A First Reconnaissance of the Atmospheres of Terrestrial Exoplanets Using Ground-Based Optical Transits and Space-Based UV Spectra

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Citation Diamond-Lowe, Hannah Zoe. 2020. A First Reconnaissance of the Atmospheres of Terrestrial Exoplanets Using Ground-Based Optical Transits and Space-Based UV Spectra. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences.

Citable link https://nrs.harvard.edu/URN-3:HUL.INSTREPOS:37365825

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A DISSERTATION PRESENTED BY HANNAH ZOE DIAMOND-LOWE TO THE DEPARTMENT OF ASTRONOMY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FORTHEDEGREEOF DOCTOROF PHILOSOPHY INTHESUBJECTOF ASTRONOMY

HARVARD UNIVERSITY CAMBRIDGE,MASSACHUSETTS MAY 2020 c 2020 HANNAH ZOE DIAMOND-LOWE.ALLRIGHTSRESERVED.

ii Dissertation Advisor: David Charbonneau Hannah Zoe Diamond-Lowe

A ﬁrst reconnaissance of the atmospheres of terrestrial exoplanets using ground-based optical transits and space-based UV spectra

ABSTRACT

Decades of ground-based, space-based, and in some cases in situ measurements of the Solar System terrestrial planets Mercury, Venus, Earth, and Mars have provided in- depth insight into their atmospheres, yet we know almost nothing about the atmospheres of terrestrial planets orbiting other stars. I present an observational reconnaissance of the atmospheres of terrestrial exoplanets orbiting nearby, low-mass stars, opening the door for an atmospheric branch of comparative terrestrial planetology. I studied three worlds, LHS 3844b, GJ 1132b, and LHS 1140b, which have equilibrium temperatures of 805 K, 580 K, and 235 K, respectively. All three planets transit stars with masses less than 20% the mass of the Sun, and lying within 15 parsecs. I employed the technique of ground-based transmission spectroscopy using the Low Dispersion Survey Spectrograph (LDSS3C) on the Magellan Clay Telescope at the Las Campanas Observatory in Chile. To observe transits of LHS 1140b I used the the Inamori-Magellan Areal Camera & Spectro- graph (IMACS) on the Magellan Baade Telescope concurrently with LDSS3C. I searched for chromatic differences in the amount of light attenuated as the planets transited across their host stars. I disfavored cloudless, hydrogen- and helium-dominated atmospheres on LHS 3844b to 5.5σ confidence, and on GJ 1132b to 3.7σ confidence. I disfavored cloudless, water steam atmospheres to 3.5σ confidence on both LHS 3844b and GJ 1132b. The cool equilibrium temperature and high surface gravity of LHS 1140b render any atmosphere around this world below my detection limits.

iii Planetary atmospheres are sculpted and in some cases removed by the high-energy radiation from their host stars. Low-mass stars spend an extended amount of time in the highly-active pre-main sequence phase compared to Sun-like stars. It is not known if terrestrial planets orbiting low-mass stars can maintain atmospheres at all, let alone provide hospitable conditions for abiogenesis. To unite my constraints on terrestrial exoplanet atmospheres with the influence of their low-mass stellar hosts I present a first look at the ultra-violet spectrum of LHS 3844 taken with the Cosmic Origins Spectrograph on the Hubble Space Telescope. I detected prominent emission lines in the ultra-violet spectrum of LHS 3844, and used them to estimate the Lyman-α and extreme ultra-violet luminosity. These data will inform models of atmospheric photochemistry on LHS 3844b and constrain rates of atmospheric escape from this world. My reconnaissance of the atmospheres of several terrestrial exoplanets excluded low mean molecular weight atmospheric cases around these worlds, and pushed current instrumentation to its limits. The pursuit of thin, secondary atmospheres similar to those on Venus and Earth must await future facilities, notably the James Webb Space Telescope and the ground-based giant segmented-mirror telescopes. Detections of terrestrial exoplanet atmospheres, in conjunction with studies of the high-energy stellar flux they encounter, will allow us to place the terrestrial worlds of the Solar System in the context of terrestrial planets as a whole.

iv ACKNOWLEDGEMENTS

This has been a long trek on a bumpy trail, and I could not have reached the summit without the support, advice, love, and tough love from my family, friends, and community. First and foremost, to my advisor Dave, who read every word of my papers, proposals, conference abstracts, and this thesis, thank you for your mentorship. Your patience and insight have made me the scientist I am today, and that is something I can be proud of. A big thank you to my committee members, Dimitar, Mercedes, and Robin, whose varied expertise has strengthened this work, and to David Sing for serving as my external reader. Thank you to Jacob and Dorian, my college advisors. Thank you to the extended MEarth team who I have gotten to know over the years, Jonathan, Jen, Raphie, Jayne, Laura K., Caroline, Laura M., Joey, Suri, Ryan, Amber, Nick, Juli, Kristo, Adrianna, and Emily, I’m glad we will never again have to meet at House of Chang, but I will miss the group conversations. To the broader Center for Astrophysics community, who keep the science, the servers, and the building running, thank you for making the CfA a warm and functioning place to work, even as a pandemic keeps us home. Christine, a very special thank you to you for being my administrative rock, for making sure I got reimbursed at lightning speed, and for sharing where to get the best Mai Tais. I have to thank some incredible friends who have been around through this process. To the past and present residents of 12 Lawrence, my grad school home, Oliver, Ali, Jas- mine, Cassandra, Katie, Allison, Molly, and Christina, thank you for every late night con- versation, every walk to the store, and of course all the backyard barbecues and holiday parties. I learned so much from all of you, and I’m so glad our paths crossed in a creaky old Cambridgeport house. Laura, thank you first for being a friend and confidant, and second for being a top- shelf astronomer. You amaze me always and I’m going to miss not working across the hall, or a floor down from you. Adrien, my oldest friend, thank you for visiting me and keeping our friendship going, now 20 years strong and counting. Erik, Sam, Jay, and Mike, from France to Norway to Chile and both coasts, we’ve been on some great (mis)adventures. Let’s do it again sometime. Zoe, my best friend, most things we talk about I probably can’t write in a Harvard thesis, so I’ll just say, I can’t wait until the next time we can sit out in the sunshine with some white wine and talk until the sun goes down. And then go to Van Kleef.

v Dan, it turns out I leaned on you more than I ever thought I would. Thank you for the day-to-day support while I finished this thesis, and for all the music, laughter, and Miller High Life a girl could want. I’m looking forward to our next adventure. Amber, I could double the length of this thesis with how many thank yous I have for you. Imagine? I’d calculate how many hours we’ve spent together over the last five years but I’d need you to do it with me on the whiteboard and we’re not allowed in our office right now. And let’s face it, it would take us like all day to work out. For all I learned about astronomy, I learned just as much about New Mexico, pecans, the whole Medina family, and your work-out regimen. Te quiero mucho chica. And finally the biggest thank you to my family. Mom and Dad, you showed me the world from day one, and you remain my fiercest supporters to this day. I am so lucky to have such cool parents. To the Diamonds — Grandma Randa, Aunt Celia, Uncle Jon, Aunt Val, Dave, Caryn, Phillip, Eve, and Noah, it is always such a treat to visit with you, whether it’s in California, Hawai’i, or Ohio. To the Chicago Diamonds, Linda, Mark, Sam, and Michael, thank you for giving me a home away from home during my college years. To the Lowes — Uncle Brian, Aunt Mary, Nick, Alexa, Liz, Tim, Miles, and Una, it’s always a good time when we get to hang out and see some art. To my extended Highland Park family, Wendy, Colin, Olivia, and Eliot, thank you for being a part of my life since the Plainfield days. To Jill and Stacy, traveling with you in Ireland is still one of my favorite vacations, and I hope we can make it happen again. And of course to Auntie Wen, Uncle Ron, and Mischa, thank you for making every Hanukkah my favorite holiday celebration. I could not ask for a more talented, more intelligent, or kinder extended family, and I love you all so much.

vi Contents

Abstract iii

Acknowledgementsv

List of ﬁgures xi

List of tables xii

1 Introduction1 1.1 What is a terrestrial exoplanet?...... 1 1.2 Small planets: terrestrial planet vs. enveloped terrestrial planet...... 3 1.2.1 What causes the small planet radius valley?...... 6 1.2.2 Secondary atmospheres on terrestrial planets...... 9 1.3 M dwarfs as terrestrial exoplanet hosts...... 10 1.3.1 Arguments for searching for terrestrial exoplanet atmospheres in mid-M dwarf systems...... 11 1.3.2 M dwarf inﬂuence on terrestrial exoplanet atmospheres...... 13 1.4 Observational opportunities for terrestrial exoplanet atmospheres...... 16 1.4.1 The sample of spectroscopically accessible terrestrial exoplanets... 16 1.4.2 Methods for detecting (terrestrial) exoplanet atmospheres...... 19 Transmission spectroscopy...... 20 Emission spectroscopy...... 21 High-resolution spectroscopy...... 22 Direct imaging...... 23 1.4.3 Other work on atmospheres of terrestrial exoplanets...... 23 1.4.4 A multi-year program to explore terrestrial exoplanet atmospheres. 24

2 Ground-based optical transmission spectroscopy of the small, rocky exoplanet GJ 1132b 27 2.1 Introduction...... 28 2.2 Observations...... 30 vii 2.3 Data Extraction...... 33 2.4 Data Analysis...... 37 2.4.1 Analyzing transits separately...... 37 2.4.2 Analyzing transits jointly...... 40 Levenberg-Marquardt ﬁts...... 40 Dynamic multi-nested sampling...... 41 White light curve...... 43 Transmission spectrum...... 48 2.5 Results...... 50 2.6 Discussion...... 55 2.6.1 Ground-based detection of terrestrial exoplanet atmospheres.... 55 2.6.2 Theoretical atmosphere of GJ 1132b...... 58 2.6.3 Searching for more terrestrial exoplanets...... 60 2.7 Conclusion...... 61

3 Simultaneous Optical Transmission Spectroscopy of a Terrestrial, Habitable- Zone Exoplanet with Two Ground-Based Multi-Object Spectrographs 63 3.1 Introduction...... 64 3.2 Observations...... 69 3.2.1 Magellan I (Baade) IMACS Observations...... 74 3.2.2 Magellan II (Clay) LSDD3C Observations...... 76 3.3 Data Extraction...... 77 3.3.1 mosasaurus extraction steps...... 78 3.3.2 Issues with Magellan I (Baade) IMACS data...... 83 3.4 Data Analysis...... 85 3.4.1 decorrasaurus decorrelation steps...... 86 3.4.2 Two data analyses...... 94 Data sets ﬁt independently...... 96 Data sets ﬁt jointly...... 98 3.5 Results & Discussion...... 105 3.5.1 Planetary atmospheric detection...... 105 3.5.2 Model transmission spectrum...... 108 3.5.3 Observed transmission spectrum...... 109 3.5.4 Atmospheric detection limits...... 109 3.5.5 Future instruments...... 110 3.6 Conclusion...... 112

4 Optical Transmission Spectroscopy of the Terrestrial Exoplanet LHS 3844b from 13 Ground-Based Transit Observations 116 4.1 Introduction...... 117

viii 4.2 Observations...... 120 4.2.1 Ground-based observing with Magellan II (Clay)/LDSS3C...... 122 4.3 Data Extraction & Analysis...... 125 4.3.1 White light curves...... 127 4.3.2 Spectroscopic light curves...... 130 4.4 Results & Discussion...... 136 4.4.1 LHS 3844b transmission spectrum compared to model transmission spectra...... 136 4.4.2 Wiggles in the LHS 3844b transmission spectrum...... 138 4.4.3 Comparison to previous results...... 139 4.5 Conclusion...... 141

5 Ultra-violet profile of the nearby planet-hosting mid-M dwarf LHS 3844 with HST/COS 144 5.1 Introduction...... 145 5.2 Constructing the UV profile of LHS 3844...... 147 5.2.1 Ly-α estimation...... 148 5.2.2 EUV estimation...... 152 5.2.3 Putting it all together...... 154 5.2.4 LHS 3844 compared to MUSCLES stars...... 155 5.3 Context for LHS 3844b...... 156 5.3.1 Scaling Proxima Centauri...... 156 5.3.2 Atmospheric mass loss...... 157 5.4 Future work...... 158 5.4.1 Flare statistics...... 159 5.4.2 Additional estimates for EUV flux...... 159 5.4.3 More detailed models of atmospheric escape...... 159 5.5 Conclusion...... 160

Bibliography 162

ix List of Figures

1.1 Mass-radius diagram...... 5 1.2 The sample of spectroscopically accessible terrestrial exoplanets...... 19 1.3 Transmission spectroscopy metric of spectroscopically accessible terrestrial exoplanets...... 26

2.1 Extraction of raw data...... 35 2.2 Stellar spectra...... 38 2.3 Observed vs. calculated times of mid-transit...... 46 2.4 White light curves...... 47 2.5 Decorrelation parameter coefﬁcients...... 49 2.6 Wavelength-binned light curves...... 52 2.7 Transmission spectrum compared to models...... 54 2.8 Transmission spectrum compared to other work...... 56 2.9 Transit depth error as a function of data sets...... 57

3.1 Schematic of LHS 1140 ﬁeld with IMACS and LDSS3C...... 73 3.2 Illustratoin of the data extraction process...... 79 3.3 Schematic of IMACS and LDSS3C detectors on sky...... 84 3.4 Extracted spectra...... 98 3.5 White light curve...... 100 3.6 Individually and jointly ﬁt transmission spectra...... 102 3.7 Fitted parameters vs wavelength bin...... 103 3.8 Wavelength-binned light curves...... 104 3.9 Transmission spectra compared to models from linear and Gaussian process methods...... 111

4.1 Schematic of LHS 3844 field with LDSS3C instrument and detector outlines 124 4.2 Spectra of LHS 3844 and comparison star...... 127 4.3 White light curves of 13 LHS 3844b transits...... 129 4.4 Band-integrated spectroscopic light curves...... 131 4.5 Transmisison spectra of LHS 3844b from 13 data sets...... 135 4.6 Mean transmission spectrum of LHS 2833b compared to atmospheric models137 4.7 Predicted stellar rotation phase with transit times...... 140 x 5.1 Profile fits to observed UV lines...... 150 5.2 Estimates of Ly-α flux from other UV lines...... 151 5.3 Estimates of EUV flux...... 153 5.4 Modified UV spectrum of LHS 3844...... 154

xi List of Tables

2.1 Observations...... 31 2.2 Stars used in this work...... 37 2.3 decorrelation parameters used to model data systematics...... 39 2.4 White light curve transit model parameter priors...... 44 2.5 White light curve derived transit model values, compared to Dittmann et al. (2017a)...... 48 2.6 Best-Fit Transit Depths...... 51

3.1 Observations with Magellan I (Baade) & Magellan II (Clay)...... 71 3.2 Stars used in this work...... 74 3.3 Systematic model parameters...... 95 3.4 Transit model parameters used in final analyses...... 97 3.5 Transit and systematic model parameters for the jointly fit white light curve, Gaussian process regression...... 99 2 2 3.6 Best fit Rp/Rs from linear regressions...... 106 2 2 3.7 Best fit Rp/Rs from Gaussian process regressions...... 107 4.1 Observations with Magellan II (Clay) and the LDSS3C Multi-Object Spec- trograph...... 121 4.2 Stars used in this work...... 123 4.3 Systematic model parameters...... 126 4.4 White light curve transit parameters and priors...... 128 4.5 Spectroscopic transit depths...... 132 4.5 Spectroscopic transit depths (continued)...... 133 4.5 Spectroscopic transit depths (continued)...... 134

5.1 Observations of LHS 3844 with HST/COS and measured molecular lines.. 148 5.2 Derived values from the UV proﬁle of LHS 3844...... 155

xii For my amazing parents, Elin and Rob, and in memory of my Uncle Josh, greatly missed

xiii Chapter 1

Introduction

1.1 What is a terrestrial exoplanet?

Exoplanet demographics are rooted in the planet populations we see in the Solar System, and the category of terrestrial exoplanets is no exception. Our home, Earth, is a habitable terrestrial planet with an iron-nickel core and a ﬂuid silicate mantle. As mammals we beneﬁt from a temperate climate in which liquid water is readily available, and an oxy- genated atmosphere, which we owe to photosynthetic life forms from the Archaean and Proterozoic eras. Earth’s closest neighbors are also terrestrial worlds. Mercury, Venus, and Mars have iron-silicate interiors, like Earth, but display a range of atmospheres.

Venus has 95 bars of carbon-dioxide (CO2) at its surface and is completely devoid of water, compared to 0.006 bar of carbon dioxide on Mars, which can rain out at the poles. Mercury has essentially no atmosphere, with only a tenuous layer of material that is constantly eroded by the solar wind. More quantitatively, these inner Solar System planets range in size from 0.4 to 1 R⊕, and in mass from 0.06 to 1 M⊕. This translates to bulk densities of 4 to 5.5 g/cm3. For comparison, silicate rock has a density of 3 g/cm3, while iron has a density of 7.8 g/cm3. Past the asteroid belt we ﬁnd a different kind of planet. Jupiter and Saturn are almost

1 Chapter 1. Introduction completely comprised of hydrogen and helium. These gas giants have small rock-and- ice cores under tens of mega-bars of pressure, though the core-atmosphere distinction is blurred for these planets. Uranus and Neptune have thick hydrogen and helium atmospheres that produce 100 bars of pressure on large ice-rock cores. The outer Solar System planets have densities ranging from 0.5 to 1.5 g/cm3, much lower that those of the inner planets. Based on their interiors and atmospheres, Jupiter, Saturn, Uranus, and Neptune are distinctly not terrestrial. The terrestrial planets in the Solar System are well characterized, and we see a range of atmospheric compositions and surface pressures. However, all of them can be characterized as high mean molecular weight (µ 2) secondary atmospheres, or as a mostly non-existent atmosphere, as in the case of Mercury. By contrast the gas and ice giants of the outer Solar System have low mean molecular weight atmospheres (µ ∼ 2). Terrestrial exoplanets orbiting stars other than the Sun bear the same broad characteristics as the Solar System terrestrial worlds. Terrestrial exoplanets have bulk densities consistent with iron cores surrounded by silicate mantles. As yet our telescopes and instruments are not sensitive enough to probe the thin layer of atmosphere that might surround a terrestrial exoplanet. In this thesis I will present a ﬁrst atmospheric investigation into three terrestrial exoplanets to determine whether, to ﬁrst order, their atmospheres are fundamentally dissimilar to those of the Solar System terrestrial planets.

2 1.2. Small planets: terrestrial planet vs. enveloped terrestrial planet

1.2 Small planets: terrestrial planet vs. enveloped terres-

trial planet

The Solar System planets are easily divisible into terrestrial planets, ice giants, and gas giants, but are these the only outcomes of the stochastic process of planet formation? From 2009 to 2013 the Kepler spacecraft stared continuously at a single patch of sky between the stars Vega and Deneb, where it monitored the brightness of hundreds of thousands of stars, looking for the signature periodic dips in starlight that indicate the presence of orbiting exoplanets. The Kepler data revealed that there are more planets than stars in the

Milky Way, and that small exoplanets, with radii less than that of Neptune (4R⊕), are the most abundant (Howard et al., 2012; Fressin et al., 2013; Petigura, Marcy, and Howard, 2013; Burke et al., 2015; Mulders, Pascucci, and Apai, 2015; Thompson et al., 2018). Planets with radii intermediate to those of Earth and Neptune have no analog in the Solar System. The question became whether these planets were scaled-up Earth-like planets, “super-Earths,” with terrestrial compositions, or scaled-down Neptune-like planets, “mini-Neptunes,” with large envelopes of hydrogen and helium. The term “mini- Neptune” is a misnomer, however. Like Jupiter, Saturn, and Uranus, Neptune formed beyond the snow line, where volatiles like water, ammonia, and methane were able to condense from the solar nebula, providing additional material for planetesimals and allowing for rapid growth. We currently ﬁnd “mini-Neptunes” interior to the snow lines of their respective systems, and whether or not they have ices in their cores is degenerate with varying proportions iron, silicate, ice, and gaseous volatiles. However, we are not completely agnostic about these worlds. Statistical evidence and theoretical models suggest that they are consistent with terrestrial-like cores enveloped in thick atmospheres

3 Chapter 1. Introduction

of hydrogen and helium gas. I will hereafter refer to the class of planets intermediate in size to Earth and Neptune as enveloped terrestrial planets. It is worth emphasizing that enveloped terrestrial planets are by nature not considered habitable; the thick hydrogen and helium envelopes around these worlds render their surfaces to be thousands of Kelvin under kilobars of pressure (Lopez and Fortney, 2014). The primary measurement made by Kepler with respect to the planets it detected is the planet-to-star radius ratio Rp/Rs, which comes directly from the observed planet transit.

The derived planetary radius Rp depends on knowledge of the stellar radius Rs. Most of the stars in the Kepler field are hundreds of parsecs away, making precise measurements of their radii difficult. The uncertainty in Rp for the Kepler planets is therefore dominated by the uncertainty in the radii of their stellar hosts. However, there are enough small planets in the Kepler sample to make some statistical inferences, even if their radii have large uncertainties. For instance, Sanchis-Ojeda et al. (2014) found a dearth of ultra-short- period (USP) planets with radii larger than 2R⊕, suggesting that planets cannot retain thick gaseous envelopes in the presence of so much stellar radiation. This study further suggested that there is a size limit for rocky core formation. These findings were in agreement with a growing body of work that similarly found a size limit for a rocky core, after which a significant amount of lighter material is present (Owen and Wu, 2013; Lopez and Fortney, 2013; Rogers, 2015). This emerging small planet radius valley became all the clearer with extensive work that beat down the error bars on the stellar host radii Rs using high resolution spectra (Fulton et al., 2017), precise distances from the Gaia mission (Gaia Collaboration et al., 2018; Fulton and Petigura, 2018), and asteroseismology (Van Eylen et al., 2018). Some further information can be gleaned with the addition of a mass measurement.

4 1.2. Small planets: terrestrial planet vs. enveloped terrestrial planet

Jupiters

Enveloped terrestrial planets Small planets

Terrestrial planets

FIGURE 1.1: Mass-radius diagram of known planets. Points are masses and radii with 1-σ error bars, with more precise measurements appearing in darker shades of grey. Large blue points are the Solar System planets. Grey curve shows the theoretical prediction for a terrestrial composition, while orange curve shows theoretical hydrogen- and helium-dominated composition (Seager et al., 2007). Terrestrial, enveloped terrestrial, and Jupiter-like planets are labeled. Figure constructed with exoplanet-atlas1, which draws data from the NASA Exoplanet Archive2.

When both a planet’s radius and mass are measured it is possible to derive its bulk composition, though this can be degenerate with many combinations of materials. Exoplanet masses are most commonly measured using the radial velocity technique, by which the planet induces a gravitational pull on its host star, causing the star to “wobble” over time. The masses of terrestrial planets in the Kepler sample are difﬁcult to measure in this way because they are far away, leading to low signal-to-noise measurements. It is possible to derive the masses of Kepler planets in tight multi-planet systems by measuring their transit timing variations (TTVs), in which the gravitational interactions between planets

1github.com/zkbt/exoplanet-atlas 2exoplanetarchive.ipac.caltech.edu

5 Chapter 1. Introduction cause them to transit earlier or later than would be expected for a Keplerian system (Hol- man and Murray, 2005; Agol et al., 2005). However, it is not feasible to retrieve the masses for many of the small planets detected by Kepler. Instead, a host of ground-based transit and radial velocity surveys are hunting for the most easily detectable small planets, and providing precise radius and mass measurements for these worlds. Though the sample of small planets with both precise radius and precise mass measurements is still small, it currently supports the picture of a small planet dichotomy.

Planets with radii less than 1.7R⊕ are the terrestrial planets, with iron-silicate cores, pos- sibly surrounded by a thin atmospheric layer that comprises a negligible fraction of their masses and radii. Planets with radii greater than 1.7R⊕ are the enveloped terrestrial planets, with rocky cores surrounded by an envelope of hydrogen and helium that comprises at least 1% of their masses, but over half of their radii. Figure 1.1 illustrates where the planets on either side of the small planet radius valley fall in mass-radius space.

1.2.1 What causes the small planet radius valley?

There are two main groups of theories to explain how small planets end up on either side of the radius valley and where they reside in parameter space: 1) Small planets all start out as terrestrial cores surrounded by thick hydrogen and helium atmospheres, and then subsequently lose or retain those atmospheres, or 2) terrestrial planets and enveloped terrestrial planets form in distinct ways, with terrestrial planets forming later after much of the gaseous protoplanetary disk has dissipated. The various mechanisms that produce the small planet radius valley predict shifts in the valley location depending on stellar mass, planetary insolation, and orbital period. As more data are gathered it will become

6 1.2. Small planets: terrestrial planet vs. enveloped terrestrial planet possible to distinguish between the formation scenarios based on how the small planet radius valley shifts in parameter space. A common mechanism for removing light, primordial atmospheres from terrestrial cores is photoevaporation, by which high energy radiation from the host star deposits energy in the upper atmosphere of the planet and drives hydrodynamic escape. It is then the right combination of initial core mass, atmospheric mass, and proximity to the host star that determines if a small protoplanet turns into a terrestrial world, which has lost its hydrogen- and helium-envelope via hydrodynamic escape, or an enveloped terrestrial world, which retains enough of this light material to be stable to atmospheric escape (Owen and Wu, 2013; Lopez and Fortney, 2013; Lopez and Rice, 2018; Owen, 2019). Atmo- spheric mass loss via hydrodynamic escape is an efﬁcient process, occurring over the ﬁrst few 100 Myr of the planet’s lifetime. A similar outcome occurs with core-powered mass loss, but with a different energy source. In core-powered mass loss the energy deposited into the planet’s atmosphere is left over from the planet formation process (Ginzburg, Schlichting, and Sari, 2018; Gupta and Schlichting, 2019). Core-powered mass loss is a slower process, occurring over Gyr-timescales. Planetary mass loss can also be caused by impacts, which lead to atmospheric erosion (Liu et al., 2015; Schlichting, Sari, and Yalinewich, 2015; Inamdar and Schlichting, 2015), though it is unclear if this stochastic process can be the sole cause of the radius valley. Of course, photoevaporation, core- powered mass loss, and impact erosion can occur concurrently, but each on their own produces a distinctive trend in the location of the small planet radius valley with respect to the system parameters. Theories of planet formation found the prevalence of enveloped terrestrial planets to be in tension with classic planet formation scenarios (Lee, Chiang, and Ormel, 2014),

7 Chapter 1. Introduction though Solar System formation scenarios are predicated on forming only two types of planets: terrestrial planets and gas giant planets (e.g., Gomes et al., 2005; Tsiganis et al., 2005). Without some additional mechanisms to prevent run-away growth, enveloped terrestrial planets would all turn into giant planets, which the Kepler data found to occur at rates of less than 1%. The work-around is to form small planets on different timescales from giant planets. In gas-poor formation scenarios, atmospheric accretion is delayed by dynamical friction induced by the gas disk, which creates drag and can dampen the ec- centricities of planetary embryos, preventing them from growing until the gas dissipates after a few Myr (Lee, Chiang, and Ormel, 2014; Lee and Chiang, 2016). The overall mass of the disk determines the timescale for gas disk dissipation, and can therefore lead to distinct outcomes in the size distributions of the resulting planets (Dawson, Chiang, and Lee, 2015). In gas-poor formation scenarios the terrestrial core never has the chance to accrete a thick gaseous envelope. This is the picture of how the Solar System terrestrial planets formed on timescales of 50 Myr, based on N-body simulations and measurements of isotope ratios from Earth and the Moon (Nemchin et al., 2009; Raymond et al., 2009), suggesting that planetary formation can continue after the gas in the disk dissipates. Both atmospheric sculpting and gas-poor formation can currently explain the small planet radius valley. Continued exoplanet detections will be able to break degenerecies between these scenarios (Lopez and Rice, 2018), especially given their various timescales of inﬂuence. For instance, the slow process of core-powered mass loss predicts that older stars will host higher proportions of terrestrial planets relative to enveloped terrestrial planets, whereas photoevaporation would predict a ﬁxed proportion of these two planet types, regardless of stellar age (Gupta and Schlichting, 2020). For the low-mass stars around which we have detected small planets, recent observational results suggest that

8 1.2. Small planets: terrestrial planet vs. enveloped terrestrial planet

photoevaporation is favored over gas-poor formation for producing terrestrial exoplanets in these systems (Cloutier et al., 2020).

1.2.2 Secondary atmospheres on terrestrial planets

Venus, Earth, and Mars have high mean molecular weight secondary atmospheres. It is worth noting that theory suggests that Mercury was the victim of an energetic impact which stripped away a large portion of its atmosphere and silicate mantle, leaving an iron-rich body mostly devoid of an atmosphere. Mercury’s fate is an unlikely outcome for

the terrestrial exoplanets discussed in this thesis. Mercury (R = 0.38R⊕) is much smaller than the terrestrial exoplanets that are observationally accessible to us today (R & 0.8R⊕). The larger the planet, the more energetic the event must be to remove a signiﬁcant portion of its atmosphere and mantle (Marcus et al., 2010), making such an event less likely to occur. Furthermore, we have not found a terrestrial exoplanet with a density that suggests a Mercury-like high proportion of iron material (70%). The secondary atmospheres of the Solar System terrestrial worlds that have not experi- enced a catastrophic impact can arise from outgassing, by which volatile material trapped in the planet’s mantle during formation is later freed through surface processes such as volcanism or a magmatic melt at the planet surface, perhaps induced by a bombardment of material (Elkins-Tanton, 2011; Lammer et al., 2018). Terrestrial planet atmospheres can be further modiﬁed by the delivery of material from solid bodies later in life. For instance, water delivery from icy comets or planetesimals from beyond the snow line is an active hypothesis for how Earth ended up with the amount of surface water it has today (Gomes et al., 2005; Izidoro et al., 2013; Raymond and Izidoro, 2017; Ida, Yamamura, and Okuzumi, 2019). Impacts can also cause erosion without destroying an atmosphere,

9 Chapter 1. Introduction which contributes to the evolution of a secondary atmosphere and affects planetary isotope fractions (Schlichting, Sari, and Yalinewich, 2015). In this thesis I will present the ﬁrst atmospheric investigations into some of our nearest terrestrial exoplanet neighbors, with the aim of empirically determining whether or not these worlds resemble the Solar System terrestrial planets. Detecting and characterizing secondary atmospheres around terrestrial exoplanets is not feasible with current telescopes and instruments, but light, hydrogen- and helium-dominated atmospheres would be detectable. We know by their radii and masses that these terrestrial exoplanets do not have substantial, thick hydrogen and helium envelopes, like the enveloped terrestrial planets, but if they retained a small atmospheric mass fraction (< 1%) of these light elements, we would be able to detect them.

1.3 M dwarfs as terrestrial exoplanet hosts

M dwarfs, which have radii and masses ranging from 10 to 60% those of the Sun, are the most abundant stellar class in the solar neighborhood, making up 75% of the stars around us (Henry et al., 2006). An important lesson from the statistical Kepler mission is that M dwarfs are frequent hosts of small exoplanets (Dressing and Charbonneau, 2015; Gaidos et al., 2016). This realization spurred investigations into the nearest M dwarf systems and led to the discovery of a small but growing sample of nearby, terrestrial exoplanets. M dwarf systems differ from the Solar System in key ways that make them amenable targets for small planet detection as well as potentially dangerous hosts for the atmospheres of those planets. The relatively low luminosities, radii, and masses of M dwarfs mean that transit and radial velocity surveys are sensitive to terrestrial-class planets, particularly for

10 1.3. M dwarfs as terrestrial exoplanet hosts the mid- to late-M dwarfs with masses less than 35% that of the Sun.

1.3.1 Arguments for searching for terrestrial exoplanet atmospheres in

mid-M dwarf systems

A back-of-the-envelope calculation presents an argument for mid- to late-M dwarfs as the optimal terrestrial exoplanet hosts if atmospheric detection is the goal. A relatively high planet-to-star radius ratio (Rp/Rs ≥ 0.04) is required for current instruments to be able to detect subtle changes in the planet radius that would point to an atmosphere (this is further discussed in Section 1.4.2). We know that terrestrial planets are those with radii R < 1.7R⊕. Taking a planet radius from the peak of the terrestrial planet size distribution (Fulton et al., 2017) of 1.3R⊕ gives an upper limit on the stellar host radius of

0.3R⊕, the radius of a mid-M dwarf. Detecting planets via the transit method requires a fortuitous alignment of the planet’s orbit with the observer’s line of sight. The probability of witnessing a planet transit can be described as ptransit = Rs/a where a is the semi-major axis of the planet (Winn, 2010). This is the simplest form of the transit probability which assumes a circular orbit and Rs Rp. Exoplanets on tighter orbits will always result in higher transit probabilities. The habitable zone, the region in a stellar system where a terrestrial planet is temperate and can host liquid water at its surface (Kopparapu et al., 2013), is a good point of reference. For a mid-M dwarf star (spectral type M4-M5; 0.15M < M < 0.20M ,

0.15R < R < 0.25R ), the habitable zone occurs at around 0.07 astronomical units

(AU). This gives a transit probability of ptransit = 0.3R /0.07AU = 2% for a habitable- zone planet around a mid-M dwarf (compare this to the transit probability for a habitable zone planet transiting a Sun-like star ptransit = 1R /1AU = 0.5%). To tie this to estimates

11 Chapter 1. Introduction of terrestrial planet occurrence rates around M dwarfs, Dressing and Charbonneau (2015) estimate that there are 0.16 habitable-zone terrestrial planets per M dwarf, using conser-

−1 vative estimates of the habitable zone. It takes a sample size of N > (ηptransit) stars in order to find a the kind of planet you are looking for, where η is fraction of stars hosting such a planet. To find a terrestrial planet in the habitable zone of a mid-M dwarf would require a conservative sample size of 300 mid-M dwarfs. For the purposes of this work, this is a highly conservative lower limit. For instance, the (Dressing and Charbonneau, 2015) study focused on early-M dwarfs. Hardegree-Ullman et al. (2019) find an occurrence rate of one short-period terrestrial-sized planet per mid-M dwarf, though not necessarily in the habitable zone. Terrestrial planet surveys are not limited to searching in the habitable zone or solely around M dwarfs with R = 0.3R . There are 400 mid- to late-M dwarfs within 15 parsecs (J. Winters, priv. comm.), and many more as the search volume increases, making mid-M dwarf systems rich hunting grounds for terrestrial exoplanets, with those closest to us the most viable options for atmospheric follow-up. A further point concerns our ability to measure terrestrial planet masses in M dwarf systems. M dwarfs exhibit magnetic activity and rotation rates that can get in the way of precise mass measurements. Radial velocity surveys search for evidence of Keplerian motion in order to identify planetary signals, but stellar rotation signatures brought on by inhomogeneities on the stellar surface can mimic these signals, frustrating our ability to detect them (Newton et al., 2016; Vanderburg et al., 2015). Later-type stars spin down to a longer characteristic rotation rate than do earlier-type stars. For radial velocity searches primarily concerned with identifying habitable-zone terrestrial exoplanets, Newton et al. (2016) find that the rotation rates of M dwarf field stars coincide with the habitable-zone orbital period for M dwarf types earlier than M4 (M = 0.3M ). M dwarfs later than M4

12 1.3. M dwarfs as terrestrial exoplanet hosts

have spun down to rotation periods of about 100 days, meaning that the signal imparted by the rotation of the M dwarf on the radial velocity measurements is easily distinguishable from the signal imparted by a planet in or interior to the habitable zone.

1.3.2 M dwarf inﬂuence on terrestrial exoplanet atmospheres

While mid- to late-M dwarfs present favorable conditions for detecting terrestrial exoplanets, it is not certain that these worlds are able to sustain atmospheres. A terrestrial exoplanet orbiting a main-sequence mid-M dwarf in or interior to the habitable zone is tidally locked, with a permanent day side and night side (Kasting, Whitmire, and Reynolds, 1993). The steep pressure gradient on a tidally-locked terrestrial world can lead to atmospheric collapse, in which the planetary atmosphere completely condenses out on the night side. The conditions leading to atmospheric collapse, and the factors that may prevent it, cover a large area of parameter space. The main drivers, however, are stellar ﬂux, atmospheric pressure, and atmospheric composition. There is a general trend towards collapse with decreasing stellar ﬂux and atmospheric pressures (e.g., Wordsworth,

2015; Koll and Abbot, 2016). Wordsworth (2015) find that for a 1R⊕ planet with a CO2 atmosphere, collapse always occurs with pressures less than 0.03 bar, for stellar fluxes up to 3.5 × 106 erg/cm2/s. However, atmospheric composition also plays a strong role, since molecular species that are efficient greenhouse gases like water and methane can trap heat and lower the collapse pressure, thereby stabilizing the atmosphere. The high energy output of M dwarf hosts in particular can sculpt and even destroy a planet’s atmosphere. All stars exhibit heightened levels of activity prior to settling onto the main sequence, producing higher levels of X-ray and ultra-violet (XUV) flux relative to bolometric flux than they do after they reach the quiescent state. M dwarfs spend an

13 Chapter 1. Introduction extended amount of time in the pre-main sequence phase, from 0.8 to 8 Gyr, compared to 50 Myr for Sun-like stars, with time to the main sequence increasing with decreasing stellar mass (West et al., 2008; Baraffe et al., 2015). Mid-M dwarfs spend 4.5 Gyr in the pre-main sequence phase, potentially subjecting the planets orbiting them to enough XUV ﬂux over time to completely remove their atmospheres. It is worth noting that mid-to-late

M dwarfs (R < 0.35R ) are fully convective (Reiners and Basri, 2009; Stassun et al., 2011), meaning that they lack a tacholine, which is the boundary between the inner convective zone and the outer radiative layer in larger stars at which drag is thought to generate magnetic fields. Despite lacking this boundary, mid-M dwarfs still produce magnetically generated phenomena, such as X-ray emission and flares (Wright and Drake, 2016; Wright et al., 2018; Hawley et al., 2014). The high energy output of mid- to late-M dwarfs can drive atmospheric chemistry. M dwarfs produce higher amounts of ultra-violet (UV) flux compared to bolometric flux than do Sun-like stars (France et al., 2016), but different regions of the high energy spectrum produce different effects in planetary atmospheres. The photodissociation cross- sections of molecular species are wavelength dependent so a planet’s atmospheric chemistry is sensitive to the spectral energy distribution (SED) of the host star. If a terrestrial exoplanet has an atmospheric composition resembling those of Venus, Earth, or Mars, the far-UV to near-UV flux ratio (FUV = 912-1700Å, NUV = 1700-3200Å) can drive this planet’s atmosphere out of thermal equilibrium. For example, CO2 is readily dissociated by FUV photons and can produce a build-up of O3 (Tian et al., 2014), while NUV emission dissociates O3 but not CO2. Different proportions of FUV to NUV flux can shift the abundances of key molecular species by more than an order of magnitude (Harman et al., 2015; Rugheimer et al., 2015; France et al., 2016). High energy flares can also disrupt planetary

14 1.3. M dwarfs as terrestrial exoplanet hosts

atmospheres on timescales of months to years (Segura et al., 2010), though some amount of NUV flux and flaring may provide the spark for abiogenesis (Ranjan, Wordsworth, and Sasselov, 2017). Terrestrial exoplanets orbiting M dwarfs may also be devoid of atmospheres. The X-ray (10-100Å) and extreme ultra-violet (EUV; 100-912Å) parts of the stellar spectrum deposit energy into the upper atmospheres of planets, which heat them and drive atmospheric mass loss via hydrodynamic escape. This is the mechanism of photoevaporation that was discussed as a potential cause of the small planet radius valley (Section 1.2.1). EUV flux can also ionize a planet’s upper atmosphere, rendering is susceptible to strip- ping by the stellar wind (Rahmati et al., 2014; Garcia-Sage et al., 2017). Measuring the high-energy spectra of M dwarfs can contextualize the atmospheres, or lack thereof, of the terrestrial exoplanets they host. However we can only take a single, current snapshot in the lifetime of a given star. This current snapshot must be paired with models of stellar evolution and planetary atmospheric mass loss in order to back out what kind of atmosphere a planet might have had, or might currently maintain (Lopez, Fortney, and Miller, 2012; Luger and Barnes, 2015; Salz et al., 2016; Garcia-Sage et al., 2017). The primary facility able to detect broad ultra-violet stellar spectra is the Hubble Space Telescope (HST), with both the Cosmic Origins Spectrograph (COS) and the Space Telescope Imaging Spectrograph (STIS) capable of observing stars in the UV. The X-ray Multi-Mirror Mission (XMM-Newton) and the Neil Gehrels Swift Observatory (Swift) can both provide X-ray information. There is no observatory that can directly measure EUV flux from stars other than the Sun because photons with wavelengths below 912Å completely ionize neutral hydrogen in the inter-stellar medium. There are no planned missions on the scale of HST to cover UV wavelengths in the future, but we will not be left in the

15 Chapter 1. Introduction

UV-dark. The Colorado Ultraviolet Transit Experiment (CUTE) is due for launch in 2020, and will have observational capabilities in the NUV. The Star-Planet Activity Research CubeSat (SPARCS) has a planned launch date of 2021, and will have both NUV and FUV wavelength coverage.

