al [1985] ). The value found by

Leach and Gursky [1979] for CCD frames obtained at Kitt Peak is 0.08 cm~2sec"1 or 58 events/hour per Reticon area. This is much higher than our observations find and probably indicates either an extraneous source of spikes in their data or possibly solar activity which can produce large changes in the muon flux ( Allkofer [1975] ).

The expected effect of a muon passing through a diode can also be roughly evaluated. The peak of the muon energy 33 spectrum is at about 400 MeV. According to Aguilar-Benitez et al [1984] these muons will lose on average 1.1 MeV/gm/cm2 when passing through carbon. Assuming a similar figure for silicon and a 30#um depth for the depletion region

( Livingston et al [1976] ) gives an average loss of

0.006 x 1.1 MeV / 400MeV muon = 7 x 103 eV, where 0.006 gm/cm2 is the area density of silicon in the depletion region. The excitation energy for the production of electrons in the depletion region is 3.6 eV/electron.

Hence the energy loss by a muon passing through a diode could produce = 2000 electrons, which is approximately that

found for the average spike value in the Reticon data.

Thus the fact that the events occur randomly across the array, are typically narrow and the- agreement of the

frequency, variation of frequency with altitude and amplitude of the observed spikes with those predicted from

the known properties of cosmic ray muons strongly suggests that this indeed is the source of the spikes. The penetration depth of these particles is so large that

shielding is not feasible. For the current generation of detectors they seem to be a fundamental limitation to precise spectrophotometry. Future detectors utilising 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

nights)"1 probably have a different origin. 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 possibility of radioactive contamination of the Reticon chip itself. To investigate this further the two chips available at UBC ( #1 and #3) were taken to the TRIUMF facility where their 7-ray spectrum was measured. 7-rays have the advantage that they suffer little attenuation in most materials and allow bulk properties to be measured. Unfortunately the 7 spectrometer was designed for much higher levels of activity than found in these chips and the actual fluxes are somewhat unreliable ( ±30% ). The 7 peaks that did stand out above the background were identified as those from the decay of

Ra226, Bi21» and Pb21• with activities of «* 0.5, 0.1 and 0.3

Bequerels. The presence of these transitions implies the decay sequence of U238 ( Walker, Kirouac and Rourke [1977] ) is being seen. The Uranium (4n+2) series produces 8 a particles whose energies range between 5 and 9 MeV. The penetration depth for such a particles is = 70vm ( Yaney et al [1979] ) although there is evidence for much longer penetrations ( Kirkpatrick [1979] ). The electrons produced by j3 decay have energies of a few MeV, their typical pathlengths are =* 1-2 cm ( Aguilar-Benitez [1984] ) and they are unlikely to interact in the silicon ( May and Woods

[1979] ).

. The location of this radioactive material is not determined from the 7-ray measurements but it could come 35 from the ceramic packaging or the quartz window material or even the gold substrate. All these materials are known to contain contain uranium from the work of May and Wood [1979] who investigated a particle 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 life of

U238 as 4.5 x 109 years gives the number of U238 atoms as =

1017. Taking the chip volume as 0.9"x0.288"x0.1" (EG & G specifications) and the density typical of a silicate of =*

2 g/cc ( Handbook of Chemistry and Physics ), gives a

fraction of U238 as = 10 ppm. This is similar to the levels

found by May and Woods (1979) in semiconductor packaging material. Until the exact location of the decaying material

is known the expected number of spikes can not be well estimated. An observed rate of activity of =*0.2 Bequerels gives an a particle flux of 10" hour"1. Although this rate

is much higher than the observed spike rate the effects of collection solid angle and attenuation by the silicon below the depletion region will reduce the figure considerably.

Notice that a typical a particle of 5 MeV, if completely

stopped in a single diode, will produce a hole-electron pair

for each 3.6eV of ionizing particle energy ( Kirkpatrick

[1979] ) or *106e". This is 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 all the observations of Cygnus X-1 used in this 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 this 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 this 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 al [1984] ) and displays well the long term stability 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 is given in table 2.04.

2.7 DIGITAL SUBTRACTION

To those accustomed to photographic plates the idea of digitally subtracting two aligned spectra may seem a little dangerous. One of the advantages of a Reticon type detector

is that the number of ADC units recorded is related to the

number of electrons produced by stellar signal photons by a Table 2.03 Details of Observations of Cygnus X-1

Date BJD Te1escope D1! V region Exposure Barycentr1c Air Re D/M/Y 2440000+ A/l A Time(secs) RV(km/sec) Mass & (

01/10/80 4513 . 770 DAO 48" 40 4686 10800 14 . 55 1 . 22 1H 02/10/80 4514 .691 DAO 48" 40 4686 10000 14.61 1 .05 1H 03/10/80 4515 .698 DAO 48" 40 4686 10800 14 . 79 1 .06 1H 04/10/80 4516 .680 DAO 48" 40 4686 10000 14.93 1 .05 1H 07/09/81 4854 . 722 DAO 48" 40 4686 10000 9. 16 1 .03 1L. 08/09/81 4855 .822 DAO 48" 40 4686 7200 9.58 1 . 18 1L 09/09/81 4856 .838 DAO 48" 40 4686 10000 9 .86 1 . 24 1L 10/09/81 4857 .818 DAO 48" 40 4686 7200 10.08 1 . 18 11 11/09/81 4858 .810 DAO 48" 40 4686 7200 10.31 1 . 17 1L 13/09/81 4860 .853 DAO 48" 40 4686 8000 10.85 1 . 36 1L 09/05/82 5098 .705 DAO 48" 40 4686 10000 -17.39 6 .79 2H 10/05/82 5099 .716 DAO 48" 40 4686 10000 -17.38 5 .41 2H 22/06/82 5142 .843 DAO 48" 40 4686 15000 -11.81 1 . 1 1 2H 23/06/82 5143 .852 DAO 48" 40 4686 15000 -11.57 1 .09 2H 24/06/82 5144 .839 DAO 48" 40 4686 15000 -11.37 1 . 1 1 2H 25/06/82 5145 .855 DAO 48" 40 4686 10600 -11.12 1 .07 2H 05/08/82 5186 . 793 DAO 48" 40 4686 12900 -0. 14 1 .03 2H 06/08/82 5187 .828 DAO 48" 40 4686 12500 0.22 1 .03 2H 07/08/82 5188 .767 DAO 48" 40 4686 10000 0.40 1 .04 2H 07/08/82 5188 .869 DAO 48" 40 4686 7700 0.59 1 .08 2H 07/08/82 5188. .953 DAO 48" 40 4686 6700 0.72 1 . 34 2H 08/08/82 5189 . 793 DAO 48" 40 4686 12000 0.75 1 .03 2H 09/08/82 5190. .762 DAO 48" 40 4686 12000 0.98 1 .04 2H 09/08/82 5190. .901 DAO 48" 40 4686 12000 1 .23 1 . 16 2H 29/09/82 5241 .707 DAO 48" 40 4686 15000 14.01 1 .06 2H 30/09/82 5242 ..66 9 DAO 48" 40 4686 8000 14.13 1 .03 2H 30/09/82 5242. , 767 DAO 48" 40 4686 10000 14 . 28 1 . 19 2H 01/10/82 5243. .697 DAO 48" 40 4686 14200 14 . 35 1 .05 2H 20/10/82 5262. .657 DAO 48" 40 4686 13000 16.90 1 .07 2H 27/06/83 5512 .. 799 DAO 48" 40 4686 13700 -10.81 1 . 19 2H 28/06/83 5513. 822 DAO 48" 40 4686 15000 -10.54 1 .. 12 2H 30/06/83 5515 . 875 DAO 48" 40 4686 13500 -9 .98 1 .0. 4 2H 29/07/83 5544 . 773 DAO 48" 40 4686 10200 -2.31 1 ,0, 6 2H 29/07/83 5544 . 907 DAO 48" 40 4686 13000 -2 .06 1 .. 10 2H 30/07/83 5545 .724 DAO 48" 40 4686 10000 -2 . 10 1 . 15 2H 30^07/83 5545 .886 DAO 48" 40 4686 10800 -1 .81 1 .07 2H 31/07/83 554G . 774 DAO 48" 40 4686 10800 - 1 . 72 1 .05 2H 31/07/83 5546 .914 DAO 48" 40 4686 13500 - 1 .47 1 . 13 2H 01/08/83 5547 .856 DAO 48" 40 4686 18000 - 1 . 28 1 .04 2H 29/ 1 1/83 5667 .635 DAO 72" 31 4686 10000 16 . 40 1 . 33 2L 30/11/83 5668 .624 DAO 72" 31 4686 1 1000 16 . 27 1 . 29 2L 01/12/83 5669 .635 DAO 72" 3 1 4686 13306 16 . 16 1 . 36 2L 02/12/83 5670. .615 DAO 72" 31 4686 1 1 120 16 .01 1 .28 2L 19/12/83 5687 .627 DAO 72" 31 4686 13100 13 .08 1 .64 2H 07/07/84 5888 . 782 DAO 48" 40 4686 7200 -8 . 19 1 . 16 3H 07/07/84 5888 .891 DAO 48" 40 4686 9000 -8 .01 1 .03 3H 08/07/84 5889 .807 DAO 48" 40 4686 851 1 -7 .90 1 .09 3H 08/07/84 5889. .904 DAO 48" 40 4686 8100 -7 .72 1 .03 3H 09/07/84 5890 . 794 DAO 48" 40 4686 8000 -7 .65 1 . 1 1 3H 09/07/84 5890 .895 DAO 48" 40 4686 10000 -7 . 47 1 .03 3H 10/07/84 5891 ,.79 9 DAO 48" 40 4686 7600 -7 . 38 1 . 10 3H 10/07/84 5891 ..89 7 DAO 48" 40 4686 9300 -7 . 20 1 .03 3H 11/07/84 5892 ..80 0 DAO 48" 40 4686 7500 -7 . 1 1 1 .09 3H 11/07/84 5892 ..89 7 DAO 48" 40 4686 9000 -6 . 94 1 .03 3H 12/07/84 5893 ,,87 8 DAO 48" 40 4686 10431 -6 . 7 1 1 .03 3H 13/07/84 5894 ..79 5 DAO 48" 40 4686 8 199 -6 . 59 1 .09 3H 13/07/84 5894 ..85 5 DAO 48" 40 4686 8020 -6 . 48 1 .03 2H 06/07/84 5887 ..80 7 DAO 72" 31 Ha 13000 -8 . 35 1 .05 2H 07/07/84 5888 .,80 0 DAO 72" 31 Ha 7 200 -8 . 17 1 . 1 1 2H 07/07/84 5888 ..89 3 DAO 72" 31 Ha 9000 -8 .00 1 .03 2H 08/07/84 5889 ..89 4 DAO 72" 31 Ha 87O0 -7 . 74 1 .03 2H 09/07/84 5890. 805 DAO 72" 31 Ha 7408 -7 .64 1 .09 2H 09/07/84 5890. 895 DAO 72" 3 1 Ha 8224 -7 . 47 1 .03 2H 10/07/84 5891 . 797 DAO 72" 31 Ha 6600 -7 . 38 1 . 10 2H 10/07/84 5891 ..89 1 DAO 72" 31 Ha 9500 -7 . 22 1 .03 2H 11/07/84 5892. 789 DAO 72" 31 Ha 7750 -7 . 13 1 . 1 1 2H 11/07/84 5892 . 895 DAO 72" 31 Ha 9600 -6 .94 1 .03 2H 12/07/84 5893 . 810 DAO 72" 31 Ha 10570 -6 . 83 1 .07 2H 13/07/84 5894 . 802 DAO 72" 31 Ha 7 100 -6 . 57 1 .08 2H 13/07/84 5894 . 892 DAO 72" 31 Ha 8243 -6 .41 1 .03 2H 14/07/84 5895 . 791 DAO 72" 31 Ha 8000 -6 . 32 1 .09 2H 14/07/84 5895 ..89 5 DAO 72" Ha 9500 -6 . 13 1 .04 1H 31 co oo 08/07/84 5889. .854 CFH 3. . 6m 2 . 4 4686 5704 -8 ..0 1 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 ..05 1 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 .30 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

Star Date Telescope Dispersion V re( Exposure Magnitude Ret 1 con D/M/Y A/mm A Time (sees) ( V ) & Gam x on 15/11/80 DAO 48" 40 4686 750 3 .66 1H HD 40111 15/11/80 DAO 48" 40 4686 3200 4 .82 1H t Per 07/09/81 DAO 48" 40 4686 200 2 .89 1L £ Per 07/09/81 DAO 48" 40 4686 200 2 .85 1L 40 Per 08/09/81 DAO 48" 40 4686 500 4 .97 1L AE Aur 08/09/81 DAO 48" 40 4686 500 5 .96 11 HD 195592 10/09/81 DAO 48" 40 4686 1500 7 .08 1L it Or t 10/09/81 DAO 48" 40 4686 250 2 .06 1L HD 199579 11/09/81 DAO 48" 40 4686 500 5 .96 1L HD 199216 11/09/81 DAO 48" 40 4686 1000 7 . 1 1L HD 217086 13/09/81 DAO 48" 40 4686 2000 7 .64 11 I on 22/10/81 DAO 48" 40 4686 500 2 . 77 1H a on 22/10/81 DAO 48" 40 4686 200 3..8 1 IH « on 22/10/81 DAO 48" 40 4686 100 1 .70 1H HD 36822 22/10/81 DAO 48" 40 4686 200 4 .41 1H 22/10/81 DAO 48" 40 4686 500 4 .4. 2 1H i/ on HD 36960 22/10/81 DAO 48" 40 4686 500 4 .78 1H n on 22/10/81 DAO 48" 40 4686 200 3 . 36 1H 42 on 22/10/81 DAO 48" 40 4686 200 4 , 59 1H 0' on c 05/03/82 DAO 48" 40 4686 1000 5 . 13 2H 15 Mon 06/03/82 DAO 48" 40 4686 500 4 . 66 2H A Leo 24/06/82 DAO 48" 40 4686 500 3 .8 5 2H 15 Sgr 07/08/82 DAO 48" 40 4686 900 5 . 38 2H 9 Sge 07/08/82 DAO 48" 40 4686 890 6 . 23 2H HD 207198 08/08/82 DAO 48" 40 4686 1500 5. 95 2H HD 218915 08/08/82 DAO 48" 40 4686 3600 7 . 18 2H S on 30/09/82 DAO 48" 40 4686 50 2 . 05 2H HD 225146 30/09/82 DAO 48" 40 4686 5000 8 .6 0 2H 6 on 01/10/82 DAO 48" 40 4686 400 2 . 23 2H HD 47432 01/10/82 DAO 48" 40 4686 2000 6 . 2 1 2H HD 194280 01/10/82 DAO 48" 40 4686 7200 8 . 39 2H HD 13745 01/10/82 DAO 48" 40 4686 4 200 7 .8 8 2H HD 204 172 20/10/82 DAO 48" 40 4686 1000 5. 94 2H y Cas 28/06/83 DAO 48" 40 4686 100 2 .4 7 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..6 2 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 .9. 4 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 Lyr 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 .0. 8 2H 19 Cep 12/07/84 CFH 3. 6m 2.4 4686 750 5. 1 1 2H 42 constant which is the same for all spectra ( i.e. the detector is linear ). Coupled with the large dynamic range of the Reticon, this enables the normalised spectra of two identical stars of very different exposure level to be subtracted directly from one another with very little residual spectrum in the difference. This is without the elaborate precautions required with photographic spectra to allow for reciprocity failure.

To illustrate how well digital subtraction can work an example of a much observed star is shown. X Per ( HR 1209 ) has been identified as a X-ray source ( Bradt and McClintock

[1983] ). Its spectrum has been detailed by Cowley et al

[1972] and Hutchings et al [1975] and a spectral type of

09.5Ve has been assigned. Its spectrum, obtained as part of the collection of standards, shows emission in the Balmer lines as expected for an 'e' star but also a considerable weakening of the He I triplet lines relative to the He I singlet lines. This may be due to a contribution from a surrounding nebula, as detailed in Osterbrock [1974]. A typical 09.5V star spectrum ( o Ori ) after suitable

shifting, 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 clearly 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 4800 5000 Nauelength (Angtsrom) 47 the problem of fitting a good continuum at the blue end of the spectrum.

Further tests were also conducted subtracting different length exposures ( i.e. different ADCU level ) of standard stars from each other. In all 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 this system.

These arguments included ;

unfortunately practically all the optical observations

available in the literature were obtained before the

advent of the current generation of low noise silicon

detectors. Most of the published spectra were therefore

of low signal to noise or the average of spectra taken

over many different orbital cycles. Any variations from

cycle to cycle or within a revolution were

conseguentialy difficult to detect. Claims of observed

changes in the spectral type as a function of phase

( Smith et al [1973] ) and in the equivalent widths at

certain epochs ( Walker, Yang and Glaspey [1978]) needed

to be investigated carefully.

long term monitoring at high precision of the velocity

curve might uncover new periods and features that would

shed new light on the system. Models of the system that

do not involve a black hole require a third body in the

48 49 system ( Bahcall et al [1974], Abt et al [1977], Bahcall

[1980] ). Bahcall [1980] makes two specific predictions for his distant triple model for Cygnus X-1 in which two heavier stars form a close binary with a lighter X-ray source moving in an extended orbit about the close pair

( a la X Tauri ). Firstly, the centre of mass velocity of the two massive stars should vary by a few kmsec"1 with a period of the order of a month. Secondly the orbital period should change by the order of

(d/dt) ln( period ) =* 10"*'5 year"1. For an observed period of 5.6 days this would imply a change in the period of about half an hour in five years. The first effect is due to an assumed 1 X-ray source perturbing the velocity of the centre of mass of the inner binary.

The second effect is due to the necessary mass loss from the inner binary to power the X-ray source. Both these effects should be measurable, if 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 third body.

There are other possibilities for longer period changes ( > orbital period ) in this system. A suggested explanation for the long period changes seen in a number of low and high mass systems is 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 attributable to this

effect ( Priedhorsky et al [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 quality spectra of both HDE 226868 and stars of

similar spectral type to determine if there are

abundance anomolies as would be expected from, stars

involved in significant mass loss ( Dearborn [1977],

Deaborn and Eggelton [1977] ) or if the primary were a

low mass, low gravity B star such as HZ 22 ( Trimble et

al [1973] ). Such high quality spectra might also reveal

any weak lines attributable to -a BV companion star to

HDE226868 as is required by triple star models of the

system. Variations in the spectrum of the primary due to

X-ray heating ( Milgrom [1977] ) or elliptical

distortion by the secondary ( Hutchings [1977], Guinan

et al [1979] ) could be expected at observable levels.

