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Home , 42 Draconis b, 51 Eridani, 51 Eridani b, HD 179949, HD 189733 b, Planetary phase

University of New South Wales

Doctoral Thesis

Polarimetry of hot- systems and radiative transfer models of planetary

Author: Supervisor: Kimberly Bott Prof. Jeremy Bailey

Co-supervisor: Prof. Chris Tinney

A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in the

Department of Astrophysics School of

March 2017 PLEASE TYPE THE UNIVERSITY OF NEW SOUTH WALES Thesis/Dissertation Sheet

Surname or Family name: Bott

First name: Kimberly Other name/s:

Abbreviation for degree as given in the University calendar: PhD

School: Physics Faculty: Science

Title: of hot-Jupiter systems and radiative transfer models of planetary atmospheres

Abstract 350 words maximum: (PLEASE TYPE)

Thousands of and candidates have been detected. The next important step in the contexts of , planetary classification and planet formation is to characterise them. This thesis aims to provide further characterisation to four exoplanets: the relatively well-characterised HD 189733 b, W ASF- l 8b which is nearly large enough to be a , and two minimally characterised non-transiting hot : HD 179949b and tau Bootis b.

For the transiting , this is done through two means. First, published data from previous observations of the secondary (and for HD 189733b) are compared to models created with the Versatile Software for the Transferof Atmospheric Radiation (VST AR). Second, new polarimetric observations from the High Precision Polarimetric Instrument are compared to Lambert-Rayleigh polarised phase curves. For the non-transiting planets, only the polarimetric measurements are compared to models, but toy radiative transfermodels are produced for concept. As an introduction to radiative transfermodels, VSTAR is applied to the planet Uranus to measure its D/H isotope ratio. A preliminary value is derived for D/H in one part of the .

Fitting a single atmospheric model to the transmitted, reflected, and emitted light, I confirm the presence of and on HD 189733b, and present a new profileand cloud profilefor the planet. ForWASP- 18b, I confirm the general shape of the temperature profile. No conclusions can be drawn from the polarimetric measurements for the non-transiting planets. I detect a possible variation with phase for transiting planet W ASP-l 8b but cannot confirm at this time. Alternative sources to the planet are discussed. For HD 189733b, I detect possible variability in the polarised light at the scale expected for the planet. However, the data are also statistically consistent with no variability and do not match the phase of the planet.

This thesis demonstrates the value of robust radiative transfer models and of polarized light detections to the characterisation of the atmospheres and orbital elements of exoplanets. Further polarimetric measurements to be taken by the HIPP! team in the near future will provide useful characterisation of these planets.

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I hereby grant to the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or in part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all property rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or partof this thesis or dissertation.

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'I hereby grant the University of New South Wales or its agents the right to archive and to make available my thesis or dissertation in whole or part in the University libraries in all forms of media, now or here after known, subject to the provisions of the Copyright Act 1968. I retain all proprietary rights, such as patent rights. I also retain the right to use in future works (such as articles or books) all or part of this thesis or dissertation. I also authorise University Microfilms to use the 350 word abstract of my thesis in Dissertation Abstract International (this is applicable to doctoral theses only). I have either used no substantial portions of copyright material in my thesis or I have obtained permission to use copyright material; where permission has not been granted I have applied/will apply for a partial restriction of the digital copy of my thesis or dissertation.'

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‘I hereby declare that this submission is my own work and to the best of my knowledge it contains no materials previously published or written by another person, or substantial proportions of material which have been accepted for the award of any other degree or diploma at UNSW or any other educational institution, except where due acknowledgement is made in the thesis. Any contribution made to the research by others, with whom I have worked at UNSW or elsewhere, is explicitly acknowledged in the thesis. I also declare that the intellectual content of this thesis is the product of my own work, except to the extent that assistance from others in the project's design and conception or in style, presentation and linguistic expression is acknowledged.’

Signed ……………………………………………......

Date ……………………………………………...... “We don’t want to conquer the cosmos, we simply want to extend the boundaries of to the frontiers of the cosmos. For us, such and such a planet is as arid as the Sahara, another as frozen as the North Pole, yet another as lush as the Amazon basin. We are humanitarian and chivalrous; we don’t want to enslave other races, we simply want to bequeath them our values and take over their heritage in exchange. We think of ourselves as the Knights of the Holy Contact. This is another lie. We are only seeking Man. We have no need of other worlds. A single world, our own, suffices us; but we can’t accept it for what it is. We are searching for an ideal image of our own world: we go in quest of a planet, a civilization superior to our own but developed on the basis of a prototype of our primeval past.”

Stanis law Lem (Solaris)

“Finally, from so little sleeping and so much reading, his brain dried up and he went completely out of his mind.”

Miguel de Cervantes (Don Quixote) UNIVERSITY OF NEW SOUTH WALES Abstract Polarimetry of hot-Jupiter systems and radiative transfer models of planetary atmospheres

by Kimberly Bott

Thousands of exoplanets and planet candidates have been detected. The next important step in the contexts of astrobiology, planetary classification and planet formation is to characterise them. This thesis aims to provide further characterisation to four hot Jupiter exoplanets: the relatively well-characterised HD 189733b, WASP-18b which is nearly large enough to be a brown dwarf, and two minimally characterised non-transiting hot Jupiters: HD 179949b and τ Bootis b.

For the transiting planets, this is done through two means. First, published data from previous observations of the secondary eclipse (and transit for HD 189733b) are com- pared to models created with the Versatile Software for the Transfer of Atmospheric Radiation (VSTAR). Second, new polarimetric observations from the HIgh Precision Po- larimetric Instrument are compared to Lambert-Rayleigh polarised light phase curves. For the non-transiting planets, only the polarimetric measurements are compared to models, but toy radiative transfer models are produced for concept. As an introduction to radiative transfer models, VSTAR is applied to the planet Uranus to measure its D/H isotope ratio. A preliminary value is derived for D/H in one part of the atmosphere.

Fitting a single atmospheric model to the transmitted, reflected, and emitted light, I confirm the presence of water and carbon monoxide on HD 189733b, and present a new temperature profile and cloud profile for the planet. For WASP-18b, I confirm the general shape of the temperature profile. No conclusions can be drawn from the polarimetric measurements for the non-transiting planets. I detect a possible variation with phase for transiting planet WASP-18b but cannot confirm at this time. Alternative sources to the planet are discussed. For HD 189733b, I detect possible variability in the polarised light at the scale expected for the planet. However, the data are also statistically consistent with no variability and do not match the phase of the planet.

This thesis demonstrates the value of robust radiative transfer models and of polarised light detections to the characterisation of the atmospheres and orbital elements of exo- planets. Further polarimetric measurements to be taken by the HIPPI team in the near future will provide useful characterisation of these planets. Acknowledgements

I’d like to thank my thesis advisor Jeremy Bailey for his guidance and support. Thank you for being accessable without being imperious. Thank you also for finding ways to aid my studies by ensuring my environment was as stable and condusive to research as possible.

I’d like to thank Lucyna Kedziora-Chudzer, Daniel Cotton, and Jonty Marshall: post- doctorates in the polarimetry and atmospheres group at UNSW who provided helpful discussion, sage advice and thoughtful feedback on my thesis. Thank you also to the postdocs and postgrads I’ve shared the office and projects with for being supportive and grounded.

Thank you to my undergraduate university, my high school and the community I grew up in. I was extremely fortunate to have grown up in such an open minded and supportive place, to have learned from brilliant and inclusive teachers and professors. Thank you for taking the concerns and intellect of the children, teens and young adults in your community seriously. Thank you for providing me with great role models. From my undergraduate I’d like to thank Richard Crowe (in mem.), William Heacox, Robert Fox, Norman Purves, John Hamilton and, in particular, Marianne Takamiya, for delightful extended discussions and encouragement. I’d like to thank Terry Welch and Barbara Ballard in particular from my schooling for encouraging me and letting me experiment with everything from rocket designs to literary critique. Thank you for providing the sort of environment that gets teens through school relatively painlessly.

Most of all I’d like to thank my parents, Robyn and Daniel Bott for bringing me up in a household that appreciates and reveres science, curiosity, and skepticism. Thank you for everything from kind words, to subscribing to science magazines, renting “Contact” for me over and over until you broke down and bought it, learning about with me, and providing further explanation of the concepts in the Timmothy Mouse books to me (rainbows and phases in particular). Thank you to my brother, David Bott, for putting up with my antics. Thank you to my entire family for being supportive. I know many people are not as lucky as I am in that regard.

vi Contents

Abstract v

Acknowledgements vi

Contents vii

List of Figures xi

List of Tables xvii

Abbreviations xix

1 Introduction 1 1.1 Planetary Atmospheres ...... 2 1.2 Exoplanets ...... 3 1.2.1 Methods for observation ...... 4 1.2.1.1 Detection methods ...... 5 1.2.2 Characterisation ...... 8 1.2.2.1 Characterisation Methods ...... 12 1.2.3 Methods for modelling ...... 18 1.2.4 Effect of stellar activity ...... 20

2 Models 23 2.1 Chemical Models ...... 23 2.2 Radiative Transfer ...... 25 2.2.1 Lines ...... 26 2.2.1.1 Broadening ...... 27 2.2.2 ...... 27 2.2.2.1 Phase Functions ...... 28 2.3 VSTAR: Radiative Transfer Modelling Software ...... 30 2.3.1 Structure of VSTAR ...... 31 2.3.2 Spectral Line Absorption ...... 32

3 Uranus 35 3.1 Deuterium ...... 38 3.1.1 Formation of the ...... 38 3.1.2 Deuterium Fractionation in the solar system ...... 39

vii Contents viii

3.1.3 Formation Hypotheses ...... 42 3.2 Observations ...... 51 3.2.1 Instrument ...... 53 3.2.2 Instrument Configuration ...... 54 3.2.3 Details of observations ...... 55 3.2.4 Calibrations ...... 56 3.2.5 Data Reduction ...... 56 3.2.6 Quality of observations ...... 58 3.3 Models ...... 58 3.3.1 VSTAR Model Set Up ...... 60 3.3.2 Isotopologues ...... 62 3.4 Results ...... 63 3.4.1 Cloud properties from low resolution fitting ...... 63 3.4.1.1 Technique ...... 63 3.4.1.2 Uranus’ cloud fit ...... 65 3.4.2 Fitting the deuterium ratio ...... 67 3.4.2.1 Technique ...... 67 3.4.2.2 Uranus’ measured D/H ratio ...... 69 3.5 Prospects ...... 71 3.6 Discussion ...... 74

4 Polarimetry 77 4.1 Polarimetry of Exoplanets ...... 81 4.1.1 Polarisation Mechanisms ...... 82 4.1.2 Stellar contributions to polarised light ...... 86 4.1.3 Scattering from atmospheres ...... 88 4.1.3.1 Orbital Parameters ...... 88 4.1.3.2 Rayleigh scattering ...... 89 4.2 HIPPI ...... 91 4.2.1 Instrument ...... 93 4.2.1.1 Ferro-electric liquid crystal modulators ...... 95 4.2.1.2 Photomultiplier detectors ...... 96 4.2.1.3 Data Acquisition ...... 97 4.2.2 Data Reduction ...... 98 4.2.2.1 Statistics ...... 101 4.2.2.2 Efficiency calibrations ...... 102 4.2.3 Performance ...... 103 4.2.4 Exoplanet Observations ...... 105 4.3 Models of Polarised Light ...... 109 4.3.1 Polarised Light Curve ...... 110 4.3.2 Polarised Light Contribution from Hypothetical Atmosphere ... 111

5 HD 189733b 113 5.1 Introduction ...... 113 5.2 Atmospheric Characterisation ...... 115 5.2.1 Context ...... 115 5.2.1.1 Observations ...... 115 Contents ix

5.2.1.2 Interpretation ...... 119 5.2.1.3 Summary ...... 129 5.2.2 Models ...... 129 5.2.2.1 Set Up ...... 129 5.2.2.2 Secondary Eclipse ...... 134 5.2.2.3 Transit ...... 136 5.2.2.4 Conclusions ...... 138 5.3 Polarimetry ...... 139 5.3.1 Context ...... 139 5.3.2 Fits ...... 142 5.3.3 Conclusions ...... 147

6 WASP 18b 151 6.1 Introduction ...... 151 6.2 Atmospheric Characterisation ...... 152 6.3 Polarimetry ...... 157 6.3.1 Fits ...... 160 6.4 Conclusions ...... 162

7 tau Bootis b 165 7.1 Introduction ...... 165 7.2 Atmospheric Characterisation ...... 165 7.3 Polarimetry ...... 169 7.3.1 Fits ...... 170 7.4 Conclusions ...... 172

8 HD 179949b 175 8.1 Introduction ...... 175 8.2 Atmospheric Characterisation ...... 175 8.3 Polarimetry ...... 178 8.3.1 Fits ...... 179 8.4 Conclusions ...... 180

9 Summary and Discussion 183 9.1 Summary of Conclusions ...... 183 9.1.1 Uranus ...... 183 9.1.2 HD 189733b ...... 184 9.1.2.1 Radiative transfer ...... 184 9.1.2.2 Polarised light ...... 184 9.1.3 WASP 18b ...... 185 9.1.3.1 Radiative transfer ...... 185 9.1.3.2 Polarised light ...... 185 9.1.4 tau Bootis b ...... 186 9.1.4.1 Polarised light ...... 186 9.1.5 HD 179949b ...... 186 9.1.5.1 Polarised light ...... 186 9.2 Discussion ...... 187 9.2.1 Forecast ...... 187 Contents x

9.2.2 Context ...... 188

Bibliography 191 List of Figures

1.1 Many different methods have discovered many different types of planets. This image is from September 2014. It thus is missing some of the more recent discoveries but illuminates our detections biases and possible real biases. Image: PHL, UPR, Arecibo ...... 5 1.2 Narrow band is compared to model spectra for the four plan- ets in a resolved HR 8799. All of these planets are farther than 14 AU from their host and greater than ∼5 MJ . Spa- tially resolved spectra have also been obtained for this system. Image: Fig 9 in original. Currie et al. [46] ...... 14 1.3 An illustration of the pressure-temperature profiles of solar system bodies with thick atmospheres. All of the worlds shown here have an inversion at these pressures except (Uranus’ is very extended). This figure is Figure 1 in Robinson and Catling [47] and is based upon the work of several others cited therein...... 15 1.4 An illustration of the path of light through an exoplanet atmosphere. The light seen by the observer moves through the periphery of the disk provid- ing more data about the upper atmosphere than the lower atmosphere. The ratios are exagerated for illustration...... 16

2.1 An example of the Henyey-Greenstein description of the angular depen- dance of light being scattered. The forward scattering direction is 0◦; backscattering is 180◦. Thus a strong backscatterer has a low anisotopy factor, g. Image: Scott Prahl and Steven Jacques 2014, Biomedical at Oregon Medical Laser Centre website ...... 28

3.1 The D/H isotope ratio for various solar system bodies, compared to the low protosolar value. The distances from the are not in or- der or to scale. Of note is the very high deuterium abundance for both and Jovian Family comets, the comparatively high value for Enceladus, the also very high value for Earth comparable to come Jovian comets and the asteroids, the similar abundances between Uranus and Neptune, higher than the lower density planets Jupiter and Saturn.Im- age: Altwegg 2014 and ESA ...... 43 3.2 Simplified illustration of planet formation and theoretical influence of each stage on Deuterium abundances. Further explanation in text...... 46

xi List of Figures xii

3.3 The fractionation factor for methane for each with atmo- spheric pressure. For Uranus, there is a constant value for the atmosphere below pressures of ∼500 bar, that is at heights where observational data is available. Below this (at higher pressures) the curve is fit to the calculated equalibrium fractionation values, with the fractionation factor f decreas- ing (the relative value of deuterium in molecular to deuterium in methane decreases, i.e. deuterium in methane should be more common at lower pressures where the processes favour the heavier molecule in the ice). The values marked with dashed arrows are from [127] and [128]. Image credit: Lecluse et al. [108] ...... 48 3.4 The location of the low resolution (LR) and high resolution (HR) GNIRS slits on the disk of Uranus. The slits are situated roughly in line with the planet’s rotation axis. The parts of the slit where data was combined are outlined in white and black boxes respectively. Data was compared for two different cloud bands on the planet with cloud fitting in LR followed by abundance fitting in HR. This aquisition image was taken with the narrowband H-G0516 filter. The NU refers to the planet’s rotational north pole. Image credit: D. Cotton ...... 52 3.5 A schematic of the GNIRS optics system with four configurations for the ‘long’ and ‘short’ camera options shown...... 54 3.6 Figure 2 in [104]. The correlated-k fit to the clouds in the H-band. Credit: Irwin et al. [104] ...... 59 3.7 Figure 4 in Irwin et al. [104]: The “zoomed in” region over which the deuterium ratio was fit in Irwin et al. [104] ...... 60 3.8 The methane profile for the chemical model based on Lindal et al. [70] from the Voyager 2 occultation observations...... 61 3.9 A plot of the best fitting parameters (in text) for the bright southern region...... 65 3.10 A cartoon of the haze and cloud layers Source: Wikipedia user ‘Ruslik0’ based upon Lindal et al. [70], Bishop et al. [137], West et al. [143], Atreya et al. [144], de Pater et al. [102] ...... 67 3.11 A plot of the chi-squared values for several outputs from the low resolution bright band data, fitting for the deuterium ratio. The x-axis values are in terms of the ratio of CH3D/CH4 as compared to Earth. The black line denotes the minimum (slope of 0)...... 71

4.1 An illustration of the Stokes parameters as used in this thesis. Q and U are linearly polarised light, which HIPPI measures. Image: Wiki Commons 78 4.2 An illustration of the Stokes vectors in Cartesian and their translation to the polarisation ellipse, a Poincare sphere. Image: Flossmann et al 2006 [152] ...... 79 4.3 An idealised case for the polarised light from a close-in giant exoplanet (hot Jupiter) with particles of effective scattering radius = 0.1 µm. The orientation of the system, particle size, multiple scattering and other fac- tors will scale the effects. The left side shows the reflected light compo- nent from the planet in micromagnitudes, while the right side shows the system’s total polarisation component per orbital . Image: Figure 4 in Seager et al. [153] ...... 82 List of Figures xiii

4.4 A simplified illustration of the effect of varying orbital parameters on the polarised light curve. Note the dashed and dotted lines show two arbitrary permutations of the value. The purple and red refer to the Stokes Q and U parameters...... 83 4.5 An illustration of the net nulling effect of the polarisation in a (unob- scured) star0s limb. In the idealised case, the polarisation intensity is equal all around the limb with changing Stokes values which cancel out. (The Q values where the U vector is shown are zero in this cartoon, and visa versa) ...... 87 4.6 Large variations in the polarised light signal from HD 189733b. Notably the amplitude of the variation in greater in shorter wavelengths (U and B vs V bands). Image: Figure 1 in Berdyugina et al. [169] ...... 90 4.7 An illustration of the basic layout of HIPPI. Note that the FLC modulator and filter wheel are forward of the rotating component. Image: Bailey et al. [58] ...... 95 4.8 A schematic diagram of HIPPi’s data acquisition system. Image: Bailey et al. [58] ...... 97 4.9 The wedges of bifringent material (calcite) in a Wollaston prism separate polarised light by its sign. Image: from Wikipedia user ”fgalore” ..... 98 4.10 An illustration of the bandpasses retrieved with HIPPI for a dummy stel- lar spectrum for a G0 V star...... 107

5.1 From the Swain et al. 2008 paper (figure 2 in that paper) on the NICMOS secondary eclipse spectrum of HD189733b. The effects of combinations of organic species with water on the fits to the NICMOS spectrum. Note that none of the combinations are fit to the blue end of the spectrum where one of the values is unphysical. Image credit: M. Swain ...... 118 5.2 Figure 5 in McCullough et al. [208] showing the combined treatment of all visible and light available for the transit spectrum of HD 189733b. Points in visible light show a rise from a combination of Rayleigh and Mie scattering and are adjusted to account for effects. Source: McCullough et al. [208] ...... 121 5.3 The temperature map of HD 189733b produced by integrating slices of the . The map shows a hot spot offset from the substellar point. Image credit: Knutson et al. [218] ...... 126 5.4 The spectrum of the assymetrically heated planet HD 189733b, for six phase angles. The bandpasses are shown at bottom. The emergent flux density is given in (ergs−1cm−2Hz−1) and should not to be confused with the comparitive flux (unitless ratio) used in my secondary eclipse models. Image credit: [233] ...... 127 5.5 The temperature profiles trialed for HD 189733b taken from literature and made ad hoc. The best fit case is a solid black line which differed significantly from anything used in literature...... 130 5.6 Dayside models for HD 189733b. The C/O = 0.6 model uses a higher (2 times solar, the rest are at a solar value). The photometric data is shown in black, and the spectral data in gray. In cases where there appear to be two photometric data points at the same x value they are from different treatments. The photometric data points are also binned (coloured dots)...... 135 List of Figures xiv

5.7 A zoomed-in plot of the fit accross the red end of the dayside, secondary eclipse, spectrum...... 136 5.8 The optical depth (divided by 10) at 1.0 µm wavelength for the enstatite scatterers with used in the best fit model. The shape of the Rayleigh curve requires a distribution in optical depths near these values. Also shown are the mixing ratios for three species in the HD 189733b atmosphere with significant effects in the wavelength regions ob- served. The mixing ratio for carbon monoxide (CO) has also been divided by 10. mixing ratios are very low for these pressures and in equilibrium condiditons...... 137 5.10 Top: HIPPI Q/I data in purple compared to Berdyugina et al. [169] in blue. Bottom: HIPPI U/I data in red, compared to Berdyugina et al. [169] in yellow. Note that the data here are not adjusted for a baseline due to interstellar polarisation. However telescope polarisation and intrumental effects have been accounted for in the data. One point at phase 0.66 is probably an outlier as it was taken during moonset. Data is binned per night, as opposed to by phase, to avoid masking long-time-scale variability.143 5.11 HD 189733b exibits some variability in the midpoints of its polarised light measurements, but not with the planet phase. Above includes dashed line as the offset from interstellar polarisation, and curves fit to the amplitude. The point at 0.66 phase is an outlier taken during moonset ...... 144 5.12 The best fit with a sliding x axis. The baseline offset is within the error bars of the secondary eclipse measurements. Position angles around 170 provide the best fit with some degeneracy. The curve was fit with a AG of 0.7 an accounting for multiple scattering. It does not appear to correspond to the IR phase curve...... 145 5.13 This figure from Wiktorowicz et al. [175] (Fig. 5 in original text) shows the reassessed measurements from POLISH and the new measurements taken by POLISH 2 for HD 189733b. The polarisation measured by Berdyugina et al. [169] is shown in red dashed lines. Notably, the measurements vary widely and do not coincide with orbital phase...... 147 5.9 The best fit for the visible light, emissions, and transmitted light, shown here applied to the transit (transmission, terminator region)...... 149

6.1 Models with varying C/O ratios for a T-P profile with no inversion taken from Nymeyer et al. [251] produced with VSTAR. A very high C/O ratio does not significantly improve the fit...... 156 6.2 Spectral models of WASP 18b with a temperature inversion, taken from Nymeyer et al. [251]. Here very high C/O ratios fits just as well as low ones. I am unable to account for the feature at 4.5 µm but note that the absorption feature found there, if strongly in emission, could produce that shift...... 157 6.3 For comparison, and isothermal 3100 K profile was modelled. It statisti- cally fits just as well as the inversion profile...... 157 6.4 A fit to the WASP 18b data with position angle 140◦, and geometric albedo 0.3. The baseline offsets (Q -62, U +182) are constrained to values within the error bars of the data point within secondary eclipse when the planet’s polarised light contribution should be obscured...... 161 6.5 This image is Figure 6.5 in Cotton et al. [87]...... 162 List of Figures xv

6.6 As in figure 6.4 but with a geometric albedo of 0.4, Q -70, U + 185, and binned per phase...... 163

7.1 τ Boo b as a pL-type from Fortney et al. [50] , having no inversion and no absorption from metal oxides (TiO and VO)...... 170 7.2 τ Boo b as a pM-type from Fortney et al. [50] , having an inversion and with absorption from metal oxides (TiO and VO)...... 171 7.3 The data for tau Boo b is coincident in phase and stokes Q is consistent with zero. Phase 0 refers to inferior conjuction for the non-transiting planet. An offset of Q+3 and U+13 is shown. The curve may slide to the left or right since the apogee is not necessarily coincident with the shown phase angle. However, with a realistic level of multiple scattering and a geometric albedo of 0.3 (shown) an offset from interstellar polarisation isn’t necessary for Q or U...... 172

8.1 HD 179949b as a pL type planet (without an inversion and no metal oxides).178 8.2 HD 179949b as a pM type planet (with an inversion and metal oxides). . 179 8.3 Although the error bars on the data for HD 179949’s polarised light mea- surements are large enough to make the Stokes U coincident with zero, an offset is possible for both Stokes parameters from the data midpoints. Shown is an example curve with interstellar offsets at Q=-31 and U=-6. Phase 0 refers to inferior . The example shown with an arbi- trary inclination of 45◦ is a reasonable example, but more data is needed to reduce the error bars...... 180

List of Tables

3.1 All observations were taken on 18 Aug 2011 while the planet was roughly at equinox. GNIRS was in long-camera mode...... 56 3.2 Table of estimates of the deuterium-to-hydrogen ratios in Uranus’ atmo- sphere. The species ratio is the ratio of the deuterated species to the non-deuterated species. D/H is the ratio adjusted for the number of hydrogen molecules in the molecule (e.g. 4 in methane), with the frac- tionation factor as quoted by the source applied to give the true ratio of deuterium-to-hydrogen (equivalent to that in H2. An additional f factor is included from Lecluse et al. [108] which accounts for species fractionation. 68

4.1 Polarised standard star measurements for determining the accuracy of HIPPI in different filters. From Table 5 in Bailey et al. [58] ...... 104 4.2 Low polarisation star measurements for determining the telescope polar- isation in the g0 filter. From Table 3 in Bailey et al. [58]...... 105

5.1 The variation seen in 2011 measurements from Berdyugina et al. [169] would require a singly scattering atmosphere [175]. Hot Jupiter atmo- spheres are expected to have multiple scattering, scaling the overall po- larisation down [153, 155]. Our measurements are more consistent with Wiktorowicz et al. [175] but still greater than expected and not with the phase of the planet. A conservative maximum polarisation (the position angle determines how much stokes Q and U contribute) is calculated based upon the general case estimates from Lucas et al. [60]...... 148

xvii

Abbreviations

VSTAR Versatile Software for the Transfer of Atmospheric Radiation AtmoF Atmospheric Fitting Routine HIPPI HIgh Prescision Polarimetric Instrument AAT Anglo- Australian Telescope GNIRS Gemini Near InfraRed Spectrograph NIFS Near Integral Feild Spectrograph STIS Hubble’s Space Telescope Imaging Spectrograph WFC3 Hubble’s Wide Field Camera 3 COS Hubble’s Cosmic Origins Spectrograph ACS Hubble’s Advanced Camera for Surveys NICMOS Hubble’s Near Infrared Camera and Multi-Object Spectrometer MACARONI MACro for the Artistic Rendering Of Noodly Information UKIRT United Kingdom InfraRed Telescope

xix

Chapter 1

Introduction

Why do we study exoplanets?

Often astronomers point to two main drivers for the identification and characterisation of exoplanets. Astrobiology drives us; we seek to pin down the numbers in Drake’s equa- tion1, to tell us how prevalent life and intelligent life are in the universe. Understanding our own solar system and planet formation drives us; we seek to know why our solar system looks different from other solar systems.

Personally, I am delighted by the strangness of the “inhospitable” places we find. There is something facinating about worlds with glass rain[1], or with enough carbon to form a composition completely different from Earth, with a plethora of diamond [2]. If we are made of star stuff, so are planets. Studying planets is just as pertinent as learning about a far-away people or an unexplored continent2.

The discovery of the first exoplanets in the mid-1990s [3] was extraordinary not only for its implications for astrobiology, but also because of the disparity of systems we found those worlds in. Exoplanet science has challenged our understanding of planet formation and migration. To understand them, we must now determine the composition of these exotic worlds. But with limited data and unexpected parameters, the description of exoplanet atmospheres has been challenging.

1Drake’s equation is a famous equation made to help us estimate the abundance of intelligent life in the universe 2This will be the only paragraph I wax poetically in and I hope you’ll accept its notion, and allow it to exist without citation.

1 Chapter 1. Introduction 2

Exoplanet atmospheres were first characterised over a decade ago [4]. These character- isations, however, were of the atmospheres of planets orbiting very close to their and thus with very hot and often extended atmospheres; these were novel worlds, heterologous to the well-studied atmospheres in our own solar system.

While these hot giant planets, dubbed hot Jupiters, were unfamiliar, the relative avail- ability of data from them, made them vital not only to understanding the variety of worlds but also to developing techniques for future studies of more solar-like systems and Earth-like planets. Solar system planets were still vital to our ability to study and understanding of exoplanets. A great deal of what we seek to understand about planetary systems depends on the study of exoplanets and the solar system planets in parallel.

1.1 Planetary Atmospheres

Stars form surrounded by a disk of gas and dust, called a proto-planetary disk, within which (exo)planets form. Theories about the formation of giant planets in our own solar system have them forming beyond or on ice lines within these disks where there is sufficient material available to form a large core which can initiate run-away gas before the gases are blow away by the activity of the star as it moves through its early phases.

The hot Jupiters, which have been the dominant source of exoplanet atmospheric data until recently [5–11], present a conundrum: their are on the scale of Jupiter’s, but their orbits are tremendously closer to their stars—a fraction of the distance between and our Sun—suggesting their presence is a result of orbital migration. Our own gas and planets are thought to form beyond or near ice lines, with Jupiter and Saturn forming near the water ice line and Uranus and Neptune perhaps forming just beyond the carbon monoxide ice line [12][13][14]. The temperature around the ice line where the giant planets are thought to have formed are approximately 150 - 170 K; water’s condensation temperature is about 183 degrees [15] for pressures akin to the early solar nebula. The tight orbits of hot Jupiters around their stars recieve significantly more flux, implying that these planets have not formed by the aggregation of material along “ice” lines in situ. Chapter 1. Introduction 3

The ability of a planet to accrete a substantial amount of solid material for its core is a defining factor in its ability to then accrete a substantial gas envelope and become a gas giant planet before the T Tauri stage (and earlier) winds drive out the remainder of the gas after ∼3-5 Myr Ribas et al. [16]. This presents an issue in our own solar system with the presence of the ice giants. The timescales required at their present orbital distance to collect the mass necessary to build their cores are longer than the lifetime of the gas disk required to provide the gas envelopes. Suggested resolutions to this issue have ranged from the migration of the ice giants early in the formation of the solar system to their present orbits from an interior, shorter and more material-rich orbit [17], to the formation of these ice giants on a different ice line: the carbon-monoxide ice line [14].

For a hot Jupiter, the notion of forming in situ is even stranger. Migration mecha- nisms have been suggested to allow the planets to migrate inwards very early in their formation(see Morton and Johnson [18] for discussion and observational assessment). Although disk instability scenarios have also been explored [19].

It seems that the mechanisms leading to planet formation are more varied than we anticipated, and that even our own solar system may have had quite a few unusual seffects at play. Studying the solar system gas giants, therefore, becomes paramount to understanding the origin of planets. It complements exoplanet studies as well, by improving our atmospheric models.

1.2 Exoplanets

The study of exoplanets improves the understanding of our place in the universe. Studies of the exoplanets are hindered not only by the remoteness of the objects compared to our own solar system planets, but also by the relatively short time we’ve known (with certainty) about them. While technology improves at an outstanding rate to characterise them, we are presented with an abundance of worlds to explore.

To understand how planets are characterised, it is helpful to understand how they are detected in the first place. Chapter 1. Introduction 4

1.2.1 Methods for observation

Exoplanets themselves were expected by popular theories of planet formation in our own solar system allowing the process to occur around other stars. Previously their presence had been suggested by observations of gaps formed in protoplanetary disks (e.g. [20–22] and many previous speculative considerations for beta Pic and others) and had been alluded to by Renaissance philosphers and science fiction authors long before their discovery. What was surprising was the arrangement of the planets in the systems we were finding. The easiest planets to detect via and transit methods—the two successful methods thus far at the time this thesis was being written— were large and close to their stars. The complication is that there are no analogues in our own solar system with which to compare to these objects in any detail.

One might expect to find most planetary systems laid out in a way similar to our own, but of course this has not been the standard configuration. Systems come is a variety of configurations, some of which challenge the paradigms of planet formation. It was not expected that astronomers would find giant planets so close to their stars, leading to a reconsideration, if not a revision, of planet formation theory parallel to exoplanet discoveries (e.g. Boss [19], Lin et al. [23]). Being relatively easy to observe, hot Jupiter planets have provided the most readily available spectra, as well as something truely “alien” to study.

Exoplanet science uses a variety of techniques for detection and a subset of these are directly applicable to exoplanetary .

The methods are not equal in their effectiveness nor in the types of planets they recover. Today, the transit method has been most successful with 1210 planets discovered at the time this thesis was being finalised (exoplanets.eu website). This is owing largely to the success of the Kepler Survey mission. Radial velocity has been the next most successful technique for discovery and was particularly preferable before the era of major space-based survey missions. Radial velocity has discovered 605 planets to date. Direct imaging of systems has come into mainstream recently, producing 59 planets, although many of them border on the definition for a brown dwarf 3. Microlensing events have

3A brown dwarf being an object intermediate to planets and stars, which possibly form through gravitational instability and have large enough (∼13 MJ ) to permit deuterium burning in their cores. Chapter 1. Introduction 5 produced 36 planet detections. Pulsar and binary timing has discovered 19. And transit timing has found 4. has only found one planet so far.

Each detection method has its own strengths and usefulness in follow-up and character- isation.

Figure 1.1: Many different methods have discovered many different types of planets. This image is from September 2014. It thus is missing some of the more recent discov- eries but illuminates our detections biases and possible real biases. Image: PHL, UPR, Arecibo

1.2.1.1 Detection methods

Planets have been detected via microlensing, direct imaging, transit, binary transit tim- ing redial velocity and through astrometry. It is probable too that astrometry will begin detecting more planets soon with the ESO’s spacecraft now launched. See: Gaia Objectives (link). The success of some of these methods is in part due to the availability of technology, detection biases and to surveys. Radial velocity, for example, was success- ful early on because it was viable from the ground. Surveys like the Anglo-Australian Planet search have been able to utilise a moderately sized (in this case, 4-meter class) telescope to successfully detect nearby planets via radial velocity since around the turn of the millenium (see Butler et al. [24]). Other techniques such as the transit method have benefitted from space-based surveys like Kepler, which allow the light from the Chapter 1. Introduction 6 system to be carefully monitored without distortions from our atmosphere. Transits have also been detected from ground based observations (e.g. Swain et al. [25]).

Microlensing is perhaps the least promising for atmospheric follow up, as it relies on the chance alignment of a foreground planet-hosting star to a background lightsource being monitored. The gravity of the planet-hosting star will have a lensing effect on the background star causing it to brighten for a period of time. If there is a planet orbiting the foreground star, that planet’s gravity will also have an effect on the lensing, causeing a momentary increase in flux from the monitored background star within the greater stellar lensing event.

This provides an estimate of the mass of the planet which is far more accurate than other methods if the distances are well known.

Astrometry uses the visible movements of a potentially planet-hosting star from the gravitational tug of a planet as it orbits with some velocity component orthogonal to our line of sight, with relation to other relatively stable stars. This method is akin to parallax wherin the motion of the Earth around the sun produces an apparent motion in stars nearby compared to background stars, but is reliant upon the actual movement of the star being observed.

Radial velocity is similar to astrometry in relying upon the movement of a star around a center-of mass with a planet, but in this case the method relies on the radial component of that velocity (in our line of sight). Thus it does not detect planets inclined face-on and has a bias for planets seen close to edge on and in short periods. The planet is detected indirectly by monitoring the spectrum from the star as the planet orbits and looking for the regular doppler shift created by a planet moving it to-and-fro about the centre of mass.

This provides an msin(i) mass, a , for the planet. This is because the inclination of the system is not determined by this method, so it is unknown if the whole of the velocity vector lies in the radial component or if there is some tangential component as well. The planet’s radial tug on the star will be strongest when the planet orbits directly along our line-of-sight (i.e. when the inclination, taken from the “plane of the sky”, is 90◦, and the sin(i) = 1). This also provides an orbital separation from Kepler’s third law 4. The inclinations of the system can be determined from observations

4 2 3 That’s the one stating that the period of a planet is proportional to its semi-major axis. P = a /M∗ Chapter 1. Introduction 7 of transits, cross-correlation detanglement of the two spectra, or from polarimetry.

Direct imaging clearly presents an opportunity for follow-up on the atmospheres of planets. The infrared light emitted by the planets is directly resolved with adaptive optics and careful post-processing. However, these planets are large, often with masses around the cut-off for being classed as brown dwarfs. They also overlap, as exoplanets often do when they are young, into brown dwarf temperatures. These planets—or brown dwarfs as the case may be for some—are interesting subjects, but attempts to retrieve their spectra have proven difficult in the past [26, 27]. The objects found through direct imaging so far contribute very different knowledge about planet and brown dwarf formation as they fill the more massive and separated part of the parameter space. In addition, while the emissions spectra are available for these planets, reflected and absorped light information is not available from them at these distances and alignments.

Transit detections of exoplanets require that a planet’s orbit be aligned nearly dead on with our line-of-sight. This method detects the periodic drop in flux from a star as a planet, relatively dim in the visible wavelengths being observed, blocks out part of the star’s disk. There is another effect, called secondary eclipse, when the planet moves behind the host star and its contribution to the combined light of the system, primarily in infrared, is momentarily lost.

This method provides a radius for the planet compared to the star’s and therefore is accurate only if the star’s radius is well constrained, with its orbital distance known. If coupled with radial velocity measurements, this can provide the absolute mass as well since the inclination must be near 90◦, and therefore the density.

Taking radial velocity measurements of the star’s light during a transit can also tell you how the spin of the star compares to the orbital motion of the planet via the Rossiter McLaughlin Effect (see Addison et al. [28] for an example and detailed description of RM measurements). This is a compliment to some measurements of the orientation that can be provided by polarimetry.

Transit timing of binaries requires a star with a dim companion (e.g. brown dwarf or another planet) orbiting aligned with our line-of-sight. The blinking the binary com- panion creates is analogus to the transit detection method for exoplanets described next but is easier to detect for a given alignment. The evidence for the planet comes from Chapter 1. Introduction 8 perturbations in the regular orbit of the binary stars around each other as the planet orbits them. The transit events of one star in front of the other will occur at slightly different times depending upon the barycenter of the (nominally) three body system.

Timing of stellar events such as the period of pulsars or a rapidly degenerating binary system can out the presence of additional companions as well.

