Pixels, photometry, and population studies: variable stars across four years of Kepler data A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy q Isabel L. Colman Supervised by Timothy R. Bedding Daniel Huber Sydney Institute for Astronomy School of Physics, The University of Sydney Q May 22, 2020 ii x x x x x x x x x x x x proximus hesperias titan abiturus in undas gemmea purpureis cum iuga demet equis, illa nocte aliquis, tollens ad sidera voltum, dicet “ubi est hodie quae lyra fulsit heri?” the next titan, about to fall beneath the western waves, removes the jewelled yoke from his brilliant steeds — that night, anyone turning their eyes to the stars will say, “where is it today, the lyre that glimmered yesterday?” – Ovid, Fasti II iii Statement of Originality I, Isabel Colman, hereby declare that all work presented in this thesis is based on research conducted by me during my PhD candidature at the Sydney Institute for Astronomy, University of Sydney, from February 2016 to December 2019, except where noted below: • Chapter 2 is a reproduction of Colman et al. (2017). I performed all analysis and wrote all the text of this paper, with advice from coauthors. A complete acknowledgement of all author contributions is provided at the beginning of the chapter. • In Section 3.2, I describe the difference image analysis I perform on Kepler-1658. The remain- der of the work summarised was performed by the authors of Chontos et al. (2019). • In Section 3.3, I describe the analysis I performed to confirm the physical association of the binary systems in question. Simon Murphy performed pulsation timing and radial velocity analysis; Tim Bedding, Daniel Huber, and Jie Yu provided asteroseismic analysis; Tanda Li performed stellar modelling analysis. • In Section 3.4, I describe the contribution of my chance alignment analysis pipeline to Hon et al. (2019). All remaining work was performed by the authors. • In Section 3.5, I describe the analysis I performed to determine the potential for contamination the sample of stars included in Bedding et al. (2020). All remaining work was performed by the authors. • In Chapters 4 and 5, Jason Drury provided cluster memberships for NGC 6791 and 6819, and Gang Li assisted with analysis of γ Doradus targets. All remaining work was performed by myself. I declare that none of this work has been submitted to obtain another degree at this or any other university. To the best of my knowledge, this thesis contains no copy or paraphrase of work by others, except where clearly acknowledged in the text. All images that I did not produce are acknowledged in figure captions. May 22, 2020 iv Acknowledgements First and foremost, I want to thank my supervisors Tim Bedding and Dan Huber for their advice, encouragement, and their help in making this thesis what it is. I’ve been working with them since my undergraduate Honours year, and it’s their support that’s enabled me to continue pursuing my interests. (Special thanks to Tim for helping me get out of jury duty a month before this thesis was due to be submitted.) I would also like to thank the extended USyd asteroseismology group for their continued good company and good advice. Thanks to the postdocs and professors who’ve offered guidance: Ben P., Dennis, Hans, Simon, Tanda, Tim V., and Tim W. Particular thanks to Tim W., who read over sections of this thesis, and to Hans, for his continued advice on my image subtraction research. Thanks also to those of you whose PhD has overlapped with mine at some point: Dan, Doug, Earl, Jason, Jie, Gang, Marc, and Yaguang. I would also like to broadly thank everyone who I’ve met at the conferences I’ve attended and who I’ve shared my research with, and vice versa. To my friends outside uni: thank you for keeping me sane. Shout-out to Akib and Vanessa, my PhD-in-another-discipline companions, who Understand. Though my PhD has meant I’ve often been too busy (being super cool and not nerdy at all, obviously) to leave my desk, I want to thank everyone who’s kept me company from behind a screen: particular thanks to Ben R., as well as Alice, JJ, Jo, Kat, Rayji, and Sabrina. And to those of you who I’ve seen in person, too: Adela, Emma, Fiona, and Viv. I also want to thank my friends in the Sydney Philharmonia Chamber Singers, particularly my companions in the alto section, for brightening my Monday nights. Finally, I want thank my housemates Alan and Julia for being there for me, both literally and metaphorically. And my utmost gratitude to my parents Marian and Graeme, for always being my biggest supporters. Contents 1 Introduction 1 1.1 Analysing variable stars . .1 1.2 Solar-like oscillators . .3 1.2.1 Red giants . .5 1.3 Classical pulsators . .7 1.3.1 δ Scuti stars . .8 1.3.2 γ Doradus stars . 