THE OSCILLATION MODES OF DELTA SCUTI STARS By Edward J. Kennelly B. Sc. (Astronomy) University of Western Ontario M. Sc. (Astronomy) University of British Columbia A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES GEOPHYSICS AND ASTRONOMY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1994 © Edward J. Kennelly, 1994 __________________________ advanced In presenting this thesis in partial fulfilment of the requirements for an the Library shall make it degree at the University of British Columbia, I agree that that permission for extensive freely available for reference and study. I further agree 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. (Signature) Department of cc’d Aroror The University of British Columbia Vancouver, Canada 199L( Date SpI. O DE-6 (2/88) Abstract Many S Scuti stars exhibit multiperiodic oscillations and are therefore considered to be good candidates for studies in stellar seismology; the modes of oscillations act as probes of the internal stellar structure. For S Scuti seismology to be successful, both the oscifiation modes and frequencies must be determined observationaily, then compared with theoreti cal models. Standard photometric observations can provide direct information only about the frequencies of those low-degree oscillations which give rise to large disk-integrated variations. In this thesis, oscillations of both low- and high-degree were studied by ana lyzing the variations introduced in the Doppler-broadened profiles of rapidly rotating S Scuti stars. The incidence of high-degree variability within the S Scuti instability strip was inves tigated with an spectroscopic survey of ‘ 50 bright stars, carried out at the Dominion Astrophysical Observatory. Evidence for high-degree variations was discovered in 14 stars which were located both on the main sequence and in more evolved stages of evolution. A few stars (e.g., r Peg and 92 Tau) were investigated further with high-resolution (2.4 A/mm) spectra obtained at the Canada-France-Hawaii telescope. Using a two- dimensional Fourier technique to transform the variations within the line profiles in both time and Doppler space, a representation of the variations was produced from which the apparent frequency and the apparent azimuthal order (or degree) could be directly determined. The technique was especially successful at uncovering multiple modes of oscillation. The observed mode spectra were found to be consistent with prograde, sec toral modes which oscillate with nearly equal frequency in the corotating frame of the star. However, the frequencies of the high-degree modes were lower than expected if they U result from pressure waves trapped near the stellar surface. To study the oscillations in detail, observations lasting several days are required in order to provide adequate frequency resolution. As part of the 1992 MUSICOS campaign, 4 days of nearly continuous observations of 82 Tau were obtained from sites in China, France, the Canary Islands, and Kitt Peak. Analysis of the MUSICOS data has revealed several low- and high-degree modes (1 8) at frequencies between 11 and 17 cycles day1. in Table of Contents Abstract ii List of Tables vii List of Figures ix Acknowledgements xii 1 The Oscillations of S Scuti Stars 1 1.1 Introduction 1 1.2 A Description of Stellar Oscillations 2 1.3 The Properties of S Scuti Stars . 7 1.4 Stability Analysis of S Scuti Stars 10 1.5 The Problem of Mode Selection 14 1.6 Seismology of S Scuti Stars - A Test for Convective Overshooting . 15 1.7 Seismology of S Scuti Stars - The Internal Rotation Proffle 16 1.8 Goals for this Thesis 18 2 The Identification of Oscillation Modes 19 2.1 Methods of Mode Identification: A Summary 19 2.2 Fourier Analysis 22 2.3 Analysis of Radial Velocity Variations 25 2.4 2-D Fourier Representation of Line-Proffle Variations 26 2.5 Demonstrations of the 2-D Fourier Technique 30 iv 2.6 2-D Fourier Prewhitening 49 2.7 Discussion 50 3 Line-Profile Variations in the S Scuti Instability Strip 52 3.1 Introduction 52 3.2 Organization of the Survey 54 3.3 Observations 55 3.4 Analysis of the Survey 70 3.5 Discussion 79 4 The Line-Profile Variations of r Pegasi 82 4.1 Introduction 82 4.2 The 1990 CFH Observations 83 4.3 The 1992 DAO Observations 91 4.4 Discussion 95 5 The Line-Profile Variations of 62 Tauri 99 5.1 Introduction 99 5.2 The 