1.4 Observational opportunities for terrestrial exoplanet

atmospheres

The vast majority of exoplanet atmospheric studies have focused on the high signal-to- noise cases of hot Jupiters (e.g., Sing et al., 2016). Some studies have taken on the atmospheres of mini-Neptunes and found a thick aerosol layer that precludes the detection of molecules (Kreidberg et al., 2014a; Knutson et al., 2014), though cooler mini-Neptunes exhibit observable water features (Benneke et al., 2019). As yet the realm of terrestrial exoplanet atmospheres remains largely untapped, owing to the difﬁculty in distinguishing a terrestrial exoplanet with a thin layer of atmosphere from a bare rock.

1.4.1 The sample of spectroscopically accessible terrestrial exoplanets

The Kepler mission delivered thousands of exoplanet detections, but the terrestrial planet systems in this sample lie too far away for atmospheric follow-up. To remedy this, in- tensive ground-based planet surveys went in search of terrestrial exoplanets whose atmospheres are more readily accessible. As discussed in Section 1.3.1, prospects for atmospheric detection for terrestrial worlds (R < 1.7R⊕) are best for those orbiting small stars

(R < 0.3R ) such that the planet-to-star radius ratios Rp/Rs are maximized. In order to

16 1.4. Observational opportunities for terrestrial exoplanet atmospheres

collect enough photons for an atmospheric detection, it is also necessary to find terrestrial exoplanets around nearby stars (< 15 parsecs) that will present high signal-to-noise detections (Rodler and López-Morales, 2014; Morley et al., 2017). Two ground-based surveys that contributed terrestrial exoplanet detections that meet these criteria are MEarth (Nutzman and Charbonneau, 2008; Irwin et al., 2015) and the Transiting Planets and Planetesimals Small Telescope (TRAPPIST; Gillon et al., 2013). The MEarth telescope arrays consist of twin sets of eight 40-cm telescopes. The MEarth arrays are remotely operated and cycle through a set of targets every 20 minutes during nighttime operations. If a target returns a low point, the MEarth telescopes are “triggered” to collect additional data (Nutzman and Charbonneau, 2008). MEarth North began operations in 2008, out of the Fred Lawrence Whipple Observatory on Mount Hopkins, in Ari- zona. Soon after coming online MEarth North returned the enveloped terrestrial world GJ 1214b (Charbonneau et al., 2009). MEarth South began operations in 2014, out of Cerro Tololo Inter-American Observatory on Cerro Tololo in Chile. Refinements in the “trigger- ing” algorithm helped produce the detection of the terrestrial exoplanet GJ 1132b (Berta et al., 2012b; Berta-Thompson et al., 2015), and further improvements in processing false “triggers” with machine learning led to the discovery of the habitable-zone terrestrial exoplanet LHS 1140b (Dittmann et al., 2017b). Subsequent observations found additional planets in both the GJ 1132 and LHS 1140 systems. GJ 1132c is likely an enveloped terrestrial world and does not transit (Bonfils et al., 2018), but LHS 1140c is terrestrial and interior to LHS 1140b (Ment et al., 2019). Both GJ 1132 and LHS 1140 are mid-M stars within 15 parsecs. TRAPPIST consists of two 60-cm remotely operated telescopes, one in the north and one in the south. TRAPPIST South began operations in 2010, out of La Silla Observatory

17 Chapter 1. Introduction in Chile, while TRAPPIST North came online 2016, at the Oukaïmeden Observatory in the Atlas Mountains of Morocco. TRAPPIST South hunted for small planets orbiting ultracool dwarfs, as well as comets in the Solar System. TRAPPIST South is a precursor to the upcoming Search for habitable Planets Eclipsing Ultra-cool Stars (SPECULOOS) program (Gillon et al., 2016; Burdanov et al., 2017; Delrez et al., 2018). TRAPPIST South detected three terrestrial planets in orbit around TRAPPIST-1, a late-M dwarf 12 parsecs away (Gillon et al., 2016). With the help of the Spitzer Space Telescope, four additional terrestrial- class planets were found in this system, bringing the total to seven (Gillon et al., 2017b). The detection rate of terrestrial exoplanets increased with the 2018 launch of the Tran- siting Exoplanet Survey Satellite (TESS; Ricker et al., 2015), in many ways the successor to Kepler. Over its nominal two-year mission TESS is surveying 85% of the sky using four wide ﬁeld-of-view cameras, each covering a 24◦ × 24◦ patch of sky, over a photometric band that ranges from 600 to 1000 nm (Sullivan et al., 2015; Sullivan et al., 2017). The northern and southern hemispheres are each divided into 13 sectors, and TESS spends 27 days on each sector. As of this writing, TESS is observing its 24th sector, out of a total of 26 in the nominal mission. As it scans the skies TESS avoids observing in the galactic plane, but continuously observes at the poles. Exposure times for TESS are 30 minutes for the full-frame images, and 2-minutes for select targets. TESS has already delivered a handful of nearby, terrestrial planets and has been approved for an extended mission to continue its monitoring. The terrestrial exoplanets that meet the criteria of orbiting stars with R < 0.3R that are less than 15 parsecs away are (so far) LHS 3844b (Vanderspek et al., 2019), LP 98-59b,c,d (Kostov et al., 2019), and LTT 1445Ab (Winters et al., 2019). An upcoming work on TOI-540b suggests that this world also meets the criteria (K. Ment, priv. comm.). Figure 1.2 provides a schematic of the nearby terrestrial exoplanets amenable

18 1.4. Observational opportunities for terrestrial exoplanet atmospheres

Planets with Planets with hydrogen- secondary and helium-dominated atmospheres envelopes

(TERRESTRIAL!) (NOT TERRESTRIAL!)

TRAPPIST-1 b,c,d,e,f,g,h

FIGURE 1.2: Schematic of the spectroscop- LHS 11140c LHS 11140b ically accessible (less than 15 parsecs away,

orbiting stars with radii R < 0.3R ) terres-

GJ 1132b LTT 1445Ab trial exoplanets. Adapted from (Fulton et al., 2017). TOI-540b LHS 3844b

L 98-59 d L 98-59 b L 98-59 c

Planet Size (Earth Radii) to atmospheric detection.

1.4.2 Methods for detecting (terrestrial) exoplanet atmospheres

Detecting an exoplanet with the transit method requires photometry, by which the telescope and detector collect as many photons as possible and attempt to distinguish a transit signal from a stellar baseline. Planetary atmospheres produce a small, chromatic effects that can only be distinguished with spectroscopic studies. Successful atmospheric investigations of giant planet atmospheres used techniques of transmission spectroscopy, emission spectroscopy, high-resolution spectroscopy, and direct imaging. The former two techniques require a transiting (or eclipsing) planet, but the latter two do not. In some cases, combining these techniques can bolster a detection.

19 Chapter 1. Introduction

Transmission spectroscopy

Transmission spectroscopy requires observations during planet transit. Starlight filters through the planet’s atmosphere on its way to the telescope. Because atmospheric molecules absorb at characteristic wavelengths, the planet will appear larger at wavelengths where a molecular species is opaque, and smaller where it is transparent. These relative changes in transit depth can give rise to an atmospheric detection. Sodium, potassium, and water make up the most common atmospheric detections in hot Jupiters (e.g., Charbonneau et al., 2002; Sing et al., 2011; Deming et al., 2013; Kreidberg et al., 2014b). Transmission spectroscopy provides little constraint on a planet’s temperature-pressure profile since observations are integrated around the limb of the planet (Kempton et al., 2017), but detecting the transmission spectrum of a planet is a relatively high signal-to-noise process since it depends on the number of photons collected during transit, which increases for brighter stars, all else being equal (Kreidberg, 2018). Some of the most successful atmospheric studies involving small planets have employed the technique of transmission spectroscopy using both ground- and space-based observatories (e.g., Bean, Miller-Ricci Kempton, and Homeier, 2010; Kreidberg et al., 2014a). This technique will also be employed with the James Webb Space Telescope (JWST), a 6.5 m telescope which will allow for observations from 0.6 to 30 µm and is scheduled to launch in 2021. Guaranteed Time Observations (GTO) from the NIRISS and NIRSPEC instrument teams (two of the four instruments that will fly on JWST) currently include programs to observe the atmospheres of terrestrial exoplanets in transmission.

20 1.4. Observational opportunities for terrestrial exoplanet atmospheres

Emission spectroscopy

Emission spectroscopy requires observations during secondary eclipse, when the planet passes behind the star. As the planet is approaching secondary eclipse, light is observed from the star-plus-planet system. When the planet is in secondary eclipse, only light from the star remains. Comparing the star-plus-planet flux to just the stellar flux reveals the portion of the light coming directly from the planet. Emission spectroscopy can return a direct measurement of the temperature-pressure profile over the pressure ranges probed, with signal-to-noise depending on the relative temperatures of the planet and star in addition to planet-to-star radius ratio (Kreidberg, 2018; Deming, Louie, and Sheets, 2019). This makes detecting planets smaller and cooler than hot Jupiters difficult, though not impossible. Emission spectroscopy has most successfully be performed at near-infrared wavelengths where the difference in thermal emission between the planet and star is minimal (e.g., Deming et al., 2005; Charbonneau et al., 2005; Knutson et al., 2008; Diamond- Lowe et al., 2014; Kreidberg et al., 2014b). The Spitzer Space Telescope was the optimal space-based instrument for this work until its cryogenic reserves ran out in 2009. Without this coolant most of Spitzer’s longer wavelength capabilities were lost. However, Spitzer continued to operate in “warm” mode, with two photometric bands centered at 3.6 and 4.5 µm. Even with scaled-back capabilities Spitzer continued to make landmark discoveries in the infrared, including capturing the secondary eclipse of the terrestrial exoplanet LHS 3844b (Kreidberg et al., 2019), until it was decommissioned in early 2020. Infrared emission spectroscopy will again be possible for a subset of small planets with JWST and may provide the most efficient method for detecting the atmospheres of these worlds (Koll et al., 2019; Mansfield et al., 2019).

21 Chapter 1. Introduction

High-resolution spectroscopy

In high-resolution spectroscopy, high-resolution spectra are taken during planetary orbit, but planet does not necessarily have to transit (or eclipse). This method capitalizes on the fact that molecular species produce unique distributions of spectroscopic lines, that are revealed at high resolution. At low resolution they are blended together and only the deepest features are distinguishable. Observing a planet throughout its orbit will reveal these line distributions offset from stellar lines, as well as telluric ones (Birkby, 2018). Cross-correlation template matching is used to identify molecular signatures. This technique has been successfully used to detect molecules in the atmospheres of hot Jupiters (Snellen et al., 2010; Birkby et al., 2013), including hot Jupiters which do not transit (Birkby et al., 2017), and has even provided detections of atmospheric circulation on hot Jupiters (Louden and Wheatley, 2015; Brogi et al., 2016). High-resolution spectroscopy is a completely ground-based effort, owing to the high stability needed by the instruments in order to make their measurements. The primary directive of these instruments with re- gards to exoplanets is to measure precise radial velocities, and thereby determine planet masses to high precision, but they can also be used for atmospheric detection. The classic high-resolution instruments that led to the aforementioned discoveries are the Cryo- genic High-Resolution Infrared Echelle Spectrograph (CRIRES), which has recently been updated to expand its wavelength coverage, on the Very Large Telescope (VLT) at the European Southern Observatory on Cerro Paranal, and the High Accuracy Radial Veloc- ity Planet Searcher (HARPS), located at the La Silla Observatory also in Chile. A host of new high resolution spectrographs are coming online, many of which will support near- infrared observations (e.g., SPIRou, MAROON-X, and NIRPS), where M dwarfs produce the bulk of their photons.

22 1.4. Observational opportunities for terrestrial exoplanet atmospheres

Direct imaging

Directly imaged plants are observed at maximum angular separation from their host stars. To directly image a planet it is necessary to obscure the overwhelming flux from the host star. This method has so far been most successful for young, giant planets, which are still hot enough from formation to produce significant amounts of thermal emission, even though they orbit tens of astronomical units away from their host stars. This technique has led to the detection of four giant planets orbiting the young bright star HR 8799 (Marois et al., 2008; Marois et al., 2010), as well the giant planet β Pictoris b still embed- ded in a dust disk (Lagrange et al., 2009). Direct imaging can provide both the planet mass and direct detections of planetary photons, meaning that temperature-pressure profiles can be tightly constrained, as with emission spectroscopy. The Gemini Planet Im- ager (GPI) mounted on the Gemini South Telescope in Chile and the Spectro-polarimetric High-contrast Exoplanet Research Instrument (SPHERE) installed on the Very Large Tele- scope (VLT), also in Chile, are state-of-the art adaptive-optics enabled high-contrast im- agers that continue to search for planet signals. Future improvements in coronagraphs will make direct imaging accessible to cooler bodies closer to their host stars, which will be necessary to push down to direct imaging detections of small planets.

1.4.3 Other work on atmospheres of terrestrial exoplanets

Apart from the work presented here, there are only two other systems to have observational atmospheric constraints on their terrestrial planets. TRAPPIST-1, a late-M dwarf

(M = 0.09M ), is too faint to allow for most atmospheric studies of its seven terrestrial worlds, but de Wit et al. (2016) and de Wit et al. (2018) were able to use Wide Field Camera 3 (WFC3) on HST to rule out clear, low mean molecular weight atmospheres on

23 Chapter 1. Introduction

TRAPPIST-1b,c,d,e, and f. The low luminosity of TRAPPIST-1 also hinders radial velocity mass measurements for its planets, but TTV observations are able to constrain them with modest uncertainties (Grimm et al., 2018). Though all of the TRAPPIST-1 planets are solidly in the terrestrial planet regime, the bulk compositions derived by (Grimm et al., 2018) imply that TRAPPIST-1b,d,f,g, and h require thick atmospheres of volatiles, a large surface ocean, or ice; they place an upper limit on the water content of these worlds at 5%. The other terrestrial planet system with atmospheric constraints is LHS 3844, with the ultra-short-period terrestrial exoplanet LHS 3844b. Kreidberg et al. (2019) used 100 hours of time on Spitzer to observe nine consecutive orbits of this planet at 4.5µm. Stacking these together, Kreidberg et al. (2019) constructed a phase-folded light curve, which showed no evidence of energy advection from the planetary day side to its night side, ruling out atmospheres with surface pressures greater than 10 bar. (Kreidberg et al., 2019) make theoretical arguments based on the high irradiation of LHS 3844b to suggest that lower pressure atmospheres would not be able to withstand the high incident ﬂux coming from LHS 3844.

1.4.4 A multi-year program to explore terrestrial exoplanet atmospheres

For the work presented in this thesis I employed the technique of ground-based transmission spectroscopy using the Magellan Telescopes at the Las Campanas Observatory in Chile. The twin 6.5 m Magellan Telescopes each have a multi-object spectrograph, with wavelength coverage from the optical to red-optical. When making ground-based time series of exoplanet systems, telluric features are imprinted on the observed stellar spectra, and can vary during observations by an order of magnitude. This is enough to wipe out

24 1.4. Observational opportunities for terrestrial exoplanet atmospheres small changes in transit depth that would point to a transmission signal from a terrestrial exoplanet atmosphere (0.05%). Multi-object spectrographs provide for simultaneous monitoring of the target star with the orbiting planet, and additional stars with which to decorrelate telluric influence. The instrument masks are custom made with wide slits such that light from the target and comparison stars is not lost during observations, and an accurate measurement of the sky background can be made (Bean, Miller-Ricci Kemp- ton, and Homeier, 2010). This allows for precise measurements of stellar baselines even in variable seeing conditions. When performing ground-based multi-object spectroscopy for planets orbiting low-mass stars, an additional difficulty is that there is only one bright M dwarf per square degree of sky, so calibrator stars are of different spectral types, which experience different levels of chromatic extinction as a function of airmass or precipitable water vapor. All of these discrepancies must be corrected for during data extraction and analysis. At the start of my PhD, in the fall of 2015, there was one known terrestrial exoplanet whose atmosphere was spectroscopically accessible. Today, with the help of MEarth, TRAPPIST, and TESS, there is a small sample that meet this criteria. I will present my atmospheric findings for GJ 1132b in Chapter2, for LHS 1140b in Chapter3, and for LHS 3844b in Chapter4. To round out this multi-year program I will observe transits of LTT 1445Ab in the fall of 2020. Two transits of this object were already observed with Magel- lan Clay/LDSS3C in the fall of 2019, but the other two observations that were awarded to that program were lost to bad weather. LTT 1445A is part of a hierarchical triple system 7 parsecs away, with the close binary LTT 1445BC currently 7” away. The BC component are also mid-M dwarfs, of comparable magnitude to LTT 1445A. This system presents a rare opportunity to use an M dwarf (the combined BC component) as a calibrator for an

25 Chapter 1. Introduction

IGURE 45 LTT1445Ab F 1.3: Spectroscopically accessible LHS3844b terrestrial exoplanets by transmission spec- TRAPPIST-1b TOI-540b 40 LHS1140c troscopy metric (TSM; Kempton et al., 2018)

35 TRAPPIST-1d GJ1132b as a function of equilibrium temperature. L98-59b Note that the TSM is calculated for J-band, 30 TRAPPIST-1c but the transmission spectra presented in L98-59c

25 L98-59d this thesis were taken in the optical. At op-

TRAPPIST-1f tical wavelengths TRAPPIST-1 is too faint 20 TRAPPIST-1g TRAPPIST-1e for our detectors; transmission spectra of 15 TRAPPIST-1h d < 15 pc planets in the TRAPPIST-1 system are op- Rs < 0.3 R timally observed at near-infrared wave- 10 LHS1140b Transmission Spectroscopy Metric Rp < 1.7 R lengths (Gillon et al., 2017a; de Wit et al., 200 400 600 800 2018). Teq (K)

M dwarf target (LTT 1445A). Figure 1.3 provides an overview of the known spectroscopically accessible terrestrial exoplanets to date, with red stars indicating which planets are included in my multi-year program. As discussed in Section 1.3.2, high-energy inﬂuence from M dwarf host stars can shape or even destroy terrestrial exoplanetary atmospheres. In Chapter5 I present a UV spectrum of the host star LHS 3844 from HST/COS (GO Program 15704; PI Diamond-Lowe). The exploratory work that I describe in this thesis seeks to place constraints on the atmospheres of three spectroscopically accessible terrestrial exoplanets. Future programs will build on this work to improve the sample size and scope of characterization of terrestrial exoplanet atmospheres, and determine whether they look anything like the atmospheres of the Solar System terrestrial planets.

26 Chapter 2

Ground-based optical transmission spectroscopy of the small, rocky exoplanet GJ 1132b

Abstract

Terrestrial Solar System planets either have high mean molecular weight atmospheres, as with Venus, Mars, and Earth, or no atmosphere at all, as with Mercury. We do not have sufficient observational information to know if this is typical of terrestrial planets or a phenomenon unique to the Solar System. The bulk of atmospheric exoplanet studies have focused on hot Jupiters and Neptunes, but recent discoveries of small, rocky exoplanets transiting small, nearby stars provide targets that are amenable to atmospheric study. GJ 1132b has a radius of 1.2 R⊕ and a mass of 1.6 M⊕, and orbits an M-dwarf 12 parsecs away from the Solar System. We present results from five transits of GJ 1132b taken with the Magellan Clay Telescope and the LDSS3C multi-object spectrograph. We jointly fit our five data sets when determining our best-fit transit parameters both for the

This chapter was originally published as Diamond-Lowe, et. al., The Astronomical Journal, 2018, 156, 42D, in collaboration with Zachory Berta-Thompson, David Charbonneau, and Eliza M.-R. Kempton.

27 Chapter 2. GJ 1132b white light curve and wavelength-binned light curves. We bin our light curves into 20 nm wavelength bands to construct our transmission spectrum. Our results disfavor a clear, 10× solar metallicity atmosphere at 3.7σ conﬁdence and a 10% H2O, 90% H2 atmosphere at 3.5σ conﬁdence. Our data are consistent with a featureless spectrum which suggests that GJ 1132b has a high mean molecular weight atmosphere or no atmosphere at all. This result is in agreement with theoretical work which suggests that a planet of GJ

1132b’s mass and insolation should not be able to retain a H2 envelope.

2.1 Introduction

Four years of transit data from the Kepler mission showed us that terrestrial planets are common around low mass stars (Dressing and Charbonneau, 2013; Dressing and Char- bonneau, 2015; Gaidos et al., 2016). The Kepler data set also led to theories suggesting that small planets retain hydrogen and helium envelopes from formation, comprising a small fraction of their total masses (Wolfgang and Lopez, 2015). These H/He envelopes are subsequently sculpted by incident extreme ultra-violet (EUV) and X-ray radiation from the host stars which, in the absence of a strong planetary magnetic ﬁeld, drives atmospheric escape (Ehrenreich et al., 2015). M dwarfs have extended pre-main sequence phases (Baraffe et al., 2015) and remain active on long timescales (Newton et al., 2017), so it is possible that terrestrial planets orbiting M dwarfs have been stripped of any primordial atmospheres early on (Lopez and Fortney, 2013; Luger and Barnes, 2015). For instance, the terrestrial planets TRAPPIST-1b and c orbiting an ultracool dwarf do not exhibit transmission spectra consistent with a low mean molecular weight atmosphere at the level of ≥ 10σ conﬁdence (de Wit et al.,

28 2.1. Introduction

2016). TRAPPIST-1d, e, and f also do not exhibit evidence for such atmospheres at the level of ≥ 4σ conﬁdence (de Wit et al., 2018). We might expect a similar result for other small planets in close-orbits around cool stars. In this work we use ground-based observations to investigate the idea that terrestrial exoplanets orbiting M dwarfs do not possess low mean molecular weight atmospheres.

We focus on the terrestrial exoplanet GJ 1132b (1.2 R⊕, 1.6 M⊕) orbiting a M4.5V dwarf which is 12 parsecs away from the Solar System. The radius and mass of GJ 1132b are consistent with an iron and silicate composition similar to that of Earth and Venus (Berta- Thompson et al., 2015). The surface gravity and estimated atmospheric temperature of GJ 1132b mean that a solar composition, hydrogen-dominated atmosphere might be detectable with ground- based instrumentation. Though we are looking for the signature of a low mean-molecular weight atmosphere, hydrogen itself is not a strong absorber, making it a difﬁcult to detect via transmission spectroscopy. Instead, we assume the atmosphere to be well-mixed and search for tracer molecules like water (H2O) and methane (CH4), which have large absorption cross sections in the visible to near-infrared wavelengths. Understanding the nature of terrestrial exoplanet atmospheres will bolster efforts to constrain planet formation and atmospheric evolution, and ultimately inform our search for biosignatures on other worlds. We do not expect life as we know it to exist on the highly irradiated surface of GJ 1132b, but understanding the atmospheres of hot rocky planets will contextualize an eventual search for life on cooler, habitable zone exoplanets. Though our current sample size of terrestrial exoplanets is small, it is important to understand them in the context of the well-studied Solar System inner planets. Whether a terrestrial exoplanet resembles Earth or Venus or Mercury has vast implications for its

29 Chapter 2. GJ 1132b formation history and life-hosting capabilities. Still more intriguing is the chance to un- cover terrestrial planets with compositions and characteristics unseen in the Solar System (e.g., Morley et al., 2017). In Section 2.2 we describe our observations of GJ 1132b in transit. In Section 2.3 we describe our customized data reduction pipeline and in Section 2.4 we describe our customized data analysis pipeline. We present the results of this work in Section 2.5. We discuss the implications of ground-based investigations of terrestrial planet atmospheres in Section 2.6 and conclude with Section 2.7.

2.2 Observations

A joint program between Harvard and MIT (PIs Diamond-Lowe and Berta-Thompson, respectively) to observe transits of GJ 1132b received eight nights on the Magellan II (Clay) Telescope with the LDSS3C multi-object spectrograph at Las Campanas Obser- vatory (Stevenson et al., 2016). Of the eight observing opportunities we observed ﬁve transits of GJ 1132b and lost the remaining three nights to clouds and high winds. The details of our observing program are presented in Table 2.1. GJ 1132 (V = 13.49, K = 8.322) is an M4.5V star (Berta-Thompson et al., 2015). In the 40 ﬁeld of view of LDSS3C there are no stars of comparable magnitude or spectral type, so we opted to simultaneously observe nine comparison stars which we later used to remove telluric effects from the GJ 1132 spectrum. Of these comparison stars one was brighter than GJ 1132 but it saturated our detector and we were not able to use it in our analysis.

30 2.2. Observations a −− −−− −− −− −− −− −− −− −− −− −−− −− −− −− −−− −−− 2.1: Observations ABLE T On nights 1, 2, and 4 the seeing remained relatively stable throughout the night while on nights 3 and ** -03-21 – -03-22 -05-04 – -05-05 * -05-22 – -05-23 123 -02-28 06:01:14 – -02-28 09:15:13 -03-04 02:28:11 – -03-04 06:29:564 -03-08 23:50:48 – -03-09 05:41:205 12 -04-17 13 02:20:47 – -04-17 06:12:37 -04-21 13 23:30:33 – -04-22 05:34:25 401 13 481 13 694 1.109 1.119 1.321 464 1.523 1.055 725 1.849 1.077 1.190 1.080 0.54 1.136 1.100 1.294 0.90 0.7-1.1 1.113 1.938 1.780 0.80 0.60-1.01 a 5 the seeing deteriorated over the course of the observations. No. [2016 UTC] [s] Exposures Start Middle End [arcsec] We were not able to take data on these nights due to poor weather conditions. Data set Date Exp. Time Number of Airmass Seeing *

31 Chapter 2. GJ 1132b

Our LDSS3C masks include slits for GJ 1132 and the nine comparison stars. At the time of our observations there was a background star 7.3 arcseconds away form GJ 1132; because GJ 1132 is a high proper motion star this separation will change over time and future observers of GJ 1132 should account for this. We oriented our mask such that the background star did not contaminate the dispersed spectrum of GJ 1132. We cut our slits 1000 in width to avoid slit losses and 2000 in length to provide sky background with which to perform our subtraction (Bean, Miller-Ricci Kempton, and Homeier, 2010). We also cut identical masks with 100 wide slits which we used to take wavelength calibration arcs during the afternoon prior to each observation. We used 2x2 binning of the detector pixels and a 13 second detector read out speed (fast mode). We set the gain to 0.6 ADU/electron. With our observation mask we took biases, darks, quartz flat fields, and a mask image with which to align our stars in the slits during observations. With our 100 mask we took helium, neon, and argon arcs so that we could determine a wavelength solution for each dispersed stellar spectrum. Both during calibrations and observations we kept every detector pixel that we used to perform our analysis below 53,000 counts. The full pixel well is 64,000 counts, but past 53,000 the detector stops counting photoelectrons linearly. We chose to use the VPH-Red grism which provides a wavelength coverage of 640- 1040 nm with a central wavelength of 850 nm (Stevenson et al., 2016). The VPH-Red grism allowed us to expose for longer at wavelengths where GJ 1132 emits more photons relative to the VPH-all grism which extends farther in the blue. We exposed for 13 seconds and achieved a duty cycle of 43%. The VPH-Red grism introduces order contamination onto the detector, which we mitigated with the OG590 order-blocking filter as advised in the LDSS3C user manual. This filter blocks spectral contamination from higher-order

32 2.3. Data Extraction lines but produces internal reflections. (Stevenson et al. (2016) noted this contamination and decided against using the OG590 filter.) After inspecting the calibration arc frames during the day we decided that the OG590 contamination was less problematic than the higher-order line contamination. We therefore used the OG590 filter during observation and also while taking our calibration images. We note that our first night of observation (data set number 1 in Table 2.1) differed from the rest for two reasons. Firstly, we neglected to use the OG590 order blocking filter, which is why we exposed for 12 seconds on this night instead of 13. In spite of this, the order contamination was not drastic since GJ 1132 emits few photons blue-ward of 700 nm. Secondly, we used a slightly different mask. The first amplifier (C1) of LDSS3C’s CCD has several columns of bad pixels which over-lapped with one of our comparison stars. We cut a second, identical mask with the slits slightly shifted in order to avoid the bad pixels. In the end we did not end up using this comparison star since the bad pixels near it saturated and leaked light into its dispersed spectrum. For all five of our data sets we acquired at least one transit-durations’s worth of out-of- transit baseline both before and after the transit event with which to correct for correlated noise in the data.

2.3 Data Extraction

We transform our raw Magellan/LDSS3C images into 1D stellar spectra by running them through our custom pipeline, mosasaurus (Z. Berta-Thompson, private communication). From each bias image we estimate a 1D bias from the overscan region. We then create a mean bias image using a median absolute deviation (MAD) to reject outliers that are

33 Chapter 2. GJ 1132b

10× the MAD. We subtract this mean bias image from all of our other images in order to remove any readout signals. We create a mean dark image in the same way that we do the mean bias image and subtract this mean dark image from all other images (except the biases). We also multiply our flat and science images by the amplifier gain before stitching these images together. We correct for cosmic ray contamination by flagging pixels that are 10× the MAD of the ten closest images in time as bad. We interpolate over these bad pixels using the surrounding pixels in the image. We cut out a 60×2048 pixel region around each of our dispersed spectra. We cut out corresponding regions using the same pixels on our quartz flat and arc images. The spectra recorded on the detector are curved. We fit a second order polynomial to the spectral trace, which maps where the peak flux is in each column in the cross-dispersion direction. We calculate the full-width-half-maximum (FWHM) in each column. To create an extraction window we extend by a multiple of the FWHM from the centroid in the spatial direction (Figure 2.1). We create a range of extraction window sizes for each stellar spectrum. We identify the appropriate extraction window for each star by plotting the science images with an overlayed extraction window, and then inspecting the aligned extraction window containing the stellar flux along with the background (Figure 2.1). At this stage we determine that several comparison stars are unusable – the bright one that saturated the detector and four others that turned out to have multiple stars clustered together in the slit. Having multiple stars in a single slit is problematic as we would have to combine their spectra in a large extraction window, which leads to a poor estimate of the sky background. We end up with four comparison stars for our analysis. Though we use the same comparison stars for each night of data the extraction windows may vary from

34 2.3. Data Extraction

FIGURE 2.1: Intermediary steps in the mosasaurus open source extraction pipeline for multi-object spectrographs (Z. Berta- Thompson, private communication). This ﬁgure corresponds to a single spectrum of GJ 1132. Top: Extracted raw spectrum of GJ 1132 prior to wavelength calibration. Middle: Spectral trace of GJ 1132 in which the curvature is apparent. Orange lines show the bounds of the extraction aperture. Shaded purple regions are data that we dis- card when doing our analysis. This includes a region directly beneath the GJ 1132 trace that is masking out the spectrum of a faint background star. The (0,0) point in the trace is where the star is located in the undispersed image Bottom: After ﬁtting a second- order polynomial to the trace in the middle panel we are able to align the spectrum. Or- ange lines and purple shaded regions are the same as in the middle panel.

night to night. This is because the seeing conditions on a given night influence the PSF of the stars on the detector. We therefore stand to benefit from using different extraction windows for each star for each data set. Using the quartz flat regions we create median-pass filters by dividing each pixel by the 20×100 pixels surrounding it. This process corrects for the intrinsic pixel-to-pixel inconsistencies of the detector. We then divide each spectrum region in the time-series by the filter made from the quartz flats over the same region. We create a 1D stellar spectrum

35 Chapter 2. GJ 1132b from each flat-fielded stellar region by summing up the flux in each column in the spatial direction in the extraction window. We create a 1D sky-background spectrum from each flat-fielded stellar region by fitting a two-degree polynomial to each column in the spatial direction outside the extraction window, and then summing over the column. We then subtract the sky-background spectrum from the stellar spectrum. We use the He, Ne, and Ar arcs taken during calibration to develop a rough wavelength solution for each star. The LDSS3C user manual provides a wavelength solution for the VPH-Red grism that gives the pixel position of prominent features in the He, Ne, and Ar spectra. Using a customized graphical user interface we match up the features in the provided wavelength solution to those in each arc, corresponding to our stellar spectrum regions, and create a polynomial wavelength solution for each star. This lines up the spectra with each other to within 5 nm. We then choose one exposure of one star and use five prominent features in its spectrum (the O2 doublet, each line of the Ca triplet, and the forest of water lines) as a basis against which to cross-correlate all of the exposures of all of the stars in a given night. Given the small field-of-view of the instrument we are not concerned about the different lines-of-sight to each star. This process reveals that there is both a shifting and stretching of the spectra over the course of the observations. For instance, in data set number 1, the difference between the positions of the O2 doublet and the water line forest in the GJ 1132 spectrum increases by a pixel from the start of the observation relative to the end. We use this information to apply a second wavelength solution that interpolates the spectra in each exposure such that they are lined-up with one another in wavelength space to within 0.35 nm. This is the final step in achieving 1D spectra which we can use to make our light curves.

36 2.4. Data Analysis

TABLE 2.2: Stars used in this work

Star RA Dec Flux/ GJ 1132 Flux GJ 1132 10:14:50.09 -47:09:17.5 1.0 Comp A 10:14:57.51 -47:05:39.9 0.35 Comp B 10:14:58.22 -47:09:35.1 0.14 Comp C 10:15:05.74 -47:07:43.9 0.11 Comp D 10:15:16.26 -47:06:44.3 0.11

Note. The relative ﬂux column indicates the full wavelength-band integrated ﬂux of each star relative to that of GJ 1132. The comparison star labels in this table correspond to those in Figure 2.2

2.4 Data Analysis

To perform this analysis we constructed the code detrendersaurus1. Though it is not generalized for data sets other than LDSS3C multi-object spectroscopy, the code is fairly modular and some routines may be useful to others performing similar analyses.

2.4.1 Analyzing transits separately

GJ 1132 is brighter than the four comparison stars (Figure 2.2, Table 2.2). We therefore create our light curves by summing up the flux from the comparison stars and dividing the GJ 1132 spectrum by the summed comparison spectrum for each point in the light curve. GJ 1132 is still brighter than the summed flux of the four comparison stars so we are limited by the photon noise of the summed comparison star flux. We detrend our light curve using decorrelation parameters that either have the same values for all the stars (e.g., airmass) or are associated with GJ 1132 (e.g., width of the

1github.com/hdiamondlowe/detrendersaurus, v0.1

37 Chapter 2. GJ 1132b

FIGURE 2.2: Wavelength-calibrated spectra of GJ 1132 and the four stars we use to remove telluric features from the GJ 1132 spectrum. The vertical dotted lines show the boundaries of the wavelength we use to make our transmission spectrum. The comparison stars are all fainter than GJ 1132. By summing the comparison stars’ flux we achieve 71% of GJ 1132’s flux when integrat- ing over the full wavelength bandpass (700- 10400 nm). This means that our results are limited by the combined photon noise of the comparison stars. spectral trace). The parameters that are unique to each star have similar values for all stars in the, data set but because we detect the most photons from GJ 1132 its decorrelation parameters have higher signal-to-noise ratios. We create white light curves for each data set and also bin the light curves from each data set into narrow wavelength bands for the purpose of atmospheric characterization. We restrict our analysis to the wavelength range common to GJ 1132 and the four comparison stars, which is 700-1040 nm. We then determine which decorrelation parameters are necessary to remove the effects of correlated noise. In a given data set we choose a single 20 nm wavelength bin without any prominent stellar, telluric, or atmospheric features (we use 830 - 850 nm) and calculate the Bayesian Information Criterion (BIC) value for every combination of possible decorrelation parameters. Once this is done for all five data sets we take the union of all the best decorrelation parameters and marginalize over them in all wavelength bins in all data sets. A list of these parameters, what vectors they depend on, and how they are derived can be found in Table 2.3. From the results of a Levenberg-Marquardt minimizer we run a makeshift Bayesian test in order to determine whether our five nights of data should be analyzed separately

38 2.4. Data Analysis

TABLE 2.3: decorrelation parameters used to model data systematics

Parameter Vector Description airmass t average airmass of the ﬁeld rotator angle t instrument rotator angle width t, star median width across wavelengths of the stellar trace in the cross-dispersion direction stretch t, star wavelength solution coefﬁcient associated with spectrum stretching in the dispersion direction peak t, λ, star brightness of the brightest pixel in the cross-dispersion direction normalization t unit array

Note. All parameters are functions of time t. They can also vary by wavelength λ and by star. For all parameters that are star-dependent we use the values associated with GJ 1132 as it has the highest signal-to-noise ratio. or taken together in a joint fit. For each 20 nm bin in each of the five data sets we compare the resulting χ2 value for a fit in which the transit depth is allowed to vary to one in which the transit depth is fixed to a inverse-variance weighted depth derived from the five nights. We account for the change in the number of fitted parameters between these two scenarios. We find that the χ2 values for the case of the fixed transit depth in a given wavelength bin can be higher, lower, or identical to the case where the transit depth parameter is allowed to vary. In other words, fixing the transit depth does not provide a uniformly worse fit. We therefore decide to fit the five nights of data jointly, allowing the transit parameters to be shared across all nights.

39 Chapter 2. GJ 1132b

2.4.2 Analyzing transits jointly

Levenberg-Marquardt ﬁts

In analyzing the transits jointly we must account for the different uncertainties associated with the individual data sets, as well as clip outlying data points. We use a three-step Levenberg-Marquardt process to settle on initial guesses for our parameters to use in a dynamic nested sampler. To run our Levenberg-Marquardt fits we employ the open- source lmfit package (Newville et al., 2016). In the first pass at the Levenberg-Marquardt fit we build a linear model unique to each night of data following the formula

M(t) = S(t)T (t) (2.1) where S(t) is the systematics model and T (t) is the transit model. The systematics model S(t) can further be broken down to

N S(t) = ∑ an pn(t) + 1 (2.2) n=1 where N is the number of decorrelation parameters used in the fit, an are the coefficients we are fitting for, and pn are the arrays of decorrelation parameters that describe the correlated systematics in the data, which are all functions of time. For decorrelation parameters which are functions of wavelength we sum over wavelength space. The decorrelation parameters are either common to all stars (airmass and rotator angle) or are taken from the GJ 1132 spectral extraction (width, stretch, peak). We build the transit model T (t) using the open-source batman code (Kreidberg, 2015) and feed in the free transit parameters. The transit parameters that can be shared across

40 2.4. Data Analysis

data sets are the planet-to-star radius ratio Rp/R∗, period P, inclination i, scaled orbital distance a/R∗, and uncorrelated quadratic limb darkening coefﬁcients 2u0 + u1 and u0 −

2u1 as used by Holman et al. (2006). The residuals that we calculate from dividing our light curves by the linear models are weighted by the calculated photon noise of each data set. At this stage we fix the uncorrelated quadratic limb darkening coefficients to values derived from the Limb Darkening Tool Kit (ldtk), an open-source package that takes in stellar parameters and uncertainties and calculates the limb darkening coefficients in a given wavelength range based on the PHOENIX library of stellar models (Husser et al., 2013; Parviainen and Aigrain, 2015). During the next stage of analysis (Section 2.4.2) we instead allow the uncorrelated quadratic limb darkening parameters to vary. In the second Levenberg-Marquardt fit we calculate the MAD of the residuals and clip the 29 data points (for the white light curve) or ≤ 27 points (for the wavelength- binned light curves) that deviate by 5× the MAD. In the third Levenberg-Marquardt fit we change the weighting from the calculated photon noise to the uncertainties we derive from each night’s data as a result of our second fit. Levenberg-Marquardt fits with lmfit are inexpensive and quick but running a dynamic nested sampler can be expensive if the priors are too wide. Since we derive our sampling priors from the covariance matrix output by the Levenberg-Marquardt fit we find it worthwhile to constrain the fit parameters as much as possible at this stage.

