The Structures and Extents of the Chromospheres of Late-Type Stars
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The Structures and Extents of the Chromospheres of Late-type Stars A dissertation submitted to the University of Dublin for the degree of Doctor of Philosophy Neal O´ Riain Trinity College Dublin, September 2015 School of Physics University of Dublin Trinity College Declaration I declare that this thesis has not been submitted as an exercise for a degree at this or any other university and it is entirely my own work. I agree to deposit this thesis in the University's open access institu- tional repository or allow the library to do so on my behalf, subject to Irish Copyright Legislation and Trinity College Library conditions of use and acknowledgement. Name: Neal O´ Riain Signature: ........................................ Date: .......................... Summary The chromosphere is the region of a star, above what is traditionally defined as the stellar surface, from which photons freely escape. As the definition implies, this region is characterised by complexity, non- equilibrium, and specifying its structure is a vastly non-linear, non- local problem. In this work we are concerned with the chromospheres of late-type stars, objects of spectral type K to M, the thermodynamic structure, extent, and heating mechanisms of whose chromospheres are not well understood. We use a number of observational and computa- tional methods in order to gain a detailed quantitative understanding of these chromospheres. We construct a model to compute the mm, thermal bremsstrahlung flux from the chromospheres of late-type objects, based on a number of simplifying assumptions concerning their thermodynamic structure. We compare this model with archival and recent observations, and find that the model is capable of reproducing the observed flux from objects of spectral type K to mid-M in the frequency range 100 GHz { 350 GHz. We suggest that, while this model is quite simple, it provides an accurate reflection the structure of the chromosphere of late-type stars. We also make use of the unique insights into stellar structure provided by the eclipsing ζ Aurigae binaries. We present the \rediscovery" of periodic Si I emission in these objects. We hypothesise that this effect arises as a result of the UV radiation of the secondary object, which photo-ionizes Si I in the chromosphere of the primary. Since this UV radiation falls only on a portion of the visible hemisphere of the primary at a given phase, the line is periodic, and as a locally formed line in disk-averaged spectrum this is a novel and powerful diagnostic. While we rule out this line being a result of simple reflection, we expect it to have the same phase variation as broadband reflection. We construct a geometric model of the system, and find that the computed reflection curve matches the observed line periodicity very well. As the primary of ζ Aurigae undergoes an eclipse it is possible to ef- fectively resolve its chromosphere, which allows us to place direct con- straints on its structure. However, despite the unique insights afforded by the study of this system, no semi-empirical model has yet been con- structed. Using archival observations of ζ Aurigae A we construct a full one-component, semi-empirical model of its chromosphere. As this binary system is detached its chromosphere is thought to be compara- ble to that of single stars | λ Velorum being a specific example | and we use the model constructed to comment on the structure of late-type chromospheres generally. For my family Acknowledgements I'd like to acknowledge the scientific contribution of Dr. Graham Harper to the research of this thesis, I am very grateful for his in- put and direction at the early stages of this work. A sincere thanks to Dr. Peter Gallagher for all of his help and advice throughout my time at Trinity, and especially in the somewhat rocky final months of my PhD. The staff of the School of Physics, academic, administrative, and technical, have always been so welcoming and accommodating, and for that I am deeply appreciative. A big thanks to all of the members of the Astrophysics Research Group, past and present, that I've had the misfortune and pleasure to work with. You're a great group of lads. The most important and lasting part of the past four years is my friendships with each of you. The science is a distant second. Thanks also all my friends, you've put up with my complaints over the past few years; thanks for the patience and all the good times. Most importantly thanks to my family, for everything. Without your support and