From Brown Dwarfs to Super-Earths: an Observational Study of Weather and Atmospheric Composition

UNIVERSITY OF EXETER

From Brown Dwarfs to Super-Earths: An Observational Study of Weather and Atmospheric Composition

Submitted by Paul Anthony Wilson

to the University of Exeter as a thesis for the degree of Doctor of Philosophy in May 2014

This thesis is available for Library use on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement.

I certify that all material in this thesis which is not my own work has been identiﬁed and that no material has previously been submitted and approved for the award of a degree by this or any other University.

Signature:

Abstract

This PhD thesis presents work on the atmospheres of both brown dwarfs and exoplanets from an observers viewpoint. The composition and weather of these worlds are explored starting with M-type brown dwarfs and continuing through the L, T and Y spectral sequence, before entering the planetary regime of hot- Jupiters and super-Earths. The similarities and differences between these objects such as their radii, surface gravities, pressures, temperatures and composition are discussed. This thesis presents new results from an extensive near-infrared monitoring survey of a uniform and unbiased sample of 69 L & T dwarfs spanning the L0 to T8 spectral range. Results show that amongst 14 identified variables, nine of them newly identified, variable brown dwarfs are not concentrated at the L - T transition, nor are they observed in a specific colour, or preferentially in binary systems. The thesis also presents narrow-band photometric measurements of the hot-Jupiter HAT-P-1b and the super-Earth GJ 1214b using the 10.4 m Gran Tele- scopio Canarias (GTC) and the OSIRIS instrument. Results for HAT-P-1b show a strong presence of potassium in the atmosphere caused by a large scale height, possibly due to higher than anticipated temperatures in the upper atmosphere or the dissociation of molecular hydrogen caused by the UV flux from the host star. Results for GJ 1214b, which constitute the first tunable filter measurements of a super-Earth, find no evidence for the presence of methane showing a featureless transmission spectrum consistent with previous studies.

Acknowledgements

I still remember those cold winter nights sat outside my childhood house in Norway, staring at the night sky with the small telescope my father bought me in London. There was something magical about seeing Jupiter, Saturn and the countless other objects with my own eyes. Unlike the photographs in the books I had gotten from the local library or seen in the astronomy magazines, this was the real thing, the photons my eyes where collecting came directly from these celestial objects.

It was my father, Anthony Berry Wilson, who discovered my interest for what it was and who helped me with my education. It is because of his encouragement and motivation in allowing me to pursue my love for astronomy that I undoubtedly owe the biggest thank you. I am also indebted to my friends and my family for their love and support.

Along my long journey towards this PhD there have been many people which deserve a mention. Dr. Kim Venn for helping me with various applications. My office mates Alex Pettitt, Matt Willson and Hannah Wakeford with whom I have had many interesting conversations, and with whom I have managed to take so much of their productive time away from. My girlfriend at the time, Hollie Swain, for her understanding and support. Luke Smith for asking how my day has been and for bringing me coffee in the morning, accompanied by music. Francesca Booker for supporting me though the final stages of my PhD and for supporting me in her own unique way. Nathan Mayne, for being a great friend, mentor, make shift psychologist, advice machine and unofficial third supervisor. Abhijith Rajan and Prof. Jenny Patience for their fruitful collaboration and feedback on my work on brown dwarfs. Prof. FrédéricPont for his supervision throughout the bulk of my PhD and for his support and humor. My internal and external assessors Dr. Sean Matt and Prof. David Pinfield for testing my knowledge during the viva. Last but not least, I would like to thank my supervisor, Dr. David K. Sing, for supervising me through the latter part of my PhD, for taking me on as a PhD student and for being an excellent collaborator and colleague.

This research has beneﬁted from the economic support of STFC and the free and open software provided by the Python communities and the developers of Ubuntu and all you other people contributing to various forums on the internet. You know who you are.

“The sun, with all those planets revolving around it and dependent on it, can still ripen a bunch of grapes as if it had nothing else in the universe to do.”

– Galileo Galilei

Contents

Abstract ii

Acknowledgements iv

List of Figures xii

List of Tables xvi

Declaration of Authorship xviii

Abbreviations xx

Physical Constants xxii

1 Introduction1 1.1 Brown Dwarfs...... 1 1.1.1 Deﬁnition...... 1 1.1.2 Detection Techniques...... 2 1.1.3 Brown Dwarf formation and evolution...... 3 1.1.4 Characterising BD Atmospheres...... 6 1.1.4.1 Spectral features of L,T and Y dwarfs...... 6 1.1.4.2 Chemistry and Composition...... 10 1.1.4.3 Variability at the L-T transition...... 14 1.2 The Exoplanet-Brown Dwarf Connection...... 17 1.2.1 The Shared Parameter Space...... 17 1.2.1.1 Comparison of mass...... 17 1.2.1.2 Comparison of radii...... 17 1.2.1.3 Comparison of surface gravities and pressures... 18 1.2.1.4 Comparison of temperatures...... 21 1.2.1.5 Comparison of composition...... 24 1.3 Exoplanets...... 27 1.3.1 A brief overview...... 27

viii Contents ix

1.3.2 Detection techniques...... 27 1.3.2.1 Direct imaging...... 29 1.3.2.2 The Transit Method...... 30 1.3.3 Exoplanet formation and evolution...... 36 1.3.3.1 Formation via disk instability...... 36 1.3.3.2 Core accretion model...... 37 1.3.3.3 Planet-disk interaction and migration...... 38 1.3.3.4 Inflated radii of extrasolar giant planets...... 40 1.3.3.5 Compact radii of extrasolar giant planets...... 42 1.3.4 Characterising Exoplanet Atmospheres...... 45 1.3.4.1 Transmission Spectroscopy...... 45 1.3.4.2 The Transmission Spectrum...... 48 1.3.4.3 The effects of temperature on ...... 50 R 1.3.4.4 The effects of changes in abundance on ..... 51 R 1.3.4.5 The effects of mean molecular weight on .... 52 R 1.3.5 The Impacts of Stellar activity...... 54 1.3.6 Thermal inversions...... 54 1.3.7 Clouds and Hazes in Exoplanet Atmospheres...... 57 1.3.7.1 Cloud models...... 58

2 Observations & Data Reduction 61 2.1 Observations in the optical...... 61 2.1.1 The night sky in the optical...... 61 2.1.2 Reducing optical imaging data...... 62 2.1.3 Narrowband Spectrophotometry using tunable ﬁlters.... 63 2.1.4 The Fabry-P´erotInterferometer...... 63 2.2 Observations in the near-IR...... 66 2.2.1 The near-IR sky...... 66 2.2.2 Reducing near-IR imaging data...... 67 2.2.3 High precision near-IR photometric monitoring of brown dwarfs...... 69 2.3 Sources of noise...... 71 2.3.1 Detector noise...... 71 2.3.2 Shot noise...... 72 2.3.3 The Signal-to-noise ratio...... 72 2.3.4 Systematic noise...... 74

3 Weather in the atmospheres of Brown Dwarfs 75 3.1 The brown dwarf atmosphere monitoring (BAM) project. I. The largest near-IR monitoring survey of L and T dwarfs...... 75 3.1.1 Abstract...... 75 3.1.2 Introduction...... 76 3.1.3 The BAM sample...... 79 3.1.4 Observations...... 81 3.1.5 Data Reduction and Photometry...... 84 Contents x

3.1.5.1 Processing the images...... 84 3.1.5.2 Generating the light curves...... 87 3.1.5.3 Identifying variables...... 91 3.1.6 Results of the BAM survey...... 92 3.1.6.1 Comparison of variables with previous studies... 95 3.1.6.2 BAM Variables...... 96 3.1.6.3 Variables in previous studies not conﬁrmed with BAM...... 97 3.1.7 Discussion...... 97 3.1.7.1 The sensitivity of the BAM survey...... 97 3.1.7.2 Frequency and amplitude of variability across spectral types...... 102 3.1.7.3 Variability as a function of colour within a spectral type...... 105 3.1.7.4 Binarity and variability...... 105 3.1.7.5 Persistence of variability...... 106 3.2 Summary...... 107 3.3 Developments since publication...... 108 3.3.1 Follow-up observations at the NOT and NTT...... 112

4 The Atmospheres of Exoplanets 115 4.1 Detection of potassium in HAT-P-1b from narrowband spectrophotometry...... 115 4.1.1 Disclaimer...... 115 4.1.2 Abstract...... 115 4.1.3 Introduction...... 116 4.1.4 Observations...... 117 4.1.4.1 Instrumental setup...... 118 4.1.4.2 Observing log...... 118 4.1.5 Reductions...... 119 4.1.6 Analysis...... 119 4.1.6.1 Light curve fits...... 119 4.1.6.2 Noise Estimate...... 124 4.1.7 Results and Discussion...... 124 4.1.7.1 The detection of potassium...... 124 4.1.7.2 The effects of temperature...... 124 4.1.7.3 The effects of potassium abundance and mean molecular weight...... 127 4.1.7.4 The effects of resolution...... 129 4.1.7.5 The effects of stellar variability...... 130 4.1.7.6 The effects of systematics...... 130 4.2 Conclusions...... 131 4.3 A Search for Methane in the Atmosphere of GJ 1214b via GTC Narrow-Band Transmission Spectrophotometry...... 133 4.3.1 Abstract...... 133 Contents xi

4.3.2 Introduction...... 133 4.3.3 Observations...... 135 4.3.3.1 8100 A˚ Transit, 17 August 2010...... 136 4.3.3.2 8550 A˚ Transit, 2 June 2010...... 137 4.3.3.3 8770 and 8835 A˚ Transit, 28 August 2010..... 137 4.3.3.4 8770 and 8835 A˚ Transit, 10 June 2011...... 138 4.3.3.5 8784.5 and 8849.6 A˚ Transit, 21 July 2010..... 139 4.3.4 Data Reduction...... 140 4.3.5 Analysis...... 141 4.3.5.1 Light curve ﬁts...... 141 4.3.5.2 The eﬀects of Earth’s Atmosphere...... 147 4.3.5.3 The presence of sky lines...... 147 4.3.5.4 Noise Estimate...... 149 4.3.6 Results and Discussion...... 150 4.3.6.1 Variability due to Stellar Activity...... 153 4.3.6.2 The impact of the observed wavelength drifts... 154 4.3.6.3 Probing the methane feature...... 156 4.3.6.4 Atmosphere models...... 158 4.3.7 Conclusions...... 159 4.3.8 Appendix: Short baselines and the radius ratio uncertainty. 160 4.4 Developments since publication...... 162

5 Conclusions 163

A Markov Chain Monte Carlo 165

B p -value 167 B.1 Deﬁnition...... 167 B.2 Calculating the p -value...... 167

Bibliography 169 List of Figures

1.1 Eﬀective temperature vs age for objects with masses ranging from 1 MJup to 2.0 M ...... 5

1.2 The spectral standards VB 10 (M8), 2M0423 (T0) and 2M0415 (T8) shown with various different atomic and molecular bands...... 7 1.3 Pressure-temperature profiles of model atmospheres...... 12 1.4 Absolute MKO J magnitude as a function of J K colour and absolute MKO J magnitude as a function of spectral− type...... 15 1.5 Mass - Radius diagram showing the parameter space of stars, field BDs, young BDs and planets...... 19

1.6 Teﬀ & Teq Vs. log(g)...... 20 1.7 Brightness temperature at Ks wavelengths as a function of dayside equilibrium temperature...... 23

1.8 Planetary mass (log(MJup)) as a function of semi-major axis..... 29 1.9 The impact parameter b...... 31 1.10 Star-planet impact parameter geometry...... 31 1.11 Star-planet impact parameter geometry...... 32 1.12 Limb darkening geometry...... 33 1.13 Light curves with different limb darkening coefficients...... 34 1.14 Light curves with different inclination values...... 35 1.15 Planetary radii as a function of incident flux...... 43

1.16 Radius evolution tracks of a 4 MJup object, representative of CoRoT- 20b...... 44 1.17 The transit light curve...... 46 1.18 Vmag as a function of the atmospheric signal required to detect an atmospheric features 1 scale height in size...... 47 1.19 Potassium line profiles showing the effects of temperature...... 50 1.20 Potassium line profile showing the effects of abundance...... 51

1.21 Potassium line proﬁle shown for various mu...... 52 1.22 The diﬀerence in transmission spectra with TiO/VO and without for a 1500 K isothermal, hydrostatic and uniform abundance model. 55

2.1 A wavelength and flux calibrated sky spectrum (black line) showing prominent emission lines together with broadband filter throughput curves...... 62 2.2 The optical path of the Fabry-Pérotinterferometer...... 64 2.3 Fabry-Pérot fringe profile...... 66

xii List of Figures xiii

2.4 The near-IR sky transmission spectrum shown together with broadband filter throughput curves...... 67 2.5 A wavelength and flux calibrated sky spectrum (black line) showing prominent emission lines together with broadband filter throughput curves...... 68 2.6 A frame from the special flat sequence...... 69 2.7 A raw SofI nodding image of a crowded field...... 70

3.1 Colour-magnitude diagram of the M-L-T spectrum...... 80 3.2 Histogram of the BAM sample across their respective spectral classes and the correspondin colour-colour diagram...... 80 3.3 Target photometric uncertainty of the BAM survey...... 88 3.4 p-value histogram of the full brown dwarf sample...... 89 3.5 Final target light curves of the 14 variable objects...... 93 3.6 Final target light curves of the candidate variables...... 94 3.7 Final target light curves of a subset of constant objects in this survey with the master reference light curves...... 94 3.8 Proportion of the survey sensitive to variability as a function of peak-to-trough amplitudes for diﬀerent detection thresholds..... 100 3.9 Variability frequency as a function of amplitude...... 101 3.10 Percentage of simulated sinusoidal light curves detected as variable, as a function of period from 1 hour to 12 hours, for three diﬀerent amplitudes...... 101 3.11 Amplitude of the BAM variables and the target photometric uncertainty of the non-varying objects (coloured triangles) across the entire spectral range of the sample...... 103 3.12 Histogram of the BAM sample across their respective spectral classes.110 3.13 Histogram of the Radigan et al.(2014) sample across their respective spectral classes...... 110 3.14 2M1010-04 observations with the NOT...... 112 3.15 2M1010-04 observations with the NTT...... 113

4.1 The 6797.2A˚ HAT-P-1b light curve...... 121 4.2 Light curves probing the potassium feature of HAT-P-1b...... 122 4.3 Transmission spectrum of HAT-P-1b...... 125 4.4 Best ﬁt potassium line proﬁle to the GTC observations of HAT-P-1b.127 4.5 The HST/STIS G430L transmission spectrum of HAT-P-1b..... 128 4.6 Changes in the planet-to-star radius ratio as function of bin width and resolution...... 129 4.7 A surface plot of GJ 1214 showing an uneven PSF due to a misalignment of the M1 mirror...... 138 4.8 The OSIRIS CCD1 (red) and CCD2 (blue) 500kHz exposure curves showing the linearity of the detector...... 139 4.9 The posterior MCMC distribution showing the relationship between the radius ratio and the slope of the sky term...... 141 4.10 Raw (non-detrended) transit light curves of GJ 1214b...... 142 List of Figures xiv

4.11 GTC OSIRIS narrow band light curves...... 142 4.12 The GTC OSIRIS narrow band light curves at the oﬀ-methane target wavelengths...... 143 4.13 The observed drift in OH sky emission observed during an observing sequence...... 144 4.14 The GTC OSIRIS narrow band light curves...... 148 4.15 Stellar variability of GJ 1214b...... 151 4.16 The combined transmission spectrum of GJ 1214b...... 152 4.17 The drift in wavelengths during each observation together with the changes in seeing and airmass...... 155 4.18 The spectrum of GJ 1214...... 156 4.19 The weighted average of the on-methane and oﬀ-methane radius ratios...... 157 4.20 The uncertainties on the radius ratio determinations...... 161

List of Tables

3.1 L dwarf Sample...... 83 3.2 T dwarf Sample...... 86 3.3 Variables identiﬁed in this study...... 90 3.4 Limits on constant targets in this survey...... 98 3.5 Summary of variable sources...... 99 3.6 Summary of constant sources...... 100 3.7 Variability frequency...... 103 3.8 Summary of Persistence Results...... 107 3.9 Variability frequency from Wilson et al.(2014)...... 111 3.10 Variability frequency from Radigan et al.(2014)...... 111

4.1 Light curve system parameters for HAT-P-1b...... 123 4.2 System parameters for GJ 1214ba...... 146

xvi

Declaration of Authorship

Work presented in 3.1 has been published in the Astronomy & Astrophysics § journal with the title: The brown dwarf atmosphere monitoring (BAM) project. I. The largest near-IR monitoring survey of L and T dwarfs, 2014, A&A, Volume 566, p. 111. I obtained the data, lead the analysis of the work, and wrote the paper in colaboration with Abhi Rajan and Prof. Jenny Patience. I developed the software used in the analysis and was responsible for the analysis and interpetation of the results.

Credit: Wilson, P. A., Rajan, A. & Patience, J., reproduced with permission, c ESO.

Work presented in 4.1 is work in preparation and will be submitted to Monthly § Notices of the Royal Astronomical Society with the title: Detection of potassium in HAT-P-1b from narrowband spectrophotometry. I wrote the paper, performed the analysis and intepretation of the data under the supervision of Prof. Fr´ed´eric Pont and Dr. David Sing.

Credit: Wilson, P. A., Sing, D. K., Nikolov, N., Pont, F., Fortney, J. J., Ballester, G. E., L´opez-Morales, M., Vidal-Madjar, A., D´esert,J.-M. and Lecavelier des Etangs, A.

Work presented in 4.3 has been published in published in Monthly Notices of § the Royal Astronomical Society with the title: A search for methane in the atmosphere of GJ 1214b via GTC narrow-band transmission spectrophotometry, 2014, MNRAS, Volume 438, Issue 3, p. 2395-2405. I wrote the paper, performed the analysis and intepretation of the data under the supervision of Dr. David Sing. Parts of the data reduction was done in collaboration with Col´on,K. D.

Credit: Wilson, P. A., Colón,K. D., Sing, D. K., Ballester, G. E., Désert,J.-M., Ehrenreich, D., Ford, E. B., Fortney, J. J., Lecavelier des Etangs, A., López- Morales, M., Morley, C. V., Pettitt, A. R., Pont, F., Vidal-Madjar, A.

xviii

Abbreviations

ADU Analogue to Digital Unit AU Astronomical Unit BAM Brown dwarf Atmosphere Monitoring BD Brown Dwarf CNO Carbon Nitrogen Oxygen CTIO Cerro Tololo Inter-American Observatory CMD Colour Magnitude Diagram DIT Detector Integration Time E-ELT European Extremely Large Telescope EGP Extrasolar Giant Planet GTC Gran Telescopio Canarias HST Hubble Space Telescope IMF Iitial Mass Function IR Infra Red JWST James Webb Space Telescope MCMC Markov Chain Monte Carlo MKO Mauna Kea Observatories NDIT Number of Detector Integration Times NGTS Next-Generation Transit Survey NOT Nordic Optical Telescope NTT New Technology Telescope OSIRIS Optical System for Imaging and low-Intermediate-Resolution Integrated Spectroscopy SED Spectral Energy Distribution xx Abbreviations xxi

SofI Son of Isaac TESS Transit Exoplanet Survey Satellite TTV Transit Time Variation Physical Constants

27 Atomic mass unit m = 1.66053892 10− kg u × 23 1 Boltzmann’s Constant k = 1.3807 10− JK− × 34 Planck’s Constant h = 6.6262 10− J s × 8 1 Speed of Light c = 2.997 924 58 10 m s− × 2π5k4 4 2 1 Stefan-Boltzmann Constant σ = 15c2h3 = 5.670 J K− m− s−

xxii

Dedicated to my father, Anthony Berry Wilson, who made my dream of becoming an astronomer possible.

xxiv

Chapter 1

Introduction

1.1 Brown Dwarfs

1.1.1 Deﬁnition

Brown Dwarfs (BDs) are regarded as sub-stellar objects with a mass ranging from

about 73 times that of Jupiter (MJup) down to a few Jupiter masses. The upper mass boundary dividing BDs from stars is well defined and set at the hydrogen burning limit, whereby an object with a central temperature insufficient for sustained hydrogen fusion in its core is considered a BD. Without hydrogen fusion in the core, thermal equilibrium is never reached and the BD steadily cools with time. The boundary between BDs and planets is currently unclear and is still a subject of much debate with no IAU official definition1. Numerous studies have used the deuterium burning limit as a lower BD limit, whereby an object is no longer able to fuse deuterium in its core. For a solar metallicity object, the lower limit for deuterium burning is 13 M (Burrows et al. 2001). The deuterium burning ∼ Jup limit however, is dependant on a number of different factors such as the objects helium abundance, the initial deuterium abundance as well as the metallicity of the object (Spiegel et al. 2011). More importantly there is no robust physical justification for this limit. It has been suggested that the overlapping BD and planet regimes should be distinguished by their formation mechanisms (Chabrier et al. 2014), with planets forming via core accretion in protostellar discs and BDs akin to stars which form in molecular clouds. For the remainder of this thesis,

1http://www.iau.org/public_press/news/release/iau0601/q_answers/ 1 Introduction 2 the formation based distinction will be used to differentiate BD from exoplanets. Differentiating between the two formation scenarios observationally remains a challenge as observations are difficult to constrain. One way of differentiating between the two formation mechanisms is by studying the composition of the object. If the object has formed through disk instabilities it will have a chemical composition similar to the original star forming material, whereas if it formed via core accretion it may be enhanced or depleted in some elements. The limiting factor for spectroscopically differentiating between the two scenarios are spectral resolution and signal to noise which are ultimately governed by the brightness of the object. The high resolution observations are further limited to young self luminous objects with wide enough separations from their host star to allow for spectroscopic observations. Observations of HR 8799C, a 10 M (Marois et al. ∼ Jup 2008) planet, by Konopacky et al.(2013) found an enhanced C/O ratio together with an under abundance of C and O in the atmosphere of HR 8799C compared to its host star. These results favour a core accretion scenario although, as the authors suggest, the results are subject to caveats related to planet migration and chemical evolution history which are unknown. Mean density measurements can also give important clues to the formation history of low mass objects within the exoplanet / BD mass regime. A measured radius which is significantly smaller than what is expected for a near solar metallicity object can indicate an enhanced abundance of heavy elements in favour of the core accretion scenario. The opposite is not necessarily true as a larger than expected radii does not necessarily mean there is an under abundance of heavy materials (Leconte et al. 2009), but could instead be due to a radius inflation which is observed in many hot-Jupiter atmospheres (Bodenheimer et al. 2003; Burrows et al. 2007; Charbonneau et al. 2000). Hot-Jupiters, jovian planets on close orbits to their host star, will be discussed in 1.3. §

1.1.2 Detection Techniques

There are three techniques currently used to discover BDs, which depend on the properties of the BD itself. One of the most straightforward techniques is the direct detection of an object outside the luminosity and eﬀective temperature domain occupied by stars. This is the case for old BDs, but not for young BDs (. 100Myr), who frequently occupy the luminosity and eﬀective temperature domain of the very low-mass stars (VLMS). To successfully distinguish young BDs from a VLMS, it Introduction 3

is necessary to acquire spectra and look for signatures of youth, or to obtain proper motions to confirm the membership to a nearby association and from that infer the age. Obtaining spectra are not only important for finding signatures of youth, but also because by obtaining the spectral type one can constrain the temperature and mass of the object. It is common practice to use both optical colour magnitude diagrams coupled with proper motion measurements for initial identification of possible group members. Wide field photometric and astrometric surveys are commonly used to confirm if the BD candidate is a part of a association or not (e.g. Faherty et al. 2009; Pinfield et al. 2014). In the most ideal case one would obtain spectral signatures of youth coupled with measurements of distance (via parallax), proper motion and radial velocity. Quite often only a subset of the aforementioned properties are required for determining membership. The last technique used in detecting BDs is through dynamical interactions with other objects (e.g. binary systems), where orbital dynamics suggest a mass below the stellar minimum mass.

1.1.3 Brown Dwarf formation and evolution

Stars are formed from molecular clouds which collapse under self gravity, forming cloud cores which eventually become dense enough to trigger sustained hydrogen fusion. Planets on the other hand, form in circumstellar disks, whereby gas ac- cretes onto rocky cores. BDs (both free ﬂoating and companion BDs) do not have a universally accepted formation mechanism. The formation of BDs as scaled down versions of stars (e.g. Elmegreen 1999) and through instabilities in circumstellar disks akin to other stars and planets (e.g. Pickett et al. 2000) are both regarded as viable theories. In the ﬁrst scenario, a BD could form if the star formation process was aborted before the onset of hydrogen burning. One such example is the ejection of a stellar embryo from small newborn multiple systems (Boss 2001; Reipurth & Clarke 2001) which could go on to producing self gravitating objects with masses down to 1 M . For this scenario to happen, the ejection has to ∼ Jup occur on a timescale less than the dynamical timescale of the parent core (on the order of 105 years), and the distance between the embryos has to be a few orders ∼ of magnitude smaller than the parent core.

The hydrogen burning limit could also be avoided without the ejection of a stellar embryo. In the presence of a forming stellar cluster, BDs could form out of the Introduction 4

ﬁlaments in the molecular gas which form due to the local self-gravity of the molecular gas and the gravitational potential of the cluster. In this case any subsequent accretion is stopped by the tidal sheer and high velocity dispersion present within the cluster (Bonnell et al. 2008).

In star forming regions, OB stars deplete their surrounding area with their pho- toionizing radiation. Pre-existing protostellar cores in the vicinity of such stars could therefore have their accretion halted by removal of their envelope and surrounding disk (Whitworth & Zinnecker 2004). This is unlikely to be a dominant eﬀect as the initial mass function (IMF) remains largely unchanged even in the presence of O stars (Luhman 2012). Turbulent fragmentation, whereby supersonic turbulence fragments the molecular cloud into dense sheets, ﬁlaments and cores over a wide range of masses, could also lead to the formation of cores small enough to produce BDs (Hennebelle & Chabrier 2008; Padoan & Nordlund 2002).

In the second scenario, whereby BDs form more akin to planets, unstable circumstellar disks of high mass that surround stars can produce low mass companions which are later ejected by dynamical interactions (Bate et al. 2002). Stellar density (Taurus) compared to clusters with higher density (Trapezium) have been shown to have similar BD to star ratios, indicating that dynamical interactions may not be essential in forming BDs (Kroupa & Bouvier 2003).

There are a number of observations which can be used to distinguish between the different formation models such as the shape of the low-mass IMF function (e.g. Chabrier et al. 2014), stellar multiplicity and kinematic distributions (e.g. Joergens 2006a; White & Basri 2003). However, different models often predict similar properties such as a low binary fraction amongst BDs and similar velocity distribution between stars and BDs making it particularly hard to distinguish between the different scenarios and therefore they are still very much a topic of debate.

As BDs age, they cool, releasing the gravitational and internal energy generated during the earliest stages of their evolution. BDs with masses greater than 0.012 M will undergo deuterium burning in their core, however, this phase of the evolution is short lived and typically does not last longer than 20 Myr (Baraﬀe ∼ 2014). The BDs with the highest eﬀective temperatures are both young ( 100 ≤ Myr) and have masses close to the hydrogen burning limit ( 73 M ), which ∼ Jup combined result in a spectral type M6. Following the models of Burrows et al. ∼ Introduction 5

3500 M 0.2 ⊙

M 3000 M 0.1 ⊙

0.075 M 2500

0.05 M ⊙ 2000 0.025 M ⊙ L

1500 0.01 M ⊙

Effective Temperature (K) ⊙ 1000 T 1.0 M Jup 500

10-3 10-2 10-1 100 101

log10 (Age) (Gyr)

Figure 1.1: Eﬀective temperature vs age for objects with masses ranging from 1 MJup to 0.2 M . The horizontal dashed lines represent typical upper and

lower bounds of the M, L and T spectral types. Since BDs are not capable of sustained deuterium fusion, they steadily cool whilst stars, capable of hydrogen fusion, achieve a stable eﬀective temperature. The models are from Burrows et al.(1993).

(1997) and Baraffe et al.(1998) these BDs have an effective temperature 3000 K, ∼ which fall within the temperature regime of older M-dwarf stars. Compared to an M-dwarf star, the young BDs are both lower in mass and also have a larger radius (Gray & Corbally 2009) as they are still contracting to their final radius, roughly the size of Jupiter. As a result, young BDs exhibit a lower surface gravity compared to other BDs. The difference between BDs and M-dwarfs are clearly seen through their evolutionary tracks in Fig 1.1 where stars (top curves) achieve stable nuclear burning (thermal equilibrium) and thus stop cooling. In the case of BDs, only hydrostatic equilibrium is reached with radiation continuously escaping the upper atmosphere (photosphere).

All stars at the substellar boundary together with BDs are thought to be fully convective causing the surface material to be eﬃciently mixed into the core. Since the temperatures required for sustained hydrogen fusion have to be greater than Introduction 6

3 106 K(Nelson et al. 1993) which is only slightly higher than the temperatures ∼ × required to burn Lithium 2 106 K(Pozio 1991), lithium may be used as an ∼ × indicator of hydrogen fusion in the core. Unlike low-mass stars and those BDs with a greater mass which burn lithium during the early stages of their evolution, BDs with masses less than 0.06 M never reach the core temperatures necessary

to burn lithium providing a robust test to distinguish the two objects. Young BDs in open clusters can aid in the determination of the age of the open cluster as well as the BDs themselves as they are assumed to have the same age as the cluster. The presence of lithium as a function of mass allows an age determination to be made of open clusters (where the stars and BDs are young). The boundry where lithium is no longer seen in the spectra (the lithium depletion boundry) depends on the age of the open cluster with the boundry migrating towards lower masses as the cluster age increases (corresponding to later spectral types) (Dobbie et al. 2010; Rebolo et al. 1992).

Another way of distinguishing between low mass stars and BDs is to perform dynamical mass measurements. A BD low-mass star or BD - BD binary pair would be suitable for this sort of measurement. Using astrometric and spectroscopic measurements the dynamical mass of each component can be determined allowing the conﬁrmation of BDs without being bound to any theoretical assumptions other than gravity (Zapatero Osorio et al. 2004). Therefore, low-mass binaries can provide excellent benchmarks with which to test models of ultracool atmospheres and inferred structure.

1.1.4 Characterising BD Atmospheres

1.1.4.1 Spectral features of L,T and Y dwarfs

The spectral energy distribution (SED) of a BD is primarily governed by the eﬀective temperature, which depends mainly on the mass and age of the BD. As the BD cools the peak of the SED steadily moves redwards. For the most part, the SEDs are characterised by large molecular absorption bands. This is seen in Fig. 1.2 where the SED of a M8 dwarf star together with two BDs with spectral type T0 and T8 are shown with the most prominent atomic and molecular features labeled. Introduction 7

2.0 VB 10, M8 (IR) Na I KI H2O 2MASSW J1146345+223053, L6 2 (IR) FeH ± 2MASS J04234858-0414035, T0 (IR) 2MASS J04151954-0935066, T8 (IR) 1.5

TiO VO CO

TiO CH4 1.0 Normalized Flux CH4 0.5

CH4

0.0 1.0 1.5 2.0 2.5 Wavelength (µm)

Figure 1.2: The spectral standards VB 10 (M8), 2M0423 (T0) and 2M0415 (T8) shown with various different atomic and molecular bands. Identification done with the help of figures in (Burgasser et al. 2008, 2004). The spectra are from the SpeX Prism Spectral Libraries maintained by Adam Burgasser (http://pono.ucsd.edu/~adam/browndwarfs/spexprism).

The hallmarks of M-type spectra are the optical signatures of TiO molecular bands with VO bands growing in prominence towards later spectral types. The neutral alkali metals Na I and K I are also prominent. For the later M-types (later than ∼ M6) the formation of dust weakens the molecular line absorption and contributes signiﬁcantly to the overall continuum opacity. The species which start to condense are corundum (Al2O3), perovskite (CaTiO3) and other Al, Ti and Ca bearing molecules, iron (Fe), enstatite (Mg2SiO3) and fosterite (Mg2SiO4)(Burrows & Liebert 1993; Jones & Tsuji 1997; Lodders & Fegley 2002; Tsuji 2002) with the latter two molecules typically condensing at the transition between M-type and L-type brown dwarfs.

The spectra of early L-type BDs are similar to older low-mass dwarf stars with a SED rich in atomic and molecular bands. The strong features caused by TiO and VO disappear whilst the neutral alkali lines such as Na I, K I persist together with Introduction 8

the much less abundant Rb I and Cs I lines and occasional Li I for the younger L’s as well as the hydride bands CrH, FeH and CaOH (Kirkpatrick et al. 1991; Lodders & Fegley 2002). The early L-type objects mark the changeover from CO

to CH4 as the main carbon bearing molecule, whilst the oxides are converted to hydrides with the alkali lines increasing in strength with the Na I and K I line wings dominating much of the optical spectrum. It is only for the latest L-types that the hydrides loose their strength with water features starting to increase in strength. Hot-Jupiter exoplanets have similar temperatures and many of the atmospheric signatures seen in L-dwarfs are also seen in exoplanets e.g.: Na I

and K I (Charbonneau et al. 2002; Jensen et al. 2011; Sing et al. 2011) and H2O (Knutson 2007). The similarities and diﬀerences between BDs and exoplanets are discussed in more detail in 1.2. § Moving into the domain of the early T-type BDs, a further deepening of the water bands is observed with the introduction of CH4 absorption. By the end of the T- type sequence, water and CH4 molecules completely dominate the spectrum giving the late T-types their characteristic three peaked shape in the near-IR.

The subclasses associated with Y-type dwarfs have not yet been well defined. From the spectra obtained thus far, Y-dwarf spectra inherit many of the same traits as the late T-dwarfs. The emergence of ammonia features have been proposed as a trigger for Y-dwarfs, which are expected to belong to the temperature regime T eff ≤ 500 (Cushing et al. 2011; Lucas et al. 2010). Tentative detections of ammonia have been seen in high resolution spectra of Y-dwarfs although more observations are required to confirm the detection (Burrows et al. 2003; Cushing et al. 2011).

As Y-dwarfs emit most of their flux at mid-IR wavelengths, the classification of the Y-dwarf subclasses will likely occur when this wavelength range is more readily accessible. Mid-IR observations from the ground are hard due to the interfering heat flux from Earth’s atmosphere and currently there are no spaced based missions capable of mid-IR observations. The mid-IR capabilities of the James Webb Space Telescope (JWST) will be suitable for the continued development of a Y-dwarf classification scheme (Cushing et al. 2011).

In summary, M-dwarfs are characterised by their strong TiO absorption bands. L-dwarfs are deﬁned by the metallic oxides (e.g. TiO/VO) being replaced by metallic hydrides (CrH,FeH and CaOH) and neutral alkali metals (e.g. Na I, K

I). T-dwarfs are deﬁned by the onset of CH4 absorption and show deeper H2O Introduction 9

absorption bands. The Y-dwarfs discovered to date have similar SEDs to T-

dwarfs, but show tentative signatures of NH3 absorption bands which might very well deﬁne this class of objects. No universally accepted classiﬁcation scheme for Y-dwarfs currently exists. Introduction 10

1.1.4.2 Chemistry and Composition

The observed spectra described in the previous subsection, are dependant on the elemental composition and how these elements chemically react under different temperatures and pressures. BDs provide the ideal environment for the emergence and dissipation of condensate clouds, which govern the atmospheric chemistry and dominate their emergent spectra. The presence of clouds can have profound effects on the opacity of the atmosphere as well as alter the pressure-temperature profile and albedo.

Clouds form through the condensation of condensible species present in the atmosphere. The efficiency of this process will depend on the nucleation process, which is the first stage of cloud formation allowing condensation to take place. There are two nucleation processes which occur in the atmospheres of BDs. The first, homogeneous nucleation, occurs when the partial pressure of a certain species in its gas phase exceeds its saturation vapour pressure. The condensation happens as a result of chance collisions between the molecules of the super saturated vapour, and is favoured when the concentration of condensation nuclei is low. An example of a homogeneously nucleating species is iron, one of the most refractory2 elements present in the atmospheres of early-L type BDs. The second nucleation process is heterogeneous (or chemical) nucleation which occurs when nuclei are formed on pre-existing surfaces (different from the condensing species) which lowers the level of supersaturation required for nucleation to begin. Heterogeneous nucleation occurs when the partial pressure of a certain species in its gas phase exceeds its heterogeneous condensation pressure (instead of its saturation vapour pressure). Examples of heterogeneous nucleation from Earth include the formation of water clouds which occur as the result of condensation of water gas into water droplets via the nucleation of dust, sea salt and pollen suspended in the atmosphere (Marley et al. 2013).