Polarimetry has not detected a planet yet, but is discussed as a characterisation tech- nique in this thesis. It is possible to detect planets from polarimetric signatures; the lack of polarised light from the star means that polarised light from a system without a significant or significant stellar activity is most likely from a planetary source. If the system is not seen face on, there will be a periodic change in the polarised light, allowing an observer to rule out the source being a disk.

As a detection method alone polarimetry can provide the planet’s inclination and posi- tion angle as well as how effectively the planet scatters light (polarimetric efficiency and albedo).

1.2.2 Characterisation

Many of the first planets discovered were very hot gas giant worlds. These first planets were often over 1000 K, producing a significant amount of . This radiation is detectable as it disappears behind its star as a periodic reduction in the combined infrared spectrum. A signicant loss of the system’s light is also detectable as the planet passes in front of the star; a giant planet is extended enough to provide a significant annulus at a particular optical depth, providing a significant amount of absorption at select wavelengths.

The hot Jupiters were indeed the first planets to have information on their spectra or multi-wavelength photometry available from their secondary and transits, thus giving us the first data for the characterisation of an exoplanet atmosphere.

At the time this thesis was being written, 15 planets have had species (either atomic such as potassium or molecular such as water) detected in their atmospheres according to the Exoplanet Encyclopedea website. While a few of these planets have several species now detected (one example, HD 189733b is discussed in this thesis), the first Chapter 1. Introduction 9 species detected are usually either sodium (Na), potassium (K), carbon monoxide (CO) or water (H2O). These species benefit from having either very strong lines in these atmospheres or substantial continuum absorption.

Sodium, for example, has been found on hot Jupiters HD 209458b and WASP 17b (among others). In the case of HD 209458b, broadband photometry was taken over the sodium doublet and off for a comparison in the transit depth [4] . For WASP 17b, a full spectrum was taken and binned at two wavelengths for a more detailed contrast from the Magellan telescope [29].

Water is commonly detected because it is theoretically abundant in the relatively well studied hot Jupiters, and because its broad absorption features lend themselves well to the low resolution spectra and broadband photometry obtained from exoplanets, particularly in near-infrared light, where secondary eclipse observations are typically taken.

Along with water, a few other (relatively) easily detected species are expected to be abundant in hot Jupiter atmospheres. Methane is also expected in atmospheres with equilibrium chemistry. Carbon monoxide is another molecule likely to appear in exo- planet atmospheres. Although the absoption bands of CO overlap many of the wave- lengths covered by the bands of methane, producing a degeneracy in low resolution spectra.

The carbon-to-oxygen ratio (or C/O ratio) is an important parameter for an exoplanet atmosphere. When the ratio is high the chemistry changes dramatically as in the case of hypothesized “carbon-planets”. In cases where the temperature of the planet is also quite high, most of the oxygen goes to making carbon-monoxide, leaving less oxygen available to form water and metal oxides. More obvious consequences of the high C/O ratio are the production of organic compounds such as hydrogen cyanide (HCN) and acetylene (C2H2).

The presence of clouds and hazes depends on the temperature and size of the planet as well as the atmospheric constituents and whether or not there is non-equilibrium chemistry. In general, clouds are not unexpected phenomena for exoplanet atmospheres although some planets have not shown evidence of them. They could reproduce the flattened spectra observed in others [30]. Chapter 1. Introduction 10

Along with the effect of flattening, clouds and hazes can affect pressure-temperature profiles (by insulating) and affect the light scattered off of the planet.

HD 80606b is giant planet in a highly eccentric orbit [31] bringing it into its star’s habitable zone (∼0.77 to 1.53 AU [32]), then back very close to the star to be heated again to hot Jupiter conditions every 111 days. Potassium has been detected in its atmosphere. Being in such an eccentric orbit and having a spin-orbit mis-alignment [33] could mean that it first formed in a very different orbit and has since been perturbed, thus its atmosphere is of interest not only for the serious temperature variations it must experience but because of the clues we might gain into its history as well. Like many, but not most, mis-aligned hot Jupiters, it is in a binary system. This fits the description for hot Jupiters having migrated to their current orbits via the Kozai-Lidov mechanism, but does not exclude other migration mechanisms such as planet-planet scattering (see: Kozai [34], Innanen et al. [35], Schlaufman et al. [36], Marchi et al. [37]).

The first claimed detections of direct spectra from resolved exoplanets (i.e. not using methods comparing combined spectra of the star and planet at different stages during the orbit) arrived only five years ago. In 2010 the VLT () in Chile, NACO (adaptive optics aided spectral coverage of 3.88–4.10µm) on Unit Telescope 1 (the VLT is actually four telescopes), retrieved a spectrum from one of the planets in the HR 8799 system [26]. The planets in this system are on the order of ten times the mass of Jupiter. The planet the spectrum was retrieved for, HR 8799c, is 10 MJ , 1100 K and orbits at a distance akin to the ice giants in our own solar system at 38 AU. An object of this size pushes the deuterium burning limit of 13 MJ , which is debatable since the masses are not measured but calculated based on the estimated age of the system being 60 Myr [26]. The objects represent an important intersection of object classes.

The spatially distinguishable L band (near infrared) spectra for this system were a great proof of concept, and provided rough data about HR 8799c. Most notably, the unex- pected (based on models) drop in flux at the red end of the L band. This system would be revisited later with extremely low resolution spectra taken for all four recognised planets and possible detections of water, ammonia, acetylene and methane [38].

These discoveries are perhaps more beneficial to the study of very large exoplanets and brown dwarfs than to studies of Earth-like planets, in spite of ever-improving resolution. But for a smaller planet, not directly resolved, the data must be collected through other Chapter 1. Introduction 11 means. At the time this thesis was being finalised, the first direct imaging observation of a Jupiter-mass exoplanet was published ( b, Macintosh et al. [39]).

Transit (and/or secondary eclipse) spectra have been obtained for planets as small as

6.5 M⊕([8]), 22.2 M⊕ (GJ 436b [40]) and 71 M⊕ (GJ 3470b [41]) in the past few years. These have largely been flat, arguably featureless, spectra though (with the possible exception of the data obtained by Crossfield et al. [41]). These observations are still in their infancy but their novelty is encouraging. One of the main drives for studying exoplanet atmospheres is to one be able to characterise Earth-like planets. The improvements on this front have happened quickly.

The techniques that will one day allow us to characterise smaller planets in detail and to possibly detect biosignatures with detailed models are, in some respect, being honed currently through studies of these hot sub-Neptune planets and detailed studied of hot Jupiters.

The atmospheres of exoplanets, even of the highly-irradiated hot Jupiters, for the most part, have temperatures under ∼2000 K (see Mancini et al. [42] and Zhou et al. [43] for good discussions of an exception to this generalisation, WASP 19b, in transmisison and secondary eclipse respectively). At these temperatures condensates of solids and liquids can form which complicates the spectra of planets when compared to those of stars. The types of condensates will depend on the environment, that is, the relative abundance of atomic species that the planet forms from. The carbon-to-oxygen ratio (commonly “C/O ratio”) is of particular importance because these species bond with other atoms, such as hydrogen, monopolising them and producing non-strightforward chemistry. This parameter is often based on the C/O ratio for the star, but it is not nessisarily the same as the star’s [10, 44]. The size and temperature of the planet will also play a role, as some clouds such as the titanium oxide (TiO) and vanadium oxide (VO) condense in the upper atmosphere of exoplanets then producing inversions in temperature as they insolate the atmosphere.

The metallicity of the star the planet orbits is itself not indicative of the abundances available in the disk. In our own solar system the gas giants have enrichment of most species at 2–4 times that of the sun, and in carbon the ice giants are enriched 30–40 times. This means that there is little to guide the modelling of exoplanets and the Chapter 1. Introduction 12 atmospheres must therefore be retrieved from the spectra available with a broad coverage of parameters.

Other broad features detectable through photometry include collision-induced-absorption and molecular absoprtion from species such as methane and water which have compli- cated rotational-vibrational modes producing many absorption lines bleeding into major absorption bands. Water is predicted to be abundant in hot Jupiter atmospheres with moderate to low C/O ratios; in atmospheres with high C/O ratios the carbon creates molecules with hydrogen, disallowing the formation of water with the remaining oxygen

1.2.2.1 Characterisation Methods

So how do we retrieve data about a planet we can’t (or can barely) resolve?

Observations at different wavelengths can be used to provide colour photometry or spectral information about the planet.

Planets that can be spatially resolved through photometry can also have their spectra spatially resolved. These are usually planets near the mass-based cut-off for the definition of planets. This is done either by placing the slit to retrieve just the planet’s light (e.g. Janson et al. [26]) or using inherently spatially resolved spectral retrieval methods, such as integral-field (IFS) (e.g. Bowler et al. [27]).

Massive planets that have been directly imaged and have had their spectra taken directly, often have spectra similar to that of a late L-type brown dwarf (early L dwarfs have methane dominated atmospheres without features from metal oxide condensates, but instead from metal hydrides and alkali metals; molecular species dominate the cooler T-type brown dwarfs) with the effects of clouds complicating the spectrum.

Some directly imaged giant planets, such as those in the HR 8799 system, appear to tra- verse the L/T brown dwarf transition but with redder J-K colours and lower so that they appear to be a continuation of the L-dwarfs beyond the L/T transition. The planets are brighter at 3.3/mu m than expected by equilibrium models for brown dwarfs which would predict that the planets be dim at these wavelengths because of methane opacity [45]. This could be due to the lower as the spectra are reproducable when one introduces both clouds and non-equilibrium conditions in Chapter 1. Introduction 13 the form of mixing. This mixing could prohibit the formation of the methane clouds thought to at similar temperatures appear much more blue in the infrared [46].

For smaller, indirectly detected planets, the most successful characterisations of atmo- spheres have been for planets that transit their star. For an exoplanet in an orbit very nearly aligned with our line of sight, the planet will pass in front of its star and behind it from our point of view. This provides a differential setting as the light curve is as- sessed with the planet passing in front of and behind its star. The secondary eclipse is a comparison of the combined flux from the system to that when the planet is hidden behind the star, giving the flux of the planet in the wavelengths being observed. It is derived straightforwardly from the depth of the curve, δSE.

F? δSE = (1.1) FP + F?

A dip in the light curve as the planet blocks part of the star’s disk is referred to commonly as transit, and the change in the flux in the curve relates to the radii of the planet and star as,

2 FP RP ≈ 2 . (1.2) F? R?

This value is typically given as a radius ratio, but if the radius of the star is known, the actual radius (or radii if taken in multiple wavelengths) of the planet can be obtained, which is useful when modelling the atmosphere. The above approximation omits the flux contribution of the planet while in transit, which, in visible light, is minor.

In secondary eclipse, when the planet is moving behind the star, a drop in the amount of combined light from the system is seen. If this is observed in different wavelengths (photometric bands or with a spectrograph), it provides information about the atmo- sphere of the planet. The difference in the spectrum when the planet is eclipsed will be most prominent in infrared light since the planet will be a thermal emitter and a solar- type star’s flux will peak in visible light. For this reason, many of the first detections of extrasolar atmospheres have been well suited to the hot giant planets close to their stars. This ensured that 1) the infrared flux from the planet was substantial, and 2) the planet was close enough to its star to pass behind the star if slightly misaligned with the Chapter 1. Introduction 14

Figure 1.2: Narrow band photometry is compared to model spectra for the four planets in a resolved planetary system HR 8799. All of these planets are farther than 14 AU from their host star and greater than ∼5 MJ . Spatially resolved spectra have also been obtained for this system. Image: Fig 9 in original. Currie et al. [46] line of sight (i.e. there are more inclinations that will appear to take the star between us and the planet if the planet is closer to it).

Pressure-temperature profiles in models determine the abundances and condensation layers in the atmosphere, and they can be retrieved if the spectra are detailed enough. From the Voyager mission, for example, very detailed pressure-temperature (P-T) pro- files for the four giant planets were obtained through radio occultation measurements 1.3.

For exoplanets, the pressure-temperature profile can be somewhat constrained from the infrared dayside emissions retrieved with secondary eclipse. In general, an atmosphere that cools with height will show absoption features while one with a temperature inver- sion will show emissions for some species. If an atmosphere were isothermal it would be featureless. Chapter 1. Introduction 15

Figure 1.3: An illustration of the pressure-temperature profiles of solar system bod- ies with thick atmospheres. All of the worlds shown here have an inversion at these pressures except Venus (Uranus’ is very extended). This figure is Figure 1 in Robinson and Catling [47] and is based upon the work of several others cited therein.

There is some evidence to suggest that hot Jupiter planets orbiting less active stars are more likely to have temperature inversions [48]. The increased UV flux from chro- mospherically active stars may photodissociate the species in the upper atmosphere responsible for the inversion, likely to be sulferic compounds as suggested by Zahnle et al. [49]. Other species have been suggested as drivers for the inversion. Metal ox- ides such as TiO and VO are good absorbers that would be present in gaseous form in the upper atmospheres of more irradiated planets [50], however some inconsistencies with a straightforward temperature relation have been discovered, so it is likely that an additional mechanism such as the stellar activity is at play [48].

Monitoring of the full light-curve through all phases is possible and has been used to create temperature maps of some hot Jupiters. Full-phase light curves provide in- formation on the amount of day-night heat redistribution. A change in the thermal signature in sync with the orbital phase shows the temperature distribution and this in turn provides information on the winds and mixing. Chapter 1. Introduction 16

A planet close to its star is also well suited to block part of that star’s light during part of orbit; this is typically referred to as transit or sometimes primary eclipse. Large planets will block a larger fraction of the disk than a smaller planet for a given orbital distance and if the planet is very hot the atmosphere may still be extended (the collapse having been damped by early migration to a highly irradiated orbit, where Ohmic heating keeps the planet inflated [51]). Transit observations are well suited to provide useful information about the planet’s chemical profile, particularly for species with signatures in visible light.

Clouds in transit spectra flatten and mask features, essentially driving up the radius of the opaque sphere for some wavelengths. In secondary eclipse they have a similar flattening effect in visible light by masking the constituents of the atmosphere below them. That is to say, wavelengths of light from the star for which the clouds are opaque will be reflected with information about the atmosphere down to the pressures of the clouds, but information about the atmosphere below the clouds will not be retrievable at those wavelengths. An additional consideration in transit spectroscopy is that the light is taking a “tangential path” through the atmosphere so it is affected more by the upper atmosphere.

Figure 1.4: An illustration of the path of light through an exoplanet atmosphere. The light seen by the observer moves through the periphery of the disk providing more data about the upper atmosphere than the lower atmosphere. The ratios are exagerated for illustration. Chapter 1. Introduction 17

Multi-wavelength determination of the radius of the planet can be determined from observation of the transit in multiple bands. The variations of the planet’s radius with wavelength provide information about the verticle structure of the atmosphere. The comparison of the projected opque disk at different wavelengths gives an absorption spectrum for the planet atmosphere most sensitive to the upper parts of the atmosphere. In fitting the spectra to models, it is important to keep in mind that the radius of the planet will vary slightly between wavelengths. This can affect estimates of the gravity, although in practise these are not substantial enough to cause problems for the relatively low resolution spectra. The limb darkening of the star also effects the transit curve. This is usually accounted for with a parameterised treatment of the limb darkening, although this can still produce errors in the estimates of planetary radius compared to the stellar radius (RP/R?) by 1-3% [52].

Transits could be observed for a , although today they have only been observed for larger planets (as small as super-Earth size[6, 53, 54]). The difference between the radius of the opaque disk of the planet and the extent of the thin atmosphere on a terrestrial planet is minor and could be difficult to detect.

Systems that are not aligned so that they transit, can still have information retrieved through cross correlation or polarimetry.

Cross correlation has also been used to retrieve high resolution data about a planet’s spectrum.

Radial velocity planet detection does not directly contribute to atmospheric detection, but radial velocity can be used to detect atmospheric species in exoplanets through cross-correlation. Carbon monoxide was detected from thermal emissions combined with the light of the star for the planet around τ Boo Brogi et al. [55]. This technique requires very high resolution spectra and careful post-analysis though as one is discerning the doppler shift in the relatively weak planet spectrum from those in the star.

In this method, a high resolution spectrum is taken of the combined light of the system to find the variations in the signal consistant with the radial velocity variations of the planet in amplitude and systemic velocity. The technique essentially disentangles the light from the planet from that of the star, providing a direct detection of the planet’s Chapter 1. Introduction 18 light. This is often performed within a broad molecular band to attempt to detect that molecule.

Since this method retrieves simultaneous radial velocity for the star and planet it can also provide the .

Polarimetry allows for the differentiation of the sources of light because the light from the star in most cases is not significantly polarised, while the light from the planet atmosphere is [56, 57]. If the planet’s orbit is inclined the polarisation will change along with the phase. This technique provides information about the size and type of particles in the atmosphere which provide constraints on the constituents of the atmosphere. However the signatures even for highly irradiated hot Jupiter exoplanets is only 1×10−5 to 1×10−6 polarisation of the combined signal. This means that this technique requires extremely sensitive which have only become available in recent years [58–60].

1.2.3 Methods for modelling

The interpretations of data collected through the techniques discussed in the last section are strengthened by their comparison to atmospheric models.

There is more than one approach to modelling the radiative transfer in an exoplanet atmosphere. Our models use a line by line approach but another popular option for exoplanets is called correlated-k.

Correlated-k uses the a distribution of absorption coefficients (k), assuming the k values correspond to given temperatures and pressures at a given layer. The distribution of absorption coefficients is based upon a parametric band model. It is faster than line-by- line models but less complete in its treatment, allowing for the possibility of errors when matching to high resolution data. In HD 189733b, which has somewhat detailed data available for an exoplanet, the overlap of absorption bands is an issue. The method can overestimate spectral mean transmittance, and abundances can differ from line-by-line by ∼0.1–0.01%.

Circulation models are also possible. For some planets, such as HD 189733b there are observations in the form of temperature maps from which one can infer the winds Chapter 1. Introduction 19 and circulation patterns. Circulation is particularly important for hot Jupiters as some planets seem to have less heat redistribution to the night side than others (they are in orbits expected to have tidal locking). Models for hot Jupiters often show superrotating jets which can displace the hot spot, otherwise at the substellar point, east or west (e.g. Showman et al. [61], Rauscher and Menou [62]).

My thesis focuses on the modelling of the atmospheric constituents based upon the findings of previous retrieval models and forward model fitting (to provide a starting point for such things as a parameterised pressure-temperature profile) and compars these radiative transfer spectroscopic models to the findings of other chemical-radiative transfer models to date. My thesis then pairs these with observations and models of the polarised light from these exoplanets.

Producing a model of an exoplanet atmosphere is similar to producing one for a star or solar system planet in that it is dependant upon similar input parameters. However since exoplanets have such sparse spectral and photometric data available, retrieval of informa- tion about the planet is fairly limited to things such as a simplified pressure-temperature profile (i.e. is there an inversion, and if so approximately at what pressure?).

A major concern for modelling a hot Jupiter is having the appropriate line lists available. This means having line lists for species such as water for temperatures over 1000 K. Water is expected to be a major constituent in most hot Jupiter atmospheres.

Atmospheric models also require assumptions about the chemical composition of the atmosphere. This can be calculated for an ideal, equilibrium case. The chemical model is based on equilibrium chemistry for a given metallicity, gravity, and pressure-temperature profile. Some deviations from equilibrium chemistry are explored in this thesis in an ad hoc sense. Previous attempts at modelling deviations from equilibrium are also described in the literature reviews of the backgrounds for these objects.

In line-by-line radiative transfer models the atmosphere is broken into many layers and the opacity is calculated for each layer at each wavelength being modelled, with adjust- ments then made for scattering and absoption. It is important that these models have a full treatment for scattering; the non-isotropic scattering that will be produced by some atmospheres can contribute to the path of the beam (stellar source ray) by scattering Chapter 1. Introduction 20 back into it. The chemical model should also account for the effects that the formation of condensates have on the surrounding gases and opacities.

Models for Uranus’ atmosphere are included in this thesis as an introduction to atmo- spheric modelling with many parallels to the less constrained exoplanet models. The Uranus model is created to solve the inverse problem: we have very detailed spectra, calculate the opacity and solve the radiative transfer equation to fit a few specific pa- rameters precisely. This serves to provide a more familiar example of radiative transfer as well as relating to one of the underlying themes of exoplanet characterisation and this thesis: planet formation.

1.2.4 Effect of stellar activity

An additional contribution to the environment that should always be considered when studying planetary atmospheres is that of the star’s activity. The magnetic field of the star and activity it produces can have numerous known effects on the atmospheres of closely orbiting planets..

The relationship between atmospheric heating (stellar type and orbital distance being central considerations), stellar activity and the atmosphere’s effects on the heat distri- bution (and conversely that heat’s effect on the atmospheric constitutents) have been a focus of hot Jupiter studies. It is important in understanding how planets form to understand whether hot Jupiters appear to fall into two types (with and without tem- perature inversions) because of their current circumstances or because of some inherant condition.

Perez-Becker and Showman [63] explored this possible dichotomy. Previous to the study, the hottest hot Jupiters had seemed to be the least efficient at redistributing the stellar energy incident upon them, producing extreme day-night contrasts. In general, for syncronously rotating planets with weak friction in their atmosphere and which are weakly irradiated, zonal flows will be produced. Conversly, if there is high friction in the atmosphere and the planet is more strongly irratidated, the planet will have a greater temperature difference.

This is not surprising but suggest that irradiation may affect the friction of the con- stituents (either those that remain at certain levels in the atmosphere or by the densities Chapter 1. Introduction 21 the constituents encounter). The relationship is largely controlled by the timescale for gravity waves to propogate over the planetary scale. The heat redistribution is governed then by wave-like prosesses akin to the low temperature gradients of Earth’s tropical zones. In hot Jupiters the timescale of the horizonal day-night advection is approx- imately equal to the time for a fluid parcel to move vertically over the difference in equivalent density thickness [63]. That is, the hot Jupiters are of the size where it is thermodynamically nominal whether or not the heat moves to equilize on the far side of the planet. This makes them particularly susseptable to variations in the density of the atmosphere and the specific heat of the condensates and atmospheric gases.

This could be induced be absorbing compounds in the upper atmosphere. Knutson et al. [48] found a correlation between the activity of host stars and the atmospheric emissions of the hot Jupiters orbiting them suggesting that such absorbers could be the device if they are then destroyed by the ultraviolet activity of an active host star. This would explain the lack of inversion in these planets around active stars as well. There is some debate over the species responsible for the absorption (for example metal oxides like we see in brown dwarfs were initially suggested by Fortney et al. [64]), but the photochemical sink suggested by Knutson et al. [48] would compliment the sulfer-based species suggested by Zahnle et al. [49].

A relation between stellar activity and an extended atmosphere isn’t always present though. The hot Jupiter WASP 12b has hot exopheric gas beyond the Roche lobe but its star isn’t particularly active. Radio and optical show it has a circumstellar gas cloud. Along with core emission of Ca II H and K lines and radio observations as an indecator of circumstellar gas clouds, polarimetry can provide evidence of such structures in distinguishing the way the light reflects [65].

Stellar effects have been explored as the source of the asymmetric light curves seen in some exoplanets. Some exoplanets show an asymmetry in ingress and egress which could be related to the interaction of the planet’s magnetic field with that of the star [66]. Asymmetry in the near ultraviolet can be explained by shock waves produced by magnetic recombination events. These can be produced by different mechanisms depending on the magnetic field of the star. If the magnetic field of the star is strong enough to confine the coronal plasma out to the distance of the planetary orbit, or in Chapter 1. Introduction 22 the case of a weaker stellar magnetic field, by coronal material escaping as the stellar wind, this can drive .

Even in cases where there may be a relation, observationally these effects may be minor. Modelling the reflection of planets as they diverge from a shape confined by the Roche lobe, Budaj [67] found that the Roche shape of two planets described in this thesis, HD 189733b and WASP 18b, would diverge from a sphere only by 1% and that HD 189733b’s reflected light curve was reproduced reasonably well by the Roche limit. This is still important to consider since atmospheric asymmetry can create non-straightforward vari- ation in the secondary elipse and may enhance polarimetric signals from the planet.

Shocks can potentially be observed; if the orbit is prograde and outside of the ‘co- rotation’ radius, the shock position will trail the planet producing a late egress. The planetary magnetic field can be described to some detail by this effect as the “stand off radius” (offset from substellar) of the shock correlates to strength of the planetary magnetic field.

The possible detectability of radio emissions to confirm these shocks has been explored by Vidotto et al. [68]. Shocks appear when planets are supermagnetosonic. Three of the four planets described in this thesis have estimated radio emissions from their stellar magnetic field interactions: τBoo b at 0.5 – 0.9 mJy, HD 189733b at ∼0.47 mJy and HD 179949b at 0.112 mJy. No planet to date has been detected in radio.

This thesis explores applications of atmospheric modelling to solar system and exo- planets, and the relatively unexplored science of exoplanet polarimetry. The polarimetry measurements included here are compared to simple models of polarised light from an unresolved system. Chapter 2

Models

The models created for this thesis were completed with the Versatile Software for the Transfer of Atmospheric Radiation (hereafter referred to as VSTAR) [69] developed by Prof. Jeremy Bailey and with significant contributions from Dr. Lucyna Kedziora- Chudczer. Additionally the ATMOsferic Fitting (ATMOF) routine developed by Dr. Daniel Cotton was used to produce accurate telluric models for line removal as well as fitting for the Uranus models. ATMOF was not used for fitting of exoplanet data be- cause the data is not detailed enough to require thorough coverage of parameter space. Preceeding the use of VSTAR, chemical models for the exoplanets were produced with our ICE routine, however for Uranus, the far more accurate Voyager 2 occultation mea- surements were used for the pressure-temperature and methane profiles.

2.1 Chemical Models

For planets in our own solar system, the chemical profile is predominantly retrieved from observation. For Uranus, a combination of radio occultation measurements from Voyager 2 [70], and atmospheric profile fitting by Sromovsky et al. [71] provides the species abundances with pressure. For Uranus our main concern was the methane profile which is reasonably well constrained for pressures below ∼10 bar (this is discussed in more detail in the section on Uranus, Chapter 3 ). Methane abundance is a particular concern since its lines dominate the H band spectra used in our deuterium fitting models.

23 Chapter 2. VSTAR 24

On the other hand, for exopanets, a chemical model is required to predict the compo- sition. This is difficult to constrain with the limited data on exoplanets available, so theoretical models on the composition of the planets provide a good starting point. The chemical model is for a given temperature, pressure and elemental abundance and is, in our case, based upon chemical equilibrium. Either solving for the mass balance and charge balance from the equilibrium constants of formation per compound or minimiz- ing the total Gibbs free energy produces appropriate mixing ratios for each pressure- temperature regime. This predicts the abundances for gas and ionized species as well as the condensates. The mean molecular weight, specific heat and adiabatic gradient can then also be derived.

Disequilibrium chemistry can certainly be a contributing factor to the spectra of exoplan- ets, currently we do not include these effects directly but can adjust the abundances ad hoc within VSTAR after the initial chemical model is made. Alternatively our chemical model can be circumvented if a retrieved model is provided by literature or a simplified model is being tested. VSTAR simply reads in the output file from the chemical model.

Disequilibrium chemistry is speculated to play a role in the atmosphere of at least one hot Jupiter studied here: HD 189733b [72]. The haze, which may exist in its upper atmosphere, may be the product of photochemistry for example, causing a species to appear that otherwise would not have or depleting an species expected to be abundant (as in through photodissociation) [72–74]. Also the dayside winds may be too fast to allow methane to stably bond [75]. These deviations are dealt with by adjusting the abundences as described in the pertinent section.

Our chemical model code ICE determines the mixing ratios of species for a given pressure (height) and temperature. This is required to model the energy budget of an atmosphere, and thus its emergent spectrum, according to chemical equilibrium (with options for rainout and simple gas-phase-only atmospheres available). Thus it requires the input of a temperature-pressure profile for the planetary atmosphere. ICE relies on the accuracy of several other inputs. The metallicity is taken into account. The gravity of the body is needed to provide an accurate density structure for the layers and for an exoplanet relies on the accuracy of radius and mass measurements provided by radial velocity and transit observations. Finally the carbon-to-oxygen ratio is taken into account as it dictates a Chapter 2. VSTAR 25 large portion of the chemistry on the planet. For exoplanets, which typically do not have this value well constrained, this value is fitted with the ICE derivitive ICECO.

ICE and ICECO calculate the layers at which species condense out as liquid and solid as well mixing ratios.

Condensation to solid and liquid phase contributes to the emergent spectrum in two major ways. First, by producing opacities at the level they develop into clouds. We adjust scattering cloud layers within VSTAR itself to account for this effect. Second, by altering the structure of the atmosphere, contributing to temperature gradient fluctua- tions and to changes in the mixing ratio for gases. The latter issue is well accounted for by our chemical models which predict the heights at which species will condense out. The particular of the species that form the condensate will dictate the influence they have on the emergent spectrum. A very opaque cloud layer for example can create a “floor” or a variation in the opaque sphere at different wavelengths. This is important in considering transmission through exoplanet atmospheres (broadband transmission measurements measure this varying opaque sphere) but is also important when modelling reflection spectra for solar system planets. The species in a cloud can affect the behavior of the light in the methane transmission windows of Uranus, for example.

2.2 Radiative Transfer

For planetary atmospheres, the energy budget of the atmosphere determines its state and the way it will interact with light. This relationship is exploited by planetary atmosphere scientists as a way to retreive atmospheric characteristics from their effect on light, from both the planet itself and the star it orbits. The radiative transfer through absorption, emission and scattering light determines the appearence of the emergent light.

The radiative transfer for an atmosphere will depend first on the light source itself, in this case the star, providing the continuum spectrum. The planet’s atmospheric constituents and their abundances at different atmospheric depths then determine how that light is absorbed or scattered. Chemical and molecular mixing ratios can be determined based upon the pressure and temperature at a given height, which are largely dependant upon the size of the planet and its orbit. These are also scaled to the relative chemical Chapter 2. VSTAR 26 abundance for the planet which is expressed by the metallicity in the star and the carbon-to-oxygen ratio for the planet.

To derive an appropriate model of the radiative transfer requires the understanding of the clouds or condensates, the appropriate inclusion of spectral lines and the atmospheric chemistry of the planet.

From a modelling perspective we can first consider that an atmosphere will be subject to a (nearly) blackbody spectrum1 from the star and emit its own blackbody spectrum at its surface. These will each contribute to the observed spectrum: the planet primarily in infrared and the star primarily in visible light if it is sun-like. The light will then undergo (multiple) scattering, absorption and reemission.

2.2.1 Lines

The physicist Max Plank decribed the linear relationship between the wavelength of light and the energy of atomic transitions. From this it follows that the emission or absoption lines created by the interaction between light and an atom would be monochromatic (i.e. for a specific wavelength). In reality, many atoms contribute to an atmospheric spectrum and many additional phenomena contribute to how the lines are expressed, so that they are not observed as perfectly quantised lines. This is, in part, owing to the fact that the orbitals in an atom are described by probability density functions. The Heisenburg uncertainty principle requires that the lines be broadened. This line shape is Lorentian and dependent upon the quantum structure of the species. This is referred to as the natural broadening of a line.

As atoms bond in molecules, the lines become more complicated and other factors affect the expressed spectrum.

VSTAR includes other line lists from physical phenomena of the environment. Collision- induced absorption is due to the inelastic collisions of molecules and can be included in our models in the form of special line lists.

1Blackbody spectrum refers to the emergent flux from a body, derivable by integrating the Plank Function over all wavelenths, and is dependant upon the absolute temperature of the body (i.e. ∝ T 4) Chapter 2. VSTAR 27

2.2.1.1 Broadening

Spectral lines in atmospheres are subject to further broadening. Doppler broadening is due to the movement of molecules in a gas. The movement is approximated by a Maxwell distribution of velocities in the gas proportional to the inverse of the square-root of the temperature, and this produces a Gaussian distribution of frequencies.

A third source of broadening, pressure broadening, is due to increasing interactions between the electric fields of molecules and their orbitals as one goes to deeper and deeper atmospheric depths (or in any case where pressure increases in pressure). This is the net product of collisional broadening which produces a Lorentzian profile. The two Lorentzian profiles from pressure and natural broadening are referred to as a damping profile.

The Gaussian Doppler profile and the damping profile combine to create the Voigt profile. In the Voigt profile which describes a line’s convolved shape (a Voigt profile is a Lorentzian profile convolved with a Gaussian profile) the Doppler broadening dominates the core of the line while the damping from Heisenburg uncertainty and collisions will primarily affect the wing shape.

Deviations from a purely Lorentzian wing shape in VSTAR are defined through a sub- routine called LIN SET SHAPE which is based largly on the application of Perrin and Hartmann [76] to line profiles of carbon dioxide for Venus as described in Meadows and Crisp [77]. This subroutine is described in more detail in 2.3

2.2.2 Scattering

Finally the aerosols in an atmosphere can dramatically affect the emerging spectrum. The aerosols act to insulate and reflect,, sheilding lower layers of the atmosphere in reflected light wavelengths and insulating the emerging light at some wavelengths in emission. Thus they often have the primary effect of flattening an emission spectrum with variations owing to the cloud and haze layers properties. In transmission they create an opaque (or partially opaque) layer for visible light and thus will flatten a primary transit spectrum as well. Chapter 2. VSTAR 28

We model both Mie scattering from aerosols and Rayleigh scattering from molecules. Mie scattering is the description of the scattering of waves of light encountering a spherical partical. The solution is an infinately long series expansion of spherical harmonics. To allow for computation an approximation must be made. For very small particles the Rayleigh scattering approximation is a good description. For Rayleigh scattering, light is scattered predominantly within the plane of the incident light; as particles become larger and a fuller treatment of Mie scattering becomes nessisary, and the particles scatter primarily in the forward direction.

2.2.2.1 Phase Functions

Figure 2.1: An example of the Henyey-Greenstein description of the angular depen- dance of light being scattered. The forward scattering direction is 0◦; backscattering is 180◦. Thus a strong backscatterer has a low anisotopy factor, g. Image: Scott Prahl and Steven Jacques 2014, Biomedical Optics at Oregon Medical Laser Centre website

If we simplify the atmosphere to be plane-parallel (which for a planetary scale is locally appropriate) we can produce a solvable general equation for radiative transfer inclusive of multiple scattering.

dI(τ; µ, φ) µ = I(τ; µ, φ) − S(τ; µ, φ) (2.1) dτ

Where I is the radiance (or specific intensity) at a given frequency, S (sometimes written J) represents the source function, µ is the cosine of the inclination to the normal (up), τ is the optical depth and φ is the azimuthal angle. The change in the optical depth Chapter 2. VSTAR 29 over a layer, dτ, includes continuum absorption, line absorption, and extinction due to aerosols.

The emergent flux then at the top of the atmosphere (as measured for a planet remotely) is described by

τ∗ 0 Z 0 −τ∗/µ 0 −τ /µ dτ I(0; µ, φ) = I(τ∗; µ, φ)e + S(τ ; µ, φ)e (2.2) 0 µ wherein τ∗ is the optical depth at the surface or maximum atmospheric depth considered and the other variables are as described in equation 2.1. To solve this we introduce a workable source function.

One challenge of radiative transfer is to utilise a source function that is solvable but still accurate. The source function used by VSTAR is based on DISORT [78], a DIScrete Ordinate Radiative Transfer code which includes multiple scattering. de Kok et al. [79] has shown that even the case of exoplanets, which have much more sparse data than the solar system planets available, incomplete treatment of scattering can produce errors. For solar system planets a complete treatment of scattering is necessary to fit the detail of the data.

Mathematically, the source function can be considered in three parts.

$(τ) Z 2π Z 1 S(τ; µ, φ) = P (µ, φ; µ0, φ0)I(τ, µ0, φ0) dµ0 dφ0 4π 0 −1 (2.3) $F −τ + (1 − $)B(T ) + P (µ, φ; µ , φ ) e µ0 4π 0 0

The first part of this source equation is the component of the light scattered into the beam from all directions (hence the double integral) and is dominated by the single scattering albedo, $. Within the double intregral is the phase function, P and radiance for that layer, I; τ is the optical depth again, which essentially corresponds to a specific layer of the atmosphere.

The second part of the equation corresponds to the thermal emissions, wherein B(T ) is the Planck function. Chapter 2. VSTAR 30

The third part of the equation is the direct beam from the external source (the Sun or appropriate host star). The flux of the star is described as µ0F ; while µ0 and φ0 give the direction of the incoming beam.

In the first part of equation 2.3, the double-integral describing the contribution of any beam by the scattered light from other beams, is difficult to model. This is where a simplification of scattering is often included to some detriment. VSTAR therefore uses a non-isotropic phase function for the scattered light, which is of particular im- portance for modelling clouds. The phase function in VSTAR can be estimated with a Henyey-Greenstein approximation[80] which is more complete than isotropic scatter- ing approximations (or ignoring the scattering contribution outright) but lacks in its hangling of backscattering [81]. The anisotropy for the Henyey-Greenstein approxima- tion is described by a parameter, usually denoted g, that describes the contribution of backscattering compared to forward scattering for a particle [80]. The source function, which is an expansion of a Legendre polynomial, can also be calculated for a number of moments with VSTAR; the polynomial is expanded for a number of moments and terms dependant upon the number of streams being modelled.

2.3 VSTAR: Radiative Transfer Modelling Software

VSTAR (Versatile Software for the Transfer of Atmospheric Radiation) is a FORTRAN 77 code for solutions to radiative transfer. It has been successfully applied to high res- olution transmission spectra through Earth’s atmosphere[82], emissions and reflections from solar system bodies such as Venus, Jupiter, Titan, Uranus and Neptune[83–88], and brown dwarfs[89] and most recently to modelling the atmospheres of transitting exoplanets [90].

While VSTAR has been used previously to fit atmospheric data on exoplanets, those attempts have been compared to data far more sparse than HD 189733b (the primary subject of this thesis) and have excluded polarimetric measurements. Chapter 2. VSTAR 31

2.3.1 Structure of VSTAR

One of VSTAR’s strengths is that it is modular, allowing parts of the code to be combined in different ways to solve for different types of problems. For example, if comparing secondary eclipse and transit data for an exoplanet, one could use essentially the same code, switching out only the radiative transfer solution approach at the end. Similarly if one has reason to believe different sets of data arise from distinct parts of the atmosphere (e.g. latitude on Uranus, or the day-night sides on a tidally locked exoplanet) the models can be run with differnt inputs, easily altered owing to the modular structure of VSTAR.

The main modules are MOD, LIN, RAY, PART, and RT and each contain several subroutines which can be used—or not—as needed.

MOD sets up the wavelength grid for the model and reads in the atmospheric chemical model (ICECO) from which the spectral model (VSTAR) will be based.

