Investigating Exoplanet Habitability and the Stellar Magnetism of Cool Stars Across Half the Southern Sky Via Superflares, Starspots, and Stellar Rotation

INVESTIGATING EXOPLANET HABITABILITY AND THE STELLAR MAGNETISM OF COOL STARS ACROSS HALF THE SOUTHERN SKY VIA SUPERFLARES, STARSPOTS, AND STELLAR ROTATION

Ward S. Howard

A dissertation submitted to the faculty at the University of North Carolina at Chapel Hill in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy in the Department of Physics and Astronomy.

Chapel Hill 2021

ii ABSTRACT

Ward S. Howard: Investigating exoplanet habitability and the stellar magnetism of cool stars across half the Southern sky via superﬂares, starspots, and stellar rotation (Under the direction of Nicholas M. Law)

Stellar flares are stochastic events that occur when a star’s magnetic field re-connects, releasing intense radiation across the electromagnetic spectrum. Rocky planets in the habitable zones of M-dwarfs are often subjected to superflares, events of at least 1033 erg and 10-1000× the energy of the largest solar flares. Frequent superflares can erode the ozone layer of an Earth-like atmosphere and allow lethal amounts of UV flux to reach the surface. Conversely, too few flares may result in insufficient UV radiation to power pre-biotic chemistry due to the inherent faintness of M-dwarfs in the UV. Cool stars are often found to exhibit superflares. Cool stars are the most common type of star, and are known to frequently host rocky planets. As a result, they may host most of the universe’s Earth-size planets orbiting in the habitable zones of main sequence stars. My EvryFlare Survey uses observations from the Evryscope array of small telescopes and the Transiting Exoplanet Survey Satellite (TESS) to answer two questions about superflares and their impacts on the habitability of terrestrial planets orbiting cool stars: (1) How frequently are superflares emitted from the nearby cool stars, both in the present and in the first 200 Myr after formation? (2) What impact does superflare UV emission have on planetary atmospheres and surface habitability of planets orbiting cool stars? The EvryFlare Survey has resulted in the detection of 575 superflares from 284 stars. Results include a superflare from Proxima Cen, the nearest host star to a rocky planet in the habitable zone. I used these events to measure a decrease in superflare rates with increasing age, rotation, and starspot coverage. I will discuss the effects of superflares on ozone loss to planetary atmospheres, including one superflare with sufficient energy to photo-dissociate

iii all ozone in an Earth-like atmosphere in a single event. I present the largest-ever survey of simultaneous observations of dozens of M-dwarf superflares with Evryscope and TESS to measure the flare blackbody and estimate UV-C continuum emission. I find superflare temperatures increase with flare energy. The largest and hottest flare briefly reached an estimated 42,000 K. During superflares, I estimate rocky HZ planets orbiting <200 Myr stars typically receive a top-of-atmosphere UV-C flux of ∼120 W m−2 and up to 103 W m−2, 100-1000× the time-averaged XUV flux from Proxima Cen. Finally, I will describe a data analysis project with Robo-AO, exploring the performance of laser guide star adaptive optics systems in the absence of tip-tilt correction.

iv To my wife, Katelyn Tassan Howard.

v ACKNOWLEDGMENTS

The research contained in this dissertation would not have been possible without the support of a number of people. I am incredibly grateful for the formative roles that each of them has played during my time here at UNC. Pursuing a PhD is a long and grueling journey that brings to mind stories such as The Lord of the Rings. As Frodo wouldn’t have got far without Sam, I wouldn’t have made it to this point without each of the following people. First, special thanks are due to my dissertation advisor, Nicholas Law. Nick showed me how “good science” is done, and how to be a good collaborator. Nick’s years of insightful comments such as “Starting a sentence with ‘whereas’ is something only the Declaration of Independence can do,” have helped me write more clearly and concisely. Nick, thank you for introducing me to the field of stellar flares and habitability. I enjoyed learning about the topic alongside you. Thank you for showing me so many times how to handle success and failure with a level head. On a related note, thank you for teaching me how to write grants. Since I popped my head into the CTIO dome and asked you “Is that Alestorm?” I have found countless hours of research motivation from your little-known Scottish power metal bands. Finally, your confidence in my ability to succeed has often given me the nudge I needed to do the next hard thing. Next, I would like to recognize each of my other committee members for their thoughtful questions, directions, and time. To Profs. Andrew Mann, Fabian Heitsch, Daniel Scolnic, and Reyco Henning: thank you for partnering with me in this dissertation journey. Andrew, thank you for letting me stop by your office to discuss active M-dwarfs on so many occasions when you had a million spreadsheets to finish. I would also like to acknowledge my academic mentors who helped me reach graduate school in the first place: Profs. Brad Barlow, Steven Gibson, Geoffrey Poore, Bill Nettles, Fonsie Guilaran, David Ward, Michael Salazar, and

vi Lorin Matthews. Brad, thank you for mentoring me and helping me to pursue my dream of doing astronomy all the way from high school to PhD applications, the quals, and into post doc applications. Throughout the PhD, I have learned so much from the other members of my lab and from my cohort. Hank, thank you for always sparing a listening ear or imparting wisdom from your coding wizardry. I also owe you a debt of gratitude for your help with Evryscope light curves. Amy, thank you for good discussions of flare stars and planets while humoring my bad puns. Carl, thank you for taking me under your wing and teaching me the ropes when I was a new grad student. Octavi, Jeff, Phil, Ramses, Nathan, Alan, and Lawrence, I am grateful to have worked alongside each of you. To my friends from my graduate cohort (broadly defined), thank you for keeping me sane while working Jackson problems and studying for quals. Particular thanks are due to Joseph Karlik, Anna Reine, Chris Haufe, Paul Smith, Andrew Loheac, and Emilia Zywot for good conversations and outrageously funny tabletop game nights. In my broader Chapel Hill community, I want to thank my pastors and mentors Eric Gravelle, Blair Waggett, AJ Farthing, Ricky Harris, Don Tyndall, and Hank Tarlton for their guidance. I would also like to thank Drs. Glynis Cowell and Tacia Kohl for their wisdom. I am eternally grateful to Fred and Nancy Brooks for hosting the Intervarsity retreat at Caswell where I met my wife. To my friends Mark Stouffer, David Little, Jeffrey Robbins, Mark Reeves, and Serge Severenchuk: I am grateful for each of you. Beyond Chapel Hill, thank you to my friends Connor Ferrell, Grant Riley, Seth Brake, Kenan Keller, Hans and Meredith Noyes, Kelly and Liam Goldsmith, and Tai and Micah Donor. I would like to thank my family for their continual encouragement. Mom and Dad, your example encouraged me to do my best in my studies without finding my identity in them. You’ve supported me since day one. Lauren, I am grateful for your years of sisterly encouragement and support. Beth Tassan, Mimi, Papaw, and Grandpa, thank you for your calls, kind cards, and good food. You lifted my spirits on so many days. Gina, your help

vii moving and lunch visits are greatly appreciated. Phil and Christie, thank you for reminding me that my studies aren’t everything. To my wife, ever since we went on our long walk at Caswell, I’ve known I wanted to marry you. You’ve been my constant encouragement on all the good and hard days of the PhD and have inspired me to achieve my best work. Working on our doctorates together has been the best of adventures! I am beyond grateful for your consistent and selﬂess support. Lastly, I want to thank my Savior for drawing me to faith and into the family of God. Jesus, you are my best hope, greatest treasure, and best inspiration to do good science.

viii TABLE OF CONTENTS

LIST OF TABLES ...... xv

LIST OF FIGURES ...... xvi

LIST OF ABBREVIATIONS ...... xix

1 INTRODUCTION ...... 1

1.1 The occurrence of superﬂares from the Sun and nearby cool stars ...... 1

1.2 Blackbody temperature of solar and stellar ﬂares ...... 4

1.3 The complex relationships between ﬂares, starspots, and spin-down ...... 6

1.3.1 Starspots and the magnetic environments that trigger ﬂares ...... 6

1.3.2 Stellar ﬂares, starspots, and rotation as a probe of spin-down ...... 7

1.4 The curious case of ﬂares that do not occur randomly ...... 8

1.5 The eﬀect of superﬂares on potentially-habitable exoplanets...... 10

1.5.1 The habitability impacts of the increased UV radiation of hot superﬂares 12

1.5.2 Proxima b: a case study for the habitability of temperate rocky planets orbiting ﬂare stars ...... 13

1.6 Superﬂare discovery ...... 14

1.7 Photometric surveys of rotating cool stars ...... 18

1.8 Long-term Evryscope observations of all bright ﬂare stars in the South ...... 18

1.9 Overview of Contents ...... 21

1.9.1 Breakdown of Work by Chapter ...... 21

1.9.2 Signiﬁcant Contributions to Other Research ...... 22

2 THE FIRST NAKED-EYE SUPERFLARE DETECTED FROM PROX- IMA CENTAURI ...... 24

ix 2.1 Evryscope Flare Discovery and Observations ...... 26

2.1.1 Simultaneous high-resolution spectra from HARPS ...... 27

2.2 Proxima Superﬂare Properties ...... 27

2.2.1 Peak brightness...... 27

2.2.2 Energy release and planetary-impact-relevant ﬂuxes ...... 28

2.2.3 Proxima’s ﬂare frequency distribution ...... 29

2.2.4 High-resolution ﬂare spectrum ...... 30

2.2.5 UV and particle ﬂuxes ...... 31

2.3 Astrobiological Impact of the Superﬂare ...... 32

2.3.1 Demise of the Ozone Column ...... 32

2.3.2 Eﬀects on surface life ...... 34

3 LONG-TERM EVRYSCOPE MONITORING OF FLARES FROM THE COOL STARS ACROSS HALF THE SOUTHERN SKY...... 37

3.1 The EvryFlare all-sky superﬂare search...... 38

3.1.1 Evryscope observations ...... 38

3.1.2 Flare search targets...... 39

3.1.3 Automated search for ﬂares ...... 41

3.1.4 Manual light curve inspection for superﬂares ...... 42

3.1.5 Determination of ﬂare parameters ...... 46

3.1.6 Flare frequency distributions ...... 47

3.2 Evryscope ﬂare discoveries ...... 48

3.2.1 Flare stars, spectral type, and stellar age ...... 49

3.2.1.1 Superﬂare energy and duration ...... 49

3.2.1.2 Flare Frequency vs. Spectral Type and Galactic Latitude. . . . 50

3.2.1.3 Mean Flare Energy vs. Spectral Type ...... 52

3.2.1.4 Superﬂare Rate vs. Spectral Type ...... 52

3.2.1.5 High-amplitude Flare Occurrence vs Spectral Type ...... 53

x 3.2.1.6 Starspot coverage and superﬂares ...... 54

3.2.2 Comparing Evryscope and TESS ﬂares ...... 55

3.2.3 Most extreme superﬂares ...... 57

3.2.4 Superﬂares from TESS planet hosts ...... 58

3.3 Astrobiological Impact of Superﬂares ...... 59

4 ROTATION PERIODS OF THE COOL FLARE STARS IN TESS ACROSS HALF THE SOUTHERN SKY ...... 67

4.1 EvryFlare: all-sky stellar activity search ...... 68

4.1.1 Evryscope observations ...... 68

4.1.2 TESS observations...... 69

4.1.3 Evryscope+TESS sample of cool ﬂaring rotators ...... 69

4.1.4 Characterizing Stellar Properties ...... 70

4.1.4.1 Estimating Photometric Spectral Type ...... 71

4.1.4.2 Estimating Stellar Eﬀective Temperature, Mass, and Radius . . 71

4.1.4.3 Characterizing Starspots and Flares...... 71

4.2 Evryscope rotation periods ...... 75

4.2.1 Initial detection of periods in Evryscope...... 75

4.2.2 Bootstrap Measurement of period uncertainty ...... 77

4.2.3 Period validation using TESS light curves ...... 79

4.2.4 Detection of Evryscope periods in TESS ...... 81

4.2.5 TESS vs. Evryscope sinusoidal amplitudes ...... 81

4.3 Discussion: Stellar Activity and Rotation Relations ...... 82

4.3.1 Stellar rotation periods ...... 82

4.3.2 Spot Coverage and Maximum Flare Energies ...... 84

4.3.3 Flaring and stellar rotation ...... 86

4.3.3.1 Statistics of fast and slow rotators ...... 86

4.3.3.2 Quantifying rotation with the Rossby number ...... 89

xi 4.3.3.3 Flare stars in the mass-Rossby plane ...... 93

4.3.3.4 Inconclusive increased activity of intermediate rotators ...... 94

5 TEMPERATURE EVOLUTION AND HABITABILTY IMPACTS OF DOZENS OF SUPERFLARES OBSERVED SIMULTANEOUSLY BY EVRYSCOPE AND TESS ...... 97

5.1 Photometry ...... 98

5.1.1 Evryscope observations ...... 98

5.1.2 TESS observations...... 98

5.1.3 The EvryFlare stellar sample ...... 100

5.2 Identifying simultaneous TESS and Evryscope ﬂares ...... 101

5.3 Flare energetics ...... 103

5.4 Flare temperature Methods ...... 107

5.4.1 Fitting model temperatures ...... 110

5.5 Flare energetics and morphology predict temperature ...... 112

5.5.1 Flare energetics and temperature ...... 112

5.5.2 Flare impulse and temperature...... 113

5.5.3 Classical versus complex ﬂares ...... 114

5.6 Habitability impacts of hot ﬂares ...... 116

5.6.1 UV-C ﬂux in the HZ versus stellar mass ...... 118

5.6.2 UV-C ﬂux in the HZ versus stellar age ...... 118

6 BAYESIAN DETECTION OF PERIODICITY IN FLARE OCCURRENCE FROM COOL STARS WITH TESS ...... 121

6.1 TESS ﬂare observations ...... 122

6.2 Flare periodicity search methods ...... 125

6.2.1 Phased-ﬂares Bayesian Likelihood periodogram ...... 125

6.2.2 Wide-ﬂare Lomb-Scargle periodogram ...... 129

6.2.3 Performance of each method ...... 129

6.2.4 Identifying which stars may be phased-ﬂare candidates ...... 130

xii 6.2.5 Determining the threshold ﬂare amplitude...... 132

6.2.6 False-alarm Probabilities ...... 133

6.3 Detection of phased ﬂaring in TESS light curves ...... 134

6.3.1 Phased-ﬂaring at high amplitudes ...... 136

6.3.2 Phased-ﬂare periodogram results ...... 137

6.4 Periodicity related to starspot evolution ...... 138

6.4.1 Spot evolution and lack of periodicity in Cycle 3 ...... 138

6.4.2 Could the look-elsewhere eﬀect be the cause of periodicity? ...... 140

6.4.3 Companion stars and evolving spot properties ...... 142

7 LASER-ONLY ADAPTIVE OPTICS ACHIEVES SIGNIFICANT IMAGE QUALITY GAINS COMPARED TO SEEING-LIMITED OBSERVATIONS OVER THE ENTIRE SKY ...... 144

7.1 Improving the ability of adaptive optics to distinguish real planets orbiting faint M-dwarfs from false positives ...... 145

7.2 Methods...... 147

7.2.1 Observations and Instrument Setup ...... 148

7.2.2 Generalized Tracking and Correction Pipeline ...... 150

7.2.3 Measuring Performance ...... 151

7.3 Results ...... 152

7.3.1 System Performance and Resolution Improvement with Laser- only Correction ...... 152

7.3.2 Sensitivity of Improvement to Guiding Timescale ...... 157

7.4 Summary and suggestions for the implementation of laser-only AO ...... 158

8 CONCLUSIONS AND OUTLOOK...... 161

8.1 Long-term Monitoring of Flares from the Cool Stars Across Half the Southern Sky ...... 161

8.2 Implications of superﬂares on planetary habitability and astrobiology ...... 163

8.3 Flare periodicity as a probe of starspots and magnetic interactions companions165

xiii 8.4 Using Laser-only AO to increase sky coverage ...... 165

8.5 Future Outlook ...... 166

8.5.1 Habitability of TESS planets...... 166

8.5.2 Flare temperatures across the sky and across geological time ...... 166

8.5.3 An all-sky ﬂare periodicity survey ...... 167

8.5.4 Multi-wavelength ﬂare surveys ...... 167

8.6 Final Thoughts ...... 168

REFERENCES ...... 169

xiv LIST OF TABLES

3.1 Flare wait-times and FFD ﬁt parameters for average K5-M4 ﬂare stars ...... 50

3.2 Flare wait times & flare amplitudes-FFD fit parameters for average K5-M4 flare stars ...... 53

3.3 Starspot coverage of average K5-M4 ﬂare stars ...... 56

4.1 Activity of short period (PRot <10 d) vs. long period (PRot >10 d) rotators . . 90

4.2 Activity of fast (Ro <0.04), intermediate (0.040.44) rotators ...... 91 5.1 Relationships between ﬂare temperature observables and ﬂare energy and impulse ...... 115

7.1 Laser-only AO Results Summary ...... 155

xv LIST OF FIGURES

1.1 Illustration of a solar/stellar ﬂare ...... 2

1.2 Fast-rise, exponential decay ﬂare morphology ...... 3

1.3 Decrease in stellar activity with increased rotation period ...... 4

1.4 Sinusoidal variability of light curves from rotating starspots ...... 8

1.5 Eﬀect of ﬂare temperatures on dose rates of prebiotic chemistry ...... 13

1.6 The RV detection of Proxima b ...... 15

1.7 Complementary Evryscope and TESS observations of ﬂare stars ...... 17

1.8 The Evryscopes...... 19

2.1 Time evolution of the Proxima superﬂare ...... 25

2.2 Multi-year Evryscope light curve of Proxima Cen ...... 28

2.3 FFD of Proxima Cen as measured by Evryscope and MOST ...... 30

2.4 Spectra of Proxima during and outside of the superﬂare ...... 31

2.5 Potential ozone loss and surface UV levels of Proxima b ...... 36

3.1 Cool stars searched and ﬂare stars detected...... 40

3.2 Vetted and rejected candidate ﬂare events ...... 43

3.3 Vetted and conﬁrmed ﬂare events ...... 44

3.4 Superﬂares consistent with magnetic reconnection ...... 61

3.5 Superﬂare occurrence and energy vs. SpT ...... 62

3.6 Superﬂare occurrence vs. galactic latitude ...... 62

3.7 Typical FFDs as a function of SpT ...... 63

3.8 Annual superﬂare rates vs. SpT ...... 63

3.9 Typical FFDs for ﬂare amplitudes (not energies) vs. SpT ...... 64

3.10 Largest expected ﬂares in a 10 d window from K7-M4 ﬂare stars ...... 65

3.11 Starspot coverage required to generate observed superﬂares ...... 65

3.12 Evryscope vs. TESS ﬂare energies and amplitudes ...... 66

xvi 3.13 The largest superﬂares detected ...... 66

4.1 Subset of detected Evryscope rotation periods ...... 73

4.2 Rotational variability compared between Evryscope and TESS ...... 74

4.3 Example detection of Evryscope rotation period ...... 76

4.4 Binarity detected in Evryscope and TESS light curves ...... 83

4.5 Histograms of rotational variability properties ...... 85

4.6 Starspot coverage vs. maximum ﬂare energy...... 86

4.7 Activity observables vs. stellar rotation and Rossby number ...... 87

4.8 Flare stars in the mass-Rossby plane ...... 96

5.1 Simultaneous ﬂare events observed by Evryscope and TESS...... 99

5.2 Eﬀect of interpolation between Evryscope and TESS timestamps on ﬂuxes . . . 102

5.3 Relative ﬂuxes in the Evryscope and TESS bands vs. temperature ...... 104

5.4 Methods used to measure ﬂare temperatures...... 105

5.5 Temperature evolution of simultaneous ﬂare events ...... 106

5.6 Energy and amplitude scaling relationships between surveys ...... 108

5.7 Temperature, energy, and impulse scaling relations ...... 111

5.8 Temperatures of classical and complex ﬂares...... 116

5.9 UV-C ﬂuxes reaching the HZ during superﬂares ...... 117

6.1 TESS light curves of the 6 candidate phased-ﬂares targets ...... 123

6.2 Flare periodogram methods ...... 124

6.3 Flare periodogram power vs. number of ﬂares ...... 126

6.4 Flare amplitude threshold determination ...... 128

6.5 Flare amplitudes versus phase-folded positions...... 131

6.6 Wide-ﬂares Lomb-Scargle periodograms of each phased-ﬂare candidate ...... 134

6.7 Bayesian-likelihood periodograms of each phased-ﬂare candidate ...... 139

6.8 Phased ﬂares and TESS Cycle 1 Rotation Periods ...... 141

6.9 Phased ﬂares and TESS Cycle 3 Rotation Periods ...... 141

xvii 7.1 Improvement in seeing with laser-only AO ...... 148

7.2 Description of GenSTAC algorithm...... 149

7.3 Contour plots of laser-only AO performance ...... 153

7.4 Laser-only AO improvement vs. magnitude ...... 154

7.6 Histograms of laser-only AO performance ...... 156

7.5 PSF quality depends on autoguider timescale employed ...... 158

xviii LIST OF ABBREVIATIONS

AAVSO American Association of Variable Star Observers AB Dor AB Doradus A-D Anderson-Darling ADS Astrophysics Data System ALMA Atacama Large Millimeter Array AO Adaptive Optics APASS AAVSO Photometric All Sky Survey AutoELFS Automated Evryscope Light-curve Flare Searcher ASAS All Sky Automated Survey ASAS-SN All Sky Automated Survey for Supernovae ATLAS Asteroid Terrestrial-impact Last Alert System BMJD Barycentric Modiﬁed Julian Day CCD Charge-coupled device CME Coronal mass ejection Coma Ber Coma Berenices CTIO Cerro Tololo Inter-American Observatory DB Database Dec Declination DR Data release

Ebol Bolometric energy ED Equivalent duration EFTE Evryscope Fast Transient Engine EM Electromagnetic EMCCD Electromagnetic charge-coupled device ESO European Southern Observatory

xix ESPRESSO Echelle´ SPectrograph for Rocky Exoplanets and Stable Spectroscopic Observation EUV Extreme UV FFD Flare frequency distribution FITS Flexible Image Transport System FoV Field of View FRED Fast rise exponential decay FUV Far UV FWHM Full Width at Half Maximum GALEX Galaxy Evolution Explorer GenSTAC Generalized Stellar Tracking And Correction GMM Gaussian Mixture Model GUI Graphical user interface HARPS High Accuracy Radial Velocity Planet Searcher HST Hubble Space Telescope HZ Habitable Zone IFS integral ﬁeld spectrograph JD Julian Date KELT Kilodegree Extremely Little Telescope KOI Kepler Object of Interest LGS Laser guide star LGS+P1 LGS + Peripheral WFS 1 LS Lomb-Scargle LWA Long Wavelength Array MAST Mikulski Archive for Space Telescopes MC Monte Carlo MLO Mount Laguna Observatory

xx MOST Microvariability and Oscillations of Stars MPix Megapixel MP-LS Modiﬁed pre-whitened Lomb Scarge MJD Modiﬁed Julian Day NGS Natural guide star NGTS Next Generation Transit Survey NIR Near infrared

NOx Nitrogen Oxides NUV Near UV PDC Pre-search Data Conditioning

Prot Period of stellar rotation PSF Point spread function QPP Quasi-periodic pulsation RA Right ascension

Ro Rossby number RPM Reduced proper motion RTS Rapid Transient Surveyor SAP Simple aperture photometry SEP Stellar energetic particle SIMBAD Set of Identiﬁcations, Measurements and Bibliography for Astronomical Data SNR Signal-to-noise ratio SpT Spectral type SXR Soft X-ray

Teﬀ Eﬀective temperature TESS Transiting Exoplanet Survey Satellite TIC TESS Input Catalog

xxi TOI TESS Object of Interest Tuc-Hor Tucana-Horologium UV Ultraviolet VLT Very Large Telescope WFS Wavefront sensor XUV X-ray and EUV YMG Young moving group β Pic β Pictoris

θ50 Full width at half-enclosed ﬂux

τconv Convective turnover time

xxii CHAPTER 1: INTRODUCTION

One of the deepest questions accessible to science is “Are we alone?” Earth orbits a G dwarf star, but smaller cool stars (Teff <4000 K) make up ∼75% of the stellar population and frequently host terrestrial planets in their habitable zones. Planets orbiting nearby cool stars are excellent targets for atmospheric characterization due to the large signals of Earth-sized planets compared to their stars. However, cool stars frequently emit large stellar flares throughout their lifetimes. “Superflares” (flares with ≥1033 erg) play an outsized role in the habitability of terrestrial planets orbiting these stars. Prior to my dissertation work, the long-term rates of superflares were unconstrained for most nearby planet-hosting cool stars. Because superflares are rare and unpredictable events, multi-year high cadence observations are needed to determine their occurrence rates and impacts on planets. For the first time, the Evryscope array of small telescopes has enabled me to directly measure these rates with long-term optical observations. In this chapter, I describe superflare emission from cool stars and how superflares are a key driver of exoplanet habitability.

1.1 The occurrence of superﬂares from the Sun and nearby cool stars

Solar/stellar flares occur on main-sequence stars when convection of the photosphere distorts the star’s magnetic field, leading to a magnetic re-connection event that releases large quantities of stored magnetic energy. Electrons are accelerated down magnetic field lines toward the photosphere, colliding with and heating plasma to temperatures above 20 MK. The depths at which these electrons brake during the flare determines the wavelengths at which the plasma radiates. White-light flares are thought to result from electron collisions in the photosphere [2] as illustrated in Figure 1.1, although additional mechanisms have been

1 Figure 1.1: A flare from the Solar Dynamics Observatory is compared with a plasmoid- induced reconnection model, reproduced from Fig. 2 of [1]. The pinching off of the plasmoid induces the flare. Thermal and non-thermal emission at various wavelengths results from the acceleration and braking of electrons and subsequent heating of the plasma. Most white light emission probably results from electrons that brake in and heat the photosphere. proposed (e.g. [3–5]). White-light flares may last from minutes to hours, following a fast-rise and exponential-decay (FRED) profile in time-domain observations, e.g. [6] and Figure 1.2. Both the sun and later-type cool stars emit flares. Flares on the Sun usually range in energy from 1029 to 1032 erg [7]. The Carrington Event of 1859 released 1032 erg and remains the largest Solar flare to be observed [8]. Cool dwarf stars are frequently observed to emit flares in excess of 1033 erg. [9]. These “superflares,” or flare events with energy ≥1033 erg release 10-1000× the energy of most solar flares [10]. While superflares have not been directly observed from the Sun to date, other G-dwarf stars similar to the Sun have been observed to emit them [7, 11]. Furthermore, the solar proton event of 774 AD recorded in tree ring cosmogenic nuclides is consistent with a solar superflare [12]. The Sun is the only main-sequence star that can be resolved spatially at present. As a result, our understanding of flaring mechanisms and structures is largely based upon comparing light curves of solar

2 Figure 1.2: Reproduced from Figure 4 of [6], the empirical Davenport flare template is displayed in red. The template is a fit to 885 flares observed from GJ . Note the fast-rise, exponential decay (FRED) morphology common to all flares. These flares are overlaid on top of each other in a contour plot and the 1σ upper and lower contours in morphology are shown in orange.

flares with the simultaneous sequence of spatial imagery and extending these results to flares observed from other stars [7]. The enhanced flaring often observed from late K-dwarf and M-dwarf cool stars with

Teff < 4000 K [13] is due to a deep convection zone and fast stellar rotation. Fast rotation increases the available magnetic energy and may result in high flare rates and flare energies compared to those from the Sun (e.g. [2, 14] and references therein). Stellar flares are easier to observe from cool stars than solar-type stars. Not only are cool stars the most populous stellar types in the galaxy [15–17], but the quiescent luminosity is lower and the resulting flare contrast is higher [2, 18]. Because flaring depends on the magnetic field of the star, increased flare activity is correlated with stellar age [19–21], rotation (e.g. [22–25]), starspot coverage [26], and spectral type [20, 22, 25, 27, 28]. As stars age on the main sequence, they rotate more slowly. Slowly- rotating stars generate less magnetic energy at the stellar surface, resulting in fewer flares and smaller starspots [29]. The rate at which this process occurs also depends on stellar mass

3 0 Figure 1.3: Stellar activity emission lines (e.g. RHK ) remain at saturated levels for cool stars with rotation periods of less than 10 d but decrease steadily at longer periods. Flare rates have recently been demonstrated to follow similar relationships, e.g. [29, 31]. This ﬁgure is reproduced from Figure 6 of [23].

as the depth of the convective layer changes [14]. Flare activity remains at a consistently-high level for stars with rotation periods less than 10 d [30–32]. At ages corresponding to longer periods, ﬂare activity quickly declines. This is consistent with other stellar activity diagnostics

such as Hα and Ca II H and K line emission that decrease from a saturated state [23, 24]. This decrease in line emission with rotation period is shown in Figure 1.3.

1.2 Blackbody temperature of solar and stellar ﬂares

Flares radiate energy in both emission lines and in the continuum, with the continuum dominating the energy budget from the FUV to the optical. During the peak phase of most flares, only ∼4% of the total energy is found in the emission lines. During the gradual decay phase, line emission may contribute 20% of the total energy budget [33]. In several flares, however, line emission has been found to contribute up to 50% of the total flare energy [34]. The combined line and continuum emission of stellar flares has often been approximated by a 9,000-10,000 K blackbody [35]. The blackbody temperature governs the energy budget of the flare, especially the fraction of the energy emitted at the UV wavelengths that most strongly react with exoplanet atmospheres [36]. The canonical value of 9000 K provides a

4 lower limit to the energy emitted in the UV, with higher-temperatures resulting in more UV radiation. The effective blackbody temperatures of superflares are tremendously uncertain. Continuum temperatures of M-dwarf flares usually range from 9000 K to 14,000 K [33] but temperatures may extend above 40,000 K [37–39]. Significant temperature changes occur over the course of individual flares as the dominant source of flare heating transitions from the base of the stellar atmosphere into the corona [33]. Superflares are rare [40], making observations to measure their temperatures difficult. Drawing broad conclusions about the temperatures of superflares is stymied by only a handful of observations. For example, it is currently unknown whether the thermal emission of superflares is consistently higher than for typical flares. It is also unknown if the impulse (i.e. how peaked a flare appears in photometry) is consistently higher for hot superflares. Few M-dwarf superflares have been observed with UV colors directly. Two examples of such events include the Great Flare of AD Leo [41] and the Hazflare [42]. The Great Flare of AD Leo (M4) released 1034 erg and exhibited a continuum consistent with a temperature of 9000 K. To date, most atmospheric modeling of potentially-habitable planets orbiting flare stars assume spectral evolution templates based upon this singular event [42–45]. The Hazflare (emitted by a 40 Myr M2 dwarf) released 1033.6 erg with a blackbody temperature of 15,500 K. Large flares observed by the Galaxy Evolution Explorer (GALEX; [46]) in the UV have reached temperatures as high as 50,000 K, measured from FUV and NUV colors. Most superflares from cool stars seen by GALEX are from late K-dwarfs, with only 1 superflare recorded from an M-dwarf in [37] and 7 superflares from 4 M-dwarfs recorded in [47]. Multi-wavelength superflares in other band-passes indirectly estimate UV emission through the blackbody. However, non-thermal emission may lead to under-estimates of the UV emission. Multi-wavelength superflare observations are uncommon. Apart from the GALEX events, only 19 superflares from 13 M-dwarfs have been recorded with multi- wavelength, high cadence observations since 1976 [40–42, 48–55] 1. These known flare stars

1The count includes only ﬂares recorded on ADS with clearly-quoted integrated ﬂare energies. Events were required to have ∼2 min or higher cadence with simultaneous multi-wavelength observations or spectra.

5 include AD Leo, YZ CMi, EQ Peg, EV Lac, UV Ceti, CN Leo, Wolf 424 AB, YY Gem, GL 644 AB, AT Mic, DG Cvn, the Tuc Hor star GSC 8056-0482, and BX Tri. These stars were largely selected for monitoring during “staring” campaigns designed to capture stochastic ﬂaring, biasing the sample toward a handful of extremely active stars.

1.3 The complex relationships between ﬂares, starspots, and spin-down

Stellar rotation and surface magnetic activity (e.g. surface field topology, starspots, and flares) are intrinsically related phenomena. Quickly-rotating young stars drive increased surface magnetic activity, while surface magnetism controls the spin-down of stellar rotation with age [56, 57]. Spin-down from angular momentum loss depends on the coupling of the field to the stellar wind, with complex fields resulting in orders-of-magnitude weaker coupling than dipole-dominant fields (e.g. [58–61]).

1.3.1 Starspots and the magnetic environments that trigger ﬂares

Starspots and flares are closely linked. The largest flare a star may emit is limited by the stored magnetic energy of the starspot group that produced it. By comparing the largest flare observed from each star and the starspot coverage fraction of that star, the stellar magnetic field strength may be constrained. This is because the surface magnetic field strength adjusts the conversion from starspot size to flare energy; the field must allow the observed flares given the observed spot sizes [62]. Similarly, estimates may be made for the surface magnetic field strengths of cool rotators as they spin down. Spots are often used to measure the stellar rotation period (e.g. [63–66]). Starspots are a form of stellar activity that appear on the photosphere of a star and are effects of the interior stellar magnetic dynamo. Starspots are cooler than the rest of the photosphere, resulting in a flux difference between the spotted and non-spotted surfaces of a star [67]. As the photosphere rotates, starspots often induce regular brightness variations in stellar photometry (Figure 1.4). The fraction of the stellar hemisphere covered by starspots, or starspot coverage fraction,

6 decreases at long rotation periods for stars above the fully-convective mass limit, probing the evolution of the star’s surface magnetic field throughout spin-down (e.g. [62, 65, 68–70]). Combining a large sample of stellar flares and rotation periods allows estimates of their minimum surface magnetic fields to be tested against typical magnetic field strengths of cool stars [71]. Because flares are intimately connected with the surface fields of starspots and depend on stellar rotation, it is hypothesized they may be useful in separating M-dwarfs with complex and simple fields. An increased flare rate from late M-dwarfs has been observed at

intermediate rotation periods (10< PRot <70 d), supporting this hypothesis [30]. Directly measuring whether surface field topology is simple or complex with Zeeman-Doppler Imaging is difficult and expensive, and has only been performed in detail for about 102 cool stars with well-constrained stellar rotation periods [71]. However, measuring the surface magnetic activity levels of many stars at a range of rotation periods may indirectly probe magnetic topology throughout spin-down. Two common photometric measurements that may trace the evolution of the magnetic field are the sinusoidal oscillations in brightness from starspots and the amount of stellar flaring. If the amplitudes of variability from rotating starspots or the rates of stellar flares in the light curves increase for a brief time during spin down, this would be evidence for changing magnetic topologies.

1.3.2 Stellar ﬂares, starspots, and rotation as a probe of spin-down

Large surveys of stellar rotation periods provide insight into the periods at which the magnetic field may change from simple to complex topologies. Stellar rotation surveys find few cool stars with rotation periods between ten and seventy days, but many faster and slower rotators (e.g [65, 66, 72]). The transition from the quickly-rotating phase to slowly-rotating phase is therefore thought to occur rapidly for cool stars [65, 72] due to a change in the state of the surface magnetic field and the sudden increased rate of mass and angular momentum

7 Figure 1.4: Reproduced with alterations from Figure 5 of [73], this ﬁgure demonstrates how starspots on the rotating photosphere induce periodic variability in light curves. This periodic variability is often used to measure stellar rotation periods from photometry.

loss (AML) that results [58]. High mass stars spin down earlier than low mass stars; many ﬁeld-age M-dwarfs are still actively spinning down [65].

1.4 The curious case of ﬂares that do not occur randomly

M-dwarf flares are generally thought to be stochastic events [74]. There are exceptions, however. Over the years, various authors have searched for periodicity in the timing between flare events with various degrees of success (e.g. [75–79]). If present, flare periodicity would serve as a unique probe of stellar rotation, star-planet interaction, or the surface magnetic properties of starspot groups. The possible explanations of apparent flare periodicity generally fall into four categories: rotating starspots, magnetic interaction with a companion star or planet, magnetic “reservoir hypotheses,” and random chance. The rotation of spotted stars can induce regular variability in light curves. Stellar activity present in the photosphere and chromosphere of M-dwarf stars are frequently coupled (e.g. [80, 81] and references therein). Flares associated with these spots may therefore preferentially occur at a certain rotational phase (such as when the dominant spot group is

8 facing us). Preferentially-phased flares have been reported for individual stars (e.g. [77, 82– 85]). Other observations show little to no preference for flaring at particular rotational phases for individual stars (e.g. [76, 81, 86–88]). Non-detections may be due to unfavorable spot geometries such as polar spots or spots across all longitudes [79, 89, 90]. Larger surveys have also reported mixed results. For example, [79] do find a correlation of flares with spots in a sample of 119 late F to early M stars observed during the primary Kepler mission [91]. However, preferential flaring with rotational phase was not supported in a study of 34 flaring M-dwarfs [78] observed during the K2 mission [92] or 119 flaring M-dwarfs observed in TESS Sectors 1 through 3 [93]. [89] do not find evidence for a correlation of spots and flaring in a sample of 1500 young rotators in 2 min TESS data, hypothesizing spots that cover the entire photosphere. Binary companions or exoplanets in close orbits around M-dwarfs may induce flares and otherwise alter the stellar atmosphere via electromagnetic interactions, e.g. [94–98]. [99] observed a clear 48 min periodicity in 4 large flares from the eclipsing binary YY Gem with a false positive probability of <0.5%. [96] were able to reproduce this periodicity via a star-star interaction. Star-star interactions have also been proposed as an explanation for phased flaring from V711 Tau [100] and UX Ari [101]. Planets may also induce regular chromospheric changes by depositing magnetic energy in the stellar atmosphere. Electromagnetic star-planet interactions (SPIs) may occur when the convection velocity of the stellar wind is sub-Alfvénic, coupling the star and planet and enabling efficient transfer of energy [102–104]. SPIs may also occur when the star and planet couple via magnetohydrostatic force-free magnetic fields [98, 105–107]. Most electromagnetic SPIs are observed as periodic changes to emission lines or photometry and are due to close-in giant planets. Examples include HD 179949 and ν And [108–110], τ Boo A [111], WASP-43 [112], HD 189733 [113], and Gliese 1151 [114, 115]. Recently, RV data from CARMENES has called the existence of the Gliese 1151 planet into doubt [116]. Flare periodicity due to SPIs rather than stellar companions has a firm theoretical basis in [98] but remains unconfirmed

9 with observations. A tentative flaring SPI has been suggested in the TRAPPIST-1 system from interactions with TRAPPIST-1 b and c [104]. As an alternate source of periodicity, the “flare reservoir hypothesis” describes the release of stored magnetic energy in an active region. After a flare occurs, some amount of time may be needed to increase the stored energy before another flare of similar energy can be triggered. If the amount of time needed to reach a critical energy remains consistent, flare periodicity would result [76, 99, 100]. The reservoir hypothesis is qualitative and may be consistent with a range of physical models [76]. The hypothesis shares similarities with the phenomenon of quasi-periodic pulsations (QPPs) but might operate at longer timescales [117]. [76] did not find any evidence for a flare reservoir in observations of 17 flares from V780 Tau. [100] found a 2.8 d periodicity in 7 large X-ray flares from V711 Tau with a false positive probability of ∼0.5%. Flares occur twice per stellar rotation, but the preciseness of the event timing suggests the periodicity is not due entirely to rotating starspots and could involve a reservoir [100]. A final explanation of apparent flare periodicity is random chance. When a small number of flares from a star show apparent periodicity, the chance that the signal is due to a random Poisson process must be rejected [99, 100]. In contrast, a periodicity search across a sample of hundreds to thousands of flare stars such as those observed by Kepler (e.g. [14, 26, 118]) or TESS (e.g. [89, 93, 119]) may also result in false-positive signals. False-positives arise from the look-elsewhere effect or problem of multiple comparisons [120–122]. For example, if 330 flare stars are searched for periodicity, at least one 3σ detection will result by chance alone.

1.5 The eﬀect of superﬂares on potentially-habitable exoplanets

Because Earth-sized planets orbiting cool stars are both common [123, 124] and produce high-SNR transit and radial velocity signals, cool stars are popular targets in the search for nearby Earth-like exoplanets. Temperate rocky planets have already been discovered in orbit around several nearby cool stars, e.g. [125–128]. However, intense ﬂaring may pose problems

10 for the habitability of planets orbiting cool stars. The so-called “habitable zone” (HZ) is defined as the distance from a star at which the stellar flux and planet atmosphere would allow for the existence of liquid water on the surface [129]. The low luminosity of cool stars requires HZ orbital distances to be very close to the star. Planets orbiting in the close-in habitable zones of late K and M-dwarfs therefore receive ∼400× more flux from a given superflare than Earth would receive. M-dwarfs can remain active for ∼10 Gyr, stripping both primary [45] and secondary [130] atmospheres. Quiescent M-dwarfs emit orders of magnitude less UV flux than the Sun, making large flares the dominant source of UV radiation at wavelengths that impact biology. Combined with the intrinsically-high flare rate of active cool stars, the ozone layers of Earth-like planets may be suppressed or destroyed on geologically-short timescales [44, 45, 131]. High-energy particles that may be associated with large flares deplete atmospheric ozone through the creation of nitrogen-oxide species. While the ozone layer of an Earth-like planet may withstand single superflare events of 1034 erg [43, 132, 133], the cumulative effect of multiple superflare events per year does not allow the planetary atmosphere to recover [45]. The largest flares may fully photo-dissociate an ozone column in a single event without consideration of high energy particles at all [131]. Long-term X-ray and UV flare emission may contribute to the complete stripping away of Earth-like atmospheres [134, 135]. [136] notes that photoevaporation of mini-Neptune atmospheres may lead to habitable worlds rather than prevent them. However, this outcome is only likely for specific H/He-envelope mass fractions, core sizes, and incident stellar fluxes [135]. The increased activity of the young Sun altered the atmosphere of the early Earth (e.g. [137–139]) but did not prevent life on our planet. [140] find that superflares may have even increased the habitability of our planet by fixing inert atmospheric nitrogen. Furthermore, the atmospheres of nearby M-dwarf planets may be capable of shielding life from the most extreme UV radiation [141]. If the RNA world hypothesis is correct, the UV radiation

11 needed to power pre-biotic chemistry on M-dwarf worlds can only come from flares [142]. Too much flare radiation, however, would likely force exposed surface life to undergo complex adaptations to survive [44]. Although superflares have an outsized role in M-dwarf planetary habitability, their rates, UV emission, and effects on surface life are not well constrained [142–144].

1.5.1 The habitability impacts of the increased UV radiation of hot superﬂares

The blackbody temperature is a key ingredient in modeling the effects of optical superflares upon the atmospheric photochemistry of Earth-like planets. The UV energy of a ∼30,000 K optical superflare computed assuming a 10,000 K blackbody will be under-estimated by a factor of 16 [145]. Furthermore, temperatures in the FUV in excess of 40,000 K increase the rate of photo-dissociation in exoplanet atmospheres by 10-100× [39, 131]. Errors in the temperatures of optical superflares propagate to the estimated UV emission that determines the space weather environment of orbiting planets. Laboratory experiments to determine the effects of M-dwarf superflares on prebiotic chemistry have previously explored the UV emission for a single superflare of 9000 K, the 1034 erg event reported in 1985 from AD Leo (e.g. [142, 146]). While it has been assumed this flare can adequately represent the UV emission of superflares from all stars in the lab, it is possible that superflares vary considerably in temperature. If a superflare has an effective blackbody temperature of 30,000 K instead of 9000 K, the consequences for prebiotic chemistry or the survival of life could be significant (Figure 1.5). The dose rates of stressor and eustressor processes and survival curves for superflares of various temperatures are shown in Figure 1.5, using data from [142] and [141]. A stressor is a chemical reaction that breaks down chemicals needed for life, while a eustressor is a chemical reaction that builds products necessary for life to occur [142]. A dose rate is the relative effect of UV light on the rate of a chemical process. Given that the dose rates of both stressor and eustressor reactions are 7× higher for a hot superflare than a typical 9000

12 Figure 1.5: Left panel: The relative effectiveness of flux per wavelength of a UV-hardy bacterium is convolved with the surface UV radiation from a 30,000 K flare, a 9000 K flare, the young Sun, and a non-flaring M-dwarf. The UV flux of the hottest flare considerably exceeds that experienced by the Early Earth, potentially decreasing habitability. Right panel: the dose rates of stressor and eustressor chemical processes from each UV source normalized by the dose rates on the Early Earth. Eustressors promote the origin of life while stressors discourage it. Both panels assume an anoxic atmosphere. Across both panels, the hotter flare leads to more significant impacts on life.

K flare, constraining the temperatures of superflares is a necessary step in characterizing the habitability of planets orbiting flare stars.

1.5.2 Proxima b: a case study for the habitability of temperate rocky planets orbiting ﬂare stars

The small and cool star Proxima Centauri (hereafter Proxima) hosts Proxima b, a likely rocky planet [125, 147] within the habitable zone (e.g. [148, 149]). Proxima b does not transit [150], but its signal is clearly present in radial velocity (RV) observations from HARPS [125] and ESPRESSO [151]. The most recent RV evidence for its existence from ESPRESSO is shown in Figure 1.6. Proxima b has potential difficulties in maintaining a habitable atmosphere, both due to possible tidal locking [152] and incident stellar activity (e.g. [9, 14, 153–155]). Proxima is well-known to exhibit large stellar variability and to produce bright flare events. It is hypothesized that it can produce superflares, extreme stellar events with an estimated bolometric energy release of at least 1033 erg [43, 45, 131]; if detected, they would

13 be one of the largest potential threats to the habitability of Proxima b [14]: while ozone in an Earth-like planet’s atmosphere can shield the planet from the intense UV flux associated with a single superflare [43, 132, 133], the atmospheric ozone recovery time after a superflare is on the order of years [45]. A sufficiently high flare rate for Proxima could therefore permanently prevent the formation of a protective ozone layer, leading to UV radiation levels on the surface which are beyond what some of the hardiest-known organisms can survive [132]. Many previous studies have explored low- and moderate-energy flare events on Proxima. Optical surveys have found events with detected energies up to 1031.5 erg (1032 erg bolometric) in visible light [14]. ALMA recently detected a large sub-mm flare (1028 erg in ALMA’s Band 6), although multiwavelength flare studies are needed to determine how large sub-mm flares relate to flares in other bands and their habitability effects [156]. In the X-ray, events up to 1032 erg (1032.7 erg bolometric) have been detected [157]. The MOST satellite [158] performed the most comprehensive previous measurement of the Proxima flare rate. MOST observed Proxima for 37.6 days, observing 66 white-light flare events, the largest of which was 1031.5 erg in the MOST band-pass (∼4500–7500 A˚ ). No superflares were observed; extrapolating the cumulative flare frequency distribution (FFD) obtained by [14] from the MOST flare sample out by 1.5 dex predicts ∼8 1033+ erg events in the MOST bandpass occur per year. Prior to my dissertation work, no superflares were observed.

1.6 Superﬂare discovery

Measuring superflare rates requires long-term, high cadence monitoring. Many late-type stars, such as Proxima, only emit superflares several times per year [44]. High cadence observations are required because the impulsive phases of superflares that most impact habitability generally last 5-15 minutes [144]. A number of space-based and ground-based surveys have discovered large flares from nearby stars.

14 Figure 1.6: The likely-rocky planet Proxima b was initially discovered by [125] in the habitable zone of Proxima Cen using radial velocities (RVs) from HARPS but is confirmed here at higher precision with ESPRESSO [151]. This figure is reproduced with alterations from Figures 3 and 4 of [151]. In the top panel, the generalized Lomb Scargle periodogram of the RVs is shown, with Proxima b’s signal clearly visible at 11.2 d. The RVs are phase-folded to the 11.2 d signal in the bottom panel, showing a clear RV semi-amplitude and providing independent confirmation of the existence of the planet.

15 High-cadence observations by the Next Generation Transit Survey (NGTS, [159]) recorded two 1034 erg superflares from a bright G8 star [160]. NGTS also captured one of the largest M-dwarf flares to be observed to date at high cadence, a 1036.5 erg event from a 2 Myr-old M3 star [161]. An M-dwarf superflare search using data obtained by the All-Sky Automated Survey for Supernovae (ASAS-SN,[162]) observed 53 large flares, with a bolometric energy range of approximately 1033 to 1036 erg [18]. Another M-dwarf flare search in data obtained by the MEarth project [163, 164] discovered 54 large flares from 34 flare stars out of 2226 stars searched [30]. These and other ground-based flare surveys probe different but overlapping regimes: MEarth and ASAS-SN are best at capturing flares from late M-dwarfs. The ultra- high cadence of NGTS allows unprecedented observations of flare morphology and evolution but from fewer stars. Since July 2018, the Transiting Exoplanet Survey Satellite (TESS, [165]) has been searching for transiting exoplanets across the entire sky, split into 26 sectors. Each TESS sector is continuously observed in the red by four 10.5 cm optical telescopes for 28 days at 21 arcsec pixel−1. TESS regularly down-links 2-minute cadence light curves of selected targets and half-hour cadence full-frame images per sector. TESS is optimized to observe cool stars at high precision in order to detect Earth-sized planets. TESS observations of cool stars also capture many stellar flares. In sectors 1 & 2 alone, 763 flare stars were observed in the 2-minute cadence TESS light curves, with 3247 individual flares recorded [119]. Cool stars comprise 83% of these flare stars. More recently, [89] observed flares from TESS in a sample of ∼2400 late K and M-dwarf flare stars. Small flares occur much more frequently than large flares. Although TESS observes each star at high photometric precision for a sufficient amount of time to characterize the occurrence of low-to-moderate energy flares from each cool star, observation times spanning 1-2 sectors are often not long enough to capture the largest superflares. For example, the well-studied flare star Proxima Centauri emits flares of 1032 erg or greater on 10 day time scales, but flares of 1033 erg or greater on 100 day timescales [44]. Furthermore, TESS flare

16 Figure 1.7: The full 2016-18 Evryscope light curve of flare star L 173-39. This flare star demonstrates how the Evryscope light curve complements the TESS light curve. While 2 sectors of TESS observations captures the frequent flares of lower to moderate energy, long-term Evryscope observations at more moderate photometric precision capture the rare, high-energy flares. Combined, these surveys sample a broader flare distribution from each star.

observations of each star outside the continuous viewing zone are insensitive to cyclic changes to stellar flaring on timescales longer than 28 days per sector. Multi-year, high cadence observations of all bright M-dwarfs are needed to constrain the superflare rates of these sources. While TESS is not ideally-suited to measuring the long-term superflare rates of most stars, it is ideal for searching for flares that are not emitted at random but instead are emitted with a clear periodicity. At least 15,000 late K and M-dwarfs have been observed at 2 min cadence for at least 1 sector [166], enabling comprehensive searches for flare periodicity from individual stars across a wide sample [89]. Previous large-scale periodicity surveys have only explored periods at the stellar rotation period, e.g. [79, 89, 93]. These surveys primarily explore periodicity on a statistical rather than case-by-case basis, although [93] also inspected 45 flare stars for rotational modulation of flares. We develop and test new flare periodogram tools on a sub-sample of 284 very active and well-studied flare stars from [143] as a step toward a broader survey. Following the insight of transit surveys designed to detect periodicity that may only be present in a small fraction of stars, we search for flare periodicity star by star to avoid diluting strong periodic signals from individual stars.

