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Interferometric Stellar Spectrometry

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Interferometric Stellar Spectrometry INTERFEROMETRIC STELLAR SPECTROMETRY by Ian Wynne Wynne-Jones Astronomy Group Blackett Laboratory, Imperial College, London SW7 2BZ Submitted to the University of London for the degree of Doctor of Philosophy London, December 1980 2 "Truth is the child of time, not of authority. dcwHnc^uk Our ignorance is infinite, so let us .diminition by a fraction. Why try to be so clever now, when at last we can become a little less stupid? I have had the unbelievable good fortune to lay my hands on a new instrument by means of which one can see one tiny corner of the universe a little clearer. Not much - but a little. Make use of it I " From The Life of Galileo By Bertolt Brecht. 3 ABSTRACT The theory of Fourier transform spectrometry is surveyed. The use of the Michelson interferometer for the Isaac Newton telescope is described. The instrument was used to study stellar spectra at high spectral resolution and high signal-to-noise ratio ^ 100 . The atmospheric motions of the luminous K stars, Arcturus, Hamal, Kochab and Pollux were studied. The profiles of their neutral iron absorption lines were measured and synthesized to obtain the microturbulent, macroturbulent and rotational velocities of their atmospheres. A Fourier technique was employed to dissect the line profiles, but it was concluded the method has no advantages compared with more traditional statistical tests. Evidence suggests a more realistic model for spectral line formation in turbulent media is required to synthesize the line profiles consistently. The hyperfine structures of the interstellar sodium D1 and D2 absorption lines in the directions of <X and S Cygni were observed for the first time. Synthesis of the profiles yielded velocity dispersions of *-250 ms ^ ,indicating diffuse interstellar cloud temperatures of 200°K and subsonic internal cloud motions. It was also concluded that the number density of interstellar clouds and variation of cloud column density was greater than previously thought. 4 ACKNOWLEDGEMENTS Firstly, I am indebted to Dr. R.C. Wayte for his guidance and example. I greatly appreciated the opportunity to learn from him and latterly, with him. Secondly, I am most grateful to Professor J. Ring for his supervision and constant encouragement. Thirdly, I would also like to thank Dr. A.P. Thome and Dr H.J. Walker for their constructive criticisms of the draft of this thesis. For their discussion and interest I am grateful to: Professor D. Blackwell, Professor D. Gray, Dr. R.Griffin, Professor B. Pagel, Dr. N.K Reay, Dr. M.A. Smith and Dr. S. Wychoff. To Professor J. Brault, Mr. C. Amos, Dr. K. Hartley, Mr. D. King and Dr. D. Youll I am thankful for advice on computing. I. should also like to thank members of staff and research students in the Astronomy Group at Imperial College and the Royal Greenwich Observatory, Herstmonceux for their help and friendship. Thanks also goes to Mrs. T. Wright for so patiently typing this thesis . X would like to acknowledge the PATT committee for their generous allocation of telescope time on the Isaac Newton telescope and to the Science Research Council for their financial support. Thanks is also due to the R.G.O. and I.C., computing and library sections for use of their resources. Finally, I should like to thank my parents, to whom I dedicate this thesis, for their understanding, and example of diligence and perseverance. 5 CONTENTS Page No CHAPTER 1 FOURIER TRANSFORM SPECTROMETRY 1.1 Introduction ^ 1.2 Theory of the interferogram ^ 1.3 Recovering the spectrum 1.4 The discretely sampled interferogram ^ 1.5 Discrete sampling restrictions ^0 1.6 Flux and acceptance ^4 1.7 Throughput and Luminosity ^9 6 97 1.8 Internal modulation ^ 1.9 Path difference errors 29 1.10 Demodulating the secondary interferogram JO 1.11 Sample interval measurement oJ/ 7 1.12 Interferogram sample signal-to-noise ratio ^7 CHAPTER 2 DATA REDUCTION OF INTERFEROGRAMS 2.1 Introduction 39 ,2.2 Theory 39 2.3 Spike elimination 41 2.4 Normalization of the spectra 48 2.5 The signal-to-noise ratio in the spectrum 50 2.6 Radial velocity measurements 53 CHAPTER 3 SYNTHESIS AND ANALYSIS OF STELLAR LINE PROFILES 3.1 Introduction 57 3.2 Line profile synthesis in local thermodynamic 58 equilibrium 3.2.1 Level populations 60 3.2.2 The absorption coefficient 61 3.2.3 Van der Waa^s