LIN retrieves lines and related continuum absorption and adds them to the model using a line-by-line approach. The lines are retrieved from appropriate databases pertaining to the species at particular temperatures (such as HITRAN or HITEMP). Line shape can be manipulated based upon the equations in Hartmann et al. [91]. For a gas giant hydrogen-helium atmosphere a sub-Lorenzian line shape is required to accomodate the line wing shape. The LIN module is easily adapted and expanded as new line lists become available for species. For example new line lists for methane at low tempertures, which is important for the ice giants, recently became available (e.g. Rothman and Gordon [92] ). Line lists for collision-induced absorption are also included here.

LIN also allows the user to adjust the isotope ratio, which is useful for deuterium fitting, by applying a simple scaling factor to the input model atmosphere.

RAY is an extension for the addition of Rayleigh scattering from molecules. It includes Rayleigh scattering effects to be added to the model for ‘Air’ (nitrogen dominated Earth- like atmospheres), N2 itself, H2 and/or He dominated atmosphere as on a gas giant.

PART allows for the addition of scattering particles such as those in clouds or hazes. These are included for both transmission and reflection spectra as they have a slightly different effect in each. The inclusion of accurate cloud layers is vital to fitting high resolution spectra on Uranus and our data for the planet are fitted for the opacity Chapter 2. VSTAR 32 and base pressure that are inputs for this subroutine. The scattering phase function is described using the Henyey-Greenstein function. Cloud properties may be either calculated with the subroutine PART ADD SPHERE or added directly (as from the literature) using PART ADD PCALC.

When the subroutine PART ADD SPHER is used to calculate the properties, this is based on a refractive index file covering the wavlength range being tested, an optical depth file for the appropriate heights in the atmosphere, a description of the distribution of sizes of the scattering particles, and the scattering phase function approximation to be used. This portion of the code is based on the description of Lorentz-Mie scattering properties for small spherical particals in Mishchenko et al. [93].

RT is the radiative transfer solution that is dependant upon either the subroutine DIS- ORT [78] for reflection and emissions spectra or TRANSMISSION which calculates the equivalent absorbing disk for transmission of light for exoplanets (based on the direc- tional transmission code used for telluric absortion).

Finally, RT also runs direct beam (source, e.g. sun) and albedo contributions for the “surface” although these are relatively negligable for giant planet atmospheres.

2.3.2 Spectral Line Absorption

The absorption contributing to the emergent flux of a planet is due to the gaseous species present in its atmosphere. The chemical model predicts the possible abundances of all gases. The inclusion of line lists for the absorption component of the radiative transfer solution depend largely on theoretical research and previous detections when it comes to exoplanets.

For Uranus, the primary constituents of the atmosphere at pressures under ∼10 bar is predominantly methane, hydrogen and helium gas with some possible contributions of other gases such as ammonia and nitrogen gas. The lines in the fitting region should also be considered. For example, our H band observations of Uranus are dominated almost solely by methane; there is no significant contribution from hydrogen or helium gas line absoption in this region. Chapter 2. VSTAR 33

Exoplanets should be dominated by water, carbon monoxide, methane, and ammonia with, in some cases, metal oxides, metal hydrydes and/or carbon species. The contribu- tions of these will vary from planet to planet. There are also contributions from atomic species such as sodium and potassium possible, these produce electronic absoptions at specific wavelengths with a broadening component and line wing profile vital to the fit.

In the case of molecular species there are rotational and vibrational effects which are also quantised in addition to the electronic emissions (or absorptions). Rotational energy changes are small producing long wavelength (microwave or infrared) lines. Vibrational energy changes are much greater and occur alongside a rotational energy change (called rovibrational changes or lines), these are observed as a complimentary set of lines in the infrared. A line from electronic transition will be much higher energy still and be produced in visible or ultraviolet light. For a molecular species therefore, the spectral signature produced is more band-like as it is the combination of many of these lines (sometimes referred to as continuum absoption).

The line shape in VSTAR is described by the subroutine LIN SET SHAPE. As the Voigt profile of a line is the convolution of the Gaussian and Lorentzian curves, we can correct the discrepancies between a pure Lorentzian wing contribution and our observations. Four parameters correct the profile (for a given wavelength), taking into consideration the the line’s postion, pressure-broadening and integrated intensity, producing a “χwing factor” which defines the ratio between the line profile and a Lorentzian profile. This is especially useful in cases where the far wing of a line may be more divergent from a Lorentzian than the inner wing (excluding the effects of the Gaussian contribution).

The line lists differ for the species at different temperatures. For Uranus it is important to use line lists for temperatures around 80 K, while for the hot Jupiter type exoplanets for which data is retrieved, the appropriate temperature will be closer to ∼1000 K.

Collision induced absoption (CIA) is also important for planets. Here the net effect of small molecular collisions increases the opacity of the atmosphere. VSTAR allows the inclusion of both H2-H2 and H2-He collisions read in as additional line lists.

The completness of line lists is important for atmospheric models. For this thesis for example the line lists for complex molecules such as methane are vital both at high temperatures for hot Jupiters and at low temperatures for the planet Uranus. Chapter 2. VSTAR 34

With the abilities of VSTAR in mind, we begin with an example of fine-tuned fitting of the spectrum of a solar system planet, Uranus. Chapter 3

Uranus

As astronomers learn about the variety of planetary systems from characterising the exoplanets they find, they are also learning about planet formation and dynamics. Mi- gration is of interest for multi-planet systems which require stable orbits and for the hot-Jupiter systems that likely migrated to their tight orbits early in their formation.

In our own solar system a key element to planet formation presents itself in the form of the ice giants, Neptune and Uranus. The composition of these planets is notably different from both the terrestrials and the gas giants in our solar system. Their intermediate mass does contain a hydrogen-helium gas envelope but their bulk interior is believed to be comprised of water and other ices. There is some dispute over the bulk material that created their cores, and this is related to the debate over where their cores formed in the . Both planets have had their D/H isotope ratios measured in the past , our high resolution data have higher spectral resolution. This chapter shows the preliminary results from the low resolution fitting. Refined fitting with high resolution in the future will allow for a more accurate measurement of the deuterium abundance, which, since deuterium is related to the location the materials in the planet formed, tells us about how and where the ice giants formed. In this section, I will outline new high resolution observations and models I have used to determine the deuterium-to-hydrogen ratio in methane for Uranus.

The radiative transfer modelling code, VSTAR (Chapter 2), has been applied to a va- riety of solar system bodies including Earth, Venus, , Jupiter, Titan, Uranus and Neptune. In its application to Uranus, it was coupled with high resolution H-band

35 Chapter 3. Deuterium on Uranus 36 spectra to detect the amount of deuterium (heavy hydrogen isotope) present in the up- per atmosphere. Deuterium measurements using VSTAR and high resolution spectra are being completed for all the Solar System gas giants[88, 94], and has already been published in peer-reviewed proceedings for Titan [86] and Neptune [87].

Deuterium was created almost solely during the big bang. Its fractionation (tendancy towards a particular species through phase changes or similar processes) in ices and gases through photodisassociation provides a diagnostic for planet formation. Planets formed very near to a star within ice lines (such as our terrestrial planets) are expected to have very low deuterium levels. Planets formed largely from the ices, such as our solar system’s ice giants Neptune and Uranus, should have larger deuterium abundances. Larger planets, such as Saturn or Jupiter, have lower abundances than ice giants because their cores were large enough to accrete a large amount of surrounding gas, therefore they tend to have values akin to the estimated protosolar nebular values, which is slightly higher than that of the ISM.

Modelling the atmosphere of Uranus, and indeed of any solar system body is useful to refine and verify the applicability of the methods and models for the improved spectra of exoplanets we will be able to retrieve in the future. Determining the deuterium levels in it is useful in understanding at least one case of how a planetary system can form.

To retrieve the deuterium ratio, fitting the clouds is also important.

Increasingly improved line lists for low temperature methane and its isotopologues in recent decades have allowed astronomers to produce better deuterium ratios for the ice giants and to better handle the degeneracies inherant in the cloud heights and methane abundances [95][96][97] . The new line lists we use were utilised by Irwin et al. [98] successfully for Neptune’s atmosphere, improving our confidence in their application.

These models tend to focus largely on the characteristics of cloud layers, as these greatly affect the outcome of the spectra and can obscure the methane abundance. Uranus is unique in its energy budget in that its residual heat from formation is matched by the flux recieved making its thermodynamics particularly interesting. Karkoschka and Tomasko [99] used near infrared, visible light and ultraviolet data from the to characterise the hypothesised haze layer in Uranus’ atmosphere finding the best fit for an extended haze layer into the upper atmosphere (rather than distinct cloud layers), Chapter 3. Deuterium on Uranus 37 at around 1 bar the atmosphere would be clear with opacity then increasing rapidly at pressures above 1.2 bar. Their models included fitting a varying methane profile for different latitudes. Haze (optically thin cloud above 1 bar) is also suggested as a solution by Tice et al. [100]

More recently using observations from NIFS (Near Integral Field Spectrograph) on Gem- ini North in 2009 in conjunction with UKIRT (United Kingdom InfraRed Telescope) ob- servations, Irwin et al. [101] found that the opacity of the clouds below 2 bar diminishes toward the poles with the lower cloud darkening toward the equator. The bright cloud at approximately 45◦S , for which we have data from our own run on Gemini South, probably lies at a lower pressure than clouds at other latitudes [101]. These clouds are most likely methane clouds, although clouds at other latitudes, such as equatorial clouds for which we also have data, may be condensates of H2S (hydrogen sulfide) or

NH3 (ammonia) [102].

In 2010 Irwin et al. [103] observed Uranus again with NIFS to determine the affect of true seasonal variability on the apparent observational changes as the planet moved through its autumnal equinox. The methane profile still did not need to change if the relative humidity of methane– rather than cloud height– could change with latitude (20% near poles to 80% equatorial of 45◦N/S.

Models have been further refined with the release of improved line lists for methane at very low (∼80K) temperatures by Wang et al. [97]. Irwin et al. [104] applied the improved lists to their previous observations as well as data from KPNO/FTS (Kitt Peak National Observatory’s Fourier Tranform Spectrograph) to determine deuterium abundances in methane. Initial fitting of cloud parameters (varying the extinction cross section and single scattering albedo for a cloud deck at 2-3 bar) was done using the correlated-k method (see section 1.2.3), then line-by-line was used to derive the deuterium ratio. Their cloud model required a reduction in scattering with wavelength which would be expected for a Rayleigh scattering aerosol. The clouds also get higher and thinner poleward, maximising at ∼45◦ which correlates to the bright band our group observed in the southern hemisphere. Here too the relative humidity of methane varies, maximising near the equator as before but at only 60%.

Irwin et al. [98] found a difference in the fit of cloud thickness with height for the dark and light bands across the surface of Uranus. Because our data are integrated across Chapter 3. Deuterium on Uranus 38 the surface, these fits are not adopted. The best fit should not be a conglomeration of the two, but rather an apparently different lower cloud deck, with an apparently thinner upper haze. This combined situation as well as the best fits for just the dark belt or bright belts are tested by first applying Irwin et al. [98] parameters as a starting point.

Karkoschka and Tomasko [99] used near infrared, visible light and ultraviolet data from the Hubble Space Telescope to characterise the hypothesised haze layer in Uranus’ at- mosphere finding the best fit for an extended haze layer into the upper atmosphere rather than two distinct cloud layers, at around 1 bar the atmosphere would be clear with opacity then increasing rapidly at pressures above 1.2 bar. Their models included fitting a varying methane profile for different latitudes.

3.1 Deuterium

Methane is a relatively common species throughout the solar system. Its most common form is the protium (1H) and carbon-12 (12C) isotopologue. Methane is tetrahedral with four equal bonds between the carbon and four hydrogen atoms. The overlap of the valence orbitals and bending-stretching vibrational modes of the molecule, create a complicated spectrum for the species, making it vital to have good labratory measure- ments at different temperatures when applying the line lists to the atmospheres of the planets.

There are a few other isotopologues of methane, but the one measured in this chapter is the next most abundant form: CH3D, or deuterated methane. Deuterium of course has the addition of a neutron in its nucleus. It, like protium, is also stable. The change in the nucleus of the molecule changes the spectrum produced, affecting dipole moment of the molecule. The expression of the rovibrational lines in the spectrum change with the addition of the isotope in the nucleus.

3.1.1 Formation of the solar system

The way our solar system formed is, like all hypothesis, open to some debate. However the current preferred model is the which has the progenitor of the system being the collapse of a small dense and unstable part of a giant . Chapter 3. Deuterium on Uranus 39

From this collapse the mass will have a net rotational velocity that will set in motion a rotating disk around the dense central mass. From that dense central mass (protosun) the sun will form, and from the disk, planets will form.

This is likely the case in most (if not all) planetary systems. The main revolution that resulted from the variety of exoplanets discovered was regarding the role migration played in the early disk, before the lighter material was blown away by the star’s early wind activity after formation. In our own solar system we believe the planets migrated. The gas and ice giants show evidence for migration in their compositions and their masses. Previous to the discovery of exoplanets, however, astronomers had little evidence of anything so dramatic as the (possible) early inward migration of a hot Jupiter. The time at which these migrations occur will have lasting effects on the material planets are comprised of. There is also evidence in our own solar system of collisions in the form of our own moon and probably in the strange orbit of Uranus.

Isotope ratios provide us with a way to measure the environment a planet formed in, or rather the materials a planet formed from.

3.1.2 Deuterium Fractionation in the solar system

Historically, isotopes have been used to establish a framework for the formation of the solar system. Carbon-14 —a carbon atom with two extra neutrons in the nucleus— for example, was measured in comets providing evidence that the chemicals in the outer solar system were largely homogeneous, and that the presolar cloud experienced very little fractionation. The study also showed that comets coevolved with the rest of the solar system, allowing their other properties to be assessed homologously [105].

Another isotope, deuterium, has been used extensively in data from a host of different solar system bodies (e.g. Kedziora-Chudczer et al. [86] and Hartogh et al. [106]). Deu- terium is heavy hydrogen; that is to say the nucleus of the atom contains a neutron as well as the singular proton.

Deuterium was formed during the big bang and has since been destroyed in the inte- riors of stars (it is produced momentarily during the proton-proton chain reaction but destoyed even faster). Therefore on a cosmic scale the deuterium-to-hydrogen ratio is falling, however deuterium can appear in higher quantities locally. Chapter 3. Deuterium on Uranus 40

Observational estimates of deuterium-to-hydrogen (D/H) ratios as well as models of solar system formation suggest that in a protoplanetary disk, such as the one our solar system formed from, the D/H ratio for water will increase as the radial distance from the primordial star increases [107][108][109].

Deuterium in the planets is imparted by water ice. In equilibrium conditions, the de- crease in temperature as one moves away from the sun effectively favours deuteration in water.

H2O + HD HDO + H2 (3.1)

This is due in large part to the preference for the right hand side of the chemical reaction (equation 3.1) at low temperatures within the protoplanetary disk. Within the protoplanetary disk, D/H also tends to be higher in the thicker parts, because the depletion of molecules onto grains provides a more stable environment for the deuterated species to exist in [107].

Nearer to the sun volatile materials like water are less abundant and more likely to be photodissociated, destabilising the deuterated water.

Overall, there is a preference for deuterated water in the protoplanetary disk and a preference for that deuterated water to remain stable as the temperature decreases with distance from the sun.

Locally the deuterium can be affected by fractionation into other species. This is thought to occur within the far more dense environment of the , producing the frac- tionation factors for different species which vary between locations.

The terrestrial planets probably formed after the depletion of most of the lightweight materials in the inner protoplanetary disk with meter-sized and larger surviving the T-Tauri winds.

Earth in particular formed too close to the sun for significant contributions from deuter- ated hydrogen gas or water, but the later bombardment by outer solar system icy bodies provided it with the relatively high deuterium levels seen today. The relative abundance of water, nitrogen and carbon along with traces of Krypton (Kr) and Xenon (Xe) in spite of a general lack of the “rare gases” on Earth is thought to be due to delivery Chapter 3. Deuterium on Uranus 41 of ices from small outer solar system bodies. The infall of material was also a major contributor for the disparities in some species in the inner solar system that do not fit a simple temperature-dependant gradient through the protoplanetary disk [110–114].

Jupiter and Saturn would have formed cores from marginally deuterated material but the run-away gas accumulation that made them the gas giants they are today provided them with an envelope of less deuterated gas from the protosolar nebula.

Some captured satellites of gas giants have D/H ratios suggesting they are either cap- tured outer solar system bodies or were subject to major impacts by such bodies. For example, Enceladus has a D/H ratio akin to Oort cloud comets [115] and, Titan’s D/H (∼143 ±15×10−6 [86]) is much higher than for other bodies at that distance.

The four giant planets of our solar system have all formed beyond the ice line but the dramatically different masses and notably different compositions between the larger two (Jupiter and Saturn) and smaller two (Uranus and Neptune) suggest a past that likely included a different formation mechanism for the two groups. Comparing isotope (D/H) ratios for H2O and HCN in the giant planets, it becomes apparent that Uranus and Neptune likely underwent a large portion of their formation after the disappation of the gaseous solar nebula if the currect estimates of the mass of their cores are accurate. As deuterium trapped in water ice is a function of distance from the star during the formation of the planets it can be used to determine where and, depending on the disk model, to some degree when a planet formed.

Uranus exists in a region of our solar system where the long dynamical timescale would limit the core growth with the material available in situ. Uranus’ axial tilt, the orbits of Neptune and Uranus, and the respective masses and compositions point to formation interior to their current orbits with migration to their current distances. Within the constraints of the Nice Model there are different interpretations of the details of how this happened, with additional cores forming near the water ice line [116], or the cores of Uranus and Neptune forming further out yet still interior to their current orbits, likely with Uranus forming exterior to Neptune and orbital instability clearing the more minor bodies from the outer solar system as well [17, 117, 118]. Chapter 3. Deuterium on Uranus 42

3.1.3 Formation Hypotheses

The different formation scenarios accounting for this include:

1. the ice giants forming closer to the sun and migrating out before reaching a large enough mass for runaway gas accretion,

2. planets forming on ice lines which largely determine the core mass,

3. forming in situ and simply not having enough material to accumulate over the long orbit to cause run-away gas accretion. The determination of the deuterium- to-hydrogen ratio can provide information about the core materials and gases that contributed to the formation of the planet.

The most popular models have explained the presence of Jupiter and Saturn by sug- gesting that they formed on the “ice line”, viz. the distance in the protoplanetary disk where water transitions between vapourised and condensed states. Here a large amount of slushy ice material would be available to quickly build large planetesimals over the minimum mass of ∼ 10M⊕ to allow for run away gas accretion. This gas accretion would have occured before the FU Orionus stage winds (and later the T Tauri winds) swept the lighter materials out of the solar system. The protosolar nebula is expected to have a very low deuterium abundance (only slightly higher than the ) so its contribution to the make up of the gaseous planets affects the deuterium in their atmospheres today. Chapter 3. Deuterium on Uranus 43

Figure 3.1: The D/H isotope ratio for various solar system bodies, compared to the low protosolar nebula value. The distances from the sun are not in order or to scale. Of note is the very high deuterium abundance for both Oort Cloud and Jovian Family comets, the comparatively high value for Enceladus, the also very high value for Earth comparable to come Jovian comets and the asteroids, the similar abundances between Uranus and Neptune, higher than the lower density planets Jupiter and Saturn.Image: Altwegg 2014 and ESA

Neptune and Uranus appear to share their early stages of formation—but over much larger timescales— with Jupiter and Saturn. Like the gas giants, the ice giants accreted solid cores in the protosolar nebula, then accreting smaller icy planetesimals and some gas in the nearby vicinity.

Neptune and Uranus probably did not form in the same way as the true gas giants, Jupiter and Saturn. The timescales for planetesimal growth at the distances they cur- rently orbit would be so long that they would not reach the minimum ∼10M⊕ required for runaway gas accretion. By conservative estimates their protoplanetary cores would only be about the mass of Mars by the time (∼×107 years) that the gas cleared. [119]. The planets are also distinguished by both containing a large amount of material similar to the composition of comets and a substantial fraction of hydrogen and helium gases (several Earth masses worth). This might suggest that the isotope ratios for their cores should be similar to those of comets from the same region.

The suggestion that the planetesimal sizes might have been smaller allowing for faster accretion, is precluded by the theory that the Oort cloud was produced by the outward Chapter 3. Deuterium on Uranus 44 scattering of the remaining planetesimals after the ice giants formed, as these larger particles would not have been as easily scattered. This is reliant upon another theory which suggests that the ice giants formed much closer to the ice line [120].

In Thommes et al. [116] and [121] the formation of ice giants is explained by considering them as failed gas giants. Perturbations in their orbits send them to their current semi-major axes, with the order of planets possibly changing before the accumulation of a significant gas envelope shortly before stellar nucleosynthesis begins. While this can be fit with dynamical models, the formation of the ice giants nearer to the current orbit of Jupiter and Saturn should produce similarities in isotope ratios to the icy bodies remaining there (such as Jovian comet families had they formed in situ themselves). Uranus and Neptune D/H measurements in the past have produced very similar values for the two planets to each other, substantially greater than those of Jupiter and Saturn. Yet these are still much lower than cometary values from either Jupiter family comets or the Oort cloud, due in part, possibly, to their moderate gas accretion during formation.

The unusual axial tilt of Uranus is not well described by simple formation scenarios, suggesting that it probably experienced some perturbations (possibly in the grand form of catastrophic collisions) and migration in its past. The central idea that planets form in a rotating disk of gas and dust, set in motion by a net rotational velocity and the conservation of momentum around a protosun, then collapsing with similar rotation to conserve the energy of the material, does not account for Uranus’ 97.7 ◦ axial tilt (nor would it explain the retrograde rotation of Venus with respect to its orbit). But the planets do seem to have formed in some convoluted derivation of this method as they orbit in roughly the same plane and in the same direction as the sun’s own rotation. The variations in axial tilt therefore are likely due to migration ephoch phenomena. Alternative formation scenarios for giant planets such as gas instability collapse [122] do not fit the isotope patterns or structure of the ice giants as well.

Thommes et al. [116] finds through n-body simulations that with several planetesimals in the Jupiter-Saturn region once one of them accretes its massive gas envelope, the others are scattered outwards, less able to acrete beyond this gas-core phase.

In fact, in Thommes et al. [121], a model for the migration of the is produced with the protoplanets all forming near the current orbit of Jupiter (near the material-rich ice-line). One planetesimal moves to 25 AU then back in (near 15 AU) which would fit the Chapter 3. Deuterium on Uranus 45 orbit of Uranus, the formerly penultimate protoplanet moves to a highly eccentric and distant orbit (>100 AU) before settling near 25 AU, presumably representing Neptune. In other words, the protoplanet that might become Uranus is initially the outermost (still far within its current orbit) protoplanet, and the protoplanet that becomes Neptune starts interior to that. The ensuing, wildly-varying orbit during the migration of the giant planets coincides with the expulsion of smaller bodies from the inner solar system to the present day Oort cloud. This provides a prediction of a migration history possibly producing more deuteration for Neptune from migration through Oort cloud ices and a lower than expected D/H ratio for the Oort cloud comets themselves. This exchange and variation could explain the current differences in Neptune and Uranus and relative similarity between the various families of comets. This wild migration is not nessisarily the only explanation for these features.

There is a possibility that the protoplanetary disk was not disjunct from the surrounding presolar (stellar) nebula for at least the beginning of its formataion. Drouart et al. [123] created nebular models of deuterium enrichment in water compared to that in protosolar

H2 in a novel way by including the effects of diffusion. Comparing these modelled trends to observations for planets, meteors and comets led the group to claim that the presolar discoid would have been enriched by infalling, deuterium-rich ices from the prestellar cloud. The theory that the Oort cloud comets formed in the same region as the ice giants and then were pushed out before the planets finished forming would imply that comets were further affected by the presolar cloud in this scenario. Early expulsion of the comets would be difficult with most mechanisms that would push out large planetesimals also able to push out the gas still forming the planets. So it is possible that the Oort comets as well as the Jovian families of comets had formed beyond the ice giants and then fell inwards toward the sun. The timescales for this could align well with the late heavy bombardment event on Earth [117, 123] Chapter 3. Deuterium on Uranus 46

Figure 3.2: Simplified illustration of planet formation and theoretical influence of each stage on Deuterium abundances. Further explanation in text. Chapter 3. Deuterium on Uranus 47

In the far outer solar system the D/H ratio is indicative of radiation and photopressure effects of the sun and rain-in interactions of the nebula. The ratio of D/H increases + with distance in the outer solar system for H2O, HCO and NH3 ices, however the relatively refactory ices of CH4 and H2CO do not undergo this trend in the far outer solar system [107]. The HCN in comets and meteors can also be used to determine deuterium enrichment in much the same way that water can. Mousis et al. [109] estimated the D/H ratio in comets to be ∼4×10−3 which would be akin to the hot molecular core of the protosolar nebula (and is akin to similar measurements for Neptune and Uranus). This might suggest that the source of deuterated ices for the far–outer solar system was largely from infalling material from the surrounding nebula after the disk formed. An exchange of isotopes could have occured after this stage with H2 and water from the inner nebula.

Recently, Ali-Dib et al. [14] found an alternative that provides a mechanism for the ice giants to form nearer to their current orbits on a carbon monoxide (CO) iceline. This could explain the relative abundance of carbon in the planets concurrent with nitrogen depletion. In this scenario much of the water ice thought to make up the interior of the planets would have been transformed from carbon monoxide ice, with the deuterium fractionation1 factor for CO lower than in water. This, therefore, is a less effective deuteration process than that between H2 and H2O. The deuterium-to-hydrogen ratio would be lower for the planet cores than that of the comets. The D/H ratio for the cores is, in practice, masked by the low D/H in the gas envelope so if the lower D/H detected in these planets is in fact due to this mechanism, it would be detectable only for a protoplanet that remained well mixed post gas envelope accretion. Additionally, this theory is in good agreement with previous findings that the formation distance for the ice giants would have to be further than Saturn’s orbit to account for the methane abundance [12] as it provides a sufficient mass source at that distance. The carbon abundance in the ice giants is notably high, with a relative metallicity 20-30 times that of the sun (most other species in gas giants are enriched only 2-4 times).

1Fractionation refers to processes that favour the inclusion of isotopes in some species over others. For example a tendancy for heavier deuterated hydrogen gas to sink lower in an atmosphere than non-deuterated hydrogen gas might mean that one would find less deuterium in the species at high altitudes and the difference in atmospheric compositions with altitude might mean that deuterium migrates to other species found at lower altitudes more. Fractionation can be driven by pressure, temperature, chemical processes, etc. Chapter 3. Deuterium on Uranus 48

This requires the unusual scenario of both Neptune and Uranus forming at the same distance from the sun. With the timescales currently estimated for their formation this would require some sort of truncation of the material or a less monotonic temperature gradiant through the disk. The model also requires a more turbulent disk than some models suggest [124–126].

Figure 3.3: The fractionation factor for methane for each giant planet with atmo- spheric pressure. For Uranus, there is a constant value for the atmosphere below pres- sures of ∼500 bar, that is at heights where observational data is available. Below this (at higher pressures) the curve is fit to the calculated equalibrium fractionation values, with the fractionation factor f decreasing (the relative value of deuterium in molecular hydrogen to deuterium in methane decreases, i.e. deuterium in methane should be more common at lower pressures where the processes favour the heavier molecule in the ice). The values marked with dashed arrows are from [127] and [128]. Image credit: Lecluse et al. [108]

The mixing history and distribution of materials in Uranus is of particular interest be- cause it can produce a non-strightforward fractionation relationship. The fractionation effect of vapour pressure on deuterium, which produces a loss in deuterium in vapourised methane above the condensation layers, is probably negligable for Uranus today [129].

A precise measurement of the deuterium-to-hydrogen ratio for Uranus is useful in provid- ing a better comparison to Neptune and icy outer solar system bodies, thereby allowing the breaking of the degeneracy between formation schemes. Chapter 3. Deuterium on Uranus 49

The recent resurgence in isotopic characterisation of the ice giant is fuelled in part by new, improved line lists—the lists of absoprtion lines used in creating atmospheric models—in recent years, and also by the recent equinox view of the planet.

As it spins effectively ‘on its side’, Uranus’ orbit takes it around the sun not as a ball rolling through a gravity well the way a tidally locked planet does with one side always facing the star, but rather with different sides facing the star at different points in the so that the north pole nearly points to the sun during northern hemisphere summer solstice and vice versa. The equinox last decade saw many observation attempt to characterise the planet, able to take into account the differences between the latitudes from this vantage.

Our models are not the first endevour to accurately measure the deuterium of the ice giant, Uranus. They do, however, benefit from higher resolution spectra than used pre- viously and from the previous efforts of groups to map the methane abundance primarily by latitude.

Our models also include more complete line lists for methane and its isotopologues than some previous attempts. Similar model fitting was published for Neptune in 2014 by Irwin et al. [98] using the newest methane low temperature line lists.

Increasingly improved line lists for low temperature methane and its isotopologues in recent decades [95][96][97] have allowed astronomers to produce better deuterium ratios for the ice giants and to better handle the degeneracies inherant in the cloud heights and methane abundances.

Previous models tend to focus largely on the characteristics of cloud layers, as these greatly affect the outcome of the spectra and produce a degeneracy with methane abun- dance. Uranus’ energy budget is unique in the solar system: the residual heat from formation is matched by the flux recieved. Thorough modelling and high resolution ob- servations therefore become paramount to understanding what lead to such an unusual world. Details of our high- and low-resolution settings with GNIRS are available in Table 3.2.

The molecules formed in the protoplanetary disk should have deuterium concentration higher than in the protosolar cloud, although the physical mechanisms for fractionation + in each environment would be the same [130]. H3 preferentially gains high D/H ratios Chapter 3. Deuterium on Uranus 50

[130]. This happens because being ionised makes the molecule more prone to rapid reactions with deuterium bearing molecules, and once deuterated the lower zero-point energy and two valence electrons increase the likelihood of interaction (as it takes less energy to break the bonds in the deuterated species[131] ).

The chemical reaction that favours ionised H3 in the cold environment is

+ + H2 + H2 *H3 + H (3.2)

+ The molecule is then deuterated through equation 3.3. The H2D is favoured in a cold interstellar environment because the reaction is strongly exothermic. This produces an enhanced deuteration over the general D/H ratio (fractionation) [132].

+ + H3 + HD*H2D + H2 (3.3)

+ From here, other species gain deuterium through interactions with H2D (and further deuterated isomers) via chemical reactions.

There is more than one path for most species’ deuteration, but a good example of the deuteration of water from Pineau des Forets et al. [133],

+ + H2D + O*OD + H2 (3.4)

+ + OD + H2 *HDO + H (3.5)

+ HDO + H2 *H2DO + H (3.6)

All three of these reactions are rapid, 3.5 and 3.6 in fact are more rapid than an isotope exchange in the conditions in the early solar nebula. While the reaction 3.5 creates ionised HDO, this is prone to dissociative recombination through,

HDO+ + e− *OD + H (3.7) Chapter 3. Deuterium on Uranus 51

To create neutral HDO we carry on from 3.6,

 HDO + H + −  H2DO + e * (3.8) OD + H2

A complication of this theory is that a lower ionisation rate than what is considered to be standard in this part of the disk is required to explain the DCN/HCN (hydrogen cyanide) and HDO/H2O (water) ratios seen. The non-ionised form of H3 is unstable and therefore does not contribute to this deuterium exchange. At higher temperatures though, the reaction 3.3 is reversed as it is endothermic.

3.2 Observations

Considering the nearness of the two deuterium ratios for the ice giants Neptune and Uranus, it is advantageous to try to achieve a more accurate measure of the value as improved data becomes available. The ice giants are thought to have “switched places” however their deuterium ratios have not yet proved this because they are similar enough to suggest that they formed from essentially the same material. If a high resolution measure of the deuterium ratio could be achieved, credence to the theory of orbital exchange could be attained.

For Uranus, high and low resolution observations from Gemini North were used in con- junction, having been taken over the same observing run for two latitudinal band re- gions. The low resolution data covers a larger range of wavelengths, allowing us to fit the cloud structures, which have broad features and effects, first. The high resolution data can then be fit with similar cloud parameters, focusing rather on fine features such as the deuterium abundance. The low resolution data also includes wavelengths outside of the window, which provides some confidence in the large scale effects of the upper atmosphere.

In this thesis only the low resolution data is analysed for cloud parameters and deuterium abundances. It is ideal to take the parameters fit to the low resolution data as both a starting point for fitting and for a check on consistency in fitting the high resolution Chapter 3. Deuterium on Uranus 52 data. For that reason the potential treatment of the high resolution data is alluded to throughout this chapter, although it has not yet been applied.

Figure 3.4: The location of the low resolution (LR) and high resolution (HR) GNIRS slits on the disk of Uranus. The slits are situated roughly in line with the planet’s rotation axis. The parts of the slit where data was combined are outlined in white and black boxes respectively. Data was compared for two different cloud bands on the planet with cloud fitting in LR followed by abundance fitting in HR. This aquisition image was taken with the narrowband H-G0516 filter. The NU refers to the planet’s rotational north pole. Image credit: D. Cotton

The signal-to-noise-ratio will vary with wavelength. The low resolution spectrum for the equatorial region has an average S/N of 130 (including count statistics and read noise), while the low resolution spectrum for the 45◦ “bright” region has an average S/N of 153. These values are reasonable for observations of a planet that fills the slit.

Each retrieved region (“equatorial” and “bright”) spans 5 pixels (∼0.25”) within the two pixel wide slit covering 0.1” of sky. Chapter 3. Deuterium on Uranus 53

3.2.1 Instrument

Observations were taken with the Gemini Near-Infrared Spectrograph (GNIRS) on the Gemini North 8 meter telescope, at Mauna Kea Observatory, Hawai‘i, USA.

GNIRS is a near infrared long-slit spectrograph. In the long-camera mode that was used for these observations the slit is between 50 –100” long and 0.1” wide. The slit placed near the longitudinal center meridian of the planet’s visible disk thus covers the entire disk in the x-dimension, i.e. it covers all latitudes visible.

Gemini North also has an integral field spectrograph (NIFS) with a shorter wavelength range (1–2.5µm compared to 1–5µm for GNIRS in long-slit mode). Although use of the integral field spectrograph on Gemini is well-suited to characterising different regions of the disk, we sought to obtain a much higher resolution spectrum that could well-constrain the isotopologue abundances. GNIRS also offers a cross-dispersal mode which was not needed for this observation.

GNIRS provides a range of configurations to cater to the observations sought. Either a 9900 slit ‘short camera’ or an effectively higher resolution 4900 ‘long camera’ can be used. Resolution can also be varied by changing the grating with 10.44, 31.7 or 110.5 `/mm available. Increasing the grating improves the resolution at the cost of the loss of wavelength range because of the higher dispursion from the larger angle of seperation between orders.

High and low resolutions on GNIRS are accomplished by changing the grating and slit width. The ‘short camera’ has a 0.30” slit and the ‘long camera’ has a 0.10” slit providing 0.15” per pixel and 0.05” per pixel respectively for the two pixel wide slit typically used, and which is used in our observations. The three groove densities for the available diffraction gratings allow some overlap with the different camera settings so that the wider slit of the short camera can provide the same resolving power (R ∼1700) with the 31.7 l/mm grating for the H band (1.65µm as the shorter slit long camera using a 10.44 l/mm grating as one would expect, but with different instrumental effects. Chapter 3. Deuterium on Uranus 54

Figure 3.5: A schematic of the GNIRS optics system with four configurations for the ‘long’ and ‘short’ camera options shown.

3.2.2 Instrument Configuration

For Uranus, GNIRS was configured to utilise the long camera 4900 slit with grating spacings of 31.7 and 110.5 lines per millimeter to give H-band resolving powers of ∼ 5100 and 17800 respectively (henceforth refered to as the low and high resolution data sets). The reduction in the band coverage with the tighter-spaced grating for the high resoltuion data meant that while the low resolution data covered the wings of the H-band, ensuring a good fit for cloud parameters, the high resolution data was centered well within the window over the 1.56 µm methane band including the CH3D 3ν2 transitions near 1.55 µm.

The data was taken in adjacent longitudinal regions to allow fitting of the cloud prop- erties with the low resolution data to be adopted by the high resolution data.

Both high resolution and low resolution spectra were taken, both times with the slits running roughly aligned to Uranus’ orbital axis and completely covered by the disk. The low resolution data is used in models to get a rough fit for clouds, but in this case, Chapter 3. Deuterium on Uranus 55 the low resolution spectrum was taken further from Uranus’ equator in a brighter band region than the high resolution data. For this reason the cloud models will need to be adjusted between the two fits as discussed in the “Models” section.

The observations used here both relied on the long camera’s 0.10” slit with the 31.7 `/mm grating used for the low resolution data at a resolving power of R ∼5100, and with the 110.5 `/mm grating for the high resolution data at a resolving power of ∼17,800.

The two-pixel wide slits were taken longitudinally adjacent (see Figure 3.4) . Within these slits, two different latitudinal regions were reduced together to have low resolution and high resolution data over comparable areas of two different cloud bands.

3.2.3 Details of observations

The observations were completed in one night: August 18th, 2011. This is (relatively) shortly after Uranus’ equinox (vernal for the northern hemisphere) which occured in December of 2007. Uranus is on a nearly circular 30687 day orbit, putting its northern hemisphere summer solstice in 2028. Uranus’ 97.77 ◦ axial tilt places its north pole (in the classical convention which is dependant upon the Sun’s north pole) just above its orbital plane (which is nearly coplanar with our own). These observations, therefore, having occured near an equinox, were over most latitudes for the planet, allowing us to place the slit roughly along a meridian and retrieve data from specific band regions within it.

Acquisition images were taken before each observation. The clouds on these timescales do not notably change. One-dimensional spectra were obtained by taking the average of 10 pixels along the slit in two different regions.

At the start of the observation for low resolution, the zenith angle was 21.59 ◦ corre- sponding to an airmass of 1.08; for high resolution observations, the zenith angle was 24.67◦ corresponding to an airmass of 1.10.

Two slit positions were used (A and B) in the ABBA pattern for averaging the data and for sky subtraction. For the low resolution spectra we obtained a single set of four nodded exposures (1 x ABBA) with each exposure lasting 400 seconds (total integration time being 4 x 400 = 1600 seconds). For high resolution observations two sets of four Chapter 3. Deuterium on Uranus 56

Uranus GNIRS Observations Low Resolution High Resolution Zenith angle 21.59◦ 24.67◦ Airmass ∼1.08 ∼1.10 Integration time 400 sec. 600 sec. Total integration 1600 sec. 4800 sec. Grating 31.7 l/mm 110.5 l/mm Resolving Power ∼5100 ∼17800 Wavelength Range 1.462–1.625µm 1.532–1.574µm

Table 3.1: All observations were taken on 18 Aug 2011 while the planet was roughly at equinox. GNIRS was in long-camera mode.

nodded exposures (2 x ABBA) were obtained with each exposure lasting 600 seconds (total integration time being 2 x 4 x 600 = 4800).