Dynamic multi-nested sampling

Our joint ﬁt comprises a minimum of 30 free parameters – the same 6 light curve parameters to ﬁt for each of the 5 nights of data. In addition to this there can be free transit

41 Chapter 2. GJ 1132b model parameters, like the transit midpoint for each night or the transit depth, which is shared between the five nights. With so many free parameters traditional Markov Chain Monte Carlo ensemble samplers are slow and inefficient at exploring the parameter space (Huijser, Goodman, and Brewer, 2015). We instead use the open-source dynamic nested sampling package dynesty2 (J. Speagle, private communication) to estimate our posteriors. dynesty samples each free parameter from 0 to 1 and then requires a prior transform function to map the outputs from the sampling onto the parameter space we want to explore. For all but the uncorrelated limb darkening coefficients we set the priors for the light curve fitting parameters by taking the estimated 1σ uncertainties from the covariance matrix of our Levenberg-Marquardt fit and multiplying by 25 such that the prior bounds for each parameter are 25σ from the estimated parameter value. These priors are so wide they are essentially uninformed. Following the work of Berta et al. (2012a) we place Gaussian priors on the uncorrelated quadratic limb darkening coefficients 2u0 + u1 and u0 − 2u1. To determine what these Gaussian priors should be we first get the quadratic limb darkening coefficients in each wavelength bin from ldtk. ldtk has an option to run a Markov chain Monte Carlo (MCMC) with the input stellar parameters and uncertainties in order to derive the limb darkening coefficients. We use the samples from the MCMC to calculate arrays of uncorrelated parameters using the formulation 2u0 + u1 and u0 − 2u1, where u0 and u1 are the quadratic coefficients derived with ldtk. We calculate the median and standard deviation of these uncorrelated arrays and use these values to set the Gaussian priors.

2github.com/joshspeagle/dynesty

42 2.4. Data Analysis

Also following Berta et al. (2012a) we achieve a χ2 value of unity by including a scaling parameter s (Equations 2 and 3 of that paper). We automatically marginalize over this during our dynamic multi-nested sampling by modifying our log-likelihood function such that s is a multiplier of the theoretical uncertainty associated with each data point. Each data set has its own value of s associated with it. An s value of unity implies that we are reaching the theoretical photon noise limit with our ﬁts, while a value less than unity implies an over-ﬁtting of the model to the data.

White light curve

We jointly ﬁt the white light curve of our ﬁve data sets and allow the time of mid-transit

δt0 to vary for each data set, along with the shared parameters of the radius ratio Rp/R∗, inclination i, scaled orbital distance a/R∗, and uncorrelated quadratic limb-darkening coefficients 2u0 + u1 and u0 − 2u1. In doing so we leverage the five nights of data, which have the same transit model parameter values, except for the mid-transit time. Where appropriate we adopt the same priors as those quoted by Dittmann et al. (2017a) (Table 2.4). The photometric bandpass of MEarth is not identical to the wavelength coverage of our white light curves, and so we use stellar models to set Gaussian priors on the uncorrelated quadratic limb darkening coefficients, as described in Sec- tion 2.4.2.

For the time of mid-transit we ﬁt for an offset δt0 from the calculated mid-transit time using the ephemeris T0 given by Dittmann et al. (2017a):

δt0 = t0 − T0 + nP (2.3)

43 Chapter 2. GJ 1132b

TABLE 2.4: White light curve transit model parameter priors

Parameter Value Priors a δt0,1 [days] -0.0015 [-0.0075, 0.0044] a δt0,2 [days] -0.0017 [-0.0057, 0.0023] a δt0,3 [days] -0.0019 [-0.0108, 0.0069] a δt0,4 [days] -0.0016 [-0.0093, 0.0060] a δt0,5 [days] -0.0017 [-0.0060, 0.0027] a Rp/R∗ 0.0493 [0.0081, 0.0904] P [days] 1.628925 [1.628744, 1.629116]b i 88.68 [85, 90]b b a/R∗ 16.54 [12, 20] c 2u0 + u1 — [0.8756, 0.0128] c u0 − 2u1 — [-0.3672, 0.0566] d s1,2,3,4,5 1 [0.01, 10] a Uniform that are 25× the 1σ uncertainties taken from the lmfit covariance matrix, as described in Section 2.4.2. The δt0 parameter is the offset from the calculated time of mid- transit (Equation 2.3). Rp/R∗ is the planet-to- star radius ratio. b Uniform priors taken from Dittmann et al. (2017a). P is the period, i is the inclination, and a/R∗ is the scaled orbital distance. c Gaussian priors calculated with ldtk outputs, as described in Section 2.4.2, given as [mean, standard deviation]. 2u0 + u1 and u0 − 2u1 are the uncorrelated quadratic limb darkening parameters. In the Levenberg- Marquardt ﬁts these parameters are ﬁxed to the ldtk outputs, but when sampling the parameter space with dynesty we use the Gaus- sian priors; dynesty does not require starting values as inputs. d Wide uniform priors set by hand. Each data set has a scaling parameter s as described in Section 2.4.2

44 2.4. Data Analysis

where n is the number of elapsed transits since the ephemeris transit, P is the period,

th and t0 is the time of mid-transit for the n transit. We fit for the offset as opposed to the mid-transit time itself as the mid-transit time in BJDTBD is too large relative to the model coefficients for the Levenberg-Marquardt fitter (lmfit) to handle. In our full band-integrated white light curve fit from 700 - 1040 nm we see significant features in the residuals. After experimenting with decorrelation parameters and wavelength clipping we conclude that the deep water absorption bands redward of 920 nm are leaving imprints on the white light curve, suggesting changes in precipitable water vapor in Earth’s atmosphere during some of our observations. The white light curves presented here do not include these problematic bands and are instead integrated from 700 - 920 nm. At this stage we investigate any transit timing variations by comparing our five derived mid-transit times to those quoted in the discovery paper (Berta-Thompson et al., 2015) and subsequent work with MEarth and Spitzer (Dittmann et al., 2017a) (Figure 2.3). The mid-transit times from the Spitzer data set reported by Dittmann et al. (2017a) are the

BJD−OBS values taken from the Spitzer header ﬁles. We correct these values to BJDTBD, which accounts for leap seconds. We note that our times of mid-transit are consistently two minutes earlier than the predicted time. We have simultaneous transit observations with the MEarth telescope array, which do not agree with our transit times. This timing offset in this analysis could be due to some unexplored systematic in the instrument or the data reduction. We check our header-time conversions to BJDTDB multiple times following Eastman, Siverd, and Gaudi (2010), making sure to account for the exposure and read-out times. As a test we perform a simple data reduction using only polynomials and the batman transit light

45 Chapter 2. GJ 1132b

FIGURE 2.3: Observed minus calculated (O- C) times of mid-transit for GJ 1132b by transit number with 1σ error bars derived from ﬁt- ting each transit. Values for MEarth (green data points) and Spitzer (red data points) are taken from Dittmann et al. (2017a, Ta- ble 4). The Spitzer points are corrected here to include leap seconds. Values for the data presented in this work from the Magel- lan/LDSS3C instrument are shown in blue. All values were converted to BJDTDB for the purpose of direct comparison. We do not know why the Magellan/LDSS3C times of mid-transit are consistently 2 minutes early compared to the MEarth and Spitzer points.

curve package (i.e., without the detrendersaurus pipeline) and were unable to derive transit times in agreement with those of the MEarth array. This discrepancy does not affect our results with respect to the atmospheric analysis since we ﬁx the times of transit to the best ﬁt values when performing our atmospheric analysis, and the time of mid-transit does not affect the transit depth at the time resolution of our data.

We compare our derived values of the planet-to-star radius ratio Rp/R∗, period P, inclination i, and scaled orbital distance a/R∗ to those reported by Dittmann et al. (2017a) and ﬁnd that our results are in agreement (Table 2.5). We present the raw white light curves, jointly-ﬁt white light curve, time-binned white light curve, and time-binned white light curve residuals in Figure 2.4.

46 2.4. Data Analysis

FIGURE 2.4: Panel a: Raw white light curves integrated from 700 - 920 nm from each of the ﬁve data sets with models over-plotted in grey. The systematic parameters for these models are unique to each data set but the transit parameters are free and shared jointly between the data sets. The derived values for the transit parameters are given in Table 2.5. Panel b: Unbinned white light curves from the ﬁve data sets with the systematics component of the models divided out. The over-plotted black line is the transit model. Panel c: White light curve binned in time at a 3-minute cadence. The over- plotted black line is the transit model. Panel d: Residuals after dividing the systematics models and subtracting the transit models from the raw white light curves and binning at a 3-minute cadence.

47 Chapter 2. GJ 1132b

TABLE 2.5: White light curve derived transit model values, compared to Dittmann et al. (2017a)

Parameter Value (this work) Value (D17a) +0.00022 δt0,1 [days] −0.0015−0.00023 — +0.00017 δt0,2 [days] −0.0017−0.00017 — +0.00055 δt0,3 [days] −0.0017−0.00054 — +0.00027 δt0,4 [days] −0.0016−0.00027 — +0.00017 δt0,5 [days] −0.0017−0.00018 — +0.0012 +0.0006 Rp/R∗ 0.0488−0.0009 0.0455−0.0006 +0.00013 +0.0000024 P [days] 1.62893−0.00013 1.6289246−0.0000030 +0.90 +0.40 i [deg] 88.54−0.90 88.68−0.33 +1.236 +0.63 a/R∗ 15.91−1.761 16.54−0.71 +0.012 2u0 + u1 0.876−0.012 — +0.055 u0 − 2u1 −0.371−0.056 — +0.19 s1 4.27−0.18 — +0.12 s2 2.73−0.12 — +0.28 s3 6.08−0.26 — +0.24 s4 5.24−0.22 — +0.13 s5 2.89−0.12 —

Transmission spectrum

We investigate the atmosphere of GJ 1132b by creating a transmission spectrum. We divide our light curves into 20 nm wavelength bins and jointly fit for Rp/R∗ and the uncorrelated quadratic limb darkening coefficients 2u0 + u1 and u0 − 2u1, along with the systematic parameters for each respective data set. We fix the times of mid-transit t0 for each night to the values determined from the white light curve fit. We fix the values of P, i, and a/R∗ in our binned wavelength fits to those reported by Dittmann et al. (2017a) as these are derived from a higher resolution Spitzer time-series.

Our joint fit produces single values for the radius ratio Rp/R∗ and the uncorrelated quadratic limb darkening coefficients 2u0 + u1 and u0 − 2u1 for each wavelength bin, but each of the five data sets has its own linear fit to the systematics in the light curve. In order

48 2.4. Data Analysis

FIGURE 2.5: Coefficients associated with each decorrelation parameter (given in Table 2.3) that we use in our light curve fit. Our joint fit produces a single value for the transit depth and the two uncorrelated quadratic limb-darkening parameters (top 3 panels), but each of the 5 data sets has its own set of decorrelation parameters which we marginalize over (bottom 6 panels, colors correspond to those in Figure 2.4). We do not see any obvious correlations between the coefficients and the transit depth as a function of wavelength.

49 Chapter 2. GJ 1132b to make more meaningful comparisons between the systematic parameters in a given data set we scale each of them by subtracting off the mean value and then dividing by the standard deviation. This ensures that all of our systematic parameters are on the same relative scale and so comparing their fitted coefficients describes the relative importance of each parameter to the fit (Figure 2.5).

2.5 Results

In Figure 2.6 we present our light curves after dividing out the systematic models for each data set. The wavelength boundaries, RMS, transit depth, and median factor of the expected photon noise limit for each wavelength bin are given in Table 2.6. We achieve an average transit depth precision across 17 wavelength bands of 100 ppm. We compare this to 80 ppm for two GJ 1132b transits with the Spitzer 4.5µm channal and 55 ppm with 25 MEarth transits in its photometric band (Dittmann et al., 2017a). We present our transmission spectrum in Figure 2.7 and compare it to two sets of four model transmission spectra generated by the Exo-Transmit open source code (Kempton et al., 2017). As inputs we use custom double-grey temperature-pressure profiles and associated equation-of-state files (provided by Eliza Kempton, private communication) as well as GJ 1132b’s surface gravity and radius at 1 bar of atmosphere and GJ 1132’s stellar radius (Miller-Ricci, Seager, and Sasselov, 2009; Miller-Ricci and Fortney, 2010). The 1 bar planet radius is smaller than the transit radius by an amount that depends on the atmospheric composition, temperature, and gravity. As these values are uncertain we allow the 1 bar planet radius to float in order to achieve the best transmission model fits to our data. Changing the 1 bar planet radius alters the amplitude of the model features

50 2.5. Results

TABLE 2.6: Best-Fit Transit Depths

Wavelength RMS Transit Depth × Expected Å (ppm) % Noisea +0.010 7000-7200 1311 0.240−0.011 1.47 +0.010 7200-7400 1288 0.206−0.010 1.55 +0.009 7400-7600 1148 0.219−0.009 1.85 +0.009 7600-7800 1213 0.233−0.010 1.63 +0.009 7800-8000 1193 0.214−0.010 1.89 +0.009 8000-8200 1093 0.234−0.009 1.80 +0.009 8200-8400 1118 0.212−0.009 1.71 +0.009 8400-8600 1141 0.229−0.009 1.67 +0.009 8600-8800 1111 0.229−0.009 1.84 +0.009 8800-9000 1171 0.233−0.009 2.03 +0.008 9000-9200 1102 0.218−0.009 1.98 +0.009 9200-9400 1186 0.222−0.009 1.66 +0.010 9400-9600 1271 0.206−0.011 1.82 +0.010 9600-9800 1261 0.220−0.010 2.02 +0.010 9800-10000 1187 0.210−0.010 1.56 +0.012 10000-10200 1510 0.223−0.012 1.68 +0.016 10200-10400 2088 0.228−0.017 1.65

aThough we are jointly fitting the five data sets we can estimate the expected photon noise limit and resulting RMS for each data set separately. This column represents the median of the five resulting RMS values divided by the expected photon noise for each data set. These values are similar to the average s values that we fit for for each night and for each wavelength bin.

51 Chapter 2. GJ 1132b

FIGURE 2.6: Left: Detrended light curves (colored points with each color representing one of the 5 data sets used in this analysis) with best ﬁt transit model over-plotted (black lines). The text states the wavelength range in angstroms covered by the light curve directly underneath it. Right: Residuals given by the detrended light curves minus the products of the best ﬁt systematics models and transit models. For clarity the y-axis labels in both panels are given only for a single light curve, but all light curves and residuals are plotted52 on the same scale. For reference, the colors correspond to those in Figure 2.4 and the transit depths and RMS values for each wavelength bin are given in Table 2.6. 2.5. Results

as well as the overall depth of the model. The Spitzer data from Dittmann et al. (2017a) can resolve the ingress and egress of a transit of GJ 1132b so we adopt the stellar mass and radius quoted in that paper in order to create the temperature-pressure proﬁles and model transmission spectra. One set of four model transmission spectra assumes solar elemental abundances (dom-

inant in H2 and He) with metallicities that are 1, 10, 100, and 1000× solar by volume. In these solar composition atmospheres the dominant sources of opacity that contribute

to the transmission features are CH4 and H2O, with modest contributions from NH3,

H2S, and K. Higher metallicity atmospheres have higher opacities, which strengthen the model features, but also higher mean molecular weights, which dampen the model features. These competing effects are the reason why they highest amplitude features are associated with the 10× solar metallicity model.

The other set of four model transmission spectra assume H2 and H2O atmospheres

where H2O makes up 1, 10, 50, and 100% of the atmosphere by volume. The solar com-

position models account for collision-induced absorption but the H2/H2O do not. Given how flat the model transmission spectra are this should not impact the results. All models assume a clear atmosphere (i.e., no aerosols). We also compare the GJ 1132b transmission spectrum to a flat line at the inverse- variance weighted-average transit depth and to a 1-degree polynomial fit to the transit depths. The wavelength bin-averaged values for the Exo-Transmit models are weighted by the recorded counts of a GJ 1132 spectrum across the same wavelength range. Because our wavelength bins are so narrow this weighting is virtually indistinguishable from a simple mean across the model wavelength bins. We use the wavelength bin-averaged values of the model transmission spectra to calculate the χ2 values associated with the

53 Chapter 2. GJ 1132b

FIGURE 2.7: Transmission spectrum of GJ 1132b with 1σ error bars derived from a joint fit of the five data sets analyzed in this work (both top and bottom). Top: We compare the GJ 1132b transmission spectrum to four clear, solar composition models at 1, 10, 100, and 1000× solar metallicity by volume. We label the molecular sources of the most prominent features in the model spectra. Bottom: We compare the GJ 1132b transmission spectrum to four clear, H2 and H2O models where H2O makes up 1, 10, 50, and 100% of the atmosphere by volume. All features in these models are due to H2O. Both figures also compare the GJ 1132b transmission spectrum to a flat line at the inverse-variance weighted-average transit depth (black dashed line) and a 1-degree polynomial fit to the transit depths (black dotted line). In the legends of each figure we provide the mean molecular weights of the atmospheres used to create the model transmission spectra and confidences to which the measured GJ 1132b transmission spectrum disfavors the model atmospheres. The data disfavor low mean molecular weight atmospheres.

54 2.6. Discussion

model ﬁts to the measured transit depths. Our results disfavor a clear, 10× solar metallicity atmosphere at 3.7σ conﬁdence and

a 10% H2O, 90% H2 atmosphere at 3.5σ conﬁdence. Our transmission spectrum is consistent with a ﬂat line and with metallicities in excess of ∼10× solar or water abundances greater than ∼10%, for aerosol-free atmospheres. We compare our results to those of other groups (Figure 2.8). Our spectrophotometric transit depths are in agreement with photometric transit depths from the MEarth survey and the Spitzer 4.5µm bandpass (Dittmann et al., 2017a), but not in agreement with the photometric transit depths from the GROND multi-band imager (Southworth et al., 2017).

2.6 Discussion

2.6.1 Ground-based detection of terrestrial exoplanet atmospheres

Our data-reduction process highlights the difficulties of trying to detect terrestrial exoplanet atmospheres from the ground. The signal we are looking for is small (0.24%) and we are not able to reach the photon noise limit (Table 2.6). One question is whether more data could disfavor higher mean molecular weight atmospheres, or if we needed less data to reach the same conclusions. To answer this question we select a test-case 20 nm wavelength bin, from 830-850 nm, and jointly fit for Rp/R∗ and the uncorrelated quadratic limb darkening coefficients

2u0 + u1 and u0 − 2u1, as we did in our analysis, using 1, 2, 3, 4, and 5 data sets in each ﬁt. We then look at the error on the transit depth after each data set is added to the analysis. We compare these to the errors in transit depth from the ﬁrst data set, scaled by the inverse of the square-root of the number of data sets included.

55 Chapter 2. GJ 1132b

FIGURE 2.8: The transmission spectrum of GJ 1132b from this work (blue points) with 1σ error bars in the context of other GJ 1132b transit data. The dashed line is the inverse-variance weighted average of these transit depths. We plot the photometric transit depths from the MEarth survey (green point) and the Spitzer 4.5µm bandpass (red point) from Dittmann et al. (2017a), as well as the photometric transit depths in g, r, i, z, J, H, and K bands (purple points) from Southworth et al. (2017).

As shown in Figure 2.9, we require all 5 transits of GJ 1132b to rule out low mean molecular weight atmospheres at high conﬁdence. Theoretically, 8 transits are needed to rule out the highest mean molecular weight atmospheres we tested (1000× solar metallicity and 100% H2O), though this is a minimum estimate since we do not achieve the photon noise limit and therefore our error bars do not decrease by the square-root of the number of data sets included in the analysis. In the coming era of extremely large ground-based telescopes (ELTs) detecting and characterizing terrestrial exoplanet atmospheres may be in reach. For example, the Giant

56 2.6. Discussion

FIGURE 2.9: Transit depth error as a function of the number of data sets included in the analysis. The blue line and circles shows how the transit depth error decreases when performing the analysis with additional data sets. The black line and squares shows the transit depth error of our ﬁrst data set divided by the square-root of the number of data sets used in the analysis. We extend the calculated error to investigate what would happen if we captured more than 5 transits of GJ 1132b. The dashed horizontal lines denote the transit depth error that would disfavor low mean molecular weight atmospheres (10× solar metallicity and 10% H2O, 90% H2) at 1, 2, and 3σ. We require all ﬁve transits to disfavor the low mean molecular weight atmospheres we tested. We theoretically require 8 transits to rule out higher mean molecular weight atmospheres (1000× solar metallicity and 100% H2O), though likely more given that we do not reach the photon noise limit.

57 Chapter 2. GJ 1132b

Magellan Telescope (GMT) will have a diameter of 24.5 m, compared to the 6.5 m diameter of Magellan Clay. This means that the GMT will receive about (24.5/6.5)2 = 14.2 times the number of photons per observation. The science and instrument requirements for the GMT-Consortium Large Earth Finder (G-CLEF), an optical-band echelle spectrograph with a multi-object spectrograph setting and the ﬁrst-light GMT instrument, suggest that with a single transit observation of GJ 1132b, GMT/G-CLEF would be able to rule out the high mean molecular weight atmospheres we tested in this analysis (Szentgyorgyi et al., 2014). The caveat for all ELT observations is that reaching the photon noise limit from the ground will still be difﬁcult and future ELT programs must take this into account.

2.6.2 Theoretical atmosphere of GJ 1132b

It would be surprising a planet with such a small radius (1.12 R⊕) and high insolation (19× Earth insolation) possessed a low mean molecular weight atmosphere. Based on thermal evolution models and extreme ultraviolet mass loss, GJ 1132b falls into a class of planets that would be unable to retain a H/He envelope (Lopez and Fortney, 2013). There is statistical evidence from the Kepler data set that close-in planets with small radii (< 1.6

R⊕) are rocky and lacking in low-density envelopes (Rogers, 2015; Fulton et al., 2017). Schaefer et al. (2016) ran models that couple GJ 1132b’s atmosphere and interior, allowing for oxygen exchange between the two. They determine that the most likely atmosphere for GJ 1132b is a tenuous one dominated by abiotic molecular oxygen (O2).

This arises as follows: water (H2O) in the GJ 1132b atmosphere is photolysed by the intense UV radiation from the GJ 1132 host star. The hydrogen escapes to space, taking some oxygen with it, but the different escape rates along with uptake by the interior mean that some oxygen can combine to form O2 and remain in the planet’s atmosphere

58 2.6. Discussion

(Schaefer et al., 2016). Further modeling that includes additional atmospheric gasses such

as N2 and CO2 would be of interest.

If the atmosphere of GJ 1132b is dominated by O2 this would be difﬁcult to detect with any currently existing instrumentation. Not only is the mean molecular weight of

O2 relatively high (µ = 32) but it also has few spectroscopic features. Fortunately the photolysis of O2 leads to the production of ozone (O3). Given the asymmetry of this molecule it produces higher-amplitude spectroscopic features and is more amenable to detection. An atmosphere around GJ 1132b may also dominated by other molecules. We see examples in the Solar System of small bodies with high mean-molecular weight atmospheres other than Earth’s. Venus, for instance, has a thick atmosphere of CO2 (µ = 44) and Titan is dominated by CH4 (µ = 16). These molecules have many prominent spectroscopic features and these atmospheres would be detectable on GJ 1132b in transmission with instruments aboard the James Webb Space Telescope (JWST) with 10 transits, according to online predictive tools like PandExo (Batalha et al., 2017; Morley et al., 2017). They may also be detectable in transmission with the GMT though the predictive tools are not yet available to test this. Other observing strategies, such as taking emission spectra, will also be useful in constraining the atmospheric properties. With its 19× Earth insolation and small radius it is likely that GJ 1132b has a high mean molecular weight atmosphere or atmosphere at all. The same can be said for many of the TRAPPIST-1 planets (Gillon et al., 2017a; de Wit et al., 2018). Terrestrial planets farther from their host stars may fare better. LHS 1140b recieves 0.46× Earth insolation and has a high surface gravity; it therefore may not experience the same rates of atmospheric escape (Dittmann et al., 2017b).

59 Chapter 2. GJ 1132b

2.6.3 Searching for more terrestrial exoplanets

Perhaps the terrestrial planets with the most accessible atmospheres have not yet been discovered. The GJ 1132, LHS 1140, and TRAPPIST-1 systems are all about 12 parsecs away (Berta-Thompson et al., 2015; Dittmann et al., 2017b; Gillon et al., 2017a, respectively). Dressing et al. (2015) investigated the occurrence rate of terrestrial planets around nearby M dwarfs using the full Kepler survey. They predict that nearest M dwarf systems

+0.7 hosting non-transiting or transiting exoplanets are 8.6−0.8 parsecs away, so there may be still undiscovered transiting exoplanets that would be amenable to atmospheric detection and characterization. M dwarfs, with their small sizes, high occurrence rates, and close-in habitable zones, are now the targets of several dedicated transit and radial velocity surveys that aim to identify planets amenable to atmospheric follow-up. Notable transit surveys include MEarth and TRAPPIST (Irwin et al., 2015; Gillon et al., 2013), with SPECULOOS and TESS waiting to come online shortly (Burdanov et al., 2017; Ricker et al., 2015). Radial velocity surveys focusing on M dwarfs stand to make more detections since they are not as limited by a planet’s inclination. Though many of the planets discovered by this method will not transit, their atmospheres may be amenable to phase curve (Koll and Abbot, 2016; Kreidberg and Loeb, 2016) or high-resolution spectroscopy (Snellen et al., 2013) observations. The radial velocity surveys (listed by their acronyms) focused on M dwarfs that are either currently taking data or in the production phase include CARMENES (Quir- renbach et al., 2010), HZPF (Mahadevan et al., 2010), MAROON-X (Seifahrt et al., 2016), NEID (Schwab et al., 2016), NIRPS (Bouchy et al., 2017), and SPIRou (Artigau et al., 2014).

60 2.7. Conclusion

2.7 Conclusion

We investigate whether or not the small, rocky terrestrial exoplanet GJ 1132b possesses a low mean molecular weight (µ ∼ 2) atmosphere using ground-based telescopes and instrumentation to construct a transmission spectrum. Our analysis disfavors a clear,

10× solar metallicity and a clear 10% H2O at high conﬁdence. GJ 1132b likely possesses a high mean molecular weight or depleted atmosphere. While we search for new terrestrial exoplanets we should also continue to learn more about the GJ 1132b atmosphere. Obtaining transits with HST/WFC3 will allow us to con- ﬁrm the results from this work. Morley et al. (2017) suggest that GJ 1132b is the most amenable planet of its kind, currently known, for observation in secondary eclipse with JWST. Small, rocky exoplanets like GJ 1132b challenge our limits of detection and characterization but also present the most exciting opportunities for comparative planetology with the Solar System terrestrial exoplanets, including Earth.

We thank the contributors to the LDSS3C project, the operations team and staff at Las Campanas Observatory, and the writers and contributors of the open-source software used in this work. We also thank Mercedes Lopez-Morales, Robin Wordsworth, Dimitar Sasselov, Laura Kreidberg, and Kevin Stevenson for helpful comments and conversations. H.D.-L. recognizes support from the National Science Foundation Graduate Research Fel- lowship Program (grant number DGE1144152).

Facilities: Magellan II (Clay) LDSS3C

Software: astropy (Astropy Collaboration et al., 2013; Astropy Collaboration et al., 2018),

61 Chapter 2. GJ 1132b

batman (Kreidberg, 2015), decorrasaurus (github.com/hdiamondlowe/decorrasaurus), dynesty (Speagle, 2020), Exo-Transmit (Kempton et al., 2017), LDTk (Parviainen and Aigrain, 2015), mosasaurus (github.com/ zkbt/mosasaurus)

62 Chapter 3

Simultaneous Optical Transmission Spectroscopy of a Terrestrial, Habitable-Zone Exoplanet with Two Ground-Based Multi-Object Spectrographs

Abstract

Investigating the atmospheres of rocky exoplanets is key to performing comparative planetology between these worlds and the terrestrial planets that reside in the inner Solar System. Terrestrial exoplanet atmospheres exhibit weak signals and attempting to detect them pushes at the boundaries of what is possible for current instrumentation. We focus on the habitable zone terrestrial exoplanet LHS 1140b. Given its 25-day orbital period and 2-hour transit duration, capturing transits of LHS 1140b is challenging. We observed two transits of this object, approximately one year apart, which yielded four data sets thanks to our simultaneous use of the IMACS and LDSS3C multi-object spectrographs

This chapter has been accepted for publication by The Astronomical Journal, in collaboration with Zachory Berta-Thompson, David Charbonneau, Eliza M.-R. Kempton, and Jason Dittmann.

63 Chapter 3. LHS 1140b

mounted on the twin Magellan telescopes at Las Campanas Observatory. We present a jointly ﬁt white light curve, as well as jointly ﬁt 20 nm wavelength-binned light curves from which we construct a transmission spectrum. Binning the joint white light curve residuals to 3-minute time bins gives an RMS of 145 ppm; binning down to 10-minute

2 2 time bins gives an RMS of 77 ppm. Our median uncertainty in Rp/Rs in the 20 nm wavelength bins is 260 ppm, and we achieve an average precision of 1.3× the photon noise when ﬁtting the wavelength-binned light curves with a Gaussian process regres-

2 2 sion. Our precision on Rp/Rs is a factor of four larger than the feature amplitudes of a clear, hydrogen-dominated atmosphere, meaning that we are not able to test realistic models of LHS 1140b’s atmosphere. The techniques and caveats presented here are applicable to the growing sample of terrestrial worlds in the TESS era, as well as to the upcoming generation of ground-based giant segmented mirror telescopes (GSMTs).

3.1 Introduction

Planetary atmospheres hold clues about surface processes, formation histories, and the potential for habitability for the planets they surround. Under the right circumstances, they can also reveal the presence of life on other worlds via biomarker gases (e.g., Domagal- Goldman et al., 2011; Meadows, 2017, and references therein). In the Solar System we see a great diversity of atmospheres, from the puffy hydrogen and helium envelopes around Jupiter and Saturn to the heavy carbon dioxide layer around Venus and the nitrogen-rich sky of Titan. The terrestrial bodies of the Solar System boast a wide variety of atmospheric compositions and masses, but all are secondary, high mean molecular weight atmospheres.

64 3.1. Introduction

Results from the Kepler mission, combined with statistical and empirical follow-up, reveal that such worlds also exist in abundance outside the Solar System, along with a completely new kind of terrestrial planet that has retained a hydrogen- and helium- dominated envelope (Fressin et al., 2013). For planets with radii < 10R⊕, those with radii

> 1.6R⊕ have low bulk densities and likely host puffy hydrogen and helium envelops captured from the stellar nebula, while those with radii < 1.6R⊕ are rocky in nature and likely host high mean molecular weight secondary atmospheres (Rogers, 2015; Owen and Wu, 2013; Lopez and Fortney, 2013; Fulton et al., 2017; Fulton and Petigura, 2018; Van Eylen et al., 2018), though given the difﬁculties in detecting secondary atmospheres around small planets, we have not yet spectroscopically characterized any. The 1.6R⊕ mark is not a hard cut-off. Another way to look at this is that planets with bulk densities less than that of rock (2.5 − 3.0 g/cm3) must have signiﬁcantly large envelopes of hydrogen and helium in order to explain their low masses relative to their radii, whereas planets with bulk densities at or above that of rock are likely compositionally similar to the terrestrial objects found in the Solar System. To understand the rocky exoplanets we must probe their atmospheres and determine their compositions. In this paper we focus on the technique of transmission spectroscopy, whereby observations of a planet’s transit across its star, taken over a range of wavelengths, can reveal the planet’s atmospheric composition, since different molecules absorb stellar light at different wavelengths. Within the limits of current instrumentation we begin the exploration of small planet atmospheres by looking for small planets that orbit the small stars closest to us. This is a simple function of the planet-to-star radius ratio Rp/Rs (the larger the ratio, the easier it is to detect the planet) and the need for high signal-to-noise measurements to differentiate the planet radius at one wavelength from

65 Chapter 3. LHS 1140b

another (the closer the star, the more photons can be collected per observation). Before the launch of the Transiting Exoplanet Survey Satellite (TESS; Ricker et al., 2015), the ground-based transit surveys MEarth and TRAPPIST (Nutzman and Charbonneau, 2008; Gillon et al., 2013; Irwin et al., 2015) discovered a handful of small planets around three small, nearby stars: GJ 1132, TRAPPIST-1, and LHS 1140, which follow-up observations by the Spitzer Space Telescope and K2 confirmed and, for the TRAPPIST-1 and LHS 1140 systems, bolstered with additional planet discoveries (Berta-Thompson et al., 2015; Gillon et al., 2017a; Dittmann et al., 2017b; Dittmann et al., 2017a; Ment et al., 2019). Follow-up by radial velocity instruments such as the High Accuracy Radial-velocity Planet Searcher (HARPS; Pepe et al., 2004) provided masses for planets in the GJ 1132 and LHS 1140 systems, thereby confirming their rocky natures. HARPS also discovered an additional, non-transiting planet in the GJ 1132 system (Bonfils et al., 2018). In the case of the two nearest terrestrial planets HD 219134b,c (Gillon et al., 2017b), their presence was detected via radial velocities from HARPS-North (Cosentino et al., 2012), and were later found to transit by Spitzer. The dimness of TRAPPIST-1 makes radial velocity measurements challenging, so masses for the TRAPPIST-1 planets are instead estimated using transit timing variations (TTVs; Wang et al., 2017), revealing that some of the TRAPPIST- 1 planets may have bulk densities comparable to that of water. Now in the era of TESS the

sample of terrestrial exoplanets orbiting small (< 0.3 R ), nearby (< 15 pc) stars is growing, with LHS 3844b and LTT 1445Ab added recently (Vanderspek et al., 2019; Winters et al., 2019). Though the presence of these terrestrial planets provides a tantalizing opportunity for atmospheric follow-up, the most we are able to do with current instrumentation is rule out the lowest mean molecular weight atmospheres dominated by hydrogen and

66 3.1. Introduction

helium, which conﬁrms the aforementioned work on Kepler planets with radii < 10 R⊕. So far cloud-free low mean molecular weight atmospheres are ruled out for TRAPPIST- 1b,c,d,e,f and for GJ 1132b (de Wit et al., 2016; de Wit et al., 2018; Diamond-Lowe et al., 2018). With the goal of eventually detecting atmospheric biomarkers on habitable zone worlds, we designed a project to characterize the atmosphere of LHS 1140b (Dittmann et al., 2017b), a habitable zone terrestrial exoplanet orbiting a nearby mid-M dwarf. Since the planet’s discovery, and our subsequent observing program, Data Release 2 of the Gaia mission (Gaia Collaboration et al., 2016; Gaia Collaboration et al., 2018) moved LHS 1140 farther away than was initially though, to its current distance of 14.993 ± 0.015 pc. This means that the stellar radius of LHS 1140 is larger than initially thought, which in turn increases the derived planet radius. With this new information, we ﬁnd that LHS 1140b has a radius of 1.727 ± 0.032 R⊕ and a mass of 6.98 ± 0.89 M⊕, making its density of 7.5 ± 1.0 g/cm3 consistent with a terrestrial composition (Ment et al., 2019). The planet’s

2 surface gravity is 23.7 ± 2.7 m/s with an estimated effective temperature (Te f f = 235 ± 5 K), assuming an albedo of zero. The atmospheric scale height of a planet is directly proportional to the planet’s temperature, and inversely proportional to its surface gravity. In the case of LHS 1140b, its atmospheric scale height, and therefore the amplitudes of its atmospheric features, are below what it detectable with our observations. We note that when we began this project, we assumed a lower surface gravity for the planet. This came about because the initial mass and radius estimates of LHS 1140b gave a bulk density consistent a composition of more than 50% iron, which is implausible and in stark deﬁance of conventional planetary formation scenarios (Zeng, Sasselov, and Jacob- sen, 2016; Dittmann et al., 2017b). As such, it seemed likely that the mass of LHS 1140b

67 Chapter 3. LHS 1140b would be refined and lowered in a subsequent season of radial velocity measurements (Figure 2 of Morley et al. (2017) provides an illustration of this thinking). At the start of this project we adopted values for the stellar distance and planet radius from Dittmann et al. (2017b). In predicting the atmospheric signal we assumed a terrestrial core-mass fraction, which implied a surface gravity of 17.5 m/s2. With Gaia DR2 it became apparent that the initial measured mass of LHS 1140b was actually correct, and it was the initial radius measurement which was wrong. The revised parameters imply a terrestrial composition, and yield a surface gravity of 23.7 m/s2. While many parallaxes of nearby stars were refined by the Gaia mission, LHS 1140 was a particularly pathological case due to how sparse its field is. For a relatively bright star like LHS 1140, pre-Gaia parallaxes are generally reliable, but if there are too few additional stars in the observing field against which to compare the position, the derived distance is unreliable. Despite the difficulty involved in detecting the atmosphere of LHS 1140b, it is one of the few terrestrial planets orbiting a nearby M star for which liquid water could potentially exist on the planet surface. However, equilibrium temperature is not the sole determinant for habitability. M stars like LHS 1140 spend more time in the pre-main sequence phase than G stars like the Sun before settling onto the main sequence branch (Baraffe et al., 2002; Baraffe et al., 2015). This means that M stars have longer periods of high energy activity which can strip the atmospheres of the planets orbiting them (Luger and Barnes, 2015). However, some high-energy flux, particularly in the near-ultraviolet (NUV), may be necessary to jump-start life (Ranjan, Wordsworth, and Sasselov, 2017). Spinelli et al. (2019) use the UV and X-ray capabilities of the space-based Swift observatory to investigate the high-energy nature of LHS 1140. They find that while LHS 1140 exhibits low levels of UV activity, its relatively high ratio of far-ultraviolet (FUV) to NUV

68 3.2. Observations

ﬂux could produce O2 and H2O abiotically through the dissociation of CO2. The low amounts of NUV received by LHS 1140b (2% the amount that Earth receives) may not provide enough of a spark for abiogenesis. However, these current measurements of LHS 1140 do not represent its past levels of UV radiation. Detecting the atmosphere around LHS 1140b would provide a clue to past behavior of LHS 1140, and vice versa. In this work, we are not ultimately able to investigate the atmosphere of LHS 1140b, illustrating the need for more observationally accessible habitable-zone terrestrial planet targets. LHS 1140b has an orbital period of 24.736959 ± 0.000080 days and a transit duration of 2.1 hours (Ment et al., 2019), making transits of this object rare and difﬁcult to observe due to the 6 hours of observing time necessary to capture both the transit and adequate baseline on either side from which to measure the depth. Spitzer observed transits of LHS 1140b in its 4.5 µm broadband photometric bandpass (DDT Program 13174, PI Dittmann; Ment et al., 2019, Dittmann, et. al., in prep); this infrared point complements the optical observations we undertake here. In this paper we present our observing program in Section 3.2. We detail our data extraction process, along with an illustrative diagram in Section 3.3. We then detail the analysis of our extracted spectra in Section 3.4. The results of this work, along with a discussion of their implications, are presented in Section 3.5, followed by our conclusions in Section 3.6.

3.2 Observations

Given the period (24.7 days) and transit duration (2.1 hours) of LHS 1140b, opportunities to observe a complete transit of this object from Las Campanas Observatory in Chile,

69 Chapter 3. LHS 1140b

where we could also capture data before and after transit, were rare. However the 2-hour transit duration offers the advantage that a single transit observation yields a high signal- to-noise measurement of the transit depth. In 2017 and 2018, there was one opportunity per year to observe a complete transit of LHS 1140b, along with baseline before and after transit. We were awarded two nights on the Magellan I (Baade) and Magellan II (Clay) telescopes through the Center for Astrophysics | Harvard & Smithsonian (PI Diamond-Lowe) to simultaneously observe the 2017 and 2018 transits of LHS 1140b with both telescopes. We used the IMACS (Dressler et al., 2011) and LDSS3C (Stevenson et al., 2016) multi- object spectrographs on Baade and Clay, respectively, to observe the transit across the optical and near infrared spectrum. We were able to capture both transits, yielding a total of four data sets (two with IMACS and two with LDSS3C) for our project. The details of these observations are presented in Table 3.1.