The atmospheres of L-dwarfs consists of hot dust grains of iron, silicates (solids containing Si-O groups) and oxides (at least one oxygen atom and one other element). These refractory condensates initially form at temperatures below T eﬀ ∼ 3000 K in the atmospheres of M-dwarfs. The newly formed dust condensates present in the photosphere, absorbs the heat coming form the interior of the BD, causing the temperature to rise and the dust to sublimate. This processes repeats

2Highest equilibrium temperatures (opposite of volatile). Introduction 11

itself until Teﬀ < 2800 K at which point chemical equilibrium is reached (Tsuji et al. 1996). The dust cloud layer which forms remains optically thin until the

M-dwarf photosphere reach temperatures Teff < 2600 K (equivalent to M6 dwarfs Rajpurohit et al. 2013) where the impact of dust clouds on the SEDs become significant (Allard et al. 2013). In a static atmosphere, the formation of dust grains will continue and eventually become too heavy to stay suspended in the photosphere and subsequently they rain out. However, due to the dynamic nature of BDs atmospheres, convection will keep the dust suspended high in the atmosphere at lower temperatures. This suspension of dust results in a greenhouse effect which gives the L-dwarfs their characteristic red colour. The dust in the atmospheres of late-M and L-dwarfs also results in Rayleigh scattering which acts as the dominant opacity source throughout the visible part of the spectrum (Allard et al. 2012).

The efficiency of the dust settling will depend on the Teff and surface gravity of the BDs, and has a direct impact on the emergent flux (see 1.3.7.1 for models which § incorporate this sedimentation efficiency). Inevitably the temperature will become sufficiently low for a transition from a dusty to a clear atmosphere to occur, which occurs at the transition between the L and T spectral types (see 1.1.4.3). § Chemical equilibrium models are used to predict which species are expected to condense out of the atmosphere at a given temperature and pressure. Fig. 1.3 shows a variety of condensation equilibrium curves for species expected to condense in the atmospheres of BDs (dashed lines). These lines show the pressure and temperature conditions necessary for condensation to occur. The solid curves are model atmospheres of various temperatures. Cloudless models are shown in blue, with orange and red curves representing a sedimentation efficiencies of fsed = 4 and 2 respectively. For L-type BDs ( 1300 2200 K, Kirkpatrick et al. 1999; Mart´ın ∼ − et al. 1999), dust clouds of corundum (Al2O3), iron (Fe), fosterite (Mg2SiO4) and enstatite (MgSiO ) dominate. For T-type BDs ( 700 1300 K) a variety of 3 ∼ − condensates are expected to form such as Cr, MnS, Na2S, ZnS and KCl (Morley et al. 2012). These sulfide and salt clouds are expected to condense in mid- to late T-dwarfs, likely resulting in photometric variability (Morley et al. 2014). As a result the first searches for variability for late-type BDs are under way (Rajan et al. 2014).

3 For the coolest BDs known to date , the Y-dwarfs, water (H2O) and ammonia (NH ) are expected to condense. This happens at temperatures of T 350 3 eﬀ ∼ − 3The coldest BD known to date has a temperature of T 250 K (Luhman 2014). eﬀ ∼ Introduction 12

−3

Na MnS

NH KCl ZnS 2 MgSiO S

4 Cr −2 H 2

PO 3

Al 2 400 K SiO −1 2 Fe O

4 3 600 K 900 K 1300 K

0 O log(pressure) (bar) log(pressure)

2 0 500 1000 1500 2000 Temperature (K)

Figure 1.3: Pressure-temperature proﬁles of model atmospheres showing cloudless models (blue) and models with fsed = 4 (orange) and 2 (red). The thicker lines represent the 1–6 µm photosphere. Adopted from (Morley et al. 2012) and used with permission from C. Morley.

375 K for water and T 200 K for ammonia (Morley et al. 2014). eff ∼ Given data on the composition and abundance of various species (often assumed solar), and armed with a chemical equilibrium model such as Burrows & Sharp (1999), the equilibrium composition of the atmosphere can be obtained. This is done by calculating which chemical species are thermodynamically favoured by minimizing the Gibbs free energy of the system (Cooper et al. 2003). Once the chemical species have been determined, their particle size distribution and number densities above the base of the cloud are computed. The methodological approach used in these calculations varies between the model atmospheres and are discussed in more detail in 1.3.7. Regardless of the models used, it is important § the properties of the cloud be taken into account when computing the chemical equilibrium of the atmosphere. This is not only due to the influence of clouds on atmospheric temperature and the emergent flux, but because once a species has condensed, it is no longer available to react at lower temperatures and pressures higher up in the atmosphere (Marley et al. 2013). Introduction 13

As it is the gas in the atmosphere which provides the atoms and molecules needed for the condensation processes to take place, the composition of the gas plays an important role in cloud formation (liquid and solid) and the chemistry of BD atmospheres. At temperatures below 1300 K methane becomes the dominant carbon ∼ bearing molecule rather than CO. This leads to the emergence of the methane clouds, greatly aﬀecting the ﬂux received in the H and K bands (Burgasser et al. 1999; Geballe et al. 2002; Leggett et al. 2000). The conversion between CO and

CH4 proceeds according to the following thermochemical reaction,

CO(g) + 3H2(g) CH4(g) + H2O(g) (1.1) under the assumption of chemical equilibrium. Carbon is preferentially in the form of CO at higher temperatures deep in the BD atmosphere, whereas CH4 is more stable thermodynamically in the upper atmosphere where the temperature is lower (Lodders & Fegley 2002). The convective nature of BD means vertical mixing takes place, which causes an upwelling of CO from the deep atmosphere to the upper atmosphere, as observed in Jupiter (Prinn & Barshay 1977). This causes an overabundance of CO compared to that which equilibrium predicts as the double bond between the carbon and oxygen atoms make the conversion back to CH4 very slow (Fegley & Lodders 1996; Seager 2010). The same sort of chemical disequilibrium happens to molecular nitrogen (N2), which is the preferred state of nitrogen at hotter temperatures and ammonia (NH3), which dominates at lower temperatures. The net thermochemical reaction

N2(g) + 3H2(g) 2NH3(g) (1.2)

proceeds more slowly to the right due to the strong triple bond in N2. Although the eﬀects of disequilibrium chemistry are well known, and despite disequilibrium chemistry being a mature ﬁeld (Barshay & Lewis 1978; Fegley & Prinn 1985; Lod- ders & Fegley 2002), predicting the abundances of various elements and molecules as well as their particle size distribution becomes hard due to the dependence on atmospheric parameters such as temperature and vertical mixing. Introduction 14

1.1.4.3 Variability at the L-T transition

As BDs age, and as a result cool with time, their atmospheres undergo a plethora of physical and chemical changes. Nowhere along the BD spectral sequence are these changes so abrupt as at the L-T transition. The transition itself is marked by a rapid change in near-IR colours from red to blue (J K 2.0 mag) over a narrow − ∼ temperature range (∆T 100 200 K) resulting in a brightening in J-band eﬀ ∼ − ( 1 mag). A colour magnitude diagram (CMD) of BDs at various temperatures ∼ show the colour transition (Fig. 1.4, left) and the J-band brightening (Fig. 1.4, right). L-type BDs (shown as circular points in Fig. 1.4), owe their red colour to the reradiation of heat absorbed by the high opacity of the dust clouds in the upper atmosphere. The T-dwarfs on the other hand (diamond points in Fig. 1.4), have clear atmospheres with the dust having condensed out below the observable photosphere, allowing ﬂux from deeper and hotter layers to emerge which are both bluer and brighter at near-IR colours.

Understanding the causes behind the change from a dusty to a clear atmosphere is one of the outstanding problems of BD evolution. One theory is that the dynamical state of the atmosphere changes due to different sedimentation efficiencies, leading to the sudden disappearance or clearing of condensate clouds (Knapp et al. 2004; Saumon & Marley 2008). Tsuji & Nakajima(2003) using the unified cloudy models of L and T dwarfs, proposed that the blue ward shift in J-K colours and brightening in the J-band was due to the migration of a thin dust cloud from the optically thin (τ < 1) to the optically thick (τ & 1) inner region of the photosphere. Instead of being an evolutionary effect, the J-band brightening could be explained by BDs with varying surface gravities and ages. Observations of flux reversal binaries (binary systems where the later type binary is brighter in J and fainter in H and Ks) has since discounted this theory. Since the flux reversal binaries are presumably formed at the same time, wast differences in ages and surface gravities between the two binaries components can be ruled out. This indicates that the brightening seen between late-L to early T-type objects are an intrinsic property of the objects and not a selection effect (Gelino et al. 2014).

The change from a dusty to a clear atmosphere also induces changes in the observed ﬂux on timescales comparable to the rotation rate of the BD which are likely due to variations in cloud thickness. This breakup in clouds, also referred to as the patchy cloud hypothesis, has been suggested by (Ackerman & Marley 2001; Burgasser Introduction 15

HD 44627b HD 44627b

14 ) g

a 16 m

( 2M1207b 2M1207b

J M

1 0 1 2 3 M6 M8 L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 Y0 Y2 J K (mag) Spectral Type − Figure 1.4: Absolute MKO J magnitude as a function of J K colour (left). − The symbols are representative of BDs with spectral type M (triangles), L (circles), L-T transition L7-T4 (squares), T (diamonds) and Y (crosses). Absolute MKO J magnitude as a function of spectral type (right), showing the J band brightening at T2-T5. The two planet candidates HD 44627b and 2M1207b are labelled highlighting the similarity between BDs and planets by allowing both objects to be placed in the same CMD. The data is a compilation of various studies available at the Database of Ultracool Parallaxes maintained by Trent Dupuy. et al. 2002; Folkes et al. 2007). There is a growing body of evidence supporting the patchy cloud hypothesis from photometric variability studies showing periodic variations possibly caused by partial cloudiness and cloud thickness variations (e.g. Apai et al. 2013; Artigau et al. 2009; Radigan et al. 2012). Observations using Doppler imaging techniques have also shown large-scale features indicative of patchy clouds (Crossﬁeld et al. 2014).

Variability might also be caused by the coupling of clouds to the global atmosphere circulation (Showman & Kaspi 2013; Zhang & Showman 2014), with the variability emerging as a consequence of thermal perturbations emitted from deeper layers within the brown dwarf atmosphere (Robinson & Marley 2014). Introduction 16

Results from a large near-IR photometric monitoring campaign which was aimed at quantitatively determining the level and frequency of variability across a uniform and unbiased sample of 69 ultracool L & T type BDs (Wilson et al. 2014) are presented in 3.1. One of the main results to emerge from this survey was that § the frequency of variables across the L-T transition is indistinguishable from earlier or later spectral types. This may suggest the early onset of cloud condensation of mid-L dwarfs and the emergence of sulﬁde clouds in mid-T dwarfs (Morley et al. 2012). It could also be that the patchy cloud scenario may not be the only source of variability with thermal perturbations being a possible candidate for variability. Introduction 17

1.2 The Exoplanet-Brown Dwarf Connection

1.2.1 The Shared Parameter Space

BDs and hot-Jupiter exoplanets frequently overlap the same parameter space with comparable radii, effective temperatures, composition and surface gravities. Fur- thermore BD and exoplanet observations compliment each other. BDs are generally easier to characterise as they can be observed in isolation (in the absence of a host star) and because they are in most cases more luminous than exoplanets. Exoplanets on the other hand allow us to further extend the probable parameter space, such as to lower pressures. Despite an overlap in several parameter spaces, the two types of objects can differ significantly in detail. Below follows a comparison between some of the most important characteristics between the two types of objects.

1.2.1.1 Comparison of mass

From the discussion of the deﬁnition of a BD in 1.1.1, it is clear that without § a universally accepted deﬁnition, it is to be expected that the mass regimes of low mass BDs and high mass exoplanets will overlap. For isolated BDs, the mass estimates are generally not as accurate (especially if the age is not well constrained) when compared to exoplanets which orbit a host star allowing for dynamical mass measurements to be made. The overlap in mass can bee seen in the mass-radius diagram shown in Fig. 1.5.

1.2.1.2 Comparison of radii

Stars on the main sequence maintain hydrostatic balance when their gravitational potential energy equals two times their thermal energy and be expressed 2 as GM /R (M/mp)kT . As such the radius of a star is proportional to its ∼ nucl mass, R M. This relationship remains constant due to the fusion temperature ∝ of hydrogen at a constant 5 106 K (the exact value depends on density) and ∼ × persists as long as the fusion of hydrogen to helium occurs via the proton-proton chain (as opposed to the CNO cycle). Young BDs, follow a similar mass-radius relationship as stars. This is due to the young BDs having a larger radii as they Introduction 18

are still contracting from their formation, and for those with a greater mass, these might still be burning deuterium.

The gravitational potential energy of BDs are partially supported by electron degeneracy pressure. The Pauli exclusion principle states that two identical fermions (in this case electrons) can not occupy the same quantum state. Therefore when the the lower energy states become occupied, the electrons have to move to higher energy states which contributes to the degeneracy pressure. This temperature independent pressure inhibits the BDs from contracting further. For a fully degenerate object (such as a white dwarf), an equilibrium is reached when the gravitational 2 5/3 2 potential energy, Ep GM /R, is balanced by the kinetic energy, Ek M /R . ∝ ∝ 1/3 This results in a radius which scales with mass as R M − . ∝ BD dwarfs and hot-Jupiters, are however only partially degenerate in their core and Coloumb pressure plays a significant role in the hydrostatic balance. The electron degeneracy is strongest for those BDs with a larger mass, taking on a mass-radius 1/8 1/3 relation of about R M − (less than the fully degenerate case R M − ). For ∝ ∝ objects with a lower mass, the Coloumb pressure (constant density, R M 1/3) ∝ becomes ever more significant. When the Coloumb pressure (R M 1/3) and ∝ 1/3 0 the degeneracy pressure (R M − ) become similar in magnitude (R M ) ∝ ∝ (Burrows et al. 1993; Oppenheimer et al. 2000) a flattening in the mass-radius relation is seen for BDs with a lower mass and hot-Jupiters as shown in Fig. 1.5.

For planetary mass objects Coloumb pressure dominates. Coloumb pressure, which is caused by the electromagnetic repulsion between the electrons of one molecules from those of another is characterised by a constant density. It follows from the constant density (ρ M/R3) that the radius scales as R M 1/3. Neptunian and ∝ ∝ Super-Earths objects ( 0.1 2 M ) are found in this regime. ∼ − Jup

1.2.1.3 Comparison of surface gravities and pressures

A natural consequence of BDs and hot-Jupiters having similar radii and a partial overlap in the mass regime, is that their surface gravities also partially overlap. As the radii are almost constant amongst the two types of objects, the surface gravities depend strongly on mass. The overlap happens between the dense hot- Jupiters of high mass and the young low mass BDs. The surface gravities of BDs and Exoplanets is shown in Fig. 1.6. Hot-Jupiters typically have surface gravities Introduction 19

101

Young BDs

Hot-Jupiters Stars ] Jup

R 100 BDs Radius [

Super-Earths

1 10−

2 1 0 1 2 3 10− 10− 10 10 10 10 Mass [MJup]

Figure 1.5: Mass - Radius diagram showing the parameter space of stars (red star shaped markers) with data from Ségransanet al.(2003), field BDs (purple) and young BDs (orange) from the BD lists maintained by Wm. Robert Johnston and planets (open circles) with data from exoplanets.org. HAT-P-1b featured in 4.1 is shown amongst the hot-Jupiters (blue), whilst GJ 1214b is shown § amongst the super-Earths (green). in the range 10 30 m/s2 whilst BDs in most cases have a larger mass and thus − commonly have surface gravities 10 100 times greater. Age also has an affect − on surface gravity, with younger objects (. 100 Myrs) having larger radii as they are still contracting from formation. Surface gravities of BDs can be inferred from signs of youth present in their spectra. Weak pressure broadening leading to narrow alkali lines, enhanced metal oxide absorption bands and a triangular peaked spectrum in H-band are all signs of youth (Faherty et al. 2014). These spectroscopic signatures are however dependant on temperature and/or metallicity which results in degeneracies, which only loosely constrain the surface gravity (Rice et al. 2011). Transiting exoplanets on the other hand, have the advantage of accurate radii and mass measurements which allow the surface gravity to be determined directly.

The affect of a larger surface gravity is higher photospheric gas pressures. Thus, in the case where a BD and an exoplanet have similar temperatures, the surface gravity will inevitably affect the temperature-pressure structure of the atmosphere. This has a direct effect on which species condense out of the atmosphere due to the resulting changes in partial pressure. The photospheric pressure can also directly Introduction 20

4000 C69-Sub-003 Kepler-20 f 3500 LOri-SOC 11 CoRoT-27 b LOri-SOC 13 Kepler-39 b 3000 CoRoT-3 b

(K) 2500 eq T 2000 & eﬀ

T 1500

1000

500

102 103 104 105 106 log(g) (cgs)

Figure 1.6: Teﬀ (for BDs) & Teq (for Exoplanets) Vs. log(g). A number of BDs (purple pentagons) and exoplanets (blue circles) have overlapping surface gravities although BDs usually have higher surface gravities, a result of larger masses with radii similar to most hot-Jupiters. The BD data is from lists maintained by Wm. Robert Johnston whilst the exoplanet data is from exoplanets.org

aﬀect the opacity of the atmosphere such as the width of the alkali lines through pressure broadening. Changes in pressure alter chemical reaction rates and lead

to non-equilibrium eﬀects such as the interplay between CO and CH4 (described in the section on chemistry and composition, 1.1.4.2). At the high temperatures § and pressures present deep in the atmosphere, chemical reactions proceed faster, increasing the likelihood of reaching chemical equilibrium. However, as material is dredged up to parts of the atmosphere where the temperatures and pressures are lower, the timescale for chemical equilibrium, τchem, becomes longer than the

vertical mixing timescale, τmix, which leads to disequilibrium chemistry. The mix-

ing timescale τmix at the radiative layer in the atmospheres of BDs and exoplanets 2 is given as τ H /KE, where H is the scale height (defined in 1.3.4.1) and mix ∼ § KE is the eddy diffusion coefficient. For the convective zone of the atmosphere Introduction 21

τ H/vc, where vc is the convective velocity. In either case τ is dependant mix ∼ mix on the pressure scale height H, which varies with surface gravity which is linked directly to the pressure as P g/κ, where κ is the Rossland mean opacity. As ∝ such, the atmospheric pressure can also directly aﬀect the equilibrium chemistry, despite similar atmospheric temperatures and composition.

1.2.1.4 Comparison of temperatures

The atmospheric temperatures of both BDs and planets govern the chemical equilibrium of the atmosphere which directly affects the SED’s and is thus one of the most important parameters when characterising their atmospheres. The heat present in BDs atmospheres comes from their interiors whilst hot-Jupiters are also heated from above by their host star. Thus when comparing temperatures it is important to consider which sort of measure of temperature is discussed. The effective temperature, Teff , is the temperature of a blackbody which radiates the same total flux as the emitting object, in this case a BD or an exoplanet. It describes the global temperature of the object at the altitude where the bulk of the radiation leaves the object and is generally regarded as the temperature of the photosphere. This quantity can be determined for BDs either by fitting theoretical spectra to observed spectra or by bolometric luminosity (L ) measurements. For ∗ field-age L and T type BDs, their radii (R ) are fairly constant allowing a Teff ∗ estimate to be made using the Stefan-Boltzmann law,

2 4 L = 4πR σTeff (1.3) ∗ ∗ where σ is the Stefan-Boltzmann constant. This can be done providing the bolometric luminosity is known. Hot-Jupiters are dominated by radiation from their host star. As such, no internal luminosity can be measured and since spectra most often are of low resolution and low signal to noise, measuring the Teff becomes very difficult. The exception to this are the directly imaged planets, where much higher resolution spectra are obtainable allowing Teff to be measured either using theoretical spectra (Lagrange et al. 2009) or atmospheric retrieval techniques

(Lee et al. 2013). For planets, the thermal equilibrium temperature (Teq) is typically calculated instead as a way of estimating Teﬀ . The Teq is never measured directly as it is only a theoretical number. Using the principles of conservation Introduction 22

of energy, whereby energy in the form of incident stellar radiation balances out the energy absorbed by the planetary atmosphere (an isothermal atmosphere) the relationship can be expressed as:

2 4 2 L 4πR σT = (1 AB)πR ∗ (1.4) p eq − p 4πd2

2 where Rp is the radius and AB the bond albedo of the planet and the term L /4πd ∗ is the energy per unit area per unit time at a distance d from the star. Equation 1.4 can be rearranged such that:

1 4 1 (1 AB)L T = − ∗ . (1.5) eq 2 πσd2

Substituting Eq. 1.3 into Eq. 1.5 allows Teq to be calculated given the effective temperature of the host star, Teff . As it is only possible to observe one hemisphere at a time and since the stellar radiation is not uniformly distributed around the planet, such as for tidally locked or slowly rotating exoplanets, a correction factor, f, is used (Seager 2010). The relationship between Teq and Teff is expressed as

1 2 R 1 T = T ∗ [(1 AB)f] 4 (1.6) eq eﬀ d −

where a perfect heat redistribution has f = 1/4 whilst in the case of no advection (no dynamical redistribution of heat) f = 2/3.

Both the Teﬀ and Teq have been measured for all the planets in our solar system and the two temperatures have been found to be constant within 15 K of each ∼ other. This precision is due to the accurate determination of the parameters in Eq. 1.6. For an exoplanet, the calculated equilibrium temperature will largely

depend on how accurate the stellar properties (Teff and R ) are determined. Teff ∗ can be obtained by fitting synthetic model spectra to observations4. R can be ∗ obtained through photometric or spectroscopic measurements with interferome- try giving the most accurate values down to within 1% accuracy (von Braun ∼ et al. 2011). Regardless of the technique used to derive a radius, the distance

4Stellar temperatures can also be obtained by photometric measurements in combination with theoretical colour-temperature relations (VandenBerg & Clem 2003). Introduction 23

3000 WASP-12b (K) B

T WASP-3b WASP-19 2500 CoRoT-1b

= TB HAT-P-1b Teq 2000 WASP-4b OGLE-TR-113b CoRoT-2b WASP-43 TrES-3b

Brightness Temperature, TrES-2b 1500 Ks-band (2.0 - 2.3 µm)

1200 1400 1600 1800 2000 2200 2400 2600 2800 Equilibrium Temperature, Teq (K)

Figure 1.7: Brightness temperature at Ks wavelengths as a function of dayside equilibrium temperature (isotropic reradiation and AB = 0). The dashed red line shows the 1:1 relationship between TB and Teq which corresponds to f = 1/4. TB and Teq are from: HAT-P-1b (de Mooij et al. 2011), OGLE-TR-113b (Snellen & Covino 2007), WASP-43 (Wang et al. 2013), TrES-2b (Croll et al. 2010), CoRoT-2b (Alonso et al. 2010), TrEs-3b (Croll et al. 2010), WASP-4 (C´acereset al. 2011), CoRoT-1b (Rogers et al. 2010), WASP-3b (Zhao et al. 2012), WASP-19 (K-band) (Gibson et al. 2010; Mancini et al. 2013) and WASP- 12 (Cowan et al. 2012).

(via trigonometric parallax) has to be known. The orbital characteristics are required to obtain d and lastly an albedo has to be assumed. Eccentricity eﬀects as well as large day/night temperature contrasts make the equilibrium temperature measurements of exoplanets a poor proxy for the photospheric temperature, and stellar irradiation can lead to the formation of a thermal inversion where the upper atmosphere is much hotter than the equilibrium temperature (see section on thermal inversions, 1.3.6). Not knowing the photospheric temperature leads § to a multitude of possibilities for atmospheric structure as several elements can condense to form clouds.

The only temperature we can measure for exoplanets (without model assumptions) is the brightness temperature, TB. This temperature is defined as the temperature a black body of similar size in thermal equilibrium would have if placed at the same distance away from the star as the exoplanet, and emitting the same flux within a specified wavelength range. Since the atmospheric opacity changes depending on the wavelength probed, it is important to state the wavelength the brightness temperature is measured at. Brightness temperatures have been measured for Introduction 24 several planets both from space and the ground (see Fig. 1.7). Using a 1-D chemical code Venot et al.(2014) demonstrated that the brightness temperature of the sub- Neptune GJ 3470b could vary by a factor 2 at infrared wavelengths depending ∼ on the thermal profile used and the metallicity of the model. An increase in metallicity would increase the opacity, causing secondary eclipse measurements to probe higher in the atmosphere where the temperature is lower, giving a lower brightness temperature. In general a large difference between Teq and TB may suggest a poor energy redistribution.

In the interest of comparing the atmospheric temperatures of exoplanets and BDs, great care must be taken, as temperatures are measured and/or calculated differ- ently. For instance, TB is always greater than Teq, and neither are directly comparable to Teff as the measurements are fundamentally different and in some cases depend on the thermal profile and metallicity which are unknown.

1.2.1.5 Comparison of composition

BDs have the clear observational advantage over exoplanets that they are in most cases not orbiting closely to a host star, often million times brighter at near- IR wavelengths, making observations a challenge. BD spectra can be obtained directly often covering a broader wavelength range and at much higher resolution. It is therefore no surprise that we have more direct detections of various species within their atmospheres. In 1.1.4.2 the chemistry and composition of BDs were § discussed with focus on how it changed primarily as a function of temperature. With exoplanets, especially closely orbiting hot-Jupiter and super-Earths which are tidally locked, the situation can be quite diﬀerent, especially as there are two temperature regimes, a highly irradiated day side, and 400-600 K cooler night side. This causes fast km/s winds (Snellen et al. 2010) which drive atoms and molecules from the dayside to the night side where they are expected to condense out. M- type and L-Type BDs show clear signs of TiO/VO in their spectra (see Fig. 1.2). Although many attempts have been made at detecting TiO/VO expected to be present in exoplanet spectra (Fortney et al. 2010), no clear evidence of TiO/VO has yet been found in exoplanet atmospheres. This strengthens the theory that TiO/VO might condense out on the night side of the planet, or get depleted via a cold trap (see section on thermal inversions, 1.3.6). § Introduction 25

The way in which spectra are obtained, generally diﬀer from BDs and exoplanets, the exception being directly imaged planets on wide orbits, which allow spectra to be obtained directly (see section on direct imaging 1.3.2.1). Transmission spec- § troscopy, a technique used to probe the atmospheres of exoplanets using transits (explained in detail in 1.3.4.1), only probes the composition of the gas at the § planet terminator, where the stellar light ﬁlters through the atmosphere. This occurs at low pressures (mbar to µbars), orders of magnitude lower than the pressures of the photosphere, which is observed when direct spectra of BDs are obtained. As such, the composition is only valid for the gas at the limb of the planet and at low pressures (mbar to µbars).

The atmospheres of hot-Jupiters contain many of the same constituents as BD atmospheres such as Na I (Charbonneau et al. 2002; Redﬁeld et al. 2008), K I

(Sing et al. 2011), CO, CH4 (Swain et al. 2008) and H2O(Grillmair et al. 2008; Wakeford et al. 2013). The consequence of closely orbiting a host star has allowed for the detection of C II, O I (Vidal-Madjar et al. 2004), S III (Linsky et al. 2010) and Mg II (Fossati et al. 2010) in hot-Jupiter atmosphers. Although C, O, S and Mg have all been detected in BD atmospheres, exoplanets have the advantage that they can be studied at ultraviolet wavelengths, which are not possible for BDs as they have no detectable ﬂux at these wavelengths.

Jupiter, Saturn, Uranus and Neptune all have metal5 enriched atmospheres. For example, Jupiter has a 2 4 higher abundance of carbon, oxygen, nitrogen, − × sulphur and various noble gasses (Atreya et al. 2003) compared to solar composition. Saturn has a 10 solar abundance of carbon (Flasar et al. 2005) and ∼ × an enhanced abundance of water and oxygen (Visscher & Fegley 2005). This enhancement of metals is likely the result of the core accretion formation mechanism, whereby the planets formed from within a protoplanetary disk rich in heavy elements. The core accretion model, which will be covered in more detail in 1.3.3.2 § has emerged as the dominant formation mechanism for exoplanets, so it is likely that exoplanets will also possess super solar abundances. BDs on the other hand are expected to have metallicities similar to stars, with the most metal rich BDs having abundances that generally do not exceed 3 5 solar abundances. For BDs − × in the metal poor thick disk and halo, their metallicities are expected to extend well below solar metallicites (Burningham et al. 2013; Mace et al. 2013; Pinfield et al. 2014). This difference in metallicities has a profound effect on the chemistry

5Metals in this context means all elements heavier than H and He. Introduction 26 and molecular composition of the atmospheres. Furthermore, the composition of the gas determines which species condense to form clouds. Chemistry and cloud formation has previously been discussed in 1.1.4.2. § Introduction 27

1.3 Exoplanets

1.3.1 A brief overview

”There are inﬁnite worlds both like and unlike this world of ours. For the atoms being inﬁnite in number are borne on far out into space.” – Epicurus, 341 - 270 BC

An exoplanet is any planet which is not in our solar system. The prefix ”exo” originates from Greek and translates into ”outside”. Although exoplanets were thought to exist in ancient times, it was not until 1992 when the first confirmed discovery of an exoplanet, was made by Wolszczan & Frail(1992). They discovered two planets which orbited a 6.2 ms pulsar 500 pc away by studying timing ∼ variations using the biggest telescope in the world, the 305 m Arecibo radio telescope. The subsequent discoveries of exoplanets, notably the first detection of an exoplanet around a sun like star (Mayor & Queloz 1995), the first detection of a transiting planet (Charbonneau et al. 2000) and an exoplanet atmosphere (Charbonneau et al. 2002), used a range of techniques which will be described in more detail below. Thanks to a number of exoplanet surveys aimed at detecting exoplanets, and the subsequent follow-up studies aimed at characterising them, the first few steps to understanding these new worlds have been made. With exoplanets known to outnumber stars (Cassan et al. 2012), and with new pow- erful telescopes and instruments on their way (e.g., JWST, E-ELT) the future of exoplanet research has an exciting future ahead.

1.3.2 Detection techniques

When it comes to detecting exoplanets, there are several techniques available at the disposal of the exoplanet hunter. Each technique, quite often sensitive to diﬀerent types of planets, is brieﬂy summarised below and shown in Fig. 1.8. Amongst these techniques the direct imaging and observations of transiting exoplanets have had the greatest impact on atmosphere characterisation and as such these methods will be discussed in more detail in the subsections below.

The main techniques used to detect exoplanets are: Introduction 28

Direct imaging: The exoplanet is imaged directly using large telescopes ﬁtted with adaptive optics and coronagraphs. The technique is most sensitive to the warmer, bright (young) and massive exoplanets on wide and/or eccentric orbits (large sky projected separations, e.g. Marois et al. 2008). The separation from the host star allows for spectra to be obtained directly and allows for the direct measurement of the luminosity.

Radial velocity: The exoplanet is detected by measuring the Doppler shift in the host star light, a consequence of the gravitational aﬀects between the two bodies. The technique is most sensitive to exoplanets with a large mass orbiting close to their host star perpendicular to the plane of the sky. The radial velocity technique allows for a minimum mass (dependant on orbital inclination) to be calculated (e.g. Pepe et al. 2011).

Transits: The exoplanet is detected by measuring a periodic decrease in the ﬂux received from the host star, as a consequence of the exoplanet transiting in front of the host star (e.g. Charbonneau et al. 2000). The transiting technique is most sensitive to large exoplanets orbiting close to their host star stars and provides an accurate determination of the planetary radius relative to the host star.

Microlensing: The exoplanet is detected by measuring characteristic light curve changes caused by changes in the lensing eﬀect observed when a star with a planet passes in front of a distant star (e.g. Gaudi 2012). The technique is limited to distant one time events and by the lack of accurate determinations of the planet and orbit parameters. It is however a very valuable technique due to the lack of strong radii or mass biasses making it ideal for statistical population studies.

Transit timing variations: The exoplanet is detected by observing a change in periodic phenomena due to the presence of an exoplanet. Examples include a change in transit time (known as TTV) of one planet, due to the presence of others in multiple planet systems (e.g. Holman et al. 2010) and pulsar timing (e.g. Bailes et al. 2011), where anoma- lous movement (measured at radio wavelengths) can be used to infer the presence of a planet. Introduction 29

2 10

1 10

0 10 ) p u J M

( -1 g

o 10 l

s s a

m -2

t 10 e n a l

P -3 10 Radial Velocity Transit -4 10 Timing Microlensing Direct Imaging -5 10 -2 -1 0 1 2 10 10 10 10 10 Semi-major axis log(a[AU])

Figure 1.8: Planetary mass (log(MJup)) as a function of semi-major axis. The shapes represent the various detection techniques; radial velocity (red circles), transits (blue diamonds), timing (black downward triangle), microlensing (orange upward triangle) and direct imaging (green stars).

1.3.2.1 Direct imaging

Amongst the different detection techniques, direct imagining is the only technique which allows for the direct measurement of the exoplanet itself. Despite the basic principle behind directly imaging a planet, it is a notoriously difficult technique in practice. This is due to the the enormous luminosity contrast between the exoplanet and the host star and the small angular separation between the two bodies. At optical wavelengths, where the black body curve of the host star peaks, the brightness contrast is on the order of 109. Towards longer wavelengths the ∼ situation improves as the black body curve of the planet peaks, whilst that of the host star diminishes, resulting in a more favourable contrast ratio of 106. For this ∼ reason, direct imaging observations are done at near-IR to mid-IR wavelengths. The diffraction limit of a telescope is the minimum angular resolution before the the two objects observed can no longer be separated. The angular resolution, θ can be expressed as Introduction 30

1.22λ θ = (1.7) D

where D is the diameter of the telescope and λ the wavelength at which the observations are done. To be able to directly image planets which orbit close to the host star, it is most favourable to use a telescope with a large mirror diameter and also observe at longer wavelengths.

The technique is most sensitive to high mass (M 5 10 M ), young ( 100 Myr) & − J . exoplanet systems on wide orbits (& 5 AU) and therefore complements the other techniques (especially the transit method and RV method) which are more likely to detect planets which orbit close to their host star. Unlike the transit and phase curve measurements (described in the next section), which are the only other methods capable of detecting an exoplanet atmosphere, the direct imaging method allows for photometric and spectroscopic observations across a range of wavelengths to be obtained directly. The wide orbits means the exoplanet atmospheres are not subjected to strong irradiation from the host star (see thermal inversions 1.3.6) nor inﬂuenced much by stellar activity (see 1.3.5). Directly § § imaged planets therefore occupy a lot of the same parameter space as BDs allowing comparisons to be made (see section on the exoplanet-BD connection, 1.2.1). § An added beneﬁt of wide orbits is that the observations are not time critical, a natural consequence of Kepler’s 3rd law.

1.3.2.2 The Transit Method

When exoplanets pass in front of their host star (as seen from Earth), a portion of the start light is blocked out and a decrease in the photon flux is measured. Measuring the change in flux over time, allows for the creation of a light curve (see Fig.1.17). Fitting models to the light curve, various characteristics such as orbital motions and atmospheric composition can be extracted. Both the size of the host star and the planet will determine the decrease in flux during the transit. The orbital distance between the exoplanet and its host star does not affect the transit depth due to the enormous distance from Earth.

The transit method is particularly useful for calculating the radius of an exoplanet. To ﬁrst order (assuming the stellar disc is of uniform brightness, and neglecting Introduction 31

a b i

Figure 1.9: The impact parameter b varies from b = 0 centre of stellar disk with b = 1 being on the cusp of the disc.

R R*p b = a cos i /R* R*

Figure 1.10: Star-planet geometry showing the distance traversed by the planet, 2l, impact parameter of the system, b and the stellar and planetary radii, R and Rp respectively. ∗ any flux from the planet) the ratio of the observed change in flux, ∆F , to that of the stellar flux F can be expressed as:

∆F R2 = p (1.8) F R2 ∗ where Rp and R are the planetary and stellar radii respectively. As described ∗ below, limb-darkening will have an aﬀect on the transit light curve, but to ﬁrst order, the equation above holds. Introduction 32

i B

2l ⍺ A

Figure 1.11: The orbital geometry of a transiting exoplanet system showing the projected distance travelled across the surface of the star, 2l, between the points A to B and the angle α this geometry forms, with the inclination, i, and semi major axis, a, shown.

Impact Parameter: The total transit duration is heavily dependent on the impact parameter b, which is deﬁned as the sky-projected distance between the centre of the stellar disc and the centre of the planetary disc at conjunction6 and is shown in Fig. 1.97. Assuming a circular orbit the impact parameter is expressed as:

a cos i b = . (1.9) R ∗ Transit Duration:

The total transit duration, Tdur, deﬁned as the time during which any part of the planet obscures the disc of the star, depends on how the planet transits the host star. If the exoplanet crosses the centre of the stellar disc (b = 0), the transit duration is the longest with b = 0 signifying a shorter transit duration. With the 6 help of Fig. 1.10 and using Pythagorass theorem, the length the planet has to travel across the disk of the star can be expressed as,

q 2 2 2l = 2 (R + Rp) b . (1.10) ∗ −

6Conjunction: The point in the orbit where two objects are most closely aligned, as viewed from Earth. 7The ﬁgures and derivations are adapted from ”Transiting Exoplanets”, by Carole A. Haswell. Introduction 33

Figure 1.12: Limb darkening of a star showing how the intensity and temperature diminishes as an observer looks towards the limb of the star.

With the aid of Fig. 1.11, the exoplanet moves from A to B around its orbit, creating an angle α (measured in radians) with respect to the centre of the host star. With the assumption of a circular orbit, the distance around an entire orbit is 2πa, where a is the radius of the orbit. The arclength between points A and B is αa and the distance along a straight line between A and B is 2l.

