On the Atmospheres of the Smallest Gas Exoplanets

Home , 31 Pegasi, 32 Pegasi, 33 Pegasi, 35 Pegasi, 51 Pegasi, 55 Pegasi

Erin M. May

A dissertation submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy (Astronomoy and Astrophysics) in The University of Michigan 2019

Doctoral Committee: Assistant Professor Emily Rasucher, Chair Professor Fred Adams Professor Michael Meyer Professor John Monnier

Erin M. May [email protected] ORCID iD: 0000-0002-2739-1465 c Erin M. May 2019 For my cat. May she learn to love me at least as much as I love this dissertation.

ii ACKNOWLEDGEMENTS

“I don’t have emotions. And sometimes that makes me very sad.” – Bender, the Robot

I’ve never been much for emotions, but if it’s a required component of this dissertation...

First, thank you to Alex. I may have been a pain to deal with during parts of this process, but we both made it through. Thank you to Li’l B who taught me that not everything that’s perfect is perfect for you and that love isn’t unconditional. Especially from a cat.

Thank you to the humans in the department who were there for me along the way. In particular, Emily, who was the advisor I needed but didn’t deserve.

To Renee for conﬁrming that there’s no such thing as too many macarons on a Friday, and for the constant commiserating throughout the past year. And because this human requested this acknowledgement, to Adi for saving me that one time from that one thing.

Thank you to the regular GB@3 crew, even those who showed up late or barely at all. Thank you to Danilyn who made GB feel like a home. Also to Brian who always knew that the only thing that mattered was tacos and how many we wanted (needed).

Thank you to all the other humans, mostly those who were especially nice humans. You know who you are.

Finally, to the humans who told me I couldn’t do it, thank you for giving me someone to prove wrong. Because, well, I did it.

iii TABLE OF CONTENTS

DEDICATION ...... ii

ACKNOWLEDGEMENTS ...... iii

LIST OF FIGURES ...... viii

LIST OF TABLES ...... xi

ABSTRACT ...... xiii

CHAPTER

I. Introduction ...... 1

1.1 Detection of Exoplanets ...... 1 1.1.1 The Transit Method ...... 2 1.1.2 The Radial Velocity Method ...... 12 1.1.3 Current Status of Exoplanet Detection and the Future of the Field ...... 16 1.2 Basic Parameters and Classiﬁcations of Exoplanets ...... 17 1.3 Transmission Spectroscopy ...... 21 1.3.1 Space-based Observations ...... 25 1.3.2 Ground-based Observations ...... 26 1.4 Atmospheric Modeling ...... 27 1.4.1 Energy Balance Models ...... 28 1.4.2 General Circulation Models ...... 29 1.5 Dissertation Overview ...... 30

II. MOPSS I: Flat Optical Spectra for the Hot Jupiters WASP-4b and WASP-52b ...... 31

2.1 Preface ...... 31 2.2 Abstract ...... 31 2.3 Introduction ...... 32

iv 2.4 Observations ...... 34 2.4.1 The IMACS Instrument ...... 34 2.4.2 The planet WASP-4b ...... 36 2.4.3 The planet WASP-52b ...... 36 2.5 Data Analysis ...... 38 2.5.1 Reduction Pipeline ...... 38 2.5.2 Light Curves ...... 42 2.5.2.1 White Light Curves ...... 43 2.5.2.2 Binned Light Curves ...... 44 2.5.3 Error Analysis and Noise Removal ...... 50 2.6 Results ...... 51 2.6.1 Transmission Spectra ...... 51 2.6.2 WASP-4b ...... 52 2.6.3 WASP-52b ...... 54 2.6.3.1 Unocculted Star Spots ...... 54 2.6.3.2 Star Spots on the Stellar Limb ...... 55 2.7 Conclusions ...... 59 2.8 Acknowledgements ...... 60 2.9 Facilities and Software Used ...... 60 2.10 Appendix ...... 61 2.10.1 Check Star ...... 61 2.10.2 Tables of Results ...... 63

III. MOPSS II: Extreme Optical Scattering Slope for the Inﬂated Super- Neptune HATS-8b ...... 67

3.1 Preface ...... 67 3.2 Abstract ...... 67 3.3 Introduction ...... 68 3.4 Observations ...... 71 3.4.1 The Inamori-Magellan Areal Camera & Spectrograph In- strument ...... 71 3.4.2 The planet HATS-8b ...... 72 3.5 Data Analysis ...... 73 3.5.1 Reduction Pipeline ...... 73 3.5.2 Removing Airmass Trend ...... 74 3.5.3 Correlated Noise Model ...... 75 3.5.4 Light Curves ...... 76 3.5.4.1 White Light Curves ...... 77 3.5.4.2 Binned Light Curves ...... 78 3.6 Results ...... 79 3.6.1 Transmission Spectrum ...... 79 3.6.2 Unocculted Star Spots ...... 84 3.6.3 A Clear Atmosphere ...... 88 3.6.4 Clouds and the Scattering Slope ...... 88

v 3.7 Conclusions ...... 92 3.8 Acknowledgements ...... 93 3.9 Facilities and Software Used ...... 93

IV. Living On the Edge: The Eﬀects of a Surface on Atmospheric Cir- culation and Emission for 1.5R⊕ Planets ...... 95

4.1 Preface ...... 95 4.2 Abstract ...... 95 4.3 Introduction ...... 96 4.4 Method ...... 98 4.4.1 General Circulation Model ...... 98 4.4.2 Surface-Atmosphere Interactions ...... 99 4.4.2.1 Surface Heating ...... 100 4.4.2.2 Atmospheric Drag ...... 101 4.4.3 Choice of Model Resolution ...... 102 4.5 Model Validation ...... 103 4.5.1 Earth ...... 103 4.5.1.1 Model Inputs ...... 104 4.5.1.2 Results: Earth ...... 106 4.6 Transition Planet ...... 106 4.6.1 Planetary Properties ...... 108 4.6.2 Model Iterations ...... 110 4.7 Results: Transition Planet ...... 111 4.7.1 Band Integrated Emission and Top of the Atmosphere Albedos112 4.7.2 Zonal Averaged Emission and Reﬂection ...... 113 4.8 Conclusions and Future Directions ...... 117

V. Examining Tatooine: Atmospheric Models of Neptune-like Cir- cumbinary Planets ...... 118

5.1 Preface ...... 118 5.2 Abstract ...... 118 5.3 Introduction ...... 119 5.4 Method ...... 121 5.4.1 Calculation of Orbits and Resulting Irradiation ...... 121 5.4.2 Energy Balance Model ...... 122 5.4.2.1 C: Heat Capacity Per Unit Area ...... 124 5.4.2.2 D: Diﬀusivity ...... 124 5.4.2.3 S(1-A): Stellar Irradiation and Albedo . . . . . 125 5.4.2.4 I: Cooling Function ...... 126 5.4.3 General Circulation Model ...... 126 5.4.3.1 GCM Heat Transport - applications to the EBM 128 5.5 Results ...... 128 5.5.1 Kepler 47b ...... 129

vi 5.5.1.1 Kepler 47b - EBM ...... 129 5.5.1.2 Kepler 47b - GCM ...... 131 5.5.2 Expanding Models to More Planets ...... 134 5.5.3 Introduction of Obliquity ...... 136 5.6 Conclusions ...... 139 5.6.1 Modeling of Circumbinary Planets ...... 139 5.6.2 Habitability of Circumbinary Planets ...... 140 5.6.3 Observables ...... 140

VI. Conclusion ...... 142

6.1 Summary ...... 142 6.1.1 Transmission Spectroscopy and the Future of Exoplanet Ob- servations ...... 142 6.1.2 Atmospheric Modeling and the Future of Atmospheric Char- acterization ...... 144 6.2 Future Directions ...... 145

BIBLIOGRAPHY ...... 148

vii LIST OF FIGURES

Figure

1.1 Schematic of a Transit ...... 3

1.2 Geometry of a Transit ...... 4

1.3 Schematic of Limb Darkening ...... 7

1.4 Limb Darkening and its eﬀect on transits ...... 8

1.5 Occulted Spots and their eﬀect on transits ...... 10

1.6 Exoplanets discovered with the transit method to-date...... 11

1.7 Radial Velocity data of 51 Pegasi b ...... 13

1.8 All exoplanets discovered to-date...... 16

1.9 Mass vs. Radius for known Exoplanets ...... 19

1.10 Composition Curves with Known Exoplanets Plotted ...... 20

1.11 Transmission Spectroscopy Schematic ...... 22

2.1 Field of Views for WASP-4b and WASP-52b Observations...... 35

2.2 WASP-4 Spectrum ...... 37

2.3 WASP-52 Spectrum ...... 39

2.4 White light curve and baseline models for WASP-4b ...... 43

2.5 White light curve for WASP-52b ...... 45

viii 2.6 Binned light curves for WASP-4b ...... 46

2.7 Binned light curves for WASP-52b ...... 48

2.8 Limb Darkening results for WASP-4b and WASP-52b ...... 50

2.9 Transmission Spectra for WASP-4b ...... 53

2.10 Combined Transmission Spectra for WASP-52b ...... 54

2.11 The eﬀects of star spots on measured transmission spectra ...... 56

2.12 The eﬀects of occulted spots on the stellar limb on the transit light curve . 57

2.13 The eﬀects of occulted spots on the stellar limb on the ﬁt limb darkening parameters ...... 57

2.14 The effects of occulted spots on the stellar limb on the fit limb darkening parameters for WASP-52b specifically ...... 58

2.15 Check-star Spectrum ...... 61

2.16 Check-star reduction process ...... 62

3.1 Field of View for HATS-8 ...... 72

3.2 Airmass correction for HATS-8b observations ...... 75

3.3 Correlated Noise Model for HATS-8b ...... 77

3.4 Light curves for HATS-8b ...... 81

3.5 Limb Darkening Fits from HATS-8b ...... 82

3.6 Transmission Spectrum for HATS-8b ...... 83

3.7 Eﬀects of Unocculted Spots on the Transmission Spectrum ...... 87

3.8 Necessary atmospheric parameters to explain the measured scattering slope for HATS-8b in a clear atmosphere ...... 89

3.9 Necessary atmospheric parameters to explain the measured scattering slope for HATS-8b in a cloudy atmosphere ...... 91

4.1 Earth GCM - Resolutions dependencies of temperature ...... 107

ix 4.2 Earth Temperature-Pressure Proﬁle Comparison ...... 108

4.3 Deﬁnitions of Transition Regime Base GCM Models ...... 109

4.4 Long wave to Short Wave Comparison ...... 112

4.5 Emitted Flux for 1.5R⊕ Planets ...... 114

4.6 Equator-to-Pole Emitted Long Wave Flux Diﬀerences ...... 116

5.1 Incident ﬂux variations for representative circumbinary systems...... 123

5.2 Time variable temperature patterns as predicted by the EBM for Kepler-47b.131

5.3 Temperature and wind maps as predicted by the GCM for Kepler-47b with both time-varying and constant irradiation inputs...... 132

5.4 Expected temperature ﬂuctuations for diﬀering levels of modeling complexities for Kepler-47b...... 133

5.5 Variability of known circumbinary planetary atmospheres as compared to their single star cases...... 136

5.6 Variability of a grid of circumbinary systems as compared to their single star cases, for a variety of axial obliquites...... 137

5.7 Time variable temperature patterns as predicted by the EBM for Kepler-47b with a 30◦ obliquity...... 138

x LIST OF TABLES

Table

1.1 Current Status of MOPSS ...... 27

2.1 WASP-4b: Calibrator Stars ...... 37

2.2 WASP-52b: Calibrator Stars ...... 39

2.3 WASP-4b Stellar and Orbital Parameters ...... 49

2.4 WASP-52b Stellar and Orbital Parameters ...... 49

2.5 WASP-4b: Wavelength dependent variables ...... 63

2.6 WASP-52b: Wavelength dependent variables, ut20160811 ...... 64

2.7 WASP-52b: Wavelength dependent variables, ut20160922 ...... 65

2.8 WASP-52b: Wavelength dependent variables, Combined Rp/Rstar values . . 66

3.1 HATS-8b Calibrator Stars ...... 73

3.2 HATS-8b Stellar and Orbital Parameters ...... 78

3.3 HATS-8b: MCMC Fit Results ...... 86

4.1 Surface Heat Equation Parameters ...... 103

4.2 Earth GCM Input Parameters ...... 105

4.3 GCM Parameters for set of 4 Base Models ...... 111

5.1 Circumbinary Exoplanet Energy Balance Model Parameters ...... 126

xi 5.2 Circumbinary Exoplanets General Circulation Model Parameters ...... 127

5.3 Kepler 47 System Parameters ...... 130

xii ABSTRACT

With nearly 4000 unique exoplanets detected to-date, the ﬁeld of exoplanet characterization has numerous questions to answer about these diverse planets and plenty of targets to observe as we work to understand the population of exoplanets as a whole, and where Earth

1 fits in. In particular, planets larger than Earth but smaller than Neptune (3.88 R⊕ ) are the most common exoplanet detected, yet we lack a direct comparison in our Solar System to study and extrapolate from. Because there must be some point at which exoplanets transition from having a higher likelihood of being terrestrial (thin gaseous envelope compared to the total radius) to having a higher likelihood of being gaseous (large gaseous envelope compared to the total radius), this size-regime has been dubbed the ‘transition regime’. With this in mind, in this dissertation, I outline the most prominent current detection methods and how the information we gain from them, specifically mass and radius, informs our understanding of detected exoplanets both within and outside the transition regime. I further discuss how these parameters alone are not enough to classify planets as terrestrial or gaseous within the transition regime due to degeneracies in inferred composition from mass-radius relations. In this dissertation I take a two-pronged approach to work towards a better understanding of the classification of these transition planets through both direct observations and theory. First, in Chapters II and III I present my work to directly measure the compositions of the smallest observable gas planets using ground-based transmission spectroscopy. This technique, while not immediately probing the transition regime, is a step towards small-planet characterization as instrumentation and observational techniques improve. In Chapter IV I use a three-dimensional general circulation model to study the influence of solid surfaces on atmospheric circulation for transition regime planets and study how the surface imprints

1 Where R⊕ refers to the radius of Earth

xiii itself on the emitted and reflected light from the exoplanet with an eye toward observing these differences. In Chapter V, I further explore the atmospheres of small, Neptune-sized planets in circumbinary orbits with time varying incident flux patterns due to their orbits around their pair of host stars to explore how this environment impacts the circulation. Together, these approaches are unique, yet complementary, in their contribution towards understanding the population of exoplanets as a whole.

xiv CHAPTER I

Introduction

“There are countless suns and countless earths all rotating round their suns in exactly the same way as the seven planets of our system.” – Giordano Bruno

1.1 Detection of Exoplanets

Four centuries after the philosopher Giordano Bruno famously suggested that every star in the night sky might be host to planets of their own, the ﬁrst objects of conﬁrmed planetary masses were detected around the pulsar PSR B1257+12. Dubbed PSR B1257+12 B and PSR

B1257+12 C, these planets were small at 4.3 M⊕ and 3.9 M⊕, respectively, and skirted the very line of terrestrial planets vs. gaseous planets. (Wolszczan & Frail, 1992). Though they orbited a ‘dead’ star, these first two exoplanets were representative of what we would come to learn are the most common types of exoplanets around main sequence stars (Batalha, 2014). Now, almost 30 years after the detection of the pulsar planets, just over1 4000 exoplanets have been officially confirmed (NASA Exoplanet Archive2). The detection of these exoplanets

1I’m so excited that we hit #Exoplanet4k between writing and turning in this dissertation! 2exoplanetarchive.ipac.caltech.edu

1 is dominated by two techniques: (1) transits of the exoplanet across the disk of the host star to enable measurements of the exoplanet’s radius; and (2) radial velocity measurements of the host star to enable measurements of the exoplanet’s mass. Here I outline the science behind these detection techniques as well as their limitations and successes to-date before discussing the current and future status of the subﬁeld of exoplanet detection.

1.1.1 The Transit Method

Events such as the Transit of Venus in 2012 and even the North American Total Solar Eclipse in 2017 grab the public’s attention and demonstrate the broad reach of astronomical transit observations. As applied to exoplanet science, transit observations have been a key component dictating the fast expansion of our knowledge of other worlds. Simply put, a transit event occurs when an orbiting body, such as an exoplanet, crosses in front of the host star as viewed along an observer’s line-of-sight. During such an event, a portion of the stellar light is blocked from view resulting in the star appearing to be dimmer in the sky for the duration of the transit event. If this occurs on a regular, predictable, schedule, one can surmise that a body is in a orbit around the studied star. Figure 1.1 demonstrates a schematic of a transit event. As shown, the exoplanet blocks out an amount of light proportional to the ratio of the area of the exoplanet disk to stellar disk, and to ﬁrst order the relative dimming of the star is given by

2 Rp f = 2 (1.1) R?

where f is the fractional decrease in detected light; Rp is the radius of the exoplanet; and

R? is the radius of the host star. If we know the stellar radius, we can derive the exoplanet radius3. For the same size host star, larger exoplanets create larger transits and smaller exoplanets create smaller transits.

3Of course, the measurement of exoplanet radius is only as precise as our knowledge of the stellar radius. And so, here one could go on a long aside titled, as many a conference and tweet has been, “To know thy planet, one must ﬁrst know thy star”. But alas, I leave this as an exercise to the reader.

2 Figure 1.1: A schematic representation of a transit.

While analytical forms of the transit light curve equation can be derived (see Pál,2008), here we walk through the derivation of the integral form, typically solved numerically. For a radial symmetric intensity profile (with the radial dimension in units of R?=1), the total flux during a point of time during transit can be written as

1 2π Z Z Ftransit(t) = I(r)dφrdr 0 2δ(r,t) (1.2) 1 Z = 2 (π − δp(r, t)) I(r)rdr 0

where δ is half of the arc obscured by the exoplanet (see Figure 1.2, panel a), I(r) is the intensity proﬁle of the star (for a uniform disk, this would be constant with r, see below for a discussion of I(r), namely limb darkening and its eﬀects on transits). Note that the angular

integral runs from 2δp(r) through 2π, which covers the entire radial arc while skipping the

region obscured by the exoplanet. Figure 1.2 panel b shows the angle δp(r) speciﬁcally for

r = R?, but it can be generalized for any arc of radius r such that

2 2 2 r + zp − Rp δp(r, t) = arccos (1.3) 2rzp(t)

3 Figure 1.2: A schematic of various transit geometries highlighting relevant angles.

where r is the radial direction of integration; Rp is the exoplanet radius; and zp is the distance from the center of the star to the center of the exoplanet, all deﬁned in a coordinate system centered on the star where R?=1.

p 2 2 To calculate zp(t) where zp(t) = xp(t) + yp(t) and xp(t) is the planet’s motion in the plane of its orbit and yp(t) is the planet’s motion perpendicular to the plane of its orbit, we first follow the derivation for planar coordinates in Pál(2009), adapted from Murray & Dermott (1999) which define

ξ = ξ0 cosω ¯ − η0 sinω ¯ (1.4)

η = ξ0 sinω ¯ + η0 cosω ¯ (1.5) with

ξ0 = a(cos(E − e)) (1.6) √ 2 η0 = a 1 − e sin E (1.7) where ξ is the projected vertical motion (motion perpendicular to the plane of the orbit); ω¯and η is the projected horizontal motion (motion in the plane of the orbit);ω ¯ is the longitude of pericenter; E is the eccentric anomaly; and e is the eccentricity of the orbit.

4 From Kepler’s equation, E is given by

E − e sin E = M (1.8)

where M is the mean anomaly, deﬁned by 2πt/T , with t the time and T the orbital period. The mean longitude of the orbit is deﬁned as λ = M +ω ¯. For circular (or nearly circular) orbits,ω ¯ = 0, one can write Equations 1.6 and 1.7 as

ξ0 = a cos λ (1.9)

η0 = a sin λ (1.10)

noting, that in this case, ξ and η reduce to ξ0 and η0, respectively. Finally, one can non- dimensionalize the vertical and horizontal elements of the planet’s motion in units of stellar radii as bξ y = (1.11) p a η xp = (1.12) R?

where a is the semi-major axis of the orbit and b is the impact parameter (deﬁned in Figure

1.2 panel c) given by b = a cos i/R?, with i the inclination of the orbit. Equations 1.9-1.10 and 1.11-1.12 then reduce to

2 2 2 2 2πt a 2 2πt zp = b cos + sin (1.13) T R? T

which now allows us to calculate δ(r, t) (Equation 1.3), and integrate over the radial axis to

obtain Ftransit(t). As one can surmise, a variety of system parameters (e.g. semi-major axis, orbital period, orbital inclination, exoplanet radius, stellar radius) play an important role in the determination of the transit light curve. Now I’ll look speciﬁcally at the stellar intensity proﬁle

5 component, I(r). Because the host star is in reality a non-uniform disk, its intensity profile adds complexity to transit studies, both with the treatment of limb darkening and due to the presence of star spots on the disk4. Limb darkening is a geometric effect resulting in the observer receiving photons from different depths in the stellar photosphere at different annuli of the observed stellar disk. As described by panel a in Figure 1.3, the τ = 1 surface probes different depths in the photosphere at the outer radial regions of the star (i.e. larger φ angles) than the central regions of the star (lower φ angles). Because photons emitted at the same radial distance from the stellar center, but at varying values of φ, have different amounts of material to pass through on their way to the observer, those at larger values of φ will be absorbed before those at smaller values of φ. At larger values of φ we then detect photons from the higher/cooler regions in the photosphere from which photons are able to escape before being absorbed and which appear darker than the deeper/warmer regions. This is a wavelength dependent effect wherein limb darkening appears stronger at shorter (bluer) wavelengths. This effect impacts transits by resulting in a lower relative amount of stellar flux being blocked by the exoplanet as it passes either limb during ingress and egress as compared to the central regions of the stellar disk. As demonstrated by Figure 1.4, with all else the same, the shape of the bottom of the transit is determined by the strength of limb darkening; stronger limb darkening (i.e. the limb is much darker than the central regions of the star) corresponds to a smoother transition from out-of-transit through ingress/egress. In contrast, weaker limb darkening creates a sharper transition. The radial intensity profile of the stellar disk due to limb darkening can be parameterized in a number of ways with varying levels of complexity and accuracy. Commonly in transit

4Once again, “To know thy planet, one must ﬁrst know thy star”

6 Figure 1.3: A schematic representation of limb darkening. a: showing the τ=1 surface eﬀect. b: showing the geometry of the parameterized limb darkening laws.

observations limb darkening is parameterized as one of three relations given by

I(µ) = I0 [1 − c1 (1 − µ)] (linear law) (1.14)

2 I(µ) = I0 1 − c1 (1 − µ) − c2 1 − µ (quadratic law) (1.15)

1/2 I(µ) = I0 1 − c1 1 − µ − c2 (1 − µ)

3/2 2 −c3 1 − µ − c4 1 − µ (nonlinear law) (1.16)

where µ ≡ cos θ, with θ the angle between the line of sight and a normal vector from the √ surface of the star (or equivalently µ = 1 − x2 with x the distance from the center of the host star in units of stellar radii), as demonstrated by panel b in Figure 1.3. The parameters c1, c2, c3, and c4 are limb darkening coefficients that must be either fit for during transit analysis, or derived from stellar models5. In practice, the nonlinear law provides the best representation of the intensity profile of the star (Espinoza & Jordán,2015) but limitations

5For a select number of nearby stars, it is possible to measure limb darkening directly, e.g. Lacour et al. (2008)

7 Figure 1.4: Sample light curves showing the effects of limb darkening on the transit light curve. Light curves were generated with the code batman (Kreidberg, 2015) and a quadratic limb darkening parameterization. in transiting fits (e.g. correlated parameters and/or convergence timescales) typically mean the quadratic law is used when modeling transits, which deviates from the true intensity profile of ATLAS stellar models (Kurucz, 1970) at a level of a few percent for low values of µ (large θ, Figure 1.3 panel b) up to ∼7% for PHOENIX stellar models (Allard & Hauschildt, 1995) as calculated by Espinoza & Jordán(2015). Deviations are <1% for the nonlinear law at the same angles with ATLAS models and a few percent for PHOENIX models . Further complicating matters is that the geometry of a transit is such that an exoplanet does not necessarily transit across the central chord of the star, resulting in a bias in limb darkening parameters derived from transit observations compared to expected values (Howarth, 2011). The authors also stress that even for a transit across the central chord limb darkening coefficients derived from transit fits are not directly comparable to those from stellar model intensity profile fits. However, if we ignore this issue of geometry for a moment, EXOFAST (Eastman et al., 2013) becomes a useful tool that interpolates limb darkening parameters from the Claret & Bloemen (2011) tables for inputs into transit light curve models. The Claret & Bloemen (2011) tables contain calculated limb darkening derived from

8 stellar models for a discrete set of stellar parameters integrated over common band passes and serve as a good starting point when fitting transit models. However, because of uncertainties in stellar models, limb darkening parameters derived from them inherently have some biases, which are further exacerbated by the the non-exact parameterizations outlined in Equations 1.14-1.16. Specifically these biases can result in derived limb darkening coefficients, for the same stellar parameters, that differ by up to 20% depending on the method and models used (Sing, 2010; Csizmadia et al., 2013; Espinoza & Jordán,2015). And so, if one chooses to fix the limb darkening coefficients when fitting transit light curves Csizmadia et al. (2013) show that this can lead to uncertainties between 1-20% on the exoplanet radius due to the uncertainties in the coefficients themselves, but by allowing these coefficients to float in fitting routines, one can achieve better than 1% accuracy on transit parameters. Because of this and the issue outlined above from Howarth (2011), one should never fix limb darkening coefficients in transit fits and instead include them as additional parameters, even if it takes longer for results to converge, and especially when using the less-precise quadratic law (Espinoza & Jordán,2015). Limb darkening is an area of transit science that often poorly addressed in the literature, with every group approaching the issue differently, though recently the importance of “knowing thy star” is being more broadly recognized and a focus on transparent treatment of limb darkening is arising in the transit community. A further effect we must consider is that of stellar spots. Star spots are dark regions on the photosphere associated with regions of high magnetic activity that exhibit temperatures cooler than the surrounding photosphere at levels of ∆T up to ∼ 2000K where ∆T is defined as T? − Ts and Ts is the temperature of the spot. As an exoplanet transits in front of a spot on the stellar photosphere, it is temporarily occulting less stellar flux compared to when it is not occulting a spot. This corresponds to a temporary decrease in transit depth, as demonstrated in Figure 1.5. A complete derivation of the in-transit flux in the case of occulted star spots is done in Békyet al. (2014) for an arbitrary number of spots, and, for

9 Figure 1.5: Data from a transit of WASP-52b showing the occultation of a dark spot at several instances in time throughout the transit event. Note the temporary decrease in transit depth at the moment the spot is occulted in panel b. (May et al., 2018b). a single spot, is given by

1  2γ∗ 2π  Z Z Z   Ftransit(t) =  fI(r)dθ + I(r)dθ rdr (1.17) 0 0 2(γ∗−δ) where γ∗ describes the unobscured half-arc of the spot, δ is the same as in Equation 1.2, and f is the spot-photosphere contrast ratio. As with limb darkening, spots are a wavelength dependent effect, with their effect more pronounced at shorter (bluer wavelengths). This can be explained to be a result of the two different blackbody functions – i.e. because the blackbody function of the spot peaks at longer (redder) wavelengths than the stellar blackbody function and is overall less intense, the spot contrast is larger at bluer wavelengths where the two blackbodies differ more strongly. For this reason, spots affect transit observations at optical wavelengths more so than infrared wavelengths. The wavelength dependence of spots that are not occulted during transit are further addressed in Section 1.3. While transit observations are complex and prone to various uncertainties, only some

10 Figure 1.6: To-date as of the writing of this dissertation, this figure shows the radius vs. period for exoplanets detected with the transit method. Data from the NASA exoplanet archive. of which I’ve addressed here, it has been arguably the most successful exoplanet detection method to-date. In particular, the Kepler space telescope (Borucki et al., 2010), which was launched in 2009, has confirmed over 2,600 exoplanets, with most falling in a only a 115 square degree patch the sky (0.25% of the sky) during the primary mission. Even though Kepler was officially retired in October 2018, more exoplanets continue to be found in archival data with improved analysis techniques (Shallue & Vanderburg, 2018; Dattilo et al., 2019). In April 2018 the Transiting Exoplanet Survey Satellite (TESS, Ricker et al., 2015) was launched as a follow up to Kepler, covering 85% of the sky over it’s nominal mission. In contrast to Kepler, TESS is targeting nearby bright stars which will enable ground-based follow up studies of the targets, including both radial velocities (Section 1.1.2) and atmospheric characterization (Section 1.3). As of writing, TESS has detected 9 confirmed exoplanets6 and nearly 500 targets-of-interest (i.e. transit-like events that cross some threshold and may be exoplanets, instrumental, or other astrophysical objects). In addition to these space- based transit missions, many ground-based transit surveys have had success in contributing

6Please speculate wildly about how high this number is as of reading.