70 3.2. Observations 3.1: Observations with Magellan I (Baade) & Magellan II (Clay) ABLE T Data Set Date Exp. Time Duty Cycle Number of Minimum Seeing IMACS 2018 2018-11-02, 00:34:47 – 07:15:41 15 32.3 508 1.029 0.50 LDSS3C 2017 2017-10-27,LDSS3C 00:28:15 2018 – 07:14:14 2018-11-02, 01:10:51 – 07:11:45 15 15 46.9 46.9 766 686 1.029 1.029 0.80 0.40 IMACS 2017* 2017-10-27, 00:37:10 – 07:09:02 15 32.3 510 1.029 0.60 * Due to instrument systematics discussed in Section 3.3.2 , we do no include this data set in the analysis. (Instrument, Year) (UTC) (s) (%) Exposures Airmass (arcsec)

71 Chapter 3. LHS 1140b

When designing these observations we wanted to keep as many aspects in common as possible between the LDSS3C and IMACS instruments so as to minimize the systematic differences between the two. The field of view of LDSS3C is 8.30, while the f/2 camera on IMACS has a field of view of 300. The field of LHS 1140 is relatively sparse. Fortunately, there is a comparison star, 2MASS J00450309-1518437, located 145.3400 away (Figure 3.1, Table 3.2). This main-sequence G-type star is non-variable in the MEarth photometry down to the 1 mmag level (Jonathan Irwin, priv. comm.), and is brighter than LHS 1140. To compare, T = 11.2991 for LHS 1140, while T = 10.5629 for the comparison star, where T stands for TESS magnitude (Stassun et al., 2019). Because the comparison star is brighter, we are limited by the photon noise of LHS 1140, not the comparison. To get the same wavelength coverage for LHS 1140 and the comparison star, we ide- ally want to orient our mask such that the two stars are aligned in the cross-dispersion (spatial) direction. However, there is a background star that was 16.500 away from LHS 1140 during the observations. Lining up LHS 1140 with the comparison star would have placed this background star within a few arcseconds of the edge of the slit. To ensure that this background star did not contaminate the LHS 1140 spectrum by peaking in and out of the slit during observations, we oriented the LDSS3C and IMACS masks such that the spectra of LHS 1140 and the background star are dispersed parallel to each other, with the comparison star almost aligned in the cross-dispersion direction (Figure 3.1). Because LHS 1140 is a high proper motion star it will be necessary to re-check its position with respect to any background stars in future observations.

72 3.2. Observations

LDSS3C mask

LHS 1140

Comparison LDSS3C detector

Cross-Dispersion Direction Cross-Dispersion

IMACS mask IMACS detector

Dispersion Direction

FIGURE 3.1: On sky projection of the LHS 1140 field from the Digitized Sky Survey (DSS), which is available in SAOImageDS9 (Joye and Mandel, 2003). The solid grey circle and square outlines are the mask and detector footprint, respectively, of the IMACS instrument. The dashed grey circle and rectangle outlines are the mask and detector footprint, respectively, of the LDSS3C instrument. Light blue rectangles are the IMACS science slits; the LHS 1140 and comparison star 2MASS J00450309-1518437 slits are marked. LHS 1140 is a high proper motion star. The yellow circle in the LHS 1140 slit shows the position of LHS 1140 at the time of the 2018 observations (Ta- ble 3.1). We observe four other comparison stars with IMACS but do not use them in the analysis in order to minimize the difference between the IMACS and LDSS3C observations. Orange squares indicate the IMACS alignment holes. There is at least 5000 separation in the cross-dispersion direction between the IMACS alignment holes and the science slits in case we needed to model out-of-slit flux (see Section 3.4). For LDSS3C, the sizes of the LHS 1140 and comparison star slits are slightly shorter in the cross-dispersion direction than shown (see text, Section 3.2.2). For clarity, we do not show the alignment star holes for LDSS3C. The grey-filled strip on the LDSS3C detector indicates a region of bad pixels where slits should not be placed.

73 Chapter 3. LHS 1140b

TABLE 3.2: Stars used in this work

Target Comparison Name LHS 1140 2MASS J00450309-1518437 RA 00:44:59.33 00:45:03.09 Dec -15:16:17.54 -15:18:43.87 V mag 14.15 11.01 T mag* 11.2219 10.5629 J mag 9.612 9.975 Spectral type M4.5 G3 *The TESS bandpass ranges from 600 - 1000 nm, which is the range over which our observations are made with Magellan Baade/IMACS and Magellan Clay/LDSS3C.

3.2.1 Magellan I (Baade) IMACS Observations

The Inamori-Magellan Areal Camera & Spectrograph (IMACS) can perform both imaging and spectroscopy. Its detector is made up of eight CCDs which produce an 8192×8192 pixel mosaic, or 27.50 × 27.50 (IMACS User Manual). We use the f/2 camera, which has a 300 field-of-view diameter. With this field-of-view we are able to capture five comparison stars, but we only use 2MASS J00450309-1518437 (Table 3.2) in the analysis in order to be consistent with the LDSS3C observations. Between the 2017 and 2018 observations we discovered large instrument systematics that led us to redesign our 2018 mask. These systematics and potential solutions are discussed in detail in Section 3.3.2, but we present this new mask in Figure 3.1. The key improvements to the 2018 mask are 1) slits that are 7000 long in the cross-dispersion direction in order to estimate the sky background outside of the extended point-spread- function of the stellar spectra, and 2) ensuring that the area on either side (in the cross- dispersion direction) of the slits has no alignment holes in case we need to model and remove out-of-slit flux. The slit widths in the dispersion direction are 1000 to avoid light

74 3.2. Observations losses. We recommend that future users of IMACS for similar observations adopt these features when designing their masks. We also cut a calibration mask which is identical to the science mask except with slit widths in the dispersion direction of 0.500. For our detector settings we use 2×2 binning and a Fast readout speed. These settings allow for a readout time of 31.4 seconds, making the duty cycle for these observations 32.3%. Gains and readout noise levels for each of the eight IMACS chips can be found in the IMACS user manual. During the afternoon prior to observations we use the science mask to take biases, darks, and quartz flats, and we use the 0.500-slit calibration mask to take helium, neon, and argon arcs. During nighttime observations, we take a non-dispersed reference image of the LHS 1140 field with the science mask before and after the science observations. After the nighttime observations we take another set of biases and darks. The 16-bit analog-to-digital converter (ADC) has a saturation limit of 65,535 analog-to-digital units (ADUs), which we do not surpass for all pixels used in the data analysis. We note that with IMACS, the overscan region is sufficient for bias-level subtraction and dark current adds only a few e−/hour. While biases and darks do not greatly affect our data reduction, taking enough flats is crucial. We were careful to collect at least as many photons in our quartz flats as we do in-transit photons of LHS 1140 in order to not be noise-limited by the flats. For all observations requiring a disperser (i.e., flats, arcs, and science spectra), we use the Gri-300-26.7 grism (300 lines/mm with a blaze angle of 26.7◦). This grism has a wavelength range of 500-900 nm and a central wavelength of 800 nm. This gives a dispersion of 0.125 nm/pixel. With this grism we use the WBP 5694-9819 order blocking filter to mitigate any blue light that could cause second-order contamination in our spectra.

75 Chapter 3. LHS 1140b

3.2.2 Magellan II (Clay) LSDD3C Observations

The Low Dispersion Survey Spectrograph (LDSS3C) has gone through several upgrades to make it more sensitive at redder wavelengths. The instrument has a single CCD detector made up of 2048×4096 pixels or 6.40 × 130 (LDSS3C User Manual). The 8.30 diameter field of view radius of LDSS3C means that 2MASS J00450309-1518437 (Table 3.2) is the only comparison star we are able to observe simultaneously with LHS 1140. We cut our slits 1000 wide in the dispersion direction to avoid light losses as seeing and airmass change throughout the night. We cut the comparison star slit 2000 long in the cross- dispersion direction in order to capture enough photons to remove the sky background. We cut the LHS 1140 slit 3000 longer on one side to account for the background star near LHS 1140. We also cut a mask for wavelength calibrations, which is identical to the science mask except with slit widths of 0.500 in the dispersion direction. We present the alignment of our science mask on the sky in Figure 3.1. The LDSS3C detector suffers from some hot pixels, which can saturate and ruin a spectrum. We mark these pixels with a grey-filled rectangle over the LDSS3C detector. Our detector settings are as follows: 2×2 detector binning, Fast readout speed, and Low gain. We find that this allows for a 15.6 s readout time, bringing the duty cycle to 46.9%. Gains and readout noise can be found in the LDSS3C user manual. Note that the Low gain setting actually refers to the inverse gain, and therefore allows for longer exposure times than the High gain setting. The full well depth of the detector is 200,000 e−, with a linear pixel response up to 177,000 e− (Stevenson et al., 2016). Like IMACS, the 16-bit analog-to-digital converter (ADC) of LDSS3C has a saturation limit of 65,535 analog-to-digital units (ADUs), which we do not surpass for all pixels used in the data analysis.

76 3.3. Data Extraction

Using the science mask we take biases, darks, and quartz flats during the afternoon prior to observations. We also take helium, neon, and argon arcs using the 0.500 calibration mask. During nighttime observations, we take a non-dispersed reference image of the LHS 1140 field with the science mask before and after the science observations. After the nighttime observations we take another set of biases and darks. For all observations that require a disperser (i.e., flats, arcs, and science spectra) we use the VPH-Red grism which provides a wavelength coverage of 640-1040 nm (see Steven- son et al. (2016) for details). The VPH-Red grism has a high throughput at redder wavelengths where LHS 1140, an M-star, is brightest. We use the OG590 order-blocking filter to mitigate order contamination introduced to the spectra by the VPH-Red grism.

3.3 Data Extraction

In this section we discuss how we turn the raw IMACS and LDSS3C data—a time-series of FITS ﬁles containing 2D stellar spectra—into a time-series of 1D stellar spectra, for both LHS 1140 and the comparison star. This ﬁnal product of the extraction will be the starting point of the data analysis (Section 3.4), where we investigate the planet radius of LHS 1140b at different wavelengths. The process for extracting the IMACS and LDSS3C spectra of LHS 1140 and the comparison star is identical. We use the custom pipeline mosasaurus to perform the extraction. This pipeline has evolved from earlier versions (e.g., Diamond-Lowe et al., 2018) and is now generalized for IMACS and LDSS3C. Though still specialized, this code is modular and may be useful to others performing multi-object transmission spectroscopy of exoplanets.

77 Chapter 3. LHS 1140b

3.3.1 mosasaurus extraction steps

Turning raw images into a time-series of wavelength-calibrated 1D spectra is a long process. Here we outline the steps of our pipeline. A visual representation of the steps can be see in Figure 3.2.

1. Set-up We read in the FITS ﬁles we need for the extraction. These are the darks, biases, quartz ﬂats, arcs (helium, neon, and argon), undispersed reference images, and science images. Following the prescription of Eastman, Siverd, and Gaudi (2010), we convert the UTC time stamps recorded in the headers of these images into a

single BJDTDB time stamp marking the middle of the exposure.

2. Master images For each type of image we stitch the raw FITS ﬁles together to create a coherent image for each of the input ﬁles. For IMACS, this results in a 4096×4096 pixel image, and for LDSS3C, a 1024×2048 pixel image (recall that we used 2×2 binning on each instrument). In the process of stitching, we trim the bias overscan regions from each CCD chip (eight for IMACS, two for LDSS3C) and subtract their median in the cross-dispersion direction from the rest of the image. We then take an average of each image type to create the master images. We do this by comparing all of the images of a type and rejecting outliers that deviate by 5× the median absolute deviation (MAD), and then taking the mean of the images. We refer to this rejection of outliers and averaging of the images as “stacking.” Depending on the image type, we perform extra calibrations:

(a) Biases We simply stitch and stack all bias images to make the master bias image.

(b) Darks We stitch each dark image, and then subtract the master bias. Then, we stack the dark images to create the master dark image.

78 3.3. Data Extraction

Step 1: Set-up Step 2: Master reference image Step 3: Extraction rectangle, LHS 1140 Read in FITS files:

Darks Flats LHS 1140 Biases LHS 1140 dispersed Arcs Reference images Comparison Science images Comparison dispersed

Step 6a,b: Estimated sky background with stellar extraction region Step 5: Normalized flat Step 4: Spectrum & sky background

Step 7: Rough wavelength calibration

Step 6c: Extracted spectrum Step 8: Fine wavelength calibration (Final extracted spectra)

Step 7: Rough wavelength calibration

FIGURE 3.2: Steps of the extraction process performed with the custom mosasaurus pipeline. For a full description of each step, see Section 3.3.1. These data products are from the 2018 LDSS3C data set.

79 Chapter 3. LHS 1140b

(c) Flats, arcs, reference images, science images In the process of stitching these files together, we multiply each CCD chip by the appropriate gain listed in the IMACS and LDSS3C user manuals. After stitching, we subtract the master bias and master dark from each image, and then stack each image type to create the master flat, arc, reference, and science images. In Figure 3.2 we show a master reference image, with red ×’s marking LHS 1140 and the comparison star in their slits. From the master flat we also create a bad pixel mask.

3. Extraction rectangles Using an interactive plotting tool developed for mosasaurus, we indicate which stars on the master reference image we wish to extract. mosasaurus then cuts out a rectangle around each of the desired spectra on the master science image, and a corresponding rectangle from the master ﬂat and arc. The extraction rectangle for LHS 1140 spectrum is shown in red in Figure 3.2.

4. Stellar spectra and sky-background Using the rectangle cut from the master science image, we use an interactive plotting tool to indicate the spectral traces of LHS 1140 (purple line, Figure 3.2) and the comparison star. An extraction region is defined as a set number of pixels away from the center of the stellar trace (purple band). We also indicate portions of sky-background on either side of the spectral trace (light blue bands). These are used to fit and remove the sky-background flux from the stellar flux during extraction.

5. Normalized flat for each star We use the extraction rectangles cut from the master flat to create a normalized flat for each star (flat for LHS 1140 shown in Fig- ure 3.2). The normalized flat is made by dividing each column of pixels in the cross-dispersion direction by the median value of that column. When making the

80 3.3. Data Extraction

median filter we only use portions of the flat extraction rectangle that correspond to pixels that are included in the spectral extraction, i.e., the stellar extraction region, the sky-background regions, and any intervening regions. We divide the extraction rectangles for each science exposure by the corresponding normalized flat.

6. Extract spectra We cycle through the science exposures and extract spectra of LHS 1140 and the comparison star in the following steps:

(a) Sky background For each column of pixels in the cross-dispersion direction of an extraction rectangle we use the sky-background regions (designated in Step 4) to make a 2nd-order polynomial ﬁt to the pixel column. This makes a 2D, polynomial-smoothed estimate of the sky background in the extraction rectangles of each exposure (Figure 3.2). We note that a median of the sky-background pixels can also be used, with similar results.

(b) Sky in stellar extraction region We take the portion of the 2D sky background that covers the stellar extraction region designated in Step 4 (purple) and sum in the cross-dispersion direction, creating a 1D estimate of the sky background (light blue spectrum in Figure 3.2).

(c) Extracted spectrum We divide the extraction rectangle (Step 4) by the normalized ﬂat (Step 5) and sum the stellar extraction region in the cross-dispersion direction (purple spectrum in Figure 3.2). We then subtract the 1D sky background estimate (blue spectrum) to get the extracted spectrum (red spectrum).

7. Rough wavelength calibration We need to create a wavelength solution to convert the extracted spectra from ﬂux vs. pixel to ﬂux vs. wavelength. Using another interactive plotting tool, we take the arc extraction rectangles for each star and mark the

81 Chapter 3. LHS 1140b

helium, neon, and argon lines. We then compare where our marked wavelengths are in pixel space to a template of lines for the grisms we used with the LDSS3C and IMACS detectors. We fit the marked arc lines to the template lines using Legendre polynomials, and apply this wavelength solution to each of the extracted spectra. Finally, we re-sample each spectrum so that they are on a common, uniform wavelength grid; we ensure that flux is conserved in this process. We enforce flux conser- vation by performing the interpolation on the cumulative distribution function of the flux, thereby ensuring that an integration of the flux over any wavelength range returns the same value as it would had we not re-sampled the spectrum. The result works reasonably well, but there are visible mismatches in spectral features between LHS 1140 and the comparison star, and also between exposures taken at different times throughout the night (zoomed-in inset, Figure 3.2). This rough wavelength calibration aligns the spectra to within 0.5 nm for IMACS spectra, and 1.0 nm for LDSS3C spectra (0.2 and 0.4 pixels, respectively). We will eventually bin these spectra into 20 nm wavelength bins, and this slight misalignment can introduce additional noise.

8. Fine wavelength calibration For a single spectrum we isolate prominent telluric

and stellar spectral features—the O2 doublet (760.5 nm), the Ca triplet (849.8, 854.2, and 866.2 nm), and the water line forest (930-980 nm)—and cross-correlate them with the same features in all other spectra in a data set. Our stars are close enough (in the Sun’s local moving group) and our spectral resolution low enough (upper limits of 250 km/s/pixel for IMACS and 165 km/s/pixel for LDSS3C) that com-

paring telluric O2 and H2O features to stellar Ca features is not introducing errors

82 3.3. Data Extraction

in to our wavelength calibration. After the cross-correlation, we re-run the ﬂux- conserving re-sampling routine to reﬂect the new wavelength grid for each spectrum. With this technique we align our spectra to within 0.25 nm (or 0.10 pixels; zoomed-in inset, Figure 3.2). We use multiple data sets for this work so we also wavelength calibrate between the data sets.

We note that one improvement to our pipeline would be to change the extraction region around the stellar spectra such that it evolves over the time-series. This would entail re-tracing the stellar spectra in every exposure (Jordán et al., 2013; Rackham et al., 2017; May et al., 2018) or utilizing an optimal extraction routine (Stevenson et al., 2016; Bixel et al., 2019). Systematics introduced by using a ﬁxed aperture are decorrelated against during analysis (Section 3.4), and do not alter the results of this work.

3.3.2 Issues with Magellan I (Baade) IMACS data

The 2017 IMACS data set exhibited anomalies that led us to perform a deep exploration of this data set, and ultimately decide not to include it in our analysis. The ACCESS collaboration (Lopez-Morales et al., 2014) noticed similar systematics, which are thoroughly outlined in Espinoza (2017)1. We find that the source of these anomalies is an excess of light scattered by the IMACS instrument that occurs when the disperser is in place (Chapter 3, Espinoza, 2017). Fig- ure 3.3 shows that this excess light adds non-negligible flux in portions of the detector which should be masked. We call this excess flux, unimaginatively, “mask flux.” We also see an excess of flux in the wings the stellar profile in the cross-dispersion direction. In Figure 3.3 we show the extraction rectangle of the comparison star from the 2017 IMACS

1repositorio.uc.cl/handle/11534/21313

83 Chapter 3. LHS 1140b

Alignment Excess star profile flux

Mask Mask flux flux (comparison star) 2017 IMACS extraction

No excess

No alignment profile flux star

No mask flux (comparison star) 2018 IMACS extraction

FIGURE 3.3: Right: Comparison star extraction rectangles for exposures from the 2017 and 2018 IMACS and data sets (similar to Step 4 for in Section 3.3.1), as well as a cut in the cross-dispersion direction (white dashed line). Exposure times are 15 seconds for both observations. Left: Cut of flux profiles in the cross-dispersion direction. The 2017 IMACS profile exhibits excess “mask flux”, as well as excess flux in the wings of the stellar profile. Light blue and purple bands correspond to the bands in the extraction rectangles; they indicate which points in the profile are used to estimate the sky background (light blue) and which points are summed to extract the stellar spectrum (light purple). data set, as well as a cut across the extraction rectangle in the cross-dispersion direction, to demonstrate the excess flux that we see. We compare these to the same figures for the 2018 IMACS data set, which does not exhibit excess flux. Espinoza (2017) outlines a process to model and remove the mask flux. We were able to remove the mask flux from the comparison star spectra, however due to the alignment star holes near the LHS 1140 slits and the closeness of LHS 1140 to the edge of the slit, the flux profile in the cross-dispersion direction is difficult to model for this star. We therefore

84 3.4. Data Analysis

do not include the 2017 IMACS data set in our analysis. For the 2018 IMACS data set we made significant changes to our mask (see Sec- tion 3.2.1) to ensure that we captured the full PSF of LHS 1140 and the comparison star, and were able to model and remove the mask flux. The 2018 observations occurred on a dark night (no moon) and we did not see the same excess mask flux in these data. The extra-long slits in the cross-dispersion direction did help us to capture the full PSF of LHS 1140 and the comparison star, along with enough sky background to do the extraction.

3.4 Data Analysis

In Section 3.3 we turned the raw FITS ﬁles that we collected during our observations into time-series of 1D wavelength-calibrated spectra of LHS 1140 and the comparison star. These time-series spectra exhibit two types of systematic trends which we address before constructing a transmission spectrum: 1) instrument systematics from the Magellan telescopes and the IMACS and LDSS3C spectrographs, and 2) telluric systematics from Earth’s atmosphere, which we peer through as we observe. So as to not tamper with the transit information buried in the time-series, we model the systematics at the same time as we model the transit properties of LHS 1140b. We ultimately want to simultaneously analyze the spectra from each data set in order to construct the transmission spectrum. We built a custom data analysis pipeline that picks up where mosasaurus left off. The pipeline, named decorrasaurus2, is built to take in IMACS and LDSS3C data cubes from mosasaurus and return systematic-removed light curves that can be turned into transmission spectra. The decorrasaurus pipeline supports two methods of treating these effects

2This pipeline is the new-and-improved cousin of the detrendersaurus pipeline, which is no longer used.

85 Chapter 3. LHS 1140b in the light curves: 1) with a linear ﬁt, and 2) with a Gaussian process (GP) regression. Where the methods differ in the analysis, we split the steps into a part A and a part B, respectively.

3.4.1 decorrasaurus decorrelation steps

Turning time-series of wavelength-calibrated 1D spectra into decorrelated light curves and a transmission spectrum is also a lengthy process. Here we outline the steps of our pipeline.

1. Set-up We read in the mosasaurus data cubes that we wish to analyze. decorrasaurus can work with a single data set, or multiple data sets simultaneously if parameters are to be jointly fit across multiple data sets. We also specify which parameters should be fixed or varied and how to bin the light curves in wavelength-space. At this stage we specify which transit parameters and which systematic parameters we will fit. The input vectors, associated with the systematic parameters, are normalized by subtracting the mean and dividing by the standard deviation for each vector.

2. Make light curves Here we transform a time-series of wavelength-calibrated 1D spectra of LHS 1140 and the comparison star into a time-series of normalized ﬂuxes, or a light curve. This requires summing up each of the spectra in a given wavelength bin. We chop the spectra in wavelength space (recall that all spectra were interpo- lated onto a common wavelength grid in Step 8 of Section 3.3.1) in order to make the wavelength bins. If necessary, we take fractions of pixels in order to meet the chosen wavelength cut-offs. We normalize each wavelength-binned time-series of ﬂuxes by

86 3.4. Data Analysis

the median ﬂux for that time-series. We then divide the LHS 1140 time-series by the comparison star time-series to make the light curve.

3A. Model the data: linear The linear model assumes that the noise in the light curves is Gaussian. We construct a model to the data that has two components:

(a) Systematics The systematics component of the model S(t) is comprised of a Legendre polynomial speciﬁed during set-up and the input vectors recorded from the data extraction. Table 3.3 lists the input vectors used in the systematics model, along with explanations. In the linear model, we decorrelate the light curves against these input vectors. This model component can be described as:

Npoly Mphys ∗ S(t) = 1 + ∑ cnPn−1(t) + ∑ cmRm(t, λ) (3.1) n=1 m=1

where t is the time-array covered by the light curve, Pn−1 are the set of Leg- ∗ endre polynomials, Rm(t, λ) are the input vectors derived from the extraction (they are all functions of time t but some also have a wavelength λ depen-

dency), and cn, cm are the coefﬁcients we ﬁt for.

(b) Transit The transit component of the model T (t) is made with the batman package (Kreidberg, 2015). Table 3.4 explains which transit parameters we ﬁx or vary for each ﬁt we perform.

The complete model M(t) that we ﬁt to the light curve is:

M(t) = S(t)T (t) (3.2)

87 Chapter 3. LHS 1140b

In steps 5 & 6 we fit for the systematics coefficients and the transit parameters simultaneously to achieve the best fit to the light curve data.

3B. Model the data: GP Using the open-source package george (Foreman-Mackey, 2015), we implement a Gaussian process regression to model the data. Now, we assume that noise in the data can be correlated as well as Gaussian. Again, there are two components that go into the model:

(a) Noise Following a long line of work using a Gaussian process regression to model light curves (e.g., Gibson et al., 2012; Gibson, 2014; Evans et al., 2017; Kirk et al., 2019), we use a covariance function, or kernel, to model the data. We do this by computing the covariance matrix using the input vectors. Here, we do not directly decorrelate the light curves against the input vectors. Rather, we use these vectors to construct a covariance matrix that is used to predict the noise in the light curves. We use a Matérn 3/2 kernel of the form

r r ! 2 r2 − 3 r k(r2) = A2 1 + 3 e L2 (3.3) L2

where A2 is the amplitude, L is the length scale, and r is the distance between two points in the light curve. In practice, the amplitude A2 multiplies a sum- mation of Matérn 3/2 kernels, each of which corresponds to a input vector. A2 itself is a constant kernel in the george framework. We set the length scale L as the hyperparameter of each kernel, which describes how correlated the light curve points are, given the input vector. The hyperparameter of a kernel has a physical meaning in that it determines how close points in the input vectors have to be in order to be correlated with each other. If the length scale is too

88 3.4. Data Analysis

small, the Gaussian process will try to ﬁt every single point, thereby over-ﬁtting the data. We choose to use Matérn 3/2 kernels with the assumption that in the light curves, points closer together in time are more likely to be correlated than those farther away. In this regard the functional form of a Matérn 3/2 kernel is similar to that of a squared exponential kernel. We also include a white noise component, which is an optional input in the george implementation of the Gaussian process, and is an additive parameter that accounts for the Gaussian and independent nature of the uncertainties associated with counting photons.

(b) Transit As in the linear method, we use the batman package (Kreidberg, 2015) to construct the transit. Table 3.4 explains which transit parameters we fix or vary for each final fit we perform. This transit model is set as the mean, around which the data deviates, in the george Gaussian process object.

In step 5B we fit for the kernel hyperparameters but keep the transit parameters (the mean of the GP) fixed. In Step 6B we fit for the kernel hyperparameters and the transit parameters simultaneously to achieve the best fit to the light curve data.

4. Limb-darkening coefﬁcients The parameters that describe the opacity at the stellar limb are crucial for constructing an accurate transit model. Following the conclusions of Espinoza and Jordán (2016) regarding the optimal limb-darkening model

for stars with effective temperatures Te f f < 4000 K, we employ a logarithmic limb- darkening law, which is supported by batman. We use the Limb Darkening ToolKit (LDTk; Parviainen and Aigrain, 2015) to interpolate stellar models from the PHOENIX library (Husser et al., 2013) and calculate the logarithmic limb-darkening coefﬁ- cients for the wavelength range of interest. (The ldtk package does not include

89 Chapter 3. LHS 1140b

the logarithmic law but it is simple to add additional laws to the package; it is the interpolation of the stellar models that is important.) In order to decorrelate

the limb-darkening coefﬁcients, we re-parameterize l0 and l1 returned by LDTk to 2 q0 = (1 − l1) and q1 = (1 − l0)/(1 − l1) (Equations 2-5, Espinoza and Jordán, 2016). With this re-parameterization we can sample the space of physically plausible loga-

rithmic limb-darkening coefﬁcients by sampling q0 and q1 uniformly between (0, 1) when we do a full sampling of the parameter space in Step 6. This is the most conservative choice we could make for the priors when ﬁtting for the limb-darkening

parameters, and likely degraded our precision on Rp/Rs.

5A. Simple minimization: Linear We perform three iterations of a Levenberg-Marquardt least-squares ﬁtting routine using the lmfit package (Newville et al., 2016). The advantage of this ﬁt is that it is fast, which means we can test different systematic parameters and choose the best ones to marginalize over.

(a) Iteration 1 We use the calculated photon noise for each data set to weight the residuals in the least-squares minimization.

(b) Iteration 2 We clip any points that are 5× the median absolute deviation of the residuals. We again use the calculated photon noise to weight the residuals.

(c) Iteration 3 We calculate the standard deviation of the residuals for each data set in the ﬁt. We use this calculated error to weight the residuals in the least- squares minimization.

After the three iterations we use the best-ﬁt values to compare different models to each other, employing both the Bayesian Information Criterion (BIC; Schwarz, 1978) and the Akaike information criterion (AIC; Akaike, 1998), which penalize excessive

90 3.4. Data Analysis

model parameters. When we have found the best input vectors to decorrelated against (Table 3.3), we continue to the next step where we more fully sample the parameter space in order to estimate the uncertainties of the free parameters.

5B. Simple minimzation: GP We perform two iterations of a minimizing routine using scipy.optimize and the L-BFGS-B method, which allows for the computation of a gradient vector, as well as bounds on the input variables.

(a) Iteration 1 We construct the GP object using george. When pre-computing the GP object, it is necessary to provide uncertainties in the data. We use the calculated photon noise to create the GP object. We then compute the conditional predictive distribution of the GP model on the light curve. This does not yield an optimal ﬁt, but does allow us to clip any data points 5× the median absolute deviation of the residuals. We then perform the minimzation.

(b) Iteration 2 We calculate the standard deviation of the residuals for each data set and then re-construct the GP object using these calculated uncertainties to pre-compute the GP object. We then perform the minimization.

We do not allow the transit parameters to vary at this stage, making the minimization computationally efﬁcient. The hyperparameters we ﬁnd from this minimization are used as the starting values for the hyperparameters in the full exploration of the parameter space (Step 6). The task of which input vectors to include in computing the covariance matrix is left until Step 6.

6. Dynamic nested sampling To estimate the uncertainties in our free parameters we need to perform a more complete exploration of the parameter space. This has frequently been done with a Markov-Chain Monte Carlo algorithm, such as the one

91 Chapter 3. LHS 1140b

provided in the emcee package (Foreman-Mackey et al., 2013). Here we employ dynesty (Speagle, 2020), an open-source dynamic nested sampling routine. dynesty samples all parameters between (0, 1) and requires a prior transform function to translate these values in to the real parameters space. It is therefore necessary to provide priors for all parameters in the ﬁt.

6A. Dynamic nested sampling: linear We use the 1σ uncertainties derived from the Levenberg-Marquardt fits (Step 5A) to set the priors for dynesty. For all free parameters we use flat priors bounded at 10× the Levenberg-Marquardt uncertainties, except for the limb-darkening parameters where we use a Gaussian prior with the standard deviation equal to 1× the uncertainty calculated by LDTk (Step 4). We assume that our data is drawn from an uncorrelated Gaussian distribution, but we multiply the standard deviation σ by a scaling parameter s to account for excess noise that our model doesn’t capture (see Berta et al., 2012a, for a detailed explanation). Our modified log-likelihood function is:

1 lnL = Nlns − χ2 + constant (3.4) 2s2

where N d − m 2 χ2 = ∑ i i (3.5) i=0 σi where N is the number of data points, d is the data, and m is the model.

6B. Dynamic nested sampling: GP With dynesty we can sample both the posterior distribution and the Bayesian evidence, which we use for model comparison to determine the best input vectors to use to compute the covariance matrix (Table 3.3).

92 3.4. Data Analysis

For the transit parameters we set uniform priors. We ﬁt the amplitude, kernel hyperparameters, and the white noise with log-uniform priors. We set the priors as so:

(a) Amplitude The amplitude is described by a constant kernel which multiplies all of the kernels associated with the noise parameters. We set the lower and upper bounds as U(ln(0.01σ2), ln(100σ2))

where σ2 is the variance of the light curve.

(b) Kernel hyperparameters We ﬁt for the hyperparameter in each of the kernels associated with the input vectors. We set the lower and upper bounds as

U(ln(δd), ln(∆d))

where δd is the absolute value of the average difference between consecutive

points in the input vector and ∆d is 3× the total range of the input vector (i.e., the maximum value minus the minimum value). Recall that the input vectors were normalized in Step 1.

(c) White noise The white noise parameter accounts for the Poisson statistics associated with measuring stellar ﬂux. We set the lower and upper bounds of this additive parameter as

U(ln((250 ppm)2), ln((2500 ppm)2))

where some guess-and-check work went in to choosing this range such that it

93 Chapter 3. LHS 1140b

was broad enough to not bias the ﬁt, but narrow enough to explore the parameter space efﬁciently.

3.4.2 Two data analyses

In order to marginalize over the appropriate parameters, we build up to the transmission spectrum by first analyzing our data sets separately, and then analyzing them jointly. Each analysis involves constructing both a white light curve and a set of wavelength- binned light curves. Table 3.4 lists the transit parameters and whether they are free or fixed in each fit. The breakdown of the white light curves into wavelength-binned light curves (20 nm bins) is shown in Figure 3.4. For all analyses we assume a circular orbit for LHS 1140b.

94 3.4. Data Analysis

TABLE 3.3: Systematic model parameters

Decorrelation Use in data sets2,3 Parameter Decorrelation Parameter Definition f () 1 L17 I18 L18 Name A B A B A B time From the header files, the average time from t – X – X – X the start of the exposure to the end of the CCD read out for that exposure. airmass From the header files, the average airmass of t XX XX XX the field recorded at each exposure during observation. rotation angle From the header files, rotation angle of the in- t XX XX XX strument recorded at each exposure. This can be correlated with changes in illumination or flexure during observation. centroid Derived during extraction, the stellar cen- t, s troid measured in the cross-dispersion direction. This is the median of the centroids across all wavelengths for each star in each exposure. width Derived during extraction, the width of the t, s X X X spectral trace in the cross-dispersion direction. This is the median of the measured widths across all wavelengths for each star in each exposure. peak Derived during extraction, the brightness of t, s, λ X X the brightest pixel in the cross-dispersion direction measured at every wavelengths for each star in each exposure. This is summed in wavelength space for each wavelength bin. shift Derived during extraction, the linear change t, s X X X in the dispersion direction needed to align the spectra with each other. This is calculated for each star in each exposure. stretch Derived during extraction, the multiplicative t, s change in the dispersion direction needed to align the spectra with each other. This is calculated for each star in each exposure. polynomial Specified during analysis, the degree of t 3 – 2 – 3 – the Legendre polynomial component of the model. 1 Parameters can be functions of time t, star s, and wavelength λ 2 Data sets: L17 = LDSS3C 2017, I18 = IMACS 2018, L18 = LDSS3C 2018 3 Decorrelation method: A = linear, B = Gaussian process

95 Chapter 3. LHS 1140b

Data sets ﬁt independently

We ﬁrst treat our data sets independently. The main purpose of this step is to decide which input vectors should be used in the modeling of each light curve. Table 3.3 lists all possible input vectors along with an explanation of how they are constructed, and which are used in the analysis of each light curve in both the linear and GP modeling methods. We use the white light curves to determine the best input vectors to use for each data set. We use the same input vectors in the wavelength bins of a given data set as we do for the white light curve. We ultimately focus on the results from the GP method, and we provide the derived parameters from the simple minimization and full sampling of the parameter space (Steps 5B & 6B of Section 3.4.1), along with the priors for the white light curves. We use the same priors for the wavelength bins.

96 3.4. Data Analysis -binned L.C.s λ -binned L.C.s White L.C λ FreeFree Fixed Free Free Free, joined Free, joined Fixed White L.C. s R 0 t / p ∆ R 3.4: Transit model parameters used in final analyses 1] Free Free Free, joined Free, joined ABLE q T 0, q = parameter is fixed and the same for all data sets = parameter is allowed to vary, but must be the same for all data sets We assume a circular orbit for all fits; L.C. = light curve = parameter is fixed = parameter is allowed to vary Note. Free Fixed Free, joined Fixed, joined Parameter nameMid-transit time difference, Planet-to-star radius ratio, Limb-darkening, [ Data sets fit independently Data sets fit jointly

97 Chapter 3. LHS 1140b

7 LHS 1140 LHS 1140 LHS 1140 LDSS3C 2017 IMACS 2018 LDSS3C 2018 Comparison Comparison Comparison 6 LDSS3C 2017 IMACS 2018 LDSS3C 2018

5 4 e 1 / FIGURE 3.4: Representative spectra of LHS s

n 4 1140 (solid lines) and the comparison star o r t (dotted lines) from the three data sets we ana- c e l lyze in this work. Grey vertical lines indicate

e 3 o

t the 20 nm wavelength bins that we use to con- o

h struct the transmission spectrum. P 2

0 650 700 750 800 850 900 950 1000 Wavelength (nm)

Data sets ﬁt jointly

Once the input vectors associated with each data set are determined by analyzing them separately, we then use those input vectors to perform a joint fit across all three data sets. To construct this white light curve we only use those data that correspond to wavelengths common to all data sets. In the case of the LHS 1140b white light curve we use data from 610-950 nm, where all three data sets have measured fluxes (as can be seen in Figure 3.4. The raw, decorrelated, and time-binned white light curves are shown in Figure 3.5. We achieve an RMS of 145 ppm when binning the fitted joint white light curves to 3-minute time bins, and an RMS of 77 ppm when binning to 10-minute time bins. The parameters we use or derive from the joint white light curve fit are presented in Table 3.5, along with their priors. We note that it is not technically correct to assume the same limb-darkening values for

98 3.4. Data Analysis

TABLE 3.5: Transit and systematic model parameters for the jointly ﬁt white light curve, Gaussian process regression

Parameter name Initial value Fitted value Priors for Fitted value for Step 5 from Step 5 Steps 5 & 6 from Step 6 1 ∆t0, L17 (days) 0.0 — U(-0.005, 0.005) -0.0027 ± 0.00024 1 ∆t0, I18 (days) 0.0 — U(-0.005, 0.005) 0.0022 ± 0.00020 1 ∆t0, L18 (days) 0.0 — U(-0.005, 0.005) 0.0023 ± 0.00022 Rp/Rs 0.074 — U(0.055, 0.085) 0.073 ± 0.0023 q0 0.36 — U(0, 1) 0.47 ± 0.26 q1 0.39 — U(0, 1) 0.65 ± 0.13 +0.57 ln(amplitude), L17 -11.7 -15.7 U(-17.0, -7.0) −15.6−0.42 +0.78 ln(time), L17 2.05 2.05 U(-5.39, 2.34) −3.95−0.60 +0.39 ln(airmass), L17 2.25 2.53 U(-6.91, 2.54) 2.01−0.87 +0.48 ln(rotation angle), L17 1.76 -6.10 U(-6.10, 2.05) 1.40−1.1 +0.10 ln(white noise), L17 -15.2 -16.9 U(-16.6, -12.0) −16.5−0.053 +0.84 ln(amplitude), I18 11.8 -14.8 U(-17.1, -7.15) −12.6−0.82 +1.4 ln(time), I18 2.05 -3.53 U(-5.00, 2.34) 0.37−0.95 +0.26 ln(airmass), I18 2.22 2.51 U(-5.70, 2.51) 2.17−0.54 +0.36 ln(rotation angle), I18 1.80 2.09 U(-5.61, 2.09) 1.55−0.65 +0.059 ln(white noise), I18 -15.2 -15.1 U(-16.2, -11.3) −16.1−0.029 +0.87 ln(amplitude), L18 -11.8 -14.8 U(-17.1, -7.2) −11.3−1.2 +0.72 ln(time), L18 2.05 -3.87 U(-5.28, 2.34) 1.4−1.3 +0.62 ln(airmass), L18 2.19 0.80 U(-5.70, 2.47) 1.62−0.92 +0.46 ln(roataion angle), L18 1.88 2.17 U(-5.74, 2.17) 1.58−0.96 +0.11 ln(white noise), L18 -15.2 -16.9 U(-16.6, -11.0) −16.5−0.61

L17 = LDSS3C 2017; I18 = IMACS 2018; L18 = LDSS3C 2018 Note. The steps referenced in the columns refer to those in Section 3.4.1. For the purpose of this study, we assume a circular orbit for LHS 1140b. 1The measured transit midpoint time for each data set can be calculated as t0 = T0 + nP + ∆t0, where ephemeris T0 = 2456915.71154 ± 0.00004 days and period P = 24.736959 ± 0.000080 (Ment et al., 2019). For the LDSS3C 2017 data set n = 46 and for the IMACS and LDSS3C 2018 data sets n = 61.