From the triangle formed by A, B and the centre of the star,

α l sin = (1.11) 2 a

thus

p 2 2 ! α P 1 l P 1 (R + RP ) b T = P = sin− = sin− ∗ − (1.12) dur 2π π a π a

an expression of the full transit duration.

The Eﬀects of Limb Darkening: The eﬀect caused by the stellar disk being brighter in the centre compared to the limb of the disk is called limb darkening. Photons emitted from the limb of the stellar disc at a certain atmospheric depth L, follow a more oblique path through Introduction 34

0.9875

0.9870

∗ 0.9865 /R p R 0.9860

0.9855

0.015 0.010 0.005 0.000 0.005 0.010 0.015 − − − Phase (days)

Figure 1.13: Two model light curves of the super-Earth GJ 1214b for observations at 5000 A˚ (blue) and 1 µm (orange) using a tunable filter with a width of 12 A.˚ Observations at shorter wavelengths result in a deeper and narrower transit. the stellar atmosphere compared to the photons emitted from the centre of the stellar disc as seen in Fig. 1.12. For the photons escaping the edge of the stellar disc, an optical depth of unity is reached at a higher altitude where the temperature is cooler (TLO) and the radiation is less intense causing the apparent darkening. The limb darkening effect is largest at short wavelengths where a highly rounded light curve is observed. For longer wavelengths the effect is less severe and the centre of the transit takes on a flatter shape (see Fig. 1.13).

Orbital Inclination: Radial velocity observations provide information about the minimum mass, of

Mp sin i, assuming the stellar mass is known. To constrain the actual mass of an exoplanet, the orbital inclination, i, has to be measured. This is done by ﬁtting a analytical transit light curve to the data using the transit equation of Mandel & Agol(2002). A transiting exoplanet which has an impact parameter b = 0 or 6 i < 90, will have a shorter transit duration, a shallower transit depth and longer ingress and egress times. This is seen in Fig. 1.14 where the eﬀects of varying i from 90◦ to 80◦ is shown. Introduction 35

1.000

0.995 ∗

/R 0.990 p R

0.985

0.980 0.10 0.05 0.00 0.05 0.10 − − Phase (days)

Figure 1.14: Inclination values ranging from 90◦ to 80◦ at 1◦ intervals, with the shallowest light curve corresponding to i = 80◦. Introduction 36

1.3.3 Exoplanet formation and evolution

The way exoplanets form and evolve has a direct impact on the composition and dynamics of their atmospheres. The local conditions at their birth, the accretion mechanism and how they interact with their parent star, disk and potentially other planets, govern the diversity of compositions and atmospheric dynamics seen in exoplanet atmospheres today.

Before the discovery of exoplanets in the 1990’s, our own solar system was the only planetary system able to provide us with observables allowing us to test theories of planetary formation. With space missions exploring the solar system throughout the latter part of the 20th century, an enormous amount of geophysical data describing the chemical composition and internal structure of the giant planets was obtained giving clues to the origin of the solar system. With the subsequent discovery of many new planetary systems, most notably by the Kepler satellite (Borucki et al. 2010), the knowledge of planet formation was complimented by statistical properties of planetary systems with which to test hypotheses, weak- ening the anthropic bias (Carter 1974) of our planetary system being the only one.

The birthplace of exoplanets is within the predominantly gaseous disk which sur- rounds protostars. The way they form however, can be divided into two formation mechanisms which all giant planet formation models rely on: disk instability model which best explains giant planets with a large mass on wide orbits, and the core accretion model, which has emerged as the dominant formation mechanism. Each of these mechanisms are described in more detail below.

1.3.3.1 Formation via disk instability

The disk instability model (Boss 1997; Cameron 1978; Kuiper 1951) entails the formation of planets from the breakup of a protoplanetary disk due to gravitational instability forming self gravitating clumps of gas, which eventually evolve into planets. The thermodynamic state of the disk is a critical part of the model. For a disk to form, self-gravity has to dominate the thermal pressure and sheer inside the disk. The threshold for axisymmetric density perturbations to occur in a thin gaseous disk is given by the Toomre criterion (Safronov 1960; Toomre 1964), Introduction 37

c κ Q = s (1.13) πGσg

where cs is the speed of sound, κ the epicyclic frequency and σg the gas surface density. Disk fragmentation will only occur if Q . 1. As such, disks with a p p large mass (high gravity) at low temperatures (cs = kT/m P/ρ) and high ∼ densities (σg) are more likely to form gravitational instabilities. Disk instability is however not enough for planets to form as a result of the fragmentation. The disk must also be able to cool efficiently on a timescale comparable to the local disk orbital period8. Disk fragmentation is expected to more readily occur further out in the protoplanetary disk (several tens of AU) where the radiative cooling rates are higher and Q lower (Cai et al. 2006; Rafikov 2007). As such, one would expect a large number of planets on wide orbits if disk instability is the dominant formation mechanism. Janson et al.(2012) found that < 10% of FGKM-type stars form and retain companions through disk instability at 99% confidence, independent of outer disk radii (within the regime 5 500 AU) taking disk migration into account. − Only companions with masses < 100 MJupwere considered. Despite this result, some observations are best explained by formation via disk instability. Examples are the four giant planets (or BDs using the formation based definition of BDs) around HR 9799 with semi-major axis of 14.5, 24, 38, 64 AU (Marois et al. 2008, 2010) and Fomalhaut b (Kalas et al. 2008) at 119 AU. Although core accretion is the dominant planet formation model, the disk instability model is still a viable formation theory for gas giants with a large mass on wide orbits (Boley 2009; Dodson-Robinson et al. 2009).

1.3.3.2 Core accretion model

The core accretion model (Lissauer 1993; Pollack et al. 1996; Safronov 1972) is a multi-step formation process which starts with the formation of a heavy element core which forms when small solid dust grains and ices ( µm) sediment and ≤ coagulate through collisions into larger particles. These particles ( cm in size) ∼ proceed to stick together until eventually objects 1 100 km in size form, known ∼ − as planitesimals. Beyond this size, gravity becomes important in the development

8 τcool/τrot < ffrag where τcool and τrot are the cooling and rotation time scales of the disc and ffrag the ratio between them. Introduction 38 of pairwise planetesimal accretion forming planetary embryos. The embryos eventually form into a planetary cores or protoplanets. When the thermal speed of the surrounding gas drops below the escape velocity of the newly formed core, gas starts to accrete around the core. Thermal pressure dictates the ever increasing growth rate which deﬁnes the runaway gas accretion phase (D’Angelo et al. 2011). This continues until the reservoir of gas within the gravitational reach of the planet is exhausted.

The core accretion model has in recent years emerged as the dominant formation mechanism with a large body of observations supporting it. One such observation is the steep increase in the giant planet occurrence rate as a function of host star metallicity above solar metallicity (Fischer & Valenti 2005; Santos et al. 2004). The terrestrial planets of the solar system together with the supersolar compositions and likely high mass cores of Jupiter and Saturn (Atreya et al. 2003; Guillot 2005; Militzer et al. 2008) are further examples in favour of the core accretion model. Uranus and Neptune also have envelopes enriched in heavy elements, however pose more of a challenge with their predicted formation timescales exceeding clas- sical calculations of the lifetime of the solar nebula (Safronov 1969). More recent studies have found that this timescale can be lowered significantly under certain assumptions such as a modest enhancement of the initial surface density and if the growth takes place preferentially during the runaway planetesimal accretion phase (Pollack et al. 1996). These results are echoed by Helled & Bodenheimer(2014) who highlight the fact that different conditions in the protoplanetary disk, as well as the birth environments of the planetary embryos, can lead to the formation of planets with vastly different masses and compositions. This would provide a natural explanation for the large diversity of intermediate mass exoplanets currently observed.

1.3.3.3 Planet-disk interaction and migration

Armed with planet formation models derived from our solar system, it came as a great surprise to ﬁnd so many gas giants orbiting very close (< 0.1 AU) to their host stars in the late 90’s. This discovery is naturally biassed by observational techniques such as the radial velocity and transit techniques which are most sensitive to detecting giant planets on close orbits. A study by Howard et al.(2012) looked at 1235 planets from the Kepler mission (Borucki et al. 2010) and found Introduction 39 that the occurrence rate for hot Jupiters (P < 10 days, R = 8 32 R ) around GK p − E type stars is only 0.005 0.001. For super-Earths and hot-Neptunes the frequency ± rises exponentially to the order of a few percent. Despite the lack of planets with a large mass and small semi major axis, the presence of these exoplanets sparked a widespread interest in orbital migration theory.

Orbital migration occurs as a result of the gravitational and viscous interaction between the planet and the protoplanetary disk. The sheer presence of a planet in the protoplanetary disk leads to a non uniform distribution of gas within the disk. This causes torques to emerge. These torques directly influence the planets’ orbits during their formation periods and later the inclination and eccentricity of their orbits. The migration can occur in both directions, with local disk properties such as surface density and temperature gradients governing whether inward or outward disk migration occurs. Planets which form early on are the most likely to eventually either be ejected or consumed by the host star, while planets which form later experience a higher likelihood of developing stable orbits (Chambers 2009). The way migration proceeds also depends on the disk parameters and the mass of the planet with terrestrial planets having different formation scenarios from the EGPs (extrasolar giant planets). In the case of a low mass planet (terrestrial planet), spiral density waves form in the disk driven by the planet. The density waves which emerge introduce differences in torque between the outer and inner disk, which cause a transfer of angular momentum from the planet to the disk, leading to inward migration. For EGPs (with masses similar to Jupiter and above) a gap forms in the protoplanetary disk as a result of strong tidal interactions which acts as a tidal barrier causing the EGP to lock into the angular momentum process of the disk and prevents the flow of gas, halting accretion (Lin & Papaloizou 1986; Ward 1997). The orbital evolution of the planet gets tied to the disk causing the planet to migrate inwards on the viscous timescale of the disk. For masses in between terrestrial planets and Jupiter mass planets, such as Saturn mass planets, a partial gap in the disk might form. In such cases it is though that gas in the gap could cause torques proportional to the migration speed which could lead to both outward and inward migration (Masset & Papaloizou 2003).

Migration theory is successful in explaining the orbital distribution of exoplanets and is compatible with the observed distribution exoplanet semi-major axis. A lot of work still remains to be done, especially within the migration of low-mass Introduction 40 planets where there is still a great deal of uncertainty regarding the direction and rate of migration (Chambers 2009).

1.3.3.4 Inﬂated radii of extrasolar giant planets

Accurate radii measurements are required to calculate the average density and surface gravity, which determine atmospheric and internal composition as well as the dynamics, structure and evolution of exoplanet atmospheres. With such a fundamental impact on the important properties of exoplanets, understanding the diversity of measured radii is vital.

A large number of transiting EGPs exhibit radii larger than predicted by models of gaseous planets with a solar composition. This inflated radius can not be explained by thermal irradiation effects from the host star alone, as a deep deposition of heat is required. This has lead to the emergence of several mechanisms aimed at explaining the inflation. Following the classification of Weiss et al.(2013) the mechanisms can be placed into three categories: tidal mechanisms, incident flux- driven mechanisms, and delayed contraction.

Tidal mechanisms: Work by Bodenheimer et al.(2001) showed that planets with an eccentric orbit or non synchronous rotation could be significantly heated through internal tidal dissipation, causing the planet to inflate until thermal equilibrium is reached. The tidal heating caused by circularisation of an initially eccentric orbit is a transient process expected to occur on time scales much shorter than the lifetime of the host star. For the eccentricity to be maintained requires the presence of a planetary companion at a few AU, capable of pumping the eccentricity. Many of the transiting exoplanets discovered to date, have small measured eccentricities consistent with a circular orbit, but still have an inflated radii. This suggests that, although tidal dissipation can be a source of internal heating, the process alone can not explain the inflated radii (Leconte et al. 2010).

Incident ﬂux-driven mechanisms: Atmospheric circulation models by Showman & Guillot(2002) demonstrated that the kinetic energy of the planets atmosphere, held in strong winds at the surface, if transported into the interior could explain the inﬂated radii. The winds emerge as a consequence of the strong temperature contrast between the dayside and Introduction 41

nightside of the planet, a result of a tidally locked planet orbiting close to the host star. Their simulations showed that 1% of the incident stellar ﬂux if deposited ∼ into deeper layers, could slow down the planet evolution and provide a solution to the inﬂated radius anomaly.

Magnetic field generation in planets on close-in orbits can result in Ohmic dissipation, thought to keep some hot-Jupiters inflated (Batygin & Stevenson 2010). The high level of stellar irradiation from the host-star results in a small but non- negligible fraction of free electrons released by species with a low ionisation potential (such as atomic Na and K). These weakly ionized strong zonal winds carry the free electrons which advect across the magnetic dipole field of the planets causing an induced current which flows inwards described by Lenz law. The heat generated can either be released in the radiative part of the atmosphere, which can act as in- sulation for the heat present in the interior, or directly heat the interior convective zone of the planet itself (Huang & Cumming 2012; Spiegel & Burrows 2013). Work by Rauscher & Menou(2013) showed that deep Ohmic heating could successfully inflate the radius of HD 209458b providing the magnetic field strengths occupied the 3 30 G regime, however, magnetohydrodynamic simulation studies of the ≥ − atmosphere of the same planet conducted by Rogers & Showman(2014) found that the Ohmic dissipation rates can not account for the inflated radius of this planet. The difference in results emerges due to how the magnetic field geometry and evolution is treated suggesting that a self-consistent magnetohydrodynamic treatment is needed. As such, although there is no disagreement that Ohmic dissipation likely has an effect on hot-Jupiter atmospheres (it is active in Jupiter and Saturn, e.g., Liu et al. 2008), the debate whether or not it can explain the inflated radii is ongoing. A large step in the right direction from an observers viewpoint would be to observe and constrain the magnetic field of an exoplanet, a task which remains to be done.

Delayed contraction: A theory which does not necessarily rely on the need for an internal energy source, is that of an enhancement of atmospheric opacities which naturally retain the heat required to keep EGPs inﬂated (Burrows et al. 2007). The enhanced opacities could be a product of non-equilibrium chemistry, hazes, an enhancement in metallicity or simply be due to missing or underestimated opacities in current model atmospheres. This theory can not by itself explain the most highly inﬂated planets such as WASP-17b (Bento et al. 2014) and TrES-4b, where the opacities would Introduction 42 have to be unreasonably large (much higher than 10 solar equivalent) (Liu et al. × 2008).

Another possible energy transporting mechanism is that of inefficient convection in the planets interior caused by heavy element gradients which have the effect of reducing the heat transport, thereby slowing down the radius contraction (Chabrier & Baraffe 2007). Similar to the enhancement of atmospheric opacity theory outlined above, this mechanism does not require an extra source of heating based on strong irradiation levels from the host star, and can thus operate on much wider orbits. The theory has its roots in the double-diffusive convection theory whereby two different compositional density gradients emerge as a result of different diffusion rates. These gradients separate the convective interior into multiple convection layers separated by diffusive layers which prohibit large-scale adiabatic convection and leads to a strong reduction of the rate of heat escape. The compositional gradients are thought to be the result of the formation history (supports the core accretion theory), giant impacts, or by the core of the planet eroding during its evolution. Observations of an inflated planet with either a sufficiently large semi major axis (a 0.1 AU for a solar type star) or observations of a reduced ≥ heat flux would support the theory of EGPs being influenced by double-diffusive convection. It is however uncertain at this point if the diffusive interfaces can last long enough (characteristic time-scale of planet formation: gigayears) to support the reduction in heat flux.

Although none of the theories above can currently be ruled out, work by Demory & Seager(2011) suggests that whatever is causing the inflation is correlated with the incident stellar flux received by the planet. This signifies that enhanced opacities or the layered convection theories can not by themselves explain the inflated radii as no observations of cold inflated planets currently exist. From a sample of 115 Kepler giant planet candidates, Demory & Seager(2011) determined that radius inflation becomes effective above the orbit-averaged stellar irradiation level 8 1 2 of 2 10 erg s− cm− . In Figure 1.15 this level is shown in a plot showing the ∼ × planetary radius as a function of host star flux.

1.3.3.5 Compact radii of extrasolar giant planets

The majority of EGPs show smaller radii than predicted by models which only take the irradiation from the host star into account. This is unsurprising as many Introduction 43

2.0 8 1 2 2 10 erg s− cm− × 0. < M 0.1 M ≤ Jup 0.1 < M 1.0 M ≤ Jup 1.5 M > 1.0 MJup ] Jup

1.0 Radius [R

0.5

0.0 105 106 107 108 109 1010 1011 1 2 Flux [erg s− cm− ]

Figure 1.15: Planetary radii as a function of incident flux with the different mass regimes noted in the figure legend. A rise in planetary radius is observed for planets which receive an incident flux above 2 108 erg s 1 cm 2. Data ∼ × − − is from exoplanets.org. plausible scenarios would result in smaller radii, such as dense cores of rock and ice (in favour of the core accretion theory) and/or metal rich envelopes (Burrows et al. 2007). An example of an EGP which could be explained by a denser core or metal rich envelope is HD 149026b, which has a substantially smaller radius than expected, R = (0.725 0.05)RJ compared to R = 1.14 RJ for a planet of ± equal mass but pure solar composition (Sato et al. 2005). Not all objects can be explained by this theory however, as is the case with CoRoT-20b which has 3 one of the highest densities discovered to date (8.87 1.10 g cm− )(Deleuil et al. ± 2012), challenging planet formation and interior structure modelling. Such a high 3 density (Earth average density is 5.52 g cm− ) would require an enormous amount

of heavy elements, approximately > 700 MEarth of heavy materials in the central core (see Fig. 1.16) which compared to current planet formation models (Alibert et al. 2005; Mordasini et al. 2009) would require an extraordinary high eﬃciency in processing heavy material from the disk to the planet. An alternative theory which would require a smaller amount of heavy material is if the heavy elements are more evenly distributed throughout the planets interior and not just in the central core (red solid line in Fig. 1.16). Although this would reduce the requirement for enrichment, it would imply a disk-to-planet processing eﬃciency of 60% which is ∼ roughly twice of what current planet formation models predict. A simple solution Introduction 44

H/He

CoRoT-20b

Figure 1.16: Radius evolution tracks of a 4 MJup object, representative of CoRoT-20b. The black dotted line corresponds to a pure H/He planet. The magenta dashed curve is a model for a planet with a 850 MEarthcentral core and the red solid line is a model with about 500 MEarthof heavy material evenly distributed across interior of the planet (models created by I. Baraffe following Baraffe et al. 2008). Figure used with permission from I. Baraffe. to the problem would be if the radius of CoRoT-20b was underestimated due to an incorrect determination of the host star radius caused by the presence of an unresolved binary companion to the exoplanet host star or by a line of sight blend with another star. In this case the combined flux from both stars will be measured, causing the radius ratio of the exoplanet (which relies on a correct determination of the stellar radius) to be underestimated. At a distance of 1.23 0.120 kpc ± and with a magnitude of 14.66 Vmag, CoRoT-20b becomes a challenging object for direct imaging follow up, suggesting that the radial velocity holds the most promise of finding a companion.

WASP-12b, a very inﬂated hot Jupiter is a good example of how an incorrect radius determination can occur as a result of an unresolved companion. At a Introduction 45

projected distance of roughly 100 away from WASP-12, a close by M-type com- ∼ panion candidate9 called Bergfors-6 (Bergfors et al. 2013), went unnoticed. Not accounting for the companion candidate caused an underestimation of the transit depth in previous studies. Correcting for this made WASP-12 hotter and larger which also had a knock on eﬀect on the inferences of its atmospheric composition (see Crossﬁeld et al. 2012; Sing et al. 2013 and references therein).

1.3.4 Characterising Exoplanet Atmospheres

Once the mass and radius of an exoplanet has been inferred from indirect observations of the exoplanet host star, the average density of the exoplanet can be calculated. This, together with chemical and physical properties of the planet, can give us important information about the bulk composition. To obtain information beyond bulk composition and to lift possible degeneracies, requires information about the atmospheric composition and structure. Observations of an exoplanet atmosphere might help lift the degeneracy between an extended atmosphere covered by clouds and hazes or a compact atmosphere composed of heavier elements, both of which have similar average densities. Transiting planets provide excellent opportunities for atmospheric studies as their atmospheres can be studied during primary eclipse (transmission spectroscopy), during secondary eclipse (emission spectroscopy) and in between the two extrema (phase curve observations). The atmospheres of an exoplanet can also be studied by obtaining spectra from directly imaged planets (e.g., Barman et al. 2011) or by observing the phase curve of a planet which does not transit (e.g., Lockwood et al. 2014).

1.3.4.1 Transmission Spectroscopy

Transmission spectroscopy is a technique used to gather details about the chemical composition and vertical extent of a planets atmosphere. The opacity of an exoplanet atmosphere decreases as density decreases with altitude. As light from the host star passes through this atmospheric shell, a small portion of the starlight is absorbed. The amount of starlight absorbed is wavelength-dependant due to the scattering properties of the atoms and molecules in the exoplanet atmosphere. The

9(Bergfors et al. 2013) note that Bergfors-6 has been observed to have an elongated shape at two diﬀerent epochs, suggesting the companion candidate might itself be a binary. Introduction 46

1-2%

~0.02%

Figure 1.17: A transit light curve schematically showing the light blocked out by the opaque disk of the planet (black line) and the light blocked by the semi-transparent atmosphere. A typical hot-Jupiter transit depth is 1 2% ∼ − wheras the transit depth caused by the atmosphere is 0.02%. ∼ presence of a strong atomic or molecular transition will make the exoplanet atmosphere more opaque. This effectively increases the radius of the planet. Observing the different transit depths (caused by the different radii) at specific wavelengths, allows the presence of specific light absorbing atoms and molecules to be inferred. This difference in depth of the light curve as a function of wavelength allows for the creation of a transmission spectrum which can be used to derive the chemical composition and physical properties of an exoplanet atmosphere. The transit depth is usually expressed as a radius ratio between the planetary and stellar radius, which is measured during transit, instead of the absolute radius of the planet. This allows the planetary radius to be updated as the stellar radius becomes better constrained through observations.

To detect a certain atmospheric constituent, and to possibly estimate the abundance, the radius of the planet is measured at multiple wavelengths during a transit event. This is done either using filters with a specific band pass, or using a spectrograph. At certain specific wavelengths, the atmospheric species of molecules and atoms at high altitudes will make the exoplanet atmosphere more opaque. The expected variation in transit depth are on the order of a hundredth of a percent, requiring high signal to noise measurements (Fig. 1.17). It is therefore essential that as many photons as possible are collected to increase the signal to noise ratio. Introduction 47

7 HD 189733b 8 HD 149026b HD 209458b

10 HAT-P-1b

11 mag V 12

15 GJ 1214b

16 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040 Atmospheric signal required to detect a 1 atmospheric scale height feature [%]

Figure 1.18: Vmag as a function of the atmospheric signal required to detect an atmospheric features 1 scale height in size. The curved lines represent lines of constant S/N. The top red dotted line indicates the required S/N for mmag photometry (S/N 1087), whilst the solid blue line below represents a S/N ∼ ∼ 2000 which is typically achieved with a single HST orbit (based on data from Nikolov et al. 2014). The three bottom curves in green represent the S/N which would be achieved with 5, 10 and 20 times the incident photons compared to the solid blue line. Favourable targets for atmospheric studies orbit bright stars and have an extended atmosphere making the atmosphere easier to detect (direction towards the top right of the plot). The hot-Jupiter HAT-P-1b (blue) and the super-Earth GJ 1214b (green), which are discussed in more detail later in 4.1 § and 4.3 respectively are shown for comparison. Data from exoplanets.org. § Introduction 48

Transit observations intended to detect atmospheric constituents are usually carried out using either large ground based telescopes, or space telescopes which are not aﬀected by the turbulence in Earths atmosphere. An exoplanet atmosphere will be easier to characterise if the host star is bright, if the radius ratio between the planet and star is large and if the atmosphere has a large scale height. The super-Earth GJ 1214b, despite having a small radius compared to hot-Jupiters, has been a favourable target to study as it orbits a M-type star which has a smaller radius leading to a more favourable radius ratio. Fig. 1.18 shows the brightness of the exoplanet host star (providing high S/N measurements), as a function of atmospheric signal.

1.3.4.2 The Transmission Spectrum

Transmission spectroscopy observations are commonly compared to detailed atmosphere models which incorporate variations in temperature, pressure, and composition as a function of altitude which the data can in principle constrain. The propagation of photons through these models are calculated using radiative transfer equations, which are solved using numerical integration allowing theoretical transmission spectra to be produced. However, by interpreting observations with an analytical model, which includes the relevant physics, valuable insight can be gained into the physical phenomena which impact the transmission spectrum.

An extended exoplanet atmosphere with a large atmospheric scale height H, is easier to detect and characterise compared to an atmosphere with a small H, as more light is obscured by the atmosphere at a given wavelength. The atmospheric scale height, which describes the distance over which the pressure decreases by a factor e is deﬁned as:

kT H = (1.14) µmg

where k is Boltzmann’s constant, T is the atmospheric temperature, µm is the mean molecular weight, and g the local gravitational acceleration. The optical depth τ of the planet’s atmosphere is dependent on the atomic and molecular opacity of the gas and the structure and composition of the clouds. τ can be expressed as function of wavelength λ and altitude z as, Introduction 49

p τ(λ, z) σ (λ)n(z) 2πR H (1.15) ≈ abs p

following the procedures of Fortney(2005), where σabs is the cross section of the

main absorbing species, n(z) the volume density at height z, and Rp the radius of the planet. The number density can be assumed to vary with height exponentially z/H (n(z) = n0e− ) in accordance with the barometric formula.

Lecavelier Des Etangs et al.(2008) showed that as the light passes through the exoplanet atmosphere at slant angles, the optical depth remains approximately constant at τ 0.56, providing R /H is between 30 and 3000. The effective ≈ p ∼ ∼ radius of an exoplanet can thus be approximated by an optical thickness of τeq defined as τ = 0.56 τ. eq ≈ Under the assumption of an isothermal atmosphere in hydrostatic equilibrium, and assuming H R and that the abundance or mean molecular weight does not p change with height, the effective altitude of the transmission, z, can be expressed as a function of wavelength following the procedures of Lecavelier Des Etangs et al. (2008):

q z(λ) = H ln ξ Pz σ (λ)/τ 2πR /kT µg , (1.16) abs =0 abs eq × p

where ξabs and σabs are the abundance and cross section of the dominant absorbing

species respectively, Pz=0 the pressure at the reference altitude and Rp the radius of the planet. To illustrate which parameters affect the transmission spectrum and to what extent, the ratio of the altitude difference between two model trans- R mission spectra is derived. The change in altitude is expressed as the difference

between the central line core z(λcore) and the line wing z(λwing) of a potassium line. Mathematically the ratio is expressed as, R

z(λ ) z(λ ) = core − wing |II , (1.17) R z(λ ) z(λ ) core − wing |I where the subscript I represents the ﬁrst model, and II the second. Substituting Eq. 1.16 into Eq. 1.17 the ratio becomes, Introduction 50

0.145 2000 K 0.140 1500 K 1000 K 0.135

∗ 0.130 /R p R 0.125

0.120

0.115 7300 7400 7500 7600 7700 7800 7900 8000 Wavelength [A]˚

Figure 1.19: Potassium line profile showing the effects of temperature. As the model temperature increases from 1000 K (blue) to 1500 K (orange) and finally to 2000 K (red), the line cores increase in strength whilst the line wings steepen.

1/2 kT ξcore σ µwing Twing ln core µg ξwing σwing µcore Tcore = II . (1.18) 1/2 R kT ξcore σ µwing Twing ln core µg ξwing σwing µcore Tcore I

Following the assumptions stated above, ξcore , µwing and Twing are all equal to ξwing µcore Tcore one as they do not change with altitude. However, by evaluating the terms in equation 1.18 individually (done in the next subsections), the eﬀects of changing the temperature, abundance or mean molecular weight, on the altitude diﬀerence , can be assessed. R

1.3.4.3 The eﬀects of temperature on R

Considering the effect a temperature change has on the potassium line profile keeping all other parameters fixed, can be expressed as, R Introduction 51

0.145 100 ξ × K 0.140 10 ξK × 1 ξ × K 0.135

∗ 0.130 /R p R 0.125

0.120

0.115 7300 7400 7500 7600 7700 7800 7900 8000 Wavelength [A]˚

Figure 1.20: Potassium line profile showing the effects of abundance. As the model abundance of potassium increases from 1 (blue) to 10 (turquoise) × × and finally to 100 (green) solar abundance, the entire profile shifts upwards, × retaining it’s shape.

T = II (1.19) R TI where TI and TII represent the temperatures of model I and model II respectively. For the altitude diﬀerence between the line core and the continuum to double in size would require the temperature to double. The eﬀects of changing the model temperature can be seen in Fig. 1.19 where the parameters of HAT-P-1 b were used. In addition to the amplitude of the spectrum increasing, an increase in temperature causes an increase in the thermal motion of the potassium atoms causing an enhanced Doppler broadening seen as an increase in opacity in the line core and steeper line wings, a result of a wider Gaussian velocity distribution.

1.3.4.4 The eﬀects of changes in abundance on R

Considering the effect an abundance change has on the potassium line profile keeping all other parameters fixed, becomes equal to one as ξcore = 1. As such R ξwing Introduction 52

0.145 1 mu 0.140 2.35 mu 5 mu 0.135

∗ 0.130 /R p R 0.125

0.120

0.115 7300 7400 7500 7600 7700 7800 7900 8000 Wavelength [A]˚

Figure 1.21: Potassium line profile showing the effects of changing the mu of the model with mu = 1 (blue), mu = 2.35 (pink) and mu = 5 (purple). Since Eq. 1.16 assumes a constant mu, the various models do not show the affect of mu changing as a function of altitude, but rather various models using a constant mu throughout. A decrease in mu results in a steeper profile with the line cores increasing in strength. An increase in mu results in a decrease in a flattening of the line wings and a line core which diminishes in strength. the potassium profile does not increase in size. Instead the increase in abundance causes a uniform increase in opacity at all wavelengths and as a result the entire profile shifts upwards retaining it’s shape as shown in Fig. 1.20.

1.3.4.5 The eﬀects of mean molecular weight on R

As the scale height of an exoplanet atmosphere is inversely proportional to the mean molecular weight (µ), only a decrease in molecular weight would cause an increase in the altitude diﬀerence. There is however a limit to how low µ can become limited by the fact that hydrogen can not be divided further, requiring the mean molecular weight to be µ m , where m is the atomic mass unit. ≥ u u A typical value for µ is taken to be 2.35 mu due to the composition of gas giant exoplanet atmospheres being predominantly composed of H2 (2 mu) and He (4 mu) together with molecules of higher molecular weight. For observations which probe Introduction 53

the upper most atmosphere, where the fraction of ionized atoms are greater, such

as with UV observations, a value of µ = 1.2 mu is used instead (Bourrier et al. 2014). Considering the effect a change in mean molecular weight has on the potassium line profile keeping all other parameters fixed, can be expressed as, R

µ = II (1.20) R µI

The effects of changing the mean molecular weight can be seen in Fig. 1.21. An increase in the mean molecular weight causes a flattening of the potassium profile with widening line wings. This is caused by an increase in pressure with the line

cores diminishing in strength as the scale height (H = kT/µmg) decreases. Introduction 54

1.3.5 The Impacts of Stellar activity

Stellar activity can have a profound impact on exoplanet transit measurements. The presence of star spots during a transit can easily complicate the interpretation of the transit data introducing the need for activity corrections, as the transit depth is directly influenced by the presence of star spots. It will be underestimated in the event where the planet transit crosses a star spot, and overestimated with the presence of unocculted star spots on the stellar surface. A wavelength dependence is also introduced, as the stellar flux lost by the spots, at a given wavelength, will depend on the blackbody temperature difference between the stellar surface and the spots (Czesla et al. 2009). The stellar spots also create a quasi-periodic photometric variability, as the spots rotate into and out of view with the stellar rotation period, changing their shape as they evolve. Activity corrections are also crucial for phase curve observations. For these events the modulations in flux due to the star must be carefully subtracted from that of the exoplanet in order to accurately interpret the phase curve. To determine the level of flux contribution of the star and to what degree this influences the amplitude of the exoplanet phase curve, the magnitude of the stellar variability needs to be accurately measured.

An example of how photometric variability monitoring of exoplanet host stars aid in the accurate determination of transit depths and phase curves is presented in the work by Huitson et al.(2013, 2014) and Nikolov et al.(2014) who used observations taken at the 1.3 m CTIO (Cerro Tololo Inter-American Observatory) telescope during the 2012AB (PI: Wilson, P. A.) and 2014A (PI: Wilson, P. A.) semester.

1.3.6 Thermal inversions

Stellar irradiation is one of the most important factors in determining the atmospheric properties of exoplanets as it has direct impact on the structure, chemistry and temperature of the exoplanet atmosphere. Furthermore, stellar irradiation is directly linked with atmospheric escape, for example the evaporation of the upper atmosphere of HD 189733b has been shown to be caused by X-ray/EUV-radiation being deposited (Lecavelier Des Etangs et al. 2008) in the upper atmosphere. Highly irradiated exoplanets are predicted to have thermal inversions as a result of a high altitude opacity source absorbing the incoming stellar irradiation in Introduction 55

0.125 TiO/VO ∗ 0.120 /R p R no TiO/VO

0.115

4000 6000 8000 10000 12000 14000 16000 18000 Wavelength [A]˚

Figure 1.22: The difference in transmission spectra with TiO/VO (upper orange) and without (lower blue) for a 1500 K isothermal, hydrostatic and uniform abundance model (Fortney et al. 2008, 2010). The TiO/VO model has been vertically offset for clarity. the UV/optical. Thermal inversions of this sort are not uncommon in the solar system planets. Earth and Jupiter are excellent examples with temperature inversions caused by the absorption of UV flux by ozone (O3) and by hazes caused by methane photochemistry respectively. Amongst the hottest hot Jupiters, there are a number of observations, which when interpreted using model atmospheres, have shown to be consistent with a thermal inversion such as HD 209458b (Burrows et al. 2007; Knutson et al. 2008), HD 149026b (Harrington et al. 2007), XO-1b (Machalek et al. 2008) and CoRoT-1b (Deming et al. 2011). It has been suggested that this could be due to the presence of TiO and VO (Burrows et al. 2007; Fortney et al. 2008; Hubeny et al. 2003) or due to photochemical hazes (Zahnle et al. 2009) (products of photochemistry or other non-equilibrium processes, see 1.3.7) with high optical opacity. The absorption at high altitudes, leading to a § thermal inversion also makes the exoplanets appear brighter in secondary eclipse measurements at mid-infrared wavelengths, with molecular bands such as water seen in emission rather than absorption.

A classification scheme which divided exoplanets with dramatically different spectra (see Fig. 1.22) and day/night contrast due to TiO/VO was suggested by Fort- ney et al.(2008). In this scheme the hotter pM class of exoplanets are hot enough to have their opacity dominated by TiO and VO absorbing in the optical. The Introduction 56 pL class on the other hand, with temperatures below the condensation curve of Ti and V bearing compounds, will have their spectra dominated by the alkali metals in the optical, and H2O and CO in the near-IR with shallow secondary eclipse depths and a small day/night contrast being the hallmark of this type of planet. Observations have not yet shown a clear cut-off between the pM and pL types. WASP-14b and TrES-3b which are highly irradiated planets do not have a temperature inversion, suggesting that either stellar or planetary characteristics other than temperature affects the presence of inversions (Blecic et al. 2013; Fressin et al. 2010). An example of such a characteristic is the proposed correlation between stellar activity and thermal inversions (Knutson et al. 2010), whereby an active star with a high UV flux may destroy any compounds which would otherwise cause an inversion.

The carbon-to-oxygen (C/O) ratio has a direct influence on the relative concentra- tions of several species, such as H2O and CO2, which greatly affect the emergent spectra. A C/O 1 causes a natural underabundance of TiO/VO which can ≥ prevent a thermal inversion from occurring. As such, Madhusudhan(2012) suggested a classification scheme based on both a C/O ratio and stellar temperature / irradiation. More observations are needed to conclusively constrain the C/O ratios of exoplanetary atmospheres, although several planets observed thus far are consistent with C-rich atmospheres.

The lack of inversion seen in some of the highly radiated planets like WASP-19b (Huitson et al. 2013) and WASP-12b (Sing et al. 2013), could be due to the depletion of TiO/VO either through gravitational settling (Spiegel et al. 2009) or by TiO/VO raining out of the atmospheres at colder temperatures. In the first scenario macroscopic mixing such as turbulent diffusion or large scale convective motions is essential for TiO/VO to stay aloft in the atmosphere as TiO/VO which are significantly heavier molecules compared to molecular hydrogen, would otherwise sink and settle deeper in the atmosphere. In the second scenario, TiO/VO could rain out of the atmosphere at lower temperatures and higher pressures as TiO/VO condense into solid grains and sink. This could happen in a cooler region of the atmosphere below the inversion known as the cold trap. Hot Jupiters are thought to be tidally locked which causes large temperature differences which introduces strong winds which flow from the hot day side to the cool night side at speeds on the order of a few km/s (Snellen et al. 2010). Such strong winds could transport the gaseous TiO/VO to the cooler night side where it condenses Introduction 57 out causing a significant TiO/VO depletion on timescales of a few hundred mil- lions of years in the upper dayside atmosphere (Spiegel et al. 2009). There has been no clear detection of TiO/VO through means of transmission spectroscopy to date. This statement follows a caveat that since transmission spectroscopy is only sensitive to the atmosphere at the terminator of a planet, it could still exist in the hotter upper atmosphere of the dayside of the planet.