3.2.4 Calibrations

For our observations flat fields were taken as well as arc lamp exposures with Argon and Xenon lamps. The telluric standard star, HIP 3033 (G0 V type) was observed after the high resolution and low resolution observations seperately. The position was nodded in the same ABBA pattern and used for the initial data reduction, however an improvement over this telluric removal was made using the ATMOF code (see section on Data Reduction below).

3.2.5 Data Reduction

The initial data reduction was done using the Gemini IRAF package application for GNIRS.

The data was visually examined and corrections were made for the variable bias, frame alignment, non-linearity and bad pixels (from the Aladdin III InSb detector). The arc lamps were used for initial wavelength calibration and the Uranus data and standard star were flat-fielded. The wavelength calibration was done using an interactive procedure due to the sparseness of the Argon and Xenon lines in some spectral regions.

Sky subtraction was performed by combining the A position frames together, and the B position frames together, then substracting the B position frames from the A position Chapter 3. Deuterium on Uranus 57 frames. Finally a dispersion correction was applied and the data was retrieved from the two regions on the disk (equatorial and the “bright” region around 45 ◦).

GNIRS suffers from moving electronic partterns in the data caused by the GNAAC con- troller. This manifests as vertical and horizonal bands and quadrant offsets. We used the nvNoise routine in the IRAF Gemini package to address this successfully. Another common issue for the GNIRS instrument is the radioactive Thorium anti-reflection coat- ing on the lenses. This affected the K–band observations of Uranus which required long integration times, but not the H–band results discussed here. Other known problems were addressed by normal data reduction.

High precision telluric removal was performed using ATMOF (ATMOspheric Fitting code) [134]. This code uses the Versatile Software for the Transfer of Atmospheric Radition (VSTAR) coupled with a high resolution solar spectrum from Kitt Peak to identify telluric lines for removal more accurately than can be done with a standard star alone by allowing a model for the atmosphere to be retrieved. The Kitt Peak spectrum serves as a baseline, which is then flux adjusted and stitched based on the flux slope of a Kurucz model.

Telluric carbon dioxide and water vapour are then varied to match the conditions at the place (in our case, Gemini North at Mauna Kea) and conditions of observation using VSTAR. Carbon dioxide is changed with a multiplicative factor (thereby scaling the entire abundance curve). Water vapour in this case was adjusted only for the lower layers of the atmospheric model [134]. The H-band is affected by water vapour at short wavelengths affecting our low resolution spectral band, and carbon dioxide affects the center of the band to a much lesser degree.

The instrumental response was modeled by an augmented filter function, whereby a draft fit to the telluric spectrum is Fourier transformed and the low resolution com- ponent is fit to account for the response due to other components in the instrument, the filter response, and the slope [135]. The data is then scaled and adjusted to fit a quadratic describing the wavelength shift. A solar spectrum, transmitted through the Earth atmosphere model, is matched to the observational data to provide the wavelength shift. Chapter 3. Deuterium on Uranus 58

With the values for the Earth’s atmosphere retrieved, the model is run again for the appropriate zenith angle. The solar spectrum is multiplied by the modelled Earth atmo- sphere transmission, then with the instrument response. This is then divided into the observed spectrum to produce a fitable spectrum corrected for telluric and solar effects.

These methods are described for similar sets of GNIRS data in more detail in Cotton et al. [87].

3.2.6 Quality of observations

The observations we have obtained through GNIRS are of similar quality or better to those used in the past and should be reliable. The instrument is well established, with instrumental effects well-documented. Our observations for the H J and K bands all fit expectations set by known physical parameters and from comparison to similar observations with other instruments performed by other groups. It is unlikely that the reduced spectra include relics due to anything besides variations in the physical parameters of Uranus’ atmosphere.

3.3 Models

The ATMOF fitting routine top end for VSTAR is not only used in telluric removal, but also the fitting of the model Uranus atmospheres to the observed data.

Preliminary fitting, largely for cloud deck heights and general chemical constituents were performed with low resolution GNIRS spectra (R ∼5000). The deuterium fitting will be completed with the high resolution data from GNIRS (R ∼18000) in the future. Previous fitting for deuterium with the updated line lists was done with NIFS (Near infrared Integral Field Spectrograph) on Gemini North with R ∼5200 by Irwin et al. [104] . This is the most comparable deuterium estimate, notably with a similar resolving power to the low resolution spectra used here. My modelling approach was to perform fitting focused on cloud parameters using the least-squares fitting abilites of ATMOF, running atmospheric models with VSTAR, then to apply these fit parameters to the high resolution data to provide starting points for ATMOF to then fit the methane parameter. Comparatively, Irwin et al. [104] used a correlated-k radiative transfer model Chapter 3. Deuterium on Uranus 59 called NEMESIS to provide their initial fits. For both Irwin et al. [104] and this paper, the final fits are performed using the far more accurate line-by-line method.

While [104] do get an excellent fit to the H-band window, they only include the re- gion around the deuterium lines in the 1.525–1.565 µm region. Figure 3.6 shows the correlated-k fit to the cloud properties and Figure 3.7 shows the region where deuterium was fit. This was done because the region 1.6–1.62 µm is heavily dependent on the methane far-wing line shape. Irwin et al. [104] trialed different line shapes for methane. In this chapter the far-wing line shape for methane was initially modified based on Hart- mann et al. [91] for H2 broadening. A better fit came from the methane line shape from the fitted S parameters (see [89]) from the Neptune methane cloud fitting (D. Cotton, private communication) fit for a methane cloud. These values come from preliminary fitting of Neptune’s H-band spectra for a model that has a lower cloud of solid methane particles. Since these line parameters are dependent on the methane mixing ratio and temperature structure of the atmosphere, improvements can probably be made to the fit futher in this regard.

Figure 3.6: Figure 2 in [104]. The correlated-k fit to the clouds in the H-band. Credit: Irwin et al. [104] Chapter 3. Deuterium on Uranus 60

Figure 3.7: Figure 4 in Irwin et al. [104]: The “zoomed in” region over which the deuterium ratio was fit in Irwin et al. [104]

3.3.1 VSTAR Model Set Up

My models benefit from previous attmepts to accurately measure the deuterium on the ice giants and to describe its cloud properties. Previous to Irwin et al. [104], Karkoschka and Tomasko [136] found that the line wing profile was important to rule out as the cause of the variation in methane abundance ratios measured in different wavelength regions. The wing shape in an extended atmosphere will be an important parameter, and with the cloud properties fit suggesting that the clouds on Uranus may be quite thin, the methane gas’s profile may vary over large distances. Furthermore, as pointed out by Irwin et al. [104] the wing shape dramatically influences one region where deuterated methane lines are most readily measured.

The methane mixing ratio profile—methane the dominant obsorbing species in the H- band region for Uranus—is taken from Voyager occultation measurements [137].

The model includes collision-induced-absorption (CIA), and line lists for methane and its isotopologue CH3D. The effects of atomic H and He absorption are negligible for this Chapter 3. Deuterium on Uranus 61

Figure 3.8: The methane profile for the chemical model based on Lindal et al. [70] from the Voyager 2 occultation observations.

region, and while N2 is likely present in this part of the atmosphere Irwin et al. [104], this region is largely unaffected by these lines.

The far-wing line shape for methane is altered as discussed in the last subsection, based upon the fits for Neptune’s methane far-wing line shape from D. Cotton (private com- munication). The S(1) parameter was set to 28.0 and the S(2) parameter was set to 47.0.

The clouds are fit in two layers with the pressure, optical depth and single scattering albedo variable.

Each cloud band will probe different depths of the atmosphere and therefore provide information on changes in deuterium fractionation within a varying methane abun- dance. Tice et al. [100] suggest based upon observations over 0.8 to 1.8 µm on SpeX (a 0.7–5.3 µm medium-resolution spectrograph at the InfraRed Telescope Facility (IRTF) on Mauna Kea) that for high altitudes, methane abundance on Uranus increases towards the planet’s equator. With a maximum near 4◦ S, having migrated north since similar measurements were taken by Irwin et al. [138].

Scattering particles follow a gamma distribution [93]. The partical size between the upper cloud and lower cloud differ. For the upper cloud the effective radius is 0.05 µm with an effective variance of 0.05 µm. For the lower cloud the effective radius is 0.45 Chapter 3. Deuterium on Uranus 62

µm with an effective variance of 0.05 µm. These are very small particals which could contribute to the Rayleigh scattering seen in visible wavelengths. The optical depths, effective at 1.6 µm, are caluclated seperately for the two clouds as single compressed layers. The single scattering albedo is also a fitted parameter but is the same value for both clouds.

The index of was trialed with either a constant value of n = 1.7 and k = 0i or with n and k varying for the wavelength range accordant with methane at ∼80 K.

Trials with a third cloud layer were attempted. Interestingly, a third cloud would con- sisitently (several starting points and opacity values were attempted) “walk” down to a depth very far below the other two clouds where the scattering component would be negligible.

3.3.2 Methane Isotopologues

The description of physical characteristics in Uranus’ cloud layers appears to be largely dependant upon the completeness of the line lists used for methane. In 2009 Irwin et al. [138] found no evidence of the purported 1.2-1.3 bar cloud layer [70] and modeled a cloud at 3-4 bar, but with improved line lists in 2010 Irwin et al. [139] found evidence of a cloud deck instead at 2-3 bar (or even higher altitude depending on the pressure-temperature profile and methane abundances). The suggested fits of a diffuse haze have been resolved by the alternative reduced helium concentration in the planet to accomodate the radio observations[71]. The methane clouds at these layers can have a great affect on the H band, where vibrational lines of CH3D exist.

It is possible that the observations fit a single cloud layer provided that the aerosols are good backscatterers at wavelengths shorter than 1.2 µm[139], however this only provides a fit between 1–1.75 µm, and thus is unlikely to be a true solution.

Taking into account variations in the cloud structure with latitude can also accomodate a more constant temperature-pressure profile and hence methane abundances, at least for mid-latitudes (30◦S-20◦N) [71]. Over the latitude variation between the equatorial region and the poles, the methane abundance likely does vary, perhaps dramatically so [104]. Chapter 3. Deuterium on Uranus 63

The isotope ratio in methane found by Irwin et al. [104] of ∼2.9×10−4 is in agreement within error with de Bergh et al. [140] and perhaps more notably is very similar to the value using the Gemini-N/NIFS and the VLT/CRIRES (The Very Large Telescope’s CRyogenic InfraRed Eschelle Spectrometer) and the same line lists for Neptune, which might suggest the planets formed out of the same ice source [98]. The VSTAR models are compared to the spectra with line-by-line Levenberg-Marquart fitting for all stages and across the entire retrieved H-band spectral region.

With higher resolution data, the ATMOF telluric removal system and a rigorous line-by line approach it is possible to achieve an even more accurate fit. Accurate measurements of D/H provide a way to distinguish between dissimilarities between Uranus and Neptune and judge their formation scenarios in the context of the protoplanetary disk.

3.4 Results

3.4.1 Cloud properties from low resolution fitting

3.4.1.1 Technique

For both the equatorial region and “bright” southern region, ATMOF was used to first fit for the cloud parameters, before fitting the deuterium ratio simultaneously with the other variables. This was done to provide a quick, realistic starting point for fitting.

The cloud parameters ATMOF fit were a cloud base pressure and net opacity for a lower cloud, a cloud base pressure and a net opacity for an upper cloud, and the single- scattering albedo. The values used start with values in literature. It is the nature of the fitting algorithm that a defined parameter space explored is not reported (not every iteration is reported by ATMOF and Levenberg-Marquart does not use “bounds” in the strictest sense).

To retrieve cloud properties before the more finely tuned fitting of methane isotopo- logues, the base cloud pressure and optical depth were fit to the low resolution data (R∼5200). The lower cloud layer is better constrained by previous literature so it was fit for first using ATMOF. The values from Irwin et al. [103] were used as a starting point for the Levenberg-Marquart [141, 142] nonlinear least-squares fitting algorithm Chapter 3. Deuterium on Uranus 64 utilised by ATMOF. This type of fitting requires a good first guess to avoid converging on a local error minimum. The cloud pressure and optical depth parameters in Irwin et al. [103] thus provided a good starting point. The fitting routine therefore started with the suggested values for the lower cloud at 2 bar and an optical depth of 0.4.

The proceedure for the two low resolution bands was to first fit the resolution with the lower cloud opacity, lower cloud base pressure and upper cloud opacity and base pressure constant at the suggested values from literature. This ensured an optomised fit with concurrent fitting of the resolution in the first run the next parameters the pressure and opacity of the upper cloud or haze, was then fit.

For these cloud fitting runs the methane isotope ratio was set to that of Neptune as estimated by Cotton et al. [87] at approximately 0.43×D/H⊕. With recent findings suggesting that the two ice giants have very similar D/H ratios [98], this was a more resonable constraint than a D/H value equal to Earth’s which is the default for VSTAR. The parameters can be fit simultaneously, but the rough fitting independantly first with the lower resoultion spectra was meant to both save time and correct for the shortcoming of the Levenberg-Marquart Algorithm converging to a false minimum when initial estimates are not near the best fit.

The atmospheric model includes abundances for methane at a given pressure to be applied to the line lists. Lines for methane as well as hydrogen and helium collision- induced-absorption were included. It is unlikely that for the bright region where the clouds are believed to be comprised of methane [101] that other species would con- tribute significantly to the lines in this wavelength range. Since lower clouds may be comprised of other species, future work aims to include line lists (which should be neg- ligable in these regions) and cloud parameters for a third cloud of ammonia (NH3) or

Hydrogen Sulfide (H2S).

The simplified cloud models use two layers with a single optical depth to represent the cloud which may in fact be more extended than this. However, Irwin et al. [98] found that for Neptune, extended clouds offer only marginal improvements to fits over a compressed cloud model. Chapter 3. Deuterium on Uranus 65

3.4.1.2 Uranus’ cloud fit

Notably the best fit as shown in Figure 3.11 does not fit very well in the extremities of the window. This could potentially be due to noise in the data at low levels or an unaccounted for instrumental effect in the reduction. It may also be due to error introduced at the wings of the filter file as it is augmented for reduction. Errors on the scale of 10%, such as these, were seen in the fits from Irwin et al. [104] as well.

In thousands of iterations of fitted models, none simultaneously fit the window region and its periphery. The fit is also weak near the center of the window ( ∼1.53–1.565 µm). The continued improvement of these models and the fitting routine is a priority for our group. With the fit reasonably close in the region aroud 1.58 µm where deuterated methane lines are readily measurable, I can derive a preliminary value.

Figure 3.9: A plot of the best fitting parameters (in text) for the bright southern region.

For the bright “temperate” southern region the best fit produced was for an upper cloud with a base pressure at 2.08 Bar and optical depth 2.0×10−1 and a lower cloud at 2.29 Chapter 3. Deuterium on Uranus 66

Bar and an optical depth of 3.24×10−1. With such similar pressures we may picture this as a single cloud, but the particle size of the lower cloud (with a greater optical depth) is larger than that of the upper (∼0.45 µm compared to 0.05 µm respectively). The single scattering albedo for both clouds in this bright region is fit to 7.5×10−1.

For the equatorial region, the fits were not as good (the minimised χ2 value was much higher). The best upper cloud base pressure was at 1.59 Bar with an optical depth of 9.21×10−2. The lower cloud was fit with a pressure of 2.22 Bar and optical depth of 8.67×10−1. Again the particles were larger in the lower cloud (the same sizes as for the bright region). The single scattering albedo for both clouds in the equatorial region was 7.56×10−1.

Although we may wish to not take the fits to the equatorial region into account until a better fit is retrieved, if these values hold, it would suggest that the opacity of the cloud or clouds in the brighter region is greater, which is intuitive. Furthermore, it is interesting to note that all of these clouds approximately coincide with the pressures expected for the methane cloud layer on Uranus at temperatures of around 100–200 K, although additional hazes have been detected much higher in the atmosphere, and other cloud species are expected lower in the atmosphere, possibly from Ammonia (NH3) or

Hydrogen Sulfide (H2S) at cooler temperatures [102]. Chapter 3. Deuterium on Uranus 67

Figure 3.10: A cartoon of the haze and cloud layers Source: Wikipedia user ‘Ruslik0’ based upon Lindal et al. [70], Bishop et al. [137], West et al. [143], Atreya et al. [144], de Pater et al. [102]

These values for the cloud are in good agreement to those found previously (e.g. Irwin et al. [104]).

3.4.2 Fitting the deuterium ratio

3.4.2.1 Technique

Feuchtgruber et al. [145] estimated the D/H ratio in hydrogen gas (i.e. (D/H)H2 ) in Uranus’ atmosphere to be between 9 – 13×10−5. This number is based upon the comparison of rotational and quadrupolar rotational lines in the isotopes to models and would require that the nebula experienced mixing in the past. This mixing, however, is rebutted by the evidence from the variation in isotopes within families of comets suggesting that the nebula was probably inhomogeneous to some degree.

Once a fraction of deuterated molecules to nondeuterated molecules has been retrieved by model fitting the value can be converted to more expository values. To convert Chapter 3. Deuterium on Uranus 68

Source D/H Species Ratio Species f

−5 +3.6 −4 deBergh 1986 [140] ∼5–9×10 ? 3.6−2.6 × 10 CH3D 1–1.8 +3.5 −5 −5 Feuchtgruber 1999 [145] 5.5−1.5 ×10 9–13 ×10 HD N/A Feuchtgruber 2013 [146] 4.4±0.4×10−5 ∼8–9.6×10−5 ? HD N/A +1.5 −5 +0.9 −4 Irwin 2012 [104] 4.3−0.9 × 10 2.9−0.5 × 10 CH3D 1.68±0.23

Lecluse 1996 [108] – – CD4 1.68 ? Inferred from given published values

Table 3.2: Table of estimates of the deuterium-to-hydrogen ratios in Uranus’ atmo- sphere. The species ratio is the ratio of the deuterated species to the non-deuterated species. D/H is the ratio adjusted for the number of hydrogen molecules in the molecule (e.g. 4 in methane), with the fractionation factor as quoted by the source applied to give the true ratio of deuterium-to-hydrogen (equivalent to that in H2. An additional f factor is included from Lecluse et al. [108] which accounts for species fractionation. to the fraction of deuterium to hydrogen for a molecule from the ratio of the deuter- ated molecule to the non-deuterated molecule one simply multiplies by the fraction of hydrogen atoms in the molecule. Equation 3.9 is an example of this for methane.

1 CH3D (D/H)CH4 = (3.9) 4 CH4

To then convert this to the D/H ratio for any other species (deuterium ratios are often compared in H2) requires the careful consideration of fractionation processes. de Bergh et al. [140] constrained the fractionation factor for the outer atmosphere (∼1 bar) of Uranus to be between 1.0 and 1.8. This was further refined in 1996 by Lecluse et al. [108] to a value of 1.68 ±0.09. Mixing could drive the error to a larger value and as the fractionation will change with processes affecting different altitudes, so too will the fractionation factor. Thus for methane a conversion to hydrogen gas can be derived using the fractionation factor as in equation 3.10 ([140][108]).

1 (D/H) = (D/H) (3.10) H2 f CH4

Finally to understand how this relates to the ices that made up the planet, we can use equation 3.11 from Feuchtgruber et al. [145]. xH2 is the per volumn ratio of H2

(gas/ice ratios) in Uranus, estimated to be ∼0.51 by Podolak et al. [147]; (D/H)proto is the protosolar value of deuterium-to-hydrogen which is believed to be close to the D/H Chapter 3. Deuterium on Uranus 69 ratio of Jupiter contigent upon the theory that the planet accumulated a large amount of its gas envelope from this material. Measurements of the D/H ratio for Jupiter −5 −5 place the (D/H)ices value at ∼9.4×10 corresponding to a (D/H)proto of 2.25×10 while measurements of the protosolar value based upon helium isotopes measured by the Galileo space probe in the solar wind place the value closer to 8.5×10−5 [145, 148].

As previously alluded to, the equation used by Feuchtgruber et al. [145] is true for the scenario where the gas is well mixed at some point prior to planet formation. Otherwise the material may have been fractionated earlier in the history and the relationship between the deuteration of hydrogen and methane may be less straightforward. [108]

(D/H)planet − xH2 (D/H)proto (D/H)ices = (3.11) 1 − xH2

These equations are referenced in my calculations for the D/H ratio of Uranus in the discussion of our own data and model fitting.

In this case an additional conversion factor is introduced because VSTAR uses line lists from laboratory measurements

3.4.2.2 Uranus’ measured D/H ratio

Although the fits in the center of the H-band window are improvements from previous fits. The perifery of the window could not be fit. This means that the cloud parameters are not well constrained. Taking this into consideration, I calculate a preliminary D/H value as a proof of concept.

In the case of the equatorial region, the cloud is too poorly fit to retrieve an accurate D/H ratio. Therefore I will follow through the steps outlined in the last subsection with the value retrieved for the bright, southern region.

Previous to the steps outlined in the last subsection to convert the values, VSTAR’s ratios must be converted. The ratio used in VSTAR and fit in Figure 3.11 is a ratio of Uranus’ CH3D/CH4 value to that of the Earth. In other words, it is a comparitive fraction to the isotopologue abundance on the Earth. Often the Earth’s D/H value is based upon the Vienna Standard Mean Ocean Water value of 1.56×10−4 (which would Chapter 3. Deuterium on Uranus 70

−4 correspond to a CH3D/CH4 of ∼6.237×10 ). For the Uranus models the line lists used for the isotopologues are from labratory measurements [149] of natural gas and similar terrestrial sources which have dramatically different, depleted values. In this case the −4 equivalent Earth CH3D/CH4 value is 5.0×10 [150].

The plot of the χ2 values shown in Figure 3.11 are for the final single variable fits (the χ2 values are very high because there are still many more degrees of freedom since this is spectral fitting). Fitting for only the D/H ratio with the best cloud parameters set as constant, I obtain a spread of χ2 values. The χ2 minimum, where the fitting would converge, is calculated by fitting a second-order polynomial to the points.

The black vertical line is the minimum value (slope = 0) and is at CH3D × Earth ≈ CH4 0.67(69). The 3σ limits can be roughly ascertained from the plot. The derivative of the polynomial is approximately equal to the square of the σ value. This would provide a 3 σ range of 0.676908 ±2.4×10−5. This is clearly over-fitted due to the additional degrees of freedom inherant in a spectral fit. However, we can take the minimum value as likely accurate, contingent upon the cloud fitting, because the minimum should not change with the removal of the spectral degrees of freedom. Chapter 3. Deuterium on Uranus 71

Figure 3.11: A plot of the chi-squared values for several outputs from the low reso- lution bright band data, fitting for the deuterium ratio. The x-axis values are in terms of the ratio of CH3D/CH4 as compared to Earth. The black line denotes the minimum (slope of 0).

First to convert my value (0.677) from the comparitive (to Earth) value VSTAR has solved for to a true CH3D ratio, it must be multiplied by the factor 5.0×10−4 as cited CH4 in Bailey [150]. This provides a CH3D = 3.34 × 10−4. CH4

−5 Next, using Equation 3.9, I convert this to the (D/H)CH4 value, at 8.50×10 . And

finally to convert to the common H2 value I encorporate the fractionation factor as in −5 Equation 3.10. We arrive at a (D/H)H2 value of 5.04×10 .

3.5 Prospects

No further observations are planned for this project, although the high resolution data still have yet to be utilised. The impedance lies in the ability of the ATMOF fitting routine. ATMOF was designed for a specific function: the fitting of telluric models. Chapter 3. Deuterium on Uranus 72

Since the routine is a top end script for a specific purpose, the fitting does not necessarily translate to other problems. For Uranus and Neptune, because the clouds have so many free parameters a different optimisation needs to be used.

An accurate fitting routine accounting for the degeneracies is needed to fit the low reso- lution spectra to cloud models, which in turn is needed to accurately fit high resolution spectra to cloud models, which then in turn is needed to accurately fit the high resolu- tion spectra to deuterium abundances. It is imperative that the clouds are fit accurately before the deuterium because they shift the flux over broad regions of the spectrum up and down depending on their optical properties and structure. Thus, too great a flux in the methane window where the deuterium lines of interest are present can change the apparent depths of the more finely structured lines and dramatically effect the measured deuterated methane abundance.

There is a lingering issue even with these improvement to the fitting routine. Because the low resolution and high resolution data are over slightly different parts of Uranus’ disk, they may be affected by varying cloud structure over these small differences. This could produce a notable shift in the spectrum between regions retrieved with low resolution versus high resolution.

Objectively and specifically, the problem with the fitting routine lies in using the Levenberg- Marquart algorithm for this data set. Although the spectra constitute a well-sampled data set, the parameters contributing to the spectra for Uranus are still ill-constrained. For fitting the Earth’s atmosphere the data is well sampled and the contributing factors are well studied.

To understand why it shouldn’t be applied to ice giant spectra (and moreso to exo- planets), it is helpful to understand how the fitting routine works. Levenberg-Marquart fits by utilising gradient descent when the guiding delta value is high, and then using Gauss-Newton to hone-in when delta values are low. The initial delta value is set by the user in ATMOF, and in essence is a proxy for how close to the real value the starting point, also supplied by the user, is expected to be. For an atmosphere like the Earth where the values of parameters have known boundaries (or probability boundaries) this works well. In cases where there may be many local minima (many locally optimised permutations of parameter values) the fitting routing needs the gradient decent portion of the fitting to work robustly initially and not converge on a local minimum (it also Chapter 3. Deuterium on Uranus 73 requires the user start with a sufficiently high delta value to weight the gradient decent fitting well over the Gauss-Newton fitting early on). Thus the alpha value (learning rate) for the gradient descent needs to be large enough to allow the parameter space to be explored. The learning rate was not a value that the user could change with AT- MOF, which itself is problematic. The fitting routine is now being updated to allow this to be set to appropriate values for atmospheres with more unknowns contributing to their spectra. It is worth noting, however that even after this change, ATMOF will still not be appropriate for use with exoplanets because the number of unknowns isn’t even well constrained much less the values they may hold. To allow ATMOF to be applied to these problems a learning algorithm such as a Metropolis-Hastings Markov Chain Monte Carlo (MCMC-MH) should be employed.

Once the alpha value (learning rate) is adaptable, ATMOF should be applicable to Uranus and other Solar System planets, allowing us to move on to recover reliable cloud models. Once the cloud models are retrieved for the low resolution data with some confidence, we can constrain the initial parameters in the high resolution data which is over an adjacent segment of the atmosphere. And once these values have been retrieved for the high resolution data, we will then be able to fit for the deuterium abundance without perpetually finding local minima where unrealisitic clouds may mask the deuterium levels.

To summarise, for this work the current hindrance is not the quality of the observational data, or the molecular data we are fitting it with. Rather it is the appropriate adaptation of the fitting routine primarily, to be capable of fitting a spectrum with some poorly- constrained parameters (namely, the species/optical properties and pressure heights of the cloud layers) before we can move on to the fine-tuned fitting of deuterium abun- dances. This could alternatively be better constrained by developing self-consistent chemical models utilising spectral data from a wider range of wavelengths. Our data is complicated by variations over the disk and temporal variations in the clouds, however this alone is not a hindrance, in fact our approach of constraining the parameters first with lower resolution spectra should provide a good fit. The difficulty in fitting the periphery of the H-band is due to the unknown nature of the clouds and their optical properties. As stated previously, this is usually “overcome” by ignoring this part of the H-band, but we seek to achieve a robust fit by using the low resolution fits and covering an open parameter space. Chapter 3. Deuterium on Uranus 74

3.6 Discussion

Measuring the D/H ratio in methane is a good test for the formation scenarios as it would provide some constraint on the origin of the bulk materials that made Uranus and Neptune. Beyond our Solar System’s planetary orbits, Aikawa and Herbst [107] have shown that the ratio of column densities in CH3D/CH4 do not change significantly with distance compared to the variation seen in the deuteration in other species such as water.

Thus the implications for the deuterium fractions in different species for the sources of the ices on Uranus and Neptune are also of interest.

Referring to Table 3.2 we see that the D/H ratio derived from the bright region of Uranus is in good agreement with early values from de Bergh et al. [140] and Feuchtgruber et al. [145] (1999), as well as from the more recent value from Irwin et al. [104].

The value derived by Feuchtgruber et al. [146] in 2013 was based upon measurements of the deuterated hydrogen molecule (HD). Assuming that Uranus was well-mixed though its interior and atmospheric material at some point in its history, this lower value would require that the protoplanetary ices that enriched the planet have a far lower D/H value than any other source of ice in the solar system, or that, contrary to the popular model, their interiors are in-fact rock dominated [146].

The core structure of the planet is likely to be heavily dependent on its formation. Distinuishing where the material came from—and how it might have escaped deuteration if that is the case—could have profound implications for determining which formation process for the ice giants is correct, particularly where their cores came from (e.g. carbon monoxide ice line, water ice line with migration, etc.).

The fact that the values we tentatively retrieve and which others have retrieved are very similar between Neptune and Uranus is interesting. This is sometimes attributed to the fact that they may have formed cores from well mixed material or formed very closely to one another, but it seems unlikely that two significant cores would form so close together. There is a possibility that if the planet Uranus did suffer a large impact in its past, this impact could have contributed to the mixing of materials throughout the planet. Neptune today has a seemingly more actively mixing atmosphere. Thus the Chapter 3. Deuterium on Uranus 75 possibilty that the early material in each ice giant may have not differentiated in the same manner or rate.

My value, using Equation 3.11 and the values quoted in the preceeding paragraph, relates −5 to an ice value of (D/H)ices = 7.94 × 10 . While this is not as low as the values found in Feuchtgruber et al. [146], it is still notably lower than the cometary ice values noted therein such as carbonaceous chondrites at 1.4×10−4 and comet Hartley 2 at 1.6×10−4

(Oort comets have even higher values). Even with a (D/H)ices value allowing for an ice core, a lack of deuteration may suggest the planets formed well inside of their current orbits as suggested by some applications of the Nice Model [151].

My value for CH3D of 3.34 × 10−4 is notably also similar to the value derived in prelimi- CH4 nary results in the conference proceeding by Cotton et al. [87] of 3.0×10−4 for Neptune. This shows VSTAR and our data sets should be self-consistent. If the refined derived values prove to be similar to these, the increase in deuteration seen in Uranus could be indicative of its formation originally outside the original orbit of Neptune. Ours are not the first models to fit very similar D/H ratios for the two planets, with Uranus’ slightly greater. Irwin et al. [98] retrieved a similar value for Neptune 3.0×10−4, also slightly lower than that of Uranus.

While this dance of planets may sound exteme to such small creatures as we, if we look to hot Jupiters we find, quite possibly, an even more extreme case.

Chapter 4

Polarimetry

Methods focused on transit and secondary eclipse spectra have been utilised substantially to characterise exoplanets. Another method which has been relatively overlooked is polarimetry. Along with photometry and spectral analysis, polarimetry is a useful tool in learning about distant worlds from their light. It provides some advantages over other observational methods and complements some methods of characterisation. The method is well suited to exoplanet studies and could potentially be used for direct detection.

Polarisation of light is the tendancy for the electric (or magnetic) field vector to oscillate in a particular direction. The electric field vector of unpolarised light oscillates in all directions. Purely linearly polarised light oscillates in a planar direction. In practice light often isn’t 100% polarised in a single direction and can be described by a percentage degree of polarisation.

The measurements of polarised light are described by Stokes parameters. Linearly po- larised light (like HIPPI measures) is described by Stokes Q and U. The positive and negative components of each are orthogonal to each other while Q and U are at 45◦ to each other. This orientation ensures that light which is not perfectly polarised in one planar direction is well described. Stokes V refers to circularly polarised light and describes its chirality. Stokes I refers to the total intensity.

77 Chapter 4. Polarimetry 78

Figure 4.1: An illustration of the Stokes parameters as used in this thesis. Q and U are linearly polarised light, which HIPPI measures. Image: Wiki Commons

Mathematically, there are many ways to represent polarisation. Trigonometrically it can be described with spherical coordinates of an eliptoid so that the more removed from a perfect sphere the elipsoid becomes, the more polarised the light. In spherical coordinates the four Stokes parameters are defined as,

S0 = I (4.1)

S1 = Ip cos 2α cos 2ω = Q (4.2)

S2 = Ip sin 2α cos 2ω = U (4.3)

S3 = Ip sin 2ω = V (4.4)

In these equations, ω and α are angles of the polarisation ellipse with the semimajor axis as the “adjacent” and “hypotenuse” sides respectively. There are therefore three dimensions, three sphereical coordinates, for describing the polarisation: two angles (2α and 2ω) and the magnitude desbribed by Ip (i.e. the intensity of the light multiplied by the polarisation factor). Light polarised fully along an axis (or perfectly orthogonal to is) would have α at 0 or 90 degrees, so that the sine or cosine (respectively) would be zero causing to be zero and the elipse would be a line. A visual aide of this concept and the relationship between the polarisation ellipse and the spherical coordinate definition is seen in Figure 4.2. Chapter 4. Polarimetry 79

The Stokes parameters are also reffered to by I, Q, U, and V . I is the intensity, Q and U are semiorthogonal linear polarisation, and V is the circular polarisation. When we measure polarisation we are typically considering the amount of polarised light compared to the overall intensity to provide intensity units. For this we normalise the Stokes parameters as Q/I or U/I.

Figure 4.2: An illustration of the Stokes vectors in Cartesian and their translation to the polarisation ellipse, a Poincare sphere. Image: Flossmann et al 2006 [152]

In systems where scattering and the reflection of light occur, polarised light may result. Light can be polarised through transmission, reflection, refraction or scattering.

Polaroid materials polarise light through transmission by only allowing the light vi- brating (we will simplify the idea of the E~ or B~ field oscilating by saying the light is vibrating in that direction) in one plane to pass through. Unpolarised light passing through a polarising filter or polaroid will become polarised as all other directions of vibration are not permitted. In a this effect is used to detect the direc- tion of polarisation in polarised light, that is when the filter0s permissivity axis and the light’s polarisation axis are aligned one would recieve the strongest signal, when they are orthogonal no light would pass through to be detected.

On a “microscopic” level the filter is comprised of molecules or crystals (liquid crystals in the case of our polarimeter) aligned in one direction throughout. The light vibrating in that same direction is absorbed while the orthogonally aligned light is the component which passes. The alignment of the molecules effectively in unidirectional strings means that their degree of freedom is orthogonal to the ”string”. A polarising filter is not getting Chapter 4. Polarimetry 80 rid of the light that isn’t aligned with the transmission axis, but rather is modifying the polarity of the light. In the case of the ferroelectric liquid crystal modulator used in our instrument, the voltage applied to the crystals unwinds them, changing their polarising orientation property (without a current applied they act as a half wave plate).

Light can be polarised by reflecting off a surface such as a liquid body, as we see in the glint off the ocean. Metallic surfaces do not polarise light as they reflect light with many directions of vibration. Non-metallic surfaces such as water will polarise light parallel to the surface since the vibrations of the molecules will tend to align this way. This occurs because the electrons in the water or other material act like dipole radiators which will not transmit energy along their vibrational axis. The vibrational axis at the surface of water is aligned to the surface— so the transmitted light is perpendicularly polarised, but the reflected light is polarised along the parallel axis.

When light is refracted it becomes polarised to some degree. This is related to the polarisation produced by reflection, as the light that is reflected tends to be polarised parallel to the surface and the light refracted as it enters the material, such as water, is polarised perpendicular to the surface. In birefringent material, such as calcite, the light can be refracted at two different angles and thus with two different polarisations. In most cases light polarises with an axis normal to the surface; in calcite one beam will polarise normal to the surface and the other parallel.

Scattering can produce polarisation and is the primary process expected to be behind the polarised light observations discussed in this thesis. The repeated absoprtion and reemission of light can be anisotropic and anisopolar as in regular Mie scattering, or, depending on the particles scattering the light and the wavelengths undergoing the process, there can be isotropy and a tendancy for a particular angle of polarisation as well. Rayleigh scattering is an example of this.

Mechanisms for polarisation in the material, which polarise light interacting with it, rely on the polarising material containing ions or dipoles. The exception to this is when electronic polarisation takes place (this is due to the charge asymetry in the electron cloud).

The type of polarisation that occurs depends heavily on the type of material; those comprised of a single element will produce electronic polarisation, and some materials, Chapter 4. Polarimetry 81 such as water, will be capable of producing electronic, ionic, and dipolar polarisation as the molecules are mixed elements and dipolar. In an atmosphere a combination of these mechanisms can occur.

In addition, the wavelenths of light affected by these different mechanisms vary. Blue light, where we see Rayleigh scattering in most atmospheric conditions, is sensitive to electronic polarisation. Slightly longer wavelengths will begin to show sensitivity to ionic polarisation.

Phenomena such as rainbows, Rayleigh scattering, effects from magnetic fields and glint produce signatures of linearly polarised light.

A related manifestation of polarised light that is not discussed here in detail but could one day be used to detect biosignatures in the form of chiral molecules is circularly polarised light. Circularly polarised light is a spiraling vector in polarised light, which is akin to two linearaly polarised light vectors out of phase by a quarter of the wavelenth and with an axis of vibration at ninty degrees from one another.

4.1 Polarimetry of Exoplanets

Polarimetry is a valuable tool for exoplanet studies. Observations of exoplanetary sys- tems in polarised light are of the combined light from the star(s) and planet(s), however because under normal circumstances light directly from the star is not polarised, this creates a great contrast and way to discern the source of the light. The measurements of polarised light from these systems is usually related as a fractional polarisation of the total light from the system, so that ratio will be very small since the portion of the light reflected by the planet, even if wholly polarised, is a small fraction of the light detected from the system overall.

Scattering from exoplanets was determined to be just outside the detectable limits in 2000 [153] at tens of parts-per-million level. At that time, polarimeters were less sensitive, at about the thousands to hundreds of parts-per-million level. Today, sev- eral polarimeters achieve tens-of-parts-per-million sensitivity. A few have demonstrated parts-per-million sensitivity including the one used for this work [58]. Chapter 4. Polarimetry 82

Figure 4.3: An idealised case for the polarised light from a close-in giant exoplanet (hot Jupiter) with particles of effective scattering radius = 0.1 µm. The orientation of the system, particle size, multiple scattering and other factors will scale the effects. The left side shows the reflected light component from the planet in micromagnitudes, while the right side shows the system’s total polarisation component per orbital phase angle. Image: Figure 4 in Seager et al. [153]

4.1.1 Polarisation Mechanisms

Polarimetry of exoplanetary systems is complementary to other characterisation tech- niques, adding and confirming a great deal of information about both transiting and non-transiting exoplanets. Observing the polarised light from an exoplanet system over the course of its orbital phase can provide a tremendous amount of information about its orbit.

The polarisation of light from the atmosphere provides information on the shape, size and distribution of the particles. Along with an improvement to atmospheric char- acterisation, polarised light can provide constraints on orbital parameters which are complemented by other techniques such as the Rossiter-McLaughlan effect.