11 to transit detections such as HARPS (>100 confirmed since 2003, Mayor et al., 2003); HAT- Net/HATSouth (61 confirmed since 2001, Bakos et al., 2004); and WASP (>100 confirmed since 2006, Pollacco et al., 2006). Figure 1.6 shows all exoplanets on the NASA exoplanet archive detected via the transit method as of writing. Clearly the transit method has played a pivotal role in our detection and understanding of exoplanets, but the information learned from a standard transit observation is limited to the radius7 and orbital properties of the exoplanet. Therefore, other observational methods must be used to expand our understanding and characterization of other worlds.

1.1.2 The Radial Velocity Method

The ﬁrst exoplanet around a main sequence star, 51 Pegasi b (Mayor & Queloz, 1995, see Figure 1.7), was discovered with the radial velocity technique. Originally borrowed from binary star observations, the radial velocity technique use measurements of stellar motion to determine the gravitational eﬀects of an orbiting body. Kepler’s third law describes the orbital properties of two massive objects in a binary system by balancing the centripetal force and gravitational force such that

M1M2 2 M1M2 rω = G 2 (1.18) M1 + M2 a

where ω, the angular velocity, is equal to 2π/T with T the orbital period. Here M1 refers to

the mass of the larger body and M2 the mass of the smaller body while a is the semi-major

axis of the two bodies and is equal to a1 + a2 with a1 and a2 the semi-major axes of the orbits of object 1 and 2 around the center of mass, respectively. With this, we can rearrange Equation 1.18 to arrive at the familiar form of Kepler’s second law:

a3 G(M + M ) = 1 2 (1.19) T 2 4π2 7I do not discuss transit timing variations in this dissertation, but this method enables the determination of masses in multi-planet systems and even the prediction and conﬁrmation of unseen additional bodies (like the (potential) Kepler-1625b exomoon?! (Teachey & Kipping, 2018))

12 Figure 1.7: From Mayor & Queloz (1995), the measured radial velocities of the ﬁrst exoplanet detected around a main sequence star, 51 Pegasi b.

In visual binary systems, this relation plus the deﬁnition of center of mass (M1a1 = M2a2), allows us to calculate the masses of the two bodies after a direct on-sky measurement of the orbital period and angular separation. However, with the exception of directly imaged systems 8, exoplanet systems are not visual binaries due to the smaller size and luminosity of the companion body (henceforth the exoplanet, denoted by subscript p). Therefore, we instead use techniques inherent to spectroscopic binaries. Recalling that orbital velocity, V , is given as 2πa/T and that conservation of momentum requires that M?V? = mpVp (subscript ? references the host star), and by applying Kepler’s third law (Equation 1.19) with M = mp + M?, we arrive at

!1/3 2πa 2π m 2π m T 2 2π G 1/3 V = ? = p a = p GM = m (1.20) ? T T M T M 2π p T M 2

where V? is the velocity of the star due to the gravitational inﬂuence of the orbiting planet.

8This is another detection technique which I do not discuss here, but it is the only method that currently gives us amazing videos of real exoplanets orbiting their stars like in the HR 8799 system! (Marois et al., 2008, 2010)

13 We must also include the on sky projection eﬀects of an inclined orbit where the measured radial velocity is reduced by sin i with i the angle between the orbital axis and the line-of- sight (90◦ is edge-on) such that, for a circular orbit,

2π G 1/3 V = V sin i = m sin i (1.21) r,? ? p T M 2

The assumption of a circular orbit, while acceptable for certain planetary types (e.g. close in Hot Jupiters with T / 3 days whose orbits are mostly consistent with circular from observational data), does not hold broadly. The derivation of Vr,? in such a case is beyond the scope of this introduction, and is given by

1/3 mp sin i 2π G Vr,? = √ (1.22) 1 − e2 T M 2 where e is the orbital eccentricity. From Equation 1.22, we see that the radial velocity technique is most powerful for massive exoplanets (high mp) with short orbital periods (low T ) around smaller stars. Namely, Hot Jupiters around M-dwarfs. This stellar motion is imprinted on the stellar spectrum by Doppler shifting the absorption lines throughout the course of the orbit. The Doppler shift of spectral lines in the case9 that

Vr,? c is described by

s λ − λ 1 + V /c V z ≡ o r = r − 1 ≈ r (1.23) λr 1 − Vr/c c

Over the course of one planetary orbit, one measures the instantaneous stellar motion towards or away from us in the form of spectral line shift, where the semi-amplitude of the signal corresponds to Vr,? (Equation 1.22). Figure 1.7 demonstrates radial velocity measurements for the ﬁrst detected exoplanet around a main-sequence star, which allows for a determination of the orbiting exoplanet’s period as well as the exoplanet’s mass (speciﬁcally an lower limit

9I for one wouldn’t want to dial my Stargate to a system where this wasn’t true. We all saw what happened in SG-1 Season 2 Episode 15.

14 on mass, i.e. mp sin i). In practice, measurements of radial velocities (henceforth RVs) are limited by the precision of the spectrographs used to determine the spectral shifts and the noise level of the host stars. Current RV detectors have precisions below 1 m/s, while the signal of an Earth- equivalent planet around a Sun-like star would impart a radial velocity of only ∼10 cm/s, the ‘magic’ precision level many RV instruments aspire to. However, recent work by Cegla (2019) suggests that the detection of Earth-similar planets around sun-like stars may be more difficult than anticipated, but not impossible, due to stellar-induced signals. Currently, HARPS and HARPS-N, as well as the new ESPRESSO instrument, are two of the more well known instruments in radial velocity work. HARPS and HARPS-North (Mayor et al., 2003), the High Accuracy Radial velocity Planet Searcher, are installed on the the 3.6-m telescope at La Silla Observatory and the 3.5-m Telescopio Nazionale Galileo (TNG10), respectively. The measurement precision is ∼0.8 m/s for both instruments, the first instruments to reach below 1 m/s precision (Fischer et al., 2016). ESPRESSO is installed on the Very Large Telescope (Pepe et al., 2014; Cupani et al., 2018; GonzálezHernández et al., 2018) and is designed as a successor to HARPS with a goal of reaching the 10 cm/s precision level over 10 years to detect Earth-similar planets. As shown11 in Figure 1.8, the radial velocity method is particularly useful for detecting more massive planets. Because more massive planets impart larger radial velocity signals, they are inherently over-represented in radial velocity surveys, an observational bias that impacts our understanding of the entire population of exoplanets. While it appears from this figure that radial velocity prefers longer period planets as compared to the transit technique, this is an observational bias of space-based transit searches which typically have a relatively short observing time period for regions of the sky, limiting the maximum orbital period that can be detected.

10No, not the Jean-Luc Picard kind. 11My obligatory “Go Green!” reference in a sea of Maize and Blue ﬁgures.

15 Figure 1.8: To-date as of the writing of this dissertation, this ﬁgure shows mass vs. period for exoplanets detected with radial velocity (maize), transits (blue), and other detection methods (green and white) not discussed here. Data is from the NASA exoplanet archive.

1.1.3 Current Status of Exoplanet Detection and the Future of the Field

As we rapidly approach 4000 confirmed exoplanets, the field of exoplanet detection remains an important part of classification studies. All detection techniques and missions have their own selection and observational biases, and while we can correct a sample for completeness based on our understanding of these biases, a continued search for planets in regimes we have not been sensitive to in the past is critical to our understanding of exoplanets as a population rather than as individual, unconnected, data points. As mentioned in Section 1.1.1, the Transiting Exoplanet Survey Satellite (TESS) is detec- ing exoplanets around brighter host stars, enabling follow-up studies including radial velocity measurements and atmospheric characterization. TESS has the precision necessary to detect numerous Sub-Neptunes, and is expected to fill in the dearth of Earth-sized planets with

hundreds of new exoplanets with radii less than 2.0R⊕ (Sullivan et al., 2015; Barclay et al., 2018; Ballard, 2019). While TESS has two continues viewing zones at each ecliptic pole,

16 it’s primary mission is to scan the entire night sky by staring at a single 3200 square degree sector for 27.4 days before moving onto a new region of the sky, meaning most TESS planets will have orbital periods less than half of that in order to detect two transit events, resulting in an observational bias for short orbital period exoplanets12. While radial velocity exoplanet detection surveys have less of a constraint in terms of orbital periods compared to space based transit surveys, they are, in general, less sensitive to low mass planets. However, as mentioned in Section 1.1.2, specially built spectrographs are pushing to the 10 cm/s precision level, and we can expect the detection of Earth-similar targets with RVs to be an inevitability. Together, space-based transit surveys and ground- based radial velocity surveys are well paired to develop a complete picture of the exoplanet population in our nearby region of the galaxy.

1.2 Basic Parameters and Classiﬁcations of Exoplanets

Knowing the mass, radius, and equilibrium temperature13 of an exoplanet gives us a general idea of the ‘type’ of exoplanet an object is. Typically, we refer to Hot Jupiters as anything that is Jupiter-sized and orbiting close to their host stars with equilibrium temperatures in the thousands of Kelvin. Additional break-downs of the “Jupiter” classification have been coined such as Warm and Cool Jupiters based on equillibirum temperature expectations. We may expect such differentiations to represent variations in atmospheric properties such as cloudiness and circulation patterns. Astronomers also regularly refer to exoplanets based on similarity in size to Saturn, Neptune, and Earth14. In this dissertation, I specifically explore how small gaseous exoplanets are unique, where “small” is a relative classification and varies for my observational and theoretical approaches.

12There are regions of overlap in the TESS mission, with areas nearer the continuous viewing zone having a longer observing baseline, allowing for longer period planet detection. 13The temperature a planet would be from basic energy conservation assuming it is a blackbody and heated only from the incident radiation of the host star, which is determined by the planet’s orbit. 14Though, notably, there is little love for comparing things to Venus. I suppose that’s what happens when your twin sister, Earth, is more popular amongst the Humans.

17 For purposes of clarity, I refer to a Super-Earth as an exoplanet which is rocky in nature with the gaseous envelope a small fraction of the planet’s total radius. In contrast, a Mini-Neptune is an exoplanet which has an gaseous envelope that dominates the radius. Because mass and radius are commonly the two most important factors diﬀerentiating ‘types’ of exoplanets as we currently deﬁne them, an active area of research is determining a robust relation between the two. Such a relation is useful in determining the composition of an exoplanet, due to its bulk density being a strong indicator of its composition. The most common type of exoplanet detected to date has been what we refer to as

‘transition-regime’ exoplanets, those larger than Earth but smaller than Neptune (3.88 R⊕, Batalha (2014)). In this regime, there must be a transition from terrestrial Super-Earths to gaseous Mini-Neptunes. We do not expect such a transition to be a sharp cut-oﬀ between the two populations, but rather a gradual transition in likely composition with radius. This transition radius has been studied by Rogers (2015) who found that, from the available exoplanet sample at the time, at 1.6R⊕ an exoplanet had an equal likelihood of being terrestrial or gaseous based on its probability to be dense enough that it was considered a Super-Earth. Further, Lopez & Fortney (2014) applied thermal evolution models to study how a planet’s radius evolves with time due to cooling and stellar inﬂuence, and concluded that a radius of

1.75 R⊕ was an appropriate division between these two populations of planets and that radius alone is a good indicator of a planet’s composition. Observationally, Fulton et al. (2017) demonstrate a bi-modal distribution in planetary radius with a gap at 1.5 R⊕ pointing to two distinct populations of planets. While these populations could be formed in a variety of ways, and are possibly a result of photo evaporation, they are concrete evidence for the existence of semi-discrete radii regimes for Super-Earths and Mini-Neptunes. However, in this work, the determination of if a planet is terrestrial or gaseous is only concerned with the current presence of a detectable surface and not necessarily how and/or why it got to where it is now. To further understand these populations, a measurement of mass for each planet is im-

18 Figure 1.9: Mass vs. Radius for known exoplanets with their quoted errors. Earth is shown in green, Neptune in blue, Saturn in yellow, and Jupiter in red. Typical Super-Earth and Mini-Neptune regimes are highlighted. Data is from the NASA exoplanet archive. portant. Because a majority of Kepler target stars are too faint for ground-based radial velocity follow up to measure this mass, alternative methods to derive the mass must be applied. Among others, Wolfgang et al. (2016) and Ning et al. (2018) work to fit analytical equations to the mass-radius data. The importance of such work is not to be underestimated, but because the uncertainties in the measured mass and radius parameters can be large (see Figure 1.9) and the intrinsic astrophysical scatter is unknown, the usefulness of such relations is questionable for planets near the transition from Super-Earths to Mini-Neptunes where numerous compositions match measured densities, making predicting mass from radius alone more difficult. In addition to deriving mass-radius relations, one can compare the observed mass and radius to calculate composition curves which describe the expected relation between mass and radius for a body of a given composition, as shown in Figure 1.10. In this figure, composition curves from Zeng et al. (2016) are shown, where solid lines represent uniform compositions while dashed lines represent a two-layer Mg-silicate/Fe or Mg-silicate/H2O composition of

19 Figure 1.10: A zoom in of Figure 1.9 around the transition from gaseous to terrestrial. Plot- ted are composition curves from Zeng et al. (2016). The left grey dot is Earth and the right grey dot is Neptune. The same typical Super-Earth and Mini- Neptune regimes are highlighted. Data is from the NASA exoplanet archive. the indicated percentages.

While planets between the size of Earth and Neptune (3.88R⊕) are common, they also have densities that are consistent with many possible compositions. Even for precisely known masses and radii, the presented composition curves in Figure 1.10 only represent a handful of possible compositions. Further, the consideration of atmospheric mass fraction allows results in the shifting of these curves to larger radii by removing solid material and adding a relatively less dense gaseous envelope. This suggests that mass and radius alone are not a strong determining factor in the composition of an exoplanet in this transition regime and we must use alternative techniques to decipher their internal structures. The classification of these planets is important in the grand scheme of understanding exoplanets as a population rather than individual, unrelated, data points. We are now in an era where we have sufficient data to make comparisons and develop classification schemes that include parameters beyond just mass and radius by including sizes of measured atmospheric

20 spectral features. The Hubble Space Telescope (HST) has been an important tool for this type of comparison, with Crossﬁeld & Kreidberg (2017) studying the 6 Neptune-sized planets with HST observations at the time and determining that there exists a positive correlation

between the 1.4µm H2O absorption features and atmospheric temperature and H/He mass fraction. Further, Fu et al. (2017) analyze 34 exoplanet transmission spectra and find a positive correlation between the same H2O absorption feature and atmospheric temperature for a sample of primarily Hot Jupiters. In this dissertation I take a two-pronged approach to studying the atmospheres of planets near this Super-Earth to Mini-Neptune transition. If the planets have a substantial atmosphere, they are classified as Mini-Neptunes and are candidates for direct atmospheric observations to study their compositions and place constraints on atmospheric metallicity. This method is called transmission spectroscopy and is addressed in Section 1.3 and Chap- ters II and III. However, for planets which are not good candidates for direct atmospheric observations due to their sizes and/or current instrumental limitations, I turn to models to determine exactly how a surface at varying surface pressures affects the circulation, and study how a surface imprints itself on observational signatures within this transition regime. In the following sections I present brief introductions to the methods used in the remainder of this dissertation, but leave many of the details to the chapters themselves.

1.3 Transmission Spectroscopy

Transmission Spectroscopy is an application of the transit method that uses spectroscopic observations during a transit event to study the stellar light that ﬁlters through the exoplanet’s atmosphere in order to directly measure the transmittance and infer the composition. The ﬁltered light interacts with the atmosphere and certain wavelengths are either absorbed or scattered out of our line-of-sight based on the atmosphere’s constituents. Fig- ure 1.11 demonstrates a not-to-scale representation of this method. Absorption through the planet’s atmosphere is a perturbation on the nominal transit depth given in Equation 1.1,

21 Figure 1.11: Stellar light ﬁlters through the planet’s atmosphere and interacts with it’s constituents resulting in a variable transit depth with wavelength. referred to as either the transmission signal or absorption signal. The strength of this signal is proportional to the scale height of the atmosphere (H) and is given by

2 2 (Rp + βH) Rp 2βRpH ∆f = 2 − 2 ≈ 2 (1.24) R? R? R? where H is deﬁned as k T H = B limb (1.25) µg with kB the Boltzmann constant; Tlimb the temperature at the limb of the exoplanet; µ the atmospheric mean molecular weight; g the exoplanet’s surface gravity; and Rp and R? the exoplanet and stellar radii, respectively. β is a scaling factor describing how many scale heights a typical feature in the atmosphere extends over. Traditionally this has been set from 1-2.5 (Kreidberg, 2018; Fu et al., 2017; Stevenson, 2016) which is supported by observational results. From Equations 1.24 and 1.25 we see that warm exoplanets with low gravity and mean molecular weight atmospheres will have stronger (larger) absorption signals. Typical sizes of signals range from 10s of parts-per-millions (ppms) to hundreds of ppms. Planets with inﬂated atmospheres (low densities) are great targets for transmission spectroscopy because

22 we expect their absorption signals to be on the larger end of this scale, making their features easier to detect with certainty. At optical wavelengths, we are primarily searching for signs of scattering in the atmosphere wherein shorter (bluer) wavelengths of light are scattered more strongly within the atmosphere and out of the observer’s line of sight than longer (redder) wavelengths of light, resulting in deeper transit depths at shorter wavelengths15. First described by Lecavelier Des Etangs et al. (2008), the strength of scattering in the atmosphere is determined based on the slope of the transmission spectrum and is given by

1 dR 1 k T p = α B (1.26) R? dlnλ R? µg where α describes the strength of the wavelength dependence of the scattering and all other parameters have been previously defined. Typical Rayleigh scattering is described by α = −4, though scattering by other particulates can introduce slopes with α as strong as −13 (Pinhas & Madhusudhan, 2017). Spots and other inhomogeneities on stellar photospheres have become a large topic of study in recent years in terms of how they affect transmission spectroscopy and how they can be removed from data sets. The impact of occulted star spots was addressed above, however unocculted spots and other features can impact data sets as well, and perhaps in more annoying and less immediately obvious ways. Unocculted star spots can introduce a Rayleigh-like slope in data. Because unocculted spots are much dimmer than the surrounding star with a more pronounced difference at bluer wavelengths, when there are significant unocculted star spots the relative flux blocked by the exoplanet during transit appears even higher at shorter wavelengths, imparting a bias on the measured transit depth. This effect

15Sometimes the sky is blue in Michigan instead of cloudy and grey. On these rare days one can see this eﬀect from the perspective of an observer on the planet for ones self. Of course if it’s cloudy and grey, one is experiencing a diﬀerent common transmission spectroscopy observation too.

23 is described by Louden et al. (2017) as

1 δe(λ) = δ(λ) (1.27) 1 − η Fλ(spot) Fλ(star) where δe(λ) is the measured transit depth, δ(λ) is the true transit depth, η is the spot covering fraction, and Fλ are the blackbody functions of the spot and star. For a further discussion of stellar effects on transmission spectroscopy, Rackham et al. (2017) discuss the effects of inhomogeneous stellar photospheres, Rackham et al. (2018) and Zhang et al. (2018) explore how M-dwarfs can impart incorrect spectral signatures due to spots and faculae and time-variations, and Apai et al. (2018) and Rackham et al. (2019) discuss how what has been dubbed ‘the transit light source effect’ will impact our ability to characterize small Earth-similar exopanets. In transmission spectroscopy observations one of the largest considerations is photometric precision owing to the small signals we seek to measure. For this reason, we typically trade spectral resolution for higher photon counts to improve our signal-to-noise (hereafter SNR). Most transmission spectroscopy observations are around stars bright enough that the observations are photon limited and we can ignore the contribution of background and √ √ read noise such that expected SNR is ∝ N/ N = N where N is the number of photons detected. By binning together pixels (e.g. averaging in wavelength space), we can increase our SNR and improve the precision of results. In reality, photon-limited observations are hard to obtain due to instrumental and observational uncertainties. This correlated noise in transmission spectroscopy is discussed in Chapter III with Chapter II also discussing white noise removal. Space and ground-based transmission spectroscopy observations vary, and below I will discuss the observational set-ups and trade-offs of both.

24 1.3.1 Space-based Observations

As of writing, there are two primary space missions that are used for atmospheric studies of transiting exoplanets, the Hubble Space Telescope (hereafter HST) and the Spitzer Space Telescope. The two are often used in complementary way, with the relatively higher spectral resolution of HST’s infrared wide ﬁeld camera 3 (WFC3) and optical Space Telescope Imaging Spectrograph (STIS) and the mid-infrared (3.6µm and 4.5µm) bands on Spitzer’s IRAC instrument working together to constrain atmospheric retrievals to determine composition. HST transmission spectroscopy observations commonly use the Wide Field Camera 3

(WFC3) instrument covering 1.1-1.7 µm allowing a constraint on H2O absorption at 1.4 µm in the atmospheres of the observed exoplanets, with the Space Telescope Imaging Spectro- gaph (STIS) also used from ∼0.58 micron to 0.8 micron. HST WFC3 observations typically reach photon precision with binned uncertainties less than 100 parts per million (ppm). While Spitzer IRAC has extreme inter-pixel sensitivity variations and was not designed for the high precision work needed for exoplanet transmission spectroscopy, it none the less has become a powerful tool for the community with photometric bins centered at 3.6 and 4.5 microns. Representative HST and Spitzer observations can be found in Sing et al. (2016), where the authors present a comparison of the optical to infrared spectra of 10 Hot Jupiters, the first of its kind which remains a benchmark study in the field. The James Webb Space Telescope (hereafter JWST) is currently expected to launch16 in 2021 and will be unmatched in its capabilities to characterize exoplanet atmospheres. JWST will be particularly useful for exoplanet transmission spectroscopy from 0.6 microns through 12 microns by combining observations from the NIRISS, NIRSpect, NIRCam, and MIRI instruments over 2-4 individual transit events (Bean et al., 2018). This extended wavelength coverage, combined with an estimated noise floor in the 10s of ppm, will allow high precision spectral detection of multiple H2O absorption bands, as well as CO, CO2, CH4, and NH3, enabling highly precise retrieved abundances.

16...remind me to update this after the next delay.

25 1.3.2 Ground-based Observations

Although ground-based transmission spectroscopy observations are further complicated by absorption through a secondary atmosphere17 (Earth’s), it is growing to become an equally reliable and accurate method which will continue to be an important characterization tool in the era of JWST. While JWST will be unmatched at near to mid infrared wavelengths, its optical observations will be limited to red-wards of 0.6µm using the low-resolution prism disperser on NIRSpec. Ground-based observations will match or best this spectral resolution while obtaining data as blue as 0.3µm depending on the instrument. Several ground-based instruments have the benefit of allowing simultaneous multi-object spectroscopic observations to correct for the secondary atmosphere effect. Typical observational setups for these instruments allow for the selection of a handful of calibration stars that are know to be non-variable over the timescale of the observations. The data from these calibrator stars allow for a time-dependent correction of atmospheric and instrumental induced variations so that the only variations left in the host star’s data are that of the transiting exoplanet’s signal. The Gran Telescopio Canarias (GTC) exoplanet transit spectroscopy survey has been the leading force in ground-based studies (Sing et al., 2012; Murgas et al., 2014; Parviainen et al., 2016; Palléet al., 2016; Nortmann et al., 2016; Chen et al., 2017a; Murgas et al., 2017; Parviainen et al., 2018; Chen et al., 2018) with published observations on numerous targets. In addition, the Arizona-CfA-CátolicaExoplanet Spectroscopy Survey (ACCESS) at the Magellan telescopes is another larger survey program (Rackham et al., 2017; Espinoza et al., 2019; Bixel et al., 2019) with several results in recent years. Of particular importance to this dissertation is the ground-based Michigan Optical Plane- tary Spectrum Survey (MOPSS). Through this project, I target low-density exoplanets with the largest expected transmission signals to search for signs of atmospheric scattering at optical wavelengths, as well as any absorption due to the alkali metals sodium and potas-

17Why observe just one atmosphere when we can observe two for twice the diﬃculty?!

26 sium or features indicative of clouds. MOPSS uses the IMACS instrument on the 6.5-meter Magellan Baade telescope, a multi-object spectrograph. Chapters II and III discuss the ﬁrst results from MOPSS and outline the methods in detail. Here I also include information on all data obtained to date with the MOPSS program and its analysis status in Table 1.1. MOPSS is complementary to other ground-based transmission spectroscopy surveys by focusing on the lowest mass gaseous planets possible in contrast to the typical Hot Jupiter targets of other surveys. By overlapping our initial targets with those from other groups and telescopes we are able to prove the robustness of our methods and results while further enabling an era of comparative exoplanet studies.

Planet Date Status WASP-4b 08/19/2015 Published: May et al. (2018b), see Chapter II WASP-52b 08/11/2016 Published: May et al. (2018b), see Chapter II 09/22/2016 HAT-P-26b 04/09/2017 (4” seeing, full transit) 05/13/2017 (Weather prohibited full transit) HATS-8b 07/23/2017 Submitted: May et al. (2018a), see Chapter III 08/28/2017 WASP-18b 08/28/2017 (Weather prohibited full transit) WASP-67b 05/22/2018 To Be Analyzed HATS-29b 05/23/2018 Currently being analyzed by K. Meyer and E. May (06/13/2019) (Scheduled) CoRoT-11b 05/24/2018 Partially analyzed by J. Lisowski and E. May HATS-35b 05/25/2018 Currently being analyzed by T. Gardner (06/16/2019) (Scheduled) HATS-28b 07/22/2018 To be analyzed HATS-3b 07/23/2018 To be analyzed HATS-34b 09/14/2018 To be analyzed (06/21/2019) (Scheduled) WASP-124b 09/15/2018 Currently being analyzed by J. Lisowski and E. May (06/15/2019) (Scheduled)

Table 1.1: All MOPSS targets with at least half of a transit observed.

1.4 Atmospheric Modeling

While direct observations of exoplanet atmospheres provide answers as to the conditions on speciﬁc planets, they are limited by the instrumentational capabilities of the era we live

27 in. Through atmospheric modeling, we can learn about and predict these conditions for planets beyond the reach of our telescopes and better understand those within our reach. Here I discuss two modeling approaches that are applicable to this dissertation.

1.4.1 Energy Balance Models

Energy Balance Models (hereafter EBMs) are one-dimensional representations of the temperature conditions in a gaseous atmosphere. While this approach does not include the eﬀects of a planet’s circulation on the temperature outside of the relevant meridional heat transport, it provides latitudinal information that can be evolved in time as exterior conditions change. The relative simplicity of EBMs compared to the other method I discuss below allow them to be run quickly and for a greater number of planetary conditions. EBMs are a powerful tool for climate studies, and have historically been used to study the climate evolution of terrestrial worlds (North et al., 1981; Forgan, 2014; Vladilo et al., 2015). The general form of an EBM is given by

∂T ∂ ∂T C − D 1 − x2 = S (1 − A) − I. (1.28) ∂t ∂x ∂x where x ≡ sin ϕ is the single dimension in the model, with ϕ being latitude. T is the local temperature at some time; C is the atmosphere’s heat capacity per unit area; D is the diffusivity of the atmosphere describing the efficiency of meridional heat transport from the equators to the poles; S is the stellar irradiation; A is the atmosphere’s albedo, and I is the cooling function of the atmosphere given by I = jσT 4 where j is the emissivity of the atmosphere. Chapter V discusses the specifics of how this model is applied in this dissertation.

28 1.4.2 General Circulation Models

General circulation models (hereafter GCMs) are a three-dimensional representation of the circulation and temperature structure in the atmosphere of a planet. GCMs are com- prised of a dynamical core which solve a set of fluid equations in the frame of the rotating planet and a radiative component to describe the differential heating in the atmosphere. Various groups have their own private or public GCMs, each with their own strengths and weaknesses. In this work, we use the GCM described in (Rauscher & Menou, 2012, , hereafter RM12) which solves the primitive equations of meteorology, a simplification of the Navier- Stokes equations under the assumption of an inviscid flow, vertical hydrostatic equilibrium, and small relative vertical flow and scales compared to the horizontal component. Further, the RM12 GCM uses a two-stream double grey radiative setup in which the radiation is treated as two independent bands, a visible band for the incoming stellar radiation and an infrared band for the emitted radiation, each with their own wavelength-independent absorption coefficient. RM12 was developed from the dynamical core created at the University of Reading (Hoskins & Simmons, 1975) which was originally formulated for Earth-like planets. GCMs have been used to study a wide range of atmospheric circulation regimes, some with focuses on observational implications. Numerous groups have their own models with differing assumptions to improve model efficiency such as but not limited to the radiative scheme, the heating patterns, the complexity and/or existence of clouds, and the chemical evolution of the atmosphere. For a selection of terrestrial GCM studies see Showman et al. (2013); Kaspi & Showman (2015); Koll & Abbot (2016); Way et al. (2018); Komacek & Abbot (2019) and Pierrehumbert & Hammond (2019) and for a selection of gaseous GCM studies see Perez-Becker & Showman (2013); Rauscher & Kempton (2014); Showman et al. (2015); Kataria et al. (2016); Komacek & Showman (2016) and Rauscher (2017). Chapters IV and V discuss my work with the RM12 GCM, including updates to allow for time variable irradiation sources and a solid surface bottom boundary to extend its uses to terrestrial bodies.