broadening 63 6 Contents (Continued) Pa^e No 3.3 Radiative transfer 53 3.3.1 Flux integration gg 3.3.2 Continuous opacities gg 3.4 Model atmospheres gg 3.5 Macro turbulence 7^ 3.6 Rotation 72 3.7 Fourier analysis of line profiles 74 3.8 Macroturbulent and rotation filters 76 3.9 Synthetic line profiles 77 CHAPTER 4 STUDIES OF Fe I ABSORPTION IN LUMINOUS K STARS 4.1 Introduction gp 4.2 Selection of line profiles gg 4.3 Choice of star ^ 4.4 Analysis of line profile data 94 4.5 The Fourier analysis method 4.6 Results and discussion 4.6.1 Accuracy of profile measurements 4.6.2 Abundance and microturbulence ^24 4.6.3 Macroturbulence and rotation ^q 4.7 Conclusions 2.30 CHAPTER 5 INTERSTELLAR Na I D ABSORPTION LINE STUDIES 5.1 Introduction ^32 5.2 Interstellar absorption line profile synthesis ^34 5.3 Instrumental profile broadening ^35 5.4 Saturated line profiles ^3g 5.5 Synthesis of Na I D1 and D2 interstellar lines ^39 5.6 Observational data 7 Contents (Continued) Page No 5.7 Data Analysis 152 5.8 Results of model fitting 5.8.1 The °C Cygni sight line 153 5.8.2 The S Cygni sight line 169 5.8.3 The Tau sight line. 169 5.9 Discussion and comments. 175 8 TABLES 2.1 Number of spikes eliminated versus standard deviation. 47 3.1 Comparison of continuum opacities. 69 401 Atomic transition data of line profiles measured. 92 4.2 Stars observed. 95 4.3 Equivalent width grid for Fe I ^6151 X of Arcturus. 97 4.4 Mean square difference grids for Fe I ^6151 X of Arcturus. 98 4.5 Best fit parameters of line profiles. Ill 4.6 Average values for velocity parameters of each star. 112 4.7 Ratio of collisional to radiative ionization excitation rates 126 in the photosphere of a late type star. 4.8 Equivalent width verses ^29 5ol Atomic parameters used to synthesize Na I D1 and D2 lines. 141 5.2 Details of interstellar Na I D1 and D2 observing runs. 14$ 5.3 Stars observed for their insterstellar spectra. 151 5.4 Properties of well resolved interstellar components. 160 5.5 Seven cloud fit to o( Cygni line of sight. 160 5.6 Nine cloud fit to Cygni line of sight. 170 5.7 Model fits to S Cygni and At Tau. 176 9 FIGURES Page No 1.1 A schematic diagram of a Fourier Transform Spectrometer. 15 1.2 A discretely sampled interferogram instrumental profile. 21 1.3 A continuously sampled interferogram instrumental profile. 22 1.4 The output intensity for an off-axis ray. 25 1.5a Asymmetric instrumental profiles. 31 1.5b Asymmetric absorption profiles. 32 1.6 Internal modulation amplitude error. 35 2.1 An interferogram before spike elimination. 45 2.2 An interferogram after spike elimination. 46 2.3 A spectrum before normalisation 51 2.4 A spectrum after normalisation. 52 3.1 Specific intensity. 64 3.2 Line profile dependence on element abundance. 78 3.3 Line profile dependence on microturbulence. 80 3.4 Line profile dependence on rotation. 84 3.5 Line profile dependence on macroturbulence. 86 3.6 Rotation profile Fourier transform filter. 87 3.7 Macroturbulence profile Fourier transform filter. 88 4.1a The spectrum of Dubhe around ^6065 8. 93 4.1b The spectrum of Aldebaran around "A5379 8. 93 4.2 The Fe I ^6151- 8 line* ofr-Arcturus. 99 4.3a The Fe I ft6151 8 line of Arcturus. 101 4.3b The Fe I ft6151 8 line of Arcturus. 103 10 FIGURES (Continued) Page No. 4.4 The Fe I A6027 X profile of Arcturus. 106 4.5 The Fe I 7\6027 X profile transform of Arcturus. 107 4.6 The Fe I 7\6065 X profile of Arcturus. 108 4.7 The Fe I ft6151 X profile of Arcturus. 110 4.8 The Fe I ^5379 X profile of Hamal. 113 4.9 The Fe I TV 6027 X profile of Hamal. 114 4.10 The Fe I J\6065 X profile of Hamal. 115 4.11 The Fe I 7*6151 X profile of Hamal. 116 4.12 The Fe I ft5379 X profile of Kochab. 117 4.13 The Fe I ft 6027 X profile of Kochab. 118 4.14 The Fe I ft 6065 X profile of Ko chab. 119 4.15 The Fe I ft6151 X profile of Kochab. 120 4.16 The Fe I ft5379 X profile of Pollux. 121 4.17 The Fe I ft6027 X profile of Pollux. 122 4.18 The Fe I A60 65 X profile of Pollux. 123 4.19 Non-LTE Fe I A6151 X profile of Arcturus. 128 5.1 Synthetic interstellar Na I D1 lines for various velocity dispersions. 142 5.2 Synthetic interstellar Na I D1 lines for various column densities. 143 5.3 Instrumental broadening of an unsaturated line. 145 5.4 Instrumental broadening of a saturated line. 146 5.5 Resolving power verses profile accuracy. 147 5.6 The +lkm/s D1 line in Cygni: a) Gaussian velocity distribution, 155 b) exponential velocity distribution.
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