99 Chapter 3. LHS 1140b

1.0125 LDSS3C 2017 IMACS 2018 LDSS3C 2018 1.0100

1.0075

1.0050

1.0025

1.0000

Normalized Flux FIGURE 3.5: Panel a: Raw white light curves 0.9975

0.9950 a from the three data sets used in this work. 1.002 Over-plotted grey lines are the ﬁtted models to each data set using the GP regression 1.000 method. Panel b: Light curves with the noise 0.998 component of the model divided out, leaving just the transit data and model. Panel c: All 0.996 of the data are combined, and binned into 3- Normalized Flux 0.994 b minute time bins. The transit model is sam-

0.992 pled at high cadence and smoothed with a 3- 1.002 minute box-car kernel. Panel d: Residuals of 1.000 Panel c. The RMS of the 3-minute time binned white light curve (Panel c) is 145 ppm; binning 0.998 down to 10 minutes gives an RMS of 77 ppm. 0.996 Data in all three data sets are summed from

Normalized Flux 610-950 nm, where the wavelength range in 0.994 c common to all three data sets. 0.992

250

250 d

Residuals (ppm) 200 100 0 100 200 Time from Mid-Transit (min) the LDSS3C and IMACS data sets, since these two instruments do not produce the same spectral energy distribution. However, this difference is not likely to affect the times of mid-transit derived from the white light curve fit, which is the only parameter we take from the white light curve fit and use in the wavelength-binned fits. The Ment et al. (2019) analysis included high cadence (2 second integrations) Spitzer data. We adopt the period P, inclination i, and semi-major axis a/Rs derived from that work as fixed parameters in the white light and wavelength-binned light curve analysis.

100 3.4. Data Analysis

We then bin the light curves into 20 nm bins. We analyze the three data sets jointly in each wavelength bin, but the wavelength bins are independently analyzed from each other. We fix the orbital parameters that are common to all wavelength bins to their fitted values or literature values. In Figure 6 we compare independently fit wavelength-binned transit depths to those that are jointly fit. We also compare Gaussian process versus linear fitting methods. It is apparent that the Gaussian process fit produces larger error bars, as it should, but also more scatter in transit depths. This could be due to the fact that we used a minimal number of input vectors in the GP fit in order to reduce computation time. In Figure 3.7 we graphically present the the final parameter values from the joint fit Gaussian process regression in each wavelength bin. We present the wavelength-binned data along with the best light curve fits from the GP regression in Figure 3.8. Tables 3.6

2 2 and 3.7 provide the measured values of Rp/Rs for the Gaussian process and linear fitting methods, as well as a further break down to the independently and jointly fit transit depths. We also provide the RMS of each set of transit depths in the table, as compared to the inverse-variance weighted mean of each transmission spectrum. At the end we provide light curve RMS for each wavelength bin in the GP joint fit, along with how close we were able to get to the photon noise limit in that bin. Across all 20 wavelength bins

2 2 we achieve an average uncertainty in Rp/Rs of 0.026% (260 ppm) and an average RMS value of 1.3× the photon noise.

101 Chapter 3. LHS 1140b ) % (

2 s 0.6 R / 2 p R

n o i

s 0.5 s e r g e r

s 0.4 s e c o r p

n 0.3 a i s s u a

G 0.2 LDSS3C 2017 IMACS 2018 LDSS3C 2018 Mean Joint GP fit

0.6 ) % (

2 0.5 s R / 2 p R

t i

F 0.4

r a e n i L 0.3

0.2 LDSS3C 2017 IMACS 2018 LDSS3C 2018 Mean Joint Linear fit

650 700 750 800 850 900 950 1000 Wavelength (nm)

FIGURE 3.6: Comparison of independent and jointly fit wavelength-binned transit depths, and of transit depths computed with a Gaussian process regression and a linear fit. Top: The independently fit transit depths from the LDSS3C 2017, IMACS 2018, and LDSS3C 2018 observations are presented, with the inverse-variance weighted mean of these values over-plotted in black. The jointly fit transit depths are presented in green. Error bars represent 1σ uncertainties in the transit depth. Vertical grey lines denote the limits of the wavelength bins, as in Figure 3.4. The transit depths are offset in the x-axis for clarity; the analyses were performed over the same wavelength ranges in the independent and joint fits. Bottom: Same as the top, but transit depths are derived using a linear fit. Transit depths for each transmission spectrum presented here are provided in Tables 3.6 and 3.7.

102 3.4. Data Analysis

0.5 (%) Depth 0.4

0.75

0 0.50 q

0.25

0.75 1

q 0.50

0.25 FIGURE 3.7: Results from the wavelength-

) 10 binned joint ﬁt using a Gaussian process re- e d

u gression. The radius ratio and scaled limb-

t 12 i l

p darkening coefﬁcients are shared across all

m 14

a three data sets, and so there is only one re- ( n l sulting value in each wavelength bin (green points with error bars). The rest of the param- )

s 2 s eters are ﬁt simultaneously, but separately for a

m 1 each data set (colors correspond to the same r i a

( data sets as in Figure 3.5). We do not see 0 n l any obvious correlations between any of the

2 parameters and the resulting measurement of n 2 2 o

i Rp/Rs . t

a 1 t o r angle) ( 0 n l

2 ) e

m 0 i t ( n

l 2

12 e t i h 14 w ( noise) n l

16 600 650 700 750 800 850 900 950 1000 Center of Wavelength Bin (nm)

103 Chapter 3. LHS 1140b

610-630 nm 1.000

630-650 nm

650-670 nm

0.975 670-690 nm

690-710 nm

710-730 nm 0.950

730-750 nm

750-770 nm

0.925 770-790 nm

790-810 nm

810-830 nm 0.900

830-850 nm Residuals (ppm)

Normalized Flux (+offset) 850-870 nm

0.875 870-890 nm

890-910 nm

910-930 nm 0.850

930-950 nm

950-970 nm

0.825 970-990 nm

5000 990-1010 nm 0

5000 200 100 0 100 200 Probability 0.800 Time from Mid-Transit (min) Density 200 100 0 100 200 Time from Mid-Transit (min)

FIGURE 3.8: Left Light curves in each 20 nm wavelength bin with noise components mod- eled with a GP regression, and removed. Right Residuals in each wavelength bin. The y-axes of each residual panel are the same, but for clarity we only label them in the bottom-most panel. We also show the residual histograms for each data set, compared to a Gaussian distribution (grey line) of the combined residuals from all three data sets. Because each of the three component data sets has a different Poisson noise, the three component Gaussians are not expected to be identical, and hence the single grey curve is simply meant to be representative of the average behavior. The colors of the points and histograms in this ﬁgure represent the three data sets, and follow the same color scheme as in Figure 3.5 104 3.5. Results & Discussion

3.5 Results & Discussion

From our observations we produce a transmission spectrum and compare it to models. In doing so we demonstrate the limits of the ground-based transmission spectroscopy technique employed here to investigate the atmosphere of LHS 1140b.

3.5.1 Planetary atmospheric detection

For the purposes of transmission spectroscopy, we are interested in the scale height H of a planet’s atmosphere, or how extended the atmosphere is, and what kinds of features it produces. The scale height is calculated by

k T H = B (3.6) µg where kB is the Boltzmann constant, T is the planet’s mean atmospheric temperature, µ is the mean molecular weight of the planet’s atmosphere, and g is the planet’s surface gravity. We do not know the mean temperature of LHS 1140b’s atmosphere, but because the transmission spectrum is an integration of light paths across multiple atmospheric layers, it is not sensitive to varying temperature gradients throughout the atmosphere (Kempton et al., 2017). We can therefore estimate a temperature-pressure proﬁle for the transmission spectrum using the planet’s equilibrium temperature. An estimate of the amplitude of features in the transmission spectrum of an atmosphere is given by

105 Chapter 3. LHS 1140b

2 2 TABLE 3.6: Best ﬁt Rp/Rs from linear regressions

Wavelength Linear Fit Transit Depths (%) (nm) L17 I18 L18 Joint 610-630 0.652 ± 0.035 0.505 ± 0.081 0.435 ± 0.042 0.502 ± 0.032 630-650 0.554 ± 0.023 0.442 ± 0.040 0.445 ± 0.029 0.485 ± 0.020 650-670 0.368 ± 0.020 0.470 ± 0.035 0.532 ± 0.028 0.520 ± 0.018 670-690 0.518 ± 0.037 0.486 ± 0.042 0.607 ± 0.033 0.512 ± 0.020 690-710 0.507 ± 0.028 0.483 ± 0.029 0.571 ± 0.023 0.528 ± 0.015 710-730 0.461 ± 0.031 0.499 ± 0.033 0.628 ± 0.029 0.526 ± 0.017 730-750 0.495 ± 0.022 0.498 ± 0.022 0.541 ± 0.023 0.510 ± 0.013 750-770 0.483 ± 0.023 0.487 ± 0.025 0.545 ± 0.020 0.520 ± 0.013 770-790 0.495 ± 0.023 0.483 ± 0.026 0.535 ± 0.021 0.502 ± 0.013 790-810 0.540 ± 0.023 0.499 ± 0.022 0.559 ± 0.020 0.529 ± 0.012 810-830 0.522 ± 0.020 0.518 ± 0.020 0.551 ± 0.017 0.535 ± 0.010 830-850 0.517 ± 0.021 0.463 ± 0.022 0.552 ± 0.018 0.520 ± 0.011 850-870 0.520 ± 0.021 0.496 ± 0.026 0.547 ± 0.020 0.530 ± 0.012 870-890 0.496 ± 0.019 0.492 ± 0.024 0.564 ± 0.019 0.520 ± 0.012 890-910 0.572 ± 0.022 0.543 ± 0.026 0.597 ± 0.019 0.572 ± 0.012 910-930 0.554 ± 0.019 0.536 ± 0.028 0.534 ± 0.017 0.544 ± 0.011 930-950 0.580 ± 0.022 0.453 ± 0.035 0.590 ± 0.021 0.548 ± 0.014 950-970 0.491 ± 0.021 — 0.508 ± 0.022 0.529 ± 0.016 970-990 0.502 ± 0.022 — 0.588 ± 0.022 0.531 ± 0.015 990-1010 0.548 ± 0.032 — 0.653 ± 0.031 0.547 ± 0.020 RMS (ppm) 540 257 513 186 1 Note In this table we present transit depths and uncertainties derived from the linear regression method. We present the transit depth of each data set individually, along with the joint ﬁts, in which the transit depths was a shared parameter between the three data sets. These values correspond to those in Figure 3.6. The last row provides the RMS of each column of transit depths, as compared to the inverse-variance weighted mean (i.e., a ﬂat line) of that column.

106 3.5. Results & Discussion

2 2 TABLE 3.7: Best ﬁt Rp/Rs from Gaussian process regressions

Wavelength GP Fit Transit Depths (%) RMS × Exp. (nm) L17 I18 L18 Joint (ppm) Noise 610-630 0.466 ± 0.073 0.536 ± 0.072 0.509 ± 0.076 0.511 ± 0.511 2659 1.51 630-650 0.311 ± 0.062 0.480 ± 0.095 0.533 ± 0.044 0.458 ± 0.458 1464 1.27 650-670 0.423 ± 0.054 0.517 ± 0.059 0.459 ± 0.072 0.464 ± 0.464 1217 1.23 670-690 0.398 ± 0.034 0.527 ± 0.069 0.431 ± 0.062 0.411 ± 0.411 1376 1.25 690-710 0.408 ± 0.037 0.500 ± 0.042 0.535 ± 0.048 0.480 ± 0.480 989 1.20 710-730 0.274 ± 0.056 0.528 ± 0.106 0.455 ± 0.100 0.392 ± 0.392 1210 1.40 730-750 0.387 ± 0.041 0.561 ± 0.053 0.470 ± 0.065 0.447 ± 0.447 849 1.36 750-770 0.443 ± 0.053 0.546 ± 0.054 0.531 ± 0.059 0.478 ± 0.478 894 1.36 770-790 0.296 ± 0.044 0.539 ± 0.061 0.524 ± 0.048 0.451 ± 0.451 887 1.36 790-810 0.430 ± 0.038 0.531 ± 0.060 0.537 ± 0.047 0.488 ± 0.488 823 1.40 810-830 0.470 ± 0.021 0.552 ± 0.033 0.535 ± 0.044 0.499 ± 0.499 710 1.23 830-850 0.453 ± 0.023 0.516 ± 0.034 0.524 ± 0.047 0.487 ± 0.487 760 1.29 850-870 0.454 ± 0.031 0.533 ± 0.037 0.552 ± 0.039 0.487 ± 0.487 783 1.30 870-890 0.446 ± 0.021 0.517 ± 0.039 0.558 ± 0.039 0.480 ± 0.480 771 1.31 890-910 0.493 ± 0.031 0.537 ± 0.045 0.532 ± 0.042 0.530 ± 0.530 836 1.35 910-930 0.521 ± 0.026 0.551 ± 0.038 0.550 ± 0.032 0.536 ± 0.536 808 1.26 930-950 0.564 ± 0.029 0.522 ± 0.055 0.578 ± 0.037 0.556 ± 0.556 1089 1.24 950-970 0.494 ± 0.036 0.522 ± 0.055 0.554 ± 0.040 0.515 ± 0.515 789 1.30 970-990 0.520 ± 0.027 0.522 ± 0.055 0.543 ± 0.053 0.511 ± 0.511 742 1.18 990-1010 0.481 ± 0.041 0.522 ± 0.055 0.553 ± 0.057 0.489 ± 0.489 972 1.24 RMS (ppm) 736 193 380 388 1 Note In this table we present transit depths and uncertainties derived from a Gaussian process regression. We present the transit depth of each data set individually, along with the joint fits, in which the transit depths was a shared parameter between the three data sets. These values correspond to those in Figure 3.6. The last row provides the RMS of each column of transit depths, as compared to the inverse-variance weighted mean (i.e., a flat line) of that column. The final two columns pertain to the joint GP fit (third-to-last-column) and provide the light curve RMS for each wavelength bin and compare this to the expected noise for that wavelength bin.

107 Chapter 3. LHS 1140b

2 2 Rp + NH Rp ∆δ = − R R s s (3.7) 2R NH ≈ p 2 Rs where N is the number of scale heights we can observe before the atmosphere becomes

2 2 optically thick (when optical depth τ ∼ 1). The last term (NH) /Rs is negligible.

3.5.2 Model transmission spectrum

The relative feature amplitudes of a planetary atmosphere observed over a range of wavelengths can be compared to models in order to reveal the presence of an atmosphere and its composition. We construct a model transmission spectrum for LHS 1140b using the open-source code Exo-Transmit (Miller-Ricci Kempton, Zahnle, and Fortney, 2012; Kempton et al., 2017). The code inputs are a temperature-pressure profile, an equation-of- state specific to the atmospheric composition, the 1-bar planet radius and surface gravity, and the stellar radius. Following the same procedures outlined in Miller-Ricci, Seager, and Sasselov, 2009 and Miller-Ricci and Fortney (2010), we use custom double-grey temperature-pressure profiles for the LHS 1140b atmosphere. (The default temperature-pressure profiles that come with Exo-Transmit are isothermal). The equation-of-state files corresponding to the atmospheres we test in this work are readily available in Exo-Transmit. Since we do not know the 1-bar planet radius exactly, we adjust it until the model transmission atmosphere best fits the data. This adjustment changes both the absolute depth of the model as well as the amplitude of the features.

108 3.5. Results & Discussion

3.5.3 Observed transmission spectrum

From the wavelength-binned jointly fitted Rp/Rs values, we construct a transmission spectrum. In Figure 3.9 we present the final transmission spectrum and compare it to model transmission spectra calculated for the LHS 1140b system using Exo-Transmit (Kempton et al., 2017). Given the small atmospheric features of the LHS 1140b atmosphere, we are not able to rule out even the lowest mean molecular weight cases. We therefore only present these cases – clear 1× and 10× solar metallicity atmospheres – and do not address models of higher mean molecular weight atmospheres. We do not expect a terrestrial planet like LHS 1140b to possess such light atmospheres (Rogers, 2015; Owen and Wu, 2013; Lopez and Fortney, 2013; Fulton et al., 2017; Van Eylen et al., 2018), but these end-member compositions are the first atmospheres to rule out. We note that the points in the range of 890-950 nm appear systematically high. Indeed, removing these three points from the GP joint fit transmission spectrum yields χ2 = 18 for the flat line fit, as opposed to χ2 = 41 when the three points are included. Between 890-950 nm is a forest of water lines. If there is water present in the photosphere of LHS 1140, which is possible given its effective temperature of 3216 ± 39 (Ment et al., 2019), then this could artificially deepen the transit depths in the water band.

3.5.4 Atmospheric detection limits

To explore the limits of our observed transmission spectrum we can perform simple calculations using Equations 3.6 and 3.7. LHS 1140b’s surface gravity (23.7 ± 2.7 m/s2) and cool equilibrium temperature (235 ± 5 K, assuming a Bond albedo of 0 and a planet-wide energy distribution; Ment et al., 2019) combine to make the scale height of this planet’s

109 Chapter 3. LHS 1140b

atmosphere 40.9 ± 4.7 km for the lowest mean molecular weight case (µ = 2) for the unrealistic, pure light H2 atmosphere.

For the LHS 1140 system where Rp = 1.727 ± 0.032 R⊕ and Rs = 0.2139 ± 0.0014 R , the amplitude of the transmission features for the lowest mean molecular weight case is 65.3 ± 7.7 ppm, assuming we can see down 1.6 scale heights. (We estimate N = 1.6 from the 20 nm wavelength-binned model transmission spectrum). This is a factor of four below the median precision we are able to achieve in this project. For a more realistic atmosphere dominated by CH4,H2O, O2, or CO2, the feature amplitudes are at the level of 8 ppm or lower, a factor of 35 below our precision.

3.5.5 Future instruments

The heavily anticipated James Webb Space Telescope will be capable of robust detections of planetary atmospheres with instruments capable of performing transmission spectroscopy across a broad wavelength range. Morley et al. (2017) simulated JWST observations with NIRSpec/G235M and the F170LP filter for several nearby planets orbiting small stars, assuming equilibrated atmospheres derived from Titan, Earth, and Venus elemental compositions. The authors conclude that it will not be possible to detect an atmosphere around LHS 1140b with JWST due to an unrealistic amount of observing time. This conclusion is still valid, despite a refinement some of the LHS 1140 system parameters (Ment et al., 2019). The next generation of ground-based optical telescopes—the Giant Magellan Telescope, the Thirty Meter Telescope, and the European Extremely Large Telescope—will be larger than any we currently have. All three have planned multi-object spectrographs as either first- light or second generation instruments. Exposure time calculators are not yet available

110 3.5. Results & Discussion

0.60 ) % (

2 s 0.55 R / 2 p R

n 0.50 o i s s e r

g 0.45 e r

s s e

c 0.40 o r p

a 0.35 i s s

u 1 x solar, = 2.36, = 2.82 flat fit, = 3.02 Joint GP Fit a

G 0.30 10 x solar, = 2.51, = 2.69 linear fit, = 1.04

0.60

0.55 )

% 0.50 (

2 s R / 2 p 0.45 R

t i F

a 0.40 e n i L 0.35

1 x solar, = 2.36, = 1.78 flat fit, = 2.17 Joint Linear Fit 0.30 10 x solar, = 2.51, = 1.56 linear fit, = 0.78

650 700 750 800 850 900 950 1000 Wavelength (nm)

FIGURE 3.9: Transmission spectrum of LHS 1140b. Top: Transmission spectrum constructed using a Gaussian process regression to jointly fit three data sets taken with the IMACS and LDSS3C spectrographs on Magellan I (Baade) & II (Clay), respectively. We compare the observed transmission spectrum (green points with 1σ error bars) to model transmission spectra with compositions that are 1 and 10× solar metallicity by volume (orange and red lines, respectively). For the model transmission spectra we state the mean molecular weight associated with each model in the legend. The grey dashed line is the inverse-variance weighted mean of the observed transmission spectrum, while the grey dotted line is a linear fit. We also state the σ-confidence with which we rule out the fit or model presented. The linear fit is marginally better than the flat fit, however none of the models or fits are significantly dis-favored to the precision that we report in the figure, so none can be ruled out by the observations. Bottom: Same as top, but using a linear regression to jointly fit the data sets. 111 Chapter 3. LHS 1140b for these modes, but a simple scaling to the larger collecting areas of these telescopes reveals that the low mean molecular weight atmospheres tested in this study could be ruled out on LHS 1140b with as few as seven transits with GMT or five transits with TMT. These ground-based observatories will still have to contend with LHS 1140b’s infrequent transits. High resolution spectroscopy (Snellen et al., 2013; Birkby, 2018) will be possible with the GSMTs, but LHS 1140b will still likely be below the detection thresholds for this technique. Perhaps the most promising avenue for detecting the atmospheres of habitable-zone terrestrial exoplanets is to find more amenable targets. As TESS continues to discover new worlds around our closest stellar neighbors, we are likely to find planets with more accessible atmospheres than that of LHS 1140b. TESS has already grown the sample of nearby (< 15 pc) terrestrial exoplanets, including prime targets such as LHS 3844b (Van- derspek et al., 2019) and LTT 1445Ab (Winters et al., 2019), though neither planet resides in the habitable zone.

3.6 Conclusion

LHS 1140b orbits in the habitable zone of its host M dwarf. This world is at the upper end of the radius regime that deﬁnes terrestrial planets (Fulton et al., 2017), but we know from radius and mass measurements that it is rocky in nature (Ment et al., 2019). How- ever, given the high surface gravity and cool equilibrium temperature of LHS 1140b, its atmosphere is not readily accessible to transmission spectroscopy. With this work we set out to capture two transits of LHS 1140b while also exploring the synergy between the IMACS and LDSS3C spectrographs. Because LHS 1140b transits

112 3.6. Conclusion infrequently, ground-based opportunities for observation are rare. We designed a multi- year program that employed both Magellan I/IMACS & II/LDSS3C, though LDSS3C is preferred for M dwarf observations because its red observing mode collects more than twice as many photons as IMACS at the wavelengths where M dwarfs emit the bulk of their photons (Figure 3.4). Though we are not able to investigate the atmosphere of LHS 1140b in this work, we detail our extraction and analysis pipelines in order to illustrate how we convert raw spectroscopic information into wavelength-calibrated time series. We construct both a white light curve and 20 nm wavelength-binned light curves by jointly ﬁtting our data sets. In the joint ﬁt white light curves, we achieve an RMS of 145 ppm when binning the data to 3-minute time bins; we achieve an RMS of 77 ppm when binning to 10-minute time bins. The data bin down predictably with the calculated RMS. Large ground-based telescopes like the Magellans can be used as high-precision white-light photometers to probe deviations in transit shape that may arise from, for example, planetary oblateness or moons. Across all of the wavelength-binned light curves we achieve an average uncertainty

2 2 in Rp/Rs of 0.028% and an average precision in the wavelength-binned light curves of 1.3× the photon noise. We will employ the techniques laid out in this work for ground- based transmission spectroscopy studies of the recently discovered terrestrial worlds LHS 3844b and LTT 1445Ab (Vanderspek et al., 2019; Winters et al., 2019) with Magellan II (Clay)/LDSS3C (PI Diamond-Lowe). These worlds do not reside in the habitable zones of their systems, but they are more amenable to atmospheric follow-up. Finally, in the TESS era, we emphasize the need for robust mass and radius measurements of newly discovered transiting exoplanets. Without knowledge of the bulk

113 Chapter 3. LHS 1140b densities of these worlds we will under- or over-estimate our ability to detect their atmospheres.

This paper includes data gathered with both of the 6.5m Magellan Telescopes (Baade & Clay) located at Las Campanas Observatory, Chile. We thank the contributors to the IMACS and LDSS3C projects, the telescope operators and staff at Las Campanas Observa- tory, and the writers and contributors of the open-source software used in this work. We make use of the Digitized Sky Surveys in Figure 1 of this paper, as well as during observations. The Digitized Sky Surveys were produced at the Space Telescope Science Institute under U.S. Government grant NAG W-2166. The images of these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. The plates were processed into the present compressed digital form with the permission of these institutions. We especially thank members of the ACCESS collaboration Néstor Espinoza, Benjamin Rackham, David Osip, and Mer- cedes Lopez-Morales for in-depth conversations about the workings of the IMACS multi- object spectrograph. We also thank Robin Wordsworth, Dimitar Sasselov, Laura Kreid- berg, James Kirk, and Amber Medina for helpful comments and conversations. We thank Erik Strand for assistance during the 2017 observations. H.D.-L. recognizes support from the National Science Foundation Graduate Research Fellowship Program (grant number DGE1144152). J.A.D. would like to acknowledge support from the Heising-Simons Foun- dation for their support, whose 51 Pegasi b Postdoctoral Fellowship program has enabled this work. The work of E.M.-R.K. was supported by the National Science Foundation under Grant No. 1654295 and by the Research Corporation for Science Advancement through their Cottrell Scholar program. This publication was made possible through the

114 3.6. Conclusion support of a grant from the John Templeton Foundation. The opinions expressed here are those of the authors and do not necessarily reﬂect the views of the John Templeton Foundation.

Facilities: Magellan I Baade (IMACS), Magellan II Clay (LDSS3C)

Software: astropy (Astropy Collaboration et al., 2013; Astropy Collaboration et al., 2018), batman (Kreidberg, 2015), decorrasaurus (github.com/hdiamondlowe/decorrasaurus), dill (McKerns et al., 2012), dynesty (Speagle, 2020), Exo-Transmit (Kempton et al., 2017), george (Foreman-Mackey, 2015), LDTk (Parviainen and Aigrain, 2015), mosasaurus (github.com/ zkbt/mosasaurus), SAOImageDS9 (Joye and Mandel, 2003)

115 Chapter 4

Optical Transmission Spectroscopy of the Terrestrial Exoplanet LHS 3844b from 13 Ground-Based Transit Observations

Abstract

Atmospheric studies of the growing sample of spectroscopically accessible terrestrial exoplanets lay the groundwork for comparative planetology between these worlds and the Solar System terrestrial planets. LHS 3844b is a highly-irradiated terrestrial exoplanet

(R = 1.3R⊕) orbiting a mid-M dwarf 15 parsecs away. Work based on a near-infrared Spitzer phase curve ruled out atmospheres with surface pressures of 10 bars and higher on this planet. We present 13 transit observations of LHS 3844b taken with the Magellan II (Clay) telescope and the LDSS3C multi-object spectrograph, which covers the optical part of the spectrum from 620-1020 nm. We analyze each of the 13 data sets individually using a Gaussian process regression, and present both white light curves and spectroscopic light curves. In the combined white light curve we achieve an RMS precision of 70

This chapter will be submitted to AAS Journals, in collaboration with David Charbonneau, Matej Malik, Eliza M.-R. Kempton, and Yuri Beletsky.

116 4.1. Introduction

2 ppm when binning to 10-minute time bins. The mean white light curve value of (Rp/Rs) is 0.4143 ± 0.0036%. To construct the the transmission spectrum, we split the white light curves into 20 spectrophotometric bins, each spanning 20 nm, and compute the mean val-

2 ues of (Rp/Rs) in each bin. We compare the final transmission spectrum to two sets of models of LHS 3844b’s atmosphere. We disfavor a clear, solar composition atmosphere (mean molecular weight µ = 2.34) with a surface pressures 0.01 bar and greater to 3.1σ confidence. We disfavor a 100% H2O steam atmosphere (µ = 18) at surface pressures of 0.01 bar and greater to 3.2σ confidence. Our observed transmission spectrum is consistent with a flat line. We cannot address the possibility of tenuous higher mean molecular weight atmospheres. Our results add further evidence that LHS 3844b is devoid of an atmosphere. Future observations of cooler terrestrial planets orbiting M dwarfs will determine if any of these worlds can retain atmospheres.

4.1 Introduction

Like the terrestrial planets of the Solar System, terrestrial exoplanets have radii R < 1.6R⊕ and bulk densities that imply iron cores surrounded by rocky mantles. As yet we do not know what the atmospheres around these worlds look like, or if they bare any similarity to the high mean molecular weight secondary atmospheres that surround Venus, Earth, and Mars, or the tenuous envelope around Mercury. Terrestrial exoplanets are distinct from another class of small planets called min-Neptunes (Owen and Wu, 2013; Lopez and Fortney, 2013; Rogers, 2015; Dressing et al., 2015; Fulton et al., 2017; Van Eylen et al., 2018). These worlds have iron-rock interiors surrounded by thick envelopes of hydrogen- and helium-dominated gas, are unlike any planets we see in the Solar System.

117 Chapter 4. LHS 3844b

Current instrumentation allows for atmospheric follow-up of mini-Neptumes (e.g., Kreidberg et al., 2014a; Benneke et al., 2019), but the the small signals produced by terrestrial exoplanets make in-depth studies of their atmospheres out of reach for our telescopes. The most spectroscopically terrestrial exoplanets orbit nearby (< 15 pc), small

(< 0.3M⊕) stars, or M dwarfs. Ground-based surveys, like MEarth (Nutzman and Char- bonneau, 2008; Irwin et al., 2015) and TRAPPIST (Gillon et al., 2013), and the space-based Transiting Exoplanet Survey Satellite TESS; Ricker et al., 2015 have compiled a small sample of terrestrial exoplanets that meet these requirements. One such terrestrial exoplanet is the highly irradiated world LHS 3844b (Vanderspek et al., 2019), discovered with TESS. As of this writing there is no published mass for LHS

3844b, but its radius of 1.3R⊕ places it squarely in the radius regime of terrestrial planets. LHS 3844b is the third in a series of four terrestrial exoplanets whose atmospheres we address with ground-based transmission spectroscopy. A clear, low mean molecular weight atmosphere is disfavored on GJ 1132b (Berta-Thompson et al., 2015; Diamond-Lowe et al., 2018), while the atmosphere of the habitable-zone terrestrial planet LHS 1140b was below the detection limits of our instruments (Dittmann et al., 2017b; Diamond-Lowe et al., 2019). A data set on the nearby terrestrial planet orbiting LTT 1445A is forthcoming (Winters et al., 2019). Clear, low mean molecular weight atmospheres are also ruled out for ﬁve of the seven TRAPPIST-1 planets (Gillon et al., 2016; Gillon et al., 2017a; de Wit et al., 2016; de Wit et al., 2018). It is an outstanding question whether or not terrestrial worlds orbiting M dwarfs can retain atmospheres at all. Unlike their solar-type counterparts, M dwarfs spend more time in the pre-main sequence phase (Baraffe et al., 2015) during which they exhibit enhanced magnetic activity and emit high levels of damaging ultra-violet and x-ray radiation. This

118 4.1. Introduction

high energy radiation can drive atmospheric mass loss, as well as the photochemistry of any remaining atmosphere (France et al., 2013). LHS 3844b orbits so close to its host star,

with an orbital period of 11 hours (Teq=805 K, S=70S⊕; Vanderspek et al., 2019), that any atmosphere around this world has likely been driven away via photodissociation and hydrodynamic escape (Tian et al., 2014; Luger and Barnes, 2015; Rugheimer et al., 2015). Using 100 hours of almost continuous observations with the Spitzer Space Telescope, Kreidberg et al. (2019) observed nine orbits of LHS 3844b to determine whether or not this world has an atmosphere. Short-period terrestrial planets like LHS 3844b are tidally locked, so energy advection from the day-side to the night-side can only occur through atmospheric transport, with thicker atmospheres more efﬁcient at doing so (Showman et al., 2013; Wordsworth, 2015; Koll, 2019). Phase curve information can reveal evidence of energy advection if there is an offset in the peak of the phase curve from the substellar point, and if the peak-to-trough variation is smaller than predicted for a bare rock. Kreid- berg et al. (2019) found a day-side brightness temperature of 1040 ± 40 K and a night-side temperature consistent with 0 K for LHS 3844b, which rules out atmospheres with surface pressures >10 bar. Based on theoretical calculations authors argue that more tenuous atmospheres, those with surface pressures less than 1 bar, are not stable to the high energy radiation from LHS 3844 over the planet’s lifetime. Kreidberg et al. (2019) used Channel 2 of Spitzer’s IRAC camera, which has a broad photometric band of 4-5µm, to gather phase curve and emission data of LHS 3844b. In this work we use the Magellan II (Clay) telescope and the LDSS3C multi-object spectrograph to gather spectra from 620-1020 nm of LHS 3844 before, during, and after transit. With this data we employ the technique of transmission spectroscopy to address the atmosphere of LHS 3844b.

119 Chapter 4. LHS 3844b

This paper is laid out as follows: In Section 4.2 we detail our observing program. We brieﬂy describe our extraction pipeline and analysis in Section 4.3 (a more detailed description has already been published in Diamond-Lowe et al., 2019). We present our results along with a discussion in Section 4.4. Our conclusions can be found in Section 4.5.

4.2 Observations

LHS 3844b orbits rapidly about its mid-M dwarf host, with an orbital period of 0.4629279 ± 0.0000006 days (11.11 hours) and a transit duration of 0.02172 ± 0.00019 days (31.3 minutes) (Vanderspek et al., 2019). Transits of LHS 3844b occur frequently and easily ﬁt within an observing night. However, the signal-to-noise is proportional to the number of in-transit photons that are detected, so the short transit duration means that we must stack many transits together in order to build up the signal. Between June and October of 2019, the Center for Astrophysics | Harvard & Smithso- nian awarded us 18 opportunities to observe transits of LHS 3844b with the Magellan II (Clay) telescope and the LDSS3C multi-object spectrograph at the Las Campanas Obser- vatory in Chile (PI Diamond-Lowe). Each observation opportunity comprised 2.5 hours to observe the LHS 3844b transit, along with baseline on either side with which to remove systematic noise and accurately measure the transit depth. Of the 18 opportunities, 13 resulted in data sets that we use in our analysis (Table 4.1).

120 4.2. Observations 2458325.72559 (Kreidberg et al., 2019 ). = 0 T 4.1: Observations with Magellan II (Clay) and the LDSS3C Multi-Object Spectrograph (UTC; 2019) (UTC) (s) (%) Exposures Airmass (arcsec) ABLE T 1 * 698 06-14 ————————– — — — —— — †12 7003 7114 713 06-155 715 06-196 741 06-21 ————————–7 765 06-228 07:49:47 767 – 10:11:36 07-049 05:58:56 — 769 – 08:09:05 07-15 04:13:42 808 – 06:21:48 07-16 30 05:27:48 810 – 07:04:30 07-17 30 07:48:43 – 09:47:45 08-04 30† — 05:47:09 – 07:58:02 08-05 30 04:12:47 – 06:17:07 63.8 27† 05:20:53 834 – 07:34:27 63.8 27† 03:27:11 – 05:48:52 63.8 27 — 879 63.8 08-16 27 177 881 61.4 27 167 61.4 09-06 ————————– 165 —— 61.4 1.308 09-07 123 61.4 1.340 ————————– 163 — 61.4 1.491 ————————– 179 — 1.352 1.1 170 — 1.308 1.0 184 — 1.308 1.5 195 — 1.349 0.8 1.308 1.0 — 1.317 0.6 — 1.2 — 0.6 0.6 — — —— —— —— — — — 1011 81212 821 82513 08-06 08-10 838 08-12 01:39:09 – 03:59:24 05:44:13 – 07:54:41 08-18 02:25:08 – 04:24:47 27 27 02:52:19 – 04:49:56 27 61.4 27 61.4 61.4 193 61.4 179 164 1.425 1.308 161 1.359 0.9 1.321 1.0 2.0 1.0 Set Num. Data Transit Night Time Exp. Time Duty Cycle Num. Min. Avg. Seeing Observations not taken due to bad weather. Transit number is counted from the transit ephemeris Observation lost due to instrumental problems. † * 1

121 Chapter 4. LHS 3844b

4.2.1 Ground-based observing with Magellan II (Clay)/LDSS3C

The Low Dispersion Survey Spectrograph (LDSS3C) has a single CCD detector with 15µ pixels arranged in a 2048 × 4096 conﬁguration. Two ampliﬁers are used to read out the detector and convert incoming photons to electrons. The detector has a full well of 200,000 e−, but the 16-bit analog-to-digital converter (ADC) saturates at 65,536 analog-to-digital units (ADUs). We ensure that no pixels used in our analysis exceed this saturation limit. We use the Fast readout mode with the Low gain setting and 2 × 2 binning to optimize the duty cycle. LDSS3C was upgraded in September 2014 to enhance sensitivity in the red optical part of the spectrum (Stevenson et al., 2016), where M dwarfs emit the bulk of their photons. This is the primary reason we chose LDSS3C for these observations. We use the VPH-Red grism to observe over the nominal wavelength range of 620-1020 nm. Our observing program on LDSS3C is similar to ones we employed for GJ 1132b and LHS 1140b, two terrestrial exoplanets also transiting nearby mid-M dwarfs (Diamond-Lowe et al., 2018; Diamond-Lowe et al., 2019). We achieve a duty cycle of 63.8% or 61.4% for all 13 of our observations of LHS 3844b. Observing with a ground-based spectrograph means that telluric features are imprinted on stellar spectra before they reach the detector. Variations in precipitable water vapor translate into variations in the spectra of LHS 3844 large enough to wash out the signal we are looking for from LHS 3844b’s atmosphere; telluric signatures can induce variations in the raw light curve of LHS 3844 by as much as 80% on a bad night, while the largest features we might observe in the atmosphere of LHS 3844b produce variations of 0.04% in transit depth. We are able to compensate for the telluric variations with LDSS3C, a multi- object spectrograph with which we can simultaneously observe spectra of the target star, LHS 3844, and spectra of comparison stars. The comparison stars are used to calibrate the

122 4.2. Observations

TABLE 4.2: Stars used in this work

Target Comparison Name LHS 3844 2MASS 22421963-6909508 RA 22:41:58.12 22:42:19.64 Dec -69:10:08.32 -69:09:50.92 V (mag) 15.24 12.557 TESS (mag) 11.9238 12.015 J (mag) 10.046 11.438 Values are from TESS Input Catalog version 8.

LHS 3844 light curve, and they should be at least as bright as the the target star so as to not be the photon-limiting factors, though not so bright as to bring down the duty cycle. The comparison stars must be selected before the observations so that an LDSS3C mask can be cut with slits corresponding to LHS 3844 and the comparison stars. The field-of-view of LDSS3C is 8.30 in diameter. The field-of-view is further cropped to 6.40 in the cross-dispersion direction when translated onto the CCD. As of June 2019, amplifier two on the LDSS3C detector, which corresponds to the left side of the CCD chip, suffers from poor electronic connections. After our first observations we re-made our observing masks so as to avoid putting any science spectra on that part of the chip, and instead used it only for alignment stars (Figure 4.1). This further curtailing of the LDSS3C field-of-view means that we were limited in our choice of comparison stars. In the re- duced field-of-view of LDSS3C we were able to observe two comparison stars, only one of which, 2MASS 22421963-6909508, is bright enough to calibrate LHS 3844 (Table 4.2).

123 Chapter 4. LHS 3844b

Amplifier 2 Amplifier 1

FIGURE 4.1: Image of the LHS 3844 ﬁeld from the Digitized Sky Survey (DSS), which is available in SAOImagesDS9. The dashed circle indicates the ﬁeld of view of the LDSS3C

multi-object spectrograph, with the solid rectangle showing the extent of the LDSS3C detector. LDSS3C has two ampliﬁers, which read out separately. These are labeled at the top of the detector rectangle, with the vertical dotted line indicating the split on the detec- LHS 3844 tor. Light blue rectangles indicate slits for LHS Comparison Dispersion Direction 3844 and comparison stars. A red line shows the path of LHS 3844 from 2000, when DSS observed this part of the sky, to 2019, when our observations were made. Only one comparison star is bright enough to use in the analysis.

N Orange squares indicate alignment star holes.