encouragement I'd be nowhere. List of Publications 1. O´ Riain, N., Harper, G. M. \Non-LTE model of the Chromosphere of ζ Aurigae A" in prep, 2015 2. Harper, G. M., O´ Riain, N., Griffin, R.E.M., Bennett, P.D. \Periodic Photoexcited Si I Emission in Composite-Spectrum Binaries" in prep, 2015 3. O´ Riain, N., Harper, G. M., Griffin, R.E.M., Bennett, P.D. \ζ Aurigae: Periodic Photoexcited Si I Emission" Proceedings of the 18th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, 2014 4. Harper, G.M., O´ Riain, N., Ayres, T.R. \Chromospheric thermal continuum millimetre emission from non-dusty K and M red giants" Monthly Notices of the Royal Astronomical Society, 2013 vii Contents List of Publications vii List of Figures xii List of Tables xx 1 Introduction 1 1.1 Motivation . .2 1.2 Evolution of Late-type Stars . .3 1.3 Structure of Late-Type Stars . .6 1.4 Stellar Observation & Theory . 11 1.5 Radiative Transfer . 13 1.6 ζ Aurigae Binaries . 16 1.7 Thesis Overview . 18 2 Background & Theory 20 2.1 Absorption and Emission Mechanisms . 21 2.1.1 Free-free absorption & emission . 21 2.2 Bound-bound Absorption and Emission . 24 2.2.1 Atomic Structure . 25 2.2.2 Transitions . 27 2.2.2.1 Line Profiles . 30 2.2.3 Bound-Free Transitions . 37 2.3 Rate Equations . 38 2.3.1 Density Sensitive Transitions . 40 2.4 Solving the Transfer Problem . 43 2.5 Computation of Fluxes . 50 viii CONTENTS 2.5.1 Escape Probability . 50 2.5.2 Feautrier Method . 52 2.6 Modelling Binary Stars . 56 2.6.1 System Geometry . 56 2.6.2 Radiative Properties . 62 3 Instrumentation 65 3.1 Spectrometers . 66 3.1.1 Ground-based Observations . 66 3.1.2 Hubble Space Telescope . 69 3.2 Interferometry . 73 3.2.1 Principles of an Interferometer . 73 3.2.2 Interferometry with CHARA . 77 3.3 Radio Observations . 78 3.3.1 CARMA . 78 3.3.2 APEX . 79 4 Thermal Continuum Millimetre Emission from non-dusty K and M Giants 82 4.1 Introduction . 83 4.2 Initial Model . 84 4.2.1 Semi-Empirical Constraints on Stellar Chromospheres . 84 4.2.2 Scale Height & Chromospheric Extent . 86 4.2.3 Millimetre Optical Depth . 87 4.2.4 Linear Source Function Method . 88 4.2.5 α Tau Calibration . 90 4.3 Extensions to the Model . 92 4.3.1 Spherical Geometry . 92 4.3.2 Exponential Layer . 93 4.4 Calibration and Results . 98 4.4.1 Solar Brightness Temperature . 98 4.4.2 Stellar Fluxes . 100 4.5 Predictions of the Model . 104 4.5.1 Recent Observations . 104 ix CONTENTS 4.5.2 Spectral Indices . 106 4.6 Summary and Conclusions . 108 5 Geometric Modelling of the ζ Aurigae System 110 5.1 Introduction . 111 5.1.1 Spectroscopic Observations . 112 5.2 Geometric Model & Light Curve . 118 5.2.1 Stellar Parameters & Orbital Elements . 118 5.2.2 Synchronicity . 121 5.2.3 Limb-Darkening & Gravity Darkening . 124 5.2.4 Light Curve . 125 5.3 Reflection Effect . 125 5.3.1 Sobolev Reflection . 128 5.3.2 PHOEBE Reflection Curve . 131 5.3.3 Line Reflection . 135 5.4 Conclusions . 138 6 Chromospheric Model of ζ Aurigae A 140 6.1 Introduction . 141 6.2 Construction of the Initial Model . 142 6.2.1 MARCS Model Photosphere . 142 6.2.2 Empirical Mass Column Densities . 143 6.2.3 Empirical Temperatures and Turbulent Velocities . 144 6.2.4 Electron Densities . 146 6.3 Atomic Models . 151 6.3.1 Hydrogen Model . 152 6.3.2 Aluminium Model . 154 6.3.3 Carbon Model . 156 6.4 Spectral Observations . 161 6.4.1 HST Data . 161 6.4.2 Synthetic Spectra . 171 6.4.3 Contribution Function . 176 6.4.4 λ Velorum Ca K & H-α Profiles . 178 6.5 Chromospheric Model . 179 x CONTENTS 6.5.1 Best-fit Chromospheric Model . 179 6.5.2 Chromospheric Extent . 183 6.6 Conclusions . 186 7 Conclusions & Future Work 188 7.1 Radio Model . 189 7.2 Periodic Si I Emission . 193 7.3 Chromospheric Model of ζ Aurigae A . 195 7.4 Concluding Remarks . 198 A Atomic Models 203 A.1 H atom . 203 A.2 Al atom . 204 A.3 C atom . 209 B Atmospheric Model 211 References 214 xi List of Figures 1.1 The Hertzsprung-Russell diagram with the stellar evolutionary tracks annotated for objects of various initial masses. This figure contains both the observational and theoretical HR diagrams. The observa- tional diagram has axes of color and magnitude, which are directly observable, and the theoretical form has axes of effective temper- ature and luminosity, which require a model to determine. Image Credit: Australia Telescope National Facility. .............4 1.2 The internal structure of red giant (left) and asymptotic giant branch stars (right), showing the different shells of internal burning. Image Credit: Australia Telescope National Facility. .............5 1.3 The complexity of the solar atmosphere from the photosphere and above.