Rayleigh scattered light, which is currently detectable, is dependant upon the size of the scattering particles (as is reflected light from oceans and the refractive angle across which a rainbow is detected). Thus a well constrained measurement of polarised light would provide a way of determining the range of size of scatterers in a planet’s atmosphere. The Rayleigh relationship is also dependent upon the index of refraction, so that could potentially serve as an additional constraint. Chapter 4. Polarimetry 83

Comparing the polarised light constraints on the index of refraction and scattering par- ticle size to the effect of Rayleigh scattering on visible light, observations in secondary eclipse and transit can confirm the observations.

Figure 4.4: A simplified illustration of the effect of varying orbital parameters on the polarised light curve. Note the dashed and dotted lines show two arbitrary permutations of the value. The purple and red refer to the Stokes Q and U parameters.

In the idealised case of a lambertian sphere, a planet is simplified to diffuse, single- scattering with intensity dependent upon the angle. A Rayleigh model is then applied to this scattered light curve. This produces a stronger polarisation signal than is seen in practise, so it provides upper limits. In models this scattering can be reduced by a factor to better represent the multiple scattering we might expect in an atmosphere. The Lambert-Rayleigh phase models of polarised light are unphysical, however until quite recently, their divergence from a more robust model has been smaller than polarimeters can measure. Chapter 4. Polarimetry 84

This approximation of the polarisation of light is heavily influence by the orbital pa- rameters which drive the amount of light scattered in the first place. The closer the planet is to a star and larger the planet’s radius is, the greater the amount of fractional polarisation for the system [153]. A further deviation from this simplified relation is due to interactions between the magnetic field of the star and planet when the planet is very close, leading to anisotropies from magnetic field reconnection. For most of the planets discussed in this dissertation this is a minor issue and will be discussed individ- ually. In general, the magnetic fields of most planet hosting stars do not seem to differ substantially from those of stars that do not host planets[154].

For the Lambertian case, the maximum of polarisation driven by scattering occurs at a phase angle of 70◦ (and at 290◦). This is due to the modulation of the polarisation curve with that of the reflected light; the maximum of polarised light signal is at the position angle (PA) = 90◦ but the maximum reflection occurs at 0◦ [153]. This remains true for more detailed, multiple-scattering models where the scatterer is molecular, however the maximum phase angle of the polarisation signal varies if the scatterer is instead a larger particle from a haze or cloud with haze also producing more of a depolarising effect from the effective multiple scattering [155]. For extremely small particles much smaller than the wavelength of light, interference can also cause peaks in the phase curve [153]. particles from debris disks in planetary systems can also produce polarised light [65]. Three of the four exoplanets considered in this thesis have had infrared photometry measurements taken with Spitzer and for all three of them no infrared excess is reported [156], meaning that scattering from large particles in debris disks effects are not a concern for these systems.

Rayleigh scattering occurs when the particle is much smaller than the wavelength of light 1 (less than ∼ 10 the wavelength). An approximation of the size of the particles, or rather the Rayleigh scattering cross section can be retrieved by considering the wavelength of light with angle, depending on the type of scattering occuring.

A particle will scatter some wavelengths of light parameterised by the relation

2πr x = s λ Chapter 4. Polarimetry 85 wherein x is the size parameterisation and r is the scattering radius of the particle. For x  1, simple geometric scattering takes place just as it does on the surface of an ocean, according to the shape of the particle, where the scattering can be modelled by ray optics.

For x ≈ 1, Mie scattering takes place where wavelengths are subject to resonances for di- electric particles as they are reflected back off of the particle’s surface (usually simplified to a sphere when considering calculable Mie scattering) producing a complicated inter- ferrence effect. The particle in this case re-radiates the energy in the same phase but in random directions so that the percieved effect is that the wavelengths most sensitive are scattered out incoherantly and diffusely. This can be modelled by Lorentz-Mie Theory, an exact solution of the scattering from spheres that can be derived from Maxwell’s equations.

For x  1, Rayleigh scattering takes place. Again the light is scattered in all directions but preferentially forwards and back. The scattering cross section for a particle inducing Rayleigh scattering is described by

2π5 d6 n2 − 12 σ = s 3 λ4 n2 + 2

.

Wherein n is the refractive index, λ is the wavelength of the light, and d is the diameter of the scattering particle. Here we can see the strong dependence upon the size of the particles and on the wavelength. A larger value of λ (implying a longer wavelength) re- duces the fraction for a given particle size, thus reducing the effect of Rayleigh scattering. Hence for any particle, shorter wavelengths will be scattered more efficiently.

The light response with wavelength will provide the approximate diameter of the scat- tering particle. While the refractive index will affect the scattering cross section, the relationship between the size of the scattering particle and the wavelength of the light is the driving term in the equation.

The inclination, separation, type of scattering (such as Rayleigh), position angle of the orbital plane, eccentricity, geometric albedo, level of multiple scattering, and amount of interstellar polarisation from the ISM all affect the polarised light curve. Depending on the system some of these parameters may be constrained by other methods, allowing Chapter 4. Polarimetry 86 the remaining parameters to be retrieved to greater accuracy. Even in systems where little is known about the planet and its orbit, if the polarised light phase curve can be thoroughly measured, these parameters can be derived because their influence on the light curves is not degenerate.

The interstellar medium polarises light between distant stars and the Solar System [157]. It is discernable from the polarisation from an exoplanet atmosphere in that it does not vary with the phase of the planet, but will manifest as a constant offset from zero polarisation. It is due to the anisotropic interstellar medium molecules, aligned by galactic-scale magnetic fields, producing a net polarisation. Its effect (position angle and intensity) differs throughout the sky as trends in the alignment of the interstellar medium itself varry [87]. It may in some cases also have a different polarisation ‘colour’ than the planet’s signal if the scattering from the planet is from larger molecules or small haze particles.

Polarised light is a practical tool for exoplanet studies not only because of the fantastic contrast it provides with the star, as we will discuss in the next subsection, but also because it can be used for both transiting and non-transiting planets to characterise their atmospheres. With no transit or secondary eclipse measurements available for non-transiting planets, polarimetry can add a lot of information about the orbit and the atmosphere of a non-transiting planet, which is otherwise limited to phase curves and cross-correlation for molecular bands.

4.1.2 Stellar contributions to polarised light

One strength of polarimetry lies in the relatively low polarisation of a star compared to an orbiting planet. For sun-like stars, the star emits its own light roughly homogeneously over its surface without scattering from condensates in the upper atmosphere. There is a measureable [158] polarisation effect at the limb of the star where one is seeing the small amount of scattered light from the upper atmosphere, but in most cases this will be negated by the star having an unobscured circular limb so that the vector of the polarised light cancles out, producing a null net effect (Fig. 4.5). There are deviations from this if the star is very active (particularly M-type stars) or the atmosphere is more extended as in cool giants. Chapter 4. Polarimetry 87

Figure 4.5: An illustration of the net nulling effect of the polarisation in a (unob- scured) star0s limb. In the idealised case, the polarisation intensity is equal all around the limb with changing Stokes values which cancel out. (The Q values where the U vector is shown are zero in this cartoon, and visa versa)

This contrast lends itself to detection as it no longer becomes as vital to remove the 0 1 star s light from an image, although the amount of relfected light will reduce as d2 , where d is the distance (star-planet separation), so it is easier to detect polarised light for planets closer to their stars

For stars with transiting planets, the ingress and egress of the planet block part of the polarised limb, shifting the net effect a detectable amount [158].

For a similar reason star spots are a concern as their local magnetic field anomolies can break the nulling effect upon reaching the limb. The most dramatic effect will be when the spots are in the limb.

In a transiting system a similar effect can be produced in Stokes Q and U between the planet transit’s effect on the polarised light curves and the effect of the spots. This is most effective when the planet and starspot are at 90◦ separation across the star0s surface (i.e. as seen from the center of the star/ stellar longitude) [159]. The specific effect on the light curve will vary for the orbital parameters and scale of the system.

Not only can a star0s magnetic field affect the atmosphere of a planet by driving atmo- spheric escape through recombination of magnetic field lines, but a planet’s magnetic Chapter 4. Polarimetry 88

field can also affect the activity on the star itself. This happens when a planetary mag- netic field sufficiently close to that of the star can perturb the open field lines of the star, producing bright spots. The activity is typically offset to the subplanetary point on the stellar surface by ∼70◦ [160].

Supermagnetosonic hot Jupiter systems could have bow shocks of material. Bow shocks for when the speed of the magnetised material in the stellar wind suddenly drops from encountering a planet’s magnetic feild. The relative speed of the wind, therefore, is important. Hot Jupiter planets very close to their stars move a high orbital velocity, so the stellar wind is submagnetosonic and a bow shock would not occur [161].However once the system becomes supermagnetosonic at a greater distance or with an accelerated stellar wind, bow shocks could occur.

In the case of one hot Jupiter orbiting in a 2.2 day orbit, models of a bow shock match the asymmetric transit curves observed [162]. The material in the bow shock is modeled as being an aborbing material which occults the star preceeding the planet, this material is compressed in the model (by a factor of 4). Larger scale bow shocks have been hypothesized as a source of polarised light for stellar objects (see, for example, discussion within Neilson et al. [163]).

4.1.3 Scattering from exoplanet atmospheres

4.1.3.1 Orbital Parameters

Measurements of the spin-orbit alignment of a system complement the polarimetry mea- surements. The Rossiter McLaughlan (RM) effect provides the angle between the spin- axis of the star and the orbital axis of the planet by measuring deviations in the radial velocity curve as the planet transits the star and obscures part of the star’s light from the side moving either towards or away from the observer (see Addison et al. [164] and Addison et al. [28] for further description and application to other exoplanet systems). Coupled with the polarimetry measurement of the inclination, eccentricity and position angle, this provides a fairly complete portrait of the projected orbital parameters of the system.

The orbital parameters relate to the origin of hot Jupiter exoplanets. The entended atmospheres of many hot Jupiter exoplanets are likely owing to the hinderance of of Chapter 4. Polarimetry 89 their collapse from planetary embryos as they rapidly moved to a shorter orbital distance very early in their formation. However many hot Jupiter systems show evidence of the Kozai mechanism in that their spin-orbit alignment is near 90 degrees and there is a larger body (e.g. an M dwarf) orbiting at a significant seperation. These hot Jupiters are driven in to very close orbits with their primary star as energy is transferred with the secondary star. The inclination of the secondary transfers energy to the planet’s eccentricity causing it to swing close to the primary. The eccentricity is then removed by tidal damping driving it to a circular orbit. The Kozai mechanism removes the need for type I or type II migration [165]. Whether this happens often, when it happens, and whether there is a correlation with planets with extended atmospheres is extremely important in understanding the way these unusual planetary systems have formed.

Some parameters, such as the obliquity, are thought to be more stable than, say, eccen- tricity [165], so the variations in some parameters could correlate to the point in their formation and migration they are observed. There may also be some connection to the mass of these hot Jupiters. Triaud et al. [165] found from combining long term radial velocity measurement from Coralie and the HARPs Rossiter McLaughlin measurements that the majority of planets less than 2 MJ are aligned with the stellar rotational axis. For hot Jupiter exoplanets however the group found that most are mis-aligned with many have spin-orbit angles greater than 30◦. Additionally, from a statistical perspec- tive, hot Jupiters are not preferentially found in binary systems [166], nor are they any less likely to have other planetary companions [36]. Planet-planet scattering could also produce their unusual configurations and does not preclude the spin-orbit misalignment seen in many systems.

4.1.3.2 Rayleigh scattering

Previous attempts to detect polarised scattered light from an exoplanet atmosphere have primarily produced nondetections [60]. The notable exception to this is from Berdyugina et al. [167] who measured an exceptionally high level of polarised light from the planet orbiting HD 189733. An attempt to reproduce this measurement by Wiktorowicz [168] showed no significant variation in the polarised light curve with the phase of the planet. In turn, Berdyugina et al. [169] confirmed their original observation, with a refinement to the values. They did not detect the level they had seen previously in blue light, but Chapter 4. Polarimetry 90 they still detected about two times the level of variation one would expect from a hot Jupiter atmosphere with multiple scattering. The group posited that this was due to a singly scattering atmosphere.

In redder wavelengths, Berdyugina et al. [169] detected far less polarised light, although still more than was detected in a similar wavelength band by Wiktorowicz [168] (V band (centered ∼540 nm) versus a custom filter in POLISH covering ∼400-675 nm) ). The dramatic decrease in polarised light with redder wavelengths was attributed to Rayleigh scattering. This trend was confirmed by secondary eclipse measurements by Evans et al. [1], although the corresponding albedos from photometry are lower than those predicted by the significant polarisation variaitons from Berdyugina et al. [169].

Figure 4.6: Large variations in the polarised light signal from HD 189733b. Notably the amplitude of the variation in greater in shorter wavelengths (U and B vs V bands). Image: Figure 1 in Berdyugina et al. [169]

Of the four exoplanets explored in this dissertation two have had previous attempts at polarised light detection. The planet τ Boo b produced a nondetection of polarised light using the extremely sensitive—better than parts per million level—polarimeter PlanetPol at the La Palma observatory [170]. PlanetPol was built with red-sensitive avalanche photodiode detectors [171]. HIPPI is far more sensitive in blue light where the extended atmospheres of many hot Jupiters are predicted to dominate [172]. Chapter 4. Polarimetry 91

4.2 HIPPI

In April of 2004, the high precision polarimeter, PlanetPol saw first light at the William Herschel Telescope at La Palma. The instrument was extremely sensitive, reaching its goal of one part-per-million level detections for bright objects, with a night-to-night scatter on unpolarised objects suggesting a sensitivity of 1 ppm. The polarimeter was a success in many respects, providing detailed information on the interstellar medium (the low density gas and dust between stars) and the shape of the Local Bubble (the relative void in this interstellar medium near the Sun) in spite of complications from a dust from a haboob [171][173].

However the polarimeter did not detect [60] polarised light from exoplanets (planets of τ Boo and the 55 Cnc system)[60]. The planetary system 55 Cnc did produced a measurable amount of polarised light, but this was not modulated as light from an orbiting planetary system would be [60]; with two of the planets in the system inclined to the sky plane at 85◦ and one inclined at 53◦, the system is expected to have a notable modulation if the polarised light was from a planet [60]. τ Boo however, which was observed with HIPPI as well, showed more scatter than other planetary systems inspite of less photon noise, but without planet-like modulation, so it is hypothesised that the scatter is due to the stellar activity detected by the MOST satellite [160]. The studies did retrieve upper limits to the geometric albedos for each planet, reporting AG ≤ 0.13 and 0.37 for 55 Cnc and τ Boo planets respectively within 4σ. So why was such a sensitive polarimeter unable to detect polarised light signals in these systems corresponding to planetary orbital periods?

The non-detection could be in part due to the atmospheric complications, although the dust affecting the polarised light from a Saharan dust storm around that time was well studied and accounted for as the polarisation had a preferred orientation [173]. More likely it is due to the fact that the instrument was built to be most sensitive in red light. This, along with the fact that hot Jupiters should be good Rayleigh scatterers and the disparity between observations for at least one hot Jupiter depending on wavelength, are the primary motivation for building HIPPI as a blue-light sensitive polarimeter.

Since blue light is scattered more readily, HIPPI was built to reach the same sensitivity that PlanetPol acheived in red light, in blue light. This increases the chances of detecting Chapter 4. Polarimetry 92 the polarised scattered light from planets around FGK spectral type stars (later types will of course produce less blue light). Red light from scattering of thermal radiation primarily from the planet itself could potentially play a role, but this would be a smaller effect and has not been observationally detected. [174]

Hot Jupiters are expected to be great Rayleigh scatterers. Burrows et al. [172] called the dominance of blue in the albedo of a hot Jupiter counter intuitive, but it is due to the abundance of absorbers in the lower atmosphere creating a “high pressure plateau” which allows the upper atmosphere to be realitively cool and effectively scatter the light.

The level of polarisation an observer can expect to see from a hot Jupiter atmosphere was estimated theoretically by Seager et al. [153] to be only 3–4 ×10−5. This has been outside the ability of visible light polarimeters largely with a few exceptions such as PlanetPol which produced non-detections [60], POLISH, which produced a non-detection [168] and TurPol which detected a surprisingly high polarised light signal for the same planet, HD 189733b [169]. Berdyugina et al. [169] estimated the fractional sensitivity of TurPol to be 1–2×10−5, while PlanetPol could detect fractional polarisation better than 1×10−6 [171]. TurPol, unlike PlanetPol is a dual beam polarimeter which, while typically a less sensitive design, does provide a better sky subtraction (see discussions in Berdyugina et al. [169] and Lucas et al. [60]).

Today HIPPI is the most sensistive visible light polarimeter in the world in use (Plan- etPol has been decommisioned) with a fractional polarisation sensitivity of 4.3×10−6. Another polarimeter, POLISH2, has, at the time this thesis is being finalised, no claimed detections of polarised light from an exoplanet, however its high sensitivity and circu- larly polarised light capabilites make it a valuable tool for the field. The sensitivity of POLISH2 from telescope polarisation measurements is 3ppm, the polarimeter system is “stable” to 7ppm for their observations of the asteroid Vesta [59].

HIPPI’s quoted sensitivity is not derived from telescope polarisation but from night- to-night variaitons. Considering the variation in non-polarised sources measured by POLISH2 [175] we estimate the fractional polarisation sensitivity of the instrument is nearly as low as HIPPI’s, probably at 5.4ppm.

Recently, POLISH2 observed the HD 189733b system, measuring a variation in polarised blue light form the sytem but not with the phase of the planet [175]. Chapter 4. Polarimetry 93

POLISH (the predecessor to POLISH2) which retrieved a non-detection of red polarised light from the HD 189733b system, claims 1 ppm sensitivity for bright stars, we estimate from the published results in Tabel 3 of Wiktorowicz and Matthews [176] that the equivalent sensitivity measurement for POLISH would be about 8.5ppm.

4.2.1 Instrument

This and the following two subsections are based on the published paper Bailey et al. [58] of which I am a coauthor.

HIPPI is a relatively small and lightweight instrument allowing it to be easily attached to the Cassegrain f/8 focus with its computer (a rack-mountable computer the size of a desktop tower) and electronics rack-mounted within the Cassegrain cage. HIPPI uses different components (refer to Figure 4.7) than its red light predecessor, PlanetPol, in several respects.

The modulation is different: HIPPI utilises a ferroelectric liquid crystal (FLC) modulator which, as with the liquid crystal displays encountered in everyday life, changes the orientation of the crystals by varying the voltage across them. Like other FLCs and photoelectric modulators (PEMs) it provides an advantage over by allowing Stokes Q and U to be measured simultaneously although an alternative approach is used in HIPPI’s case. Their modulation is also very fast, reducing the turn around time between measurements to allow faster and more accurate measurements, and thus making HIPPI insensitive to seeing and tracking effects.

The modulator is placed first in the optics to avoid other components introducing un- wanted instrumental polarisation. Further discussion on the advantages of the compo- nents used in HIPPI are available in its comissioning publication from Bailey et al. [58]. PlanetPol used a photoelastic modulator [171].

Using two modulators rotating, Wiktorowicz et al. [175] is able to produce a sinusoidal modulation. Our modulation is produced by switching the current, flipping the crystals and thus the polarising filter field. It modulates by a roughly square wave. The square wave allows a rough calculation of the polarisation signal to be provided on the spot. The data from the switch is retrieved for our published work but is not included here. Chapter 4. Polarimetry 94

The 1 mm aperture that follows the FLC translates to 6.7 arc seconds when placed at the AAT f/8 focus, as it was during the observations presented in this thesis.

HIPPI included filters for r0 (roughly red light ∼550–700 nm), g0 (roughly blue light ∼400–550 nm) SDSS bands [177], and 500 short pass (a blue end filter with a sharp cut off at 500 nm, also called 500SP) as well as a 425 SP, a clear channel and a blank, blocked channel for taking darks. For the three exoplanets in this thesis without previous detections we used the clear filter, for HD 89733b we used the 500SP. HIPPI’s calcite prism introduces absorption below ∼350 nm, making the range of the 500SP effectively ∼350–500 nm (refer to Figure 4.10).

Polarisation is seperated into two beams at 20◦ for analysis by a calcite Wollaston prism. Lenses on either side of the prism collimate the light through the prism and refocuses. The Fabry lenses following that follow image the light onto the detectors. All optics in HIPPI have an anti-reflection coating covering wavelengths between 350–700 nm.

HIPPI’s detectors are high quantum efficiency ultra-bialkali photomultipliers (43% QE at 400 nm), which have lower noise than the avalanche photodiodes used in PlanetPol.

A Thorlabs NR360S NanRotator rotates the optical system form the collimating lens through to the detectors about the optical axis. By rotating this portion of HIPPI relative to the modulator 90◦ the sign of the polarised light is changed. This contributes a “second stage chopping”, eliminating some systematic effects [178]. PlanetPol used a similar method of rotational second stage chopping.

HIPPI is also relatively inexpensive to manufacture. This is due in part to the use of pre-manufactured, widely available, high quality optical components along with some components (mostly casings) being built with a 3D printer. The components made with the 3D printer are comprised of a polymer (ABS plastic) and thus had their measure- ments and structural integrity tested to ensure no critical mophing would occur. HIPPI was built by a team of just a few people and is a small (fitting onto a 300 mm2 alu- minium optical breadboard), lightweight (10 kg) instrument. It is mounted to the back of the telescope by a mounting plate at 90◦ to the breadboard. Chapter 4. Polarimetry 95

Figure 4.7: An illustration of the basic layout of HIPPI. Note that the FLC modulator and filter wheel are forward of the rotating component. Image: Bailey et al. [58]

4.2.1.1 Ferro-electric liquid crystal modulators

HIPPI has used two types of FLC modulators (the time at which they were switched is discussed in Section 4.2.4 ). One from Micron Technology (LV1300-AR-OEM) is calibrated for wavelengths 400–700 nm with a half-wave retardance at ∼500 nm. The other from Boulder Non-linear Systems (BNS) is calibrated for use at 425–675 nm and also has a half-wave retardance at ∼500 nm. The BNS modulator is slightly larger in diameter at 22 mm opposed to 12.7.

A ±5 volt drive is applied to them in each case, providing good polarisation modulation. The driving waveform is produced via software built in LabView and is a square wave. The frequency of modulation can be set anywhere between 200 Hz and 2kHz. We use 500 Hz for our observations as it is infrequent enough to maintain a wave very close to a square, and frequent enough to keep measurements insensitive to intensity fluctuations. Chapter 4. Polarimetry 96

Both modulators produced internal systematic polarisation with the BNS modulator producing less, making it the current preferred option.

The modulators are electrically equivalent to capacitors of ∼200 nF. They can be dam- aged by a sustained DC voltage. Electronic high pass filters are used to ensure that no direct current or low frequency reaches the device. The FLCs are also temperature sen- sitive; the rate of switching is faster at higher temperatures and the angle between which they switch may change as well. HIPPI’s FLC is therefore mounted in a temperature- controlled lens tube kept at a constant 25 ±0.1◦ C.

4.2.1.2 Photomultiplier detectors

HIPPI uses compact photomultiplier tube modules (PMTs). PMTs have large detectors areas and low dark noise compared their solid state alternatives such as the avalanche photodiodes used in PlanetPol or silicon photomultipliers. The detectors on HIPPI can be easily switched out should the observer wish to use others with different sensitivities. The amplifiers they use have been built with a surface-mount on a compact printed circuit board, fitting onto the back of the small PMT module which slides into a 3-D printed casing.

The PMTs used for observations of exoplanets as presented in this these were Hama- matsu (H10720-210) PMT modules with ultrabialkali photocathodes [179]. The quantum efficiency is 43 % at 400 nm. They operate from a single 5V supply.

The rate of photon aquisition in HIPPI is too high to use the PMTs in photon counting mode so a transimpedance amplifier is used to amplify the photocurrent. The amplifiers were designed and built specifically for HIPPI utilising ulta low noise (input current noise ∼0.1 fA Hz1/2) operational amplifiers (Texas Instruments OPA 129). The tran- simpedence can be switched remotely between 105, 106 and 107 V/A.

The PMT’s high tension supply voltage can be set to voltages between 500 and 1100 V, which corresponds to a variation in the gain from 5×103 to 3×106 e−/ν. This ability to remotely vary the photomultiplier and amplifier gain has been central to providing HIPPI with a large dynamic range, allowing it near photon noise limited performance whether observing bright stars or distant planets. Chapter 4. Polarimetry 97

4.2.1.3 Data Acquisition

HIPPI uses software built through LabView (National Instruments) run on a rack mount computer (Intel quad core i7, 8 GB RAM, two 1 TB disks). The interface driving the FLC and acquiring data from the detectors utilises two data acquisition modules (Na- tional Instruments PCIe 6341) each providing 16-bit analog input and output channels. The drive produced by the software is output through one of the modules. A digital trigger signal is generated by the rising edge of the square wave input and fed to both modules allowing the retrieved data input to be in phase with the modulator wave- form. The signals from the detectors are read via analog channels for each module (see schematic in Figure 4.9).

Figure 4.8: A schematic diagram of HIPPi’s data acquisition system. Image: Bailey et al. [58]

The software provides control over the LFC temperature, filter wheel, rotation of the Wollaston prism and detector section, and detector gain and the high tension voltage setting for the detectors.

The input channels from the detectors are sampled at 10 µs intervals with an integration time of 1 second during operations, retrieving 100,000 data points for each channel. The data are folded within the software over the cycle. When operating at 500 Hz this thus results in 200 points from each channel. Each channel of course has an opposite sign as they collect light seperated by the Wollaston prism (see Figure for clarfication). Chapter 4. Polarimetry 98

Figure 4.9: The wedges of bifringent material (calcite) in a Wollaston prism separate polarised light by its sign. Image: from Wikipedia user ”fgalore”

As mentioned previously, HIPPI is driven by a square wave form, meaning there is a short (100 µs) delay in the signal, also affected by the time constant of the amplifiers. The waveforms are displayed for the user and their amplitude corresponds to the strength of the polarised signal. A rough estimate is produced by an on-the-spot data reduction pipeline built into the software to allow the user to judge the signal on-the-fly and detect problems early on although it does not include the dark subtraction or efficiency correction. These and other corrections are applied to the data, as discussed in the next section, for the final measurements presented in this thesis.

4.2.2 Data Reduction

In polarimetry, a Mueller matrix is a 4 × 4 matrix used to describe the change in po- larised light as it moves through a system or material. It is a transformation of the input polarised light matrix (a vector, or 1 matrix) to the output—or measured— polarised light matrix. Differential transmission of orthogonal vibration, phase delays with differ- ent values for orthogonal vibrations and rotations of the of linear vibrartions may all be expressed through the Mueller matrix using different combinations of elements.

The polarisation effects within HIPPI are thus described by a Mueller matrix accounting for each of it’s pertinent optical elements in order. The parameters in the system overall will vary over an integration as the voltage applied varries.

If we write the relation between the input and output polarised light vectors (sin and sout respectively), and the Mueller matrix of the optical system, M: Chapter 4. Polarimetry 99

sout = M sin (4.5)

We can describe the full integration over changing parameter space by using a system matrix, W. This represents the ordered matrices describing the components in order and can be represented as an n × 4 matrix wherein each row is a state of the system corresponding to a single data point in the modulation curve. If we multiply the input Stokes vector by the system matrix, we retrieve a vector x for n observed intensities through the modulation cycle.

x = W sin (4.6)

The n rows of the system matrix W are the top rows of the Mueller matrices for HIPPI for each state n within its cycle. Only the top row, which determines the intensity of the output light is needed because HIPPI is designed only to measure the intensity, for a state of the system, at the detector.

The optical components of HIPPI are the FLC and the Wollaston Prism. The FLC is a retarder. A perfect retarder has a Mueller matrix of the form,

  1 0 0 0     0 1 0 0    (4.7)   0 0 cos δ sin δ   0 0 − sin δ cos δ wherein δ is the retardance. Taking into account the angle to the fast axis of the retarder, φ, and simplifying cos 2φ = C and sin 2φ = S, we describe HIPPI’s retarder, the ferroelectric liquid crystal modulator, as:

  1 0 0 0    2 2  0 C + S cos δ SC(1 − cos δ) −S sin δ MRet =   . (4.8)  2 2  0 SC(1 − cos δ) S + C cos δ C sin δ    0 S sin δ −C sin δ cos δ Chapter 4. Polarimetry 100

Additionally we should add a linear depolarisation component to the FLC [180]. We can describe this by an additional Mueller matrix as,

  1 0 0 0     0 1 − d 0 0  MDepol =   (4.9)   0 0 1 − d 0    0 0 0 1 − d wherein d is the degree of polarisation.

The Wollaston prism’s two calcite slabs act as two perpendicular polarisers. By simplify- ing η, the angle of the polariser’s axis to that of the incoming beam, into the expressions cos 2η = C and sin 2η = S we can describe the polariser with a Mueller matrix of the form,

  1 eC eS 0    2  eC eC eSC 0 MP ol =   (4.10)  2  eS eCS eS 0   0 0 0 0 wherein e is the polariser efficiency. Typically Wollaston prisms have a very high effi- ciency so we assume e = 1.

From the above matrices (4.8, 4.9, 4.10) we can combine to form the Mueller matrix for HIPPI,

M = MP ol MRet MDepol (4.11) and from this the system matrix. The values of φ, η and d will vary throughout the modulation, with n rows in the matrix corresponding to the n points throughout the modulation. The retardance, δ does not vary over the course of the modulation. Instead it varies with wavelength; it is a half-wave (πradians) only at one wavelength. This effectively reduces the amplitude of the modulation by a factor of (1 − cos δ)/2. In practice we assume a half-wave retardance in reduction and account for the wavelength Chapter 4. Polarimetry 101 dependence by encorporating this into an efficiency model which is also confirmed by observations of standard stars.

With the system matrixW now defined we can invert its relation to Equation 4.17, by using its pseudo-inverse, W+ [181]. This allows us to retrieve the input Stokes parameters in terms of what we observe through HIPPI rather than apply the optical effects to the incoming beam.

+ sin = W x. (4.12)

Since HIPPI does not measure circularly polarised light, we use only the first three columns of W+. This provides a least squares estimate of the components in the vector sin.

  Iin     Qin sin =   (4.13)   Uin    (V )

We then divide Stokes Q and U by I to retrieve the normalised values.

To calibrate the varying components of the system matrix throughout the cycle, HIPPI was tested in the labratory with a controlled polarised light source stepped through a full rotation. The intensity with angle was fit to a modified Malus Law (see Bailey et al. [58] for detailed discussion of the cailbrations.

4.2.2.1 Statistics

The coordinate frame of HIPPI is always chosen to match the calibrated rotator posi- tions; this means that most of the data points taken are for a particular Stokes parameter. The data points for the other Stokes parameter have greater relative noise per data point and from the instrinsic polarisation of the modulator. The off-axis Stokes parameter is therefore discarded per integration. Switching positions then allows the other Stokes parameter to be obtained. Chapter 4. Polarimetry 102

The error is calculated from the standard deviation of the integration data points, then combined with the statistical errors for each position and averaged by dividing by the square root of the number of statistical errors combined.

4.2.2.2 Efficiency calibrations

For the exoplanet polarised light detections we have utilised a bandpass model for the efficiency correction. In [58] these models were checked against measurements of stan- dard polarised stars. A bandpass model is useful because the effective wavelength can vary based upon the stellar type as the bands are quite broad. For this we used an approach similar to that described in Hough et al. [170].

The bandpass model begins with an input stellar model. For the exoplanets in this thesis, these were obtained from the Castelli & Kurucz stellar atmospheres catalogue [182] for the appropriate stellar type. The spectral energy distribution (SED) is modified for extinction based upon the model of Cardelli et al. [183].

A model of the transmission though Earth’s atmosphere for Siding Spings Observatory (where the AAT is located) is created with parameters such as water vapour and air mass adjusted for the observing conditions, and parameters such as Rayleigh scattering included. This is then applied to the SED to provide the transmitted stellar spectrum.

The effects of the components of the instrument are then applied via an instrument response model which takes into account the transmission of the filters, the cathoode’s sensitivity in the PMT (mA/W) from the Hamamatsu data sheet, and the absorption of the calcite prism.

If we call the output detector signal with wavelength then S(λ), we can decribe the effective wavelength of the observation by,

R λS(λ) dλ λ = (4.14) eff R S(λ) dλ wherein the integral is over all wavelengths at which S(λ) is non-zero.

The efficiency correction fro the polarisation is described by, Chapter 4. Polarimetry 103

R e(λ)S(λ) dλ P = (4.15) c R S(λ) dλ wherein e(λ) is the wavelength dependence of the modulation efficiency. This varies primarily in accordance with the retardance with wavlength for an FLC. The relationship of the optical path difference, ∆, for an FLC is from Gisler et al. [184].

λ0  1 1  ∆ = + Cd 2 − 2 (4.16) 2 λ λ0 wherein λ0 is the half-wave wavelength, C is a parameter for describing the dispersion in the bifringence of the FLC material and d is the thickness of the FLC layer. Cd can be treated as a single parameter. Fitting this relationship to laboratory measurements we are able to retrieve these parameters. The BNS and Micron modulators used in HIPPI have very similar parameters (see Bailey et al. [58]).

The modulation efficiency can be calculated by,

e  ∆ e(λ) = max 1 − cos 2π (4.17) 2 λ

wherein emax is the peak efficiency at wavelength λ0. This number would ideally be equal to one. HIPPI achieved 0.98 with laboratory measurements. An illustration of an application of the bandpass, with the above described components, to a G0 V star is available in Figure 4.10.

4.2.3 Performance

HIPPI’s calibrations with polarised and unpolarised standard stars at the AAT showed the polarimeter to have high precision—0.01% on bright stars and within 0.1◦ of the position angle—and to be very sensitive, acheiving 4.3 ppm conservatively. The po- larimeter is nearly photon-noise limited, as it measures within the error, for very bright stars. Taking into account internal error from noise and effects of the photomultiplier tubes the sensitivity may be closer to 3 ppm. Chapter 4. Polarimetry 104

Star Date Filter Measured Expected P(ppm) θ (deg) Efficiency P(ppm) θ (deg) Efficiency HD 23512 Aug 28 g0 18 852 ±37 30.5 ±0.1 87.8 21 469 29.9 90.0 HD 147084 Aug 29 g0 33 919 ±11 32.0 ±0.1 90.1 37 664 32.0 91.0 Aug 30 g0 33 972 ±12 32.0 ±0.1 90.2 37 665 32.0 91.0 Aug 30 r0 34 910 ±17 32.1 ±0.1 81.9 42 619 32.0 84.2 Aug 30 500SP 29 349 ±17 32.0 ±0.1 81.6 35 958 32.0 80.7 Aug 31 500 SP 29 337 ±12 31.9 ±0.1 81.6 35 956 32.0 80.7 HD 187929 Aug 28 g0 15 450 ±9 93.5 ±0.1 91.1 16 950 93.8 91.2 Aug 29 g0 15 493 ±9 93.6 ±0.1 91.3 16 960 93.8 91.4 Sep 2 g0 15 560 ±13 93.6 ±0.1 91.8 16 944 93.8 91.1 Sep 2 500 SP 14 213 ±16 93.8 ±0.1 85.7 16 570 93.8 84.7

Table 4.1: Polarised standard star measurements for determining the accuracy of HIPPI in different filters. From Table 5 in Bailey et al. [58]

HIPPI also benefits from a good dynamic range. This has allowed for its application to a variety of objects and calibrations with a range of standard stars. HIPPI is limited at the low end by dark noise from the PMT at about 16th magnitude.

The standard stars used in our observations are both polarised standards, for which the polarisation level is well established and consistently measured to the same approximate values (see table 4.1), and non-polarised standards (see table 4.2), which have no intrinsic or interstellar polarisation present. Observations of these objects allow the sensitivity of the polarimeter and instrumental polarisation to be established.

The bright standard polarised stars are used to calibrate HIPPI and determine its ac- curacy in each filter. These calibrations are then used to correct observations of less established objects (like planet-hosting systems) for efficiency. The unpolarised stan- dards are used to estimate the telescope’s polarisation and, by monitoring the variation (standard deviation) in the measured polarised light over time, to determine how sensi- tive HIPPI is. Chapter 4. Polarimetry 105

Star Date Filter P(ppm) θ (deg) BS 5854 Aug 28 g0 35±5 113±6 Aug 29 g0 46±4 115±17 Aug 30 g0 50±4 114±4 Sep 2 g0 45±5 110±6 Average g0 44±2 114±3 Beta Hyi Aug 28 g0 52±3 113±4 Aug 29 g0 62±3 106±3 Aug 30 g0 58±3 109±4 Aug 31 g0 52±3 106±4 Average g0 56±2 109±2 Sirius Aug 31 g0 55±1 112±1 Sep 2 g0 48±4 108±5 Average g0 51±2 110±3 Adopted TP g0 48±5 111±2

Table 4.2: Low polarisation star measurements for determining the telescope polari- sation in the g0 filter. From Table 3 in Bailey et al. [58].

4.2.4 Exoplanet Observations

Observations of the four exoplanets discussed in this thesis were taken over three runs in August of 2014 and May and June of 2015 at the Anglo-Australian Telescope near Coonabarrabran, NSW, Australia. The AAT is a 4m, equatorially mounted telescope, which, while larger than many of the telescopes used previously to detect polarised light from exoplanets, presents a hurdle in removing telescope polarisation since the telescope cannot be rotated on axis. This was overcome by taking observations of standards throughout the campaign, taking sky measurements at each angle throughout, and by taking measurements at otherwise redundant angles to remove the degeneracy.

A previous run on June 2014 included the nights of the 8th through the 12th used for calibrations of HIPPI. The first night was classed as gray time, and the remainder were bright time. The sky at 90◦ to the moon was avoided when possible to avoid Rayleigh scattering effects although the sky subtraction also corrects for this.

The August 2014 run included four nights of observations for HD 189733b (28th through 31st), and five nights of observations (12 observations) for WASP 18b (28th through the Chapter 4. Polarimetry 106

31st and September 2nd ). The first two nights (28th and 29th) were dark, the rest were classed as gray. Typically three sets of observations are taken in a row for an object to reduce error. For WASP 18b these observations are not binned because the planet’s is only 0.94 day long, therefore three, one-hour sets would cover about one-sixth of the orbit, over which the polarised light signal could vary dramatically. The longer orbit of HD 189733b (2.2 days) allows for all three sets per night to be binned together. A fourth observation of the system taken on the night of the 31st is omitted from fitting as an outlier because it was taken partially before and partially after moonset, while the moon was at ∼90◦ from the object maximising the Rayleigh scattering from the moon in our field.

Each sequence consists of a number of repeats, each repeat consists of a sequence of rotations of the aft, independently rotating, section of the polarimeter as shown in Figure 4.7 which includes the Wollaston prism and detectors. The rotation is sequenced in an ABBA pattern: positions A and B are orthogonal, effectively measureing the maxima and minima (sign change) of a Stokes parameter in the idealised case that the polarisation is exactly aligned with the polarising filter. This measures only one Stokes parameter at a time; the instrument is rotated 45◦ and the sequence repeated.