3.2 THE SPECTRUM ITSELF

With these goals in mind this study was concentrated on the blue region of the spectrum. There were a number of good reasons for this choice;

the blue region is free of telluric lines

the Reticon detector works well in this region

early type stars are bright in the blue and contain 51

spectral lines with a range of excitation energies

the mysterious emission line 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 orbital cycles as possible. This was expected to show clearly the effects of variations between different epochs.

Shown in figure 3.01 is 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 details of data collection can be found in Chapter 2. The identification of features in figure 3.01 is listed in Table 3.01. Wavelengths for stellar lines are from Moore [1959], for night sky lines from Meinel et al [1975] and for interstellar lines from

Herbig [1975] and Scholz [1972], There are a number of lines not previously identified in the literature. The weak interstellar feature seen at X4963 stands out in spectra of

HDE 226868 as it does not share in the large velocity variations associated with binary motion. This line is also clearly seen in spectra obtained of other well reddened early type stars such as HD 206267 and HD 207198. There are also two unidentified emission lines at X6667 and X6700 in the spectrum of 19 Cepheus reminiscent of the line pair at 52

Figure 3.01 The Spectrum of HDE 226868 (upper) and 19 Cep (lower). Tic marks indicate lines identified in table 3.01.

Mivfltngth (Angstrom)

Table 3.01a Line list for early type stars (blue).

N2 (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 Call (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 Call (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 Oil 4699.21 0 II 4153.30 on 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- on 4319.93 H7 4340.468 on 4349.426 Hgl (Nightsky) 4358.3 0 II 4366.896 N III 4379.09 He I 4387.928 on 4414.909 ? (is) 4428.

Table 3.01b Line list for early type stars (red). He II 6406.3 He II 6527.3 Ha 6562.817 ? IS 6613.63 ? IS 6660.71 ? 6667.0 He I 6678.149 ? 6700.0 He II 6683.2 58

X4486 and X4504.

3.3 EQUIVALENT WIDTH DETERMINATION To investigate properly the spectra that have been collected, the equivalent widths of the lines need to be measured. For spectra of lower dispersion this can prove difficult to do due to blending of lines. Conventionally one determines the equivalent width by first finding the limits of the line wings by visual inspection, and then integrating the area between the continuum and the line profile, using these limits, either digitally or with a planimeter. In our observations the major contributor to the width of the lines observed is the instrumental profile. From arc lines we find that typical half widths are on the order of 2.5 pixel or about 1.5 A. The broadening due to rotation is not more that 90 km/sec or about 1 A. The line we see is the convolution of the naturally broadened line convolved with the rotational broadening and the instrumental profile. As the broadening terms are essentially the same for all lines, the equivalent width will be a function of the central depth of the line. Therefore one merely needs to find the constant term relating the depth to the equivalent width to determine all the equivalent widths in a spectrum. This technique thus allows the equivalent widths of blended lines to be determined. In order to check on how well the above technique worked, the observations of 19 Cepheus from July 1984 were 59 inspected and lines were selected with a range of central depths for which the limits of the line wings could be well determined. The equivalent widths, using the visually selected line limits, were evaluated using a numerical

Simpson's Rule integrating routine while the line depths were found fitting a Gaussian to the six points straddling the line 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 is quite good. Figure 3.03 shows a plot of the line depth and corresponding equivalent width as determined by the technique descibed above. It is clear that the two are approximately related by merely a constant over the entire range of line strengths. The deviations from linear due to line saturation effects do not significantly affect the results. Thus on any spectrum all that is needed

is to determine the equivalent width and line strength for one line and all the remaining lines can then have their

line depth determined and scaled to give the equivalent width. For heavily blended lines this method may not give

the absolute equivalent width but in this work the primary concern is with relative values where the technique is adequate. 60

Figure 3.02 Equivalent Width here Vs. Equivalent Width from work of others (in mA) for 19 Cepheus. Stars are from Takada [1977], circles from Conti's series of papers (see text). 61

500 1000 E Ul (mi 1 1 iAngstrom) others 62

Figure 3.03 Line depth, as fraction of continuum, vs. equivalent width (mA) determined using line limit 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.

Firstly 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 its spectral class has been made, differences from the mean stellar spectrum for this class due to the primary's history or current configuration can be looked for.

The ultimate aim of spectral classification is to place particular stars in homogeneous spectral type and luminosity bins by using spectral lines, blends and bands for the classification criteria. There has been a long history of improvements in this 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 lines. This was followed by the monumental Henry

Draper Catalogue ( Cannon and Pickering [1918-1924] ). The widely accepted criterion today is the Morgan-Keenan System

( Morgan et al [1943], Morgan and Keenan [1973] ) which is defined by a basis set of standard stars located on a two dimensional spectral type vs luminosity class plane. The process of classification is a differential comparison to these standards. Such a system forces stars to fit into a finite array of cells when in fact that really form a continuum of possibilities. The simplicity of arranging this 65 system in terms of two simple parameters, temperature and luminosity, however makes the system extremely attractive. A word of caution should however be noted for classification of early type stars under such a system. If spectral type is to be correlated monotonically with effective temperature then the effective temperature must be the parameter which most stongly determines what the conditions in the photosphere are like. Underhill [1983] has shown that for

03,04,05 stars this assumption breaks down completely and in

Underhill [1984] it is shown that mechanisms other than the underlying radiation field can affect the line forming region in spectral types 04 to 09. We shall proceed with this caution in mind.

Over small ranges of spectral type it is possible to quantitatively define variation of spectral type. In the MK system the variation of the ratio of Hel X4471 to Hell X4541

is the primary classification criteria for 0 type stars. In

09 stars the former is strongest but the ratio changes slowly so that by 05 the latter predominates. Conti and

Aschuler [1971] and Walborn [1971a] attempted to improve on the original MK classification by carefully looking at a

large number of 0 stars and attempting to classify them uniformly. They found the most consistent system resulted when the variation of ratios of certain Hel, Hell and

ionized silicon lines was used. Unfortunately neither paper gave quantitative values for these ratios and unless one is an expert in classification it can be difficult to determine 66

the exact spectral type. For this reason, and to be able to carefully compare HDE 226868 to stars of similar spectral

type, high signal to noise spectra of a number of like stars was obtained.

The stars of primary interest were confined to those with spectral type 08 to B1 as this might have been the maximum expected region of variability of HDE 226868 with phase due to the presence of the compact secondary. Listed

in Table 3.02 are all 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

classification of early type stars. This is the most

consistent set of spectral types available as they were

determined by the same person using objective criteria.

Column 4 has the spectral type from the Bright Star Catalog

( Hoffeit and Jaschek [1982] ) for all stars sufficently

bright. Column 5 has the effective 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 al [1979] from fitting the ultraviolet

continuum.

The equivalent widths of all significant lines in the

spectra of the standards were evaluated using the technique

described previously. The ratios of a number of lines which

appeared sensitive to spectral type(S) and/or luminosity(L)

were evaluated. The most sensitive ratios were found to be Table 3.02 Standard Star Characteristics

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 BOV 29500 34347 i/ Or 1 36512 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 CTi X Per 24534 (BOV) Ope 29500 -J 09.5111 290CX) 3^078 188209 09.5 lab 09V/ 34700 34°75 1993322 08.5111 09V 08. 5111 33200 14 Cep 209481 06f 39000 206267 06 5V(

08 35600 08 . OV 68 Cyg 203064 09V 35600 35401 214680 08.0111 10 Lac 38700 37721 06.0I(n) FP osif V. Cep 210839 B1I3 22900 2905 BC 0.7 la K Cas 2 00 09.51b 09.51b 9° 19 Cep 209975 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 all the standards and figures 3.04 to 3.07 give a graphical representation of this data. In these figures the dashed line represents the ratio to be found for HDE 226868, the star symbols that for supergiant standards, the squares for class Ills and the hourglass symbols for class Vs. It can be seen there is considerable scatter in using any one set of lines as a criterion of spectral type for a particular star.

The first determination of spectral type for HDE 226868 was made by Seyfert and Popper [1941 ] who gave BO.

Subsequently Morgan at al [1955] found BOIb, Murdin and

Webster [1971] also gave BOIb, Smith et al [1973] quoted

'between 09.5 and BO1 and then Walborn specified it 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 it can be seen that the primary of Cygnus X-1 does indeed fall in the part of each graph that gives a consistent spectral type of between 09.5 and 09.7. No peculiarities are noted.

In order to more clearly 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 class. Figure 3.08 70

Figure 3.04 Ratio of Si IV X4116 / He I X4121 for all available standards in table 3.2. Dashed line indicates ratio measured HDE 226868. OJ OJ

\ CD

o

• z z • X • E Z Z z X

•* L 06 07 08 09 09.7 B0.5 B1

Spectral Type 72

Figure 3.05 Ratio of Si III X4552 / He I X4387 for all available standards in table 3.2. Dashed line indicates ratio measured for HDE 226868. 73

ID

06 07 08 09 09.7 ' B0.5 B1 Spectral Type 74

Figure 3.06 Ratio of Si III X4552 / He II X4541 for all available standards in table 3.2. Dashed line indicates ratio measured for HDE 226868. 75

\ OJ tn in

Spectral Type 76

Figure 3.07 Ratio of Si IV X4089 / He I X4121 for all available standards in table 3.2. Dashed line indicates ratio measured for HDE 226868. Ra t io 4089/4121 • 1 2 3 4 'l r 1 i | 1 1— 1 T 1— "I T 1 1 o *

[BJ

9 - M M -

- - TJ <0 8- • M • * - o c* - • • * -J o • * - CD H N N * * * CC TJ OCO * _ 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 4552/4387 4552/4541 4089/4121

X Ori 36861 1.33 0 . 14 1 .07 2 . 37 139 Tau 40111 0.694 1 .09 5 . 57 1 .08 « 24760 0.43 0 .50 9 .46 0 . 77 5 Per 24398 0.44 0 . 74 >> 0 .724 40 Per 22951 0.42 0 . 32 12 . 93 0 . 76 AE Aur 34078 0.67 0 .09 >> 0 .82 195592 1 . 2 1 K. Or i 2004 1.12 0 .86 4 .54 1 .71 199216 0.41 0 .88 8 . 18 0 . 75 217086 1.05 0 . 54 0 . 35 1 .60 l Ori 37043 0 . 35 0 . 16 1 . 27 a Ori 37468 0.84 0 . 34 0. 76 1 .04 l Ori 37128 1.63 0 .87 2 . 79 2 . 18 36822 0.72 0 .63 3 . 39 1 . 10 v Ori 36512 0.72 0.. 34 0. 97 1 .. 12 36960 0.50 0 54 4 .3 4 0 8 1 n Ori 3541 1 0.73 0 . 35 >> 0 . 94 42 Ori 37018 0.39 0 . 32 4 .7 6 0. 64 0' Ori C 37027 0.66 0.. 35 0. 16 1.. 25 S Mon 47839 0.83 0. 19 0. 08 1. 35 p Leo 91316 0.49 0 99 3 .1 5 0. 76 15 Sgr 167264 1.62 0. 73 1 .7 9 2 .2 5 9 Sge 188001 1.69 0. 26 0. 10 3 .8 5 207198 1.58 0. 28 0. 25 2 .2 4 218915 1.69 0. 42 0. 56 1 .8 1 5 Ori 37742 1.69 0. 46 0. 61 2 .6 6 225146 1.39 0. 63 1 .4 5 1 .8 5 6 Ori 36486 1.40 0. 48 0. 59 1 .9 5 47432 1.65 0. 46 0. 77 2 .1 8 194280 1.57 0. 76 1 .7 5 2 .0 0 13745 1.41 0. 54 , o.78 1 .9 1 69 Cyg 204172 1.37 0. 79 3 .0 6 1 .9 4 T Cas 5394 0.79 0. 47 1 .1 6 1 .O O a Cam 30614 2.57 0. 44 0. 46 3 .6 8 X Per 24534 0.97 0. 50 0. 86 0. 38 188209 2.,0 2 0. 46 0.64 2 .67 1993322 0.,9 2 0,, 28 0. 33 1 . 47 14 Cep 209481 1 ,. 38 0. 47 0.65 2 .08 206267 0.,9 0 0. 27 << 2 .00 199579 0.,7 1 0. 31 0.76 1 . 99 68 Cyg 203064 0. 80 0. 27 << 1 . 47 10 Lac 214680 1 ,0. 8 0. 28 0. 33 1 .61 V Cep << 1 . 19 ix Cas 2905 0.,8 1 1. 06 >> 1 . 19 80 is 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 this thesis. The peculiarity of He II X4686 emission at spectral type 09.7lab of HDE 226868 is clearly seen in the diagram. No significant difference is seen in the strength of the metal lines ( of N, C and 0 ) as might be the case if significant mass loss from the primary affected abundances ( Dearborn and Eggleton [1977] ).

3.5 THE ROTATIONAL VELOCITY

It is of considerable interest to determine accurately the rotational velocity of the primary in this system for two

reasons. It has been stated by Hutchings [1982] that vrot / vsync nas va^-ue n«5, meaning that the secondary is orbiting much faster than the primary is rotating. Current orbital solutions show that there is no significant eccentricity.

Hence it appears we have a system in which orbital circularization has had time to occur but synchronization has not. If true this 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 ratio of the orbital velocity to the rotational velocity, if

synchronization is assumed, can give an estimate for the mass of the unseen secondary. gure 3.08 Spectral Mosaic for Wavelength Range centered on X4686. A Cep 9 Sge a Cam HD195592 e Ori Ori 061 081a K 09.51a 09.71a BOIa B0.5la

K Cas B0.7la

A Ori 19 Cep Cyg X-1 08.5lab 09.5lab 09.7lab

HD188209 15 Sgr 09.5lab 09.7lab

HD218915 HD194280 09.5!ab 09.7lab

C Ori 69 Cyg <; Per 09.71b BOIb Bllb

HD225146 HD 40111 09.71b Bllb

HD207198 HD47432 p Leo 09lb-ll 09.71b Bllb

6 Ori HD13745 HD199216 09.511 09.711 Bill 00 83 84

The estimation of rotational velocities began with the simple idea that the observed widths of lines of stars are too broad to be due to natural line broadening processes and that the measured width could be due to the range of velocities produced between the receding and forward moving edges of a rotating stellar surface. Carroll and Ingram

[1933] were the first to developed the technique of using the position of the zeros of the fourier transform of a spectral line to estimate rotational velocities. Gray

[1973,1976] has used the shape of the entire transform profile to estimate vsini for a variety of stars. Ebbets

[1979] has used this technique to estimate both rotational broadening and macroturbulence in the 0 type stars.

Many different mechanisms exist for the broadening of a stellar line and their effect can be thought of as a convolution with some intrinsic profile. Assume a spherical star rotating as a rigid body whose intrinsic profile is the same over the entire stellar surface. Taking O(AX) as the observed profile, P(AX) as the intrinsic profile, R(AX) as the rotation profile, M(AX) as the macroturbulence broadening function, and I(AX) as the instrumental profile, 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 this transform is that the first zero crossing is determined by the rotation profile alone. 85

The rotational broadening function has been determined previously in Huang and Struve [1953] and Gray [1976] and

from Ebbets [1979]

R(x) = a[ 2 * ( 1 - x2 )°"5A + 0.5 * /J * ( 1 - x2 ) ] where

x = AX / AXR

AXR = V sini X/c

a = 3 / ( 3 + 2/3 ) |3 = limb darkening parameter ( 0 ^ 0 £ 1.5 ) and

r(s) = [a/*] * J,(2TTS) - [ 2a/3 / (2TTS)2 ] COS(2JTS) +

[ 2a/3 / (2TTS)3 ] sin(27rs) / (2TTS)3 ] sin(2irs) If the zeros of this transform function are then observed at frequencies z^ (measured in units of cycles/angstrom), the vsini is given by

vsini = s. c / z. . 1 1 A

where s, = 0.665 , s2 = 1.162 , s3 = 1.663 , . . .

The instrumental function will be the result of a convolution of a Lorentzian ( the projected slit ) and the filtering function used on the data ( Gaussian ). For the CFHT data we have a dispersion giving approximately 0.036A/pixel. On average the width of the arc lines observed is 2 pixels and this results in the transform dropping to half the value of that at the zero frequency at a frequency of 14 cycles/A. The intrinsic profile can be obtained from 86 suitable models of early type stars such those found in Auer and Mihalas [1972]. Their NLTE model for a T = 30000°K and log g = 3.3 star (typical of HDE 226868 and 19 Cep ) gives profiles of the He I lines that drop to half their value in less than 0.5A, and their transform drops to half its value by about 2 cycles/A. Thus both these broadening terms result in zeros that would occur at much higher frequencies than that expected from rotational broadening in the early type stars being looked at. In order to test that this method works, the rotationally broadened NLTE theoretical profiles of Stoeckly and Mihalas [1973] were Fourier transformed in order to test how well the vsini they used to generate the profiles could be recovered. Their profiles allowed for the full limb-distance variation of both continuum intensity and line shape, and hence also allow us to see how seriously the assumption of a constant profile over the entire surface affects the Fourier transform technique. Figure 3.09 shows the vsini derived by determining the vsini using the first zero of the fourier transform of the Hel X 4713 line. It is clear that for values of vsini less than 100 kmsec"1 the technique works well in recovering the vsini. Above 100 kmsec"1 there is a progressively greater difference between measured and actual velocities. This is due to the Stoeckly and Mihalas [1973] paper only providing values for the profiles within 2A of the line centre. For the more rapidly rotating stars this results in most of the line information 87

Figure 3.09 vsini derived from FT Technique versus vsini used to generate profiles by Stoeckley and Mihalas [1973]. 88 89 being lost and the consequentially poor results.