1.3.7 Clouds and Hazes in Exoplanet Atmospheres

Clouds are generally regarded as a mass of liquid or solid particles which form when the vapour pressure of the particles exceeds their saturation vapour pressure. Hazes on the other hand are generally considered as products of photochemistry or other non-equilibrium processes (Marley et al. 2013). ”Aerosols” is the all encompassing term which includes particles of any size and kind which are suspended in the atmosphere, although it is commonly used to describe very small particles which do not precipitate out of the atmosphere (Seager 2010).

Clouds and hazes play an essential role in the atmospheric energy balance of substellar objects and are closely linked with atmospheric dynamics. Their opacities affect the emergent flux and atmospheric temperature-pressure profiles which directly influences observations. For example, their obscuration of emergent spectral features alter the resulting transmission spectra and their reflective properties, which changes the geometric albedo, impacting phase curve observations. The impact of clouds and hazes is evident in roughly half of the exoplanet atmospheres discovered to date (D. K. Sing. priv. comm.)10. Clouds and/or Hazes have been observed in hot-Jupiters such as HD 189733b (Pont et al. 2008), WASP-12b (Sing et al. 2013), HAT-P-32b (Gibson et al. 2013) and WASP-6b (Jordánet al. 2013). Clouds have also been found to be present in the super-Earth GJ 1214b, where a featureless transmission spectrum has been observed across a wide range of wavelengths from the optical to the near-IR, due to the presence of clouds (Kreidberg et al. 2014). Clouds are also likely present in the atmosphere of HD 97658b, a super-Earth with a transmission spectrum best described by an obscuring cloud deck or a metal-rich atmosphere (Knutson et al. 2014).

There are a number of different cloud models which differ significantly in their approach. Despite the different approaches, most of the cloud models have many

10Based on preliminary results from a large HST program, GO-12473 Introduction 58 similarities. Cloud models all need to assume a gas composition which in most cases is assumed solar or super-solar (enhanced abundances). The temperature- pressure (T-P) proﬁle, which governs when the constituents of the atmosphere condense out is derived from radiative - convective equilibrium calculations which are dependent on lower boundary conditions from interior models (e.g., Baraﬀe et al. 1998). Beyond the above description, cloud models start to diverge in their approach. Some of the main cloud models are summarised in the next section.

1.3.7.1 Cloud models

Ackerman & Marley(2001) presented a method of calculating vertical proﬁles of particle size distributions in condensation clouds of giant planets and BDs. The method assumes a balance between a downward transport of particles by sedimentation and the upward turbulent mixing of condensate and vapour. Assuming a uniform cloud deck (globally averaged) the balance is presented as:

∂qt Kzz f w∗qc = 0 (1.21) − ∂z − sed where Kzz is the vertical eddy diffusion coefficient, qt the mixing ratio of condensate and vapour (qt = qc+qv), qc the mixing ratio of the condensate, w∗ is the convective velocity scale, and fsed, a dimensionless parameter describing the efficiency of the sedimentation. A high sedimentation efficiency produces clouds with large particles which settle into vertically thin layers. A low sedimentation efficiency on the other hand, produces vertically extended clouds composed of smaller particles, making them optically thicker (Morley et al. 2012; Stephens et al. 2009). The method does not rely on the treatment of microphysical processes to compute particle sizes and the formation of clouds in BD and planetary atmospheres. This makes the solution numerically rapid, allowing a large number of models to be generated within a relatively short time frame (Marley et al. 2013). The solution of the equation provides the total amount of condensate and particle sizes for each layer in the atmosphere above an arbitrary cloud base.

In the previous model, vapour and condensate is dredged up from deeper in the atmosphere before being transported downwards by sedimentation. Models by Helling & Woitke(2006) have taken a different approach by modelling the complex process of condensate grain formation which starts off with seed particles a the Introduction 59 top of the atmosphere. The nucleation process itself is computed as the seeds fall reacting with the gas and accreting condensate material. The top-down approach adopted by Helling and collaborators compared to the bottom-up approach by models akin to Ackerman & Marley causes a difference in predicted composition. Although a number of cloud models have been compared (Helling et al. 2008) to each other, the complexity of the Helling et al. models has made the computational approach challenging, and limited comparison between models and observations (Marley et al. 2013). As such, which model best matches observations for range of conditions, remains to be fully determined.

Chapter 2

Observations & Data Reduction

2.1 Observations in the optical

2.1.1 The night sky in the optical

Compared to the near-IR night sky, the optical night sky is relatively free of emission lines towards bluer wavelengths with the strong neutral oxygen lines (see Fig. 2.1) being the exception. Moon light does affect the sky background (dependant on phase) by reflecting sunlight onto molecules in the atmosphere thereby increasing the sky background. Even in the absence of the Moon, Zodiacal light which is sunlight reflected off dust grains located in the inner solar system can also increase the brightness off the sky background. Zodiacal light predominantly affects observations during dark time with objects located towards the ecliptic and is most dominant in the V-band. The zodiacal light is one of the major contributors to the total HST sky background, together with Earthshine light and geocoronal line emission (originating from photochemical reactions involving hydrogen and oxygen atoms in the Earth’s exosphere) (Giavalisco et al. 2002). The geocoronal line emission, also known as airglow, changes on timescales of years to minutes getting systematically fainter as the night progresses (Krisciunas 1997).

Down on Earth, light pollution can be a major contributing factor on sky-background in the optical especially as many street lights use sodium-vapor lamps. Solar activity will also aﬀect the sky brightness within all optical bandpasses. As the level

61 Observations & Data Reduction 62

2.5

) OI [5577 ] 2 − c e

s U B V R I c 2.0 r a 1 − 2

− 1.5 m

c OI [6300 ] 1 − s

r 1.0 e 6 1 − 0 1

× 0.5 OI [6364 ] OH Meinel bands ( Na I D x u l NI [5200 ] F 4000 5000 6000 7000 8000 Wavelength ( )

Figure 2.1: A wavelength and flux calibrated sky spectrum (black line) showing prominent emission lines together with broadband filter throughput curves. The night sky spectrum is taken from the FORS1 night sky spectral library (Patat 2008) where observations were done with a 100 slit using the G300V grism. The spectral resolution is ∆λ = 12 A.˚ The filter throughput curves (coloured lines) are the Bessel filters from the Nordic Optical Telescope (Filters #1,2,3,4,5) and have been arbitrarily normalised. of solar activity decreases, so does the sky background in a linear fashion (Patat 2008).

2.1.2 Reducing optical imaging data

Reduction of optical imaging data in its most basic form, consists of subtracting the pixel value bias added to the images to avoid negative pixel values in the science images, before subsequently dividing the science images by a flat field. The flat field is created by imaging a uniform screen or the sky at dusk/dawn. The purpose of the flat field is to remove as much of the non-uniform ADU count variations across the detector which occur as the result of pixel to pixel sensitivity variations, time-varying dust accumulation on optical elements and alterations to the throughput such as vignetting. In the event where thermal noise is significant, dark frames should be acquired with exposure times equal to that of the observations. With instruments cooled sufficiently such as with liquid nitrogen, dark frames are not necessary as the dark current is negligible. Such is the case with the OSIRIS instrument at the GTC telescope. Observations & Data Reduction 63

2.1.3 Narrowband Spectrophotometry using tunable ﬁl- ters

Narrowband spectrophotometry is a technique which bridges the gap between imaging observations and low resolution spectroscopy. Tunable filters (TFs) are a special type of narrowband filters which have the unique capability of altering the wavelength of maximum transmission and in some cases the bandpass. This is particularly useful when studying specific features such as Lyα emitter galaxies at high redshift (de Diego et al. 2013; Swinbank et al. 2012) or atmospheric absorption in the atmospheres of hot-Jupiters (Colónet al. 2010; Sing et al. 2011) and super- Earths (Wilson et al. 2014). Tunable filters provide high signal-to-noise S/N at good resolutions which is necessary for studying the atmospheres of exoplanets. Altering the wavelength of the tunable filters also makes it possible to avoid major sky lines such as the O I and OH emission lines described in 2.1.1 and shown in § Fig 2.1, which might otherwise interfere with the observations.

2.1.4 The Fabry-P´erotInterferometer

To allow for high S/N measurements at specific wavelengths, such as when probing a specific part of the transmission spectrum, a Fabry-Pérotinterferometer can be used. In 1899 C. Fabry and A. Pérotdesigned the interferometer, which unlike the Michelson interferometer which splits the light into two beams, the Fabry-Pérot Interferometer splits the light into multiple beams creating a fringe pattern which is much sharper due to the interference of multiple rays of light. The setup consists of two parallel, semi-transparent, reflective plates at a fixed distance apart, known as the etalon. As the incident light enters the system it is reflected a number of times before exiting the system forming sharp fringes. These fringes are the interference pattern caused by constructive interference, a result of two or more light beams which have a path difference equal to a integer multiple of λ. Shown in Fig. 2.2 are two partially reflective surfaces a distance d apart being illuminated by light incident at an angle φ.

The diﬀerence in path lengths ∆P between the emerging beams of light is:

∆P = 2d cos φ (2.1) Observations & Data Reduction 64

Figure 2.2: The optical path of the Fabry-P´erotinterferometer. with constructive interference occurring when the path is an integer multiple of the wavelength, µ∆P = Nλ (µ is the refractive index of air) such that

µ2d cos φ λ = . (2.2) N

The OSIRIS instrument at the GTC telescope uses a very narrow plate separation resulting in a wide separation between the successive interference peaks. Using a blocking ﬁlter, the order of interest is isolated allowing the system to only let through light over narrow wavelength range. Moving outward from the optical center causes a shift towards bluer wavelengths. In the case of relative photometry, the target of interest and reference star has to be placed at the same distance from the optical center to ensure observations at the same wavelength.

As the light passes through the etalon it is either transmitted or reﬂected. To

calculate the transmitted light intensity IT we need to know the complex amplitude of the electric ﬁeld E since:

cµ I = 0 E 2 (2.3) 2 | |

where c is the speed of light, µ the refractive index and 0 vacuum permittivity. Following Fig. 2.2 the transmitted electric ﬁeld can be expressed as: Observations & Data Reduction 65

2 2 2 iδ 2 4 2iδ ET = E0t + E0t r e + E0t r 2e + ... (2.4)

which is a geometric series whose sum is given as

E t2 E = 0 (2.5) T 1 r2eiδ − 2 2 Substituting Eq. 2.5 into Eq. 2.3 and expressing T = t , R = r and ∆ = δ + δr | | | | gives

T 2 IT = I0 , (2.6) 1 Reiδ 2 | − | were the denominator can be expressed in terms of trigonometric functions as:

T 2 1 IT = I (2.7) 0 1 R2 1 + F sin2(∆/2) −

where F = 4R/(1 R)2 is the finesse of the interferometer describing the sharp- − ness of the interference fringes. Ideal Fabry-Pérotfringe profiles with various reflectivities are shown in Fig. 2.3. Observations & Data Reduction 66

1.0 R = 0.95 R = 0.50 0.8 R = 0.25 ) 0

I/I 0.6

0.4 Transmission (

0.2

0.0 6500 7000 7500 8000 8500 9000 Wavelength (A)˚

Figure 2.3: An ideal Fabry-Pérotfringe profile showing transmitted intensity as a function of wavelength for plates with 95%, 50% and 25% reflectivity and plate separation of 3µm. By adjusting the plate separation, a desired wavelength can be chosen and together with a blocking filter the contribution from the other orders can be removed.

2.2 Observations in the near-IR

2.2.1 The near-IR sky

Observations in the near-IR are challenging for a number of reasons. Compared to the optical, the near-IR sky is dominated by the vibrationally excited OH molecules which are created when hydrogen and ozone react. The highly variable OH emission contributes significantly to the sky background making it variable on time scales of tens of seconds to minutes. Beyond a wavelength of 700 nm, ∼ the OH emission lines start to dominate and continue to do so until wavelengths longward of 2.3 µm where a steep increase in flux density is observed due to thermal black body radiation from the sky and the telescope itself. This effect is amplified by the presence of thin clouds (e.g. cirrus clouds) which have the effect of reflecting heat of Earths surface. Although the OH emission lines can be a nuisance for astronomical observations, especially low resolution spectroscopy and imaging of faint objects, they can also serve as good wavelength calibrators (Osterbrock et al. 1996; Rousselot et al. 2000). At near-IR wavelengths (1 to 2.5 microns) many absorption features caused by water vapour and carbon dioxide Observations & Data Reduction 67

1.0

Ks 0.8 Js

0.6 J H K

Transmission 0.4

0.2

0.0 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Wavelength (µm)

Figure 2.4: The near-IR sky transmission spectrum shown together with broadband filter throughput curves. The transmission spectrum is generated by ATRAN (Lord 1992) and is hosted on the Gemini Observatory webpages. The tranmission spectrum is specifically generated for Mauna Kea assuming an airmass of 1.0 and a water vapour coloumn of 1.6 mm. The filter throughput curves (coloured lines) are the standard SofI filters at the ESO NTT telescope. exist. The near-IR transmission spectrum is shown in Fig. 2.4 whilst the emission spectrum is shown in Fig. 2.5. Both figures are shown with common near-IR filter profiles for reference.

2.2.2 Reducing near-IR imaging data

To account for the pixel response variation of the near-IR array, flat fields are acquired to create a master flat which the science images can be divided by. Sky flats, or dome flats are taken in two groups, a set of brighter flats and a group of fainter flats all with the same exposure time. This is to allow for the thermal emission from the telescope and instrument to be subtracted. As the array expe- riences noise due to thermal noise, darks are taken and subsequently subtracted from the array.

For the brown dwarf monitoring observations with SofI at the NTT, a set of special flats were done. This was done to remove a residual shading pattern which varies as a function of the DIT (Detector Integration Time) and the incident flux. In addition to the regular flats (bright and a dark flat), the focal plane mask was placed such that the array was partly obscured with one part evenly illuminated and the other part dark (see Fig. 2.6). The dark section can then be used to Observations & Data Reduction 68 ) 2 −

c 50

e Ks s

c Js r a 1

− 40 2 − m

c J H K

1 30 − s

g r e 6

1 20 − 0 1 × (

10 x u l F 0 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 Wavelength (µm)

Figure 2.5: A wavelength and flux calibrated sky spectrum (black line) showing prominent emission lines together with broadband filter throughput curves. The night sky spectrum is generated by ATRAN (Lord 1992) and is hosted on the Gemini Observatory webpages1. The sky emission data is specifically generated for Mauna Kea assuming an airmass of 1.0 and a water vapour coloumn of 1.6 mm. The filter throughput curves (coloured lines) are the standard SofI filters at the ESO NTT telescope and have been arbitrarily normalised. characterise the shading pattern. This pattern, becomes especially important when dithering or nodding in the y-direction as this is the direction the shading changes the most.

In the near-IR, the sky background is orders of magnitude brighter than the optical sky, primarily due to a plethora of OH emission lines, but also due to molecular oxygen (1.27 µm) and water (end of K-band) (see 2.2.1). To be able to detect faint § sources, the sky background emission has to be removed. This can be done either by using sky suppressing filters, which have shown to be capable of supressing 400 OH lines across the 1 1.8 µm range, resulting in a background 30-60 times − fainter (Bland-Hawthorn et al. 2011), or by using dithering techniques. The latter technique works by taking multiple images, dithering the telescope between each exposure allowing a median combined image without stars to be created (a sky image), which then can subsequently be subtracted. Sources in the sky subtracted images will have a greater S/N allowing for measurements of higher photometric precisions to be made. For photometric time series measurements, sky subtracted images provide a better centring of the photometric aperture. The drawback of the dithering technique is that it inevitably introduces systematic errors as the objects of interest falls on different pixels, each with different responses. The flat Observations & Data Reduction 69

1000 180 160 800 140

600 120 ADU

y (pix) 100 400 80 200 60

0 40 0 200 400 600 800 1000 0 250 500 750 1000 x (pix) y (pix)

Figure 2.6: A frame from the special ﬂat sequence with focal plane mask partially obscuring the array (left) allowing the residual shading pattern to be measured. Median combining along the columns of the white box, the shading pattern is clearly seen (right).

field calibration images limit this variation, but is not able to remove the variations completely, in part due to the sensitivity of the flat field varying depending on the illumination level. To limit the systematic noise, stare mode observations whereby the object of interest is kept on the same set of pixels throughout the observing sequence can be used. This is a technique commonly used with observations from space where Earth’s sky background is no longer an issue, although it can also be used from the ground. The technique works best for bright objects, but is not suitable for ground observations of faint targets such as T-type brown dwarfs which have magnitudes comparable to the sky background. In such cases the centring of the aperture becomes unreliable introducing systematic effects. The best photometric technique will also depend on the seeing conditions and airmass.

2.2.3 High precision near-IR photometric monitoring of brown dwarfs

Nodding Technique: For the BAM follow-up study of variable brown dwarfs a nodding technique was adopted. This technique, is based on doing only one dither step to obtain an on and oﬀ-ﬁeld image allowing for the sky background to be subtracted. The technique is frequently used in other parts of astronomy such as when observing extended Observations & Data Reduction 70

1000

800

600 y (pix) 400

200

0 0 200 400 600 800 1000 x (pix)

Figure 2.7: A raw SofI nodding image of a crowded field created by median combining two set of images and subtracting one combined image from another. objects, where a dither pattern is not sufficient. For the brown dwarf monitoring observations the nodding technique was used stepping 20 – 30 00 between two pixel locations on the array. This had the benefit of allowing the sky background to be properly subtracted whilst at the same time minimising the inter-pixel variations by having the objects of interest fall on the same two pixel locations on the array. To further minimize the systematic pixel variations which could occur in the event of poor guiding (caused by a faint guide star or bad seeing) or because of instrument

flexure, which might affect the sub-pixel tracking, a slight defocus (seeing 1.2 00) ∼ was used. To obtain the best possible guiding, a red guide star (most similar in colour to the BDs) was selected, when possible, to minimise guiding errors due to differential atmospheric refraction. For the technique to work efficiently, the array also needs to be checked to ensure the object of interest and some of the best reference stars do not fall on faulty pixels. The drawback of this technique is that for crowded fields, some objects will inevitably fall on the previous position of other stars in the field, causing their flux values to become unreliable. Fig. 2.7 shows a typical unprocessed nodding image. Observations & Data Reduction 71

Illumination correction: As the illumination of the sky is not accurately represented by dome screen flats or sky flats, residual low frequency sensitivity variations exist in the SofI data after the sky subtraction and the division by a normalised flat has been done. To account for this low frequency sensitivity variation across the array (typically a few percent), illumination corrections were done for the BAM survey. By observing a standard star in a grid like pattern across the array, a low order polynomial can be fitted by placing a standard star of known brightness at various positions across the array in a grid pattern. This 2D surface is subsequently normalised and multiplied by the normalised flat to create an illumination corrected flat which the science data can be divided by. As both the flats and the intensity of the dome lamps change with time, a set of illumination correction observations were done every night of observing.

2.3 Sources of noise

2.3.1 Detector noise

Read noise The read noise is the noise (independent of signal level) associated with converting measured electrons to an analogue voltage and subsequently converting this to a Analogue to Digital Unit (ADU). Subtracting one bias image from another (∆B) and creating a histogram of the pixel values, results in a gaussian distribution with a width characterised by the read noise and the gain of the detector:

G σ∆B NR = × (2.8) √2 which for multiple read outs (NDITs) becomes:

σRN = √npix NR (2.9) × where G is the gain of the detector in units of e−/ADU and npix the number of pixels. The speed at which the detector is read out aﬀects the read noise with faster readouts causing larger temperature variations in the on-chip ampliﬁer which leads Observations & Data Reduction 72 to a greater read noise per pixel (Howell 2006). With modern day detectors this source of noise is in most cases not dominant.

Dark current Dark current is quantum mechanical property of the detector whereby electrons accumulate within a pixel due to thermal noise. As such, detectors are cooled to a constant temperature to limit this noise source. Dark current is not much of an issue for CCD detectors, however for near-IR detectors doing longer integrations, dark current can become a signiﬁcant source of noise, warranting calibrations with dark frames. The dark current is expressed as

p σ = n ND t (2.10) dark pix × × in units of e−/second/pixel where ND is the total dark count per pixel in units of electrons.

2.3.2 Shot noise

The quantum nature of light causes the photons to arrive at the detector spo- radically and uncorrelated with time. When the number of photons detected are sparse, such as for observations of faint objects, or when the exposure times are very short, diﬀerent amount of photons are detected causing variations in the signal. This variation in the measured signal is known as shot noise. The probability of arrival is described by a Poisson distribution:

k n n Pois(n; k) = e− (2.11) n! which has a standard deviation of σ = √n where n are the average number of events within a given time interval and k the number of events detected (number of electrons detected).

2.3.3 The Signal-to-noise ratio

The complete CCD equation describing an estimate of the signal-to-noise ratio (S/N), derived in Merline & Howell(1995), takes the following form: Observations & Data Reduction 73

S N ? (2.12) N ' r npix 2 2 2 N? + n 1 + NS + ND + N + G σ pix nB R f

where N? is the total star counts (electrons), npix the number of pixels used in integration of source, nB number of pixels used in background determination, NS total sky counts per pixel (electrons), NR read noise (electrons/pixel/read), G gain of CCD (electrons/ADU) and σf the uncertainty caused within the A/D converter.

The fraction npix/nB decreases with increasing resolution. As an example, consider a large diameter telescope using adaptive optics, which results in a seeing improvement from 1.000 to 0.100. In this scenario, this noise term would decrease by a factor 100 (not accounting for Airy rings) as the signal is preserved, since the sky background contribution diminishes due to an area reduction from 1.000 squared to 0.100 squared.

When observing bright sources such as exoplanet host stars the dominant source (not accounting for systematic noise) is the object itself (see Shot noise 2.3.2) § which allows Eq. 2.12 to be approximated as:

S N? p = N? (2.13) N ' √N?

When limited by the sky background such as when looking at faint sources or during near-IR observations (or both), the term NS (shot noise from the sky) dominates giving:

S N? r (2.14) N ' npix n 1 + NS pix nB

Once the S/N value has been measured it can be converted to magnitude errors using the relation: σ(m) = 2.5 log (1 + N/S) . (2.15) ± Observations & Data Reduction 74

2.3.4 Systematic noise

Correlated noise which does not follow the noise properties associated with random noise and depart from a √N improvement in the uncertainities for N number of measurements, is considered systematic noise. Time-correlated noise, sometimes referred to as ”red noise” can have a profound effect on observational data and is often hard to account for in the final estimation of measurement uncertainties. This is because the systematic noise can be made up of multiple components which do not follow a clear deterministic model. For instance, an increasing airmass can lead to differential refraction effects, but also affect the shape of the PSF and FWHM values as the seeing worsens. There are several techinques in place for estimating the red noise contribution. One of these techniques is the ”time- averaging” method by (Pont et al. 2006), where the variance of time-averaged data for various bin sizes are calculated and compared to the scatter of the un-binned residuals. In the event where the noise is random and uncorrelated with time ”white noise”, the scatter of the time-averaged bins should follow a √N relation, and only depart form it if the data is affected by red noise (see 4.3.5.4 to see § how this method affects the uncertainties). There are also various other methods used to estimate the red noise contribution such as the ”wavelet” method (Carter & Winn 2009a) and the ”residual-permuation” method (Jenkins et al. 2002).

To remove the red noise constribution, auxillary parameters such as airmass, FWHM, detector positions in conjuction with deterministic models (mainly poly- nomials and trigonometric functions) have been used. Recently there have been developments in alternative approaches such as blind extraction techniques based on principle component analysis (Waldmann et al. 2013) and Gaussian processes (Gibson et al. 2012). They diﬀer in their use of auxillary parameters with the latter method using them whereas the former does not. The advantage of the methods is their move away from the parametric approach with the systematics model not having to be set a priori. Chapter 3

Weather in the atmospheres of Brown Dwarfs

3.1 The brown dwarf atmosphere monitoring (BAM) project. I. The largest near-IR monitoring survey of L and T dwarfs

3.1.1 Abstract

Using the SofI instrument on the 3.5 m New Technology Telescope, we have conducted an extensive near-infrared monitoring survey of an unbiased sample of 69 brown dwarfs spanning the L0 to T8 spectral range, with at least one example of each spectral type. Each target was observed for a 2 – 4 hour period in the J -band, and the median photometric precision of the data is 0.7%. A total of s ∼ 14 brown dwarfs were identiﬁed as variables with min-to-max amplitudes ranging from 1.7% to 10.8% over the observed duration. All variables satisfy a statistical signiﬁcance threshold with a p-value 5% based on comparison with a median ≤ reference star light curve. Approximately half of the variables show pure sinusoidal amplitude variations similar to 2MASSJ2139+0220, and the remainder show multi-component variability in their light curves similar to SIMPJ0136+0933. It has been suggested that the L/T transition should be a region of a higher degree of variability if patchy clouds are present, and this survey was designed to test the patchy cloud model with photometric monitoring of both the L/T transition 75 Weather in the atmospheres of Brown Dwarfs 76

+10 and non-transition brown dwarfs. The measured frequency of variables is 13 4 % − across the L7 – T4 spectral range, indistinguishable from the frequency of variables +11 +10 of the earlier spectral types (30 8 %), the later spectral types (13 4 %), or the − − +7 combination of all non-transition region brown dwarfs (22 5%). The variables are − not concentrated in the transition, in a speciﬁc colour, or in binary systems. Of the brown dwarfs previously monitored for variability, only 60% maintained the ∼ state of variability (variable or constant), with the remaining switching states. The 14 variables include nine newly identiﬁed variables that will provide important systems for follow-up multi-wavelength monitoring to further investigate brown dwarf atmosphere physics.

3.1.2 Introduction

The L, T, and Y-type brown dwarfs represent a link between the coolest stars and giant planets. Many brown dwarfs are even cooler than currently observable exoplanetary atmospheres (e.g. HR 8799b, HD 189733b; Barman et al. 2011, Sing et al. 2009, 2011a). The recently discovered Y dwarfs (Cushing et al. 2011) approach the temperature of Jupiter. Since brown dwarfs never achieve a stable nuclear burning phase, they cool throughout their lifetimes, and temperature, rather than mass, is the dominant factor in deﬁning the spectral sequence. As they cool, their atmospheres undergo changes in the chemistry and physical processes that sculpt their emergent spectra. While spectroscopy can be used to investigate atmospheric constituents and chemistry, photometric monitoring is an eﬀective means to search for evidence of surface brightness inhomogeneities caused by cloud features, storms, or activity.

The transition region from late-L to early-T encompasses a particularly interesting change in physical properties, as the atmospheres transform from dusty to clear over a narrow effective temperature range, and the observed infrared colours reverse from red to blue. This is predicted to be an effect of the formation and eventual dissipation of dusty clouds in brown dwarf atmospheres (Burrows et al. 2006; Chabrier & Baraffe 2000; Marley et al. 2002). Broadly, as brown dwarfs cool through the spectral sequence, the lower temperatures allow more complex molecules to form, resulting in condensate clouds. When the temperature is cool

Based on observations made with ESO Telescopes at La Silla Observatory under programme ID 188.C-0493. Weather in the atmospheres of Brown Dwarfs 77 enough, large condensate grains cannot remain suspended high in the atmosphere and sink below the observable photosphere, allowing methane and molecular hydrogen to become the dominant absorbers. Although there are several existing models for condensate cloud evolution, most cannot easily explain the rapid colour change from red to blue over the L-to-T transition. A systematic survey of variability in brown dwarfs including both L/T transition objects and comparison hotter/cooler objects is required to search for diﬀerences in the structure of condensate clouds in this important regime.

Existing photometric monitoring campaigns of brown dwarfs have been conducted at different wavelengths: optical bands (e.g. Tinney & Tolley 1999 and Koen 2013), near-IR bands (e.g. Artigau et al. 2003, Khandrika et al. 2013 and Buenzli et al. 2013), mid-IR (e.g. Morales-Calderónet al. 2006), and radio frequencies (e.g. Berger 2006). From small (< 20 objects) initial samples of ultracool field dwarfs, frequencies of variables ranged from 0% to 100% (e.g. summary in Bailer- Jones 2005), and results from larger studies ( 25 objects) have measured the ∼ frequency of variables to be in the range of 20% to 30% (e.g. Buenzli et al. 2013; Khandrika et al. 2013). Examples of objects that vary in multiple wavebands have been identified (e.g. 2MASS J22282889-4310262 Buenzli et al. 2012; Clarke et al. 2008, SIMP J013656.5+093347.3 Artigau et al. 2009, 2MASS J21392676+0220226 Radigan et al. 2012), as well as objects recorded as variable in one wavelength range, but not another (e.g. 2MASS J15344984-2952274, Koen et al. 2004). A small set of variable sources have been monitored contemporaneously at multiple wavelengths, with the combined results being used to infer the vertical extent of atmospheric features and to investigate atmospheric circulation patterns (e.g. Buenzli et al. 2012). Given the unique probe of the atmospheric structure that multi-wavelength observations provide, it is essential to identify a larger set of known variables across a broad range of effective temperatures.

Most monitoring programs have involved observation sequences spanning a few hours, but some studies have searched for longer timescale variations (e.g. Enoch et al. 2003; Gelino et al. 2002). A time scale of a few hours is well-matched to a search for rotation-modulated variability, since expected rotation periods are 2 ∼ – 12 hours for L and T dwarfs, considering the range of measured v sin i values (10 – 60 km/s for L dwarfs and 15 – 40 km/s for T dwarfs – Zapatero Osorio et al. 2006) and the radius of the 0.08 – 0.10 M objects from evolutionary models at ∼ the age of the ﬁeld (Baraﬀe et al. 2003). Periodogram analysis of some variables Weather in the atmospheres of Brown Dwarfs 78 has shown clear peaks associated with periods in the range of 2 – 8 hours (e.g. ∼ Clarke et al. 2008; Radigan et al. 2012) which is consistent with an atmospheric feature rotating into and out of view. Other variables exhibit multi-component light curves (e.g. Artigau et al. 2009) that are suggestive of a rapid evolution of atmospheric features.

An unresolved BD binary system which consists of two BDs each with a different spectral type, can mimic a single BD with a spectral type somewhere between the individual BDs. This can lead to an incorrect spectral typing which may alter the statistics on the number of variables as a function of spectral type. A BD binary pair with only one variable BD will cause an underestimate of the measured variability amplitude if the binary system is unresolved as the non- variable component of the system dilutes the variability signal. As such, binaries play an important role in both the frequency and amplitudes of brown dwarfs. BD binary systems are typically found using high-resolution imaging (adaptive optics or HST) (e.g. Burgasser 2007), radial velocity variations (e.g. Joergens 2006b) or by carefully studying the spectra of possibly unresolved BD binary systems which may lead to the identification of spectroscopic binaries (e.g. Burgasser et al. 2010). The direct imaging method is most sensitive to BD binary separations greater than 3 AU whereas, RV measurements are most sensitive to close in ∼ binaries (typically 0.6 AU) (Joergens 2008). The binary frequency is observed ≤ to decrease as a function of primary mass with 60 % of solar type stars being ∼ found in binary systems, 30 40 % for M-dwarfs and 15 % for BDs (see ∼ − ∼ Dhital et al. 2010 and references therein). The peak of the BD binary separation distribution is found at 4–7 AU (Allen 2007; Maxted & Jeffries 2005) although the width of the distribution is still loosely constrained, something which orbital characterisation and the detection of more spectral binaries will help constrain (Duchêne& Kraus 2013). All the known binary BDs in the BAM sample are unresolved.

To investigate the variability of brown dwarfs across the full L-T spectral sequence, we have performed a large-scale Js-band photometric monitoring campaign of 69 ﬁeld brown dwarfs with the SofI instrument on the 3.5 m New Technology Telescope (NTT). This survey is a part of the BAM (Brown dwarf Atmosphere Monitoring) project. In Section 3.1.3, the properties of the sample, including magnitudes, spectral types, and companions are summarised. Details of the observations are reported in Section 3.1.4, followed by the data reduction procedure, Weather in the atmospheres of Brown Dwarfs 79

and methodology used to characterise each target as variable or constant in Section 3.1.5. Section 3.1.6 presents the results of the program and a comparison to previous variability studies. Finally, we discuss the sensitivity of the BAM survey and investigate possible correlations between variability and various observables such as spectral type, colour and binarity in Section 3.1.7. The results are summarized in Section 3.2.

3.1.3 The BAM sample

The 69 objects in the BAM sample were drawn from the brown dwarf archive (dwarfarchives.org) and were selected to span the full sequence of L- and T- spectral types from L0 to T8. An equal proportion of targets with spectral types above, across and below the L/T transition region were included. In this paper, we consider the L-T transition to range from L7 – T4, following Golimowski et al. (2004). Spectral types including a fractional subtype have been rounded down - for example, an L6.5 is considered L6 for the statistics. For the 48 targets with parallax measurements (e.g. Dupuy & Liu 2012; Faherty et al. 2012), a colour- magnitude diagram was constructed and is shown in Figure 3.1. The histogram of target spectral types and a plot of the colour as a function of spectral type are shown in Figure 3.2. The spectral types are based on IR spectroscopy for 54 targets and on optical spectroscopy for the remaining 15 targets that lacked an IR spectral classiﬁcation. The spectral types, parallaxes, and apparent 2MASS magnitudes of the targets are listed in Table 3.1 for L dwarfs and Table 3.2 for T dwarfs.

Additional factors that inﬂuenced the target selection were the magnitudes and coordinates. To obtain high signal-to-noise individual measurements, the targets were limited to objects with magnitudes brighter than J 16.5 mag. To avoid ∼ observations at high airmass, the target declinations were limited to South of +20 degrees. Pairs of targets were observed for sequences of 2 to 4 hours, which also impacted the range of target coordinates observed each observing run.

The majority of the sample, 47 targets, have been observed in programs designed to detect binary companions with radial velocity variations (Blake et al. 2010), or spectra showing features of diﬀerent spectral types (Burgasser et al. 2010), or high angular resolution imaging (i.e. Bouy et al. 2003; Burgasser et al. 2006, 2003a, 2005; Looper et al. 2008; McCaughrean et al. 2004; Reid et al. 2008, 2006). Weather in the atmospheres of Brown Dwarfs 80

L0-L6 10 L7-T4 T5-T8

12 ) g a m (

S 14 S A M 2 , J M

-1 0 1 2 (J-K)2MASS (mag)

Figure 3.1: Colour-magnitude diagram of the M-L-T spectrum (small grey circles). All brown dwarfs with known parallax in the BAM sample are overplotted, with red representing the L dwarfs, yellow the L/T transition dwarfs, and blue the T dwarfs (see Table 3.1 and 3.2). Half spectral types have been rounded down in the study. The photometry and parallaxes for the ﬁeld M-L-T objects are from Dupuy & Liu(2012).

3.0 10 23 Targets 23 Targets 23 Targets 2.5

2.0

8 ) g

a 1.5 m (

6 1.0 S S A 0.5 M 2

4 ) BD Number K 0.0 - J ( 0.5 2 1.0

0 1.5 L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 Spectral Type Spectral Type

Figure 3.2: Diagram on the left shows a histogram of the sample across their respective spectral classes, whilst on the right is a colour-colour diagram showing the J-K colours of the same (coloured circles) overplotted on the full brown dwarf L-T spectral sequence (small grey circles). The L/T transition is indicated by the dashed lines deﬁned in Golimowski et al.(2004). Weather in the atmospheres of Brown Dwarfs 81

Based on the companion search programs reported in the literature, a total of 12 targets are members of spatially resolved binary pairs, and the results of all the binary searches are reported in Table 3.1 and 3.2. The proportion of binaries in this sample is comparable to the overall brown dwarf binary frequency (Burgasser et al. 2003a), indicating that the sample is not biased in the level of multiple systems included. All of the binaries in the sample have separations less than the seeing limit, so the photometric measurements in this study record the combined ﬂux from both components. A variable brown dwarf that is part of an unresolved binary system can be more diﬃcult to detect, as the variability is diluted by the non variable companion.

Previous observations designed to search for photometric variability have been reported for approximately half the sample – 34 targets – and cover optical (Gelino et al. 2002; Koen 2013), near-IR (Buenzli et al. 2013; Clarke et al. 2008; Enoch et al. 2003; Khandrika et al. 2013; Koen et al. 2004, 2005), and radio (Berger 2006) wavelengths. It is important to note that the diﬀerent variability monitoring studies apply diﬀerent criteria to categorise a target as variable or constant, and a range of observation wavelengths have been employed. Most of the previous monitoring has been conducted over timescales of hours similar to this program, though a few studies covered longer timescales with lower cadence measurements (e.g. Gelino et al. 2002, Enoch et al. 2003).