29 1.5 Dissertation Overview

Chapter II outlines the MOPSS observational strategy and data analysis and reduction process in detail, as well as present transmission spectra for the exoplanets WASP-52b and WASP-4b, which are shown to agree with previously published spectra. By bench marking against previous observations of these targets, this chapter demonstrates the robustness of the MOPSS project and is published in the Astronomical Journal. Chapter III presents a transmission spectrum for HATS-8b, an inflated warm Neptune observed on two nights in 2018. This planet sits near the limit of our observational capabilities with a mass near that of Neptune and a radius near that of Jupiter. In this chapter I show that the scattering slope found in the transmission spectrum is significantly stronger than expected for this planet, as well as being the strongest scattering slope measured to date for any exoplanet. I further outline possible explanations for such a strong slope including the presence of strongly scattering particulate hazes and unocculted star spots. This chapter has been submitted to the Astronomical Journal. Chapter IV explores how a surface impacts the circulation and observational features for a 1.5 R⊕ planet. By varying the surface pressure we change how the planet interacts with its incident radiation resulting in differences in circulation as well as reflected and emitted radiation. We identify key observational differences between Super-Earths and Mini- Neptunes based on a uniform modeling scheme across the transition regime. This chapter is based on work in progress and will be submitted to the Astrophysical Journal. Chapter V describes my work to study the atmospheres of planets in circumbinary orbits. Of the dozen known, these exoplanets are all of approximately Neptune mass in orbit around two stars. We explore how the time varying flux may impact the circulation and place constraints on the extent of the impact for a grid of stable planetary orbits around a given set of host stars. This chapter is published in the Astrophysical Journal. Finally, in Chapter VI concludes by summarizing the work presented in this dissertation and discuss future directions of the field of exoplanet characterization.

30 CHAPTER II

MOPSS I: Flat Optical Spectra for the Hot Jupiters

WASP-4b and WASP-52b

2.1 Preface

Results in this chapter were published in: May, E. M., et. al 2018. MOPSS I: Flat Optical Spectra for the Hot Jupiters WASP-4b and WASP-52b. The Astronomical Journal, 156, 122 and are reproduced here with minor style revisions by permission of the American Astronomical Society under the non-exclusive right of republication granted to authors.

2.2 Abstract

We present the first results from MOPSS, The Michigan Optical Planetary Spectra Sur- vey, aimed at creating a database of optical planetary transmission spectra all observed, reduced, and analyzed with a uniform method for the benefit of enabling comparative exoplanet studies. We discuss our methods, and present results for our first two targets observed with the Magellan Baade 6.5m telescope, one transit of the Hot Jupiter WASP-4b and two transits of the Hot Saturn WASP-52b. Both targets present flat, featureless spectra, corresponding to the presence of aerosols. We find that the cloud decks must begin no lower than 10−4 bar for both planets. For WASP-52b, we also consider the effects of star spots on the transmission spectrum, including unocculted spots and spots on the stellar limb influencing

31 the light curve limb darkening parameters. We discuss the usefulness of this program in the coming James Webb Space Telescope era.

2.3 Introduction

The study of exoplanet atmospheres has been a rapidly growing field for many years. Observationally, transmission spectroscopy has grown into a robust way to constrain the composition of a planet’s atmosphere, assuming a well-understood host star. The increasing number of planets with observed transmission spectra has moved us towards comparative studies of planetary atmospheres, rather than studies of planets as single, non related, data points (see Sing et al. (2016) for a discussion of the variety of Hot Jupiter atmospheres, Fu et al. (2017) for an updated look at Hubble spectra, and Crossfield & Kreidberg (2017) for a look at Neptune-sized planets). With this, comes the need to have sets of uniformly observed and reduced planetary transmission spectra to better make comparisons between planets. In this work, we discuss our first steps towards contributing our own catalog of such planets observed with the Magellan Baade telescope at Las Campanas Observatory in Chile. Transmission spectroscopy measures the relative size of an exoplanet compared to its host star as a function of wavelength. Because a fraction of the stellar light will filter through the planet’s gaseous atmosphere before reaching our observatories, the exact transit depth measured is a combination of the light blocked out by the optically thick portion of the exoplanet and the amount of absorption and scattering of stellar light by the atmosphere. This allows us to reconstruct likely compositions of the atmosphere, including mean molecular weight, molecular and atomic atmospheric constituents, and clouds. In the presence of absorbers or scatterers, the transit depth will appear larger, due to the star light that is removed from our line of sight by the planet’s atmosphere. The expected strength of such features scales with the planet’s atmospheric scale height; related to the planet’s gravity, limb temperature, and mean molecular weight. Therefore, a typical ‘good’ target for transmission spectroscopy is a planet with a high limb temperature, low atmospheric mean molecular weight, or a low

32 gravity. To date, planet atmospheres are best described as being ‘cloudy’, with a flat and featureless transmission spectrum (uniform transit depth with wavelength); ‘clear’, showing evidence of atomic and molecular absorption; or ‘hazy’, showing evidence of scattering, but few, or diminished, absorption features. The characterization of a planet’s atmosphere benefits from the detection or non-detection of this absorption and/or scattering through the atmosphere. At optical wavelengths, the primary source of scattering is Rayleigh scattering. Rayleigh scattering has a wavelength dependence of λ−4, resulting in a stronger effect at shorter, bluer, wavelengths. These higher amounts of scattering at shorter wavelengths corresponds to a deeper planetary transit, as more light is scattered from our line of sight. Meanwhile the primary source of absorption at optical wavelengths is due to the alkali metals Sodium and Potassium. The presence or lack-there-of of any of these features tells us information about the composition of the planet’s atmosphere. In order to best understand the shapes of transmission spectra, we need to leverage multiple types of observatories to combine data from a variety of wavelength regimes. Hubble has been a leading force in infrared transit observations; from small, Neptune-like planets (e.g. Ehrenreich et al., 2014; Kreidberg et al., 2014); to large, Hot Jupiters (e.g. Vidal- Madjar et al., 2003; Sing et al., 2008). More recently, Tsiaras et al. (2018) did a re-analysis of the Hubble observations for 30 exoplanets in order to provide a uniformly reduced and analyzed sample of planets. At optical wavelengths, numerous ground-based observatories are working on surveys; including the ACCESS group, also at the Magellan telescopes at Las Campanas, with results for GJ 1214 b (Rackham et al., 2017); and the Gran Telescopio Canarias exoplanet transit spectroscopy survey, currently with results for numerous planets (see Sing et al., 2012; Murgas et al., 2014; Parviainen et al., 2016; Palléet al., 2016; Nortmann et al., 2016; Chen et al., 2017a,b; Murgas et al., 2017; Parviainen et al., 2018). Because telescope time is limited, it is important to make use of all resources available to us to study the atmospheres of new planets, as well as ensure reproducibility of results across telescopes,

33 instruments, and reduction methods. In this work, we present the first results of the Michigan Optical Planetary Spectra Survey (MOPSS) at the 6.5-meter Magellan Baade Telescope. This survey is designed to create a catalog of uniformly observed and reduced transmission spectra for the benefit of enabling comparative exoplanet studies. WASP-4b and WASP-52b provide two case studies with which we built our complete reduction and analysis pipeline. Both planets were selected for their size, expected transmission signals, and/or ease of observations from the Magellan Baade Telescope. In Section 2.4, we discuss the instrument used, our observational set-up, and previous observations of our targets. In Section 2.5, we outline the steps in our data reduction pipeline, as well as the steps we take in the analysis of the resulting light curves. Section 2.6 details our resulting transmission spectra for both targets, and discusses the affects of star spots on our transits. Section 2.7 discusses the future steps and goals for MOPSS, as well as the benefit of ground based optical planetary studies in the coming James Webb Space Telescope (JWST) era.

2.4 Observations

2.4.1 The IMACS Instrument

34 nfs oead11bnig hc scmaal oteepsr iefrec rm for frame each for time exposure seconds the to 81 comparable at is targets. CCD; which these the binning, for 1x1 and time night). mode read-out each fast the for in by data seeing limited is for was 2.4.3 resolution efficiency and our observational 2.4.2 setup, Sections Our (see this night With each minimize seeing to subtraction. the (20”) by background lengths limited for large fits with improve (16”) and slits losses wide within used slit similar we be most object, star each the the For that with target. requirement those main a or with type colors, spectral J-K was same and type the spectral B-V are if color calibrators their stars Ideal or Calibrator type, available. spectral 2.2). not and Figure magnitudes (see their chip on central wavelength based a chosen complete on were with target stars main calibrator the of keeping number while coverage the instrument maximize Our to wavelengths). designed longer are to masks contamination this push to 8000 designed beyond filter contamination blocking order second and atmosphere), our in from 17.5 of stars calibrator with (right) WASP-52b and (left) WASP-4b for Views of Field 2.1: Figure ∼ ◦ 4600 eutn ntertclwvlnt oeaefo 3900 from coverage wavelength theoretical in resulting , etmss h ml elwmrsaeainetsasfrtems ntused (not mask instru- the the for on stars cut alignment slits are collection). the marks data of yellow for size small the the represent masks, boxes ment yellow large The marked. to A ˚

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Cal #7 Cal #8 2 absorption 2.4.2 The planet WASP-4b

WASP-4b is a ∼1600K Hot Jupiter orbiting a G-type star. WASP-4b has previously been targeted for transmission spectroscopy by Hubble, with both transit and secondary eclipse measured (See Ranjan et al., 2014). Ranjan et al. (2014) find that their transmission measurements heavily depend on their reduction methods due to chip saturation, and as such, do not report results. Recent work by Huitson et al. (2017) presents complete optical transmission spectra for WASP-4b observed at the Gemini South telescope from 4400-9400A.˚ We compare their results to ours in Section 2.6.2. WASP-4b was observed on the night of August 19th, 2015 with an exposure time of 90 seconds and a total of 112 exposures, for an observational efficiency of 53%. Thin clouds passed during the night, with increased cloud coverage toward the end of the night. We discard the final 15 exposures due to these clouds, leaving us with 97 science frames. Seeing ranged from 1” to 1.3” during the course of the night, with the object’s airmass ranging from ∼1.0 to ∼1.5. Our wide slits mean that we are not concerned with slit losses even during these unfavorable seeing conditions. In addition to our main target, our instrument mask allowed us to simultaneously target 11 calibrator stars (see Table 2.1). The large number of calibrator stars observed allows us to be highly selective when choosing those to use for flux calibration, as well as reserve one calibrator to serve as a ‘check’ star. Since these calibrators should be constant throughout the night, this ‘check’ star provides a method to ensure our pipeline is correctly accounting for airmass and seeing effects throughout the night.

2.4.3 The planet WASP-52b

WASP-52b is a ∼1300K inﬂated Hot Saturn orbiting a K-type star. WASP-52b has been targeted for transmission spectroscopy by Kirk et al. (2016), Mancini et al. (2017), Chen et al. (2017b), and Louden et al. (2017). In addition, Tsiaras et al. (2018) recently analyzed archival Hubble transits of WASP-52b. Kirk et al. uses wide band ﬁlters on the William Herschel Telescope, while Mancini et al. (2017) uses multiple medium-sized

36 Figure 2.2: Spectra for WASP-4 (grey line) and the representative calibrator (red line) from 4600 A˚ through 8200A.˚ The edges of our 200 A˚ binning are plotted as grey lines, with the integrated values for those bins over plotted.

Identiﬁer R.A Dec. V mag. R mag. I mag. WASP -4 23:34:15.09 -42:03:41.05 12.48 11.90 12.09 Cal #1 23:35:09.73 -41:54:36.47 13.24 13.07 12.90 Cal #2 23:35:34.59 -41:52:34.75 12.09 11.86 11.52 Cal #3 23:35:41.22 -41:57:40.27 11.77 11.41 11.01 Cal #4 23:35:27.70 -42:04:15.13 13.07 12.99 12.84 Cal #5 23:35:44.41 -42:06:19.16 12.41 12.40 12.40 Cal #6 23:36:03.58 -42:06:10.32 11.66 11.52 11.37 Cal #7 23:35:37.94 -42:10:46.97 13.18 13.04 12.87 Cal #8 23:35:09.24 -42:15:10.52 13.75 13.57 13.39 Cal #9 23:34:44.80 -42:14:05.85 12.50 12.28 12.04 Cal #10 23:34:18.36 -42:04:50.99 12.93 12.76 12.56 Cal #11 23:34:04.52 -42:02:43.22 14.52 14.31 14.07

Table 2.1: WASP-4b: Calibrator Stars. See Figure 2.2 for a visual representation of the layout of the calibrator stars.

37 telescopes to obtain 13 light curves with wide band filters. In this work, we report higher spectral resolution light curves, with resolution similar to that reported in Chen et al. (2017b) and Louden et al. (2017). Chen et al. (2017b) report a detection of the sodium line with a single transit observed from the Gran Telescopio Canarias from 5220 A˚ to 9030 A.˚ Louden et al. (2017) similarly cover the entire optical range, from 4000 A˚ to 8750 A,˚ with two discrepant transits observed from the William Herschel Telescope. The Hubble observations reported in Tsiaras et al. (2018) cover 1µm to 1.6µm and are binned at higher spectral resolutions than ground-based optical studies. Because of the spotty nature of WASP-52, additional transits of WASP-52b allow us to provide tighter constraints on the atmosphere’s transmission spectra. In this work, WASP-52b was observed on the nights of August 11th and September 21st, 2016 with exposure times of 70 seconds for both nights, resulting in an observational efficiency of 46%. We obtained 154 exposures from the first night and 170 exposures on the second night. Seeing was very good on night 1, ranging from 0.6” to 0.9”. The second night had high wind throughout, with seeing generally above 1.0” but below 1.5”. The airmass of WASP-52 ranged from ∼2.5 → ∼1.2 → ∼1.7 on the first night, with similar values on the second night. As with WASP-4b, we are unconcerned about these seeing conditions due to our wide slits. In addition to our main target, our instrument mask allowed us to simultaneously target 8 calibrator stars (see Table 2.2). One calibrator is reserved as a ‘check’ star to ensure our pipeline accurately accounts for airmass and seeing effects throughout the night

2.5 Data Analysis

2.5.1 Reduction Pipeline

Our data reduction pipeline was developed in python from scratch in order to better understand the various sources of error. Our pipeline follows the standard spectroscopic

38 Figure 2.3: Spectra for each night of WASP-52 observations from 4600 A˚ through 8200 A.˚ The grey line shows WASP-52, and the red line shows the calibrator. The edges of our 200 A˚ binning are plotted as grey lines, with the integrated values for those bins over plotted.

Identiﬁer R.A Dec. V mag. R mag. I mag. WASP-52 23:13:58.76 +08:45:40.60 12.00 11.98 11.79 Cal #1 23:14:23.71 +08:27:56.76 12.21 12.99 12.92 Cal #2 23:14:16.72 +08:42:16.92 11.76 12.73 12.47 Cal #3 23:14:07.26 +08:39:29.28 12.26 11.74 11.39 Cal #4 23:13:31.96 +08:40:55.47 11.25 12.03 11.88 Cal #5 23:13:19.57 +08:30:35.68 11.22 11.93 11.84 Cal #6 23:13:29.15 +08:45:10.21 11.60 12.33 12.22 Cal #7 23:13:17.19 +08:38:25.27 12.43 12.89 12.68 Cal #8 23:13:20.30 +08:47:17.94 11.30 12.01 11.89

Table 2.2: WASP-52b: Calibrator Stars. See Figure 2.2 for a visual representation of the layout of the calibrator stars.

39 reduction techniques as outlined in this section. All data is first dark-corrected using dark frames taken in the afternoon prior to each observation. For each night, we took approximately one dozen dark frames, with exposure length equal to the science frames, which are combined into a median-filtered master dark frame before being subtracted. The variance in the master-dark is taken to be a source of error in pixel count levels. To begin data extraction, our pipeline uses flat frames taken with the mask and dispersing grism in place to identify the extent of the spectra on the chips for each object observed. A box is generated encompassing this entire region, which corresponds to approximately 200 pixels wide by nearly 3000 pixels long. This process accounts for curvature in the spectrum by extending the width of the extracted 2D region as needed if there is curvature detected. Because the size of the target is much smaller than the size of our slits, the width of these 2D boxes is always more than sufficient to capture the entire spectrum. For each target, the 2D regions are stitched across the y-direction chip gap of 57 pixels. In each 2D spectrum, we perform cosmic ray rejection following the process described in Nikolov et al. (2014). We do not find that cosmic rays are a problem in our data, but use this step to ensure that we remove as many sources of error as possible From the 2D spectrum, we first account for outliers in the background in order to improve our background fit. This is done row-by-row searching for ‘flared’ pixels more than 3σ the surrounding median background level, while masking the central region consisting of the object’s spectrum. Outlier background pixels are mapped to the median of the surrounding pixels. A first-order polynomial is then fit to the background and subtracted off. Next, for each row in spectral space of the 2D spectrum, a gaussian is fit to the data to determine the x-centroid and size of the aperture (from the FWHM) to be used for each exposure. We again map 3σ outliers from the gaussian fit to the surrounding median and then re-fit the gaussian to ensure there are no outliers significantly affecting the x-centroid and FWHM. It is important to note is that we do allow the aperture size to vary from exposure to exposure,

40 but it is constant across all wavelengths for a given exposure (We find this method useful to account for variations in seeing and airmass throughout the night). Each exposure’s aperture is computed from the median FWHM across all spectral rows for each individual exposure and object. The aperture size is defined to be 3× the median FWHM for each exposure and object. Shifts in the star’s position in the spatial direction on the chip are accounted for by allowing the central position of the gaussian to float for each row, but in reality, the centroid also remains fairly constant throughout the extraction, due to the stability of the pointing of the Baade telescope. Finally, we sum the region within the aperture size around the x-centroid, accounting for the 57 chip gap by assigning non-number values to those rows in spectral space (This later allows us to discard the binned spectra including this region). Prior to applying a wavelength solution, we first account for shifts in the star’s position in the spectral direction on the chip. This involves oversampling each spectrum in the time- series by a factor of 10 and correlating them with the first exposure to measure pixel shifts in the spectral direction down to 1/10th of a pixel. Just like we previously account for stellar shifts in the spacial direction on this chip by fitting the x-centroid location, this step allows us to correct for stellar shifts in the spectral direction. Each exposure is then shifted to the same pixel space as the first exposure as needed. Because the large size of our target slits would result in our arc frames being saturated at the shortest exposure time, here we instead use small 1” ‘mini-slits’ directly to the side of our object slits for wavelength calibration. The IMACS instrument has available a HeNeAr lamp with 24 identified lines from ∼ 3900A˚ to ∼8500A.˚ Our pipeline requires an initial manual marking of several lines and from there extrapolates a polynomial with a user-defined order while matching up additional lines. The user can then accept or reject each newly matched line. Because a line matched by the pipeline must be within 0.25 pixels of the known arc spectrum, obvious matches are sometimes not identified by the routine. At this point, the user can manually feed in the locations of these additional lines to improve the fit. Once the user accepts a fit, a pixel-to-wavelength conversion is calculated and applied to the spectra

41 for that object. This process is done for each object on the mask (the main target and each calibration star). Because the lines below ∼5000A˚ are weak in our arcs, we do not currently use the wavelength solution below approximately ∼4600A.˚ We ﬁnally bin the spectra for each star into 200A˚ wide bins from 4600 - 8200 A,˚ for a total of 18 bins; 100A˚ wide bins, for a total of 36 bins; as well as 20A˚ wide bins, for a total of 180 bins. For this step, we make use of the python package SpectRes (Carnall, 2017).

Bins containing a chip gap and/or the large O2 absorption near 7600A˚ are discarded. The wide binning allows for measurements of any Rayleigh slope, while minimizing noise in the light curves. The ﬁnest binning allows for detection of Alkali absorption features. Applying a variety of binning ensures we return the overall shape of the transmission spectrum, while not averaging over any narrower features. Figures 2.2 and 2.3 show spectra from one point in time for all three nights at the widest binning, as well as the combined calibrator star.

2.5.2 Light Curves

To generate our binned and white light curves, we first create ‘master’ calibrators. Each master calibrator consists of all reference stars, minus the one chosen as the ‘check’ star. This master calibrator is divided out for both our target star and the check star before an out-of-transit time series model is fit. We fit both models of time (2nd, 3rd, and 4th order polynomials) and airmass (3rd order polynomial). We determine the 3rd order polynomial in time to be the best reproduction of our observed baseline after dividing out our calibrator stars. Figure 2.4 shows our white light curve for WASP-4b, with several baseline models in time. Although the 3rd and 4th order polynomials show similar fits, we choose the 3rd order fit to minimize the number of free parameters involved when fitting the binned light curves which naturally are noisier.

42 Figure 2.4: White light curve for WASP-4b, overlaid with several baseline models. The inset shows a zoomed-in portion of the light curve after transit, demonstrating that the 3rd and 4th order fits are similar, but that the 2nd order does not properly capture the baseline. While the 3rd order and 4th order fits are similar, we choose the 3rd order fit to minimize free parameters.

2.5.2.1 White Light Curves

White light curves are generated from the entire spectral range, covering 4600A˚ to 8200A.˚ These white light curves are used to fit for orbital parameters using the python package Batman(Kreidberg, 2015) with a quadratic limb-darkening function, in conjunction with a MCMC fitting routine, emcee (Foreman-Mackey et al., 2013). We adopt the quadratic limb darkening coefficients from Claret & Bloemen (2011) as starting points for the fits based on the stellar parameters in Tables 2.3 and 2.4. We fit for the center of transit, period/semi- major axis, inclination of orbit, white-light planet radius, and white-light limb darkening, where orbital and stellar parameters are fit with a gaussian prior defined by the values and errors given in Tables 2.3 and 2.4. The relation between period and semi-major axis (in units of stellar radii) is maintained for the assumed stellar mass and radii values by only fitting for period, while simultaneously calculating a corresponding semi-major axis with a stellar mass and radii drawn from a gaussian distribution around the errors defined by the

43 parameters in Tables 2.3 and 2.4. For the second transit of WASP-52b, there is a clear star spot crossing event visible in the white light curve (see Figure 2.5). In exoplanet transits light curves, star spots appear as ‘bumps’ in transit due to the planet blocking out less light while occulting a dark spot. Spots occulted during transit require fitting a light curve with 4 additional parameters per spot; spot x and y location relative to the stellar center, spot radius, and spot contrast. Similarly to orbital parameters, the spot location and size will not change as a function of wavelength. We employ a python package named SPOTROD (Békyet al., 2014), which generates light curve models in combination with any number of spot occultations. Although our first transit of WASP-52b does not show a star spot feature, we chose to model both transits with this package for consistency. For both transits, the white light curve fitting searches for the best orbital parameters and star spot location and size parameters, with the expectation that the spot radius should be 0 for the first transit. In order to ensure that the joint spot-orbital parameter fitting does not alter our orbital parameters, we also run white light curve fits for just orbital parameters with the spot masked in the data. We find that both techniques provide the same orbital parameters, within errors. For all transits, the orbital parameters are then assumed to be constant with wavelength. For spotted transits, spot location and size are held constant across wavelengths as well. Additionally, we perform the same analysis on our check stars from each night. In these cases, the light curves should be best fit by a flat line, finding no planet transit. In all cases, this is found to be true.

2.5.2.2 Binned Light Curves

As discussed in Section 2.5.1, we bin the data into 200A,˚ 100A,˚ 50A,˚ and 20A˚ wide bins in wavelength space. Light curves and their ﬁts are shown in Figures 2.6 and 2.7. For each binning we perform MCMC ﬁts using either Batman (WASP-4b, no stellar spots)

44 Figure 2.5: White light curve for the second transit of WASP-52b, showing a clear spot crossing feature at approximately -0.5 hours. or SPOTROD (WASP-52b, spot crossing events), as well as noise removal as discussed in 2.5.3. Because orbital parameters are fit using only the white light curve, we need only fit for radius and limb darkening coefficients for WASP-4b in the binned light curves, and the same plus spot contrast for the binned WASP-52b light curves. For each bin, the quadratic limb darkening coefficients are interpolated between the Johnson filter values from Claret & Bloemen (2011) and fit together across bins by requiring that the shape of the limb darkening wavelength-dependent interpolation remains approximately constant, while allowed to shift to better fit the data and to account for uncertainties in the stellar parameters and limb darkening tables. For WASP-4b and the first transit of WASP-52b, our fit limb darkening values agree with those from Claret & Bloemen (2011) For the second transit of WASP- 52b, see Section 2.6.3.2. Figure 2.8 shows our fit limb darkening values as compared to the Claret & Bloemen (2011) values, which demonstrates our fitting procedure, where, for all three transits, the limb darkening parameters show the same wavelength-dependent shape as the Claret & Bloemen (2011) values, but may be systematically shifted higher or lower to account for the uncertainties in the stellar parameters and limb darkening tables.

45 Light Curves Residuals 4700Å

1.25 4900Å 5100Å 5300Å 5500Å 1.20 5700Å 5900Å 6100Å 1.15 6300Å 6500Å 6700Å 1.10 6900Å 7100Å 7300Å Relative Flux + shift 1.05

7900Å 1.00 8100Å

2 0 2 2 0 2 Time from Center of Transit [hrs]

Figure 2.6: Light curves for the low resolution binning (200A)˚ for WASP-4b. The left frame shows our reduced light curves and best ﬁt model in black. The right panel shows the residuals for the ﬁts. We do not include bins that are contaminated by major O2 absorption in Earth’s atmosphere.

46 Light Curves Residuals 4700Å 1.30 4900Å 5100Å 5300Å

1.25 5500Å 5700Å 5900Å 6100Å 1.20 6300Å 6500Å 6700Å 1.15 6900Å 7100Å 7300Å 1.10 7500Å 7700Å Relative Flux + shift 7900Å 1.05 8100Å 8300Å 8500Å 1.00 8700Å

0 2 4 0 2 4 Time from Center of Transit [hrs]

47 Light Curves Residuals

1.30 4900Å 5100Å 5300Å

1.25 5500Å 5700Å 5900Å 6100Å 1.20 6300Å 6500Å 6700Å 1.15 6900Å 7100Å 7300Å 1.10 7500Å 7700Å Relative Flux + shift 7900Å 1.05 8100Å 8300Å 8500Å 1.00 8700Å

0 2 4 0 2 4 Time from Center of Transit [hrs]

Figure 2.7: Light curves for the low resolution binning (200A).˚ Top: WASP-52b Transit 1 (unspotted, 08/11/2016). Bottom: WASP-52b Transit 2 (spotted, 09/22/2016). For both transits, the left frame shows our reduced light curves and best ﬁt model in black. The right panel shows the residuals for the ﬁts. We do not include bins that are contaminated by major O2 absorption in Earth’s atmosphere.

48 Stellar Parameter Value Mass, [M ] 0.89±0.01 Radius, [R ] 0.92±0.06 Teff , [K] 5436±34 [Fe/H], [dex] -0.05±0.04 ξ, [km/s] 0.85±0.10† (Microturbulent Velocity) log g, [cm/s] 4.28±0.06 Planet Parameter Value Mass, [MJup] 1.22±0.01 Radius, [RJup] 1.33±0.16 Teq, [K] 1664±54 Period, [days] 1.3382325±3e-7 Semi-major axis, [AU] 0.0232±0.0005? Eccentricity 0.0 Inclination, [deg] 86.85±1.76 Table 2.3: WASP-4b: Stellar and Orbital Parameters: All values have been adopted from Petrucci et al. (2013) with the exception of those marked with a ?, which come from Southworth (2012), and those marked with a †, which come from Doyle et al. (2013).

Stellar Parameter Value Mass, [M ] 0.87±0.03 Radius, [R ] 0.79±0.02 Teff , [K] 5000±34 [Fe/H], [dex] 0.03±0.12 ξ, [km/s] 0.9±0.1 (Microturbulent Velocity) log g, [cm/s] 4.58±0.01 Planet Parameter Value Mass, [MJup] 0.46±0.02 Radius, [RJup] 1.27±0.03 Teq, [K] 1315±35 Orbital Period, [days] 1.749780±1e-6 Semi-major axis, [AU] 0.0272±0.0003 Eccentricity 0.0 Inclination, [deg] 85.35±0.20 Table 2.4: WASP-52b: Stellar and Orbital Parameters: All values have been adopted from H´ebrardet al. (2013).