1990 CFHT Observations 103 5.3 Observations from DAO 111 5.4 Discussion 112 6 Four Line-Profile Variables Re-Visited 114 6.1 Introduction 114 1 6.1.1 HR 1298: En 114 6.1.2 HR 2707: 21 Mon 115 6.1.3 HR 3888: v UMa 115 2 6.1.4 HR 5329: Boo 116 V 6.2 Fourier Analysis of the 1987 CFHT Observations 116 6.3 Discussion 123 7 The MUSICOS Observations of 62 Tauri 126 7.1 Introduction 126 7.2 The Goals of MUSICOS 126 7.3 Organization of the MUSICOS 92 Campaign 127 7.4 The MUSICOS Observations 129 7.5 Reduction of the MUSICOS Spectra 131 7.5.1 Reduction of the Xinglong Data 131 7.5.2 Reduction of the OHP Data 133 7.5.3 Reduction of the WilT Data 134 7.5.4 Reduction of the Kitt Peak Data 136 7.5.5 Corrections to the Line-of-Sight Velocity 138 7.5.6 Continuum Normalization 138 7.5.7 Spectral and Temporal Resolution 141 7.6 Radial-Velocity Variations 142 7.7 Line-Profile Variations 150 7.8 Discussion 167 8 Summary and Conclusions 176 Bibliography 180 vi 21 36 45 List of Tables 2.1 Methods of Mode Identification 2.2 Numerical Simulations of High-Degree Modes . 2.3 Simulations of Low-Degree Modes 2.4 Fourier Representation of Multiple Modes 46 3.1 Survey Selection Criteria • . 55 3.2 Survey of S Scuti Candidates 56 3.3 Survey Observations 59 3.4 Detection of Line Profile Variations 65 4.1 Fourier Analysis of the Line-Proffle Variations of r Peg (CFHT) 87 4.2 Fourier Analysis of the Velocity and Light Variations of r Peg (CFHT & UH) 88 4.3 Fourier Analysis of the Line-Profile Variations of T Peg (DAO) 94 92 5.1 Summarizing Tauri 102 5.2 Fourier Analysis of the Line-Profile Variations of 92 Tau 110 5.3 Fourier Analysis of the Velocity Variations of 92 Tau 110 6.1 Characteristics of the Observed Stars 124 7.1 MUSICOS 92: Requirements 128 7.2 MUSICOS 92: Sites and Instruments 129 92 7.3 MUSICOS 92: Observations of Tau 130 vii . 7.4 MUSICOS 92: Spectral Resolution 141 7.5 MUSICOS 92: Analysis of the Radial Velocity Variations 147 7.6 MUSICOS 92: Further Analysis of the Radial Velocity Variations . 149 vu’ 41 42 43 44 47 48 74 76 80 List of Figures 1.1 Velocity Maps of Surface Oscillations 4 2.1 Simulated High-Degree Line-Profile Variations 33 2.2 Fourier Representation of High-Degree Line-Profile Variations 34 2.3 Fourier Representation of Large Amplitude Variations 38 2.4 Fourier Representation of Inclined stars with 0 —m £ 40 2.5 Fourier Representation of Radial Oscillations. 2.6 Fourier Representation of £ = 1 Oscillations 2.7 Fourier Representation of £ = 2 Oscillations 2.8 Fourier Representation of £ = 3 Oscillations 2.9 Line-Profile Simulations with Multiple Modes 2.10 Fourier Representation of Multiple Modes - 3.1 Detection of Line-Profile Variations Example One • 62 3.2 Detection of Line-Profile Variations - Example Two 63 3.3 Mean Spectra and Their Variations 68 3.4 Mean Spectra and Their Variations 69 3.5 Line-Profile Variations in the Instability Strip 3.6 The Period-Luminosity-Colour Relation for S Scuti Stars. 3.7 The Distribution of Projected Rotational Velocities 4.1 The Line-Profile Variations of r Peg (CFHT) 84 4.2 Fourier Representation of the Line-Profile Variations in r Peg (CFHT). 85 ix 4.3 Simultaneous Radial Velocity and Light Variations of r Peg (CFHT & UH). 89 4.4 The Line-Proffle Variations of r Peg (DAO) 92 4.5 Fourier Representation of the Line-Proffle Variations in r Peg (DAO). 93 4.6 Radial Velocity Variations of r Peg (DAO) 95 4.7 Identification of the High-Degree Modes 97 5.1 The Orbital Radial Velocity Variations of 92 Tau 104 92 5.2 Mean Spectra of Tau at Different Phases of the Orbit 106 92 5.3 The Line-Proffle Variations of Tau 108 92 5.4 The Fourier Representation of the Line-Profile Variations of Tau. 109 92 5.5 The Radial Velocity Variations of Tau. 111 6.1 Fourier Representation of the Line-Profile Variations in o1 En (I) 118 1 6.2 Fourier Representation of the Line-Proffle Variations in Eri (II) 119 6.3 Fourier Representation of the Line-Profile Variations in 21 Mon 120 6.4 Fourier Representation of the Line-Proffle Variations in v UMa 121 6.5 Fourier Representation of the Line-Proffle Variations in ic2 Boo 122 7.1 Spectral Coverage for the Individual MUSICOS Sites. 131 7.2 The Observational Window Functions 132 7.3 Stability at the MUSICOS Sites 137 92 7.4 The Radial Velocity Variations of Tau 144 92 7.5 The Spectral Window Function and Amplitude Spectra of Tau .