17 Previous large-scale periodicity surveys have only explored periods near the stellar rotation period, e.g. [79, 89, 93].

1.7 Photometric surveys of rotating cool stars

In order to explore the dependence of flaring upon rotation, a large number of stars with both their flare rates and rotation periods are needed. Large numbers of photometric rotation periods of cool stars have been or are being catalogued by various space-based and ground-based surveys. Examples include 5257 Kepler [91] K5 and later rotators (at least 80% of which are M1 or earlier) from [69], at least 105-106 K5 and later rotators from the Transiting Exoplanet Survey Satellite (TESS; [165]) estimated from [166, 167], ∼800 K5 or later rotators in the Kilodegree Extremely Little Telescope (KELT; [168–170]) from [66], and 628 mid-to-late M-dwarf rotators from MEarth [163, 164][65, 72]. While about 1-10% of late K-dwarfs and early M-dwarfs are flare stars, about 30% of mid-to-late M-dwarfs are flare stars (e.g. [26, 119, 143]). Cross-matching stars in each survey with rotation periods against stars with stellar flares therefore significantly reduces the sample size. Optimized to observe low-amplitude variation from all nearby cool stars, TESS will contribute the majority of fast and intermediate-period cool rotators. However, the TESS primary mission observes most stars for only 28 days, decreasing its ability to measure the periods of slow rotators. Furthermore, the uncertainties to the periods of intermediate and slow rotators obtained by TESS will be large (e.g. errors from approximately ∼0.1-to-∼1 days) compared to longer-duration observations.

1.8 Long-term Evryscope observations of all bright ﬂare stars in the South

The Evryscopes [171, 172] are performing long-term high-cadence monitoring of ﬂares and other short-timescale phenomena across the Southern sky, for much longer periods than does TESS. Together, Evryscope-North (California) and Evryscope-South (Chile) are producing light curves of all ∼20,000 nearby cool dwarf stars and tens of millions of other stars. Each

18 Figure 1.8: The Evryscopes are two arrays of small telescopes together observing all bright nearby stars at 2 min cadence in the optical blue. Individual 60mm telescopes are housed in a hemispherical dome that tracks the sky for 2 hr at a time before ratcheting back into its initial conﬁguration and repeating the process. Multi-year Evryscope light curves of each star capture many large ﬂares and other transient sources of variability [173]. The Evryscopes also record periodic variability at periods ranging from hours [174] to potentially several years.

Evryscope is an array of small telescopes which simultaneously images the entire accessible sky. Each system is composed of 22 60mm telescopes and observes in the optical blue g0 bandpass at 13 arcsec pixel−1. The systems are illustrated in Figure 1.8. Combining the frequent flares seen in the TESS light curves themselves with rarer Evryscope flares provides for more comprehensive flare monitoring. Evryscope complements TESS by monitoring the high-energy end of each star’s flare distribution, as well as any other changes in flare activity that occur on timescales longer than the 28 day observation time per sector. For example, we illustrate in Figure 1.7 flares in the combined Evryscope and TESS light curves for the case of the active star TIC-231017428 (L 173-39). TESS observed TIC-231017428 for 2 sectors during its Primary Mission, finding many flares with amplitudes too small to recover with Evryscope, while missing the rarest and largest flares captured by Evryscope. For example, in March 2016, the Evryscope detected the first-known superflare from Proxima Cen. Although no M-dwarfs are usually visible to the naked-eye [e.g., 155], Proxima briefly became at least a magnitude-6.8 star during this superflare, at the limit of visibility to dark-site naked-eye observers. This observation would have been much more difficult without

19 both the high cadence, multi-year coverage of each bright star that Evryscope provides. This event typifies the conditions that potentially habitable exoplanets orbiting flare stars may experience. In this dissertation, we explore the physics and habitability impacts of Evryscope-detected superflares from the brightest cool stars across half the Southern sky. We measure blackbody temperatures of dozens of these superflares observed simultaneously at 2 min cadence by the Evryscope [172, 175] and Transiting Exoplanet Survey Satellite (TESS; [165]) surveys as shown in Figure 5.1. Each night, the southern Evryscope system observed the entire TESS Cycle 1 field simultaneously in g0-band for hours. In order to obtain a representative sample of superflares from stars of various activity levels, we search multi-band photometry of hundreds of late-type stars. With the 2 min cadence of Evryscope and TESS, we robustly quantify the amount of time superflares emit at temperatures in excess of 9000 K. Evryscope light curves also allow detection of significantly longer rotation periods than is possible from TESS data alone. While TESS observes each star for ∼28 days per year in the red at high photometric precision, Evryscope observes each star at moderate precision for several years in the blue. Combined rotation periods in the blue and in the red allows not only better error analysis of the rotation rate for large numbers of field stars during spin-down, but also an estimate of the color-dependence of starspot modulation during this process. Long-term monitoring by Evryscope also confirms whether periodic brightness modulation seen in TESS is transient or stable over the course of multiple years to better inform RV follow-up efforts of planet candidates. In this dissertation, we focus on the subset of Evryscope rotation periods of previously- identified flare stars in the Evryscope dataset of [143]. This subset of the Evryscope data was selected from cool stars with 2-minute cadence light curves from both Evryscope and TESS, allowing a comparison of Evryscope and TESS rotation. Future work will further explore the combined flare rate and starspot coverage in both the TESS and Evryscope bands.

20 1.9 Overview of Contents

For the first time, my dissertation has measured the long-term superflare rates of cool stars across half the southern sky and measured superflare temperatures from a large sample of flare stars. I have also explored correlations between flaring, starspots, spin-down, and habitability.

1.9.1 Breakdown of Work by Chapter

This dissertation is divided into 6 chapters containing my original contributions to the field followed by a conclusion. In Chapter 2, I describe the Evryscope detection of the Proxima superflare and how its bolometric energy and peak brightness are measured. The occurrence of similarly-large superflares is also explored. The impacts of superflares on the atmosphere of an Earth-like planet at the orbital distance of Proxima b and astrobiological implications are investigated. In Chapter 3 of this work, I describe the Evryscope flare search program, EvryFlare. I also describe our flare-search sample, algorithms, and discoveries. These include a number of superflare events similar to the Proxima superflare that increased the stellar brightness by at least 3 g0 magnitudes, and correlations of flaring with stellar astrophysics. I describe a superflare observed from the LTT 1445 system, which hosts one of the nearest transiting rocky planets. The implications of extreme flaring observed from M-dwarfs across the sky for the retention of planetary ozone layers and resulting planetary habitability are explored. In Chapter 4, I describe the relationship between superflare rates, starspots, and stellar rotation periods. Rotation periods are explored in both Evryscope and TESS light curves. I describe how the sinusoidal amplitude of rotational variability is greater in the Evryscope g0 bandpass than in the red TESS bandpass and how this effect is greatest for low-mass stars. The distributions of rotation periods, starspot coverage fractions, and surface magnetic field constraints are investigated. I discuss the decrease in activity with rotation period, and describe a possible increase in superflare rates at intermediate rotation periods.

21 In Chapter 5, I describe the first statistical sample of the temperatures of M-dwarf superflares recorded at high cadence. Superflares observed simultaneously by Evryscope and TESS are catalogued and their temperatures estimated from the ratio of flux in each bandpass. Newly-discovered power law relationships of increasing flare temperature with energy and impulse are explored, and implications for the planetary atmospheres of HZ planets orbiting young stars are discussed. In Chapter 6, I describe the discovery of flare stars with periodically-spaced flares in TESS light curves. Two new flare periodograms are developed, including a Bayesian periodogram. These periodograms are used to perform the first flare periodogram survey of a large sample of TESS flare stars. Detected periodicity is often correlated with stellar rotation but may indicate further drivers including star-star magnetic interactions. In Chapter 7, I describe the first large-scale experiment with laser-only adaptive optics and my GenSTAC adaptive optics pipeline. Empirical measurements of laser correction using the Robo-AO database are given. These include measurement of the relative contributions of tip-tilt and laser correction. I discuss the performance of GenSTAC from targets bright enough for full tip-tilt correction to laser-only targets at the limiting magnitude of the telescope for a given exposure time. In the Conclusion, I summarize the work and explore implications for the fields of stellar astrophysics and planetary habitability.

1.9.2 Signiﬁcant Contributions to Other Research

In addition to the work contained in the following chapters, I have also made signiﬁcant contributions as a co-author to several other publications. Each co-authored paper and my speciﬁc contribution to it is listed below:

• MacGregor, M.A., Weinberger, A.J., Loyd, R.O.P., et al. 2021, ApJ Letters 911, L25. “Discovery of an Extremely Short Duration Flare from Proxima Centauri Using Millimeter Through FUV Observations.” – I contributed FFDs of Proxima to place

22 constraints on the likely optical emission from a large sub-mm and FUV ﬂare observed from Proxima on May 1st, 2019.

• Gan, T., Wang, S.X., Teske, J.K., et al. 2020, MNRAS 501, 6042. “Revisiting the HD 21749 Planetary System with Stellar Activity Modeling.” – I contributed an Evryscope rotational analysis of the host star, adding independent photometric evidence for the correct period originally found in its TESS light curve.

• Teske, J.K., Wang, S.X., Wolfgang, A., et al. 2020, Submitted to AAS Journals. “The Magellan-TESS Survey I: Survey Description and Mid-Survey Results.” – I contributed Evryscope and TESS photometric stellar rotation periods and candidate periods for 17 host stars to TESS planetary candidate systems.

• Glazier, A.L., Howard, W.S., Corbett, H., et al. 2020, ApJ 900, 27. “Evryscope and K2 Constraints on TRAPPIST-1 Superﬂare Occurrence and Planetary Habitability.” – I mentored this project and contributed ﬂare analysis codes used in the paper from my previous work in [143].

• Kosiarek, M.R., Crossﬁeld, I.J.M., Hardegree-Ullman, K.K., et al. 2019, AJ 157, 97. “Bright Opportunities for Atmospheric Characterization of Small Planets: Masses and Radii of K2-3 b, c, d and GJ3470 b from Radial Velocity Measurements and Spitzer Transits.” – I contributed an Evryscope rotational analysis of the host star to K2-3 b, adding independent photometric evidence for the correct period originally found in its K2 light curve. I reduced the period uncertainty signiﬁcantly compared to the K2 measurement.

23 CHAPTER 2: THE FIRST NAKED-EYE SUPERFLARE DETECTED FROM PROXIMA CENTAURI

Proxima b is a terrestrial-mass planet in the habitable-zone of Proxima Centauri. Prox- ima Centauri’s high stellar activity however casts doubt on the habitability of Proxima b: sufficiently bright and frequent flares and any associated proton events may destroy the planet’s ozone layer, allowing lethal levels of UV flux to reach its surface. In March 2016, the Evryscope observed the first naked-eye-brightness superflare detected from Proxima Centauri. Proxima increased in optical flux by a factor of ∼68 during the superflare and released a bolometric energy of 1033.5 erg, ∼10× larger than any previously-detected flare from Proxima. Over the last two years the Evryscope has recorded 23 other large Proxima flares ranging in bolometric energy from 1030.6 erg to 1032.4 erg; coupling those rates with the single superflare detection, we predict at least five superflares occur each year. Simultaneous high-resolution HARPS spectroscopy during the Evryscope superflare constrains the superflare’s UV spectrum and any associated coronal mass ejections. We use these results and the Evryscope flare rates

to model the photochemical effects of NOx atmospheric species generated by particle events from this extreme stellar activity, and show that the repeated flaring may be sufficient to reduce the ozone of an Earth-like atmosphere by 90% within five years; complete depletion may occur within several hundred kyr. The UV light produced by the Evryscope superflare would therefore have reached the surface with ∼100× the intensity required to kill simple UV-hardy microorganisms, suggesting that life would have to undergo extreme adaptations to survive in the surface areas of Proxima b exposed to these flares1.

1Content from this chapter previously appeared in Howard et al. 2018, ApJ Letters 860, L30. For this project, I assembled and led a team of researchers from UNC, Barcelona, ASU, and UW investigating the astrophysics and habitability impacts of the ﬁrst superﬂare observed from Proxima Cen. I personally performed the science for about 50% of the paper and wrote the vast majority of the paper, with multiple contributions from other team members. Nicholas Law supervised and contributed science and text to the work.

24 a b c d e 40 c 35

weaker flares 15 Normalized flux

10 b quiescent d 5 flux a e 0 20 0 20 40 60 80 Time / minutes

Figure 2.1: The Evryscope discovery of a naked-eye-brightness superflare from Proxima. The y-axis is the flux increase over Proxima’s median g’-band flux from the previous hour. Bars show the integration time of each individual flux measurement. Insets display cutout images over the course of the flare. For clarity, we here show only one camera’s light curve; another Evryscope camera simultaneously observing the event showed a very similar light curve offset by 2.2 seconds.

25 2.1 Evryscope Flare Discovery and Observations

We discovered the Proxima superflare as part of the Evryscope survey of all bright Southern stars. The Evryscope is an array of small telescopes simultaneously imaging 8000 square degrees of the sky every two minutes [171]. The Evryscope observes essentially the entire Southern sky above an airmass of two, at two-minute cadence in g 0 and at a resolution of 13” pixel−1. The system has a typical dark-sky limiting magnitude of g 0=16 and tracks the sky for 2 hours at a time before ratcheting back and continuing observations, for an average of ∼6 hours of continuous monitoring each night on each part of the sky. The Evryscope image archive contains 2.5 million raw images, ∼350TB of data. A custom pipeline analyzes the Evryscope dataset at realtime rates [175]. Each image, consisting of a 28.8 MPix FITS file from one camera, is calibrated using a custom wide-field solver. After careful background modeling and subtraction, forced-aperture photometry is extracted based on known source positions in a reference catalog. Light curves are then generated for approximately 15 million sources across the Southern sky by differential photometry in small sky regions using carefully-selected reference stars and a range of apertures; residual systematics are removed using two iterations of the SysRem detrending algorithm [176]. In extremely crowded fields, such as for Proxima (−2◦ galactic latitude), we re-run the pipeline for particular targets, optimizing the aperture sizes to avoid nearby stars. As a very large event, the Proxima Superflare was discovered in routine by-eye checks of interesting targets in the Evryscope data set. Smaller flares are discovered and characterized with an automated flare-analysis pipeline which uses a custom flare-search algorithm, including injection tests to measure the flare recovery rate. First, we search for flares by attempting to fit an exponential-decay matched-filter similar to that of [177] to each contiguous segment of the Evryscope light curve. Matches with a significance greater than 2.5σ are verified by eye. The entire Proxima lightcurve is visually examined for flares to account for false-negatives in the automated search.

26 The fractional flux and equivalent duration (ED) for each flare are calculated as described in [74], and flare start and stop times are initially chosen where the flare candidate exceeds the local noise and are subsequently confirmed or adjusted by eye. We inject simulated flares separately into each light curve and perform 20 trials of randomly-located flare injection and attempted recovery per contiguous lightcurve segment. We average the results across the lightcurve to measure recovery completeness as a global function of flare contrast and ED and to quantify the error in contrast and ED for each flare.

2.1.1 Simultaneous high-resolution spectra from HARPS

The superflare reported here occurred during the three-month Pale Red Dot campaign, which first revealed the presence of Proxima b [125] using the HARPS spectrograph on the ESO 3.6m at La Silla, Chile [178]. The HARPS spectrum was taken at 2016 March 18 8:59 UT, 27 minutes after the flare peak at 8:32 UT. This single 1200 second exposure captured the majority of the flare tail, including 20% of the total radiated flux.

2.2 Proxima Superﬂare Properties

The Evryscope detected the Proxima Superflare on 2016 March 18, 8:32:10 UT (MJD 57465.35568, see Figure 2.1). The flare lasted approximately one hour. The flare energy release was dominated by a single large event but subsequently showed a complex morphology, with three weaker flares (each more than doubling Proxima’s g 0 -band brightness) observed.

2.2.1 Peak brightness

Within the Evryscope’s two-minute integration during the flare peak, Proxima reached an average flux of 38× the quiescent emission. By fitting a instantaneous-flux flare template [6] we estimate the superflare’s brightness on human-eye timescales to have reached 68× Proxima’s flux. Proxima, an 11.4 g0 magnitude star, thus briefly became a g0=6.8 star, at the limit of visibility to trained observers at very dark sites [179–181].

27 4.0 1.5 a b c 3.5 0 1.0 g M 3.0 0.5 0.0 2.5

superflare -10m 0m 10m 20m -10m 0m 10m 20m -10m 0m 10m 20m

0 2.0 g

M b 1.5 a 1.0 c 0.5

0.0

0.5 57400 57500 57600 57700 57800 57900 58000 58100 Time / MJD

Figure 2.2: The full 2016-18 Evryscope Proxima light curve. Detected flares are highlighted in red; to show short-term activity Proxima’s long-term variability has been removed. The superflare is 2.5-magnitudes brighter than any other Evryscope-detected flare from Proxima. For clarity, we plot only 20% of the 40,486 light curve points. Three representative flares are shown in detail. Because of the two-minute sampling, low-energy, short flares such as the rightmost individually-displayed flare often do not show classical rapid-rise flare shapes, although these flares are often confirmed by multiple cameras simultaneously.

2.2.2 Energy release and planetary-impact-relevant ﬂuxes

Calculation of the superflare’s atmospheric impacts requires an estimate of the flare’s energy in multiple bandpasses, from the far-UV to the infrared. We measure the superflare energy in the g 0 Evryscope bandpass and subsequently convert into the bolometric energy using the energy partitions of [35]. We accomplish this by estimating the bolometric flare energy of a 9000 K flare blackbody with emission matching the measured Evryscope flux;

0 the fraction of the bolometric energy found in the Evryscope g bandpass is fg0 =0.19. The canonical value of 9000 K provides a lower limit to the flare energy; a higher-temperature flare blackbody, as has been sometimes measured for larger flares [51] results in more short- wavelength energy. The energy seen in any bandpass ∆λ is then given by the approximate

relationship E∆λ = f∆λ × Ebol. We obtain the quiescent ﬂux in the Evryscope g 0 bandpass by scaling directly from the Evryscope-measured calibrated magnitude, and by weighting the ﬂux-calibrated spectrum of Proxima used in [14] by the Evryscope response function and scaling using Proxima’s

28 distance [182]. Both methods measure Proxima’s quiescent ﬂux in the Evryscope bandpass

28.6 −1 32.8 to be L0 = 10 erg s , giving the superﬂare energy in the Evryscope bandpass of 10 erg, and a bolometric energy of 1033.5 erg.

2.2.3 Proxima’s ﬂare frequency distribution

The Evryscope observed Proxima for a total of 1344 hours between January 2016 and March 2018. We discovered 24 large flares (Figure 2.2), with bolometric energies from 1030.6 erg to 1033.5 erg. To obtain the cumulative flare frequency distribution (FFD), we calculate the uncertainty in the cumulative occurrence rate for each Evryscope flare with a binomial 1σ confidence interval statistic (following [14]). Errors in energy for high-energy flares are calculated using the inverse significance of detection; low-significance flares use the injection-and-recovery error estimate instead, to account for the possibility of correlated noise introducing bias. To sample both the rare high-energy events detectable by Evryscope and the frequent moderate-to-low energy events detectable by MOST, we also include flares from the MOST sample [14] with energy in the MOST bandpass greater than 1030.5 erg (we exclude lower- energy MOST flares due to a possible knee in the FFD biasing the occurrence of superflares ∼1000X larger). We fit a cumulative power-law FFD to the MOST and Evryscope flares, and determine the uncertainty in our fit through 10,000 Monte-Carlo posterior draws consistent with our uncertainties in energy and occurrence rates. We represent the cumulative FFD in the Evryscope bandpass (Figure 2.3) by a power law of the form log ν = (1 − α) log E + b, where ν is the number of flares with an energy greater than or equal to E erg per day, α gives the frequency at which flares of various energies occur, and b is the y-intercept and crossover into the unphysical energy region E < 0. Evryscope constrains the expected occurrence of 1033 erg bolometric events to be at least

+0.2 5.2−3.0 per year. It is evident from Figure 2.3 that it is difficult to fit a single power law which reproduces both the lower-energy flares and the Evryscope-observed superflare. This

29 Evryscope MOST 1.0

0.1

superflare

region of incomplete Cumulative Flares per Day 0.01 Evryscope recovery

30.5 31.0 31.5 32.0 32.5 33.0 33.5 log Total Flare Energy (erg)

Figure 2.3: The cumulative flare frequency distribution of Proxima fit to all Evryscope flares and the largest MOST flares, scaled to bolometric energy from the g 0 and MOST bandpass, respectively. The best fit, which excludes the Evryscope superflare, is displayed in red. 10,000 posterior draws (1000 shown) estimate the error of this power-law fit.

could mean the probability of reaching superflare energies is higher than would be expected by a simple power-law extrapolation from lower energies; it could also be that the Proxima Superflare is just a statistically-rare event. We therefore report two separate FFDs; the first excludes the Proxima Superflare, while the second includes it. For the no-superflare case,

+0.26 +8.4 we report an FFD of log ν = −1.22−0.003 log E + 38.1−0.07, displayed in Figure 2.3, in good agreement with both the Evryscope and MOST sample. Including the prior of the observed

+0.02 +0.83 superflare, we obtain log ν = −0.98−0.24 log E + 30.6−7.6 . We note αEvryscope is significantly steeper in our higher-energy flare sample in both cases than that for Proxima FFDs from previous studies, e.g. [14, 183].

2.2.4 High-resolution ﬂare spectrum

The spectrum of Proxima, in both the median quiescent and ﬂare states, is shown in Figure 2.4. During the superﬂare, chromospheric metals and the Balmer series show sharply

−1 increased emission. A −30 km s splitting of the Hα,Hβ, and He I lines is detectable, and is indicative of a flow of highly ionized plasma generated by the flare, most likely correlated to a hot stellar wind moving outwards from the star [184]. No significantly-blueshifted emission or anomalous emission lines are visible; the superflare spectrum is similar to other smaller

30 Mar 07 Mar 07

Mar 13 Mar 13

Mar 19 Mar 19

Mar 24 3932 3933 3934 3935 Mar 24 6561 6562 6563 6564 Ca II K (Angstrom) H (Angstrom)

Median Quiescence H 1000 H Mar 18 Flare

Fe I 500 H Ca II Ca II Fe I Ca I He I He I { Fe I Na {

Relative Flux H Ti I Si II {

0 4000 4500 5000 5500 6000 6500 Angstroms

Figure 2.4: Top: Chromospheric activity evolution traced by the Ca II (K) and Hα indicators in the month leading up to the flare. Bottom: Flux-normalized median quiescent spectrum from the month leading up to the flare (black) and active (red) spectrum 27 minutes after the superflare peak. Flare spectrum is relative to the normalized quiescent spectrum.

ﬂares recorded from Proxima and is therefore likely to be amenable to emission-line scaling relations to estimate Far-UV (FUV) and particle ﬂuxes (Section 2.2.5).

2.2.5 UV and particle ﬂuxes

FUV (912–1700 A)˚ photons are capable of photolyzing most molecules in planetary atmospheres. The Hubble Space Telescope archive contains 13.3 h of FUV spectrophotometry by the STIS spectrograph of Proxima. From this data, we aggregated 9 flares spanning FUV energies of 1029.3 – 1030.8 erg to construct a FUV energy budget for Proxima flares. We scale to a 9000 K blackbody and EUV emission via a “fiducial flare” prescription [131], tailored to the Proxima data. The 1032.5 erg FUV energy of the Proxima Superflare obtained by the fiducial flare prescription is found to be consistent with an independently-obtained estimate using the quiescent scaling relations of [185] applied to a measurement of the Ca II K equivalent width in the HARPS spectrum (Section 2.1.1). Coronal mass ejections (CMEs) are often assumed to accompany large flares [186]. [185] measures a relation for predicting >10 MeV proton fluxes based on the energy of the flare in Si IV. These particles can initiate nonthermal chemical reactions in the planetary atmosphere.

31 From the [185] relation and the HARPS spectrum, we estimate a proton ﬂuence at Proxima b’s 0.0485 AU distance of 107.7 protons cm−2.

2.3 Astrobiological Impact of the Superﬂare

2.3.1 Demise of the Ozone Column

We employ a 1D coupled, photochemical and radiative-convective climate model to determine the effects of the observed flare activity on the potential habitability of Proxima b. We assume the planet to have an Earth-like atmosphere, but neglect the planetary magnetic field, which may be weaker than Earth’s due to tidal-locking [152]. The details of the coupled model can be found in [43] and [45], which discovered that the results of only electromagnetic

flaring cannot significantly drive O3 column loss, while flares with proton events can rapidly

destroy the O3 column. Proton events lead to the dissociation of N2 in the planet atmosphere

into constituent, excited N-atoms, which then react with O2 to produce NO and O. NO reacts with O3 to produce NO2. The NOx species generated during the proton events therefore drive the evolution of the ozone column (see [45] for further details). Using the cumulative FFD measured in the present work and the scaling from [74], we generate a sequence of flares for a 5-year time span in the U-band energy range of 1029.5 erg to 1032.9 erg (scaled to represent the Evryscope-measured FFD). We assume a time-resolved UV superflare spectrum scaled from AD Leo to Proxima flares, following [45]. This flare sequence drives the evolution of volatiles in an Earth-like atmosphere at a distance of 0.0485 AU to an active M dwarf. Flares are selected at random to produce a proton event, with proton flux scaling with event amplitude. The probability for each flare to generate a planet-oriented energetic particle event was assumed to be a moderate P = 0.08, following [45].

The evolution of the O3 column as a result of the impacting ﬂares and proton events is shown in the top panel of Figure 2.5. At the end of the simulation, 846 of 10,724 ﬂares had

generated a proton event that impacted the atmosphere of the planet, resulting in an O3

32 column loss of 90%. The system does not appear to reach steady state with increasing time. We assess that it is likely that Proxima b has suﬀered extreme ozone loss. At Proxima’s

current activity rate, >99.9% of Proxima b’s O3 is likely to be lost within 100s of kyr, leaving the planet’s surface largely unprotected from UV light.

A complete lack of O3 would particularly aﬀect the amount of germicidal UV-C reaching

the surface. Although other volatiles capable of absorbing UV-C (i.e., O2,H2O) are not necessarily destroyed, they do not eﬀectively block UV-C for wavelengths longer than ∼2500A.˚

No significant Earth-like atmospheric gas but O3 effectively absorbs in the UV-B and UV- C wavelengths ∼2450-2800A[˚ 45]. During the Proxima Superflare, the top-of-atmosphere receives ∼3.5 J cm−2 of UV-C in the wavelength range 2400-2800 A.˚ Absent ozone, most of this reaches the surface. We caution that our result assumes an Earth-like atmosphere and is exploratory in nature. Ozone loss depends on indirect scaling relations between flare and particle flux, which exhibit 3-4 orders-of-magnitude of scatter (e.g. [185, 188]). Our primary result shown in the top panel of Figure 2.5 assumes solar SXR-particle scaling relations [189] and active M-dwarf UV-SXR scaling relations [190], resulting in a median proton fluence of 5.5 × 109 pr cm−2. Even if we assume a 105 times lower median proton fluence, a value from the lowest end of the proton-scaling distribution, we find that the ozone layer is severely depleted after 5 years. In this second run, we use the “fiducial flare” template spectrum of Section 2.2.5 and employ a planet-oriented energetic particle event probability of P = 0.25 and solar EUV-particle scaling relations and then an M dwarf synthetic spectrum [191] to relate EUV to FUV [185] for a median proton fluence of 6.1 × 104 pr cm−2. We measure 40% ozone loss after 5 years. While the difference between these two models is large, it is unsurprising in light of the large scatter in the correlations between solar flare intensity and proton flux. Further work is needed to more rigorously constrain the energetic particle environments of these stars.

33 2.3.2 Eﬀects on surface life

Figure 2.5 shows the UV-B and UV-C flux at the surface of Proxima b during the superflare, given the g 0 flux measured in the Evryscope light curve, the flare spectral modeling in Section 2.2.2, and assuming an orbital radius of 0.0485 AU [125]. We plot two flare regimes: (1) the expected fluxes for an intact Earth-like ozone layer (where essentially no UVC reaches the surface, and ∼ 10% of UVB reaches the surface; [192] and references therein); and (2) an extreme ozone-loss scenario, where UVC in the wavelength range ∼2450-2800A˚ reaches the surface unimpeded by ozone or other atmospheric absorption (see Section 2.3), resulting in UV-B'UV-C surface fluxes (this equivalence is coincidental: the lack of ∼2500 A˚ UV-C reaching the surface counters the proximity to the flare blackbody peak). We assume cloudless skies. While UV-B accounts for only 5% of the solar UV radiation incident upon Earth, it has the largest impact upon terrestrial biology because shorter UV-C wavelengths are blocked by the Earth’s atmosphere [193]. During the Proxima Superflare, 3.5 J cm−2 of UV-B reached the surface under the assumption of extreme ozone attenuation, which is below a lethal dose of 4 J cm−2 for Deinococcus radiodurans but lethal for most UV-hardy organisms, even when protected by a shallow layer of freshwater. For example, in the top 50 cm of water, 1.5 J cm−2 of UV-B will kill 50% of freshwater invertebrates [194]. Zooplankton’s UV-B lethal dose is 0.5 J cm−2 [195]. UV-C is much more efficient at damaging DNA than UV-B [196, 197]. Although D. radiodurans is amongst the most UV-resilient organisms on Earth, its UV-C D90 dose (i.e., the amount of radiation required to kill 90% of the population) of 0.0553 J cm−2 [198] is a factor of 65× smaller than the 3.6 J cm−2 reaching the surface during the Proxima Superflare, given no ozone. Recent results have suggested that more complex life such as lichens evolved for extreme environments and with adaptations such as UV-screening pigments may survive these radiation levels [199]. These results suggest that surface life on areas of Proxima b

34 exposed to these flares would have to undergo complex adaptations to survive2, even if the planetary atmosphere survives the long-term impact of the stellar activity. Earth may have undergone significantly higher UV fluxes during the early evolution of life. [138] give diurnally-averaged values of the surface UV-B and UV-C flux on Earth during the pre-biotic (3.9 Ga ago) and early Proterozoic (2.0 Ga ago) epochs. Assuming the full-ozone-loss scenario, the surface UV-B flux during the Proxima superflare was an average of 2× higher than that 3.9 Ga ago and a factor of 3× higher 2.0 Ga ago, although between flares the UV flux was much lower than Earth’s, because late M-dwarfs are far fainter in the UV than solar-type stars. The UV-C superflare flux was a factor of 7× higher than that 3.9 Ga ago and a factor of 1750× higher than 2.0 Ga ago; again, the UV-C flux potentially reaching Proxima’s surface is the critical difference compared to Earth’s environment.

2although superﬂares would have a greatly reduced direct impact on organisms that may exist underground, under deep water, on the dark side of a tidally-locked world, etc.

35 Proxima Centauri b, 5 yr. flaring 0.2

-0.2 column depth 3 -0.4

-0.6

-0.8 Φ × 4 -2 med = 6.1 10 pr cm -1 Φ × 9 -2 med = 5.5 10 pr cm Fraction change in the O 4 5 6 7 8 9 10 log10 time (seconds)

Figure 2.5: Top panel: The solid black line represents the evolution of the O3 column for a planet with an Earth-like atmosphere orbiting Proxima under flares with a median proton fluence of 5.5 × 109 pr cm−2. The vertical lines represent the 1- and 5- year times. The dash-dotted red line is a projection of future O3 evolution. The dash-dotted projection assumes continued flare activity; the solid black line assumes no further activity after 5 years and hence returns to Earth-like conditions. The blue line is a model from the lowest end of the proton-fluence distribution (median fluence of 6.1 × 104 pr cm−2) consistent with the scatter in flare and particle scaling. The brief spikes in ozone in both models and the end-of-flaring dip in the lowest-fluence model are from generation of ozone via free O atoms from photodissociation of other species. Bottom panel: Surface UV-B and UV-C flux during the superflare. Surface flux is calculated with (purple) no atmospheric attenuation from volatiles, and (red) an Earth-like, intact ozone column. UV surface levels during the superflare result in 30× lethal doses for simple microorganisms [187].

36 CHAPTER 3: LONG-TERM EVRYSCOPE MONITORING OF FLARES FROM THE COOL STARS ACROSS HALF THE SOUTHERN SKY

We search for superflares from 4,068 cool stars in 2+ years of Evryscope photometry, focusing on those with high-cadence data from both Evryscope and TESS. The Evryscope array of small telescopes observed 575 flares from 284 stars, with a median energy of 1034.0 erg. Since 2016, Evryscope has enabled the detection of rare events from all stars observed by TESS through multi-year, high-cadence continuous observing. We report ∼2× the previous largest number of 1034 erg high-cadence flares from nearby cool stars. We find 8 flares with amplitudes of 3+ g 0 magnitudes, with the largest reaching 5.6 magnitudes and releasing 1036.2 erg. We observe a 1034 erg superflare from TOI-455 (LTT 1445), a mid-M with a rocky planet candidate 1 2. We measure the superflare rate per flare-star and quantify the average flaring of active stars as a function of spectral type, including superflare rates, FFDs, and typical flare amplitudes in g 0. We confirm superflare morphology is broadly consistent with magnetic re- connection. We estimate starspot coverage necessary to produce superflares, and hypothesize maximum-allowed superflare energies and waiting-times between flares corresponding to 100% coverage of the stellar hemisphere. We observe decreased flaring at high galactic latitudes. We explore the effects of superflares on ozone loss to planetary atmospheres: we observe 1 superflare with sufficient energy to photo-dissociate all ozone in an Earth-like atmosphere in one event. We find 17 stars that may deplete an Earth-like atmosphere via repeated flaring. Of the 1822 stars around which TESS may discover temperate rocky planets, we observe 14.6±2% emit large flares.

1Content from this chapter previously appeared in Howard et al. 2019, ApJ 881, 9. For this project, I designed and carried out this survey in Evryscope light curves produced by the team. Nicholas Law advised the project and suggested several modiﬁcations to the survey science ultimately done. I wrote the paper. 2During proofs, a pre-print of a paper by Winters et al. conﬁrming LTT 1445Ab was released. See arxiv.org/abs/1906.10147

37 3.1 The EvryFlare all-sky superﬂare search

In order to measure the occurrence of rare superflares, Evryscope monitors the long- term flare activity of all cool stars. We focus the current analysis on bright stars across half the Southern sky. Stellar flares in Evryscope data are discovered and characterized in two independent ways. A brief manual inspection of each Evryscope light curve discovers the largest flares captured by Evryscope. An automated flare search discovers flares of all amplitudes above the photometric noise; these candidate flares are further inspected by eye.

3.1.1 Evryscope observations

As part of the Evryscope survey of all bright Southern stars, we discover many large stellar flaring events. The Evryscope is an array of small telescopes simultaneously imaging 8150 square degrees and 18,400 square degrees in total each night on the sky at two-minute cadence in g 0 [171]. The Evryscope is optimized for bright, nearby stars, with a typical dark-sky limiting magnitude of g 0=16. The Evryscope is designed to observe the entire Southern sky down to an airmass of two and at a resolution of 13” pixel−1. To achieve ∼6 hours of continuous monitoring each night on each part of the sky, the Evryscope tracks the sky for 2 hours at a time before ratcheting back and continuing observations [172]. The Evryscope image archive contains 3.0 million raw images, ∼250 TB of data. The Evryscope dataset is reduced at realtime rates by a custom data reduction pipeline [175]. Each image, consisting of a 28.8 MPix FITS file from one camera, is calibrated using a custom wide-field solver. Careful background modeling and subtraction is performed before raw photometry is extracted with forced-apertures at known source positions in a reference catalog. Light curves are then generated for approximately 9.3 million sources across the Southern sky by differential photometry in small sky regions using carefully-selected reference stars and across several apertures [172]. Any remaining systematics are removed using two iterations of the SysRem detrending algorithm [176].

38 The Evryscope light curve database is periodically regenerated across the sky for improved photometric precision and longer baseline of observations. The current generation of light curves at the time of this work spans Jan 2016 through June 2018, with an average of 32,000 epochs per star. Light curves of bright stars (g 0=10) attain 6 mmag to 1% photometric precision (depending on the stellar crowding level); light curves of dim stars (g 0=15) attain 10% precision. We note Evryscope precision for dim stars is comparable to TESS precision on dim stars [172].

3.1.2 Flare search targets

We select cool stars that have both TESS and Evryscope light curves for this subset of the larger EvryFlare search program. We begin with the list of all target stars being observed at two-minute cadence by TESS in sectors 1 through 6. Due to the large pixel scales of Evryscope and TESS (13” and 21” respectively), we cross-match each target star with Gaia DR2 [201, 202] sources within a 13” aperture. Any star with multiple cross-matches within that radius is discarded if the parallaxes of the cross-matched source diﬀer by more than 1% or if the distance to the source is greater than 600 pc. The Evryscope forced-photometry catalog is based upon APASS DR9 [203]; we cross-match each target with its g 0-magnitude, discarding any sources without a match. Using the distance and apparent g 0-magnitude, we compute the absolute g 0-magnitude

and select only targets with Mg0 > 8 to constrain our analysis to cool stars with spectral types of ∼K5 and later [13, 204]. We update the J2000 coordinates of high proper motion stars to correct for movement between pixels by J2018 and query the Evryscope light curve database. Of these sources, 20% do not produce light curves in the Evryscope DB, and 10% of those remaining are aﬀected by source blending from stellar crowding.

Applying the above constraints, we select 1679 Mg > 8 Evryscope light curves from a list of 24,816 2-minute cadence targets observed by TESS in Sectors 1 and 2, 1904 Evryscope light curves from a list of 28,577 TESS targets in Sectors 3 and 4, and 1773 Evryscope light

39 Mg0 8.0 8.6 9.9 10.5 11.4 12.4 13.6 3 10 searched stars flare stars

102 # stars

101 K5 K7 M0 M1 M2 M3 M4 Spectral Type

Figure 3.1: Top panel: Evryscope-detected flare stars (red) compared to the full sample of Evryscope light curves of the cool stars (blue). Bottom panel: Our flare-search sample and flare stars plotted on an absolute magnitude versus color diagram. The Evryscope light curves with Mg0 > 8 (K5 and later cool stars) are selected in blue and plotted against their Evryscope minus TESS color to ensure main-sequence dwarfs are primarily selected by our simple brightness cut. Evryscope targets earlier than K5 are removed from this analysis of flaring cool stars. The flare stars we observe are plotted as red asterisks. We note the distribution of cool flare stars is slightly offset from the cool star distribution we searched. Because active stars are younger and therefore higher in metallicity than most stars, we expect them to cluster toward the right edge [200], as we observe. curves from a list of 30,840 TESS targets in Sectors 5 and 6. Because some targets are observed in multiple sectors, repeated Evryscope light curves in each list are allowed; we analyze a total of 4068 unique Evryscope light curves.

TESS observes 4212 targets at 2-minute cadence with Mg0 >8, which we ﬂag as likely K5 and later dwarfs. Of these, we analyzed Evryscope light curves for 4068 targets. We exclude earlier-type stars in this ﬂare search. To ensure we are primarily selecting K5 and later stars on the main sequence, we compute the Evryscope g’ -magnitude minus TESS magnitude of

40 our sample of light curves. We plot g’-TESS color versus Mg0 of our final sample of light curves in Figure 3.1. Light curves with Evryscope flares are highlighted. We search for flares in this cool star subset of the Evryscope light curves. We break up our flare search into sets of Evryscope light curves of two TESS sectors at a time: 1 & 2, 3 & 4, and 5 & 6. The number of epochs (and hence number of flares) in the Evryscope light curves from each batch of sectors will vary by season; seasonal variation of the length of the night is a function of right ascension and therefore TESS Sector. Sectors 1 & 2 have a median number of 25,134 individual epochs per light curve; sectors 3 & 4 have a median number of 17,164 epochs per light curve, and sectors 5 & 6 have a median number of 17,652 epochs per light curve. Stars at the southernmost declinations average ∼ 5× these numbers of epochs.

3.1.3 Automated search for ﬂares

We perform an automated flare search in the Evryscope light curves using a custom flare- search algorithm, Auto-ELFS (Automated Evryscope Light-curve Flare Searcher). Due to the Evryscope ratchet observing length, duration of the night, and various weather interrupts to observing, Auto-ELFS first splits up the light curve into separate “contiguous” segments of uninterrupted observations, each of which is analyzed separately. Before attempting to locate flares, Auto-ELFS tries to determine which epochs represent the quiescent baseline flux; excluding brightness excursions improves our estimation of the local photometric noise. Likely-quiescent epochs are defined to exclude any epoch that occurs less than 20 minutes following any brightening in magnitude with a significance of 4.5σ above an initial estimate of the noise. Auto-ELFS then searches for flares by applying an exponential-decay matched-filter similar to that of [177] to the contiguous light curve segment. Peaks in the matched-filter with a filter significance above 4.5σ that correspond with peaks in the actual g0 magnitude light curve with a significance above 2.5σ are considered flare candidates. The matched-filter significance is defined as the median-subtracted filter value divided by the standard deviation

41 of the filter values of likely non-flaring epochs. The g0 light curve significance is defined as the median-subtracted magnitude divided by the standard deviation of the magnitudes of likely non-flaring epochs. We require the flare candidate to be significant in the matched filter in order to recover flares from noisy light curves; we require the flare candidate to be significant in the light curve magnitudes to ensure the flare rises sufficiently above its surrounding epochs to be vetted by eye. Flare start and stop times are determined as the first and last epochs with significance in magnitude (not in filter product) that exceed 1σ around the flare peak time. Significant candidates are verified by eye in an interactive vetting tool. During interactive vetting, flare candidates from the automated pipeline are confirmed or rejected based on the following criteria: similarity to a FRED profile, dis-similarity to known systematics (such as a Gaussian or box-shaped flare light curve), and a lack of similar flaring behavior at the same time in 3 nearby reference stars. We also exclude from consideration flare candidates that increase in brightness by multiple magnitudes but last less than 10 minutes. Full-frame image cutouts of several of these short multi-magnitude excursions consistently display telescope shake. An example of four flare candidates rejected during vetting for each of these reasons is shown in Figure 3.2, and an example of four flares confirmed during vetting are shown in Figure 3.3.

3.1.4 Manual light curve inspection for superﬂares

We also perform a brief manual inspection of the entire light curve of each star. Although less sensitive to smaller flares than the automated pipeline, this approach allows us to consistently record the largest flares. Large flares easily observable from the light curve by eye sometimes occur in contiguous segments that last only ∼ 20-30 minutes (in periods where due to weather or other observing programs the Evryscope was executing shorter- than-usual ratchets). Auto-ELFS is not designed to operate on contiguous segments of such a short duration due to difficulty in distinguishing in-flare epochs from out-of-flare epochs.

42 A B Target star

Matched-filter

’ ’

g g Δ Δ Reference star

Reference star

Time [minutes] Time [minutes]

C D

’

Δ Δ

Time [minutes] Time [minutes]

Figure 3.2: Rejected stellar flare candidates resulting from by-eye vetting. In each vetting image (i.e. A,B,C,D), target star and reference star light curves are displayed, along with the flare matched-filter product. All light curves displayed are in g 0, except for the matched-filter (orange) which is unit-less. For each target star, epochs flagged by Auto-ELFS for possible stellar brightening are displayed in blue. Start and stop times for each flare are displayed as vertical dashed red lines. Candidate A is rejected for failing to follow a FRED profile. Candidates B and C are rejected because reference stars display similar behavior. Candidate D is rejected for having an amplitude of multiple magnitudes while lasting less than 10 minutes. This event occurred during telescope shake.

43 E F Target star

Matched-filter

’ ’

g g Δ Δ Reference star

Reference star

Time [minutes] Time [minutes]

G H

’ ’

g g

Δ Δ

Time [minutes] Time [minutes]

Figure 3.3: Confirmed stellar flare candidates resulting from by-eye vetting. In each vetting image (i.e. E,F,G,H), target star and reference star light curves are displayed, along with the flare matched-filter product. All light curves displayed are in g 0, except for the matched-filter (orange) which is unit-less. For each target star, epochs flagged by Auto-ELFS for possible stellar brightening are displayed in blue. Start and stop times for each flare are displayed as vertical dashed red lines.

44 Similar difficulties arise when the flare length and the contiguous segment observing length are comparable, e.g. for the largest and longest-lasting superflares, where the slow decay dominates the local background estimation. Light curve inspection remedies this. Finally, some rare systematic brightness excursions of 1-2 magnitude occur consistently across the sky in particular observing seasons but not others. These systematics are readily separated from real flares during manual inspection of all light curves, although they do not occur on the same night for each star and hence do not appear in the 3 nearest reference stars at exactly the same time as the target star. Flares discovered during manual light curve inspection are assigned start and stop times by eye. Flare candidates from this pipeline are subsequently compared against 3 reference stars using the same vetting criteria described in Section 3.1.3. Flares from both automated and manual pipelines are cross-matched against one another and compiled into a single list, keeping one entry for each flare. Because we perform separate searches in each batch of 2 TESS sectors, some of our flare stars will be discovered multiple times. Furthermore, many flares are discovered with an entry from each pipeline. We find 75% of flares discovered by the manual pipeline are also found by the automated one, and 45% of flares from the automated pipeline are found in the manual search. Duplicate flares may also occur when long-lasting flares are sometimes “rediscovered” multiple times by the automated pipeline. Whatever the source of duplicate flare entries, if multiple flare entries are found within 0.1 day of each other, the flare entry with the larger peak magnitude is kept, ensuring the entire flare has been captured and not just the decay tail. This process loses ∼2% of small flares observed near a large flare. Future work will examine the relationships of complex versus single flares occurring in rapid succession after each other [74, 205] in the Evryscope data-set. Quasi-periodic pulsation (QPP; [117]) may be detectable in these complex flares at Evryscope’s 2-minute cadence for the brightest flare stars, although most QPPs have periods and amplitudes below our detection thresholds [206].

45 3.1.5 Determination of ﬂare parameters

We describe below how we measure the physical parameters of each individual ﬂare and describe relevant uncertainties:

• The fractional ﬂux is calculated as described in [74]. Fractional ﬂux is computed as

|F −F0| ∆F/F= where F0 is the out-of-flare flux. F0 is determined from the median of F0 the entire light curve in the automated pipeline and from a ∼5 day window around the flare in the manual pipeline.

• The equivalent duration (ED) for each flare is calculated as described in [74]. We compute the ED as “area-under-the-curve” using the trapezoidal rule, with upper and lower limits of the flare start and stop times. We compute ED as “area-under-the- curve” rather than as a direct sum of flux received during each 2-minute exposure in order to avoid double-counting flux from flares seen by multiple Evryscope cameras simultaneously. We may safely approximate the ED as “area-under-the-curve” because the dominant source of error in flare energy is estimation of a star’s quiescent energy

L0.

0 −1 • We compute the quiescent luminosity in g (L0) in erg s using the apparent g 0 magnitude of the star in the AAVSO Photometric All Sky Survey (APASS) DR9 [203], g 0 =0 to ﬂux calibration [207], and the Gaia DR2 parallax [201, 202].

0 • Flare energy in the Evryscope g bandpass is given in erg by ED×L0.

• We convert the flare energy in the Evryscope bandpass into bolometric energy using the energy partitions of [35]. We estimate the bolometric flare energy of a 9000 K flare blackbody with emission matching the measured Evryscope flux; the fraction of the

0 bolometric energy found in the Evryscope g bandpass is fg0 =0.19.

• The full-width-at-half-maximum (FWHM, in minutes) of each ﬂare was recorded by an automated algorithm to estimate the distribution of highly impulsive ﬂares as

46 described in [33]. As such, we estimate the FWHM as 2 minutes of rise/decay time plus the elapsed time between the first and last points at or above 50% of the peak flare flux. We compared the FWHM computed this way versus a FWHM computed as 2 minutes times the number of points above the 50% flux and found both values agreed for dozens of flares, but only when one camera recorded each flare. The number-of-points method doubled the FWHM when the flare was observed by 2 overlapping cameras.

• The impulse of each flare was then recorded as the flare peak fractional flux divided by the FWHM in minutes.

These values and relevant uncertainties are recorded for each flare. We here summarize the errors of our flare parameters. Uncertainties in peak flare time and FWHM result from the observing cadence and should average ∼2 minutes. Uncertainties in ED and flare energy are computed as the inverse significance of detection; these uncertainties are computed at an

7 average ∼10% error because the median and 1σ spread in significance of detection is 10.2−4. Errors in flare amplitude are computed as the photometric errors at the peak flare times.