The July 1984 CFHT data is of suitable dispersion to be able to carefully measure the vsini of HDE 226868. A disperion of 2.4 Amm"1 corresponds to 0.036 Apixel"1 which in turn gives a nyquist frequency of 25 cycle/A"1. The data collected at the DAO is of dispersion 40 Amm"1 which gives

0.6 Apixel"1 and therefore a nyquist freqency of 1.7 cyclesA"1, clearly unsuitable for any fourier transform work. Figure 3.10 shows the fourier transform of the mean

HDE 226868 and 19 Cep Hel X4713 profile from the CFHT July

1984 data. The straight line in this figure is an estimate of the noise level as derived from the expression given in

Smith and Gray [1976] and Smith [1976] which is

Sf = SXAX/N where

S^ is the transform noise to signal ratio

S^ is the noise to signal ratio in the data

AX is the wavelength interval between data points

N is the number of real profile data points

From the first zero in figure 3.10 one can derive a value of the vsini for 19 Cep of 75.1 kmsec"1 which is 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 vsini is 94.3 ±5 kmsec"1 which is quite different from the value of 140 kmsec"1 given by

Bolton [1975], The error in the vsini is estimated from the 90

Figure 3.10 Fourier Transform of mean CFHT He I X4713 profile for 19 Cep (upper) and HDE 226868 (lower). 91

1 1 1 1 r

Ql TJ 3

£

c

TJ Ql in

CCS £ JL ' v ; • i_ _ o

+ 4- ° 0-5 1 1.5

Frequency (cyc1es/Angstrom) 92 scatter in the individual vsini measures from the five nights observing at CFHT. Ebbets [1979] has fitted profiles to the fourier transform to extract a value for a macroturbulence parameter which is postulated to characterise large scale velocity fields on the stellar surface. Mihalas [1979] has severely criticized this technique on the grounds that the assumption of a constant line profile over the stellar disc is 'simply invalid'. Note that the technique used above for estimating the vsini of

HDE 226868 whilst using this assumption as a basis to proceed, calibrates against stars with theoretical

rotational velocities and can in that way be considered an empirical technique. Figure 3.11 shows the He I X4713 line profile for HDE 226868, used in the fourier transform, plotted with theoretical profiles from Stoeckly and Mihalas

[1973] over a range of input vsini. As can be seen any small

systematic errors ( 2% ) in placing the continuum will not affect the determined vsini significantly.

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 it

is in digital —f-orm—from a Reticon makes it possible to

obtain relatively good velocity estimates. After reduction

of the raw data as outlined in Chapter 2 all lines listed in

table 3.04 had their doppler velocity shift determined. The position of each line was found using a centre of weight 93

Figure 3.11 Actual HDE 226868 He I X4713 profile together with profiles from Stoeckly and Mihalas [1973] for the range of vsini labeled (in km/sec). KD Uavelength (Angstrom) 95 criterion in which

P =( I. I• p. ) / ( I. I.) where

P = the estimated line position p^ is the position of each pixel in the line profile

1^ is the associated absolute intensity relative to the continuum at each pixel position

The summation is performed over some consistent estimate of the line limits. These limits are, if possible, the positions where the line merges into the continuum but, as this is usually not possible due to blending, some other appropriate level ( 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 shift between them determined by taking one of the spectra, applying small shifts in the fourier domain and then creating a difference function, summed over all points on the line profile at each shifted position. After all the shifts are performed a high order polynomial is fitted to the difference function values and the position of the minimum gives the shift in position between the two lines

(Yang [1985]). This technique gave good results when tested on some of this data but the increased cost in terms of computing time did not allow its use.

Listed in table 3.05 and shown in figures 3.12 to 3.15

( folded on the orbital period found from figure 3,16 ) are 96 the radial velocities found using the centre of gravity method on the lines in HDE 226868 and the corresponding date of observation. These velocities are corrected to the solar system barycentre ( corrections given in table 2.2 ) using the parameters from Stumpff [1979], The velocities presented are given in four groups; the 'H' velocities are the mean hydrogen line velocities, the 'He I' velocities are those of neutral helium, the 'He II' are from singly ionized helium and the metal lines are from all others combined ( i.e. all

C, N, O, Si lines ). The lines used in each group and the weight assigned each line in calculating a mean group velocity for each night is given in table 3.04. The weights were assigned subjectively depending on the strength of the line, and its location in the spectrum. Note that for the

1984 DAO 72" red data only the He I X6678 line was available to determine an absorption line velocity.

There are a number of sources of error in determining velocities from the spectra obtained on the DAO 48" telescope at 40Amm"1. The technique of fitting a centre of gravity to a profile will yield different values depending on how many points are available in the profile, this is a

form of digitization error. Also blends with weak lines will perturb the shape of the line of interest and cause error.

Various experiments have been conducted to test for these effects using multiple spectra of bright standard stars. It

is found that these errors occur at a level of * 0.1 pixel or = 4 kmsec"1 in these spectra. Another, and unexpected, Table 3.04 Line weights for least squares fitting radial velocity curve and excitation potential for line groups.

Line Excitation Weight Potential (eV)

Hydrogen Lines ="1 0 4101.737 0.5 4340.468 1 .0 4861 .332 0.8

He I Lines ="21 4009.270 0.1 4026.189 0.8 4120.812 0.4 4143.759 0.8 4387.928 0.8' 4471 .477 1 .0 4713.143 1 .0 4921.929 0.8 5015.675 0.8 5047.736 0.5

He II Lines ="75 4199.83 0.4 4541.598 0.4 4685.685 1 .0

Metal Lines ="50 4069.897 0.2 4075.86 0.1 4088.863 1 .0 4097.31 0.4 4116.104 0.8 4349.426 0.1 4366.896 0.1 4379.09 0.8 4481.228 0.6 4510.92 0.5 4514.89 0.5 4552.654 0.5 4567.872 0.5 4574.777 0.1 4630.537 0.1 4634.16 0.2 4640.64 0.5 4647.40 0.2 4650.74 0.2 Table 3.05 Calculated Velocities for Spectra of HDE 226868

JO Binary X-ray H He I He II Meta 1 240000+ Phase Phase 1980 48" DAO

4513.76806 0.282 0. 322 61.72 64.85 75 .06 87 .05 4514.68889 0.447 0.325 10. 14 5.89 39.23 20. 55 4515.69653 0.627 0.329 -52.80 -65.01 -26.45 -56.67 4516.67778 0.802 0. 332 -92.65 -89.63 -82.67 -91.38

1981 48" DAO

4854.71944 0. 169 0.482 128.08 122.09 137.94 132.98 4855.81944 0. 366 0. 486 42 .69 47 . 38 55.09 65 . 27 4856.83542 0.547 0.489 - 17.94 -22.49 -28.59 -8 .95 4857.81528 O. 722 0.493 -98.33 -96. 12 -71.91 -94.79 4858.80764 0.899 0.496 -93.43 -60.87 -69.23 -67.55 4860.85069 0.264 0.503 53.84 67 . 50 93.85 71 .86

1982 48" DAO

5098.70486 0.740 0.312 -81.43 -77.29 -50.26 -70.71 5099.71528 0.921 0.315 -43.10 -30.07 -26.57 -28.94 5142.84028 0.622 0.462 -47 . 47 -39. 14 -47.32 -41.82 5143.84931 0.802 0.465 -85.83 -72.22 -70.09 -70.46 5144 .83681 0.978 0.469 -29.33 -26.06 - 13.34 -22.67 5145.85278 0. 160 0.472 55 . 10 54 . 50 74 . 29 70.53 5186.78958 0.470 0.612 7 .65 12 .98 1 1 .35 21 .85 5187.82431 0.655 0.615 -70.62 -59.97 -66.74 -61 .85 5188.76319 0.823 0.618 -66.81 -74.25 -55.90 -60.97 5188.86597 0.841 0.619 -64.83 -70.47 -55. 1 1 -61.07 5188.94931 0.856 0.619 -63.09 -65.28 -55.34 -54 . 18 5189.78958 0.006 0.622 -7 . 25 - 10. 14 11.18 4 .02 5190.75903 0. 179 0.625 52 .94 56.52 52.91 47 . 87 5190.89792 0.204 0.626 69 . 72 66 .04 75. 16 67 . 89 5241.70486 O. 277 0.798 70. 25 74 . 78 83.71 62.91 5242.66736 O. 449 0.802 14 . 32 10.48 26.71 1144 vo 5242.76458 0.466 0.802 -20.91 -2.92 18.84 - 1 . 75 CO 5243.69514 0.632 0.805 -80.50 -78.69 -94.02 -73.89 5262.65625 0.019 0.870 0. 27 -3 .02 7.59 2 .03

1983 DAO

5512.79653 0.689 0.720 -79 . 18 - 77.98 -61.77 -62.89 5512.93819 0.714 0. 721 -77.45 -86.05 -53.54 -61 .50 5513.81944 0.871 0.724 -66.41 -65.96 -46.62 -56.96 5515.87222 0.238 0. 731 76 . 34 70. 94 79.04 80. 49 5544.76944 O. 398 0.829 28 . 22 37 . 19 50.08 45 .26 5544.90347 0.422 0.830 26 .43 31 .54 47.40 40. 16 5545.72083 0.568 0.832 -41 .58 -30.91 -31 .72 -24 .68 5545.88264 0. 597 0.833 -45.99 -36.51 -35 . 19 -37 . 24 5546.77014 0.756 0.836 -90.54 -75.88 -76.07 -68.62 5546.91042 0.781 0.836 -92.09 -82.44 -80.40 -75.72 5547.85278 0.949 0.840 -37.78 -42.77 -42 .79 -35.66 5667.63681 0. 340 0. 247 49 . 70 70. 58 108.16 76 . 97 5668.62500 0.516 0.250 -27.64 -9.31 12 .77 6 .45 5669.63681 0.697 0.254 -99.58 -80.16 -55.55 -73.38 5670.61667 0.872 0. 257 -60.58 -53.31 -31.06 -61 .96 5687.62917 0.910 0.315 -60.82 -55.71 -48 . 22 -49.23

1984 48" Data

5888.77847 0.831 0.999 -84.51 -74.56 -72 .63 -7 1.47 5888.88819 0.851 0.000 -64.92 -65 .89 -67.59 -61.69 5889.80347 0.014 0.003 - 11 .58 -5 . 70 7 .05 -2 . 75 5889.90139 0.032 0.003 -1.13 5.72 14.19 6 .44 5890.79097 O. 191 0.006 7 1 . 54 68 . 70 76 .93 64 . 7 1 5890.89236 0.209 0.006 73.51 68 .58 69 . 1 1 76 . 32 5891.79583 0.370 0.010 47 . 52 55 . 32 67 .06 61 .58 ' 5891.89444 0. 388 0.010 59 . 18 50.61 66 .52 55 .97 5892.79653 0.549 0.013 -24.63 -23.69 -14.65 -8 . 52 5892.89375 0.566 0.013 -26.57 -31.59 -20.28 -19.77 5893.87431 0.741 0.017 -86.91 -85 . 12 -67.78 -74 . 10 5894.79236 0.905 0.020 -6 1.72 -52.39 -48.20 -47.31 1984 72" DAO

5887.83889 0.663 0.996 -61 .59 5888.79653 0.834 0.999 -66.80 5888.89028 0.851 0.000 -60.21 5889.89792 0.031 0.003 -6 . 38 5890.80208 O. 193 0.006 63 .90 5890.89167 0.209 0.006 64 .89 5891 . 79444 0. 370 0.010 56 .80 5891 .88750 0. 386 0.010 47 .82 5892.786 1 1 0. 547 0.013 -33.36 5892.89167 0.565 0.013 -34.24 5893.80694 0. 729 0.016 -78.40 5894.7993 1 0.906 0.020 52 .03 5895.78750 0.083 0.023 19.23 5895.89167 0. 102 0.023 28.22 1984 CFHT

5889.85069 0.023 0.003 2 . 35 5889.97986 0.046 0.003 16.26 5890.06875 0.062 0.004 24.23 5890.85417 0.202 0.006 61.18 5890.95625 0.220 0.007 71 .60 5891.04792 0. 237 0.007 71 .80 5891.93542 0.395 0.010 49.59 5892.01944 0.410 0.010 49.90 5892.10139 0.425 0.011 38.65 5892.85069 0.558 0.013 -24 . 11 5892.93681 0.574 0.013 -29.60 5893.07500 O. 599 0.014 -41.50 5893.82083 0.732 0.016 -73.74 5893.94375 O. 754 0.017 -75.42 5894.05625 0.774 0.017 -73.43 101

Figure 3.12a Mean He I line radial velocity curve for for HDE 226868. Crosses denote data from the DAO, circles indicate CFHT data, dotted curve is best orbital solution to the data. Uelocity (km/sec) 100 • 100

o

~0

ro

201 103

Figure 3.12b Residuals for best fit orbital solution to He I radial velocity curve of HDE 226868. Crosses denote data from the DAO, circles indicate CFHT data. vol 105

Figure 3.13a Mean Hell radial velocity curve for HDE 226868 using data from the DAO. Dotted line is best orbital solution to the data. Uglocity (km/sec) 100 • 100 i—•—•—•—•

o -J cr

ZT

Ul ro

90 L 107

Figure 3.13b Residuals for best fit orbital solution to Hell absorption radial velocity curve for HDE 226868 using data from the DAO. o -I

"0 3*

ro

801 109

Figure 3.14a Mean Balmer line radial velocity curve for HDE 226868 using data from the DAO. Dotted line is best orbital solution to the data. Uelocity (km/sec) 100 • 100 i . . . . ^ •

o cr

ro

OU 111

Figure 3.14b Residuals for best fit orbital solution to Balmer line radial velocity curve for HDE 226868 using data from the DAO. o ZT

"0 3"

ro

Zl I 113

Figure 3.15a Mean Metal line radial velocity curve for HDE 226868 using data from the DAO. Dotted line is best orbital solution to the data. Uelocity (km/sec ) -100 • 100

o cr

TJ zr in ID

Ul 115

Figure 3.15b Residuals for best fit orbital solution to Metal line radial velocity curve for HDE 226868 using data from the DAO. o

ro

9L I 117 error was of small random shifts in the spectra. Comparing standard stars taken on the same night or a series of arcs taken over many hours small shifts in the position of the lines can be measured. These shifts are of order 0.2 pixel or roughly lOkmsec"1. Yang et al [1982] have noticed such shifts in the similar design spectrograph at the coude of the CFHT. One suggestion to explain the shifts is that are due to guiding errors, however this is unlikely as an image slicer was used, and exposures were typically of three hours duration, factors that would minimise this effect. Fletcher

[1983] has also ruled out image motion due to air currents in the coude room by direct observation of images. Flexure in the Reticon mounting is possible but it is difficult to then understand why the shifts change direction at random.

As these shifts are seen both at CFHT and DAO it may be that they are integral to the readout of the Reticon system.

These shifts are quite small and would only cause problems if attempting to measure accurate radial velocities at low dispersion. This means that such measurements are not detector (signal to noise) limited but limited by the stability of the system.

One method of eliminating these shifts is to use the interstellar lines distributed across the spectrum as a set of fiducials. In practise however most of the lines are weak and/or blended, thus estimating their position accurately is not possible. The strong line at X4428 is heavily blended and unuseable. The Call H and K lines were not available on 118 all the spectra and when available fell near the edge of the array where removal of the fixed pattern is not as well executed as at the centre ( see Chapter 2 ). This affects determining the line position accurately and thus finding the small random shift. The errors in velocity determination for the DAO 72" red data were smaller. This was because of the presence of

telluric lines of H20 in the spectrum which can be used to accurately remove any shifts ( Griffin and Griffin [1973] ). Campbell [1983] gives in his review that the variation in the telluric lines from natural source such as upper atmospheric winds and topocentric variation is in the range 10-50 msec"1. At a dispersion of 3lAmm"1 this is more than adequate for a fiducial system as the line fitting routines have an accuracy of =*0.1 pixel or 3 kmsec"1. Shifts of the kind noted in the above chapter were masked by larger shifts that occurred with motion of the telescope. The most significant error in the CFHT 2.4Amm"1 data was from broad cosmic ray events distorting the line shape and producing shifts in the centre of weight. Quantifying the magnitude of this effect is difficult but the fact that the CFHT velocities for He I X 4713 fall within the range of scatter of the DAO He I velocity curve ( see figure 3.-4-2 j— makes it reasonable to assume it is small. All other sources of error for the CFHT data are minimal as a result of the velocity resolution (2 kmsec"1). 119

As a check on our errors and on any absolute offset, the velocity of 19 Cepheus for all nights it was observed

(1980 to 1984) was measured. The mean velocity so obtained was -14.5 ± 1.5 kmsec"1, close to the value of -14.3 ± 1-2 kmsec"1 by Conti et al [1977], -10.7 ± 3 kmsec"1 by Garmany et al [1980] and -13 kmsec"1 by Hoffleit and Jaschek [1982].

No long term change was measured in the velocity of this star over the four years of observations and no spectroscopic variations were noted, thus it seems likely that 19 Cepheus is a bona fide single O-star.

The first step in determing orbital parameters for

Cygnus X-1 is 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 radial velocity data obtained. The method essentially entails folding data on a

series of trial periods and then searching for significant upgoing followed by downgoing modulation. The longest period that could be detected is 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 this data set a period of 5.60172 ± 0.00003 days

is found to be the most significant peak in the pseudo power

spectrum. No significant peak is found at 294 days, which is

the period found for the long timescale X-ray variations (

Priedhorsky et al [1983] ).. 120

In order to better search for any long period variation

in this system and to see if there has been any long term change in the orbital period, all historic velocity measures were compiled and combined with the data from this work to

form a data set spanning 45 years. The historic data set

included data from Seyfert and Popper [1941], Webster and

Murdin [1972], Brucato and Kristian [1973], Smith et al

[1973], Brucato and Zappala [1974], Mason et al [1974], Abt et al [1977], and Gies and Bolton [1982] ( includes all of

Bolton's earlier data ). The most significant period found was at 5.59964 ± 0.00001 days, shown in fig 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 historic data would imply a P/P =* 10"7

day"1, over the time of observation of the system. In order

to further test this possibility all historic and new

observations with two or more velocity measures at similar

epochs were fitted to a velocity sinusoid. The procedure

used the best estimates for the period from above and

orbital parameters determined latter in this section, and

left the T0 parameter (epoch of zero phase) to be fitted.