A target is typically measured 2-5 times in a row per night. A measurement consists of taking data at four position angles of the telescope Cassegrain rotator at 0, 45, 90 and 135 degrees. These angles provide data for both Stokes parameters with a redundant angle each to reduce systematic error. For planetary system targets, sky measurements are taken at each of these four angles, typically after the target observation for that angle. The sky measurements require shorter integration times.

At each rotator position, there are a set of integrations, and within those integrations there are a number of modulation points (i.e. sampling points) which comprise the modulation curve.

The data are binned by averaging; their errors based on a weighted average. The data then have an efficiency correction applied. The bandpass, which determines the effi- ciency is based upon the absolute visual magnitude, the airmass, the extinction which is estimated by the distance and the total to selective extinction set to RV = 3.1 which is reasonable for local stars. The maximum polarisation was presumed to occur in blue visible light for the exoplanet systems, since hot Jupiters are expected to be good Chapter 4. Polarimetry 107

Rayleigh scatterers. The object’s expected bandpass efficiency is then dependent upon the spectrum and the filter used as illustrated for a general case in Figure 4.10.

Figure 4.10: An illustration of the bandpasses retrieved with HIPPI for a dummy stellar spectrum for a G0 V star.

The May 2015 run produced two more nights of observations for HD 189733b (23rd & 26th), two for τ Boo b (23rd & 26th), and five for HD 179949b (22nd through 26th). The first two nights (21st and 22nd) were dark, the rest were gray.

The June 2015 run included one more observation for HD 189733b (26th) and two more for WASP 18b (on the night of the 27th). Both the 26th and 27th were bright nights.

The first observing run, in May of 2014 was used primarily as a commissioning run with observations of standard stars (polarised and unpolarised) performed over most of the nights. Thin and passing clouds were an issue over the last three nights of the run in particular and so observations of bright stars and solar system bodies were completed. Observations of HD 189733b were also attempted but with the effects of the clouds, a reliable signal could not be detected. Chapter 4. Polarimetry 108

The complete measurements are comprised of:

1. npt modulation points in the modulation curve sampled at approximately 10 µs producing about 200 data points in a second after folding at 500 Hz.

2. nint number of integrations

3. nrot,A, nrot,B number of rotations of ortogonal angles A and B

4. nrep number of repeats for object

5. 2 channels at orthogonal positions within the rotating section

6. 4 sequences at telescope position angles of 0, 45, 90 and 135◦

The sky measurements are taken after each set, for each angle (i.e. a set of measurements is taken at one angle, then the sky, then at each of 3 more angles, each with a sky follow up). The series of angles is typically repeated 2 to 5 times in a row, each taking about 15 minutes). When binning the data those 2 to 5 observations are combined, except in the case of WASP 18 because the orbit is so short.

Sky exposures are taken before each set of observations for each object and these account primarily for the effects of moonlight.

The sky subtractions per angle account for most instrumental effects along with the standard stars and sky exposures. However the ferro-electric liquid crystal modulator (FLC) used in HIPPI produces intrinsic polarisation likely due to internal reflection between its plates. This is accounted for by turning the internal rotating section of HIPPI so that one of the output channels has a maximised signal, making the angle of the instrument polarisation and the Stokes parameter orthogonal. This is possible because only one Stokes parameter is measured at a time by HIPPI. The effect was also reduced slightly with the use of a different modulator (Boulder Nonlinear Systems) in the August 2014 and May and June 2015 runs.

A new modulator was tested to help account for instrumental polarisation detected in the commisioning survey completed in May of 2014. The ferroelectric liquid crystal modulator from Micron Technology which was used in the May 2014 observing run pro- duced a greater intrumental polarisation than the one from Boulder Nonlinear Systems used in August 2014. Even with the improvement, both produce internal systematic Chapter 4. Polarimetry 109 polarisation at ∼1000 ppm (parts-per-million). This effect is not corrected via the extra rotational angles that account for most other effects, so the effect is corrected for by choosing the angles to measure a Stokes parameter (orthogonal to each other) to have the maximum value of polarised light possible. This is obtainable by monitoring the signal read out live as one moves through the angles. The remaining instrumental effect (on the order of 50 ppm) is removed by utillising four rather than two rotation angles at 0◦, 45◦, 90◦ and 135◦ ensuring that the sign for the instrument’s polarisation reverses with respect to that of the star.

The efficiency estimated to be on average (some variation with the airmass changing was taken into account) 92.6% for HD189733, 87.7% for HD 179949, 87.5% for WASP 18 and 88.6% for τ Boo. There is some margin for error in those estimates since a portion of the infrared light will come from the planet when visible as well.

4.3 Models of Polarised Light

Fluri and Berdyugina [174] describe the derivation of parameters from a fitted, simplified Rayleigh scattering curve either by modelling the light scatter from a Lambertian sphere and then applying Rayleigh scattering for polarisation, or the slightly more robust tech- nique of retrieving both intensity and polarisation from the Rayleigh Law. At the time the paper was written (2010), the small deviations between the two techniques were not a concern as they mainly affect the rate of change between maxima and minima in the polarised light curve at a scale less than 5 parts-per-million. Fluri and Berdyugina [174] also includes a treatment of the size of the star, which matters for hot Jupiters aroud Giant Stars giving up to a 5% error when ignored. The paper also outlines treatments for transit effects. The retrieval provides the inclination, position angle, eccentricity, and the oblateness of the planet when the full Rayleigh Law treatment is used.

For this thesis the simple Lambert-Rayleigh model is used because the error in HIPPI is nearly the scale of the variations between the two approaches (a few parts-per-million). A more thorough, full Rayleigh treatment of the scattered light is currently being developed to be integrated with VSTAR (based upon VLIDORT [185]) since polarimeters today can nearly acheive the level of accuracy that would warrant this treatement. Chapter 4. Polarimetry 110

4.3.1 Polarised Light Curve

“The First Option”

The intensity of the light can be calculated angularly for the scattering light curve form a Lambertian sphere approximation. Rayleigh scattering is then applied to derive the polarisation. In other words the curves for the scattered light and the Rayleigh scattering per phase angle are summed to produce the resultant polarised light curve.

For the simplified Lambert-Rayleigh curve, the parameters are the inclination of the planet’s orbit (from the plane of the sky) i, the radius of the planet RP , distance to the star d, the geometric albedo of the planetAG, and the position angle, PA. The interstellar medium will create an offset from zero for the curve in Stokes Q and U. Multiple scattering is taken into account with a scaling factor.

For a phase angle, θin degrees, the projected phase in radians is,

 π π  φ = arccos sin(θ − ) sin(i ) . (4.18) 2 180

The Lambertian phase function is then (based on equation 3 in Seager et al. [153]) is,

(π − φ) × cos φ q = sin φ + (4.19) π

The scattering angle, ϕ, is just the inverse of the phase ratio,

ϕ = π − φ. (4.20)

And the polarisation phase function, pp, to be combined with the Lambertian reflection is then,

sin2 ϕ pp = . (4.21) 1 + cos2 ϕ

And the combined polarised light curve is then,

R 2 P ol = P × q × pp × A . (4.22) d G Chapter 4. Polarimetry 111

To then retrieve Stokes Q and U from this curve,

2π × PA Q = Q + P ol × cos (4.23) ISM 180

2π × PA U = U + P ol × sin (4.24) ISM 180

4.3.2 Polarised Light Contribution from Hypothetical Atmosphere

“The Second Option”

A more complete treatment is to derive both the intesity of the scattered light and its polarisation from the Rayleigh Law.

dI(τ; µ, φ) µ = I(τ; µ, φ) − J(τ; µ, φ) (4.25) dτ

dI µ = I − S (4.26) dτ

κ B + σ S S = C R R (4.27) κC + σR

0 The Rayleigh source function, SR, is expressed by the Rayleigh phase matrix P(µ, µ ) [174] while the the thermal component B is dependent upon the partical size and while always non-zero, is not significant unless the partical size is large [186]. In blue light the thermal component from the star and the planet itself can be ignored.

1 S(τ, µ0) = P(µ, µ0) I(τ, µ) (4.28) 4π

For single scattering this simplifies further,

−τ I(τ, µ) = I∗e µ (4.29) Chapter 4. Polarimetry 112

VSTAR was first developed to be used on solar system planets and thus focused on a treatment of radiative transfer based on the DISORT code which solves for reflected light in atmospheres with low temperatures. The VSTAR code, being modular, was able to be expanded to include the non-directional reflected light from exoplanets at any temperature line lists for major constituents were available for. Capabilites for transmitted light were also added to VSTAR for cases on Earth (looking at a star through our own atmosphere, which is used in telluric removal for our group in ATMOF as well as applications monitoring atmospheric consentrations of greenhouse gases) and to transitting planets.

What remained was a model of the reflected light from an exoplanet that is polarised.

The following sections report the findings and confirmations of emissions, scattered light and polarised scattered light detections for the systems studied in this thesis. These planets all have had atmospheric transfer models made and fit to a variety of data sources and have also been observed with HIPPI polarimeter. The polarimetric models and measurements, and how they relate to the atmospheric models is discussed in consecutive sections. Chapter 5

HD 189733b

5.1 Introduction

HD 189733b is one of the best characterised exoplanets to date (see references throughout this chapter). It was an obvious test case for VSTAR for this reason. Applying VSTAR to HD189733b for secondary eclipse and primary transit spectra allowed us to calibrate the models for their application to less well-studied exoplanets and provided a proof of VSTAR’s robustness.

The planet is in a 2.21857 day orbit at a semi-major axis of 0.03142 AU [187][165]. The planet was initially detected via RV measurements with spectroscopic and photometric follow-up confirmation [188]. Since the planet transits, the radial velocity measurements can be used in conjunction with transits to fit orbital parameters, and the combined light can be compared when it passes in front of or behind its host star.

The planet is slightly more massive than Jupiter at 1.144 MJ . Its radius is estimated to be 1.138 RJ in V band [189] which will vary depending upon the transmission properties of the atmospheric constituents at different wavelengths. The orbit of the planet is circular [165] as would be expected of such a short orbit. Planets in very close orbits such as this, are also be expected to be tidally locked with one side always facing the host star, possibly causing a significant thermal gradient dependent upon radiation driven mixing.

113 Chapter 5. HD 189733b 114

The planet’s host star, HD 189733A, is actually part of a binary. The primary star, which the planet orbits, is a K1.5 V type star with a nearly solar metallicity (Fe/H ≈ -0.03). The secondary star in the binary HD189733B (not to be confused with the planet in lower case, and often denoted with a different name), is a well seperated M4 star.

The Rossiter McLaughlin1 measurements of the system’s radial velocity curve as the planet transits suggest its orbital plane is inclined 85.51 degrees to the rotational plane of the star. Planets are thought to form in orbits coplanar with the star’s rotational equatorial plane, so this orbit is unusual in that regard. However mechanisms such as the Kozai mechanism [34] suggest that extrasolar giant planets which formed further from their stars, at distances more akin to our own solar system’s giant planets, could be driven inwards by the transfer of energy from an the inclination of exterior binary stellar companion to the planet’s eccentricity which eventually stabalises at a closer distance to the primary (see: Addison et al. [164] for further description and application of the RM effect and Kozai mechanism).

The environment of a planet should be considered as well. We can see the effects of the largely sun-driven space in our own solar system on the planets. Stellar activity can increase the rate that a planet’s atmosphere escapes and complicate observations. HD189733A is a BY Draconis type variable star: a star whose brightness varies due to star spots moving across its surface. This has to be taken into account when interpreting radial velocity and transit observations (spots both dim the star and produce doppler effects). In addition this could affect the polarised light recieved from the system. If broadband photometry over different wavelengths during transit, starspot activity can affect some wavelengths more than others being generally cooler regions.

The magnetic fluctutions of the parent star are a serious consideration for planets orbit- ing very close to them. The enhancement to the stellar magnetic field’s driving dynamo by a closely orbiting planet can influence the evolution of the system [190]. Recombi- nation events in the stellar atmosphere can also drive atmospheric escape for the planet [191, 192].

1The Rossiter McLaughlin effect uses the small deviation in the radial velocity curve of the system (convolved curves) as a transiting planet blocks part of the rotating disk of the star, masking the star’s spin contribution to the RV curve. Chapter 5. HD 189733b 115

Starspots can also complicate polarimetric observations by creating an inhomogenatity in the radial symmetry of the star, so that the polarised light from the limb does not cancel itself out [193].

5.2 Atmospheric Characterisation

HD 189733b has the benefit of being already well studied, with data ready for analysis. Compared to the other exoplanets in this thesis, the pressure-temperature profile is already constrained to some degree, allowing the chemical model and ensuing spectral model to be honed more precisely.

5.2.1 Context

5.2.1.1 Observations

Most of the observations used to characterise the atmosphere of HD 189733b and its environment come from two space telescopes: Hubble Space Telescope (HST) and (“Spitzer”). Other telescopes have had important contributions to its characterisation. In 2008 Redfield et al. [194] impressively detected the sodium doublet from the ground using the Hobby-Eberly telescope at McDonald Observatory. The spectrum however, suggested strong absorption and a cloudless atmosphere for the terminator, which is opposed to most other transit observations.

Bakos et al. [195] combined transit measurements from other ground based telescopes such as the Submillimeter Array on Mauna Kea (SMA), TopHat at McMurdo in Antarc- tica, the Observatoire de Haute-Provence, with those of the space-based telescope, the Wide-Field Infrared Survey Explorer (WISE) to provide very accurate transit timing measurements for the system. Findings from Keck’s Near InfraRed SPECtrograph (NIR- −3.4 SPEC) placed a flux limit on the planet in the 2–2.4 µm region at FP /F? < 10 ) with a non-detection [196].

Even the space based Microvariability and Ocillations of STars satellite (MOST) has contributed to research of HD 189733b by determining there were no companions (down to about 1-1.5 R⊕)[197]. This was an important discovery early in the characterisation Chapter 5. HD 189733b 116 of the planet not only because additional planets would complicate atmospheric charac- terisation but also because the lack of planets interior to hot Jupiters could be insightful into how the planets form.

Spitzer The space-based infrared telescope, Spitzer has provided the astronomical com- munity with a great deal of information about HD 189733b. Data have come via Spitzer’s InfraRed Array Camera (IRAC), InfraRed Spectrograph (IRS) and its Multiband Imag- ing Photometer for Spitzer (MIPS). The interpretation and reduction of the data from these instruments is perhaps less disputed than, say, NICMOS on HST, but the four wavelength channels of IRAC in particular have had a great variety of treatments.

The IRS data taken for the dayside secondary eclipse of the planet shows a great deal of scatter towards the red end. In Grillmair et al. [198] the authors suggest the scatter is from unaccounted for systematic errors and treat the scatter as uncertainty in the measurements. The flux measured by different parts of the array can vary due to the tilt of the fitlers. In my models I fit generally to the trend of this data. Some degree of the unsual slope can be fit with non-equilibrium species like hydrogen cyanide (HCN) [72].

IRS produces low resolution (R ∼60-130) spectra at 5.3–14 and 14–40 µm, or high resolution spectra at 10–19.5 and 19–37 µm. In addition bandpasses centered at ∼16 and 22 µm are availble through the telescopes “peak-up” mode which offsets the telescope.

The four bandpasses (centered at ∼3.6, 4.5, 5.8, 8.0 µm) available from IRAC have often been reanalysed.In some cases as with its two shortest wavelength channels, 3.6 and 4.5 µm, this has dramatically changed the measurement in a region that is vital to understanding whether the dayside of HD 189733b is in equilibrium [73].

MIPS is sensitive to longer wavlengths (broadbands at ∼24, 70 and 160 µm). For HD 189733b, only the 24 µm band has been used in published measurements. Along with data from IRAC, MIPS was used to determine the temperature profile for HD 189733b lacks an inversion, contrary to some other hot Jupiters [199].

In 2014 Todorov et al. [200] revisited the Spitzer emissions data for HD 189733b with a new approach to the removal of the systematic errors. They confirm general features such as the water features seen in Grillmair et al. [198] while refining the data. This Chapter 5. HD 189733b 117 allows it to be better fit to models, which they adopt primarily from the Burrows models [201]. This refined Spitzer spectrum is used in my model fits.

Hubble Space Telescope

The Hubble Space Telescope has proven to be a valuable investment for many topics in astronomy, not the least of which is the characterisation of exoplanets. A great number of observations of the HD 189733b system have come from this telescope’s instruments. Successful observations of the transit and secondary eclipse have been performed with HST’s Adavanced Camera for Suveys (ACS), Space Telescope Imaging Spectrograph (STIS), Wide Field Camera 3 (WFC3) and Cosmic Origins Spectrograph (COS). An additional instrument, the Near Infrared Camera and Multi Object Spectrometer (NIC- MOS) provided some detailed data but with some controversy. Unphysical data points lead to a heated debate on the reduction and interpretation of the data.

Unusual issues (more familiar ones like dark current and amplifier glow are more readily accounted for) present in the NICMOS instrument include “super-shading” where the shading bias across a quadrant as the pixels are read out will vary in intensity over time, bias jumps caused by detectors being read while others are being reset, and most notably, the count rate non-linearity (in addition to the expected and accounted-for typ- ical count non-linearity) which varies the intensity of the light measured dependent upon the amount of light measured and varies additionally with wavelength. The count-rate non-linearity also varies between arrays.

In June 2007 a routine to correct this count-rate variation was distributed by the Space Telescope Science Institute. The initial version contained an error which was subse- quently updated in the October 2007 version.

Shortly after these corrections became available spectral observations with NICMOS (covering ∼1.5 – 2.5 µm) of HD 189733b in transit were released in a preprint by Swain et al. [202] in 2008 2. These transit spectra showed evidence of molecules ( water, carbon monoxide) and a limit to the abundance of methane. Secondary eclipse measurements with NICMOS were published by Swain et al. [203] the following year, showing evidence

2I realise it is unconventional to refer to preprints if they were subsequently published but I find the minor changes and time line are easier to understand in the case of the first few years of NICMOS data for HD 189733b. Chapter 5. HD 189733b 118 of a few species but with unphysical data points at the blue end. Narrowband observa- tions (1.87 and 1.66 µm) of the transit of HD 189733b produced data that showed no water features but rather evidence of haze (higher, flattened spectra) [204].

In response, to the inconsistencies in NICMOS’ measurements, a serious review of the treatment of the data ensued. A paper (and preceeding arXiv preprint which was rea- sonably similar) by Gibson et al. [205] reexamined the NICMOS data. They suggested that the original molecular features in Swain et al. [202] were owed to the incorrect treat- ment of systematics. An offset in the baseline function, data selection and decorrelation technique were all cited as possible explainations for the systematic noise that remains in the transit data. The spectrum they reduce from the raw NICMOS data has larger error bars, making any molecular features far less certain.

Figure 5.1: From the Swain et al. 2008 paper (figure 2 in that paper) on the NIC- MOS secondary eclipse spectrum of HD189733b. The effects of combinations of organic species with water on the fits to the NICMOS spectrum. Note that none of the combi- nations are fit to the blue end of the spectrum where one of the values is unphysical. Image credit: M. Swain

A retort to this appeared on arXiv by Deroo et al. [206] (the Swain 2009 group) in response to the arXiv version of the Gibson et al. [205] paper around the same time that it was published. They claimed that Gibson et al. [205] had in fact retrieved the same model a poorly formed instrument model in their treatment accounted for the difference. The data was re-treated again and again in ensuing years. In 2014 Swain et al. [207] reviewed these approaches and a Baysian approach to the molecules detected found that the approaches all showed (two of them strongly) evidence for water. Chapter 5. HD 189733b 119

The results from other instruments have been less controversial.

McCullough et al. [208] obtained transit data with HST’s WFC3 showing further ev- idence of water for the terminator. They combined these observations with previous observations in the visible and infrared to account for star spot effects. Their corrected data combined with the corrected visible light data for is the data set I fit models to in this thesis.

5.2.1.2 Interpretation

The NICMOS data, for all its disputes and different reductions consistently showed evidence of water, a species that is expected to be prevalent on hot Jupiters [153] and is backed up by numerous other observations.

The features of other molecules have been met with far more prevalent skepticism. Both the day and nightside observations fitting water, carbon monoxide and carbon dioxide, and placing limits on methane (e.g. Swain et al. [203] 2009) are disputed and should be considered appropriately.

Along with the contenteous NICMOS observations of water vapour and possibly carbon monoxide and negligable amounts of methane, scientists using Hubble Space Telscope found evidence of molecules and helped to characterise the atmosphere through its other instruments.

Hubble Space Telescope’s ACS instrument helped astronomers to define the radius, effects of starspot and eliminate the possibility of [209]. Early evidence of haze— important for the interpretation of NICMOS data—from a flat transmission spectrum devoid of even atomic (Na, K) spectral features in transit also came from ACS [209]. Similarly the same year the particle size of the scattering haze was estimated to be be- tween 1×10−1 – 1×10−2 µm and requiring a low imaginary component (extinction) to the refractive index [210].

In 2010, Lecavelier Des Etangs et al. [210] using data from ACS, would identify deep Lyman αabsorption requiring that the atmosphere of HD 189733b be escaping. The possibility of an escaping atmosphere is an important one, especially if that escape might be temporally variable, particularly for our polarimetric observations. Chapter 5. HD 189733b 120

Studies using HST’s STIS also have also had multiple contributions to the character- isation of this strange world. Transit observations in visible light have contributed additional evidence for a Rayleigh scattering atmosphere and helped to further charac- terise the impact of star spots on visible light transit observations [211]. While the data from ACS did not show evidence of atomic species through the haze in the terminator, the data from STIS detected the sodium doublet, however largely obscured by the haze (or as suggested, possibly due to a low abundance) [212].

Two pivotal discoveries by the instrument have been evidence of Rayleigh scattering on the dayside (that the planet is a deep blue colour, although there already existed evi- dence of Rayleigh scattering from the polarised light increase towards blue wavelengths observed by Berdyugina et al. [169]), and the Lyman αobservations during the planet’s transit varying over time suggesting the atmospheric escape discovered by Lecavelier Des Etangs et al. [210] actually varies over time [192]. The varying levels of atmospheric escape also correlated to an increase in x-ray activity on the active stellar host [192].

The extent of the haze was furthered by near-infrared observations with the time aver- aged spectra from the WFC3 instrument on Hubble Space Telescope [213]. The contin- ued dominance of the haze into the near infrared differed from the radius ratios suggested by the NICMOS spectra and required a more substantial haze (a greater optical depth further down) for the planet. These findings as well as the later WFC3 observations by McCullough et al. [208], which confirmed the continuation of the haze’ effects from the Rayleigh scattering in visible through to the near infrared, are central to the cloud properties I fit in my models.

The McCullough et al. [208] observations also showed water absorption features, con- firming the detection by other instruments in other wavelength regions. For the dayside, WFC3 observed the 1.1–1.7 µm region to confirm or correct the NICMOS data (1.5–2.5 µm) already available but with unphysical data points in the blue end. These obser- vations confirmed the finding of water features in the region but could not constrain other species that had been fitted to the features previously (i.e. water, carbon dioxide, carbon monoxide) [214].

In 2013 Pont et al. [215] combined the STIS, ACS, and WFC3 HST data from transit to the available Spitzer data to find evidence for condensates, which could help explain Chapter 5. HD 189733b 121

Figure 5.2: Figure 5 in McCullough et al. [208] showing the combined treatment of all visible and infrared light available for the transit spectrum of HD 189733b. Points in visible light show a rise from a combination of Rayleigh and Mie scattering and are adjusted to account for starspot effects. Source: McCullough et al. [208] the inhomogenaity of thermal signatures across the “surface” of the planet in spite of being otherwise well-mixed.

Recently, Ben-Jaffel and Ballester [216] utilised Hubble Space Telescope’s COS instru- ment detecting early absorption in the transit (early ingress) via the Ca II ion. This is an important discovery for our models, particularly those of polarised light curves. A sufficient amount of material extended from the planet with strong scattering proper- ties could offset the polarised light signal. Furthermore, ionised material can linearly polarise circularly polarised light (and starspots can create circularly polarised light sig- nals), though the Faraday Effect as we see with other astronomical objects, although typically for longer wavelengths.The exploration of this latter source of polarisation is outside the scope of this thesis, however the former option is explored superficially.

Spitzer’s mid- and near-infrared coverage nicely complements the near-infrared and visi- ble light covered so thoroughly by HST’s instruments. It is from these thorough infrared measurements that we begin to grasp the pressure-temperature profile of the planet which is central to confining other parameters. Chapter 5. HD 189733b 122

In 2006 Deming et al. [217] was able to detect the strong infrared emissions for the first time from HD 189733b using the IRAC 16 µm bandpass, providing a high brightness temperature of 1117 ±42 K. IRAC was utilised again the following year at 8.0 µm to monitor the phase curve of the planet showing a variation in the brightness temperature from 973 ±33 to 1212 ±11 K for the well-mixed planet [218]. However this phase curve had one very strange feature: it was asymmetric with a peak brightness occuring 16.6◦ before superior conjunction, which they attribute to a east-shifted hot spot.

In the same year, photometry in the 3.6, 5.8 and 8.0 µm IRAC bands [219–221] as well as a low resolution spectrum (IRS 7.5–14.7) [222] were obtained and assessed for the transit of the planet. The spectrum was flat and featureless, wheras the broadband photometric channels showed evidence of water features, although some found the errors in some bands to be too large to firmly claim its detection [220, 221]. The possibility that both the featureless spectrum and the variations in the photometric bands could be real lead to the some heights might be isothermal or that clouds could flatten the longer wavelength data.

A similar IRS spectrum was obtained for the dayside but with strong water features [198]. The dramatic scatter seen in the red end of their data was attributed to systematic errors and taken as undertainties when fitting models.

Measurements in 5 different wavelength bands from Spitzer MIPS, IRAC with a reanaly- sis of the 16 µm IRS peak-up band from Deming et al. [217], allowed Charbonneau et al. [199] to determine the planet’s temperature profile to some level, ruling out a profile with a temperature inversion.

IRAC measurements would be reanalysed and revisited in the coming years for the transit and secondary eclipse. These reassesments accentuating the importance of con- sidering the effects of the stellar variability for this system orbiting such an active star [5, 223]. A new measurement of IRAC’s 4.5 µm bandpass would lead [224] to suggest carbon monoxide as the culprit of a feature (a drop in the otherwise ”flat” infrared trans- mission) there. The 3.6 µm IRAC band would be revisted again in 2014 by Morello et al. [225] finding a value between those previously measured and re-measured. Along with the importance and influence of systematic removal this is surely a testiment to need for accurate removal of star spots when trying to take accurate transit measurements. Chapter 5. HD 189733b 123

Spectra from Spitzer’s IRS instrument were also reanalysed in 2014, confirming a water feature near 6 µm [200].

In the midst of this these secondary eclipse and transit observations, phase curves were obtained for 3 other Spitzer bandpasses [73, 226]: MIPS’ 24 µm band and IRAC’s 3.6 and 4.5 µm band. The phase curve from the latter was particularly important, as the excess of carbon monoxide on the nightside and in the terminator would suggest non-equilibrium chemistry was present [73].

It is unclear if the disequiibrium chemistry of the nightside and terminator is present on the dayside as well. As Knutson et al. [73] point out, attempts to fit non-equilibrium chemistry products to the dayside by others [72, 74] have had the inverse effect of what is needed when it comes to adjusting bandpass fluxes. The direction of the exchange between carbon monoxide and methane is highly dependent upon the vertical mixing in a hot Jupiter atmosphere Visscher and Moses [74]. For the dayside of HD 189733b the lower altitudes may have an enhancement in methane and ammonia in the lower atmo- sphere while higher in the atmosphere those species are removed. Other species such as the hydrogen cyanide (HCN) and acetylene (C2H2) are also enhanced by disequilibrium chemistry [72]. Quenching along with photodissociation may drive a complex profile of varying disequilibrium effects for HD 189733b.

This is of course not a comprehensive history of the interpretations of the observations for HD 189733b. Observations of this planet have been amoung the most successful, however contested some of them may be.

Structure

Highly irradiated atmospheres with incident fluxes over 2×108 erg s−1 cm−2 have inflated atmospheres; this inflation is not driven by the irradiation itself. Rather, the collapse of the atmosphere from formation is slowed down by the irradiation [227] suggesting that many hot Jupiters may either form in situ or have early migration events within the first 1×107 years or so. The amount by which the planet is inflated therefore depends on the mass of the planet itself [228]. Ohmic dissipation can also heat the interior and drive inflation, but requires a strong magnetic field [120].

A further interaction between the closely orbiting planet and stellar magnetic field, a shock wave, can provide insight into whether or not the planet and stellar magnetic Chapter 5. HD 189733b 124

fields are indeed strong currently. The offset of a shock wave preceeding a planet is potentially detectable in the asymmetry of the light curve and is related to the strength of that planet’s magnetic field [66]. A relationship between the radius of the planet and of its magnetic field, dependent upon the offset bow shock, is directly relatable depending on the strength of the magnetic field: for a planet with a magnetic field of 14 G, and a star with a 1 Gauss magnetic field for example this ratio will be about 8.6, for a star with a 100 Gauss field the radius ratio would be about 1.9 [66]. The ratio between the magnetic field of the star and planet (B∗ and BP respectively) is related to the ratio of the star’s radius to the orbital distance (R∗ and Rorb) and the stand-off radius of the planet’s magnetic field (where the bow will form, rm) compared to the radius of the planet itself by equation 6.5.

3 R∗/Rorb BP = B∗ (5.1) RP /rm

The magnetic field of the host star in this case is ∼20 – 40 Gauss [193, 229]. We can estimate the strength of the planet’s magnetic field from the equation 6.5 and the stand off distance of the bow shock from the planet estimated at 16.7 RP from early ingress of secondary eclipse as measured by Ben-Jaffel and Ballester [216]. Taking the larger estimate for the stellar magnetic field of 40 Gauss, this would imply that the planet’s magnetic field is ∼5.3 Gauss (this is also derived in Ben-Jaffel and Ballester [216]), which is comperable to our own solar system planet, Jupiter. Upper limits placed by radio non-detections of the planet would suggest that the magnetic field of the planet is actually quite weak[230, 231].

As well as lingering inflation, planet’s atmosphere appears to be escaping. HD189733b was the second planet found to have evidence of an evaporating atmosphere, [210]. The width of the HI Lyman-α line is a diagnostic for collisional excitation in an atmosphere [210]. Transit light curves of HD 189733b centered about the HI Lyman-α line in visible wavelengths show a 5% absorption around Lyman-α (corresponding to a change in the radius) which suggests that the planet is losing hydrogen at a rate of 109 to 1011 g/s.

The line width of Lyman-α in these Hubble Space Telescope observations requires either a 1.65 RJ cloud with a velocity of ν = 150 km/s or core absorption of 20%. In the case of the former, the velocity exceeds the escape velocity for that altitude (49 km/s) and Chapter 5. HD 189733b 125

the latter case would require clouds past the Roche limit at ∼ 4 RJ . Thus, in either case the atmosphere would be evaporating. A larger EUV flux will correspond to a larger escape rate and could be measured independently. Both ionisation and collisional excitation can drive atmospheric escape [232]. If driven by the EUV radiation from the star, the Lyman-α width of 0.61 Angstrœms˚ suggests an EUV (extreme ultraviolet: 10 to 124 nm) flux from the parent star to be ≈ 20 times that of the sun.

The secondary eclipse spectrum is flattened in near infrared and shows evidence of Rayleigh scattering, possibly indicative of the presence of a scattering aerosol haze.

Circulation models of hot Jupiters are particularly important as some seem to have better heat redistribution than others. In the case of HD 189733b, some observations are available from temperature mapping. Temperature maps can illustrate thermal gradients allowing astronomers to infer wind and circulation patthens.

In 2007 Knutson et al. [218] retrieved a very detailed map by monitoring the phase curve of HD 189733b 5.3, producing longitudinal slices of the planet’s thermal signa- ture. From this the offset hot spot was detected as well as a further delay in secondary eclipse ingress. The tremendous varaition in temperature across the planet can be in- terpreted a extremely high winds across the planet with a mid-lattitude jet. Theoretical extrapolations of the temperature map lead to detailed wind maps–the first of their kind— for HD189733b (and HD 209458b) by Showman et al. [233] in 2009 and, en- corporating magnetic field effects and atmospheric pressure, by Rauscher and Menou [234, 235] in 2013. Showman et al. [233] also discusses the effects on the spectrum that the dramatic phase variations can cause (see: Figure 5.4).

Knutson et al. [218] mapped the temperature across HD 189733b from its phase finding further evidence for the offset hot spot that had been suggested by the offset ingress and egress. Knutson et al. [218], in mapping the temperatures across HD189733b, also found the day and night temperature contrast (at 8µm) to be 973±33K for the minimum (nightside) and 1212±11K for the maximum (dayside hot spot). This relative lack con- trast is indicative of the good mixing on the planet. The hot spot is offset approximately 16±6 degrees east of the substellar point (before opposition, i.e. the phase curve appears unusually hot at ingress). The secondary eclipse seems to occur 120±24 seconds later than predicted, although this is not necessarily a related phenomenon. Chapter 5. HD 189733b 126

Figure 5.3: The temperature map of HD 189733b produced by integrating slices of the phase curve. The map shows a hot spot offset from the substellar point. Image credit: Knutson et al. [218]

The asymmetry of the thermal signature of the planet will produce an asymmetrically changing spectrum through phases. This means that spectra taken during ingress of secondary eclipse will be different than those taken at egress. Potentially, issues could arise if the hot spot is variable. Furthermore the hot spot asymmetry can have an influence on the polarised light curve. The atmospheric escape, which could be related to the hot spot, is variable [192].

Composition and Chemistry

In Tinetti et al. [220], global simulations of the planet suggested a tremendous abun- dance of water (mixing ratio ∼5×10−4) for the planet and indeed for most hot Jupiter −7 atmospheres. Ammonia (NH3) was expected to be relatively rare though ( 10 ). Water has been detected by others on the dayside with bands at various wavelengths such as in Grillmair et al. [198] and Barman [236].

Water, which is detected by these groups, is actually expected to be abundant in the atmospheres of hot Jupiters and effects the region around 4µm within the opacity window Chapter 5. HD 189733b 127

Figure 5.4: The spectrum of the assymetrically heated planet HD 189733b, for six phase angles. The bandpasses are shown at bottom. The emergent flux density is given in (ergs−1cm−2Hz−1) and should not to be confused with the comparitive flux (unitless ratio) used in my secondary eclipse models. Image credit: [233] with abundant emission lines [199].

Swain et al. [203] constrained the water mixing ratio to be between 10−5 and 10−4 in good agreement with the simulated estimate. Also a non-detection of NH3 constrains that mixing ratio to a nil value, also in agreement with Tinetti et al. [220] simulated predictions. Other species were detected such as CO2 and CO with mixing ratios of −7 −6 −4 10 to 10 and 3×10 respectively. CO2 is expected to form in low abundance in exoplanet atmospheres [237], but the NICMOS detection of it in HD 189733b is at a much higher abundance than models suggest, assuming that the planet is in equilib- rium. The unusual abundance suggested by the NICMOS data can’t be explained by non-equilibrium chemistry though: it requires enrichment in metals. This could be ex- plained by the data being faulty; the NICMOS data is unreliable [205] at least in its original forms. The NICMOS spectrum can be fit with a pressure-temperature profile that is strongly isothermal at higher altitudes [238]. In fact reanalysis of the NICMOS −3 data’s CO2 abundance places it even higher (∼1×10 ), furthuring the argument for the possibility of non-equilbrium chemistry.

While methane is spectroscopically difficult to discern from carbon monoxide (CO) with the incomplete coverage of the data available, Swain et al. [203] suggested an upper limit of 10−7 for the species. The spectra from the NICMOS spectrograph seemed to suggest Chapter 5. HD 189733b 128 the presence of methane, while cross-correlation has suggested a better fit for carbon monoxide looking at absorption in the k-band.

Methane is expected to exist in most hot Jupiter atmospheres. If methane is absent from the dayside atmosphere of HD 189733b, the planet would need a driver of non- equilibrium chemistry in order to keep methane from forming. The day-night terminator of the planet appears to have methane present. It is possible that the high levels of ir- radiation the dayside experiences inhibits the stable production of methane.

Like secondary eclipses, transits rely on the alignment of a planetary orbit with our line of sight. Unlike secondary eclipse emissions, transits are best suited for observation in visible light–rather than infrared–as it relies on the gases in the atmosphere absorb- ing the light of the star. Transits also probe different depths of the atmosphere than the emissions since they are more sensitive to the upper atmosphere and dramatically affected by clouds.

To garner information about the planet’s atmosphere, the transit depth is measured (over multiple transit events) in at least two different photometric bands. Transit information is comparitive, describing the projected radius of the planet compared to that of the star and thus is dependent upon the model for the star accurately predicting the star’s radius.

[203] determined a water mixing ratio akin to that of the dayside at 5×10−4. Carbon monoxide (CO) and ammonia (NH3) lines in the available wavelength regions for the transit spectra are degenerate without spectroscopic coverage. Swain et al. [203] deter- mined that either of these elements may be present with mixing ratios on the order of −5 <10 for one or the other. The NH3 required to fit the problematic NICMOS data also presents insight into the question of equilibrium for the planet. In the heavily irradiated upper atmospheres of hot Jupiters, ammonia and methane are photodissociated, form- ing hydrgen cyanide (HCN) and molecular hydrogen in their stead Moses et al. [72]. If, on a well-mixed world, the upper atmosphere of the terminator is in equilibrium while on the dayside it is not, how?

Methane was detected by Swain et al. [75] in the terminator at a much higher mixing ratio than other groups have found for the dayside emissions (5×10−5at the terminator versus ∼10−7 for the dayside). Chapter 5. HD 189733b 129

Transit data for HD 189733b consistently shows a rise in the radius towards blue wave- lengths. This is almost certainly due to Rayleigh scattering. Further evidence for Rayleigh scattering may come from the dayside polarimetric and photometric obser- vations from Berdyugina et al. [169] and Evans et al. [1] respectively. The dramatic increase in radius with shorter wavelength attributed to Rayleigh scattering was con- firmed again in transit recently with the HIPO instrument on the SOFIA space telescope [239].

5.2.1.3 Summary

The data used in fitting my models are from McCullough et al. [208] for the transit. For the dayside measurements I have combined the data from Evans et al. [1] Deming et al. [217], and Charbonneau et al. [199] with corrections from Knutson et al. [73] shown as points at the same (central) wavelength with smaller error bars.

The inclusion of revisted data should compensate for some of the issues outlinned above. Data from Hubble Space Telescope’s NICMOS and the ”noise” in Spitzer’s IRS spectrum should be considered as guides but with some degree of flexibility in their fits.