0 0.03 In ∆g , the median and spread of the errors is given by 0.02−0.01, and in fractional-ﬂux, the

0.05 median and spread of the errors is given by 0.01−0.009. The median and spread of the errors

0.05 in ﬂare impulse is given by 0.05−0.3. Errors in L0 and Mg0 both depend only on Gaia DR2 parallaxes and APASS DR9 g-magnitudes, which both have typical errors below the 10%

level. Photometric spectral types estimated from Mg0 are approximate, and are accurate within 1-2 spectral sub-types.

3.1.6 Flare frequency distributions

To estimate the superflare rate for each star, the number of flares observed and the total observing time are calculated. We compute the total observing time as the number of epochs in each light curve times a two-minute exposure. We ignore the effect of double-counting epochs from occasional camera overlaps on the total observing time, as only ∼10% of epochs are doubled and the observing time is not the dominant source of error.

47 For stars with less than five flares, we estimate the superflare rate as the number of superflares actually observed divided by the total observing time. Limits on non-flaring stars are large; we focus this work upon stars with at least one flare observed. The upper and lower limits on the superflare rate are given by a 1σ binomial confidence interval. For stars with at least five flares, we calculate the cumulative flare frequency distribution (FFD) by fitting a cumulative power-law to the flares, and estimating the uncertainty in our fit through 1000 Monte-Carlo posterior draws consistent with our uncertainties in occurrence rates. We represent the cumulative FFD in bolometric energy by a power law of the form log ν = α log E + β, where ν is the number of flares with an energy greater than or equal to E erg per day, α gives the frequency at which flares of various energies occur, and β is the y-intercept and sets the overall rate of flaring. We calculate the uncertainty in the cumulative occurrence for each Evryscope flare with a binomial 1σ confidence interval statistic (following [14]). The observation time, number of flares observed, estimated α, β, superflare rates, and uncertainties on these parameters are recorded. Following [119], we also record the maximum and mean amplitude and bolometric energy of each Evryscope flare star for comparison. Because we are observing a large sample of large flares, we compute the FFD of each star without weighting recovery completeness using flare injection-and-recovery.

3.2 Evryscope ﬂare discoveries

We detect 575 high-energy flare events from 284 flare stars in TESS sectors 1-6. Such a large sample of high-energy flares from cool stars probes both the dependence of superflaring on other astrophysical parameters and the potential habitability of planets orbiting cool star stars: we present ∼ 2× the previous-largest sample of high-cadence 1034 erg flares from nearby cool stars (e.g. [119]). We detect at least an order of magnitude more large flares than other ground-based flare surveys due to the high-cadence and multi-year coverage of the entire accessible sky. Precision Evryscope light curves of flare stars later than M4 are only possible for the brightest sources

48 across the sky, although this does not rule out the detection of multi-magnitude flare events from late M and L dwarfs in future work using a separate pipeline. In comparison, the large flare yield of ASAS-SN displayed in Figure 1 of [18] increases significantly at later types.

3.2.1 Flare stars, spectral type, and stellar age

We explore how superﬂare rates correlate with drivers of stellar surface magnetic activity.

3.2.1.1 Superﬂare energy and duration

Because flares are thought to result from magnetic re-connection, we begin by attempting to confirm that our very large superflare events distribute their energy release according to the predictions of magnetic re-connection models. [208] describe how flares generated by

1/3 magnetic re-connection follow the scaling relation τdecay ∝ Ebol between ﬂare energy Ebol

and flare duration τdecay (i.e. the approximate decay time). Our distribution of flare energy versus duration shown in the top panel of Figure 3.4 follows a broken power law that is flat

34 0.34 at energies below 10 erg and best fit by τdecay ∝ Ebol above this energy. The flat power law at lower energies is due to the flare decay tail falling below the photometric noise level and biasing the measured duration. However, when we split up our flares into late K and early M bins and re-compute the power laws separately as shown in the bottom panel of Figure 3.4, we observe coefficients of ∼0.4, slightly larger than those expected from re-connection. We estimate our broken power law knee in flare energy to be approximately 1033.5 for late K flares and 1034.1 for early M flares. In fact, our coefficients for the late K and early M bins are within the errors of the G-dwarf superflare coefficient measurement of 0.38±0.06 discussed in [208]. [208] also considers a number of additions to magnetic re-connection that may steepen the power law. Because the scatter in the data is large, it is unclear whether the larger coefficients we find for the separate populations imply emission mechanisms beyond magnetic re-connection.

49 Table 3.1: Flare wait-times and FFD ﬁt parameters for average K5-M4 ﬂare stars

SpT αenergy βenergy Max energy Max energy Waiting-time seen in 10 d seen in 28 d for 1033 erg ﬂare [log erg] [log erg] [d]

Active K5 -1.34 44.55 34.0 34.3 0.5 Active K7 -1.34 44.55 34.0 34.3 0.5 Active M0 -0.96 31.05 33.5 34.0 3.2 Active M1 -0.88 28.5 33.5 34.0 3.7 Active M2 -0.84 26.82 33.3 33.9 5.4 Active M3 -1.25 40.02 32.9 33.3 12.0 Active M4 -0.97 30.45 32.5 33.0 30.8

Notes. Fit parameters to the “averaged” FFD for K5-M4 flare stars, shown in Fig- ure 3.7. α and β are given by the power law of the form log ν = α log E + β as described in Section 3.1.6, where ν is the number of flares observed per day at an energy of at least Ebol. We estimate the largest flare expected from a typical active star of each spectral type during 10 and 28 days of continuous observing, respectively. We also estimate the waiting-time between successive flares of at least 1033 erg.

We note that we exclude durations measured by hand in the manual pipeline of Section 3.1.4 due to bias in the measured flare start and stop times (increased to ensure the flare fell between the selected times). We conclude that our superflares are broadly consistent with being generated by the re-connection process, but may be affected by additional mechanisms, as in [208].

3.2.1.2 Flare Frequency vs. Spectral Type and Galactic Latitude

Superﬂare energy and occurrence will impact the atmospheres of temperate planets

differently depending on the host star’s spectral type. We use Mg0 to estimate the spectral type of each flare star. Due to the faintness of stars later than M4 in the blue, we do not include later types in this analysis. Both the average number of flares per star and the fraction of searched stars that flare increase from K7 toward M4. This may be a result of approaching the fully-convective

50 boundary. We define the average number of flares per star per spectral type as the number of flares observed from all stars of a given spectral type divided by the total number of stars of that spectral type in our flare search. Error bars are given by 1σ binomial confidence intervals for each spectral type in the two panels to the left in Figure 3.5. Remarkably, the fraction of cool flaring stars per spectral type is identical to the fraction of flaring M-dwarfs found at lower flare energies in [119], indicating that superflares from late-type stars follow a similar increase in flare activity as small flares. The fraction of flaring M-dwarfs per spectral type is also comparable to that found by [26] in Kepler light curves. The fraction of active stars for each spectral type measured in [22, 27] and [18] are 2-10X as high as those we measure here. This is likely a result of choosing to measure activity using a sample of infrequent superflares rather than elevated Hα emission in spectra. We also check if the occurrence of large flares depends upon galactic latitude. Stars in the disk are generally younger and therefore more active than stars at higher latitudes [27]. In Figure 3.6, we do observe an apparent decrease in flare stars at high latitudes. This may be due in part to target selection, as there are fewer cool stars at high latitudes than low latitudes. Flare surveys in Kepler and K2 data ([91, 92]) also find increases in flare rate and fraction of stars flaring for K5 and later spectral types, and decreased flaring with greater age across spectral type [20, 21, 26, 118, 209, 210]. However, Kepler and K2 only observed several hundred active M-dwarfs (e.g. [210, 211]). Evryscope and TESS observations of orders-of- magnitude more M-dwarfs will provide comprehensive flare monitoring in the M-dwarf regime [119]. Several caveats are in order: Figure 3.5 gives the occurrence of the largest flares; surveys observing smaller flares may therefore observe higher rates of flaring. Next, the increased flaring of M4 dwarfs involves small-number statistics. Although larger than for other spectral types, M4 errors are still <20%. Last, we do not perform flare injection and recovery in this sample, so Evryscope systematics in the light curves could alter the true number of stars

51 from which we would have been able to see ﬂares. Because 10% of Evryscope light curves experience source contamination from stellar crowding outside the galactic plane, we conclude this is not a dominant source of error.

3.2.1.3 Mean Flare Energy vs. Spectral Type

Next, we find that the mean flare energy decreases as a function of spectral type, as shown in the right panel of Figure 3.5. Error bars are the 1σ spread in energy. As [119] and [20] note, the lower luminosity of the later types means the same ED results in less bolometric energy. In Kepler, the maximum flare energy as a function of spectral type shows a similar decline toward later types [210]. We compute the hemispherical starspot coverage necessary to generate flares at the mean flare energies we observe for each spectral type in Figure 3.5 as described later in Section 3.2.1.6. We assume a stellar magnetic field of 1 kG and compute starspot coverage as described in Section 3.2.1.6. We find that spots corresponding to the observed mean flare energies cover 1-2% of the stellar hemisphere across all K5-M4 spectral types. Although the mean flare energy of late K and early M stars in our sample is high, future work is needed to determine if the increased orbital distance to the HZ will protect the atmospheres of Earth-like planets around these stars.

3.2.1.4 Superﬂare Rate vs. Spectral Type

To investigate superflare frequency, we construct cumulative FFDs for an “average” flaring star of each spectral type. Binning all flare observations by spectral type, we find similar power-law slopes α for early and mid-M stars, but higher y-intercepts β and therefore occurrence of flares at a given energy for the earlier types. The FFDs are displayed in Figure 3.7. We estimate the annual rate of 1033 erg superflares in Figure 3.8. We record the fitting functions of each FFD and the expected waiting-times for a superflare to occur in Table 3.1.

52 Table 3.2: Flare wait times & flare amplitudes-FFD fit parameters for average K5-M4 flare stars

SpT αampl βampl Max Max con- Max Max con- Waiting- ampl. trast seen ampl. trast time seen in in 10 d seen in 28 seen in 28 for 3-mag 10 d d d ﬂare

[∆F/F] [∆Mg0] [∆F/F] [∆Mg0] [yr]

Active K5 -0.44 -2.34 0.0 0.0 0.0 0.0 N/A Active K7 -1.04 -2.26 0.1 0.1 0.2 0.2 8.2 Active M0 -0.84 -1.98 0.1 0.1 0.2 0.2 2.5 Active M1 -0.91 -1.65 0.2 0.2 0.6 0.5 1.4 Active M2 -0.97 -1.41 0.4 0.3 1.1 0.8 1.0 Active M3 -2.19 -0.69 1.4 0.9 2.2 1.3 4.9 Active M4 -1.46 -1.14 0.8 0.6 1.6 1.0 2.0

Notes. Fit parameters to the “averaged” flare amplitudes “FFD” for K5-M4 flare stars, shown in Figure 3.9. α and β are given by the power law of the form log ν = α log A + β following the discussion in Section 3.2.1.5, with ν being the number of flares observed per day at an amplitude with a fractional flux peak of at least A. We estimate the largest flare amplitude expected from a typical active star of each spectral type during 10 and 28 days of continuous observing, respectively. Each amplitude is given in units of both fractional flux and g0 magnitudes. We also estimate the waiting-time between successive flares of at least 3 g 0 magnitudes.

Although these rates are high, they are constructed from active stars of each spectral type and do not hold for inactive stars. [131] ﬁnds inactive stars to be 10× less active in the FUV-130 bandpass. Should similar relationships hold for white-light superﬂares, the impacts on planet atmospheres would be greatly reduced for inactive stars.

3.2.1.5 High-amplitude Flare Occurrence vs Spectral Type

Sky surveys performing rapid transient discovery and follow-up must be able to characterize the degree to which M-dwarf ﬂare stars contaminate desired triggers from extra-galactic sources of rapid brightening events (e.g. [212–214]).

53 We construct cumulative FFDs for flare amplitudes rather than energies in order to predict how often an average flare star of a given spectral type will emit a flare of a given amplitude. We fit parameters α and β to the power law log ν = α log A + β following the discussion in Section 3.2.1.5, with ν being the number of flares observed per day at an amplitude with a fractional flux peak of at least A. Recorded in Table 3.2 and displayed in Figure 3.9, the resulting amplitude-FFDs may be used to predict how often a flare of a given amplitude will occur, as well as the largest flare expected within a certain observing baseline. For example, a survey observing an M2e star for 10 continuous days would observe a flare with a stellar peak fractional flux of least 0.4. The best-fit parameters for these amplitude-FFDs for each spectral type are given in Table 3.2. We find the largest flare amplitude expected from a typical active star of each spectral type increases as the quiescent luminosity of the star decreases as shown in Figure 3.10. We also find the waiting-time between successive flares of at least 3 g 0 magnitudes decreases from nearly a decade for late K-dwarfs to only two years for M4 dwarfs.

3.2.1.6 Starspot coverage and superﬂares

41 of our flare events exceed 1035 erg. If the energy released by extreme flares is stored in surface magnetic fields, then the area of the smallest spot that could have produced such a

B2 3/2 flare is given by Eflare = 8π Aspot [7, 62]. Eflare is the bolometric flare energy, B is the surface

magnetic field strength, and Aspot is the smallest spot group area expected to generate Eflare. We note that this model is a very simplified assumption and true spot sizes could be at least

an order of magnitude larger. We estimate the starspot coverage by dividing Aspot by the

projected area of the approximate stellar hemisphere Astar. To calculate stellar area, we

estimate the stellar mass from Mg0 using [204] and then estimate the stellar radius using the mass-radius relationship provided by [200]. We note that the spot group area scaling law was discovered for solar-type stars and extrapolation into the cool star regime may introduce further error.

54 Early to mid M-dwarf surface magnetic fields are often 1-4 kG in strength [71]. We therefore estimate the approximate starspot coverage as a function of flare energy for 1, 2, and 4 kG fields, shown in Figure 3.11. As the field strength increases, the necessary spot coverage to generate a given superflare decreases [62]. We compute three separate scaling relationships between flare energy and starspot coverage of K5-M4 stars for 1, 2, and 4 kG

fields assuming a power law of the form log fcoverage = a log E + b, where fcoverage is the spot coverage and E is the flare energy. The fits are also shown in Figure 3.11. We attempt to constrain the largest flare a cool star may emit by assuming 100% hemispherical spot coverage and solving for the flare energy. The hypothesized maximum- allowed flare energies are displayed in Table 3.3 along with an estimate of the waiting-time between successive flares at these energies obtained from the K5-M4 FFDs in Section 3.2.1.4. We caution readers that these upper limits are dependent on large uncertainties in the flare energy-spot model and in the FFDs. Cool star flare energies associated with 100% spot coverage are comparable to those estimated by [62] for Solar-type stars.

3.2.2 Comparing Evryscope and TESS ﬂares

Evryscope flare monitoring of TESS flare stars complements flare studies done in the TESS light curves themselves. While TESS has the high photometric precision necessary to observe the most frequent low-to-moderate energy flares, long-term Evryscope monitoring captures the largest and rarest flares the star is capable of releasing. Flares observed by Evryscope are approximately an order of magnitude more energetic than those found in the TESS light curves themselves due to the longer observing baseline and lower photometric precision of Evryscope compared to TESS, as displayed in the left panel of Figure 3.12. These energies are comparable, however, to the flares discovered by [18] in ASAS-SN data.

55 Table 3.3: Starspot coverage of average K5-M4 ﬂare stars

Stellar aspot bspot Emax K5-K7 M0 M1 M2 M3 M4 B- Wait- Wait- Wait- Wait- Wait- Wait- ﬁeld time time time time time time for for for for for for Emax Emax Emax Emax Emax Emax

[kG] [log erg] [kyr] [kyr] [kyr] [kyr] [kyr] [kyr]

1 kG 0.70 -25.96 37.0 0.3 0.07 0.03 0.05 4 0.7 2 kG 0.70 -26.36 37.5 1.5 0.3 0.09 0.1 20 2.4 4 kG 0.70 -26.76 38.1 8.7 0.9 0.3 0.4 110 8.8

Notes. Fit coefficients for the power law of the form log fcoverage = a log E + b describing the scaling relationship between hemispherical spot coverage of cool stars fcoverage and superflare energy E. We perform separate fits at representative cool star magnetic field strengths. We also hypothesize for each field strength the maximum allowed flare energy Emax assuming 100% spot coverage. We urge caution in applying these maximum-allowed flare energies, because real spots do not necessarily release all of their energy in a single flare event. As a result, the flare energy and spot size scaling used to compute these values introduces at least order-of-magnitude-level uncertainties. Using the FFDs computed in Table 3.1, we estimate the waiting-time between successive flares of energy Emax for an active star in each spectral type.

56 Evryscope also observes the largest and rarest flare amplitudes, as displayed in the right panel of Figure 3.12. Flares emit more strongly in the blue than in the red, so our flare peak amplitude of a given flare will be several times higher than for TESS [215].

3.2.3 Most extreme superﬂares

In 2 years of Evryscope monitoring of the nearest star, the common red dwarf Proxima Centauri, we discovered three-magnitude stellar flare events occur 2-5 times per year [44], with 2 total superflares observed [216]. Here, we constrain how frequently similarly-large events occur across the sky. Out of 284 flare stars, we observe 8 stellar flares that increased their star’s brightness by at least 2.9 g 0 magnitudes; they are displayed in Figure 3.13. These flares have also been checked against Evryscope image cutouts in addition to the regular systematics checks described in Section 3.1.3. The largest of these is a 5.6 magnitude flare from a 40 Myr M4 star in the Tuc-Hor cluster, TIC-160008866, which increased the stellar brightness by ∼ 90× and released 1036.2 erg. These superflare stars are as follows:

• TIC-160008866: (UCAC2 14970156) an M4 that increased in brightness 5.6 magnitudes and released 36.2 log erg. To estimate the energy of this flare, we fit the flare template of [6] and computed the area-under-the-curve. Other large flares were also observed from this star in the Evryscope light curve. Stellar activity from this young star in the Tuc Hor moving group [217] has been measured in the UV by [218]. The extreme UV “Hazflare” observed by [219] is from the same cluster.

• TIC-326446019: (RBS 1877) an M3.5 [220] that increased in brightness 3.5 magnitudes and released 1035.3 erg

• TIC-224225152: (LTT 9582) an M3 [220] that increased in brightness 3.1 magnitudes and released 1034.9 erg

57 • TIC-231017428: (L 173-39) an M2 [221] that increased in brightness 3.1 magnitudes and released 1035.4 erg

• TIC-206478549: (WISE J035122.95-515458.1) an M4 [217] (also in the Tuc-Hor moving group) that increased in brightness 2.9 magnitudes and released 1035.6 erg

• TIC-231799463: (L 57-11 B) an M4 [222] that increased in brightness 3.5 magnitudes and released 1035.4 erg. Due to Evryscope’s large pixel scale and the high PM of this system, it is possible this ﬂare came from the M4, L 57-11 A or the semi-regular pulsator 2MASS J05125971-7027279 in the LMC [223]. All 3 stars are within ∼13 arcsec.

• TIC-262575578: (UCAC3 63-25310) an M1 that increased in brightness 3.2 magnitudes and released 1035.8 erg

• TIC-167457891 (LP 767-17), an M2 that increased in brightness 3.6 magnitudes and released 1035.2 erg.

3.2.4 Superﬂares from TESS planet hosts

Out of 284 Evryscope ﬂare stars, one is a TESS Object of Interest (TOI). TOI-455 (TIC-98796344) was observed in TESS Sector 4, when it was found to host a candidate 1.37

R⊕ planet interior to the star’s habitable zone (HZ). Subsequent follow-up may find a larger radius for the planet (e.g. [224]), as another star is in the same pixel of the TESS CCD. At a distance of 20 pc, TOI-455 is close enough to make future planetary atmospheric study a possibility [165]. We observe a single 1034.2 erg superflare, and predict a superflare rate

23 −1 of 15.1−9 yr . Although this rocky planet candidate lies outside the habitable zone, TESS is expected to discover many compact multiple-planet systems around M-dwarfs [225]. The atmospheres of any additional rocky planets in this star’s HZ will also be impacted by these superﬂares.

58 3.3 Astrobiological Impact of Superﬂares

[45] find that the cumulative effect of multiple 1034 erg superflares per year and any associated stellar energetic particles (SEPs) may destroy an Earth-like planet’s ozone layer on timescales of years to decades. [119] generalizes this result from [45] to estimate that a 1034 erg superflare rate of 0.1 to 0.4 flares day−1 is sufficient to deplete ozone. In our sample of 284 flare stars, we observe 17 flare stars in this regime. However, the ozone loss modeling by [45] depends on the assumed distribution of particle energy versus flare energy. Efforts to directly measure the SEP environment of nearby stars by observing their stellar coronal mass ejections (CMEs) have resulted in a lack of evidence for stellar CMEs in the radio [226, 227], although candidate CMEs have been identified in optical/X-ray data at lower SEP velocities than previously thought [228]. The lack of CMEs in the radio and reduced SEP velocities in the optical/X-ray may be due to the strong dipoles of quickly-rotating cool stars that trap SEPs before they can escape the star’s magnetic field [229]. We therefore inquire how many of our superflares may have sufficient energy in the UV alone to fully deplete an ozone column in a single event. [131] finds that single superflares with equivalent durations in the Si IV FUV bandpass greater than 108 seconds release enough energy to fully photo-dissociate an Earth-like planet’s ozone column. [131] approximates the Si IV ED of a 3×1035 erg g 0 -band flare to be 108 seconds. We here extend this approximation to the bolometric energy of our g 0 flare energies. The in-band energy of an Evryscope flare is 19% of the bolometric energy [44]. As a result, a bolometric energy of 1036.2 erg is required to exceed 108 seconds in Si IV. In our flare sample, we observe 1 superflare that meets this criteria. This is the 5.6 magnitude flare from the young star TIC-160008866 described in Section 3.2.3. We also observe 23 more superflares in our sample that attain at least 10% of our estimate of the required energy to dissociate an ozone layer. Such large flares from very young stars may not prevent planets orbiting these stars from being conducive to life. Recent modeling by [141]

59 of the surface UV environment of Earth-analogues orbiting M-dwarfs suggests that extreme stellar activity may not prevent the formation of life, if the planet atmospheres follow the evolution of the Earth’s atmosphere through time. We note that the photo-dissociation estimates from [131] do not include modeling of the thermochemistry occurring after each flare, but rather describe how far a flare of a given energy is able to push an Earth-like atmosphere out of chemical equilibrium if the flare were to deposit its energy instantaneously. Si IV flares of 108 seconds could severely disrupt atmospheric equilibrium. During the thermochemical aftermath of such a large flare, ozone would rapidly return to equilibrium and overshoot its original value due to the creation of

additional, slowly recombining free oxygen from the photolysis of O2 by FUV photons. While ozone rapidly reforms after a single event, sufficiently-frequent extreme superflares would further and likely permanently disrupt atmospheric equilibrium. We also note that extreme UV radiation and high energy SEPs from superflares will alter planetary atmospheric chemistry and surface environments through more pathways than ozone depletion. For example, the atmospheric volatile composition of close-in planets may be altered by SEPs associated with superflares through the production of secondary particles. These SEPs would also increase the surface radiation dosage, although potentially not to un-inhabitable levels [230]. As a second example, SEPs from superflares may fix inert atmospheric nitrogen in Earth-like atmospheres, creating greenhouse gasses and compounds necessary for life [140]. Although an Earth-like atmosphere may not survive repeated flaring, many HZ planets

may orbit inactive stars. During the 2-year primary TESS mission, planets as small as 2R⊕

and 1.6R⊕ may be detected within the HZ of only 1822 and 1690 stars, respectively [231]. We observe a total of 49 stars in the TESS HZ catalog to exhibit large ﬂares. Due to the faintness of many of these catalog stars in the blue, we only search 335 catalog stars, for a physical rate of 14.6±2% with large ﬂares.

60 100.0

10.0 Duration [min]

0.34 Decay Ebol

1.0 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 log Energy [erg]

K5-M1 flares 100.0 M2-M4 flares

10.0 Duration [min]

0.39 M2-M4: Decay Ebol

0.43 K5-M1: Decay Ebol 1.0 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 log Energy [erg]

Figure 3.4: Top panel: Flare energy and duration (i.e. decay timescale) of all flares discovered by the automated pipeline in Section 3.1.3. Errors in energy and duration are computed as the inverse significance of detection. A broken power law is fit, with photometric scatter dominating below 1034 erg. At energies above 1034 erg, the best-fit power law coefficient of 0.34 is consistent with that predicted by magnetic re-connection, 1/3. Bottom panel: Same as top panel, but with separate power laws fit to early M and late K flares. We observe a gradient in the flare duration at a given energy as a function of spectral type. Both power law coefficients are slightly larger than 1/3, although it is unclear if this is due entirely to the large scatter in the data or implies emission mechanisms beyond magnetic re-connection.

61 Mg0 Mg0 Mg0 8.0 8.6 9.9 10.5 11.4 12.4 13.6 8.0 8.6 9.9 10.5 11.4 12.4 13.6 8.0 8.6 9.9 10.5 11.4 12.4 13.6 0.6 35.0 25 0.5 34.5 20 0.4 34.0

0.3 15 33.5

0.2 10 33.0 % stars flaring 5 mean # flares / star 0.1 32.5 log Total Energy [erg] 0.0 0 32.0 K5 K7 M0 M1 M2 M3 M4 K5 K7 M0 M1 M2 M3 M4 K5 K7 M0 M1 M2 M3 M4 Spectral Type Spectral Type Spectral Type

Figure 3.5: Flaring as a function of spectral type. Left panel: the average number of individual flares observed per star as a function of spectral type. Error bars are 1σ binomial confidence intervals. Middle panel: the fraction of flare stars observed as a function of spectral type. Error bars are 1σ binomial confidence intervals. We note a rise in the average number of flares and the fraction of flare stars towards the M4 fully-convective boundary. Right panel: the flare energy as a function of spectral type. Error bars are the standard deviation in energy.

6 % flare stars 4 Region of stellar crowding 2

0 80 60 40 20 0 Galactic latitude

Figure 3.6: The percentage of flare stars in our sample of cool stars is displayed as a function of galactic latitude. Error bars are 1σ binomial confidence intervals. We note an apparent decrease in the flare rate at high galactic latitudes. This may be due to the decreased activity of old stars above the galactic plane; it may also be a result of sampling the decreasing density of both flaring and non-flaring M-dwarfs at high latitudes.

62 0.1 0.1 0.1

0.01 0.01 0.01 1 y

a 0.001 0.001 0.001 d

s e r a l

f 33.0 33.5 34.0 34.5 35.0 35.5 36.0 33.0 33.5 34.0 34.5 35.0 35.5 36.0 33.0 33.5 34.0 34.5 35.0 35.5 36.0

f o 0.1 0.1 0.1 #

K5-K7 e

v M0 i t

a M1 l

u M2 m

u M3 C 0.01 0.01 0.01 M4

0.001 0.001 0.001

33.0 33.5 34.0 34.5 35.0 35.5 36.0 33.0 33.5 34.0 34.5 35.0 35.5 36.0 33.0 33.5 34.0 34.5 35.0 35.5 36.0 log Total Flare Energy [erg]

Figure 3.7: We construct averaged cumulative FFDs for each spectral type classification. We bin all flares observed and the total observing time by the estimated spectral types. As a result, these relations do not hold for inactive stars. Errors in the number of flares d−1 are given by 1σ binomial confidence intervals. The curve at the lower-energy end of each FFD is an artifact of sometimes failing to observe the smallest flares.We remove all flares with an ED<102.44 from the fit, below which the lost flares dominate. Because this incompleteness limit is higher for later types, this curve remains visible at the leftmost end of each panel.

Mg0 8.0 8.6 9.9 10.5 11.4 12.4 13.6

800

600 ] 1

r 400 y [

s 200 e r a

l 150 f r e

p 100 u S 50

0 K5 K7 M0 M1 M2 M3 M4 Spectral Type

Figure 3.8: The annual superflare rate of a typical active flare star as a function of estimated spectral type. We extrapolate the superflare rate from each averaged cumulative FFD for each spectral type displayed in Figure 3.7. As a result, this distribution does not hold for inactive stars. Due to the low numbers of K-dwarf flares, we bin all K5-K7 flares and display the averaged result in both the K5 and K7 bins for consistency with other plots in this work. Error bars on superflare rates are calculated with 1000 posterior draws to each FFD.

63 1.0 1.0 1.0

0.1 0.1 0.1

0.01 0.01 0.01 1 y a d

0.001 0.001 0.001 s e r a l

f 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0

f o 1.0 1.0 1.0 # K5-K7 e v

i M0 t a

l M1 u 0.1 0.1 0.1 M2 m

u M3 C M4

0.01 0.01 0.01

0.001 0.001 0.001

0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 log Amplitude [normalized flux]

Figure 3.9: We construct averaged cumulative FFDs from flare amplitudes instead of flare energies. We bin all flare amplitudes observed and the total observing time by the estimated spectral types. As a result, these relations do not hold for inactive stars. Errors in the number of flares d−1 are given by 1σ binomial confidence intervals. The curve at the lower end of each FFD is an artifact of sometimes failing to observe the smallest flares. We remove all flares with an ED< 102.44 from the fit, below which the lost flares dominate. Because this incompleteness limit is higher for later types, this curve remains visible at the leftmost end of each panel (strongest for M3). We further manually adjust the fit to include only the linear-in-log-log region of the M3 and M4 amplitude power laws to avoid bias at the lower end.

64 Mg0 8.0 8.6 9.9 10.5 11.4 12.4 13.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

Highest amplitude expected / 10 days 0.0

K5 K7 M0 M1 M2 M3 M4 Spectral Type

Figure 3.10: We estimate the largest flare amplitude expected from a typical active star of each spectral type during 10 days of continuous observing. These estimates are obtained by extending the amplitude FFDs in Figure 3.9 and Table 3.2 to the typical flare amplitude per 10 days of observing. Flare amplitudes are displayed as peak increases in fractional flux. We find expected amplitudes increase for less luminous spectral types. The large uncertainty in M3 is due to the knee in the power law in Figure 3.9.

1.0 1 kG 2 kG

] 4 kG 2 r a t s R / t o p s 0.1 A [

e g a r e v o c

t o p

s 0.01 r a t S

35.0 35.2 35.4 35.6 35.8 36.0 36.2 log Flare energy [erg]

Figure 3.11: Estimated starspot coverage required to generate the largest superflares we observed as a function of stellar magnetic field strength and flare energy. We compute the starspot coverage as the spot group area divided by the projected area of the stellar hemisphere. The minimum spot group area required to generate each superflare is computed from the flare energy using scaling relations from [7, 62]; true spot coverage could be at least an order of magnitude larger. We fit a power law of the form log fcoverage = a log E + b to the spot coverage fcoverage and flare energy E for representative cool star field strengths. Fit coefficients are given in Table 3.3. Error in energy is computed as the inverse significance of detection; 100% error in spot coverage is assumed due to the approximate nature of the spot group area scaling law.

65 3000 Evryscope Evryscope 2500 0.7 TESS TESS 2000 0.6 1500

0.5 1000

500 0.4 50

0.3 # flares 40 flare frequency 30 0.2 20

0.1 10

0 0.0 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 32.0 32.5 33.0 33.5 34.0 34.5 35.0 35.5 36.0 Peak amplitude [ F/F] log E [erg]

Figure 3.12: Left panel: Normalized distributions of recovered bolometric flare energies from Evryscope and TESS. Right panel: Histogram of flare amplitudes from Evryscope and TESS. TESS flares in both panels are from light curves of K5 and later stars in [119]. Although TESS observes an order of magnitude more flares, Evryscope captures the largest-amplitude and highest-energy flare events.

100 40 40 30 37.5 80 F/F=84X F/F=32X 30 F/F=27X F/F=25X 30 60 20 20 20 40 37.0 10 20 10 10

0 0 0 0 ] 36.5 g TIC-160008866 TIC-326446019 TIC-167457891 TIC-231799463 r e [

0 1 2 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 1.25 0.0 0.5 1.0 1.5 l o b E

20 36.0 g o 20 20 l 15 F/F=18X F/F=18X 20 F/F=17X F/F=17X Normalized flux 15 15 10 35.5 10 10 10 5 5 5 35.0 0 0 0 0 TIC-262575578 TIC-206478549 TIC-231017428 TIC-224225152 0.5 1.0 1.5 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 0.00 0.25 0.50 0.75 1.00 Time [hours]

Figure 3.13: A “rogues gallery” of our highest-amplitude superflares detected by Evryscope from cool stars listed as 2-minute cadence-observed TESS stars in sectors 1-6. Each flare released at least 1035 erg and is capable of significantly altering the chemical equilibrium of an Earth-like atmosphere [131]. Each flare is color-coded by its bolometric flare energy; the energy/color scheme is given on the colorbar to the right of the figure.

66 CHAPTER 4: ROTATION PERIODS OF THE COOL FLARE STARS IN TESS ACROSS HALF THE SOUTHERN SKY

We measure rotation periods and sinusoidal amplitudes in Evryscope light curves for 122 two-minute K5-M4 TESS targets selected for strong flaring. The Evryscope array of telescopes has observed all bright nearby stars in the South, producing two-minute cadence light curves since 2016. Long-term, high-cadence observations of rotating flare stars probe the complex relationship between stellar rotation, starspots, and superflares. We detect periods from 0.3487 to 104 d, and observe amplitudes from 0.008 to 0.216 g0 mag. We find the Evryscope amplitudes are larger than those in TESS with the effect correlated to stellar mass

(p-value=0.01). We compute the Rossby number (Ro), and ﬁnd our sample selected for ﬂaring

has twice as many intermediate rotators (0.040.44) rotators; this may be astrophysical or a result of period-detection sensitivity. We discover 30 fast, 59 intermediate, and 33 slow rotators. We measure a median starspot coverage of 13% of the stellar hemisphere and constrain the minimum magnetic field strength consistent with our flare energies and spot coverage to be 500 G, with later-type stars exhibiting lower values than earlier-types. We observe a possible change in superflare rates at intermediate periods. However, we do not conclusively confirm the increased activity of intermediate rotators seen

in previous studies. We split all rotators at Ro ∼0.2 into PRot <10 d and PRot >10 d bins to confirm short-period rotators exhibit higher superflare rates, larger flare energies, and higher starspot coverage than do long-period rotators, at p-values of 3.2×10−5, 1.0×10−5 and 0.01, respectively1.

1Content from this chapter previously appeared in Howard et al. 2020, ApJ 895, 140. For this project, I designed and carried out the rotation period survey in its entirety and wrote the paper. Nicholas Law advised the project.

67 4.1 EvryFlare: all-sky stellar activity search

The EvryFlare survey is an ongoing comprehensive survey of stellar activity from all cool stars observed by Evryscope in the accessible Southern sky. Evryscope monitors large ﬂares, stellar rotation periods, and starspot coverage from all nearby cool stars.

4.1.1 Evryscope observations

As part of the Evryscope survey of all bright Southern stars, we discover many variable stars and rotating stars with starspots. The Evryscope is an array of small telescopes that simultaneously images 8150 square degrees and 18,400 square degrees in total each night on the sky. Evryscope observes at two-minute cadence in g 0 [171], and is optimized for bright, nearby stars, with a typical dark-sky limiting magnitude of g 0=16. Each night, Evryscope continuously monitors each part of the sky down to an airmass of two and at a resolution of 13” pixel−1 for ∼6 hours, The system accomplishes this by employing a “ratchet” strategy, tracking the sky for 2 hours at a time before ratcheting back into the initial position and continuing observations [172]. The Evryscope has already obtained 3.0 million raw images, which we store as ∼250 TB of data. Evryscope images are reduced at real-time rates using a custom data reduction pipeline [172, 175]. Each 28.8 MPix Evryscope image is calibrated using a custom wide-ﬁeld astrometric solution algorithm. Background modeling and subtraction is carefully performed before raw photometry is extracted within forced-apertures at coordinates in an Evryscope catalog of 3M known source positions, including all stars brighter than g 0=15, fainter cool stars, white dwarfs, and a variety of other targets. We then generate light curves across the Southern sky by diﬀerential photometry in small sky regions using carefully-selected reference stars and across several apertures [172]. Systematics are partially removed by employing two iterations of the SysRem detrending algorithm [176]. We periodically regenerate the entire database of Evryscope light curves in order to incorporate observations obtained since the last update and to improve the photometric

68 precision. At the time the data was analyzed for the present work, the Evryscope light curve database spanned Jan 2016 through June 2018, averaging 32,000 epochs per star (with factors of several increases to this number closer to the South Celestial Pole). Depending upon the level of stellar crowding, light curves of bright stars (g 0=10) reach 6 mmag to 1% photometric precision. Evryscope light curves of dim stars (g 0=15) reach comparable precision to TESS, attaining 10% photometric precision [172].

4.1.2 TESS observations

The TESS mission is searching for transiting exoplanets across the entire sky, split into 26 sectors. TESS observes each sector continuously in the red with four 10.5 cm optical telescopes for 28 days at 21” pixel−1. We chose our original sample to have calibrated, short-cadence TESS light curves during the Primary Mission, which were downloaded from MAST2 for each cool ﬂare star in our sample. We selected Simple Aperture Photometry (SAP) light curves rather than Pre-search Data Conditioning (PDC) ones to avoid removing real astrophysical variability.

4.1.3 Evryscope+TESS sample of cool ﬂaring rotators

We search for rotation periods in our sample of flaring cool stars (i.e. K5-M4 dwarfs) from [143]. Although Evryscope observes ∼0.5×105 cool stars, 2-minute cadence light curves of only 4,068 cool stars were produced by both Evryscope and TESS in the first six TESS sectors. We selected only stars with both a high-cadence light curve in the blue (Evryscope) and in the red (TESS) in order to compare the flare amplitudes, flare energies, flare rates, rotation periods and amplitudes of rotation between these bands. Evryscope observed 575 large flares with a median energy of 1034 erg from the 284 flare stars. Of these, rotation was detected for 122 stars. These stars comprise the sample of active cool rotators in this work. Future work will explore a larger sample in both Evryscope and TESS.

2https://mast.stsci.edu

69 The stellar flares were observed in the Evryscope light curves from the subset of rotators within the [143] sample. Flares are discovered and characterized as described in [143]. Briefly, we searched 2-minute cadence Evryscope light curves for large flares first by eye, and then with the Auto-ELFS automated flare-search algorithm. The algorithm applies a flare matched-filter to the light curve and records brightening events that exceed the local noise by at least 4.5σ as flare candidates. Event start and stop times are determined by the first and last epochs to exceed the noise by 1σ around the peak epoch. The light curve of each flare

F −F0 candidate is converted to fractional-flux ∆F/F using the out-of-flare flux F0: ∆F/F= . F0 The equivalent duration (ED) of each flare candidate is computed from the start to the stop time in seconds by a trapezoidal integration of the fractional-flux. We multiply the ED by

0 0 the g stellar quiescent ﬂux (L0) computed from the APASS DR9 [203] g magnitude and

−1 Gaia DR2 [201, 202] distance; L0 is given in units of erg second . Finally, we convert flare energies in g0 to bolometric energies assuming a 9000 K flare blackbody. These events are inspected by eye for systematics or astrophysics other than flares as described in [143] and subsequently confirmed or rejected. We calculated the maximum-energy flare observed from each star during 2+ years of Evryscope observations, as well as the annual superflare rate of each star. We use these two flare star parameters to investigate the dependence of flaring upon stellar rotation and starspot coverage to avoid discovering random correlations between a large number of flaring variables.

4.1.4 Characterizing Stellar Properties

Obtaining accurate values of stellar eﬀective temperature and stellar radius helps constrain the physical parameters of starspots.

70 4.1.4.1 Estimating Photometric Spectral Type

We estimate the photometric spectral type of each star. Because [143] estimated spectral type from one color and a Gaia DR2 distance, we find the g 0 blue band may over-predict the stellar effective temperature of cool dwarfs by several hundred K compared to classifiers that use several colors (e.g. [232]). To provide increased accuracy in our sub-type classification, we use the photometric spectral type classifier described in [232]. Briefly, [232] classifies main sequence dwarfs by their reduced proper motion (RPM) and multiple stellar colors using a Gaussian Mixture Model (GMM; [233]). The GMM calculates the negative-log-likelihood and confidence level each star has been correctly classified. The GMM classifies M-dwarfs to within at least 3 spectral sub-types 95% of the time. While it is possible for an RPM classifier to fail to separate dwarf and giant stars at low RPM, we do not consider this to be a concern because the entire sample of stars was separately classified on the basis of Gaia DR2 parallax and APASS DR9 g-magnitude; we desire to increase the precision of sub-type measurements made from one color toward several colors. Out of 122 stars, the GMM classified 80% of our sample. For the other 20%, no GMM classification was given, likely a result of having too few cross-matched colors. For stars without a classification, we assign the spectral type via the absolute g0 magnitude as described in [143].

4.1.4.2 Estimating Stellar Eﬀective Temperature, Mass, and Radius

We compute stellar eﬀective temperature from the estimated spectral type using the relations given in Table 5 in the Appendix of [204]. We also compute stellar mass from the estimated spectral type using the relations given in Table 5 in the Appendix of [204]. We compute stellar radius using the mass-radius relationship for cool stars given in [200].

4.1.4.3 Characterizing Starspots and Flares

Assuming that the observed sinusoidal stellar brightness variations are caused by star spots rotating into and out of view, we may investigate the nature of the star spots in

71 our sample. For each rotating star in our sample, we may estimate the following starspot parameters:

• We estimate starspot temperature using the relationship between stellar eﬀective

temperature TEﬀ and starspot temperature TSpot from [62]:

∆T (TStar) = TStar − TSpot = (4.1) −5 2 3.58 × 10 TStar + 0.249TStar − 808

We note this ﬁt was derived for solar type stars observed by Kepler and is extrapolated into the cool star regime. We therefore urge caution in the application of these values.

• We measure spot coverage as the starspot area ASpot divided by the projected

hemispherical area of the star AStar. We use the relation described in [7, 11, 62, 234]:

" #−1 A ∆F T 4 Spot = 1 − Spot (4.2) AStar F TStar

∆F/F is the normalized ﬂux diﬀerence in brightness between the brightest part of

the star and the dimmest side and is in units of fractional-ﬂux. Astar is given as

2 AStar = πRStar. The bolometric spot area will diﬀer from the spot area measured in a given bandpass.

These results and relevant uncertainties are found for each ﬂare star. The measured rotation period and period error calculated as described in Section 4.2 is also included for each rotating ﬂare star. We plot a grid of sample Evryscope period detections in Figure 4.1. We also plot a grid of sample Evryscope and TESS period detections overlaid on each other in Figure 4.2.

72 Figure 4.1: A random subset of all photometric rotation periods found in Evryscope light curves for 122 cool ﬂare stars. In each panel, we plot ∆Mg0 magnitudes versus phase. We repeat the phased epochs twice to better display the periodicity. A phased and binned Evryscope light curve is overlaid (in blue), along with a best-sinusoid ﬁt to the unbinned data (in orange). We sometimes detect periods with additional periodicity at harmonics of the strongest peak, such as in the bottom-left panel.

73 Figure 4.2: Phased and binned light curves of a subset of cool rotators for which the TESS light curve folds up exactly to the Evryscope-detected period. The phased and binned Evryscope (blue) and TESS (red) light curves are overlaid. In each panel, we plot the normalized flux ∆F/F versus phase. We repeat the phased epochs twice to better display the periodicity. We find the amplitudes of the TESS light curves are almost universally less than or equal to the Evryscope amplitudes. We note the increase in spot contrast in the blue g0 bandpass versus the red T bandpass. TESS amplitudes are further decreased beyond the initial amplitude difference by systematics-removal. In visual inspection and A-D tests, this color difference correlates with the stellar effective temperature of our K5-M4 stars but not with the presence of companion stars in the TESS pixel, which is 4× larger.

74 4.2 Evryscope rotation periods

We search for photometric rotation periods by computing the Lomb-Scargle (LS) periodogram [235–237] of each Evryscope light curve.

4.2.1 Initial detection of periods in Evryscope

We separately compute the LS periodogram of each light curve for 10,000 frequency steps over a test period range of 0.1 to 3 days, and for 10,000 frequency steps over a test period range of 1.25 to 100 d. Periodograms were computed separately in these period ranges as part of a modular data analysis and then the clearest candidate signals across both periodograms were selected. This was a result of realizing the initial lower period limit of 1.25 d had removed fast rotators from the sample. The upper limit of 102 is arbitrarily selected; we note most active stars will rotate much faster. We also note that distinguishing signal from our systematics and noise becomes increasingly difficult at very long periods, placing us in a different regime for rotation than MEarth [72], etc. We also note that if the highest LS peak for a star is at 100 d, we manually increase the period in steps of 0.1 to 0.5 d and examine the phase-folded light curve to see if the true period is slightly larger than 100 d. We subtract 27.5 day and 1 day best-fit sines from all light curves before computing the periodograms. LS power is computed as the median-subtracted LS periodogram peak of the target star over the “noise” of the periodogram. We exclude a period region within 0.05 days of the detected peak from the noise computation. In order to constrain systematics during the period analysis, we compare the LS periodogram of each target star with the combined LS periodograms of the other 283 flare stars in [143], stepping through the entire sample star by star. Systematic behavior common to all light curves will increase the LS power of each star at systematics-affected periods. We therefore combine together the LS periodograms of all rotating and non-rotating stars, computing the median and standard deviation of the detected LS powers of all stars at each test period from 0.1 to 100 d. We define the averaged LS periodogram as the 1σ upper

75 Figure 4.3: An example photometric rotation period found in an Evryscope light curve. The LS periodograms of all stars are plotted on top of each other in a transparent red color, while the “averaged” periodogram is plotted as a solid dark red line. The LS periodogram of the target star is plotted as a solid black line. The averaged LS periodogram is then subtracted from the LS periodogram of the target star and searched for the highest peak above the noise, as displayed in the middle panel of Figure 4.3. The best period is denoted by a green arrow. In the bottom panel, we plot ∆Mg0 magnitudes versus phase. A folded and binned Evryscope light curve is plotted in blue points and compared to the best-ﬁt sine in orange.

76 limit of the distribution of LS powers at each tested period. This process is illustrated in the top panel of Figure 4.3. We subtract the averaged LS periodogram from the target star periodogram to produce a “modified pre-whitened (MP) periodogram.” The MP periodogram allows the detection of high-amplitude astrophysical oscillations at periods that may also display low amplitude systematic periods while removing the low-amplitude events. For such high-amplitude signals, the height of the peak is reduced in the MP periodogram. Evryscope-detected periods within 5% of 1 d (or 1/2 d, 1/3 d, 1/4 d, 1/5 d etc) are not considered at all due to the prevalence of the day-night cycle systematic. The highest peak above the noise in the MP periodogram is selected as the best candidate period as shown in the middle panel of Figure 4.3. Candidate periods are investigated in a custom graphical user interface (GUI) by eye; the GUI is an interactive version of Figure 4.3. The light curve is folded to the period with the highest peak and visually confirmed as a sinusoid. If the highest peak is not a clear sinusoid, other large peaks above the noise are inspected in the same way. The highest peak is sometimes a harmonic of the true rotation period or even a systematic in the light curve. If a clear sinusoidal signal can be detected, that period is recorded. The light curve of the target star is folded to the best-detected period in the bottom panel of Figure 4.3. If the LS power and oscillation amplitude are small and the power spectrum is noisy or dominated by systematic periods, we record no period for that target star. The best estimate for the period of each flare star is recorded in Table I of this work.

4.2.2 Bootstrap Measurement of period uncertainty

A periodogram bootstrap may serve two closely-related purposes: (1) to measure the false-alarm probability of a signal, and (2) to measure the uncertainty of a given period on the data [237]. We use TESS light curves to assess (1), and use Evryscope light curves and our bootstrap routine to assess (2). While one might initially assume a full test period range of 0.1 to 100 d would best sample the bootstrap uncertainties, a narrower window centered

77 on the detected period provides more meaningful information. A narrow window reduces the effects of aliasing. A 0.1 to 100 d window would result in unphysically-large deviations in the average maximum-power position in the bootstrapped periodograms. The day-night cycle, the lunar cycle, seasonal changes, and instrumental effects will also each imprint on the full periodogram as a convolution of periods [237]. Therefore, we choose a window size of 20%, exceeding the FWHM of the detected LS peak. Phase-folding the Evryscope light curve at periods outside the FWHM demonstrates a highly-degraded signal compared to phase-folding at periods within the LS peak. Uncertainty to each Evryscope-detected period is computed with 1000 trials of a custom bootstrap algorithm, which randomly drops 10% of the light curve before re-computing the LS periodogram. This method assumes a light curve that is much longer than the oscillation period, and tests if some small section of that light curve may unduly bias the recovered period. In each trial, periodograms are computed with 10,000 steps in frequency within 25% of the period previously confirmed by eye (chosen to allow up to 20% error as described below). Periods are tested as follows:

1. The bootstrap begins by searching in the periodogram for candidate peaks within 10% of the period previously conﬁrmed by eye. We start with 10% of the period to avoid other large peaks in the periodogram that survived the 25% cut.

2. If the resulting periods do not converge to better than 10% (e.g. there are other large peaks in this period range causing the histogram of bootstrapped periods to not be pseudo-normally distributed), the period range of candidate peaks is then extended and the bootstrap is re-run. This time, candidate peaks within 20% of the period previously conﬁrmed by eye are allowed.

3. If the resulting periods do not converge to better than 20%, the bootstrap fails. In this case, the uncertainty to the period is reported to be the FWHM of the LS peak and no further iterations are attempted for that target. Uncertainties larger than 20% are

78 rare (2% of the sample) and generally occur only if the period selected by eye that best phases up the light curve is not the highest peak in the periodogram test window.