49 Figure 2.8: Limb darkening parameters from MCMC ﬁts (red points) compared to literature values (black curves). All three transit events are shown.

2.5.3 Error Analysis and Noise Removal

Our MCMC likelihood function takes the RMSE of the out-of-transit baseline as the input uncertainty on an individual point. From this, the error on our fit transit depths is the 1-sigma level from the converged MCMC chain. To further improve our results, we perform a noise removal algorithm to remove common mode white noise. We do not find a significant improvement when applying red noise removal techniques to these data sets. Our common mode white noise is the ratio between the baseline-uncorrected data and the white transit model fit, which we then divide out of our wavelength-binned light curves.

50 2.6 Results

2.6.1 Transmission Spectra

For all transits, we produce transmission spectra based on the binned light curve fits. Our finer binning (100A,˚ 50A,˚ and 20A)˚ serves to ensure that we do not miss absorption features that may be smeared out by wider binning (200A),˚ however, these bins naturally result in larger error bars. We find no additional features at this binning and do not show light curves at this binning, though the points for the 100A˚ binning are shown on the transmission spectra in Figure 2.9. At optical wavelengths, we are primarily searching for signs of Rayleigh Scattering, as well as sodium and potassium absorption features. Rayleigh Scattering allows us to constrain the relation between the mean molecular mass of the atmosphere and the mean atmospheric limb temperature. The slope of this scattering is given by

1 dR 1 k T p = α B (2.1) Rs d ln λ Rs µg

, ﬁrst described by Lecavelier Des Etangs et al. (2008) where Rs is the stellar radius; Rp is the planet radius; α is the power of the wavelength dependance of Rayleigh scattering, typically -4; kB is the Boltzmann constant; T is the planetary limb temperature; µ is the mean molecular weight of the atmosphere; and g is the planetary gravity. Where, as noted, µ and T are our main unknown parameters. Even for planets with temperatures determined through secondary eclipse (such as WASP-4b), transmission spectroscopy probes the average temperature of the atmospheric limb, whereas secondary eclipse probes the average dayside temperature. While secondary eclipse measurements, in combination with expected equilibrium temperatures for an assumed albedo, can help break the degeneracy between the parameters, this degeneracy points to the necessity of multi-wavelength observations to fully understand the planetary atmosphere. It is important to note that large uncertainties in temperature observations still dominate the relation between the limb temperature and the mean molecular mass, and any statement about mean molecular weight must make an

51 assumption for the temperature and albedo of the planet. The sodium (Na) and potassium (K) absorption features occur at 5890A˚ and 7665A,˚ respectively. For most planets, these are the only two absorption features detectable in the optical regime. It is important to note, however, that the detectability of these features heavily depends on the width of the wavelength bins chosen, as demonstrated by Chen et al. (2017b). Specifically calculated for WASP-52b, Chen et al. (2017b) show that for bin sizes greater than ∼30A,˚ no detectable increase due to these absorption features will be measured. Unfortunately, at these bin widths, the error in the measurements increases substantially. For this reason, we bin at 200A˚ to determine the overall shape of the transmission spectra, as well as at 100A˚ and 20A˚ to search for additional spectral features. We find no significant deviation from the 200A˚ binning in the higher spectral resolution light curves. Although the K absorption feature may be as detectable as Na, there is an oxygen absorption line in our atmosphere centered at ∼7600A.˚ If bin sizes are wide enough that they contain the potassium absorption line and any part of this wide oxygen feature, the K feature may be diluted due to high noise. Because our data is not of high enough resolution to perform atmospheric retrievals, we instead create representative transmission models using the code Exo-Transmit as described in Kempton et al. (2017). Exo-Transmit is a robust and user-friendly package which allows the user to define the planetary parameters, as well as set the composition and temperature structure of the atmosphere. The user can set the pressure level of any cloud deck, and vary the strength of scattering in the atmosphere. We explore models with varying composition, scattering strength, and cloud decks. Throughout this work, we assume isothermal temperature structures.

2.6.2 WASP-4b

Figure 2.9 shows our ﬁnal transmission spectrum for WASP-4b. We note that within errors, WASP-4b presents a fairly ﬂat, and featureless, spectrum; however one that is also

52 Figure 2.9: Transmission spectra for our one transit of the Hot Jupiter WASP-4b. For ease of comparison with values from Huitson et al. (2017), values are plotted relative to the white light transit depth. Left: We present a Rayleigh slope at the equilibrium temperature of the planet (dashed line), and a flat spectra to mimic a cloudy atmosphere (solid line). We find that the models show nearly identical goodness-of-fit χ2 values, pointing to the necessity of additional longer wavelength data to distinguish between atmospheric models for such high gravity planets. Right: Our data in comparison to Huitson et al. (2017), which agree well. We note that they obtained 3 transits of WASP 4-b, compared to our single transit. consistent with Rayleigh scattering at the equilibrium temperature of the planet (assuming zero-albedo). Observations into the infrared would help to clear up the degeneracy between models, and additional transits would improve the accuracy of measurements. Unfortunately, Hubble transit observations of this planet by Ranjan et al. (2014) were saturated and transit depth values were not reported. Additionally, WASP-4b’s high gravity means transmission signals will be small, and so we do not expect single transit ground based observations alone to disentangle the atmospheric models. The cloudy model and the nominal Rayleigh slopes both return a nearly identical χ2 value, at ∼8×10−4. Based on our Exo-Transmit modeling of a solar metallicity atmosphere, we expect a cloud deck no lower than 10−4 bar in order to obscure the Na and K absorption lines.

53 Figure 2.10: Combined transmission spectra for both transits of the Hot Saturn WASP-52b. Left: We present a linear ﬁt to the data (dotted line) and an Exo-Transmit model with solar metallicity. We prefer a ﬂat, cloudy spectra. Right: Our data in comparison to Chen et al. (2017b) and Louden et al. (2017), which agree well.

2.6.3 WASP-52b

Figure 2.10 shows our combined transmission spectrum for WASP-52b, plotted with a linear fit and an Exo-Transmit model (solar metalicity, standard scattering). We find a large discrepancy in the average transit depth between the spotted transit (Night 2) and the unspotted transit (Night 1). The offset between a spotted and unspotted transit is also seen by Louden et al. (2017). This difference may be a result of unocculted star spots on the stellar surface. See section 2.6.3.1 for a discussion of how one can correct for unocculted star spots. Further, we measure different limb darkening parameters on each night. Section 2.6.3.2 discusses one possible explanation for this difference. We do not find evidence of sodium absorption, as found by Chen et al. (2017b). Our data exhibits a flat transmission spectra, pointing to a cloudy atmosphere. Using Exo-Transmit models, we conclude that the cloud deck must be no lower than 10−4 bar.

2.6.3.1 Unocculted Star Spots

The detection of a star spot in one transit of WASP-52b suggests we must also consider the possibility of unocculted stellar features which would affect the absolute flux level of the star. Such features, if uncounted for, could mimic a Rayleigh slope, as well as introduce an offset in the absolute transit depth. We investigate the affect of unocculted star spots using

54 the prescription given in Louden et al. (2017) where the measured transit depth, δ˜(λ), can be described as a function of the true depth, δ(λ), times a function of the spot coverage, η:

˜ 1 δ(λ) = δ(λ) (2.2) 1 − η 1 − Fλ(spot) Fλ(star)

From this, we can calculate the approximate overall dimming of the star as a function of wavelength as

Fλ(star, corrected) = ηfλFλ(star) + (1 − η)Fλ(star) = [1 − η(1 − fλ)]Fλ(star) (2.3)

with fλ the spot contrast we fit with the transit light curves and fλFλ(star) equivalent to the spot’s flux. From our fit spot contrast levels, and the required spot coverage fraction to reach the observed fractional difference in transit depth (see Figure 2.11), we can calculate the observed stellar dimming due to spots between the two nights, and compare to photometric studies of WASP-52’s variations. Hébrardet al. (2013) performed photometric monitoring of WASP-52 over two different seasons, and found the star dimmed up to 0.89% over the course of a 16.4±0.04 day rotational period. Our observations were 42 days apart, which puts us at ∼2.5 periods, assuming the star presented a similar period of spot variability during our transit observations. An analysis of more recent photometric data by Louden et al. (2017) found a 17.79±0.05 day period, with a significantly higher dimming amplitude of 1.42%. Our data requires a spot coverage of ∼2-3%, corresponding to a dimming of 1.5-2%, in agreement with previous photometric measurements.

2.6.3.2 Star Spots on the Stellar Limb

Due to our diﬀering limb darkening measurements between our two transits of WASP-52b, we cannot ignore the possibility that occulted spots are present on the limb of the star, and manifest as variations in limb darkening. To determine whether this is a feasible explanation

55 Figure 2.11: Using equation 2.2, a demonstration of how increasing spot coverage changes the measured planetary-to-stellar radius ratio for a wavelength dependent spot contrast as measured in our MCMC fits, from 4000A(blue)˚ to 8000A(red).˚ Over plotted in a grey band is our measured difference in radius between our two observations of WASP-52b. for our differing limb darkening measurements, we use SPOTROD to generate light curves with 2 spots on the limb of the star, in the path of the planet’s transit. Both spots are identical in size, vertical location, and contrast to the occulted spot in the September 2016 transit of WASP-52b, but offset to the limb of the star. We compare these light curves to those expected in a spot-free transit (see Figure 2.12) and note that spots on the limb do not appear as large ‘bumps’ as they do during mid-transit occultations, but instead they slightly change the shape of the ingress and egress portions of transit. By eye, one does not detect the presence of a spot and therefore would not find it necessary to fit such a light curve as a spotted transit. To demonstrate how this assumption affects the measured limb darkening, we fit the transit with occulted spots on the stellar limb with a standard transit model, using the previously described BATMAN package. As expected, the returned limb-darkening parameters do not match those used to create the light curve. Figure 2.13 shows visually the difference between the expected limb darkening with occulted spots on the limb, and the returned limb darkening. Figure 2.14 shows

Spot-Free Limb-Spots

− −

Figure 2.12: Eﬀect of occulted spots on the limb on the shape of ingress/egress for a WASP- 52b like planet. The black curve shows a typical transit signal for WASP-52b. In red is the resulting transit with occulted spots on the stellar limb. Note that the ‘typical’ spot feature is not present, but instead the spotted transit simply appears to have diﬀerent limb darkening.

Figure 2.13: Eﬀect of occulted spots on the limb on the returned limb darkening for a WASP- 52b like planet. Expected limb darkening with occulted limb spots (left). Spots on the limb result in returned limb darkening parameters that correspond to noticeably stronger limb darkening (right). The shaded red region corresponds to the path of the planet during transit. The two limb spots are shown in the left panel, but not the right, because they are not assumed to be present when ﬁtting for the observed limb darkening parameters. The dashed black circle represents the location of the measured spot in our September 2016 transit.

57 iue2.14: Figure Limb Darkening 0.0 0.2 0.4 0.6 0.8 1.0

4000 q1 q1 q0 ∙ hpsa ntetppo.Nt httesotdtasti etfi ihlarger with fit best is limb. the transit on spotted spots the for that expected Note and as colors values, plot. same darkening top the limb with the nights, in two our as for shapes parameters darkening limb both to sdntdwt ice,adtescn udai aaee sdntdwith darkening. denoted limb returned stronger is are to parameter parameters corresponding darkening values, quadratic parameter limb larger quadratic second both as when first that the parameters The Note and darkening limb. triangles. circles, limb upside-down the returned with on the spots denoted of are is possibility red actual, spots the In or occulted ignores with expected, one limb. curve the stellar light are the the generate black on to In used parameters planet. darkening like limb WASP-52b a for parameters Left: 4500

5000 Wavelength, ﬀc focle pt ntelm ntertre ibdarkening limb returned the on limb the on spots occulted of Eﬀect 5500

6000 Returned Parameters Actual ParametersActual 6500

Å 7000

7500

8000 58 Right: CCfits MCMC how the expected and returned limb darkening differ, these results are within the variations between our August and September 2016 WASP-52b transits. We find this to be a viable explanation for the differing limb darkening, though we do not attempt to fit for the presence of these limb spots, due to the degeneracy between the limb darkening and spot parameters in this part of the transit. We acknowledge that this situation is artificially contrived. However, we do note that as spots are likely to occur along the same latitude band, and we have detected a spot at this latitude in the relevant transit, it is not completely unrealistic to place additional spots in these locations. Regardless, this exercise serves only as one possible explanation for the different limb darkening measured under the circumstances that may exist for this star and to demonstrate that this possibility does produce the effect we measure.

2.7 Conclusions

We find flat spectra for both WASP-4b and WASP-52b within the errors of our measurements, implying the presence of clouds in the atmospheres of both planets. Our group is currently working on applying noise removal techniques for future data sets in order to improve our precision. We continue to schedule observations at the Magellan Baade telescope and hope to complete observations of several more targets this year. With the launch of JWST in spring 2021, ground based optical studies of planetary atmospheres will remain a worthwhile use of ground-based telescope time. The NIRSPEC instrument on JWST, likely to be the most commonly used instrument for transmission spectroscopy studies, has a lower wavelength limit of 0.6µm when using the prism disperser element. The prism, however, is a low resolution disperser, with a resolving power ∼100, comparable to our ground-based resolution. One of the major benefits of JWST is the ability to perform higher resolution transmission spectroscopy from 0.7µm to 5.27µm, with a resolving power up to ∼2700 depending on the disperser used. Therefore, ground based observations will remain important below 0.7µm, both to compare measurements between

59 0.6µm and 0.7µm, and to provide transmission measurements bluewards of the lower limit of JWST. Additionally, the TESS mission is expected to ﬁnd of order 1000 Sub-Neptunes in the primary mission (Sullivan et al., 2015). As a result, we expect numerous new ground based targets for this project in the coming years. With our current methods, and improvements being made, we will be well prepared to observe and characterize these new targets.

2.8 Acknowledgements

We thank the staﬀ at Las Campanas Observatory, without which we would be unable to carry out the observations presented in this work. This research has made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org.

2.9 Facilities and Software Used

Facilities: Magellan:Baade Software: Astropy (Astropy Collaboration et al., 2013), batman (Kreidberg, 2015), emcee (Foreman-Mackey et al., 2013), Exo-Transmit (Kempton et al., 2017), IPython (P´erez& Granger, 2007), Matplotlib (Hunter, 2007), NumPy (van der Walt et al., 2011), SciPy (Jones et al., 2001–), SpectRes (Carnall, 2017), spotrod (B´ekyet al., 2014)

60 2.10 Appendix

2.10.1 Check Star

As a check on our reduction process, all steps are also performed on a designated ‘check star’ each night. Because we have a large number of simultaneously observed stars, we can easily select one as a check star to be treated as a second target instead of an additional calibrator. Here we include representative ﬁgures (see Figures 2.15 and 2.16) for the check star from the ﬁrst night of WASP-52b observations (ut20160811).

Figure 2.15: Spectra for our check star during our ﬁrst night of WASP-52 observations from 4800 Athrough˚ 8000 A.˚ The blue line shows our check star, and the orange line shows the calibrator spectrum at one point in time. The edges of our 200 Abinning˚ are plotted as grey lines, with the summed values for those bins over plotted.

61 Figure 2.16: Showing the reduction process from the raw white light curve through the baseline-calibrated white light curve for both the target (left) and the check star (right) on the same scale. The first (top) panel of each figure is the uncali- brated, raw white light curve. The second (middle) panel shows the light curve after dividing out the combined calibrator stars. The third (bottom) panel shows the final light curve after fitting and removing a 3rd order polynomial in time to the out-of-transit baseline.

62 2.10.2 Tables of Results

Center of Bin [A]˚ Rp/Rstar ∆ Rp/Rstar q0 ∆ q0 q1 ∆ q1 4700 0.1560 0.0014 0.618 0.036 0.078 0.035 4900 0.1590 0.0014 0.595 0.035 0.114 0.036 5100 0.1530 0.0009 0.575 0.026 0.147 0.030 5300 0.1571 0.0009 0.560 0.026 0.199 0.030 5500 0.1529 0.0006 0.516 0.020 0.213 0.025 5700 0.1534 0.0006 0.526 0.020 0.246 0.026 5900 0.1557 0.0007 0.484 0.022 0.225 0.026 6100 0.1557 0.0005 0.437 0.019 0.212 0.025 6300 0.1570 0.0006 0.442 0.018 0.246 0.024 6500 0.1549 0.0006 0.440 0.021 0.251 0.025 6700 0.1532 0.0019 0.442 0.026 0.277 0.030 6900 0.1546 0.0015 0.430 0.041 0.278 0.042 7100 0.1559 0.0027 0.407 0.060 0.271 0.058 7300 0.1557 0.0020 0.375 0.052 0.246 0.054 7500 — — — — — — 7700 — — — — — — 7900 0.1553 0.0011 0.408 0.031 0.311 0.030 8100 0.1574 0.0010 0.377 0.030 0.297 0.032

Table 2.5: WASP-4b Wavelength dependent variables: Relative planetary radius measurements and quadratic limb darkening parameters, with their corresponding errors.

63 Center of Bin [A]˚ Rp/Rstar ∆ Rp/Rstar q0 ∆ q0 q1 ∆ q1 4900 0.1703 0.0015 0.715 0.026 -0.023 0.022 5100 0.1681 0.0011 0.661 0.019 -0.009 0.018 5300 0.1682 0.0011 0.657 0.019 0.052 0.022 5500 0.1684 0.0010 0.594 0.018 0.054 0.020 5700 0.1658 0.0010 0.567 0.018 0.071 0.021 5900 0.1655 0.0009 0.566 0.018 0.098 0.021 6100 0.1649 0.0008 0.533 0.017 0.097 0.020 6300 0.1663 0.0008 0.504 0.016 0.107 0.020 6500 0.1670 0.0008 0.508 0.017 0.157 0.021 6700 0.1682 0.0013 0.423 0.024 0.103 0.017 6900 0.1675 0.0015 0.478 0.024 0.158 0.026 7100 0.1638 0.0012 0.407 0.019 0.115 0.019 7300 0.1654 0.0009 0.400 0.019 0.124 0.020 7500 0.1658 0.0013 0.375 0.025 0.122 0.020 7700 0.1672 0.0016 0.418 0.024 0.178 0.027 7900 0.1624 0.0013 0.371 0.020 0.151 0.023 8100 0.1651 0.0012 0.390 0.021 0.187 0.024 8300 0.1626 0.0012 0.352 0.020 0.157 0.023 8500 0.1659 0.0012 0.300 0.023 0.132 0.017 8700 0.1638 0.0015 0.327 0.025 0.157 0.025 8900 0.1614 0.0032 0.367 0.050 0.210 0.050

Table 2.6: WASP-52b Wavelength dependent variables, ut20160811: Relative planetary radius measurements and quadratic limb darkening parameters, with their corresponding errors.

64 Center of Bin [A]˚ Rp/Rstar ∆ Rp/Rstar q0 ∆ q0 q1 ∆ q1 4900 0.1675 0.0027 0.826 0.030 0.091 0.030 5100 0.1677 0.0014 0.774 0.022 0.104 0.024 5300 0.1647 0.0012 0.721 0.024 0.116 0.019 5500 0.1616 0.0010 0.692 0.018 0.164 0.021 5700 0.1638 0.0010 0.640 0.019 0.155 0.017 5900 0.1656 0.0009 0.628 0.021 0.165 0.019 6100 0.1647 0.0009 0.586 0.021 0.169 0.015 6300 0.1650 0.0007 0.572 0.017 0.190 0.017 6500 0.1643 0.0012 0.537 0.022 0.196 0.017 6700 0.1659 0.0019 0.545 0.028 0.214 0.024 6900 0.1637 0.0018 0.508 0.036 0.204 0.020 7100 0.1670 0.0010 0.476 0.018 0.206 0.014 7300 0.1655 0.0009 0.499 0.019 0.225 0.022 7500 0.1706 0.0028 0.457 0.030 0.212 0.017 7700 0.1600 0.0033 0.465 0.037 0.233 0.030 7900 0.1641 0.0014 0.458 0.024 0.246 0.026 8100 0.1642 0.0013 0.452 0.027 0.241 0.024 8300 0.1651 0.0013 0.443 0.024 0.253 0.024 8500 0.1680 0.0016 0.397 0.034 0.245 0.028 8700 0.1668 0.0019 0.423 0.035 0.232 0.018 8900 0.1699 0.0039 0.399 0.044 0.264 0.038

Table 2.7: WASP-52b Wavelength dependent variables, ut20160922: Relative planetary radius measurements and quadratic limb darkening parameters, with their corresponding errors. Radius values have been corrected assuming a spot coverage fraction of 3%.

65 Center of Bin [A]˚ Rp/Rstar ∆ Rp/Rstar 4900 0.1693 0.0019 5100 0.1680 0.0016 5300 0.1669 0.0012 5500 0.1649 0.0012 5700 0.1649 0.0013 5900 0.1655 0.0016 6100 0.1648 0.0010 6300 0.1657 0.0011 6500 0.1662 0.0009 6700 0.1678 0.0011 6900 0.1663 0.0012 7100 0.1661 0.0013 7300 0.1654 0.0016 7500 0.1662 0.0011 7700 0.1660 0.0012 7900 0.1634 0.0012 8100 0.1648 0.0011 8300 0.1638 0.0011 8500 0.1666 0.0011 8700 0.1647 0.0012 8900 0.1625 0.0030

Table 2.8: WASP-52b Wavelength dependent variables, Combined Rp/Rstar values: Relative planetary radius measurements and quadratic limb darkening parameters, with their corresponding errors.

66 CHAPTER III

MOPSS II: Extreme Optical Scattering Slope for the

Inﬂated Super-Neptune HATS-8b

3.1 Preface

Results in this chapter were submitted to the Astronomical Journal as May, E. M., et. al 2018. MOPSS II: Extreme Optical Scattering Slope for the Inﬂated Super-Neptune: HATS- 8b. and are reproduced here with minor style revisions and updates from the ﬁrst round of referee comments.

3.2 Abstract

We present results for the inflated super-Neptune HATS-8b from MOPSS, The Michigan Optical Planetary Spectra Survey. This program is aimed at creating a database of optical planetary transmission spectra all observed, reduced, and analyzed with a uniform method for the benefit of enabling comparative exoplanet studies. HATS-8b orbits a G dwarf and is a low density super-Neptune, with a radius of 0.873 RJup, a mass of 0.138 MJup, and a density of 0.259 g/cm3. Two transits of HATS-8b were observed in July and August of 2017 with the IMACS instrument on the Magellan Baade 6.5m telescope. We find an enhanced scattering slope that differs between our two nights. These slopes are stronger than one due only to Rayleigh scattering and cannot be fully explained by unocculted star spots. We explore the

67 impact of condensates on the scattering slope and determine that MnS particulates smaller than 10−2µm can explain up to 80% of our measured slope if the planet is warmer than equilibrium, or 50% of the slope at the equilibrium temperature of the planet for a low mean molecular weight atmosphere. The scattering slope that we observe is thus beyond even the most extreme haze case we consider. We suggest further follow up on this target and host star to determine if the temporal variation of the slope is primarily due to stellar or planetary eﬀects, and to better understand what these eﬀects may be.

3.3 Introduction

Our ability to probe the atmospheres of exoplanets is rapidly advancing, with transmission spectroscopy leading the way as a robust method to constrain the composition of a planet’s atmosphere, for a well-characterized host star. With the number of detected exoplanets increasing rapidly in the past few years, we are no longer forced to study planets as single, unrelated, data points, but rather we are moving towards an era of comparative studies (see Sing et al. (2016) for a discussion of the variety of Hot Jupiter atmospheres, Fu et al. (2017) for an updated look at Hubble spectra, and Crossfield & Kreidberg (2017) for a look at Neptune-sized planets). In this new era for exoplanet science, it becomes necessary to have sets of uniformly observed and reduced planetary transmission spectra to better make comparisons between planets. In this work, we present our third data set in our catalog of such observations. Our work makes use of the IMACS instrument on the Magellan Baade telescope at Las Campanas Observatory in Chile. Transmission Spectroscopy relies on detection of stellar light that filters through the planet’s atmosphere as it transits the host star. The transit depth as a function of wavelength is then a combination of the light blocked by the optically thick part of the planet and the scattering/absorption effects on star light that passes through the atmosphere. When the stellar light is absorbed or scattered, the transit depth becomes larger, due to additional stellar light being removed from our line-of-sight. By precisely measuring the transit depth

68 as a function of wavelength, we can probe the composition of the atmosphere based on absorption and scattering features; particularly allowing constraints on the mean molecular weight, molecular and atomic atmospheric constituents, and the presence of clouds or other scattering particles. The expected strength of a feature due to absorption and scattering scales with the planet’s atmospheric scale height; a function of the planet’s limb temperature divided by its surface gravity and atmospheric mean molecular weight. For these reasons, a typical ‘good’ target for transmission spectroscopy is a planet with a high limb temperature, low atmospheric mean molecular weight, and/or a low gravity. Observations of most exoplanet atmospheres with this method return spectra suggesting either clear atmospheres showing evidence of atomic and/or molecular absorption with the full absorption profile present, or cloudy/hazy atmospheres exhibiting few or diminished absorption features with possible evidence for scattering slopes appearing as deeper transits at shorter wavelengths. At the optical wavelengths we probe in this work, the primary source of scattering is expected to be Rayleigh scattering, which has a wavelength dependence of λ−4. This corresponds to a stronger effect at shorter, bluer, wavelengths, resulting in deeper transits as more light is scattered from our line-of-sight at the blue end of the spectrum. Meanwhile, the primary sources of absorption at optical wavelengths are the alkali metals sodium and potassium. The presence of their absorption profiles, and the exact shape, gives us information on the composition and properties of the planet’s atmosphere. Observations that only cover optical or infrared wavelengths are not always able to place unambiguous constraints on atmospheric properties alone. Therefore we are best able to characterize a planet when we combine data from multiple observations at a variety of wavelengths. The Hubble Space Telescope has been a leading force in infrared transit observations; from small, Neptune-like planets (e.g. Ehrenreich et al., 2014; Kreidberg et al., 2014); to large, Hot Jupiters (e.g. Vidal-Madjar et al., 2003; Sing et al., 2008). More recently, Tsiaras et al. (2018) and Fu et al. (2017) did a re-analysis of the Hubble observations for 30 exoplanets in order to provide a uniformly reduced and analyzed sample of planets. At opti-

69 cal wavelengths, numerous ground-based observatories are working on surveys; including the ACCESS group, also at the Magellan telescopes at Las Campanas, with results for GJ 1214 b (Rackham et al., 2017) and WASP-19b (Espinoza et al., 2019); the Gran Telescopio Canarias exoplanet transit spectroscopy survey, currently with results for numerous planets (see Sing et al., 2012; Murgas et al., 2014; Parviainen et al., 2016; Pall´eet al., 2016; Nortmann et al., 2016; Chen et al., 2017a,b; Murgas et al., 2017; Parviainen et al., 2018; Chen et al., 2018); GMOS at Gemini (Huitson et al., 2017); and FORS2 at the VLT (Nikolov et al., 2016). May et al. (2018b) (hereafter MOPSS1) is the ﬁrst paper in our survey. Because telescope time is limited, it is important to make use of all resources available to us to study the atmospheres of new planets, as well as ensure reproducibility of results across telescopes, instruments, and reduction methods. In this work, we present results for the low-density hot-Neptune HATS-8b from the Michigan Optical Planetary Spectra Survey (MOPSS) at the 6.5-meter Magellan Baade Telescope. MOPSS is designed with a goal of creating a catalog of uniformly observed and reduced transmission spectra to better enable comparative exoplanet studies. HATS-8b is the third target in the survey and was selected for its expected transmission signal, as well as the schedulability of transits at Magellan Baade. In Section 3.4, we discuss our observational set up and target. Section 3.5 discusses our reduction pipeline in brief, as well as our noise model and generation of light curves. Section 3.6 discusses our transmission spectra, as well as any impacts unocculted star spots may have on our results and the impact of particulates in the atmosphere. Finally, Section 3.7 presents our conclusions for this work.