5.2.2 Models

5.2.2.1 Set Up

The chemical models for HD 189733b were made with the icemodco program, described in Chapter 2. Several pressure-temperature profiles are tested for the dayside and ter- minator. One from Lee et al. [238] is utilised in their optimal estimation retrievals of the dayside composition; although their retrieval was for constant mixing ratios from all Spitzer and Hubble Space Telescope data available at the time. They did this by fitting the spectrum with an F-test with the NEMESIS algorithm. Similarly, Barstow et al. [240] retrieved abundances and a pressure-temperature profile, used here, while also testing the presence of clouds with Spitzer spectra using NEMISIS. With this I test a case with temperature adjusted for the presence of clouds. The third borrowed dayside pressure-temperature profile comes from Todorov et al. [200]. This is also a retrieved profile, using available Spitzer data (including the data re-visited by Knutson Chapter 5. HD 189733b 130 et al. [73]), with fitting via the Monte Carlo method. This includes a small inversion for a scattering haze in the upper atmosphere, however Todorov et al. [200] stated that the absorber was unimportant in the spectral fit. I have also trialed temperature profiles taken from the projected global mean or from dayside measurements from Heng et al. [241], using it for both the dayside and terminator (which is less sensitive to it) regions.

Our dayside observations, which are more sensitive than the terminator to the tempera- ture profile, were not fit with any of these aforementioned profiles in longer wavelengths. Other temperature profiles were made ad-hoc to fit the data. The best fitting tempera- ture profile is shown in black in Figure 5.5 along with the other profiles trialed in dashed coloured lines.

Figure 5.5: The temperature profiles trialed for HD 189733b taken from literature and made ad hoc. The best fit case is a solid black line which differed significantly from anything used in literature.

HD 189733b is not expected to have a major inversion: the level of radiation it recieves would class it as a pL-type planet by the Fortney classification scheme [50] giving it a lack of major absorption features. Chapter 5. HD 189733b 131

The Fortney classification is driven by the presence or abscence of metal oxides, which are outstanding absorbers, as gases in the upper atmosphere. For planets receiving less radiation, the metal oxides—or possibly another major absorber [49]—condense lower in the atmosphere. These less radiated planets absorb the energy deeper, they exibit a dramatic inversion and absorption lines in the infrared. Ironically, the less radiated type-pM planets will have higher dayside temperatures.

Models would suggest that HD 189733b is a pL-type planet [50]. For this reason my spectral models for HD 189733b do not include titanium oxide (TiO) and vanadium oxide (VO) absorbers. Previous models of the planet have omitted these species as well [233].

My models use methane line lists for temperatures up to 1500 K, carbon dioxide high temperature line lists from the HITEMP database, water line lists for temperatures near 1500 K, carbon monoxide for a hydrogen-helium atmosphere from Goorvitch [242]. Possibly less impactful but still included are line lists for calcium, iron, chromium and magnesium hydrides (CaH, FeH, CrH, MgH). Atomic line lists included are for rubidium (Rb), caesium (Cs), potassium (K) and sodium (Na). The far wing shape of potassium and sodium are altered within VSTAR so that the Lorentzian limit (S(1)) is set to 500 cm−1, and the wing is cut off (S(2)) after 7500 cm−1 (A(1) = 0.00005; A(2) = 1.0; B and E values = 0). The models are completed at a wavenumber step of 0.5 and smoothed for plotting using a simple 1-D Gaussian filter with a standard deviation for the kernal fitting set to 0.5 (the model data is not smoothed or otherwised altered outside of normalisation before binning or any other actual treatment, the smoothing is for illustrative purposes). Collision-induced absorption for H2H2 and H2He are also included as are the Rayleigh scattering effects of H2, He and H.

Planets of the pL-type also have more effective mixing from their day to night side, as the absorbing metal oxides in pM-types effectively insulate the planet. HD 189733b is believed to have a energy redistribution effienciency of 43% [236] although, in models higher values are sometimes used (50% would reffer to complete heat redistribution).

Presssure temperature profiles have a large influence on the chemical model. All chemical models for this planet are produced with equilibrium chemistry. Chapter 5. HD 189733b 132

In the models tested, the metallicity and carbon-to-oxygen ratio have some minor variations. The star in this case has had its metal ratios explored in some detail. Teske et al. [243] used several indecators of oxygen abundance from Keck HIRES data for the stellar host. The oxygen triplet indicated a (O/H) ten times higher if non- thermodynamic-equilibrium was assumed (∼0.12 depending on the model fitting com- pared to about 0.01 with LTE). The paper also derived iron abundance((Fe/H)∼0.01), carbon abundance((C/H)∼0.22), and nickel abundance((Ni/H)∼nil), with an average C/O of 0.9±0.15, with thermodynamic equilibrium assumed.

For the planet, Benneke [44] found HD 189733b should have a carbon-to-oxygen ratio under 0.92 (95% confidence). Their models show the probabilty of a very low C/O ratio is high only when there is a very high planetary metallicity. At most a C/O ratio between ∼0.7 to 0.9 meets the 95% confidence level. For my models, carbon-to- oxygen ratios between 0.7 and 0.9 are stepped through with a solar metallicity (the host star, HD 189733A, has 93% solar metallicty or [Fe/H] = −0.03); a carbon-to-oxygen ra- tio of 0.6 was also trialed with 2x solar metallicity. Some trials of very high metallicity were also included in initial fitting.

This produces a multitude of chemical models to be applied to the VSTAR spectral model.

The gravity also affects the distribution of species through the layers; I adopt a value of 22ms−2 based upon the measured radius and mass of the planet.

The stellar models used for the other three planetary systems’ spectral models are for the appropriate stellar type from the Castelli-Kurucz ATLAS models (available through the STScI website and described in Castelli and Kurucz [182]. An object-specific model for HD 189733A was used for the models of HD 189733b (from Kurucz’s website, the program is described in Kurucz [244]). This was nessisary because the data is sufficiently detailed beyond 10 µm and in visible light for this planet, where the sampling of the stellar models is more sparse.

The VSTAR spectral models, which solve for the radiative transfer per wavelength for a given chemical model atmosphere, were tested with non-equilibrium chemistry by omitting the methane that is expected to be present on the planet, and is possibly detected in transit. The dayside observations have not provided a detection of methane, Chapter 5. HD 189733b 133 so my secondary eclipse and transit chemical models are run with and without the lines added. The transit had a disputed detection with the NICMOS instrument (see Gibson et al. [205] and Deroo et al. [206]).

If indeed there is methane in the terminator, but not the dayside, the dayside may be experiencing photodissociation of methane and higher enthalpy not allowing the molecule to stably form. The atmosphere, although heavily mixed, would then have to stabalise enough to allow the terminator to recombine the species present in equilibrium. It is also possible that the efficient mixing dredges different species and that the change in heights probed by the different methods produces a changing apparent abundance across the planet (photodissociation would otherwise effect primarily the upper atmosphere which is probed by the transmisson spectrum more efficiently). The observed deficiency in the nightside flux from phase curves supports non-equilibrium chemistry due to vertical mixing [73].

Finally, HD 189733b’s models also trial hazes. Evidence for dusts or hazes is tenuous and requires that the aerosol be extremely transparent (i.e. have a small imaginary component to the refractive index) [210]. Lecavelier Des Etangs et al. [210] suggested that the culprit could be either Rayleigh scattering by molecular hydrogen or solid enstatite (MgSiO3) grains. In my models, the scattering species responsible for the increase in radius at blue wavelengths for the transmission spectrum uses the refractive indices of enstatite.

Rayleigh scattering from molecular hydrogen is surely present as well. But the strong Rayleigh scattering seen on HD 189733b would be due to an additional aerosol haze. Evidence from both polarimetry and visible light eclipse depths suggest the planet is a deep blue colour due to very effective Rayleigh scattering [1, 169].

Rayleigh scattering from molecular hydrogen (as well as atomic hydrogen and helium) is included for the models and creates a sufficient trend to meet the rise in blue light observed on the dayside by Evans et al. [1] but not the dramatic rise seen in the termi- nator. The large scattering sphere of the hydrogen envelope of the extended atmosphere could compensate for this.

The hazes in my models are described by an optical depth per layer and a refractive index per wavelength (for enstatite). The scattering radius of the particles tested were Chapter 5. HD 189733b 134

0.01 µm, 0.05 µm and 0.1 µm, which are all within the bound given by the Rayleigh scattering curve of 0.1µm [215], producing Mie scattering effects, near the Rayleigh limit, at the blue wavelengths they are fitting.

5.2.2.2 Secondary Eclipse

The secondary eclipse models I’ve produced for this thesis are intended to reproduce previous findings using other modelling software. The pressure temperature profiles outlined in the last subsection produced a widely varying grid of fits that could be judged qualitatively. While the temperature profile included here is the best fit of those trialed and was adjusted parametrically from the profile from Barstow et al. [240], there is some room for variation.

The reason my profile is substantially different from most of the other trialed pressure- temperature profiles is likely because most of them were from retrieval models. The retrievals provided abundances which varried less or did not vary as they were retrieved from the average of the data available. In most cases, these mixing ratios are much higher than those calculated from our equilibrium chemistry model, so they require the profile to be shifted to compensate for the opacity of the species.

The fits shown in Figure 5.6 use the same atmosphere as fit for the transmission spec- trum. Four carbon-to-oxygen ratios are shown: 0.6, 0.7, 0.8 and 0.9. The metallicity in the C/O = 0.6 model is increased to 2 × solar value. Based upon Benneke [44] these ratios meet a 95% confidence level (at 0.6 and under this confidence level is met for metalicities higher than solar, hence the adjustment).

The inset in Figure 5.6 shows that the trend in visible light wavelengths is fit with all of these models. There is little variation between the different models outside of an increase in flux for longer wavelengths with increasing C/O ratio. This is because of the strong water absorption present in this region for low values of C/O. The photometric bands at 3.6 and 4.5 µm (Spitzer IRAC) lie within another region influenced by the C/O ratio. Adjusting the carbon-bearing species, methane and cabon monoxide mixing ratios could compensate for the fits in these regions. However the adjustments predicted by disequilibrium chemistry from quenching have the inverse effect of what is needed at these wavelengths [72]. Chapter 5. HD 189733b 135

Figure 5.6: Dayside models for HD 189733b. The C/O = 0.6 model uses a higher metallicity (2 times solar, the rest are at a solar value). The photometric data is shown in black, and the spectral data in gray. In cases where there appear to be two photometric data points at the same x value they are from different treatments. The photometric data points are also binned (coloured dots).

The fit is also weak through the Spitzer IRS data. This is due in part to the offset between the photometric data and spectral data. Due to the systematic scatter in the IRS data [198], I focused the fitting on the photometric data in this region and only tried to fit the general shape of the spectral data. The fall-off at the red end is considered part of this scatter, but could be fit to some level with the inclusion of the disequilibrium product, hydrogen cyanide (HCN).

Similarly due to the varying approaches to the data reduction for the problematic HST NICMOS data ( around ∼2 µm), this region is fit only generally in both the dayside and terminator (although the terminator model fits within nearly all of the error bars). Chapter 5. HD 189733b 136

Figure 5.7: A zoomed-in plot of the fit accross the red end of the dayside, secondary eclipse, spectrum.

5.2.2.3 Transit

Producing a transit model for HD 189733b requires a scattering haze to enhance the Rayleigh scattering present in the atmosphere.

The region between 0.8 and 1.5 µm in the transit spectrum is a transitional portion of the spectrum between the Rayleigh scattering dominated bluer light, and the largely flattened cloud-deck dominated redder part. This region is possibly dominated by set- tling dust in the atmosphere [215] partially obscuring features in the atmosphere ( radius ratios in this region are between ∼0.155–0.154).

The optical depth was fit to the transmission data. A plot of the optical depth (unitless, divided by 10) is shown in Figure 5.8 .

The Rayleigh trend in the blue light seen in the transmission spectra for HD 189733b, as shown in gray in Figure 5.9 is highly dependent upon the optical depth at each layer. The optical depth between layers will direct how much light is scattered through Rayleigh Chapter 5. HD 189733b 137

Figure 5.8: The optical depth (divided by 10) at 1.0 µm wavelength for the enstatite scatterers with atmospheric pressure used in the best fit model. The shape of the Rayleigh curve requires a distribution in optical depths near these values. Also shown are the mixing ratios for three species in the HD 189733b atmosphere with significant effects in the wavelength regions observed. The mixing ratio for carbon monoxide (CO) has also been divided by 10. Carbon dioxide mixing ratios are very low for these pressures and temperatures in equilibrium condiditons. scattering so the slope can be fit to the data. The optical depths of the enstatite haze provided optical depth (effective at 1.0 µm wavelength) in Figure 5.8 are a good fit to the Rayleigh trend in the spectrum shown in Figure 5.9. If the haze optical depths become too great, this would flatten the mid-infrared wavelengths of the dayside, as well as the blue, visible light. The blue light on the day side of course has been measured to have a rise towards shorter wavelengths by Evans et al. [1]; too opaque an atmosphere, therefore, will not fit the dayside.

It is possible the the dayside has a different haze (/cloud/aerosol) structure than the terminator.

The haze is for particles with an effective scattering radii of 0.1 µm in a power law distribution with effective variance 0.01 (see: Mishchenko et al. [93] and Chapter 2). These haze parameters meet the suggestions from Lecavelier Des Etangs et al. [210] Chapter 5. HD 189733b 138 that the haze particles be 1×10−1 – 1×10−2 µm, and that they have a low imaginary component to the refractive index, as in enstatite.

To fit the transit model, the radius of the star also had to be adjusted from what is in literature. The radius of the host star was determined directly using the CHARA Array

Interferrometer to be R? = 0.805 ± 0.016R [245, 246]. The value used in this model is for a stellar radius of 0.750R which is well outside of the error quoted by Boyajian et al. [245, 246]. To some degree the radius ratio is variable: the radius that goes into the model for the planet is for the base of the atmosphere and will be lower than the measured planet radius (so only the ratio is relavent). However this is dependent also upon the accuracy of the Hipparcos distance for the star and the radius and temperature for the star do not match its K1.5 V spectral type under normal circumstances (mixing).

Along with uncertainties (beyond those included in the quoted error value) in the star’s radius, there could also be some variation in the planet’s radius. I use a value of 79559 km based upon the radius estimate from Torres et al. [189] of 1.138 ± 0.027RJ . This is based on a radius ratio from a stellar radius based on isochrones. Furthermore, the star is highly variable, and while the data set I fit the models to has tried to take this into account, it produces further uncertainty into radius estimates derived from photometric changes [189, 247]. I therefore generally treat the radius ratio as an adjustable parameter for the terminator spectral models.

Had I varried the radius of the planet in my calculations to adjust the ratio, the gravity would need to be adjusted as well in the chemical models. It is possible that the base radius should indeed be larger for the planet, driving the gravity to a lower value than the 22ms2 used in the chemical models. This would maintain the base height of the transmission spectra but could vary the depth of the features as the mixing ratios change. The mixing ratios for three vital elements to HD 189733b’s atmosphere are shown along with the optical depth in Figure 5.8.

5.2.2.4 Conclusions

By adjusting the ’base-of-atmosphere’ radius ratio, and introducing a parameterised optical depth file for the Rayleigh scattering by enstatite, I am able to produce a very Chapter 5. HD 189733b 139 good fit for the transmission spectrum. Importantly, I use the same atmospheric model, solved for emissions and reflected light, to fit the dayside of the planet.

I produce qualitatively identical models for the dayside of HD 189733b to previous model fits by other groups using different modeling software, but find that my best fit requires a novel pressure-temperature profile with a more isothermal upper atmosphere, likely because it is not a retrieval.

The evidence for water is strong in the blue end of the Spitzer IRS spectrum in particular, I can confirm the presence of water on the planet.

This is among the earliest cases for HD 189733b of fitting a forward model to all of the transmission data, and is the first case where the dayside model has been fit through to the visible wavelength data. Furthermore these models are unusual in that they provide a good fit to both the dayside and terminator.

Further models including disequilibrium chemistry would be useful in characterising the planet particularly in understanding the features detected by the IRAC bandpasses centered at 3.6 and 4.5 µm.

5.3 Polarimetry

5.3.1 Context

The only previous claim for polarisation from an exoplanet atmosphere is by Berdyugina et al. [167], using the DIPol polarimeter, for the planet HD 189733b. The 2×10−4 amplitude of the B-band polarisation curve was surprisingly large for a hot Jupiter which, as mentioned in the introduction to polarimetry (see section 4.1.3), should only have variations on the order of a few parts per million. Lucas et al. [60] predicted a maximum signal for the system of 2.6×10−5.

This amplitude of variation seen in Berdyugina et al. [167] requires the size of the scat- tering sphere from Rayleigh scattering to be 1.5 ±0.2 RJ , or 30% larger than the opaque sphere. The geometric albedo is also constrained from this measurement, however at a minimum of AG & 0.14 it merely provides the insight that it is no less matte than Mars or the Moon. While the scale of the detection was disputed, it did provide orbital Chapter 5. HD 189733b 140 parameters. The longitude of the ascending node, Ω≈16◦ (or 196◦) ±8◦ and the orbital inclination, i ≈98◦ ±8◦, while the eccentricity is next to nil. These values were used in the original fitting as a starting point for comparison.

The Berdyugina et al. [169] reduced polarised light measurements still require a blue light geometric albedo of ∼0.6 which would require a perfectly singly scattering atmosphere (if from the planet atmosphere alone), which is highly unlikely to be the case with such a high albedo Wiktorowicz et al. [175].

The formal retort to the unusually high polarisation came from Wiktorowicz [168] who attempted to reproduce the detection with the original POLISH polarimeter at Mount Palomar’s Hale 5 metre telescope. This placed an upper limit to the polarisation vari- ability at 7.9×10−5 for the 400–675nm coverage (to a 99% confidence with significance determined by a Kolmogorov-Smirnov test). Although this is still quite substantial, the author also points out that the Berdyugina et al. [167] detection was also too high for previously observed albedos for other hot Jupiters and would require no multiple scattering in the highly extended atmosphere. With an upper limit of AG . 0.22, the polarised light should only be on the scale of about 1×10−5 at most (2×10−5 if assuming a Lambertian sphere).

The process was repeated again in Berdyugina et al. [169] with the TurPol polarimeter. Since Rayleigh scattering is predicted to be the dominant source of the polarisation signature, one would expect that the blue light be far more scattered than the red. The observations were taken in U band, B band and V band, with V band approximately covering the same wavelength region used by Wiktorowicz. Again an unusually high polarisation modulation was detected for the B band, although in this case only about −5 half the level of the original discovery paper at ∆qB ≈9×10 . Bluer to this, ∆qU ≈9×10−5 and in the region measured by Wiktorowicz [168], Berdyugina et al. [169] −5 measured a lower value of ∆qV ≈4.5×10 . This corresponds to a geometric albedo

(dependent on the radius used) and ∆qV within the limits set by Wiktorowicz for those wavelengths. Different radii measurements are used to calculate each geometric albedo, retrieved from transit depth measurements. The equivalent radius in B band is 1.23

RJ —about 0.4% deeper than in the V band [188].

The star, HD 189733, was monitored with spectropolarimetry for topographic magnetic variations using circular polarisation coupled with Zeeman-doppler imaging by Fares Chapter 5. HD 189733b 141 et al. [154]. The hot Jupiter orbiting the star crosses different stellar field configurations throughout its orbit, producing possible reconnections between the planet’s and star’s magnetic fields throughout its orbit. The system has an observed hot spot, but this hot spot is predicted to be of thermal planetary origin as it preceeds the planet only slightly [248] and not at the ∼70◦ associated with magnetic field interactions between planets and stars peak variability in some hot Jupiters including HD 189733b preceeds the sub-planetary longitude on the star’s surface by 70◦ and can affect the light curves [248]. HD 189733 also has a rather strong field compared to other planet hosting stars thus far studied: the field is estimated to be 20 to 40 Gauss and predominately toroidal [193, 229].

The secondary stellar companion is unlikely to contribute to the variations in the po- larised light curve. At 11.38” [195], the M4 dwarf should be outside of the 6” aperture of HIPPI. Variations from the clouds in M dwarfs also are not believed to have timescales comperable to the 2.2 day orbit of the planet.

Recently, Wiktorowicz et al. [175], observed the HD189733 system again with the very sensitive POLISH2 polarimeter. The polarimeter has a sensitivity comperable to HIPPI or PlanetPol: a few parts-per-million (although I estimate from the variation in the measurements of standard stars in Wiktorowicz and Nofi [59] that our instrument sensi- tivity is slightly better). The polarimeter utilises a photo-electric modulator allowing for fast curve modulation and reducing error while improving the time needed for exposure. Unlike HIPPI, POLISH2 uses two PEMs to produce a sine-like curve rather than the square curve produced by HIPPI, further improving the collection time and allowing the polarimeter to measure circularly polarised light. The error the group reports in the HD 189733b paper for the unbinned data Stokes Q and U are ∼29.6 ppm on average for a nightly mean. The HIPPI results presented for all four planets before binning have an average error of 16.5 ppm, and for the HD189733 data alone, only 13.9 ppm (furthermore, omitting the outlier discussed in the next sections, the average error in our data is 12 ppm).

The data presented by Wiktorowicz et al. [175] are limited by systematic effects. HIPPI’s data is close to the photon noise limit on bright objects.

HD 189733 likely has no circumstellar disk that would affect the polarisation measure- ments, according to a measurement of infrared excess by Bryden et al. [156]. Chapter 5. HD 189733b 142

5.3.2 Fits

In fitting the data to my Rayleigh-Lambert phase models, the HD 189733b data is binned per night, as opposed to by phase. This is done to avoid masking long-time-scale variability for this system since the star is variable and may interact with the planet.

The outlier in the data is a point taken around moonset. The object was near 90◦ separation from the moon during this observing run. This produces a large amount of foreground polarisation from Rayleigh scattering in the sky (peaking at an angle of 90◦). This is usually well accounted for by sky subtraction. However the outlier seen at phase 0.66, had two angles taken roughly before moonset and two taken roughly after, with the sky for one taken during the moonset, it is difficult to account for the subtleties of the moons effect on the sky to be subtracted and the added accuracy of our measurements which comes from measuring redundant angles to remove instrumental effects is compromised for this point. Chapter 5. HD 189733b 143

Figure 5.10: Top: HIPPI Q/I data in purple compared to Berdyugina et al. [169] in blue. Bottom: HIPPI U/I data in red, compared to Berdyugina et al. [169] in yellow. Note that the data here are not adjusted for a baseline due to interstellar polarisation. However telescope polarisation and intrumental effects have been accounted for in the data. One point at phase 0.66 is probably an outlier as it was taken during moonset. Data is binned per night, as opposed to by phase, to avoid masking long-time-scale variability.

The system is calibrated each observing run by the measurements of polarised and unpo- larised standard stars taken throughout each observing run. This helps to compensate for any variation in the instrumental effects.

HIPPI’s observations of HD 189733b do show a variation in the polarised light but one that is wildly variable within a limit, and does not modulate to the phase of the planet assuming a Rayleigh-like scattering curve. Chapter 5. HD 189733b 144

Figure 5.11: HD 189733b exibits some variability in the midpoints of its polarised light measurements, but not with the planet phase. Above includes dashed line as the offset from interstellar polarisation, and curves fit to the amplitude. The point at 0.66 phase is an outlier taken during moonset

In figure 5.11, the minimum amplitude is fit to the data excluding the data point at phase 0.66 because it was taken over moonset. This fit to the variation in the curve includes a minimum interstellar offset that is within the error bars of the data taken at secondary eclipse since these should not include the polarised light contribution of the planet. The interstellar polarisation offsets for these data are Q +29 and U +39.

The minimum variation of the polarised light signal is then fit with curves of the ap- propriate amplitude. They correspond to a position angle of the polarised light at ∼168 degrees for a multiple scattering atmosphere (polarisation signal scaled by 0.3) with a very high geometric albedo of 0.68. This albedo is well outside of the photometric albe- dos measured by Evans et al. [1] in all but the bluest bandpasses the group observed, which are not well inside the instrument sensitivity of HIPPI [58]. This albedo can be reduced somewhat by the light undergoing less multiple scattering (being multiplied by Chapter 5. HD 189733b 145 a factor greater than 0.3). While it is possible that the atmosphere is a more efficent po- lariser, singly scattering more of the light than 30%, it is unlikely that it singly scatters at 100% as suggested by the fits from Berdyugina et al. [169].

While the minimum albedo for a multiply scattering atmosphere is very high, the vari- ation in the polarised light in each Stokes parameter is far closer to what would be expected for an exoplanet than other reported findings. For the minimum amplitude, ∆Q is ∼3.0×10−5 and ∆U is only ∼1.1×10−5 (not to be confused with the midpoint variation quoted in the table). This level of polarisation(P = 3.2×10−5) is very near to the value one would expect for HD 189733b as calculated based on the estimate of P = 1.7×10−5 from Lucas et al. [60].

Figure 5.12: The best fit with a sliding x axis. The baseline offset is within the error bars of the secondary eclipse measurements. Position angles around 170 provide the best fit with some degeneracy. The curve was fit with a AG of 0.7 an accounting for multiple scattering. It does not appear to correspond to the IR phase curve. Chapter 5. HD 189733b 146

As a first order exploration into the assymetric atmosphere’s effect on the polarised light curve, the thermal phase curve was taken as a metric for possible extended atmosphere asymmetry.

The variation detected by HIPPI in the polarised light signal does not seem to correspond to the asymmetric heat distribution. The binned data from HIPPI were fit to the data with a sliding x axis (whist keeping the insterstellar polarisation offset within the error bars of the data taken during secondary eclipse) to see if there was an offset period to the polarised light signal. Position angles around 170 provide the best fit with some degeneracy. The curve was fit with a AG of 0.7 an accounting for multiple scattering. It does not appear to correspond to the IR phase curve, although one of the Rayleigh peaks would occur near the coolest part of the infrared phase curve at around phase = 0.1. The baseline interstellar polarisation offsets for the sliding x-axis plot are adjusted slightly to Q +29 and U +40.

The paper from Wiktorowicz et al. [175] combined data from POLISH and POLISH2 polarimeters with new error handling for the original refutation to Berdyugina et al. [167] detection of a very strong, periodic polarised light signal from the system (Figure 5.13; see Wiktorowicz [168] for original treatment). The combined data points show no trend with the phase of the planet, however there is a peak in the amount of polarised light at a phase of 0.1. This is roughly coincident with the minimum temperature in the infrared phase curve caused by the minimum temperature just west of the hot spot on the planet.

Wiktorowicz et al. [175] also note a great deal of variation between nightly measurements for the data taken at orbital phases of 0.5 and at 0.85. Notably, those taken very close to 0.5, between roughly 0.48 and 0.52 would be during the planet’s secondary eclipse. A great deal of variation at that phase might suggest that the polarisation is due to the star or variable atmospheric escape that could be seen after the “planet proper” has passed behind the star. Whether shifted along the axis for the thermal phase or not the polarisation at 0.85 should be near a minimum. Chapter 5. HD 189733b 147

Figure 5.13: This figure from Wiktorowicz et al. [175] (Fig. 5 in original text) shows the reassessed measurements from POLISH and the new measurements taken by POLISH 2 for HD 189733b. The polarisation measured by Berdyugina et al. [169] is shown in red dashed lines. Notably, the measurements vary widely and do not coincide with orbital phase.

Our observations do not match these observations precisely, and we also have fewer observations (albeit with a slightly more sensitive instrument on a larger telescope). The best fit of a curve shifted along the x axis does however produce an expected peak polarisation roughly near 0.1 phase angle.

Wiktorowicz et al. [175] suggested that the polarisation is not from Rayleigh scattering in the planet, as their observations do not show a variation that matches the planetary phase, and that instead the apparent blue colour of the planet from transit and secondary eclipse observations would be due to inaccurate removal of starspots.

5.3.3 Conclusions

The variation in polarised light from the system with a 500SP filter on the HIPPI polarimeter is nearly within the range estimated by Seager et al. [153] and constrained by transit observations by Stam et al. [155] of 3–5×10−5. This is a total polarisation Chapter 5. HD 189733b 148

Berdyugina ’11 Wiktorowicz ’15 Bott ’15 Max? ∆Q 9.1 × 10−5 4.4 × 10−5 4.8 × 10−5 ∼1.7 × 10−5 ∆U 9.4 × 10−5 8.3 × 10−5 4.0 × 10−5 ∼1.7 × 10−5 ◦ ? ∆P Based on Lucas et al. [60] estimate for RP = 1.138RJ at 0.03 AU and nearly edge on (∼85 )

Table 5.1: The variation seen in 2011 measurements from Berdyugina et al. [169] would require a singly scattering atmosphere [175]. Hot Jupiter atmospheres are ex- pected to have multiple scattering, scaling the overall polarisation down [153, 155]. Our measurements are more consistent with Wiktorowicz et al. [175] but still greater than expected and not with the phase of the planet. A conservative maximum polarisation (the position angle determines how much stokes Q and U contribute) is calculated based upon the general case estimates from Lucas et al. [60]. value, so for an aligned Stokes parameter it is a maximum value (assuming there is no contribution in the other linear Stokes parameter).

Comparing our data with that presented in Wiktorowicz et al. [175], we can see that we observe similar levels of polarisation in the system (although we see more variation in Stokes Q, while Wiktorowicz et al. [175] saw more variation in U). We rule out polarisation to the level reported by Berdyugina et al. [169]. The HIPPI observations, like Wiktorowicz et al. [175] also do not detect variation with the phase of the planet as claimed by Berdyugina et al. [169]. Both HIPPI’s measurements of the HD 189733 system and our own are closer to the level of polarisation expected from this exoplanet.

For such an active star, the polarimetric (and photometric) effects of star spots must be considered. Furthermore, more exploration into the interactions between the active star and the planet (magnetic, stellar wind, etc.) should be a focus of further research. A polarised light model for trailing extended atmospheres and a quantification of the effects of bow shocks would be valuable subjects for further exploration.

Detection of polarisation from this system at likely levels should be feasible with a more extended set of observations or a larger telescope. Chapter 5. HD 189733b 149 The best fit for the visible light, emissions, and transmitted light, shown here applied to the transit (transmission, terminator region). Figure 5.9:

Chapter 6

WASP 18b

6.1 Introduction

The other transiting system explored by this thesis is the hot Jupiter WASP 18b. The planet is the largest of the four planets we observe with a mass of 10.43 MJ [187]. The planet’s radius (1.165 RJ ) is not substantially larger than that of the other planets, since the increase in mass increases the pull of gravity. Hydrostatic equilibrium keeps even brown dwarfs at approximately the same radius as their large mass is then countered by pressure from deuterium burning. This means that the gravity at that radius will be greater, which is an important consideration in modeling the atmosphere, particularly the transit spectrum.

WASP 18b orbits very close to its star; with a semimajor axis of only 0.02 AU it orbits closer than any of the other hot Jupiters I investigate in this thesis. The short orbit of the planet presents a possibility to detect transit timing variations which might otherwise have been difficult to detect [249].

Transit timing variations can be caused by tidal dissipation via the Applegate effect [250]. The Applegate effect creates the appearence of light-time travel variation due to a second gas giant. The star will change shape with variations in angular momentum as it goes through its activity cycle, this can couple gravitationally to a hot Jupiter producing orbital period variations [250]. WASP 18b does not show evidence of these transit timing variations, however [251] meaning it probably does not have a companion of substantial mass. 151 Chapter 6. WASP 18b 152

More anomolous variations in transit can be due to an escaping atmosphere and unac- counted for stellar activity.

Like many other hot Jupiter planets, WASP 18b has evidence of hot exospheric gas beyond its Roche Lobe. The star is likely surrounded by a circumstellar gas cloud, based on the detection of emissions in the cores of the Ca II H&K lines. Theoretically the planet would not lose enough mass to be the source of the material as is likely to be the case in some other hot Jupiter systems. The anomolous H & K lines could potentially be explained by the presence of a moon ( but a moon of substantial size would affect the transit timing [252]). Or it could be due to material loss from the planet. This option would require an additional energy source to drive the mass loss such as magnetic field reconnections within the atmosphere. The material lost from the planet can fall into the star in an accreting stream; the spot where the material accretes can produce flares from the shock of the infalling mass [253].

Again, while this is possible for the planet, the transits are consistent [251] meaning that the stream and mass loss would need to be fairly consistent and that the ensuing stellar activity would be surprisingly steady. The activity and mass loss of the planet are of interest in polarimetric observation because both can affect the polarised light curve. Infalling material could explain the offset secondary eclipse

6.2 Atmospheric Characterisation

Although WASP 18b is not as extensively studied as HD 189733b it does have the benefit of having substantial observational information available since its discovery in 2009 [254]. Assuming the tidal dissipation is not weak, the planet orbiting so closely to its star is likely at the end of its life.

The age of the system is still moot. Isochrone fitting for the star suggests it is ∼600 Myr, however the nondetection of x-rays from a star that old is unusual [190]. The star’s H & K lines are narrow suggesting it is a slow rotator, and this would suggest the star is not young (the spin stars slow over time). At the same time, the star does show lithium absorption which is normally only seen in young stars [190]. Lithium can be an indicator of age in stars that host giant, close-in exoplanets but is dependant upon the Chapter 6. WASP 18b 153 convective zone height. The magnetic dynamo mixes the convective zone if deep enough within the star, depleting the lithium.

It is possible that the planet, orbiting so closely to the star, disrupts the stellar magnetic dynamo created within its thin convective layers, reducing the mixing and allowing the lithium to last longer. This is highly dependent upon the orbit of the planet (and how long it has been in that orbit) and the magnetic dynamo structure of the star. In the case of WASP 18b the planet creates 498 km tides on the star, a much higher tide compared to the pressure scale height than seen in many other close-in systems [190].

Full phase curves for the planet were obtained with the Spitzer Space Telescope [255] in 3.6µm and 4.5µm but were somewhat limited in accuracy due to systematic noise. These observations found no evidence for large variations in the eclipse timing. They did show that there is probably very little recirculation of heat for the planet, and that the heat distribution is symmetric from the substellar point (i.e.there is no offset hotspot as in HD 189733b) by showing the peak-to-peak amplitude to be similar to the eclipse depth and the peak brightness to occur around mid-eclipse respectively [256].

The evidence for poor heat redistribution was confirmed by time-dependent radiative transfer models with parameterised day-to-night redistribution of heat from Maxted et al. [256]. Unlike the jet-dominated atmosphere of HD 189733b, WASP 18b has no rotation of its atmosphere, which provides its tremendous day side flux and temperature.

Secondary eclipse depths from Spitzer in four bands (IRAC’s 3.6 µm, 5.8µm, 4.5µm and 8.0µm) provided evidence of a temperature inversion for the planet’s dayside from the variations in brightness temperature derived from each eclipse depth [251]. The planet also likely has a near zero bond albedo in infrared [257].

WASP 18b does not benefit from a substantial body of previous research and observa- tion. Since its discovery in 2009 [254] WASP 18b has produced limited phase curve and secondary eclipse measurements. No transit depths sufficient for atmospheric character- isation have yet been measured for the planet.

The secondary eclipse has thus far been the primary source of successful data. The eclipse depths from Nymeyer et al. [251] in four IRAC bands suggest that the planet has an albedo near zero and that the dayside temperature pressure profile likely has a temperature inversion. Chapter 6. WASP 18b 154

Both the pressure-temperature profile with and that without an inversion from Nymeyer et al. [251] are used in our fits along with an isothermal profile.

The temperature estimates for the isothermal profiles are based on theoretical estimates from Cowan and Agol [258], the near zero albedo, and the lack of energy redistribution across the surface of the planet [255, 256]. From Cowan and Agol [258], the dayside temperature can be estimated by

1 1 2 5  4 T = T (1 − A ) 4 − ε (6.1) d 0 B 3 12

wherein AB is the bond albedo (approximated to zero), ε is the efficiency parameter (approximated to zero, trivially at 0.01) and

1 R 2 T = T p (6.2) 0 eff,∗ a for a roughly circular orbit (a is actually r, the distance between the star and planet, in the orginal derivation. The small variations from the minor eccentricity are negligible for WASP 18b [256]).

The nightside is calculated by

1 1 ε 4 T = T (1 − A ) 4 . (6.3) n 0 B 4

The night side is more sensitive to low values of ε, and although the planet is expected to have no internal energy source [257], the day-to-night energy redistribution is not exactly ever zero. The inference that the energy redistribution is poor is made based upon the fact that the dayside temperatures, measured from multi-band infrared measurements is proportional to the amount of radiation recieved.

Notably the system is the youngest of the four presented here at “only” 0.4 Gyr (the oldest is τ Boo at an estimated 2.52 Gyr; the solar system is 4.6 Gyr for comparison). Internal energy sources for objects this size are expected to be the residual heat from planet formation, but since it is young and relativley near the 13 MJ deuterium burning limit, it ispossible that WASP 18b has internal energy sources . “Planets” with high Chapter 6. WASP 18b 155 metallicities can burn deuterium at much lower masses [259], as can planets with larger cores which form more quickly [260].

This is important for the yongest, most massive and tightest orbiting of all four planets explored here, because we might expect it to be the most likely to have an internal heat source. It also orbits the hottest star of all four systems. If the stellar heating is the main driver for the apparent infrared flux from the planet and the planet is highly irradiated as in this case, there is less heat transport around the planet [50, 257].

The eclipse depth is approximately equivalent to the amplitude of the phase curve at

3.6µm and 4.5µm [256]. The value of 0.01 used for ε, and zero for AB provide a dayside temperature of about 3100 K which is in good agreement with the brightness temperature measurements from secondary eclipse [251], and a nightside temperature well under 1000 K (highly sensitive to ε), in our case, at about 800K. The isothermal profile for the dayside is set to 3100 K. No model is produced for the terminator of the planet since it has no data currently to compare to, but the lack or heat redistribution can help constrain profiles when data does become available.

There is little information about the metallicity or carbon-to-oxygen ratio of the planet. The host star’s metallicity is solar ([Fe/H] = 0.0 ±0.09 [254] or [Fe/H] = 0.1 [256]). The only indication of the carbon-to-oxygen ratio of the planet is from secondary eclipse measurements from Nymeyer et al. [251], which suggested that for the dayside a very small abundance of CO2 was present, 10x smaller for the temperature-pressure profile without inversion. The abundance of CO2 is itself a weak diagnotic for the ratio unless it is paired with precise measurements of other carbon-bearing species such as C2H2. As we saw with HD 189733b, the prevalence of carbon monoxide can be highly dependent on the combined effect of the temperature profile and the carbon-to-oxygen ratio, and is dependent upon the presence of equilibrium chemistry.

In my chemical models of WASP 18b, the metallicity is set to 1x solar, and the carbon- to-oxygen ratio is stepped through from 0.2 to 5. The carbon-to-oxygen ratio of our solar system is about 0.55, but many exoplanets (1–5%) have ratios over unity [261].

The gravity for the planet is 197 ms−2.