4. The final bootstrapped period error is chosen to be the standard deviation of the histogram of bootstrapped values. We ensure at least 250 of the 1000 MC trial values are used in the standard deviation calculation and did not center on another large peak within 25% of the input period. We also allow for small systematic offsets between the input period (measured by the MP-LS process and not the bootstrap LS) and the distribution of bootstrapped values. When the offset between the input MP-LS period and the median of the bootstrapped period histogram is larger than the standard deviation of the histogram, we increase the error to the larger of the two values. Such offsets are small (3σ-clipped median of 0.0002 d).

We inspected the bootstrap errors versus the amplitude of rotation to ensure that as amplitudes increase above the photometric noise, the bootstrap errors decrease. This trend loosely holds from amplitudes of 0.008 up to 0.05 mag in g0. Above 0.05 mag in g0 the trend of bootstrap error versus amplitude of rotation becomes less clear. Visual conﬁrmation of period errors indicates the smallest errors (<10−4 d) may be under-estimated.

4.2.3 Period validation using TESS light curves

As a further validation step, we fold the corresponding 2-minute cadence TESS light curve to our detected period. If we observe no coherent behavior at that period in TESS data, we record that information. We note that a lack of TESS periodicity at our detected period does not mean our period is not astrophysical. Starspots evolve over time [238], may display a change in contrast against the star at different wavelengths [62], and may even be altered by large flares [167]. Many TESS SAP flux light curves demonstrate long term trends; to prevent these trends from altering TESS amplitudes of rotation, we pre-whiten the light curves at timescales longer than the Evryscope-detected periodicity. This is done by subtracting a 1D Gaussian-blurred

79 light curve with a blurring kernel equal to the rotation period. We record whether the TESS light curve folds exactly to the Evryscope period. If so, we also record the amplitude of the oscillation in TESS-magnitude and normalized flux for comparison to the Evryscope values. The range of folded TESS light curves that phase to Evryscope periods is visible in Figure 4.2. While folding TESS light curves to the Evryscope period of each rotator identified by eye above, we discovered 27 of our rotation periods in the 1.25+ d range were aliases of an obvious rapid-rotator in TESS. As a result, we re-computed the LS periodogram of all Evryscope light curves down to 0.1 d. For stars with periods already detected in the original 1.25-100 d period search range, we exclude shorter periods at exact beat frequencies of the previously-detected period and 1 d. We may sometimes detect a period not evidenced in the TESS light curve or vice versa. Systematics in the TESS light curve, in the Evryscope light curve, or in both may cause difficulty in comparing the two periods. In particular, uncorrected TESS systematics in multi-sector light curves may obscure periods of slow rotators.

80 4.2.4 Detection of Evryscope periods in TESS

During inspection of the TESS light curves of Section 4.2.3, we observe 75 periods that exactly match in both surveys (shown in Figure 4.2), and 7 periods that are probably confirmed but do not fold to the exact period detected by Evryscope, possibly due to spot evolution and differential rotation. 4 of our periods appear to be simple harmonics of the fundamental TESS period, and 4 of our periods correspond exactly to the beat frequency of 1 d and the period observed in TESS (all are from the 0.1d to 3 d periodogram). Because astrophysical signals in LS periodograms are well-known to produce power at harmonic frequencies close to the true frequency (i.e. 1/2×, 2×, 1/3×, 3×)[237], we include our “harmonic” and “beat” detections as genuine detections of the stellar rotation in both surveys. For stars labeled “harmonic” or “beat,” we record the unambiguous TESS period. Finally, 3 of our periods are too long to confirm in the TESS light curve. 29 of our periods do not correspond to any period in the TESS light curve.

4.2.5 TESS vs. Evryscope sinusoidal amplitudes

While folding the high-cadence TESS light curves of each rotator to the Evryscope period as described in Section 4.2, we noticed the Evryscope sinusoidal amplitudes are consistently greater than or equal to those in TESS. We compute the normalized fractional ﬂux diﬀerence between Evryscope and TESS amplitudes for the TESS periods of our 75 exact period-matches, 4 harmonic periods, and 4 harmonic-beat periods from Section 4.3.3.1, for

+0.03 a median flux difference and 1σ spread in the distribution of flux difference of 0.04−0.02. It is likely this is an effect of the differing blackbody temperatures of the spot and star. We hypothesized the rotators with the greatest amplitude differences should correlate with stellar effective temperature and therefore color. We checked the correlation visually and observed a weak trend toward larger differences in amplitude at lower masses; we also performed a two-sample Anderson-Darling test on the flux amplitude differences of early and late rotators,

81 and found some correlation (p=0.01, see Section 4.3.3.1 for more information on the test statistic). To be thorough, we also hypothesized the 4X larger TESS pixels capture more flux from companion stars, diluting the amplitude. We checked the number of Gaia DR2 sources for each star, and found the larger flux differences in amplitude do not correlate with more companion stars (p≈1). We find between 1 and 17 Gaia DR2 sources per 21” aperture; 94% of our 83 targets have fewer than four nearby sources and display no trend with a difference in flux amplitude. Although not statistically significant, the remaining 6% of the targets with four or more sources do display flux amplitude differences. We do not see similar amplitude offsets between Evryscope and TESS for other targets (e.g. [239, 240]) as might be expected if our detection were due to systematics, further supporting our detection of increased contrast with spots at later types.

4.3 Discussion: Stellar Activity and Rotation Relations

In this section, we characterize stellar rotation, starspot coverage, and ﬂare energy in the [143] ﬂare star sample.

4.3.1 Stellar rotation periods

We discover 122 stellar rotation periods out of 284 ﬂare stars. We detect rotation periods

+31 ranging from 0.3487 to 104d, a median and 1σ spread of 6.3 −5 d. Phase-folded light curves of a random subset of our detected rotation periods are displayed in Figure 4.1. M-dwarf periods of ∼7 d are relatively rare in MEarth data, suggesting our sample contains many young stars and stellar binaries. Periods of ∼7 d occur when stars are either young and still activity spinning down, or else when they are members of a multiple system that has slowed spin-down [241]. Indeed, several stars in the sample are well-known ﬂaring binaries (e.g. GJ 841 A, CC Eridani and V* V1311 Ori, all BY Dra systems [242, 243]). One way to determine if rotators like these BY Dra are in multiple systems is by multiple periods imprinted on the

82 Figure 4.4: Binarity is observable via multiple rotation periods for the ﬂaring BY Dra variable TIC-50745582 (V* V1311 Ori). Two Evryscope periods were detected and then validated in the TESS light curves. Top panel: The LS periodogram of the TESS light curve and modiﬁed pre-whitened LS periodogram of the Evryscope light curve are compared, and the best peaks with Prot <1.25 d and Prot >1.25 d are selected, respectively. Bottom panels: The TESS light curve is folded to each period, demonstrating clear rotational modulation.

light curve. Of all our Evryscope rotators, only the BY Dra system V* V1311 Ori clearly showed rotation in both components, as displayed in Figure 4.4. Because the Evryscope light curves are high-cadence and multi-year, many of our detected periods are good to 2-5 signiﬁcant ﬁgures, with better uncertainties for short periods than

+0.57 long periods. The period uncertainties have a median and 1σ range of 0.0061−0.0058 days. We detect all periods at signiﬁcance levels greater than 5σ, with greater signiﬁcance for shorter

+13 periods. The median signiﬁcance of detection and its 1σ range is 18.5 −9 .

83 4.3.2 Spot Coverage and Maximum Flare Energies

Starspots are easily observed on low-mass stars because the amount of light blocked by spots creates a high-amplitude signal [69]. Starspot coverage fractions are inferred from either the amplitude of rotational modulation in the light curve [7, 11, 62, 234], or comparing TiO bands in stellar spectra with simulated template spectra of the spot and star [70, 244, 245]. We search for spots using rotational modulation. Not all spotted stars will produce photometric rotation periods; rotational variation from spots is suppressed for spots at the poles and stars with spots evenly distributed across the stellar surface [70]. We measure a distribution of sinusoidal amplitudes ranging from 0.008 to 0.216 g0 magnitudes, with a median amplitude and 1σ spread in the distribution of amplitudes of

+0.026 0 0.033−0.014 g magnitudes, as shown in the left panel of Figure 4.5. We convert amplitude of rotation in g0 magnitudes to the normalized peak-to-trough flux amplitude ∆F/F, which may be understood as the fraction of starlight blocked by spots (∆F/F is mathematically equivalent to fractional-flux). The median flux amplitude and 1σ spread in the distribution

+0.05 of normalized ﬂux amplitudes is 0.06−0.03 as shown in the middle panel of Figure 4.5. The fraction of starlight blocked by spots ∆F/F is not equivalent to the hemispheri-

cal starspot coverage fraction ASpot/AStar. This is because starspot area depends on the temperature of the star and the temperature of the starspots as given in Equation 4.2. We estimate spot coverage fractions ranging from 0.03 up to nearly an entire stellar hemisphere; the median spot coverage fraction and 1σ spread in the distribution of spot coverage fractions

+0.12 is 0.13−0.06. We note that coverage fractions depend on the assumed spot temperature, stellar radius, and fraction of bolometric spot ﬂux observed in g0, which may each be in excess of 10% error; we urge readers to exercise caution in the use of these values where precision better than 50% is required. Energy stored in starspots may be released in the form of stellar ﬂares. The area of the

smallest spot that could have produced a ﬂare of bolometric energy Eﬂare is given by [7, 62]

84 50 60 50

50 40 40 40 30 30 30

20 20 # flare stars # flare stars # flare stars 20

10 10 10

0 0 0 0.00 0.05 0.10 0.15 0.20 0.0 0.1 0.2 0.3 0.4 0.0 0.2 0.4 0.6 0.8 1.0 Amplitude of rotation [g0-mag] Amplitude of rotation [ F/F] Spot coverage fraction [ASpot/AStar]

Figure 4.5: Left panel: Histogram of the amplitudes of rotation detected by Evryscope, +0.026 0 with a median amplitude and 1σ spread in the distribution of amplitudes of 0.033−0.014 g magnitudes. Middle panel: Same as left panel, except in normalized flux units ∆F/F, or the fraction of light blocked by spots, with a median amplitude and 1σ spread in the distribution +0.05 of normalized flux amplitudes of 0.06−0.03. Right panel: Histogram of the distribution in hemispherical starspot coverage fraction, with a median spot coverage fraction and 1σ spread 0.12 in the distribution of spot coverage fraction of 0.13−0.06. as: B2 E = A3/2 (4.3) flare 8π Spot

B is the surface magnetic ﬁeld strength, and ASpot is the smallest spot group area that could

release a flare of energy Eflare. We note that true spot sizes could be at least an order of magnitude larger than those given by this simplified model. We plot the largest flares we observed from each star as a function of the estimated starspot coverage of that star in Figure 4.6. We then overlay lines of minimum starspot coverage capable of generating the maximum-observed flare energy from each star, for representative magnetic field strengths of 0.5 kG, 1 kG, and 2 kG as shown in Figure 4.6. Because the true spot coverage ought to lie to the right of this line (i.e. greater spot coverage), we may constrain the minimum field strength B associated with our starpots (in certain line-of-sight spot geometries, a smaller field could be several kG larger). We find most stars in our sample lie to the right of the 0.5 kG field line, and all stars lie to the right of the 2 kG line. We therefore find a minimum magnetic field of 0.5 kG and a largest value for the minimum field strength of several kG, in broad agreement with previous measurements of the magnetic strengths of cool stars ([71] and references therein). Interestingly, these field strengths are smaller than but comparable to those measured for

85 0.7 1036

0.6

1035

0.5 ] M [

B=2kG s a

0.4 M 1034

B=1kG 0.3 Largest flare energy observed [erg]

1033 B=1/2kG 0.2 0.001 0.01 0.1 1.0 Measured spot coverage [ASpot/AStar]

Figure 4.6: Measured starspot coverage of each rotating star versus the maximum-observed flare energy from that star. Scaling relations for the minimum spot coverage needed to generate flares at the observed energies are overlaid for representative field strengths of 0.5 kG, 1 kG, and 2 kG. For each scaling relation for a particular field strength, the measured spot coverage should lie to the right of that line. We find most of our rotators lie to the right of the 0.5 kG field line, and all lie to the right of the 2 kG line, placing upper limits on the minimum field strength of our sample. We also color-code each data point representing a rotating flare star by its stellar mass, finding a gradient between early and mid M-dwarf stars in the plane of stellar mass and flare energy. rotating solar-type stars by [62]. We also note that Figure 4.6 shows a gradient in stellar mass across the plane of spot coverage versus maximum flare energy, implying late-type stars may sometimes have a smaller minimum field strength than earlier-type stars.

4.3.3 Flaring and stellar rotation

[23] and [24] explore an increase in stellar activity as a function of rotation until the increase in activity shows saturation at periods shorter than ∼10 days. For those stars in our sample with recovered ﬂares, we compare the amplitudes, energies and frequencies of their ﬂares as a function of stellar rotation.

4.3.3.1 Statistics of fast and slow rotators

We find an apparent increase in flare energy, amplitude, and superflare occurrence at short rotation periods, in general agreement with earlier results (e.g. [11, 20, 28]). However,

86 ] r a t S M* < 0.33M 1036 70 A 0.4 / t M > 0.33M o *

p 60 S 1 A [

0.3

r 50

n 35 10 y

o i s t 40 e c r

a 0.2 a r l f f

30 r e 34 e g

10 p a 0.1 u 20 r S e

v 10 o c

t 0.0 1033 o 0 p S 100 101 Largest flare energy observed [erg] 100 101 102 100 101 102

PRot [d] PRot [d] PRot [d] ] r a t 4 4 S 36 70

0 4 10 A 0.4 . . / t 0 0 o

p 60 = = S o o 1 A R R [

0.3

r 50

n 35 10 y

o i s t 40 e c r

a 0.2 a r l f f

30 r e 34 e g

10 p a 0.1 u 20 r S e

v 10 o c

t 0.0 1033 o 0 p S 10 2 10 1 100 Largest flare energy observed [erg] 10 2 10 1 100 10 2 10 1 100 Rossby number Rossby number Rossby number

Figure 4.7: Stellar activity observables as functions of stellar rotation and Rossby number. All points have periods confirmed in both TESS and Evryscope. Red points have stellar masses M∗ < 0.33 M , while purple points have stellar masses 0.33 < M∗ < 0.7 M . Top panels: The starspot coverage fraction, largest observed flare energy from each star, and superflare rate versus rotation period. All three types of activity decrease at longer rotation periods, as described by Table 4.1 and Table 4.2. To guide the eye, a grey line is overlaid on the decrease in stellar activity with period. The superflare rate changes significantly between periods of roughly 3 to 11 d. Bottom panels: The starspot coverage fraction, largest observed flare energy from each star, and superflare rate versus Rossby number. Vertical red dashed lines indicate the boundaries between the Rossby numbers of fast, intermediate, slow rotators. All three types of activity decrease at longer rotation periods, as described by Table 4.1 and Table 4.2. However, the superflare rates of intermediate rotators show an apparent increase in flaring, if extremely-active stars (up arrows) are excluded. If real, this tentative evidence for changing surface magnetic field geometry during spin down may correlate with the increased activity of [30].

87 some previous superflare surveys do not find any correlation of flare energy with rotation period, e.g. [11, 119]. [11] suggest the maximum energy of a flare is thought to be dependent on the stored energy of a local active region, which does not necessarily depend on the stellar rotation. [62] report the [11] result is a result of giant contamination. More recently, [20] do find that flare strength decreases with increasing stellar rotation for all slowly-rotating cool stars. We note [119] studied short-period rotators and [11] studied solar-type superflare stars instead of cool stars. The relative difficulty in recovering long rotation periods means we may be sampling all activity levels at short periods and only the most common activity at long periods. This bias means that we must exercise caution in interpreting our results. To correct for differences in stellar activity observables as functions of the rotation period, we group all recovered flare stars into <10 day (Ro <0.2) and >10 day (Ro >0.2) period bins of short-period and long-period rotators, respectively. We select these bins to directly compare our results to [23] and [24] who observed a break in rotation-activity power laws at this period. Looking ahead to Section 4.3.3.2, we include the approximate Rossby number of a 10 d M-dwarf rotator because [23] find a break in the power law describing M-dwarf activity versus period at 10 d but [24] find the break at Ro=0.2. We hypothesize our short-period and long-period rotators are drawn from the same underlying distribution of superflare rates. Because we sample more short-period rotators than long-period rotators, we construct our random distribution of superflare rates based upon the observed distribution of short-period rotators. We perform a Monte Carlo test of 10,000 trials with the goal of distinguishing if 79 short-period and 43 long-period rotators from the same simulated population can differ as much as our actual rotators do. In each trial, we simulate the same numbers of short-period rotators and long-period rotators as we actually observed, and test how often these simulated rotators differ as much as our observed rotators do by using the SciPy [246] implementation of the two-sample Anderson-Darling (A-D) test [247].

88 All three stellar activity observables easily distinguish between our actual short-period and long-period rotators, with large A-D statistics and small p-values. This suggests they do not come from the same population. The MC trials support this interpretation: the A-D statistic and p-value of simulated rotators randomly drawn from the same underlying population do not distinguish between short and long-periods. Across 10,000 trials, the minimum p-values are 0.07, 0.06 and 0.04 and maximum A-D statistic values are 1.55, 1.71 and 2.33 for the superflare rate, maximum flare energy, and starspot coverage respectively. Since the simulated rotators cannot reproduce the difference in the activity of our actual rotators, we conclude the difference between our actual short-period and long-period rotators is unlikely to be due to sample bias. These results are shown in Table 4.1. We note running the same statistics excluding the 29 periods that do not correlate with TESS reduces the significance of the tests, although the activity-versus-period trends are still visible when only including periods confirmed in both surveys. See the top panel of Figure 4.7.

4.3.3.2 Quantifying rotation with the Rossby number

In addition to the rotation period, stellar rotation is also quantiﬁed by the Rossby number:

Ro=PRot/τConv, where τConv is the convective turnover timescale in the star. Ro gives the relative strength of Coriolis forces and inertial forces in the star (i.e. when the Rossby number is small, the star rotates quickly, and Coriolis forces have the greatest impact upon the surface magnetic ﬁeld). Convective turnover time is calculated using Equation 11 of [248].

This equation is valid in the mass range 0.09 < MStar/M < 1.36. Because the convection turnover time depends upon the stellar mass, inaccuracy in the determination of the mass used in calculating convection turnover timescale will be propagated to the Rossby number.

In the cool star mass range, uncertainty in the stellar mass of 0.1M can propagate to errors in the Rossby number of up to ∼0.15 dex.

We ﬁnd 30 (24.6%) of our ﬂare stars to be fast rotators (Ro <0.04), 59 (48.4%) to be

intermediate-period rotators (0.04

89 Table 4.1: Activity of short period (PRot <10 d) vs. long period (PRot >10 d) rotators

Activity observable pobs A-Dobs Fraction ptrials Fraction A-Dtrials trials min trials max psim < pobs A-Dsim >A-Dobs

Superﬂare rate 3.2×10−5 13.12 <10−4 0.07 <10−4 1.55 Largest ﬂ. energy 1.0×10−5 17.52 <10−4 0.06 <10−4 1.71 Spot coverage 0.01 3.74 <10−4 0.04 <10−4 2.33

Notes. We perform A-D tests on the stellar activity of our 79 short-period (PRot <10 d) and 43 long-period (PRot >10 d) rotators to distinguish if they arise from two distinct populations. We observe higher superflare rates, maximum flare energies, and starspot coverage from short-period rotators than long-period ones. While short-period and long-period rotators have distinct activity levels to significant p-values, we perform MC tests of 10K trials each to ensure our results are not entirely dependent on the larger number of short-period rotators. In each trial, we simulate the distribution of short-period rotators using acceptance-rejection sampling and draw the number of short-period and long period rotators we observed. We find that the fraction of the trials in which the A-D statistic and p-value of our simulated rotators more strongly distinguishes between short and long-periods than do the A-D statistic and p-value of our actual rotators is essentially zero. Across 10K trials, the minimum p-values of the simulated rotators are 0.07, 0.06 and 0.04 and the largest A-D statistic values are 1.55, 1.71 and 2.33 for the superflare rate, maximum flare energy, and starspot coverage respectively. The p-values of the observed rotators are more than an order of magnitude better (with the exception of spot coverage), and the A-D statistic values of the observed rotators are at least 60% higher.

90 Table 4.2: Activity of fast (Ro <0.04), intermediate (0.040.44) rotators

Activity observable Fast vs. Fast vs. Intermed. Intermed. intermed. pobs intermed. vs. slow pobs vs. slow A-Dobs A-Dobs

Superﬂare rate 0.22 0.43 2.4×10−5 13.87 Largest ﬂ. energy 0.66 -0.61 0.01 3.36 Spot coverage 0.28 0.21 0.003 5.05

Notes. We perform A-D tests on the stellar activity observables of our 30 fast rotators (Ro <0.04), 59 intermediate-period rotators (0.040.44) to distinguish if they arise from distinct populations. We do not observe significant A-D statistic values or p-values between the stellar activity of our fast and intermediate rotators. We do observe a significant difference between the superflare rate and starspot coverage of the intermediate and slow rotators. The largest flare energies of the intermediate and slow rotators do not demonstrate significant differences, likely due to the small numbers of flare stars observed since the flares in Table 4.1 do display a difference. We note that we do not conclusively confirm the higher activity of intermediate rotators detected in MEarth light curves by [30]. We believe this to be a result of our sample size and urge future work with larger samples of cool stars.

91 the surface magnetic field during spin-down, and 33 (27.0%) to be slow rotators (Ro >0.44). We define fast, intermediate, and slow rotators this way to be consistent with the convention of [30]. In Figure 4.8, we explore the stellar mass and Rossby number as functions of the spot coverage, maximum flare energy observed per star, and the superflare rate. We find our flare star sample explores the period-gap reported in earlier works (e.g. [72]).

92 4.3.3.3 Flare stars in the mass-Rossby plane

We compare our rotators against rotators from other surveys. We plot low-mass and long-period rotators from the MEarth survey [72], and early M-dwarf to late K-dwarf rotators from the KELT survey [66]. We convert the stellar effective temperatures from [66] to stellar masses using the relations given in Table 5 in the Appendix of [204]. We find that Evryscope flare stars occupy a similar parameter-space in the mass-rotation plane as these surveys. However, our sample does not reach masses as low as some MEarth targets. What is unique about our sample compared to these MEarth and KELT targets is that our sample is selected on the basis of flaring, allowing us to probe changes in flaring in the mass-rotation plane. We note the lack of fast rotators compared to intermediate rotators. We observe twice as many intermediate rotators as fast rotators. We check this lack is not a result of unexpected

large errors in calculating Ro. Because our typical uncertainty in stellar mass is ∼0.1-0.2M (i.e. a few spectral sub-types) can lead to errors in the Rossby number of up to 0.2-0.3 dex, our uncertainties are unlikely to account for the nearly order-of-magnitude diﬀerence necessary to move data-points between the the intermediate and fast rotator regime (visible

as the bottom gray sequence below Ro=0.04 in Figure 4.8). We hypothesize that selecting rotators on the basis of a high flare rate is likely the cause of the high number of intermediate rotators. It is possible selection effects are present in Evryscope periodograms, suppressing the detection rates of fast rotation periods. Ruling out this possibility will require statistical analysis on a larger sample of Evryscope rotators that are not selected on the basis of flaring. Low-mass stars comprise the vast majority of fast rotators and therefore most of the fast rotators that have high superflare rates as shown in Figure 4.7 and Figure 4.8. In Figure 4.7, we split our rotation-activity plots into low mass and high mass groups to determine if rotation-versus-activity changes across the fully-convective boundary. [30]’s sample of flaring

MEarth rotators are all M∗ < 0.33 M , motivating our choice of boundary.

93 4.3.3.4 Inconclusive increased activity of intermediate rotators

We divide up all 122 rotating flare stars into fast, intermediate, and slow rotators and test if the stellar activity of the intermediate rotators is increased compared to the stellar activity of the fast and slow rotators. We perform 2-sample A-D tests as described in Section 4.3.3.1 separately for the starspot coverage, maximum flare energy, and the superflare rate. We limit our hypothesis testing to three observables to avoid searching for random correlations. We choose observables that probe a broad range of stellar activity: a flare rate, a flare size, and the extensiveness of the active regions that emit flares. For each observable, we test whether the fast and intermediate rotators come from the same population, and we test whether the intermediate and slow rotators come from the same population. We observe a general decrease in activity with decreasing rotation, in agreement with Table 4.1 and earlier studies (e.g. [20, 21, 24]). However, we do not statistically confirm the increased activity of intermediate rotators reported by [30]. This is likely due to the small number of flare stars we observe; we urge more extensive studies of rotating flare stars be made. These results are displayed in Table 4.2. We plot the stellar activity observables versus period and Rossby number in Figure 4.7 to verify the statistical results by visual inspection. While the statistical tests are performed on all 122 stars, we plot here only those stars with periods observed in both Evryscope and TESS. Although this cut removes some periods longer than the TESS observing window, it enables a simpler visual inspection of possible trends between the fast and intermediate rotator groups. We overlay grey lines indicating the trends in maximum activity versus rotation and search for excursions above these trend lines. There appear to be two groups of fast rotators, with one group showing lower superflare rates and the other group showing very high superflare rates. There is only one group of intermediate rotators, but this single group has a higher flare rate than the low activity group of fast rotators. It is possible the two groups of fast rotators evolve with age into the single group of intermediate rotators.

94 Our M∗ < 0.33 M stars include both high and low activity groups of fast rotators and display the same patterns at longer periods as earlier-type stars. If a difference in mass between this work and [30] explained their non-detection of the high-activity fast rotators, we would expect the high activity fast rotators to be earlier-type stars. However, Figure 4.8(c) shows the high-activity fast rotators are mostly late-type stars. We urge further work with a larger sample of rotators and flare stars. The spot coverage trend has high noise compared to the flare rate trend in Figure 4.7 and Figure 4.8(a). The maximum energies display a decrease with increasing period in Figure 4.7 and a diagonal gradient in the mass-Rossby plane of Figure 4.8(b).

95 0.30

100 0.25 Ro=0.44

0.20 10 1

Ro=0.04 0.15

Rossby Number 10 2

0.10 Spot coverage fraction

0.05 10 3

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Mass [M ]

100 35

10 1 34

Rossby Number 10 2 33

32 10 3 Largest flare energy observed [log erg]

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Mass [M ]

35 100 30 ] 1

25 r y [

1 10 s e

20 r a l f r e

15 p u

Rossby Number 2 10 S 10 Grey points are cool rotators from other surveys 5 10 3 0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Mass [M ] Figure 4.8: Evryscope flare stars in the mass-Rossby plane. Flare stars are scaled in color by (top panel to bottom) the spot coverage, maximum flare energy observed per star, and superflare rate, respectively. MEarth and KELT rotators not selected for flaring are plotted in grey for reference. Evryscope flare stars explore the spin down transition region from fast to slow rotation where [30] report increased flaring.

96 CHAPTER 5: TEMPERATURE EVOLUTION AND HABITABILTY IMPACTS OF DOZENS OF SUPERFLARES OBSERVED SIMULTANE- OUSLY BY EVRYSCOPE AND TESS

Superflares may provide the dominant source of biologically-relevant UV radiation to rocky habitable-zone M-dwarf planets (M-Earths), altering planetary atmospheres and conditions for surface life. The combined line and continuum flare emission has usually been approximated by a 9000 K blackbody. If superflares are hotter, then the UV emission may be 10× higher than predicted from the optical. However, it is unknown for how long M-dwarf superflares reach temperatures above 9000 K. Only a handful of M-dwarf superflares have been recorded with multi-wavelength high-cadence observations. We double the total number of events in the literature using simultaneous Evryscope and TESS observations to provide the first systematic exploration of the temperature evolution of M-dwarf superflares. We also increase the number of superflaring M-dwarfs with published time-resolved blackbody evolution by ∼10×. We measure temperatures at 2 min cadence for 42 superflares from 27 K5-M5 dwarfs. We find superflare peak temperatures (defined as the mean of temperatures corresponding to flare FWHM) increase with flare energy and impulse. We find the amount of time flares emit at temperatures above 14,000 K depends on energy. We discover 43% of the flares emit above 14,000 K, 23% emit above 20,000 K and 5% emit above 30,000 K. The largest and hottest flare briefly reached 42,000 K. Some do not reach 14,000 K. During superflares, we estimate M-Earths orbiting <200 Myr stars typically receive a top-of-atmosphere UV-C flux of ∼120 W m−2 and up to 103 W m−2, 100-1000× the time-averaged XUV flux from Proxima Cen1.

1Content from this chapter previously appeared in Howard et al. 2020, ApJ 902, 115. For this project, I designed and carried out the ﬂare temperatures survey in its entirety. I wrote the paper. Nicholas Law both advised the project and suggested small modiﬁcations to the science done.

97 5.1 Photometry

We discover ﬂares in photometry from TESS and Evryscope.

5.1.1 Evryscope observations

Evryscope-South is located at Cerro Tololo Inter-American Observatory in Chile, and Evryscope-North is located at Mount Laguna Observatory in California, USA. Each Evryscope is an all sky array of small telescopes that continuously and simultaneously images 8150 square degrees and 18,400 square degrees in total each night at a resolution of 13” pixel−1 and down to an airmass of two. Evryscope-South observes at two-minute cadence in g 0 [171] for ∼6 hr each night and has a typical dark-sky limiting magnitude of g 0=16 [172]. The system accomplishes this coverage by employing a “ratchet” strategy that tracks the sky for 2 hours before ratcheting back into the initial position and continuing observations. Evryscope images are processed using the Evryscope Fast Transient Engine (EFTE; [173]). EFTE performs simple aperture photometry at the catalog location of each source. The resulting magnitudes are calibrated to the ATLAS All-Sky Stellar Reference Catalog [249] using a smoothly interpolated zero-point across each individual camera’s ﬁeld of view.

5.1.2 TESS observations

The TESS mission is looking for transiting exoplanets across the entire sky, split into 26 sectors. TESS observes each sector continuously with four 10.5 cm optical telescopes in a red (600-1000 nm) bandpass for 28 days at 21” pixel−1. Calibrated, short-cadence TESS light curves of each ﬂare star were downloaded from MAST2. We selected Simple Aperture Photometry (SAP) light curves rather than Pre-search Data Conditioning (PDC) ones to avoid altering the impulsive ﬂare structure.

2https://mast.stsci.edu

98 Figure 5.1: Simultaneous flare events observed at 2 min cadence by Evryscope (blue) and TESS (red) for multi-wavelength coverage. Multi-wavelength, high-cadence observations of superflares are necessary to understand their influence on the evolution of planet atmospheres; however such observations have been previously obtained for only a handful of superflares from a handful of highly-active stars such as AD Leo. Our sample of 44 large flares expands our knowledge to a diverse population of cool dwarfs. Flare fits are shown as grey lines. UT identifiers are approximated from barycentric TESS epochs and may differ by up to 10 min from the exact flare peak time.

99 5.1.3 The EvryFlare stellar sample

The EvryFlare survey is an ongoing search for stellar activity from all cool stars observed by the Evryscopes across the accessible sky. We select 306 K5-M6 ﬂare stars observed simultaneously by Evryscope and TESS during Cycle 1. The EvryFlare targets are some

+27 0 +1.4 of the nearest (23−12 pc) and brightest (g =12.3−1.0) flare stars. A number of flare stars in our sample are also planet-search targets, with 3 targets (Proxima Cen, LTT 1445, and the WD+M4 binary RR Cae (AB)) already known to host planets; constraining their space weather will benefit future atmospheric characterization [143]. We obtain spectral types of our late K and M-dwarf stars from SIMBAD [250] if possible and then from [31]. SIMBAD types were used for 80% of our flares, and the analysis from [31] incorporating multi-band photometry and stellar distances was used for the other 20%. We use SIMBAD if available because nearly all (97%) of the SIMBAD entries of flares in our sample had types classified by spectra, and spectral absorption lines in M-dwarf reconnaissance spectra are a reliable way to identify sub-types in our mass range. Most of the SIMBAD types were identified by several spectroscopic surveys (e.g. [251–257]). The stellar mass is estimated from the spectral type using [204]. Most stellar rotation periods are from [31]; missing periods are supplemented by strong rotational modulation seen in the TESS light curves.

100 5.2 Identifying simultaneous TESS and Evryscope ﬂares

We identify flares in the TESS light curves, then search the Evryscope light curves for simultaneous events. We pre-whiten the TESS light curves of sinusoidal variability and systematics before searching for flares. We then search each TESS light curve for large flares by selecting photometric brightening events 5σ above the local photometric noise. Flares in TESS smaller than 5σ above the noise are not considered since they will likely be too noisy for high-signal detections in the lower-precision Evryscope light curves. We remove any TESS flare candidates that occur between 9:00 and 23:00 UT. We vet each remaining candidate in the TESS light curves by eye, removing common TESS systematics and marginal detections. We consider multiple flare peaks within the start and stop time to be a single event. In sum, we find 806 TESS flares that occur during the night from 163 K5-M5 stars. We search the Evryscope database at the coordinates and time of each flare event and produce light curves where we have data. We visually inspect each Evryscope light curve at the time of the TESS flare, looking for epochs exhibiting rapid-rise, slow-decay profiles that exceed the local noise. Because low-signal events do not produce useful data for temperature measurement, we only include flares large enough to be clearly visible by eye and that produce a well-defined flux increase during the rapid phase. We convert the MJD time stamps of the Evryscope light curves into barycentric MJD (BMJD). Because TESS time stamps are recorded in the middle of each exposure while Evryscope stamps are recorded at the beginning, we must add 1 min to correct offsets between the surveys. Next, we remove any flares with peak amplitudes comparable to the noise in the Evryscope light curve ensuring clear signals for flare temperature measurement. To place both surveys on an identical time axis, linear interpolation of the Evryscope epochs, fluxes, and uncertainties is performed, and subsequently evaluated at the TESS timestamps. Because impulsive flare heating features in optical light curves may evolve at timescales as short as ∼10 s [258], it would be best to observe each flare at ∼10 s cadence with TESS. At 2 min cadence however, we may either (1) directly compare flux values at the

101 Figure 5.2: Evryscope light curves of several of the largest flares are shown in light blue. In dark blue, the epochs are interpolated to the timestamps of the TESS epochs to provide simultaneous flux estimates. While the peak epoch of each flare is under-estimated at 2 min cadence by the linear interpolation process, it is necessary to sync up the physics occurring in each light curve: the two closest epochs in Evryscope and TESS can occur up to 1 min apart, but impulsive flare heating events may evolve at timescales much faster than 1 min. Ultimately, the new TESS 20 s cadence mode will alleviate the need for this technique.

Evryscope and TESS epochs with the smallest separation in time, which assumes the physics captured by timestamps up to 1 min apart is still simultaneous, or (2) estimate simultaneous behavior using linear interpolation for timestamps within each two minute window. Option (1) biases instantaneous temperatures since different impulsive flare heating events may be recorded even 1 minute apart. We choose option (2) since it attempts to minimize the time lag between the physics captured in each light curve. This process does not significantly alter the profile of most superflares, which typically last for tens of minutes to hours; it may under-represent the rapidly-changing flux near the flare peak resulting in a lower temperature. The drop in flux depends on how far away the Evryscope and TESS timestamps are from each other. Essentially no under-estimation of the peak occurs when the timestamps are within seconds of one another; ∼25% percent drops are possible when timestamps differ by up to 1 min as shown in Figure 5.2. The peaks of the largest flares (i.e. those that increase

+18 the stellar brightness by a factor of 2) are under-estimated by a median and 1σ drop of 8 −8 %.

+14 The peaks of the smaller ﬂares are under-estimated by a median and 1σ drop of 5 −4 %.

102 5.3 Flare energetics

We measure the quiescent luminosity of each flare star in erg s−1 for the g0 and TESS bandpasses, respectively. The quiescent luminosity is computed using the method of [44, 143], which relies upon the g0=0 to flux calibration [207], the T =0 to flux calibration [259], the stellar distance, the g0 magnitude, and the T magnitude of the star. Stellar distances and uncertainties are primarily obtained from the TESS Input Catalog version 8 (TIC; [166, 260]). g0 magnitudes and uncertainties are primarily obtained from the Asteroid Terrestrial-impact Last Alert System (ATLAS) catalog [249]. TESS magnitudes and uncertainties are obtained from the TIC. Errors in distance and apparent magnitude in each band-pass are propagated to the quiescent luminosity. The quiescent luminosity of 8 stars found in stellar binaries is corrected in both Evryscope and TESS data for blending due to the brightest two stars within 21” of each target pixel, preventing significant under-estimates of the flare energy in most cases. Flare start and stop times are determined from the TESS light curves as the initial and final epochs near the flare peak that exceed 1σ above the photometric noise. TESS start and stop times are subsequently adjusted by eye to include the flare tail. Start and stop times are used only for the purposes of providing limits of integration, so we do not worry about the 1 min before the rapid rise is timestamped at the middle of the 2 min exposure- this flux is included in the integration and not lost. The fractional flux is calculated as described

|F −F0| in [74]. Fractional flux is computed as ∆F/F= where F0 is the out-of-flare flux and F0

is determined from the local median. The uncertainty in F0 is determined by a bootstrap analysis of the median out-of-flare flux within a few hours of each event. The equivalent duration (ED) for the entire duration of each flare is calculated as described in [74], between upper and lower limits of the flare start and stop times. The energies computed for each flare within the FWHM of the flare peak are computed between the start and stop times at which the flare exceeds half its peak amplitude. The quiescent luminosity in each bandpass is

103 0.6 TESS bandpass 0.5

0.4

0.3

0.2 Evryscope bandpass

0.1

0.0 Fraction of total blackbody flux in band 0 10000 20000 30000 40000 50000 TEff [K]

Figure 5.3: The fraction of the total blackbody flux in the Evryscope and TESS bands is shown versus the blackbody temperature. The highest fraction of flux relative to temperature seen in the red TESS bandpass will occur for 4000 K flares, while the highest fraction of flux seen in the blue Evryscope g0 bandpass will occur at 7300 K. The two curves converge above ∼46000 K, dis-allowing temperature estimation. This plot is inspired by Figure 12 of [261].

multiplied by the ED in each bandpass to measure energy. Errors in energy are computed with 200 MC trials varying each input. We fit the [6] flare model to each flare’s light curve. Flares are often best-fit by a superposition of multiple emission events. We visually inspect each light curve and determine the number of flare peaks in each event, then fit a superposition of 1-3 flares. Flare amplitude, FWHM, and timing are all set as free parameters. TESS and Evryscope light curves of the same events are fitted separately to allow for differences between band-passes. Looking ahead to Section 5.4.1, the purpose of fitting the flare light curves with a model is to provide a second estimate of the flare temperature evolution; a smoothly-varying function reduces noise in the individual temperature measurements obtained at 2 min cadence during the flare decay. It is useful to compare both the measured temperature evolution and the model temperature evolution for each flare.

104 Figure 5.4: Methods. Top left: a 10,000 K flare blackbody compared to a 30,000 K blackbody. The Evryscope and TESS band-passes are overlaid. The UV energy of a hot flare may be under-estimated from the optical by ∼10× if the canonical temperature is assumed. Top right: The ratio of flare energies observed in the Evryscope and TESS band-passes uniquely determines the effective blackbody temperature. A blackbody of temperature TEff is separately convolved with the response functions of each instrument to produce a ratio R. The wide wavelength range of TESS offsets reduced emission at longer wavelengths, allowing sensitivity to temperatures as high as 46,000 K. Above this value, the TEff -R relation becomes asymptotic due to insufficient flux in the TESS bandpass. Bottom panels: temperatures of individual epochs are compared with temperatures from the flare models fitted to the light curves. We confirm our model temperatures broadly reproduce trends in the data for low-uncertainty flare signals (left) and use our models to understand the temperature evolution of high-uncertainty data (right).

105 Figure 5.5: The continuum temperature evolution of the sample flares identified in Figure 5.1. Temperature measurements of 44 flares were obtained at 2 min cadence, providing a statistical sample of how long M-dwarf superflares emit at high temperatures. Flare A is our largest and hottest flare, briefly peaking at 42,000 K. Formal errors are represented in black and systematic errors in grey. Temperature non-detections are displayed as hollow circles.

106 5.4 Flare temperature Methods

We define the color-temperature of a flare as the effective continuum temperature inferred from a flare’s spectral properties. We measure the color-temperature as follows:

1. We compute the radiation spectrum for a blackbody of temperature T as a function of wavelength using Planck’s law from 1 to 1500 nm, ensuring coverage of the tail of the Planck curve beyond the TESS bandpass.

2. We separately convolve the blackbody spectrum with the Evryscope and TESS response functions and integrate over all wavelengths to obtain the energy in each bandpass. The fraction of total blackbody ﬂux in each band is shown in Figure 5.3.

3. We take the ratio R of the energy observed in the Evryscope bandpass to the energy in the TESS bandpass.

4. We repeat the above process for blackbody temperatures from 500 K to 50,000 K to

create a one-to-one function R(TEﬀ ).

5. Since our data is in the form of Evryscope and TESS light curves, we estimate the values of R for each ﬂare using the values of observed ﬂare energies in the two bandpasses.

We therefore invert the function to ﬁnd TEﬀ (R).

The function TEﬀ (R) is plotted in Figure 5.4. Because both the Evryscope and TESS bandpasses are in the tail of the Planck curve, high temperatures result in very small amounts of energy in the TESS bandpass, making a temperature determination increasingly diﬃcult.

Our R-TEﬀ relationship indicates the temperature information that may be gleaned from our

bandpasses ceases above ∼46,000 K when TEff (R) becomes asymptotic. We note this method is essentially identical to that of Equation 1 of [262], except that we do not simultaneously fit the flare area since it cancels out with two colors. We reproduce

their Equation 1 here. Fλ is the flux in a given bandpass, Afl is the projected area of the flare,

2 2 deﬁned as XπR∗, X is the ﬂare area as a fraction of the projected stellar area A∗ = πR∗,

107 Figure 5.6: Scaling relationships for ﬂare energy (left) and amplitude (right) between the Evryscope and TESS bands. While Evryscope amplitudes are approximately an order of magnitude larger than the TESS amplitudes, the energies are comparable between bandpasses.

d is the stellar distance, and Bλ(Tfl) is the emission of a blackbody of temperature Tfl in a given bandpass. A B (T ) F = fl λ fl (5.1) λ d2

0 Assuming Aﬂ does not vary appreciably between the g and T bandpasses and the areas

cancel, dividing Fg0 by FT results in the following equation:

F 0 X 0 B 0 (T ) B 0 (T ) g = g g fl ≈ g fl (5.2) FT XTBT(Tfl) BT(Tfl)

This last expression is identical to the approach we used to estimate ﬂare temperatures using only the Evryscope and TESS bandpasses. Because a ﬂare’s spatial extent should be

approximately the same in either bandpass, we may solve the system of equations for Tﬂ

and Aﬂ separately. More recently, [263] make this same assumption in their Appendix A,

Equation 4 to find the same result as our Equation 5.2 if Tfl/T∗ >> 1 or T∗ ≈ 0 K. They note this approximation is valid for M-dwarfs but not G-dwarf stars. Two min cadence allows three unique measurements of the flare temperature:

108 1. We compute ﬂare temperatures epoch-by-epoch across the ﬂare light curve to understand how the temperature changes with time, demonstrated in Figure 5.5.

2. We compute the global flare temperature by integrating the flare light curve in each bandpass. The integral in each bandpass uses limits of integration equal to the start and stop times of the flare. We then divide the energy of the entire flare in the Evryscope bandpass by the energy in the TESS bandpass to obtain R. We then convert R to

TEff (R) as described above. This measures the energy associated with the average photon from the flare. The global or total flare temperature estimates the average temperature at which the flare emitted each photon. This in turn provides an estimate of the amount of UV energy associated with each photon from the flare continuum. Giving a single flare temperature representative of the entire flare duration is occasionally done when the signal to noise of the time-evolution is low (e.g. [55]).

3. We measure the peak temperature, defined as the mean temperature during the flare FWHM. We use the average temperature within the FWHM instead of the maximum temperature so that it will be useful for estimating UV space weather and the habitability conditions of surface life during superflare events. For example, [264] subject microorganisms to likely UV conditions occurring near the peak of the 2016 Proxima superflare reported in [44]. Typical fluxes during the rapid-rise and rapid-decay phases near the flare peak are usually well-described by those within the FWHM, which is why we denote this the “peak temperature.” We compute the peak temperature by randomly drawing temperatures from within the temperature uncertainties of each epoch in the flare FWHM measured in (1) and then determine the average temperature across 1000 Monte Carlo trials. The temperature near the flare peak depends on the specific flare heating conditions, so we do not assume that that the maximum (not “peak”) temperature must coincide with the epoch at the peak of the flare flux light curve. This may be too conservative of an assumption, as we find for most flares in our sample that

109 at such low cadence the peak ﬂux and maximum temperature do indeed coincide. This result has also been reported at 10 s cadence by [265].

Temperature measurements of epochs above 46,000 K are close to the asymptotic limit and depend strongly on small changes in the Evryscope energy measurements; we therefore ﬂag and remove these epochs. The uncertainty of each 2 min epoch temperature measurement is estimated by error propagation. Formal errors are estimated by propagating the uncertainties in the quiescent luminosity and in the ED measurement. Systematic errors are estimated by propagating the remaining uncertainties from Section 5.3. Uncertainty in the global ﬂare temperatures is estimated by integrating the total energy in each bandpass, then varying the ED and quiescent luminosity across 200 MC trials.

5.4.1 Fitting model temperatures

In some cases, photometric scatter during the flare obscures temperature trends from epoch to epoch. To obtain smoothly-varying model flare temperatures, we sample the energies in each bandpass from the flare fits described in Section 5.3. We test the model on both flares with strong signals and clear temperature trends and on flares with weak signals and noisy trends to ensure the model accurately reproduces the data as shown in Figure 5.4. Uncertainty in the model fits is computed by randomly drawing the ED and quiescent luminosity from their distributions of allowed values and re-fitting the model temperatures across 200 MC trials. For ∼10% of flares where the temperature evolution is unclear in the epoch-by-epoch temperature measurements but clear from the model fits, we use the model temperatures in conjunction with the epoch by epoch data to determine how long each flare emitted in excess of 14,000 to 30,000 K so long as the model largely agrees with the error bars of the single epoch temperatures.

110 Figure 5.7: In each panel, flares are color-coded as M>0.42M or M≤0.42M . In each row of panels, flare energy and impulse are plotted respectively against the peak temperature (TEff ), total TEff , amount of time a flare emits at TEff > 14,000 K, and peak flare color. Peak 0 TEff follows a power law with g energy. The mass gradient results from higher-mass stars producing higher-energy flares and a selection effect for small flares from later-type stars. A weaker correlation is visible between peak TEff and impulse. Total TEff is an integrated measurement over the entire flare. Total TEff power law relationships and mass stratification are similar to those for peak TEff , but with a lower y-intercept. The amount of time a flare emits at TEff >14,000 K describes higher-than-expected UV emission. A power law is only visible versus energy. Peak color is the difference in the normalized-flux amplitudes.

111 5.5 Flare energetics and morphology predict temperature

We find g0-band flare energies that range from 1031.2 to 1035.0 erg and fractional-flux amplitudes in g0 that range from 0.08 to 7.24. 44 large flares from 29 stars and 42 superflares from 27 stars were detected. All but two flares were from M-dwarfs, with one from a K5 and

another from a K9 dwarf. The ﬂare energy emitted in the TESS bandpass ET is related to

0 the energy in the g bandpass Eg0 by log10 Eg0 = 0.98 log10 ET + 0.62. The ﬂare amplitude

0 in the TESS bandpass AT is related to the amplitude in the g bandpass Ag0 by log10Ag0 =

0.92 log10 AT + 0.86. These relationships are plotted in Figure 5.6. The flare amplitudes and energies in these relationships do not use interpolated light curves and do not suffer from the under-estimated peak flux. Only the 2 min cadence temperatures from Section 5.2 use timestamps with interpolated flux measurements to ensure simultaneity of each 2 min epoch.

We measure the mean and 1σ distribution of the peak TEﬀ of our 44 ﬂare events to be

+8,300 14,000−3,400 K, while the mean and 1σ distribution of the total TEﬀ , integrated across the

+3,600 flare, is slightly lower at 11,000−2,600 K. 43% of the flares emit at a peak TEff above 14,000 K

(the upper limit of the typical range quoted in [33]). 23% emit at a peak TEﬀ above 20,000

K and 5% emit at a peak TEff above 30,000 K. The largest and hottest flare in our sample briefly reached 42,000 K.

5.5.1 Flare energetics and temperature

Flare energy correlates with TEff as shown in the left-side top and second row panels of Figure 5.7, with 1035 erg M-dwarf flares often demonstrating twice the peak temperature of 1033 erg flares. That larger flares are hotter is not necessarily surprising, as X-class solar flares are hotter than smaller events [266, 267]. A handful of M-dwarf superflares have also indicated a similar trend, e.g. [37, 51]. We find such results extend to energies of 10-1000× that of the largest solar flares and are consistent across a ∼10× increase in the published number of M-dwarfs with flare optical blackbody measurements at such high energies.

112 While a general pattern of higher peak temperature at higher flare energy is supported on our data, the scatter in the relationship is large. For example, the 1033.6 erg “Hazflare” [42] had a peak temperature of 15,500 K and the 1034 erg Great Flare of AD Leo [41] had a temperature consistent with 9000 K. Both of these events are consistent with the top left panel of Figure 5.7. Potentially more puzzling is the ∼1031 erg hot flare from GJ 674 reported by [39]. However, it too is consistent with our optical relation since its temperature was expected to be only 9000 K in the optical while being ∼40,000 K in the FUV. It is well-known that flares may emit more flux in the FUV than expected from the optical [268]. We note a differentiation in stellar mass in our plots. This is partly because flares from early M-dwarfs are typically larger than those from mid and late M-dwarfs [119, 143] and partly because of selection effects that remove the smallest flares from the sample. We discover for the first time that a typical 1035 erg M-dwarf flare emits above 14,000 K for ∼10× longer than a 1033 erg flare, as shown in the third row left-side panel of Figure 5.7. We note some superflares never reach a temperature of 14,000 K. A clear differentiation by mass in our sample is also apparent. The differentiation seen as a function of mass is not inconsistent with the similar flare properties seen across a large range of stellar masses (e.g. [269, 270]). Rather, higher-energy flares occur more frequently on more massive M-dwarfs prior to spin-down (e.g. [20, 21, 119, 143]), and we find that higher-energy flares are often hotter flares. In the same span of time, more high-energy flares are likely to be observed from a young early M-dwarf than from a young mid M-dwarf star according to their respective flare frequency distributions.

