thesis.tex

% thesis.tex
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% Copyright 2022 Alexander Lyttle.
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\addbibresource{lyttle21.bib}

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  % chapters/outline,
  chapters/introduction,
  chapters/hbm,
  chapters/lyttle21,
  chapters/glitch,
  chapters/glitch-gp,
  chapters/conclusion,
  chapters/software,
  appendices/lyttle21
}

%% TITLEPAGE DETAILS ----------------------------------------------------------
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% Add your details here
\author{Alexander J. Lyttle}
\title{%
Hierarchically Modelling Many Stars\\
to Improve Inference with\\
Asteroseismology}
\group{Sun, Stars and Exoplanets Group}
\school{Physics and Astronomy}
\college{Engineering and Physical Sciences}
\submitted{April}{2023}  % Change this to the month you submit your thesis

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% https://intranet.birmingham.ac.uk/staff/resources/brand-resources/university-logo-guidelines.aspx
\logo{uob-logo.eps}  % Optional, comment this out if logo not wanted


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%% DEDICATION -----------------------------------------------------------------
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% Optional dedication, edit this or comment out if not appropriate
\dedication{%
\begin{center}
  \textsc{Dedicated to}\\
  Hannah\\
  \pgfornament[width=1.5cm,ydelta=-3pt]{70}\\  % Fancy divider
  % \pgfornament[width=2.5cm,ydelta=-3pt]{80}\\  % Simple divider
  \textsc{In Loving Memory of}\\
  Angela and Barry
\end{center}
}


%% ABSTRACT -------------------------------------------------------------------
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\abstract{%
  Astronomers want accurate physical properties of stars like age, mass, and radius. We can estimate these by comparing observable parameters to those from models of stellar evolution. This has been made possible on a large-scale with recent astronomical surveys and the field of asteroseismology probing inside stars. In the first chapter of this thesis, I introduce asteroseismology --- the study of stellar oscillations. I choose to focus on stars which oscillate like the Sun with masses from \SIrange{0.8}{1.2}{\solarmass} undergoing their main sequence and subgiant phases of evolution. To date, we have observed oscillations in hundreds of these stars. With the upcoming space-based \emph{PLATO} mission, we anticipate observations of \(\sim 10^4\) more solar-like oscillators. 
  % Modelling stars to understand stellar physics and characterise their ages and masses is crucial for studying exoplanetary systems and the evolution of the Milky Way. 
  % As stellar modelling advances with the advent of high-precision asteroseismology, it is becoming increasingly important to account for the systematic effects that arise from our physical assumptions. 
  In this thesis, I aim to develop probabilistic modelling methods which can quickly and easily scale to such huge numbers of stars. Furthermore, we know our stellar models are wrong. It is important to accurately quantify this uncertainty if we are to use stellar parameters to understand stellar populations. In Chapters \ref{chap:hbm} and \ref{chap:hmd}, I present a novel approach for improving the inference of fundamental stellar parameters using a hierarchical Bayesian model. I introduce a statistical treatment which `pools' helium abundance (\(Y\)) and the mixing-length theory parameter (\(\mlt\)) to incorporate information about their distributions in the population. Specifically, I model \(Y\) as a distribution centred on a linear enrichment law parametrised by \(\Delta Y/\Delta Z\). I test our method on a sample of dwarfs and subgiants observed by \emph{Kepler} with \(0.8 < M/\mathrm{M}_{\odot} < 1.2\). Exploring various levels of pooling parameters, with and without the Sun as a calibrator, I report \(\Delta Y/\Delta Z = 1.05^{+0.28}_{-0.25}\) when the Sun is included in the sample. Despite marginalising over uncertainties in \(Y\) and \(\mlt\), I am able to report statistical uncertainties of 2.5 per cent in mass, 1.2 per cent in radius, and 12 per cent in age. Moreover, my approach can be extended to larger samples. This will enable further uncertainty reduction in fundamental parameters and data-driven insight into population-level distributions.