10 1.4 Spots and rotation . 11 1.5 Binary and multiple stellar systems . 13 1.6 Stellar clusters . 15 1.7 Asteroseismology before Kepler .............................. 19 1.8 Kepler and K2 ....................................... 21 1.9 TESS ............................................ 24 2 Detailed Pixel Analysis of Anomalous Red Giants 27 2.1 Introduction . 28 2.2 Methods and Analysis . 31 2.2.1 Data preparation . 31 2.2.2 Pixel power spectrum analysis . 32 2.2.3 Difference imaging . 34 2.3 Discussion . 36 2.3.1 Spatial distribution . 36 2.3.2 Amplitude distribution . 39 2.3.3 Modelling of chance alignments . 39 2.3.4 Nature of the population . 41 2.4 Conclusions . 41 2.5 Acknowledgments . 42 2.6 Appendix: Tables . 42 3 Variability in the Kepler Field: Further Work 49 3.1 Distribution and classification of KOIs . 49 3.1.1 Introduction and motivation . 49 3.1.2 Methods and analysis . 51 3.1.3 Results and discussion . 57 3.2 Stellar surface rotation in Kepler-1658 . 58 v vi CONTENTS 3.3 Red giant–δ Scuti binaries . 63 3.3.1 KIC 6753216 . 64 3.3.2 KIC 9773821 . 64 3.3.3 Continuing work . 68 3.4 Supplementing machine learning . 69 3.5 Confirming high frequency δ Scuti stars . 71 4 Image Subtraction Photometry: Methods 77 4.1 Aperture photometry . 77 4.2 Image subtraction . 78 4.3 The image subtraction algorithm . 79 4.4 Cluster centroids . 83 4.5 Aperture selection . 86 4.6 Running the pipeline . 89 4.7 Light curve analysis and vetting . 90 5 Image Subtraction Photometry: Results 97 5.1 NGC 6791 . 97 5.1.1 Surface rotation . 98 5.1.2 Binary stars . 102 5.1.3 Solar-like oscillations . 104 5.1.4 Blue stragglers . 107 5.1.5 Compact pulsators . 108 5.1.6 Data anomalies and artefacts . 112 5.2 NGC 6819 . 112 5.2.1 Rotation . 114 5.2.2 Binary stars . 117 5.2.3 Solar-like oscillations . 118 5.2.4 Classical pulsators . 121 5.2.5 Blue stragglers . 125 5.2.6 Data anomalies and artefacts . 125 5.3 Summary and conclusions . 127 6 Conclusions and Future Work 129 Bibliography 131 Chapter 1 Introduction The Kepler space telescope observed one area of the sky for four years, resulting in an exceptional and rapid increase in both the scope and finesse of our understanding of variable stars. The nominal Kepler mission ended in 2013, and the final release of processed data products was in 2016, but work has continued. Throughout this thesis, I examine methods of analysing stellar variability in Kepler data, including looking at different populations of variable Kepler targets, examining pixel data in great detail, and performing my own photometry to search for variable stars. A common thread between these projects is a focus on stars in crowded fields, whether searching for contaminated signals or performing photometry. In this chapter I will introduce the concepts explored throughout my doctoral studies. I will begin with an introduction to the different types of variable stars featured in this thesis, followed by an overview of the history and current state of space-based telescopes, with a focus on those that observe stellar variability. 1.1 Analysing variable stars Variable objects can be divided into two main classes: intrinsic and extrinsic. Figure 1.1 shows the great diversity of variability seen in astronomical objects. In this study, we focus on variable stars. Intrinsic variability in stars is due to physical processes causing changes within the object itself, such as pulsation or eruption; extrinsic variables experience changes in brightness caused by motion events at the stellar surface and beyond, such as the transit of another astronomical body, or the rotation of the star. Of the intrinsic variables, we focus on pulsating stars, in particular red giants (Section 1.2.1) and the so-called classical pulsators (Section 1.3). The extrinsic variables we study are rotating stars (Section 1.4) and binary star systems (Section 1.5); we also briefly look at exoplanet host stars (Section 3.1). For sufficiently long time series data of variable stars, we are able to observe periodicity, and with the Fourier transform of a time series we are able to observe this star in frequency space. The essence of the Fourier transform is fitting sinusoids to time series data at a range of frequencies. 1 2 CHAPTER 1. INTRODUCTION Figure 1.1: A flowchart showing the different types of variable star. In this study we focus on binary stars, rotating stars, and pulsating stars.