5.5.2 Flare impulse and temperature

Impulse, a measure of how pronounced and rapid the flare peak is in photometry, helps to estimate when and for how long the NUV flux is greatest. [33] defines the impulse as the fractional-flux amplitude over the FWHM in minutes, leveraging it as a proxy for the duration and intensity of flare heating at various depths in the stellar atmosphere. It is likely

113 that photochemistry in Earth-like atmospheres may respond differently to superflares with higher impulse values [131]. Impulse appears to correlate with flare temperature, but the power law slope is shallow as shown in the right-side top and second row panels of Figure 5.7. A relationship between impulse and TEff would indicate flare heating conditions in the stellar atmosphere are a determining factor in the blackbody properties. Flare amplitudes and FWHM values are altered by the host star’s luminosity. A larger sample of temperature and impulse measurements is needed to fit power laws within each spectral sub-type to account for this effect. Binning the peak TEff into high and low-impulse sets and then randomly shuffling TEff values between bins in 10,000 MC trials, we find our observed impulse-TEff power law is reproduced by chance 1.7% of the time for all M-dwarfs and 3.4% of the time for M≤0.42M dwarfs only. However, an Anderson-Darling test finds the difference between the high- and low-impulse

M≤0.42M ﬂares to be statistically signiﬁcant, rejecting the null hypothesis that the peak

TEff of low-impulse and high-impulse events come from the same population at a p-value of 0.037. The null hypothesis is not rejected for the full M-dwarf sample. Impulse does not clearly correlate with the time a flare emits at high temperatures. We do not find strong evidence for trends in flare temperature as a function of other variables such as stellar rotation rate. This may be due to our small sample size.

5.5.3 Classical versus complex ﬂares

We classify the morphology of each flare’s light curve in our sample into either “classical” or “complex” events. Classical flares exhibit a single flare peak while complex flares exhibit multiple peaks. Complex flares comprise the majority of the largest flares [74], making statistical comparisons of the temperatures of simple and complex flares challenging. While some flares are easily classified as having one or multiple large peaks, there is some ambiguity in the classification of other flares. While some secondary peaks significantly change the shape of the overall light curve, other flares exhibit small secondary events with an energy

114 Table 5.1: Relationships between ﬂare temperature observables and ﬂare energy and impulse

Flare Observable Oﬂ αE βE αI βI

Peak TEff 0.128 -0.193 0.115 4.193 Entire flare TEff 0.064 1.811 0.114 4.07 Time abv. 14,000 K 0.285 -8.969 – – Peak color – – 0.792 0.507

Notes. We tabulate the fitted power law coefficients for each power law shown in Figure 5.7. Power laws for each flare temperature observable are given where appropriate versus flare energy and flare impulse. The power law fit for each flare observable Ofl versus flare energy Eg0 is of the form log10Ofl = αE log10 Eg0 + βE. Likewise, the power law fit for each flare observable Ofl versus flare impulse I is of the form log10Ofl = αI log10 I + βI .

contribution that only perturbs the total energy (dominated by the primary peak). We include such flares in the “classical” bin to ensure the numbers needed to assess the properties of classical versus complex superflares. For example, flare A in Figure 5.1 has a small secondary event that is unlikely to significantly change its total energy budget, so its light curve is best described as falling into the classical bin. Flare D, however, is best described as complex. While the total flare energy of our sample appears to correlate with the peak flare temperature, the relationship may only hold for classical flares and not complex flares. The large amplitude and short duration of a classical flare may produce the same energy as a complex flare with a small amplitude and long duration. However, these two flares may have very different heating environments and therefore different peak temperatures. We plot the peak temperatures of the classical and complex flares in our sample against their energy and impulse in Figure 5.8. We do not observe different behavior between the classical and complex flares, especially for the energy relationship. The complex flares do show lower impulse values on the same power law. We also checked these relationships for the total or “global” flare temperatures instead of the peak temperatures and observe no difference. If this effect is physical and not a result of our small sample of superflares, it may be because secondary peaks are often of lower energy than the primary peak, acting as a perturbation to the total flare energy. Because we do not observe distinct relationships from classical and

115 Figure 5.8: We investigate the dependence of our peak temperature, energy, and impulse relationships on the shape of the flare. Classical flares with a single peak may correlate with temperature in a more straightforward way than complex flares do. However, we do not observe a significant difference in the energy or impulse versus temperature relationships between classical or complex flares in our (admittedly small) sample. We do note complex flares appear to have relatively lower impulse values. The appropriate trend lines from Figure 5.7 are also displayed.

complex flares, we only fit one power law for each relationship in Table 5.1 rather than fit classical and complex flares separately.

5.6 Habitability impacts of hot ﬂares

The relationship between UV and optical emission is not yet well-understood [39, 42, 131, 271, 272]. As a result, estimating the UV emission of stellar flares from the optical continuum may under-represent the true UV flux. For stars lacking direct UV flare observations, placing a probable lower limit on UV emission via the blackbody continuum allows us to also estimate lower limits on photo-evaporation of planetary atmospheres and constrain the conditions that

116 103 0.25 ] 2 0.50 m / W [

0.75 e 2

c 10 n a

t 1.00 s i d

Z 1.25 H

t 1

a 10

1.50 log Rossby number u l f

C 1.75 V U

0 10 2.00

0 100 200 300 400 Stellar age [Myr]

0.100

3 0.075

] 10 2 m / 2 0.050 W 10 [

e c

n 0.025 1 a 10 t s i d

0.000

Z 100 H

t 0.025 a

1 log Rossby number

u 10 l f

0.050 C

V 2

U 10 M 0.075 3 3 .

3 0 10 0.100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Stellar mass [M ]

Figure 5.9: We plot the estimated UV-C flux emitted during the FWHM of each flare and scaled to the HZ distance from its flare star; we compare these fluxes against stellar age and mass. UV-C fluxes are estimated using the blackbody temperature of each flare. Flares are color-coded by stellar rotation rate, expressed as the Rossby number. The Rossby number is a stellar mass-independent rotation parameter useful in the large M-dwarf regime; smaller Rossby numbers correspond to faster stellar rotation periods. Top panel: Stellar ages are computed from YMG membership. The UV-C fluxes of the largest flares appear to remain approximately constant from 102 m−2 to 103 W m−2 for ages up to at least 200 Myr, with potentially significant consequences for young planetary atmospheres and the evolution of life during this period. Bottom panel: The UV-C fluxes at the distance of HZ planets do not appear to change significantly across the fully-convective boundary near 0.33 M , although a tentative but statistically-insignificant increase at higher masses may be visible in our small sample. Fully-convective stars appear to rotate more quickly.

117 might impact the evolution of surface life. The true UV emission may in fact be higher than that estimated from the optical.

5.6.1 UV-C ﬂux in the HZ versus stellar mass

Larger and hotter flares are more common from more massive M-dwarfs prior to spin- down. However, the distance to the HZ is also larger for more massive stars. To determine if M-Earths orbiting lower-mass M-dwarf flare stars are more habitable, we estimate the UV-C energy of each flare using the peak blackbody temperature and the g0 energy. We estimate the UV-C flux by dividing UV-C energy by the FWHM during which the energy was observed, and compute the HZ distance for each stellar mass using [129]. Since the fully-convective

boundary occurs around ∼0.33 M [30], we bin our sample of UV-C fluxes by flares from fully-convective and from earlier M-dwarfs. A slight trend towards higher UV-C fluxes at larger masses may exist in Figure 5.9, but it is not clear if it is physical. We perform an Anderson-Darling test on the UV-C fluxes in each mass bin and do not find the difference to be statistically-significant (p-value >0.05). We therefore cannot reject the hypothesis that the UV-C space weather environment of M-Earths orbiting more massive M-dwarfs may be comparable to that for less massive M-dwarfs as estimated from the optical blackbody. A larger sample may be able to determine the relative habitability effects of hot flares as a function of mass. Because early M-dwarfs spin down faster than mid M-dwarfs, it is helpful to compare flares from stars of the same ages and different masses and different ages but similar masses. We use the Rossby number as a mass-independent relative age indicator and find our sample of flares come primarily from young stars with activity levels near the

saturated regime (Ro < 0.2).

5.6.2 UV-C ﬂux in the HZ versus stellar age

Fourteen of our ﬂares were emitted by members of young moving groups (YMG). These include 6 ﬂares from Tuc-Hor, 4 from AB Dor, 2 from Coma Ber, 1 from Columba, and 1

118 from β Pic [255, 257, 273, 274], allowing us to precisely estimate their ages using Table 3 in [257]. 16 of our flares were emitted by dwarfs that are likely to be young according to their spectral features reported in the literature but are not identifiable with any known moving group [253, 257], and 13 flares come from stars with no age information available in the literature. One flare is from a ∼6 Gyr star (Proxima Cen) [275]. The UV-C fluxes at the HZ distance are estimated as described in Section 5.6.1. We find the median and 1σ range of UV-C fluxes estimated at the HZ distance of flares from the YMG

+800 −2 sample to be 120−110 W m . We ﬁnd the median and 1σ range of young stars not known to

+137 −2 be members of YMGs to be 4.6−4.3 W m , although this sample is very small and heavily biased by one flare star with unusually-low UV-C fluxes. We find the median and 1σ range

+178 −2 of flares with no stellar age information to be 161−158 W m . We plot the stellar age versus UV-C flux at the HZ distance for our sample of known ages less than 500 Myr and observe similar fluxes at all ages in this range in Figure 5.9. [24] and [23] find fast stellar rotators with

Rossby numbers Ro < 0.2 and rotation periods less than 10 d demonstrate similarly-high

levels of stellar activity. Our sample is almost entirely composed of rotators with Ro < 0.2, potentially explaining our consistently-high activity levels at these ages. [21] find the flare activity of cool stars decreases with increasing open cluster age, so we expect the typical flare energy (and therefore typical UV flux) will decrease at some threshold age greater than 200 Myr (not 500 Myr- only one data-point at this age). Further work is warranted. If HZ planets orbiting <200 Myr stars typically receive ∼120 W m−2 and often up to 103 W m−2 during superflares, then significant photo-dissociation of planetary atmospheres may occur [45, 148]. As a point of comparison, the likely water loss of Proxima b is due to the long-term effects of a time-averaged XUV flux (including flares) of less than 1 W m−2 [148]. The median value from the flares observed in YMGs is comparable to the ∼100 W m−2 of UV-C flux estimated at the distance of Proxima b during the [44] Proxima superflare. While [264] found 10−4 micro-organisms would have survived the Proxima superflare, it is presently unclear what effects a 10× increase in UV-C flux would have on the evolution and

119 survival of life prior to 200 Myr; it is possible such high rates of UV radiation could drive pre-biotic chemistry [142, 146], suppress the origin of life on worlds orbiting young M-dwarfs [28], or not impact astrobiology at all if the timescale for life to emerge is longer than 200 Myr [28, 276].

120 CHAPTER 6: BAYESIAN DETECTION OF PERIODICITY IN FLARE OC- CURRENCE FROM COOL STARS WITH TESS

Phased flaring, or the periodic occurrence of stellar flares, may probe electromagnetic star-planet interaction (SPI), binary interaction, or local magnetic conditions in spots. For the first time, we explore flare periodograms for a large sample of flare stars to identify periodicity due to magnetic interactions with orbiting companions, magnetic reservoirs, or rotational phase. Previous large surveys have explored periodicity at the stellar rotation period, but we do not assume periods must correspond with rotation in this work. Two min TESS light curves of 284 cool stars are searched for periods from 1-10 d using two newly-developed periodograms. Because flares are discrete events in noisy and incomplete data, typical periodograms are not well-suited to detect phased flaring. We construct and test a new Bayesian likelihood periodogram and a modified Lomb-Scargle periodogram. We find 6 candidates showing apparent periodicity with a false-alarm probability below 1%. Three targets are ≥3σ detections of flare periodicity; the others are plausible candidates which cannot be individually confirmed. Periods range from 1.35 to 6.7 d and some, but not all, correlate with the stellar rotation period or its 1/2 alias. Event timings from the two strongest detections both show a clear preference for near-exact periodicity with little scatter in phase. This suggests mechanisms beyond rotational modulation such as binary interactions might exist. The detected periodicity does not persist from TESS Cycle 1 into Cycle 3. This is likely to result from the significant spot evolution observed from each candidate between Cycle 1 and 3. The link between phased flaring and spot evolution suggests magnetic conditions play an important role in sustaining periodicity1.

1Content in this chapter has been submitted for publication in AAS Journals. I designed and carried out the phased-ﬂare survey in its entirety. Nicholas Law both advised the project and developed the mathematical framework for the ﬂare periodograms which I then implemented and used for my survey.

121 Flares are discrete and stochastic events, motivating periodograms for incomplete, noisy data. Discrete Fourier Transforms, auto-correlation approaches, histograms of arrival time separations, and string comparison methods are not designed for incomplete or pseudo- periodic event times [277, 278]. [277] and [279] create periodograms employing probabilistic likelihoods for various test periods. Whenever the test period approaches a real periodicity, the phase-folded points line up in phase and create high likelihoods. [278] searched for periodicity in incomplete data with Bayesian particle bootstrap filters. They model periodicity with incomplete data and where the preferred phase is not fixed in time. We present a new Bayesian likelihood periodogram for discrete events in noisy and incomplete data. We also present a modified Lomb-Scargle periodogram for comparison. Our Bayesian periodogram is similar to the [277] approach but is fully Bayesian, making it an efficient and robust way to characterize flare signals that can easily incorporate priors. Our approach is simpler than the bootstrap filter since we do not need to perform online prediction, but rather to search many stars.

6.1 TESS ﬂare observations

TESS is continuously monitoring each part of the sky for 28 d at a time in the red with four 10.5 cm optical telescopes at 21” pixel−1. During the primary mission, TESS Cycle 1 observed the southern hemisphere split into 13 sectors. TESS Cycle 3 is now re-observing this field as part of the extended mission. We downloaded 2 min cadence simple aperture photometry (SAP) light curves from TESS Sectors 1-9 of 284 late K and M-dwarf flare stars from [143]. Following [280], SAP rather than pre-conditioned light curves were selected to avoid altering or removing flares or other astrophysical variability. We identify flares in the light curves of all targets with the [144] automated pipeline and then again independently in a visual search for 11 targets with apparent periodicity to ensure no flares are missed. In both, flares are discovered as brightening events above the photometric noise following the rapid-rise, slow-decay [6] flare profile. This is done to ensure the start

122 Figure 6.1: TESS Cycle 1 light curves of the 6 candidate phased-flares targets with FAP<1%. Periodicity from these flare stars was detected with our newly-developed flare periodograms. Flares large enough to comprise the phased-flares signal (i.e. with amplitudes above the threshold amplitude Athresh) are highlighted in red. Smaller flares are highlighted in light orange. Predicted times when high-amplitude flares will occur are shaded in grey. Out-of-flare variability in the light curve is de-trended with a Savitsky-Golay filter. Some phased-flare targets are stronger detections than others, with A and B as the clearest.

123 Figure 6.2: Top panel: A TESS light curve modified for input into the wide-flares LS periodogram. Y-values in the light curve are replaced with a small constant value where there are no flares and a Gaussian where there is a flare. The Gaussian is made much wider than the original flare in order to be picked up by the LS basis functions. Bottom panel: The flare probability comb with period P used to compute Bayesian likelihood periodograms L(P |ti) = L(ti|P )L(P ) for a set of discrete flare times ti. The comb determines L(ti|P ) as phased-flares with period P occur near the peaks of the comb teeth more often than flares phased to a different period (or no period). The comb is swept through the flare times to account for phase and the maximum likelihood is recorded for each period in the periodogram.

and stop times of each flare are correct and that no artifact of automated flare detection is the cause of flare periodicity. Out-of-flare variability is removed using a Savitzky–Golay (SG; [281]) filter, carefully inspecting each flare to ensure out-of-flare variability is correctly subtracted. Carefully removing rotational variability is essential to ensuring flux is not added to or removed from the flares in a periodic way. Finally, flare amplitudes are measured in the de-trended light curves using fractional fluxes instead of magnitudes to observe linear

|F −F0| relationships between flare peaks. Fractional flux is computed as ∆F/F= where F0 is F0 the out-of-flare flux and is determined from the local median. Stellar distances and the T magnitude of the star are primarily obtained from the TESS Input Catalog version 8 (TIC; [166, 260]). Stellar rotation periods are identified by strong rotational modulation in the TESS light curves in both Cycle 1 and Cycle 3. LS periodograms are computed for the out-of-flare variability and the light curve is folded in phase to confirm the period.

124 6.2 Flare periodicity search methods

We outline the identification of flare periodicity in TESS light curves and the development of two new phased-flares periodograms. Because the Bayesian periodogram is a fundamentally- new approach to flare periodicity, we construct a modified LS periodogram as a way to assess the dependence of signal power on the type of periodogram. In the following subsections, we discuss the steps required to measure and assess each periodogram:

1. §6.2.1: Generate the Bayesian likelihood periodogram.

2. §6.2.2: Generate the Wide-ﬂares LS periodogram.

3. §6.2.3: Assessing the performance of the periodograms as a function of the number of ﬂares.

4. §6.2.4: Use the periodograms and a visual inspection of each of the 284 light curves to identify candidate phased ﬂare signals for further study.

5. §6.2.5: Find the threshold amplitude separating large, phased flares from smaller, non-phased flares. This threshold is necessary to select the finalized sample of events from each discovery on which periodograms and false-alarm probabilities will be run.

6. §6.2.6: Identify strong periodogram signals for all ﬂares above the threshold amplitude for each star using FAP calculations.

6.2.1 Phased-ﬂares Bayesian Likelihood periodogram

We employ Bayes’ theorem to to compute the likelihood that a set of discrete stellar flare times demonstrates periodicity at a given period. Computing L(P |F ), the likelihood of periodicity at period P for a set of discrete flare times F , is more difficult than computing the likelihood that a set of flare times F occur at a period P , L(F |P ). This is because it is a

125 Figure 6.3: Simulated detection of a 3.142 d phased-flares periodicity with the wide-flares LS periodogram (top panels) and Bayesian likelihood periodogram (bottom panels). Peri- odograms of randomly-timed flares are also shown. The leftmost panels show phased and random flare detections from just 12 events, while the middle panels show phased and random flare periodograms from 48 events. As the number of flares increases, the signal to noise increases and the ability to discriminate phased flares from random flaring also increases. The rightmost panels extend this observation with MC trials on sets of 3, 6, 12, 24, 48, and 74 flares. The Y-axes of the rightmost panels LSphased-LSrandom and log L phased-log L random gives the typical increase in power between real detections versus non-detections. These differences in power allow us to explore the ability of the periodograms to distinguish between phased and random flaring scenarios as a function of the number of flares. The most improvement is seen from 3-24 flares.

126 straightforward matter to compute whether ﬂares occur at high-probability intervals on a periodic probability distribution at a given period P . We therefore compute L(P |F ) as

Y L(P |F ) = L(F |P ) × L(P ) = L(Fi|P ) × L(P ) (6.1) i

where Fi is the time at which each discrete ﬂare event occurs and L(P ) is the prior likelihood of each period (i.e. a period of at a known systematic would be unlikely). In this work, we set L(P ) to one.

Flare likelihoods L(Fi|P ) are evaluated in log L(t|P ) as the composition of the log of a P∞ Gaussian function G centered at zero (µG=0) with a comb of delta functions k=−∞ δ(t−kP ).

∞ X log L(t|P ) = log G(t, µG, σG) ∗ δ(t − kP ) (6.2)

k=−∞ Fi

Each delta function is spaced P days after the previous delta function in the comb. The delta function builds in the periodicity, while the Gaussian allows for the stochastic nature of ﬂare events emitted before or after the exact center of the probability peak of the comb tooth. The resulting likelihood function consists of a comb of evenly-spaced Gaussian teeth with a separation of P days as shown in the bottom panel of Figure 6.2. Each Gaussian tooth

has a spread of σG=0.1 d about the predicted time. Since reconnection is stochastic, flare events triggered by a periodic mechanism will not occur at exactly periodic intervals, but may be clustered about the expected phase within some interval of time. We account for this pseudo-periodicity by using Gaussian-shaped probability envelopes for the teeth (which makes it most probable the flares occur at exactly the same phase at each period, but admits a range of possible occurrence times). The choice of a Gaussian ensures the periodogram will detect flare periodicity even when the events are not strictly periodic, but vary before

or after the expected time by ∼0.1 d. The chosen value of σG has two implications for the ﬁnal Bayesian periodogram. First, the periodogram will break down at periods P for which

127 Figure 6.4: The method by which flares from each light curve are sorted into the high- amplitude phased-flares and into the low-amplitude random flares. Because low-amplitude flares often appear uncorrelated with each phased-flares signal, we define a threshold amplitude Athresh to isolate the larger flares for periodogram and statistical analysis. In the right panel, we plot flare amplitudes versus the phase-folded flare times. For each flare in the right panel, we measure the spread in phase σA for all flares with amplitudes Aflares ≥ Athresh. As the flare amplitude decreases, σA increases. This creates the A − σA distribution shown in the left panel. The amplitude Athresh is selected to correspond to the half-maximum of σA. For all Nabove flares above Athresh, the standard deviation of their phase-folded times is computed. Phased-flares FAP are computed for each candidate signal by randomly-shuffling flare times and amplitudes to see how often Nabove random flares can produce a smaller standard deviation than the actual flares.

σG/P ≥∼1. Second, the amount of random scatter in the ﬂare times around the exact period

P that will generate high probabilities is set by σG. Once a likelihood function log L(P |F ) has been defined for a given period P , a periodogram is created across all periods. For each period P , the comb is swept through the flare times to account for any mismatch in phase between periodic flares and the placement of the teeth. The highest likelihood is recorded for that test period. The normalization constant of the likelihood scales as ∼ P 2 due to the decrease in the area under the comb at longer periods, similar to the effect seen by [277]. At short periods (<2 d), the periodogram power noise floor begins to increase due to the closeness of the comb spacing. This slight excess in power compared to longer periods is well-described by an exponential function and is removed in plots to guide the eye.

128 6.2.2 Wide-ﬂare Lomb-Scargle periodogram

Lomb-Scargle (LS) periodograms are a standard method of detecting periodicity in a light curve [236, 237]. Because they correlate sinusoidal functions with the light curve, they are not automatically a good matched filter for very short-term impulsive events like flares. To make the LS basis functions applicable to periodic flare signals we artificially widen the flare signals by replacing the light curve with a synthetic light curve consisting of a near-zero constant value C where no flares are observed, and wide Gaussian-shaped bumps G where

ﬂares Fi do occur. This synthetic light curve y(t) is constructed as the convolution

N X y(t) = G(t, µG, σG) ∗ δ(t − Fi) + C (6.3) i=1 with N being the number of flares and the Gaussian mean and spread as before. If exactly zero is used for C, the window function is not preserved as out-of-flare times no longer contribute to the convolution. The wide-flares process is illustrated in the top panel of Figure 6.2 where Gaussian flux increases at the flare times are highlighted in red and the non-flare times are displayed in blue. The TESS observing window is preserved since only the flux values in the light curve are synthetic, not the epoch times. For example, the mid-sector TESS observing gap can be seen in Figure 6.2. Once y(t) has been constructed, the normal LS periodogram can be computed as LS(y(t)). Since LS periodograms are well-understood, they provide a good check on the performance of the new Bayesian likelihood periodogram.

6.2.3 Performance of each method

For a TESS sector of 28 days and a phased-flares period of 1-5 days, between 6-30 periodic flares will occur. How well do the Wide-flares LS and Bayesian-likelihood periodograms distinguish a phased-flares signal from random flaring for so few flares? We first verify both periodograms recover injected flares at periods from 1 to 10 d, with stronger signals for higher numbers of flares as illustrated in the left and middle panels of Figure 6.3. By necessity, both

129 types of periodograms generate power at the primary period and also a signal at the 1/2 alias. More flares are required at 10 d periods than 2 d periods to reach the same peak strength. To determine the typical periodogram power obtained with flares in periodic versus random configurations, 10,000 MC trials are performed on each sample of N random and N phased-flares. We separately test samples of N=3, 6, 12, 24, 48, and 74 random flares; we test the same numbers of phased-flares. As expected, larger numbers of flares better distinguish a phased-flares signal from random flaring as described in Figure 6.3. The ability to distinguish between periodogram power from phased flaring and power arising from random flaring is

quantified by LSphased-LSrandom and log Lphased-log Lrandom. These expressions give the typical increase in power from real detections versus non-detections. Intriguingly, the difference in power seen between phased and random flaring increases significantly in samples containing 3-24 flares, but the ability to discriminate a real signal from random flaring increases very modestly for samples larger than 24 flares. The difference in power from 3 to 74 flares is illustrated in the right panels of Figure 6.3. Injected phased-flares are given a 3.142 d periodicity with a Gaussian 1σ spread of 0.1 d while random flares are drawn from a uniform distribution of flare times sampled from the light curve.

6.2.4 Identifying which stars may be phased-ﬂare candidates

For each of the 284 flare stars in our sample, the light curve and wide flares LS periodogram are plotted in separate panels of a graphical user interface (GUI). In a third panel, the light curve is folded in phase to the period at the highest peak of the flare periodogram. Stars with a clear peak in their periodogram or flares that appear to be regularly spaced in the light curve are recorded as potential candidates. Once the candidate periodicity is identified,

the spread σA in the preferred phase positions of each ﬂare is measured and the threshold

amplitude Athresh is computed as described in §6.2.5. Potential candidates are not considered actual candidates until the false alarm probabilities are computed as described in §6.2.6.

130 Figure 6.5: Larger panels: Flare flux amplitudes of each candidate versus flare times, folded in phase to the flare period. Flares are color-coded by position in the light curve to show whether groups of flares were emitted in the same day or different days. High amplitude flares are often emitted periodically at a particular phase. Smaller flares often appear to occur randomly. The dividing line is the threshold flare amplitude, Athresh. Inset panels: De-trended TESS light curves are folded in phase to the phased-flare period. The amplitude is in flux units, with the peak flux equivalent to the recorded amplitude values in the larger panels. For plotting purposes, the excess high-amplitude flares that occur at a particular periodic phase are plotted on the right-hand side of both larger and smaller panels.

131 6.2.5 Determining the threshold ﬂare amplitude

For many of our targets, the largest flares in each light curve seem to exhibit the strongest periodicity. Unless the large flares can be separated from the smaller non-periodic flares, the period-power of the signal will be diluted. We therefore need a way to define a flare amplitude cutoff that distinguishes large flares from small non-phased flares. To avoid arbitrarily picking

a threshold amplitude by hand, we deﬁne this threshold as the half-maximum of the A-σA distribution (described below) and illustrated in the left panel of Figure 6.4. This is done as follows:

1. The peak flare amplitudes A are sorted from largest to smallest. The event times of each flare in the light curve are phase-folded to the candidate flare period.

2. Starting with the largest ﬂare, we select a sub-sample of ﬂares Asub = Ampl(A ≥ Acur)

with amplitudes equal to or greater than that of the current ﬂare amplitude Acur. The

next step is to compute σA, the standard deviation of the event times of Asub folded in phase to the candidate ﬂare period as shown in the right panel of Figure 6.4.

3. This process is repeated for each smaller ﬂare in the sorted list, creating sorted (A, σA) pairs.

4. The halfway point between the smallest and largest σA values as located and shown in the left panel of Figure 6.4. The amplitude corresponding to the half-maximum of the

σA values is called Athresh.

5. All ﬂares are divided into two categories using the threshold (as shown in the right

panel of Figure 6.4). Flares above Athresh are selected as candidate phased-ﬂare events and are subsequently used in periodogram detections and FAP calculations.

Across all candidate phased-flare systems, we find Athresh does a good job separating the strongly-phased flares from the lower-amplitude background flares.

132 6.2.6 False-alarm Probabilities

We compute two different types of FAP on phased flares candidates. In the first type of FAP (denoted the phased-flare FAP), all flare times and amplitudes are randomly shuffled

10,000×. In each trial, shuﬄed ﬂares with amplitudes above Athresh are selected and the

standard deviation of the phased-up times σA is computed. The FAP is deﬁned as the fraction

of trials where σA is more tightly phased than the real signal. The beneﬁt of this method

is that it takes into account both the number of flares above Athresh and also the degree to which the flares are tightly clustered in phase. For example, a low FAP may be due to a small number of extremely well-aligned flares in the phase-folded graph, or due to a larger number that all occur within half of the period but not in the other half. Both situations are observed in Section 6.3. We cut all flare stars with a phased-flares FAP above 1% from our sample as randomly-shuffled flares can too easily reproduce these signals. This cut flags the plausible candidates and keeps the number of false-positives to a manageable level in both the current and future larger survey of all TESS flare stars. In the current survey we would expect ∼3 false positives, and a full survey of all bright flare stars should result in 10-100 false positives (depending on the bright limit cutoff used). The second type of FAP (denoted the periodogram FAP) describes how often random flaring reproduces detections in the two types of periodograms. For each detection, the

number of flares with amplitudes above Athresh is determined and an equivalent number of flare times are randomly drawn from the light curve. The Wide-flares and Bayesian-likelihood periodograms are computed across 10,000 MC trials for the randomly-drawn flares and the maximum power in the 1-10 d search range is recorded. The fraction of times the power at the period of interest is equal to or greater than the real signal gives the FAP. We note this FAP assumes no prior exists on the number of periods searched. Sometimes the phased-flare period correlates with the stellar rotation period (e.g. peaks near a close

harmonic of Prot in Figures 6.6 and 6.7), which provides a prior on the period search range. In such a case, the FAP is reduced by recording the maximum period per trial in a period

133 Figure 6.6: Wide-flares Lomb-Scargle periodograms of the strongest phased-flare candidates. Only candidates A,B, and D are detections. In each periodogram, the candidate Pflares is displayed with a blue arrow and is the most significant peak in its periodogram. Some peaks are clearer than others: for example the peaks in panels A and B are clearer than those in panels C and E. FAP are computed for each candidate period across 10,000 trials and are displayed in blue. For reference, the stellar rotation period is displayed as a solid orange line and the 1/2 alias as a dashed orange line.

range within the percent diﬀerence between the true phased-ﬂares period and Prot (or its

closest harmonic). When the ﬂare period is close to the nth harmonic of Prot, random power

at Prot and all harmonics up to n is included in the FAP. For example, if the ﬂare period is

closest to 1/2Prot, then random periodogram power higher than the true phased-ﬂares signal

at Prot and 1/2Prot are both counted in each MC trial. The periodogram FAP will be higher than the phased-flares FAP since large LS peaks generated from 5-15 randomly-timed flares are easier to produce. The large range of the period search window will also increase these values relative to the single period tested in the phased-flares FAP.

6.3 Detection of phased ﬂaring in TESS light curves

We find 6 flare stars with candidate phased-flare signals in their TESS Cycle 1 data and a phased-flares FAP<1%. These flare stars are TIC-80427281, TIC-95328477, TIC-279615427,

134 TIC-220432563, TIC-326446019, and TIC-177255827. Only Candidates A (TIC-80427281), B (TIC-95328477), and D (TIC-220432563) are secure detections unlikely to be due to random peaks or look-elsewhere eﬀects. Candidate F (TIC-177255827) is 2.5σ. The other two are non-detections (TIC-279615427 and TIC-326446019). Flare periods range from 1.3 to 6.7 d. 4 are M-dwarfs and 2 are likely late K dwarfs. We describe each detection below:

• TIC-80427281 (ASAS J004211-4252.7): A moderately nearby (53 pc) M2.2 dwarf [217] observed for 1 sector by TESS in Cycle 1. We observe a ﬂare period of 1.67 d with a phased-ﬂares FAP of 0.1%. This period is close to the half-alias of the stellar rotation

period of Prot=3.715 d. Phase-folding the ﬂares to Prot does not reveal an obvious correlation (candidate A in the ﬁgures).

• TIC-95328477 (UCAC4 368-011078): A moderately nearby (51 pc) M0 dwarf [220] observed for 1 sector by TESS in Cycle 1. We observe a ﬂare period of 1.35 d with a

phased-ﬂares FAP of 0.1%. The stellar rotation period Prot=2.609 d is twice the phased-

flare period. Phase-folding the flares to Prot does show a clear sinusoidal modulation in flare amplitudes with rotational phase (candidate B).

• TIC-279615427 (UCAC3 63-21199): A moderately nearby (57 pc) K9 dwarf [31] in the TESS Cycle 1 Continuous Viewing Zone (CVZ). We observe a flare period of 5.05 d with a phased-flares FAP of 0.4%. The flare period does not correlate to the stellar rotation

period Prot=1.1882 d and the ﬂares do not show clear modulation when phase-folded

to Prot (candidate C).

• TIC-220432563 (2MASS J04534379-5836247): A moderately nearby (30 pc) K9 dwarf [31] observed for 12 sectors by TESS in Cycle 1. We observe a ﬂare period of 6.62 d

with a phased-ﬂares FAP of 0.1%. The phased-ﬂares period is ∼3X the Prot of 2.274

d, making a correlation likely. However, phase-folding the ﬂares to Prot only shows a possible correlation between the largest ﬂares and the dominant starspot (candidate D).

135 • TIC-326446019 (RBS 1877): A moderately nearby (35 pc) M3.5 dwarf [282] observed for 1 sector by TESS in Cycle 1. We observe a ﬂare period of 3.63 d with a phased-ﬂares

FAP of 0.9%. With a stellar rotation period Prot=0.8022 d, it is not likely the ﬂare

signal is correlated with the rotation period. Phase-folding the ﬂares to Prot shows no correlation either (candidate E).

• TIC-177255827 (ASAS J064643-7700.4): A moderately nearby (64 pc) K7 dwarf [31] in the TESS Cycle 1 CVZ. We observe a ﬂare period of 6.68 d with a phased-ﬂares

FAP of 0.2%. The stellar rotation period of Prot=6.26 d is nearly identical. While the ﬂares phase up strongly at 6.68 d, they do not phase up well at 6.26 d, possibly due to diﬀerential rotation (candidate F).

6.3.1 Phased-ﬂaring at high amplitudes

We inspect the distributions of ﬂare amplitudes versus their position in phase. Phase- folding the event times to the best ﬂare period found with the periodograms, we observe

that the flares cluster in phase as shown in Figure 6.5. The threshold amplitude Athresh separating large phased flares from small non-phased ones is shown in each panel. Some flare stars show a tighter clustering in phase than others. For example, the flares from Candidate A (TIC-80427281) occupy a very small range of positions in phase while the flares from Candidate F (TIC-177255827) cover almost half the phase. Large spreads in phase at periods close to the stellar rotation period as seen from Candidate F are likely indicative of stochastic flaring from active regions rotating into and out of the field of view. Alternately, they could be due to differential rotation and spot evolution. Very tight clustering may be indicative of

triggering mechanisms [96, 100]. These plots ensure Athresh is accurately selecting the sample of flares for which the finalized periodograms are computed (i.e. those on which proper false-alarm calculations may be performed, not the initial search periodograms in high SNR flares).

136 In our sample, the high amplitude flares display the clearest signal. Flare periodicity amongst the highest-amplitude flares from a star has been detected in the past. [88] found the brightest flares occurred when the dominant starspot was facing our line of sight, similar to our Candidate B (see panel B, Figure 6.8). [81, 283] found the strongest flares from V374 Peg and TRAPPIST-1 were concentrated at particular rotational phases, but not necessarily when the dominant spot was in our line of sight. Following [81, 283], we also phase-fold the light curves themselves to the flare period. The phase-folded light curves are shown as inset panels in the phase-amplitude plots of Figure 6.5. Each inset light curve is pre-whitened of non-flare variability with a SG filter and phase-folded to the flare period. The light curves help to ascertain at a glance if the amplitudes increase and decrease from a mean phase with the strongest flares as seen in Panel C, for example.

6.3.2 Phased-ﬂare periodogram results

Wide-flares LS and Bayesian-likelihood periodograms for each candidate are shown in Figure 6.6 and Figure 6.7. In each periodogram, the phased-flare period is highlighted as the most significant detection in the period range searched. The detections are consistent between the LS and Bayesian likelihood approaches, although the peaks are higher in the LS periodograms. This is a result of the logarithm used in the Bayesian approach. The phased-flare periods are associated with either the stellar rotation period or an alias of it in 4/6 cases. This suggests the contrast of the flare against the stellar brightness changes as the emitting starspot rotates through our line of sight. The most secure detections are from Candidates A and B (TIC-80427281 and TIC- 95328477), which are 3.3σ and 4σ, respectively. The next strongest signals D and F (TIC- 220432563 and TIC-177255827) are 3.3σ and 2.5σ, respectively. Candidates C and E (TIC- 279615427 and TIC-326446019) are not detections. These σ significance values are from the periodogram FAPs with constraints from stellar rotation included as described in Section 6.2.6. The FAP of candidate D is computed slightly differently from the others. The flare period is

137 close to 3Prot, for a 2.3σ signal (FAP=2.5%). However, the rotational phases of the flares agree with the rotational phase of the dominant spot (at the light curve minimum) as shown in Figure 6.8. We multiply the periodogram FAP by the probability that randomly-timed flares would correlate with the rotational phase of the dip. Across 10,000 MC trials, the root mean square error (RMSE) between the rotational phase of the dip and randomly timed flares is smaller than the RMSE of the real flares only 5.1% of the time. This increases the signal strength to a 3.3σ detection. Across all 6 candidates, the least clear signals often have fewer flares with amplitudes

above Athresh, although there are exceptions. For example, Candidate A has the second- strongest signal with only 6 periodic flares while the weaker Candidate C has 9 high-amplitude flares. The degree to which the phased flares are tightly-packed at a particular position in phase also affects the peak power. Candidate A’s signal is relatively high because its flares are tightly clustered at a particular position in phase.

6.4 Periodicity related to starspot evolution

We found each phased flares candidate in TESS Cycle 1 data, leaving Cycle 3 data for validation purposes and exploring the persistence of phased flaring through time. The Cycle 3 data is also leveraged to determine if phased flaring is caused by spot rotation, magnetic interaction with a companion, a flares reservoir, or the look-elsewhere effect.

6.4.1 Spot evolution and lack of periodicity in Cycle 3

None of the Cycle 3 data shows phased flaring at the periods or phases detected in Cycle 1. This could indicate the signals depend on magnetic properties that may have changed through time, or this could indicate the signals were a result of the look-elsewhere effect. Intriguingly, the rotational modulation seen in the Cycle 3 light curves of Figure 6.9 has evolved significantly from the modulation seen in the Cycle 1 light curves of Figure 6.8. The difference is especially pronounced for the multi-spot rotators in panels A and D in Figure

138 Figure 6.7: Bayesian-likelihood periodograms of the 6 strongest phased-flare candidates. Only candidates A,B, and D are detections. In each periodogram, the signal Pflares is displayed with a blue arrow and is the most significant peak in its periodogram. Peaks are smaller than in the LS periodogram due to the logarithm used in computing periodogram power. Some peaks are clearer than others: for example the peaks in panels A and B are clearer than those in panels C and E. FAP are computed for each candidate period across 10,000 trials and are displayed in blue. For reference, the stellar rotation period is displayed as a solid orange line and the 1/2 alias as a dashed orange line.

139 6.8. Candidate D shows 2 dips in Cycle 1 reminiscent of a W UMa, but in Cycle 3 shows only a single dip. The changes in number of dips and the amplitudes and phases of variability strongly indicates each star is undergoing significant spot evolution as in [79]. The similarity of our samples may explain why we also find flare periodicity.

6.4.2 Could the look-elsewhere eﬀect be the cause of periodicity?

Could the lack of periodicity in Cycle 3 mean the Cycle 1 signals are due to the look- elsewhere effect? The look-elsewhere effect is not a plausible explanation for the secure detections (candidates A, B, and D) but is plausible for the unconfirmed detections. For example, the probability that our strongest detection (Candidate A) could arise from the look-elsewhere effect in a survey of 300 stars is 2.3% (based on the phased-flares FAP). The probability that both Candidates A and B arise from the look-elsewhere effect is ∼0.1%. In each of 10,000 MC trials, we search 300 flare stars for stronger phased flaring than the target signal. The strength of phased flaring in each trial is defined as the degree of

clustering at a particular position in periodic phase as described in §6.2.6. The number of stars in the sample with a tighter clustering than that of the actual flare star(s) is recorded as a “success”, and the fraction of trials with a success is given as the final look-elsewhere probability. However, the look-elsewhere effect cannot be excluded as an explanation of periodicity for candidates C, E, or F. Candidate F is the most likely to be astrophysical since it correlates with the stellar rotation period, but this probability is difficult to quantify: If the phased-flares FAP is used, the chance of a signal like F resulting from the look-elsewhere effect in a sample of 300 stars is ∼5%. However, if the periodogram FAP is used, a 2.5σ event should occur by chance ∼4 times in a sample of 300 stars. Individual 2.5σ candidates near the rotation period or another period of interest (such as a candidate at a period expected from SPI) may still be astrophysical and should be investigated.

140 Figure 6.8: TESS Cycle 1 light curves are phase-folded to the stellar rotation period for each flare star and plotted in grey. Binned epochs are overlaid in white. Although it is difficult to distinguish between rotational modulation from multiple spots or EB scenarios in panels A and D, the phases and amplitudes of the variability are completely different a year later in Cycle 3, confirming the evolving starspot scenario. Flares are also phase-folded to the stellar rotation period and are shown in red. Only panels B and D show a convincing modulation in flare amplitude at the stellar rotation period. This does not mean other signals are not correlated with stellar rotation, just that they don’t phase up well at the exact Prot value. Differential rotation at the spot latitude or external flare triggers could modulate phased-flares signals away from the precise Prot value.

Figure 6.9: TESS Cycle 3 light curves are phase-folded to the stellar rotation period for each flare star and plotted in grey. Binned epochs are overlaid in white. Significant spot evolution has occurred in all stars but Candidate B since Cycle 1 a year earlier. This suggests magnetic properties generating flare periodicity may also have changed.

141 6.4.3 Companion stars and evolving spot properties

Since the look-elsewhere eﬀect is not the best explanation for the periodicity of our best candidates in Cycle 1, we consider astrophysical interpretations. Since the periodicity changed when the spot structures present in the light curves changed, a connection between the two is probable. The phased-ﬂare signals from candidates A, B, D, and F indicate rotational

modulation because they are close to either Prot, the 1/2 Prot harmonic, or the 3 Prot harmonic.

A 3 Prot harmonic might result from delayed ﬂare events or a juxtaposition of the eﬀects

of the wait-time between flares and Prot. Two show more power at the 1/2 alias than the primary period, likely a result of the basis functions of the periodograms. Candidate B in particular shows a clear modulation of amplitudes with rotational phase (Figure 6.8). When the dominant spot is facing us at light curve minimum, we observe the largest flares. However the smallest flares occur at light curve maximum. Likewise, the largest flares correlate with the dominant spot in panel D of Figure 6.8. As seen in Figure 6.1, the periodicity of our clearest candidates prefers a very small range of rotational phases. As the spot rotates into and out of our line of sight, the largest flares should be observed at phase positions covering up to half the period. Furthermore, the preference of candidates A and B for two phase positions separated by half a stellar rotation period is suggestive of the phased flaring detected from the binaries YY Gem and V711 Tau by [99] and [100]. RVs would be necessary to rule out a similar situation here since binarity is not evident in the TESS light curves. Spot evolution is observed in each light curve via changes in the amplitudes and phases of rotational variability (with the possible exception of Candidate B). Spot evolution is especially pronounced in Candidate F, making reflection/ellipsoidal modulation highly unlikely. The lack of phased flaring in Cycle 3 could also suggest there is no external trigger such as a companion star. However, if both a companion star and the right magnetic conditions are both required for periodicity to occur, then phased flaring could come and go as spots evolve. If no companion star or planet is

142 forcing the periodic release of magnetic energy, it is possible that conditions in the dominant spot may create a temporary ﬂare reservoir. We note this possibility is highly speculative.

143 CHAPTER 7: LASER-ONLY ADAPTIVE OPTICS ACHIEVES SIGNIFICANT IMAGE QUALITY GAINS COMPARED TO SEEING-LIMITED OBSERVATIONS OVER THE ENTIRE SKY

Adaptive optics laser guide star systems perform atmospheric correction of stellar wavefronts in two parts: stellar tip-tilt and high-spatial-order laser-correction. The requirement of a sufficiently bright guide star in the field-of-view to correct tip-tilt limits sky coverage. Here we show an improvement to effective seeing without the need for nearby bright stars, enabling full sky coverage by performing only laser-assisted wavefront correction. We used Robo-AO, the first robotic AO system, to comprehensively demonstrate this laser-only correction. We analyze observations from four years of efficient robotic operation covering 15,000 targets and 42,000 observations, each realizing different seeing conditions. Using an autoguider (or a post-processing software equivalent) and the laser to improve effective seeing independent of the brightness of a target, Robo-AO observations show a 39±19% improvement to effective FWHM, without any tip-tilt correction. We also demonstrate that 50% encircled-energy performance without tip-tilt correction remains comparable to diffraction-limited, standard Robo-AO performance. Faint-target science programs primarily limited by 50% encircled- energy (e.g. those employing integral field spectrographs placed behind the AO system) may see significant benefits to sky coverage from employing laser-only AO1.

1Content from this chapter previously appeared in Howard et al. 2018, AJ 155, 59. Nicholas Law designed the laser-only AO project, but I carried it out and wrote the paper. Nicholas Law and Carl Ziegler both advised the project and helped with the science done.

144 7.1 Improving the ability of adaptive optics to distinguish real planets orbiting faint M-dwarfs from false positives

Correcting atmospheric distortion of stellar wavefronts involves two components: tip-tilt (e.g. stellar image displacement) and point-spread-function (PSF) irregularities. The image quality of laser adaptive optics suffers without a sufficiently-bright guide star nearby to correct tip-tilt error [284]. High-resolution-imaging science programs that include faint targets are thus susceptible to tip-tilt errors. In the case of Kepler Objects of Interest (KOIs – i.e. stars that host planet candidates), follow-up using high-resolution observations is a key step to rule out false-positive scenarios. Kepler looks for the dip in brightness due to transits of the planet in front of the host star, and uses the transit depth and stellar radius to estimate planetary radius [285–287]. Any blending of associated stars on the sky to the host dilute the transit depth and artificially decrease the calculated planetary radius [288]. [289] notes that faint hosts have received less focus in high-resolution follow-up efforts. For example, M-dwarfs, the most populous stellar type in the Galaxy [290], are a class of intrinsically faint stars; Earth-sized planets orbit within the habitable zones of approximately one in six M-dwarfs [291]. Although M-dwarfs account for only 2% of all KOIs, the percentage of M-dwarfs amongst the faintest 12% of KOIs is three times higher than in the overall KOI population1. The ability to detect companion stars amongst the faintest KOIs disproportionately affects the confirmation of M-dwarf rocky planets. A KOI companion-star survey with Robo-AO, the first autonomous laser guide star adaptive optics system [292], has already observed 3857 KOIs due to its low observation overheads [287, 289, 293]. With hundreds of KOIs too faint for full Robo-AO post-facto

image registration (mV > 15.5), even modest gains in resolution above the seeing-limit allow discovery of companions deep within the Kepler ∼4” pixel scale [294].

1https://exoplanetarchive.ipac.caltech.edu/

145 In order to increase AO coverage of faint targets, methods to minimize tip-tilt error have been developed. The standard approaches are natural guide star (NGS) AO, laser guide star (LGS) AO [295], off-axis tip-tilt correction, e.g. [296–298], and laser-only AO [299]. NGS AO employs bright guide stars to correct both tip-tilt and high-order errors. LGS AO supplies a laser guide star to correct high-order errors, although a natural guide star is still necessary to correct tip-tilt. Off-axis tip-tilt correction employs an off-axis guide-star with respect to the observation target for approximate tip-tilt correction. Laser-only AO employs an LGS AO system, but with no natural guide-star, and hence no tip-tilt correction. Correcting high-order errors requires a brighter guide star than does correcting tip-tilt, vastly expanding the sky coverage of LGS AO over NGS AO. Even with LGS, the necessity of sufficiently-bright guide stars significantly limits AO sky coverage [284]. For large apertures, off-axis tip-tilt error is reduced compared to smaller 1- or 2-meter aperture AO systems [300]. Off-axis guide stars approximate the tip-tilt of the target star, improving effective seeing. Using the Altair AO system on the Gemini-North telescope [301], [297] designed and tested LGS + Peripheral WFS 1 (LGS+P1 henceforth), an off-axis guiding mode with low-Strehl “super-seeing.” LGS+P1 NIR observations of 101 to 102 targets give 2-to-3x improvement in effective seeing [297]. However, off-axis guiding is intended for large apertures, as scintillation and tip-tilt anisoplanatism decrease as aperture increases. Also relying upon reduced tip-tilt for large apertures, [299] and references therin explore the use of an LGS system while foregoing the tip-tilt guide star entirely. Employing the VLT in K-band for a handful of observations, they demonstrate significant improvement to FWHM and encircled energy using laser-only AO. Off-axis guiding is less applicable to AO systems on intermediate-class telescopes, such as on the Palomar 60-inch [292] or Kitt Peak 2.1-meter [302], the respective past and present host telescopes to Robo-AO. Scintillation also impacts the performance of laser-only AO on smaller apertures more than on larger telescopes, but the loss in effective seeing has been poorly characterized for large numbers of targets on smaller telescopes.