70 3.4 Observations

3.4.1 The Inamori-Magellan Areal Camera & Spectrograph Instrument

IMACS (Inamori-Magellan Areal Camera & Spectrograph) is a wide-field imager and optical multi-object spectrograph located on the 6.5-meter Magellan Baade Telescope at Las Campanas Observatory. We use the f/2 camera on IMACS and custom-made observing masks to simultaneously observe our target and a number of calibration stars. The IMACS f/2 CCD consists of 8 separate rectangular chips in a 4x2 arrangement. There is a gap of ∼57 pixels between the short edges of the chips, and ∼92 pixels between the long edges of the chips. We use the 300 lines/mm grism at a blaze angle of 17.5, resulting in theoretical wavelength coverage from 3900A˚ to 9000A,˚ but practically, from ∼4600A˚ to ∼8000A˚ . The shortened wavelength coverage on the blue end is due to the use of a blocking filter for light below 4550A˚ . The throughput at these wavelengths is low, so we choose this addition in order to eliminate spectral contamination from 7800A˚ to 9000A˚ from the grism’s second order. On our first night we did not use this filter, so we do not use wavelengths past 7800Ain˚ our analysis. Further, the gap between chips occurs at ∼7800A˚ for our target star, with the main O2 absorption in our atmosphere at ∼7600A˚ . In our analysis, we skip any bins that contain either of these features. As mentioned above, we use a custom-made observing mask designed to maximize the number of calibrator stars, all aligned in a way to allow the full wavelength span to fall across the chips. The main target is placed on a central chip (see Figure 3.1). Calibrators were selected based on their magnitudes and spectral type if available, or their color in the common case that a spectral type was not determined. We select those stars that are most similar in color and are within ∼0.75 magnitudes of the main target when possible. Each calibrator and the main target is centered in a wide slit (15”) with large lengths (20”) so that we are not concerned with slit losses, and to improve background subtraction. With this

71 #1 #3#4 #5 #7 HATS-8b #6 #2

25 2429 Figure4332 3.1: Field6254 of View for8158 HATS-8, with10080 calibrator11984 stars marked.13888 The15810 large yellow17713 boxes 196 represent the size of the slits cut on the instrument masks. The dispersion direction is in the vertical plane. Star #3 serves as our ‘check star’.

setup, our resolution is limited by the seeing each night (see Sections 3.4.2 for seeing data). Our observational eﬃciency was limited by the read-out time for the CCD; 82 seconds in fast mode and 1x1 binning, 29 seconds in fast mode and 2x2 binning).

3.4.2 The planet HATS-8b

HATS-8b is an ∼1300K Hot Neptune orbiting a G-type star with a V-mag of 14.03. Dis- covered in 2015 (Bayliss et al., 2015), HATS-8b was immediately noted to be an ideal target for transmission spectroscopy. However, as of writing, there are no previous transmission spectra observations in the literature. HATS-8b was observed on the nights of July 23rd 2017 in 1x1 binning, with exposure times of 300 seconds and 72 exposures; and August 11th 2017 in 2x2 binning, with exposure times of 180 seconds and 92 exposures. This corresponds to an observational eﬃciency of 78% and 86%, respectively. Seeing was between ∼0.8” and 1.5” throughout the ﬁrst night, with the seeing improving as the night went on. Our wide slits mean we were not concerned

72 Identiﬁer R.A Dec. V mag. R mag. J mag. HATS-8 19:39:46.08 -24:44:53.90 14.03 — 13.10 Cal #1 19:40:14.20 -25:49:23.23 14.47 14.22 13.39 Cal #2 19:39:56.82 -25:48:59.63 13.51 13.30 12.14 Cal #3 19:39:59.75 -25:46:15.68 13.71 13.50 12.33 Cal #4 19:39:57.51 -25:45:16.27 13.53 13.27 11.81 Cal #5 19:39:47.79 -25:43:09.70 14.30 14.15 12.97 Cal #6 19:39:31.70 -25:41:22.72 13.56 13.29 12.14 Cal #7 19:39:07.93 -25:34:29.86 14.46 14.21 13.41

Table 3.1: Simbad does not list an R magnitude for HATS-8. See Figure 3.1 for a visual representation of the layout of the calibrator stars. Star #3 serves as our ‘check star’. with slit losses, even at the 1.5” seeing. We were not impacted by clouds or wind throughout the night. During the second night, seeing was around 0.6”-0.7” throughout the night with no cloud coverage. In addition to our main target, we observed an additional 7 calibrator stars which are listed in Table 3.1. We reserve 1 of the calibrators (star #3 in Figure 3.1 and Table 3.1) to serve as a ’check’ that our calibrators have a constant ﬂux throughout the night. This allows us to ensure that our pipeline is correctly accounting for airmass, seeing, and other instrumental eﬀects throughout the night.

3.5 Data Analysis

3.5.1 Reduction Pipeline

Our reduction pipeline was developed in Python and is described in detail in MOPSS1. It follows the traditional techniques for spectral reduction. We follow the process outlined in Nikolov et al. (2014) for cosmic-ray removal. We use SpectRes (Carnall, 2017) for fast ﬂux-conserving binning when down sampling the spectra to lower resolutions. Wavelength calibration is done using a second mask with small, 1” square slits, at the locations of each object. We use a HeNeAr lamp and take several frames at the beginning of the night. By measuring shifts in the spectral direction as described in MOPSS1, we can shift the spectrum back to the wavelength frame of the ﬁrst exposure, which should most

73 exactly match the pixel locations of our arc frames. This paper includes improvements to our treatment of biases introduced due to atmospheric and instrumental eﬀects, as described in the following sections.

3.5.2 Removing Airmass Trend

Because our red noise model is best applied to normalized data, we ﬁrst correct for extinction due to airmass. This process requires ﬁtting for extinction as a function of wavelength following the relationship

mobserved(λ, t) = mtrue(λ, t) + k(λ)Z(t) (3.1)

where mobserved is the observed magnitude at a given time and wavelength, mtrue is the true magnitude of the object, k(λ) is the wavelength dependent extinction coefficient, and Z(t) is the airmass as a function of time. We can use the observed magnitude and airmass from our first exposure and the definition of magnitudes to write Equation 3.1 as

−k(λ)(Z(t)−Z0)/2.5 Fobserved(t) = FZ0 10 (3.2)

where Fobserved(t) is the number of counts detected at time t, FZ0 is the number of counts at time=0, k(λ) is the wavelength dependent extinction, Z(t) is the airmass at time t, and Z0 is the airmass at t=0. We ﬁt for the average k(λ) across all objects except the target (the transit event will bias the ﬁt), and then remove the trend described in Equation 3.2 from all objects. Figure 3.2 shows an example of the extinction curve for the white light binning of our check star on night 1. Typically, this trend is addressed simply through the division of the target star by the calibrator star(s). However, because we wish to model the correlated noise component in each star independently, we choose to remove the airmass trend in the manner described

0 o 0

− − − −

Figure 3.2: Here we plot raw, uncorrected, white-light data for our check star as well as an extinction curve derived from the mean extinction coefficient for all calibrator stars. This step removes the overall trend in the data, while keeping each object completely separate for our red-noise models. here. We find that treating each star independently in our noise model provides a greater precision in our final results.

3.5.3 Correlated Noise Model

We expect the dominate source of correlated noise in our data to be caused by variations in seeing and the spectra shifting on the chips throughout the night. Though IMACS has very stable pointing, our night-long coverage of the object results in the objects shifting on the chips throughout the night at a measurable level of a few pixels. We extract these shifts during our data reduction process so that we can de-correlate the data against these shifts. The seeing is calculated by converting the spatial FWHM measured when ﬂattening the 2D spectra to 1D, multiplied by the detector’s plate scale of 0.2”/pixel. In addition to the spectral and spatial shifts and seeing, we de-correlate the data against the background counts as well. We use a linear combination of all of the above parameters

75 ﬁt to the out-of-transit times to predict in-transit data. Our model is described as

f = Xβ (3.3) where f is the data; X is a matrix containing the spatial and spectral positions relative to time=0, seeing, background counts, and a column of unity values to account for a constant offset; and β is an array containing the relative importance of each term. By inverting Equation 3.3, −1 β = XT X f (3.4) one can solve for β during the out-of-transit times, and use the results to calculate the predicted flux during transit under the current conditions (chip location, seeing, background). We perform this fit for each object and bin independently. Though relative pixel shifts are the same for all objects, due to differences in pixel response, a shift of 1 pixel in the spatial direction may mean an increase in counted photons for one object or wavelength bin, but a decrease for another object or wavelength bin. Figure 3.3 shows an example of our noise model as applied to the white light data for our check star on night 2. We are able to explain the majority of the trends and scatter with this method. Any trends left over we attribute to instrumental effects we are unaware of or do not include. Theses trends are small in comparison to what we fit for here, and are removed through dividing our target by a master calibrator star.

3.5.4 Light Curves

To generate our light curves, we first create our ‘master’ calibrator which consists of all reference stars except the one chosen as the ‘check’ star. The master calibrator allows us to correct for instrumental effects not captured in our noise model. After applying the master calibrator, a small systematic generally remains in the light curve. Though this trend is smaller than in previous work due to our airmass and red noise corrections, we still find it

76 1.5 1.0 0.5

Shift 0.0 Spatial

Relative 0.5 1.0 A 1.5 2 1 0 1 2 3 1.0 0.5 0.0 Shift 0.5 Relative Spectral 1.0 B 1.0 2 1 0 1 2 3

0.8 Counts Relative 0.6

Background C 1.2 2 1 0 1 2 3

1.0

Seeing ["] D 1.005 2 1 0 1 2 3

1.000

0.995

0.990

0.985 Relative Counts E 0.980 2 1 0 1 2 3 Time from Mid-Transit [hrs]

Figure 3.3: For our check star’s white light binning, here we show the following: A: Pixel shift in the spatial direction. B: Pixel shift in the spectral direction. C: Background counts. D FWHM. E Airmass extinction corrected data with our red-noise model (see Equation 3.3) over plotted. The red box represents the in-transit times and are not used in the fit, but are predicted on. necessary to include a baseline fit. For night 1, we fit this as a 3rd order polynomial in time, as detailed in MOPSS1. For night 2, we use a 2nd order polynomial in time due to there being relatively few data points before transit to constrain the fit.

3.5.4.1 White Light Curves

The white light curves for HATS-8b are generated from 4200-8000A˚ on night 1 and 4600- 9000A˚ on night 2. The difference is due to a blocking filter we implemented on night 2 as described in Section 3.4.2. The white light curves are used to fit for orbital parameters in the same manner as in MOPSS1. We use Batman (Kreidberg, 2015) with a quadratic limb- darkening function, as well as emcee (Foreman-Mackey et al., 2013) to fit for center of transit, period/semi-major axis, inclination of orbit, white-light planet radius, and white-light limb darkening. All orbital parameters are fit with a Gaussian prior defined by the values and errors given in Table 3.2. We find that our MCMC chains do not converge as easily if

77 Mass, [M ] 1.056±0.037 +0.149 Radius, [R ] 1.086−0.059 Teff , [K] 5679±50 [Fe/H], [dex] 0.210±0.080 ξ, [km/s] 2.00±0.50 (Microturbulent Velocity) log g, [cm/s] 4.386±0.071 Planet Parameter Value Mass, [MJup] 0.138±0.019 +0.123 Radius, [RJup] 0.873−0.075 +79 Teq, [K] 1324−38 Period, [days] 3.583893±0.000010 Semi-major axis, [AU] 0.04667±0.00055 Eccentricity <0.376 +1.2 Inclination, [deg] 87.8−1.8 Table 3.2: HAST-8b: Stellar and Orbital Parameters: All values have been adopted from Bayliss et al. (2015). Our fits use an eccentricity of 0.0 due to the lack of strong constraint from previous work. we have both the period and semi-major axis as free parameters, and so we maintain the relation between period and semi-major axis by only fitting for period while simultaneously calculating a corresponding semi-major axis based on the stellar mass and radius and their errors cited in Table 3.2. In all light curve fits we check for convergence by calculating the autocorrelation time (τ) of our chains for each parameter. We use the autocorrelation function suggested by the emcee package from Goodman & Weare (2010). We run our chains long enough that τ approaches a consistent value regardless of chain length. We find that for all bin sizes (white and binned in wavelength space) all parameters converge to τ ∼100 steps fairly quickly. Our chains are run at least 500× longer than τ.

3.5.4.2 Binned Light Curves

We bin the data from each night into bins of width 400A,˚ 200A,˚ 100A,˚ 50A,˚ 40A,˚ and 20A˚ in order to capture the overall shape of the transit at high precision, while also searching for absorption features that may be averaged over in wider binnings. For each resultant light

78 curve, we use emcee to fit for Rp/RS, and the two quadratic limb darkening parameters. We do not fit for orbital parameters as a function of wavelength as they should not have a wavelength dependence. We use the orbital parameters we retrieve from our white light emcee runs. Figure 3.4 shows the 400A˚ binned light curves and their fits from our MCMC runs. Our initial quadratic limb darkening parameters are interpolated between the Johnson filter values from Claret & Bloemen (2011). While it is understood that these may not be completely accurate, our use of them as a starting value does not affect our results since we use a non-informative flat prior which allows our walkers to fully explore the parameter space without being biased to our initial guess. We confirm this by also starting white light chains at values of 0.0 for both limb-darkening parameters and the planet radius, which return the same results as those that begin at the Claret & Bloemen values. Because the unconstrained runs take longer to converge, we choose to use the starting guesses from Claret & Bloemen and a more informed initial guess for the planet radius. For this planet, we find that our returned limb darkening values agree well with those from Claret & Bloemen (2011). Figure 3.5 shows the theoretical quadratic limb darkening coefficient values and our fit values for both nights.

3.6 Results

3.6.1 Transmission Spectrum

We fit our data from each night independently. We present results here for the 400A˚ binnings, which demonstrate the overall scattering slope. We find no definitive evidence of sodium or potassium absorption at any of our finer binnings. Figure 3.6 shows our transmission spectra and scattering slopes. Table 3.3 lists our results for both nights. Our data covers only optical wavelengths, which can only constrain combinations of atmospheric properties by itself. Due to the lack of absorption features, we report only

79 Light Curves Residuals

1.175 5100Å

5300Å 1.150 5500Å

1.125 5700Å

5900Å 1.100 6100Å

1.075 6300Å

6500Å

Relative Flux + shift 1.050

6700Å

1.025 6900Å

1.000 7100Å July 23rd 2017 2.5 0.0 2.5 2.5 0.0 2.5 Time from Center of Transit [hrs]

80 Light Curves Residuals 1.08

5600Å

6000Å 1.06

6400Å

1.04 6800Å

7200Å 1.02 Relative Flux + shift

1.00 8000Å

Aug 28th 2017 2 0 2 2 0 2 Time from Center of Transit [hrs]

Figure 3.4: Light curve data and MCMC ﬁts. Top: Results from the night of July 23rd 2017. Bottom: Results from the night of August 28th 2017. For both, the left panel shows the data and ﬁts, and the right panel show the residuals (data-model).

81 0.8 Claret et al. (2011) Values 0.7 Returned Parameters 0.6

0.5 q0 0.4 q1

0.3

0.2

0.1 Limb Darkening Aug 28th 2017 0.0 0.5 0.6 0.7 0.8 0.9 Wavelength, m

Figure 3.5: Limb darkening parameters from our MCMC fits. For both, the secondary axis presents feature size in relative scale heights calculated with the equilibrium temperature of the planet and µ=2.3, which we demonstrate is not representative of the data. Left: Results from the night of July 23rd 2017. Right: Results from the night of August 28th 2017. For both, the theoretical values from Claret & Bloemen (2011) are shown in black and our results in red. Points denoted by circles show the first quadratic coefficient, an upside down triangles show the second. Our 1-sigma uncertainty on individual points is shown by the shaded region. measurements of the strength of the scattering slope. The optical slope we detect is typically a signature of scattering, given by

1 dR 1 k T p = α B limb (3.5) RS d ln λ RS µg

ﬁrst described in Lecavelier Des Etangs et al. (2008), where RS is the stellar radius, Rp is the planetary radius, α is the power of the wavelength dependence in the scattering cross section

(−4 for Rayleigh Scattering), kB is the Boltzmann constant, Tlimb is the temperature at the limb of the planet, µ is the mean molecular weight of the atmosphere, and g is the planetary

gravity. 1/RS is included on both sides of the equation because transmission spectra are typically plotted as the planet radius relative to the stellar radius. Our main unknowns in Equation 3.5 are the atmospheric mean molecular weight (µ) and

the limb temperature (Tlimb). Typical values for µ range from 2.2 for Jupiter to 2.5-2.7 for Neptune. If the atmosphere of the planet is clear, the gas should produce Rayleigh scattering and α will be equal to −4 as on Earth. However, if there exist particles in the atmosphere

82 0.10 35 0.095 July 23rd 2017 Fit Slope Fit Slope 30 Nominal Rayleigh 30 0.090 Nominal Rayleigh 0.09 25 25 -95 0.085 -55

0.08 -85 20 -75 -45

/R /R 0.080 -65 15 20 -35 0.07 -55 R -45 R 10 0.075 -25 -35 15 0.06 -25 5 -15 -15 0.070 Aug 28th 2017 0 10 0.05 Height Scale Relative 0.065 Height Scale Relative 0.5 0.6 0.7 0.8 0.9 0.5 0.6 0.7 0.8 0.9 Wavelength, μm Wavelength, μm

Figure 3.6: Left: Night one (July 23rd 2017) transmission spectrum. Right: Night two (August 11th 2017) transmission spectrum. The two nights are plotted sepa- rately due to diﬀerences in the measured scattering slope. On both panels, the vertical green dashed line at 5890A˚ is where we would expect sodium absorption, while the orange dashed line at 7665A˚ is where we would expect potassium absorption if they were present (though the features would not show up at the wide binning plotted here). The dashed gray line is the nominal Rayleigh slope, the solid gray line is the ﬁt slope. Both panels include the same slopes for varying α parameters in blue for easy comparison of the two nights. The nominal Rayleigh 2 slope has α = −4, Tlimb=Teq (1321 K), µ=2.3, and g=gplanet (464.51 cm/s . large enough to produce Mie scattering, α can take on a wider range of values.

Our measured transmission slope on night 1, July 23rd 2017, is (1/RS)(dRp/d ln λ) = −0.146±0.024, ∼27.7 times stronger than nominal Rayleigh scattering, deﬁned as the right

2 hand side of Equation 3.5 with α = −4, Tlimb=Teq, µ =2.3, and g=464.51 cm/s (calculated from the planetary parameters given in Table 3.2. With these parameters, there is no reasonable combination of µ and limb temperature to explain the slope at α = −4.0. At the equilibrium temperature of the planet and a mean molecular weight of 2.3, we can match the slope with an extremely strong wavelength dependence of λ−70 for scattering.

On night 2, the measured slope is (1/RS)(dRp/d ln λ) = −0.101±0.024, approximately

70% of that from night 1. Prior to searching parameter space for a combination of µ,Tlimb, and α that matches this slope, we first discuss the effect unocculted star spots may have on the measured scattering slopes. An important consideration is how uncertainties on planetary properties may affect the nominal Rayleigh slope, which in turn affects our expectations. Taking our parameters and

83 uncertainties from Table 3.2, we note that Rplanet has the highest relative uncertainty. When estimating the Rayleigh slope, planet radius matters only for the planet gravity. This results

2 in a factor of Rplanet. If the true planet radius sits at the edge of the upper error bar, so that

Rplanet=0.996×RJupiter, the nominal Rayleigh slope will increase by a factor of 1.3. This is not a significant change when compared to the factor of ∼28 we are looking to explain and so we do not explore this option further. In addition, HATS-8b is a low density, low gravity, exoplanet, with ρ=0.259 g/cm3, 2.6× lower than Saturn. It is possible that the extended atmosphere requires a different treatment for atmospheric models. In particular, Exo-Transmit (Kempton et al., 2017) does not account for variations in scale height with altitude, a potentially important factor for these low-density, inflated planets. As noted above, we also search for the presence of sodium absorption (5890A)˚ and potassium absorption (7665A)˚ with our narrow bins. We find that the presence or lack of potassium absorption could not be well established due to the deep O2 telluric line at ∼7600A˚ diluting any signal. We do not find strong evidence of sodium absorption.

3.6.2 Unocculted Star Spots

Although the star HATS-8 is known to be an inactive star from exoplanet discovery observations (Bayliss et al., 2015) and we do not detect an occulted spot during either of the observed transit events, we cannot rule out that the host star has some amount of spot coverage. Particularly because unocculted spots can appear as a scattering slope in transmission spectrum, and our results suggest a stronger than expected slope with differences between the two nights. If the rotational period of the host star is approximately twice the time between observations, we would be viewing the planet against a different side of the star, and different spot coverage. Following the approach of May et al. (2018b), we use the formulation of Louden et al. (2017) to investigate the influence unocculted spots may have on our results. Here we assume

84 that night 1 is heavily inﬂuenced by spots, while night 2 is relatively uninﬂuenced by spots

because of the stronger slope measured on night 1. The measured transit depth, δm(λ), is described as a function of the true transit depth, δ(λ), the spot coverage fraction, η, and the

relative ﬂux from a spot, Fλ(spot), compared to the stellar photosphere, Fλ(star).

1 δm(λ) = δ(λ) (3.6) 1 − η 1 − Fλ(spot) Fλ(star)

The overall dimming of the star due to unocculted spots can be written as

Fλ(star, corrected) = ηfλFλ(star) + (1 − η)Fλ(star) = [1 − η(1 − fλ)]Fλ(star) (3.7)

with fλ the spot contrast given as Fλ(spot)/Fλ(star). When the star dims due to unocculted spots, the transit depth looks relatively larger compared to transits with no unocculted spots. Because the spot’s black body spectra peaks at longer (redder) wavelengths, while the star peaks at relatively shorter (bluer) wavelengths, the spot contrast level is higher at short wavelengths, and lower at red wavelengths. This is therefore a wavelength dependent eﬀect, with blue wavelengths more heavily aﬀected than red, resulting in a star-induced slope being injected into the data.

Following equation 3.6, we calculate the required δm(λ)/δ(λ) to match the observed night 1 slope to both the nominal Rayleigh slope and the observed slope on night 2. Figure 3.7 shows the corrected/expected slopes (where a ratio of 1 can fully explain the slope) at a variety of spot coverage fractions (η) and ∆T=Tstar-Tspot. The required spot coverage fraction to fully explain our night 1 slope vs. nominal Rayleigh slope at a ∆T of 1500K is ∼75%, much higher than one would expect. HATS-8 is a G star with an age of 5.1±1.7 Gyr (Bayliss et al., 2015), comparable to the Sun. On magnetically active low-mass stars, Jackson & Jeﬀries (2013) suggest that the spot coverage could be as high at 40% with Tspot/Tstar=0.7 (similar to our value). Further, long term spot-coverage studies by Alekseev & Kozhevnikova (2018) ﬁnd spot coverages up to 42% for 13 active

85 July 23rd 2018 λ0 Rp/R? ∆Rp/R? q0 ∆q0 q1 ∆q1 RMSE [ppm] Phtn [ppm] RMSE/phtn 5100 A˚ 0.0824 0.0031 0.723 0.038 0.235 0.03 2373.65 1041.29 2.28 5300 A˚ 0.086 0.002 0.693 0.029 0.268 0.015 1651.75 891.48 1.85 5500 A˚ 0.0801 0.0031 0.623 0.047 0.268 0.045 1761.51 822.02 2.14 5700 A˚ 0.0794 0.0029 0.611 0.041 0.289 0.029 1572.61 760.34 2.07 5900 A˚ 0.0801 0.0034 0.534 0.073 0.267 0.053 1297.26 725.53 1.79 6100 A˚ 0.0684 0.0029 0.531 0.064 0.28 0.053 1277.48 704.54 1.81 6300 A˚ 0.0712 0.0034 0.43 0.065 0.214 0.066 1475.78 684.14 2.16 6500 A˚ 0.0665 0.0028 0.385 0.06 0.18 0.043 1083.74 678.73 1.6 6700 A˚ 0.0705 0.002 0.371 0.053 0.192 0.046 783.24 673.06 1.16 6900 A˚ 0.0624 0.0026 0.322 0.039 0.171 0.031 1306.35 670.4 1.95 7100 A˚ 0.0676 0.0021 0.31 0.039 0.168 0.024 1012.04 663.38 1.53 August 28th 2018 λ0 Rp/R? ∆Rp/R? q0 ∆q0 q1 ∆q1 RMSE [ppm] Phtn [ppm] RMSE/phtn 86 5200 A˚ 0.0971 0.002 0.575 0.05 0.141 0.05 2424.69 847.2 2.86 5600 A˚ 0.0842 0.0013 0.551 0.04 0.223 0.043 2251.51 698.24 3.22 6000 A˚ 0.0789 0.0012 0.534 0.039 0.273 0.037 1011.98 632.42 1.6 6400 A˚ 0.0777 0.0013 0.479 0.044 0.262 0.045 701.46 602.73 1.16 6800 A˚ 0.0803 0.0017 0.522 0.035 0.329 0.023 868.91 594.28 1.46 7200 A˚ 0.0729 0.0019 0.476 0.043 0.326 0.026 1467.92 595.38 2.47 7600 A˚ ————————— 8000 A˚ 0.0747 0.0026 0.383 0.067 0.302 0.051 1152.9 625.8 1.84

Table 3.3: HATS-8b: MCMC Fit Results: Here q0 is the ﬁrst quadratic limb darkening parameter and q1 is the second quadratic limb darkening parameter. Night 1 does not have values reported past Earth’s 7600 O2 absorption feature due to second order contamination. For both nights, the bin centered on this absorption feature is discarded. The column labeled RMSE contains the RMSE of the light curve ﬁt in parts per million, the column labeled Photon contains the photon noise level in parts per million, and the column labeled RMSE/Photon contains a value describing how close we are to photon limited observations 0 0 1.5 1.6 20 24

15 1.4 21 Level that can 500 500 0.5 fully explain slope 1.2 T [K]T 18 [K]T Δ Δ "Typical" Values "Typical" Values 1.0 1000 15 1000 η=0.3 η=0.3

ΔT=1000K Level that can ΔT=1000K 0.8 12 "Maximum" Values fully explain slope "Maximum" Values 1500 1500 0.6 η=0.5 9 η=0.5 ΔT=1500K ΔT=1500K

6 0.4 Corrected Slope/Night 2Slope Slope/Night Corrected

2000 Rayleigh Slope/Nominal Corrected 2000

Spot-Photosphere Spot-Photosphere 3 Spot-Photosphere 0.2

10 5 2500 0 2500 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Spot Coverage Fraction Spot Coverage Fraction

Figure 3.7: Equation 3.6 applied to our observed slope. Left: The corrected slope is divided by the nominal Rayleigh slope. Right: The corrected slope is divided by the night 2 slope. In both panels, The black dashed line denotes the level that would correct our data back onto the nominal Rayleigh slope or night 2 slope, at a ratio of 1. The higher the value, the further the corrected slope is from the ‘goal’ slope. The shaded gray regions result in a positive slope, and so are considered “unallowed”. Regardless, it is highly unlikely that a star would have such a high spot coverage and ∆T.

G and K stars. In agreement with these literature values for G stars, we can explain the diﬀerence between our two nights with a spot coverage fraction of 40% and a ∆T of 1500K. We note, however, that HATS-8 is a slowly rotating G-dwarf and aside from metallicity is very similar to our sun (Bayliss et al., 2015). Typical spot coverage fractions for inactive stars such as the sun range from 0.05% to 0.5% at solar minimum and solar maximum, respectively. (Bogdan et al., 1988; Solanki & Unruh, 2004). Further, if HATS-8 had 40% spot coverage on night 1, it is rather unlikely that the observed transit did not exhibit a spot crossing event unless the orbit and rotational axis of the star are very well aligned and the spots are strongly bound to latitudes away from the path of the transit. In addition, a 40% spot coverage fraction on night 1 is even more unlikely because our two observations are only one month apart. Therefore, because our two slopes are consistent within 1.3-σ, we instead move forward by computing a weighted average of the slopes of our two nights. Our weighted slope is then (1/RS)(dRp/d ln λ) = −0.123±0.017.

87 3.6.3 A Clear Atmosphere

With this slope, we explore the range of atmospheric parameters that can explain the observed slope in a clear atmosphere. In Figure 3.8 we show a range of possible parameters to satisfy the observed combined scattering slope in our data. Based on the unreasonable parameter vales shown in Figure 3.8, we require a strong wavelength dependence of approx-

−25 imately λ and a low mean molecular weight atmosphere (µ .2.0) to explain our slope. This is inconsistent with a clear atmosphere, where α must equal −4. Further, because a µ<2.0 suggests a large fraction of the atmosphere is atomic rather than molecular (unphysical at these temperatures), we choose to exclude solutions for such low mean molecular weight values. As described below, we prefer an explanation that involves a portion of the slope due to clouds (see Section 3.6.4), and the remainder resulting from diﬀerences between our expected and realized values of mean molecular weight and the limb temperature.