The results are given in table 3.6 and shown in figure 3.17

where the vertical axis is the change in T0 found for a best

fit and the horizontal axis is the Julian . Date of

observation using 2445513.770 as a zero (my first

observation of Cygnus X-1). A linear least squares fit ( 121

Figure 3.16 Pseudo power spectrum of all HDE226868 velocity measures (1939 to 1984).

Table 3.06 Fitted 6To values for all velocity data on Cygnus X-1.

Mean epoch of Number of JTo Source of observation (JD) observations (days) Data

2429664 2200 2 -0 .968 Seyfert 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 Brucato and Kristian [1973] 2441476 8595 4 -0 003 Brucato and Kristian [1973] 2441495 8498 5 -0 023 Smith et al [ 1973] 2441587 7885 2 +0 067 Smith et al [ 1973] 244 1859 7022 1 3 +0 007 Brucato and Zappala [1974] 2441919 7360 3 +0 002 Brucato and Zappala [1974] 2441269 7975 2 -0 079 Mason et al [ 1974 ] 2441400 3493 3 -0 037 Mason et al [ 1974 ] 2441424 1528 4 . +0 061 Mason et al [ 1974 ] 2441453 5910 2 -0 343 Mason et al [ 1974 ] 2441525 4365 2 -0 698 Mason et al [ 1974 ] 2441935 0195 2 +0 092 Mason et al [1974] 2442205 854 5 +0 038 Abt et al [ 1977 ] 2442229 4679 18 +0 086 Abt et al [1977] 2442257 7712 4 -0 006 Abt et al [1977] 2442266 3144 7 -0 052 Abt et al [1977] 2442286 8819 35 +0 033 Abt et al [ 1977] 2442680 3177 6 +0 087 Abt et al [ 1977] 2442909 6020 6 +0 053 Abt et al [1977] 2441225 1380 2 -0 216 Gies and Bolton [1982] 2441257 8820 3 -0 161 Gies and Bolton [1982] 2441464 7885 4 -0 010 Gies and Bolton [1982] 2441535 1965 2 -0 071 Gies and Bolton [1982] 2441893 1980 6 -0 065 Gies and Bolton [1982] 2441929 9543 3 -0 032 Gies and Bolton [1982] 2442306 1300 2 -0 129 Gies and Bolton [1982] 2442542 7823 3 -0 045 Gies and Bolton [1982] 2443342 2 Gies and Bolton [1982] 7575 +0. 029 00 2443373 .6688 4 +0. 111 G1es and Bolton [1982] 2444058 . 3552 13 +0. 088 Gies and Bolton [1982] 2444795 .0557 3 +0. 131 Gies and Bolton [1982] 2444514 .7178 3 -0. 057 this work 2444858 .0783 4 +0 . 120 this work 2445099 .2101 2 -0. 007 this work 2445144 . 3448 4 +0. 103 this work 2445189 .0799 8 +0. 224 this work 2445243 .0424 3 -0. 125 this work 2445513 . 3080 2 +0 145 this work 2445545 .9832 6 +0. 183 this work 2445669 . 6208 2 +0. 145 this work 2445891 . 2030 1 1 +0. 231 this work 2445891 .9116 15 +0. 230 this work 2445892 . 1 149 13 +0. 188 this work 125

Figure 3.17 Change in T0 with epoch of observations for all velocity measures (1939 to 1984). Crosses and circles indicate two and greater than two observations at that particular epoch respectively. © ...© ©+ + © o © © ^' © ^+

$ + +

i ^ • j • 1 1 i •15000 -13000 -4000 -2000 • 2000

Epoch (- 2444513.770 JD) 127

Bevington [1969] ) to these observations using the historic measures from 1939/40 ( at -14850 days in figure 3.17) yields

S 6T0 = 0.13(08) + 6.3(3.1) x 10" T

Not including these earliest observations gives a best fit of

5 5T0 = 0.12(08) + 5.7(3.7) x 10" T where T is the days from Julian day 2444513.770.

In either case a P/P =* 10"5 day"1 is implied. This is larger than the value found from period folding previously but this may be because for the period folding all points were of equal weight while in the fitting 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 disc. The period change predicted due to mass transfer from the primary into this disc is given by

1 3 1 P/P = - 10"* yr" [ - M/10" M@yr" ]

The estimated present mass loss rate is 5.7 x 10"6 M^yr"1, which yields an expected P/P * 2 x 10"9 day"1 which is far

too small to explain the observed change. If the system were

in a period of disc filling the estimated mass loss ( 10"3

1 7 1 M0yr" , Kundt [1979] ) would give a P/P =* 3 x 10" day " ,

still less than that found above. The reason for the probable large period change is therefore unknown. More data at longer time baseline are needed to confirm the reality of

the period change. 1 28

Again no significant power was found at the 294 day period in this longer time span data set. This is in agreement with the findings of Gies and Bolton [1984] who, however, used a much shorter data base in their period search. Kemp et al [1978] have claimed to have detected a

39/78 day effect in the U band flux, the X-ray flux and their polarization data. No significant power was found at this periodicity in the data compiled here. A null result was also found for the 91 day possible periodicity suggested by Walker and Quintanilla [1978].

The velocities measured were fitted to a velocity curve from which orbit parameters could be derived. Herbison-Evans and Lomb [1971] outline this physical problem well and the technique for solution (• a more accessible summary is by

Petrie [1962] ). The velocity expected for a single line binary is v = r + K [ e cos OJ + cos( u + v) ] where

T is the mean velocity

K is the amplitude of the orbital velocity curve e is the eccentricity of the orbit

CJ = CJ0 + 2ir( t - T0) / Pa a

CJ is the longitude -of-periastron

CJ0 is the longitude of periastron at epoch T0 t is the epoch of observation

PQ is the period of the apsides v is the true anomly 129 where tan( v/2 ) = tan( E/2 ) • [ (e+1) / (1-e) ] and

E is the eccentric anomaly which is derived from Kepler's

Equation

E - e sin E = M where

M = 2JT ( t - T ) / Pfa and is the orbital period.

The above was put into a subroutine function which could then be called 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 statistical software package which optimises the parameters using a least squares approach. The velocities were weighted according to the quality of the spectra which was mainly a function of which year the data was collected

(i.e. of which Reticon System was used). These weights are listed in table 3.07. The best estimates of the orbit parameters for the H, He I, Hell and metal absorption lines are to be found in Table 3.08. The best solution for all the lines was found with an eccentricity of essentially zero ( <

0.03 ). Lucy and Sweeny [1971] have outlined a test for objectively deciding if a derived eccentricity is significant. In all cases here the significance of the eccentricity was < 5% according to their criteria. Thus no significant eccentricity was found in this data as opposed to Bolton's [1975] analysis, and in agreement with Gies and 130

r

Table 3.07 Weights for least squares fitting radial velocity 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 Orbit Solutions for Cygnus X-1

Element H He I He II Metal

Period held 5.6017(1) held held (days)

TO held 1869.17(1) held held (2440000+) -9.15(70) -4.44(50) 6.27(70) 0.10(70) V0

1 (kmsec" ) 78.1(16) 75.0(10) 75.4(20) 75.9(15) K 0.0 0.0 0.0 0.0 (kmsec"1 ) 6.5 6.2 9.5 5.6 e a fit (kmsec"1) 131

Bolton [1982]. This result of a circular orbit disagrees with interpretation of the photometric observations by

Hutchings [1978] and Guinan et al [1979] who found that to explain the light curve an eccentricity between 0.015 and

0.04 is required.

3.7 MASSES OF THE COMPONENTS

It is normally accepted that the components in a tidally linked binary after a suitable time are in circular, synchronous . Press et al [1975] give expressions for the circularization and synchronization timescales due to dissipative 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 circular orbit (shown earlier in this chapter) and if indeed it was only formed 400 years ago as suggested by historic Chinese records ( Li Qi-Bin [1979] ) then it would seem that the supernova that created the compact companion did not seriously perturb the original binary system. Alternatively

Savonije and Papaloizou [1983] have suggested that circularization could occur on a much shorter timescale

(^100 years) if the system passed through a resonance between the orbit and a stellar pulsation mode.

Unfortunately without an independent estimate for the inclination of the system it is not possible to know for certain whether synchronization has occurred. Let us proceed however with this normal assumption that the angular 132 rotational velocity of the star is the same as its orbital angular velocity, hence vsini / K = R / R . cm ' star where

Rcm is the distance from the star's centre to the system centre of mass

Rstar *s tne °^stance between the surface and centre of the star

As we believe that the star is close to filling its Roche

Lobe in this system ( denote F as the fraction filled ) we can use the expression from Kopal [1959] and more recently

Plavec [1968], Paczynski [1971] which gives

Rstar " Rsep * [ °'38 + °'2 lo9( »p / mx } ] to find vsini /K=F*[(m+m)/m ]* p X X [ 0.38 + 0.2 log( m / m ) ] P x where vsini = 94.3 kmsec"1

K = 75.0 kmsec"1

F = 0.95 ( from Conti [1978] )

This gives a m_/m ratio of 2.0 ( a vsini = 140 km/sec gives P x a ratio of * 3 ). Taking an assumed mass for the primary of

25 M@, typical of an 09.7Iab ( Schmidt-Kaler [1982] ), gives

a mass estimate for the secondary of 12 M@. Underhill 133

[1983a] collates 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 this estimate is independent of the system inclination and only assumes that the axis of the primary is the same as that of the binary.

Hutchings et al [1979a] suggested that the mass of all 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 is certain 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 entirely normal for its MK spectral type. Thus a

minimum mass for the primary bf 20 MQ appears reasonable.

Thus

The mass ratio for a single line spectroscopic binary is given by Bachall [1977] as

3 2 f(mpfmx,i) = mx(sini) [ mx / ( mx + mp) ]

= [ 4 *r2/G ] * [ ( a, sini )3 / P2 ]

Knowing the masses for the two components from above and setting a,sini = P * K / 2* gives a derived inclination for the system of 40°. This is in agreement with the independent UV line modeling estimate of i £ 40° ( Davis and Hartman [1983] ) and in the range 25° 134

< i < 40° as determined from X-ray polarization measures (

Long et al [1980] ).

An independent lower limit for the mass of the secondary can be made using the method of Paczynski [1974] and Bachall [1978] if an estimate for the distance can be made. This technique relies only on the geometrical constraint implied by lack of observed eclipses. A value for the distance of HDE 226868 can be calculated using the equivalent width of H7. Using early type supergiants in h and x Per Walker and Millward [1984] have recently produced a calibration of H7 equivalent width vs absolute magnitude which they give as

Mv = -9.456 + ( 2 - 0.0942s) * W( H7 ) where s is the number of spectral sub-classes from BO.

The measured H7 equivalent width is 1.5 ± 0.1A, when the same criteria as that of Walker and Millward [1984] are used in avoiding the effect of blends. This gives an absolute magnitude for HDE 226868 of -6.46 ± 0.2 using the above relation. Using the standard value of E(B-V) = 1.12 from the work of Bregman et al [1973], a value of R of 3.2 ( Seaton

[1979] ) and the observed V magnitude of 8.81 (Kemp et al

[1981] ) gives a distance modulus of 11.68 or a distance of

2170 pc. It has been noted that HDE 226868 lies about one degree from the centre of NGC 6871 which is the nuclear centre of the Cyg OB3 Association. Janes and Adler [1982] give a distance modulus for the cluster 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 it seems HDE 226868 can be considered a cluster member. The magnitude expected for normal stars of spectral type 09.7lab in the MK system is -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

2 of the secondary of Mx > 3.4 d , where d is 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@ is found.

In passing we mention that we checked that the H7 equivalent width calibration 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 orbital period 3.4 days ( Jones et al [1973] ). It is 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 this type has B-V = -0.31. This therefore

gives for HD153919 a My = -7.05. Conti and Cowley [1975] find log[ W(mA {H7}) ] = 3.00 which using the above

calibration gives My = -7.17 . The absolute magnitudes derived from the two different 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 this study by measuring the equivalent widths of the interstellar features seen towards Cygnus X-1. The best line for this purpose is at X6613 which is narrow, strong and unblended. The feature at X4430 although strong is blended with stellar lines and may have a circumstellar contribution ( Tug and Schmidt-Kaler [1981] ). The Ca II K line could also be used but it is more prone to measurement errors as it is close to the edge of the spectrum in all cases. As well Bromage and Nandy [1973] find that this line is not well correlated with E(B-V) in the Cygnus direction.

All the the other interstellar lines in the available spectra are too weak to be useful.

The correlation of equivalent widths of the interstellar lines with E(B-V) has been investigated by

Herbig [1975] and by Bromage and Nandy [1973]. They both find that the lines in stars between 1^75° and 82° are 30% weaker per unit E(B-V) than the average of all other areas on the sky. Table 3.09 shows the E(B-V) as determined for

Cygnus X-1 from the X6613 line for both the Cygnus and non-Cygnus directions.

If HDE 226868 is indeed a normal 0 supergiant

( therefore {B-V}0 - -0.25 ) then its measured B-V colour of

0.85 gives an E(B-V) = 1.10, which is the accepted value in the literature.This value however is higher than the independent estimate of E(B-V) to be found in table 3.09. 137

Table 3.09 E(B-V) as determined from the Interstellar lines using the calibration of Herbig [1975] for the whole sky and just the direction of Cygnus.

line EW E(B-V) E(B-V)

A mA all Cygnus

6613 0.16(2) 0.56 0.76

4430 1.5(3) 0.56 0.79

Note that this lower value makes no assumption at all about

the Cygnus X-1 primary as it relies only on the interstellar

line strengths. A value of the E(B-V) of 0.95 was deduced

from the UV observations of Wu et al [1982].

This smaller E(B-V) can be explained in two ways ;

HDE 226868 does not have the normal colours for an O

supergiant. The change in intrinsic colour required to

agree with the measured (B-V) would move the (B-V)0

colour to that expected from a late B supergiant. As the

spectrum is obviously that of an O supergiant this would

imply the primary is perculiar. However the fact that

the H7 equivalent width is in such good agreement with

that found for stars of its type makes this unlikely.

The interstellar extinction law is unique in the

direction of Cygnus X-1. As the interstellar lines are

already weakest per E(B-V) towards Cygnus ( compared to

any other direction in the sky ) this would mean an even 1 38

weaker dependence in the particular direction 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] lists seven different mass loss indicators in early type stars. One of these indicators is particularily useful as it can be used to quantitively estimate the mass loss rate without detailed modelling. As lines in a star are formed at different depths due to varying excitation energies, in the expanding atmosphere of an early type star lower energy lines are systematically blue shifted relative to those of higher energy ( Karp

[1978] ). The amount of initial energy provided to drive the wind is related to this velocity gradient and to the total mass loss. Suitable calibration of the mass loss vs velocity gradient relation allows its use to determine mass loss rates for individual stars.

Table 3.08 lists the relative zero velocities of lines of different excitatation energy in HDE 226868 ; namely H,

He I, He II and Metal lines having excitation energys 10,

21, 75 and 50 eV ( Hutchings [1976] ). Figure 3.18 shows these quantities plotted together with the best least squares fit ( dotted line ) given by

Velocity(km/sec) = 0.224(20)(km/sec/eV)* Energy(eV)

-10.4(9) (km/sec) 139

Figure 3.18 Zero velocity vs excitation energy for lines from HDE 226868. 140

o OJ in \ £

o o

Ql

100

Excitation Energy (eU) 141

The value obtained for the gradient is higher than the 0.13 km sec"1eV- Hutchings [1976] lists for HDE 226868.

A mass loss rate for HDE 226868 can now be obtained by comparing this value of the velocity excitation gradient to that of stars with known mass loss rate and velocity excitation gradients. The only such compilation comes from

Hutchings [1976]. However this work is tied to only seven stars whose mass loss rates were believed well known at the time from modelling of optical P-Cygni profiles.

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 lines. Table 3.10 is a compilation of those stars for which a velocity gradient is 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 listed in table

3.10 have been criticised by Castor and Simon [1983] and

Abbott et al [1984] as they require the assumption of the

form of the velocity 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 excitation gradient. The least squares fit to the data below a gradient of 20 eV/kmsec"1 is s 1 Table 3.10 Mass loss rates ( 10" MQyear- )from different techniques

Star Name Spectral Gradient Radio UV IR Opt i ca1 HD Type 2eV/kmsec

108 06- 7f 8.5" 50' 10'

14947 05-6If 4.0' 2.4" 29s 9.1'° 81

24398 £ Per B1Ib 20 0. 45'

3G486 6 Orl 09.511 >40 0.5" 1.3' 1.2' 1 ' '

37128 t Or1 BOIa 10 3.5' 1.7': 3. r

37742 s on 09.51b >40 2.3s 0.5" 2.2' 1 .0" 3.2'° 1.2'

46150 05- 6f 15 0.8'

46223 04-5Vf >40 2.5'

47839 5 Mon 07- 8Vf >40 0.15' 0.85'

48099 07V >40 0.6'

s 6681 1 £ Pup 04If 9 3.5 6. 3.5' 4.1' 3.5' 8 ' ' 9 '

91316 p Leo B1 lb 15 1.4'

93129 03 10 1.4' 21 1

101190 06- 7V 34 1.0'

151804 09f 9.3 7.9' 16.6'"- 10"

152236 B1Ia 4 10' 152408 08f 3 10' 2 1 . 41 0 1001

152424 091 >40 0.81 5 . 21 0

188001 9 Sge 08If 7 6.3' 1 1 '

193237 P Cyg B1p 1.4 13" 350'

210839 V. Cep OGIf 12 4.8 7.8s 4.0' 6 . 5 1 = Garmany et al [1981] ' = Gathler et al [1981] 3 = Garmany and Conti [1984] ' = Olson and Castor [1981] 5 = Abbott et al [1980] 8 = Abbott et al [ 1981 ] ' = Morton and Wright [1978] • = Barlow and Cohen [1977] ' = Persei et al [1983] 10 = Klein and Castor [1978] '1 = Cassinel1i et al [1978] 1 ! = Morton [ 1967 ] '1 = Conti and Frost [1977] '• = Hutchings [ 1968] 1' = Hutchings [1970] 15 = Peppel [ 1984] 144

Figure 3.19 Mass loss rates, determined by different methods vs velocity excitation gradient. Stars are UV determinations, open circles from radio measure and filled circle that predicted for Cygnus X-1. 20 >40

Slope 2(eU/[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 al [1980].