Cross-Dispersion Direction

124 4.3. Data Extraction & Analysis

4.3 Data Extraction & Analysis

To extract and analyze our data we use two custom pipelines developed for ground-based multi-object spectroscopy. The extraction pipeline, mosasaurus1, turns the raw images collected by Magellan II/LDSS3C into wavelength-calibrated spectra for LHS 3844 and the comparison star (Diamond-Lowe et al., 2019). We subtract biases and darks from every science images and cut out extraction rectangles around the LHS 3844 and comparison star spectra. We divide the extraction rectangles by their associated flats and designate a fixed-width aperture around the stellar trace. We sum the flux in the cross-dispersion direction to create a spectrum, and then subtract off the estimated sky background. We use He, Ne, and Ar arcs taken during daytime calibrations to perform an initial wavelength calibration, and we use a cross-correlation function to adjust all spectra in a data set onto a common wavelength grid. We present spectra of LHS 3844 and the comparison star for each of the 13 data sets (Figure 4.2). Unlike LHS 3844, the comparison star is not an M dwarf; it is brighter than LHS 3844 at optical wavelengths, but becomes dimmer than LHS 3844 at wavelengths redder than 800 nm. This means that in wavelength bins redder than 800 nm we are photon-limited by the comparison star rather than by LHS 3844. The analysis pipeline, decorrasaurus2 takes the wavelength-calibrated spectra and creates decorrelated, spectroscopic light curves that can be used to construct a transmission spectrum (Diamond-Lowe et al., 2019). We divide the LHS 3844 time series by the comparison star time series to create our light curves. We then process this light curve to remove remaining correlated noise while simultaneously fitting a transit model. For this

1github.com/zkbt/mosasaurus 2github.com/hdiamondlowe/decorrasaurus

125 Chapter 4. LHS 3844b

TABLE 4.3: Systematic model parameters

Decorrelation Data set numbers Parameters 1 2 3 4 5 6 7 8 9 10 11 12 13 airmass XX X XX XX XX XX X rotation angle X centroid X width XX XX X X peak XX XX XX X shift X X X X stretch time X X X X X X A more detailed explanation of the decorrelation parameters can by found in (Diamond-Lowe et al., 2019). work we use the Gaussian process regression capabilities of decorrasaurus. For this project we make some changes to our process of choosing the best decorrelation parameters to use in in the fit (Section 4.2.1 of Diamond-Lowe et al., 2019). We still use the white light curve to test combinations of decorrelation parameters, and then select the optimal combination using the Bayesian evidence derived from the dynamic nested sampler, dynesty (Speagle, 2020). We then find the optimal decorrelation parameters for two 20 nm spectroscopic bands, one towards the blue end of the spectrum (710-730 nm), and one towards the red end of the spectrum (930-950 nm). If additional decorrelation parameters are needed in either of the spectroscopic bands, we include those in the fit. We also fix the priors for all length scales to be in the range of [ln(10−2), ln(105)]. This ensures equal prior volumes for all length scales. As before, we use the same decorrelation parameters for the white light and spectroscopic fits for a given data set. The decorrelation parameters we use in each data set are provided in Table 4.3. More detailed explanations of the physical meanings of these parameters are found in Table 3 of Diamond-Lowe et al. (2019).

126 4.3. Data Extraction & Analysis

5 1 2 3 4 5 6 7 8 9 10 11 12 13 4 4 e 1 /

s FIGURE 4.2: Spectra of LHS 3844 (solid lines) n 3 o

r and the comparison (dotted lines) from each t c

e of the 13 data sets used in this work. Verti- l e

o cal gray lines are the edges of the 20 nm spec- t 2 o trophotometric bands. h P

0 650 700 750 800 850 900 950 1000 Wavelength (nm)

4.3.1 White light curves

For each of our 13 data sets, we perform a white light curve fit from 620-1020 nm. We fix the inclination i and scaled semi-major axis a/Rs to the values found in the initial TESS analysis (Vanderspek et al., 2019). LHS 3844b has a short circularization timescale, and Kreidberg et al. (2019) find the secondary eclipse of LHS 3844b at phase 0.5; we therefore

fix the orbital eccentricity of zero. We fix the period P and transit ephemeris T0 to the values revised by Kreidberg et al. (2019). Note that there is an 0.5 JD error in T0 given in Kreidberg et al. (2019); we use T0=2458325.72559 BJDTDB (L. Kreidberg, priv. comm.). Similar to the analysis performed in Diamond-Lowe et al. (2019), we employ a logarithmic limb-darkening law and re-parameterize the coefficients that we fit for according to Espinoza (2017). In this analysis we place Gaussian priors on the re-parameterized limb- darkening coefficients q0 and q1; the transit of LHS 3844b is so short that measurements

127 Chapter 4. LHS 3844b

TABLE 4.4: White light curve transit parameters and priors

a c Param. δt (days) Rp/Rs q0 q1 RMS Prior U(-0.003, 0.003)b U(0.055, 0.075) N (0.38, 0.027) N (0.47, 0.012) (ppm) 1 0.00124 ± 0.00023 0.437 ± 0.029 0.380 ± 0.068 0.475 ± 0.028 1141 2 0.00136 ± 0.00019 0.387 ± 0.019 0.378 ± 0.063 0.472 ± 0.025 927 3 0.00113 ± 0.00025 0.433 ± 0.022 0.380 ± 0.083 0.481 ± 0.034 1187 4 0.00121 ± 0.00011 0.431 ± 0.012 0.381 ± 0.026 0.476 ± 0.011 597 5 0.00129 ± 0.00010 0.372 ± 0.012 0.376 ± 0.025 0.471 ± 0.010 553 6 0.00150 ± 0.00009 0.414 ± 0.009 0.372 ± 0.024 0.475 ± 0.011 513 7 0.00137 ± 0.00015 0.407 ± 0.016 0.382 ± 0.025 0.474 ± 0.010 988 8 0.00133 ± 0.00011 0.399 ± 0.012 0.375 ± 0.026 0.475 ± 0.011 553 9 0.00145 ± 0.00008 0.429 ± 0.008 0.382 ± 0.026 0.472 ± 0.011 474 Transit Number 10 0.00139 ± 0.00009 0.402 ± 0.011 0.383 ± 0.028 0.471 ± 0.012 557 11 0.00175 ± 0.00011 0.424 ± 0.011 0.374 ± 0.026 0.470 ± 0.011 490 12 0.00121 ± 0.00015 0.469 ± 0.021 0.378 ± 0.022 0.478 ± 0.009 1102 13 0.00117 ± 0.00008 0.430 ± 0.027 0.380 ± 0.025 0.474 ± 0.011 535 a δt is the difference between the predicted time of mid transit and the derived time-of mid transit from fitting each white light curve. The predicted time of mid-transit is calculated as t0 = T0 + nP where T0 = 2458325.72559BJDTDB, P = 0.46292792 (days), and n is the transit number provided in Table 4.1. b U denotes a uniform prior; N denotes a Gaussian prior. c The RMS values in the bottom row refer to the white light curve RMS values in each individual data set compared to the model. The RMS of the combined data sets is discussed in Figure 4.3. of the ingress and egress do not constrain these parameters well. Furthermore, the Gaus- sian priors on these parameters cut down on parameter space to explore, and therefore decrease the computational time to perform the fit. Table 4.4 presents the priors we place on the white light curve transit parameters, and the derived parameters for each data set. We also provide the RMS of each white light curve fit compared to the model. We analyze each white light curve individually, and then take the inverse-variance weighted mean of their planet-to-star radius ratios Rp/Rs and limb-darkening coefficients

q0 and q1 to create a combined transit model. We present the raw white light curves

128 4.3. Data Extraction & Analysis

1 2 3 4 5 6 7 8 9 10 11 12 13

1.015

1.010

1.005

1.000 FIGURE 4.3: Panel a Raw white light curves for 0.995

0.990 the 13 data sets included in this work. Data

0.985 set numbers correspond to those in Table 4.1. 0.980 a Over-plotted grey lines are models computed Normalized Flux + Offset 1.004 by the Gaussian process regression, which in-

1.002 cludes the transit model as the mean function. We ﬁt each of the data sets individually. Panel 1.000 b White light curves of the 13 data sets with 0.998 the Gaussian process model removed. The 0.996 grey lines are the derived transit model for Normalized Flux 0.994 each data set. Panel c Data from all 13 data sets b are combined and binned down to 3-minute 1.004 time bins. The grey transit model is con- 1.002 structed using the inverse-variance weighted 1.000 mean of the 13 derived values of Rp/Rs and

0.998 limb-darkening coefﬁcients. Panel d: Resid- uals of Panel c. With 3-minute time bins we 0.996

Normalized Flux achieve an RMS of 137 ppm; binning to 10- 0.994 c minute bins gives an RMS of 70 ppm.

200

200 d

Residuals (ppm) 60 40 20 0 20 40 60 Time from Mid-Transit (min)

129 Chapter 4. LHS 3844b in Panel a of Figure 4.3, along with the combined systematics and transit models over- plotted. In Panel b we remove the systematics component of each model so that just the transit models are left. We plot each of the 13 transit models, and it is apparent that there is some dispersion in transit depth across the data sets. In Panel c we bin the data to 3- minute time bins and plot the combined transit model. In 3-minute bins we and achieve an RMS precision of 137 ppm. Binning in time to 10-minute bins gives an RMS of 70 ppm, √ but past that the residuals to not bin down as predicted for 1/ N where N is the number of data points in a time bin.

4.3.2 Spectroscopic light curves

We split the white light curves into 20 spectroscopic bands of 20 nm each to create our band-integrated spectroscopic light curves. In each band, and for each data set, we we ﬁx the times to of mid-transit to the values derived from the white light curves (Table 4.4).

We then ﬁt for the planet-to-star radius ratio Rp/Rs and the re-parameterized logarithmic limb-darkening coefﬁcients q0 and q1. We present the resulting light curves with the GP 2 model component removed in Figure 4.4, and list the transit depths (Rp/Rs) for each data set in Table 4.5. In Table 4.5 we also provide the inverse-variance weighted mean of the transit depths in each spectroscopic band, and the RMS of all 13 combined data sets (without any time binning).

130 4.3. Data Extraction & Analysis

620-640 nm 1.00

640-660 nm

660-680 nm

680-700 nm

700-720 nm 0.95 720-740 nm

740-760 nm

760-780 nm

780-800 nm

0.90 800-820 nm

820-840 nm

840-860 nm Normalized Flux +Offset 860-880 nm

0.85 880-900 nm

900-920 nm

920-940 nm

940-960 nm

0.80 960-980 nm

980-1000 nm

1000-1020 nm

60 40 20 0 20 40 60 60 40 20 0 20 40 60 Time from Mid-Transit (min) Time from Mid-Transit (min)

FIGURE 4.4: Left: Band-integrated spectroscopic light curves with GP models removed for each of the 13 data sets. The transit model (GP mean function) is plotted in grey for each data set. Spectroscopic bands are offset for clarity. Right: Residuals of all 13 data sets, in each spectroscopic band, also offset for clarity. The spectroscopic transit depths and uncertainties are provided in Table 4.5 and Figure 4.5. 131 Chapter 4. LHS 3844b

TABLE 4.5: Spectroscopic transit depths

Wavelength Transit depths by data set (%) 1 2 3 4 5

620-640 0.364 ± 0.151 0.307 ± 0.128 0.277 ± 0.089 0.395 ± 0.045 0.395 ± 0.063 640-660 0.369 ± 0.093 0.498 ± 0.080 0.321 ± 0.051 0.377 ± 0.024 0.394 ± 0.056 660-680 0.172 ± 0.099 0.357 ± 0.095 0.429 ± 0.048 0.360 ± 0.027 0.398 ± 0.036 680-700 0.382 ± 0.139 0.359 ± 0.062 0.372 ± 0.049 0.415 ± 0.027 0.388 ± 0.030 700-720 0.408 ± 0.066 0.533 ± 0.059 0.444 ± 0.041 0.376 ± 0.026 0.339 ± 0.026 720-740 0.315 ± 0.050 0.392 ± 0.039 0.468 ± 0.034 0.376 ± 0.024 0.392 ± 0.025 740-760 0.399 ± 0.037 0.448 ± 0.028 0.451 ± 0.031 0.405 ± 0.015 0.398 ± 0.017 760-780 0.351 ± 0.041 0.357 ± 0.054 0.493 ± 0.029 0.410 ± 0.025 0.402 ± 0.022 780-800 0.445 ± 0.050 0.403 ± 0.049 0.467 ± 0.029 0.425 ± 0.015 0.407 ± 0.025 800-820 0.423 ± 0.029 0.405 ± 0.025 0.452 ± 0.027 0.399 ± 0.015 0.408 ± 0.019 820-840 0.466 ± 0.057 0.443 ± 0.026 0.441 ± 0.025 0.430 ± 0.015 0.405 ± 0.018 840-860 0.403 ± 0.089 0.466 ± 0.029 0.446 ± 0.024 0.406 ± 0.014 0.373 ± 0.020 860-880 0.427 ± 0.032 0.413 ± 0.027 0.457 ± 0.025 0.393 ± 0.015 0.421 ± 0.018 880-900 0.338 ± 0.048 0.406 ± 0.028 0.409 ± 0.029 0.413 ± 0.016 0.407 ± 0.021 900-920 0.432 ± 0.032 0.400 ± 0.033 0.459 ± 0.026 0.417 ± 0.018 0.371 ± 0.020 920-940 0.421 ± 0.040 0.421 ± 0.035 0.422 ± 0.028 0.380 ± 0.017 0.387 ± 0.019 940-960 0.391 ± 0.080 0.407 ± 0.042 0.460 ± 0.029 0.422 ± 0.017 0.407 ± 0.029 960-980 0.415 ± 0.051 0.399 ± 0.037 0.464 ± 0.022 0.383 ± 0.021 0.386 ± 0.022 980-1000 0.415 ± 0.055 0.453 ± 0.056 0.482 ± 0.028 0.384 ± 0.019 0.392 ± 0.035 1000-1020 0.345 ± 0.087 0.358 ± 0.048 0.502 ± 0.037 0.420 ± 0.031 0.419 ± 0.040

132 4.3. Data Extraction & Analysis

TABLE 4.5: Spectroscopic transit depths (continued)

Wavelength Transit depths by data set (%) 6 7 8 9 10

620-640 0.395 ± 0.095 0.204 ± 0.102 0.352 ± 0.045 0.440 ± 0.040 0.484 ± 0.043 640-660 0.364 ± 0.042 0.512 ± 0.051 0.396 ± 0.032 0.459 ± 0.026 0.435 ± 0.022 660-680 0.388 ± 0.045 0.369 ± 0.055 0.383 ± 0.029 0.459 ± 0.024 0.438 ± 0.025 680-700 0.411 ± 0.034 0.318 ± 0.041 0.395 ± 0.024 0.459 ± 0.026 0.417 ± 0.022 700-720 0.402 ± 0.033 0.399 ± 0.037 0.407 ± 0.028 0.398 ± 0.020 0.455 ± 0.018 720-740 0.413 ± 0.025 0.451 ± 0.041 0.435 ± 0.019 0.415 ± 0.018 0.405 ± 0.017 740-760 0.426 ± 0.019 0.381 ± 0.027 0.394 ± 0.021 0.425 ± 0.014 0.438 ± 0.017 760-780 0.443 ± 0.023 0.476 ± 0.036 0.464 ± 0.017 0.441 ± 0.019 0.423 ± 0.019 780-800 0.432 ± 0.021 0.396 ± 0.029 0.424 ± 0.016 0.435 ± 0.014 0.417 ± 0.016 800-820 0.449 ± 0.022 0.374 ± 0.022 0.398 ± 0.017 0.416 ± 0.012 0.425 ± 0.013 820-840 0.412 ± 0.015 0.436 ± 0.027 0.450 ± 0.013 0.407 ± 0.012 0.433 ± 0.015 840-860 0.412 ± 0.017 0.392 ± 0.018 0.418 ± 0.014 0.404 ± 0.014 0.445 ± 0.019 860-880 0.422 ± 0.015 0.393 ± 0.023 0.381 ± 0.017 0.418 ± 0.013 0.412 ± 0.016 880-900 0.389 ± 0.016 0.369 ± 0.027 0.405 ± 0.017 0.408 ± 0.017 0.427 ± 0.016 900-920 0.412 ± 0.017 0.364 ± 0.025 0.401 ± 0.016 0.413 ± 0.012 0.387 ± 0.016 920-940 0.423 ± 0.018 0.375 ± 0.022 0.410 ± 0.016 0.392 ± 0.016 0.446 ± 0.018 940-960 0.411 ± 0.017 0.399 ± 0.026 0.375 ± 0.023 0.391 ± 0.017 0.388 ± 0.020 960-980 0.430 ± 0.018 0.354 ± 0.023 0.407 ± 0.020 0.385 ± 0.017 0.433 ± 0.018 980-1000 0.369 ± 0.025 0.366 ± 0.036 0.392 ± 0.030 0.373 ± 0.022 0.408 ± 0.023 1000-1020 0.351 ± 0.032 0.319 ± 0.028 0.402 ± 0.032 0.350 ± 0.025 0.388 ± 0.034

133 Chapter 4. LHS 3844b

TABLE 4.5: Spectroscopic transit depths (continued)

Wavelength Transit depths by data set (%) 11 12 13 Mean RMS (ppm)

620-640 0.349 ± 0.078 0.565 ± 0.150 0.355 ± 0.060 0.3963 ± 0.0173 5470 640-660 0.460 ± 0.030 0.380 ± 0.082 0.409 ± 0.039 0.4182 ± 0.0099 2793 660-680 0.448 ± 0.030 0.311 ± 0.107 0.435 ± 0.035 0.4133 ± 0.0099 3016 680-700 0.439 ± 0.029 0.357 ± 0.056 0.345 ± 0.033 0.4030 ± 0.0090 2162 700-720 0.407 ± 0.021 0.347 ± 0.050 0.394 ± 0.029 0.4063 ± 0.0079 1984 720-740 0.380 ± 0.019 0.393 ± 0.037 0.388 ± 0.025 0.4042 ± 0.0068 1600 740-760 0.410 ± 0.016 0.423 ± 0.030 0.382 ± 0.020 0.4130 ± 0.0055 1220 760-780 0.396 ± 0.031 0.409 ± 0.038 0.386 ± 0.025 0.4289 ± 0.0069 1494 780-800 0.404 ± 0.016 0.428 ± 0.030 0.377 ± 0.021 0.4197 ± 0.0056 1418 800-820 0.434 ± 0.017 0.414 ± 0.037 0.415 ± 0.026 0.4153 ± 0.0051 1121 820-840 0.410 ± 0.016 0.474 ± 0.034 0.374 ± 0.021 0.4226 ± 0.0049 1177 840-860 0.420 ± 0.015 0.449 ± 0.032 0.435 ± 0.025 0.4150 ± 0.0052 1143 860-880 0.421 ± 0.015 0.436 ± 0.032 0.371 ± 0.022 0.4108 ± 0.0051 1104 880-900 0.426 ± 0.019 0.445 ± 0.028 0.410 ± 0.019 0.4087 ± 0.0056 1263 900-920 0.408 ± 0.021 0.403 ± 0.027 0.391 ± 0.020 0.4038 ± 0.0053 1192 920-940 0.409 ± 0.018 0.393 ± 0.037 0.368 ± 0.023 0.4031 ± 0.0057 1307 940-960 0.405 ± 0.018 0.420 ± 0.045 0.432 ± 0.024 0.4068 ± 0.0064 1512 960-980 0.408 ± 0.019 0.431 ± 0.036 0.387 ± 0.021 0.4056 ± 0.0060 1363 980-1000 0.410 ± 0.023 0.395 ± 0.040 0.424 ± 0.026 0.4002 ± 0.0077 1790 1000-1020 0.354 ± 0.029 0.345 ± 0.053 0.457 ± 0.035 0.3831 ± 0.0095 2105

134 4.3. Data Extraction & Analysis Mean (Bins) About Spread 0.7

0.6

0.5 ) % (

) 0.4 s R / p

R 0.3 (

0.2

1 2 3 4 5 6 7 0.1 8 9 10 11 12 13 Mean

650 700 750 800 850 900 950 1000 Wavelength (nm)

FIGURE 4.5: Transmission spectra of LHS 3844b from each of the 13 data sets analyzed. Values of 2 (Rp/Rs) along with 1-σ error bars are provided for each of the 13 data sets in each spectroscopic band. Transit depths are offset in the x-axis for clarity. Black points with 1-σ error bars are the inverse-variance weighted mean transit depths in each band. Horizontal bars on the black point denote the span of each 20-nm spectroscopic band. On top are the spread of each transit depth ¯ about the inverse-variance weighted mean in each band; i.e., (Di − D)/σDi , compared to Gaussian distributions. The dots above the histograms show where this value lands for each data set. We do not ﬁnd that any data sets are systematically offset from the others.

We present transmission spectra from each data set, ﬁt individually, along with the inverse-variance weighted mean of the transit depths in Figure 4.5. The histograms above ¯ each spectroscopic band show the spread in transit depths according to (Di − D) /σDi , where Di and σDi are the transit depth and 1-σ transit depth uncertainty for each data set i, and D¯ is the inverse-variance weighted mean transit depth in that band. The dots on top of the histograms show where each data set is in relation to the others. We do not ﬁnd that any data set is consistently lower or higher than the mean.

135 Chapter 4. LHS 3844b

4.4 Results & Discussion

4.4.1 LHS 3844b transmission spectrum compared to model transmis-

sion spectra

We use the inverse-variance weighted mean of the derived transit depths in each of the 20-nm spectrophotometric bands as our ﬁnal transmission spectrum. We compare this observed transmission spectrum to model transmission spectra in order to address the atmosphere of LHS 3844b. We construct the model transmission spectra using two open source codes, HELIOS (Malik et al., 2017; Malik et al., 2019) and Exo-Transmit (Miller-Ricci Kempton, Zahnle, and Fortney, 2012; Kempton et al., 2017). With HELIOS we compute temperature-pressure proﬁles, and then reformat these and feed them into Exo-Transmit. Like Kreidberg et al. (2019), we assume an Earth-like bulk composition for LHS 3844b, which gives a surface gravity of 16 m/s2 in our models. Both HELIOS and Exo-Transmit use a reference base of the atmosphere, such as a planet’s rocky surface or an impenetrable cloud deck, where the optical depth τ ≈ 1. We do not know a priori where the bottom of the atmosphere is, so we vary the planet radius input to Exo-Transmit such that each model transmission spectrum best aligns with the observed transmission spectrum. We focus on two groups of atmospheric models of LHS 3844b: 1) a solar composition atmosphere (µ = 2.34), and 2) a water steam atmosphere (µ = 18). Within each group we test surface pressures ranging from 0.01 to 10 bars. The solar composition model is dominated by hydrogen and helium, and the main optical absorbers are water and

methane. The water steam atmosphere is 100% H2O, which is such a strong absorber

that in the 100% H2O steam atmosphere cases it produces strong features down to 0.01

136 4.4. Results & Discussion

0.44

0.43

0.42 ) % ( 0.41 2 ) s R / p R

( 0.40

0.39

0.01 bar solar, = 3.1 0.01 bar H2O, = 3.2 Flat line, = 2.5 0.38 0.1 bar solar, = 5.5 0.1 bar H2O, = 3.5 Mean Transit Depths 1 bar solar, = 8.1 1 bar H2O, = 3.5

10 bar solar, = 8.0 10 bar H2O, = 3.5

650 700 750 800 850 900 950 1000 Wavelength (nm)

FIGURE 4.6: Transmission spectrum of LHS 1844b compared to model atmospheres. The observed transmission spectrum (1σ bars) is constructed from the inverse-variance weighted mean transit depths across the 13 data sets used in this analysis. They are the same 1-σ black vertical bars as in Figure 4.5, and the transit depth values are provided in the grey columns of Table 4.5). We test two sets of clear atmospheric models: 1) solar composition, and 2) 100% H2O steam. For each model case we test surface pressures from 0.01 - 10 bar. The σ values in the legend are the confidence to which we can rule out each model. We also compare the observed transmission spectrum to a flat line, which are more consistent with the observations. bar We disfavor a clear, solar composition atmosphere at 0.01 bars of surface pressure and greater to 3.1 σ confidence, and a clear H2O steam atmosphere down to 0.01 bars of surface pressure to 3.2σ confidence (Figure 4.6). We cannot rule out a flat line fit as a potential explanation of the data, meaning that our data allow for a tenuous high mean molecular weight atmosphere, or no atmosphere at all.

137 Chapter 4. LHS 3844b

4.4.2 Wiggles in the LHS 3844b transmission spectrum

Though we are able to rule out clear, low mean molecular weight atmospheres around LHS 3844b, we cannot rule out a flat line at the inverse-variance weighted mean of the transit depths (σ=2.48). However this flat line is still poor fits to the data. We investigate the possibility that the “wiggles” about the mean in the observed transmission spectrum are due to inhomogeneities in the stellar photosphere, which we are effectively prob- ing as we observe the planet transit. These inhomogeneities can arise from star sports, cooler (and darker) regions on the stellar surface, or faculae, hotter (and brighter) regions more often seen at the limb of the star (Spruit, 1976; Foukal, 2004). Both phonomena arise from magnetic activity. Rackham, Apai, and Giampapa (2018) refer to the imprint of stellar photosphere inhomogeneities on observed transmission spectra as the transit light source effect, and have observed it robustly in the optical transmission spectrum of GJ 1214b (Rackham et al., 2017), a mini-Neptune orbiting another nearby mid-M dwarf (Charbonneau et al., 2009). Star spots and faculae have temperatures different than that of the rest of the stellar photosphere, so their presence produces a chromatic effect. M dwarfs are known to have inhomogeneities in their photospheres, allowing for variations large enough to track their rotation periods (Newton et al., 2018). The transit light source effect in M dwarf transits can spuriously increase optical transit depths by a fac-

2 tor of 0.5% × (Rp/Rs) , with an overall slope upwards towards the blue, or spuriously

2 decrease transit depths by a factor of 2.5% × (Rp/Rs) if faculae are present, with a steep downwards slope towards the blue (Figures 6 & 7 of Rackham, Apai, and Giampapa, 2019). In our observed transmission spectrum we ﬁnd a mean transit depth in our spectrophotometric bands of 0.4089% and with a mean uncertainty of 0.0073% (Table 4.5). A 2.5% change in our observed transit depths would be within most of our 1σ error bars,

138 4.4. Results & Discussion

and the slight slope that we do see towards the blue is not statistically distinguishable from a flat line. For comparison, the average transit depth of GJ 1214 in the optical is 1.3133 ± 0.0045% (Rackham et al., 2017); the larger planet-to-star ratio of GJ 1214 makes changes in transit depth due to the transit light source effect larger. We further note that our mean white light curve transit depth of 0.4143 ± 0.0036% is in agreement with the transit depths found by TESS (0.403 ± 0.011%; Vanderspek et al., 2019) and Spitzer (0.4109 ± 0.0038%; Kreidberg et al., 2019) for this planet. In particular, the Spitzer bandpass from 4-5µm should be less susceptible to the transit light source effect because the temperate differences due to photospheric inhomogeneities are minimized at longer wavelengths. Finally, we consider the stellar rotational phase over which our observations were made. The rotation period of LHS 3844 is 128 days (Vanderspek et al., 2019). The 13 transits presented here span 60 days, meaning that our data set covers half of the stellar rotation period. We did not did not find a correlation between white-light transit depths or slopes in the transmission spectrum with stellar rotational phase, suggesting that the transit light source effect is not apparent in our data. We propagate the rotation period of LHS 3844 forward in time to cover our observations, and find that if the rotation period is stable from 2018 to 2019, our observations sampled a peak, rather than a rapid change from peak to trough, further diminishing our chances of detecting heterogeneity in the photosphere of LHS 3844 (Figure 4.7).

4.4.3 Comparison to previous results

Kreidberg et al. (2019) were able to rule out atmospheres with surface pressures greater than 10 bar with their 100-hour campaign with Spitzer to observe the phase curve of LHS 3844b. By nature, those data are most sensitive to thick atmospheres which can efﬁciently

139 Chapter 4. LHS 3844b

0.01 0.04 0.00 FIGURE 4.7: Stellar rotation phase of LHS 0.01 3844. Black points are photometric data from 650 700

) 0.02 MEarth South (Irwin et al., 2015). Grey line is e d u

t a sinusoidal ﬁt to the photometric data points, i n

g which was also presented in Vanderspek et al. a 0.00 M ( (2019). Vertical lines indicate the times of mid- transit for the 13 data sets analyzed in this 0.02 work, with colors corresponding to those in other ﬁgures.

0.04 600 400 200 0 200 400 600 800 Time From Ephemeris (BJD-2458000)

redistribute heat from the day-side to the night-side of the planet. Kreidberg et al. (2019) argue based on theory that lighter atmospheres are not stable over the lifetime of the planet due to atmospheric erosion over time. We provide an observational constraint by addressing cases of clear, low mean molecular weight atmospheres from 0.01 - 10 bar, and disfavoring them to >3 sigma conﬁdence.

Kreidberg et al. (2019) speciﬁcally test atmospheric compositions involving O2 and

CO2. Models of atmospheric evolution on terrestrial planets around M dwarfs ﬁnd that

several bars of O2 can result from hydrodynamic escape driven by high energy stellar

radiation (Tian et al., 2014; Luger and Barnes, 2015; Schaefer et al., 2016). CO2 exhibits spectral features in the Spitzer Channel 2 bandpass. Unlike Kreidberg et al. (2019), we do not address model transmission spectra comprised of O2 (µ = 32) and CO2 (µ = 44) because we cannot distinguish these high mean molecular weight cases from a ﬂat line. This leaves open the possibility of a constantly replenished high mean molecular weight tenuous atmosphere around LHS 3844b.

140 4.5. Conclusion

4.5 Conclusion

We observed 13 transits of the highly irradiated terrestrial exoplanet LHS 3844b in the fall of 2019 with the Magellan II (Clay) telescope and the LDSS3C multi-object spectrograph at the Las Campanas Observatory in Chile. From these 13 transits we construct both white light curves and spectroscopic light curves. When combining all 13 data sets we achieve an RMS precision of 137 ppm in 3-minute time bins of the white light curve, and an RMS

2 of 70 ppm if we bin down to 10-minutes. We derive a combined value of (Rp/Rs) = 0.4143 ± 0.0036%. We chop the light curves into 20 spectrophotometric bands of 20 nm each. We take the inverse-variance weighted mean of the 13 transit depths in each band to construct our

2 ﬁnal transmission spectrum. We achieve an average transit depth precision on (Rp/Rs) of 0.0073%, and an average of 1.7 × the expected noise in the spectroscopic light curves. We compare the ﬁnal transmission spectrum to models of LHS 3844b’s atmosphere. We exclude clear low mean molecular weight solar composition atmospheres with surface

pressures of 0.01 bar and greater to 3.1σ conﬁdence, and a clear, 100% H2O water vapor atmosphere with surface pressures of 0.01 bar and greater to 3.2σ conﬁdence. Our results are in good agreement with theoretical models and observational evidence demonstrating that terrestrial worlds do not retain low mean molecular weight atmospheres (de Wit et al., 2016; de Wit et al., 2018; Diamond-Lowe et al., 2018). The question remains if terrestrial exoplanet orbiting M dwarf can retain high mean molecular weight atmospheres, like the Solar System terrestrials have. In the case of the highly irradiated planet LHS 3844b, the answer is likely no (Kreidberg et al., 2019). But cooler worlds in the growing sample of nearby terrestrial exoplanet orbiting small stars may prove differently.

141 Chapter 4. LHS 3844b

These cooler terrestrials are not spectroscopically accessible to us today, but the next generation of space-based observatories beginning with the James Webb Space Telescope, and ground-based telescopes like the Giant Magellan Telescope, the Thirty Meter Telescope, and the European Extremely Large Telescope, will be able to characterize the atmospheres, or lack there of, around these worlds.

This paper includes data gathered with the 6.5m Magellan II Telescope (Clay) located at Las Campanas Observatory, Chile. We thank the contributors to the LDSS3C instrument and documentation, the telescope operators and staff at Las Campanas Observatory, and the writers and contributors of the open-source software used in this work. We make use of the Digitized Sky Surveys in Figure 1 of this paper, as well as during observations. The Digitized Sky Surveys were produced at the Space Telescope Science Institute under U.S. Government grant NAG W-2166. The images of these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain and the UK Schmidt Telescope. The plates were processed into the present compressed digital form with the permission of these institutions. We thank Jonathan Irwin for providing MEarth photometric data of LHS 3844 and the model for stellar rotation. H.D.-L. recognizes support from the National Science Foundation Graduate Research Fellowship Program (grant number DGE1144152). This publication was made possible through the support of a grant from the John Templeton Foundation. The opinions expressed here are those of the authors and do not necessarily reﬂect the views of the John Templeton Foundation.

Facilities: Magellan II (Clay), LDSS3C

142 4.5. Conclusion

Software: astropy (Astropy Collaboration et al., 2013; Astropy Collaboration et al., 2018), batman (Kreidberg, 2015), decorrasaurus (Diamond-Lowe et al., 2019), dynesty (Speagle, 2020), Exo-Transmit (Kempton et al., 2017), george (Foreman-Mackey, 2015), LDTk (Parvi- ainen and Aigrain, 2015), mosasaurus (github.com/zkbt/ mosasaurus), SAOImageDS9 (Joye and Mandel, 2003)

143 Chapter 5

Ultra-violet proﬁle of the nearby planet-hosting mid-M dwarf LHS 3844 with HST/COS

Abstract

To fully characterize the atmospheres, or lack thereof, of terrestrial exoplanets we must have a clear understanding of the high energy environments provided by their host M dwarfs. The nearby mid-M dwarf LHS 3844 hosts a highly irradiated terrestrial world that is unlikely to retain an atmosphere. We present an ultra-violet spectrum of LHS 3844 from 1125-3216Å captured by HST/COS. From these observations we estimate the Ly-α, EUV, and XUV flux from the star. We estimate a Ly-α flux compared to the total UV flux of 88 ± 0.10%. We compare the FUV, NUV, and XUV flux of LHS 3844 compared to its bolometric luminosity and derive values of log10(band/LBol) = -4.1, -5.3, and -3.65, respectively. These values are in agreements with those found by the MUSCLES collaboration for their sample of mostly early-M dwarfs. By scaling the X-ray and EUV portions of the

This chapter will be submitted to AAS Journals, in collaboration with Allison Youngblood, David Charbon- neau, Laura Kreidberg, and Jennifer Winters.

144 5.1. Introduction

spectrum of Proxima Centrauri, we estimate that LHS 3844b receives 2.1 × 104 erg cm−2 s−1 in XUV ﬂux, corresponding to an estimated hydrodynamic mass loss rate of 2 × 1010 g/s. The data we present here will complement the forthcoming extended MUSCLES program, Mega-MUSCLES, to address a larger sample of mid- to late-M dwarfs.

5.1 Introduction

Studying the atmospheres of terrestrial exoplanets can provide insights into their histories and current process which are not available from radius and mass measurements alone.

The most accessible terrestrial planet atmospheres are those that transit small (< 0.3M M dwarfs), nearby (< 15 pc) stars. These systems provide large planet-to-star radius ratios Rp/Rs and high signal-to-noise observing opportunities. The Transiting Exoplanet Survey Satellite (TESS Ricker et al., 2015), along with other ground-based survey programs (Nutzman and Charbonneau, 2008; Gillon et al., 2013; Irwin et al., 2015), are expanding the known sample of transiting terrestrial exoplanets orbiting nearby mid-M dwarfs, and these worlds are becoming prime targets for in-depth characterization. Mid-M dwarfs have masses and radii 20% that of the Sun, and exhibit stark differences from their G-type counterparts. M dwarfs have extended pre-main sequence phases (Baraffe et al., 2015) and remain chromospherically active on long timescales (Newton et al., 2017). A large fraction of M dwarf surfaces are covered by magnetic ﬁelds, which heat their upper atmospheres and produce strong emission lines and ﬂaring in these fully convective stars (Saar and Linsky, 1985; Wright et al., 2018; Loyd et al., 2018).

145 Chapter 5. LHS 3844 UV

For planets in orbit around such stars, this adds up to a harsh high-energy environment that can alter their atmospheric chemistry and even strip their atmospheres alto- gether. Molecular photodissociation cross-sections are wavelength dependent, so planetary atmospheric chemistry is highly sensitive to the stellar spectral energy distribution (SED). For instance, the far-ultra-violet (FUV = 912-1700Å) to near-ultra-violet (NUV = 1700-3200Å) flux ratio can shift the abundances of key molecules for habitability studies like water, methane, carbon dioxide, ozone, and diatomic oxygen by more than an order of magnitude (Rugheimer et al., 2015; Harman et al., 2015; France et al., 2016). While high energy radiation may damaging to biologic material, there is evidence that some amount is needed for abiogenesis (Ranjan, Wordsworth, and Sasselov, 2017). Studies of atmospheric escape of terrestrial exoplanets orbiting M dwarfs are rooted in theoretical studies of what early Venus, Earth, and Mars might have looked like in the presence of a young, more active Sun (e.g., Watson, Donahue, and Walker, 1981; Zahnle, Kasting, and Pollack, 1990). Extreme ultra-violet and X-ray flux (EUV = 100-912Å; XUV = 10-1000Å) are responsible for hydrodynamic escape, by which photolysis of atmospheric molecules, namely water, can produce a stream of escaping hydrogen which can drag heavier molecules with it. It remains an open question whether or not terrestrial worlds around M dwarfs can retain atmospheres. Knowing where the divide between those that can and those that cannot is a key piece of missing information when it comes to identifying optimal terrestrial targets for atmospheric follow-up. This divide, known as the cosmic shoreline, relies on many inputs that are unknown, including high-energy stellar flux levels over planetary lifetimes (Zahnle and Catling, 2017). In this work we focus on the nearby mid-M dwarf LHS 3844, which hosts a terrestrial exoplanet discovered by TESS (Vanderspek et al., 2019). Kreidberg et al. (2019) observed

146 5.2. Constructing the UV proﬁle of LHS 3844 nine orbits of the terrestrial exoplanet LHS 3844b with 100 hours of Spitzer time. From the phase curve data they determined that surface pressures of 10 bars or higher are disfavored on this planets, for a range of atmospheric compositions. Clear, low mean molecular weight atmospheres are also disfavored (Diamond-Lowe et al., 2020). Kreidberg et al. (2019) disfavored tenuous high mean molecular weight atmospheres on the basis of stellar wind the high energy ﬂux over the planetary lifetime. We do not know the high energy history of LHS 3844, but we here provide a current snapshot as an anchor for stellar evolution and atmospheric escape models. In Section 5.2 we describe in detail our data, as well as the high-energy estimates we derive. We discuss the implications of our data for the terrestrial exoplanet LHS 3844b in Section 5.3. We outline future projects for this data set in Section 5.4, and present our conclusions in Section 5.5.

5.2 Constructing the UV proﬁle of LHS 3844

We observed the UV spectrum of mid-M dwarf LHS 3844 from 1125-3216Å with 10 orbits of the Hubble Space Telescope (HST) and the Cosmic Origins Spectrograph (COS) (GO Program 15704, PI Diamond-Lowe). We used the G130M and G160M grisms to observe prominent molecular lines in the far ultra-violet (FUV; 912-1700Å), and the G230L grism to observe lines in the near ultra-violet (NUV; 1700-3200Å). A list of the lines that we measure, along with which grism we use and exposure times to measure them can be found in Table 5.1.

147 Chapter 5. LHS 3844 UV

TABLE 5.1: Observations of LHS 3844 with HST/COS and measured molecular lines

Grism Total Exposure Time Line Line Centers log10(Surface Flux) (s) (Å) (erg cm−2 s−1) SiIII 1206.50 3.29 ± 0.062 NV 1238.82, 1242.8060 3.58 ± 0.062 G130M 17802 SiII 1264.74 2.40 ± 0.099 CII 1335.71 3.55 ± 0.040 FUV SiIV 1393.72, 1402.74 3.42 ± 0.13 CIV 1548.19, 1550.78 3.91 ± 0.12 G160M 8854 HeII 1640.4 3.01 ± 0.66 G230L 716 MgII 2796.35, 2803.53 4.38 ± 0.71 NUV Surface ﬂuxes are calculated by scaling the observed ﬂux by the distance d and stellar 2 radius R of LHS 3844: FSur f = FObs × (d/R ) . We use d = 14.89 ± 0.011 pc and R = 0.189 ± 0.006 (Vanderspek et al., 2019).

5.2.1 Ly-α estimation

The most prominent source of flux by far in the UV is the Ly-α line, so having a measurement or estimation of the Ly-α flux is key to understanding the UV profile of LHS 3844. However, for all stars other than the Sun, Ly-α emission is absorbed by neutral hydrogen in the inter-stellar medium before it can reach our telescopes. The MUSCLES survey was able to gather enough flux in the wings of the Ly-α profile to perform a reconstruction of the line, and thereby measure the flux (Youngblood et al., 2016). We make a distinction between the MUSCLES method of Ly-α reconstruction, and the method we present here for Ly-α estimation. An additional barrier to measuring the Ly-α flux from LHS 3844 comes from the COS instrument. COS is optimal for measuring the FUV (Green et al., 2012; France et al., 2013), but because it is a slit-less spectrograph, the Ly-α line becomes contaminated by geocoronal emission, whereby solar photons interact with neutral hydrogen in Earth’s

148 5.2. Constructing the UV proﬁle of LHS 3844

atmosphere, producing local Ly-α emission. The Space Telescope Imaging Spectrograph (STIS) aboard HST has a slit and can therefore measure the wings of the Ly-α profile (France et al., 2016; Youngblood et al., 2016), but at a lower efficiency. Given how faint LHS 3844 is in the UV we estimate that it would take a prohibitive amount of HST/STIS time (70 orbits) to build up enough signal-to-noise in the wings of the Ly-α profile to perform a reconstruction. To estimate the Ly-α flux from LHS 3844 we instead build upon the work of the MUS- CLES survey to establish correlations between UV line strengths across their stellar sample. Though the early-M stars in the MUSCLES samples have orders-of-magnitude variations in their measured line fluxes, there exist statistically significant correlations between line fluxes within a given star’s UV profile Youngblood et al., 2017. Because the MUS- CLES survey successfully reconstructed the Ly-α profiles for their sample, and measured correlations between line strengths, including the Ly-α line, we can build upon that work in order to estimate the Ly-α flux from LHS 3844. We start by fitting Gaussian profiles1 to each of the lines listed in Table 5.1. Visuals of these fitted profiles are shown in Figure 5.1. We then integrate under the fitted profiles to establish the line flux. (For double-peaked lines–those with two centers–we fit separate profiles to each peak and then sum the integrated flux, except for the MgII line.) We normalize the observed flux in each line to the surface flux of the star using the stellar distance and radius, and take the base 10 log. In this format, we can use the UV- UV emission line scaling relations established by Youngblood et al. (2017) to estimate this

1We tried to fit Voigt profiles to the UV lines, which should be the correct profile to use, but because our data are so noisy the extra free parameter made for an indistinguishable fit, but with larger uncertainties.