3.1.4 Observations

The observations took place from 4 - 11 October 2011 and 3 - 9 April 2012 with the SofI (Son of ISAAC) instrument (Moorwood et al. 1998) mounted on the NTT (New Technology Telescope) at the ESO La Silla observatory. Observations were 1 performed in the large field imaging mode that has a pixel scale of 000.288 px− and a field-of-view of 4.92 4.92. During the first observing run, some of the targets 0 × 0 were observed in both the Js-band and Ks-band, but only the Js-band was used during the second run. As a consequence, six of the targets from the first run have

Js-band data with lower cadence. The Js filter (1.16-1.32 µm) was used to avoid contamination by the water band centred at 1.4 µm that would have otherwise affected the photometry. An increase in the telluric water column would have caused an anti-correlation between the brightness of the brown dwarfs and the reference stars in the J-band, since an increase in the water column will decrease Weather in the atmospheres of Brown Dwarfs 82 the flux from the reference stars to a greater extent compared to the brown dwarfs that have deep intrinsic water bands. The Js data should not suffer from this effect.

Three sets of two target fields were observed most nights, alternating between each target roughly every 15 min over a 3.5 hour window. This procedure allowed ∼ six targets to be observed every night. During clear conditions, the observations had a detector integration time (DIT) of 5s, with three DITs (NDIT) taken and averaged together with about 25 exposures in each observing block. During poorer conditions, such as the presence of cirrus clouds, and for fainter objects, the exposure times were increased. The flux was kept below 10,000 ADUs for the brightest targets in the field to prevent any non-linearity effects. Weather in the atmospheres of Brown Dwarfs 83 S radial velocity BCW10 S SpeX spectraSS BC10 radial velocity SpeX spectra BCW10 BC10 Binary/ Instrument References 0.070.03 S B (120 mas) HST HST imaging imaging K99, B06, D02, B03 K07, R08 0.03 B (264 mas) HST imaging D97, K04, D12, B03 0.03 B (730 mas) HST imaging R08, R06 0.03 B (409 mas) HST imaging R06, K04, D02, B03 0.0220.071 S0.0390.162 S0.029 B HST0.027 (130 imaging S mas) S SpeX spectra HST imaging Giz00, B06, R08 F00, K04, HST V04, imaging BC10 Ken04, SpeX D12, spectra RL06 R08, F12, R06 C06, S13, BC10 R08, F12 0.0590.032 C03, F12 F07, B06 0.138 K04 0.0610.0440.027 S0.0280.0390.055 SpeX0.032 spectra0.0870.058 S0.0290.026 K08, BC10 0.024 HST0.024 imaging S S S K08, F12, S R08 HST imaging HST imaging R08 radial velocity K07, D07 C03, HST F12, C03, imaging R06 W03, C03, BCW10 F12, K08, K07 R06 R08 C03, And11, R06 C07, K08 R08, R08 B06 0.027 S HST imaging R00, K04, D02, R06 0.0350.077 S SpeX spectra K04, F12, BC10 Giz02, And11 0.035 R08 0.029 S HST imaging R08, F12, R06 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± MASS 2 J L dwarf Sample. 0.6 12.83 7.9 13.775 4.0 14.408 5.68.1 14.48 15.508 1.8 14.378 1.5 14.587 7.7 15.569 4.94.5 13.393 11.2 14.48 13.169 62.15.4 16.103 4.7 15.867 1.6 14.486 16.625 5.6 14.313 13.577 10.2 15.66 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 3.1: Type (mas) (mag) Single Target Name Spectral Parallax DENIS J0205.4-1159 L5.5 50.6 SDSS J204317.69-155103.4 L9 22.8 [R00], Reid et al. ( 2006 ) [R06], Reid et al. ( 2006 ) [RL06], Reid et al. ( 2008 ) [R08], Smart et al. ( 2013 )[S13], Vrba et al. ( 2004 ) [V04]. 2MASS J19360187-55023222MASS J23224684-3133231 L5* 66.3 L0* 58.6 2MASS J13262981-00383142MASS J15074769-16273862MASS J22521073-17301342MASS J22551861-5713056 L5.5 L5.5 136.4 50 L7.5 L5.5 63.2 14.083 2MASS J11263991-5003550 L6.5 13.997 2MASS J10043929-33351892MASS J10101480-04064992MASS J12281523-1547342 L4* L6* 54.8 L6 59.8 44.8 2MASS J00165953-40565412MASS J00184613-63561222MASS J01062285-59331852MASS J01282664-55453432MASS J02284355-63250522MASS J02572581-31055232MASS J03185403-3421292 L3.5* L2*2MASS J03400942-6724051 L0*2MASS J03582255-4116060 L12MASS J04390101-23530832MASS L0 J04455387-3048204 L8*2MASS J05233822-1403022 15.24 L7*2MASS J06244595-4521548 L7* 15.316 L5* 72.9 15.224 L6.5* 14.33 L2* 110.4 L5 L5* 13.556 14.672 78.5 83.9 14.742 15.846 13.084 2MASS J08354256-0819237 L5* 117.3 2MASS J16322911+1904407 L8 65.6 2MASS J13004255+1912354 L3 12.717 2MASS J11555389+0559577 L7.5 57.9 2MASS J09153413+04220452MASS J09310955+0327331 L7* L7.5 14.548 16.615 2MASS J04070752+1546457 L3.5 15.478 Note: *Spectral classification using optical data et al. ( 2000 ) [Giz00], Gizis ( 2002 ) [Giz02], Kendall et al. ( 2004 ) [Ken04], Kendall et al. ( 2007 ) [K07], Kirkpatrick et al. ( 1999 )[K99], Kirkpatrick et al. ( 2008 )[K08], Knapp et al. ( 2004 ) [K04], Reid et( 2000 ) al. References: Andrei et al. ( 2011 )[And11], Bouy et al. ( 2003 ) [B03], Blake et al. ( 2010 ) [BCW10], Berger ( 2006 ) [B06], Burgasser et al. ( 2010 ) [BC10], Cruz et al. ( 2003 ) [C03], Chiu et al. ( 2006 ) [C06], Cruz et al. ( 2007 ) [C07], Dahn et al. ( 2002 ) [D02], Deacon &( 2007 ) Hambly [D07], Delfosse et al. ( 1997 ) [D97], Dupuy & Liu ( 2012 )[D12], Folkes et al. ( 2007 )[F07], Faherty et al. ( 2012 ) [F12], Fan et al. ( 2000 ) [F00], Gizis Weather in the atmospheres of Brown Dwarfs 84

3.1.5 Data Reduction and Photometry

3.1.5.1 Processing the images

For each image, basic data reduction steps consisting of correcting for the dark current and division by a flat field and sky subtraction were applied. Developing flat field images for the NTT/SofI instrument involved generating two different flats, a special dome flat and an illumination correction flat as documented by the observatory. The dome flat requires observations of an evenly illuminated screen with the dome lamp turned on and off in a particular set sequence. To correct for low frequency sensitivity variations across the array that are not completely removed by the dome flat, an illumination correction was applied. By observing the flux from a standard star in a grid pattern across the array, a low order polynomial was fitted to the flux measurements, allowing large scale variations across the array to be characterised and removed. Flat field images were produced using the IRAF1 scripts provided by the observatory2. As the flat fields are documented to be extremely stable over several months, a single set of flat fields were used for all the targets in a given run.

For the SofI instrument, the dark frames are a poor estimate of the underlying bias pattern, which varies as a function of the incident flux. Consequently, the darks are subtracted from the science frames through the computation of a sky frame, which also removes the sky background from the science data. Sky frames were generated by median combining the dithered science frames. The final calibration step involved measuring the offsets between the individual images and aligning all the science frames. The aligned frames within each 15 min interval were ∼ subsequently median combined. We compared the photometric uncertainties on the median combined images calculated using IRAF, to the standard deviation of the unbinned images within each bin. For most objects, the two methods for calculating uncertainties gave very similar results. The IRAF uncertainties on the median combined images were used for all the objects for consistency. Median combining the images before performing photometry rather than measuring the individual frames had the advantage of improving the centring, measurements

1IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. 2http://www.eso.org/sci/facilities/lasilla/instruments/sofi/tools/reduction/ sofi_scripts.html Weather in the atmospheres of Brown Dwarfs 85 of the full width at half maximum (FWHM), and the photometry of the fainter comparison stars in the ﬁeld. Weather in the atmospheres of Brown Dwarfs 86 Binary/ Instrument References B (100.9 mas) AO imaging S11 0.070.030.05 S HST imaging B03, BK06 T05, B06, D12 A06 0.0510.0710.0540.056 B0.118 (349 mas) S0.049 ?B (weak candidate) S ?B0.073 (strong candidate) HST SpeX imaging spectra0.068 SpeX spectra B02,0.057 B06, D12, BK06 HST C06, imaging R08, D12, B06, BC10 S13, BC10 HST B02, imaging B06, S T03, BK03 S99, B06, T03, BK06 S HST imaging B03, F12, B06, HST BK06 imaging B04, F12, B06 B02, B06, S13, BK03 B04, B06 0.0450.0580.0270.0870.079 B (160 mas) S S HST imaging G02, B06, V04, HST B05 imaging B02, B06, V04, HST BK06 imaging B03, F12, B06, B04, BK06 B06, F12 L07 0.0240.0240.117 ?B (weak S candidate) SpeX spectra T05, F12, B06, BC10 0.035 HST0.062 imaging0.0790.102 B00, B06, ?B D02, (strong BK03 candidate) B (130 mas) SpeX S spectra S A11, AO F12, imaging BC10 HST imaging L07, D12, L08 L00, A10 B06, D02, SpeX BK06 spectra K04, F12, B06, BC10 0.0680.0910.083 B (172 mas) HST imaging L00, B06, T03, BK06 L07, F12 T05, B06, D12 0.0770.1060.0610.0470.072 B (282 mas) S HST imaging B99, B06, T03, BK03 HST imaging B99, B06, T03, BK06 L07, F12 T05, B06, B08 B04, B06 0.071 ?B (weak candidate) SpeX spectra H02, F12, B06, BC10 0.04*0.0740.04* S SpeX spectra K04, F12, B06, BC10 E05, F12, B06 S10, B10 T dwarf Sample. 0.054 B (65 mas) HST imaging B02, B06, T03, BK03 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± MASS 2 J 1 13.802 7.5 15.535 1.7 15.695 8.3 15.92 4.6 15.98 1.4 15.858 2.0 15.264 0.91.2 15.825 7.7 15.494 7.9 15.175 0.8 16.85 16.334 6.77.0 15.73 15.662 3.5 15.824 2.4 15.928 1.1 14.465 6.5 15.984 136.6 13.613 16.149 2.22.5 15.86 1.9 15.26 1.1 14.891 6.4 15.577 7.2 16.016 1.3 16.399 14.9 5.21.3 15.653 16.253 12.2 15.58 1.9 15.631 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Table 3.2: ± ± Type (mas) (mag) Single Note: *MKO to 2MASS conversion using transformations from Stephens & Leggett ( 2004 ). [S13], Strauss et al. ( 1999 ) [S99], Tinney et al. ( 2003 ) [T03], Tinney et al. ( 2005 ) [T05], Vrba et al. ( 2004 ) [V04]. Target Name Spectral Parallax DENIS J081730.0-615520 T6 203 2MASS J1511145+060742 T2 36.7 SIMP J013656.5+093347.3 T2.5 13.455 SDSS J204749.61-071818.3 T0 49.9 SDSS J042348.56-041403.5 T0 72.1 2MASS J18283572-48490462MASS J20523515-1609308 T5.52MASS J21513839-4853542 T1 83.7 2MASS J22282889-43102622MASS J23312378-4718274 T4 33.9 2MASS T6.5 J23565477-1553111 T5 50.4 94.0 T5.5 57.9 15.659 2MASS J00501994-33224022MASS J03480772-60222702MASS J04151954-0935066 T72MASS J05103520-4208140 T72MASS J05160945-0445499 T8 94.6 2MASS J05591914-1404488 T5 T5.5 175.2 T4.5 44.5 96.6 15.318 16.222 2MASS J09490860-1545485 T22MASS J12255432-2739466 55.3 2MASS J12545393-0122474 T6 T2 75.1 2MASS J15462718-3325111 84.9 T5.5 88 2MASS J07290002-39540432MASS J09393548-2448279 T82MASS J10073369-4555147 T8 126.3 T5 187.3 71.0 2MASS J14044941-31593292MASS T2.5 J15344984-2952274 42.1 T5.5 62.4 2MASS J12171110-0311131 T7.5 90.8 2MASS J10210969-03041972MASS J11145133-2618235 T3 T7.5 179.2 29.9 ULAS J232123.79+135454.9 T7.5 17.04 2MASS J00345157+0523050 T6.5 105.4 2MASS J21392676+0220226 T1.5 101.5 2MASS J15530228+15323692MASS J16241436+0029158 T7 T6 75.1 90.9 2MASS J12314753+0847331 T5.5 15.57 2MASS J15210327+0131426 T2 41.3 2MASS J12074717+0244249 T0 44.5 et al. ( 2003b ) [B02], Burgasser et al. ( 2003a ) [BK03], Burgasser et al. ( 2004 ) [B04], Burgasser et al. ( 2005 ) [B05], Burgasser et al. ( 2006 ) [BK06], Burgasser et al. ( 2008 ) [B08], Burgasser et al. ( 2010 ) [BC10], Burningham et al. ( 2010 ) [B10], Chiu et al. ( 2006 ) [C06], Dahn et al. ( 2002 ) [D02], Ellis et al. ( 2005 ) [E05], Faherty et al. ( 2012 ) [F12], Gelino et al. ( 2002 ) [G02], Hawley et al. ( 2002 ) [H02], Knapp et al. ( 2004 ) References: Albert et al. ( 2011 ) [A11], Artigau et al. ( 2006 ) [A06], Artigau et al. ( 2010 ) [A10], Berger ( 2006 ) [B06], Bouy et al. ( 2003 ) [B03], Burgasser et al. ( 1999 ) [B99], Burgasser et al. ( 2000 ) [B00], Burgasser [K04], Leggett et al. ( 2000 ) [L00], Looper et al. ( 2007 ) [L07], Looper et al. ( 2008 ) [L08], Reid et al. ( 2008 ) [R08], Scholz et al. ( 2003 ) [S03], Scholz et al. ( 2003 ) [S10], Stumpf et al. ( 2011 ) [S11], Smart et ( 2013 ) al. Weather in the atmospheres of Brown Dwarfs 87

3.1.5.2 Generating the light curves

Aperture photometry was carried out using the APPHOT package in IRAF. A median value of the FWHM was measured per image using all the stars in the field-of-view. A range of aperture radii were explored and the size of 1.5 FWHM × was selected, as it minimised the root-mean-square (RMS) scatter of the reference star light curves that were created by dividing each reference star by the weighted mean of the remaining reference star light curves. The aperture was kept constant for all the stars in a single image, but was allowed to vary between individual images to account for variations in seeing. The variable aperture also yielded higher signal-to-noise measurements compared to a constant aperture, which would otherwise cause a loss in the flux measured within the aperture during poorer seeing conditions. We checked each target field to ensure that the photometry was not impacted by nearby astrophysical sources.

The steps taken to generate the target light curves in the survey are given in the following list:

For each target, a list of reference star candidates was generated by consid- • ering all stars visible in the ﬁeld of view, discarding stars with peak counts less than 20 ADUs or greater than 10, 000 ADUs. These limits were im- posed to ensure enough signal was present to accurately centre the aperture around the object and to ensure that none of the reference stars were in the non-linear regime of the detector.

Reference candidates were trimmed by selecting up to 15 of the reference • stars with the most similar brightness to the target.

Candidate reference star light curves were calculated by dividing each refer- • ence star by a weighted mean of the remaining reference stars.

Candidate reference stars with light curves exhibiting a standard deviation • greater or equal to the median standard deviation for all reference star candidates were removed.

A master reference light curve was subsequently created by median combin- • ing the normalised light curves of all the qualifying reference stars.

The ﬁnal target light curve was produced by dividing the target brown dwarf • ﬂux by the weighted mean of all the qualifying reference stars. The light Weather in the atmospheres of Brown Dwarfs 88

10 8 6

Number 4 2 0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Target Photometric Uncertainty, Q (%)

Figure 3.3: Target photometric uncertainty of the survey deﬁned as the median value of the ﬁnal target light curve uncertainties. The median target photometric uncertainty is 0.7%.

curve was normalised by dividing the light curve by the median ﬂux value of the light curve.

The target and reference star light curves were all airmass de-trended by • dividing the light curves by a second order polynomial ﬁt to the relative ﬂux of the master reference as a function of airmass.

The number of reference stars used for each target is given in Table 3.3 and Ta- ble 3.4, with six to eight references being typical (with the fewest number of reference stars being three). The automatic selection process was applied uniformly throughout the entire sample of objects. The uncertainties were calculated using IRAF. The target photometric uncertainty (Q) is deﬁned as the median value of the target light curve uncertainties. A histogram of the Q values for each object is shown in Figure 3.3, and the value for all targets are listed in Table 3.3 and Table 3.4. The median Q value for the entire survey is 0.7%. Weather in the atmospheres of Brown Dwarfs 89

10 BD Number 5

0 0 20 40 60 80 100 p-value (%)

Figure 3.4: p-value histogram of the full brown dwarf sample. The objects in the first bin includes 16 targets with p-value 5%, and three targets with ≤ p-values from 5 – 10%. Of the 16 targets with p-value 5% listed in Table 3.3, ≤ two targets are not listed since they failed the robust criterion (˜η 1). The large ≥ number of objects in the last two bins (80 to 100) is suggestive of conservative errorbars. Weather in the atmospheres of Brown Dwarfs 90 (%) 3 2 9 2 5 6 1 5 7 1 5 6 7 5 6 9 1 ...... ∗ 1 1 0 1 0 1 1 0 0 1 0 0 0 0 0 1 1 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 8 3 6 8 7 4 1 6 2 2 7 0 9 4 0 6 2 ...... -value (%) Amplitude p (%) ˜ η Q 0 . 1 0 ≥ . 2 ν 1 η χ ≥ η 10% and ˜ 5% and ˜ ≤ ≤ -value -value p < p Variables identified in this study. Variables with Variables with 5% Table 3.3: Object2MASS J01062285-5933185 L0 Spectral Type Obs. Dur. (hours) 3.14 Refs.DENIS J0205.4-1159 DOF 7 5 L5.5 4.4 1.3 1.07 3.22 0.12 5 4 5 2.0 1.5 0.50 7.9 2 2MASS J13004255+19123542MASS J03582255-41160602MASS J08354256-08192372MASS J22551861-57130562MASS J10101480-0406499 L32MASS J04390101-23530832MASS L5 J11263991-50035502MASS L5 J12074717+0244249 L5.52MASS J21392676+0220226SIMP L6 J013656.5+093347.3 L6.52MASS J22282889-4310262 L6.52MASS J00501994-3322402 T02MASS T1.5 J03480772-6022270 3.06 1.97 T2.5 T6.5 3.32 3.162MASS J09310955+0327331 T7.02MASS J12171110-0311131 T7.0 3.08 2.53 3.23 5 2.76 L7.5 2.62 6 6 T7.5 3 2.94 9 3.08 4 8 2.63 4 8 2.85 10 6 3.6 7 7 4.2 8 5 5.8 2.6 3.21 5 12 4.0 8 1.9 2.78 2.0 7 1.21 6 7 4.3 2.5 2.7 3.3 7 0.88 7 0.33 2.0 1.7 7 1.55 18.1 2.1 1.4 6 3 0.0 3.9 1.18 6 2.3 0.50 1.4 0.52 6 2.6 0.2 0.0 5.6 0.42 2.2 0.0 0.91 10 1.3 2.5 3.3 5 0.0 0.72 1.8 0.0 1.6 0.51 1.8 9 1.24 0.0 4 4.2 1.9 0.42 1 1.0 9 2.3 1.2 1.8 1.55 5 2 3 0.0 0.93 1.9 4 5 6.1 3 3 9.3 10 2 7 4 These peak-to-trough amplitudes are calculated as the difference between the minimum and maximum points in the light curve. In some cases, these might represent the lower limit of the true amplitude, ∗ Notes: especially for brown dwarfs which exhibit variability on longer time scales. Weather in the atmospheres of Brown Dwarfs 91

3.1.5.3 Identifying variables

The significance of the variations were assessed in comparison to two criteria. For the first assessment, the final target light curve was compared against a flat line using the reduced robust median statistic (˜η)(Enoch et al. 2003). The definition ofη ˜ is expressed as N 1 X ∆Fi median(∆F ) η˜ = − (3.1) d σi i=1

where d deﬁnes the number of free parameters and σi, the uncertainty on each photometric measurement in the ﬁnal target light curve.

2 For the second assessment, the reduced chi squared (χν) value for each target light curve was calculated relative to the master reference light curve. The deﬁnition 2 of χν is expressed as N 2 1 X (Oi Ei) χ2 = − (3.2) ν ν σ2 i=1 i

where ν is the degrees of freedom, Oi is the ﬁnal target light curve, Ei is the master

reference light curve and σi is the uncertainty on the ﬁnal target light curve and master reference light curve added in quadrature.

2 Astrophysical variability was better determined calculating χν relative to the master reference light curve instead of a straight line, which was more prone to classify- 2 ing variable conditions over intrinsic variability. We make use of the χν to estimate the cumulative distribution function and thus the p-value for each final target light curve. The p-value is the probability that the final target light curve is the same as (p-value > 10%) or different from (p-value 10%) the master reference light ≤ curve. In Figure 3.4, we plot the histogram of the calculated p-values for the full sample, and the large number of objects in the first bin gives an indication of the variables in the survey. The first bin contains 16 objects with p-value 5%, and ≤ the level of false positives expected with an equivalent p-value is 3 to 4 objects (5%) for a sample of 69 targets. For the identification of variables, both p-value and anη ˜ thresholds were applied. The number of targets with p-value 5% but ≤ η˜ > 1 was two, which is similar to the level of expected false positives. The excess of targets in the last two bins of Figure 3.4 suggests that the uncertainties for the sample are conservatively estimated. Weather in the atmospheres of Brown Dwarfs 92

The p-value is the probability, under the assumption that we detect no variability (our null hypothesis), of observing variability greater or equal to what was observed in the master reference light curve. The survey has 39 targets satisfying the criterion ofη ˜ 1 and 16 targets with p-value 5%. Objects classified as variable ≥ ≤ in this study satisfied two criteria, defined by p-value 5% andη ˜ 1, and they ≤ ≥ are listed in Table 3.3. Candidate variables with a less restrictive p-value 10% ≤ andη ˜ 1 are also listed in Table 3.3. ≥ The min-to-max amplitudes of the variable objects were calculated as the difference between the highest and the lowest point in the light curve, using the uncertainties on these two points to calculate the uncertainty on the amplitude. Using this method to calculate the amplitude is dependent on how the data is binned, with the unbinned data showing larger amplitude variations. The amplitudes listed in Table 3.3 use the more conservative estimate from binned data. For objects with periods larger than the duration of observations, the amplitude is likely an underestimate, as the entire period is not observed. An example of a target with a known variable period exceeding the observation timescale is 2M2139, and the reported amplitude in this study is lower than longer timescale results (Radigan et al. 2012). Due to the limited duration and cadence of the observations, it is not possible to measure the periods of the variables in the BAM study.

3.1.6 Results of the BAM survey

The primary result from the BAM survey is the identification of a set of 14 variable brown dwarfs with p-value 5% and a further three candidate variables ≤ with 5% < p-value 10% (see 3.1.6.2). For the remaining analysis, we only ≤ § consider the p-value 5% variables. The BAM variables appear to show two ≤ morphologies. The first type of light curve shows pure sinusoidal trends, akin to 2M2139 (Radigan et al. 2012). Variables like 2M0050, 2M0348, 2M1010, and possibly 2M2255 appear to have sinusoidal light curves. The second group consists of targets that appear to display multi-component variations in their light curves akin to SIMP0136 (Artigau et al. 2009; Metchev et al. 2013). SIMP0136 shows remarkable evolution in its features over multiple epochs, possibly caused by rapidly varying cloud features (Metchev et al. 2013). Objects with light curves similar to SIMP0136 object, such as 2M0106, 2M0439, 2M0835, 2M1126, 2M1207, 2M1300 are interesting for future follow up, to confirm whether or not they also Weather in the atmospheres of Brown Dwarfs 93

1.04 1.08 1.04 1.03 L0 J0106-5933 1.06 L3 1.03 L5 1.02 1.04 1.02 1.01 1.01 1.02 1.00 1.00 1.00 0.99 0.99 0.98

Relative Flux 0.98 0.96 0.98 0.97 J0358-4116 0.94 J1300+1912 0.97 0.96 1.08 1.04 1.02 L5 1.06 J2255-5713 1.03 L6 J1010-0406 1.04 1.02 1.01 1.01 1.02 1.00 1.00 1.00 0.99 0.98 Relative Flux 0.99 0.98 J0835-0819 0.96 L5.5 0.97 0.98 0.94 0.96 1.03 1.04 1.02 1.03 L6.5 J0439-2352 1.02 L6.5 T0 1.02 1.01 1.01 1.01 1.00 1.00 1.00 0.99 0.99 Relative Flux 0.99 0.98 0.98 J1126-5003 0.97 J1207+0244 0.98 0.96 1.04 1.025 1.03 1.020 1.03 J2139+0220 T2.5 1.02 T6.5 1.015 1.02 1.010 1.01 1.01 1.005 1.00 1.00 1.000 0.995 0.99 0.99 Relative Flux 0.990 0.98 0.98 T1.5 0.985 J0136+0933 J2228-4310 0.97 0.980 0.97 0 1 2 3 1.08 1.015 Time (Hours) 1.06 J0050-3322 1.010 1.04 1.005 1.02 1.000 1.00 0.995 0.98 0.990 Relative Flux 0.96 T7 0.985 T7 J0348-6022 0.94 0.980 0 1 2 3 0 1 2 3 Time (Hours) Time (Hours)

Figure 3.5: Final target light curves of the 14 variable objects (blue points) with a p-value 5% andη ˜ 1.0 together with the master reference light curves ≤ ≥ (yellow points). The uncertainties on the variable light curve incorporates the uncertainties in the master reference light curve. Weather in the atmospheres of Brown Dwarfs 94

1.015 1.03 1.08 1.010 J0205-1159 T7.5 J0931+0327 1.02 J1217-0311 1.06 1.005 1.01 1.04 1.000 1.00 1.02 0.995 0.99 1.00 0.990 0.98 Relative Flux L5.5 0.98 T7.5 0.985 0.97 0.96 0 1 2 3 0 1 2 3 0 1 2 3 Time (Hours) Time (Hours) Time (Hours)

Figure 3.6: Final target light curves of the candidate variables (larger blue points) with 5% < p-value 10% andη ˜ 1.0 together with the master reference ≤ ≥ light curves (yellow smaller points).

1.010 1.015 1.010 J0559-1404 J0407+1546 J2322-3133 1.010 1.005 Q =0.37 Q =0.43 1.005 Q =0.49 1.005 1.000 1.000 1.000

Relative Flux 0.995 0.995 0.995 0.990 0.990 1.015 1.015 1.010 J2151-4853 1.010 J1534-2952 1.010 J0510-4208 1.005 Q =0.62 Q =0.66 1.005 1.005 1.000 1.000 1.000 0.995 0.995 0.995 Relative Flux 0.990 Q =0.51 0.990 0.990 0.985 0.985 0.985 1.025 1.020 1.04 1.020 J1155+0559 1.015 J1404-3159 1.03 J1007-4555 1.015 Q =0.74 1.010 Q =0.82 1.02 Q =1.62 1.010 1.005 1.01 1.005 1.000 1.00 1.000 0.995 0.995 0.99

Relative Flux 0.990 0.990 0.98 0.985 0.985 0.97 0.980 0.980 0.96 0 1 2 3 0 1 2 3 0 1 2 3 Time (Hours) Time (Hours) Time (Hours)

Figure 3.7: Final target light curves of a subset of constant objects in this survey (larger blue points) with the master reference light curves (yellow smaller points). The target photometric uncertainty decreases from top to bottom and includes the light curve with the best photometry (top left) and light curve with the worst photometry (bottom right). Weather in the atmospheres of Brown Dwarfs 95 show rapidly evolving light curves. Finally, the light curve of 2M0358 may be a fast rotating variable, since 2M0358 appears to oscillate through more than one cycle within the limited timespan of the BAM monitoring. The light curve of 2M2228 shows similar short time scale variations as 2M0358 and was previously +0.16 found to be variable with a period of P= 1.43 0.15 hours by Clarke et al.(2008). − Final target light curves for the 14 BAM variables and the associated comparison master reference light curves are shown in Figure 3.5. Similar plots for the candidate variables are given in Figure 3.6. The amplitudes and p-values are reported in Table 3.3.

Representative light curves of nine constant targets with a range of photometric qualities are shown in Figure 3.7. These light curves show the full range of the data quality for brown dwarfs of similar brightness to the variables identified in the study. The constant light curves are not all flat, however their variations are not statistically distinct from their associated master reference. The constant targets do not satisfy the two separate criteria used to identify the variables (specified in section 3.1.5.3) which require the final target light curve to be distinct from the master reference light curve (p-value) and a flat line (˜η). The p-values for constant sources are given in Table 3.4.

Since the p-value 5% cutoﬀ is a statistical measure, there remains a likelihood ≤ of a contamination level of 3 – 4 false variables that are statistical ﬂuctuations, 5% of the entire sample. Continued monitoring of the variables should help ∼ identify false positives.

3.1.6.1 Comparison of variables with previous studies

This Js-band SofI program is the largest uniform monitoring survey conducted in the near-IR. Several previous surveys have targeted smaller sample sets (e.g. Buenzli et al. 2013; Clarke et al. 2008; Enoch et al. 2003; Girardin et al. 2013; Khandrika et al. 2013; Koen et al. 2004, 2005) or searched in different wavelengths such as I-band (e.g. Gelino et al. 2002; Koen 2004, 2013). Apart from results of the study by Koen(2013), previous surveys have typically targeted fewer than 25 objects and detected variability frequencies of 30% in their sample sets, ∼ ∼ with a significant amount of overlap in the target samples used in different studies (Khandrika et al. 2013). The BAM sample was designed to uniformly cover the L- T spectral range (see Figure 3.2) and includes 35 brown dwarfs that have not been Weather in the atmospheres of Brown Dwarfs 96 previously monitored in different surveys. There are nine new BAM variables, six of which have not been previously monitored for variability – 2M0050, 2M0106, 2M0358, 2M1010, 2M1207 and 2M2255. The survey has three variables that were previously found to be constant, and found nine brown dwarfs previously classified as variable to be constant. Finally, there are five variables that were found to vary in the literature and in this BAM study. A synopsis of the variables in the BAM and previous surveys is presented in Table 3.5. These objects are used to investigate the persistence of variability in section 3.1.7.5. Table 3.6 presents the constant brown dwarf sample in the BAM study. These are targets that were monitored in previous surveys and were found to be constant in the literature and in this study. In the following two subsections, we compare our results with literature measurements for the variables identified in this sample and in previous work.

3.1.6.2 BAM Variables

In Table 3.5, we present information for all the targets that were considered variable, either in this BAM study or in the literature. Three of the BAM variables – 2M0348, 2M0439 and 2M1126 – were identified as constant brown dwarfs in prior surveys but appear to be variable in this survey. A further five brown dwarfs – SIMP0136, 2M0835, 2M1300, 2M2139 and 2M2228 – were confirmed to be variable both in this study and in the literature. Of these five, SIMP0136, 2M2139 and 2M2228 were previously found to vary in the near-IR, similar to this study. The other two variables 2M0835 and 2M1300 were originally measured to vary in the Ic band, and also display multi-component variations at near-IR wavelengths. Amongst the known variables with measured periods (from previous studies), only 2M2139 and 2M1300 have periods longer than the duration of the BAM monitoring data (> 7 hours, and 238 hours, respectively). The latter period is much longer than the expected rotation for a brown dwarf (Zapatero Osorio et al. 2006), which indicates that the periodic feature might not be related to the rotation of the brown dwarf (Gelino et al. 2002). The three remaining targets with previously measured periods - SIMP0136, 2M0835 and 2M2228 - were monitored in this study with a time span greater than one of their rotational periods. All three objects that we monitored over an entire period had amplitudes consistent with what has been previously published. Weather in the atmospheres of Brown Dwarfs 97

3.1.6.3 Variables in previous studies not conﬁrmed with BAM

There are nine targets from the BAM sample that have been previously reported as variable, but were found to be constant in this survey. These sources are listed in Table 3.5, with a summary of the previous results pertaining to variability, including the observation wavelength and any notes on the amplitudes and timescales of the variations in brightness. One of these nine variables from literature – 2M0228 – has only been monitored in the optical. The remaining eight variables exhibited modulations in the near-IR. 2M0559, 2M0624, DENIS0817 and 2M1624 were found to have small amplitude variations in the Buenzli et al.(2013) survey carried out using the HST grism data. In the HST survey, 2M1624 showed variability in the water band (1.35-1.44 µm) but was found to be constant at J-band wavelengths. Similar to other ground based surveys that found some of these targets constant, this BAM survey likely does not have the photometric sensitivity necessary to confirm the HST variables, nor is it possible to monitor the water bands from the ground. Another four targets – SDSS0423, 2M0939, 2M1534 and 2M2331 – also appear constant in the data. The photometric uncertainties on SDSS0423 and 2M2331 are too large to confirm their lower amplitude variability of 0.8% ∼ and 1.2%, respectively. Despite 2M0939 having been observed as a variable in ∼ the K’ band with an amplitude of 3.1% (Khandrika et al. 2013), we are unable to confirm any variability in Js with the BAM observations. 2M1534 was detected to vary in the JHKs bands initially in (Koen et al. 2004), but was constant in a later epoch (Koen et al. 2005). Koen(2013) further discounts the likelihood of detecting short period variability in 2M1534, but maintains that the target likely varies on the timescale of a few days. The reported amplitudes in the H-band and K-band are below the detection threshold in the data for this target.

3.1.7 Discussion

3.1.7.1 The sensitivity of the BAM survey

To obtain an estimate of the variability frequency for brown dwarfs across spectral types, it is essential to quantify the sensitivity of the data to detecting diﬀerent amplitudes of variability. We estimate the sensitivity to variables of a certain amplitude as three times the target photometric uncertainty of each ﬁnal target light curve. This places a limit on the minimum amplitude required for a detection Weather in the atmospheres of Brown Dwarfs 98

Table 3.4: Limits on constant targets in this survey.