  There is additional information on \(Y\) to be gained from detailed asteroseismology. Acoustic glitches, which arise from rapid changes in stellar structure (e.g. from helium ionisation), leave a periodic signature in the mode frequencies (\(\nu_{nl}\)) of solar-like oscillators. I explore the theoretical background behind this effect in Chapter \ref{chap:glitch}. Then, in Chapter \ref{chap:glitch-gp}, I present a new method for modelling glitch signatures in the radial mode frequencies using a Gaussian Process (GP). The GP provides a statistical treatment of uncertainty in the functional form of our model for \(\nu_{nl}\). Using a model star and 16 Cyg A, I compare this approach to another method which models the smooth component of the function using a 4th-order polynomial. My results show that the GP method accurately determines the strength and location of glitches caused by He\,\textsc{ii} ionisation and the base of the convective zone. I find that using a prior to inform the glitch parameters in my method reduces the occurrence of extreme, unrealistic solutions in the posterior. Furthermore, I demonstrate that the GP approach outperforms the polynomial by marginalising over the lesser signature of He\,\textsc{i} ionisation. However, inclusion of the He\,\textsc{i} ionisation glitch in the model remains a question. Overall, my results suggest that the GP method should be further tested on more solar-like oscillators and then integrated into the hierarchical model presented in this work.}


%% ACKNOWLEDGEMENTS -----------------------------------------------------------
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\acknowledgements{%
I am tremendously grateful to my PhD supervisor Guy R. Davies for his support and excellent mentorship throughout my postgraduate research. Additionally, I thank my first co-supervisor Andrea Miglio for his guidance before his move to the University of Bologna. I extend my thanks to Amaury Triaud, who took over from Andrea as my co-supervisor and has since been an inspiring mentor and leader of our research group. I would like to thank in advance my PhD examiners Daniel Reese and Chris Moore, and viva chairperson Annelies Mortier.

\begin{CJK*}{UTF8}{gbsn}
  % INTERNAL SUPPORT
  It has been a pleasure to work with the Sun, Stars, and Exoplanets research group here at the University of Birmingham. I would like to thank all of my fellow current and former PhD students with whom I have exchanged ideas, advice, laughs, and stories.
  % : T. Baycroft, L. Carboneau, Y. Davies, A. Dixon, G. Dransfield, A. Freckleton, O. Hall, E. Hatt, V. Hod\v{z}i\'{c}, S. Khan, E. Ross, O. Scutt, M. Standing, W. Van Rossem, and E. Willett. 
  I also appreciate the support of the Head of School Bill Chaplin, and other postdoctoral researchers in our group, notably M. Nielsen, Tanda Li (李坦达), and W. Ball. I extend my thanks to the support staff in the School of Physics and Astronomy, particularly our office secretary Lou for her unwavering support over a challenging few years. I also thank my external collaborators, for example Nick Saunders at the University of Hawaii and Simon Murphy at the University of Southern Queensland, with whom I have worked during my graduate studies.
\end{CJK*}

% FUNDING
I acknowledge the support of the public who have indirectly funded the research in this work via various publicly funded agencies. Specifically, I thank the Science and Technology Facilities Council (STFC) who funded my PhD. I also acknowledge that this work is a part of a project that has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (CartographY; grant agreement ID 804752). Finally, I am grateful for the financial and academic support from the Alan Turing Enrichment scheme. This scheme provided me the opportunity to learn from and collaborate with the wider world of machine learning in science.

Last but not least, I am hugely grateful for the support of my loving family and friends. Particularly, I thank my fianc\'{e} Hannah, my parents Katy and Paul, and my brother Dom.
}


%% DOCUMENT ===================================================================
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\begin{document}

  \maketitle  % Title page

  \frontmatter

  %% FRONT MATTER -------------------------------------------------------------
  \makefrontmatter  % Adds abstract, dedication and acknowledgements

  %% CONTENTS -----------------------------------------------------------------
  \tableofcontents
  \listoffigures                                              % Figures
  \listoftables                                               % Tables
  % \printglossary[type=\acronymtype,title={List of Acronyms}]  % Acronyms
  % \printglossary[title={List of Terms}]                       % Terms

  % \include{chapters/outline}

  \mainmatter

  %% CHAPTERS -----------------------------------------------------------------
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  % Add your chapters here
  \include{chapters/introduction}
  \include{chapters/hbm}
  \include{chapters/lyttle21}
  \include{chapters/glitch}
  \include{chapters/glitch-gp}
  \include{chapters/conclusion}
  \include{chapters/software}

  %% BIBLIOGRAPHY -------------------------------------------------------------
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  %% APPENDICES ---------------------------------------------------------------
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  \appendix

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  \include{appendices/lyttle21}

\end{document}