Garmany et al [1981] find that the mass loss and the stellar luminosity for many stars can be related by

5 log[ M ] = -7.15(10) + 1.73(16) log [ L / 10 L@ ]

For the mass loss found above this gives a luminosity for

6 HDE 226868 of 1.3 ± 0.5 x 10 LQ. Schmidt-Kaler [1982] gives a typical value for a 09.7 supergiant of between 2.6 and 5.3 x 105 LQ. AS the luminosity of the primary found earlier from the H7 calibration was entirely 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 earlier in this chapter all lines, except the Balmer series, of sufficent strength had their equivalent widths determined. These values were then placed in orbital phase bins of width 0.1 and normalised to the average. The Balmer series lines are much broader than other lines due to stark broadening, 147 consequentially their equivalent widths were determined by numerical intergration between the line limits. All the equivalent width measures are listed in table 3.11 and plotted in figure 3.20 to 3.23 .

The interstellar line at 4726.OA provides a useful check on the consistency of our methods. The scatter found in that line is about 10%, which is similar to the maximum difference found between equivalent width measures from spectra of the same star taken on the same night. The cause of this scatter in the interstellar line may be because the line is fairly weak and not strictly Gaussian as can be seen in figure 4.1. As the equivalent width measurement technique relies on the profile being approximately Gaussian, measurement of this line is difficult. It is likely that an error of 10% in the equivalent width can be considered as typical for a single line measurement.

As can be seen from the plots no significant phase variation is seen in the equivalent widths ( as opposed to the claim by Smith et al [1973] ) except possibly in the hydrogen lines which will be discussed further in the next chapter. The magnitude of the variation expected from the effect of the ellipsoidal distortion of the primary has been modeled by Hutchings [1977]. He predicts a 10% variation 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 limit here but no such variation is apparent. As the photometric light curve observed is that characteristic 148

Figure 3.20 Phase variation of hydrogen lines equivalent width in Cygnus X-1 . Circles are from H7, stars from H/3. Normalised Equivalent Width 0.9 1 1.1 1 . 2 -i 1 1 1 1 1 1 1 1 1 r

* 0

ro a

M o o s s

to

\ -rj \ 0 * / / ro CT) / I 6. *

: I a : I oo ':»

/ / /

6*1 150

Figure 3.21 Phase variation of mean He I line equivalent width in Cygnus X-1. Norma 1 ised Equ iwa lent Ulid t h 0.9 1 1 . 1 1 .

1 1 l • 1 1 1 I 1 1 1 1

• (J / / / M 1

»

ro i

- i - i • o o \ \ m i i "0 m j • OJ j

•

- \_ -

*\

'•

•*

•

m / •''

I

\

•

• 1 • 1 1 1 - L 1 1 1 1 1 1 1 1 1 1 1 1

191 152

Figure 3.22 Phase variation of He II (absorption lines) equivalent width in Cygnus X-1. Circles are X4200, stars are X4542. Normalised Equivalent Width 0.9 1 1.1 1 T 1 1 1 tI 1 1 1 r t T 1 r

3K 0 O s a y ro

Q o o a- ^

"0 3"

Ul a N. ro

a • oo

/ / X ©

_i i i_ -i i I i i_ -i i i i_

£91 154

Figure 3.23 Phase variation of mean metal line equivalent width in Cygnus X-1. Normalised Equivalent Width 0.9 1 1.1 1.2

-i 1 1 r T r t

ro

ro

o a a- j> so

P

ro CT)

O 00

J I L. J • 1_

SSI 156

Figure 3.24 Phase variation of interstellar lines equivalent width in Cygnus X-1. Squares are X4726, circles are Ca II K, stars are X4763. Normalised Equivalent Ulidth 0.9 1 1.1 1 ~i 1 1 r T 1 r t T 1 r

s. ¥ .* a ro ,K \ \ w * -. A #© p o o /

/• \

\y "TJ A'. ZT / \\ $" a ID cn V* ^.

o . I \ 00 >. \ ; \ " V v '. / v / v / •

_i i L.

Z.SI Table 3.11 Normalized Equivalent Width Variations with Orbital Phase

Line Mean EW 0 .0- 0 . 1 - 0 . 2- 0 . 3- 0 . 4 0 .5- 0 .6- 0 . 7- 0 . 8- 0 . 9- A . (mi) 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 .6 0 . 7 0 . 8 0 . 9 1 .0

Hydrogen 4340. 468 1744.99 1 . 135 1 .052 0 .966 1 .093 0 .931 0 .922 0 .911 1 .010 1 .022 0 .997 4861 . 332 1232.04 1 .013 0 .977 1 .018 1 .030 '0 .946 0 .957 0 .932 1 .027 1 .021 0 .978

He I 4026 . 189 547 .45 1 .056 0 .997 0 .995 0 . 957 0 .990 1 .035 0 .970 1 .038 0 .988 0 . 975 4120. 812 233 . 15 1 .017 1 . 1 10 0 .909 0 .918 0 .968 1 .029 0 .977 1 . 108 0 .965 0 .999 4143 . 759 236 . 83 1 .032 1 .036 0 . 959 0 . 94 1 1 .009 1 .017 1 .020 1 .016 0 . 934 1 .038 4387 . 928 318 .20 1 .087 0 .958 0 .966 1 .022 1 .020 0 .989 0 .960 1 .040 1 .006 0 .952 447 1 .47 7 645 . 23 1 .032 0 .979 0 .959 0 .985 1 .003 1 .009 0 .990 1 .028 1 .006 1 .01 1 4713 . 143 273 .06 1 .068 0 .976 0 .96 1 1 .003 1 .005 1 .005 0 .985 1 .032 0 .983 0 . 981 4921 . 929 406 .43 1 .053 0 .989 0 .980 0 .932 1 .071 0 .964 0 .964 1 .074 0 .984 0 . 991 5015 .67 5 292 . 23 1 .061 0 .979 1 .031 0 .983 1 .042 0 .965 0 .961 1 .045 0 . 940 0 .994

He II 4199 .8 3 193 .90 1 .025 1 .06. 8 0 . 993 0 . 943 1 .00. 1 0 .968 1 .067 0 .983 1 .045 1 .024 454 1 .59 8 190 .54 0 .947 1 .03. 0 0 .934 1 .047 1 .07. 2 1..01 0 0 .925 1 .089 0 .955 0.. 990

Metal 4069 . 897 243 .06 1 .053 1 .01. 2 0. 88 1 1..04 6 1 .05. 0 0. 886 0..98 4 1 .083 0..99 3 1. 031 4075 . 86 163 . 73 0 .973 1 .09 9 1. 005 0..88 6 0. 960 1. 022 1. 031 0..97 3 0. 918 1. 102 4088 . 863 598 .71 0 .986 0. 959 1. 008 1. 010 0. 992 1. 019 0. 968 1..06 6 1. 029 0. 964 4097 . 31 628 .56 1 .026 1. 003 0. 997 0. 935 1. 003 0. 97 1 0. 980 1. 088 0. 997 1. 001 41 16. 104 434 . 36 1 .045 1. 015 0. 897 0. 938 0. 976 1. 037 0. 983 1. 117 0. 979 1. 010 4379 . 09 148 .53 1.. 100 1. 094 0. 897 1. 104 1. 049 0. 956 0. 876 1. 011 0. 972 0. 963 4481 . 228 91 . 13 0..95 7 0. 996 0. 907 0. 998 1. 014 1. 102 1. 041 0. 983 0. 983 1. 018 4510. 92 142 .43 0..94 0 0. 927 0. 907 1. 068 0. 964 1. 013 1. 057 1. 045 1. 048 1. 032 4514 . 89 175 .91 0. 963 0. 894 0. 878 1. 047 1. 024 1. 04 1 0. 978 1. 109 1. 032 1. 035 4552 . 654 164 . 39 1. 061 0. 982 0. 977 0.98 0 0. 993 0. 957 1. 002 1. 087 0. 903 1. 059 4630. 537 129 .66 1. 018 1. 01 1 0. 986 0. 955 0. 992 1. 002 0. 991 1. 103 1. 047 1. 013 4634 . 16 132 .26 0. 978 1. 092 1. 017 0.94 4 1. 001 0. 931 0. 902 1 .04 6 1. 140 0. 950 4640. 64 238 . 34 1. 087 1. OOO 0.96 4 0.99 3 0. 964 0. 977 1. 002 1 .06 7 1. 05 1 1. 07 1 4647 . 40 4 17 .98 1. 076 0. 970 0. 954 1. 000 1. 000 0. 973 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 ellipsoidal variables, it seems likely therefore that the prediction for the size of the ellipsoidal effect on the absorption lines is in error.

3.11 LINE HALFWIDTH VARIATIONS

Priedhorsky et al [1983] have suggested that the most satisfactory way in which to explain the observed 294 day period in the X-ray flux is 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 line of sight and the outer disc plane. Sokolov and Tsymbal [1984] have explained the long period light variations in this way and find that the primary's rotation axis is varying in orientation by =* 16° on a period 39 days. Kopylov and

Sokolov [1984] support this interpretation with spectroscopic data.

A change in the inclination of the primary of ±8° would produce a change in the vsini of ± 15%. To search for such a variation the halfwidths of the He I X4471 and X4713 were measured. These lines were chosen as they are relatively insensitive to temperature fluctuations, have no emission component, are relatively unblended and are quite deep. In order to ensure that instrumental changes were not affecting the results, the halfwidths of the He I lines 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 orbital phases and the results are tabulated in table 3.12 and illustrated in figure 3.24. There is no significant variation connected with the 5.6 day period. The period searching technique described previously was applied to this data and no periodic variations were found in the range 1 to

350 days. It is unlikely that a variation with an amplitude as large as predicted would have been missed. 162

Table 3.12 Normalized phase variations of He I halfwidth

phase Hel X4713 He I X4471 bin Cyg X-1/19 Cep Cyg X-1/19 Cep

0.0-0,, 1 13 .15 0.1-0,, 2 13 .16 0.2-0,, 3 10 . 1 1 0.3-0,, 4 12 .12 0.4-0,, 5 14 .09 0.5-0, 6 15 .13 0.6-0,, 7 1 2 .10 0.7-0.8 17 .16 0.8-0.9 16 .15 0.9-1 .0 12 .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> •©, • .©• —5K ZP ©• •••o-^v © s ©. V> ' / s: '©

3 5*

0 0.2 0.4 0.6 • . 8 Or b i t a 1 Phase Chapter 4

THE EMISSION LINE SPECTRUM

4.1 RATIONALE FOR THE STUDY

The identification 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 it was thought that it might give

insight into conditions in the postulated disc. It was however Hutchings et al [1973] who realised that in order to

study the He II emission line properly the absorption line contribution from the primary had to be accounted for.

Walker et al [1978] went into the details of this

subtraction process and produced corrected profiles which,

unfortunately, were of poor signal to noise. The Ha line has

also been the subject of study using similar techniques by

Hutchings et al [1974, 1979b] and Brucato and Zappala

[1974]. All this data however lacked sufficent detail to

give good information on the emission lines and to answer

the principal question of where do they originate.

165 166

4.2 ANALYSIS OF THE HE II X4686 DATA

4.2.1 FINDING A GOOD REFERENCE STAR

The observed He II emission line is the result of

some unknown emission profile coming from an

unidentified region in the binary system combined with

the absorption profile from the primary. As the primary

moves in orbit its absorption profile is doppler

shifted. In order to correct the observed profile for

this effect the intrinsic profile of the He II X4686

from the primary must be known. This can be done by

finding a comparison star of similar spectral type that

would have He II lines of similar strength. The He II

line at the spectral type of HDE 226868 ( 09.7Iab as

determined in Chapter 2 ) is particularily sensitive to

changes in effective 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 identified

in order left to right in table 4.01 . The two stars

with spectral type closest to HDE 226868 had lines 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. Tic marks indicate lines identified 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 list for CFHT data.

Line Wavelength (A) on 4673.75 on 4676.234 Nil 4677.93 He II 4685.682 O II 4699.21 0 II 4705.355 Oil 4710.04 He I 4713.143 Oil 4713.373 ? IS 4726.0

spectra of these stars could be made to match that of

HDE 226868 they needed to be broadened to the same vsini. The broadening was done by convolving the observed profile with a function that simulates the effect of rotational broadening ( Huang and Struve

[1953], Gray [1976] ). This function has the the form

2 0>5 2 G(AX) = C,[ 1 - x ] + C2 [ 1 - x ] where

x = AX / AXL

AX_ = X vsini / c JLi

C, = 2( 1 - e ) / ( TTAXl ( 1 - e/3 )

C2 = ire / [ 2?rAXL ( 1 - e/3 )

e is the limb darkening parameter =* 0.6 ( Gray [ 1976] )

Figure 4.02 shows the result of convolving this function

with the X4713 line profile of the standards. The solid

line in each case is the HDE 226868 X4713 profile, the

dashed line is the profile of the standard and the 170

Figure 4.02 Broadened Profiles of Standards Solid line = HDE226868 He I X4713 profile Dashed line = indicated standard's profile Dot-Dash line = broadened standard's profile 171

Wavelength (Angstrom) 172 dashed dot line is the profile resulting from a convolution to 94 kmsec"1, the vsini of HDE 226868 (see

Chapter 3 for details). The profiles look as if they fit those of HDE 226868 approximately. For the subsequent analysis HD 167264 broadened to a vsini 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 different dispersion from which the intrinsic He II X4686 profile was recovered. Firstly there is the five years of 40

Amm"1 data taken mainly (except for four profiles) on the DAO 48" Telescope. For this low dispersion data the profile is essentially determined by the projected slit width meaning that all the absorption lines will essentially have the same profile 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 this;

It would serve as a check on any long term errors

that might creep into the reduction technique

it would provide a profile, taken under identical

conditions of a star of similar spectral type, for

correction of the effect of the primary on the He II

emission feature. 173

The correction for the primary absorption must be done fairly accurately or it may affect the resultant velocity curve for the He II emission. If the correction is too large the velocity curve for the emission will be influenced too much by the assumed absorption profile and the velocity curve will tend to reflect too much this component (i.e. it will follow the velocity curve of the primary). If too little is subtracted then the line wings will be weighted too heavily and a more extreme range velocity curve will result. From the CFHT data HD 167264 seems like a close fit to HDE 226868 in spectral type and the equivalent widths of He II X4686 should therefore be similar. As the profile.of a line in the DAO data is independent of line depth it is then possible to use the ratio of the equivalent widths for the He II line from the CFHT data for 19 Cep and

HD167264 to alter the DAO 19 Cepheus He II X4686 equivalent width to that expected for HDE 226868. The equivalent widths for these lines are listed in table

4.02 and it can be seen that the HD 167264 He II X4686 line is 0.872 that of 19 Cepheus.

The procedure then for correcting the He II emission is as follows. The He I X4713 for both Cygnus

X-1 and 19 Cepheus on each night are shifted and aligned to zero velocity ( i.e. they are put in the primary's centre of mass frame ). As has been seen in the previous chapter lines of different excitation energy are formed 174

Table 4.02 Equivalent Widths (mA) for selected lines from CFHT data. Star He I X4713 He II X4686 19 Cep 275.1 329.3 HD 167264 316.2 287.1 HDE 226868 319.6

at different depths in the atmosphere ; the low excitation energy lines are formed higher and have less blue shifted velocities than the high excitation lines. The velocity difference between the He I lines and the He II absorption lines is 18.2 kmsec"1 for 19 Cepheus and 8.3 kmsec"1 for HDE 226868. Thus after alignment the 19 Cepheus line is shifted by -9.9kmsec"1 to ensure that the underlying He II absorption line is aligned. The 19 Cepheus spectrum is weakened by 13% in order to make the line strengths more like those of HDE 167264 ( and HDE 226868 ). The two spectra are then subtracted and the resultant shifted back into the centre of mass rest frame. Figure 4.03 shows the He II X4686 profiles of Cygnus X-1 without any correction (dashed lines) together with the profile of 19 Cepheus taken on the same night (solid line). Figure 4.4 shows the result of the subtraction procedure outlined above. The subtraction at the He I X4713 is not perfect because the two profiles are not aligned for that line. 175

Figure 4.03 He II X4686 profiles from Cygnus X-1 (dashed line) and from 19 Cep (solid line). Cyg X-1 : 1980-1984 : He II

-^f\/—""V—y—^ 0.006 Vs 0.014 0.019 0.032 0.160 0.169 0.179 0.191 0.204 0.209 0.238 0.264 0.277

0.282

0.340 0.366 0.370

4600 4650 4700 4750 Uavelength (Angstrot) Cyg X-1 : 1980-1984 : He II

"V ~\T 0.568 ~^rr~v\j ~~V V" 0.597 - 0.622 0.627 0.632 -~v~—v-*" 0.655 0.689 0.597 —V^Yy^-t jj* Y" 0.7U 0.722 0.740 0.741 0.756

-NC^y^- y—^ 0.781 -vrv\y^ —^"V^ 0.802 0.802

0.823

0.831 -^v^ -v*—\r 0.9-11 -x/^r*y^—^ "~V~ 0.851 0.856

0.871 ~^rr*y\jy~~-—'~yr v— 0.872 0.899 0.905 0.910 -v^^^

4600 4650 4700 4750

Wavelength (Angstroi) 1 78

Figure 4.04 He II X4686 profiles after correction for absorption from primary. 179 Cyg X-1 1980-1984 : He II

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 line 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 is used after broadening it to 94 kmsec"1 to

match the vsini of HDE 226868. The two profiles

superposed are shown in figure 4.05. The result of the

subtraction is shown figure 4.06 and from this it is

clear that the profiles exhibit considerable structure

at high dispersion not visible in the low dispersion DAO

data. Chapter five will deal with this structure.

4.3 THE HE II EMISSION RADIAL VELOCITY CURVE

The previous data on the radial velocity curve of the He II

X4686 line is quite limited and of variable quality. Bolton

[1975] collated the available He II velocities to that time and the data showed great scatter partially because some of

the measurements did not take into account correction • for the primary's absorption. Walker et al [1978] made a careful analysis of their He II profiles but a limited amount of low

signal to noise data resulted in no firm conclusions being

reached.