149 Chapter 5. LHS 3844 UV

1e 16 SiIII at 1206.50Å 1e 15 NV at 1238.82Å 1e 16 NV at 1242.81Å 8 6 COS data 1.0 Profile fit 5 6 0.8 4

4 0.6 3

0.4 2 2 0.2 1

0 0 0.0 )

1 1205.5 1206.0 1206.5 1207.0 1207.5 1238.0 1238.5 1239.0 1239.5 1242.0 1242.5 1243.0 1243.5 Å SiII at 1264.74Å CII at 1335.71Å SiIV at 1393.72Å 1 1e 16 1e 15 1e 16 s

2.0

2 8 1.5 1.5

m 6 c 1.0 1.0 g

r 4

e 0.5 ( 0.5 2 y

t 0.0 i

s 0

n 0.5 0.0 e

D 1264.0 1264.5 1265.0 1265.5 1335.0 1335.5 1336.0 1336.5 1393.0 1393.5 1394.0 1394.5

x u

l 1e 16 SiIV at 1402.74Å 1e 15 CIV at 1548.19Å 1e 16 CIV at 1550.78Å F 1.75 3 1.50 6 1.25 2 1.00 4

1 0.75

0.50 2

0 0.25 0 0.00

1402.0 1402.5 1403.0 1403.5 1547.5 1548.0 1548.5 1549.0 1550.0 1550.5 1551.0 1551.5

1e 16 HeII at 1640.40Å 1eM16gII at 2796.35, 2803.53Å 3 4 2 2 1 0 0 2 1

1639.5 1640.0 1640.5 1641.0 2795 2800 2805 Wavelength (Å)

FIGURE 5.1: UV molecular lines listed in Table 1505.1. The observed COS spectrum (blue) zoomed in to each of the observed lines, with the fitted Gaussian profile (orange). For double-peaked lines (except for MgII) we fit each peak separately. 5.2. Constructing the UV profile of LHS 3844 )

1 7 s

2 6 FIGURE 5.2: Ly-α ﬂux estimates from UV-UV m c line emission correlations found by Young- g

r 5 e

( blood et al. (2017). We take the inverse-

) x

u 4 variance weighted mean of the individual l F

e line correlations to get our ﬁnal Ly-α ﬂux c

a 3

f estimate (last bar in the graph) of FIXME r u

S ( ) = ± 2 log10 FSur f .,Ly−α 5.55 0.000003, which -

y corresponds to FLy−α = (2.91 ± 0.0000171) × L ( −14 0 1

1 10 . g o l 0 MgII HeII CIV SiIV SiIII NV CII SiII Mean Line

value for Ly-α according to:

( ) = × ( ) + log10 FSur f ., UV1 m log10 FSur f ., UV2 b (5.1)

where FSur f ., UV1 in this case is the Ly-α surface flux, FSur f ., UV2 is the surface flux of the lines we measure (Table 5.1), and m and b, along with their uncertainties, are taken from Table 9 of Youngblood et al. (2017). We propagate the errors in stellar distance, stellar radius, m, and b in order to estimate the uncertainty in Ly-α flux established by each line. The UV-UV scaling estimates for the Ly-α flux are all in agreement. We take the inverse-variance weighted mean of the individual line estimates to get our final Ly-α flux

estimate Figure 5.2. We ﬁnd log10(FSur f .,Ly−α) = 5.55 ± 0.000003, which corresponds to −14 FLy−α = 2.91 ± 0.0000171 × 10 .

151 Chapter 5. LHS 3844 UV

5.2.2 EUV estimation

The extreme ultra-violet (EUV; 100-912Å), for stars other than the Sun, is not observable to any current or future telescope. Energies corresponding to wavelengths below 912Å are high enough to completely ionize the neutral hydrogen in the inter-stellar medium. We must therefore rely on estimates similar to those we used for the Ly-α line to estimate the EUV flux of LHS 3844. We compare two methods for EUV estimation which produce, on the whole, similar results. The first is based on measurements of the Solar spectrum and relies on scaling relations from the Ly-α lineLinsky, Fontenla, and France (2014). The Linsky, Fontenla, and France (2014) relations provide broadband estimates of the EUV flux (Figure 5.3, top panel). The second method from France et al. (2018) develops scaling relations between the SiIV and NV lines in the FUV and the 90-360Å range measured by the Extreme-ultraviolet Explorer (Craig et al., 1997). These scaling relations work the same way as in Equation 5.1. X-ray data would be required to estimate the rest of the EUV spectrum in this manner. The SiIV and NV lines are particularly suited to estimating the EUV because they form in a plasma similar to the coronal region where the EUV radiation is emitted. The SiIV and NV lines do not suffer from ISM extinction as other FUV lines which form at lower temperatures, like CII (France et al., 2018). We in general find good agreement between the France et al. (2018) and Linsky, Fontenla, and France (2014) methods where they over- lap, but the uncertainty in m and b from the France et al. (2018) method dominate our uncertainties and therefore only provide upper limits on the EUV flux from LHS 3844 at 90-360Å (Figure 5.3, bottom panel).

152 5.2. Constructing the UV proﬁle of LHS 3844

Estimated EUV flux ) 1 Å 10 16 1 s

m FIGURE 5.3: EUV estimates of LHS 3844. c

r Top: EUV estimates from Ly-α ﬂux (Linsky, e ( Fontenla, and France, 2014). Blue line shows y t i

s best estimates and shaded region indicates 1- n e 17 σ uncertainties. Bottom: EUV estimates from D

10 x

u 90-360Å based on correlations with SiIV and l F NV lines (France et al., 2018). We integrate the 10 13 estimates in the top panel in wavelength space SiIV, France+ (2018) NV, France+ (2018) in order to compare them to the estimates Linsky+ (2014) from the SiIV (purple) and NV (pink) lines. ) 1 Error bars are 1-σ uncertainties. Dashed ver- s

2 tical grey lines indicate the edges of the Lin-

m 10 14 c sky, Fontenla, and France (2014) photometric

r bands. Shaded grey area indicates photomet- e ( ric band from 90-360Å. x u l F

10 15

200 400 600 800 1000 Wavelength (Å)

153 Chapter 5. LHS 3844 UV

1e 15 2.00 1e 14

) 1.75 1 1.0 Å

1 1.50 s

2 1.25 0.5 m c

g 1.00 r e

( 0.0

t 0.75 1210 1215 1220 i s n e 0.50 D

x u l

F 0.25

0.00 500 1000 1500 2000 2500 3000 Wavelength (Å)

FIGURE 5.4: Modified UV spectrum of LHS 3844. This UV spectrum includes an estimate of the Ly-α line (inset), and an estimate of the EUV flux (blueward of 1170Å) using the Linsky, Fontenla, and France (2014) method. Flux between lines has been binned down and averaged such that flux does not dip below zero. The continuum is below the noise floor of the COS observations, except at the reddest end of the NUV (redward of 3000Å). There is a gap in our observations between 2125 and 2750Å.

5.2.3 Putting it all together

Finally, we put all the pieces together to present a UV spectrum of LHS 3844 (Figure 5.4. We construct a Ly-α line using a Gaussian profile that integrates to the value we derive for the Ly-α flux. We include an estimate of the EUV using the scaling method from Linsky, Fontenla, and France (2014). The COS spectrum from HST is noisy and includes flux points below zero, which is not physical. Except for the very reddest end of the NUV, the UV continuum is below the COS noise floor. We remove contamination in the UV profile from geocoronal Ly-α emission, as well as local emission of OI (1302Å, 1305Å, 1306Å) and NI (1200Å). In between the detected lines and the estimated Ly-α and EUV fluxes we bin the measured flux. For bins where the mean flux is less than zero we take the mean of the neighboring bins.

154 5.2. Constructing the UV proﬁle of LHS 3844

TABLE 5.2: Derived values from the UV proﬁle of LHS 3844

Value FUV/NUV 15.7 ± 25.5 Ly-α/UV 0.88 ± 0.10 f (FUV) -4.10 f (NUV) -5.30 f (XUV) -3.65 The large uncertainty in the value of FUV/NUV comes from the large uncertainty in the NUV ﬂux, which is dominated by the MgII line (Ta- ble 5.1). Following France et al. (2016), f (band) = log10(L(band)/LBol).

5.2.4 LHS 3844 compared to MUSCLES stars

The MUSCLES survey featured few stars of similar spectral type to LHS 3844 (France et al., 2018). The extension to MUSCLES for low mass stars, Mega-MUSCLES, will focus on this parameter space but it is not yet published. We present some derived values from the observed and estimated UV profile to compare to those presented by the MUSCLES survey in Table 5.2. We find a higher FUV/NUV flux ratio than for MUSCLES (France et al., 2013; France et al., 2018), but with such a large uncertainty that this value is not useful. We find that the Ly-α line makes up 88 ± 10% of the total UV flux, which in good agreement with the MUSCLES stars. We also provide the fraction of the FUV and NUV

−3 luminosities to the bolometric luminosity. We use (2.72 ± 0.4) × 10 L as the bolometric luminosity for LHS 3844 (Vanderspek et al., 2019).

155 Chapter 5. LHS 3844 UV

5.3 Context for LHS 3844b

The highly irradiated terrestrial planet in orbit around LHS 3844 likely does not have an atmosphere. Atmospheres with surface pressures greater than 10 bars are disfavored (Kreidberg et al., 2019), and clear, low mean molecular weight atmospheres are disfavored down to 0.01 bar (Diamond-Lowe et al., 2020). Tenuous high mean molecular weight atmospheres are not addressed empirically, but theoretical arguments based on the stellar wind and high energy radiation that LHS 3844b would encounter strongly imply that this world is a bare rock (Kreidberg et al., 2019). We do not have direct measurements of the X-ray and extreme-ultra-violet (XUV; 10-1000Å) portion of LHS 3844’s spectrum, but we can use the observed UV proﬁle of LHS 3844 to anchor estimates, which in turn can provide insight into the high energy history of LHS 3844 and the atmospheric evolution of LHS 3844b.

5.3.1 Scaling Proxima Centauri

There is not a perfect analog to LHS 3844 in the MUSCLES sample, but the MUSCLES collaboration put together a data product for Proxima Centauri using archival data2. Prox- ima Centauri, our nearest stellar neighbor, is a mid-M dwarf like LHS 3844, and there has been extensive theoretical work on the potential survival of an atmosphere of habitable- zone exoplanet around it (Anglada-Escudé et al., 2016; Ribas et al., 2016; Dong et al., 2017; Garcia-Sage et al., 2017; Zahnle and Catling, 2017). We scale the panchromatic spectrum of Proxima Centauri for the MUSCLES catalog to LHS 3844, and use this scaled spectrum to estimate the XUV ﬂux of LHS 3844. Proxima Centauri has a faster rotation period (82.6

2archive.stsci.edu/prepds/muscles/

156 5.3. Context for LHS 3844b days; Collins, Jones, and Barnes, 2017) than LHS 3844 (128 days Vanderspek et al., 2019), and is likely more active (Davenport et al., 2016; MacGregor et al., 2018). We therefore take estimates from the scaled Proxima Centauri spectrum as upper limits for LHS 3844. We scale the Proxima Centauri spectrum to LHS 3844 using the SiIV and NV lines, as these have the highest correlations with high energy radiation beyond FUV (France et al., 2018). We integrate the scaled Proxima Centauri spectrum from 10-1000Å and compare

−3 this value to LHS 3844’s bolometric luminosity of (2.72 ± 0.4) × 10 L (Vanderspek et

−4 al., 2019). We ﬁnd an XUV fraction LXUV/LBol = 2.2 × 10 . At a distance of 0.00622 ± 0.00017 AU from LHS 3844 (Vanderspek et al., 2019), LHS 3844b receives an XUV ﬂux of 2.1 × 104 erg cm−2 s−1. Kreidberg et al. (2019) explore a parameter space for LHS 3844’s XUV saturation fraction from 10−4 to 10−2. Our estimate of the current XUV fraction falls within this range, though it is likely that with a 128-day rotation period, LHS 3844 is no longer in the saturation state (Wright et al., 2018). Models activity evolution predict that M dwarfs spend an extended amount of time in the highly active pre-main sequence phase before settling on to the main sequence (Baraffe et al., 2002; Baraffe et al., 2015). Our estimate of the current XUV fraction can be an anchor to those models.

5.3.2 Atmospheric mass loss

An open question for exoplanetary science is the rate of atmospheric mass loss for terrestrial planets orbiting M dwarfs. Atmospheric escape can take many forms. The data and associated estimates presented here, can address cases of thermal escape, which is driven by EUV and XUV ﬂux from the star.

157 Chapter 5. LHS 3844 UV

Basic mass loss equations for energy-limited escape show that hydrodynamic escape from LHS 3844b would be rapid and efﬁcient (Lopez and Fortney, 2013; Salz et al., 2016;

Johnstone et al., 2019). We calculate the evaporation efﬁciency log10(ηeva) to be -0.55, placing LHS 3844b solidly in the regime of efﬁcient atmospheric evaporation (compare to Figure 2 of Salz et al., 2016). This is unsurprising given that this is a terrestrial planet with a relatively low gravitational potential. Basic estimates of mass loss rates for the hydrodynamical regime using

2 ηπRpRXUV FXUV M˙ = (5.2) GKMp

where we take η = ηeva, Rp is the planet radius, RXUV is the planet radius at which XUV

ﬂux can be absorbed (for this simple calculation we assume Rp = RXUV), FXUV is the XUV ﬂux at the planet, K is correction factor because mass only needs to reach the Hill

radius to escape, and Mp is the planet mass (Salz et al., 2016). We ﬁnd a hydrodynamic mass loss rate of 2×1010 g/s for LHS 3844b.

5.4 Future work

We present here an initial look at the UV proﬁle of LHS 3844 from HST/COS. This data set has additional potential which cannot be explored here. Below we consider future directions for this project.

158 5.4. Future work

5.4.1 Flare statistics

All COS data were observed in TIME-TAG mode. With this time-sensitive information we can place constraints on the flare rate of LHS 3844. Though LHS 3844 is an inactive star, with H-α emission consistent with 0 EW and no optical flares detected in 28 days of 2-minute TESS data (Vanderspek et al., 2019), M dwarfs are known to flare at high energies even when quiescent at optical wavelengths (Loyd et al., 2018). Our data were taken over three separate visits between August 7 and August 12, 2019, with each visit lasting approximately 5 hours, including 45-minute Earth occultations during the HST orbit. Loyd et al. (2018) developed flare statistics from the MUSCLES sample using similar HST/COS data, and we can compare the flare frequency distribution for LHS 3844 to their results.

5.4.2 Additional estimates for EUV ﬂux

One of the key deliverables of this UV data set is an estimation of the EUV ﬂux, which has implications for atmospheric mass loss. In this work we explore two methods of estimating the EUV of LHS 3844 from the observed and estimated lines in the FUV, however there are additional methods that take into account the peak formation temperature for different lines (Garcia-Sage et al., 2017), and would therefore provide a more accurate estimate of the EUV ﬂux, or at least provide a conservative spread of estimates.

5.4.3 More detailed models of atmospheric escape

A leading motivation in observing the high-energy radiation of nearby mid-M dwarfs is to determine whether or not the terrestrial planets in orbit around them are able to

159 Chapter 5. LHS 3844 UV retain atmospheres. A more sophisticated modeling approach could use the results presented here as a benchmark for XUV radiation. Models of LHS 3844’s high-energy ﬂux can be evolved backwards from this point to estimate what XUV environment around LHS 3844b earlier looked like a few billion years ago (e.g., Luger and Barnes, 2015).

5.5 Conclusion

We present the observed UV spectrum of LHS 3844 from 1126-3216Å using COS instrument aboard HST. Because COS is a slit-less spectrograph, we cannot directly observe Ly-α flux from LHS 3844 due to geocoronal contamination in this band. We instead use UV-UV scalings from the MUSCLES survey to estimate the Ly-α flux (France et al., 2016; Youngblood et al., 2017). We estimate the EUV flux using the Linsky, Fontenla, and France (2014) scalings, and the XUV flux by scaling a panchromatic spectrum of Proxima Cen- tauri to the flux levels of the SiIV and NV lives measured in the LHS 3844 spectra. We find our resulting band-integrated measurements and estimates of the FUV, NUV, and XUV are in agreement with those found for other M stars (France et al., 2013; France et al., 2016). Ultimately the forthcoming Mega-MUSCLES survey will place LHS 3844 in the context of other planet-hosting mid-M stars. The MUSCLES survey found orders-of-magnitude variations in line fluxes in their sample, which largely consisted of earlier-type stars. It remains to be seen if this trend holds for older, slowly rotating mid-to-late-M dwarfs (Newton et al., 2018). We can place preliminary, empirical constraints on thermally-driven atmospheric escape from the highly-irradiated terrestrial world LHS 3844b. Scaling the UV spectrum we

160 5.5. Conclusion detect for LHS 3844 to other planet-hosting mid-M dwarfs can provide the ﬁrst empirically- driven inputs to models of atmospheric mass loss on other terrestrial exoplanets. We stress, however, the need for results from the Mega-MUSCLES program to know the limits on such a scaling for mid-M dwarfs like LHS 3844. We do note that it will not be possible to measure the UV spectrum of every planet-hosting M dwarf, and that our ability to do so only lasts as long as HST can gather data. With no planned successor to HST in the UV, these data of planet-hosting mid-M dwarfs are crucial for future efforts to understand atmospheric observations of the terrestrial worlds around them.

This paper includes data gathered with the Cosmic Origins Spectrograph on board the Hubble Space Telescope. We thank HST program coordinator Tricia Royle for assistance in scheduling these observations. Support for Program number 15704 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. H.D.-L. recognizes support from the National Science Foundation Graduate Research Fellowship Program (grant number DGE1144152). This publication was made possible through the support of a grant from the John Templeton Foundation. The opinions expressed here are those of the authors and do not necessarily reﬂect the views of the John Templeton Foundation.

Facilities: Hubble Space Telescope, Cosmic Origins Spectrograph

Software: astropy (Astropy Collaboration et al., 2013; Astropy Collaboration et al., 2018), ldtk (Newville et al., 2016)

161 Bibliography

Agol, Eric et al. (May 2005). “On detecting terrestrial planets with timing of giant planet transits”. In: MNRAS 359.2, pp. 567–579. DOI: 10.1111/j.1365-2966.2005.08922.x. arXiv: astro-ph/0412032 [astro-ph]. Akaike, Hirotogu (1998). “Information theory and an extension of the maximum likelihood principle”. In: Selected papers of hirotugu akaike. Springer, pp. 199–213. Anglada-Escudé, G. et al. (Aug. 2016). “A terrestrial planet candidate in a temperate orbit around Proxima Centauri”. In: Nature 536, pp. 437–440. DOI: 10.1038/nature19106. arXiv: 1609.03449 [astro-ph.EP]. Artigau, Étienne et al. (July 2014). “SPIRou: the near-infrared spectropolarimeter/high- precision velocimeter for the Canada-France-Hawaii telescope”. In: Ground-based and Airborne Instrumentation for Astronomy V. Vol. 9147, p. 914715. DOI: 10 . 1117 / 12 . 2055663. Astropy Collaboration et al. (Oct. 2013). “Astropy: A community Python package for astronomy”. In: A&A 558, A33, A33. DOI: 10 . 1051 / 0004 - 6361 / 201322068. arXiv: 1307.6212 [astro-ph.IM]. Astropy Collaboration et al. (Sept. 2018). “The Astropy Project: Building an Open-science Project and Status of the v2.0 Core Package”. In: AJ 156.3, 123, p. 123. DOI: 10.3847/ 1538-3881/aabc4f. arXiv: 1801.02634 [astro-ph.IM]. Baraffe, I. et al. (Feb. 2002). “Evolutionary models for low-mass stars and brown dwarfs: Uncertainties and limits at very young ages”. In: A&A 382, pp. 563–572. DOI: 10.1051/ 0004-6361:20011638. eprint: astro-ph/0111385. Baraffe, I. et al. (May 2015). “New evolutionary models for pre-main sequence and main sequence low-mass stars down to the hydrogen-burning limit”. In: A&A 577, A42, A42. DOI: 10.1051/0004-6361/201425481. arXiv: 1503.04107 [astro-ph.SR]. Batalha, N. E. et al. (June 2017). “PandExo: A Community Tool for Transiting Exoplanet Science with JWST & HST”. In: PASP 129.6, p. 064501. DOI: 10 . 1088 / 1538 - 3873 / aa65b0. arXiv: 1702.01820 [astro-ph.IM]. Bean, J. L., E. Miller-Ricci Kempton, and D. Homeier (Dec. 2010). “A ground-based transmission spectrum of the super-Earth exoplanet GJ 1214b”. In: Nature 468, pp. 669–672. DOI: 10.1038/nature09596. arXiv: 1012.0331 [astro-ph.EP].

162 Bibliography

Benneke, Björn et al. (Dec. 2019). “Water Vapor and Clouds on the Habitable-zone Sub- Neptune Exoplanet K2-18b”. In: ApJL 887.1, L14, p. L14. DOI: 10.3847/2041-8213/ ab59dc. arXiv: 1909.04642 [astro-ph.EP]. Berta, Z. K. et al. (Mar. 2012a). “The Flat Transmission Spectrum of the Super-Earth GJ1214b from Wide Field Camera 3 on the Hubble Space Telescope”. In: ApJ 747, 35, p. 35. DOI: 10.1088/0004-637X/747/1/35. arXiv: 1111.5621 [astro-ph.EP]. Berta, Zachory K. et al. (Nov. 2012b). “Transit Detection in the MEarth Survey of Nearby M Dwarfs: Bridging the Clean-ﬁrst, Search-later Divide”. In: AJ 144.5, 145, p. 145. DOI: 10.1088/0004-6256/144/5/145. arXiv: 1206.4715 [astro-ph.EP]. Berta-Thompson, Z. K. et al. (Nov. 2015). “A rocky planet transiting a nearby low-mass star”. In: Nature 527, pp. 204–207. DOI: 10 . 1038 / nature15762. arXiv: 1511 . 03550 [astro-ph.EP]. Birkby, J. L. (June 2018). “Exoplanet Atmospheres at High Spectral Resolution”. In: arXiv e-prints, arXiv:1806.04617, arXiv:1806.04617. arXiv: 1806.04617 [astro-ph.EP]. Birkby, J. L. et al. (Nov. 2013). “Detection of water absorption in the day side atmosphere of HD 189733 b using ground-based high-resolution spectroscopy at 3.2 µm”. In: MN- RAS 436, pp. L35–L39. DOI: 10.1093/mnrasl/slt107. arXiv: 1307.1133 [astro-ph.EP]. Birkby, J. L. et al. (Mar. 2017). “Discovery of Water at High Spectral Resolution in the Atmosphere of 51 Peg b”. In: AJ 153, 138, p. 138. DOI: 10.3847/1538-3881/aa5c87. Bixel, Alex et al. (Feb. 2019). “ACCESS: Ground-based Optical Transmission Spectroscopy of the Hot Jupiter WASP-4b”. In: AJ 157.2, 68, p. 68. DOI: 10.3847/1538-3881/aaf9a3. arXiv: 1812.07177 [astro-ph.EP]. Bonﬁls, X. et al. (Oct. 2018). “Radial velocity follow-up of GJ1132 with HARPS. A precise mass for planet b and the discovery of a second planet”. In: A&A 618, A142, A142. DOI: 10.1051/0004-6361/201731884. arXiv: 1806.03870 [astro-ph.EP]. Bouchy, F. et al. (Sept. 2017). “Near-InfraRed Planet Searcher to Join HARPS on the ESO 3.6-metre Telescope”. In: The Messenger 169, pp. 21–27. DOI: 10.18727/0722- 6691/ 5034. Brogi, M. et al. (Feb. 2016). “Rotation and Winds of Exoplanet HD 189733 b Measured with High-dispersion Transmission Spectroscopy”. In: ApJ 817.2, 106, p. 106. DOI: 10. 3847/0004-637X/817/2/106. arXiv: 1512.05175 [astro-ph.EP]. Burdanov, Artem et al. (2017). “SPECULOOS Exoplanet Search and Its Prototype on TRAP- PIST”. In: Handbook of Exoplanets, Edited by Hans J. Deeg and Juan Antonio Belmonte. Springer Living Reference Work, ISBN: 978-3-319-30648-3, 2017, id.130, p. 130. DOI: 10. 1007/978-3-319-30648-3_130-1. Burke, Christopher J. et al. (Aug. 2015). “Terrestrial Planet Occurrence Rates for the Kepler GK Dwarf Sample”. In: ApJ 809.1, 8, p. 8. DOI: 10.1088/0004-637X/809/1/8. arXiv: 1506.04175 [astro-ph.EP]. Charbonneau, David et al. (Mar. 2002). “Detection of an Extrasolar Planet Atmosphere”. In: ApJ 568.1, pp. 377–384. DOI: 10.1086/338770. arXiv: astro-ph/0111544 [astro-ph]. 163 Bibliography

Charbonneau, David et al. (June 2005). “Detection of Thermal Emission from an Extraso- lar Planet”. In: ApJ 626.1, pp. 523–529. DOI: 10.1086/429991. arXiv: astro-ph/0503457 [astro-ph]. Charbonneau, David et al. (Dec. 2009). “A super-Earth transiting a nearby low-mass star”. In: Nature 462.7275, pp. 891–894. DOI: 10.1038/nature08679. arXiv: 0912.3229 [astro-ph.EP]. Cloutier, Ryan et al. (Apr. 2020). “TOI-1235 b: a keystone super-Earth for testing radius valley emergence models around early M dwarfs”. In: arXiv e-prints, arXiv:2004.06682, arXiv:2004.06682. arXiv: 2004.06682 [astro-ph.EP]. Collins, John M., Hugh R. A. Jones, and John R. Barnes (June 2017). “Calculations of peri- odicity from Hα proﬁles of Proxima Centauri”. In: A&A 602, A48, A48. DOI: 10.1051/ 0004-6361/201628827. arXiv: 1608.07834 [astro-ph.SR]. Cosentino, Rosario et al. (2012). “Harps-N: the new planet hunter at TNG”. In: Proc. SPIE. Vol. 8446. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Se- ries, p. 84461V. DOI: 10.1117/12.925738. Craig, N. et al. (Nov. 1997). “The Extreme Ultraviolet Explorer Stellar Spectral Atlas”. In: ApJS 113.1, pp. 131–193. DOI: 10.1086/313052. Davenport, J. R. A. et al. (Oct. 2016). “MOST Observations of Our Nearest Neighbor: Flares on Proxima Centauri”. In: ApJL 829, L31, p. L31. DOI: 10.3847/2041- 8205/ 829/2/L31. arXiv: 1608.06672 [astro-ph.SR]. Dawson, Rebekah I., Eugene Chiang, and Eve J. Lee (Oct. 2015). “A metallicity recipe for rocky planets”. In: MNRAS 453.2, pp. 1471–1483. DOI: 10.1093/mnras/stv1639. arXiv: 1506.06867 [astro-ph.EP]. de Wit, J. et al. (Sept. 2016). “A combined transmission spectrum of the Earth-sized exoplanets TRAPPIST-1 b and c”. In: Nature 537, pp. 69–72. DOI: 10.1038/nature18641. arXiv: 1606.01103 [astro-ph.EP]. de Wit, Julien et al. (Mar. 2018). “Atmospheric reconnaissance of the habitable-zone Earth- sized planets orbiting TRAPPIST-1”. In: Nature Astronomy 2, pp. 214–219. DOI: 10 . 1038/s41550-017-0374-z. Delrez, Laetitia et al. (July 2018). “SPECULOOS: a network of robotic telescopes to hunt for terrestrial planets around the nearest ultracool dwarfs”. In: Proc. SPIE. Vol. 10700. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, p. 107001I. DOI: 10.1117/12.2312475. arXiv: 1806.11205 [astro-ph.IM]. Deming, Drake, Dana Louie, and Holly Sheets (Jan. 2019). “How to Characterize the At- mosphere of a Transiting Exoplanet”. In: PASP 131.995, p. 013001. DOI: 10.1088/1538- 3873/aae5c5. arXiv: 1810.04175 [astro-ph.EP]. Deming, Drake et al. (Mar. 2005). “Infrared radiation from an extrasolar planet”. In: Na- ture 434.7034, pp. 740–743. DOI: 10 . 1038 / nature03507. arXiv: astro - ph / 0503554 [astro-ph].

164 Bibliography

Deming, Drake et al. (Sept. 2013). “Infrared Transmission Spectroscopy of the Exoplanets HD 209458b and XO-1b Using the Wide Field Camera-3 on the Hubble Space Tele- scope”. In: ApJ 774.2, 95, p. 95. DOI: 10.1088/0004-637X/774/2/95. arXiv: 1302.1141 [astro-ph.EP]. Diamond-Lowe, Hannah et al. (Nov. 2014). “New Analysis Indicates No Thermal Inver- sion in the Atmosphere of HD 209458b”. In: ApJ 796.1, 66, p. 66. DOI: 10.1088/0004- 637X/796/1/66. arXiv: 1409.5336 [astro-ph.EP]. Diamond-Lowe, Hannah et al. (Aug. 2018). “Ground-based Optical Transmission Spec- troscopy of the Small, Rocky Exoplanet GJ 1132b”. In: AJ 156, 42, p. 42. DOI: 10.3847/ 1538-3881/aac6dd. Diamond-Lowe, Hannah et al. (2019). “Simultaneous Optical Transmission Spectroscopy of a Terrestrial, Habitable-Zone Exoplanet with Two Ground-Based Multi-Object Spec- trographs”. In: submitted to AJ, arXiv:1909.09104, arXiv:1909.09104. arXiv: 1909.09104 [astro-ph.EP]. Diamond-Lowe, Hannah et al. (2020). “Optical Transmission Spectroscopy of the Terres- trial Exoplanet LHS 3844b from 13 Transit Observations”. In: in prep. Dittmann, Jason A. et al. (Oct. 2017a). “A Search for Additional Bodies in the GJ 1132 Plan- etary System from 21 Ground-based Transits and a 100-hr Spitzer Campaign”. In: AJ 154, 142, p. 142. DOI: 10.3847/1538-3881/aa855b. arXiv: 1611.09848 [astro-ph.EP]. Dittmann, Jason A. et al. (Apr. 2017b). “A temperate rocky super-Earth transiting a nearby cool star”. In: Nature 544, pp. 333–336. DOI: 10.1038/nature22055. arXiv: 1704.05556 [astro-ph.EP]. Domagal-Goldman, Shawn D. et al. (June 2011). “Using Biogenic Sulfur Gases as Re- motely Detectable Biosignatures on Anoxic Planets”. In: Astrobiology 11.5, pp. 419–441. DOI: 10.1089/ast.2010.0509. Dong, Chuanfei et al. (Mar. 2017). “Is Proxima Centauri b Habitable? A Study of Atmo- spheric Loss”. In: ApJL 837.2, L26, p. L26. DOI: 10.3847/2041- 8213/aa6438. arXiv: 1702.04089 [astro-ph.EP]. Dressing, C. D. and D. Charbonneau (Apr. 2013). “The Occurrence Rate of Small Planets around Small Stars”. In: ApJ 767, 95, p. 95. DOI: 10.1088/0004-637X/767/1/95. arXiv: 1302.1647 [astro-ph.EP]. — (July 2015). “The Occurrence of Potentially Habitable Planets Orbiting M Dwarfs Es- timated from the Full Kepler Dataset and an Empirical Measurement of the Detec- tion Sensitivity”. In: ApJ 807, 45, p. 45. DOI: 10.1088/0004- 637X/807/1/45. arXiv: 1501.01623 [astro-ph.EP]. Dressing, Courtney D. et al. (Feb. 2015). “The Mass of Kepler-93b and The Composition of Terrestrial Planets”. In: ApJ 800.2, 135, p. 135. DOI: 10.1088/0004-637X/800/2/135. arXiv: 1412.8687 [astro-ph.EP]. Dressler, Alan et al. (Mar. 2011). “IMACS: The Inamori-Magellan Areal Camera and Spec- trograph on Magellan-Baade”. In: PASP 123.901, p. 288. DOI: 10.1086/658908. 165 Bibliography

Eastman, Jason, Robert Siverd, and B. Scott Gaudi (Aug. 2010). “Achieving Better Than 1 Minute Accuracy in the Heliocentric and Barycentric Julian Dates”. In: PASP 122.894, p. 935. DOI: 10.1086/655938. arXiv: 1005.4415 [astro-ph.IM]. Ehrenreich, D. et al. (June 2015). “A giant comet-like cloud of hydrogen escaping the warm Neptune-mass exoplanet GJ 436b”. In: Nature 522, pp. 459–461. DOI: 10.1038/ nature14501. arXiv: 1506.07541 [astro-ph.EP]. Elkins-Tanton, Linda T. (Apr. 2011). “Formation of early water oceans on rocky planets”. In: Ap&SS 332, pp. 359–364. DOI: 10.1007/s10509- 010- 0535- 3. arXiv: 1011.2710 [astro-ph.EP]. Espinoza, Néstor (Sept. 2017). “Unveiling Exoplanet Atmospheres with the ACCESS Sur- vey”. URL: https://repositorio.uc.cl/handle/11534/21313. PhD thesis. Av. Vicuña Mackenna 4860. Santiago de Chile: Pontiﬁcia Universidad Católica de Chile. Espinoza, Néstor and Andrés Jordán (Apr. 2016). “Limb darkening and exoplanets - II. Choosing the best law for optimal retrieval of transit parameters”. In: MNRAS 457.4, pp. 3573–3581. DOI: 10.1093/mnras/stw224. arXiv: 1601.05485 [astro-ph.EP]. Evans, Thomas M. et al. (Aug. 2017). “An ultrahot gas-giant exoplanet with a strato- sphere”. In: Nature 548.7665, pp. 58–61. DOI: 10.1038/nature23266. arXiv: 1708.01076 [astro-ph.EP]. Foreman-Mackey, D. et al. (Mar. 2013). “emcee: The MCMC Hammer”. In: PASP 125, pp. 306–312. DOI: 10.1086/670067. arXiv: 1202.3665 [astro-ph.IM]. Foreman-Mackey, Daniel (Nov. 2015). George: Gaussian Process regression. ascl: 1511.015. Foukal, Peter V. (2004). Solar Astrophysics, 2nd, Revised Edition. France, K. et al. (Apr. 2016). “The MUSCLES Treasury Survey. I. Motivation and Overview”. In: ApJ 820, 89, p. 89. DOI: 10 . 3847 / 0004 - 637X / 820 / 2 / 89. arXiv: 1602 . 09142 [astro-ph.SR]. France, K. et al. (Nov. 2018). “Far-ultraviolet Activity Levels of F, G, K, and M Dwarf Exoplanet Host Stars”. In: ApJS 239, 16, p. 16. DOI: 10.3847/1538-4365/aae1a3. arXiv: 1809.07342 [astro-ph.SR]. France, Kevin et al. (Feb. 2013). “The Ultraviolet Radiation Environment around M dwarf Exoplanet Host Stars”. In: ApJ 763.2, 149, p. 149. DOI: 10.1088/0004-637X/763/2/149. arXiv: 1212.4833 [astro-ph.EP]. Fressin, François et al. (Apr. 2013). “The False Positive Rate of Kepler and the Occurrence of Planets”. In: ApJ 766.2, 81, p. 81. DOI: 10 . 1088 / 0004 - 637X / 766 / 2 / 81. arXiv: 1301.0842 [astro-ph.EP]. Fulton, Benjamin J. and Erik A. Petigura (Dec. 2018). “The California-Kepler Survey. VII. Precise Planet Radii Leveraging Gaia DR2 Reveal the Stellar Mass Dependence of the Planet Radius Gap”. In: AJ 156.6, 264, p. 264. DOI: 10.3847/1538-3881/aae828. arXiv: 1805.01453 [astro-ph.EP].

166 Bibliography

Fulton, Benjamin J. et al. (Sept. 2017). “The California-Kepler Survey. III. A Gap in the Radius Distribution of Small Planets”. In: AJ 154.3, 109, p. 109. DOI: 10.3847/1538- 3881/aa80eb. arXiv: 1703.10375 [astro-ph.EP]. Gaia Collaboration et al. (Nov. 2016). “The Gaia mission”. In: A&A 595, A1, A1. DOI: 10. 1051/0004-6361/201629272. arXiv: 1609.04153 [astro-ph.IM]. Gaia Collaboration et al. (Aug. 2018). “Gaia Data Release 2. Summary of the contents and survey properties”. In: A&A 616, A1, A1. DOI: 10.1051/0004-6361/201833051. arXiv: 1804.09365 [astro-ph.GA]. Gaidos, E. et al. (Apr. 2016). “They are small worlds after all: revised properties of Kepler M dwarf stars and their planets”. In: MNRAS 457, pp. 2877–2899. DOI: 10.1093/mnras/ stw097. arXiv: 1512.04437 [astro-ph.EP]. Garcia-Sage, K. et al. (July 2017). “On the Magnetic Protection of the Atmosphere of Prox- ima Centauri b”. In: ApJL 844.1, L13, p. L13. DOI: 10.3847/2041-8213/aa7eca. Gibson, N. P. (Dec. 2014). “Reliable inference of exoplanet light-curve parameters using deterministic and stochastic systematics models”. In: MNRAS 445.4, pp. 3401–3414. DOI: 10.1093/mnras/stu1975. arXiv: 1409.5668 [astro-ph.EP]. Gibson, N. P. et al. (Jan. 2012). “A Gaussian process framework for modelling instrumental systematics: application to transmission spectroscopy”. In: MNRAS 419.3, pp. 2683– 2694. DOI: 10.1111/j.1365-2966.2011.19915.x. arXiv: 1109.3251 [astro-ph.EP]. Gillon, M. et al. (Apr. 2013). “TRAPPIST-UCDTS: A prototype search for habitable planets transiting ultra-cool stars”. In: European Physical Journal Web of Conferences. Vol. 47. European Physical Journal Web of Conferences, p. 03001. DOI: 10 . 1051 / epjconf / 20134703001. Gillon, M. et al. (Feb. 2017a). “Seven temperate terrestrial planets around the nearby ultracool dwarf star TRAPPIST-1”. In: Nature 542, pp. 456–460. DOI: 10.1038/nature21360. arXiv: 1703.01424 [astro-ph.EP]. Gillon, Michaël et al. (May 2016). “Temperate Earth-sized planets transiting a nearby ultracool dwarf star”. In: Nature 533.7602, pp. 221–224. DOI: 10.1038/nature17448. arXiv: 1605.07211 [astro-ph.EP]. Gillon, Michaël et al. (Mar. 2017b). “Two massive rocky planets transiting a K-dwarf 6.5 parsecs away”. In: Nature Astronomy 1, 0056, p. 0056. DOI: 10.1038/s41550-017- 0056. arXiv: 1703.01430 [astro-ph.EP]. Ginzburg, Sivan, Hilke E. Schlichting, and Re’em Sari (May 2018). “Core-powered mass- loss and the radius distribution of small exoplanets”. In: MNRAS 476.1, pp. 759–765. DOI: 10.1093/mnras/sty290. arXiv: 1708.01621 [astro-ph.EP]. Gomes, R. et al. (May 2005). “Origin of the cataclysmic Late Heavy Bombardment period of the terrestrial planets”. In: Nature 435.7041, pp. 466–469. DOI: 10.1038/nature03676. Green, James C. et al. (Jan. 2012). “The Cosmic Origins Spectrograph”. In: ApJ 744.1, 60, p. 60. DOI: 10.1088/0004-637X/744/1/60. arXiv: 1110.0462 [astro-ph.IM].