3.6.4 Clouds and the Scattering Slope

Naturally, the next consideration is that the atmosphere of HATS-8b is not clear, and instead contains scattering particulates of some kind. The well known hot Jupiter, HD 189733b is a natural comparison here, due to its strong optical slope and similar equilibrium temperature (1200-1400K). A detailed analysis of the optical slope for HD 189733b is presented in Pont et al. (2013). As demonstrated in Sing et al. (2016), HD189733b has the strongest scattering slope among Hot Jupiters observed with STIS. Of importance, however, is that Pont et al. (2013) state that the optical slope for HD 189733b can be explained by an α = −4 Rayleigh scattering slope at a temperature of ∼1300K for particle sizes below 0.1µm. This is not the case for HATS-8b, as the slope is steeper than α = −4 even after considering the possibility of an extreme level of unocculted star spots. Therefore we note that the optical scattering slope of HATS-8b is the strongest detected scattering slope to date.

88 3.0 1.20

0.04 0.05 0.03 2.8 0.02 1.05

0.90 2.6 0.75 2.4 0.60 2.2 0.45 2.0 0.30

1.8 0.15 =-4.0 1.6 Theoretical/Observed Slope 0.00 400 600 800 1000 1200 1400 1600 1800 2000 Planet Limb Temperature [K]

1.20 0.10 10 =2.3 1.05 0.25 0.90 20 0.75

0.50 30 0.60

0.45 40

0.75 0.30 50 0.15

60 Theoretical/Observed Slope 0.00 600 800 1000 1200 1400 1600 1800 2000 Planet Limb Temperature [K]

1.20

10 Tlimb=Teq=1321 K 1.05

0.90 20 0.25 0.75 0.50 30 0.60

0.45 40 0.30

50 0.75 0.15

60 Theoretical/Observed Slope 0.00 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Figure 3.8: For all frames we show the theoretical Rayleigh slopes (see equation 3.5) divided by the combined measured slope. The thick dashed black line denotes the values that can explain the measured slope (if possible). Dark red lines represent the nominal values. The shaded grey region denote values which are unphysical. Top: for a constant α Middle: for a constant mean molecular weight of 2.3 (a value typical of Jupiter) Bottom:. for a constant limb temperature set to Teq.

89 Pinhas & Madhusudhan (2017) explore the eﬀects of a variety of species on the wavelength dependence (α) of the scattering cross section. In their work, Pinhas & Madhusudhan show that in some cases, the presence of cloud particles can result in a slope as strong as α = −13. Of the species Pinhas & Madhusudhan discuss, they suggest that transmission spectra which show strong optical slopes are likely to contain sulphide clouds - Na2S, MnS, or ZnS. These three species have condensation temperatures of 1176 K, 1139 K, and 700K,

−3 respectively at 10 bar (Wakeford & Sing, 2015). It is probable that Na2S and Mns could condense out in the nightside atmosphere of HATS-8b, which has an equilibrium temperature of 1321K for an albedo of 0. If a large amount of scattering particles are present, we would expect a higher albedo, and therefore lower temperature that allows the condensation of these species. Cloud formation along the limbs is an expected (Parmentier et al., 2016; Roman & Rauscher, 2018) consequence of atmosphere dynamics. Speciﬁcally, Pinhas & Madhusudhan ﬁnd that MnS produces the steepest slopes at a

−2 modal particle size of 10 µm for a cloud scale height (Hc) equal to the gas scale of kB

Teq/(µ g). Under these conditions, one can attain a scattering slope with α = −13 for a hot Jupiter of g = 24.79 m/s2, µ=2.3, and a solar abundance of MnS The slope models in

Pinhas & Madhusudhan (2017) depend on the cloud scale height (a smaller Hc brings the slope closer to the standard Rayleigh slope), the modal particle size based on their assumed distribution (smaller particles cause steeper slopes), the reference pressure (only varies the absolute depth), the grain abundance, and the molecular abundance of the species. Pinhas & Madhusudhan state that the slopes are insensitive to the planet gravity, because the same value is assumed for both the the gas scale height and the cloud scale height.

Additional condensates at these wavelengths and temperatures may include SiO2, Al2O3,

Fe2O3, Mg2SiO4, and MgSiO3 with condensation temperatures of 1725 K, 1677 K, 1566 K, 1354K, and 1316 K, respectively at 10−3 bar (Wakeford & Sing, 2015). Of these, Pinhas

& Madhusudhan ﬁnd that MgSiO3 can result in the strongest scattering slope, with an

−2 α ∼ −5 for small grains (a modal particle size of 10 µm) if Hc=H. However, this is not

90 3.0 0.48 0.15 = 13.0 0.10 2.8 0.42

2.6 0.36 0.20 0.30 2.4 0.24 2.2 0.18 2.0 0.25 0.12

1.8 0.06 0.30

1.6 Theoretical/Observed Slope 0.00 400 600 800 1000 1200 1400 1600 1800 2000 Planet Limb Temperature [K]

Figure 3.9: Here we show the necessary combinations of planetary limb temperature and mean molecular weight to match our observed data with an α=-13, a value that may be attainable if MnS clouds are present with grain sizes of 10−2µm. Dark red lines denote the nominal values. The shaded grey region denotes values of µ which are unphysical for these temperatures..

much different from a nominal Rayleigh slope of α = −4, and insufficient for the scenario we explore here. We note that this large slope may also be a result of a yet to be identified photochemical haze. In Figure 3.9 we show the values of limb temperature and mean molecular weight which, combined with α = −13 for MnS clouds and small particle sizes, could explain our data. We plot the same levels as Figure 3.8 for comparison. We find that we can explain at most 40% of the observed slope through the inclusion of MnS clouds, but only for a warm, low mean molecular weight atmosphere. However, because a µ<2.0 suggests a large fraction of the atmosphere is atomic rather than molecular, for reasonable values of µ ≈2.0, we can at most explain ∼20% of the slope at the equilibrium temperature of the planet. Finally, In the limiting case that nothing is changing on the star itself, there must be a different explanation for the varying scattering slope we measure. Our two slopes differ by a factor of 3, which, following the methods of Pinhas & Madhusudhan (2017), suggests that the cloud scale height is up to 3 times larger on night 1. In order to get the strongest

scattering slope (α = −13) we assume Hc=H, which only gets us within a factor of 2 of matching our data. Invoking an increase in the vertical extent of the cloud to enhance the

91 scattering would require vigorous vertical mixing in the atmosphere, but the change between the two observations would require that the mixing also be time variable, which has not been seen in hot Jupiter atmospheric simulations, to our knowledge. Therefore, if the particulates in the atmosphere of HATS-8b are composed of small MnS particles, it is not likely that we can explain the diﬀerence between the two nights as only an increase in cloud coverage on the terminator.

3.7 Conclusions

We observed the low density super-Neptune HATS-8b on two nights during August 2017 and September 2017. Both data sets show stronger-than-Rayleigh scattering, with significant differences between the two nights which can possibly be explained by unocculted star spots. After applying a correction to account for this possibility, we find the slope in the data from the combined two nights to be 27 times stronger than a nominal Rayleigh slope at the equilibrium temperature of the planet with a mean molecular weight of 2.3. We are unable to explain this slope with reasonable atmospheric parameters and gas scattering alone, so we explore several options to model the strong slope.

• We have explored the possible condensates that could contribute to the strong scattering slope detected. MnS clouds with particle sizes no greater than 10−2µm can result in at most α = −13. This can explain 20% of our observed slope for a reasonable temperature and mean molecular weight, or up to 40% of the slope if the limb temperature is ∼2000K. No other condensates (based on work by Pinhas & Madhusudhan (2017)

and Wakeford & Sing (2015)) produce an |α| &5.

• Uncertainties on planet and stellar parameters can at most account for a factor of 1.3 in the slopes. We discard errors in system parameters as an explanation for the measured transmission slope.

While we cannot completely rule out an instrumental or reduction process systematic,

92 we are confident that they cannot explain the entire slope seen in this work. IMACS has not been previously found to have such a strong blue-red systematic. These are the most recent transits with this instrument currently in the literature, but work by Espinoza et al. (2019) includes transits from April 2017 without strong blue-red biases. We are unaware of any significant instrument work done during the three months between these transit observations. Further, our previous work (May et al., 2018b) does not show strong blue-red slopes and uses the same reduction pipeline as this work. MOPSS1 presents work that is in agreement with the literature, so we do not expect strong blue-red biases to be a result of our reduction process. Photometric monitoring of HATS-8 would determine the activity level of the star, allowing a more informed correction for unocculted star spots. Future transits of HATS-8b would confirm if this slope is a time-variable phenomenon, and simultaneous with photometric monitoring, would point to if it is primarily a result of stellar or planetary effects. We recommend future follow up from ground and space based telescopes to better explain the atmosphere of HATS-8b and compare results from various sources.

3.8 Acknowledgements

We thank the staﬀ at Las Campanas Observatory, without which we would be unable to carry out the observations presented in this work. Special thanks to Dave Osip who took the August 2018 data through a service observing program at Las Campanas, and Michael Roman who provided useful comments on condensates for this manuscript. This research has made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org.

3.9 Facilities and Software Used

Facilities: Magellan:Baade

93 Software: Astropy (Astropy Collaboration et al., 2013), batman (Kreidberg, 2015), emcee (Foreman-Mackey et al., 2013), Exo-Transmit (Kempton et al., 2017), IPython (P´erez& Granger, 2007), Matplotlib (Hunter, 2007), NumPy (van der Walt et al., 2011), SciPy (Jones et al., 2001–), SpectRes (Carnall, 2017), spotrod (B´ekyet al., 2014)

94 CHAPTER IV

Living On the Edge: The Eﬀects of a Surface on

Atmospheric Circulation and Emission for 1.5R⊕

Planets

4.1 Preface

Results in this chapter are a work in progress and will be published in May, E. M., & Rauscher, E., in prep., to be submitted to the Astrophysical Journal.

4.2 Abstract

It is well known that planets with radii between that of Earth and Neptune have been the most commonly detected to-date. To classify these planets as either terrestrial or gaseous, typically we turn to mass-radius relations and composition curves to determine the likelihood of such a planet being rocky or gaseous. While these methods have set a likely transition radius of approximately 1.5 R⊕, we cannot expect that any change between terrestrial and gaseous compositions will be a sharp cut-oﬀ, and composition curve predictions result in ambiguous designations for planets right near this transition radius. In this work we present 3D general circulation models of transition planets, wherein we study the eﬀects of a surface on observable quantities such as the latitudinal variations. We present our updated GCM,

95 validated on the circulations of Earth and Neptune, before discussing our modeling choices for this transition planet. Finally, we discuss the results of this study and explore the prospects of detecting a surface through observations of atmosphere dynamics in the future.

4.3 Introduction

From exoplanet detections to-date, planets with radii between that of Earth and Neptune

(3.88R⊕, the smallest gaseous planet in our Solar System) have been discovered to be the most common type of planet outside of our Solar System (Batalha, 2014). Naturally, there must be some point between these two radii at which we see a transition from primarily terrestrial planets to primarily gaseous planets. Without a direct comparison in our Solar System, we must turn to other methods to understand the unique properties of this class of planets. This transition from terrestrial to gaseous has been studied by Rogers (2015) which sets the transition from terrestrial to gaseous at 1.6R⊕ and Lopez & Fortney (2014) which sets the transition at 1.75 R⊕. In addition, Fulton et al. (2017) find a gap in the known planet radius distribution at 1.5 R⊕. While these two populations could be formed in a variety of ways, possibly due to photoevaporation rather than a result of formation, they are concrete evidence for the existence of separate, yet overlapping, radii regimes for Super-Earths and Mini-Neptunes. However, in this work, the determination of if a planet is currently terrestrial or gaseous is only concerned with the current presence of a surface and not necessarily how and/or why it got to where it is now. Because mass and radius are commonly the two most important factors differentiating ‘types’ of exoplanets as we currently define them, an active area of research is determining a robust relation between the two. Such a relation is useful in determining the composition of an exoplanet, due to density generally being a strong indicator of composition. Wolfgang et al. (2016); Ning et al. (2018) and Kanodia et al. (2019) are examples of mass-radius relations tuned for various types of exoplanets, with a focus on the predictive power of such

96 techniques to determine a likely mass or radius if one is not known. However, even when a mass and radius are known for a transition regime planet, uncertainties on these values, the wide number of possible compositions that match its derived density, and observed and expected scatter in mass-radius relations leave some ambiguity in its likelihood to be gaseous or terrestrial. Such compositions curves are presented in Seager et al. (2007) and Zeng et al. (2016) for various commonly considered compositions including

Iron, MgSiO3 (rock), H2O, in addition to combined multi-layer compositions. One can add more composition curves by including further combinations of compositions (Zeng et al.,

2016, do this in their computer readable tables) and by including H2/He envelopes of varying mass-fractions. In theory, there are infinite number of possible composition curves, and more than one that matches any given measured or inferred planetary density including options that would classify a planet as both terrestrial and gaseous over this intermediate-size regime. While the various composition curves that match a given exoplanet would naturally lead to composition differences that may be detected through atmospheric observations, the likely presence of aerosols in the planet’s atmosphere will inhibit our ability to make a direct determination of composition for all planets. For this reason, we seek to determine a density-independent classification scheme for transition regime planets by considering the circulation effects of having a solid surface. Ter- restrial and gaseous circulation patterns have been well studied independently; see, among others, Showman et al. (2013); Kaspi & Showman (2015); Koll & Abbot (2016); Way et al. (2018); Komacek & Abbot (2019); Pierrehumbert & Hammond (2019) for terrestrial examples and Perez-Becker & Showman (2013); Rauscher & Kempton (2014); Showman et al. (2015); Kataria et al. (2016); Komacek & Showman (2016); Rauscher (2017) for gaseous examples. Each of these looks at variations in specific key parameters that affect circulation for either terrestrial or gaseous planets independently. Here we present a single modeling scheme applied uniformly for Super-Earths and Mini-Neptunes alike. Our model is bench- marked against Earth and Neptune, two planets for which we have direct observational data

97 on circulation and emission and which book-end the transition regime we are studying. In the coming years, the launch of the James Webb Space Telescope (JWST) will enable eclipse mapping of Hot Jupiters down through even a temperate Earth-sized planet in over a dozen eclipse observations (Belu et al., 2011; Beichman et al., 2014a; Schlawin et al., 2018). Eclipse mapping enables the determination of longitudinally and latitudinally resolved maps of the planet’s emission and/or reflection (Williams et al., 2006; Rauscher et al., 2007). The shape of ingress and egress during secondary eclipse determines a map of the planet’s emission by measuring how much flux is blocked by the host star from successive arcs of the planet as it moves out of and back into our line of sight. Recently, Rauscher et al. (2018) demonstrated a new method to more accurately retrieve maps in the era of JWST. In this work, we focus on the zonally averaged latitudinal effects of a surface on the atmospheric circulation, and the observational consequences of surface in the context of the era of JWST. For non-tidally locked (quickly rotating) planets, this equator to pole heat transport, and observability of the resulting temperature gradient, is the main uncertainty we quantify in this work. In Section 4.4 we discuss our modeling framework including the general circulation model applied and updates to replicate the effects of a surface. In Section 4.5 we present our results for our Earth and Neptune models as a validation of our modeling framework. Section 4.6 outlines our modeling choices for our transition planet. In Section 4.7 we present our results, discuss the next steps in this project, and touch on the observational consequences of a surface.

4.4 Method

4.4.1 General Circulation Model

We employ a three dimensional general circulation model (GCM), a robust tool in modeling planetary atmospheres. Our GCM is outlined in detail in Rauscher & Menou (2012)

98 (and henceforth referred to as RM12), with modifications as discussed in the following sections. The GCM is built upon the primitive equations of meteorology, a standard reduction of the Navier-Stokes equations under assumptions of an inviscid flow, vertical hydrostatic equilibrium, and small relative vertical flow and scales. Vallis (2006) contains an in-depth derivation and discussion of these equations and assumptions. RM12 uses a double-grey approximation (visible band for stellar irradiation, infrared band for emitted heat), with the radiative transfer recently updated as described in Roman & Rauscher (2017), following the scheme of Toon et al. (1989). RM12 originated as an Earth-Based code, using a dynamical core developed at the Uni- versity of Reading (Hoskins & Simmons, 1975) and as such has been well tested for terrestrial planet applications (Joshi et al., 1995; de F. Forster et al., 2000; Menou & Rauscher, 2009). Having undergone major changes for applications to gaseous exoplanets, this work re-introduces a surface into the GCM, including the relevant interactions between the surface and the atmosphere. To date, RM12 has been used to study, among other things, observational signatures of non-synchronous rotation (Rauscher & Kempton, 2014), atmospheric circulation of circumbinary planets (May & Rauscher, 2016), observational signatures of obliquity (Rauscher, 2017), the radiative effects of clouds (Roman & Rauscher, 2017, 2018), and to constrain high-resolution spectroscopic observations (Zhang et al., 2017; Flowers et al., 2019).

4.4.2 Surface-Atmosphere Interactions

We include two main surface-atmosphere interactions as outlined below. First, we consider the additional heating sources due to the surface. Second, we consider the eﬀects of drag on the atmosphere.

99 4.4.2.1 Surface Heating

The introduction of a surface requires us to consider the additional heating sources that naturally will result. Our bottom boundary flux condition is no longer the planet’s internal heat source, but is rather determined by emission and/or reflection from the surface. Each surface element below an atmospheric column is treated independently, i.e. there is no heat transport within the surface to neighboring resolution elements. This choice allows us to apply the one-dimensional heat equation to determine the surface temperature. We do not consider moist effects in this work, and as such do not include latent heating terms. Therefore, the equation governing the energy exchange with the surface is given by

∂T c ρ ∆z s = (1 − α ) F + (1 − α ) F − j σT 4 − c ρ C |−→u | (T − T ) (4.1) s s s ∂t SW SW ↓ LW LW ↓ s s a a a a s

where cs is the surface speciﬁc heat; ρs is the surface density; ∆zs is the thickness of the surface layer; Ts is the surface temperature; FSW ↓ and FLW ↓ are the downwards short wave

(optical) and long wave (infrared) fluxes, respectively; αSW and αLW are the short wave and long wave surface albedos, respectively; js is the surface emissivity; σ is the Stefan-Boltzman constant; ca is the specific heat of the atmosphere; ρa is the density of the atmospheric level directly above the surface; C is the transfer coefficient for specific heat, set to 10−3 following −→ estimates in Frierson et al. (2006); ua is the wind vector in the atmospheric level directly above the surface; and Ta is the temperature of the atmospheric level directly above the surface. This last term describes the sensible heat, which is an energy exchange as winds blow across the surface layer. This surface layer scheme is similar to that used by Kaspi & Showman (2015) and Frierson et al. (2006), however we choose to use a uniform solid surface, rather than a water slab. The surface emission plus reflection off the surface in the long wave is treated as the long wave (infrared) bottom boundary condition for the atmosphere; with the short wave reflection the bottom boundary condition in the short wave (visible), for an optically thin

100 atmosphere. This results in an additional source of heating, working to warm the atmosphere from below. In our standard RM12 GCM, the bottom boundary condition takes the downwards long wave ﬂux and adds it into the upwards long wave ﬂux in the bottom layer of the atmosphere to maintain energy conservation. With the inclusion of this new phys- ically motivated boundary condition, our lowest atmospheric levels are considered realistic representations of the dynamics that occur there.

4.4.2.2 Atmospheric Drag

We introduce drag into the atmosphere through Rayleigh Friction, following the benchmark work by Held & Suarez (1994). The friction is a decaying function of pressure, with the strongest eﬀect in the atmospheric level directly above the surface. Rayleigh friction is given by −→ ∂ |ua| σ − σb −→ (σ) = −kf max 0, |ua| (4.2) ∂t 1 − σb −→ where ua is the wind speed in the given σ level; kf is the coeﬃcient of friction, in units of the inverse of time; σ corresponds to the atmospheric level, with σb being the boundary above which friction no longer exists (sometimes referred to as the boundary level). The σ levels are a common realization of pressure in GCMs, where σ ≡ P/P0 with P0 the reference pressure, i.e. the average pressure at the bottom level of the model. Following Held & Suarez (1994)

−1 and their Earth models, we set kf =1 day and σb=0.7 to recreate an Earth-like friction proﬁle. Although it is a small fraction of the total energy budget, in order to maintain energy conservation, we choose to return the energy removed in a given cell through drag directly back to the atmosphere as heating in the same cell. The temperature increase due to returned energy is given by −→ 2 ∆ |ua| ∆Ta = (4.3) 2ca where all terms are the same as above. The general result of drag is to slow the winds near

101 the surface, and add a small amount of additional heating to the atmosphere.

4.4.3 Choice of Model Resolution

Baroclinic instabilities are a circulation pattern consisting of eddies that arises due to the rotation of the atmosphere and the missalignment of the vertical stratification with the density gradient. Typically, there are between 5 and 8 large scale eddies that form around the Earth at mid latitudes which result in efficient transport of heat pole wards in these regions compared to the transport provided by the mean flow. For a more in depth discussion of the effects of these eddies on circulation, see Washington & Parkinson (1986) and Holton (1992). The scale of the baroclinic eddies is typically thought of as being proportional to the Rossby radius of Deformation, given by

NH L = (4.4) πf

where H is the scale height; f is the coriolis parameter given by f = 2Ω sin γ with Ω the rotation rate and γ the latitude; and N is the Brunt-Väisäläfrequency given by

r g dθ N = − (4.5) θ dz

where g is the gravity; z is the vertical unit of height; and θ is potential temperature given by P R/cp θ = T 0 (4.6) P

with T the temperature; P the pressure and P0 the reference pressure. We test various horizontal resolutions around the expected necessary resolution to insure we have suﬃciently resolved these important dynamical features in the circulation.

102 4.5 Model Validation

First, we run models for both Earth and Neptune to validate the updated RM12 GCM on both ends of the transition between terrestrial and gaseous planets. Because we have direct observations of both planets’ circulations, we are able to compare our models to data and previous modeling work. Here we present results for our Earth model, with Neptune results forthcoming. In all runs which include a solid surface boundary, we treat the surface as an uniform

composition slab composed of enstatite (MgSiO3). Though the heat capacity of this surface is itself a function of temperature (Krupka et al., 1985), we choose to hold this constant to minimize variations in parameters, set to an average temperature across our models of 500 K. Table 4.1 summarizes the input parameters for our solid surface. We use a diurnally averaged heating scheme for our validation models, in which the stellar irradiation pattern is applied in a daily average around the entire globe such that the equator receives more irradiation that the poles. This is an obvious choice for Earth and Neptune based on their observed insolation patterns and rotation rates.

Parameter Value Adopted −1 −1 cs 528.99 J kg mol −3 ρs 3.5 g cm ∆z 100 cm js 1.0

Table 4.1: See Equation 4.2 and following text. Heat capacity (cs) is calculated following Krupka et al. (1985) at a temperature of 500K. Emissivity (js) is an average infrared value derived from Maturilli et al. (2016) and for modeling stability. Our surface layer is chosen to be 1 meter thick as in Kaspi & Showman (2015).

4.5.1 Earth

As in Held & Suarez (1994), we run multiple Earth-like models at resolutions of T21, T42, and T63 to study the resolution eﬀects on the induction of baroclinic instabilities in the atmosphere due to the surface-atmosphere interactions. The necessary resolution can be

103 estimated based on the scale of the Rossby radius of deformation, given in equations 4.4 - 4.6. On Earth, L at mid-latitudes is ∼1000 km. In order to suﬃciently resolve these features, we need our resolution to be at least half this size. For Earth, a T21 resolution corresponds to a resolution at the equator of 625 km, T42 corresponds to 310 km, and T63 corresponds to 210 km. We therefore expect that the T21 run might not be high enough resolution to fully resolve and excite the baroclinic instability features, while T42 and T63 should be. All Earth runs are done in linear pressure space. Typically, log pressure are used for gas giants with thick atmospheres in order to more highly resolve low-pressures where the main heating and cooling of the atmosphere driving the circulation takes place. For planets with thin atmospheres, and particularly in those cases with a surface, we are more interested in resolving regions near the surface and hence linear pressure levels makes more sense. All Earth models cover 0 - 1 bar linearly over 30 sigma-levels.

4.5.1.1 Model Inputs

The following discussion of model inputs for Earth is summarized in Table 4.2. Most important to the resulting heating profile is choosing absorption coefficients to correctly represent the observed temperature-pressure profile on Earth. We model only the troposphere and assume the temperature would continue to fall with decreasing pressure without the turnover at the tropopause (on Earth, this is a result of the ozone present in the stratosphere). We first consider the averaged optical depth of Earth’s atmosphere in the optical band to set the photospheric level. For the shortwave (visible) band, we take this band to encompass all incoming stellar irradiation. We use that ∼ 23% of incoming solar irradiation is absorbed by the atmosphere (NEO, 1999–) to approximate the optical depth of Earth’s atmosphere in the shortwave band as 0.25 at 1 bar where τ=κswP/g (for double gray radiative formu-

−4 2 −1 lation, see Guillot, 2010) gives us an absorption coeﬃcient of κsw=2.45×10 cm g and a photosphere pressure of psw=4.00 bar.

104 Parameter Value Adopted g 981 cm s−2 R (speciﬁc gas constant) 287 J kg−1 K−1 R⊕ 6.371×108 cm Ω 7.292×10−5 radians s−1 P0 1 bar −2 Fint 0.087 W m −2 Firr 1370 W m A 0.3 −4 2 −1 κv 2.45×10 cm g −3 2 −1 κth 3.50×10 cm g Table 4.2: Input parameters for our Earth model.

To set the absorption in the infrared, we assume γ=0.07 (commonly used for the super- Earth GJ 1214b, see Miller-Ricci & Fortney, 2010; Miguel & Kaltenegger, 2014) where

−3 2 −1 γ=κsw/κlw. This corresponds to an absorption coefficient of κlw=3.5×10 cm g , with a photosphere pressure of plw=0.28 bar. We find that these values reproduce the shape of Earth’s temperature-pressure profile well, but result in higher temperatures than those calculated with the Guillot (2010) profile. We explain this with the lack of surface interactions in the standard Guillot profiles which results in excess heating in the lower atmosphere. With the above absorption coefficients, our Earth model has a surface which is above the short wave (visible) photosphere but below the long wave (infrared) photosphere. In reality, the long wave absorption on Earth is slightly more complex than the short wave since Earth’s absorption spectrum is highly variable at infrared wavelengths with several windows in which the atmosphere is transparent and several at which it is opaque. Therefore, in our two- stream model, we could place the surface either above or below the long wave photosphere and replicate a physical situation on Earth. Our choice here to place the surface below the long wave photosphere is made in order to reproduce Earth’s observed temperature-pressure profile, which is the more important governing factor in the circulation of the atmosphere.

105 4.5.1.2 Results: Earth

We present temperature patterns from all three resolutions in Figures 4.1. After comparing our three resolutions, we find that the T21 resolution is not high enough to sufficiently reproduce the resulting circulation effects due to large scale baroclinic instabilities in the lower atmosphere. Figure 4.2 shows our longitudinally averaged temperature profiles from the T63 earth compared to a parameterized (NEO, 1999–) Earth temperature-pressure profile for the troposphere given as

T [K] 5.256 p[KP a] = 101.29 × (4.7) 288.08

We see a deviation at low pressures, but attribute this to our model not extending past the tropopause region, while the parameterized model is defined to match with stratosphere temperatures. Overall, we find that our Earth model does a good job of replicating real-life conditions, even with its two stream double-grey radiative scheme and uniform surface slab assumptions. These results give us confidence that our updated RM12 GCM can correctly model the transition regime.

4.6 Transition Planet

We select a hypothetical planet at the transitional radius of 1.5 R⊕. For known exoplanets near the transition radius, error bars on measurements of their masses and radii and the breadth of composition curves that can match a given mass and radius result in large uncertainties in their Hydrogen-Helium mass fractions, placing them anywhere from a terrestrial planet with a thin atmosphere, to a gaseous planet with a thick atmosphere (Lopez

& Fortney, 2014). Therefore, we are justiﬁed in modeling this hypothetical 1.5 R⊕ transition planet as both terrestrial and gaseous with a wide range of surface pressures. We explore several versions of our four classes of transition planets, placing the surface at diﬀering places in the atmosphere relative to the photospheres. Figure 4.3 shows a representation of our four

106 Figure 4.1: All plots, Temperature contours at the lowest atmospheric level (directly above the surface) for a single snapshot in time. The right panel shows a stream and contour plot of the winds on the same scale. Top: low resolution (T21) run, Middle: medium resolution (T42) run, Bottom: high resolution (T63) run. Notice that the relative scale of the temperatures is not dependent on model resolution, as expected. However, comparing the T21 and T42 runs suggests that the T21 run is not at a high enough resolution to fully resolve the baroclinic instabilities due to the surface. The T63 run further resolves these structures.