146 We evaluate the eﬀectiveness of laser-only AO systems without tip-tilt correction as an approach to sky coverage limitations for faint targets, but do so for 104 targets, using a vastly smaller robotic LGS system than the VLT or Gemini-North, and in the visible instead of NIR. To do this, we employ a new observation pipeline, Generalized Stellar Tracking And Correction (GenSTAC), described in section 7.2.2 of this paper. Robo-AO+GenSTAC (see

Figure 7.1) reaches targets from the Robo-AO guide star limiting-magnitude of ∼ mV = 15.5 to the telescope limiting magnitude for a given exposure time. GenSTAC achieves sky coverage at visible wavelengths through its ability to point anywhere in the sky, but at the cost of reduced angular resolution. For arbitrarily-long exposures, GenSTAC would need to be replaced with a physical autoguider to best perform laser-only correction. GenSTAC converts stars that are too faint for guide star correction into suﬃciently bright stars through stacking of an integer number of N binned frames and cubic-spline interpolation of stellar drift between averaged stellar positions. Any tip-tilt information inherent in brighter targets is applied for increased improvement to seeing, up to the diﬀraction limit, much

as the current Robo-AO faint-star (i.e. 15.5 < mV < 18) pipeline at Kitt Peak does [302]. When GenSTAC is instead applied to truly photon-starved targets with no remaining tip-tilt information, laser-only AO provides constant improvement down to the telescope limiting magnitude for a given exposure time. Although GenSTAC’s primary purpose is to simulate an autoguider in order to test laser-only AO, it becomes a tip-tilt optimizer when the number of averaged frames is close to one. In this limit, other image registration methods designed for the background-dominated regime of at least a few photons per frame, e.g. [303–305], may outperform GenSTAC when applied to targets bright enough for partial tip-tilt correction.

7.2 Methods

To measure the performance of operating in a laser-only mode, we ﬁrst reduce observations from the Robo-AO system with our laser-only pipeline:

147 0.8 Laser-only AO 0.8 Seeing-limited 0.4 0.4

0.0 0.0

Y / arcsec -0.4 Y / arcsec -0.4

-0.8 -0.8 -0.8-0.4 0.0 0.4 0.8 -0.8-0.4 0.0 0.4 0.8 X / arcsec X / arcsec (a) binary star

0.8 Laser-only AO 0.8 Seeing-limited 0.4 0.4

0.0 0.0

Y / arcsec -0.4 Y / arcsec -0.4

-0.8 -0.8 -0.8-0.4 0.0 0.4 0.8 -0.8-0.4 0.0 0.4 0.8 X / arcsec X / arcsec (b) single star

Figure 7.1: No tip-tilt + laser observations from GenSTAC, typifying improvement above the seeing-limit for a binary star 7.1(a) and a single star 7.1(b). Both images are selected from the one-second (no-tip-tilt correction), FWHM median-improvement bin of Figure 7.6(c) and displayed with min-max scaling.

7.2.1 Observations and Instrument Setup

Observations were acquired from May of 2012 through June of 2015 with Robo-AO, mounted on the Palomar 60-inch (1.5 m) telescope. Robo-AO eﬃciently observes hundreds of targets in a night [292]. As such, the observed-targets database resulting from hundreds of nights over four years of Robo-AO operation allows quantiﬁcation of AO performance on a large scale. While the AO system sets up for a given target, it obtains a 20-second seeing-limited observation to assess seeing conditions. The laser-launch system then pulses a 12 W, 355 nm ultraviolet beam along the host telescope line-of-sight out to a distance of 10 km to obtain a measurement of the atmospheric turbulence wavefront. A Shack-Hartmann wavefront sensor in the adaptive optics 1.2 kHz control loop feeds information to a CPU driving a MEMS actuator system, which adapts the shape of a deformable mirror in the optical path, providing wavefront correction. An Andor iXon EMCCD science camera records images at 8.6 FPS

148 Initiate GenSTAC

1st - coadd Final coadd

1. Subtract sky BKGD Frame 2. Dark sub. & flat field count modulo NO N? YES AUTOGUIDER: Corrects image NO Record star drift by centering EOF? position for N interpolated star frame stack YES position

Interpolate star positions between N EOF? points YES NO

Output co- added image

Figure 7.2: A flowchart describing GenSTAC. The first coaddition step (orange, left) reads in data and averages stellar position over N frames for interpolation. Next, the actual align-and-stack step (green, right) outputs final images. Initiation and output (blue) are also included. “EOF” abbreviates “End-of-file.” In this work, we choose N during the GenSTAC initiation step, but this choice may be scripted for fully automated use.

149 (0.1168 second frametime), allowing suﬃciently-short frametimes for after-the-fact guide star correction of tip-tilt errors, in a reduction pipeline described in [287]. The EMCCD reduces the read noise for short frametimes from about 50e− to < 1e−; Robo-AO employs typical EM-gains between 25x and 300x. The raw data are stored as frames of 1024×1024 pixels in FITS datacubes with a pixel scale of 0.043”.

7.2.2 Generalized Tracking and Correction Pipeline

We introduce a new pipeline, GenSTAC, to handle laser-only targets. The standard Robo-AO pipeline shifts-and-adds based upon cross-correlation to a diffraction-limited PSF. GenSTAC operates under the assumption of a large Gaussian PSF due to the lack of tip-tilt correction, and hence shifts-and-adds each frame based on averaged stellar positions over many frames. This enables laser-only correction on faint targets and faster operation on bright targets. When the average stellar position over N frames is reduced to N = 1, the original pipeline outperforms GenSTAC because GenSTAC does not cross-correlate with a diffraction-limited PSF. When GenSTAC finds the best solution to be N = 1 as described

below (i.e. for mV < 15.5 targets), it reverts to the original pipeline for full tip-tilt correction. GenSTAC shifts-and-adds frames according to the following steps, summarized in ﬁgure 7.2.

1. Raw frames are read into GenSTAC.

2. Choose the number of frames N to bin together for averaged stellar positions. When scripted, multiple values of N are tested and the best resulting FWHM determines the best2 N. Otherwise, the user chooses N directly.

GenSTAC binning is usually performed based upon the brightness of the target star. Extremely faint objects, producing less than one photon per frame, are binned on

2Using FWHM to determine the best N rather than magnitude avoids any danger from incorrect catalog magnitudes.

150 second-or-longer timescales to remove long-term tracking drifts. Brighter objects enable faster operation with improved performance using some tip/tilt information.

To quantify the eﬀective seeing of laser-only AO for 15,000 targets, however, N is speciﬁed by the user in order to bin away all tip-tilt information regardless of target brightness.

3. A ﬁrst-pass through the frames is performed. The average position of the star for each group of N frames throughout the observation is recorded during this ﬁrst coaddition step.

4. The averaged pixel positions are interpolated with one-dimensional cubic splines.

5. The frames are dark-subtracted, flat-fielded, shifted, and added to produce a final image. Shifting uses the output of the cubic interpolation in the previous step. While the standard Robo-AO bright-star pipeline [287] employs the Drizzle algorithm [306], Drizzle is not applied by GenSTAC due to the assumption of large Gaussian PSFs.

7.2.3 Measuring Performance

Once all frames are reduced into a final image, we use three measures to characterize the quality of each observation: the full-width at half-maximum (FWHM) diameter, the 50% encircled energy (θ50) diameter, and the Strehl ratio. FWHM is calculated as the diameter of the circle with an area of all pixels in the photometric aperture brighter than half the peak. θ50 is calculated as the diameter of the area containing half of the cumulative flux from the PSF. The Strehl is calculated as the total-flux-normalized peak intensity of the PSF divided by a theoretical diffraction-limited, normalized PSF. For the faint targets of the current paper, we are in the very low Strehl regime, making the FWHM and θ50 more relevant in quantifying faint AO performance.

151 We break up 15,000 separately-targeted Robo-AO observations into 42,000 images, typically of 30 seconds each. We desire to test laser-only image-quality over a wide range of conditions; as the seeing evolves rapidly, these 30-second exposures represent independent

realizations of the seeing. We then characterize the FWHM-, θ50-, and Strehl- improvements in eﬀective seeing. To ensure breaking up the 15,000 observations in this way does not bias

the seeing statistics, we compared median FWHM and θ50 using only one 30-second image per separately-targeted observation and observed no change in seeing statistics from using 42,000 realizations.

7.3 Results

We present measurements over the 15,000-observation Robo-AO dataset of 42,000 independent realizations of the seeing, to show eﬀective seeing for telescope-magnitude-limited targets. Although almost all Robo-AO observed targets were bright enough for tip-tilt correction (by design), we exclude all tip-tilt information from bright targets by binning frame-by-frame changes in position away in order to test laser-only AO performance on 15,000 targets. We also run statistical samples of the dataset over a range of binning timescales to quantify eﬀective seeing as tip-tilt error is added, from guide star correction all the way to laser-only correction.

7.3.1 System Performance and Resolution Improvement with Laser-only Correc- tion

For a 1.2-second binning timescale, simulating an autoguider-equipped Robo-AO for

observing a faint star, we compute the seeing-limited and laser-only FWHM, θ50, and Strehl of 14,954 separately-targeted observations, with 42,752 30-second images processed by GenSTAC. Seeing-limited performance is measured from the 20-second acquisition image for each observation. Observations with technical problems that would otherwise bias our data were removed from this list with 5σ-clips, leaving 14,158 targets and 40,521 images. The

152 1200 1.4 1050

1.2 900

1.0 750

600 0.8 450 0.6 300 Observation Density laser-only FWHM / arcsec

0.4 150

0 0.4 0.6 0.8 1.0 1.2 1.4 seeing-limited FWHM / arcsec (a) FWHM Comparison

2.25 2000

1750 2.00

c 1500

e 1.75 s c r

a 1250

1.50 0 5

1000 y l 1.25 n o

- 750 r e

s 1.00 Observation Density a l 500 0.75 250 0.50 0 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 seeing-limited 50 / arcsec

(b) θ50 Comparison

Figure 7.3: Performance contour plots of laser-only AO (Y/arcsec) versus seeing-limited performance (X/arcsec). 42,000 raw scatterplot points were 2D-binned, interpolated, and contour-plotted. Reference lines of increasing FWHMseeing/FWHMlaser−only are drawn to guide the eye. These include no increase (red) 1.5x (orange), and 3x (magenta).

153 80 280

70 240

60 200 50 160 40 120 30

80 Observation Density 20 Percent Improvement (%)

10 40

0 0 6 8 10 12 14 16 Magnitude (a) FWHM Improvement versus Magnitude

80 240

70 210

60 180

50 150

40 120

30 90

20 60 Observation Density Percent Improvement (%)

10 30

0 0 6 8 10 12 14 16 Magnitude

(b) θ50 Improvement versus Magnitude

Figure 7.4: Laser-only Improvement versus magnitude. Though median improvement (yellow) remains constant across magnitude, the spread of the data increases toward the faint end due to the eﬀects of noise while measuring resolution.

154 Table 7.1: Laser-only AO Results Summary Laser- Seeing- Improvement Laser/ only limited (%) Seeing (arcsec) (arcsec) Ratio FWHM 0.6±0.3 1.1±0.5 39±19% 0.6±0.2

θ50 (50% enc.) 1.1±0.5 1.5±0.5 23±16% 0.8±0.2 Strehl 0.024±0.017 0.010±0.007 — 2.1±1.1 Notes. – The Strehl laser/seeing ratio is equivalent to the ﬂux-normalized PSF relative peak intensity and is computed by dividing the laser-only Strehl by the seeing-limited Strehl for each observation. A 5σ cut was applied to the Strehls due to a small number of biasing outliers. – Laser-only values, seeing-limited values, percent-improvements, and ratios are computed for each observation separately. Medians and standard errors of the distributions are given; hence computing improvements directly from the quoted measurements will produce values diﬀerent from the ones above.

resulting distributions, descibed by median value and standard deviation, are as follows: Seeing-limited FWHM is 1.1”±0.5”, while laser-only AO FWHM is 0.6”±0.3”, an improvement

of 39±19%. Seeing-limited θ50 is 1.5”±0.5”, while laser-only AO θ50 is 1.1”±0.5”, an improvement of 23±16%. Strehls also showed improvement, although Strehl contrast in the faint-target regime becomes less relevant due to lower values. Laser-only Strehl is 0.024±0.017, while the seeing-limited Strehl is 0.010±0.007. Strehl improvement over the seeing-limit and the associated uncertainty are large due to the non-linear peak eﬀects of concentrating photons into a smaller area. All 42,000 individual observations are plotted against each other in Figure 7.3. Scatterplot points are 2D-binned, interpolated, and displayed as AO-resolution versus seeing-resolution contours. As a check against implicit tuning toward bright targets in the Robo-AO dataset, we examine improvement-vs-brightness contour-scatterplots in Figure 7.4, which remains relatively constant across magnitude. For faint targets close to the background-noise level, measurement of resolution becomes slightly less accurate, with a small apparent increase in improvement, although not at a signiﬁcant-enough level to obscure the constant-improvement trend.

155 700 700 700 600 laser-only laser-only laser-only laser-only 600 0.1 sec seeing-lim 600 0.2 sec seeing-lim 600 0.6 sec seeing-lim 1.2 sec seeing-lim 500

500 500 500 400

400 400 400 300

Count 300 Count 300 Count 300 Count

200 200 200 200

100 100 100 100

0 0 0 0 0.0 0.3 0.6 0.9 1.2 1.5 1.8 0.0 0.3 0.6 0.9 1.2 1.5 1.8 0.0 0.3 0.6 0.9 1.2 1.5 1.8 0.0 0.3 0.6 0.9 1.2 1.5 1.8 FWHM / arcsec FWHM / arcsec FWHM / arcsec FWHM / arcsec (a) Laser-oﬀ / Laser-on FWHM Distributions

400 600 laser-only laser-only laser-only laser-only 500 500 350 0.1 sec seeing-lim 0.2 sec seeing-lim 0.6 sec seeing-lim 1.2 sec seeing-lim 500

300 400 400 400 250 300 300 200 300 Count Count Count Count 150 200 200 200 100 100 100 100 50

0 0 0 0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 2.5 3.0 50% encircled energy / arcsec 50% encircled energy / arcsec 50% encircled energy / arcsec 50% encircled energy / arcsec

(b) Laser-oﬀ / Laser-on θ50 Distributions

350 600 500 500 FWHM FWHM FWHM FWHM 0.1 sec 0.2 sec 0.6 sec 1.2 sec 300 θ-50 500 θ-50 θ-50 θ-50 400 400 250 400 300 300 200 300

Count 150 Count Count Count 200 200 200 100 100 100 50 100

0 0 0 0 20.0 40.0 60.0 80.0 100.0 20.0 40.0 60.0 80.0 100.0 20.0 40.0 60.0 80.0 100.0 20.0 40.0 60.0 80.0 100.0 Percent Improvement (%) Percent Improvement (%) Percent Improvement (%) Percent Improvement (%)

Figure 7.6: Well-behaved normal or skewed-normal resolution distributions, for laser-on and laser-oﬀ. Distribution medians indicate system performance, as distribution wings contain some observations with technical problems. However much tip-tilt is possible for each timescale is applied to both seeing-limited and AO-images, resulting in slightly-underestimated improvement for 0.1-0.6 second timescales.

156 7.3.2 Sensitivity of Improvement to Guiding Timescale

In addition to laser-only correction, we measure AO-correction with varying amounts of tip-tilt present. Stacking more frames progressively removes tip-tilt information. In Figure 7.5 we show that the FWHM performance drops to a steady value around one-second timescales, while the θ50 remains approximately constant across timescales.

We randomly selected several observations of θ50 median improvement and measured normalized cumulative flux as a function of radius away from PSF center. For each target, the cumulative flux distribution for full-AO, partial tip-tilt “hybrid”-AO, and seeing-limited tracking were compared. A 0.6-second guiding timescale was chosen as representative of “hybrid” tracking. While seeing-limited cumulative flux always converges last, both full-AO

and “hybrid”-AO distributions quickly converge and have nearly identical θ50, within ∼ 0.1” of each other. Within the 50% encircled energy radius, the contributions from the PSF core to the cumulative distribution, which occur at very small radii, are dominated by the roughly

linear increase in PSF ﬂux that scales as enclosed-area. This agrees with the median θ50 obtained from each larger guiding-timescale sample: a diﬀraction-limited 0.1-second timescale

median θ50 of 1.04” is only 0.1” better than a 1.2-second autoguider timescale median θ50 of

1.15”. For reference, the median θ50 for slow-guided, seeing-limited observations is 1.5”. The takeaway from this 50% encircled energy behavior is that for science goals requiring high-resolution energy-encircled observations, a Robo-AO LGS system equipped with an autoguider and running the laser system should give comparable performance to full-AO correction. For faint targets especially, this greatly reduces the sky-coverage tip-tilt problem. We also estimate the limiting magnitude for which each timescale is valid. Diﬀraction- limited performance with tip-tilt correction is possible to ∼15.5th magnitude. We estimate that GenSTAC provides some improvement by using residual tip-tilt information down to ∼18th magnitude, and operates as a software slow-guider for targets down to the limiting magnitude of the instrument at a given exposure time.

157 Guiding Timescale (seconds) 0.12 0.23 0.58 1.17 2.34 100 FWHM

θ50 80

40 Percent Improvement 20

(Full AO; laser & tip-tilt) (No AO, autoguider only) 0 N=1 N=2 N=5 N=10 N=20 Binned # of Frames, N

Figure 7.5: Improvement in eﬀective seeing across guiding timescale. GenSTAC’s guide star mode lies to the left, where full tip-tilt information is employed, while the autoguider mode to the right uses no tip-tilt information. 3σ-clips are applied to the means of each FWHM distribution, as FWHM standard performance in “hybrid mode” is aﬀected by failed measurements in the distribution wings. θ50 is more robust, requiring no cuts.

Samples were randomly selected from 42,000 observations and processed at characteristic timescales (N). Assuming approximately normal distributions, mean improvements for each timescale were obtained at a 99% conﬁdence interval and margins-of-error of no more than

∼1.1 pixel and ∼2% for resolutions (FWHM and θ50) and percent improvements, respectively. A 3σ cut to FWHM was applied to each sample, removing up to 10% of observations. Without this cut, mean FWHM improvement is aﬀected by occasional observations with technical problems, where telescope shake was present, or the PSF of a binary was measured

assuming a non-binary. The margin-of-error for FWHM and θ50 remained less than ∼1.1 pixel without any sigma-clipping. Figure 7.6 veriﬁes our assumption of normal or skewed-normal distributions for each measurement, such that σ-clipping does not remove standard system performance.

7.4 Summary and suggestions for the implementation of laser-only AO

For our LGS AO system, Robo-AO, the eﬀective seeing upon arbitrarily faint targets demonstrates 39±19% improvement above the seeing-limit, even in the absence of tip-tilt correction. Faint targets with some recoverable tip-tilt information show corresponding gains

158 in seeing, culminating in diffraction-limited performance for moderately bright guide star targets. Our FWHM results on an intermediate-class telescope show a 2x-3x effective-seeing improvement similar to those of the LGS+P1 mode upon the Gemini-North telescope. Due to the lack of tip-tilt correction, laser-only AO does not require large apertures such as that of Gemini-North. Furthermore, whereas LGS+P1 improvements have been demonstrated in the NIR for 102 targets [297], our LGS without tip-tilt improvement holds for 104 targets, into the visible. 50% encircled energy demonstrates for 104 targets the same improvement upon both diffraction-limited tip-tilt correction and slow-guiding correction where tip-tilt correction is no longer possible, in agreement with [299]. These results suggest that intermediate-class telescopes equipped with LGS AO systems will see significant gains in performance upon faint targets when running the laser with a slow-guiding drift corrector, especially upon targets for which we most care about the energy encircled. For example, the proposed Rapid Transient Surveyor instrument (RTS) combines an integral field spectrograph (IFS) placed behind an LGS AO system on the robotized University of Hawai’i 2.2-meter telescope. RTS will enable precise mapping of dark matter in the local universe by characterizing SN1a in the IR, which

requires IFS for faint sources [307]. Our θ50 results motivate future exploration of laser-only IFS for those RTS targets without suﬃciently-bright guide stars. We investigate laser-only AO with GenSTAC, a new Robo-AO pipeline. GenSTAC provides post-processing options for guide-star correction, partial tip-tilt correction, and laser-only correction. GenSTAC binning on timescales longer than 1 second serves as a software equivalent to a slow-guider mounted to the telescope by converting stars that are too faint for guide star correction into adequate stars through averaging and interpolating procedures described in 7.2.2. For moderately-faint targets, it extracts any remaining tip-tilt information; very faint targets with no tip-tilt information will rely purely on laser correction.

159 As LGS AO systems continue to proliferate [308], small-to-intermediate-class observatories with LGS will beneﬁt greatly from running the laser and a slow-guider whenever observing faint targets beyond diﬀraction-limited sky-coverage.

160 CHAPTER 8: CONCLUSIONS AND OUTLOOK

This ﬁnal chapter summarizes the key results of my dissertation work and explores the implications for stellar astrophysics and planetary habitability.

8.1 Long-term Monitoring of Flares from the Cool Stars Across Half the South- ern Sky

I discussed the results of my survey to detect superflares across the Southern sky. Because superflares are rare and short-lived events, multi-year observations at high cadence are required to observe a large sample. I performed the first high-cadence survey of the long-term superflare rates of the brightest M-dwarfs in half the Southern sky. The survey observed 575 flares from 284 flare stars, with a marked increase in flaring at spectral types close to the M4 fully-convective boundary. The survey found 15% of the highest-priority TESS planet-search targets are currently emitting flares capable of impacting the habitability of their planets. Superflares from two nearby M-dwarf systems with terrestrial exoplanets were detected. The first was from the nearest star to our Sun, Proxima Cen. The other was from the LTT 1445 system, which hosts one of the closest transiting exoplanets amenable to atmospheric characterization. The system is a triple, making it unclear whether the superflare is from the planet host [309]. In all, we report approximately twice the previous largest number of 1034 erg high-cadence flares from nearby cool stars. We find 8 flares with amplitudes comparable to the Proxima superflare, with the largest reaching 5.6 magnitudes and releasing 1036.2 erg. We find a decrease in average flare energy at later spectral types arising from the decreasing size of the stellar convective region. We present average FFDs of active stars as a function of spectral type and measure the annual superflare rates of each spectral type, with

161 late-K and early-M dwarfs demonstrating the highest rates. We also find that the largest flare amplitudes expected from a flaring star of each spectral type in a given observation time increases for later types. We find that the decay times of our superflares are broadly consistent with emission caused by magnetic re-connection, although we cannot rule out the possibility of further emission mechanisms. We approximate the minimum starspot coverage required to produce superflares, and hypothesize the maximum allowed values of superflare energy and waiting time between flares corresponding to 100% hemispherical spot coverage. Such values are extrapolations from the G-dwarf superflare regime and should be treated with caution, especially since the minimum spot area we compute may be at least an order-of-magnitude less than the true spot area. Finally, we observe a decreasing superflare rate for older stars at high galactic latitude. By combining the frequently-occurring small and moderate flares seen by TESS across 28 days with rare superflares observed over multiple years by Evryscope, we may better explore the FFD of each star in the South. From a well-constrained FFD, planetary atmosphere modeling for rocky TESS planets orbiting flare stars will inform the atmospheric compositions and surface UV environments of these worlds. Well-constrained FFDs for such a large sample will also make possible large-scale statistical treatments of superflare occurrence as functions of stellar rotation, stellar age, binarity, and surface magnetic field topology. I discussed how superflare rates are related to stellar rotation rates. I compared the superflare rates of M-dwarf rotators throughout the spin-down process and found the rates of the highest energy flares follow the same age-activity relations previously observed for smaller flares. I also found that rotational variability in the light curves due to star spots shows a color dependence, with the g0-TESS color depending on stellar mass. This change in contrast with mass is likely due to the differing temperatures of spots and stars in the M-dwarf regime. The survey observed 122 rotators in our larger sample of 284 late K and early-to-mid M flare stars, with periods ranging from 0.3487 to 104 days. We observe 30 fast rotators

162 (Ro <0.04), 59 intermediate-period rotators (0.04

the surface magnetic ﬁeld, and 33 slow rotators (Ro >0.44). We ﬁnd the sinusoidal amplitudes of rotation of cool stars often exceed 1% variability, suggesting the combination of 28 d TESS observations and long-term, moderate-precision ground based observations may greatly increase the number and precision of rotation period measurements for nearby cool stars.

We ﬁnd our PRot <10 d (Ro <0.2) rotators demonstrate higher superﬂare rates, largest

ﬂare energies observed per star, and starspot coverage fractions than do PRot >10 d (Ro >0.2)

rotators. Splitting up our rotators instead into fast (Ro <0.04), intermediate (0.04

and slow (Ro >0.44) rotators do not result in statistically significant increases from the fast to intermediate rotators, although a possible rise in the superflare rate of intermediate rotators is observed visually. Therefore, we do not conclusively confirm the increased activity of intermediate rotators seen in previous studies. Because our sample is specifically selected to only include flare stars from the 2 min cadence cool stars observed by TESS, the 2× increase in intermediate rotators we find over fast or slow rotators may itself be indicative of increased activity at these periods. I discussed the first systematic exploration of the temperature evolution of M-dwarf superflares using 40 events observed simultaneously at 2 min cadence with Evryscope and TESS. I discovered for the first time in a statistical sample that higher energy superflares often have higher temperatures. The multi-band photometry and analysis within our uniform sample is well-suited to statistical studies of the flare properties. We demonstrate for the first time in a large sample that flare energy and impulse are predictors of the optical temperature evolution of M-dwarf superflares. These relationships are a key step toward tailored blackbody temperatures for flares observed in photometry only, rather than having to assume 9000 K.

8.2 Implications of superﬂares on planetary habitability and astrobiology

Among our superﬂare sample, we observe a number of extreme events. We observe 8 ﬂares that increased the brightness of their host star by at least 3 stellar magnitudes in

163 g 0 and released at least 1035 erg. The largest of these flares is a 5.6 magnitude event from an active 40 Myr-old Tuc-Hor cluster member. This flare released 1036.2 erg, enough energy to completely photo-dissociate the ozone column of an Earth-like planet in one event. If we factor in high energy particles potentially associated with flares, lesser superflares become equally dangerous. For example, we find 17 stars that may fully attenuate an Earth-like atmosphere via repeated flaring by emitting at least 0.1 1034 erg flares d−1. Of the 1822 stars

around which TESS may discover planets smaller than 2R⊕ in the HZ, we observe only 49 to emit large flares. Because most of these 1822 host stars are faint in the blue, we only searched the brightest 335 for flares, resulting in 14.6±2% with large flares. Although higher-mass young M-dwarfs may emit more biologically-relevant UV flux as a consequence of frequent superflares than do lower-mass young M-dwarfs, we do not confirm that more UV-C flux from early M-dwarf superflares consistently reaches the HZ. The relative habitability of early versus mid M-dwarf planets is a topic for future work. In particular, the shorter active lifetimes of early M-dwarfs may allow planetary atmospheres to recover as the star ages via degassing [310]. During superflares, we estimate rocky HZ planets orbiting <200 Myr stars typically receive a top-of-atmosphere UV-C flux of ∼120 W m−2 and up to 103 W m−2, 100-1000× the time-averaged XUV flux from Proxima Cen. These levels may suggest Earth-like atmospheres and surface life would be difficult to maintain on the side of the planet facing the star. I described the Evryscope discovery of the Proxima superflare. This event delivered a potentially lethal dose of UV radiation to Proxima b. I found Proxima emits 2-5 superflares/yr, a rate likely sufficient to remove the ozone layer of an Earth-like planet at the distance of Proxima b over short geological timescales. On Proxima b, the Evryscope superflare (along with Proxima’s regular and extreme activity) leads to our photochemical model predicting 90% ozone destruction within 5 years. As Proxima’s ozone column fraction does not reach a steady state at the end of that period but instead continues a clear downward trend, we conclude that Proxima b has likely suffered extreme ozone loss over long timescales. If the

164 current activity rate of Proxima holds for longer timescales, >99.9% of the planetary O3 is likely to be lost within 100s of kyr, leaving the planet’s surface largely unprotected from UV light, and forcing extreme adaptation by any organisms on the Proxima-facing surface of Proxima b.

8.3 Flare periodicity as a probe of starspots and magnetic interactions companions

We have developed and tested two new approaches to detect and statistically confirm flare periodicity. The periodograms are leveraged to perform the first large-scale survey for

periodicity in flare rates that explores periods other than Prot. After imposing the 1% FAP cut, at least 2% of flare stars are found to exhibit periodicity. Our results strengthen the correlation between flare periodicity and spot evolution from [79]. Should flare periodicity be shown to probe SPIs as predicted by [98], TESS light curves will open a new window on the discovery and characterization of close-in exoplanets. For example, the magnetic fields of M-dwarf terrestrial planets remain unexplored [311]. Probing their magnetospheres through phased flares might potentially enable the first tests of magnetic dynamo evolution of rocky planets outside our solar system and inform planetary habitability. Alternately, a search for flare periodicity across the entire TESS data set would place two orders of magnitude better constraints on the occurrence of flare reservoirs or interacting binaries like YY Gem than has previously been possible. Building on the work of [89], the conditions under which TESS flares depend on active longitude could be ascertained.

8.4 Using Laser-only AO to increase sky coverage

We used Robo-AO, the first robotic AO system, to demonstrate laser-only AO can achieve a 39±19% improvement to the PSF. We also demonstrated that 50% encircled-energy performance without tip-tilt correction remains comparable to diffraction-limited, standard Robo-AO performance. Faint-target science programs using integral field spectrographs where

165 the primary science limitation is the 50% encircled-energy may signiﬁcantly extend their sky coverage by employing laser-only AO.

8.5 Future Outlook

8.5.1 Habitability of TESS planets

The brightest M-dwarf planetary systems are prime targets for atmospheric characterization. However, at least 46 candidate and confirmed TESS Objects of Interest (TOI) are flare stars. Because superflares likely dominate UV-induced photo-dissociation in planetary atmospheres [131], host stars must be prioritized for atmospheric characterization based on the existence or non-existence of an atmosphere. TOIs will ultimately make up the majority of targets amenable to atmospheric characterization [312]. I plan to measure the flare frequency distributions of these targets, allowing me to constrain the UV flux reaching planetary atmospheres of currently-known planets.

8.5.2 Flare temperatures across the sky and across geological time

By obtaining spectra of Evryscope detected superflares within minutes of their occurrence using EFTE and the 4.1 m Southern Astrophysical Research Telescope, the high (42,000 K) temperatures of hot superflares often seen in the Evryscope and TESS light curves will also be spectrally confirmed [313]. In future work with Evryscope and TESS light curves, we will investigate enough flares observed simultaneously at 2 min cadence in order to create separate energy and impulse relationships for each spectral sub-type. We also require higher cadence to better constrain impulsive flare emission, which can occur on 10 s timescales [258]. TESS will re-observe most EvryFlare targets during Cycle 3 at 20 s cadence as part of G0 3174 to investigate the relationship between impulsive emission and temperatures of M-dwarf superflares.

166 My larger survey would determine how the UV flux driving the potential habitability of M-dwarf planets changes across geological time. 160±40 multiband flares will occur in young moving groups or clusters of known ages (e.g. [89]). The UV flux of superflares that reaches the HZ and the ages of the systems will be compared to place limits on the evolution of life on M-dwarf planets.

8.5.3 An all-sky ﬂare periodicity survey

My initial survey has demonstrated the feasibility of extending the flare periodogram analysis to all 15,000 cool stars that have high cadence TESS light curves. The amplitudes of flares sufficiently large to be part of a candidate phased-flares signal are robustly determined

by the A-σA mechanism. Once the sample of candidate flares has been identified, Monte-Carlo calculations of periodogram power and signal strength are obtained and the causes of the periodicity may be explored. At least ∼20 detections should occur in a survey of all 2 min cadence TESS light curves of late K and M-dwarf stars (assuming the fractions of flare stars from [143]). Such a survey will often detect correlations between the phased flares period and the stellar rotation period. I would confirm if SPI signals are indeed difficult to identify and/or rare.

8.5.4 Multi-wavelength ﬂare surveys

I hope to continue leveraging Evryscope and TESS flare observations by combining them with other simultaneous wavelengths. For example, multi-wavelength observations of flares from Proxima Cen spanning the FUV to the sub-mm and radio have shown that optical flares are only weakly correlated with sub-mm/FUV flares, while a tentative scaling relationship between the sub-mm and FUV appears [314]. More flares observed in many wavelengths will increase confidence in tentative and even presently undiscovered scaling relationships.

167 In conjunction with coronal-mass-ejection searches from radio arrays like the LWA [315] and Jansky Very Large Array [316], the Evryscope will also aid in constraining the long-term atmospheric eﬀects of extreme stellar activity.

8.6 Final Thoughts

Superflares are a key driver of exoplanet habitability, yet only 25% of nearby stars have received multi-year monitoring. As the effort to characterize rocky exoplanet atmospheres begins in earnest with the launch of the James Webb Space Telescope and new generations of large ground-based telescopes, the planetary effects of superflares must be considered [317]. This dissertation has demonstrated the feasibility of measuring superflare rates for each bright nearby star. The reality of a bio-signature detected from such a cool star may someday be the subject of debate: is it due to life, or due to flares?

168 REFERENCES

[1] Kazunari Shibata. Evidence of Magnetic Reconnection in Solar Flares and a Uniﬁed Model of Flares. Astrophysics and Space Science, 264:129–144, 1999. doi: 10.1023/A: 1002413214356.

[2] J. C. Allred, A. F. Kowalski, and M. Carlsson. A Uniﬁed Computational Model for Solar and Stellar Flares. Astrophysical Journal, 809:104, 2015. doi: 10.1088/0004-637X/ 809/1/104.

[3] L. Fletcher and H. S. Hudson. Impulsive Phase Flare Energy Transport by Large-Scale Alfv´enWaves and the Electron Acceleration Problem. Astrophysical Journal, 675: 1645–1655, 2008. doi: 10.1086/527044.

[4] P. Heinzel and K. Shibata. Can Flare Loops Contribute to the White-light Emission of Stellar Superﬂares? Astrophysical Journal, 859:143, 2018. doi: 10.3847/1538-4357/ aabe78.

[5] S. Jejˇciˇc,L. Kleint, and P. Heinzel. High-density Oﬀ-limb Flare Loops Observed by SDO. Astrophysical Journal, 867:134, 2018. doi: 10.3847/1538-4357/aae650.

[6] J. R. A. Davenport, S. L. Hawley, L. Hebb, J. P. Wisniewski, A. F. Kowalski, E. C. Johnson, M. Malatesta, J. Peraza, M. Keil, S. M. Silverberg, T. C. Jansen, M. S. Scheﬄer, J. R. Berdis, D. M. Larsen, and E. J. Hilton. Kepler Flares. II. The Temporal Morphology of White-light Flares on GJ 1243. Astrophysical Journal, 797:122, 2014. doi: 10.1088/0004-637X/797/2/122.

[7] K. Shibata, H. Isobe, A. Hillier, A. R. Choudhuri, H. Maehara, T. T. Ishii, T. Shibayama, S. Notsu, Y. Notsu, T. Nagao, S. Honda, and D. Nogami. Can Superﬂares Occur on Our Sun? Publications of the ASJ, 65:49, 2013. doi: 10.1093/pasj/65.3.49.

[8] R. C. Carrington. Description of a Singular Appearance seen in the Sun on September 1, 1859. Monthly Notices of the Royal Astronomical Society, 20(1):13–15, 1859. doi: 10.1093/mnras/20.1.13.

[9] J. C. Tarter, P. R. Backus, R. L. Mancinelli, J. M. Aurnou, D. E. Backman, G. S. Basri, A. P. Boss, A. Clarke, D. Deming, L. R. Doyle, E. D. Feigelson, F. Freund, D. H. Grinspoon, R. M. Haberle, S. A. Hauck, II, M. J. Heath, T. J. Henry, J. L. Hollingsworth, M. M. Joshi, S. Kilston, M. C. Liu, E. Meikle, I. N. Reid, L. J. Rothschild, J. Scalo, A. Segura, C. M. Tang, J. M. Tiedje, M. C. Turnbull, L. M. Walkowicz, A. L. Weber, and R. E. Young. A Reappraisal of The Habitability of Planets around M Dwarf Stars. Astrobiology, 7:30–65, 2007. doi: 10.1089/ast.2006.0124.

[10] Bradley E. Schaefer, Jeremy R. King, and Constantine P. Deliyannis. Superﬂares on Ordinary Solar-Type Stars. Astrophysical Journal, 529(2):1026–1030, 2000. doi: 10.1086/308325.

169 [11] H. Maehara, T. Shibayama, S. Notsu, Y. Notsu, T. Nagao, S. Kusaba, S. Honda, D. Nogami, and K. Shibata. Superﬂares on solar-type stars. Nature, 485:478–481, 2012. doi: 10.1038/nature11063.

[12] E. W. Cliver, H. Hayakawa, Jeﬀrey J. Love, and D. F. Neidig. On the Size of the Flare Associated with the Solar Proton Event in 774 AD. Astrophysical Journal, 903(1):41, 2020. doi: 10.3847/1538-4357/abad93.

[13] Philip S. Muirhead, Courtney D. Dressing, Andrew W. Mann, BárbaraRojas-Ayala, SébastienLépine,Martin Paegert, Nathan De Lee, and Ryan Oelkers. A Catalog of Cool Dwarf Targets for the Transiting Exoplanet Survey Satellite. Astronomical Journal, 155:180, 2018. doi: 10.3847/1538-3881/aab710.

[14] J. R. A. Davenport, D. M. Kipping, D. Sasselov, J. M. Matthews, and C. Cameron. MOST Observations of Our Nearest Neighbor: Flares on Proxima Centauri. Astrophys- ical Journal, 829:L31, 2016. doi: 10.3847/2041-8205/829/2/L31.

[15] G. Chabrier. Galactic Stellar and Substellar Initial Mass Function. Publications of the Astronomical Society of the Paciﬁc, 115:763–795, 2003. doi: 10.1086/376392.

[16] T. J. Henry, J. P. Subasavage, M. A. Brown, T. D. Beaulieu, W.-C. Jao, and N. C. Hambly. The Solar Neighborhood. X. New Nearby Stars in the Southern Sky and Accurate Photometric Distance Estimates for Red Dwarfs. Astronomical Journal, 128: 2460–2473, 2004. doi: 10.1086/425052.

[17] T. J. Henry, W.-C. Jao, J. P. Subasavage, T. D. Beaulieu, P. A. Ianna, E. Costa, and R. A. M´endez. The Solar Neighborhood. XVII. Parallax Results from the CTIOPI 0.9 m Program: 20 New Members of the RECONS 10 Parsec Sample. Astronomical Journal, 132:2360–2371, 2006. doi: 10.1086/508233.

[18] Sarah J. Schmidt, Benjamin J. Shappee, Jennifer L. van Saders, K. Z. Stanek, Jonathan S. Brown, C. S. Kochanek, Subo Dong, Maria R. Drout, Stephan Frank, T. W.-S. Holoien, Sean Johnson, Barry F. Madore, J. L. Prieto, Mark Seibert, Marja K. Seidel, and Gregory V. A. Simonian. The largest m dwarf ﬂares from ASAS-SN. The Astrophysical Journal, 876(2):115, 2019. doi: 10.3847/1538-4357/ab148d.

[19] V. A. Ambartsumian and L. V. Mirzoian. Flare stars in star clusters and associations. In V. E. Sherwood and L. Plaut, editors, Variable Stars and Stellar Evolution, volume 67 of IAU Symposium, pages 3–14, 1975.

[20] James R. A. Davenport, Kevin R. Covey, Riley W. Clarke, Austin C. Boeck, Jonathan Cornet, and Suzanne L. Hawley. The Evolution of Flare Activity with Stellar Age. Astrophysical Journal, 871:241, 2019. doi: 10.3847/1538-4357/aafb76.

[21] E. Ilin, S. J. Schmidt, J. R. A. Davenport, and K. G. Strassmeier. Flares in open clusters with K2 . I. M 45 (Pleiades), M 44 (Praesepe), and M 67. Astronomy and Astrophysics, 622:A133, 2019. doi: 10.1051/0004-6361/201834400.

170 [22] A. A. West, K. L. Weisenburger, J. Irwin, Z. K. Berta-Thompson, D. Charbonneau, J. Dittmann, and J. S. Pineda. An Activity-Rotation Relationship and Kinematic Analysis of Nearby Mid-to-Late-Type M Dwarfs. Astrophysical Journal, 812:3, 2015. doi: 10.1088/0004-637X/812/1/3. [23] N. Astudillo-Defru, X. Delfosse, X. Bonfils, T. Forveille, C. Lovis, and J. Rameau. Magnetic activity in the HARPS M dwarf sample. The rotation-activity relationship for very low-mass stars through R’(HK). Astronomy and Astrophysics, 600:A13, 2017. doi: 10.1051/0004-6361/201527078. [24] E. R. Newton, J. Irwin, D. Charbonneau, P. Berlind, M. L. Calkins, and J. Mink. The Hα Emission of Nearby M Dwarfs and its Relation to Stellar Rotation. Astrophysical Journal, 834:85, 2017. doi: 10.3847/1538-4357/834/1/85. [25] N. J. Wright, E. R. Newton, P. K. G. Williams, J. J. Drake, and R. K. Yadav. The stellar rotation-activity relationship in fully convective M dwarfs. Monthly Notices of the Royal Astronomical Society, 479:2351–2360, 2018. doi: 10.1093/mnras/sty1670. [26] Huiqin Yang, Jifeng Liu, Qing Gao, Xuan Fang, Jincheng Guo, Yong Zhang, Yonghui Hou, Yuefei Wang, and Zihuang Cao. The flaring activity of m dwarfs in the kepler field. The Astrophysical Journal, 849(1):36, 2017. doi: 10.3847/1538-4357/aa8ea2. [27] A. A. West, S. L. Hawley, J. J. Bochanski, K. R. Covey, I. N. Reid, S. Dhital, E. J. Hilton, and M. Masuda. Constraining the Age-Activity Relation for Cool Stars: The Sloan Digital Sky Survey Data Release 5 Low-Mass Star Spectroscopic Sample. Astronomical Journal, 135:785–795, 2008. doi: 10.1088/0004-6256/135/3/785. [28] R. R. Paudel, J. E. Gizis, D. J. Mullan, S. J. Schmidt, A. J. Burgasser, P. K. G. Williams, A. Youngblood, and K. G. Stassun. K2 Ultracool Dwarfs Survey - V. High superflare rates on rapidly rotating late-M dwarfs. Monthly Notices of the Royal Astronomical Society, 486(1):1438–1447, 2019. doi: 10.1093/mnras/stz886. [29] St. Raetz, B. Stelzer, M. Damasso, and A. Scholz. Rotation-activity relations and flares of M dwarfs with K2 long- and short-cadence data. Astronomy and Astrophysics, 637: A22, 2020. doi: 10.1051/0004-6361/201937350. [30] Nicholas Mondrik, Elisabeth Newton, David Charbonneau, and Jonathan Irwin. An Increased Rate of Large Flares at Intermediate Rotation Periods for Mid-to-late M Dwarfs. Astrophysical Journal, 870:10, 2019. doi: 10.3847/1538-4357/aaee64. [31] Ward S. Howard, Hank Corbett, Nicholas M. Law, Jeffrey K. Ratzloff, Nathan Galliher, Amy Glazier, Octavi Fors, Daniel del Ser, and Joshua Haislip. EvryFlare. II. Rotation Periods of the Cool Flare Stars in TESS across Half the Southern Sky. Astrophysical Journal, 895(2):140, 2020. doi: 10.3847/1538-4357/ab9081. [32] Ekaterina Ilin, Sarah J. Schmidt, Katja Poppenhäger,James R. A. Davenport, Martti H. Kristiansen, and Mark Omohundro. Flares in open clusters with K2. II. Pleiades, Hyades, Praesepe, Ruprecht 147, and M 67. Astronomy and Astrophysics, 645:A42, 2021. doi: 10.1051/0004-6361/202039198.

171 [33] Adam F. Kowalski, Suzanne L. Hawley, John P. Wisniewski, Rachel A. Osten, Eric J. Hilton, Jon A. Holtzman, Sarah J. Schmidt, and James R. A. Davenport. Time-resolved Properties and Global Trends in dMe Flares from Simultaneous Photometry and Spectra. The Astrophysical Journal Supplement Series, 207:15, 2013. doi: 10.1088/0067-0049/ 207/1/15. [34] Suzanne L. Hawley, Lucianne M. Walkowicz, Joel C. Allred, and Jeff A. Valenti. Near- Ultraviolet Spectra of Flares on YZ CMi. Publications of the Astronomical Society of the Pacific, 119(851):67–81, 2007. doi: 10.1086/510561. [35] R. A. Osten and S. J. Wolk. Connecting Flares and Transient Mass-loss Events in Magnetically Active Stars. Astrophysical Journal, 809:79, 2015. doi: 10.1088/ 0004-637X/809/1/79. [36] Adam F. Kowalski, Mihalis Mathioudakis, and Suzanne L. Hawley. The Evolution of T = 10,000 K Blackbody-Like Continuum Radiation in the Impulsive Phase of dMe Flares. In 20th Cambridge Workshop on Cool Stars, Stellar Systems and the Sun, Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, page 42, 2018. doi: 10.5281/zenodo.1463140. [37] Richard D. Robinson, Jonathan M. Wheatley, Barry Y. Welsh, Karl Forster, Patrick Morrissey, Mark Seibert, R. Michael Rich, Samir Salim, Tom A. Barlow, Luciana Bianchi, Yong-Ik Byun, Jose Donas, Peter G. Friedman, Timothy M. Heckman, Patrick N. Jelin- sky, Young-Wook Lee, Barry F. Madore, Roger F. Malina, D. Christopher Martin, Bruno Milliard, Susan G. Neff, David Schiminovich, Oswald H. W. Siegmund, Todd Small, Alex S. Szalay, and Ted K. Wyder. GALEX Observations of an Energetic Ultraviolet Flare on the dM4e Star GJ 3685A. Astrophysical Journal, 633(1):447–451, 2005. doi: 10.1086/444608. [38] Adam F. Kowalski and Joel C. Allred. Parameterizations of Chromospheric Condensa- tions in dG and dMe Model Flare Atmospheres. Astrophysical Journal, 852(1):61, 2018. doi: 10.3847/1538-4357/aa9d91. [39] Cynthia S. Froning, Adam Kowalski, Kevin France, R. O. Parke Loyd, P. Chris- tian Schneider, Allison Youngblood, David Wilson, Alexander Brown, Zachory Berta- Thompson, J. Sebastian Pineda, Jeffrey Linsky, Sarah Rugheimer, and Yamila Miguel. A hot ultraviolet flare on the m dwarf star GJ 674. The Astrophysical Journal, 871(2): L26, 2019. doi: 10.3847/2041-8213/aaffcd. [40] C. H. Lacy, T. J. Moffett, and D. S. Evans. UV Ceti stars: statistical analysis of observational data. Astrophysical Journals, 30:85–96, 1976. doi: 10.1086/190358. [41] S. L. Hawley and B. R. Pettersen. The great flare of 1985 April 12 on AD Leonis. Astrophysical Journal, 378:725–741, 1991. doi: 10.1086/170474. [42] R. O. Park Loyd, Evgenya L. Shkolnik, Adam C. Schneider, Travis S. Barman, Victoria S. Meadows, Isabella Pagano, and Sarah Peacock. HAZMAT. IV. Flares and Superflares on Young M Stars in the Far Ultraviolet. Astrophysical Journal, 867(1):70, 2018. doi: 10.3847/1538-4357/aae2ae.

172 [43] A. Segura, L. M. Walkowicz, V. Meadows, J. Kasting, and S. Hawley. The Eﬀect of a Strong Stellar Flare on the Atmospheric Chemistry of an Earth-like Planet Orbiting an M Dwarf. Astrobiology, 10:751–771, 2010. doi: 10.1089/ast.2009.0376.

[44] W. S. Howard, M. A. Tilley, H. Corbett, A. Youngblood, R. O. P. Loyd, J. K. Ratzloﬀ, N. M. Law, O. Fors, D. del Ser, E. L. Shkolnik, C. Ziegler, E. E. Goeke, A. D. Pietraallo, and J. Haislip. The First Naked-eye Superﬂare Detected from Proxima Centauri. Astrophysical Journal, 860:L30, 2018. doi: 10.3847/2041-8213/aacaf3.

[45] M. A. Tilley, A. Segura, V. S. Meadows, S. Hawley, and J. Davenport. Modeling Repeated M Dwarf Flaring at an Earth-like Planet in the Habitable Zone: Atmospheric Eﬀects for an Unmagnetized Planet. Astrobiology, 19:1, 2019. doi: 10.1089/ast.2017. 1794.

[46] Luciana Bianchi and GALEX Team. The Galaxy Evolution Explorer (GALEX): an All Sky Ultraviolet Survey. Mem. Societa Astronomica Italiana, 70:365, 1999.

[47] C. E. Brasseur, Rachel A. Osten, and Scott W. Fleming. Short-duration Stellar Flares in GALEX Data. Astrophysical Journal, 883(1):88, 2019. doi: 10.3847/1538-4357/ab3df8.

[48] J. G. Doyle, C. J. Butler, P. J. Callanan, G. Tagliaferri, R. de La Reza, N. E. White, C. A. Torres, and G. Quast. Rotational modulation and ﬂares on RS CVn and BY DRA systems. VIII. Simultaneous EXOSAT and H alpha observations of a ﬂare on the dMe star GL 644 AB (Wolf 630) on 24/25 August 1985. Astronomy and Astrophysics, 191:79–86, 1988.

[49] Suzanne L. Hawley, George H. Fisher, Theodore Simon, Scott L. Cully, Susana E. Deustua, Marek Jablonski, Christopher M. Johns-Krull, Bjorn R. Pettersen, Verne Smith, William J. Spiesman, and Jeﬀrey Valenti. Simultaneous Extreme-Ultraviolet Explorer and Optical Observations of AD Leonis: Evidence for Large Coronal Loops and the Neupert Eﬀect in Stellar Flares. Astrophysical Journal, 453:464, 1995. doi: 10.1086/176408.