2 Object Spectral Type Obs. Dur. [hours] Refs. DOF χν η˜ Q (%) p-value (%) 2MASS J00165953-4056541 L3.5 3.43 6 8 0.9 0.8 0.54 51.1 2MASS J00184613-6356122 L2 3.43 7 8 1.1 1.0 0.42 35.4 2MASS J00345157+0523050 T6.5 2.98 7 7 0.9 1.1 0.53 49.1 2MASS J01282664-5545343 L1 2.66 5 5 0.5 2.1 0.61 77.7 2MASS J02284355-6325052 L0 2.84 3 10 0.8 1.0 0.42 62.7 2MASS J02572581-3105523 L8 3.33 7 5 0.3 1.2 0.48 90.2 2MASS J03185403-3421292 L7 1.97 5 4 1.9 1.8 0.99 10.1 2MASS J03400942-6724051 L7 2.61 6 5 0.2 1.1 0.75 96.4 2MASS J04070752+1546457 L3.5 3.19 7 7 0.7 0.7 0.43 68.4 2MASS J04151954-0935066 T8 3.29 4 7 0.3 0.6 0.83 95.8 SDSS J042348.56-041403.5 T0 2.62 8 5 0.4 0.7 0.51 86.2 2MASS J04455387-3048204 L2 4.55 7 9 0.7 0.7 0.36 68.7 2MASS J05103520-4208140 T5 2.74 6 6 0.5 0.6 0.66 84.2 2MASS J05160945-0445499 T5.5 3.11 4 7 1.1 1.1 0.88 38.5 2MASS J05233822-1403022 L5 4.56 6 9 0.7 1.0 0.99 66.8 2MASS J05591914-1404488 T4.5 3.11 6 7 0.3 0.5 0.37 96.3 2MASS J06244595-4521548 L5 3.26 5 6 1.2 1.0 0.49 28.5 2MASS J07290002-3954043 T8 3.37 8 10 0.6 0.6 0.9 84.3 DENIS J081730.0-615520 T6 3.48 8 13 0.8 0.7 0.68 64.5 2MASS J09153413+0422045 L7 3.33 6 7 0.9 0.8 0.55 50.1 2MASS J09393548-2448279 T8 3.06 8 9 1.0 0.8 0.98 46.5 2MASS J09490860-1545485 T2 3.16 8 6 1.7 1.3 0.67 11.0 2MASS J10043929-3335189 L4 3.14 8 11 1.4 1.0 0.99 17.6 2MASS J10073369-4555147 T5 3.41 8 13 0.3 0.5 1.62 99.5 2MASS J10210969-0304197 T3 3.17 7 6 0.7 0.6 0.88 64.1 2MASS J11145133-2618235 T7.5 2.90 5 5 0.4 1.0 1.0 86.3 2MASS J11555389+0559577 L7.5 2.87 5 7 0.6 1.2 0.74 79.3 2MASS J12255432-2739466 T6 2.85 7 5 0.4 0.3 0.67 86.9 2MASS J12281523-1547342 L6 3.39 7 10 1.0 1.1 0.5 42.5 2MASS J12314753+0847331 T5.5 2.56 5 5 0.3 1.6 1.63 89.6 2MASS J12545393-0122474 T2 3.17 7 9 1.0 1.1 0.51 45.2 2MASS J13262981-0038314 L5.5 2.80 4 7 0.9 0.9 1.17 50.8 2MASS J14044941-3159329 T2.5 3.01 8 8.5 0.4 0.6 0.82 89.4 2MASS J15074769-1627386 L5.5 4.16 7 15 0.4 0.6 1.21 98.5 SDSS J151114.66+060742.9 T.0 3.85 7 11 0.8 0.6 0.8 64.1 2MASS J15210327+0131426 T2 6.37 7 12 0.5 0.6 0.9 93.6 2MASS J15344984-2952274 T5.5 3.88 8 8 0.5 0.6 0.62 85.3 2MASS J15462718-3325111 T5.5 3.50 4 7 0.4 0.5 1.45 93.3 2MASS J15530228+1532369 T7 3.82 7 8 2.7 1.0 0.72 0.7 2MASS J16241436+0029158 T6 3.21 8 8 0.3 0.4 0.66 95.6 2MASS J16322911+1904407 L8 3.89 4 14 1.1 1.0 1.76 36.4 2MASS J18283572-4849046 T5.5 3.06 8 7 0.4 0.5 0.5 88.7 2MASS J19360187-5502322 L5 3.21 7 6 0.4 0.5 0.4 86.9 SDSS J204317.69-155103.4 L9.0 3.03 8 6 1.4 1.0 1.14 22.5 SDSS J204749.61-071818.3 T0.0 2.68 8 5 1.6 1.2 1.16 15.8 2MASS J20523515-1609308 T1 3.08 8 7 0.8 0.8 0.7 62.9 2MASS J21513839-4853542 T4 3.08 8 7 0.8 0.7 0.51 63.0 2MASS J22521073-1730134 L7.5 2.34 5 5 0.8 1.3 0.65 58.9 ULAS J232123.79+135454.9 T7.5 2.94 8 7 0.3 0.6 0.9 94.9 2MASS J23224684-3133231 L0 2.69 6 4 1.1 0.9 0.49 37.8 2MASS J23312378-4718274 T5 2.63 5 6 1.7 1.1 1.13 12.0 2MASS J23565477-1553111 T6 2.98 5 7 3.5 0.6 0.64 0.1 above a certain statistical significance threshold. The proportion of the sample that is sensitive to a given variability amplitude is shown as a function of amplitude in Figure 3.8. As shown in Figure 3.8, the BAM survey is capable of detecting any object in the sample showing a peak-to-trough amplitude 2.3% during ≥ the duration of the observations. The detection probability continues to decrease with decreasing amplitude with a sensitivity of 50% occurring for variables with a 1.7% amplitude. Given that the full BAM sample is sensitive to variables with ∼ amplitudes 2.3%, Table 3.7 quantifies the frequency of variability for different ≥ subsets of spectral types using an amplitude cutoff of 2.3% and p-value 0.05; ≤ this level includes all but one BAM p 0.05 variable. Figure 3.9 shows how ≤ the variability frequency (considering all spectral types) varies as a function of amplitude to account for the declining proportion of the sample that is sensitive to lower amplitude variables. Weather in the atmospheres of Brown Dwarfs 99 ) 0.005 hr µm ± 2 mmag 18 mmag 0.16hr 0.9 hr ± K < ± K < 96 hr 1%) . . 62 hr . 4hr . 0 0.05 hr 8% ± ± -val= 6 39 – 1 . < p 11 mmag, 11 mmag, ’ K 1.7% 013 mag . 4 mmag, P=1.43 3 mmag, P=2.9 H < H < 7 mmag, P= 0 0 . . < 1 1 ’ ± K ± ± K )=(0.3, 0.18, 0.17) mag, P = 7.721 4 4 . . 9hr 176 5%, P = 2.39 7%, C at 8 mmag, P= 2 18 mag, P= 1 K . . . Jy . . , ± Jy Jy Jy Jy Jy Jy µ 0 0 Jy Jy H µ µ µ µ µ µ 15 mmag, 1.1%, 10 mmag, 141 mag , µ µ =10-16 mmag, P=3.1 hr = 12 = 0 = 4 = 15 = 6 . ± ± c 4 mmag, J 111 3% 30 10 mmag, periodic 30 87 42 7% 5 mmag 0 63 30 I J J J J J 0 3 42 36 . . < < < < < < J < < J < < < < < < J < H < < Jy µ 27 Z06 < CCCCC E03 C08 K13 K05 K13C possibly periodic K13 C KTTK05 C K13 CC K05 C KMM04 K13 CCC K13 C E03 CC K04 C K13 KTTK05 K05 C KMM04 V V V VV K04,V K13 ∆ A03 ∆ G02 P=238 V A09, Ap13 ∆ V V V V Candidate Variable ( V C08 8 V K13 V KMM04 V C08 ∆ V C08, Bu12 ∆ V R12, Ap13 ∆( C08 C likely V E03 0 Summary of variable sources. ( 2012 ) [R12], Zapatero Osorio et al. ( 2006 ) [Z06] New variables previously categorised as constant ’ C Kh13 ’ V Kh13 ∆ s s s s s s Literature variables confirmed as variable in this study K K ’ V Kh13 0.31 mag s s s s s s s s s s c c c c c c c c c c c c c New variables from this study with no prior observations I J J J J J J J I I I I I I I I I I I I I J J J J J J J K K K K + + JK Table 3.5: JHK JHK JHK JHK JHK JHK J J 8.46 GHz8.46 GHz C8.46 GHz C B06 C B06 B06 8.46 GHz C B06 8.46 GHz C B06 8.46 GHz8.46 GHz C B06 B06 8.46 GHz C B06 8.46 GHz C B06 Objects with reported IR variability measured as constants in this study Objects with reported Optical variability measured as constants in this study 3%) 8.46 GHz C B06 9%) . . -val= 7 p Target Name Band Variable/Constant References Notes 2MASS J11263991-5003550 Candidate Variable (p-val= 9 2MASS J13004255+1912354 2MASS J12074717+0244249 2MASS J22551861-5713056 2MASS J10101480-0406499 2MASS J03480772-6022270 2MASS J04390101-2353083 2MASS J08354256-0819237 2MASS J12171110-0311131 2MASS J00501994-3322402 DENIS J0205.4-1159 SIMP J013656.5+093347.3 2MASS J22282889-4310262 SDSS J042348.56-041403.5 2MASS J02284355-6325052 2MASS J01062285-5933185 2MASS J03582255-4116060 2MASS J09310955+0327331 Candidate Variable ( 2MASS J21392676+0220226 2MASS J05591914-1404488 HST G141 grism2MASS J06244595-4521548DENIS J081730.0-6155202MASS J09393548-2448279 2MASS J15344984-2952274 HST V G141 grism HST G141 grism V Bu13 V Bu13 Bu13 2MASS J23312378-4718274 2MASS J16241436+0029158 HST G141 grism V Bu13 Variability detected in water band (1.35-1.44 ( 2003 ) [E03], Gelino et al. ( 2002 ) [G02], Khandrika et ( 2013 ) al. [Kh13], Koen ( 2004 ) [K04], Koen et al. ( 2004 ) [KMM04], Koen et( 2005 ) al. [KTTK05], Koen ( 2005 ) [K05], Koen ( 2013 ) [K13], Radigan et al. References: Artigau et al. ( 2003 ) [A03], Artigau et al. ( 2009 ) [A09], Apai et al. ( 2013 ) [Ap13], Berger ( 2006 ) [B06], Buenzli et al. ( 2012 ) [Bu12], Buenzli et al. ( 2013 ) [Bu13], Clarke et al. ( 2008 ) [C08], Enoch et al. Weather in the atmospheres of Brown Dwarfs 100

Table 3.6: Summary of constant sources.

Target Name Band References Notes 2MASS J02572581-3105523 Ic K13 2MASS J04070752+1546457 JK0 Kh13 no results 2MASS J04151954-0935066 8.46 GHz B06 < µJy 2MASS J04455387-3048204 Ic K13 Ic K04 8.46 GHz B06 < 66µJy 2MASS J05233822-1403022 Ic K13 Ic K05 8.46 GHz B06 231 ± 14µJy 2MASS J12255432-2739466 J KTTK05 < 12 mmag H < 14 mmag Ks < 9 mmag JHKs KMM04 2MASS J12281523-1547342 Ic K13 8.46 GHz B06 < 87µJy 2MASS J12545393-0122474 JHKs KMM04 J Gi13 < 5mmag 2MASS J15074769-1627386 Ic K13 Ic K03 8.46 GHz B06 < 57µJy 2MASS J1511145+060742 J Kh13 < 3.3% K’ < 6.1% 2MASS J15462718-3325111 JHKs KMM04 2MASS J15530228+1532369 JHKs KMM04 2MASS J16322911+1904407 8.46 GHz B06 < 54µJy HST G141 Grism Bu13 2MASS J19360187-5502322 Ic K13 2MASS J23224684-3133231 Ic K13 References: Berger(2006) [B06], Buenzli et al.(2013) [Bu13], Girardin et al.(2013) [Gi13], Khandrika et al.(2013) [Kh13], Koen (2004) [K04], Koen(2003) [K03], Koen et al.(2004) [KMM04], Koen et al.(2005) [KTTK05], Koen(2005) [K05], Koen(2013) [K13].

To calculate the uncertainty on the variability frequency we use the binomial distribution

N! n N n B(n; N, v) = (1 v) − . (3.3) n!(N n)! v − −

100

0 Detection probability for the sample (%) 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 Amplitude (%)

Figure 3.8: Proportion of the survey sensitive to variability as a function of peak-to-trough amplitudes for diﬀerent detection thresholds. The dashed line represents the fraction of objects with a photometric accuracy good enough to have allowed for the detection of variability. The shaded area represents the region of sensitivity with the upper binomial errors and amplitude uncertainties added to the variability fraction. Weather in the atmospheres of Brown Dwarfs 101

10 Variability Frequency (%) 0 3.0 2.5 2.0 1.5 1.0 Amplitude (%)

Figure 3.9: Variability frequency as a function of amplitude (dashed line) with the binomial errors and amplitude uncertainties added to the variability fraction (shaded area).

100

Amp = 1.5% 20 Amp = 2.5% Amp = 5.0% 0 4 6 8 10 12 Variable Detection Probability (%) Period (hours)

Figure 3.10: Percentage of simulated sinusoidal light curves detected as variable, as a function of period from 1 hour to 12 hours, for three diﬀerent amplitudes. We used the measured survey median noise of 0.7%, and each sine curve was sampled at intervals of 15 minutes to imitate the binned data of the survey. Additionally, we stepped through each sine curve at 5 degree phase intervals, to ensure that we sampled the full phase of the variable light curve. Weather in the atmospheres of Brown Dwarfs 102

where n is the number of variables, N the sample size and v the variability frequency. This approach is based on Bayes’ theorem under the assumption of a uniform prior based on no a priori knowledge and is ideal for small samples such as is the case for the BAM survey.

The rotation period is another factor that can influence the detectability of a variable signal. In Figure 3.10, we present the results of simulating light curves to test the detection probability of the survey to brown dwarf variables with different periods. We simulated sinusoidal light curves with three different amplitudes, of 1.5%, 2.5%, and 5.0%, and with periods ranging from a minimum of 1 hour to a maximum of 12 hours (Zapatero Osorio et al. 2006). Gaussian noise equal to the median photometric uncertainty of the survey of 0.7% was added to each light curve. To mimic the binned SofI data, the light curves were sampled at intervals of 15 minutes, and each simulated dataset was divided into groups of 3 hours, similar to the typical duration of the BAM data. For light curves with period longer than 3 hours, we generated multiple datasets, by stepping through the sine curve in steps of 5 degrees of phase and calculating the p-value at each phase, ensuring full sampling of the phase. Figure 3.10 shows the percentage of simulated light curves that are detected as variable with a p-value 5%. For amplitudes of 5.0%, ≤ periodicities from 3 to 12 hours are easily recovered with a probability of 80 to 100%, while the required periods decrease to 6 hours for 2.5% variables and ∼ 5 hours for 1.5% variables for detection probabilities in the 80 to 100% range. ∼

3.1.7.2 Frequency and amplitude of variability across spectral types

The frequency of variables as a function of spectral type is an important topic, since models of brown dwarf atmospheres have suggested that breakup of clouds across the L/T transition may result in both a higher rate of occurrence and a higher amplitude of variability compared to earlier L and later T objects. Amongst the previously known variables, the two largest amplitude variable objects discovered to-date are L/T transition objects - SIMP0136 ( 5% in J-band but with a ∼ signiﬁcant night to night evolution, Artigau et al. 2009) and 2M2139 (as high as 26% in the J-band, Radigan et al. 2012).

As indicated by the variability frequencies reported in Table 3.7, the BAM results show no evidence that the frequency of variables in the L7 to T4 transition region is distinct from the earlier spectral types, the later spectral types, or the combination Weather in the atmospheres of Brown Dwarfs 103

Table 3.7: Variability frequency.

Sample Sp. Type No. Targets No. Variables Freq. (%) † +11 Early-L L0-L6 23 7 30 8 +10− Late-T T5-T8 23 3 13 4 −+10 L/T Transition L7-T4 23 3 13 4 −+7 Outside L/T transition L0-L6 & T5-T8 46 10 22 5 − Notes: † These are the variables with a p-value 5%, and amplitude 2.3%. ≤ ≥ Temperature Range (K) 2200 2000 1800 1600 <-----1400 1200----- > 1050 750 3.0

2.5 100 10 2.0 ) g

a 1.5 ) m g ( a ) 1.0 S S % m 25 2.5 ( A σ

m 0.5 M ( 2

) σ K 0.0 - J

10 1 ( 0.5

1.0

1.5 L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 Spectral Type Spectral Type

Figure 3.11: Diagram on the left shows the amplitude of the variables (p- value 5% – closed circles and 5% < p-value 10% – closed circles with ≤ ≤ cross) as well as the target photometric uncertainty of the non-varying objects (coloured triangles) across the entire spectral range of the sample. The diagram on the right shows the colour-colour diagram of the entire L through T spectral range with the full sample plotted with open circles, showing the colour spread of the targets. The variables from the BAM sample are overplotted (p-value 5% ≤ – closed circles and 5% < p-value 10% – closed circles with cross). The L/T ≤ transition is indicated by the dashed lines of all non-transition region brown dwarfs. The variability frequencies in Table 3.7 are calculated using the entire sample of targets and an amplitude threshold of 2.3% and p 0.05. Although no statistically significant difference in the vari- ≥ ≤ ability frequencies for transition brown dwarfs is measured with the BAM survey, the 2.3% amplitude limit of the analysis would not have detected differences at lower amplitudes, and removing the peak-to-trough amplitude threshold does not change this result. Adjusting the boundaries of the transition region by up to two spectral types does not change the result. Likewise, the amplitudes of the detected variables show no clear trends with spectral type within the capacity of the survey, as shown in Figure 3.11 (left). The measured amplitude is sensitive to deviant photometric measurements which have the effect of possibly overestimat- ing the measured amplitude (i.e. last point in 2M1300). Identifying a minimum upper limit and a maximum lower limit could avoid such a bias for some of the Weather in the atmospheres of Brown Dwarfs 104

light curves. However, for light curves showing multi-component variability it is not clear which photometric points would be best suited for the amplitude calculations (i.e. 2M1126). Light curves showing deviant points where visually inspected to insure no cosmic rays aﬀected the data. Not accounting for variables which are identiﬁed as variables due to one or two possibly deviant photometric points does not introduce a change in variability frequency amongst the earlier, transition or later spectral types. In the interest of keeping the amplitude determination uniform throughout the sample, and to remove any human bias introduced in selecting upper and lower amplitude limits, the max-min amplitude is calculated using all the points in the light curve.

The BAM variability frequency is very comparable to estimates for M stars. A variability frequency between 21–29% for 19 M-stars was measured in a multi- ∼ wavelength optical study with the Calar Alto Observatory in Spain (Rockenfeller et al. 2006). The wavelength of observations for the M-star study was shorter than the BAM survey J-band data, and the amplitude of variations is expected to decline for longer wavelengths (e.g. Reiners et al. 2010).

In a recent compilation of variability surveys, Khandrika et al.(2013) reported a variability frequency of 30 5% based on a collection of different surveys with ± observations obtained in the optical and near-IR passbands, covering 78 objects in total. Comparison between surveys is difficult as the variability frequency may depend on a variety of different factors, including the target selection criterion and the criteria used to define variability in the targets which usually differs from one survey to the next. Additionally, the observed wavelength may also alter the variability frequency with different wavelength probing different depths in the atmosphere. Koen(2013) finds a poor overlap between the variables identified with optical and near-IR filters (of the 13 variables already observed in near-IR surveys, 7 were found as constant and 6 as variable in the optical). Because of the uniform sensitivity of this survey, we did not incorporate the results of previous studies into the statistics, presented in Table 3.7. The presence of highly variable objects outside the transition region, may suggest the possibility of both early onset of cloud condensation in the atmospheres of mid-L dwarfs and the emergence of sulfide clouds in mid-T dwarfs (Morley et al. 2012). The contribution of magnetic fields to the observed variabilty, especially for early L-type objects, is still an open question althogh most brown dwarfs are likely too cool to exhibit magnetic spots (Gelino et al. 2002; Mohanty et al. 2002). Other physical processes that have been Weather in the atmospheres of Brown Dwarfs 105 suggested to possibly induce variability in the atmospheres of brown dwarfs include coupling clouds with global atmosphere circulation (Showman & Kaspi 2013; Zhang & Showman 2014), and variability caused by thermal perturbations emitted from deeper layers within the brown dwarf atmosphere (Robinson & Marley 2014).

3.1.7.3 Variability as a function of colour within a spectral type

The J K colour of the sample as a function of the spectral type is shown in − Figure 3.11. The targets span nearly the full colour spread of early-L, transition and late-T sub samples. The 14 BAM variables and the three candidates are not clustered toward either the red or the blue within any particular spectral type. Previous studies (e.g. Khandrika et al. 2013) have suggested that brown dwarfs with unusual colours (highly red or blue) compared to the median of the spectral type might be indicative of variable cloud cover. We performed a two sample K-S test to determine whether or not the detrended colors of the BAM variables were distinct from the rest of the sample. The maximum diﬀerence between the cumulative distributions was 0.18 with a corresponding p-value of 75%, indicating that the two datasets are consistent with being drawn from the ∼ same sample. The BAM study thus ﬁnds no correlation between the variables and the colour of a brown dwarf within each spectral type.

3.1.7.4 Binarity and variability

The BAM sample includes 12 confirmed binaries out of 47 targets studied for binarity with another four SpeX spectra binary candidates. Including the binary candidates, 10 out of the 16 binaries in the BAM sample fall in the L/T transition. This is consistent with previous detections of an increase in the binary frequency across the L-T transition Burgasser et al.(2006). Amongst the BAM variables, only 2M2255 is a confirmed binary, while 2M1207 and 2M2139 are binary candidates. Amongst the non-variable objects no correlation between non-variability and binarity is observed in the L/T transition. A BD binary system can mimic a L/T transition BD if the combined light from the unresolved binary system originates from a pair of BDs which individually may not have a spectral type within the L/T transition. To investigate if such an effect would alter the results we calculate the variability frequency of objects confirmed to be single within each of the Weather in the atmospheres of Brown Dwarfs 106 spectral bins. We find the measured frequency of the L/T transition to be indistinguishable from the earlier and later spectral types. The limited data provides no evidence to support a correlation between variability and binarity amongst the objects in the BAM survey.

3.1.7.5 Persistence of variability

A recent multi-epoch ( 4 years) monitoring study of the variable brown dwarf ∼ SIMP0136 (Metchev et al. 2013) revealed that the target has significant evolution in its light curve, changing from highly variable to constant in a 2 month period. When compared to the SofI light curve for SIMP0136, the target shows a fascinat- ing variation in amplitude. It appears to be variable at 3% in the SofI data, while a month later it shows large amplitude variations ( 9%) in the J-band, only to ∼ appear constant a few months later. Similar night-to-night variations have also been seen in SDSS J105213.51+442255.7 (Girardin et al. 2013). The evolution indicates a lack of persistence in the source of variability over timescales longer than a few weeks and it suggests that the brown dwarfs identified as constant in this study might similarly exhibit periods of quiescence and enhanced activity. The BAM survey only examines variability on the timescale of a single rotation period or less as compared to some surveys (e.g. Enoch et al. 2003; Gelino et al. 2002) that study the flux variations of brown dwarfs over longer timescales.

The BAM data, in combination with previous results, can be used to address the question of persistence of variability. Table 3.8 summarizes the observations related to persistence of variability, using information presented in Table 3.5 and 3.6. For greatest consistency with the BAM study, we consider other epochs of near-IR data rather than optical. A total of 34 BAM targets have an earlier epoch of observation. 2M0228 is the only source measured to be variable in the optical

(Ic) that switched from variable to constant. Table 3.8 indicates that brown dwarf variability does not necessarily persist on longer timescales, with only half the BAM variables showing variation in both epochs. The survey ﬁnds four previously constant objects to be variable and nine targets previously reported as variable in the literature to be constant, making these ideal candidates for multiple epoch monitoring programs. Weather in the atmospheres of Brown Dwarfs 107

Table 3.8: Summary of Persistence Results

Total targets with 2 epochs 34 Variable at 2 epochs 6 Constant at 2 epochs 15 Switch between variable and constant 13

3.2 Summary

We present the results of the largest near-IR brown dwarf variability survey con-

ducted in the Js-band using the NTT 3.5 m telescope. The BAM survey has an unbiased sample of 69 early-L through late-T brown dwarfs. A total of 14 variable objects were detected: six new variables not previously studied for variability, three objects previously reported as constant, and five previously known variables. The nine newly identified variables constitute a significant increase in the total number of known brown dwarf variables characterisable using ground-based facilities. In a recent study of 57 L4-T9 brown dwarfs (Radigan et al. 2014), a set of 35 targets were observed by both studies, enabling a direct comparison of results. Of the 35 targets in both samples, both studies classify a common 26 targets as not variable and a common 4 targets as variable. Of the 5 remaining variables noted in a single study (2 in BAM, 3 in Radigan et al. 2014), 4 can be explained by differences in sensitivity for the specific light curves.

Rather than quoting a single number for the variability frequency, we discuss how the frequency of variable brown dwarfs depends on different factors such as the observed wavelength and the variability amplitude. The BAM study, representing the largest and most uniform ground-based search for variability, was designed to address the important question of the physical properties of brown dwarf atmospheres including the L-T transition. One class of models has suggested that this colour change, that defines the transition, may be a manifestation of the breakup of clouds resulting in a patchy coverage across the surface (Ackerman & Marley 2001), which would have the observable consequence of enhanced variability at the L-T transition. Considering the results of this study, covering both transition and non-transition objects and statistical significance of the variability, there is no distinction between the variability frequency between the brown dwarfs in the transition region or outside the transition region. This suggests that the patchy cloud scenario may not provide the full explanation for the L-T transition or that the induced level of variability is substantially below the detection thresholds of Weather in the atmospheres of Brown Dwarfs 108 the current study. The 14 variables, including the nine newly identified variables, will provide valuable systems with which to pursue additional questions of the physics of brown dwarf atmospheres, including the longitudinal and vertical variations of clouds and active regions which can be inferred from multi-wavelength follow-up monitoring.

Acknowledgements: Based on observations made with ESO Telescopes at the La Silla Paranal Obser- vatory under programme ID 188.C-0493. We would like to thank the anonymous referee for valuable suggestions thats helped improve this paper. PAW acknowledges support from STFC. JP was supported by a Leverhulme research project grant (F/00144/BJ), and funding from an STFC standard grant. This research has made use of the SIMBAD database and VizieR catalogue access tool, CDS, Strasbourg, France. The original description of the VizieR service was published in A&AS 143, 23. This research has beneﬁtted from the M, L, T, and Y dwarf compendium housed at DwarfArchives.org. This research made use of Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration et al. 2013). We thank F. Pont, R. De Rosa and D. K. Sing for valuable feedback and discussion.

3.3 Developments since publication

Subsequently with the publication of Wilson et al.(2014) a paper addressing many of the same questions was published by Radigan et al.(2014) who studied variability in 57 L4-T9 brown dwarfs. The main difference between the studies, in terms of scientific results, is that Radigan et al.(2014) find J-band variability of BD with peak to peak amplitudes &2% to be rare outside of the L9-T3.5 spectral range whereas Wilson et al.(2014) find high amplitude variables to be more evenly distributed amongst the brown dwarf spectral classes. The reason behind the different conclusions is not yet clear and could be due to the methods used in determining variability or the initial sample or a combination of both.

Although every eﬀort was made to minimize systematics in Wilson et al.(2014), there is still a chance that unaccounted for systematics could remain in the data which mimic real variability. These false variables should be contained within the Weather in the atmospheres of Brown Dwarfs 109

3-4 false positives which exist in the data (as inferred from the p-value determination). The survey sample in Radigan et al.(2014) is distinctly lacking in number of L-type objects, with the L-type objects being biassed towards bluer colours compared to most L-dwarfs. Partial cloud cover may explain the bluer L-dwarfs and as such the L-dwarf sample may be biassed towards objects which more likely show variability. The deficiency of unbiased L-dwarfs could be complimented by studies by Koen et al.(2004) and Clarke et al.(2008) who both find no evidence for J-band variability above a peak-to-peak amplitude of 2%. However, these studies use different variability criteria. The approach by Radigan et al.(2014) assumed the variability to be strictly sinusoidal in nature and does not account for objects with more erratic variations.

The two studies also share many similarities. Amongst the 35 objects common to both studies, 86% of them were both consistent in their classification typing an object as either non-variable or variable. For the remaining five variables, which differ between the two studies, four of them can be explained by differences in sensitivity. In terms of detected variability as a function of spectral type, the surveys are very similar, as can be seen in Fig. 3.12 and Fig. 3.13 as well as Table 3.9 and Table 3.10. Weather in the atmospheres of Brown Dwarfs 110

10 23 Targets 23 Targets 23 Targets

4 BD Number

0 L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 Y0 Spectral Type

Figure 3.12: Histogram of the BAM sample across their respective spectral classes. The sample size is represented by the gray histograms whilst the variables are coloured.

10 9 Targets 28 Targets 20 Targets

4 BD Number

0 L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 Y0 Spectral Type

Figure 3.13: Histogram of the Radigan et al.(2014) sample across their respective spectral classes. The sample size is represented by the grey histograms whilst the variables are coloured. The hatched areas symbolise the marginal detections at > 96% confidence. Weather in the atmospheres of Brown Dwarfs 111 4 4 5 5 +9 − +18 − +11 − +10 − 99% 14 11 15 18 > 5 8 4 4 +7 − +11 − +10 − +10 − 3%. . 6 11 5 6 2 +9 − +18 − +11 − +10 − Freq. (%) 96% Freq. (%) ≥ > 96% confidence. † > † 99% > 96% > 5%, and amplitude ≤ -value p 99% confidence, Marginal detections: > Variability frequency from Wilson et al. ( 2014 ). Variability frequency from Radigan et al. ( 2014 ). Table 3.9: Table 3.10: These are the variables with a † Late-T T5-T8 23 3 13 Sample Sp. Type No. Targets No. Variables Early-L L0-L6 23 7 30 Significant detections: Late-T T5-T8 20 3 3 15 Sample Sp. Type No. Targets No. Variables Early-L L0-L6 9 3 1 33 † L/T Transition L7-T4 23 3 13 Notes: L/T Transition L7-T4 28 6 5 21 Outside L/T transition L0-L6 & T5-T8 46 10 22 Notes: Outside L/T transition L0-L6 & T5-T8 29 6 4 21 Weather in the atmospheres of Brown Dwarfs 112

1.020

1.015 2M 1010-04 Sim. Ref 1.010

1.005

1.000

Relative Flux 0.995

0.990

0.985

0.980 0 1 2 3 4 Time (hr)

Figure 3.14: 2M1010-04 observations with the NOT (red) shown together with a similar brightness reference star (blue). Data discarded from the analysis is marked in grey. A simple best-ﬁt sine curve gives a peak-to-peak amplitude of 2.0 % and a period 4 hours. ∼ 3.3.1 Follow-up observations at the NOT and NTT

After the initial submission of BAM survey paper, observations of 2MASS J10101480- 0406499 were conducted at the Nordic Optical Telescope (NOT) program P48-411 (PI: Wilson, P. A.), using a similar bandpass filter, aimed at confirming the variability. The resulting light curve from the NOT observations are shown in Fig. 3.14. A simple sine curve was fit to the NOT data using a modified Levenberg-Marquardt algorithm which gave an estimate of the period 4 hours and peak to peak am- ∼ plitude of 2.0 %. The uncertainties where checked against the standard deviation 2 of the similar brightness reference star. The χred of the sine fit gives 0.4 compared to a straight line which gives 5.0. No correlation with FWHM is observed.

The data from the BAM survey was revisited and the photometry performed again, this time specifically optimising the 2M1010-04 observations by selecting the most optimal aperture for this object. The resulting unbinned light curve is shown in Fig. 3.15. A sine fit to this data gives a matching period of 4 hours however with ∼ a larger peak to peak amplitude of 4.7%. During the analysis a seeing variation was observed which showed similar variations to the 2M1010-04 light curve. None of the reference stars showed this variation so it is uncertain to what degree it may have affected the light curve, especially the amplitude. As both observations Weather in the atmospheres of Brown Dwarfs 113

1.10

1.05

1.00 Relative Flux

0.95

0.90 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Time (hr)

Figure 3.15: 2M1010-04 observations with the NTT (red) shown together with a similar brightness reference star (blue). Data discarded from the analysis is marked in grey (poor seeing). A simple best-fit sine curve gives a peak-to-peak amplitude of 4.7 % and a period 4 hours. ∼ acquired on different nights using different telescopes show similar periods, it is highly likely that the period is real in both cases.

Follow-up observations of the variable BAM survey targets are currently underway at the NTT telescope. The observations will allow for the confirmation of the variables and allow their variability to be characterised as a function of time and atmospheric depth using multi wavelength observations. The contamination due to unresolved binaries, can be reduced by searching for binarity amongst the objects in the BAM survey. This can be done by looking for RV variations in the BD spectra. Obtaining low resolution spectra and comparing these spectra to synthetic models, spectral LT binaries can be identified. Parallax measruements would allow likely binaries to be flagged if the object appears brigther than is expected for a single object in the CMD.

Chapter 4

The Atmospheres of Exoplanets

4.1 Detection of potassium in HAT-P-1b from narrowband spectrophotometry

4.1.1 Disclaimer

The work below is not published and may be subject to slight change. The paper below will be published in the Monthly Notices of the Royal Astronomical Society.

4.1.2 Abstract

We present the detection of potassium in the atmosphere of HAT-P-1b using optical transit narrowband photometry. The results are obtained using the 10.4-m Gran Telescopio Canarias (GTC) together with the OSIRIS instrument in tunable filter imaging mode. We observed a total of three transits, one outside the potassium feature at 6797.2 A˚ (R=566) and two probing the potassium feature by alternating the observed wavelengths between the line wing at 7582.0 A˚ (R=632) and the line core at 7664.9 A˚ (R=639). The planet-to-star radius ratios are found to be R /R?= 0.11706 0.00072 for 6797.2 A,˚ R /R?= 0.12461 0.00081 pl ± pl ± for 7582.0 A˚ and R /R?= 0.12855 0.00089 for 7664.9 A˚ using a 12 A˚ filter pl ± width. Compared to the weighted means of previous HST observations centred at 6797.2 A˚ and 8843.7 A,˚ the detection of potassium is evident from an increase in the radius ratio of 0.00636 0.00095 at 7582.0 A˚ (6.7 σ significance) and ± 115 The Atmospheres of Exoplanets 116

∆R /R?= 0.01030 0.00102 at 7664.9 A˚ (10.1 σ significance). Fitting a potassium pl ± profile to our data we derive a temperature of 1332 407 K. We hypothesize that ± the strong detection of potassium is caused by a large scale height, which can be explained by a higher than anticipated temperature in the upper atmosphere, or by the dissociation of molecular hydrogen into atomic hydrogen caused by the UV flux from the host star. We note that high resolution observations are essential for detecting very narrow alkaline spectral features such as those seen in HAT-P-1b and HD 189733b.

4.1.3 Introduction

Transiting exoplanets provide us with a unique opportunity to study the structure and composition of their atmospheres. A valuable insight into the planet’s atmosphere is gained by measuring the amount of stellar light which passes through the exoplanet atmosphere as a function of wavelength. The amount of light obscured by the transiting exoplanet is dependent on the atmospheric composition of its atmosphere, with absorbing species letting less light through at specific wavelengths, leading to a change in the exoplanet radius as a function of wavelengths. For hot Jupiters which are not dominated by clouds and hazes, the two most dominant sources of opacity in the optical are thought to be the alkali metals sodium and potassium (Seager & Sasselov 2000), with their resonance doublets at 5890, 5896 A˚ and 7665, 7699 A˚ respectively. Sodium was first detected by Charbonneau et al. (2002) in the atmosphere of HD 209458 b using the Space Telescope Imaging Spec- trograph (STIS) on the Hubble Space Telescope (HST). These observations were later confirmed by Snellen et al.(2008) using the High Dispersion Spectrograph at the Subaru telescope. Exoplanetary sodium has also been found to be present in the atmospheres of HD 189733b (Huitson et al. 2012; Redfield et al. 2008), XO- 2b (Sing et al. 2012) and WASP-17b (Wood et al. 2011; Zhou & Bayliss 2012). Exoplanetary potassium has been detected on the hot Jupiters XO-2b (Sing et al. 2011b) and HD 80606b (Colónet al. 2010) who, similar to this work, used tunable filters (TFs) with the Optical System for Imaging and low Resolution Integrated Spectroscopy (OSIRIS) instrument at the Gran Telescopio Canarias (GTC).

TFs have the unique capability of allowing the central wavelength and filter passband tuned to a specific value. The TF consists of a Fabry-Pérotetalon made up of two parallel reflective surfaces. By varying the separation between the two plates, The Atmospheres of Exoplanets 117

the filter width and central wavelength can be chosen. TF have several advantages over low resolution spectroscopy. They provide accurate differential photometry whilst also allowing for relatively high resolution measurements (R 600-700), ≈ compared to a low-resolution grism on OSIRIS (R 100-200). TFs have the ≈ unique advantage that they can be tuned to a wavelength not contaminated by strong telluric lines such as the prominent O2 lines at 6884 and 7621 A(˚ Catan- zaro 1997). Since no diffraction gratings are used, TFs can be much more efficient (Colónet al. 2010), especially for observing atomic absorption features which typically have a narrow spectral range. Combining this technique with the 10.4 m aperture of the GTC telescope makes it possible to study the atmospheres of planets orbiting stars fainter than HD 209458 and HD 189733, which due to apparent brightness, and large atmospheric scale heights, are the two best studied cases thus far.

In this study we present the detection of potassium in HAT-P-1b (Bakos et al.

2007), a 1.319 RJup exoplanet with a mass of 0.525 MJup and thus a low average density of ρ = 0.345 g/cm3 on a 4.47 day circular orbit around a G0V star at a distance of 0.055 AU (Bakos et al. 2007; Johnson et al. 2008). The host star appears to not be very active (Knutson et al. 2010) with HAT-P-1b showing signs of a modest temperature inversion layer (Todorov et al. 2010). With its low density and large radius HAT-P-1b is an interesting test case for interior and atmosphere models. These observations are a part of our larger spectrophotometric survey aimed at detecting and comparing atmospheric features in transiting hot Jupiters (ESO programme 182.C-2018).