The centre of gravity position fitting technique was

used on all the corrected He II profiles ( both DAO and

CFHT ) and correction to the solar system barycentre was made. Listed 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 July 1984 CFHT data. 20 -15 -10 -5 0 5 10 15 20 Wavelength (Angstrom) 184

Figure 4.06 He II X4686 Profiles after correction for absorption from the primary for July 1984 CFHT data. 185

Wavelength (Angstrom) 186 velocities for the He II X4686 line in the centre of mass frame of the Cygnus X-1 system. The first thing to be noted from the plot in figure 4.07 is that the curve looks quite smooth with little of the scatter apparent in previous results ( Bolton [1975] ). It is also clear that the velocity curve is approximately 120° phase removed from the velocity curve of the primary. Emission from the region of the secondary would be shifted 180° in phase, so clearly this simple explanation is not the answer. Similarily to what was outlined in the previous chapter, the BMDP software package was used to fit this radial velocity curve to give

'orbit' parameters. The resultant parameters are listed in the second column of table 4.04. As in the case of the absorption line curve no significant eccentricity could be forced to fit the data. It is also apparent from figure 4.07 that the best solution to the data does not fit extremely well. In particular the fit around phase 0.5 ( the X-ray

source between the observer and the primary ) and phase 0.0 appears poor. Walker and Quintanilla [1978] find deviations

from an ellipsoidal light curve, in their five years of photometric data on this system, at these phases also.

There is no straight forward explanation as to where in

the system such a velocity curve would come from. A simple model would locate the emission on the line of centres between the primary and secondary. A test particle in such a position would have two velocity components, one due to orbiting about the centre of mass and the other due to some Table 4.03 He II X46B6 emission radial velocities and equivalent widths Orbital He II X4686 He II X4686 phase velocity equivalent kmsec"1 width (mA)

DAO Data

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 radial velocity curve versus orbital phase. Circles are from 1980-81 DAO data, stars from 1982-84 DAO data and filled circles from CFHT 1984 data. 061 191

Table 4.04 Orbit parameters from BMDP fit to He II X46B6 emission radial velocity curve.

Elements Orbit Solution Extra Radial Velocity Term

Period (days) 5.60172 (held) 5.60172(held)

TO 1869.17 (held) 1869.I7(held) (JD 2440000+)

V0 0.0 0.0 ( kmsec"1 )

K 76.2(20) 55.2(15) ( kmsec"1 )

Flow Velocity 52.4(15) ( kmsec 1 )

Flow Angle(°) 89.4(10)

0.0 0.0 a fit 15.1 13.6

streaming velocity from one of a variety of possibilities

(e.g. Roche Lobe overflow, stellar wind, etc ). This can be simply incorporated in the fitting by including an extra

v n tne velocity term ( ra,3iai ) * expression used in the BMDP fit to the measured radial velocities. The form of the function to be fitted is now 192

V = V + V cos( flow angle + phase*2ir ) fit orbital radial

The results of such a fit are shown in the third column of table 4.04 . They show that a good fit can be obtained using a velocity form such as the one.above. Knowing that the mass ratio is <*2 and that the velocity amplitude of the primary is 75kmsec the V then fixes the location of the orbital 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 literature that the He II X4686 line is subject to large variations ( Bolton

[1975] , Walker et al [1978] ). In order to verify this the equivalent widths of the corrected profiles were measured by determining limits to the extent of each profile and using a

Simpson's Rule Integration Routine to calculate the area.

When these results were plotted two sets of observations fell well off the smooth curve defined by the remainder of the data. The August 1982 observations consist of five nights of observation, while the Spetember 1982 data was of three nights duration. The first 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 lines in the same 193 spectra and it seems these are real changes in the He II emission equivalent width. Walker et al [1979] reported similar changes in equivalent width between data taken at two different epochs ( 1972 and 1975 ). It would of course have been interesting to see if these increases were associated with transitions 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 ( listed in table

4.03 ) were averaged in bins of 0.1 of the orbital phase and these values are listed in table 4.5 . They are plotted in figure 4.08 and it is obvious that there is a previously undetected variation with orbital phase. Possible mechanisms for producing this variation will be discussed in the next chapter. The August and September 1982 equivalent widths had the same orbital phase variations as the remainder of the data even though the actual values were much larger.

The halfwidths of the corrected X4686 line was also measured. In order to guard against instrumental variation producing changes, each value was divided by the measured halfwidth of the He I X4471 line from the spectrum of 19

Cepheus taken on the same night. 19 Cepheus is a single star and no variations in the vsini are observed. The normalized halfwidths binned on the orbital phase are listed in table

4.05 and shown in figure 4.09 . Table 4.05 He II X4686 equivalent widths and halfwidths as a function of orbital phase.

Phase Mean EW _[ mA ]_ Halfwidth All DAO 547.53

Phase Fraction of Mean Normalized 0.0-0.1 1 .000 1 .43 0.1-0.2 1 .172 1 .38 0.2-0.3 1 .073 1 .09 0.3-0.4 0.861 1.12 0.4-0.5 0.859 0.98 0.5-0.6 0.846 1 .47 0.6-0.7 0.910 1 .48 0.7-0.8 1 .022 1 .29 0.8-0.9 1 . 108 1.14 0.9-1.0 1 .067 1 .56 195

Figure 4.08 He II X4686 equivalent widths versus orbital 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. Normalized Equivalent Width 5 1 1.5 —I - ' ' • s*>i o '-\ ' ' ' r— ? M \ * © © / • / / .©* / / ©; G :© / / O © © Ul < \ / o -J © *. \ / ©° ©\ \© V © '© \ © \ ©- o ©©. : © © ro © / /©

M

M

M ° ©::G © : ©J Ul —i 1 : i__ 961 1 97

Figure 4.09 He II X4686 halfwidths versus orbital phase. 198

-1 - -1 1 1 1 -1 1 i •

•

CO

QO OJ in as _E 0_

CO

o o ©'

...© •\* nj

•—•

6

1 —i i i i i S ' T T d9D 6T/T-X 6Fi3 H1PImiIBH 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 al [1974,1979b] ). The accepted explanation of the profile seen is that it may be regarded as a single broad emission peak with a variable central absorption due to a wake effect ( Hutchings [1979] ). Unfortunately again the data was of rather poor quality and futher observations seemed appropriate.

The first stage of analysis of the data is similar to that for the He II emission line. 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 profile. Shown in figure 4.11 are the Cygnus X-1 Ha profiles, after all preliminary reduction, shifted into the rest frame of the primary. The Ha profile for 19 Cep was fitted with a smoothed curve and this profile was then subtracted from the Cygnus X-1 Ha profiles of figure 4.11 .

These first stage corrected profiles are shown in figure

4.12 as the solid line profiles. Stars at this spectral type and luminosity class are known to have Ha in emission (

Rosendhal [1973], review of Snow and Morton [1976] ). A good example is the type I P Cygni Ha profile seen in the 09.71b star $ Ori ( Conti and Leep [1974] ). The profiles 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 lines. 201

188001

^—-^i^^^ Y*^~ • HD18820 9

• 19Ce p ^^-^^^—r~Y*~~

Cyg

n—*^TY^^—"y"^ "67 Oph

I I I I u 6388 6488 6588 6688

Wavelength (Angstrom) 202

Figure 4.11 Ha Profiles shifted to primary's rest frame. 203

1 1 1—:—i 1 1 1 0.663

*~~~~+

^-~*~-«**^^ -Try—- QQS]

0.031

0.193

0.209

0.370

^lTY^M^^-^l 0.386

^^irTryrTW^^—Hf~—0.547

•^W^H^^^^T^^r^ 0-566 *~*,*<^^ 0.729

^ •^^ffY^^^^ 0,906

^p^^

^-^yrr^ —np~~o.io2

6388 6438 6488 6538 6588 6638 6688 6738

Uavelength (flnnsTroa) 204

Figure 4.12 Ha profiles corrected with 19 Cep profile (solid curves) and fitted P Cygni profile at phase 0.209 (dashed line). 205

Wavelength (flngstrot) 206 profile. This can be interpreted as the emission peak of a type I P Cygni profile ( Beals [1951] ). The profile 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 this phase any emission associated with the secondary would have the maximum velocity blue shift. Figure 4.12 shows this fitted P Cygni profile plotted as a dashed line over the first stage corrected profiles. The solid line in

figure 4.13 shows the net Ha profile after the first 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 telluric lines

found around Ha and their presence makes it very difficult to measure the final Ha profile line position and thereby compare its radial velocity curve to that of ' the He II emission. The two profiles however, except for differences

in strength, show remarkably similar forms over the cycle observed. It would therefore seem from these profiles that the two lines have a common origin contrary to the

suggestion of Hutchings et al [1974].

4.6 THE Ha PROFILE OF THE PRIMARY

The primary's intrinsic line profile was obtained above

through a number of convoluted steps. In figure 4.14 there

are three profiles visible. The dot-dashed absorption line

is the assumed 19 Cep absorption profile of Ha, the dotted 207

Figure 4.13 Ha (solid line) and He II X4686 (dashed line) corrected for underlying profile of primary for simultaneous observations at DAO(red) and CFHT(blue). 208

Velocity } km/sec I 209

Figure 4.14 Ha absorption component from fit to 19 Cepheus profile ( dot-dash line ), Ha from fit to corrected profile ( dotted line ) and sum of the two ( solid line) = HDE 226868 intrinsic Ha profile. 210 21 1

emission line is the fitted P Cygni emission profile and the

solid line is the sum of these two. This sum is the net Ha profile of HDE 226868.

Hearn [1975] has indicated a technique for determining

the region from which the Ha emission originates. Cassinelli

et al [1978] have pointed out a small error in the

application of the techique as outlined by Hearn [1975], The

method assumes that the profile observed is the result of an

absorption profile originating with the primary and a

component due to a spherically symmetric extended envelope

(the shell). The Ha line is the result of the 3=>2

transition in Hydrogen. Assuming that the shell has an inner

radius r and a thickness Ar then the absorption component of

the profile has an equivalent width proportional to the

number of absorbers in the line of sight, which is

2 2 2 W = X 7re f n2Ar / m c cl 6 where

3 n2 cm" is the average density of hydrogen atoms in level 2

f is the absorption oscillator strength for the Ha line

7re2 / mc is the intergrated absorption coefficent of a

classical atom

X is the rest wavelength of the Ha line

c is the speed of light

The Ha emission component comes from the region of the shell

visible to the observer and not on the line of sight to the 212 primary. This intensity is given by

2 1 1 I = n3A3 2 ( 47rr2 - 27rr0 ) Arh?/4ir ergs sec - sterad" where

n3 is the average density of hydrogen atoms in level 3

A32 is the Einstein spontaeous transition probability for Ha hv is the energy of a Ha photon

r0 is the radius of the primary

This intensity is observed as an equivalent width given by

2 2 2 2 2 Wg = X n3A3 2 ( 47rr - 27rr0 )Ar hv / c47r r0 B where

B = the Planck function at the Ha frequency for the

effective temperature of the star

The ratio of W to W 3give s the ratio e a

2 n3/n2 = (W /W ) * 0.549 * 1 / ( [r/r0] - 0.5 )

where the Planck function has been evaluated at a

temperature appropriate to the primary of 27500°K. If the

populations of the shell are primarily determined by the

radiation field from the primary then

n3/n2 = (CJ3/W2)( A31/ [ A31 + A32] )( exp[ "WkTstar ])

where co is the statistical weight of the level ( 2n2 )

For a 27500°K radiation field this gives a ratio of 0.619

This can now put into the earlier equation for n3/n2 to 213 finally give

r = roV/(W /Wj * 0.887 + 0.5

Figure 4.15 shows as a solid line the derived P Cygni profile, while the dashed-dot line is a NLTE Auer and

Mihalas [1972] Ha theoretical profile for a log g = 3.3 and

T = 30000°K star broadened to 95 kmsec-1 and the dotted line is a profile from Collins' [1977] LTE profiles with i = 40° and a rotation velocity = 0.2 of critical ( this gives the correct vsini value ). A number of investigations of 0 stars indicates that neither NLTE or LTE models satisfactorily fit any but a few select lines and are typically worse for the

Balmer lines < Auer and Mihalas [1972], Underhill [1983],

Takada [1977] ). Using the NLTE case ( the LTE profile is not very different ) as representing the primary's absorption profile and assuming the emission profile is symmetric then the horizontal hatched area in figure 4.15 is the emission equivalent width while the vertical hatched area is the absorption equivalent width. Measuring these areas gives a ratio of W /W * 2.5. Hence the inner radius of the Ha shell is derived as 1.37R*. This is 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 al [1980]. The X-ray source Wray 977 is also believed to have a Ha shell beginning at a radius fe 2 R* ( Parkes et al

[1980] ). 214

Figure 4.15 Derived Ha P Cygni profile (solid line), Auer and Mihalas NLTE profile (dash-dot line) and Collins LTE profile (dotted line). Uelocity (km/sQC) IT) 216

4.7 THE HYDROGEN ABSORPTION LINES

The equivalent widths of the hydrogen absorption lines were measured in the previous chapter and showed no variations when binned according to orbital phase ( 5.6 days ).

Recently Priedhorsky et al [1983] have found a periodicity

in the long term X-ray monitoring of Cygnus X-1 of 294±4 days. Kemp et al [1983] post-facto claim to have detected variations in the B photometry and polarization with the

same period. In order to test whether this variation is 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

listed in table 4.06 . The data, with the appropriate errors, are plotted in figure 4.16 a & b. It is clear from

this that the Balmer lines seem to be considerably stronger during X-ray zero phase whereas the He I lines seem to be

unchanged. Kemp et al [1983] find only a change of 0.005 magnitudes in their B photometry over the 294 day period and

this would certainly be well below the detection limit for equivalent width variations.

The results shown in figure 4.16b are quite interesting

if it is remembered that the Balmer lines are the result of

an absorption component from the primary plus a weak

emission. When binned on orbital phase the equivalent width variations were weak or non-existent which would indicate no variation from the primary profile itself. The emission contribution probably has the same origin as the He II and, 217

Table 4.06 Equivalent Widths Binned on the 294 day Period.

I I X-ray He He H0 H7 Erroi Phase X4471 X4713 +

Mean EW mA 645.23 273.06 1232.04 1744.99

Normalized

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 of, the Ha emission. As it has been found unlikely that

X-ray flux from the Cygnus X-1 secondary would produce enhanced mass loss from the primary ( London and Flannery

[1982] ) the logical conclusion seems to be that what is seen is the coupling between mass loss and accretion. For some reason the mass loss from the primary is modulated and as both the hydrogen emission component and the X-ray emission strength depend on the amount of mass loss, both are modulated also. At X-ray minimum less material is lost from the star, hence there is less Balmer emission, therefore the absorption line equivalent width increases, as seen. This is finally very clear evidence for the long held 218

Figure 4.16 upper: He I X4471 and 4713 equivalent widths as function of the 294 day X-ray period, lower: Ha and H7 equivalent widths as function of the 294 day X-ray period. Normal Ifid Equivalent Mldth Normal Ifid Equivalent Uldth ••9 1 1.1 1.2 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 its mass loss rate is not clear. One possibility is that a third body in the system perturbs the gravitational field between the primary and secondary. No evidence for extra absorption from such a star is seen in any of our spectra or in the power spectrum of the radial velocity curve. The fact that a 5.6 day periodicity is also seen in the X-ray data ( Holt et al

[1976,1979] ) makes the possibility of a third body less likely. The possibility of a precession in the system from either the compact object, the primary or from a tilted accretion disc is discussed by Priedhorsky et al [1983]. The latter two possibilities turn out to have time scales on the order of a year but such calculations are necessarily considerably simplified. However it should be kept in mind that there is no evidence for a disc about the secondary in

Cygnus X-1, it is difficult to think of a scenario where the rotation axis of the primary is very different from that of the system, and there is no evidence for the expected associated variation in the halfwidths of the primary's absorption lines.

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 itself is variable. Dolan et al [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 oscillations which occasionally align and enhance mass 221 loss. In fact photometric oscillations have been reported in

Cygnus X-1 during a transition into the high state ( Natali et al [1978] ). It may be that one mode of oscillation or a beat of different modes results 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, is the eccentric orbit LMC X-ray source

0535-668 ( Howarth et al [1984], Hutchings et al [1985] ). Chapter 5

EMISSION MECHANISMS

Although the Hell X4686 and Ha emission has been well known since the earliest days of the Cygnus X-1 optical identification ( Bolton [1972a,b], Smith et al [1973] ) little has been done to explain their origin. The He II

X4686 is clearly not a common feature in the spectra of stars at this spectral type as can be seen in Appendix A.

The model put forward to explain the emission is that it arises from material that has overflowed the Roche Lobe and is falling onto the secondary. The resultant heating in this process presumably produces the right conditions for the observed emission lines to be produced. This type of model has been variously suggested by Smith et al [1973],

Hutchings et al [1973], Bolton [1975] and Oda [1977]. There are in the literature at present five different (likely) mechanisms suggested for the production of the emission observed in massive X-ray binaries. These will be discussed below and the one most likely applicable to Cygnus X-1 will 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 result of X-ray irradiation of the surface producing a temperature increase

222 (effectively changing the spectral type for that side of the primary). There are three reasons for not believing this to be the major contributor to the emission seen in Cygnus X-1.

Firstly one would expect the equivalent widths of the emission lines to be largest near phase 0.5 where the maximum amount of the affected side of the primary is seen and minimum near phase 0.0 . This is not seen, in fact just the opposite behaviour is seen in the He II X4686 line.

Secondly, this mechanism can not produce a large component of velocity directed towards the secondary as is inferred is neccessary from the observed profiles. The major velocity component present in this model would be that due to rotation of the primary. Thirdly there is no evidence for a variation of spectral type, as defined by ratios of sensitive lines, 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 its application to cataclysmic variables. The primary loses mass either due to evolutionary pressure or to decreasing orbital seperation ( by say gravitational radiation ) and this mass is most—easily lost through the Lagrangian Point L1 , located between the primary and secondary, because of the minimum in the gravitational potential well at this point. Lubow and

Shu [1975] have made detailed calulations of this 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 this model predicts for Cygnus X-1 (taken from their table 3) is shown in figure 5.01 . There are two reasons for not believing that this is the major means of producing the observed emission. Taking the value of the mass ratio 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 ratio, the radius for their predicted disc around the secondary is 0.0683 of the orbit seperation, or 2.8 R^. This value is somewhat smaller than the accretion disc limits set by Paczynski's [1977] study of three body orbits about the central object. This is a quite substantial disc and because of its high temperature, due to

X-Ray heating, should be observable. The standard

'alpha-disc' models ( after Shakura and Sunyaev [1973] ) predicts that the temperature distribution in the disc follows

3//4 T(r) = T0 r~ .