[50] D. Garc´ıa-Alvarez, D. Jevremovi´c,J. G. Doyle, and C. J. Butler. Observations and modelling of a large optical ﬂare on AT Microscopii. Astronomy and Astrophysics, 383: 548–557, 2002. doi: 10.1051/0004-6361:20011743.

[51] Adam F. Kowalski, Suzanne L. Hawley, Jon A. Holtzman, John P. Wisniewski, and Eric J. Hilton. A White Light Megaﬂare on the dM4.5e Star YZ CMi. Astrophysical Journal, 714(1):L98–L102, 2010. doi: 10.1088/2041-8205/714/1/L98.

[52] Rachel A. Osten, Olivier Godet, Stephen Drake, Jack Tueller, Jay Cummings, Hans Krimm, John Pye, Valentin Pal’shin, Sergei Golenetskii, Fabio Reale, Samantha R. Oates, Mat J. Page, and Andrea Melandri. The Mouse That Roared: A Superﬂare from the dMe Flare Star EV Lac Detected by Swift and Konus-Wind. Astrophysical Journal, 721(1):785–801, 2010. doi: 10.1088/0004-637X/721/1/785.

173 [53] Rachel A. Osten, Adam Kowalski, Stephen A. Drake, Hans Krimm, Kim Page, Kosmas Gazeas, Jamie Kennea, Samantha Oates, Mathew Page, Enrique de Miguel, Rudolf Nov´ak,Tomas Apeltauer, and Neil Gehrels. A Very Bright, Very Hot, and Very Long Flaring Event from the M Dwarf Binary System DG CVn. Astrophysical Journal, 832 (2):174, 2016. doi: 10.3847/0004-637X/832/2/174.

[54] ChangQing Luo, XiaoBin Zhang, Kun Wang, Chao Liu, Xiangsong Fang, Chunguang Zhang, Licai Deng, Jundan Nie, Lester Fox-Machado, Yangping Luo, and Hubiao Niu. Frequent Flare Events on the Short-period M-type Eclipsing Binary BX Tri. Astrophysical Journal, 871(2):203, 2019. doi: 10.3847/1538-4357/aafafa.

[55] Kosuke Namekata, Hiroyuki Maehara, Ryo Sasaki, Hiroki Kawai, Yuta Notsu, Adam F. Kowalski, Joel C. Allred, Wataru Iwakiri, Yohko Tsuboi, Katsuhiro L. Murata, Masa- fumi Niwano, Kazuki Shiraishi, Ryo Adachi, Kota Iida, Motoki Oeda, Satoshi Honda, Miyako Tozuka, Noriyuki Katoh, Hiroki Onozato, Soshi Okamoto, Keisuke Isogai, Mariko Kimura, Naoto Kojiguchi, Yasuyuki Wakamatsu, Yusuke Tampo, Daisaku Nogami, and Kazunari Shibata. Optical and X-ray observations of stellar ﬂares on an active M dwarf AD Leonis with the Seimei Telescope, SCAT, NICER, and OISTER. Publications of the ASJ, 72(4):68, 2020. doi: 10.1093/pasj/psaa051.

[56] Edmund J. Weber and Jr. Davis, Leverett. The Angular Momentum of the Solar Wind. Astrophysical Journal, 148:217–227, 1967. doi: 10.1086/149138.

[57] Steven D. Kawaler. Angular Momentum Loss in Low-Mass Stars. Astrophysical Journal, 333:236, 1988. doi: 10.1086/166740.

[58] Timothy M. Brown. The Metastable Dynamo Model of Stellar Rotational Evolution. Astrophysical Journal, 789(2):101, 2014. doi: 10.1088/0004-637X/789/2/101.

[59] Cecilia Garraﬀo, Jeremy J. Drake, and Ofer Cohen. The Dependence of Stellar Mass and Angular Momentum Losses on Latitude and the Interaction of Active Region and Dipolar Magnetic Fields. Astrophysical Journal, 813(1):40, 2015. doi: 10.1088/ 0004-637X/813/1/40.

[60] Cecilia Garraﬀo, Jeremy J. Drake, and Ofer Cohen. The missing magnetic morphology term in stellar rotation evolution. Astronomy and Astrophysics, 595:A110, 2016. doi: 10.1051/0004-6361/201628367.

[61] C. Garraﬀo, J. J. Drake, A. Dotter, J. Choi, D. J. Burke, S. P. Moschou, J. D. Alvarado-G´omez,V. L. Kashyap, and O. Cohen. The Revolution Revolution: Magnetic Morphology Driven Spin-down. Astrophysical Journal, 862:90, 2018. doi: 10.3847/ 1538-4357/aace5d.

[62] Yuta Notsu, Hiroyuki Maehara, Satoshi Honda, Suzanne L. Hawley, James R. A. Davenport, Kosuke Namekata, Shota Notsu, Kai Ikuta, Daisaku Nogami, and Kazu- nari Shibata. Do Kepler Superﬂare Stars Really Include Slowly Rotating Sun-like Stars?—Results Using APO 3.5 m Telescope Spectroscopic Observations and Gaia-DR2 Data. Astrophysical Journal, 876(1):58, 2019. doi: 10.3847/1538-4357/ab14e6.

174 [63] Sallie Baliunas, Dmitry Sokoloﬀ, and Willie Soon. Magnetic Field and Rotation in Lower Main-Sequence Stars: an Empirical Time-dependent Magnetic Bode’s Relation? Astrophysical Journal, 457:L99, 1996. doi: 10.1086/309891.

[64] L. Aﬀer, G. Micela, F. Favata, and E. Flaccomio. The rotation of ﬁeld stars from CoRoT data. Monthly Notices of the Royal Astronomical Society, 424(1):11–22, 2012. doi: 10.1111/j.1365-2966.2012.20802.x.

[65] E. R. Newton, J. Irwin, D. Charbonneau, Z. K. Berta-Thompson, J. A. Dittmann, and A. A. West. The Rotation and Galactic Kinematics of Mid M Dwarfs in the Solar Neighborhood. Astrophysical Journal, 821:93, 2016. doi: 10.3847/0004-637X/821/2/93.

[66] Ryan J. Oelkers, Joseph E. Rodriguez, Keivan G. Stassun, Joshua Pepper, Garrett Somers, Stella Kafka, Daniel J. Stevens, Thomas G. Beatty, Robert J. Siverd, and Michael B. Lund. Variability Properties of Four Million Sources in the TESS Input Catalog Observed with the Kilodegree Extremely Little Telescope Survey. Astronomical Journal, 155(1):39, 2018. doi: 10.3847/1538-3881/aa9bf4.

[67] Svetlana V. Berdyugina. Starspots: A key to the stellar dynamo. Living Reviews in Solar Physics, 2(1):8, 2005. doi: 10.12942/lrsp-2005-8.

[68] J. D. Hartman, G. A.´ Bakos, R. W. Noyes, B. Sip˝ocz,G. Kov´acs,T. Mazeh, A. Shporer, and A. P´al. A Photometric Variability Survey of Field K and M Dwarf Stars with HATNet. Astronomical Journal, 141(5):166, 2011. doi: 10.1088/0004-6256/141/5/166.

[69] A. McQuillan, T. Mazeh, and S. Aigrain. Rotation Periods of 34,030 Kepler Main- sequence Stars: The Full Autocorrelation Sample. Astrophysical Journals, 211(2):24, 2014. doi: 10.1088/0067-0049/211/2/24.

[70] Brett M. Morris, Jason L. Curtis, Charli Sakari, Suzanne L. Hawley, and Eric Agol. Stellar Properties of Active G and K Stars: Exploring the Connection between Starspots and Chromospheric Activity. Astronomical Journal, 158(3):101, 2019. doi: 10.3847/ 1538-3881/ab2e04.

[71] D. Shulyak, A. Reiners, A. Engeln, L. Malo, R. Yadav, J. Morin, and O. Kochukhov. Strong dipole magnetic ﬁelds in fast rotating fully convective stars. Nature Astronomy, 1:0184, 2017. doi: 10.1038/s41550-017-0184.

[72] E. R. Newton, N. Mondrik, J. Irwin, J. G. Winters, and D. Charbonneau. New Rotation Period Measurements for M Dwarfs in the Southern Hemisphere: An Abundance of Slowly Rotating, Fully Convective Stars. Astronomical Journal, 156:217, 2018. doi: 10.3847/1538-3881/aad73b.

[73] D. Garc´ıa-Alvarez, A. F. Lanza, S. Messina, J. J. Drake, F. van Wyk, R. R. Shobbrook, C. J. Butler, D. Kilkenny, J. G. Doyle, and V. L. Kashyap. Starspots on the fastest rotators in the β Pictoris moving group. Astronomy and Astrophysics, 533:A30, 2011. doi: 10.1051/0004-6361/201116646.

175 [74] S. L. Hawley, J. R. A. Davenport, A. F. Kowalski, J. P. Wisniewski, L. Hebb, R. Deitrick, and E. J. Hilton. Kepler Flares. I. Active and Inactive M Dwarfs. Astrophysical Journal, 797:121, 2014. doi: 10.1088/0004-637X/797/2/121.

[75] W. E. Kunkel. A Search for Periodic Phenomena in the Activity of Solar Neighborhood Flare Stars. In Bulletin of the American Astronomical Society, volume 3, page 13, 1971.

[76] B. R. Pettersen. The ﬂare activity of V780 Tau. Astronomy and Astrophysics, 120: 192–196, 1983.

[77] Hasan Ali Dal and Serdar Evren. Rotation Modulations and Distributions of the Flare Occurrence Rates on the Surface of Five UV Ceti Type Stars. Publications of the ASJ, 63:427–447, 2011. doi: 10.1093/pasj/63.2.427.

[78] L. Doyle, G. Ramsay, J. G. Doyle, K. Wu, and E. Scullion. Investigating the rotational phase of stellar ﬂares on M dwarfs using K2 short cadence data. Monthly Notices of the Royal Astronomical Society, 480:2153–2164, 2018. doi: 10.1093/mnras/sty1963.

[79] Rachael M. Roettenbacher and Kriszti´anVida. The Connection between Starspots and Flares on Main-sequence Kepler Stars. Astrophysical Journal, 868(1):3, 2018. doi: 10.3847/1538-4357/aae77e.

[80] H. Korhonen, K. Vida, M. Husarik, S. Mahajan, D. Szczygiel,and K. Ol´ah.Photometric and spectroscopic observations of three rapidly rotating late-type stars: EY Dra, V374 Peg, and GSC 02038-00293. Astronomische Nachrichten, 331(8):772, 2010. doi: 10.1002/asna.201011407.

[81] K. Vida, Zs. K˝ovári,A. Pál,K. Oláh,and L. Kriskovics. Frequent Flaring in the TRAPPIST-1 System—Unsuited for Life? Astrophysical Journal, 841(2):124, 2017. doi: 10.3847/1538-4357/aa6f05.

[82] L. N. Mavridis, S. I. Avgoloupis, J. H. Seiradakis, and P. P. Varvoglis. Dependence of ﬂare activity on BY Draconis on the phase of the short-term periodic light variation. Astronomy and Astrophysics, 296:705, 1995.

[83] H. A. Dal and S. Evren. The Patterns of High-Level Magnetic Activity Occurring on the Surface of V1285 Aql: The OPEA Model of Flares and DFT Models of Stellar Spots. Publications of the Astronomical Society of the Paciﬁc, 123(904):659, 2011. doi: 10.1086/660820.

[84] Qing-feng Pi, Li-yun Zhang, Shao-lan Bi, Xianming L. Han, Hong-peng Lu, Qiang Yue, Liu Long, and Yan Yan. Magnetic Activity and Orbital Period Study for the Short-period RS CVn-type Eclipsing Binary DV Psc. Astrophysical Journal, 877(2):75, 2019. doi: 10.3847/1538-4357/ab19c3.

[85] P. Ioannidis and J. H. M. M. Schmitt. Keeping up with the cool stars: one TESS year in the life of AB Doradus. Astronomy and Astrophysics, 644:A26, 2020. doi: 10.1051/0004-6361/202038175.

176 [86] F. I. Lukatskaia. Time distribution of the flares of UV Cet. Soviet Astronomy Letters, 2:61, 1976. [87] Nicholas M. Hunt-Walker, Eric J. Hilton, Adam F. Kowalski, Suzanne L. Hawley, and Jaymie M. Matthews. MOST Observations of the Flare Star AD Leo. Publications of the Astronomical Society of the Pacific, 124(916):545, 2012. doi: 10.1086/666495. [88] Rachael M. Roettenbacher, John D. Monnier, Robert O. Harmon, Thomas Barclay, and Martin Still. Imaging Starspot Evolution on Kepler Target KIC 5110407 Using Light-Curve Inversion. Astrophysical Journal, 767(1):60, 2013. doi: 10.1088/0004-637X/ 767/1/60. [89] Adina D. Feinstein, Benjamin T. Montet, Megan Ansdell, Brian Nord, Jacob L. Bean, Maximilian N. Günther, Michael A. Gully-Santiago, and Joshua E. Schlieder. Flare Statistics for Young Stars from a Convolutional Neural Network Analysis of TESS Data. Astronomical Journal, 160(5):219, 2020. doi: 10.3847/1538-3881/abac0a. [90] Ekaterina Ilin, Katja Poppenhaeger, Sarah Jane Schmidt, Silva P. Järvinen,Elisabeth R. Newton, JuliánD. Alvarado-Gómez, J. Sebastian Pineda, James R. A. Davenport, Mahmoudreza Oshagh, and Ilya Ilyin. Giant white-light flares on fully convective stars occur at high latitudes, 2021. [91] W. J. Borucki, D. Koch, G. Basri, N. Batalha, T. Brown, D. Caldwell, J. Caldwell, J. Christensen-Dalsgaard, W. D. Cochran, E. DeVore, E. W. Dunham, A. K. Dupree, T. N. Gautier, J. C. Geary, R. Gilliland, A. Gould, S. B. Howell, J. M. Jenkins, Y. Kondo, D. W. Latham, G. W. Marcy, S. Meibom, H. Kjeldsen, J. J. Lissauer, D. G. Monet, D. Morrison, D. Sasselov, J. Tarter, A. Boss, D. Brownlee, T. Owen, D. Buzasi, D. Charbonneau, L. Doyle, J. Fortney, E. B. Ford, M. J. Holman, S. Seager, J. H. Steffen, W. F. Welsh, J. Rowe, H. Anderson, L. Buchhave, D. Ciardi, L. Walkowicz, W. Sherry, E. Horch, H. Isaacson, M. E. Everett, D. Fischer, G. Torres, J. A. Johnson, M. Endl, P. MacQueen, S. T. Bryson, J. Dotson, M. Haas, J. Kolodziejczak, J. Van Cleve, H. Chandrasekaran, J. D. Twicken, E. V. Quintana, B. D. Clarke, C. Allen, J. Li, H. Wu, P. Tenenbaum, E. Verner, F. Bruhweiler, J. Barnes, and A. Prsa. Kepler Planet-Detection Mission: Introduction and First Results. Science, 327:977, 2010. doi: 10.1126/science.1185402. [92] S. B. Howell, C. Sobeck, M. Haas, M. Still, T. Barclay, F. Mullally, J. Troeltzsch, S. Aigrain, S. T. Bryson, D. Caldwell, W. J. Chaplin, W. D. Cochran, D. Huber, G. W. Marcy, A. Miglio, J. R. Najita, M. Smith, J. D. Twicken, and J. J. Fortney. The K2 Mission: Characterization and Early Results. Publications of the Astronomical Society of the Pacific, 126:398, 2014. doi: 10.1086/676406. [93] L. Doyle, G. Ramsay, J. G. Doyle, and K. Wu. Probing the origin of stellar flares on M dwarfs using TESS data sectors 1-3. Monthly Notices of the Royal Astronomical Society, 489(1):437–445, 2019. doi: 10.1093/mnras/stz2205. [94] Wing-Huen Ip, Andreas Kopp, and Juei-Hwa Hu. On the Star-Magnetosphere In- teraction of Close-in Exoplanets. Astrophysical Journal, 602(1):L53–L56, 2004. doi: 10.1086/382274.

177 [95] S. Preusse, A. Kopp, J. B¨uchner, and U. Motschmann. MHD simulation scenarios of the stellar wind interaction with Hot Jupiter magnetospheres. Planetary Space Science, 55(5):589–597, 2007. doi: 10.1016/j.pss.2006.04.037.

[96] D. H. Gao, P. F. Chen, M. D. Ding, and X. D. Li. Simulations of the periodic ﬂaring rate on YY Gem. Monthly Notices of the Royal Astronomical Society, 384(4):1355–1362, 2008. doi: 10.1111/j.1365-2966.2007.12830.x.

[97] A. Strugarek, A. S. Brun, S. P. Matt, and V. R´eville. Magnetic Games between a Planet and Its Host Star: The Key Role of Topology. Astrophysical Journal, 815(2): 111, 2015. doi: 10.1088/0004-637X/815/2/111.

[98] A. F. Lanza. Close-by planets and ﬂares in their host stars. Astronomy and Astrophysics, 610:A81, 2018. doi: 10.1051/0004-6361/201731414.

[99] J. G. Doyle, C. J. Butler, G. H. J. van den Oord, and T. Kiang. A periodicity in the ﬂaring rate on the eclipsing binary YY Geminorum. Astronomy and Astrophysics, 232: 83, 1990.

[100] D. Garc´ıa-Alvarez, B. H. Foing, D. Montes, J. Oliveira, J. G. Doyle, S. Messina, A. F. Lanza, M. Rodonò,J. Abbott, T. D. C. Ash, I. K. Baldry, T. R. Bedding, D. A. H. Buckley, J. Cami, H. Cao, C. Catala, K. P. Cheng, Jr. Domiciano de Souza, A., J. F. Donati, A. M. Hubert, E. Janot-Pacheco, J. X. Hao, L. Kaper, A. Kaufer, N. V. Leister, J. E. Neff, C. Neiner, S. Orlando, S. J. O’Toole, D. Schäfer,S. J. Smartt, O. Stahl, J. Telting, and S. Tubbesing. Simultaneous optical and X-ray observations of flares and rotational modulation on the RS CVn binary HR 1099 (V711 Tau) from the MUSICOS 1998 campaign. Astronomy and Astrophysics, 397:285–303, 2003. doi: 10.1051/0004-6361:20021481.

[101] Dong-Tao Cao and Sheng-Hong Gu. Optical ﬂare events on the RS Canum Venaticorum star UX Arietis. Research in Astronomy and Astrophysics, 17(6):055, 2017. doi: 10.1088/1674-4527/17/6/55.

[102] C. K. Goertz. Io’s interaction with the plasma torus. Journal of Geophysics Research, 85(A6):2949–2956, 1980. doi: 10.1029/JA085iA06p02949.

[103] F. M. Neubauer. Nonlinear standing Alfv´enwave current system at Io: Theory. Journal of Geophysics Research, 85(A3):1171–1178, 1980. doi: 10.1029/JA085iA03p01171.

[104] Christian Fischer and Joachim Saur. Time-variable Electromagnetic Star-Planet Inter- action: The TRAPPIST-1 System as an Exemplary Case. Astrophysical Journal, 872 (1):113, 2019. doi: 10.3847/1538-4357/aafaf2.

[105] A. F. Lanza. Stellar coronal magnetic ﬁelds and star-planet interaction. Astronomy and Astrophysics, 505(1):339–350, 2009. doi: 10.1051/0004-6361/200912367.

[106] A. F. Lanza. Star-planet magnetic interaction and activity in late-type stars with close-in planets. Astronomy and Astrophysics, 544:A23, 2012. doi: 10.1051/0004-6361/ 201219002.

178 [107] A. F. Lanza. Star-planet magnetic interaction and evaporation of planetary atmospheres. Astronomy and Astrophysics, 557:A31, 2013. doi: 10.1051/0004-6361/201321790.

[108] E. Shkolnik, G. A. H. Walker, and D. A. Bohlender. Evidence for Planet-induced Chromospheric Activity on HD 179949. Astrophysical Journal, 597:1092–1096, 2003. doi: 10.1086/378583.

[109] E. Shkolnik, G. A. H. Walker, D. A. Bohlender, P. G. Gu, and M. K¨urster.Hot Jupiters and Hot Spots: The Short- and Long-Term Chromospheric Activity on Stars with Giant Planets. Astrophysical Journal, 622(2):1075–1090, 2005. doi: 10.1086/428037.

[110] Evgenya Shkolnik, David A. Bohlender, Gordon A. H. Walker, and Andrew Collier Cameron. The On/Oﬀ Nature of Star-Planet Interactions. Astrophysical Journal, 676 (1):628–638, 2008. doi: 10.1086/527351.

[111] G. A. H. Walker, B. Croll, J. M. Matthews, R. Kuschnig, D. Huber, W. W. Weiss, E. Shkolnik, S. M. Rucinski, D. B. Guenther, A. F. J. Moﬀat, and D. Sasselov. MOST detects variability on τ Bootis A possibly induced by its planetary companion. Astronomy and Astrophysics, 482(2):691–697, 2008. doi: 10.1051/0004-6361:20078952.

[112] D. Staab, C. A. Haswell, Gareth D. Smith, L. Fossati, J. R. Barnes, R. Busuttil, and J. S. Jenkins. SALT observations of the chromospheric activity of transiting planet hosts: mass-loss and star-planet interactions∗. Monthly Notices of the Royal Astronomical Society, 466(1):738–748, 2017. doi: 10.1093/mnras/stw3172.

[113] P. Wilson Cauley, Evgenya L. Shkolnik, Joe Llama, Vincent Bourrier, and Claire Moutou. Evidence of Magnetic Star-Planet Interactions in the HD 189733 System from Orbitally Phased Ca II K Variations. Astronomical Journal, 156(6):262, 2018. doi: 10.3847/1538-3881/aae841.

[114] H. K. Vedantham, J. R. Callingham, T. W. Shimwell, C. Tasse, B. J. S. Pope, M. Bedell, I. Snellen, P. Best, M. J. Hardcastle, M. Haverkorn, A. Mechev, S. P. O’Sullivan, H. J. A. R¨ottgering,and G. J. White. Coherent radio emission from a quiescent red dwarf indicative of star-planet interaction. Nature Astronomy, 4:577–583, 2020. doi: 10.1038/s41550-020-1011-9.

[115] Suvrath Mahadevan, Guthmundur Stef´ansson,Paul Robertson, Ryan C. Terrien, Joe P. Ninan, Rae J. Holcomb, Samuel Halverson, William D. Cochran, Shubham Kanodia, Lawrence W. Ramsey, Alexander Wolszczan, Michael Endl, Chad F. Bender, Scott A. Diddams, Connor Fredrick, Fred Hearty, Andrew Monson, Andrew J. Metcalf, Arpita Roy, and Christian Schwab. The Habitable-zone Planet Finder Detects a Terrestrial-mass Planet Candidate Closely Orbiting Gliese 1151: The Likely Source of Coherent Low-frequency Radio Emission from an Inactive Star. arXiv e-prints, art. arXiv:2102.02233, 2021.

[116] M. Perger, I. Ribas, G. Anglada-Escudé,J. C. Morales, P. J. Amado, J. A. Caballero, A. Quirrenbach, A. Reiners, V. J. S. Béjar,S. Dreizler, D. Galad´ı-Enr´ıquez,A. P. Hatzes, Th. Henning, S. V. Jeffers, A. Kaminski, M. Kürster,M. Lafarga, D. Montes, E. Palé,

179 C. Rodr´ıguez-L´opez, A. Schweitzer, M. R. Zapatero Osorio, and M. Zechmeister. The CARMENES search for exoplanets around M dwarfs, No evidence for a super-Earth in a 2-day orbit around GJ 1151. arXiv e-prints, art. arXiv:2103.10216, 2021.

[117] C. E. Pugh, D. J. Armstrong, V. M. Nakariakov, and A. M. Broomhall. Statisti- cal properties of quasi-periodic pulsations in white-light ﬂares observed with Kepler. Monthly Notices of the Royal Astronomical Society, 459(4):3659–3676, 2016. doi: 10.1093/mnras/stw850.

[118] Tom Van Doorsselaere, Hoda Shariati, and Jonas Debosscher. Stellar Flares Observed in Long-cadence Data from the Kepler Mission. Astrophysical Journals, 232(2):26, 2017. doi: 10.3847/1538-4365/aa8f9a.

[119] Maximilian N. G¨unther, Zhuchang Zhan, Sara Seager, Paul B. Rimmer, Sukrit Ranjan, Keivan G. Stassun, Ryan J. Oelkers, Tansu Daylan, Elisabeth Newton, Martti H. Kristiansen, Katalin Olah, Edward Gillen, Saul Rappaport, George R. Ricker, Roland K. Vanderspek, David W. Latham, Joshua N. Winn, Jon M. Jenkins, Ana Glidden, Michael Fausnaugh, Alan M. Levine, Jason A. Dittmann, Samuel N. Quinn, Akshata Krishnamurthy, and Eric B. Ting. Stellar Flares from the First TESS Data Release: Exploring a New Sample of M Dwarfs. Astronomical Journal, 159(2):60, 2020. doi: 10.3847/1538-3881/ab5d3a.

[120] R.G.Jr. Miller. Simultaneous Statistical Inference. Springer, New York, NY, New York, NY, 2 edition, 1981. doi: 10.1007/978-1-4613-8122-8.

[121] J P Shaﬀer. Multiple hypothesis testing. Annual Review of Psychology, 46(1):561–584, 1995. doi: 10.1146/annurev.ps.46.020195.003021.

[122] Adrian E. Bayer and UroˇsSeljak. The look-elsewhere eﬀect from a uniﬁed Bayesian and frequentist perspective. Journal of Cosmology and Astroparticle Physics, 2020(10): 009, 2020. doi: 10.1088/1475-7516/2020/10/009.

[123] C. D. Dressing and D. Charbonneau. The Occurrence Rate of Small Planets around Small Stars. Astrophysical Journal, 767:95, 2013. doi: 10.1088/0004-637X/767/1/95.

[124] C. D. Dressing and D. Charbonneau. The Occurrence of Potentially Habitable Plan- ets Orbiting M Dwarfs Estimated from the Full Kepler Dataset and an Empirical Measurement of the Detection Sensitivity. Astrophysical Journal, 807:45, 2015.

[125] G. Anglada-Escudé,P. J. Amado, J. Barnes, Z. M. Berdiñas,R. P. Butler, G. A. L. Coleman, I. de La Cueva, S. Dreizler, M. Endl, B. Giesers, S. V. Jeffers, J. S. Jenkins, H. R. A. Jones, M. Kiraga, M. Kürster,M. J. López-González,C. J. Marvin, N. Morales, J. Morin, R. P. Nelson, J. L. Ortiz, A. Ofir, S.-J. Paardekooper, A. Reiners, E. Rodr´ıguez, C. Rodr´ıguez-López, L. F. Sarmiento, J. P. Strachan, Y. Tsapras, M. Tuomi, and M. Zechmeister. A terrestrial planet candidate in a temperate orbit around Proxima Centauri. Nature, 536:437–440, 2016. doi: 10.1038/nature19106.

180 [126] MichaëlGillon, Amaury H. M. J. Triaud, Brice-Olivier Demory, EmmanuëlJehin, Eric Agol, Katherine M. Deck, Susan M. Lederer, Julien de Wit, Artem Burdanov, James G. Ingalls, Emeline Bolmont, Jeremy Leconte, Sean N. Raymond, Franck Selsis, Martin Turbet, Khalid Barkaoui, Adam Burgasser, Matthew R. Burleigh, Sean J. Carey, Aleksander Chaushev, Chris M. Copperwheat, Laetitia Delrez, Catarina S. Fernand es, Daniel L. Holdsworth, Enrico J. Kotze, ValérieVan Grootel, Yaseen Almleaky, Zouhair Benkhaldoun, Pierre Magain, and Didier Queloz. Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1. Nature, 542:456–460, 2017. doi: 10.1038/nature21360.

[127] Jason A. Dittmann, Jonathan M. Irwin, David Charbonneau, Xavier Bonfils, Nicola Astudillo-Defru, RaphaëlleD. Haywood, Zachory K. Berta-Thompson, Elisabeth R. Newton, Joseph E. Rodriguez, Jennifer G. Winters, Thiam-Guan Tan, Jose-Manuel Almenara, Fran¸coisBouchy, Xavier Delfosse, Thierry Forveille, Christophe Lovis, Felipe Murgas, Francesco Pepe, Nuno C. Santos, Stephane Udry, AnaëlWünsche, Gilbert A. Esquerdo, David W. Latham, and Courtney D. Dressing. A temperate rocky super-Earth transiting a nearby cool star. Nature, 544:333–336, 2017. doi: 10.1038/nature22055.

[128] X. Bonfils, N. Astudillo-Defru, R. D´ıaz, J. M. Almenara, T. Forveille, F. Bouchy, X. Delfosse, C. Lovis, M. Mayor, F. Murgas, F. Pepe, N. C. Santos, D. Ségransan, S. Udry, and A. Wünsche. A temperate exo-Earth around a quiet M dwarf at 3.4 parsec. Astronomy and Astrophysics, 613:A25, 2018. doi: 10.1051/0004-6361/201731973.

[129] Ravi Kumar Kopparapu. A Revised Estimate of the Occurrence Rate of Terrestrial Planets in the Habitable Zones around Kepler M-dwarfs. Astrophysical Journal, 767: L8, 2013. doi: 10.1088/2041-8205/767/1/L8.

[130] Kevin France, Girish Duvvuri, Hilary Egan, Tommi Koskinen, David J. Wilson, Allison Youngblood, Cynthia S. Froning, Alexander Brown, JuliánD. Alvarado-Gómez,Za- chory K. Berta-Thompson, Jeremy J. Drake, Cecilia Garraffo, Lisa Kaltenegger, Adam F. Kowalski, Jeffrey L. Linsky, R. O. Parke Loyd, Pablo J. D. Mauas, Yamila Miguel, J. Sebastian Pineda, Sarah Rugheimer, P. Christian Schneider, Feng Tian, and Mariela Vieytes. The High-energy Radiation Environment around a 10 Gyr M Dwarf: Habitable at Last? Astronomical Journal, 160(5):237, 2020. doi: 10.3847/1538-3881/abb465.

[131] R. O. P. Loyd, K. France, A. Youngblood, C. Schneider, A. Brown, R. Hu, A. Segura, J. Linsky, S. Redﬁeld, F. Tian, S. Rugheimer, Y. Miguel, and C. S. Froning. The MUS- CLES Treasury Survey. V. FUV Flares on Active and Inactive M Dwarfs. Astrophysical Journal, 867:71, 2018. doi: 10.3847/1538-4357/aae2bd.

[132] J.-M. Grießmeier, F. Tabataba-Vakili, A. Stadelmann, J. L. Grenfell, and D. Atri. Galactic cosmic rays on extrasolar Earth-like planets. II. Atmospheric implications. Astronomy and Astrophysics, 587:A159, 2016. doi: 10.1051/0004-6361/201425452.

[133] F. Tabataba-Vakili, J. L. Grenfell, J.-M. Grießmeier, and H. Rauer. Atmospheric eﬀects of stellar cosmic rays on Earth-like exoplanets orbiting M-dwarfs. Astronomy and Astrophysics, 585:A96, 2016. doi: 10.1051/0004-6361/201425602.

181 [134] M. Cuntz and E. F. Guinan. About Exobiology: The Case for Dwarf K Stars. Astro- physical Journal, 827:79, 2016. doi: 10.3847/0004-637X/827/1/79.

[135] J. E. Owen and S. Mohanty. Habitability of terrestrial-mass planets in the HZ of M Dwarfs - I. H/He-dominated atmospheres. Monthly Notices of the Royal Astronomical Society, 459:4088–4108, 2016. doi: 10.1093/mnras/stw959.

[136] R. Luger, R. Barnes, E. Lopez, J. Fortney, B. Jackson, and V. Meadows. Habitable Evaporated Cores: Transforming Mini-Neptunes into Super-Earths in the Habitable Zones of M Dwarfs. Astrobiology, 15:57–88, 2015. doi: 10.1089/ast.2014.1215.

[137] C. S. Cockell. The ultraviolet radiation environment of Earth and Mars: past and present, pages 219–232. Berlin: Springer, 2002.

[138] S. Rugheimer, L. Kaltenegger, A. Segura, J. Linsky, and S. Mohanty. Eﬀect of UV Radiation on the Spectral Fingerprints of Earth-like Planets Orbiting M Stars. Astrophysical Journal, 809:57, 2015. doi: 10.1088/0004-637X/809/1/57.

[139] S. Rugheimer and L. Kaltenegger. Spectra of Earth-like Planets through Geological Evolution around FGKM Stars. Astrophysical Journal, 854:19, 2018. doi: 10.3847/ 1538-4357/aaa47a.

[140] V. S. Airapetian, A. Glocer, G. Gronoﬀ, E. H´ebrard,and W. Danchi. Prebiotic chemistry and atmospheric warming of early Earth by an active young Sun. Nature Geoscience, 9:452–455, 2016. doi: 10.1038/ngeo2719.

[141] J. T. O’Malley-James and L. Kaltenegger. Lessons from early Earth: UV surface radiation should not limit the habitability of active M star systems. Monthly Notices of the Royal Astronomical Society, 485:5598–5603, 2019. doi: 10.1093/mnras/stz724.

[142] Sukrit Ranjan, Robin Wordsworth, and Dimitar D. Sasselov. The Surface UV Envi- ronment on Planets Orbiting M Dwarfs: Implications for Prebiotic Chemistry and the Need for Experimental Follow-up. Astrophysical Journal, 843(2):110, 2017. doi: 10.3847/1538-4357/aa773e.

[143] Ward S. Howard, Hank Corbett, Nicholas M. Law, Jeﬀrey K. Ratzloﬀ, Amy Glazier, Octavi Fors, Daniel del Ser, and Joshua Haislip. EvryFlare. I. Long-term Evryscope Monitoring of Flares from the Cool Stars across Half the Southern Sky. Astrophysical Journal, 881(1):9, 2019. doi: 10.3847/1538-4357/ab2767.

[144] Ward S. Howard, Hank Corbett, Nicholas M. Law, Jeffrey K. Ratzloff, Nathan Galliher, Amy L. Glazier, Ramses Gonzalez, Alan Vasquez Soto, Octavi Fors, Daniel del Ser, and Joshua Haislip. EvryFlare. III. Temperature Evolution and Habitability Impacts of Dozens of Superflares Observed Simultaneously by Evryscope and TESS. Astrophysical Journal, 902(2):115, 2020. doi: 10.3847/1538-4357/abb5b4.

[145] Max Planck. Ueber das Gesetz der Energieverteilung im Normalspectrum. Annalen der Physik, 309(3):553–563, 1901. doi: 10.1002/andp.19013090310.

182 [146] Paul B. Rimmer, Jianfeng Xu, Samantha J. Thompson, Ed Gillen, John D. Sutherland, and Didier Queloz. The origin of RNA precursors on exoplanets. Science Advances, 4 (8):eaar3302, 2018. doi: 10.1126/sciadv.aar3302.

[147] A. Bixel and D. Apai. Probabilistic Constraints on the Mass and Composition of Proxima b. Astrophysical Journal, 836:L31, 2017. doi: 10.3847/2041-8213/aa5f51.

[148] I. Ribas, E. Bolmont, F. Selsis, A. Reiners, J. Leconte, S. N. Raymond, S. G. Engle, E. F. Guinan, J. Morin, M. Turbet, F. Forget, and G. Anglada-Escud´e.The habitability of Proxima Centauri b. I. Irradiation, rotation and volatile inventory from formation to the present. Astronomy and Astrophysics, 596:A111, 2016. doi: 10.1051/0004-6361/ 201629576.

[149] V. S. Meadows, Arney Giada N., Schwieterman Edward W., Lustig-Yaeger Jacob, Lincowski Andrew P., Robinson Tyler, Domagal-Goldman Shawn D., Deitrick Russell, Barnes Rory K., Fleming David P., Luger Rodrigo, Driscoll Peter E., Quinn Thomas R., and Crisp David. The habitability of proxima centauri b: Environmental states and observational discriminants. Astrobiology, 18(2):133–189, 2018. doi: 10.1089/ast. 2016.1589. PMID: 29431479.

[150] D. M. Kipping, C. Cameron, J. D. Hartman, J. R. A. Davenport, J. M. Matthews, D. Sasselov, J. Rowe, R. J. Siverd, J. Chen, E. Sandford, G. A.´ Bakos, A. Jord´an, D. Bayliss, T. Henning, L. Mancini, K. Penev, Z. Csubry, W. Bhatti, J. Da Silva Bento, D. B. Guenther, R. Kuschnig, A. F. J. Moﬀat, S. M. Rucinski, and W. W. Weiss. No Conclusive Evidence for Transits of Proxima b in MOST Photometry. Astronomical Journal, 153:93, 2017. doi: 10.3847/1538-3881/153/3/93.

[151] A. SuárezMascareño,J. P. Faria, P. Figueira, C. Lovis, M. Damasso, J. I. González Hernández,R. Rebolo, S. Cristiani, F. Pepe, N. C. Santos, M. R. Zapatero Osorio, V. Adibekyan, S. Hojjatpanah, A. Sozzetti, F. Murgas, M. Abreu, M. Affolter, Y. Alibert, M. Aliverti, R. Allart, C. Allende Prieto, D. Alves, M. Amate, G. Avila, V. Baldini, T. Bandi, S. C. C. Barros, A. Bianco, W. Benz, F. Bouchy, C. Broeng, A. Cabral, G. Calderone, R. Cirami, J. Coelho, P. Conconi, I. Coretti, C. Cumani, G. Cupani, V. D’Odorico, S. Deiries, B. Delabre, P. Di Marcantonio, X. Dumusque, D. Ehrenreich, A. Fragoso, L. Genolet, M. Genoni, R. Génova Santos, I. Hughes, O. Iwert, F. Kerber, J. Knusdstrup, M. Landoni, B. Lavie, J. Lillo-Box, J. Lizon, G. Lo Curto, C. Maire, A. Manescau, C. J. A. P. Martins, D. Mégevand, A. Mehner, G. Micela, A. Modigliani, P. Molaro, M. A. Monteiro, M. J. P. F. G. Monteiro, M. Moschetti, E. Mueller, N. J. Nunes, L. Oggioni, A. Oliveira, E. Pallé,G. Pariani, L. Pasquini, E. Poretti, J. L. Rasilla, E. Redaelli, M. Riva, S. Santana Tschudi, P. Santin, P. Santos, A. Segovia, D. Sosnowska, S. Sousa, P. Spanò,F. Tenegi, S. Udry, A. Zanutta, and F. Zerbi. Revisiting Proxima with ESPRESSO. Astronomy and Astrophysics, 639:A77, 2020. doi: 10.1051/0004-6361/202037745.

[152] J.-M. Grießmeier, A. Stadelmann, J. L. Grenfell, H. Lammer, and U. Motschmann. On the protection of extrasolar Earth-like planets around K/M stars against galactic cosmic rays. Icarus, 199:526–535, 2009. doi: 10.1016/j.icarus.2008.09.015.

183 [153] J. Scalo, L. Kaltenegger, A. G. Segura, M. Fridlund, I. Ribas, Y. N. Kulikov, J. L. Grenfell, H. Rauer, P. Odert, M. Leitzinger, F. Selsis, M. L. Khodachenko, C. Eiroa, J. Kasting, and H. Lammer. M Stars as Targets for Terrestrial Exoplanet Searches And Biosignature Detection. Astrobiology, 7:85–166, 2007. doi: 10.1089/ast.2006.0125.

[154] S. Seager and D. Deming. Exoplanet Atmospheres. Annual Review of Astron and Astrophys, 48:631–672, 2010. doi: 10.1146/annurev-astro-081309-130837.

[155] Aomawa L. Shields, Sarah Ballard, and John Asher Johnson. The habitability of planets orbiting M-dwarf stars. Physics Reports, 663:1, 2016. doi: 10.1016/j.physrep.2016.10. 003.

[156] M. A. MacGregor, A. J. Weinberger, D. J. Wilner, A. F. Kowalski, and S. R. Cranmer. Detection of a Millimeter Flare from Proxima Centauri. Astrophysical Journal, 855:L2, 2018. doi: 10.3847/2041-8213/aaad6b.

[157] M. G¨udel,M. Audard, F. Reale, S. L. Skinner, and J. L. Linsky. Flares from small to large: X-ray spectroscopy of Proxima Centauri with XMM-Newton. Astronomy and Astrophysics, 416:713–732, 2004. doi: 10.1051/0004-6361:20031471.

[158] G. Walker, J. Matthews, R. Kuschnig, R. Johnson, S. Rucinski, J. Pazder, G. Burley, A. Walker, K. Skaret, R. Zee, S. Grocott, K. Carroll, P. Sinclair, D. Sturgeon, and J. Harron. The MOST Asteroseismology Mission: Ultraprecise Photometry from Space. Publications of the Astronomical Society of the Paciﬁc, 115:1023–1035, 2003. doi: 10.1086/377358.

[159] P. J. Wheatley, R. G. West, M. R. Goad, J. S. Jenkins, D. L. Pollacco, D. Queloz, H. Rauer, S. Udry, C. A. Watson, B. Chazelas, P. Eigmüller,G. Lambert, L. Genolet, J. McCormac, S. Walker, D. J. Armstrong, D. Bayliss, J. Bento, F. Bouchy, M. R. Burleigh, J. Cabrera, S. L. Casewell, A. Chaushev, P. Chote, S. Csizmadia, A. Erikson, F. Faedi, E. Foxell, B. T. Gänsicke, E. Gillen, A. Grange, M. N. Günther, S. T. Hodgkin, J. Jackman, A. Jordán,T. Louden, L. Metrailler, M. Moyano, L. D. Nielsen, H. P. Osborn, K. Poppenhaeger, R. Raddi, L. Raynard, A. M. S. Smith, M. Soto, and R. Titz-Weider. The Next Generation Transit Survey (NGTS). Monthly Notices of the Royal Astronomical Society, 475:4476–4493, 2018. doi: 10.1093/mnras/stx2836.

[160] J. A. G. Jackman, P. J. Wheatley, C. E. Pugh, B. T. Gänsicke, E. Gillen, A.-M. Broomhall, D. J. Armstrong, M. R. Burleigh, A. Chaushev, P. Eigmüller,A. Erikson, M. R. Goad, A. Grange, M. N. Günther, J. S. Jenkins, J. McCormac, L. Raynard, A. P. G. Thompson, S. Udry, S. Walker, C. A. Watson, and R. G. West. Ground-based detection of G star superflares with NGTS. Monthly Notices of the Royal Astronomical Society, 477:4655–4664, 2018. doi: 10.1093/mnras/sty897.

[161] J. A. G. Jackman, P. J. Wheatley, C. E. Pugh, D. Y. Kolotkov, A.-M. Broomhall, G. M. Kennedy, S. J. Murphy, R. Raddi, M. R. Burleigh, S. L. Casewell, P. Eigmüller, E. Gillen, M. N. Günther, J. S. Jenkins, T. Louden, J. McCormac, L. Raynard, K. Poppenhaeger, S. Udry, C. A. Watson, and R. G. West. Detection of a giant flare displaying quasi-periodic pulsations from a pre-main-sequence M star by the Next

184 Generation Transit Survey. Monthly Notices of the Royal Astronomical Society, 482: 5553–5566, 2019. doi: 10.1093/mnras/sty3036.

[162] B. J. Shappee, J. L. Prieto, D. Grupe, C. S. Kochanek, K. Z. Stanek, G. De Rosa, S. Mathur, Y. Zu, B. M. Peterson, R. W. Pogge, S. Komossa, M. Im, J. Jencson, T. W.-S. Holoien, U. Basu, J. F. Beacom, D. M. Szczygiel,J. Brimacombe, S. Adams, A. Campillay, C. Choi, C. Contreras, M. Dietrich, M. Dubberley, M. Elphick, S. Foale, M. Giustini, C. Gonzalez, E. Hawkins, D. A. Howell, E. Y. Hsiao, M. Koss, K. M. Leighly, N. Morrell, D. Mudd, D. Mullins, J. M. Nugent, J. Parrent, M. M. Phillips, G. Pojmanski, W. Rosing, R. Ross, D. Sand, D. M. Terndrup, S. Valenti, Z. Walker, and Y. Yoon. The Man behind the Curtain: X-Rays Drive the UV through NIR Variability in the 2013 Active Galactic Nucleus Outburst in NGC 2617. Astrophysical Journal, 788:48, 2014. doi: 10.1088/0004-637X/788/1/48.

[163] Philip Nutzman and David Charbonneau. Design Considerations for a Ground-Based Transit Search for Habitable Planets Orbiting M Dwarfs. Publications of the Astro- nomical Society of the Paciﬁc, 120(865):317, 2008. doi: 10.1086/533420.

[164] Z. K. Berta, J. Irwin, D. Charbonneau, C. J. Burke, and E. E. Falco. Transit Detection in the MEarth Survey of Nearby M Dwarfs: Bridging the Clean-ﬁrst, Search-later Divide. Astronomical Journal, 144:145, 2012. doi: 10.1088/0004-6256/144/5/145.

[165] G. R. Ricker, J. N. Winn, R. Vanderspek, D. W. Latham, G. A.´ Bakos, J. L. Bean, Z. K. Berta-Thompson, T. M. Brown, L. Buchhave, N. R. Butler, R. P. Butler, W. J. Chaplin, D. Charbonneau, J. Christensen-Dalsgaard, M. Clampin, D. Deming, J. Doty, N. De Lee, C. Dressing, E. W. Dunham, M. Endl, F. Fressin, J. Ge, T. Henning, M. J. Holman, A. W. Howard, S. Ida, J. Jenkins, G. Jernigan, J. A. Johnson, L. Kaltenegger, N. Kawai, H. Kjeldsen, G. Laughlin, A. M. Levine, D. Lin, J. J. Lissauer, P. MacQueen, G. Marcy, P. R. McCullough, T. D. Morton, N. Narita, M. Paegert, E. Palle, F. Pepe, J. Pepper, A. Quirrenbach, S. A. Rinehart, D. Sasselov, B. Sato, S. Seager, A. Sozzetti, K. G. Stassun, P. Sullivan, A. Szentgyorgyi, G. Torres, S. Udry, and J. Villasenor. Transiting Exoplanet Survey Satellite (TESS). In Space Telescopes and Instrumentation 2014: Optical, Infrared, and Millimeter Wave, volume 9143 of Proceedings of the SPIE, page 914320, 2014. doi: 10.1117/12.2063489.

[166] Keivan G. Stassun, Ryan J. Oelkers, Martin Paegert, Guillermo Torres, Joshua Pepper, Nathan De Lee, Kevin Collins, David W. Latham, Philip S. Muirhead, Jay Chittidi, B´arbaraRojas-Ayala, Scott W. Fleming, Mark E. Rose, Peter Tenenbaum, Eric B. Ting, Stephen R. Kane, Thomas Barclay, Jacob L. Bean, C. E. Brassuer, David Charbonneau, Jian Ge, Jack J. Lissauer, Andrew W. Mann, Brian McLean, Susan Mullally, Norio Narita, Peter Plavchan, George R. Ricker, Dimitar Sasselov, S. Seager, Sanjib Sharma, Bernie Shiao, Alessandro Sozzetti, Dennis Stello, Roland Vanderspek, Geoﬀ Wallace, and Joshua N. Winn. The Revised TESS Input Catalog and Candidate Target List. Astronomical Journal, 158(4):138, 2019. doi: 10.3847/1538-3881/ab3467.

[167] Z. Zhan, M. N. G¨unther, S. Rappaport, K. Ol´ah,A. Mann, A. M. Levine, J. Winn, F. Dai, G. Zhou, Chelsea X. Huang, L. G. Bouma, M. J. Ireland, G. Ricker, R. Vanderspek,

185 D. Latham, S. Seager, J. Jenkins, D. A. Caldwell, J. P. Doty, Z. Essack, G. Furesz, M. E. R. Leidos, P. Rowden, J. C. Smith, K. G. Stassun, and M. Vezie. Complex Rotational Modulation of Rapidly Rotating M Stars Observed with TESS. Astrophysical Journal, 876(2):127, 2019. doi: 10.3847/1538-4357/ab158c.

[168] J. Pepper, A. Gould, and D. L. Depoy. Using All-Sky Surveys to Find Planetary Transits. ACTAA, 53:213–228, 2003.

[169] Joshua Pepper, Richard W. Pogge, D. L. DePoy, J. L. Marshall, K. Z. Stanek, Amelia M. Stutz, Shawn Poindexter, Robert Siverd, Thomas P. O’Brien, and Mark Trueblood. The Kilodegree Extremely Little Telescope (KELT): A Small Robotic Telescope for Large-Area Synoptic Surveys. Publications of the Astronomical Society of the Paciﬁc, 119(858):923–935, 2007. doi: 10.1086/521836.

[170] Joshua Pepper, Rudolf B. Kuhn, Robert Siverd, David James, and Keivan Stassun. The KELT-South Telescope. Publications of the Astronomical Society of the Paciﬁc, 124(913):230, 2012. doi: 10.1086/665044.

[171] N. M. Law, O. Fors, J. Ratzloﬀ, P. Wulfken, D. Kavanaugh, D. J. Sitar, Z. Pruett, M. N. Birchard, B. N. Barlow, K. Cannon, S. B. Cenko, B. Dunlap, A. Kraus, and T. J. Maccarone. Evryscope Science: Exploring the Potential of All-Sky Gigapixel-Scale Telescopes. Publications of the Astronomical Society of the Paciﬁc, 127:234, 2015. doi: 10.1086/680521.

[172] J. Ratzloﬀ, N. M. Law, O. Fors, H. T. Corbett, W. S Howard, D. del Ser, and J. Haislip. Building the Evryscope: Hardware Design and Performance. Publications of the Astronomical Society of the Paciﬁc, page 24, 2019.