In this paper we present our results on TF observations of HAT-P-1b with the GTC telescope. In 4.1.4 we describe the observations, and in 4.1.6 we describe § § the analysis of the transit light curves. In 4.1.7 we present a discussion of the § results were we compare the observations to a model atmosphere, and conclude in 4.2. §

4.1.4 Observations

Observations were performed using the 10.4 m GTC telescope located at Obser- vatorio del Roque de los Muchachos of the Instituto de Astrof´ısicade Canarias on The Atmospheres of Exoplanets 118

the island of La Palma. Narrowband imaging was done with the OSIRIS instrument using the red tuneable ﬁlter (operating range of 6510 A˚ - 9345 A)˚ tuned to the minimum width of 12 A.˚

4.1.4.1 Instrumental setup

The OSIRIS instrument (Cepa 1998; Cepa et al. 2000, 2003) consists of a mosaic of two Marconi CCD42-82 CCDs each with a 2048 x 4096 pixel detector separated by a 72 pixel gap between them. Each pixel has a physical size of 15 µm, which gives

a plate scale of 000.125. The observations were performed without any binning with a readout frequency of 500 kHz and a gain of 1.46 e−/ ADU on CCD2. This setup

gives a readout noise of 8e−. The observations tuned to 6797.2 A˚ were performed using the whole CCD2 array. Being one of the first OSIRIS observations, a sub- array mode was not offered. Later observations have since been performed in the sub-array mode as it reduces the read time yielding a higher cadence, and because the photometry of the first observations was not improved by including other fainter stars in the HAT-P-1 field. The observations tuned to 7582.0 and 7664.9 A˚ were windowed to 600 700 pixels. To obtain the highest possible resolution the × smallest possible passband of 12 A˚ was chosen.

4.1.4.2 Observing log

HAT-P-1b was observed on three separate nights. For all observations, the companion star HAT-P-1-B (BD+37 4734p) was used for photometric comparison, and

its close 1100proximity allowed for windowed frames to be taken. The frames ∼ were also rotated to ensure that both the target and the comparison star were at the same radial distance from the centre of the CCD, ensuring that both objects were observed at the same wavelength.

22 October 2009: The tunable ﬁlters where centred on the continuum at 6797.2 A.˚ The observations began at 20:42 UT, about 15 min later than planned, due to issues with the OSIRIS setup, and ended at 02:25 UT. Due to variable seeing, ranging from about 1.4 to 0.7 arc seconds, the exposure time was frequently adjusted to avoid saturation. Being the ﬁrst observations with the OSIRIS instrument in our program there were still issues present concerning the dark current. Hardware upgrades have since solved the issue. The Atmospheres of Exoplanets 119

19 November 2010: The tunable ﬁlters where centred at 7582.0 A˚ and 7664.9 A,˚ resulting in near simultaneous light curves at two wavelengths sampling the line wing of the potassium feature and the core of the KI D2-line. The observations started late at 22:15 UT due to high humidity and ended at 01:29 UT. Seeing was variable ranging from 0.8 to 1.3 arc seconds. The exposure was adjusted to avoid saturation. An hour into the observations light cirrus clouds were present.

26 November 2013: These observations were a repeat of the 19 November 2010 observations and used the same setup. To decrease the overheads the exposure times were increased. Observations started late at 22:16 (due to high humidity) and ended at 01:29 UT (lower elevation limit of the GTC of 25 degrees).

4.1.5 Reductions

The image reductions were made by combining the bias frames and sky ﬂats using standard IRAF1 routines. Dark frames were only obtained for observations at 6797.2 A˚ as the issue with high dark current noise was corrected in time for the subsequent observations. Due to the short exposure times, the dark frames did not improve the reduction and where therefore not used. Aperture photometry was done using the APPHOT package in IRAF. In order to ensure the best possible photometry, a large range of apertures were explored varying both the aperture size as well as the dimensions of the sky annuls in order to minimise the scatter of data points in the continuum. The diﬀerential photometry was performed with the target and the nearby reference star at the same wavelength. The resulting light curves are shown in Fig. 4.1 and Fig. 4.2.

4.1.6 Analysis

4.1.6.1 Light curve ﬁts

The transit light curves were generated using only one reference star and were ﬁtted using the analytical transit equations of Mandel & Agol(2002). The best ﬁtting parameters together with their associated uncertainties were determined

by a Markov chain Monte Carlo algorithm (MCMC) in the same way as (Wilson et al. 2014). The initial starting parameters were from Nikolov et al.(2014). Time dependent correlations with airmass, FWHM and detector position were, when signiﬁcant enough as determined by the Bayesian Information Criterion (BIC), used to model the systematics in the data. No sky-rings are seen in the data making it impossible to measure a possible wavelength shift. All the transits had

the radius ratio, Rp/Rs, central transit time TC , a baseline normalising factor, N and a slope term s as free parameters. The 6797.2 A˚ light curve was fit with an additional linear FWHM term (time FWHM+1). The half transits observed at × 7582.0 A˚ and 7664.9 A˚ on 19 November 2010 showed no detectable systematic noise leading to no additional free parameters. The full transit observations conducted on 26 November 2013 were fit with both a linear FWHM term (time FWHM+1) × and a quadratic airmass term (time airmass2+1). × The fixed parameters were the period, P = 4.46529976 (55) days, impact parame- ± ter b = 0.7501 and the quadratic limb-darkening coefficients, u1 and u2, which were calculated using the ATLAS stellar atmospheric models2 following Sing(2010). A quadratic limb darkening law of the following form was used

I(µ) = 1 u (1 µ) u (1 µ)2, (4.1) I(1) − 1 − − 2 − where I(1) is the intensity at the centre of the stellar disk, µ = cos(θ) is the angle

between the line of sight and the emergent intensity while u1 and u2 are the limb darkening coeﬃcients.

The stellar and orbital parameters were also kept ﬁxed with Rs = 1.174 R , the

eccentricity e = 0 and the scaled semi-major axis a/Rs = 9.853.

2http://kurucz.harvard.edu/grids.html The Atmospheres of Exoplanets 121

1.005 1.000 0.995 0.990 0.985 Norm. Raw Flux

1.000

0.995

0.990 Normalized Flux

0.985 ) 3

− 4

10 2

× 0 2 −4

O-C ( − 0.08 0.04 0.00 0.04 0.08 − − Orbital Phase

Figure 4.1: The 6797.2A˚ observations (outside the potassium feature) with the raw light curve shown in the top panel, the corrected light curve in the middle panel and the best ﬁt residuals shown in the bottom panel. The Atmospheres of Exoplanets 122

1.005 1.000 0.995 0.990 0.985

Norm. Raw0 Flux .980 1.005

1.000

0.995

0.990

Normalized Flux 0.985

0.980 )

3 4 − 2 10

× 0 2 −

O-C ( 4 − 0.00 0.04 0.08 0.00 0.04 0.08 0.05 0.00 0.05 0.10 0.05 0.00 0.05 0.10 − − Orbital Phase

Figure 4.2: Light curves probing the potassium feature. The ﬁrst and third columns (yellow points) corresponding to observations at 7582.0 A,˚ and the second and fourth column (red points) corresponding to the core of the potassium line at 7664.9 A.˚ The half transits were obtained 19 November 2010 whilst the full transits were obtained on 26 November 2013. The Atmospheres of Exoplanets 123 00147 ˚ A . † 0 9 . 45682(27) ± . 2667 2595 00107 00032 . . . . 12919 . 00152 0 ˚ A 7664 . † 0 0 . 45685(30) 2455524 ± . 2676 0 2560 0 00127 0 00000 0 . . . . 12591 . 00111 0 ˚ A 7582 . 0 9 . 50153(29) 2455524 ± . 2667 0 2595 0 00083 0 00000 0 . . . . 12818 . Half transits † 00096 0 ˚ A 7664 . 0 0 . Light curve system parameters for HAT-P-1b 52828(26) 2456605 ± . 2676 0 2560 0 00074 0 00024 0 . . . . 12409 . Table 4.1: 00072 0 ˚ A 7582 . 0 2 . 51013(33) 2456605 ± . 3205 0 2884 0 00077 0 00025 0 . . . . 0 0 0 0 11706 . 0 ? r 1 2 w /R σ u u σ [BJD] 2455127 pl 0 R T Parameter 6797 The Atmospheres of Exoplanets 124

4.1.6.2 Noise Estimate

Following the procedures of Carter & Winn(2009b) the wavelet method was used

to calculate the uncorrelated noise term, σw, and the systematic noise term, σr. Using these terms a β-factor expressed as

s σ 2 β = 1 + r (4.2) σw

was computed and used to used to incorporate the eﬀects of systematics noise in the calculations of the uncertainties on the radius ratio. The transits are all dominated by white noise indicating the the light curves are largely aﬀected by photon noise.

4.1.7 Results and Discussion

4.1.7.1 The detection of potassium

We observed three transits, one of which was outside the potassium feature at 6797.2 A˚ (R=566) and two inside the potassium feature probing the line wing at 7582.0 A˚ (R=632) and the line peak at 7664.9 A˚ (R=639). Both the raw and detrended light curves together with their best fit light curve models are shown in Fig. 4.1 and Fig. 4.2 with their best fit model parameters shown in Table 4.1. A transmission spectrum of HAT-P-1b showing results form this study as well as Nikolov et al.(2014) and Wakeford et al.(2013) are shown in Fig. 4.3. Compared to the weighted means of previous HST observations centred at 6797.2 A˚ and 8843.7 A,˚ the detection of potassium is evident from an increase in the radius ratio of R /R?= 0.00636 0.00095 at 7582.0 A˚ (6.7 σ significance) and ∆R /R?= pl ± pl 0.01030 0.00102 at 7664.9 A˚ (10.1 σ significance). ±

4.1.7.2 The eﬀects of temperature

To assess possible scenarios for the large atmospheric scale height inferred from the observations, we explore the possibility of a temperature inversion in the upper atmosphere. We model the potassium D doublet and ﬁt it to the potassium The Atmospheres of Exoplanets 125

0.130

0.128

0.126

0.124 ∗ 0.122 /R p R 0.120

0.118

0.116

0.114 4000 6000 8000 10000 12000 14000 16000 Wavelength [A]˚

Figure 4.3: Transmission spectrum of HAT-P-1b. The data is from Nikolov et al.(2014) (red and blue points at optical wavelengths), Wakeford et al.(2013) (purple points at near-IR wavelengths) and Wilson et al.(2014) (hexagonal points). The model transmission spectra assume an isothermal hydrostatic uniform abundance with a equilibrium temperature of 1200 K. The magenta line is an isothermal model by Burrows et al.(2010) with an ’extra absorber’ at 2 1 altitude with an opacity of 0.03 cm g− from 0.4 to 1.0 µm. The brown line is a 1200 K isothermal model (without TiO/VO) by Fortney et al.(2008, 2010). probing observations at 7582.0 A˚ and 7664.9 A.˚ At the wavelengths and pressures probed, the potassium profile is dominated by natural broadening with pressure broadening providing a negligible contribution. For our calculations, we assume potassium is the dominant opacity source at the wavelengths probed. Extracting a temperature from the potassium profile also assumes an isothermal atmosphere with a constant gravity and a mean molecular weight which does not change with altitude, a valid assumption for local measurements. The cross section profiles for each data point therefore depends on the local temperature, but does not depend on the reference pressure, abundances, gravity or the mean molecular weight. We calculate the absorption cross sections for the potassium probing wavelengths by convolving the potassium absorption cross section profile with the GTC tunable filter (TF) response curves. The spectral transmission of a TF is expressed as:

( ) 1 2(λ λ )2 − = 1 + − 0 (4.3) T δλ The Atmospheres of Exoplanets 126

3 where λ0 is the wavelength at maximum transmission and δλ the passband width . Given an atmospheric structure and composition, the eﬀective altitude as a function of wavelength, can be calculated using the following relation:

q z(λ) = H ln ξ Pz σ (λ)/τ 2πR /kT µg (4.4) abs =0 abs eq × p

described in detail in Lecavelier Des Etangs et al.(2008). In the equation above

ξabs is the abundance, σabs the cross section, τeq the optical depth, Rp the radius of the planet, k the Boltzmann constant, T the temperature, µ the mean molecular weight, g the gravity and H the scale height H = kT/µg. Using Eq. 4.4 the planet-to-star radius ratio values for the two potassium probing wavelengths are calculated using the previously calculated absorption coeﬃcients. We measure the local temperature by performing a MCMC analysis with temperature and a vertical shift of the transmission spectrum as free parameters. The shift is dependent on the abundance of potassium and the reference pressure at the reference zero altitude, which we are not able to constrain independently. For our calculations we assume a solar potassium abundance and a mean molecular weight of 2.35 mu. We derive a temperature of T = 1332 407 K for our isothermal potassium model ± and shown with the convolved potassium proﬁle binned into 12 A˚ bins in Fig. 4.4.

The apparent slope seen towards shorter wavelengths in the data of Nikolov et al. (2014) could be due to Rayleigh scattering. As the composition of the gases which might affect this slope is not well known, we derive a temperature assuming a Rayleigh slope only described by molecular hydrogen, the most abundant molecule. We calculate the best fitting temperature inferred from the Rayleigh slope to be +553 1685 539 K. The best fit slope with associated uncertainties is shown in Fig. 4.5. − The temperatures derived using the above methods are primarily limited by the lack of data points and can thus only provide loose constraints on the temperature. Using Spitzer/IRAC secondary eclipse photometry Todorov et al.(2010) derived an average dayside temperature of 1500 100 K. Wakeford et al.(2013) find a ± 1000 K isothermal model by (Fortney et al. 2008, 2010) best fit the water feature ∼ detected in the planet, whereas Nikolov et al.(2014) find a 1200 K isothermal model best represents the data. The data presented here are consistent with the above previous results.

3see OSIRIS User Manual v3.1 The Atmospheres of Exoplanets 127

0.132

0.130

∗ 0.128 /R p R

∆ 0.126

0.124

0.122 7550 7600 7650 7700 7750 7800 Wavelength [A]˚

Figure 4.4: Best fit potassium line profile to the GTC observations at 7582.0 A˚ and 7664.9 A˚ (hexagonals). The potassium profile has been binned by convolving the potassium profile with the TF transmission curve. The wavelength bin sizes are indicated by the width of the symbols with the vertical error bars representing the 1σ uncertainties. The best fit potassium line is that a of a T = 1332 407 K model. The 1σ uncertainties in the fit are represented by the ± shaded regions.

The enhanced absorption measured at the potassium probing wavelengths compared to previous HST data (Nikolov et al. 2014) could be due to a larger temperature at the layers where the potassium is being probed. The result could be indicative of a thermosphere as the core of the potassium line probes higher re- 3 6 gions in the atmosphere (typically 10− to 10− bars), where a large increase in temperature is not uncommon in solar system planets (Lindal et al. 1985, 1981). This transition region between the lower atmosphere and the outermost, hottest layers of the upper atmosphere is referred to as the base of the thermosphere. High upper atmospheric temperatures are particularly relevant to hot-Jupiter planets as predicted by models (e.g., Garc´ıaMu˜noz 2007; Tian et al. 2005; Yelle 2004).

4.1.7.3 The eﬀects of potassium abundance and mean molecular weight

The observed radius ratio increase could in part be due to an enhanced abundance of potassium high in the atmosphere. Jupiter and Saturn both show an increase in metals (Atreya et al. 2003; Flasar et al. 2005), and an enhancement of metals in the atmospheres of hot-Jupiter is a well known consequence predicted by the core accretion model. An enhancement in the abundance in potassium high in the The Atmospheres of Exoplanets 128

0.121

0.120 S

/R 0.119 P R

0.118

0.117

3000 3500 4000 4500 5000 5500 Wavelength [A]˚

Figure 4.5: The HST/STIS G430L transmission spectrum from Nikolov et al. (2014) and the 1σ uncertainties (shaded region) showing the best ﬁt Rayleigh +553 slope (dashed line) giving a temperature of 1685 539 K assuming a pure H2 solar composition gas.− atmosphere can however not explain the large absorption measured as a 10 ∼ × increase in abundance compared to the base would be required. This is an unlikely explanation for the height increase, as the ionisation of potassium is expected to increase with altitude, resulting in a decrease in abundance of neutral potassium at high altitudes. The condensation of potassium at the base of the atmosphere, where the temperatures are cooler, could cause a depletion of potassium, thus serving to increase the relative abundance higher up (a cold trap). The most likely condensate to form would be KCl which would happen at a temperature of 3 600 K and at a pressure of 10− bar (Morley et al. 2012) which is too far away ∼ from the conditions of the base of the atmosphere to be a viable explanation.

The photon dissociation by UV flux could break molecular hydrogen into atomic 8 hydrogen at pressures lower than 10− bar (Garc´ıaMuñoz 2007) and could increase scale height, leading to an increase in the observed radius ratio. This would have the effect of lowering the mean molecular weight at the top of the atmosphere, by no more than a factor 2, and therefore photon dissociation can only partly ∼ account for the large absorption observed. The Atmospheres of Exoplanets 129

Resolution (λ/∆λ) Resolution (λ/∆λ) 491 295 197 118 79 59 29 20 12 639 383 255 153 102 77 38 26 15 0.008

0.007 Na I KI 0.006

0.005 ∗

/R 0.004 p R 0.003

0.002 12 75 12 75

0.001 A ˚ A ˚ A ˚ A ˚

0.000 101 102 101 102 Bin Width [A]˚ Bin Width [A]˚

Figure 4.6: Changes in the planet-to-star radius ratio as function of bin width and resolution for a 1332 K isothermal model (solid blue lines) measured by centring a bin on the D2 sodium (left) and a D2 potassium line core (right). The response is modeled with a box function. The black horizontal lines in the right hand plot show the diﬀerence in radius ratio introduced when binning the data from a 75 to a 12 A˚ bin, ∆Rpl/R?= 0.0023. The vertical axis are in units of radius ratios above the white light curve radius ratio. The slight increase in radius ratio seen at 12 A˚ in the left plot and 68 A˚ in the plot on the right is due to the 5.98 A˚ and 34 A˚ separation between the D1 and D2 doublets of the sodium and potassium lines being included in the bin.

4.1.7.4 The eﬀects of resolution

The HST observations of Nikolov et al.(2014) showed no detection of potassium with a 75 A˚ bin centred on the feature resulting in a radius ratio of Rpl/R?= 0.1182 0.0013. Compared to the GTC observations centred on the D2 potassium ± line at 7664.9 A˚ which resulted in R /R?= 0.1282 0.0011 a radius ratio diﬀerence pl ± of ∆R /R?= 0.0100 0.0017 is observed. As the GTC observations of the central pl ± potassium line are done at a resolution of R = λ/∆λ = 639 (∆λ 12 A)˚ compared ∼ to the HST observation with a resolution of R=102 (∆λ 75 A)˚ we explored the ∼ eﬀects of resolution on the measurements.

We measure the changes in the planet-to-star radius ratio as function of bin width and resolution for the HST observations by stepwise binning a high resolution sodium and potassium proﬁle model centred on the D2 sodium and D2 potassium line. For the HST line spread function we used a box function. The increase in radius ratio as a function of decreasing bin width and increasing resolution is shown in Fig. 4.6. The increase in the planet-to-star radius ratio resulting from a decrease The Atmospheres of Exoplanets 130

in bin width from 75 to 12 A˚ for the HST data, is measured to be ∆Rpl/R?= 0.0023 for the potassium line. Compared to the observed diﬀerence in radius ratio of

∆R /R?= 0.0100 0.0017 between the HST and GTC observations, it is clear pl ± that the diﬀerence in resolution alone can not explain why the large potassium absorption seen in the GTC data is not seen in the HST data. Attempts at binning the HST data down to 12 A˚ size bins (corresponding to a width of 2 pixels on ∼ the detector) resulted in a non detectable increase in the radius ratio. However, at such small bin sizes the uncertainties on the HST data become too large for a statistical signiﬁcant non-detection to be not possible.

4.1.7.5 The eﬀects of stellar variability

Stellar variability is know to alter the flux received from the host star, thereby directly affecting the measured transit depth. HAT-P-1 b is not considered to be an active star, showing low chromospheric activity (Bakos et al. 2007; Knut- son et al. 2010) without detectable spot crossings in the HST light curves and variability monitoring showing a < 0.05 per cent variability (Nikolov et al. 2014) corresponding to ∆R /R? 0.0005. Stellar variability is therefore unlikely to be pl ∼ the main cause behind the observed difference.

4.1.7.6 The eﬀects of systematics

Observations done on the 19 November 2010 and 26 November 2013, which used the same instrument setup, both show a clear increase in the radius ratio at the potassium probing wavelengths 7582.0 and 7664.9 A˚ compared to both the HST observations and the GTC observation at 6797.2 A˚ (green hexagon in Fig. 4.3). With such a large difference in radius ratio we investigated the scenario whereby the measurements at the potassium probing wavelengths are offset due to an unknown systematic caused by differences introduced by Earth’s atmosphere. To address this concern we calculate the weighted mean of the difference in radius ratios between the potassium probing wavelengths at 7582.0 and 7664.9 A˚ obtained on the same night. By comparing the difference in radius ratios derived from the two light curves (using the same systematics models) obtained near simultaneously on the same night, the effects of the systematics as well as the choice of systematics models are greatly reduced. A combined difference of ∆R /R?= 0.0038 0.0012 pl ± The Atmospheres of Exoplanets 131 is measured, resulting in an independent detection of potassium with a 3.2 σ significance.

4.2 Conclusions

We present three GTC/OSIRIS transit observations aimed at probing the presence of potassium in the atmosphere of HAT-P-1b. Two separate transit observations detect the potassium feature at high confidence providing a detection with a 6.7 σ significance at 7582.0A˚ and 10.1 σ significance at 7664.9A˚ when combined, relative to previous HST measurements. The strong potassium signature is modeled using a potassium profile which allows us to derive a temperature of T = 1332 407 K ± at the pressures where the potassium is probed. A best-fit Rayleigh slope to pre- +553 viously obtained HST data results in a temperature of T = 1685 539 K (assuming − molecular hydrogen dominates). The derived temperatures together with an enhanced potassium feature support a modest temperature inversion. The strong presence of potassium inferred from the observations could be influenced by the dissociation of molecular hydrogen into atomic hydrogen thereby decreasing the mean molecular weight or due to a super solar abundance of potassium, although it is likely that an increase in temperature at altitude is the dominant cause for the detection of potassium. Finally we discuss how spectral resolution affects radius ratio measurements. Although the effect is clearly present, it is not large enough to account for the large difference in radius ratio in the core of the potassium line compared to previous studies. Future observations aimed at sampling the slope of the potassium profile, will provide more stringent constraints on the derived temperature at the potassium probing wavelengths, and will allow for the degeneracies amongst the possible effects causing the large absorption to minimised.

The Atmospheres of Exoplanets 133

4.3 A Search for Methane in the Atmosphere of GJ 1214b via GTC Narrow-Band Transmis- sion Spectrophotometry

4.3.1 Abstract

We present narrow-band photometric measurements of the exoplanet GJ 1214b using the 10.4 m Gran Telescopio Canarias (GTC) and the OSIRIS instrument. Using tuneable filters we observed a total of five transits, three of which were observed at two wavelengths nearly simultaneously, producing a total of eight individual light curves, six of these probed the possible existence of a methane absorption feature in the 8770 – 8850 A˚ region at high resolution. We detect no increase in the planet-to-star radius ratio across the methane feature with a change in radius ratio of ∆R = 0.0007 0.0017 corresponding to a scale height (H) − ± change of 0.5 1.2 H across the methane feature, assuming a hydrogen dominated − ± atmosphere. We find a variety of water and cloudy atmospheric models fit the data well, but find that cloud-free models provide poor fits. These observations support a flat transmission spectrum resulting from the presence of a high-altitude haze or a water-rich atmosphere, in agreement with previous studies. In this study the observations are predominantly limited by the photometric quality and the limited number of data points (resulting from a long observing cadence), which make the determination of the systematic noise challenging. With tuneable filters capable of high resolution measurements (R 600–750) of narrow absorption features, ≈ the interpretation of our results are also limited by the absence of high resolution methane models below 1 µm.

4.3.2 Introduction

The discovery of close-in “super-Earths”, with masses between 1.5 and 10 M , has ⊕ opened an entirely new ﬁeld of exoplanet research. While transiting super Earths allow the radius and mass to be measured, the regime is prone to large degeneracies between their internal and atmospheric compositions and their masses (Rogers & Seager 2010). Characterising the atmospheres may be the only way to help constrain the overall bulk composition of these hot planets. A large planet-to-star The Atmospheres of Exoplanets 134 contrast is essential when measuring transmission or emission spectra, making transiting super Earths orbiting M dwarf stars ideal for such studies.

The most studied super Earth is GJ 1214b, discovered in the MEarth ground- based transit survey (Charbonneau et al. 2009). GJ 1214b is a 2.7 R , 6.55 M ⊕ ⊕ planet orbiting (P=1.58 days) a M4.5 dwarf star, and therefore has a large planet- to-star radius ratio despite the stellar radius only being 0.21 R . The result is a transit depth of nearly 1.5%. The observed mass and radius of GJ 1214b are consistent with theoretical models indicative of a signiﬁcant atmosphere (Miller- Ricci & Fortney 2010). Due to degeneracies in the models it is predicted that GJ 1214b is either composed of a rocky/ice core surrounded by a hydrogen-rich atmosphere, a water/ice core with an atmosphere dominated by water vapor, or a rocky core with a thin atmosphere formed by outgassing (Rogers & Seager 2010).

Recent studies have attempted to constrain GJ 1214b’s atmosphere through transmission spectroscopy (Bean et al. 2011, 2010; Berta et al. 2012; Carter et al. 2011; Charbonneau et al. 2009; Colón& Gaidos 2013; Croll et al. 2011; Crossfield et al. 2011; de Mooij et al. 2012; Désertet al. 2011; Fraine et al. 2013; Kundurthy et al. 2011; Murgas et al. 2012; Narita et al. 2013, 2012; Sada et al. 2010; Teske et al. 2013). In a majority of these studies, it has been found that GJ 1214b has a flat, featureless spectrum, with no evidence of any significant features either at optical ( 600–1000 nm) or near-infrared (1.1–1.7 µm) wavelengths. It is believed that ∼ the lack of significant features supports the presence of either a heavy, metal-rich atmosphere or optically thick clouds/hazes that produce a constant level of absorption across a large range of wavelengths. One exception is a study conducted by Croll et al.(2011). Specifically, they reported a significantly deeper transit depth at 2.15 µm, a wavelength where methane would be a viable source of opacity. ∼ To help reconcile these studies, we present narrow-band photometry of five transits of GJ 1214b, three of them around a methane absorption feature commonly found at optical wavelengths in the atmospheres of the jovian planets and Ti- tan (Karkoschka 1994). The observations were acquired using the tuneable filter imaging mode on the Optical System for Imaging and low Resolution Integrated Spectroscopy (OSIRIS) instrument installed on the 10.4 m Gran Telescopio Ca- narias (GTC). Tuneable filters (TFs) have several advantages over low resolution spectroscopy; they provide accurate differential photometry whilst also allowing for relatively high resolution measurements (R 600–750), compared to low- ≈ resolution grisms. The relatively high resolution has the advantage of tuning the The Atmospheres of Exoplanets 135

filters to avoid prominent telluric lines (see Hanuschik 2003 for a high-resolution sky emission atlas). Since no diffraction gratings are used, TFs can be much more efficient (Colónet al. 2010; Sing et al. 2011), especially for observing atomic absorption features that typically have a narrow spectral range. Combining this technique with the 10.4 m aperture of the GTC telescope makes it possible to study the atmospheres of planets orbiting fainter stars compared to the hot Jupiters HD 209458b and HD 189733b, which have bright host stars and large atmospheric scale heights, making them two best studied cases thus far.

The methane feature that we focus on is the blue edge of the methane absorption band at 8900 A˚ and is predicted to cause additional absorption during transit at a level of 0.1%, assuming a hydrogen-rich atmosphere (Berta et al. 2011). In ∼ 4.3.3, we describe our observations. In 4.3.4 and 4.3.5, we describe our data § § § reduction and analysis procedures. We present our results in 4.3.6, where we § also discuss the implications of stellar activity, equilibrium cloud models and the possible presence of methane in the atmosphere of GJ 1214b. Finally, we conclude with a summary of our ﬁndings in 4.3.7. §

4.3.3 Observations

Photometric observations of GJ 1214b were conducted using the GTC telescope on La Palma. For all observations, we used the tuneable ﬁlter (TF) imaging mode on OSIRIS (Cepa 1998; Cepa et al. 2000, 2003) to acquire photometry within a bandpass of 12 A.˚ The TF imager allows for custom bandpasses with a central wavelength between 651–934.5 nm and a FWHM of 12–20 A˚ to be speciﬁed.

Out of the five transits observed, three transits were observed in the 8770 – 8850 A˚ region by alternating between two narrow bandpasses, each with a full width at half maximum (FWHM) of 12 A,˚ allowing us to perform near simultaneous photometry at two wavelengths. Observing one transit at two wavelengths simultaneously allows for a more accurate comparison between two wavelengths as systematic variations caused by varying weather conditions or stellar activity are likely to affect both light curves similarly. For the observations done at two wavelengths we specifically chose our bandpasses so that one was located in the continuum, at a shorter wavelength of 8770 A˚ and 8784.5 A˚ compared to the other band located at 8835 A˚ and 8849.6 A,˚ within the methane absorption band. As described in Colónet al.(2010) and Sing et al.(2011), another property of the TF imaging The Atmospheres of Exoplanets 136

mode is that the effective wavelength decreases radially outward from the optical center, so we attempted to position the target and a single “primary” reference star (i.e., one most comparable in brightness to the target) at the same distance from the optical center so as to observe both stars at the same wavelengths.4 The other reference stars were thus observed at slightly different wavelengths than the target, due to their different distances from the optical center.

All observations were performed with 1 1 binning and a fast pixel readout rate of × 500 kHz, a gain of 1.46 e−/ADU and a read noise of 8 e− as well as a single win- ∼ dow located on one CCD chip. The size of the window varied for each observation, but was chosen to be large enough so as to contain the target and several reference stars of similar brightness. Data points with analog-to-digital unit (ADU) counts larger than 45,000 were removed to ensure the measurements were taken in the linear regime of the CCD detector. The data presented in this paper originated from two separate observing programs by PI. D. Sing (ESO program 182.C-2018 see 4.3.3.1 and 4.3.3.2) and PI. K. Colón(GTC2-10AFLO and GTC4-11AFLO § § see 4.3.3.3, 4.3.3.4 and 4.3.3.5) and each had slightly different observing strate- § § § gies. Further details regarding each specific transit observation are given in the following sections.

4.3.3.1 8100 A˚ Transit, 17 August 2010

Observations of the 2010 August 17 transit were tuned to a target wavelength of 8100 A,˚ with the target 3.7 arc minutes away from the optical centre. The observations began at 21:18 UT and ended at 23:29 UT, during which time the

airmass ranged from 1.11 to 1.44. Due to variable seeing, ranging from 0.7 to 1.2 00, the telescope was defocused to avoid saturation. Two reference stars were selected (more on the selection technique in 4.3.4). The observations were windowed using § a 1160 760 pixel section on CCD1. Twelve images containing counts greater than × 45 000 ADU were removed to ensure linearity. The exposure time was kept at 60 s throughout the sequence, with a corresponding 12 s of readout time. ∼ 4Due to technical issues, the positioning for some of the observations was not as expected, and the target and a single reference star were not always observed at the same exact wavelengths. See 4.3.5.3. § The Atmospheres of Exoplanets 137

4.3.3.2 8550 A˚ Transit, 2 June 2010

Observations of the 2010 June 2 transit were tuned to a target wavelength of 8550 A,˚ with the target 1.3 arc minutes from the optical centre. The observations began at 23:48 UT and ended at 03:04 UT, during which time the airmass ranged from 1.27 to 1.87. Due to a technical problem with the secondary mirror, re-focusing was not possible during the whole sequence. This caused an increase in the full width at half-maximum (FWHM) of the Point Spread Function (PSF) of the stars

from 0.9 to 1.9 00, resulting in a notable decrease in the peak counts levels. Three reference stars were selected. The observations were performed using CCD1 and no windowing was done. One data point with counts greater than 45 000 ADU was removed to ensure linearity (see 4.3.4). The exposure time was kept at 120 s § throughout the sequence, with a corresponding 24.5 s of readout time for the ∼ full frame.

4.3.3.3 8770 and 8835 A˚ Transit, 28 August 2010

Observations of the 2010 August 28 transit were tuned to the target wavelengths of 8770 and 8835 A,˚ with the target 3.2 arc minutes from the optical centre. The observations were done by alternating between the two wavelengths in sets of two exposures at each wavelength. The seeing was variable throughout the observations, so the telescope was defocused and the exposure time was changed to avoid saturation. The observations were done in queue (service) mode. The exposure time started at 100 s and was later increased to 150 s and then to 200 s towards the end of the observations. The observations began at 22:00 UT and ended at 00:30 UT, during which time the airmass ranged from 1.26 to 2.32 and the

FWHM varied between 1.0 to 2.6 00. There are some small gaps in the data towards the beginning of the observations due to minor technical issues. Also, there is some vignetting in the last few images due to the low elevation of the telescope, so we exclude these from our analysis. Two reference stars were selected. Two data points with counts greater than 45 000 ADU were removed to ensure linearity. The observations were windowed using a 850 4102 pixel section on CCD2 with a × corresponding 22 s of readout time. ∼ The Atmospheres of Exoplanets 138

Figure 4.7: A surface plot of GJ 1214 showing an uneven PSF due to a misalignment of the M1 mirror during the 8770 and 8835 A˚ observations on the 10th of June 2011 (see Section 4.3.3.4). The small bump seen towards § the front of the larger PSF is due to one of the hexagonal mirrors not being properly aligned. By choosing a larger photometry aperture, the eﬀects caused by the distorted PSF were removed.

4.3.3.4 8770 and 8835 A˚ Transit, 10 June 2011

Observations of the 2011 June 11 transit were tuned to the target wavelengths of 8770 and 8835 A,˚ with the target 3.2 arc minutes from the optical centre. The observations were done by alternating between the two wavelengths in sets of two exposures at each wavelength. The conditions were clear, and observations took place during bright time in visitor mode. Observations began at 23:40 UT and ended at 02:48 UT, during which time the airmass ranged from 1.09 to 1.19 and the

FWHM varied between 1.3 and 2.2 00. The observations started 25 min later than planned because one of the M1 mirror segments was found to be slightly misaligned (see Fig. 4.7). One segment of the mirror would not stack with the other segments. Attempts were made to correct this, although the problem persisted throughout the observations. As this problem had the same effect on all the stars (i.e., each star had an extended PSF, see Fig. 4.7), we have assumed the photometry was not significantly affected by this problem since we chose a larger aperture that included the photons from the unstacked segment. Three reference stars were selected. The observations were windowed using a 850 3250 pixel section on × CCD1. An exposure time of 100 s was used throughout the sequence, with a corresponding 19 s of readout time. ∼ The Atmospheres of Exoplanets 139

80000

70000

60000

50000

40000 ADUs 30000

20000

10000

0 0 2 4 6 8 10 12 14 16 Exposure time [s]

Figure 4.8: The OSIRIS CCD1 (red) and CCD2 (blue) 500kHz exposure curves showing the linearity of the detector. The measurements connected by a solid line were used to ﬁt the estimated linearity of the detector. Images which had the brighter reference star at more than 45,000 ADUs were removed in order to ensure they used data sampled within the linear regime of the CCD.

4.3.3.5 8784.5 and 8849.6 A˚ Transit, 21 July 2010

Observations of the 2010 July 22 transit were tuned to the target wavelengths of 8784.5 and 8849.6 A,˚ with the target 2.9 arc minutes from the optical centre. The observations were done by alternating between the two wavelengths in sets of two exposures at each wavelength. The conditions were clear and the observations took place during bright time in queue mode. The observations began at 00:26 UT and ended at 02:11 UT. The airmass ranged from 1.25 to 1.87. The actual seeing varied between 0.9 and 1.4 00. A slight defocus was used in order to avoid saturation. Two reference stars were selected. The observations were windowed using a 849 3774 pixel section on CCD2. An exposure time of 120 s was used × throughout the sequence, with a corresponding 22 s of readout time. ∼ The Atmospheres of Exoplanets 140

4.3.4 Data Reduction

For all our data sets, we used standard IRAF5 procedures for bias subtraction and flat-field correction. For the flat-field correction, we used dome flats that were taken after each observation and for each filter setting. For the observations done at the methane probing wavelengths 8770 A˚ (two transits), 8784.5 A,˚ 8835.0 A˚ (two transits) and 8849.6 A˚ were affected by the presence of sky lines. We therefore performed a sky subtraction of these images using the IRAF package TFred6.

Aperture photometry was done using the APPHOT package in IRAF. To obtain the best possible photometry, a large number of apertures and sky annuli were explored. The aperture and sky annulus combination which produced the least amount of scatter in the continuum (lowest χ2 value by fitting a straight line to the continuum) was chosen. The number of reference stars varied depending on the size of the CCD readout window, the location of the sky lines as well as the observed scatter in the photometry of each reference star. To determine the optimal number of reference stars all stars above 15,000 ADU were initially chosen as potential reference stars. Each star which did not help reduce the overall scatter in the continuum, such as fainter stars affected by the sky emission rings (see 4.3.5.3) were removed. § The linearities of the CCD1 and CCD2 detectors were evaluated by measuring the average ADU counts of centrally windowed flat field images as a function of exposure time (see Fig. 4.8). Using the measured points known to be within the linear regime of the CCD (< 25,000 ADU), a linear extrapolation of ADUs as a function of exposure time was created. To ensure the observations were not affected by non-linearity effects, the few images that contained a reference star with more than 45,000 ADUs were discarded, as counts above this level were shown to deviate from the linear extrapolation by more than 1σ on CCD2. The resulting light curves are shown in Fig. 4.11 and 4.12.

5IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. 6Written by D. H. Jones for the Taurus Tunable Filter, previously installed on the Anglo- Australian Telescope; http://www.aao.gov.au/local/www/jbh/ttf/adv_reduc.html The Atmospheres of Exoplanets 141

0.125

1σ

0.120 S

/R 2σ P R 0.115 3σ

0.110 −0.005 0.000 0.005 0.010 0.015 0.020 Sky slope

Figure 4.9: The posterior MCMC distribution showing the relationship between the radius ratio and the slope of the sky term for the 8770.0 A˚ observations on the 10th of June 2011. The diﬀerent shadings represents the 1σ (dark-blue), 2σ (mid-blue) and 3σ (light-blue) conﬁdence intervals.

4.3.5 Analysis

4.3.5.1 Light curve ﬁts

The transit light curves were fitted using the analytical transit equations of Mandel & Agol(2002). The best fit light curve, together with the uncertainties associated with the fits, were determined by performing a Markov chain Monte Carlo algorithm (MCMC); see, Gregory(2005) for the use of MCMC in uncertainty estimates, Collier Cameron et al.(2007) for the application to transit fitting, and Pont et al.(2009) for our specific implementation. This gave us a posterior probability distribution which we used to define the uncertainties (see 4.3.5.4 and Fig. 4.9). § For a discussion on how the short baselines affect the radius ratio uncertainties, we refer the reader to Appendix 4.3.8. Individual light curve fits were generated for each transit corresponding to different wavelengths. The initial starting parameters were from Bean et al.(2011); see below. We used 5 chains each consisting of 500,000 steps, trimming away the first 50,000 points with a 25% of the proposed ∼ parameter steps being accepted. The Atmospheres of Exoplanets 142

1.005 1.000 0.995

0.990 8770.0 Å 8835.0 Å Relative Flux Relative 0.985 2010-08-28 2010-08-28

1.020 1.015 1.010 1.005 1.000 OH-line 0.995 0.990 8770.0 Å 8835.0 Å

Relative Flux Relative 0.985 2011-06-10 2011-06-10 0.980

1.010 1.005 1.000 0.995 0.990 8784.5 Å 8849.6 Å

Relative Flux Relative 0.985 2010-07-21 2010-07-21 0.980 −0.02 −0.01 0.00 0.01 0.02 −0.02 −0.01 0.00 0.01 0.02 Phase Phase

Figure 4.10: Shown are the raw (non-detrended) transit light curves at the oﬀ-methane target wavelengths 8770 A˚ (two transits) and 8784.5 A˚ (on the left) and the methane probing target wavelengths 8835.0 A˚ (two transits) and 8849.6 A˚ (on the right). The hollow white points represent the best-ﬁt model. The red vertical line shows the phase during which the 8835 A˚ 10th of June 2011 transit shows a wavelength drift across a strong OH emission line doublet near 8829.5 A˚ (see 4.3.6.2). §

1.005 1.000 0.995

0.990 8100.0 Å 8550.0 Å 0.985 2010-08-17 2010-06-02 Relative Flux Relative 0.980

0.004 0.002 0.000 −0.002 −0.004 −0.04 −0.02 0.00 0.02 0.04 −0.04 −0.02 0.00 0.02 0.04 Phase Phase

Figure 4.11: The GTC OSIRIS narrow band light curves with the target wavelength tuned to 8100.0 A˚ (left) and 8550.0 A˚ (right). Below each light curve are the residuals from the best ﬁt. The 8550.0 A˚ light curve has a considerable shallower transit depth compared to the other transits. This could be due, in part, to a below average number of star spots on the surface of GJ 1214 eﬀectively creating a shallower transit depth. The Atmospheres of Exoplanets 143

1.000

0.995

0.990 8770.0 Å 8835.0 Å Relative Flux Relative 0.985 2010-08-28 2010-08-28

0.004 0.002 0.000 −0.002 −0.004 −0.04 −0.03 −0.02 −0.01 0.00 0.01 0.02 −0.04 −0.03 −0.02 −0.01 0.00 0.01 0.02

1.000

0.995

0.990 8770.0 Å 8835.0 Å Relative Flux Relative 0.985 2011-06-10 2011-06-10

0.004 0.002 0.000 −0.002 −0.004 −0.02 0.00 0.02 0.04 −0.02 0.00 0.02 0.04

1.000

0.995

0.990 8784.5 Å 8849.6 Å Relative Flux Relative 0.985 2010-07-21 2010-07-21

0.004 0.002 0.000 −0.002 −0.004 −0.02 −0.01 0.00 0.01 0.02 −0.02 −0.01 0.00 0.01 0.02 Phase Phase

Figure 4.12: The GTC OSIRIS narrow band light curves at the oﬀ-methane target wavelengths 8770 A˚ (two transits) and 8784.5 A˚ (on the left) and the methane probing target wavelengths 8835.0 A˚ (two transits) and 8849.6 A˚ (on the right). Below each light curve are the residuals from the best ﬁt.

The free parameters in the ﬁt were the radius ratio, Rp/Rs and the sky-ring positions outlined in 4.3.5.3 and summarised in Table. 4.2. The ﬁxed parameters were § the period P = 1.58040481 days, mid-transit time T0 = 2454966.525123 BJDTDB (see Table 4.2 for calculated ephemerides), impact parameter b = 0.27729 and the

quadratic limb-darkening coeﬃcients, u1 and u2, which varied depending on the wavelength of the observations. The stellar and orbital parameters were also kept

ﬁxed with Rs = 0.21 R , the eccentricity e = 0 and the scaled semimajor axis

a/Rs = 14.9749. We ﬁx these values to allow for a more accurate comparison with Bean et al.(2010), D´esertet al.(2011), Croll et al.(2011) and Berta et al.(2012).

The limb darkening coeﬃcients used were calculated using the ATLAS stellar The Atmospheres of Exoplanets 144

Figure 4.13: These two images exemplify the drift in OH sky emission observed during an observing sequence. The image on the left was taken at the beginning of the sequence, whilst the image on the right was taken towards the end of the sequence during the 8770.0 A˚ observations on the 10th of June 2011. For some of the observations a linear correlation with sky line position was found and used to detrend the systematic eﬀects it was causing in the data. The Atmospheres of Exoplanets 145

atmospheric models7 following Sing(2010) and are listed in Table 4.2. A quadratic limb darkening law of the following form was used

I(µ) = 1 u (1 µ) u (1 µ)2, (4.5) I(1) − 1 − − 2 − where I(1) is the intensity at the centre of the stellar disk, µ = cos(θ) is the angle

between the line of sight and the emergent intensity while u1 and u2 are the limb darkening coeﬃcients.

7http://kurucz.harvard.edu/grids.html The Atmospheres of Exoplanets 146 r σ 00020 00028 00042 00034 00043 00048 00037 00049 ...... TDB 1 σ 00141 0 00107 0 00116 0 00073 0 00102 0 00140 0 00071 0 00107 0 ...... 000032 BJD . 0 ± 525123 Trends . . a = 2454966 2 c u 3200 none 0 30293243 sky3243 ring position sky none3266 ring 0 position sky3357 ring 0 position sky3357 ring 0 position 0 sky3387 ring 0 position 0 none 0 ...... 1 u 1797 0 0552 0 0552 0 0552 0 0556 0 0577 0 0577 0 0584 0 ...... 2E-7 days and T . 1 ± Date 58040481 . System parameters for GJ 1214b = 1 P TDB Table 4.2: BJD 0013 2455426.422923 2010-08-17 0 0014 2455350.5634920025 2010-06-02 2455437.4875930016 0 2010-08-28 2455723.5390270020 0 2011-06-10 2455399.5560410032 0 2010-07-21 2455437.4875930016 0 2010-08-28 2455723.5390270024 0 2011-06-10 2455399.556041 0 2010-07-21 0 ...... s 0 0 0 0 0 0 0 0 /R ± ± ± ± ± ± ± ± pl R 12038 11042 11843 11754 11724 11556 11791 11595 ...... Ephemeris from Bean et al. ( 2011 ) with a ˚ A 0 ˚ A˚ A 0 ˚ A 0 ˚ A 0 ˚ A 0 ˚ A 0 ˚ A 0 0 0 0 0 0 5 0 0 6 ...... Wavelength 8100 8550 8770 8770 8784 8835 8835 8849 The Atmospheres of Exoplanets 147

4.3.5.2 The eﬀects of Earth’s Atmosphere

In an attempt to assess the photometric variability caused by the Earth’s atmosphere we studied the ratio of the reference star fluxes as a function of time and looked for correlations such as detector position, airmass, FWHM and the position of the OH emission sky lines present in the data (see Fig. 4.13). In order to determine which correlations were significant, the Bayesian Information Criterion (BIC) was computed and the model with the lowest BIC was accepted. The position of the OH sky emission rings, which were only visible in the images observed around the methane feature, were the dominant systematic effect occurring when a sky ring drifted across either the target or the reference stars. The sky-position was found to behave linearly throughout the observing sequence and was mod- elled by a linear fit to the position of the sky rings. For the data with no sky lines present, a slope term was used to correct for the slope of the out-of-transit flux. The effects of airmass and FWHM were present, but not strong enough to warrant any detrending. In the case of the slight FWHM trends, they seemed to mainly influence the data under variable seeing conditions. The light curves with their associated correlations were all fit simultaneously by performing a MCMC. A summary of the results can be seen in Table 4.2.

4.3.5.3 The presence of sky lines

When using the tuneable filters on the OSIRIS instrument the observed wavelength decreases radially outward from the center of the tuneable filter due to a difference in the optical path length that the light has to travel. This effectively causes most of the stars in the field to be observed at slightly different wavelengths. The functional form of this radial wavelength dependance can be described using the following equation:

λ(r) = λ 5.04 r2 + a(λ) r3 (4.6) 0 − × ×

3 where the chromatic colour term is expressed as a(λ) = 6.1781 1.6024 10− − × × 7 2 λ + 1.0215 10− λ , where λ (A)˚ is the central wavelength at which the × × 0 tuneable ﬁlter is tuned, and r (arcmin) is the distance outward from this centre. The eﬀects of the radial wavelength dependence is easily seen in Fig. 4.13 where The Atmospheres of Exoplanets 148

1.000

0.995

0.990 8770.0 / 8835.0 Å

Relative Flux Relative 0.985 2010-08-28

1.000

0.995

0.990 8770.0 / 8835.0 Å

Relative Flux Relative 0.985 2011-06-10

1.000

0.995 8784.5 Å / 0.990 8849.6 Å

Relative Flux Relative 0.985 2010-07-21

−0.02 −0.01 0.00 0.01 0.02 Phase

Figure 4.14: The GTC OSIRIS narrow band light curves with the light curves obtained on the same night over plotted with their best ﬁt models to enable direct comparison of the transit depth diﬀerences. The white points indicate the longer wavelength within each sequence. The Atmospheres of Exoplanets 149

the prominent OH sky lines are visible. Ideally, each exposure is taken at the same wavelength throughout an observing sequence within a tolerance typically of 1–2 A,˚ however, this is not the case for these observations. At the methane probing wavelengths 8770 A,˚ 8784.5 A˚ and 8835.0 A˚ a clear drift in wavelength is observed (see Fig. 4.17). This causes systematic effects in the observations when a significant portion of the sky-ring crosses either the target star or the reference stars. A linear combination of sky-ring position of the form A sky + B was × multiplied by the light curve fit, with sky being the sky ring position with A and B being parameters set to vary freely in order to detrend this systematic effect. For the observations at 8100 A,˚ 8550 A˚ and 8849.6 A˚ there were no interfering sky lines present in the data.

4.3.5.4 Noise Estimate

The resulting light curves shown in Fig. 4.11 and Fig. 4.12 are aﬀected by both white noise (noise uncorrelated with time, such as photon noise) as well as red noise (noise which correlates with time, such as airmass). In order to obtain realistic uncertainties the red noise must be taken into account, since only using Poisson noise can underestimate the uncertainties. We estimated the level of white noise

(σw) and red noise (σr) using techniques described in Pont et al.(2006). The relationship between σw and σr is given by

2 2 2 σ1 = σw + σr (4.7)

where σ1 is the standard deviation of the unbinned residuals, i.e., the difference between the individual normalised flux measurements and the best fit models of the transit light curves. In the absence of red noise the standard deviation in the binned residuals is expressed as

r σ1 M σN = (4.8) √N M 1 −

where M is the number of bins each containing N points. However, since σN is in most cases larger than the above calculated value (Eq. 4.8) due to the presence of red noise, the eﬀects of red noise on the radius ratio had to be taken into account by using a re-weighting factor. The contribution by red noise was estimated by The Atmospheres of Exoplanets 150 choosing N to be equal to the number of points in the transit, which varied in accordance with the cadence of the observations and can be written as

r 2 2 σw σr = σ . (4.9) N − N

The red noise was then used to recompute the error bars, taking systematic noise into account by using a re-weighting factor, β, expressed as

σ β = r √N. (4.10) σw

The individual parameters used in the light curve ﬁtting together with the estimated white and red noise are summarised in Table 4.2.

4.3.6 Results and Discussion

The resulting light curves with their corresponding best-ﬁt models for each transit observation are shown in Fig. 4.11 and Fig. 4.12. The measured radius ratios are compared to atmospheric models by Morley et al.(2013) and are shown in Fig. 4.16 and 4.19. The Atmospheres of Exoplanets 151

0.122 0.122

0.120 0.120

0.118 0.118

S 0.116 0.116 /R P

R 0.114 0.114

0.112 0.112

0.110 0.110

0 20 40 60 80 100 120 140 160 180 460 480 Time (BJD - 2455260)

Figure 4.15: Shown are the radius ratios as a function of time (BJD), spanning a time period from the 29th of May, 2009 until 10th of June 2011. The black diamonds are measurements by Carter et al.(2011) in the Sloan z’ band using the 1.2 meter FLWO telescope. The grey triangles represent the VLT measurements by (Berta et al. 2011) in z’ band. The grey squares represents the de Mooij et al.(2012) measurement with GROND instrument at the 2.2 m MPI/ESO telescope in the z band. The coloured hexagonal markers, represent our data within the z band wavelength range. The colours of the hexagonal points correspond to those in Fig. 4.16 The Atmospheres of Exoplanets 152 solar composition solar composition × × ˚ A bins for clarity. The 9000 8800 ˚ A bandpass), de Mooij et al. ( 2012 ) using the ′ z ] Å 8600 ˚ A bandpass). The horizontal error bars represent the width of 1 and an eﬃcient heat distribution (orange dashed line). A close-up . Wavelength [ Wavelength = 0 8400 sed f ′ 8200 i of the methane probing region is shown in Fig. 4.19 . 8000

0.122 0.112 0.118 0.120 0.110 0.116 0.114

S P /R R The combined transmission spectrum of GJ 1214b with data from Bean et al. ( 2010 ) (grey upward triangles) and Bean atmosphere model with anatmosphere efficient model heat with distribution a low (grey sedimentation dotted efficiency line) of and a worst-fit cloudy (KCl and ZnS) 50 Figure 4.16: I-filter with the(grey WFC diamond) on and the thisthe Isaac study photometric Newton (multi-coloured band. hexagonal Telescopeobservations The markers, and are 12 transmission z shown spectra filter alongside are with from a theMorley 100% et GROND water al. ( 2013 ) instrument atmosphere and on model have the been (solid 2.2 binned blue m into line), 12 MPI/ESO a telescope best-fitting cloud-free 50 et al. ( 2011 ) (grey downward triangles) using the FORS instrument on the VLT (200 The Atmospheres of Exoplanets 153

4.3.6.1 Variability due to Stellar Activity

GJ 1214, an active M4.5 type star, has been shown to exhibit a 2% peak-to-peak ∼ stellar flux variability in the wavelength range 715–1000 nm and a long rotation period on the order of 53 days (Berta et al. 2011) based on three years of data from MEarth (Nutzman & Charbonneau 2008). This is equivalent to a difference in radius ratio of ∆(Rp/Rs) 0.001 (using Eq. 7 from Désertet al. 2011). Compared ∼ to the equilibrium cloud model atmosphere which includes methane, detailed in 4.3.6.4, we would expect an increase in the radius ratio of the broad methane § absorption band at 8800 – 9000 A˚ to be Rp/Rs 0.002 at the resolution of our ∼ measurements. As such it is necessary to consider the impact of stellar variability and star spots.

The stellar activity can affect the transit depth by means of unocculted star spots, which increase the transit depth, or by the presence of occulted star spots, which lead to an underestimation of the transit depth. As the star spot coverage changes due to the evolution of the spots and stellar rotation, it is possible that small differences in the transit depths are measured at different epochs. To limit the effects of stellar activity it is essential that the different wavelength observations are done at, or close to, the same time. In this study, the light curves that probed the methane feature were acquired over three transits by alternating the tuneable filters between two wavelengths. This gave a total of 6 individual transits around the methane feature (see Fig. 4.12), two at 8770 A˚ and one at 8784.5 A˚ (off- methane) and two at 8835 A˚ and 8849.6 A˚ (on-methane).

The transit light curve at 8550 A˚ taken on the 2nd of June 2010 shows a con- siderably shallower transit depth inconsistent at the 3σ signiﬁcance level with ∼ previously measured radius ratios by (Bean et al. 2011) . Although the cause of this is unknown, it is possible the shallower light curve is partly the result of a below average number of star spots on the surface of GJ 1214, causing a shallower transit depth to be observed. No evidence for the presence of an occulted star spot is present in the data. Carter et al.(2011) also observed a shallower transit of GJ 1214b 3 nights later, during the morning of the 6th of June 2010 (see Fig. 4.15 near BJD-2455260 + 90). Considering that the estimated rotation speed of GJ 1214b is of the order of 53 days, it is likely that both observations were aﬀected by a lower number of star spots than usual. The Atmospheres of Exoplanets 154

4.3.6.2 The impact of the observed wavelength drifts

The change in sky line position during the course of the observations is indicative of a change in wavelength. By measuring the position of the sky lines in the images the corresponding drift in wavelength was estimated following Eq. 4.6 with the drifts shown in Fig. 4.17. The most signiﬁcant wavelength drift is seen in the 10th of June 2011 observations where a wavelength change of 13 A˚ was observed. ∼ No detectable sky lines were observed during the 17th of August 2010 and 2nd of June 2010 observations.

Although every attempt was made to tune the filter to a wavelength absent of strong sky lines it is likely that the sky lines still affect the data despite the sky background having been subtracted. In particular the OH-emission line doublet at 8829.514 A˚ and 8829.525 A(˚ Rousselot et al. 2000) has likely interacted with the 8835 A˚ observations conducted on the 10th of June 2011. The 8770 A˚ observations, done the same night are not affected by a similar shift in wavelength which suggests the OH-emission line is likely causing the systematic relative flux variations seen in the 8835 A˚ observations (Fig. 4.10). Shown in Fig. 4.17 (fifth panel from the top) the observed wavelength drifted towards shorter wavelengths during the night, with the OH line (red line) causing an increase in the relative flux. This is clearly seen in the raw transit light curve shown in Fig. 4.10 (middle green light curve on the right).

With the sky-rings subtracted before performing aperture photometry only very small sky-ring residuals are left in the images. It was of interest to investigate if other systematics were introduced by the wavelength drift sampling different parts of the spectrum of GJ 1214 or the spectra of one of the reference stars. Having previously conducted spectroscopic observations of GJ 1214 with the GTC telescope th using the R500R grism and a 1000 slit on the 25 of July 2012, we compared the wavelength drifts with the spectra of GJ 1214 and one of the reference stars used. The two spectra which have a resolution of about R 250 are shown in Fig. 4.18 ∼ with a rescaled view of the methane-probing region shown in the sub-window located towards the upper right of the plot. Due to the nature of the long slit, only one other reference star could be fit on the slit. Since no major absorption lines were crossed it is unlikely that the systematic wavelength trends are caused by different parts of the spectrum of GJ 1214 or the reference star being sampled. The Atmospheres of Exoplanets 155

8782 8779 8770.0Å ]

Å 8776 ∆λ =7.9Å [

λ 8773 2010-08-28 8770

8844 8835.0Å ]

Å 8841 ∆λ =6.6Å [ 8838 λ 2010-08-28 8835

2.5 2.5 Airmass 2.0 2.0 1.5 1.5 1.0 1.0 Seeing [''] Seeing 8770 8770.0Å ] 8766 Å ∆λ =-12.8Å

[ 8762

λ 2011-06-10 8758

8835 8835.0Å ] 8831 OH-line

Å ∆λ =-12.7Å

[ 8827 λ 8823 2011-06-10

2.5 2.5 Airmass 2.0 2.0 1.5 1.5 1.0 1.0 Seeing [''] Seeing 8788 8784.5Å ]

Å 8786 ∆λ =3.9Å [ 2010-07-21 λ 8784

8854 8849.6Å ]

Å 8852 ∆λ =4.6Å [ 2010-07-21 λ 8850

2.5 2.5 Airmass 2.0 2.0 1.5 1.5 1.0 1.0 Seeing [''] Seeing −0.04 −0.02 0.00 0.02 0.04 Phase

Figure 4.17: The panels above show the drift in wavelengths during each observation together with the changes in seeing and airmass. The seeing is indicated by black points (seeing scale on the left) whilst airmass is represented by a blue solid line in the same panel (airmass scale on the right). The red line shown in the ﬁfth panel from the top shows the location of the OH sky line doublet near 8829.5 A.˚ The drift in wavelength was calculated using Eq. 4.6. The Atmospheres of Exoplanets 156

3.0

1.95

2.5 ) 1.90 5 10 1.85 × (

2.0 1.80 OH-line ADU )

5 1.75 10

× 1.5 8750 8800 8850 8900 ( Wavelength [Å] ADU ADU 1.0

0.5 Reference star

GJ 1214 0.0 8000 8500 9000 9500 10000 10500 11000 Wavelength [Å]

Figure 4.18: The spectrum of GJ 1214 (black) and one of the reference stars h m s with coordinates 17 15 19.42 04◦ 560 32.600(grey). The colours indicate the wavelength probed by each ﬁler (including drifts). The reference spectrum has been multiplied by a factor 9.2 to allow for a comparison in the sub-window. The OH doublet at the vacuum measured wavelengths 8829.514 A˚ and 8829.525 A˚ is shown in red. Only the 8835 A˚ observations on the 10th of June 2011 cross this line completely with the black arrow indicating the direction of the wavelength drift.

4.3.6.3 Probing the methane feature

Here we compare our five observed transits of GJ 1214b with theoretical models presented in Morley et al.(2013) to investigate the nature of GJ 1214b’s atmosphere, in particular, to look for extra absorption due to methane (see Fig. 4.16 and 4.19). Using tuneable narrowband filters, we are able to probe the planets atmosphere at a higher spectral resolution (R 600–750) than would otherwise be possible using standard photometric filters.

The possibility of a methane feature is explored by comparing the difference in radius ratios between the on-methane, off-methane observations each done on the same night. For the observations done on the 21st of July 2010, the difference in The Atmospheres of Exoplanets 157

0.120

0.118 S /R P

R 0.116

0.114

100% H2O, 50x solar, planet-wide, cloud-free 50x solar, planet-wide, f =0.1 0.112 sed 8700 8720 8740 8760 8780 8800 8820 8840 8860 8880 Wavelength [Å]

Figure 4.19: The weighted average of the on-methane and off-methane radius ratios (black points) compared to unbinned model spectra of a 100% water atmosphere model (blue solid line), a best-fit cloud-free 50 solar composition × atmosphere model with an efficient heat distribution (grey dotted line) and a cloudy (KCl and ZnS) 50 solar composition atmosphere model with a low × sedimentation efficiency of fsed = 0.1 and an efficient heat distribution (orange dashed line). The coloured points represents the radius ratios from the individual transits. For a larger overview of the transmission spectrum see Fig. 4.16. radius ratios were found to be ∆R = 0.0013 0.0031, for the 28th of August 2010, − ± ∆R = 0.0029 0.0041, and for the 10th of June 2011, ∆R = 0.0004 0.0023. − ± ± The weighted average of the difference in radii from all three nights are calculated to be ∆R = 0.0007 0.0017 which in terms of scale heights (H) is expressed as − ± ∆R 0.5 1.2 H, using H/Rs = 0.0014 and assuming a hydrogen dominated ' − ± atmosphere. We therefore detect no increase across a possible methane feature. A close up of the probed methane region together with the weighted average of the on and off-methane planet-to-star radius ratios are show in Fig. 4.19. The Atmospheres of Exoplanets 158

4.3.6.4 Atmosphere models

We compare our observations across the methane feature to nine different atmosphere models, which include a 100% water atmosphere model, four cloud-free models and four cloudy models from the model suites of Morley et al.(2013). Each of the cloudy and cloud-free models consist of solar (1 ) and super solar × metallicities (50 ) and a variety of T-P profiles. We find that our water and × equilibrium cloud models (KCl and ZnS) fit the data well due to a large area of parameter space being allowed and are therefore not able to rule out any of the water or cloudy models. We show the worst fitting cloudy model, a 50 solar × composition atmosphere with a low sedimentation efficiency of fsed = 0.1 and an efficient heat distribution in Fig. 4.16. We are able to rule out all the cloud-free atmosphere models at the > 2.7σ-level and show the best-fitting cloud-free models together with the worst-fitting cloudy-model in Fig. 4.16.

A muted methane feature would require the presence of optically thicker clouds or a large mean molecular weight atmosphere, which would be hard to detect, such as a water dominated atmosphere. For a cloudy H-rich model to obscure the transmission spectrum, the clouds have to be optically thick high in the atmo- 3 sphere where transmission spectroscopy probes ( 10− bar). An inefficient heat ∼ redistribution would causes the P–T profile to be warmer, which would cause the profile to cross the condensation curve higher in the atmosphere. In addition, a low sedimentation efficiency would create a more vertically extended cloud. We note that photochemical models which include the formation of naturally forming photochemical hazes high in the atmosphere can also mute the transmission spectrum of GJ 1214b.

Croll et al.(2011) noted that the increased transit depth measured in the Ks-band could be due to an opacity source such as methane or water, requiring hazes in the atmosphere. Subsequent near-IR observations by Bean et al.(2011), Berta et al.(2012), Crossﬁeld et al.(2011) and Narita et al.(2013, 2012) have not been able to reproduce this result. As such it is likely the enhanced absorption in Ks is an outlier as suggested could be the case by Croll et al.(2011). With a detection sensitivity on the order of a scale height at high spectral resolution, we are capable of excluding the presence of a methane absorption band spanning multiple scale heights, which higher resolution models might reveal in the future. The Atmospheres of Exoplanets 159

4.3.7 Conclusions

We present GTC OSIRIS narrowband observations of five transits of GJ 1214b, three of which probe the presence of methane at two near simultaneously obtained wavelengths. We find no increase in radius ratios across the possible methane feature with a planet-to-star radius ratio, ∆R = 0.0007 0.0017, across the feature. − ± This corresponds to an increase in scale height of 0.5 1.2 H assuming a hydro- − ± gen dominated atmosphere. We are therefore not able to rule out any of our water and cloud based models. Cloud-free models generally provide poor fits to the data. Even the best fitting cloud free model assuming a 50 solar composition atmo- × sphere with an efficient heat distribution can be rejected at the 2.7σ confidence level form our data alone. The results, which are compatible with previous results of a largely flat transmission spectrum, do not rule out the possibility of a high altitude haze or a water dominated atmosphere in the atmosphere of GJ 1214b, but do rule out methane features spanning multiple scale heights. Observations around the methane absorption band are predominantly limited by low cadence observations and sky emission lines in Earth’s atmosphere affecting the photometric quality, making the determination of the systematic noise challenging. With tuneable filters capable of high resolution measurements (R 600-750) there is ≈ currently a need for high resolution methane models below 1 µm.

Acknowledgements: We thank the entire GTC staff and in particular Antonio Cabrera Lavers and Robert C. Morehead for their help with conducting these observations. This work is based on observations made with the Gran Telescopio Canarias (GTC), installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrof´ısicade Canarias on the island of La Palma. The GTC is a joint initia- tive of Spain (led by the Instituto de Astrof´ısica de Canarias), the University of Florida and Mexico, including the Instituto de Astronom´ıa de la Universi- dad Nacional Autónomade México(IA-UNAM) and Instituto Nacional de As- trof´ısica,Optica y Electrónica(INAOE). P.A.W, D.K.S and A.R.P acknowledges support from STFC. K.D.C. and R.C.M. were supported by NSF Graduate Re- search Fellowships. G.E.B. acknowledges support from STScI through grants HST- GO-12473.01-A. E.B.F acknowledges support from the Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium. F.P. is grateful The Atmospheres of Exoplanets 160 for the STFC grant and Halliday fellowship (ST/F011083/1). This work was also aided by the National Geographic Society’s Young Explorers Grant, awarded to K.D.C. The authors would like to acknowledge the anonymous referee for their useful comments.

4.3.8 Appendix: Short baselines and the radius ratio uncertainty

With only a few data points present in the continuum of some of the transits, it was of interest to explore the effects of a short baseline on the uncertainty of the radius ratio as calculated using the MCMC method. To asses the relationship, we generated five light curves each consisting of the the 2010 August 28 8770 A˚ transit data with additional synthetic data points added to the right hand continuum. For each of the five light curves, a series of MCMC chains, each consisting of 500,000 steps (trimming away the first 50,000 points), were calculated iteratively removing one point from the right hand continuum before calculating a new chain. This process was repeated for the five light curves with the resulting radius ratio uncertainties subsequently median combined. As shown in Fig. 4.20, as points are removed from the continuum the radius ratio uncertainties as given by the MCMC method increase following a power law. The relationship is further verified by our observations when comparing the derived uncertainties on the radius ratio between the 2010-08-28 and the 2011-06-10 transits, which were done at the same wavelengths and show a consistent decrease in uncertainties with the addition of more points in the post-egress continuum. The Atmospheres of Exoplanets 161

0.0040

0.0035 S /R

P 0.0030 R ε

0.0025

0.0020

0 2 4 6 8 10 Number of data points in the right hand side continuum

Figure 4.20: The uncertainties on the radius ratios as a function of the number of points in the right hand continuum. The results from the ﬁve light curves are shown as dashed lines with their median value represented as a red solid line. The data consists of the 2010 August 28 8770 A˚ transit data with additional synthetic data points added to the right hand continuum. As the the number of data points in the right hand side continuum decrease, the uncertainty on the radius ratio given by the MCMC method increases following a power law. The Atmospheres of Exoplanets 162

4.4 Developments since publication

Since the publication of the paper above, Kreidberg et al.(2014) published HST observations of GJ1214 b with sufficient precision to resolve the ambiguity between an atmosphere dominated by heavy molecules or an atmosphere composed of high altitude clouds obscuring the lower layers, and find the latter has to be true to be consistent with their data. Interestingly, it is still puzzling how the transmission spectra can be so flat for such a large wavelength range 0.5 5 µm. For this to − be possible requires a cloud layer with a near constant opacity at all wavelengths observed thus far, an unlikely scenario. Observations with the JWST will likely solve the issue, not just because of its increased light collecting potential over HST but because it will allow observations at IR wavelengths, were the differences in atmospheric models will become large and easily detectable.

On the theoretical front Yurchenko & Tennyson(2014) released a new methane line list encompassing the rotation-vibration spectrum of methane up to 1500 K covering the wavelength range 8264 A˚ 100 µm. This is welcome news for − tunable ﬁlter observations, which are now no longer limited by the absence of high resolution methane models (see last line of Abstract of the paper presented above). Chapter 5

Conclusions

This thesis presents an overview of the atmospheres of brown dwarfs and exoplanets from an observers viewpoint, focusing on the weather and composition of these distant worlds. An introduction to the topic is given starting with brown dwarfs before descending down the mass sequence to hot-Jupiters and super-Earths. The similarities and diﬀerences between the objects are highlighted and discussed. Ob- servational methods and data reduction techniques are discussed, covering both observations in the optical and at near-IR wavelengths.

Work on the largest near-IR variability study of a uniform and unibassed sample of brown dwarfs is presented showing that variability is common among all spectral types, and that the observed variability does not correlate with spectral type, colour or binarity. Preliminary work on the hot-Jupiter HAT-P-1b presents the detection of potassium in its atmosphere. The large potassium absorption is consistent with a weak temperature inversion or the dissociation of molecular hydrogen, a result of the incoming UV flux from the host star. The first tunable filter measurements of a super-Earth (GJ 1214b) are presented which constrain the presence of methane in the atmosphere, showing a flat transmission spectrum consistent with previous work.

Future work on brown dwarfs will include the photometric follow-up of brown dwarf variables from the BAM survey and other variable brown dwarfs to confirm and characterise their variability across multiple wavelengths. This will allow the cloud composition of the brown dwarfs to be modeled as well as provide information about the longitudinal and vertical structure of the atmospheres. By observing the targets over a range of timescales, from hours to weeks corresponding 163 Conclusion 164 to multiple rotation periods, we will study the longevity of the variability of the atmospheres. The first few results have already confirmed several of the detected variables in the BAM survey. The analysis techniques of hot-Jupiter atmospheres will be further developed, providing a better treatment and assessment of systematic noise. This will also allow for more robust estimations of uncertainties on the transit depths to be made.

The next generation of telescopes such as the JWST and the E-ELT will introduce a new era within brown dwarf and exoplanet science. In particular, JWST will allow for unprecedented photometric precision at wavelength regimes inaccessible from the ground. The E-ELT will give access to the fainter brown dwarfs and provide the precision needed to detect smaller exoplanets allowing their atmospheres to be characterised. Future exoplanet studies, in particular the identiﬁcation and characterisation of spectroscopic signatures, will allow for exoplanets to be classi- ﬁed in a way similar to what has already been done for brown dwarfs. The next generation of transit surveys such as TESS and NGTS aimed at looking at planets orbiting the brighter stars in our sky are about to come online. When they do, a whole host of new targets will be found, introducing a great leap forward in exoplanet characterisation. This is a very exciting time for brown dwarf and exoplanet astronomy, and I am very fortunate to be a part of it. Appendix A

Markov Chain Monte Carlo

The Markov Chain Monte Carlo (MCMC) method is a set of algorithms which are used as a statistical method for sampling a probability density function by constructing a Markov Chain, which itself is drawn from a probability distribution equal to the distribution being sampled. Unlike a systematic grid approach, where a calculation is done at each point of the parameter space being explored, the Markov Chain randomly explores a parameter space of arbitrary dimensionality through a random walk. This random walk is governed by a likelihood function which determines which areas are explored the most. Each step is independent of the previous step.

The MCMC method yields robust uncertainty estimates and provides a posterior probability distribution for each parameter, avoiding getting trapped in local minima on the way.

The algorithms used can be summarised as:

1. An initial ﬁt to the data is done using a parametrised model.

2. The agreement between the data and the ﬁtting model is evaluated using a merit function (good agreement means small merit function result). In χ2 this thesis a likelihood function of the form = e 2 was used as the merit L function with χ2 expressed as,

n 2 X (Oi Ei) χ2 = − , (A.1) σ2 i=1 i

165 Appendix 166

where the numerator describes the spread between the data Oi and the model

Ei, and σi is the the variance of each measurement, n.

3. A random step, drawn from a Gaussian distribution, is done for each parameter, changing the parametrised model.

4. The new model is passed to the likelihood function described in step 2, where it is calculated.

5. A ratio between the two likelihood function results (the current one and previous one) is calculated.

If this ratio is greater than 1, the new parameters give a better ﬁt and • they are stored. If the ratio is less than 1, the new parameters give a worse ﬁt and • a random number is drawn from a uniform distribution of numbers between 0 and 1.

– If the ratio is greater than this number, the new parameters are stored. The new parameters are more likely to be stored if the ratio is close to 1. In the same way it increasingly unlikely that the new parameters are stored if the ratio is close to 0. A consequence of this is the Gaussian distribution which forms for each parameter as the number of steps increase. – If the ratio is less than this number, the new parameters are discarded and the previous parameters are retained.

6. The processes is repeated N times, starting at step 3. Appendix B p -value

B.1 Deﬁnition

In the paper by Wilson et al.(2014) the p -value was used as a measure of statistical signiﬁcance. The p -value can be deﬁned the following way:

The p-value is a probability of getting the observed result or more extreme results given that the null hypothesis is true.

The null hypothesis, H0, is the hypothesis that there is no aﬀect, in the case of the BAM survey, the null hypothesis is that no variability is detected. Thus, if an object has a measured p > 0.05 it means that H0 is statistical signiﬁcant with the observed results and we can not reject H0.

B.2 Calculating the p -value

The computation of a p -value requires a null hypothesis, a test statistic (which is a function of the sample) and the observed data itself. As with any statistical hypothesis, H0 has to refer to a distribution function. In the case of the BAM survey, the distribution function is a χ2-distribution and the test statistic is the χ2 test. The distribution function, also known as the cumulative distribution function (CDF), for a χ2-distribution takes the form:

167 Appendix 168

2 Z χ zr/2 1e z/2 CDF(χ2) = − − dz (B.1) 1 r/2 0 Γ 2 r 2

1 where r is the number of degrees of freedom and Γ 2 r is the gamma function. Given the CDF the p -value is calculated as,

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