Assuming that at all radii of interest the disc radiates as

a blackbody and knowing the inner disc radius (r0) and the outer disc limit (r,) then it is a simple integration to calculate 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 ratio 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 ratio of » 0.5 a radius for the accretion disc of * 3 to 20

s s R@ ( or 2 x 10 to 8 x 10 Schwarzschild radii {rg} ). The inner bound is less well determined but Priedhorsky et al

[1979] suggest it is greater than 20 r . The'central T0 can be obtained from Pringle's [1981] estimation for it of

3 0 25 T0 = [ 3GMM/87TRO 0 ] ' where

M is the accretion rate

M is the mass of the compact object a is the Stefan-Boltzmann constant

Note that T0 is 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 al [ 1983] ) but not radiating as a blackbody and being the source of the hard X-ray flux seen in Cygnus X-1. Shapiro et al [1976] estimate that the transition to the cooler standard disc would occur at « I00r .

6 Thus estimating r0 * 100 and r, » 10 and the range of

8 7 temperature T0 as 3 x 10 to 6 x 10 °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 it can be seen that the maximum contrast between the disc and the stellar flux 228

Figure 5.02 The Flux Spectra of Accretion Discs at a

distance of 2.5 kpc. Two disc models with T0 indicated ( dotted and dash-dot lines ) and flux expected from HDE 226868 ( solid line).

230 occurs at wavelengths in the far ultraviolet. In fact at about 1200 A the flux from a disc with temperature of 3 x

108K is of the same order as that coming from the luminous primary. Pineault [1984] finds similar estimates for the visibilty of the disc from his models. Treves et al [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 all the UV flux comes from the primary. Beall et al [1984] have searched in the infrared for an excess flux from a disc but they find only that expected from the primary. It must be concluded therfore that if 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 infall of matter necessary to explain the X-ray emission can be explained by direct 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 velocities predicted at the point where the stream strikes the disc, and from where Hell emission is expected to originate. For the Cygnus X-1 case this value is (from Lubow and Shu [1975] table 3 ) =900 km/sec. For our line of sight this would imply a maximum observed radial velocity of 580 km/sec ( i = 40° ) which is far larger than found from the observed Hell velocity curve in Chapter 4. Therefore, although this model seems to well 231 describe the cataclysmic variables where a stream from the

low mass companion falls on the white dwarf ( Warner and

Peters [1972] ) it seems unlikely that it is appropriate in

the case of Cygnus X-1.

5.3 TRAILING SHOCK MODEL

Strong absorption components blue shifted relative to

the H and He absorption lines from the primary are found in

the spectra of some X-ray binaries at phases after the

secondary has crossed the line of sight to the observer (i.e

phases 0.5 to 0.8 ). The effect can be particularily strong

in the Hel X5876 and is clearly seen in the X-ray binaries

HD153919 ( Fahlman and Walker [1980] ) and Vela X-1 ( Bessel

et al [1975] ).

Fransson and Fabian [1980] propose a model in which the

stellar wind escaping from the primary in the direction of

the secondary passes through a region near the X-ray source

where the ionizing X-Ray flux is sufficently 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 its orbit this

material is left behind and eventually recombines and is

subject to acceleration again. However the wind coming

directly 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 colliding with a slower, denser medium. These are the classic conditions for a shock front to form. The results of Fransson and Fabian

[1980] program to simulate this scenario ( given in their figure 2 and 3 ) show a strong shock region trailing the

X-ray source in the orbital plane. The conditions derived

( T~105K , n^lO12 cm"2 ) are suitable for Hell lines to be enhanced and the expected velocities are ^ 0.2 V ) where esc V * 2000 km/sec. The velocities predicted ( =*400 km/sec ) esc do agree with those measured for the trailing 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 inclination of the system. However the amplitude of the Hell

X4686 radial velocity curve for Cygnus X-1 has a much smaller amplitude ( =*75 km/sec ) than would predicted ( 250 km/sec ). As the shock is produced by the Ram Pressure of the stellar wind on the slower moving material its strength is dependant on pAv . For comparison the mass loss rate of

Cygnus X-1 and HD 153919 are a factor of four different

(Hutchings [1976]) and the distances of the compact

companions from the stellar 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 is a factor of 10 larger in HD153919 than Cyg X-1 and this may explain why ram pressure is appropriate in HD

153919 and not Cyg X-1. 233

5.4 EMISSION FROM THE DISC

Hutchings et al [1974] suggested that the width of the Ha profile was best explained by having the emission originate in a rapidly rotating disc about the secondary. The profile 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 velocity component that would give a phase dependence similar to that seen in figure 4.7. In standard disc models test particles in orbit about the compact companion move in circular 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 velocity is * 450 kmsec"1, or a projected radial velocity of 290 kmsec"1 when viewed from i = 40°. This again is larger than the observed K amplitude of the He II emission radial velocity curve in

Cygnus X-1. Reducing the radius of a disc would increase this rotation velocity while reducing the mass of the secondary would decrease it. However a reduction of more than an order of magnitude in the mass of the secondary would be needed to bring the velocity down to the observed K amplitude of 74 km sec"1 seen. This is not consistent with other knowledge of the system. 234

5.5 ENHANCED STELLAR WIND

In single stars the stellar wind mass loss is assumed to be spherically symmetric ( Conti [1978], Cassinelli

[1979] ) but in the case of a close binary the presence of a companion distorts the potential field and may result in large enhancements of mass flow towards the secondary.

Friend and Castor [1982] have studied the effects of a compact companion (i.e. through gravity and continuum radiation pressure) and the centrifugal force due to orbital motion on the symmetry of the wind. They find that when these effects are included the character of the wind is a strong function of the size of the primary relative to its critical potential lobe. As the primary comes close to filling its Roche Lobe the mass loss in the direction of the secondary becomes enhanced. This idea neatly combines the two popular mechanisms of a stellar wind and Roche Lobe overflow for providing material to power X-ray sources. The

Stellar Wind progressively looks more like what is normally thought of as Roche lobe overflow as the primary star expands to fill its Roche Lobe. One of the specific stars that Friend and Castor [1982] model is Cygnus X-1 and their mass loss rate vs angle from the axis of this binary is shown in figure 5.03.

There were a number of reasons for thinking this might be a good explanation for not only the source of accretion material but also as the origin of the observed emission lines. 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 ) is primarily in that the H and Hell lines are in emission in the latter and in absorption in the former. The reason for this is that the mass loss rate is much larger in the Of stars and therefore the wind has a higher density, and the central star is hotter thereby providing a more intense radiation field.

Klein and Castor [1978] have produced dynamical models of the H and He II lines in the expanding envelopes of Of stars. Using the observed ratio of the equivalent widths of

Ha to He II X4686 in Cygnus X-1 of =* 2 ( see figure 4.12 ), their models and observation would require a radiation field 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 is also supported by dynamical considerations. The centre of mass for the system lies 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 velocity amplitude about the same as the primary but 180° out of phase. If this gas also had an outflow component this would introduce a phase effect ( i.e. it would not be exactly out of phase ), as observed in the He II X4686 radial velocity curve. 238

5.6 THE MODEL

This last suggested model for the system seemed worthy of further study and so a code was written which attempted to model the line profiles expected for an enhanced stellar wind model of Cygnus X-1. Following Friend and Castor [1982] there is a region between the secondary and primary through which substantially more mass is lost than in any other direction. This region must be quite thin as any material flowing at any distance out of the binary plane will be subject to a gravitational restoring force returning it 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 fiftieth 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 line could be determined by knowing the variation of velocity with radius. Various velocity laws exist in the literature

( see review by Cassinelli [1979] ) but the most appropriate in this case would .seem to be that used by Friend and Castor

[1982] and by MacGregor and Vitello [1982]. They both find that in the region between the primary and secondary in a 239

Figure 5.04 A schematic of the Enhanced Stellar Wind Model for Cygnus X-1 as described in text.

241

X-ray binary the velocity law is approximately linearly related to the radius. The form of the velocity law was then fixed as

V(r) = V(D) ( r / rsfcar - 1 )

where V(D) = velocity at the X-ray source

r . = radius of star star r = radius from primary's centre

The density follows from this

p(r) = M/( 47rr2 V(r) )

where M= mass loss at each angle from axis

r= distance from primary centre

v(r)= velocity of wind at r

The velocity law assumed is quite different from that conventionally accepted for single stars ( Castor et al

[1975] = CAR ) of v • vinf 1 " Rstar ' r > where

v^n£ = terminal velocity of the wind

R . = radius of the star star r is the distance from the centre of the star

1 For a v^nf * 2000 kmsec" the CAR velocity law gives a

1 velocity at the secondary ( 2Rgtar ) of * 1000 kmsec" .

MacGregor and Vitello [1982] find in their theoretical study that the presence of an X-ray emmitting secondary can change the velocity of the wind at the secondary. When they

increased the X-ray luminosity from 0 to 103"ergs/sec, the vinf °^ fc^e w*n^ was reduced by a factor of 3 and hence the 242 velocity at the secondary was also lower than what CAR

gives. Observationally there is also evidence that the CAR velocity is 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 light 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

1 velocity at 2Rstar to 250 kmsec" . Parkes et al [1980]

from a study of the P-Cygni profiles of WRA-977 conclude

that the stellar wind only reaches a velocity of 300 kmsec"1

R at 3 star' Therefore there seem to be reasons for assuming a

velocity law for the material moving between the primary and

secondary in Cygnus X-1 in which the acceleration is more

gradual than for a normal stellar wind.

The next step is to calculate what fraction of this

material is in the correct level to produce the He II X4686

transition. To rigorously determine the temperature and the

ionized fraction would require solving the local 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

al [1984] ).

2 2 2 where £ = ( Lx / nx D ) ( R v(R) / { r v(D) } ) 243

and Lx = luminosity of the X-ray source

nx = density of wind at the X-ray source

D = orbital separation

R = distance from the primary

r = distance from the X-ray source

v(R) = wind velocity at R

v(D) = wind velocity at the X-ray source

Buff and McCray [1974] and Tarter et al [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 stellar wind. The form of the X-ray spectrum they use is

dL/de - ( L / emax) * exp[ -( e - e^/e^] where

em. = 13.6 eV nun

£ 10 keV mma=vx =

The form of the X-ray spectrum of Cygnus X-1 has been the subject of considerable study ( Oda [1977], Ling et al

[1983], Liang and Nolan [1984] ). Shown in figure 5.05 is 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 is the < 2.5 keV spectrum as this is where many elements' K shell cross-sections are largest and therefore substantial heating is 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 their work. 245

nj i • i • 1

N. S. X S. N.

s.

\ \ Q-h \

'A \.\

\ -- v.. \ \ \ \ V \ \ V \ V V V \ \ i V — V \ V V 1 . .1

• 2 log [Energy (keU)] 246 distance of Cygnus X-1 ( 2 kpc ) results in substantial absorption of these soft X-rays by the interstellar medium (

Fireman [1974] ). Also there is considerable variation in the intrinsic soft X-ray absorption. This results in both the form and intensity of the soft X-ray flux not being well known and it will thus be assumed similar to that adopted by

Buff and McCray [1974] and which applies to other X-ray systems. Shown in figure 5.06 are the variations of the temperature and ionization with i- assumed in the following work. Knowing the temperature and from that the ionized fraction ( using the fraction of He/H = 0.1 from Allen

[1976] ) at each grid point now allows calculation of the populations of the appropriate levels of He.

A further effect to consider is the re-absorption of the photons emitted in the 4 => 3 He II transition. The most significant re-absorption will happen in the vicinity of where the emission occurs as the gas there is denser than that out of the plane of the binary and along the line of sight. Also most of the material out of the plane will be velocity shifted out of the doppler width of the line. The equation for reabsorption from Lang (1980) was used, namely

2 ay=( ire / mc ) f ( N / Ai>) -( 1 - expt - hv/kT ] )

where e = electron charge

m = electron mass

f = oscillator strength for the transition

N = Number of atoms in the lower state

A»> = thermal width 247

Figure 5.06 Variation of temperature with £ (upper). Variation of ionization fraction with £ (lower). From Buff and McCray [1974].

249

T = temperature of the gas

From this one can calculate the optical depth as

r—a v L where L is the pathlength through the

absorbing material.

In this situation the optical depth turned out to be less than one through most of the region of interest and thus the gas can be considered to be optically thin ( as was assumed for the X-ray flux). The inclination of the system (i » 40°) and the radius of the primary (18 R^) implies that the closest 4 RQ 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 lines as a function of orbital phase.

This implies that there is no significant contribution to the observed emission from the region close to the surface of the primary where the optical 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 line of centres form and the velocity law and from this obtain a density at each point in a spatial grid covering the region of enhanced mass loss towards the secondary. A value of £ is then calculated—at all grid points and this gives a local temperature and fraction of singly ionized helium. The equilibrium in the 4=>3 transition is then calculated following Rybicki and Lightman

[1979] and using the expression for a diluted radiation 250 field from Mihalas [1978], Allowance is then made for reabsorption. Finally the emitted flux from each grid point is appropriately velocity (for that phase) shifted, corrected to put it in the centre of mass frame of the system and summed to give a resultant profile. A summary of the basic system parameters used in this work is given in Table 5.01 . The predicted profiles from such a model are shown in figure 5.07 together with profiles obtained at the CFHT at 2.4 A/mm or 0.037A/pixel. Although the profiles do have their differences it is pleasing to see that the strength and the velocity shifts are of the correct order at phases 0.25 and 0.75. The differences at conjunction phases are substantional and this may be because of a much more complex velocity field around the secondary than has been assumed here. The presence of an off axis emission component (as in SMC X-1, Hutchings et al [1977]) would also distort the profile. It should also be remembered that the absorption profile from the primary also probably varies with phase and this effect has not been accounted for in the observed profiles. The only parameters that were manipulated in this analysis were the velocity at the X-ray source, which defines the magnitude of the velocity law, and the luminosity of the X-ray source. The best match to the observed profiles was obtained with a velocity at the X-ray source of 350 km/sec and a X-ray luminosity of 8 x 1037 ergs/sec. This velocity is approximately the value found by 251

Figure 5.07 Model (solid) and observed profiles (dotted) of He II X4686 in Cygnus X-1 for phases indicated. 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 R0

Separation = 25.2 RQ Orbital Radius of Secondary = 43.2 RQ Luminosity of the X-ray source = 4.2 x 1037 ergs/sec Temperature of Primary = 31000°K

Mass of Primary = 21 MQ

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 direction of the secondary. They did not include the effect of ionization by the X-rays on the wind however. The value is also similar to the wind velocity at the secondary deduced for the very similar X-ray binary WRA 977 ( White and Swank [1984] ). The

X-ray luminosity derived is also higher than the average value of 4x1037 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 reality. 254

In principle this technique can also be used to determine the mass ratio of the system. If the theoretical model is correct, then a different mass ratio changes the velocity transform into the centre of mass system. Model profiles using a range of mass ratios could be generated to

find the best fit to the observed data. The current models do not justify trying this. A model using full local balance equations, coupling the stellar wind acceleration to local conditions and using NLTE would produce more accurate profiles and may make such an attempt useful.

One further check on how realistic the enhanced stellar wind model is can be made by using the estimated mass loss and wind velocity to determine an expected X-ray luminosity

from the secondary. This requires estimating the accretion

rate from a stellar wind, a problem dealt with most recently

by Henrichs [1983] ( and by Shapiro and Lightman [1976],

Bondi and Hoyle [1944] ) who gives

( V /V )a "ac " % * orb w * < 1 / { 1 + tMp/Mx]}* ) *

< 1 / { 1 + a[vorb/vw]>

where

Vork = orbital velocity of the secondary

V„w = radial velocit•y* of the wind at the distance of the secondary

a - ( 1 - X{ Rp/Rsep }')*

and X = 1 for corotation.

The X-ray luminosity can then be determined from 255

x 0 ac where

$ is the efficency For the values appropriate to Cygnus X-1 ( table 5.01 and

1 1 vQrD- 250 kmsec" , vw* 350 kmsec" ) the X-ray luminosity would be predicted as $ x 2 x 1039 ergs/sec. To produce the observed X-ray flux of =•= 2 x 103'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 all concentrated on modeling a system like Her X-1 where the X-ray luminosity at the surface is much larger than the optical flux and hence the main concern is with the effect of heating high in the atmosphere. Table 5.02 lists a number of the properties of

Her X-1 and Cygnus X-1 ( from London et al [1981], Liang and

Nolan [1984] ). The Cygnus X-1 system differs from the Her

X-1 system in two significant ways. The ratio of the X-ray to optical luminosity is 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 it. 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] ). Clearly there is 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 flux this may produce effects deeper in the atmosphere of HDE 226868.

The variation of the equivalent width of He II X4686 line shown in Chapter 4 can be explained conveniently if the variation is attributed to change in the strength of the underlying absorption line. Absorption line changes in Her

X-1 are seen in coincidence with the orbital period of the secondary ( Hutchings and Crampton" [1972] ) and they indicate a change in the spectral type from B1 to B4. Oke

[1976] has modelled the changes in the equivalent widths by assuming most of this star has a normal stellar atmosphere 257

Figure 5.08 X-ray Spectrum of Cygnus X-1 (dotted line) and Her X-1 (dash-dot line). log [Flux ( photons/cm«)iE2/sec/l

o CD

m 3 ro

CO ...-•if.—-'

c

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 3X1011 1.8x10*2 surface (cm)

X-ray Luminosity

(<10 keV) ergs/s 1.5X1037 0.5-4X1037

(>10 keV) ergs/s 1.0X1037 1-3.5X1037

Temperature of Primary 7000 27500 °K

Optical Luminosity 1 . 4X1 03 5 1 . 1x1 03 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 variation 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 line in Cygnus X-1

(figure 4.8).