[173] Hank Corbett, Nicholas M. Law, Alan Vasquez Soto, Ward S. Howard, Amy Glazier, Ramses Gonzalez, Jeﬀrey K. Ratzloﬀ, Nathan Galliher, Octavi Fors, and Robert Quimby. Orbital Foregrounds for Ultra-short Duration Transients. Astrophysical Journal, 903 (2):L27, 2020. doi: 10.3847/2041-8213/abbee5.

[174] Nathan W. Galliher, Jeffrey K. Ratzloff, Hank Corbett, Nicholas M. Law, Ward S. Howard, Amy L. Glazier, Alan Vasquez Soto, and Ramses Gonzalez. Evryscope-South Survey of Upper- and Pre-main Sequence Solar Neighborhood Stars. Publications of the Astronomical Society of the Pacific, 132(1017):114202, 2020. doi: 10.1088/1538-3873/ abb010.

[175] N. M. Law, O. Fors, J. Ratzloﬀ, H. Corbett, D. del Ser, and P. Wulfken. The Evryscope: design and performance of the ﬁrst full-sky gigapixel-scale telescope. In Ground-based and Airborne Telescopes VI, volume 9906 of Proceedings of the SPIE, page 99061M, 2016. doi: 10.1117/12.2233349.

[176] O. Tamuz, T. Mazeh, and S. Zucker. Correcting systematic eﬀects in a large set of photometric light curves. Monthly Notices of the Royal Astronomical Society, 356: 1466–1470, 2005. doi: 10.1111/j.1365-2966.2004.08585.x.

186 [177] E.-S. Liang, S. Wang, J.-L. Zhou, X. Zhou, H. Zhang, J. Xie, H. Liu, L. Wang, and M. C. B. Ashley. Stellar Flares in the CSTAR Field: Results from the 2008 Data Set. Astronomical Journal, 152:168, 2016. doi: 10.3847/0004-6256/152/6/168.

[178] M. Mayor, F. Pepe, D. Queloz, F. Bouchy, G. Rupprecht, G. Lo Curto, G. Avila, W. Benz, J.-L. Bertaux, X. Bonﬁls, T. Dall, H. Dekker, B. Delabre, W. Eckert, M. Fleury, A. Gilliotte, D. Gojak, J. C. Guzman, D. Kohler, J.-L. Lizon, A. Longinotti, C. Lovis, D. Megevand, L. Pasquini, J. Reyes, J.-P. Sivan, D. Sosnowska, R. Soto, S. Udry, A. van Kesteren, L. Weber, and U. Weilenmann. Setting New Standards with HARPS. The Messenger, 114:20–24, 2003.

[179] H. F. Weaver. The Visibility of Stars Without Optical Aid. Publications of the Astronomical Society of the Paciﬁc, 59:232, 1947. doi: 10.1086/125956.

[180] B. E. Schaefer. Telescopic limiting magnitudes. Publications of the Astronomical Society of the Paciﬁc, 102:212–229, 1990. doi: 10.1086/132629.

[181] P. Cinzano, F. Falchi, and C. D. Elvidge. Naked-eye star visibility and limiting magnitude mapped from DMSP-OLS satellite data. Monthly Notices of the Royal Astronomical Society, 323:34–46, 2001. doi: 10.1046/j.1365-8711.2001.04213.x.

[182] J. C. Lurie, T. J. Henry, W.-C. Jao, S. N. Quinn, J. G. Winters, P. A. Ianna, D. W. Koerner, A. R. Riedel, and J. P. Subasavage. The Solar Neighborhood. XXXIV. a Search for Planets Orbiting Nearby M Dwarfs Using Astrometry. Astronomical Journal, 148:91, 2014. doi: 10.1088/0004-6256/148/5/91.

[183] A. R. Walker. Flare activity of Proxima Centauri. Monthly Notices of the Royal Astronomical Society, 195:1029–1035, 1981. doi: 10.1093/mnras/195.4.1029.

[184] Y. Pavlenko, A. SuárezMascareño,R. Rebolo, N. Lodieu, V. J. S. Béjar,and J. I. GonzálezHernández.Flare activity and photospheric analysis of Proxima Centauri. Astronomy and Astrophysics, 606:A49, 2017. doi: 10.1051/0004-6361/201730733.

[185] A. Youngblood, K. France, R. O. P. Loyd, A. Brown, J. P. Mason, P. C. Schneider, M. A. Tilley, Z. K. Berta-Thompson, A. Buccino, C. S. Froning, S. L. Hawley, J. Linsky, P. J. D. Mauas, S. Redﬁeld, A. Kowalski, Y. Miguel, E. R. Newton, S. Rugheimer, A. Segura, A. Roberge, and M. Vieytes. The MUSCLES Treasury Survey. IV. Scaling Relations for Ultraviolet, Ca II K, and Energetic Particle Fluxes from M Dwarfs. Astrophysical Journal, 843:31, 2017. doi: 10.3847/1538-4357/aa76dd.

[186] S. Yashiro, S. Akiyama, N. Gopalswamy, and R. A. Howard. Diﬀerent Power-Law Indices in the Frequency Distributions of Flares with and without Coronal Mass Ejections. Astrophysical Journal, 650:L143–L146, 2006. doi: 10.1086/508876.

[187] D. Slade and M. Radman. Oxidative Stress Resistance in Deinococcus radiodurans. Microbiology and Molecular Biology Reviews, 75(1):133–191, 2011. doi: 10.1128/MMBR. 00015-10.

187 [188] E. W. Cliver, A. G. Ling, A. Belov, and S. Yashiro. Size distributions of solar ﬂares and solar energetic particle events. Astrophysical Journal, 756:L29, 2012. doi: 10.1088/2041-8205/756/2/L29.

[189] A. Belov, H. Garcia, V. Kurt, H. Mavromichalaki, and M. Gerontidou. Proton Enhance- ments and Their Relation to the X-Ray Flares During the Three Last Solar Cycles. Solar Physics, 229:135–159, 2005. doi: 10.1007/s11207-005-4721-3.

[190] U. Mitra-Kraev, L. K. Harra, M. G¨udel,M. Audard, G. Branduardi-Raymont, H. R. M. Kay, R. Mewe, A. J. J. Raassen, and L. van Driel-Gesztelyi. Relationship between X-ray and ultraviolet emission of ﬂares from dMe stars observed by XMM-Newton. Astronomy and Astrophysics, 431:679–686, 2005. doi: 10.1051/0004-6361:20041201.

[191] J. M. Fontenla, Jeﬀrey L. Linsky, Jesse Witbrod, Kevin France, A. Buccino, Pablo Mauas, Mariela Vieytes, and Lucianne M. Walkowicz. Semi-empirical Modeling of the Photosphere, Chromosphere, Transition Region, and Corona of the M-dwarf Host Star GJ 832. Astrophysical Journal, 830:154, 2016. doi: 10.3847/0004-637X/830/2/154.

[192] R. H. Grant and M.G. Heisler. Obscured overcast sky radiance distributions for ultraviolet and photosynthetically active radiation. Journal of Applied Meteorology, 36 (10):1336–1345, 1997. doi: 10.1175/1520-0450(1997)036h1336:OOSRDFi2.0.CO;2.

[193] David Sliney and Myron Wolbarsht. Safety with lasers and other optical sources. In Safety with lasers and other optical sources, volume ., page 194. Plenum Press, 1980. doi: 10.1080/713820456.

[194] R. D. Hurtubise, J. E. Havel, and E. E. Little. The eﬀects of ultraviolet-B radiation on freshwater invertebrates: Experiments with a solar simulator. Limnology and Oceanography, 43(6):1082–1088, 1998. doi: 10.4319/lo.1998.43.6.1082.

[195] Milla Rautio and Atte Korhola. Eﬀects of ultraviolet radiation and dissolved organic carbon on the survival of subarctic zooplankton. Polar Biology, 25(6):460–468, 2002. doi: 10.1007/s00300-002-0366-y.

[196] A Rehemtulla, C A Hamilton, A M Chinnaiyan, and V M Dixit. Ultraviolet radiation- induced apoptosis is mediated by activation of CD-95 (Fas/APO-1). The Journal of biological chemistry, 272(41):25783–6, 1997. doi: 10.1074/JBC.272.41.25783.

[197] Lu´ısF.Z. Batista, Bernd Kaina, Rog´erioMeneghini, and Carlos F.M. Menck. How DNA lesions are turned into powerful killing structures: Insights from UV-induced apoptosis. Mutation Research/Reviews in Mutation Research, 681(2-3):197–208, 2009. doi: 10.1016/J.MRREV.2008.09.001.

[198] Jordi Gascón,Anna Oubiña,Ana Pérez-Lezaun,and Jordi Urmeneta. Sensitivity of selected bacterial species to uv radiation. Current Microbiology, 30(3):177–182, 1995. doi: 10.1007/BF00296205.

188 [199] Annette Brandt, Jean-Pierre de Vera, Silvano Onofri, and Sieglinde Ott. Viability of the lichen xanthoria elegans and its symbionts after 18 months of space exposure and simulated mars conditions on the iss. International Journal of Astrobiology, 14(3): 411–425, 2015. doi: 10.1017/S1473550414000214. [200] Andrew W. Mann, Gregory A. Feiden, Eric Gaidos, Tabetha Boyajian, and Kaspar von Braun. How to Constrain Your M Dwarf: Measuring Effective Temperature, Bolometric Luminosity, Mass, and Radius. Astrophysical Journal, 804(1):64, 2015. doi: 10.1088/0004-637X/804/1/64. [201] Gaia Collaboration, T. Prusti, J. H. J. de Bruijne, A. G. A. Brown, A. Vallenari, C. Babusiaux, C. A. L. Bailer-Jones, U. Bastian, M. Biermann, D. W. Evans, and et al. The Gaia mission. Astronomy and Astrophysics, 595:A1, 2016. doi: 10.1051/0004-6361/ 201629272. [202] Gaia Collaboration, A. G. A. Brown, A. Vallenari, T. Prusti, J. H. J. de Bruijne, C. Babusiaux, C. A. L. Bailer-Jones, M. Biermann, D. W. Evans, L. Eyer, and et al. Gaia Data Release 2. Summary of the contents and survey properties. Astronomy and Astrophysics, 616:A1, 2018. doi: 10.1051/0004-6361/201833051. [203] A. A. Henden, M. Templeton, D. Terrell, T. C. Smith, S. Levine, and D. Welch. VizieR Online Data Catalog: AAVSO Photometric All Sky Survey (APASS) DR9 (Henden+, 2016). VizieR Online Data Catalog, 2336, 2016. [204] Adam L. Kraus and Lynne A. Hillenbrand. The Stellar Populations of Praesepe and Coma Berenices. Astronomical Journal, 134:2340–2352, 2007. doi: 10.1086/522831. [205] James R. A. Davenport. The shape of M dwarf flares in Kepler light curves. In A. G. Kosovichev, S. L. Hawley, and P. Heinzel, editors, Solar and Stellar Flares and their Effects on Planets, volume 320 of IAU Symposium, pages 128–133, 2016. doi: 10.1017/S174392131600867X. [206] J. A. McLaughlin, V. M. Nakariakov, M. Dominique, P. Jel´ınek, and S. Takasao. Modelling Quasi-Periodic Pulsations in Solar and Stellar Flares. Space Science Reviews, 214:45, 2018. doi: 10.1007/s11214-018-0478-5. [207] P. C. Hewett, S. J. Warren, S. K. Leggett, and S. T. Hodgkin. The UKIRT Infrared Deep Sky Survey ZY JHK photometric system: passbands and synthetic colours. Monthly Notices of the Royal Astronomical Society, 367:454–468, 2006. doi: 10.1111/j.1365-2966. 2005.09969.x. [208] K. Namekata, T. Sakaue, K. Watanabe, A. Asai, H. Maehara, Y. Notsu, S. Notsu, S. Honda, T. T. Ishii, K. Ikuta, D. Nogami, and K. Shibata. Statistical Studies of Solar White-light Flares and Comparisons with Superflares on Solar-type Stars. Astrophysical Journal, 851:91, 2017. doi: 10.3847/1538-4357/aa9b34. [209] S. Candelaresi, A. Hillier, H. Maehara, A. Brandenburg, and K. Shibata. Superflare Occurrence and Energies on G-, K-, and M-type Dwarfs. Astrophysical Journal, 792:67, 2014. doi: 10.1088/0004-637X/792/1/67.

189 [210] J. R. A. Davenport. The Kepler Catalog of Stellar Flares. Astrophysical Journal, 829: 23, 2016. doi: 10.3847/0004-637X/829/1/23. [211] B. Stelzer, M. Damasso, A. Scholz, and S. P. Matt. A path towards understanding the rotation-activity relation of M dwarfs with K2 mission, X-ray and UV data. Monthly Notices of the Royal Astronomical Society, 463:1844–1864, 2016. doi: 10.1093/mnras/ stw1936. [212] Anna Y. Q. Ho, S. R. Kulkarni, Peter E. Nugent, Weijie Zhao, Florin Rusu, S. Bradley Cenko, Vikram Ravi, Mansi M. Kasliwal, Daniel A. Perley, Scott M. Adams, Eric C. Bellm, Patrick Brady, Christoffer Fremling, Avishay Gal-Yam, David Alexand er Kann, David Kaplan, Russ R. Laher, Frank Masci, Eran O. Ofek, Jesper Sollerman, and Alex Urban. iPTF Archival Search for Fast Optical Transients. Astrophysical Journal, 854 (1):L13, 2018. doi: 10.3847/2041-8213/aaaa62. [213] I. Andreoni, J. Cooke, S. Webb, A. Rest, T. Pritchard, M. Caleb, S. W. Chang, W. Farah, A. Lien, A. Möller,M. E. Ravasio, T. M. C. Abbott, S. Bhandari, A. Cucchiara, C. Flynn, F. Jankowski, E. F. Keane, T. J. Moriya, C. A. Onken, A. Parthasarathy, D. C. Price, E. Petroff, S. Ryder, D. Vohl, and C. Wolf. Probing the extragalactic fast transient sky at minute time-scales with DECam. Monthly Notices of the Royal Astronomical Society, 491(4):5852–5866, 2020. doi: 10.1093/mnras/stz3381. [214] J. van Roestel, P. J. Groot, T. Kupfer, K. Verbeek, S. van Velzen, M. Bours, P. Nugent, T. Prince, D. Levitan, S. Nissanke, S. R. Kulkarni, and R. R. Laher. The Palomar Transient Factory Sky2Night programme. Monthly Notices of the Royal Astronomical Society, 484(4):4507–4528, 2019. doi: 10.1093/mnras/stz241. [215] James R. A. Davenport, Andrew C. Becker, Adam F. Kowalski, Suzanne L. Hawley, Sarah J. Schmidt, Eric J. Hilton, Branimir Sesar, and Roc Cutri. Multi-wavelength Characterization of Stellar Flares on Low-mass Stars Using SDSS and 2MASS Time- domain Surveys. Astrophysical Journal, 748:58, 2012. doi: 10.1088/0004-637X/748/1/ 58. [216] John F. Kielkopf, Rhodes Hart, Bradley D. Carter, and Stephen C. Marsden. Obser- vation of a possible superflare on Proxima Centauri. Monthly Notices of the Royal Astronomical Society, 486(1):L31–L35, 2019. doi: 10.1093/mnrasl/slz054. [217] Adam L. Kraus, Evgenya L. Shkolnik, Katelyn N. Allers, and Michael C. Liu. A Stellar Census of the Tucana-Horologium Moving Group. Astronomical Journal, 147:146, 2014. doi: 10.1088/0004-6256/147/6/146. [218] Brittany E. Miles and Evgenya L. Shkolnik. HAZMAT. II. Ultraviolet Variability of Low-mass Stars in the GALEX Archive. Astronomical Journal, 154:67, 2017. doi: 10.3847/1538-3881/aa71ab. [219] R. O. Parke Loyd, Evgenya L. Shkolnik, Adam C. Schneider, Travis S. Barman, Victoria S. Meadows, Isabella Pagano, and Sarah Peacock. HAZMAT. IV. Flares and Superflares on Young M Stars in the Far Ultraviolet. Astrophysical Journal, 867:70, 2018. doi: 10.3847/1538-4357/aae2ae.

190 [220] Basmah Riaz, John E. Gizis, and James Harvin. Identiﬁcation of New M Dwarfs in the Solar Neighborhood. Astronomical Journal, 132:866–872, 2006. doi: 10.1086/505632.

[221] E. Gaidos, A. W. Mann, S. L´epine,A. Buccino, D. James, M. Ansdell, R. Petrucci, P. Mauas, and E. J. Hilton. Trumpeting M dwarfs with CONCH-SHELL: a catalogue of nearby cool host-stars for habitable exoplanets and life. Monthly Notices of the Royal Astronomical Society, 443:2561–2578, 2014. doi: 10.1093/mnras/stu1313.

[222] A. P. Cowley, D. Crampton, J. B. Hutchings, D. J. Helfand , T. T. Hamilton, J. R. Thorstensen, and P. A. Charles. Optical counterparts of the Large Magellanic Cloud X-ray point sources. Astrophysical Journal, 286:196–208, 1984. doi: 10.1086/162587.

[223] Oliver J. Fraser, Suzanne L. Hawley, and Kem H. Cook. The Properties of Long-Period Variables in the Large Magellanic Cloud from MACHO. Astronomical Journal, 136: 1242–1258, 2008. doi: 10.1088/0004-6256/136/3/1242.

[224] Carl Ziegler, Nicholas M. Law, Christoph Baranec, Tim Morton, Reed Riddle, Nathan De Lee, Daniel Huber, Suvrath Mahadevan, and Joshua Pepper. Measuring the Recov- erability of Close Binaries in Gaia DR2 with the Robo-AO Kepler Survey. Astronomical Journal, 156(6):259, 2018. doi: 10.3847/1538-3881/aad80a.

[225] Sarah Ballard. Predicted Number, Multiplicity, and Orbital Dynamics of TESS M-dwarf Exoplanets. Astronomical Journal, 157:113, 2019. doi: 10.3847/1538-3881/aaf477.

[226] M. K. Crosley and R. A. Osten. Constraining Stellar Coronal Mass Ejections through Multi-wavelength Analysis of the Active M Dwarf EQ Peg. Astrophysical Journal, 856: 39, 2018. doi: 10.3847/1538-4357/aaaec2.

[227] M. K. Crosley and R. A. Osten. Low-frequency Radio Transients on the Active M-dwarf EQ Peg and the Search for Coronal Mass Ejections. Astrophysical Journal, 862:113, 2018. doi: 10.3847/1538-4357/aacf02.

[228] Sofia-Paraskevi Moschou, Jeremy J. Drake, Ofer Cohen, JuliánD. Alvarado-Gómez, Cecilia Garraffo, and Federico Fraschetti. The Stellar CME-Flare Relation: What Do Historic Observations Reveal? Astrophysical Journal, 877(2):105, 2019. doi: 10.3847/1538-4357/ab1b37.

[229] JuliánD. Alvarado-Gómez,Jeremy J. Drake, Ofer Cohen, Sofia P. Moschou, and Cecilia Garraffo. Suppression of Coronal Mass Ejections in Active Stars by an Overlying Large-scale Magnetic Field: A Numerical Study. Astrophysical Journal, 862:93, 2018. doi: 10.3847/1538-4357/aacb7f.

[230] D. Atri. Modelling stellar proton event-induced particle radiation dose on close-in exoplanets. Monthly Notices of the Royal Astronomical Society, 465:L34–L38, 2017. doi: 10.1093/mnrasl/slw199.

[231] L. Kaltenegger, J. Pepper, K. Stassun, and R. Oelkers. TESS Habitable Zone Star Catalog. Astrophysical Journal, 874:L8, 2019. doi: 10.3847/2041-8213/ab0e8d.

191 [232] Jeffrey K. Ratzloff, Henry T. Corbett, Nicholas M. Law, Brad N. Barlow, Amy Glazier, Ward S. Howard, Octavi Fors, Daniel del Ser, and Trifon Trifonov. Variables in the Southern Polar Region Evryscope 2016 Data Set. Publications of the Astronomical Society of the Pacific, 131(1002):084201, 2019. doi: 10.1088/1538-3873/ab1d77. [233] Fabian Pedregosa, GaëlVaroquaux, Alexandre Gramfort, Vincent Michel, Bertrand Thirion, Olivier Grisel, Mathieu Blondel, Andreas Müller,Joel Nothman, and Gilles Louppe. Scikit-learn: Machine Learning in Python. arXiv e-prints, art. arXiv:1201.0490, 2012. [234] Yuta Notsu, Takuya Shibayama, Hiroyuki Maehara, Shota Notsu, Takashi Nagao, Satoshi Honda, Takako T. Ishii, Daisaku Nogami, and Kazunari Shibata. Superflares on Solar-type Stars Observed with Kepler II. Photometric Variability of Superflare- generating Stars: A Signature of Stellar Rotation and Starspots. Astrophysical Journal, 771(2):127, 2013. doi: 10.1088/0004-637X/771/2/127. [235] N. R. Lomb. Least-squares frequency analysis of unequally spaced data. Astrophysics and Space Science, 39:447–462, 1976. doi: 10.1007/BF00648343. [236] J. D. Scargle. Studies in astronomical time series analysis. II - Statistical aspects of spectral analysis of unevenly spaced data. Astrophysical Journal, 263:835–853, 1982. doi: 10.1086/160554. [237] Jacob T. VanderPlas. Understanding the Lomb-Scargle Periodogram. The Astrophysical Journal Supplement Series, 236:16, 2018. doi: 10.3847/1538-4365/aab766. [238] Helen A. C. Giles, Andrew Collier Cameron, and RaphaëlleD. Haywood. A Kepler study of starspot lifetimes with respect to light-curve amplitude and spectral type. Monthly Notices of the Royal Astronomical Society, 472(2):1618–1627, 2017. doi: 10.1093/mnras/stx1931. [239] Jeffrey K. Ratzloff, Brad N. Barlow, Thomas Kupfer, Kyle A. Corcoran, Stephan Geier, Evan Bauer, Henry T. Corbett, Ward S. Howard, Amy Glazier, and Nicholas M. Law. EVR-CB-001: An Evolving, Progenitor, White Dwarf Compact Binary Discovered with the Evryscope. Astrophysical Journal, 883(1):51, 2019. doi: 10.3847/1538-4357/ab3727. [240] Jeffrey K. Ratzloff, Brad N. Barlow, PéterNémeth,Henry T. Corbett, Stephen Walser, Nathan W. Galliher, Amy Glazier, Ward S. Howard, and Nicholas M. Law. Hot Subdwarf All Southern Sky Fast Transit Survey with the Evryscope. Astrophysical Journal, 890(2):126, 2020. doi: 10.3847/1538-4357/ab64f3. [241] David P. Fleming, Rory Barnes, James R. A. Davenport, and Rodrigo Luger. Rotation Period Evolution in Low-mass Binary Stars: The Impact of Tidal Torques and Magnetic Braking. Astrophysical Journal, 881(2):88, 2019. doi: 10.3847/1538-4357/ab2ed2.

[242] Z. Eker, N. Filiz Ak, S. Bilir, D. Doˇgru,M. T¨uys¨uz,E. Soydugan, H. Bakıs, , B. Uˇgras, , F. Soydugan, A. Erdem, and O. Demircan. A catalogue of chromospherically active binary stars (third edition). Monthly Notices of the Royal Astronomical Society, 389(4): 1722–1726, 2008. doi: 10.1111/j.1365-2966.2008.13670.x.

192 [243] N. N. Samus’, E. V. Kazarovets, O. V. Durlevich, N. N. Kireeva, and E. N. Pastukhova. General catalogue of variable stars: Version GCVS 5.1. Astronomy Reports, 61(1): 80–88, 2017. doi: 10.1134/S1063772917010085. [244] James E. Neff, Douglas O’Neal, and Steven H. Saar. Absolute Measurements of Starspot Area and Temperature: II Pegasi in 1989 October. Astrophysical Journal, 452:879, 1995. doi: 10.1086/176356. [245] Douglas O’Neal, James E. Neff, Steven H. Saar, and Manfred Cuntz. Further Results of TiO-Band Observations of Starspots. Astronomical Journal, 128(4):1802–1811, 2004. doi: 10.1086/423438. [246] Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, StéfanJ. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, CJ Carey, Ilhan˙ Polat, Yu Feng, Eric W. Moore, Jake Vand erPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E. A. Quintero, Charles R Harris, Anne M. Archibald, AntônioH. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1. 0 Contributors. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods, 2020. doi: https://doi.org/10.1038/s41592-019-0686-2. [247] F. W. Scholz and M. A. Stephens. K-Sample Anderson-Darling Tests. J. Am. Stat. Assoc, 82:918–924, 1987. [248] Nicholas J. Wright, Jeremy J. Drake, Eric E. Mamajek, and Gregory W. Henry. The Stellar-activity-Rotation Relationship and the Evolution of Stellar Dynamos. Astrophysical Journal, 743(1):48, 2011. doi: 10.1088/0004-637X/743/1/48. [249] J. L. Tonry, L. Denneau, H. Flewelling, A. N. Heinze, C. A. Onken, S. J. Smartt, B. Stalder, H. J. Weiland, and C. Wolf. The ATLAS All-Sky Stellar Reference Catalog. Astrophysical Journal, 867(2):105, 2018. doi: 10.3847/1538-4357/aae386. [250] M. Wenger, F. Ochsenbein, D. Egret, P. Dubois, F. Bonnarel, S. Borde, F. Genova, G. Jasniewicz, S. Laloë,S. Lesteven, and R. Monier. The SIMBAD astronomical database. The CDS reference database for astronomical objects. Astronomy and Astrophysicss, 143:9–22, 2000. doi: 10.1051/aas:2000332. [251] Todd J. Henry, Lucianne M. Walkowicz, Todd C. Barto, and David A. Golimowski. The Solar Neighborhood. VI. New Southern Nearby Stars Identified by Optical Spectroscopy. Astronomical Journal, 123(4):2002–2009, 2002. doi: 10.1086/339315. [252] Todd J. Henry, Wei-Chun Jao, John P. Subasavage, Thomas D. Beaulieu, Philip A. Ianna, Edgardo Costa, and RenéA. Méndez.The Solar Neighborhood. XVII. Parallax Results from the CTIOPI 0.9 m Program: 20 New Members of the RECONS 10 Parsec Sample. Astronomical Journal, 132(6):2360–2371, 2006. doi: 10.1086/508233. [253] Basmah Riaz, John E. Gizis, and James Harvin. Identification of New M Dwarfs in the Solar Neighborhood. Astronomical Journal, 132(2):866–872, 2006. doi: 10.1086/505632.

193 [254] C. A. O. Torres, G. R. Quast, L. da Silva, R. de La Reza, C. H. F. Melo, and M. Sterzik. Search for associations containing young stars (SACY). I. Sample and searching method. Astronomy and Astrophysics, 460(3):695–708, 2006. doi: 10.1051/0004-6361:20065602. [255] Adam L. Kraus, Evgenya L. Shkolnik, Katelyn N. Allers, and Michael C. Liu. A Stellar Census of the Tucana-Horologium Moving Group. Astronomical Journal, 147(6):146, 2014. doi: 10.1088/0004-6256/147/6/146. [256] E. Gaidos, A. W. Mann, S. Lépine,A. Buccino, D. James, M. Ansdell, R. Petrucci, P. Mauas, and E. J. Hilton. Trumpeting M dwarfs with CONCH-SHELL: a catalogue of nearby cool host-stars for habitable exoplanets and life. Monthly Notices of the Royal Astronomical Society, 443(3):2561–2578, 2014. doi: 10.1093/mnras/stu1313. [257] Adric R. Riedel, Munazza K. Alam, Emily L. Rice, Kelle L. Cruz, and Todd J. Henry. Young Stars with SALT. Astrophysical Journal, 840(2):87, 2017. doi: 10.3847/ 1538-4357/840/2/87. [258] T. J. Moffett. UV Ceti flare stars: observational data. Astrophysical Journals, 29:1–42, 1974. doi: 10.1086/190330. [259] Peter W. Sullivan, Joshua N. Winn, Zachory K. Berta-Thompson, David Charbonneau, Drake Deming, Courtney D. Dressing, David W. Latham, Alan M. Levine, Peter R. McCullough, Timothy Morton, George R. Ricker, Roland Vanderspek, and Deborah Woods. The Transiting Exoplanet Survey Satellite: Simulations of Planet Detections and Astrophysical False Positives. Astrophysical Journal, 809(1):77, 2015. doi: 10.1088/ 0004-637X/809/1/77. [260] C. A. L. Bailer-Jones, J. Rybizki, M. Fouesneau, G. Mantelet, and R. Andrae. Estimating Distance from Parallaxes. IV. Distances to 1.33 Billion Stars in Gaia Data Release 2. Astronomical Journal, 156(2):58, 2018. doi: 10.3847/1538-3881/aacb21. [261] J. H. M. M. Schmitt, P. Ioannidis, J. Robrade, S. Czesla, and P. C. Schneider. Superflares on AB Doradus observed with TESS. Astronomy and Astrophysics, 628:A79, 2019. doi: 10.1051/0004-6361/201935374. [262] Suzanne L. Hawley, Joel C. Allred, Christopher M. Johns-Krull, George H. Fisher, William P. Abbett, Ilya Alekseev, Stavros I. Avgoloupis, Susana E. Deustua, Alastair Gunn, John H. Seiradakis, Martin M. Sirk, and Jeff A. Valenti. Multiwavelength observations of flares on AD leonis. The Astrophysical Journal, 597(1):535–554, 2003. doi: 10.1086/378351. [263] J. SebastiánCastellanos Duránand Lucia Kleint. The Statistical Relationship between White-light Emission and Photospheric Magnetic Field Changes in Flares. Astrophysical Journal, 904(2):96, 2020. doi: 10.3847/1538-4357/ab9c1e. [264] X. C. Abrevaya, M. Leitzinger, O. J. Oppezzo, P. Odert, M. R. Patel, G. J. M. Luna, A. F. Forte Giacobone, and A. Hanslmeier. The UV surface habitability of Proxima b: first experiments revealing probable life survival to stellar flares. Monthly Notices of the Royal Astronomical Society, 494(1):L69–L74, 2020. doi: 10.1093/mnrasl/slaa037.

194 [265] S. W. Mochnacki and H. Zirin. Multichannel spectrophotometry of stellar ﬂares. Astrophysical Journal, 239:L27–L31, 1980. doi: 10.1086/183285.

[266] U. Feldman, G. A. Doschek, W. E. Behring, and K. J. H. Phillips. Electron Temperature, Emission Measure, and X-Ray Flux in A2 to X2 X-Ray Class Solar Flares. Astrophysical Journal, 460:1034, 1996. doi: 10.1086/177030.

[267] Amir Caspi, S¨amKrucker, and R. P. Lin. Statistical Properties of Super-hot Solar Flares. Astrophysical Journal, 781(1):43, 2014. doi: 10.1088/0004-637X/781/1/43.

[268] R. O. Parke Loyd, Evgenya L. Shkolnik, Kevin France, Brian E. Wood, and Allison Youngblood. When “boring” stars ﬂare: The ultraviolet activity of GJ 887, a bright m star hosting newly discovered planets. Research Notes of the AAS, 4(7):119, 2020. doi: 10.3847/2515-5172/aba94a.

[269] Andrea De Luca, Beate Stelzer, Adam J. Burgasser, Daniele Pizzocaro, Piero Ranalli, Stefanie Raetz, Martino Marelli, Giovanni Novara, Cristian Vignali, Andrea Belﬁore, Paolo Esposito, Paolo Franzetti, Marco Fumana, Roberto Gilli, Ruben Salvaterra, and Andrea Tiengo. EXTraS discovery of an X-ray superﬂare from an L dwarf. Astronomy and Astrophysics, 634:L13, 2020. doi: 10.1051/0004-6361/201937163.

[270] R. R. Paudel, J. E. Gizis, D. J. Mullan, S. J. Schmidt, A. J. Burgasser, and P. K. G. Williams. K2 Ultracool Dwarfs Survey - VI. White light superﬂares observed on an L5 dwarf and ﬂare rates of L dwarfs. Monthly Notices of the Royal Astronomical Society, 494(4):5751–5760, 2020. doi: 10.1093/mnras/staa1137.

[271] J. Sebastian Pineda, Kevin France, and Allison Youngblood. FUMES: Simultaneous Optical and UV Spectroscopy of an M-dwarf Flare. In American Astronomical Soci- ety Meeting Abstracts #233, volume 233 of American Astronomical Society Meeting Abstracts, page 204.03, 2019.

[272] R. O. Parke Loyd, Evgenya L. Shkolnik, Adam C. Schneider, Tyler Richey-Yowell, Travis S. Barman, Sarah Peacock, and Isabella Pagano. Current Population Statistics Do Not Favor Photoevaporation over Core-powered Mass Loss as the Dominant Cause of the Exoplanet Radius Gap. Astrophysical Journal, 890(1):23, 2020. doi: 10.3847/ 1538-4357/ab6605.

[273] Lison Malo, Etienne´ Artigau, RenéDoyon, David Lafrenière,Lo¨ıcAlbert, and Jonathan Gagné.BANYAN. III. Radial Velocity, Rotation, and X-Ray Emission of Low-mass Star Candidates in Nearby Young Kinematic Groups. Astrophysical Journal, 788(1):81, 2014. doi: 10.1088/0004-637X/788/1/81.

[274] Jonathan Gagné,Eric E. Mamajek, Lison Malo, Adric Riedel, David Rodriguez, David Lafrenière,Jacqueline K. Faherty, Olivier Roy-Loubier, Laurent Pueyo, Annie C. Robin, and RenéDoyon. BANYAN. XI. The BANYAN Σ Multivariate Bayesian Algorithm to Identify Members of Young Associations with 150 pc. Astrophysical Journal, 856(1):23, 2018. doi: 10.3847/1538-4357/aaae09.

195 [275] Thierry Morel. The chemical composition of α Centauri AB revisited. Astronomy and Astrophysics, 615:A172, 2018. doi: 10.1051/0004-6361/201833125.

[276] M. S. Dodd, D. Papineau, T. Grenne, J. F. Slack, M. Rittner, F. Pirajno, J. O´ Neil, and C. T. S. Little. Evidence for early life in Earth’s oldest hydrothermal vent precipitates. Nature, 543:60, 2017. doi: 10.1038/nature21377.

[277] Z. Li, J. Wang, and J. Han. eperiodicity: Mining event periodicity from incomplete observations. IEEE Transactions on Knowledge and Data Engineering, 27(5):1219–1232, 2015. doi: 10.1109/TKDE.2014.2365801.

[278] Abhirup Ghosh, Christopher Lucas, and Rik Sarkar. Finding periodic discrete events in noisy streams. In Proceedings of the 2017 ACM on Conference on Information and Knowledge Management, CIKM ’17, page 627–636, New York, NY, USA, 2017. Association for Computing Machinery. doi: 10.1145/3132847.3132981.

[279] Yunfan Gerry Zhang, Vishal Gajjar, Griﬃn Foster, Andrew Siemion, James Cordes, Casey Law, and Yu Wang. Fast Radio Burst 121102 Pulse Detection and Periodicity: A Machine Learning Approach. Astrophysical Journal, 866(2):149, 2018. doi: 10.3847/ 1538-4357/aadf31.

[280] KrisztiánVida, Katalin Oláh,Zsolt K˝ovári,Lidia van Driel-Gesztelyi, Attila Moór, and AndrásPál. Flaring Activity of Proxima Centauri from TESS Observations: Quasiperiodic Oscillations during Flare Decay and Inferences on the Habitability of Proxima b. Astrophysical Journal, 884(2):160, 2019. doi: 10.3847/1538-4357/ab41f5.

[281] A. Savitzky and M. J. E. Golay. Smoothing and diﬀerentiation of data by simpliﬁed least squares procedures. Analytical Chemistry, 36:1627–1639, 1964.

[282] Adric R. Riedel, Munazza K. Alam, Emily L. Rice, Kelle L. Cruz, and Todd J. Henry. Young Stars with SALT. Astrophysical Journal, 840(2):87, 2017. doi: 10.3847/ 1538-4357/840/2/87.

[283] K. Vida, L. Kriskovics, K. Oláh,M. Leitzinger, P. Odert, Zs. K˝ovári,H. Korhonen, R. Greimel, R. Robb, B. Csák,and J. Kovács.Investigating magnetic activity in very stable stellar magnetic fields. Long-term photometric and spectroscopic study of the fully convective M4 dwarf V374 Pegasi. Astronomy and Astrophysics, 590:A11, 2016. doi: 10.1051/0004-6361/201527925.

[284] F. Rigaut and E. Gendron. Laser guide star in adaptive optics - The tilt determination problem. Astronomy and Astrophysics, 261:677–684, 1992.

[285] D. G. Koch, W. J. Borucki, G. Basri, N. M. Batalha, T. M. Brown, D. Caldwell, J. Christensen-Dalsgaard, W. D. Cochran, E. DeVore, E. W. Dunham, T. N. Gautier, III, J. C. Geary, R. L. Gilliland, A. Gould, J. Jenkins, Y. Kondo, D. W. Latham, J. J. Lissauer, G. Marcy, D. Monet, D. Sasselov, A. Boss, D. Brownlee, J. Caldwell, A. K. Dupree, S. B. Howell, H. Kjeldsen, S. Meibom, D. Morrison, T. Owen, H. Reitsema, J. Tarter, S. T. Bryson, J. L. Dotson, P. Gazis, M. R. Haas, J. Kolodziejczak, J. F.

196 Rowe, J. E. Van Cleve, C. Allen, H. Chandrasekaran, B. D. Clarke, J. Li, E. V. Quintana, P. Tenenbaum, J. D. Twicken, and H. Wu. Kepler Mission Design, Realized Photometric Performance, and Early Science. Astrophysical Journal, 713:L79-L86, 2010. doi: 10.1088/2041-8205/713/2/L79. [286] F. T. O’Donovan, D. Charbonneau, G. Torres, G. Mandushev, E. W. Dunham, D. W. Latham, R. Alonso, T. M. Brown, G. A. Esquerdo, M. E. Everett, and O. L. Creevey. Rejecting Astrophysical False Positives from the TrES Transiting Planet Survey: The Example of GSC 03885-00829. Astrophysical Journal, 644:1237–1245, 2006. doi: 10.1086/503740. [287] Nicholas M. Law, Tim Morton, Christoph Baranec, Reed Riddle, Ganesh Ravichandran, Carl Ziegler, John Asher Johnson, Shriharsh P. Tendulkar, Khanh Bui, Mahesh P. Burse, H. K. Das, Richard G. Dekany, Shrinivas Kulkarni, Sujit Punnadi, and A. N. Ramaprakash. Robotic laser adaptive optics imaging of 715 kepler exoplanet candidates using robo-ao. The Astrophysical Journal, 791(1):35, 2014. [288] John Asher Johnson, Kevin Apps, J. Zachary Gazak, Justin R. Crepp, Ian J. Crossfield, Andrew W. Howard, Geoff W. Marcy, Timothy D. Morton, Carly Chubak, and Howard Isaacson. Lhs 6343 c: A transiting field brown dwarf discovered by the kepler mission. The Astrophysical Journal, 730(2):79, 2011. [289] C. Ziegler, N. M. Law, T. Morton, C. Baranec, R. Riddle, D. Atkinson, A. Baker, S. Roberts, and D. R. Ciardi. Robo-AO Kepler Planetary Candidate Survey. III. Adaptive Optics Imaging of 1629 Kepler Exoplanet Candidate Host Stars. Astronomical Journal, 153:66, 2017. doi: 10.3847/1538-3881/153/2/66. [290] G. Chabrier. Galactic Stellar and Substellar Initial Mass Function. Publications of the Astronomical Society of the Pacific, 115:763–795, 2003. doi: 10.1086/376392. [291] C. D. Dressing and D. Charbonneau. The Occurrence of Potentially Habitable Plan- ets Orbiting M Dwarfs Estimated from the Full Kepler Dataset and an Empirical Measurement of the Detection Sensitivity. Astrophysical Journal, 807:45, 2015. [292] C. Baranec, R. Riddle, N. M. Law, A. N. Ramaprakash, S. Tendulkar, K. Hogstrom, K. Bui, M. Burse, P. Chordia, H. Das, R. Dekany, S. Kulkarni, and S. Punnadi. High- efficiency Autonomous Laser Adaptive Optics. Astrophysical Journal, 790:L8, 2014. doi: 10.1088/2041-8205/790/1/L8. [293] C. Baranec, C. Ziegler, N. M. Law, T. Morton, R. Riddle, D. Atkinson, J. Schonhut, and J. Crepp. Robo-AO Kepler Planetary Candidate Survey. II. Adaptive Optics Imaging of 969 Kepler Exoplanet Candidate Host Stars. Astronomical Journal, 152:18, 2016. doi: 10.3847/0004-6256/152/1/18. [294] Michael R. Haas, Natalie M. Batalha, Steve T. Bryson, Douglas A. Caldwell, Jessie L. Dotson, Jennifer Hall, Jon M. Jenkins, Todd C. Klaus, David G. Koch, Jeffrey Kolodziejczak, Chris Middour, Marcie Smith, Charles K. Sobeck, Jeremy Stober, Richard S. Thompson, and Jeffrey E. Van Cleve. Kepler science operations. The Astrophysical Journal Letters, 713(2):L115, 2010.

197 [295] R. Foy and A. Labeyrie. Feasibility of adaptive telescope with laser probe. Astronomy and Astrophysics, 152:L29–L31, 1985.

[296] E. Steinbring, S. M. Faber, B. A. Macintosh, D. Gavel, and E. L. Gates. Characterizing the Adaptive Optics Oﬀ-Axis Point-Spread Function. II. Methods for Use in Laser Guide Star Observations. Publications of the Astronomical Society of the Paciﬁc, 117: 847–859, 2005. doi: 10.1086/431725.

[297] C. Trujillo, J. Ball, M. Boccas, C. Cavedoni, J. Christou, D. Coulson, A. Ebbers, K. Emig, I. Jorgensen, S. Kang, O. Lai, A. Matulonis, R. McDermid, B. Miller, B. Neichel, R. Oram, F. Rigaut, K. Roth, T. Schneider, A. Stephens, G. Trancho, B. Walls, J. White, and Gemini Software Team. Altair at Gemini North: Full Sky Coverage Laser AO Correction at Visible Wavelengths. In S. Esposito and L. Fini, editors, Proceedings of the Third AO4ELT Conference, page 51, 2013. doi: 10.12839/ AO4ELT3.13288.

[298] P. Wizinowich, R. Smith, R. Biasi, S. Cetre, R. Dekany, B. Femenia-Castella, J. Fucik, D. Hale, C. Neyman, D. Pescoller, S. Ragland, P. Stomski, M. Andrighettoni, R. Bartos, K. Bui, A. Cooper, J. Cromer, M. van Dam, M. Hess, E. James, J. Lyke, H. Rodriguez, and T. Stalcup. A near-infrared tip-tilt sensor for the Keck I laser guide star adaptive optics system. In Adaptive Optics Systems IV, volume 9148 of Proceedings of the SPIE, page 91482B, 2014. doi: 10.1117/12.2055279.

[299] R. Davies, S. Rabien, C. Lidman, M. Le Louarn, M. Kasper, N. M. F¨orsterSchreiber, V. Roccatagliata, N. Ageorges, P. Amico, C. Dumas, and F. Mannucci. Laser Guide Star Adaptive Optics without Tip-tilt. The Messenger, 131:7–10, 2008.

[300] J. W. Hardy. Adaptive Optics for Astronomical Telescopes. New York: Oxford Univ. Press, 1998.

[301] S. Roberts and G. Singh. Optomechanical design of Altair, the Gemini adaptive optics system. In D. Bonaccini and R. K. Tyson, editors, Adaptive Optical System Technologies, volume 3353 of Proceedings of the SPIE, pages 611–620, 1998. doi: 10.1117/12.321627.

[302] Rebecca Jensen-Clem, Dmitry A. Duev, Reed Riddle, Ma¨ıssa Salama, Christoph Baranec, Nicholas M. Law, S. R. Kulkarni, and A. N. Ramprakash. The Performance of the Robo-AO Laser Guide Star Adaptive Optics System at the Kitt Peak 2.1 m Telescope. Astronomical Journal, 155(1):32, 2018. doi: 10.3847/1538-3881/aa9be6.

[303] D. Gratadour, L. M. Mugnier, and D. Rouan. Sub-pixel image registration with a maximum likelihood estimator. Application to the ﬁrst adaptive optics observations of Arp 220 in the L’ band. Astronomy and Astrophysics, 443:357–365, 2005. doi: 10.1051/0004-6361:20042188.

[304] M. Guillaume, P. Melon, P. Refregier, and A. Llebaria. Maximum-likelihood estimation of an astronomical image from a sequence at low photon levels. Journal of the Optical Society of America A, 15:2841–2848, 1998. doi: 10.1364/JOSAA.15.002841.

198 [305] D. L. Snyder and T. J. Schulz. High-resolution imaging at low-light levels through weak turbulence. Journal of the Optical Society of America A, 7:1251–1265, 1990. doi: 10.1364/JOSAA.7.001251.

[306] A. S. Fruchter and R. N. Hook. Drizzle: A method for the linear reconstruction of undersampled images. Publications of the Astronomical Society of the Paciﬁc, 114(792): 144, 2002.

[307] C. Baranec, J. R. Lu, S. A. Wright, J. Tonry, R. B. Tully, I. Szapudi, M. Takamiya, L. Hunter, R. Riddle, S. Chen, and M. Chun. The rapid transient surveyor. In Adaptive Optics Systems V, volume 9909 of Proceedings of the SPIE, page 99090F, 2016. doi: 10.1117/12.2230848.

[308] R. Davies and M. Kasper. Adaptive Optics for Astronomy. Adaptive Optics for Astronomy, 50:305–351, 2012. doi: 10.1146/annurev-astro-081811-125447.

[309] Jennifer G. Winters, Amber A. Medina, Jonathan M. Irwin, David Charbonneau, Nicola Astudillo-Defru, Elliott P. Horch, Jason D. Eastman, Eliot Halley Vrijmoet, Todd J. Henry, Hannah Diamond-Lowe, Elaine Winston, Thomas Barclay, Xavier Bon- fils, George R. Ricker, Roland Vanderspek, David W. Latham, Sara Seager, Joshua N. Winn, Jon M. Jenkins, StéphaneUdry, Joseph D. Twicken, Johanna K. Teske, Pe- ter Tenenbaum, Francesco Pepe, Felipe Murgas, Philip S. Muirhead, Jessica Mink, Christophe Lovis, Alan M. Levine, SébastienLépine, Wei-Chun Jao, Christopher E. Henze, Gábor Furész,Thierry Forveille, Pedro Figueira, Gilbert A. Esquerdo, Court- ney D. Dressing, Rodrigo F. D´ıaz,Xavier Delfosse, Christopher J. Burke, Fran¸cois Bouchy, Perry Berlind, and Jose-Manuel Almenara. Three Red Suns in the Sky: A Transiting, Terrestrial Planet in a Triple M-dwarf System at 6.9 pc. Astronomical Journal, 158(4):152, 2019. doi: 10.3847/1538-3881/ab364d.

[310] Keavin Moore and Nicolas B. Cowan. Keeping M-Earths Habitable in the Face of Atmospheric Loss by Sequestering Water in the Mantle. Monthly Notices of the Royal Astronomical Society, 2020. doi: 10.1093/mnras/staa1796.

[311] Rodrigo Luger, Jacob Lustig-Yaeger, David P. Fleming, Matt A. Tilley, Eric Agol, Victoria S. Meadows, Russell Deitrick, and Rory Barnes. The Pale Green Dot: A Method to Characterize Proxima Centauri b Using Exo-Aurorae. Astrophysical Journal, 837(1):63, 2017. doi: 10.3847/1538-4357/aa6040.

[312] Thomas Barclay, Joshua Pepper, and Elisa V. Quintana. A Revised Exoplanet Yield from the Transiting Exoplanet Survey Satellite (TESS). Astrophysical Journals, 239(1): 2, 2018. doi: 10.3847/1538-4365/aae3e9.

[313] N. Galliher, W. Howard, H. Corbett, N. Law, A. Vasquez Soto, A. Glazier, and R. Gonzalez. Chasing Young Star Superﬂares Using the Evryscopes. In American Astronomical Society Meeting Abstracts, volume 53 of American Astronomical Society Meeting Abstracts, page 515.04, 2021.

199 [314] M. A. MacGregor, A. J. Weinberger, P. Loyd, E. L. Shkolnik, T. Barclay, R. Osten, W. S. Howard, A. Zic, S. R. Cranmer, A. F. Kowalski, A. Youngblood, A. Estes, D. J. Wilner, J. Forbrich, T. Murphy, N. Law, A. Hughes, A. Boley, I. I. Tristan, J. F. Fuson, and J. Matthews. Discovery of an Extremely Short Duration ’Building Block’ Flare from Proxima Cen Using Millimeter through FUV Observations. In American Astronomical Society Meeting Abstracts, volume 53 of American Astronomical Society Meeting Abstracts, page 515.02, 2021.

[315] G. Hallinan and M. M. Anderson. The OVRO-LWA: An Extrasolar Space Weather Monitoring Station. In Radio Exploration of Planetary Habitability (AASTCS5), volume 49, page 401.01, 2017.

[316] M. K. Crosley and R. A. Osten. Constraining Stellar Coronal Mass Ejections through Multi-wavelength Analysis of the Active M Dwarf EQ Peg. Astrophysical Journal, 856: 39, 2018. doi: 10.3847/1538-4357/aaaec2.

[317] Howard Chen, Zhuchang Zhan, Allison Youngblood, Eric T. Wolf, Adina D. Feinstein, and Daniel E. Horton. Persistence of ﬂare-driven atmospheric chemistry on rocky habitable zone worlds. Nature Astronomy, 5:298–310, 2021. doi: 10.1038/s41550-020-01264-1.

200