107 Longitudinaly Averaged Temperature [C] -100.0 -50.0 0.0 50.0

0.2 90 45 0 -45 -90 Latitude

0.4

0.6 Pressure [bars]

0.8

150 200 250 300 Longitudinaly Averaged Temperature [K]

Figure 4.2: A comparison of our T63 resolution longitudinally averaged temperature- pressure proﬁles and a parameterized Earth troposphere model (black line, equation 4.7). classes of models. This replicates a range of Super-Earth to Mini-Neptune conditions. Here we present preliminary results for the two shallowest cases, the shallow surface model and the intermediate surface model.

4.6.1 Planetary Properties

Our base planet has a radius of 1.5 R⊕ and a mass of 5 M⊕. We choose a Hydro- gen/Helium dominated atmosphere for consistency across all 4 of our base models. We select a long orbital period so that we may safely assume the planet is not synchronously rotating, therefore it is placed on a 100 day orbit around a solar-like star, with a rotation rate of 20 hours. With this selection, we are safe to use the same diurnally averaged heating scheme that is used for our Earth validation runs. The internal heat ﬂux is set to 0.4 W m−2. We select a resolution of T42 for all transition planets following estimates from Equations 4.4-4.6 of the mid-latitude Rossby Radius of Deformation, and from scaling oﬀ our Earth results. Table 4.3 summarizes the input parameters for our base models.

108 To Space

To Core

Figure 4.3: We deﬁne our four classes of models as shown. From bottom to top; the thick- est atmosphere is our Mini-Neptune Model, with no surface included in the modeling; the Deep Surface Model has a surface placed at higher pressures than both the short wave and long wave photospheres; the Intermediate Sur- face Model has a surface placed between both photospheres; and the Shallow Surface Model has a surface above both photospheres.

109 As in Miller-Ricci & Fortney (2010); Miguel & Kaltenegger (2014), and following our

Earth models, we set γ=0.7, where γ=κsw/κlw. For a predominately Hydrogen/Helium

−2 2 −1 −4 2 −1 atmosphere, these authors set κlw=10 cm g giving us κsw=7×10 cm g . These values are similar to Earth, but the diﬀerence reﬂects that we choose to maintain a constant atmospheric composition of slightly higher than solar-metallicity across our transition regime, rather than an Earth-like atmosphere. From these values, our two photospheres are

PP hoto,LW = 0.218 bar and PP hoto,SW = 3.114 bar. The difference between our 4 classes of models is primarily the surface pressure, which results in the atmospheric photospheres being at different locations relative to the solid surface and contributes to how the surface influences the circulation, particularly at the levels of the atmosphere we are sensitive to in observations. Table 4.3 lists the surface pressures (or bottom boundary for our mini-neptune model) for our Mini-Neptune, deep surface, intermediate surface, and shallow surface base models respectively; while Figure 4.3 shows a schematic representation of these classes of models. To maintain relative pressure resolution, the number of atmospheric levels is varied between models. We find that because of the effects of Rayleigh friction, vertical resolution becomes an important consideration for stability of the models. Our shallow surface and intermediate surface models are run with linear pressure levels due to their relatively thin atmospheres, with 10 and 40 levels, respectively. Our deep surface model and Mini-Neptune model are run with log pressure levels where the number of levels is calculated to maintain approximately the same number of levels above 2 bar as in the intermediate surface model. The result is 50 and 55 levels covering 3 orders of magnitude in pressure space, respectively.

4.6.2 Model Iterations

To further explore the eﬀects of a surface, we run iterations on our base models by varying the surface pressure around the base model. For our deep surface model we run a total of 15 variations on the surface pressure ranging from 4 bar to 15 bar. If the surface pressure is less

110 Parameter Value Adopted g 2180 cm s−2 R (speciﬁc gas constant) 3779 J kg−1 K−1 Rp 9.56×108 cm Ω 8.73×10−5 radians s−1 P0 50 bar, 10 bar, 2 bar, 0.1 bar Vertical Levels 55, 50, 40, 10 Pressure Orders of Magnitude 3, 3, 0, 0 −2 Fint 0.40 W m −2 Firr 7680 W m A (top of atmosphere) 0.3 −3 2 −1 κsw 7.00×10 cm g −2 2 −1 κlw 1.00×10 cm g PP hoto,LW 0.218 bar PP hoto,SW 3.114 bar Table 4.3: Parameters for our set of base models. In rows with one value given, it is held constant across all four base models. In rows with four options listed is our input parameter for our Mini-Neptune, deep surface, intermediate surface, and shallow surface models, respectively. than 9.5 bar we run the model with 40 levels opposed to the standard 50 for computational speed. For the intermediate surface model we run a total of 13 variations on the surface pressure ranging from 0.25 bar to 3.0 bar. If the surface pressure is less than 2.0 bar the number of levels is computed such that the relative pressure resolution in constant between runs, with a minimum of 10 levels. Finally, for our shallow surface model, we run a total of 4 variations on surface pressure including the base model ranging from 0.01 bars to 0.20 bars, all with 10 levels. There are fewer variations for the shallow surface model due to numerical stability limitations for such a thin, low mass atmosphere.

4.7 Results: Transition Planet

As discussed in the introduction to the chapter, when considering observational implications, we are primarily interested in the various latitudinal dependencies of long wave emission and the reﬂected short wave light. Because of the position of the long wave photosphere, the shallow surface model and the iterations upon it are the only models where we

111 100% No TOA Reflection With TOA Reflection

80% 100

60%

40% 10-1 Surface Pressure [bars] 20%

Fractional Wave-Integrated Emission TOA albedo = 0.3 0% 10-2 Short Long Short Long Wave Wave Wave Wave Model Waveband

Figure 4.4: In both panels, the shallow surface models are shown by dashed lines and intermediate surface models are shown by solid lines. Left: Long wave emission and short wave surface reflection Right: The same, but taking into account the top of the atmosphere reflected short wave. directly see emission from the surface instead of the atmosphere itself. For all other models, we see emission from an atmospheric level corresponding to the long wave photosphere. Fur- ther, for the shallow and intermediate surface models a significant fraction of the incoming stellar radiation reaches the surface and is reflected back into space. Finally, for the deep surface model, the surface is below the short wave photosphere and, aside from the top of the atmosphere reflection, no short wave radiation is reflected back to space, approaching the conditions of our Mini-Neptune model.

4.7.1 Band Integrated Emission and Top of the Atmosphere Albedos

Observationally, the short wave surface reflection is combined with any top-of-the-atmosphere (TOA) reflection and can not be independently determined without a-priori knowing the TOA albedo. There is a degeneracy between an atmosphere with a low TOA albedo and thin atmosphere (no TOA reflection, but a significant amount reflected from the surface) and an atmosphere with a high TOA albedo and a thick atmosphere (significant TOA reflec-

112 tion, but no surface reflection). Figure 4.4 shows a dual band representation of the relative long wave emission and short wave surface + TOA reflection contributions to the planet’s spectrum from our model runs. As expected, including TOA reflection results in a smaller difference between the long wave and short wave, and by comparing the shallow surface models with TOA reflection ignored to the intermediate surface models with TOA reflection, one can see the discussed degeneracy. Because of this degeneracy, simply measuring the disk integrated relative reflected short wave to emitted long wave light is not a robust way to determine the presence of a surface unless the TOA albedo can be determined in some other way. For example, Demory (2014) calculate geometric albedos for Super-Earths in the Kepler sample assuming there is no reflected short wave from the surface, which is a good assumption for most of the planets in the sample due to their radii being large enough that they are more likely to be gaseous, mini-Neptunes. However, as several planets in the sample skirt the line of terrestrial and gaseous and may have intermediate to shallow surfaces, the contribution from surface reflection cannot be ignored. Other work to measure the top of the atmosphere albedo focuses on large gaseous planets where all short wave light detected should be in the form of TOA reflection (for example, Angerhausen et al., 2015; Bell et al., 2017; Mallonn et al., 2019). More work needs to be done on disentangling the surface reflection before we can use spectra to determine the presence of a surface for transition regime planets.

4.7.2 Zonal Averaged Emission and Reﬂection

Figure 4.5 presents the zonal average net fluxes and relative short-wave to long-wave emission for all shallow and intermediate surface models. Models with surface pressures of 1 bar and below have finished running and are averaged over the last orbit in addition to longitude space. The remaining runs have reached equilibrium but have not yet finished their last orbit and are a zonal average of the last model output. As shown in the left panel, for the shallowest atmosphere (0.01 bars), the net flux is approximately constant, representing

113 iue45 nbt aes h hlo n nemdaesraemdl r hw ydashed by shown are models surface intermediate and shallow the panels, both In 4.5: Figure

Latitude [degrees] -50.0 50.0 0.0 einrpeet hr eeto sgetrta emission. than greater is reflection output. last where finished represents the yet of region not atmosphere. average have the zonal a of but are top equilibrium below and reached orbit and have longitude last to bar runs addition their 1 in remaining orbit of The last pressures the over space. surface averaged are with and running Models finished have respectively. lines, solid and Absorption

-200 N

e 0 t

F l u 200 x

[ W

/ 400 m 2 Emission ]

Right: 600

800 ai fttlrﬂce oeitdlgt shaded light, emitted to reﬂected total of Ratio 114 Reflection 1.1

1.0 (surface +TOAreflection) 0.9 SW/LW

0.8

0.7 Reprocessing 0.6 Left:

0.5 e u tthe at ﬂux Net

Surface Pressure [bars] 1 1 1 0 0 0 - - 0 2 1 that heat is primarily emitted back to space at the latitudes it was received, with little heat transport in the atmosphere. As we move to deeper surfaces (higher surface pressures), we find that the relative net absorption at the equator to net emission near the poles becomes more distinct, corresponding to more efficient atmospheric heat transport away from the equator, as one would expect. Further, for surfaces near the long wave photosphere there is a flattening off at mid latitudes representing heat being moved more efficiently away from these latitudes towards the poles as a result of eddy formation and heat transport. As the surface moves deeper, this effect is less pronounced due to the effects of the surface mostly occurring below the levels we see emission from. Heat transport via eddies and the mean flow, and a comparison of the two, is an ongoing part of this in-progress work. In the right panel of Figure 4.5, we see that as the surface moves deeper the short wave surface reflection becomes less important in comparison to the long wave emission. While the disk-integrated short-wave to long-wave ratio for a planet with a surface is degenerate with the contribution from the uniform TOA albedo (see Figure 4.4), the qualitative shape of this ratio as a function of latitude depends on the presence of a surface and is unaffected by the uniform TOA albedo. For models with shallow surfaces (above the long wave photosphere), the total short wave reflection to long wave emission ratio is relatively constant with latitude until a sharp drop off near the poles, while the ratio becomes more dependent on latitude as the surface moves deep enough to allow for atmospheric heat redistribution. In Figure 4.6 we show the zonally averaged equator-to-pole emission difference as a function of model surface pressure. As before, models with surface pressures of 1 bar and below are averaged over the last orbit. We find a qualitatively similar result to that of Komacek & Abbot (2019) and Kaspi & Showman (2015) wherein the measured equator to pole difference decreases with increasing surface pressure as atmospheric heat transport becomes more efficient. However, neither of these works explicitly presents zonally averaged comparisons of planets in this transition regime and discuss the observational implications of a surface. We further fill out the surface pressure dimension with detailed comparisons of various classes

115 1200

] 1000 2 m

/ surface above W

[ both photospheres

surface

e 800

c between both n

e photospheres r e f

f 600 i D

x short-wave photosphere u l F 400 d e t t i

Equator-to-Pole Long Wave surface m

E below both 200 photospheres Long-wave photosphere 0 10-2 10-1 100 101 Model Surface Presure [bar]

Figure 4.6: Equator-to-pole emitted long wave flux differences for shallow and intermediate surface models. of models and how heat transport changes within this regime. The equator-to-pole emitted light difference is an observable quantity with secondary eclipse mapping as discussed in the introduction to this chapter. Typical errors on measurements with Spitzer IRAC are too high to resolve temperature structures in a small number of orbits, however the expected noise floor of JWST is 15-30 ppm which is sufficient to resolve the eclipse depth of a temperate Super-Earth in 25 transits (Beichman et al., 2014a), however the ability to resolve temperatures through eclipse mapping is more difficult than simply detecting the eclipse itself. A detailed analysis of the detectability of the latitudinal variations in emission and reflection due to a surface is forthcoming.

116 4.8 Conclusions and Future Directions

In this chapter, I have presented preliminary results from our study of surface effects on atmospheric circulation, with a focus on observability of the presence of the surface. Current results include zonally and orbit averaged shallow surface and intermediate surface model classes, with results for the remaining two cases forthcoming. We have presented equator-to-pole emitted flux results for the shallow and intermediate surfaces. As is expected, the atmosphere becomes more efficient at transporting heat away from the equator as it becomes thicker, resulting in a lower equator-to-pole difference in emitted flux. Currently, we are working on understanding this meridional heat transport and how the surface pressure in relation to the photospheres affects the contributions to the transport via eddies and the mean flow. Results for the deep surface and mini-Neptune models will further ground our study in the context of the transition regime, while exact calculations of observability and heat transport will determine the observational implications of this study in near term exoplanet characterization studies.

117 CHAPTER V

Examining Tatooine: Atmospheric Models of

Neptune-like Circumbinary Planets

5.1 Preface

Results in this chapter were published in: May, E. M., & Rauscher, E. 2016. Examining Tatooine: Atmospheric Models of Neptune-like Circumbinary Planets. The Astrophysical Journal, 826, 225 and are reproduced here with minor style revisions by permission of the American Astronomical Society under the non-exclusive right of republication granted to authors.

5.2 Abstract

Circumbinary planets experience a time varying irradiation pattern as they orbit their two host stars. In this work, we present the first detailed study of the atmospheric effects of this irradiation pattern on known and hypothetical gaseous circumbinary planets. Using both a one-dimensional Energy Balance Model and a three-dimensional General Circulation Model, we look at the temperature differences between circumbinary planets and their equivalent single-star cases in order to determine the nature of the atmospheres of these planets. We find that for circumbinary planets on stable orbits around their host stars, temperature differences are on average no more than 1.0% in the most extreme cases. Based on detailed

118 modeling with the General Circulation Model, we find that these temperature differences are not large enough to excite circulation differences between the two cases. We conclude that gaseous circumbinary planets can be treated as their equivalent single-star case in future atmospheric modeling efforts.

5.3 Introduction

Circumbinary planets are a fascinating new regime of planets to be studied. While we have been drawn to them for decades in science fiction, it has only been in the past several years that such planets have begun to be discovered, leading to a new and exciting field of study. Orbiting two stars, circumbinary planets experience strong short-term variations in stellar irradiation over the course of their orbits owing to the motion of their host binary stars. Such variation is interesting when we begin to consider the possible effects on climate patterns for planets in these systems. Binary stars are common in our galaxy. With the fraction of single stars with planets being at least 50% (Fressin et al., 2013), we can say that planets are also a common occurrence in our galaxy. If we only consider planets which are 4 times the radius of Neptune (hereafter

1 RN) , the same study finds that just over 8% of single stars are host to such objects. If circumbinary planets were to form at a similar rate, we could assume them to be just as common. In fact, Armstrong et al. (2014) finds that the fraction of binary stars with planets larger than 6 R⊕ is at least 10% for coplanar circumbinary systems, a rate even higher than that for single-star systems. This makes circumbinary planets an extremely interesting field of study, since we can expect them to be quite numerous. As of writing, there have been 10 transiting circumbinary planets discovered around main sequence stars. The first was Kepler 16b (Doyle et al., 2011). Following this were the discoveries of Kepler 34b and 35b (Welsh et al., 2012), Kepler 47b and 47c (Orosz et al., 2012a), Kepler 38b (Orosz et al., 2012b), Kepler 64b (Schwamb et al., 2013; Kostov et al.,

1 RN = 3.88R⊕ ; RJ = 11.2R⊕

119 2013), Kepler 413b (Kostov et al., 2014), Kepler 453b (Welsh et al., 2015), and KOI 2939b (Kostov et al., 2016). With the exception of the most recent planet, which is Jupiter-sized,

all are between approximately 0.75 - 2.25 RN. This agrees with studies which conclude that

planets larger than 10 R⊕ are uncommon around binary stars (Armstrong et al., 2014). Many upcoming missions will provide opportunities to search for and discover new circumbinary planets. The Gaia mission is expected to discover between tens and hundreds of new circumbinary planets (Sahlmann et al., 2015), depending on the abundance of giant circumbinary planets. In addition, microlensing has been shown as an effective way to discover circumbinary planetary candidates, with studies predicting that this is a sufficient method for candidate detection (Luhn et al., 2016). Atmospheric modeling is one of the most important ways we can gain insights into the circulation patterns of exoplanets. Through the use of models of varying complexities, we can learn about a planet’s temperature structure and circulation and make predictions for observational signatures of various types of temperature structures due to, for example, shifted hot spots, seasonal effects, clouds, and composition. In this dissertation we study the atmospheres of circumbinary planets through the use of both a one-dimensional Energy Balance Model and a three-dimensional General Circulation Model in order to learn about the effects of flux variation on short timescales. Such a study for these types of planets has not been done previously, with the only similar study being of habitable zones around binary stars for hypothetical Earth-like planets (Forgan, 2014). By piecing together all of the information we have about the known set of circumbinary planets, and by studying them further through the use of models, we can begin to understand where such planets are similar to and different from their single-star counterparts. By modeling both a known circumbinary planet and a single-star planet with an equivalent constant irradiation, we then study the temperature and wind circulation patterns in the atmospheres of both planets in order to make comparisons between the two atmospheres. Through this work we are then able to answer the question of how a quickly varying stellar

120 irradiation aﬀects the atmosphere of a giant planet and make further statements as to the detectability of any diﬀerences between single-star and circumbinary planets. In Section 5.4 we discuss the methods and models used in this work, with particular emphasis on model parameters. The results of our work, including various known and theoretical planets, is presented in Section 5.5. Conclusions are given in Section 5.6.

5.4 Method

We begin with a one-dimensional Energy Balance Model (Section 5.4.2) to study the general behavior of a planet’s atmosphere over long periods of time. We use a three-dimensional General Circulation Model (Section 5.4.3) for more in depth studies of a specific planet in order to confirm results from the one-dimensional model. The benefits of using the Energy Balance Model (hereafter EBM) are that it is relatively simple, allowing us to model the atmosphere over many more planetary orbits and for a wide range of configurations. While the General Circulation Model (hereafter GCM) is beneficial in order to obtain more realistic and detailed three-dimensional results, it is much more computationally expensive. By using both models we are therefore able to obtain a better understanding of the effects of the varying irradiation pattern both in high detail and over a wider parameter space. We focus on Neptune-like planets, and all model parameters are derived based on this fact.

5.4.1 Calculation of Orbits and Resulting Irradiation

We calculate orbits by assuming Keplerian motion, which is a good approximation over the short number of orbits we model. For the known circumbinary systems, observations over multiple planetary orbits support our choice for Keplerian motion. Both stars are placed on Keplerian orbits around their center of mass, with the planet on a Keplerian orbit around this same center of mass. Assuming the planet is approximately Neptune-like in mass, it is not massive enough to signiﬁcantly perturb the stellar orbits away from Keplerian motion over the timescales we consider. Our assumption of planet mass is based on the measured

121 radii of known circumbinary planets, and mass-radius models and observations which do not predict a planet of this size to be dense enough to be terrestrial (Swift et al., 2012; Rogers, 2015; Wu & Lithwick, 2013). For all known systems, the irradiation pattern is non-repeating over timescales of both the stellar orbits and the planetary orbits. General patterns do emerge which depend on the location of the more luminous star or stars relative to the planet. As shown in Figure 5.1, planets with more massive secondary stars (top two panels) experience a greater variation in their stellar irradiation pattern over a given planetary orbit, while those with lower mass secondaries (bottom two panels) have stellar irradiation patterns which become much sim- pler, beginning to resemble simple sinusoidal curves. Further, planets on longer period orbits experience less extreme irradiation patterns (smaller amplitude variations) as the motions of the stars become less important simply due to the larger distance between the planets and the stars. This can also be seen in Figure 5.1 when comparing the left two panels to the right two panels.

5.4.2 Energy Balance Model

Historically, EBMs have been used to predict the long-term climate of terrestrial-like planets (see North et al., 1981; Forgan, 2014; Vladilo et al., 2015). EBMs are designed to be relatively simple, yet complex enough to encapsulate the relevant physics of atmospheric heating. The simplicity of these models comes from their single dimension in space, latitude. For terrestrial planets, models predict the planet’s surface temperature - so there is no need to study the various heights in the atmosphere. EBMs calculate the temperature at each point in latitude space, evolving it forward in time to represent the evolution of the surface or atmospheric temperature over a period of time Previous works have been applied to Earth-like planets only - here we make modiﬁca- tions to account for the thicker atmosphere of Jovian-like planets. When modeling planets dominated by a thick atmosphere, we decide to modify the coeﬃcients in such a way that we

122 (a) M2 =1.0 M ⊙ , aplanet =0.3 AU (b) M2 =1.0 M ⊙ , aplanet =0.5 AU

1.2

1.1

1.0

0.9

0.8

1.2

1.1

1.0 Binary/Constant Stellar Irradation Binary/ConstantStellar 0.9

0.8 2 4 6 8 1 2 3 4 Time (Planetary Orbits)

Figure 5.1: Flux variation for several diﬀerent systems. For (a), (b), and (d) the primary stellar mass is set to 1 M and the stellar separation is set to 0.1 AU with zero eccentricity for all orbits. Plot (c) shows the irradiation variation for the planet Kepler 47b. are integrating over the range of pressures in the atmosphere in which heating takes place. This lets us gain insight into the temperature of the thermal (infrared emission) photosphere of the planet. This choice becomes important as we discuss observables in section 5.6.3. The general form of the EBM is given by

∂T ∂ ∂T C − D 1 − x2 = S (1 − A) − I. (5.1) ∂t ∂x ∂x

Here x ≡ sin ϕ is the single dimension in the model, with ϕ being latitude. T is the local temperature at some time. C is the atmosphere’s heat capacity per unit area; D is the diffusivity of the atmosphere, S is the stellar irradiation, A is the atmosphere’s albedo, and I is the cooling function of the atmosphere. In the next few sections we discuss all parameters and their physical roles in the model, as well as our modifications to account for the specific cases we study. The adopted values are listed in Table 5.1.

123 5.4.2.1 C: Heat Capacity Per Unit Area

As discussed in the introduction, most of the currently known circumbinary planets are

approximately Neptune-sized, ranging from 0.768 RN (Kepler 47b, Orosz et al. (2012a)) to

2.20 RN (Kepler 34b, Welsh et al. (2012)), with a single outlier at 1.52 RJ (KOI 2939b, Kostov et al. (2016)) . For this reason, we chose to use a Neptune-like composition for all planets modeled in this work. This approximation allows better comparison across systems by minimizing free parameters. Previous work on circumbinary planets using EBMs (Forgan, 2014) focuses on hypothetical Earth-like planets. Here we seek to model the known planets, with much of their mass and radius being dominated by atmosphere. Because of this, we do not need to take into account the fraction of the planet covered in ice, water, and solid surfaces as is often done with EBMs. Therefore, our heat capacity is calculated based on our choice of atmospheric composition with a mean molecular weight of 2.5 g/mol (Lodders & Fegley, 1998), a value commonly used for Neptune. This corresponds to a speciﬁc gas constant of 3.2×107 erg g−1 K−1, which we can covert to heat capacity per unit area at the pressure level (thermal photosphere, 0.12 bar) we are studying. C is then set to 4.154×1010 erg cm−2 K−1.

5.4.2.2 D: Diﬀusivity

The diffusivity coefficient (D) encapsulates the atmospheric transport of heat from the equator towards the cooler poles. For Earth-like planets, the diffusivity coefficient is set based on empirically fitting models to reproduce the observed temperature structure on Earth. In a similar way, we can use more sophisticated models of gas planets to predict how meridional heat transport occurs. This is discussed in depth in section 5.4.3.1. The diffusion constant could in principle be set as a function of x (latitude), but we use a constant value in this work, which we find is able to capture the relevant physics without adding more unknowns into the model. Using results of a preliminary GCM (model details are discussed in Section 5.4.3), we

124 obtain an initial estimate of the diffusion coefficient based on the rate of energy transport in this preliminary model. This served as a base value which was then varied over multiple runs of the EBM in order to obtain a latitudinal temperature structure which corresponded to the results of the GCM. As a result, we use a diffusion coefficient of 4×103 erg cm−2 s−1 K−1. For comparison, typical values of diffusivity used for Earth-like planets are of order 102 erg cm−2 s−1 K−1. It is of importance to note that this value is the least constrained of the parameters used here. Small variances have little affect on the resulting temperature structures. However, extremely large values of the diffusion coefficient (greater than of order 104 erg cm−2 s−1 K−1) correspond to efficient heat transport to the poles, where it is then radiated out to space, leading to an global cooling effect. Similarly, extremely low values of the diffusion coefficient (smaller than of order 102 erg cm−2 s−1 K−1) correspond to heat being trapped near the equator, leading to an global heating effect.

5.4.2.3 S(1-A): Stellar Irradiation and Albedo

Stellar irradiation (S) is set by the motions of the binary stars in the system. The time (t) dependence of this parameter is determined by the speciﬁc planetary and stellar orbits for any given system. The spatial (x) dependence of this parameter is rooted in the fact that the equator receives more irradiation than the poles for zero (or very low) obliquity systems, represented by a factor of cosine of latitude in the received irradiation. Based on the small angular separation of the two stars in the planet’s sky, we do not need to account for two separate substellar points, and instead treat them as one point, again letting us make the claim that the equator is heated more than the poles. As discussed in Section 5.4.1 and demonstrated in Figure 5.1, the binary mass fraction and the planet’s semi-major axis play a large role in the stellar irradiation. Additionally, we ignore the eﬀects of stellar eclipses, as they occur on time scales which are short relative to the radiative timescale of the atmosphere.

125 Albedo (A), or the amount of light reflected off the top of the atmosphere, is set to 0.3. This value has been used for Neptune previously (such as in Liu & Schneider (2010)), so we find it appropriate to use due to other parameters being set to Neptune values as well.

5.4.2.4 I: Cooling Function

The cooling function determines the planet’s outgoing radiation for any given point in latitude. Again, we examine results from the preliminary GCM to determine the appropriate amount of outgoing radiation necessary to produce the temperature structure seen in this more complicated model. As the cooling function represents the outgoing ﬂux, we can represent it as σT 4 I(T ) = , (5.2) α

where α is a constant related to the optical thickness of the atmosphere, determined by the GCM. Our initial parameter guess from the preliminary GCM reproduces the expected temperatures in the EBM without any further ﬁne tuning. Based on results for outgoing radiation and temperature structure from the GCM, an α value of 1.682 is used.

Parameter Value Adopted Heat Capacity, C 4.154×1010 erg cm−2 K−1 Diﬀusivity Coeﬃcient, D 4×103 erg cm−2 s−1 K−1 Albedo, A 0.3 Cooling Function, I I(T ) = σT 4/α Cooling α 1.682

Table 5.1: Energy Balance Model parameters

5.4.3 General Circulation Model

GCMs are three dimensional climate models which calculate temperature and winds at every point in latitude, longitude, and pressure space using basic information about the planet we seek to model - such as atmospheric composition, solar irradiation, size, and rotation rate. Because of their complexity, these models can be used to predict observational

126 signatures in the form of infrared radiation for a wide array of planet types and provide a base for detailed study of planetary atmospheres. We use the GCM detailed in Rauscher & Menou (2012), with a modification to account for the variation in stellar irradiation, calculated as discussed in section 5.4.2.3 and 5.4.1. The model is built upon the primitive equations of meteorology, which are a standard reduction of the Navier-Stokes equations including assumptions of inviscid flow, vertical hydrostatic equilibrium, and small vertical flow and scales relative to the horizontal components. See Vallis (2006) for further explanation. Heating is treated using double gray radiative transfer such that the incoming radiation (optical) and the outgoing radiation (infrared) each have their own absorption coefficient. For a more detailed description of the model, see Rauscher & Menou (2012) and sources within. See Table 5.2 for a list of parameters used for a Neptune-like planet.

Parameter Adopted Value 3 Planet density, ρN 1.64 g/cm −4 −1 Rotation rate, ΩN 1.08×10 s Specific gas constant, R 3.2×107 erg g−1 K−1 −4 2 −1 Optical absorption, κvis 8.14×10 cm g † −2 2 −1 Infrared absorption, κIR 1.49×10 cm g † −2 Internal heat flux, Fint 0.433 W m † Irradiated flux, Firr Varies - Section 5.4.2.3

Table 5.2: General Circulation Model Parameters. Values with a subscript N are set to accepted parameters for Neptune. We chose density as the constant parameter across various Neptune-like planets. The radius of the each planet is set from observations, and density is used to obtain a mass and gravitational acceleration for use in the General Circulation Model.