167 Bibliography

Grimm, Simon L. et al. (May 2018). “The nature of the TRAPPIST-1 exoplanets”. In: A&A 613, A68, A68. DOI: 10.1051/0004-6361/201732233. arXiv: 1802.01377 [astro-ph.EP]. Gupta, Akash and Hilke E. Schlichting (July 2019). “Sculpting the valley in the radius distribution of small exoplanets as a by-product of planet formation: the core-powered mass-loss mechanism”. In: MNRAS 487.1, pp. 24–33. DOI: 10.1093/mnras/stz1230. arXiv: 1811.03202 [astro-ph.EP]. — (Mar. 2020). “Signatures of the core-powered mass-loss mechanism in the exoplanet population: dependence on stellar properties and observational predictions”. In: MN- RAS 493.1, pp. 792–806. DOI: 10.1093/mnras/staa315. arXiv: 1907.03732 [astro-ph.EP]. Hardegree-Ullman, Kevin K. et al. (Aug. 2019). “Kepler Planet Occurrence Rates for Mid- type M Dwarfs as a Function of Spectral Type”. In: AJ 158.2, 75, p. 75. DOI: 10.3847/ 1538-3881/ab21d2. arXiv: 1905.05900 [astro-ph.EP]. Harman, C. E. et al. (Oct. 2015). “Abiotic O2 Levels on Planets around F, G, K, and M Stars: Possible False Positives for Life?” In: ApJ 812, 137, p. 137. DOI: 10.1088/0004- 637X/812/2/137. arXiv: 1509.07863 [astro-ph.EP]. Hawley, Suzanne L. et al. (Dec. 2014). “Kepler Flares. I. Active and Inactive M Dwarfs”. In: ApJ 797.2, 121, p. 121. DOI: 10.1088/0004- 637X/797/2/121. arXiv: 1410.7779 [astro-ph.SR]. Henry, T. J. et al. (Dec. 2006). “The Solar Neighborhood. XVII. Parallax Results from the CTIOPI 0.9 m Program: 20 New Members of the RECONS 10 Parsec Sample”. In: AJ 132, pp. 2360–2371. DOI: 10.1086/508233. eprint: astro-ph/0608230. Holman, M. J. et al. (Dec. 2006). “The Transit Light Curve Project. I. Four Consecutive Transits of the Exoplanet XO-1b”. In: ApJ 652, pp. 1715–1723. DOI: 10.1086/508155. eprint: astro-ph/0607571. Holman, Matthew J. and Norman W. Murray (Feb. 2005). “The Use of Transit Timing to Detect Terrestrial-Mass Extrasolar Planets”. In: Science 307.5713, pp. 1288–1291. DOI: 10.1126/science.1107822. arXiv: astro-ph/0412028 [astro-ph]. Howard, Andrew W. et al. (Aug. 2012). “Planet Occurrence within 0.25 AU of Solar-type Stars from Kepler”. In: ApJS 201.2, 15, p. 15. DOI: 10.1088/0067- 0049/201/2/15. arXiv: 1103.2541 [astro-ph.EP]. Huijser, D., J. Goodman, and B. J. Brewer (Sept. 2015). “Properties of the Afﬁne Invari- ant Ensemble Sampler in high dimensions”. In: ArXiv e-prints. arXiv: 1509 . 02230 [stat.CO]. Husser, T. O. et al. (May 2013). “A new extensive library of PHOENIX stellar atmospheres and synthetic spectra”. In: A&A 553, A6, A6. DOI: 10.1051/0004- 6361/201219058. arXiv: 1303.5632 [astro-ph.SR]. Ida, Shigeru, Takeru Yamamura, and Satoshi Okuzumi (Apr. 2019). “Water delivery by pebble accretion to rocky planets in habitable zones in evolving disks”. In: A&A 624, A28, A28. DOI: 10.1051/0004-6361/201834556. arXiv: 1901.04611 [astro-ph.EP].

168 Bibliography

Inamdar, Niraj K. and Hilke E. Schlichting (Apr. 2015). “The formation of super-Earths and mini-Neptunes with giant impacts”. In: MNRAS 448.2, pp. 1751–1760. DOI: 10. 1093/mnras/stv030. arXiv: 1412.4440 [astro-ph.EP]. Irwin, J. M. et al. (Jan. 2015). “The MEarth-North and MEarth-South Transit Surveys: Searching for Habitable Super-Earth Exoplanets Around Nearby M-dwarfs”. In: 18th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun. Ed. by G. T. van Belle and H. C. Harris. Vol. 18. Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, pp. 767–772. arXiv: 1409.0891 [astro-ph.EP]. Izidoro, A. et al. (Apr. 2013). “A Compound Model for the Origin of Earth’s Water”. In: ApJ 767, 54, p. 54. DOI: 10.1088/0004-637X/767/1/54. arXiv: 1302.1233 [astro-ph.EP]. Johnstone, C. P. et al. (Apr. 2019). “Extreme hydrodynamic losses of Earth-like atmospheres in the habitable zones of very active stars”. In: A&A 624, L10, p. L10. DOI: 10.1051/0004-6361/201935279. arXiv: 1904.01063 [astro-ph.EP]. Jordán, A. et al. (Dec. 2013). “A Ground-based Optical Transmission Spectrum of WASP- 6b”. In: ApJ 778, 184, p. 184. DOI: 10.1088/0004-637X/778/2/184. arXiv: 1310.6048 [astro-ph.EP]. Joye, W. A. and E. Mandel (2003). “New Features of SAOImage DS9”. In: Astronomical Data Analysis Software and Systems XII. Ed. by H. E. Payne, R. I. Jedrzejewski, and R. N. Hook. Vol. 295. Astronomical Society of the Paciﬁc Conference Series, p. 489. Kasting, James F., Daniel P. Whitmire, and Ray T. Reynolds (Jan. 1993). “Habitable Zones around Main Sequence Stars”. In: Icarus 101.1, pp. 108–128. DOI: 10.1006/icar.1993. 1010. Kempton, E. M.-R. et al. (Apr. 2017). “Exo-Transmit: An Open-Source Code for Calcu- lating Transmission Spectra for Exoplanet Atmospheres of Varied Composition”. In: PASP 129.4, p. 044402. DOI: 10.1088/1538-3873/aa61ef. arXiv: 1611.03871 [astro-ph.EP]. Kempton, Eliza M. R. et al. (Nov. 2018). “A Framework for Prioritizing the TESS Plane- tary Candidates Most Amenable to Atmospheric Characterization”. In: PASP 130.993, p. 114401. DOI: 10.1088/1538-3873/aadf6f. arXiv: 1805.03671 [astro-ph.EP]. Kirk, James et al. (Oct. 2019). “LRG-BEASTS: Transmission Spectroscopy and Retrieval Analysis of the Highly Inﬂated Saturn-mass Planet WASP-39b”. In: AJ 158.4, 144, p. 144. DOI: 10.3847/1538-3881/ab397d. arXiv: 1908.02358 [astro-ph.EP]. Knutson, Heather A. et al. (Jan. 2008). “The 3.6-8.0 µm Broadband Emission Spectrum of HD 209458b: Evidence for an Atmospheric Temperature Inversion”. In: ApJ 673.1, pp. 526–531. DOI: 10.1086/523894. arXiv: 0709.3984 [astro-ph]. Knutson, Heather A. et al. (Oct. 2014). “Hubble Space Telescope Near-IR Transmission Spectroscopy of the Super-Earth HD 97658b”. In: ApJ 794.2, 155, p. 155. DOI: 10.1088/ 0004-637X/794/2/155. arXiv: 1403.4602 [astro-ph.EP]. Koll, D. D. B. and D. S. Abbot (July 2016). “Temperature Structure and Atmospheric Cir- culation of Dry Tidally Locked Rocky Exoplanets”. In: ApJ 825, 99, p. 99. DOI: 10.3847/ 0004-637X/825/2/99. arXiv: 1605.01066 [astro-ph.EP]. 169 Bibliography

Koll, Daniel D. B. (July 2019). “A Scaling Theory for Atmospheric Heat Redistribution on Rocky Exoplanets”. In: arXiv e-prints, arXiv:1907.13145, arXiv:1907.13145. arXiv: 1907. 13145 [astro-ph.EP]. Koll, Daniel D. B. et al. (Dec. 2019). “Identifying Candidate Atmospheres on Rocky M Dwarf Planets via Eclipse Photometry”. In: ApJ 886.2, 140, p. 140. DOI: 10.3847/1538- 4357/ab4c91. arXiv: 1907.13138 [astro-ph.EP]. Kopparapu, Ravi Kumar et al. (Mar. 2013). “Habitable Zones around Main-sequence Stars: New Estimates”. In: ApJ 765.2, 131, p. 131. DOI: 10.1088/0004-637X/765/2/131. arXiv: 1301.6674 [astro-ph.EP]. Kostov, Veselin B. et al. (July 2019). “The L 98-59 System: Three Transiting, Terrestrial-size Planets Orbiting a Nearby M Dwarf”. In: AJ 158.1, 32, p. 32. DOI: 10 . 3847 / 1538 - 3881/ab2459. arXiv: 1903.08017 [astro-ph.EP]. Kreidberg, L. and A. Loeb (Nov. 2016). “Prospects for Characterizing the Atmosphere of Proxima Centauri b”. In: ApJL 832, L12, p. L12. DOI: 10.3847/2041-8205/832/1/L12. arXiv: 1608.07345 [astro-ph.EP]. Kreidberg, L. et al. (Jan. 2014a). “Clouds in the atmosphere of the super-Earth exoplanet GJ1214b”. In: Nature 505, pp. 69–72. DOI: 10.1038/nature12888. arXiv: 1401.0022 [astro-ph.EP]. Kreidberg, Laura (Nov. 2015). “batman: BAsic Transit Model cAlculatioN in Python”. In: Publications of the Astronomical Society of the Paciﬁc 127, p. 1161. DOI: 10.1086/683602. arXiv: 1507.08285 [astro-ph.EP]. — (2018). “Exoplanet Atmosphere Measurements from Transmission Spectroscopy and Other Planet Star Combined Light Observations”. In: Handbook of Exoplanets, p. 100. DOI: 10.1007/978-3-319-55333-7_100. Kreidberg, Laura et al. (Oct. 2014b). “A Precise Water Abundance Measurement for the Hot Jupiter WASP-43b”. In: ApJL 793.2, L27, p. L27. DOI: 10.1088/2041-8205/793/2/ L27. arXiv: 1410.2255 [astro-ph.EP]. Kreidberg, Laura et al. (Aug. 2019). “Absence of a thick atmosphere on the terrestrial exoplanet LHS 3844b”. In: Nature 573.7772, pp. 87–90. DOI: 10.1038/s41586- 019- 1497-4. arXiv: 1908.06834 [astro-ph.EP]. Lagrange, A. M. et al. (Jan. 2009). “A probable giant planet imaged in the β Pictoris disk. VLT/NaCo deep L’-band imaging”. In: A&A 493.2, pp. L21–L25. DOI: 10.1051/0004- 6361:200811325. arXiv: 0811.3583 [astro-ph]. Lammer, Helmut et al. (May 2018). “Origin and evolution of the atmospheres of early Venus, Earth and Mars”. In: Astronomy and Astrophysics Review 26, 2, p. 2. DOI: 10. 1007/s00159-018-0108-y. Lee, Eve J. and Eugene Chiang (Feb. 2016). “Breeding Super-Earths and Birthing Super- puffs in Transitional Disks”. In: ApJ 817.2, 90, p. 90. DOI: 10.3847/0004-637X/817/2/ 90. arXiv: 1510.08855 [astro-ph.EP].

170 Bibliography

Lee, Eve J., Eugene Chiang, and Chris W. Ormel (Dec. 2014). “Make Super-Earths, Not Jupiters: Accreting Nebular Gas onto Solid Cores at 0.1 AU and Beyond”. In: ApJ 797.2, 95, p. 95. DOI: 10.1088/0004-637X/797/2/95. arXiv: 1409.3578 [astro-ph.EP]. Linsky, J. L., J. Fontenla, and K. France (Jan. 2014). “The Intrinsic Extreme Ultraviolet Fluxes of F5 V TO M5 V Stars”. In: ApJ 780, 61, p. 61. DOI: 10.1088/0004-637X/780/1/ 61. arXiv: 1310.1360 [astro-ph.SR]. Liu, Shang-Fei et al. (Oct. 2015). “Giant Impact: An Efﬁcient Mechanism for the Devolatiliza- tion of Super-Earths”. In: ApJ 812.2, 164, p. 164. DOI: 10.1088/0004-637X/812/2/164. arXiv: 1509.05772 [astro-ph.EP]. Lopez, E. D. and J. J. Fortney (Oct. 2013). “The Role of Core Mass in Controlling Evapora- tion: The Kepler Radius Distribution and the Kepler-36 Density Dichotomy”. In: ApJ 776, 2, p. 2. DOI: 10.1088/0004-637X/776/1/2. arXiv: 1305.0269 [astro-ph.EP]. Lopez, E. D., J. J. Fortney, and N. Miller (Dec. 2012). “How Thermal Evolution and Mass- loss Sculpt Populations of Super-Earths and Sub-Neptunes: Application to the Kepler- 11 System and Beyond”. In: ApJ 761, 59, p. 59. DOI: 10.1088/0004-637X/761/1/59. arXiv: 1205.0010 [astro-ph.EP]. Lopez, E. D. and K. Rice (Oct. 2018). “How formation time-scales affect the period dependence of the transition between rocky super-Earths and gaseous sub-Neptunesand implications for η⊕”. In: MNRAS 479, pp. 5303–5311. DOI: 10.1093/mnras/sty1707. Lopez, Eric D. and Jonathan J. Fortney (Sept. 2014). “Understanding the Mass-Radius Relation for Sub-neptunes: Radius as a Proxy for Composition”. In: ApJ 792.1, 1, p. 1. DOI: 10.1088/0004-637X/792/1/1. arXiv: 1311.0329 [astro-ph.EP]. Lopez-Morales, Mercedes et al. (2014). “ACCESS: The Arizona-CfA-Catolica Exoplanet Spectroscopy Survey”. In: American Astronomical Society Meeting Abstracts #224. Vol. 224. American Astronomical Society Meeting Abstracts, p. 120.14. Louden, Tom and Peter J. Wheatley (Dec. 2015). “Spatially Resolved Eastward Winds and Rotation of HD 189733b”. In: ApJL 814.2, L24, p. L24. DOI: 10.1088/2041-8205/814/ 2/L24. arXiv: 1511.03689 [astro-ph.EP]. Loyd, R. O. P. et al. (Nov. 2018). “The MUSCLES Treasury Survey. V. FUV Flares on Active and Inactive M Dwarfs”. In: ApJ 867, 71, p. 71. DOI: 10.3847/1538-4357/aae2bd. arXiv: 1809.07322 [astro-ph.SR]. Luger, R. and R. Barnes (Feb. 2015). “Extreme Water Loss and Abiotic O2 Buildup on Planets Throughout the Habitable Zones of M Dwarfs”. In: Astrobiology 15, pp. 119– 143. DOI: 10.1089/ast.2014.1231. arXiv: 1411.7412 [astro-ph.EP]. MacGregor, M. A. et al. (Mar. 2018). “Detection of a Millimeter Flare from Proxima Cen- tauri”. In: ApJL 855, L2, p. L2. DOI: 10.3847/2041-8213/aaad6b. arXiv: 1802.08257 [astro-ph.EP]. Mahadevan, S. et al. (July 2010). “The habitable zone planet ﬁnder: a proposed high- resolution NIR spectrograph for the Hobby Eberly Telescope to discover low-mass

171 Bibliography

exoplanets around M dwarfs”. In: Ground-based and Airborne Instrumentation for Astron- omy III. Vol. 7735. Proc. SPIE, p. 77356X. DOI: 10.1117/12.857551. arXiv: 1007.3235 [astro-ph.IM]. Malik, Matej et al. (Feb. 2017). “HELIOS: An Open-source, GPU-accelerated Radiative Transfer Code for Self-consistent Exoplanetary Atmospheres”. In: AJ 153.2, 56, p. 56. DOI: 10.3847/1538-3881/153/2/56. arXiv: 1606.05474 [astro-ph.EP]. Malik, Matej et al. (Dec. 2019). “Analyzing Atmospheric Temperature Profiles and Spectra of M Dwarf Rocky Planets”. In: ApJ 886.2, 142, p. 142. DOI: 10 . 3847 / 1538 - 4357 / ab4a05. arXiv: 1907.13135 [astro-ph.EP]. Mansfield, Megan et al. (Dec. 2019). “Identifying Atmospheres on Rocky Exoplanets through Inferred High Albedo”. In: ApJ 886.2, 141, p. 141. DOI: 10.3847/1538-4357/ab4c90. arXiv: 1907.13150 [astro-ph.EP]. Marcus, Robert A. et al. (Mar. 2010). “Minimum Radii of Super-Earths: Constraints from Giant Impacts”. In: ApJL 712.1, pp. L73–L76. DOI: 10.1088/2041-8205/712/1/L73. arXiv: 1003.0451 [astro-ph.EP]. Marois, Christian et al. (Nov. 2008). “Direct Imaging of Multiple Planets Orbiting the Star HR 8799”. In: Science 322.5906, p. 1348. DOI: 10.1126/science.1166585. arXiv: 0811. 2606 [astro-ph]. Marois, Christian et al. (Dec. 2010). “Images of a fourth planet orbiting HR 8799”. In: Na- ture 468.7327, pp. 1080–1083. DOI: 10.1038/nature09684. arXiv: 1011.4918 [astro-ph.EP]. May, E. M. et al. (Sept. 2018). “MOPSS. I. Flat Optical Spectra for the Hot Jupiters WASP-4 b and WASP-52b”. In: AJ 156.3, 122, p. 122. DOI: 10.3847/1538-3881/aad4a8. arXiv: 1807.06561 [astro-ph.EP]. McKerns, Michael M. et al. (2012). “Building a Framework for Predictive Science”. In: arXiv e-prints, arXiv:1202.1056, arXiv:1202.1056. arXiv: 1202.1056 [cs.MS]. Meadows, Victoria S. (Oct. 2017). “Reflections on O2 as a Biosignature in Exoplanetary Atmospheres”. In: Astrobiology 17.10, pp. 1022–1052. DOI: 10.1089/ast.2016.1578. Ment, Kristo et al. (Jan. 2019). “A Second Terrestrial Planet Orbiting the Nearby M Dwarf LHS 1140”. In: AJ 157, 32, p. 32. DOI: 10.3847/1538-3881/aaf1b1. arXiv: 1808.00485 [astro-ph.EP]. Miller-Ricci, E. and J. J. Fortney (June 2010). “The Nature of the Atmosphere of the Tran- siting Super-Earth GJ 1214b”. In: ApJL 716, pp. L74–L79. DOI: 10.1088/2041-8205/ 716/1/L74. arXiv: 1001.0976 [astro-ph.EP]. Miller-Ricci, E., S. Seager, and D. Sasselov (Jan. 2009). “The Atmospheric Signatures of Super-Earths: How to Distinguish Between Hydrogen-Rich and Hydrogen-Poor At- mospheres”. In: ApJ 690, pp. 1056–1067. DOI: 10.1088/0004-637X/690/2/1056. arXiv: 0808.1902. Miller-Ricci Kempton, E., K. Zahnle, and J. J. Fortney (Jan. 2012). “The Atmospheric Chem- istry of GJ 1214b: Photochemistry and Clouds”. In: ApJ 745, 3, p. 3. DOI: 10.1088/0004- 637X/745/1/3. arXiv: 1104.5477 [astro-ph.EP]. 172 Bibliography

Morley, C. V. et al. (Dec. 2017). “Observing the Atmospheres of Known Temperate Earth- sized Planets with JWST”. In: ApJ 850, 121, p. 121. DOI: 10.3847/1538-4357/aa927b. arXiv: 1708.04239 [astro-ph.EP]. Mulders, Gijs D., Ilaria Pascucci, and Dániel Apai (Jan. 2015). “A Stellar-mass-dependent Drop in Planet Occurrence Rates”. In: ApJ 798.2, 112, p. 112. DOI: 10 . 1088 / 0004 - 637X/798/2/112. arXiv: 1406.7356 [astro-ph.EP]. Nemchin, A. et al. (Feb. 2009). “Timing of crystallization of the lunar magma ocean constrained by the oldest zircon”. In: Nature Geoscience 2.2, pp. 133–136. DOI: 10.1038/ ngeo417. Newton, E. R. et al. (Jan. 2017). “The Hα Emission of Nearby M Dwarfs and its Relation to Stellar Rotation”. In: ApJ 834, 85, p. 85. DOI: 10.3847/1538-4357/834/1/85. arXiv: 1611.03509 [astro-ph.SR]. Newton, E. R. et al. (Nov. 2018). “New Rotation Period Measurements for M Dwarfs in the Southern Hemisphere: An Abundance of Slowly Rotating, Fully Convective Stars”. In: AJ 156, 217, p. 217. DOI: 10.3847/1538-3881/aad73b. arXiv: 1807.09365 [astro-ph.SR]. Newton, Elisabeth R. et al. (Apr. 2016). “The Impact of Stellar Rotation on the Detectability of Habitable Planets around M Dwarfs”. In: ApJL 821.1, L19, p. L19. DOI: 10.3847/ 2041-8205/821/1/L19. arXiv: 1604.03135 [astro-ph.EP]. Newville, M. et al. (June 2016). Lmﬁt: Non-Linear Least-Square Minimization and Curve- Fitting for Python. DOI: 10.5281/zenodo.49428. ascl: 1606.014. Nutzman, Philip and David Charbonneau (Mar. 2008). “Design Considerations for a Ground- Based Transit Search for Habitable Planets Orbiting M Dwarfs”. In: PASP 120.865, p. 317. DOI: 10.1086/533420. arXiv: 0709.2879 [astro-ph]. Owen, James E. (May 2019). “Atmospheric Escape and the Evolution of Close-In Exo- planets”. In: Annual Review of Earth and Planetary Sciences 47, pp. 67–90. DOI: 10.1146/ annurev-earth-053018-060246. arXiv: 1807.07609 [astro-ph.EP]. Owen, James E. and Yanqin Wu (Oct. 2013). “Kepler Planets: A Tale of Evaporation”. In: ApJ 775.2, 105, p. 105. DOI: 10.1088/0004- 637X/775/2/105. arXiv: 1303.3899 [astro-ph.EP]. Parviainen, Hannu and Suzanne Aigrain (Nov. 2015). “ldtk: Limb Darkening Toolkit”. In: MNRAS 453.4, pp. 3821–3826. DOI: 10.1093/mnras/stv1857. URL: http://mnras. oxfordjournals.org/lookup/doi/10.1093/mnras/stv1857. Pepe, F. et al. (Aug. 2004). “The HARPS search for southern extra-solar planets. I. HD 330075 b: A new “hot Jupiter””. In: A&A 423, pp. 385–389. DOI: 10.1051/0004-6361: 20040389. eprint: arXiv:astro-ph/0405252. Petigura, Erik A., Geoffrey W. Marcy, and Andrew W. Howard (June 2013). “A Plateau in the Planet Population below Twice the Size of Earth”. In: ApJ 770.1, 69, p. 69. DOI: 10.1088/0004-637X/770/1/69. arXiv: 1304.0460 [astro-ph.EP].

173 Bibliography

Quirrenbach, A. et al. (July 2010). “CARMENES: Calar Alto high-resolution search for M dwarfs with exo-earths with a near-infrared Echelle spectrograph”. In: Ground-based and Airborne Instrumentation for Astronomy III. Vol. 7735. Proc. SPIE, p. 773513. DOI: 10.1117/12.857777. Rackham, B. et al. (Jan. 2017). “ACCESS I: An Optical Transmission Spectrum of GJ 1214b Reveals a Heterogeneous Stellar Photosphere”. In: ApJ 834, 151, p. 151. DOI: 10.3847/ 1538-4357/aa4f6c. arXiv: 1612.00228 [astro-ph.EP]. Rackham, Benjamin V., Dániel Apai, and Mark S. Giampapa (Feb. 2018). “The Transit Light Source Effect: False Spectral Features and Incorrect Densities for M-dwarf Tran- siting Planets”. In: ApJ 853.2, 122, p. 122. DOI: 10.3847/1538- 4357/aaa08c. arXiv: 1711.05691 [astro-ph.EP]. — (Mar. 2019). “The Transit Light Source Effect. II. The Impact of Stellar Heterogeneity on Transmission Spectra of Planets Orbiting Broadly Sun-like Stars”. In: AJ 157.3, 96, p. 96. DOI: 10.3847/1538-3881/aaf892. arXiv: 1812.06184 [astro-ph.EP]. Rahmati, A. et al. (July 2014). “Pickup ion measurements by MAVEN: A diagnostic of photochemical oxygen escape from Mars”. In: Geophys. Res. Lett. 41.14, pp. 4812–4818. DOI: 10.1002/2014GL060289. Ranjan, Sukrit, Robin Wordsworth, and Dimitar D. Sasselov (July 2017). “The Surface UV Environment on Planets Orbiting M Dwarfs: Implications for Prebiotic Chemistry and the Need for Experimental Follow-up”. In: ApJ 843, 110, p. 110. DOI: 10.3847/1538- 4357/aa773e. Raymond, Sean N. and Andre Izidoro (Nov. 2017). “Origin of water in the inner Solar Sys- tem: Planetesimals scattered inward during Jupiter and Saturn’s rapid gas accretion”. In: Icarus 297, pp. 134–148. DOI: 10.1016/j.icarus.2017.06.030. arXiv: 1707.01234 [astro-ph.EP]. Raymond, Sean N. et al. (Oct. 2009). “Building the terrestrial planets: Constrained accretion in the inner Solar System”. In: Icarus 203.2, pp. 644–662. DOI: 10.1016/j.icarus. 2009.05.016. arXiv: 0905.3750 [astro-ph.EP]. Reiners, A. and G. Basri (Mar. 2009). “On the magnetic topology of partially and fully convective stars”. In: A&A 496.3, pp. 787–790. DOI: 10.1051/0004-6361:200811450. arXiv: 0901.1659 [astro-ph.SR]. Ribas, Ignasi et al. (Dec. 2016). “The habitability of Proxima Centauri b. I. Irradiation, rotation and volatile inventory from formation to the present”. In: A&A 596, A111, A111. DOI: 10.1051/0004-6361/201629576. arXiv: 1608.06813 [astro-ph.EP]. Ricker, G. R. et al. (Jan. 2015). “Transiting Exoplanet Survey Satellite (TESS)”. In: Journal of Astronomical Telescopes, Instruments, and Systems 1.1, 014003, p. 014003. DOI: 10.1117/ 1.JATIS.1.1.014003. Rodler, Florian and Mercedes López-Morales (Jan. 2014). “Feasibility Studies for the De- tection of O2 in an Earth-like Exoplanet”. In: ApJ 781.1, 54, p. 54. DOI: 10.1088/0004- 637X/781/1/54. arXiv: 1312.1585 [astro-ph.EP]. 174 Bibliography

Rogers, L. A. (Mar. 2015). “Most 1.6 Earth-radius Planets are Not Rocky”. In: ApJ 801, 41, p. 41. DOI: 10.1088/0004-637X/801/1/41. arXiv: 1407.4457 [astro-ph.EP]. Rugheimer, S. et al. (Aug. 2015). “Effect of UV Radiation on the Spectral Fingerprints of Earth-like Planets Orbiting M Stars”. In: ApJ 809, 57, p. 57. DOI: 10.1088/0004- 637X/809/1/57. arXiv: 1506.07202 [astro-ph.EP]. Saar, S. H. and J. L. Linsky (Dec. 1985). “The photospheric magnetic ﬁeld of the dM3.5e ﬂare star AD Leonis”. In: ApJL 299, pp. L47–L50. DOI: 10.1086/184578. Salz, M. et al. (Jan. 2016). “Energy-limited escape revised. The transition from strong planetary winds to stable thermospheres”. In: A&A 585, L2, p. L2. DOI: 10.1051/0004- 6361/201527042. arXiv: 1511.09348 [astro-ph.EP]. Sanchis-Ojeda, Roberto et al. (May 2014). “A Study of the Shortest-period Planets Found with Kepler”. In: ApJ 787.1, 47, p. 47. DOI: 10.1088/0004- 637X/787/1/47. arXiv: 1403.2379 [astro-ph.EP]. Schaefer, L. et al. (Oct. 2016). “Predictions of the Atmospheric Composition of GJ 1132b”. In: ApJ 829, 63, p. 63. DOI: 10 . 3847 / 0004 - 637X / 829 / 2 / 63. arXiv: 1607 . 03906 [astro-ph.EP]. Schlichting, Hilke E., Re’em Sari, and Almog Yalinewich (Feb. 2015). “Atmospheric mass loss during planet formation: The importance of planetesimal impacts”. In: Icarus 247, pp. 81–94. DOI: 10.1016/j.icarus.2014.09.053. arXiv: 1406.6435 [astro-ph.EP]. Schwab, C. et al. (Aug. 2016). “Design of NEID, an extreme precision Doppler spectrograph for WIYN”. In: Ground-based and Airborne Instrumentation for Astronomy VI. Vol. 9908. Proc. SPIE, 99087H. DOI: 10.1117/12.2234411. Schwarz, Gideon (July 1978). “Estimating the Dimension of a Model”. In: Annals of Statis- tics 6.2, pp. 461–464. Seager, S. et al. (Nov. 2007). “Mass-Radius Relationships for Solid Exoplanets”. In: ApJ 669.2, pp. 1279–1297. DOI: 10.1086/521346. arXiv: 0707.2895 [astro-ph]. Segura, A. et al. (Sept. 2010). “The Effect of a Strong Stellar Flare on the Atmospheric Chemistry of an Earth-like Planet Orbiting an M Dwarf”. In: Astrobiology 10, pp. 751– 771. DOI: 10.1089/ast.2009.0376. arXiv: 1006.0022 [astro-ph.EP]. Seifahrt, A. et al. (Aug. 2016). “Development and construction of MAROON-X”. In: Ground- based and Airborne Instrumentation for Astronomy VI. Vol. 9908. Proc. SPIE, p. 990818. DOI: 10.1117/12.2232069. arXiv: 1606.07140 [astro-ph.IM]. Showman, A. P. et al. (Jan. 2013). “Doppler Signatures of the Atmospheric Circulation on Hot Jupiters”. In: ApJ 762, 24, p. 24. DOI: 10.1088/0004-637X/762/1/24. arXiv: 1207.5639 [astro-ph.EP]. Sing, D. K. et al. (Mar. 2011). “Gran Telescopio Canarias OSIRIS transiting exoplanet atmospheric survey: detection of potassium in XO-2b from narrowband spectrophotom- etry”. In: A&A 527, A73, A73. DOI: 10.1051/0004-6361/201015579. arXiv: 1008.4795 [astro-ph.EP].

175 Bibliography

Sing, David K. et al. (Jan. 2016). “A continuum from clear to cloudy hot-Jupiter exoplanets without primordial water depletion”. In: Nature 529, pp. 59–62. DOI: 10 . 1038 / nature16068. arXiv: 1512.04341 [astro-ph.EP]. Snellen, I. A. G. et al. (Feb. 2013). “Finding Extraterrestrial Life Using Ground-based High- dispersion Spectroscopy”. In: ApJ 764, 182, p. 182. DOI: 10.1088/0004-637X/764/2/ 182. arXiv: 1302.3251 [astro-ph.EP]. Snellen, Ignas A. G. et al. (June 2010). “The orbital motion, absolute mass and high- altitude winds of exoplanet HD209458b”. In: Nature 465.7301, pp. 1049–1051. DOI: 10.1038/nature09111. arXiv: 1006.4364 [astro-ph.EP]. Southworth, J. et al. (Apr. 2017). “Detection of the Atmosphere of the 1.6 M ⊕ Exoplanet GJ 1132 b”. In: AJ 153, 191, p. 191. DOI: 10.3847/1538-3881/aa6477. arXiv: 1612.02425 [astro-ph.EP]. Speagle, Joshua S. (Apr. 2020). “DYNESTY: a dynamic nested sampling package for estimating Bayesian posteriors and evidences”. In: MNRAS 493.3, pp. 3132–3158. DOI: 10.1093/mnras/staa278. arXiv: 1904.02180 [astro-ph.IM]. Spinelli, R. et al. (July 2019). “The high-energy radiation environment of the habitable- zone super-Earth LHS 1140b”. In: A&A 627, A144, A144. DOI: 10.1051/0004-6361/ 201935636. arXiv: 1906.08783 [astro-ph.EP]. Spruit, H. C. (Dec. 1976). “Pressure equilibrium and energy balance of small photospheric ﬂuxtubes.” In: SoPh 50.2, pp. 269–295. DOI: 10.1007/BF00155292. Stassun, K. G. et al. (2011). “The M4 Transition: Toward a Comprehensive Understand- ing of the Transition into the Fully Convective Regime”. In: 16th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun. Ed. by Christopher Johns-Krull, Matthew K. Browning, and Andrew A. West. Vol. 448. Astronomical Society of the Paciﬁc Confer- ence Series, p. 505. Stassun, Keivan G. et al. (Oct. 2019). “The Revised TESS Input Catalog and Candidate Target List”. In: AJ 158.4, 138, p. 138. DOI: 10.3847/1538-3881/ab3467. arXiv: 1905. 10694 [astro-ph.SR]. Stevenson, K. B. et al. (Feb. 2016). “A Search for Water in the Atmosphere of HAT-P-26b Using LDSS-3C”. In: ApJ 817, 141, p. 141. DOI: 10.3847/0004-637X/817/2/141. arXiv: 1511.08226 [astro-ph.EP]. Sullivan, P. W. et al. (Aug. 2015). “The Transiting Exoplanet Survey Satellite: Simulations of Planet Detections and Astrophysical False Positives”. In: ApJ 809, 77, p. 77. DOI: 10.1088/0004-637X/809/1/77. arXiv: 1506.03845 [astro-ph.EP]. Sullivan, Peter W. et al. (Mar. 2017). “Erratum: “The Transiting Exoplanet Survey Satellite: Simulations of Planet Detections and Astrophysical False Positives” (2015, ApJ, 809, 77)”. In: ApJ 837.1, 99, p. 99. DOI: 10.3847/1538-4357/837/1/99. Szentgyorgyi, A. et al. (Aug. 2014). “A preliminary design for the GMT-Consortium Large Earth Finder (G-CLEF)”. In: Ground-based and Airborne Instrumentation for Astronomy V. Vol. 9147. Proc. SPIE, p. 914726. DOI: 10.1117/12.2056741. 176 Bibliography

Thompson, Susan E. et al. (Apr. 2018). “Planetary Candidates Observed by Kepler. VIII. A Fully Automated Catalog with Measured Completeness and Reliability Based on Data Release 25”. In: ApJS 235.2, 38, p. 38. DOI: 10.3847/1538-4365/aab4f9. arXiv: 1710.06758 [astro-ph.EP]. Tian, F. et al. (Jan. 2014). “High stellar FUV/NUV ratio and oxygen contents in the atmospheres of potentially habitable planets”. In: Earth and Planetary Science Letters 385, pp. 22–27. DOI: 10.1016/j.epsl.2013.10.024. arXiv: 1310.2590 [astro-ph.EP]. Tsiganis, K. et al. (May 2005). “Origin of the orbital architecture of the giant planets of the Solar System”. In: Nature 435.7041, pp. 459–461. DOI: 10.1038/nature03539. Van Eylen, V. et al. (Oct. 2018). “An asteroseismic view of the radius valley: stripped cores, not born rocky”. In: MNRAS 479.4, pp. 4786–4795. DOI: 10 . 1093 / mnras / sty1783. arXiv: 1710.05398 [astro-ph.EP]. Vanderburg, A. et al. (Oct. 2015). “A disintegrating minor planet transiting a white dwarf”. In: Nature 526, pp. 546–549. DOI: 10.1038/nature15527. arXiv: 1510.06387 [astro-ph.EP]. Vanderspek, Roland et al. (Feb. 2019). “TESS Discovery of an Ultra-short-period Planet around the Nearby M Dwarf LHS 3844”. In: ApJL 871.2, L24, p. L24. DOI: 10.3847/ 2041-8213/aafb7a. arXiv: 1809.07242 [astro-ph.EP]. Wang, Songhu et al. (Apr. 2017). “Updated Masses for the TRAPPIST-1 Planets”. In: arXiv e-prints, arXiv:1704.04290, arXiv:1704.04290. arXiv: 1704.04290 [astro-ph.EP]. Watson, A. J., T. M. Donahue, and J. C. G. Walker (Nov. 1981). “The dynamics of a rapidly escaping atmosphere: Applications to the evolution of Earth and Venus”. In: Icarus 48.2, pp. 150–166. DOI: 10.1016/0019-1035(81)90101-9. West, Andrew A. et al. (Mar. 2008). “Constraining the Age-Activity Relation for Cool Stars: The Sloan Digital Sky Survey Data Release 5 Low-Mass Star Spectroscopic Sam- ple”. In: AJ 135, pp. 785–795. DOI: 10.1088/0004-6256/135/3/785. arXiv: 0712.1590 [astro-ph]. Winn, Joshua N. (Jan. 2010). “Transits and Occultations”. In: arXiv e-prints, arXiv:1001.2010, arXiv:1001.2010. arXiv: 1001.2010 [astro-ph.EP]. Winters, Jennifer G. et al. (Oct. 2019). “Three Red Suns in the Sky: A Transiting, Terrestrial Planet in a Triple M-dwarf System at 6.9 pc”. In: AJ 158.4, 152, p. 152. DOI: 10.3847/ 1538-3881/ab364d. arXiv: 1906.10147 [astro-ph.EP]. Wolfgang, A. and E. Lopez (June 2015). “How Rocky Are They? The Composition Distri- bution of Kepler’s Sub-Neptune Planet Candidates within 0.15 AU”. In: ApJ 806, 183, p. 183. DOI: 10.1088/0004-637X/806/2/183. arXiv: 1409.2982 [astro-ph.EP]. Wordsworth, Robin (June 2015). “Atmospheric Heat Redistribution and Collapse on Tidally Locked Rocky Planets”. In: ApJ 806.2, 180, p. 180. DOI: 10.1088/0004-637X/806/2/180. arXiv: 1412.5575 [astro-ph.EP]. Wright, Nicholas J. and Jeremy J. Drake (July 2016). “Solar-type dynamo behaviour in fully convective stars without a tachocline”. In: Nature 535.7613, pp. 526–528. DOI: 10. 1038/nature18638. arXiv: 1607.07870 [astro-ph.SR]. 177 Bibliography

Wright, Nicholas J. et al. (Sept. 2018). “The stellar rotation-activity relationship in fully convective M dwarfs”. In: MNRAS 479.2, pp. 2351–2360. DOI: 10.1093/mnras/sty1670. arXiv: 1807.03304 [astro-ph.SR]. Youngblood, A. et al. (June 2016). “The MUSCLES Treasury Survey. II. Intrinsic LYα and Extreme Ultraviolet Spectra of K and M Dwarfs with Exoplanets”. In: ApJ 824, 101, p. 101. DOI: 10.3847/0004-637X/824/2/101. arXiv: 1604.01032 [astro-ph.SR]. Youngblood, A. et al. (July 2017). “The MUSCLES Treasury Survey. IV. Scaling Relations for Ultraviolet, Ca II K, and Energetic Particle Fluxes from M Dwarfs”. In: ApJ 843, 31, p. 31. DOI: 10.3847/1538-4357/aa76dd. arXiv: 1705.04361 [astro-ph.SR]. Zahnle, Kevin, James F. Kasting, and James B. Pollack (Apr. 1990). “Mass fractionation of noble gases in diffusion-limited hydrodynamic hydrogen escape”. In: Icarus 84.2, pp. 502–527. DOI: 10.1016/0019-1035(90)90050-J. Zahnle, Kevin J. and David C. Catling (July 2017). “The Cosmic Shoreline: The Evidence that Escape Determines which Planets Have Atmospheres, and what this May Mean for Proxima Centauri B”. In: ApJ 843.2, 122, p. 122. DOI: 10.3847/1538-4357/aa7846. arXiv: 1702.03386 [astro-ph.EP]. Zeng, Li, Dimitar D. Sasselov, and Stein B. Jacobsen (Mar. 2016). “Mass-Radius Relation for Rocky Planets Based on PREM”. In: ApJ 819.2, 127, p. 127. DOI: 10.3847/0004- 637X/819/2/127. arXiv: 1512.08827 [astro-ph.EP].

178