The first question to be addressed is 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 stellar atmosphere. In the soft X-ray region ( > 300 eV ) the primary means of transferring energy from X-rays to the gas is by K shell ionizations of metal atoms. The cross-sections and ionization energies for this process for the abundant metals has been tabulated by Daltabuit and Cox [1972] and more recently by London et al [1981]. The energy difference between the incoming X-ray photon and the K shell ionization energy is 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 collision is 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 distribution is strongly peaked toward forward scattering and only about 10% of the photons are backscattered.

To do this calculation properly a Monte Carlo simulation would have to be performed in which each photon

is followed through the gas. In the code here an initial flux of photons was attenuated in its passage through a planar atmosphere by allowing one interaction with the gas (

i.e. no scattering ) The result of this collision was determined by the probabilities outlined above. The resultant heating rates as a function of depth are shown in

figure 5.09 ( as the lines 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 al [1981] for that object.

The next step is to compare this X-ray heating to the energy density of the radiation field of the star. No tabulation of energy density with depth could be found in

the literature and thus it was assumed that the atmosphere was in LTE so that the energy density is 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 lines only are the resultant internal radiation 262 field energy densities. Clearly the secondary in Her X-1 has a much more substantial effect on the primary than is the case in Cygnus X-1. Note however that this heating is still present at great depth in Cygnus X-1 ( >1 gem"2 ) due to its large hard X-ray flux. This calculation is only approximate and a more detailed evaluation would be interesting to see how strong this deep atmosphere heating effect is.

The question that began this aside was why the He II

X4686 shows equivalent width variations with orbital 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 plot. In Her X-1 the entire line

forming region is strongly affected by the secondary as the

X-ray heating is two orders of magnitude larger than the

internal radiation field. This explains the large changes in

spectral type observed for this star. For Cygnus X-1 the effect is not substantial, always being less than the primary's radiation field over the entire line 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 it can be seen that at this depth the He II ions still

contribute to the line observed from outside the star. At

mass fraction 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

Figure 5.09 Model of X-ray heating of primary in Her X-1 (dashed line + symbols) and Cygnus X-1 (dotted line + symbols ). Energy density in Her X-1 (dashed line only) and Cygnus X-1 (dotted line only) 264

in 1 1 1 1 ry He I y * Hell I / £ o • i \ o Ql .• / \ in / / \ in / / o> t_ Qt i—i

° O

/ .• /

01 X ///

in o o. Ql Q V / 3>

i_ Ql -. -\ L. + -5 • Depth (1og[g/cm**2]) 265

LTE. The energy density ( E ) given by

E = aT*

where a = 4o/c = 7.56 x 10"5 ergs/cm3/deg"

Now if the effect of the X-ray heating can be treated as a

small pertubation on this energy density then

(T + 6T)« = E/a + 8E /a

which expands to give

6T <* 6E /(4Taa)

From figure 5.09 the maximum heating is about 30

ergs/cm3/sec at depth 0.1 g/cm2.The stellar temperature is

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 this is 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 optical 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 is the IUE

Spacecraft which because of its aperture can only produce low resolution, poor signal to noise spectra. The radio emission is quite weak and comes from synchrotron emission in large flares and from the terminal region of the wind.

The X-ray flux comes from near the secondary in the binary system and with the availability of EXOSAT it was decided to investigate it further.

The optical observations of July 1984 of Cygnus X-1 were obtained almost simultaneously with requested Target of

Opportunity Observations by the EXOSAT satellite. The purpose of these observations was to see whether the source was in its high or low state. Previous observations ( by the author and Walker et al [1978] ) indicated large changes in the equivalent widths at various times possibly associated with the X-ray state. Further it was expected that the optical spectroscopy could be done with sufficent time and wavelength resolution to enable observation of any changes in the optical corresponding to variations in the X-ray. The details 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 Day # Orbital ' X-ray 3-13keV Flux 1 984 Phase Phase 10"sergs/cm2/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.

Clearly seen are long dips in the flux in the second nights observations.

Cygnus X-1 was one of the first observed and strongest

sources in the X-ray region. It has been studied extensively using all available X-ray satellites ( 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 ( Li and

Clarke [1974], Mason et al [1974], Parsignault [1976],

Murdin [1976], Pravdo et al [1980], Remillard and Canizares

[1984] ). Mason et al [1974] have suggested that they occur

prior to superior conjunction, however using the the new

ephemeris for the orbit derived in Chapter 2 on all the

historic dip observations reveals no such effect. 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 is in units of UT hours. 269

CYG X-1 EXOSRT/ME

HflRONESS

s.o

0.0 5-13 KEV

ISO •Verity

CJ IU co n V u' CO 1-3 KEV o CJ 150 J

o. 10.00 12.00 14.00 16.00 OflY NO: 189.0 270

CYG X-1 EXOSAT/ME

HARDNESS

!1 5.0

o.o 5-13 KEV

130 J

UJ « 0. CO 1-3 KEV 3 o 120i

0. 0.00 2.00 4 .00 6.00 DAY NO: 190.0 271

CYG X-1 EXOSflT/ME

HARDNESS

5.0

0.0 5-13 KEV

130

o ^ 0. CO t— z 1-3 KEV O (_> 120

0. 10.30 12.30 14.30 16.30 DAY NO: 191 .0 272 attentuation of the X-ray flux ranging from a few percent to almost complete absorption. Remillard and Canizares [1984] explain their data and that of Pravdo et al [1980] as being due to partially ionized blobs of gas along the line 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 optical eclipses, meaning that the system inclination must be less than 62° with the most likely value of near 40°

( this thesis, Davis and Hartman [1983] ).

The high viewing aspect of this system makes these dips difficult to explain. They are certainly 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 is high out of the plane of the system ( because of the low inclination ) and its presence must be explained.

The fact that the dips are only seen near phase zero indicates that the absorbing region lies between the primary and secondary. There are a number of mechanisms suggested in the literature to explain a variety of X-ray observations which may pertain to this situation.

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 [1976], table 1 ). For the size of accretion disc they envisage ( * 3 RQ ) this would not be sufficent to produce the absorption features seen. The stream itself can not be the source either as it is confined essentially 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 instabilities producing an oscillation in the disc. Such oscillations have been reported in some low mass

X-ray binaries ( White and Swank [1982], Walter et al

[1982] ). The data for 4U1755-33 ( Frank and Sztajno [1984]

) is particularly clear, showing semi-periodic dips between

400 ' and 730 seconds. The deeper dips are also longer in duration which the authors interpret as being due to larger excursions in the disc. Such an interpretation predicts a characteristic time scale for such oscillations as of the order of the disc thickness divided by the local sound speed or characteristic turbulent velocity. If the disc thickness is the result of balance between gravity and turbulent pressure the time scale of oscillations is ( Frank and

Sztajno [1984] )

where

M = the mass for the secondary =* 10 MQ for Cygnus X-1

Assuming the oscillations are confined to the rim ( as is believed the case in the low mass systems ) of the disc of 274

radius =* 3 R@, the oscillation time for a Cygnus X-1 disc is

2600 sees. The data in figure 6.01 does not seem to be periodic however it is apparent that the larger flux dips mask the true number of smaller dips. A longer data set is needed to investigate if the smaller dips are periodic. The amplitude necessary for such oscillations to produce the observed dips ( assuming an inclination of 40° ) however

would have to be larger ( * 2.5 R@ ) than the disc radius.

This is clearly not possible. This explanation is therefore probably not appropriate unless the inclination of the system is in fact near the grazing eclipse limit 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 field. 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 is not high enough out of the plane to explain the observed dips for the assumed inclination. As well there is little evidence to support the existence of such a substantial disc.

It has been reported on numerous occasions in the literature that the winds of early type stars vary ( e.g.

Ebbets [1982] ). These claims are normally justified with observation of emission lines ( typically Ha ) in high mass loss stars. One needs to be particularily careful in using such data as the region near Ha is infested with telluric lines which vary independently of the star ( Carlberg 275

[1978] ) and because the underlying spectrum of early type stars can be varying ( Ninkov et al [1983] ). Better evidence for inhomogeneities in the wind come from the flickering seen in a number of X-ray sources ( Holt [1982] ) and which is attributed to accretion of clumps from the stellar wind onto the secondary. Kahn [1981] has shown that in a radiation driven wind inhomogeneities will grow with height . from the star for

M winds in which the star > X/2 where X is the maximum mass loss rate allowed. For HDE 226868 the figure is = 96% of the maximum and thus its wind may be quite susceptible to clump iness. Carlberg [1978,1980] has modeled the scale size of inhomogeneities that may exist and grow in stellar winds. The conditions used in his study were a wind that had a mass

6 loss rate 1 x 10' M@/yr, at a distance of 2R* from the star, with a velocity of 1000 kmsec"1. These conditions are very similar to what would be found in the wind of HDE 226868 at the distance of the secondary. The result of his linearised stability analysis is that there are two distinct absolute instabilities. The first results from radiation driven sound waves producing a Raleigh-Taylor Instability due to small perturbations in the velocity field ( also Nelson and Hearn [1978] ). Any velocity perturbation in a direction away from the star will move the absorbing profile further into the continuum thereby increasing the radiation force. The second is again a Raleigh-Taylor instability but due to initial fluctuations in the density of the wind. Any 276 pertubation that produces a constant outward velocity produces an increase in the density. This density is subject to an increased radiation force which in turn accelerates the vertical flow. These instabilities have characteristic wavelengths of scale I09cm and lO^cm respectively.

Two observations can be made from the data shown in figure 6.01. Firstly dips in the X-ray are seen mainly in the second night's data where the observations are near zero phase as is 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 ratio,

narrow ones with duration of < 5 minutes, with a

distribution centered on phase zero but a larger spread

in phase and with a highly variable hardness ratio.

Any inhomogeneities in the stellar wind when viewed near phase zero have their velocity primarily along the line of sight ( radial ). Thus the eclipse duration is the time it takes the background X-ray source to pass through the shadow of a wind inhomogenity in the foreground. From work in chapter three the velocity of the secondary is 350 kmsec"1.

Therefore a one hour eclipse corresponds to a length of ^

I011cm and <5 minutes to < 101ocm. These figures correspond well to the theoretical estimates of Carlberg.

The clustering of dips near phase zero imply that the the material producing the dips occupies a region between the orbit of the secondary and the primary surface. Carlberg 277

[1978] finds that his larger scale disturbances are in fact absolute instabilities ( 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 this perturbation to grow. Beyond the radius of the secondary the density of the wind drops rapidly and in consequence the more severe effects of X-ray ionization ( McCray et al

[1984] ) may destroy the instabilities. The smaller scale

instabilities are an amplifying perturbation ( they grow

from some initial pertubation under the influence of

radiative acceleration ). They too are more likely to grow

in the region between the primary and secondary due to the higher densities.

The location of the dips is possible to estimate in a

rough way if estimates for the ionization parameter £ and

the column density of the dip can be made. Pravdo et al

[1980] and Remillard and Canizares [1984] have both found

that the spectra of the X-ray source taken during eclipse is

best fit assuming attenuation by partially ionized gas. L.

Stella at the EXOSAT observatory has made fits 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

fit was made with an absorber temperature of 1.7X105 °K and

a column density of 2.40±0.05 x 1023 cm"2. From Buff and 278

McCray [1974] this implies that the ionization parameter £ =

L/nr2 > 100 . Rearranging this expression gives

r = • L D / Nc $

where

r = distance from the X-ray source

L * 2 to 8 X1037 erg/sec

I «* 100

D * 101 1 cm

This gives a value for r, the distance from the absorption

region to the X-ray source, as =*4-8 RQ. With an inclination

for the system of 40°, simple geometry indicates that the

absorption region is positioned =* 3-6 r^ out of the orbital

plane of the system and at a distance from the primary of 41

RQ or 2 R*. It is intriguing that this is also about the

distance from the star where the narrow absorption

components seen in lines in the ultraviolet in some early

type stars originates. ( Underhill and Fahey [1984] ).

Notice that r is larger than the radius of the sphere in

which complete ionization of the gas by X-rays from the

secondary occurs. It is also close, but larger than, the

inner radius of the Ha shell found in the previous chapter.

The existence and location of these dips is of

relevance to models of O star stellar winds. Cassinelli et

al [1981] suggest that the X-ray observations imply that all

OB supergiants are X-ray sources at a level >1032 ergs/sec.

This level is consistent with the Corona and Cool Wind model

for stellar winds ( Waldron [1984] ) and with the shocked 279 inhomogeneties in the wind model ( Lucy and White [1980],

Lucy [1982] ). Our studies indicate that there is 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 it 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 this region would be a number of orders of magnitude smaller than that seen from the secondary ( Cassinelli and Swank [1983] ) and consequently undetectable. An alternative explanation for these observations is due to the presence of magnetic fields 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

( Cassinelli [1985] ) using a magnetic field approach. In

fact as X-ray luminosity increases monotonically with greater rotational velocity, and as this is 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 visible 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 al 280

[1983] report on a loose correlation between X-ray absorption and flickering X-ray on a 10 minute timescale in

HD 153919 ( 06.5f + neutron star ). HD 153919 is known to suffer variable duration eclipses of the X-ray source by the primary ( Branduardi et al [1978] ). This variability may be due to the presence of large dips which would be most likely to produce absorption ( i.e. be along the line of sight) near ingress and egress. SMC X-1 ( BOI + neutron Star ) shows absorption dips of a few hundred seconds following eclipse exit ( Marshall et al [1983] ) which is also attributed to inhomogeneities in the wind. In all these cases the systems are eclipsing 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 particularily 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 is found using the historic data available in the

literature and applying both a period folding analysis

and looking for systematic changes in the T0 parameter.

No periods other than orbital were detected.

2. the absorption line velocity curve is well defined and

the orbital parameters are determined with great

accuracy.

3. the He II emission radial velocity curve is quite smooth

contrary to the results of previous studies which

attributed noise in their observations to fluctuations

in the system. The emission is 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

orbital phase, being smallest at phase 0.5 and largest

at phase 0.0 . It is due to change in strength of the He

II X4686 absorption line 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 is 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 line on some occasions which may be

associated with X-ray transitions from low to high

states.

7. after removal of the primary contribution the variation

of the shape of the Ha and He II X4686 profile with

orbital phase looks very similar, contrary to the

findings of others.

8. investigation of the Ha line profile indicates a region

of * 0.4 times the radius of the primary above the

primary which does not contribute to the Ha profile.

9. modeling of the He II emission lines indicates the 283

origin of the emission lines is in the X-ray heated

region between the primary and the secondary. A slowly

accelerating stellar wind directed toward the secondary,

with a velocity at 2RA of only 350 km/sec is 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 101° and

1011 cm. This is in agreement with stability analysis of

the wind. The location of the larger dips is 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 is needed. Observationally much remains

to be done in the optical but mainly at specific times.

It would be nice to have X-ray monitoring of the X-ray

sources that have erratic long term behaviour so as to

know when to make a concerted observing effort on them.

For example the cause of the high and low state in

Cygnus X-1 is not at all understood. It would also be

productive to continue to observe Cygnus X-1 so as to

investigate the possible change in orbital period of the

system. Whether there is fine structure in the optical

emission lines still needs to be resolved with good high 284 dispersion data, Some Be stars are known to pulsate ( e.g. 7 Cas, $ Oph ), possibly some of the X-ray source

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A Spectral Atlas for Stars 08 to Bl. All spectra are of 110A extent at a dispersion of 4OA/nun centered on wavelengths A4686, X4542 and X4100 .

302 A Cep 9 Sge a Cam e Ori « Ori 061 081a 09.51a BOIa B0.5!a

K Cas B0.7la

A Ori 19 Cep Cyg X-1 08.5lab 09.5lab 09.7lab

HD188209 15 Sgr 09.5lab 09.7lab

HD218915 HD194280 09.5lab 09.7lab

«T Ori 69 Cyg f Per 09.71b BOIb Bllb

HD225146 HD 40111 09.71b Bllb

HD207198 HD47432 p Leo 09lb-ll 09.71b Bllb

6 Ori HD13745 HD199216

09.511 09.711 Bill OJ o OJ CD O HD199579 15 Mon t Ori 06.5111 08111 09.5111

10 Lac 08111

HD193322 08.5111

7 Cas BOIV

1 Ori BOIV

HD206269 HD217086 68 Cyg 14 Cep o Ori v Ori n Ori 42 Ori 06.5V 07V 08V 09V 09.5V BOV B0.5V B1V

0l Ori C AE Aur e Per 07V 09.5V B0.5V

X Per HD36960 09.5V B0.5V

40 Per B0.5V

A Cep 9 Sge a Cam HD195592 e Ori K Ori 061 081a 09.51a 09.71a BOIa B0.5la

AC Cas B0.7la

A Ori 19 Cep Cyg X-1 08.5lab 09.5lab 09.7lab

HD188209 15 Sgr 09.5lab 09.7lab

HD218915 HD194280 09.5lab 09.7lab

C Ori 69 Cyg c* Per 09.71b BOIb Bllb

HD225146 HD 40111 09.71b Bllb

HD207198 HD47432 p Leo 091b II 09.71b Bllb

8 Ori HD13745 HD199216 09.511 09.711 Bill o 308 HD199579 15 Mon i Ori 06.5111 08111 09.5111

10 Lac 08111

HD193322 08.5111

7 Cas BOIV

HD206269 HD217086 68 Cyg 14 Cep a Ori v Ori n Ori 42 Ori 06.5V 07V 08V 09V 09.5V BOV B0.5V B1V

01 Ori C AE Aur e Per 07V 09.5V B0.5V

X Per HD36960 09.5V B0.5V

40 Per B0.5V 310

PQ

CD O A Cep 9 Sge a Cam e Ori K Ori 061 081a 09.51a BOIa B0.5la

/c Cas B0.7la

A Ori 19 Cep 08.5lab 09.5lab

HD188209 09.5lab

HD218915 09.5lab

69 Cyg c* Per BOIb Bllb

HD 40111 Bllb

HD207198 p Leo 09lb-ll Bllb

6 Ori HD199216 09.511 Bill 312 HD199579 15 Mon tOri 06.5111 08111 09.5111

10 Lac 08111

HD193322 08.5111

7 Cas BOIV

HD206269 HD217086 68 Cyg 14 Cep a Ori vOx\ TJ Ori 42 Ori 06.5V 07V 08V 09V 09.5V BOV B0.5V B1V

61 Ori C AE Aur e Per 07V 09.5V B0.5V

X Per HD36960 09.5V B0.5V

40 Per B0.5V CD O