†Adapted to our model formulation from Liu & Schneider (2010)

127 5.4.3.1 GCM Heat Transport - applications to the EBM

Using equations adapted from Pierrehumbert (2010), we can relate the heat transport in the EBM to the heat transport in the GCM by writing

∂T Φ ≡ −D , (5.3) ∂ϕ

where D is the diffusion coefficient defined in section 5.4.2.2. Φ, given by

Ps 1 Z dP Φ = v (cpT + gz) (5.4) Rp g 0

2 relates to the rate of energy transport across latitude bands, calculated as 2πRpΦ cos ϕ. In

all of the above, Rp denotes the radius of the planet, P the pressure of a given level, Ps the representative bottom boundary pressure, T the temperature at that pressure level, and g the gravitational acceleration. Using output of the GCM, Φ can be computed for a planet of our chosen composition as a function of latitude, ϕ. We can then compute the diffusion coefficient D as a function of latitude. For simplicity, we adopt an average value, which as discussed above, has been determined to be sufficient for 1D models

5.5 Results

In the following sections we study the planet Kepler 47b using both the EBM and the GCM. First, by running the one-dimensional EBM, we obtain limits on the atmosphere’s temperature variations due to the time varying flux. By then running the three-dimensional GCM, we can further study how these variances may or may not affect the planet’s circulation. We then extend our results to all known circumbinary systems as well as a grid of hypothetical circumbinary systems in order to thoroughly examine which regions of parameter space are host to planets which are most affected by their orbit around a binary star system.

128 To compare our results to a single-star system, we calculate an equivalent single-star case in which the total luminosity of both stars is held unmoving at the center of mass. This allows for a direct comparison between a single-star case and a circumbinary case with all other variables the same.

5.5.1 Kepler 47b

Kepler 47 is a multi-planet binary system, with two confirmed Neptune-sized planets (Orosz et al., 2012a). We initially decided to study Kepler 47b in the most detail due to a comparable radiative time scale of the atmosphere and timescale over which the irradiation is varying (similar to the orbital period of the stars). The radiative timescale describes how quickly or slowly a planet’s atmosphere is able to respond to changing environmental conditions, therefore a planet which has a radiative timescale nearly that of the short scale changes in irradiation may have interesting coupling between the variation in stellar heating and the atmospheric response. Atmospheres with longer radiative timescales will be unaware of the varying flux, and we can expect them to then respond to the average irradiation, while those with shorter radiative timescales will respond very quickly to changes in stellar flux. System parameters are given in Table 5.3. The irradiation pattern for Kepler 47b is shown in the bottom left panel of Figure 5.1 and is fairly regular with two superimposed sinusoidal patterns. The shorter of the two periods is due to the motions of the host stars, and the other, longer period, sinusoidal pattern is due to the slight eccentricity of the planetary orbit. This eccentricity is set to the upper limit given in Orosz et al. (2012a) in order to test the combined effect of eccentricity and binary motions.

5.5.1.1 Kepler 47b - EBM

Using the EBM, we run both the circumbinary case with ﬂux varying according the motions of the stars relative to the planet, and a single-star case set up as described above.

129 Stellar Properties Parameter Primary Star Secondary Star Mass (M ) 1.043 0.362 Radius (R ) 0.964 0.3506 Temperature (K) 5636 3357 Stellar Orbit Stellar Separation (AU) 0.0836 Orbital Period (Earth Days) 7.448 Eccentricity 0.0234 Planet b Properties Radius (RNept) 0.767 Semimajor Axis (AU) 0.2956 Orbital Period (Earth days) 49.514 Eccentricity <0.035

Table 5.3: Kepler 47 System Parameters. All values have been adopted from Orosz et al. (2012a). We chose to adopt the upper limit for the planet’s eccentricity in order to maximize any variations.

Both models run for 20 planetary orbits (where one orbit is 49.5 Earth days, see Table 5.3), which serves to give us a long enough base-line for comparison between the two cases. The atmosphere equilibrates over the first planetary orbit, so for this reason we do not include the first orbit in our analysis. As the EBM is a one-dimensional model, the output represents the temperature across all latitude bands evolved forward in time. Shown in the middle frame of Figure 5.2 is the model output at the thermal (outgoing) photosphere in the circumbinary case through the fifth planetary orbit. We find that peaks in temperature correspond to peaks in irradiation after accounting for the expected delay due to the radiative lag of the atmosphere. For this system, the radiative timescale corresponds to approximately 0.14 planetary orbits, or approximately 7 days. As shown, times of peak temperature are only a few Kelvin warmer than other times. This is reasonable, as we can not expect a direct comparison between changes in irradiation and atmospheric temperature because the atmosphere dampens out the irradiation changes. A direct comparison between flux and temperature (∆F → σ∆T 4) suggests changes of order tens of Kelvin, so our results of a few Kelvin is reasonable.

130 Flux at Planet

90 486. 0 4 8 2 .0 4 9 0 .0 474.0 478.0 470.0 466.0 462.0 546 458.0 458.0 458.0 466.0 462.0 458.0 474.0 470.0 486.0 478.0 482.0 534 494.0 490.0 502.0498.0 45 506.0 514.0 510.0 522.0 518.0 522 530.0 526.0 538.0 534.0 542.0 510 542.0 0 542.0 498 542.0 538.0 534.0 530.0 526.0 486 518.0 522.0 514.0 510.0 -45 506.0 5 0 2 .0 498.0 490.0 494.0 474 482.0 486.0 478.0 (K) Temperature 474.0 458.0 470.0 462.0 466.0 462 458.0 458.0 458.0 470.0 466.0 462.0 474.0 478.0 -90 486.0 4 9 0 .0 482.0 450 90 0.0 0.0 0.0 0.0

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Figure 5.2: Results of the Energy Balance Model for the circumbinary planet Kepler 47b. The top curve represents the stellar irradiation pattern received by the planet over the course of the 4 planetary orbits plotted. The bottom two plots represent the evolution of the thermal photosphere’s temperature over time. For the middle plot, the absolute temperature is plotted. The bottom plot shows the relative changes in temperature as compared to the equivalent single-star case.

By eye, we can see that the circumbinary planet shows variations we would not expect for planets receiving a constant amount of irradiation over the course of its orbit. We would like to quantify how different a circumbinary planet is from its equivalent single-star case, so we define a parameter η representing the mean of the absolute value of the fractional difference in temperature for the circumbinary case as compared to the single-star case. For Kepler 47b, we find an η of 0.2%. The bottom frame of Figure 5.2 shows the temperature deviations over the first through fifth planetary orbits as compared to the single-star case, demonstrating that for the case of Kepler 47b, the maximum deviation away from the single-star model is 6K, which is less than 1%.

5.5.1.2 Kepler 47b - GCM

In order to determine the magnitude of these temperature variations on the planet’s circulation, we study this planet with the full three-dimensional GCM. We do not expect

131 Temperature (K) Temperature (K) 546 547

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Figure 5.3: GCM results for the circumbinary case (left) and the single-star case (right) at a single point in time for Kepler 47b. The top panel shows the temperature of the thermal photosphere, and the bottom panel shows the east-west winds at the thermal photosphere. that a mean deviation of 0.2% is large enough to excite noticeable changes in the planet’s circulation, however, we explore the possibility here for completeness. Figure 5.3 shows the full three-dimensional model results for both the circumbinary case (left) and the single-star case (right). The top row shows the temperature of both cases at a snapshot in time, and the bottom row shows the zonal (East-West direction) winds for both cases at the same point in time. GCM results suggest diﬀerences in temperatures and wind speeds for the circumbinary case compared to the single-star case which are less than 1 K and 1 m/s, respectively, at any given point in time. We ﬁnd that for η ≈ 0.002 (as calculated from the EBM), the irradiation pattern due to the binary motion does not cause noticeable changes in planetary circulation as compared to the equivalent single-star case, unsurprisingly.

132 546

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Figure 5.4: Temperature predictions from the General Circulation Model (Purple), Energy Balance Model (Blue), and Irradiation Temperature (Black) for Kepler 47b.

A further comparison of the zonal-averaged temperature at the equator from the GCM (an average temperature across the latitude band sitting at the equator), the equator temperature of the EBM, and the irradiation temperature at the equator (T=(S(t)/σ)(1/4)) over the course of one orbit shows that the GCM produces temperature variations of even smaller amplitudes than those found in the EBM (Figure 5.4). Comparing both to the amplitudes of the temperature variations we could expect if the atmosphere responded immediately to changes in irradiation, we see that the atmosphere in both models does indeed dampen out the irradiation changes. The results of this comparison allows us to determine that any atmospheric eﬀects due to the irradiation pattern exhibited in the Kepler 47 system are negligible and become even less pronounced when we use the GCM, which more correctly models the heating and cooling of the atmosphere as compared to the EBM.

133 5.5.2 Expanding Models to More Planets

We seek to draw a conclusion for a wider range of circumbinary planets, and so we start by looking at the 10 circumbinary planets which have been confirmed. For relevant orbital parameters, see sources Doyle et al. (2011) (Kepler 16b), Welsh et al. (2012) (Kepler 34b and 35b), Orosz et al. (2012a) (Kepler 47b and 47c), Orosz et al. (2012b) (Kepler 38b), Schwamb et al. (2013); Kostov et al. (2013) (Kepler 64b), Kostov et al. (2014) (Kepler 413b), Welsh et al. (2015) (Kepler 453b), and Kostov et al. (2016) (KOI2939b). For each system, we run circumbinary-case models and single-star models for 20 orbits and calculate their η value using the EBM. Resulting η values are shown in Figure 5.5. Due to each system’s unique orbital parameters and host stars, planets such as Kepler 16b and Kepler 64b can lay close to each other in the shown parameter space, but experience different effects due to their binary stars. In this case, both of the stars in the Kepler 64 system are at least twice as massive as those in the Kepler 16 system, causing the stars to move through their orbits much faster. This causes the variations in irradiation to be much more extreme (see Figure 5.1 for a demonstration of the variation in flux across different systems). Here we also see that Kepler 35b experiences the most extreme variations over the single- star case, at an η=0.0051, or 0.51%. This matches our expectations that this planet should experience the most variations due to its closer proximity to two nearly equal mass stars. Figure 5.1 demonstrates this through the differences in irradiation patterns for stars near and far from equal mass stars. Although not shown in Figure 5.5, Kepler 47c and KOI 2939b experience the smallest variations with η=0.00013 (0.013%) and 0.00088 (0.088%) respectively due to their large orbital distances of 0.989 AU and 2.72 AU. Though there are only 10 announced circumbinary planets as of writing, we also wish to expand these results to a wider array of possible circumbinary planets. To do so, we develop a grid of hypothetical planets with a set stellar separation of 0.1 AU (corresponds to slightly less than the average stellar separation for the known systems), a set primary star mass of

134 1.0 M (corresponds to the average primary star mass of the known systems), and then vary the planetary semi-major axis and the secondary star mass. Further, because we are only focused on studying circumbinary planets orbiting two main-sequence stars, we can apply main sequence scaling relations based on a fully radiative approximation to convert stellar mass to luminosity, L M 10.1/2 = (5.5) L M and update the orbital periods of the stars and planet as necessary by Kepler’s laws with

p 3 P=2π a /(G(M1 + M2)). While low mass stars are generally fully convective, and this is likely to then over predict the luminosity of such a star, low mass stars will contribute minimally to the total luminosity of the system, and as such it is suﬃcient to simplify the general set of mass luminosity relations to one relation for all stars. Additionally, all orbits are set to zero eccentricity so that the only variation produced is due to the motions of the binary stars, and not dependent on orbital eccentricity.

We then run a grid of planets for 0.2 AU

From Holman & Wiegert (1999), we take the limit of stability (acritical) for zero eccentricity stellar orbits to be

a M M 2 critical = (1.60 ± 0.04) + (4.12 ± 0.09) 2 + (−5.09 ± 0.11) 2 (5.6) astars M1 M1

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Figure 5.5: η values for 7 of the 10 known circumbinary systems as of writing. Kepler 34b, Kepler 47c and KOI2939b are excluded due to their large semi-major axes, placing all three oﬀ the right of the plot. All have η values less than 0.1%.

when M2 / M1 is no greater than 0.5. For higher mass ratios we adopt the value of acritical=2.37 from Dvorak et al. (1989). No planet within the region of stability reaches an η value much greater than 0.01 (1% variations), which would imply that their atmospheres are similar to that of a single-star planet, with only slight changes in temperature for small periods of time. We do not expect that these systems will exhibit circulation diﬀerences, and therefore make the overarching conclusion that the atmospheres of circumbinary planets exhibit no strong or noticeable eﬀects due to their unique irradiation patterns.

5.5.3 Introduction of Obliquity

Seasons are an additional way in which we could produce variations over the single-star case. When orbiting two stars, the relative strength of a given season depends on which star is closest to the planet for the longest amount of time during that season. Therefore,

136 0.000 0.003 0.006 0.009 0.012 0.015 0.018

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Figure 5.6: η values for the grid of models with Mprimary and astars held constant at 1.0 M and 0.1 AU respectively. The top left represents no seasons, or 0 degrees obliquity. The red curve gives the approximate limit of stability as established in Holman & Wiegert (1999); Dvorak et al. (1989) with appropriate errors. Grey dots represent the planets shown in Figure 5.5. Each other frame represents a different obliquity, corresponding to stronger seasons, where the results of the zero obliquity case have been subtracted away to demonstrate which regions of parameter space are most affected by the introduction of seasons. we could expect hot summers and cold summers in a system with a low mass ratio. This is something not seen on a planet with only one star, so we investigate if the addition of a seasonal pattern (implemented by adding an axial tilt) can serve to excite large differences in a circumbinary planet’s atmosphere. We introduce seasons in the typical way (Pierrehumbert, 2010) where the daily averaged stellar irradiation at a given latitude varies with time as

F S¯(φ, t) = [H(t) sin ϕ sin δ(t) + sin H(t) cos ϕ cos δ(t)] (5.7a) π

137 90 485.0 480.0 490.0 505.0 480.0 470.0 470.0 485.0 545 465.0 460.0 470.0 490.0 475.0 460.0 475.0465.0 475.0 460.0 475.0 455.0 495.0

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455.0 485.0 480.0 455.0 .0 470.0 455 500.0 465.0 455 Latitude (Degrees) Latitude 450.0 455.0 495.0 450.0 460.0 460.0 470.0 450.0 450.0 480.0 -90 490.0 480.0 490.0 485.0 485.0 440 1.0 1.5 2.0 2.5 Time (Planetary3.0 Orbits)3.5 4.0 4.5 5.0

Figure 5.7: Temperature map for Kepler 47b with a 30◦ obliquity.

sin δ(t) = sin ψ sin λ(t) (5.7b)

cos H(t) = − tan ϕ tan δ(t), (5.7c) with F the calculated flux, based on the location of the stars relative to the planet (see Section 5.4.2.3); H is the hour angle at sunset; ϕ is the latitude; and δ is the declination of the substellar point. Because there are two substellar points, one for each star, δ is further defined as the point directly in between the two substellar points - though the separation of the stars has been found to be negligible regardless. Further, ψ gives the obliquity (tilt of the orbital axis); and λ represents the angle of the planet’s orbit relative to some standard ‘zero’ point. As before, we start by looking at the planet Kepler 47b. Using an obliquity of 30◦, and running this through the EBM, we begin to see the seasonal variation we expect with hotter summers in one hemisphere while there is a colder winter in the other hemisphere. Figure 5.7 shows the results for this case. We see no strong difference in the general seasonal pattern as compared to an equivalent single-star case with the same axial tilt. Setting up the hypothetical models as before, with the same grid of stellar and planet orbital properties, we now vary the planetary obliquity between 0◦ (no axial tilt, same as before) and 90◦ (planet rotating completely on its side). In Figure 5.6 we show results for obliquities of 15◦, 45◦, and 75◦ with the zero obliquity case subtracted off in order to focus only on the additional temperature variations caused by the seasons. Compared to the zero

138 obliquity case shown in the top left of Figure 5.6, we see the most additional variation for planets close in to any type of binary system (left region of subplots in Figure 5.6). However, these planets are on unstable orbits (compare to the red line of stability in the 0◦ obliquity case), and are therefore unimportant to this discussion. The next region with significant additional differences are those planets far away from a equal mass binary system (top left of plots in Figure 5.6). In this region, we expect planets to exhibit temperature patterns similar to their equivalent single-star case since they are far enough away from their hosts that the motions of the stars become less important as compared to their axial tilt. As with the zero obliquity case in Section 5.6, we conclude that the atmospheres of circumbinary planets with any axial tilt are no different that their equivalent single-star case. Seasons are no more extreme for circumbinary planets than single-star planets.

5.6 Conclusions

We conclude that the temperature structures and wind patterns within the atmosphere of a circumbinary planet are negligibly diﬀerent from its equivalent single-star case. This has important implications for future work, both with considerations of habitability and, more importantly to this work, continuing modeling eﬀort of these planets.

5.6.1 Modeling of Circumbinary Planets

We find a a maximum deviation in temperature of approximately 1% for circumbinary planets on stable orbits. Based on our further modeling of Kepler 47b, a planet which experiences deviations of 0.2%, we do not expect a deviation of 1% to be large enough to lead to differences in circulation patterns. Therefore we conclude that the atmospheres of circumbinary planets, in all reasonably stable orbital configurations, are negligibly different from their equivalent single-star cases. Going forward, it is therefore reasonable to model circumbinary planets as their equivalent single-star case for studies of atmospheric circulation.

139 5.6.2 Habitability of Circumbinary Planets

Although the ten known circumbinary planets are all of sufficient size to be considered gaseous, we can extend our results to make certain assumptions about the potential for habitability of moons or terrestrial planets within the habitable zone of binary star systems. We conclude that circumbinary planets should not be discounted as potential hosts for life, as their atmospheres should be of a similar nature to the single-star planets we know so well, though much more work can be done in order to study any possible circulation differences of circumbinary terrestrial planet atmospheres specifically.

5.6.3 Observables

With our growing ability to observe planetary atmospheres, it becomes interesting to consider if we could measure the temperature variations of a circumbinary planet’s atmosphere. During a secondary eclipse, we are able to determine the planet’s thermal emission - emission which originates from the depth in the atmosphere which we have studied in this work. Ideally, by observing several different secondary eclipses and noting the positions of the stars relative to the planet at these points, we can predict the expected temperature differences between the two events and test the predictions based on the observations. In reality, we do not expect these temperature variations to be large. For Kepler 47b, the maximum temperature variations between different points in orbit are of order a few Kelvin as predicted by the GCM. This is quite far out of the reach of current ground based efforts, which have errors of 100s of Kelvin (Zhou et al., 2015; von Essen et al., 2015). Recent best efforts to measure thermal emission from an exoplanet using Spitzer phase curves have achieved errors of only 20-60K (Knutson et al., 2009, 2012; Maxted et al., 2013; Wong et al., 2015; Zellem et al., 2014), but this would still not be small enough to measure the extremely small temperature differences of a circumbinary planet with any certainty. While JWST will be even more powerful than Spitzer for atmospheric characterization (Beichman et al., 2014b), it is unlikely it will have the precision necessary (only a few Kelvin) in order to

140 deﬁnitively say whether the expected small amplitude temperature variations are present in the atmospheres of circumbinary planets.

141 CHAPTER VI

Conclusion

“Somewhere, something incredible is waiting to be known.” – Carl Sagan

Incredible discoveries await us every day, and the study of exoplanets lends to us a sense of wonder about our place in the universe. We are standing on the edge of an era of these great discoveries, well positioned to unlock the secrets of worlds outside of our Solar System in the next decades with the coming launch of the James Webb Space Telescope (JWST) and ﬁrst light for the next generation of ground-based facilities. In this dissertation, I have presented my contribution towards a global understanding of exoplanets from an observational and theoretical perspective. Here I summarize this work and discuss the future of exoplanet characterization.

6.1 Summary

6.1.1 Transmission Spectroscopy and the Future of Exoplanet Observations

In Chapters II and III I discussed my work on developing the Michigan Optical Planetary Spectrum Survey (MOPSS) and presented results for three exoplanets using data obtained with the IMACS instrument on the Magellan Baade telescope at Las Campanas Observatory

142 in Chile. Two of these planets, WASP-52b and WASP-4b were observed on 2 and 1 night(s), respectively, and confirmed that our methods obtain results in line with other observing teams and methods, pointing to cloudy atmospheres for both WASP-52b and WASP-4b. The third planet, HATS-8b, is unique to all transmission spectroscopy studies with the strongest atmospheric scattering measured to-date. We observed HATS-8b on two separate nights, and on both find stronger than expected atmospheric scattering. In this work we present possible explanations including unocculted star spots affecting the data and the effects of strongly scattering particulates in the planet’s atmosphere. As discussed in Chapter I, MOPSS currently has data for more than 10 planets and this project will continue to contribute to the field in the coming years as we improve our analysis techniques and converge upon the most optimal observing strategy. Preliminary results for several of the targets look equally as beneficial to the field as those presented in Chapters II and III, and we hope to make an impact on ground based transmission spectroscopy studies so that the techniques and methods exist to study smaller planets in the era of JWST and the extremely large telescopes (ELTs). JWST will allow an unparalleled combination of spectral resolution and wavelength coverage redwards of 6000 A.˚ Current work with the Hubble Space Telescope used 60 Hubble Space Telescope orbits of Earth to observe 15 transit events of GJ 1214b, resulting in the highest precision transmission spectroscopy data for an exoplanet to date (Kreidberg et al., 2014). JWST is expected to be able to characterize the atmosphere of a temperate Earth- similar planet (such as the recently discovered TRAPPIST-1 system) in only 10 transit events (Batalha et al., 2018) with no gaps in transit coverage due to heliocentric orbit as opposed to HST’s geocentric one. It is important to note, however, that at optical wavelengths, ground based observing obtains similar spectral resolution, and bluer wavelength coverage, allowing us to get a better picture of the scattering in the atmosphere, which is key to determining absolute abundances in the atmosphere. Therefore ground based observing, and MOPSS and any future derivatives of the program, will remain extremely important in the era of

143 JWST While current ground based eﬀorts are focused on Hot Jupiters and Neptune-mass planets, the development of high precision spectrographs, improvements of reduction techniques (e.g. gaussian process correlated noise removal), instrumentation development to mitigate atmospheric eﬀects, and the introduction of new observing techniques will allow us to push towards smaller planets and contribute to a global understanding of the diversity of exoplanet atmospheres.

6.1.2 Atmospheric Modeling and the Future of Atmospheric Characterization

In Chapters IV and V I discussed my modeling work using the general circulation model (GCM) introduced by Rauscher & Menou (2012) as well as 1D energy balance models. Through this dissertation, I provided two key updates to the RM12 GCM: (1) the re- introduction of a surface and its effects on the atmospheric circulation, including additional sources of heating and drag on the lower atmosphere and (2) the introduction of time-variable irradiation patterns due to, specifically, orbits around binary star systems. I have used the first code update to study the effects of a surface on atmospheric circulation in the size regime between that of Earth and Neptune (3.88 R⊕) to identify key observational differences between planets with and without a surface near the expected transition from terrestrial to gaseous planets. Under the assumptions that a planet near 1.5 R⊕ is equally likely to be terrestrial and gaseous, Chapter IV presents models of multiple classes of planets, ranging from those with a shallow surface above both atmospheric photospheres to those with no surface and a high pressure bottom model boundary. With the launch of JWST expected in 2021, we hope to apply the results of this work in the characterization of planets between that of Earth and Neptune. JWST will be extremely well suited to eclipse mapping, allowing us to resolve the latitudinal dependence of emission from the planet and place constraints on the efficiency of heat transport, and therefore the likelihood of the presence of a surface.

144 The second code update, time varying irradiation patterns, was used to study the eﬀects of such a pattern on the atmospheric circulation for planets orbiting a binary star system. As of the writing of Chapter V, there were approximately a dozen detected planets in such an orbit, all approximately Neptune-sized. In this chapter, I presented 1D and 3D models of their atmospheres to study how they evolved over the course of many orbits. This work concludes that for these planets, the eﬀects of the time varying irradiation are largely unimportant to the global circulation patterns with negligible changes in winds and temperatures due to the radiative timescales of their atmospheres being longer than the timescales over which the irradiation pattern varies.

6.2 Future Directions

Until recently, we had little data on few exoplanets. Today, we are rapidly gathering significantly more and better data on many exoplanets. At this rate, we will soon have the capabilities of obtaining all too much data1 on all too many exoplanets2, making it harder to fully characterize and deeply understand each and every target. With this in mind, the field is moving towards global population studies and developing frameworks to describe trends in atmospheric properties. Crossfield & Kreidberg (2017) and Fu et al. (2017) are two examples of first efforts to develop characterization schemes in the era of “too much data”. Moving forward, studies like this will be key to predicting the best targets for exoplanet observations in order to maximum telescope productivity. For example, Kempton et al. (2018) provides an example of classification schemes for target selection in the era of JWST, focusing on signal to noise and expected thermal emission. As we move forward and work towards tying all observations of all planets together, these predictive schemes will include information about cloudiness and metallicities, for example, to help us understand which planets are best suited for detailed

1Though, can we ever have too much data? 2And there’s no such thing as too many planets!

145 follow up. Even with the approaching launch of JWST, ground based observations of exoplanets will remain incredibly important. While JWST’s precision will be unparalleled, its strengths will not extend into the bluest optical wavebands, regions which are critical to a full and detailed spectroscopic characterization of exoplanet atmospheres. Optical transmission spectroscopy, as discussed in Chapters II and III, gives us insights into the scattering properties of the planet’s atmosphere, and when combined with longer wavelength data, allows us to constrain absolute abundances of the constituents of the atmosphere (Benneke & Seager, 2012). With this in mind, the combination of data from optical to near-ultraviolet ground-based observatories and that from JWST is key to the advancement of characterization schemes for exoplanet atmospheres. The classification of exoplanet atmospheres requires not only broad wavelength coverage, but a wide range of planetary types studied. If we limit our focus to only the easiest to observe Hot Jupiters, we cannot hope to gain an understanding of the atmospheres of smaller, cooler, planets as well. And yet many ground based surveys do primarily target these easy to observe Hot Jupiters, resulting in a narrow understanding of the diversity of exoplanet atmospheres. With MOPSS, I am focusing on lower mass, inflated planets with a goal of extending our database of planets to a different class of targets. Still, most efforts to-date focus on gaseous planets due to the inherent difficulty of targeting terrestrial planets with, by nature, thin atmospheres. I have above touched on the limitations of JWST for gaseous planets at short wavelengths, but it is just as important to discuss JWST’s strengths where ground-based observatories reach the limits of their abilities - smaller and/or terrestrial planets. As mentioned above, while the Hubble Space Telescope (HST) required 60 orbits over 15 transit events to characterize the smallest planet attempted to-date (GJ1214b, Kreidberg et al., 2014), JWST will be be able to characterize temperate Earth-sized planets in only 10 transit events (Batalha et al., 2018) at a high enough precision to differentiate between atmospheric models and var-

146 ious biosignature gases, perhaps leading to the term “Venus-similar” coming into use. The optical scattering slope is still, however, key to obtaining the absolute abundances of these gases, and so future extremely large telescopes (ELTs) on the ground and their teams, in combination with the currently 10-meter class observatories and teams must work together to coordinate optical observations of any terrestrial JWST targets to further help classification efforts. It is my hope that, within the time frame of my career, we develop a full and robust multi- dimensional “Hertzsprung-Russell style” diagram for exoplanet atmospheres in the style of Crossfield & Kreidberg (2017), over more planetary types and adding in the constraining optical data contributed through ground based surveys. While we do not yet know what the key parameters that will describe a planet’s atmosphere will be, we can begin to make guesses from the limited complete data sets we have. Naturally temperature has already been shown to point to something about cloudiness (i.e. where and what clouds form), while rotation rate plays heavily into circulation patterns as directly observed and modeled (i.e. offset hotspots on tidally locked planets). Any such diagram for exoplanets will likely contain many more parameters than those for stars owing to the assumed complexity and “messiness” of planet formation. Presumably there are many other relationships we will discover relating to spectral features such as the heavily studied 1.4 µm water absorption line, perhaps even relations giving insights into planetary formation models. My observational work will contribute in a direct way to the data sets used for the development of such models, while my theory work will contribute to further developing and learning from observational methods and allow the identification of key trends themselves. Only once a robust classification scheme exists will we be able to say that we “understand” the diversity of the atmospheres of exoplanetary bodies.

And yet, even then, there is always more to learn. And so I, and I hope many more with me, will continue looking up...

...and cursing Earth’s atmosphere for always getting in the way.

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