The models I’ve produced for WASP 18b in this chapter sought to confirm the findings in Nymeyer et al. [251] by comparing to the secondary eclipse data presented therein, but Chapter 6. WASP 18b 156 providing a more comprehensive chemical model for equilibrium chemistry. I’ve included many species expected to be present in hot Jupiter atmospheres, but the data is cur- rently too sparse to preclude any solutions other than non-inverted temperature-pressure profiles.

The models with very high C/O ratios include the lines for appropriate organic species such as C2H2. While we don’t have the C/O ratio well constrained, we do know that exoplanet-hosting stars tend to have C/O ratios close to solar [243], and that planets can have different C/O ratios from their host stars [44].

Figure 6.1: Models with varying C/O ratios for a T-P profile with no inversion taken from Nymeyer et al. [251] produced with VSTAR. A very high C/O ratio does not significantly improve the fit. Chapter 6. WASP 18b 157

Figure 6.2: Spectral models of WASP 18b with a temperature inversion, taken from Nymeyer et al. [251]. Here very high C/O ratios fits just as well as low ones. I am unable to account for the feature at 4.5 µm but note that the absorption feature found there, if strongly in emission, could produce that shift.

Figure 6.3: For comparison, and isothermal 3100 K profile was modelled. It statisti- cally fits just as well as the inversion profile.

6.3 Polarimetry

There are currently no published detections or non-detections of polarised light from the WASP 18 system. While it is possible to detect a small amount of polarised light in red Chapter 6. WASP 18b 158 and infrared wavelengths [], WASP 18b has a very low albedo in the infrared []. Still it is possible that, if Rayleigh scattering is present in the atmosphere, blue wavelengths could be sufficiently scattered producing a polarised light signal modulating with the period of the planet in shorter wavelengths.

WASP 18b has an orbit very close to its host star, with an orbital period under one day. The lack of core absorption in the star’s H & K lines can be interpreted evidence of an exteneded gas envelope masking the stellar activity [262], which could affect the polarised light signal from the system, although this finding would need to be confirmed directly by FUV observations. Magnetic field reconnections within the atmosphere have been suggested as the driving force the circumstellar gas cloud produced by atmospheric escape [262]. This could also produce an assymetric light signal if the gas cloud opacity is assymetric (Lai et al. [263] discusses a case in WASP 12b). If the cloud itself is assymetric, this could potentially produce a varying polarised light signal as well. WASP 18b however seems to have a symmetric (photometric) light curve in infrared light at least [256].

If there is an extended, escaping atmosphere on WASP 18b is due rather to tidal effects from interactions with the star, it is quite possible that a distorted, non-spherical enve- lope could cause significant fluctuations in the polarised light from the system. The idea that a closely orbiting extrasolar giant planet could distort the shape of the host star, producing a polarisation effect from the star itself has been previously explored [264].

The 498 km tides that WASP 18b would induce on its star are notably larger compared to the pressure scale height than those in most other systems [190]. If there is an effect, it would manifest as polarised light modulation with the same period as the planet and most effective in blue light [264]. For a planet as closely orbiting and massive as WASP 18b this is a concern.

Following Hough and Lucas [264] we know that the maximum polarisation contribution of these tidal effects scale as,

MP R? P oltide = × × P ollimb (6.4) M? d

wherein MP , M?, R?, d and P ollimb are the planet mass, the star mass, the star’s radius, the distance (semimajor axis if circular), and the stellar limb polarisation respectively. Chapter 6. WASP 18b 159

In the case of WASP 18b the this reduces to ∼ 0.002 × P ollimb. If, as in Hough and Lucas [264] we use the measurements of solar limb polarisation as a first order guide, this would suggest that at 400 nm (HIPPI is most sensitive around roughly 425 nm) where the solar limb polarisation was measured to be 0.002 [265], we would expect WASP 18 to have a fractional (limb) polarisation of about 5×10−6. This is very close to the sensitivity of HIPPI (on bright stars) and this small effect should be considered in judging the polarimetric data for the system.

The offset of a shock wave preceeding a planet is potentially detectable in the asymmetry of the light curve and is related to the strength of that planet’s magnetic field [66]. A relationship between the radius of the planet and of its magnetic field, dependant upon the offset bow shock, is directly relatable depending on the strength of the magnetic field: for a planet with a magnetic field of 14 G, and a star with a 1 Gauss magnetic field for example this ratio will be about 8.6, for a star with a 100 Gauss field the radius ratio would be about 1.9 [66]. That ratio related to the orbital distance of the planet, radius of the star and ratio of the planetary magnetic field strength to that of the star by equation 6.5. In the case of WASP 18b, the light curve is symmetric around the secondary eclipse [256], suggesting there may not be a bow shock in this system, in spite of being an especially promissing candidate [66].

1 r B 3 R m = ( p ) orb (6.5) RP B∗ R∗

A constant offset can be difficult to discern from the effects of the insterstellar medium. The interstellar medium can polarise light from stars as particles over a long distance can tend to be aligned in a particular direction. Our models fit for this parameter as a bulk offset.

Triaud et al. [165]’s comparison of HARPs Rossiter-McLaughlin measurements to the CORALIE radial velocity measurements was applied to several WASP objects. WASP 18b was found to have a sky projected spin-orbit alignment of 0◦, that is the spin-orbit alignment is zero and both axis are approximately in the “plane” of the sky.

Unlike the other planets with polarimetric measurements explored in this thesis, WASP 18 has not had a search for infrared excess due to a debris disk completed. A limit to a possible disk can be inferred from WISE observations of WASP 18b. In W1 (3.4 µm) Chapter 6. WASP 18b 160 the photometric magnitude is 8.075 (σ0.023), in W2 (4.6 µm) it is 8.123 (σ0.021), in W3 (12 µm) it is 8.079 (σ0.022) and in W4 (22 µm) it is 7.753. A back-of-the-envelope conversion to a monochromatic flux equivilent is Fν,W 1 at 0.1762 Jy, Fν,W 2 at 0.0961

Jy, Fν,W 3 at 0.0158 Jy, and Fν,W 4 at 0.0064 Jy. That is, there is not a major infrared excess in this wavelength region.

6.3.1 Fits

WASP 18b shows a reasonable variation with phase as shown in Figure 6.4. WASP 18b is the only system observed with HIPPI and presented in this thesis with any variation in polarised light with planetary phase. Currently the error bars are so large that the variation is poorly constrained. It is a high priority target for follow up with HIPPI.

The curve fit to the data in Figure 6.4 is a 1.43σ fit (unweighted error) for multiple scattering (polarisation scaled by 0.3) and a geometric albedo of 0.3. The position angle used here is 140◦ providing Stokes U with most of the variaiton. A large albedo is not nessisary for significant modulation for such a tightly orbiting planet; in fact, a higher albedo will fit more poorly (AG 0.4 for example is a 1.34σ fit). Lower albedos quickly begin to produce worse fits ( AG 0.2 is a 1.25σ fit).

Another constraint for the curves is to ensure that the offset of the polarisation due to the interstellar medium is within the error bars of the data taken durning the secondary eclipse. If the polarised light it from the planet rather than the ISM (or other static sources of polarisation such as a symmetric circumstellar gas envelope) then the time when the planet is hidden will be the baseline for the polarised light variations.

In Figure 6.4 the unbinned Stokes U curve is offset by +182, while Stokes Q is offset by −62. The total contribution of polarised light is

p P = U 2 + Q2, (6.6)

neglecting the circularly polarised component which in this case should be nil.

For this system’s offsets, P = 192. The “nearby” (to WASP 18) star HD 11695 was observed with HIPPI in the clear filter as a calibrator for the system. The polarised light from that system is about 90ppm (with an efficiency correction). The star, however, Chapter 6. WASP 18b 161

Figure 6.4: A fit to the WASP 18b data with position angle 140◦, and geometric albedo 0.3. The baseline offsets (Q -62, U +182) are constrained to values within the error bars of the data point within secondary eclipse when the planet’s polarised light contribution should be obscured. is an M4 giant, which tend to have higher polarisation signals from intrinsic polarised light constributions [87], so this may not be a reliable source for gauging the polarised light from the interstellar medium. A more reliable measure may be to extrapolate the trend seen in the southern bright star survey by Cotton et al. [87].

The southern hemisphere stars observed by HIPPI saw a steeper trend in the polarised light with distance than those in the northern hemisphere. The data at large distances is sparse but in general the southern hemisphere bright stars follow a trend between 1.14×10−6 pc−1 and 2×10−6 pc−1. The variation between trends is due the dichotomy of stars being within or above (as the sun is) the local disk of the Milky Way at short distances. Galactically, from our point of view, WASP 18b is “down” (towards the galactic plane), where we might expect a great deal of interstellar polarisation [87, 266, 267]. The value we might expect for WASP 18’s interstellar polarisation offset is not well-constrained by this plot but clearly a value of P = 192 would not upset the trend of (more highly polarised) 2×10−6 pc−1 line. Chapter 6. WASP 18b 162

Figure 6.5: This image is Figure 6.5 in Cotton et al. [87].

6.4 Conclusions

By binning the data by phase, the curve can be judged more precisely. Inclusive of error we see a possible change in the polarised light signal with phase for Stokes U: the binned point at phase 0.24 does not overlap the error in the data point at phase 0.40. Although, notably, the points with error bars that do not overlap also do not fit the phase curve simultaneously. The binned data also produces a greater geometric albedo of 0.4. The offsets change for this fit as well but are of a similar scale to the last fit and still fit within the trend described in Cotton et al. [87] (P = 198).

With the data binned, assuming the errors are unweighted, this is a 1.52σ fit. It is important to consider as well that these are Rayleigh-Lambert phase curves which are somewhat simplified from a full Rayleigh treatment. Although our polarimeter’s sensi- tivity is only approaching the level to warrant a full Rayleigh treatment, for cases where a phase curve barely fits the error bars, it may be important. This is because the slope of the curve is changed by ∼1–2 ppm {Fluri2010.

The intensity of the offset is akin to that seen for stars at the same distance in the same direction (although minor changes in direction at 100 pc are significant). Chapter 6. WASP 18b 163

Figure 6.6: As in figure 6.4 but with a geometric albedo of 0.4, Q -70, U + 185, and binned per phase.

Finally, the possible additional modulation seen in the binned phase curve (three or four troughs/peaks rather than two) is of interest. The errors in the data are such that this apparent midpoint modulation may disappear with subsequent observations driving the error bars down. However for such a large planet (∼10 MJ the largest of the four considered here) at such a close orbit (a ∼0.02 AU, the shortest orbit of any planet in this thesis) tidal effects should be considered should those trends remain after subsequent observations.

Chapter 7 tau Bootis b

7.1 Introduction

The planets discussed so far (HD 189733b and WASP 18b) have been transiting planets which provide us with transit and secondary eclipse spectra, as well as a constraint on the inclination, giving us a true mass, and a measurement of the radius from the transit depth.

τ Boo b does not transit its star. It was discovered using the radial velocity method [268]. Although no spectra are retrieved for the planet, cross-corrolation has allowed for the detection of some species (see: Chapter 1 for more information on detection and characterisation methods) .

Cross-correlation also allows astronomers to estimate the inclination of the planet’s orbit, by comparing the magnitude of the radial velocity components of the planet simultaneously with those of the star. This is vital for estimating the gravity of the planet “surface” for atmospheric models as well as for comparison with polarimetric measurements.

7.2 Atmospheric Characterisation

τ Boo b was discovered in 1996 [268] and in the 19 years since has had numerous attempts to characterise its atmosphere. Although it is a hot Jupiter, τ Boo b is not

165 Chapter 7. τ Bootis b 166 a transiting planet, and so it is far more difficult to characterise the atmosphere as an observer cannot use the light absorbed during transit nor the emissions occulted during secondary eclipse.

The planet may not be particularly efficient at reflecting light either. Failed attempts to detect the reflected light from the planet (in photometry, an attempt to detect the polarised reflected light is described in this thesis) provided an upper limit to the light reflected by the planet. If the planet had a very high albedo the flux produced by the planet could be as much as 1×10−4 of the star’s light [153]. Photometric limits had been set to exclude albedos above 0.4 for the planet by Rodler et al. [269]. A previous non-detection of polarised light from the system limited the geometric albedo to 0.37 (red wavelengths) [60] and models have suggested it is likely as low as 0.175 dependent upon the scattering particles [153].

The methods used to detect light directly from a non-transitting planet are limited. Polarimetry or cross-correlation are currently the only viable options for those planets not distant, large, and young enough to be directly imaged.

Charbonneau et al. [270] attempted to detect the periodic shifts with cross-correlation in light from the planetary spectrum within the combined spectra in visible light .The non-detection down to a contrast ratio of 5×10−5 for reflected light suggests a maximum albedo for this planet of 0.3 at 0.48µm. Also based upon a non-detection, Rodler et al. [271] found from cross-corelation measurements that the relative flux of the planet in 425-632 nm is likely 3.3×10−5, with the geometric albedo under 0.4. This limit is placed ◦ with the assumptions of a gray albedo, a radius for the planet, R=1.2RJ , and i=46 .

Cross-correlation was utilised again for this planet with high resolution L-band and K- band data focused on water absorption bands, producing a detection at 6σ. In infrared, the flux ratio was limited to 1×10−4 [272]. Cross-correlation treats the system as a spectroscopic binary, so with a firm detection, the mass can be estimated. In this case +0.35 +3 ◦ the mass is estimated to be 5.90−0.20 MJ , with the inclination confined to 45−4 . The strong water absorption lines used for cross-correlation are also evidence of the abun- dance of the species in the planet’s atmosphere.Methane was not detected in these bands (where it should contribute significantly) suggesting that the species may be absent or it’s evidence suppressed by obscurring clouds. Chapter 7. τ Bootis b 167

Lockwood et al. [272] suggested that previous conflicting radial velocity detections could be due to incomplete removal of water vapour in the telluric removals for this water-rich planet.

An estimate of the mass had been provided previously by Rodler et al. [271]. The group used cross-correlation at 2.3µm with carbon monoxide lines, providing a detection of the molecule in the atmosphere. This retrieved an estimate of the inclination and the mass at MP = 5.6 ±0.7 MJ which the later value from Lockwood et al. [272] is in good agreement with.

Also in the same year as the Rodler et al. [271] study, Brogi et al. [55] had detected carbon monoxide in the atmosphere with cross-correlation using very high resolution spectra. Their estimates of inclination and planetary mass would be in good agreement with the later paper by Lockwood et al. [272] and with Rodler et al. [271], at 44.5 ±1.5◦ and 5.95 ±0.28 MJ . The strong carbon monoxide signature they detected was likely owing to the temperature profile sharply decreasing with altitude.

A steeply decreasing temperature with altitude could be induced by absorbing com- pounds in the upper atmosphere. Knutson et al. [48] found a correlation between the activity of host stars and the atmospheric emissions of the hot Jupiters orbiting them. Strong absorbers sensitive to desctruction by ultraviolet activity of an active host star could explain the tendancy for an inversion in planets receiving less ultraviolet radiation.

The mass of a non-transiting planet has upper limits placed on it by radial velocity measurements but the exact value is dependent upon the inclination of the system. Cross-correlation allows the observer to break down the degeneracy.

The radius is harder to constrain without transit depths. Taking the age into account and the stellar irradiation, and assuming inflated hot Jupiters are extended because of collapse damping, one can estimate the expected radius of the planet. This has been compared to transit observations of the hot Jupiter HD209458b, but the method cannot be applied to a planet as massive as τ Boo b.

The star that τ Boo b orbits has cycles like the sun’s but over a much shorter duration. Vidotto et al. [273] quantified the effect of the stellar wind on the planetary atmosphere by producing observationally derived surface magnetic field maps for the star and then applying those to a 3-D dynamical simulation of the stellar wind at the location of the Chapter 7. τ Bootis b 168 planet. At the distance τ Boo b orbits, if it were to have a Jupiter-like magnetic field (polar 14 Gauss) we might expect a radio flux on the order of 0.5-1 mJy (34 MHz) which is barely detectable currently. If the giant planet has a weaker magnetic field (under 4 Gauss) the radio flux would not be detectable at all.

So in inflated hot Jupiters we are met with a catch-22. The planets extended atmosphere creates a larger effective disk to scatter the light for polarimetric detection, but a planet with an inflated atmosphere is more likely to orbit an active star. Interactions with the magnetic feild can induce mass loss (and possibly further inflation), yet if the nature of the loss (whether it is symmetric, whether there is a bow shock, whether it varies temporally, etc.) is not known, it may constribute to the polarised light signal in unusual ways as well.

The periodicity of activity in the host star τ Boo has been compared to the planet’s orbital period. For τ Boo a correlation is difficult to determine but the two periods are probably not related [248].

Interactions between the planetary and stellar magnetic fields have been ruled out as the primary source of variability in the star τ Bootis [60, 274] which hosts another planet characterised in this disertation however comparing MOST photometric data with Ca II H & K activity monitoring, Walker et al. [160] found that the variable region of the star remains ∼68◦ ahead of the planet’s orbit, suggesting that it is in fact related. The group found no complementary activity at the antimeridian, suggesting that in this case the activity was magnetically, rather than tidally, induced.

τBoo likely has no circumstellar disk that would affect the polarisation measurements, according to a measurement of infrared excess by Bryden et al. [156].

Since τ Boo b is not yet well described compared to the transiting planets presented here, it behoves us to test a range of parameter space, within physicality, when we fit our model spectra.

The chemical models for τ Boo b, therefore, use the same wide range of carbon-to-oxygen ratios that were used for WASP 18b (0.2–5.0). Although the star has a metallicity nearly two times solar ([Fe/H] = +0.28) the models are run with a solar metallicity as a starting point for comparison. Chapter 7. τ Bootis b 169

−2 The gravity is kept constant at 137 ms based upon a mass of 5.95 MJ , contingent upon the inclination measurement of 44.5◦ based on cross-correlation [55]. Other estimates of the inclination from cross-correlation measurements yeild similar inclinations (and thus masses) (e.g. Rodler et al. [269]). The radius is estimated theoretically [275] based on [50].

The pressure-temperature profiles used for τ Boo are based upon the pM and pL -type models from Fortney et al. [50]. τ Boo b is at a separation of 0.048 AU from a F6 IV star (the transition occurs around 0.04 AU for a solar-type star). An isothermal profile at 1600 K was also made but is not shown in this thesis. The temperature for the isothermal profile (and appropriate pM and pL profiles) is based upon the observed low albedo of the planet in infrared, for a planet with a Bond albedo ∼0.1 .

These classes of planetary atmospheres are analogous to L and M -type brown dwarfs as Fortney et al. [50] postulated that the same metal oxide clouds responsible for the transition in spectra in brown dwarfs could be responsible for the similar phenomenon seen in hot Jupiter atmospheres. Other species look to be more promissing as the condensate [49] however major abosorbers and an inversion are typically the first data retrievable from planetary spectra [251].

Only secondary eclipse was modeled for this planet as its orbit is at an inclination from the line-of-sight from the solar system that does not transit.

The pL-type planets are so defined because of the lack of metal oxides in their atmo- sphere. Therefore the line lists for TiO and VO are omitted for the spectra with the chemical models using this profile. The spectral models using the pM-type profile do include the line lists for TiO and VO.

Without true spectra to compare to, these models are purely speculative and created for illustrative purposes.

7.3 Polarimetry

The star τ Boo undergoes a magnetic field reversal approximately every two years. The magnetic field was measured by Fares et al. [154] to be 2.7 to 3.8 Gauss and pre- dominately poloidal with the toroidal component contributing to about 12–20% of the Chapter 7. τ Bootis b 170

Figure 7.1: τ Boo b as a pL-type from Fortney et al. [50] , having no inversion and no absorption from metal oxides (TiO and VO).

field. Poloidal field 1 components are more prone to reconnection effects.

Lucas et al. [60] did not detect polarised light from τBoo with the PlanetPol polarimeter. They place an upper limit on the geometric albedo of 0.37, assuming an inclination of 40◦. Previous photometric attempts to detect reflected light from the planet have also produced non-detections, placing upper limits at AG ∼0.39 [276] to 0.4 [269].

7.3.1 Fits

Very little can be said for this data set at present, although it will prove valuable as HIPPI or other polarimeters gain more data on this system.

1The poliodal field refers to the component producing a north and south magnetic pole on the surface. For example, this is the main component that brings charged particles into Earth’s atmosphere to create the auroae. At the magnetic equator the field thus becomes weaker as you move radially out normal to the surface. On the other hand, the toroidal component’s magnetic field lines “wrap” around the planet (magnetically) lattitudinally. They thus create toroidal fields around the lines. The magnetic field from this thus becomes weaker as one moves radially into or out of the body. Chapter 7. τ Bootis b 171

Figure 7.2: τ Boo b as a pM-type from Fortney et al. [50] , having an inversion and with absorption from metal oxides (TiO and VO).

The two data points retrieved by binning per night (3 or 2 sets of observations are binned for approimately 1–1.5 hours of observing time for this object) happen to have occured close to the same point in the orbit. The data points are shown in Figure 7.3 along ◦ with a curve for a position angle of 22.5 with AG=0.3 and realisitic levels of multiple scattering. The offsets are fit to the averages of the data, at Q=+3 and U=+13. The offsets are not necessary if there is a variation with phase. If there is no polarised light variation with phase then an offset is only required for Stokes U, as Stokes Q is in agreement with zero polarisation.

The curve shown is set to 45◦ inclination, which will provide a moderate variation in the light curve and is reasonably well confined by cross-correlation. The minima and maxima position of the phase curve should be accurate if there is a non-zero inclination. The phases are calculated based on an inferior conjunction time of JD 2453450.984 and a period of 3.31 days [277]. Chapter 7. τ Bootis b 172

Figure 7.3: The data for tau Boo b is coincident in phase and stokes Q is consistent with zero. Phase 0 refers to inferior conjuction for the non-transiting planet. An offset of Q+3 and U+13 is shown. The curve may slide to the left or right since the apogee is not necessarily coincident with the shown phase angle. However, with a realistic level of multiple scattering and a geometric albedo of 0.3 (shown) an offset from interstellar polarisation isn’t necessary for Q or U.

7.4 Conclusions

Without photometric (or spectroscopic) data to compare our radiative transfer models to, the only inference we can make is that in the future when such data do become available the flux varaitions in the pL-type atmosphere are so great that they should be discernable from the inversion of a pM-type atmosphere. If the planet is a pL-type, whatever species may cause the inversion, some information about the C/O ratio may also be retrievable since the shapes of the C/O ratios over unity vary so dramatically.

Our polarimetric data for τ Boo are by far too limited to make any inferences about the planet or its orbit. The polarimetric data presented here could be added to further observations with HIPPI or other instruments. Chapter 7. τ Bootis b 173

The polarimetric data for tau Boo b are, unfortunately, all near phase 0, where minimal polarised light from the planet is expected anyway. The data show a possible offset for Stokes U at least of Q+3 and U+13 to midpoint. However including error the offset for Stokes Q could be consistent with zero. A curve with multiple scattering effects and a geometric albedo of 0.3 is shown in Figure 7.3.

Further observations taken near the time of peak polarisation in the phase would be ideal to decide whether the system is worthy of follow up at this time with the currect capabilites of the world’s currently most senstive polarimeters.

Chapter 8

HD 179949b

8.1 Introduction

HD 179949b was discovered by the Anglo-Australian planet search in 2001 [278]. The discovery paper calculated the minimum mass of the planet (its inclination was unknown so the radial velocity can only provide a minimum) to be 0.84 MJ . Knowing the radius and mass of an exoplanet to some detail is vital to modelling the atmosphere of the planet. Polarimetry can help constrain the inclination, as well as the size and shape of scattering particles in the atmosphere to some degree which may depend on the irradiation of the planet [49, 50]. The planet orbits at 0.044 AU around an F8 V type star.

With species detected through cross-correlation and a phase curve available, the next logical step for characterising this non-transitting planet was to obtain polarimetric data.

8.2 Atmospheric Characterisation

While some hot Jupiters appear to have extensive heat redistibution, HD 179949b does not.

Spitzer IRAC data in three infrared bands (3.6, 4.5, and 8 µm) produced observations of the phase variation. Systematic uncertainty was larger than the photon error in two of the bands, and at about the same level in the third (8 µm). The amplitude of the

175 Chapter 8. HD 179949b 176 variation in the 8 µm band is about f 0.00141 suggesting that the dayside and nightside emissions are very different due to a lack of heat recirculation [279]. Assuming the radius of the planet is somewhere between 1 and 1.2 RJ , which is typical for a hot Jupiter, this would mean less than 21% of the heat recirculates to the night side (50% being full recirculation) [279]. If HD 179949b has a low albedo, the mass would need to be less than 2.4 MJ to compensate for this phase variation [279].

The albedo of a planet dramatically effects the polarised light curve for a planet, al- though these IRAC measurements are of course in infrared light which is outside of the range of HIPPI (and a smaller effect than Rayleigh scattering if pressent). The circula- tion however is vitally important for radiative transfer models, as dramatically different conditions accross the surface can lead to dramatically different spectra.

Excellent spectral deconvolution data was obtained for the 2.14µm signature with the VLT1 CRIRES instrument. Comparing the spectra to models both with and without metal oxides (VO and TiO can cause atmospheric temperature inversions and have large molecular absorption bands, although other species can cause inversions [49]) the group did not detect the planet. This implies that at these near IR wavelengths the flux ratio between the planet and star would be quite, low, only about 0.0002985 [196].

The magnetic field of the planet can affect the activity on the star. HD 179949b produces bright spots on the host star by perturbing open field lines [274]. The excess in brightness for this system is postulated to be due to the consequential flares produced by the breaking of interacting field lines, a hypothesis which coincides with the x-ray excess seen from the system.

HD 179949b was the first exoplanet to have the x-ray emissions it induces upon its host star detected. Saar et al. [280] found a 30% periodic increase in the X-ray emissions of the system coincidental with the periodic Ca II K line enhancement variations with phase, using the Chandra ACIS-S. As discussed in previous chapters, magnetic feild interactions can influence the polarised light signature from the system, most simply by driving starspots and stellar activity which can break the stellar limb’s symmetry.

The period of activity for HD 179949 has been compared to the planet’s orbital period. For HD 179949 there is a clear correlation. The offset of the activity with the period of the planetary orbit is typically preceeding by a sub-planetary longitude of 70◦ [248]. This Chapter 8. HD 179949b 177 could be related to the assymmetric phase curves seen in some planets. Since stellar activity of this type can periodically disrupt the polarised light of the stellar limb it should always be considered fitting a polarised light curve to exo-planetary observations.

The approach to the chemical models for HD 179949b was very similar to that for τ Boo b. This is largely because we are faced with the same limitations. Again, this is a non-transitting planet with atmospheric measurements limited to cross-correlation phase measurements. The major notable difference between HD 179949b and τ Boo b is that the gravity for the former is at most 23 ms−2, with the mass limit being set at 2.4 −2 MJ [275], while the latter had a very high gravity of 137 ms . The radius was derived theoretically with the assumption of a 25 M⊕ core [275]. The mass for this system is constrained from cross-correlation measurements at 0.98 ± 0.04 MJ [281]. However attempts at detecting a transit have ruled out inclinations between 83◦ and 90◦ (and the redundant angles greater than 90◦)

Just as with τ Boo b, pL and pM models were utilised for test chemical models to be implemented in illustrative spectral models. The dayside and nightside temperatures were calculated using the method described in Chapter 6 from Cowan and Agol [258]. The day-to-night energy redistribution effiency was set to 0.01 as the planet appears to have a large day/night temperature difference with very little recirculation [279]. This suggests that the nightside temperature for HD 179949b would be around 500K (but, again, this nightside temperature is sesitive to the low value selected for essentially no heat redistribution). The albedo was set to AB = 0.1 in computing the Teff,p = 1533. The dayside temperature from equations 6.2 and 6.1 then is about 1950 K. Along with the pM and pL -type profiles, an isothermal profile at 2000 K was also tested.

With so little constrained for the planet, the metallicity was set to solar for all chemical models and the carbon-to-oxygen ratio was stepped through from 0.2 to 5.0.

Carbon monoxide and water have been detected through cross-correlation by Brogi et al. [281].

Depending on the chemical model used, metal oxides were either included (for pM-type planets) or excluded (for pL).

As always an atmosphere with significant absorbers will allow the differentiation be- tween an atmosphere with a temperature inversion or lacking one. The presence of Chapter 8. HD 179949b 178 carbon-bearing species and hydrogen species highly denpendent upon the C/O ratio will allow for the differentiation between a high or low C/O ratio. Interestingly because HD 179949b has such a high dayside temperature, even an isothermal atmosphere could have features at shorter wavelengths where the wavelengths are reflected (rather than emitted by the planet in the case of longer infrared wavelengths).

Figure 8.1: HD 179949b as a pL type planet (without an inversion and no metal oxides).

8.3 Polarimetry

HD 179949’s magnetic field is only a few Gauss and predominately poloidal. The star’s activity features two maxima per rotation (from observing Ca II H & K and Hαlines) but rather than being due to tidal interactions with the planet, Fares et al. [282] suggested it was due to the dipole of the star’s feild being tilted. It is tilted by 70◦ and this tilt is unlikely to have a severe effect on the system [282]. Their observations in 2009 however show additional modulation possibly caused by star-planet interactions. Chapter 8. HD 179949b 179

Figure 8.2: HD 179949b as a pM type planet (with an inversion and metal oxides).

HD 179949 likely has no circumstellar disk that would affect the polarisation measure- ments, according to a measurement of infrared excess by Bryden et al. [156].

8.3.1 Fits

The polarimetric data obtained with HIPPI for HD 179949b has errors too substantial for data too flat to make any conclusions about the system. Interestingly fitting to the midpoints of the data, a realistic offset of Q = −31ppm and U = −6ppm, equivalent to P ≈ 30ppm and a modulating curve for Rayleigh scattering is reasonable.

The Rayleigh scattering curve in Figure 8.3 is for an arbitrary inclination of 45◦.A position angle of 170◦ is shown, to give more variation in Stokes Q than in Stokes U. But considering the quality of the data, this is an arbitrary fit. If indeed the system has these parameters, it would suggest that this system would be difficult for follow up: the polarised light signal from a planet inclined less than ∼45◦ will have very minor modulation. The geometric albedo in the fit shown is for 0.4, however this cannot be constrained by this sparse data. Chapter 8. HD 179949b 180

The phases are calculated based on an inferior conjunction time of JD 2451001.510 [24] and a period of 3.09 days [196].

Figure 8.3: Although the error bars on the data for HD 179949’s polarised light measurements are large enough to make the Stokes U coincident with zero, an offset is possible for both Stokes parameters from the data midpoints. Shown is an example curve with interstellar offsets at Q=-31 and U=-6. Phase 0 refers to inferior conjunction. The example shown with an arbitrary inclination of 45◦ is a reasonable example, but more data is needed to reduce the error bars.

8.4 Conclusions

Neither the radiative transfer nor the polarimetric models are decisive at system at this time. If and when emissions data do become available, the dramatic variations in the infrared light should allow astronomers to discern between a temperature profile with and without an inversion. The polarised light also may become more telling as further observations with HIPPI or other polarimeters reduce the error in the measurements and complete the phase curve. The current data from HIPPI shown in this thesis does have a good phase spread, so better phase coverage and additional overlapping data with phase Chapter 8. HD 179949b 181 to reduce error, could produce a detection, depending, of course, on the orientation of the system which remains largely unconstrained.

Chapter 9

Summary and Discussion

9.1 Summary of Conclusions

This section recounts the conclusions of the science chapters of this thesis (Chapters 3, 5, 6, 7 and 8).

9.1.1 Uranus

The models described in Chapter 3 provide a good preliminary fit to the clouds for to two lattitudinal regions on Uranus near its recent sping equinox. Two single layers of clouds representing two compressed extended clouds are fit for each region.

The upper cloud fit to the bright, southern region, which has an effective particle radius of 0.05 µm, is at a pressure of 2.08 bar and optical depth 0.2. The lower cloud for this region, which has an effective particle radius of 0.45 µm, is at a pressure of 2.29 bar and an optical depth of 0.324.

The single scattering albedo for both clouds was fit simultaneously and has a value of 0.75 for both clouds.

Similar clouds were fit to the equatorial region but with less confidence. For the equato- rial region the upper cloud again has an effective particle radius of 0.05 µm, but with a pressure of 1.59 bar and an optical depth of only 0.092. The lower cloud in the equatorial

183 Chapter 9. Summary & Discussion 184 region again has an effective particle size set to 0.45 µm, but with a pressure of 2.22 bar and optical depth of 0.87.

The single scattering albedo for both clouds in the equatorial region was fit to 0.76.

These values are in good agreement to those found previously (e.g. Irwin et al. [104]).

For only the bright, southern region, the deuterium ratio for methane, which is measur- able within the h-band region observed, is also fit (because of the improved certainty of the cloud fitting). For this region I calculate the species ratio (CH3D/CH4) to be −4 −5 3.34×10 . This corresponds to a calculated D/H ratio ((D/H)H2 ) of 5.04×10 . This is in good agreement with most previous measurements. It is also very near to, but −4 slightly great than, the preliminary value for Neptune (CH3D/CH4) of 3.0×10 from Cotton et al. [87], which is also consistent with previous measurements.

9.1.2 HD 189733b

9.1.2.1 Radiative transfer

For the transiting hot Jupiter HD 189733b I have created new dayside reflected light and emissions and terminator transmission models. I am able to produce a reasonable fit for all of these using a single atmospheric model. This is the first time a single model has been fit to the emissions, reflected light and transmitted light for an exoplanet.

The dayside shows evidence confirming the existence of water in the atmosphere of HD 189733b. I produce a new temperature profile for the planet, adjusted from a retrieval, with a more isothermal upper atmosphere. For the terminator I am able to produce a very good fit to the possible Rayleigh scattering seen in blue wavelengths by creating a new haze optical depth profile based on a refractive index of enstatite. These findings synthesize previous suggestions for the nature of the scattering haze to provide new information on the structure of the atmosphere.

9.1.2.2 Polarised light

Using observations from the HIgh Precision Polarimetric Instrument [58] at the Anglo- Australian Telescope, we retrieved polarised light observations of this and the three Chapter 9. Summary & Discussion 185 other hot Jupiters examined in this thesis. These are compared to Lambert-Rayleigh phase curves calculated for the systems.

For HD 189733b, I am unable to reproduce the variation in polarised light for the system reported by Berdyugina et al. [169] in either the amplitude or phase relation. I find possible variation in the polarised light, seeming random, and not in phase with the planet. For ∆Q I find a variation of ∼4.76×10−5 (from midpoints), and for ∆U I find variation of ∼4.0×10−5. The possible polarised light variability is closer to the scale expected for the system, and similar to recent findings by Wiktorowicz et al. [175], but are still slightly higher than expected in an atmosphere with multiple scattering. I find no phase relation correlating to the infrared light temperature phase for the planet, which is assymetric, either.

The minimum amplitude fit to the scatter in the polarised light measurements with a position angle of 168◦ and multiple scattering scaling the polarised light by 0.3, corre- sponds to a geometric albedo of 0.68. The interstellar offsets used are Q/I +29, and U/I + 39 for the amplitude fit.

9.1.3 WASP 18b

9.1.3.1 Radiative transfer

Although WASP 18b is a transiting hot Jupiter, the observations available so far to characterise the planet are limited relative to HD 189733b. A secondary eclipse emissions spectrum is created with VSTAR to compare to the observations from Nymeyer et al. [251]. I am able to confirm that an atmospheric temperature profile without an inversion is unlikely for the planet.

9.1.3.2 Polarised light

The polarised light detections from the WASP 18 system are perhaps the most promising for follow up of all the planets reported on here. Modulation is seen in the midpoints of the data suggesting a possible variation with phase. By binning the data per phase, a curve fitting a WASP 18b with geometric albedo of 0.4, multiple scattering, and a position angle of 140◦ is able to produce a 1.52 σ fit. However it would not simultaneously Chapter 9. Summary & Discussion 186 include the points that have error bars which do not overlap. The possible additional modulation seen near phase = 0 could be due to tidal interactions from the planet’s pull on the star (creating assymmetry in the limb). The best fit to the geometric albedo decreases slightly to 0.3 if the data is not binned.

The offset from zero is consistent with the amount expected from interstellar polarisation for a system in this direction at this distance (Q -70, U +185).

9.1.4 tau Bootis b

9.1.4.1 Polarised light

In the case of tau Boo b, little can be said about the polarised light from the non- transiting system at this time. Our data points are all taken around phase zero when there should be minimal signal from Rayleigh scattering. Without more complete phase coverage, no information about the orbit can be obtained. The offsets for the midpoints of these observations from interstellar effects are also difficult to judge as the values appear to be low but the error bars are still relatively large. For the midpoints the offsets are approximately Stokes Q +3 and Stokes U +13. The error bars in Stokes Q make the offset consistent with 0.

9.1.5 HD 179949b

9.1.5.1 Polarised light

The observations for HD 179949b are in good agreement with each other but lie along stright lines within their error bars. At midpoints Stokes Q is offset -31 and Stokes U is offset -6, assuming some of the variation near Rayleigh peaks is indeed due to the planet’s orbit. The system is an excellent follow up option for HIPPI and other polarimeters since the phase coverage of our data is fairly spread out. Reducing the error bars on the data could allow the inclination and position angle of the system to be reasonably well determined. Chapter 9. Summary & Discussion 187

9.2 Discussion

9.2.1 Forecast

The further refinement of the ATMOF routine for VSTAR will allow the clouds in both regions on the planet to be characterised well enough to warrent very high precision deuterium measurements from our high resolution data. This will be both the highest resolution data used to measure the deuterium and the first time that the deuterium abundance has been fit along with the cloud properties for the entire H band simulta- neously.

WASP 18b and HD 189733b are the most important systems outlined here for follow up. HD 189733b has a varying polarised light signal that does not modulate with the planet’s phase, making it an interesting subject and important calibrator for furture polarised light observations of exoplanetary systems. Further exploration into the space environment for HD 189733b, the activity of its host star, and its interactions with its host star will aid the identification of the unusual polarised light signals from the system. WASP 18b has data which possibly modulates with the planet’s phase, making it possibly the first exoplanet to have its own polarised light detected, but further observations are vital at this stage. It is also very possible that the possible modulation in polarised light from the WASP 18 system is actually the planet’s tidal effect on the star. This potential tidal would be an excellent subject to characterise, aiding future observations of polarised light from exoplanet systems.

HD 179949b and τ Boo b may have polarised light signals from the planet. HD 179949b’s measurements have very large errors but their midpoints suggest there may be a small modulation from the planet. There is not enough data nor phase coverage to make any assertions about τ Boo b’s polarised light signal currently but sufficient follow up observations at the points of peak Rayleigh scaterring in the phase curve could provide better insight into whether this system warrents further study with the strength of polarimeters currently available.

Along with WASP 18b and HD 189733b, other hot Jupiter hosting systems are set to be observed with HIPPI in an upcoming observing run in October. Recently an adaptation of VSTAR to polarised light (solving for the polarised light signal across the surface of the planet through phases with a full Rayleigh treatment, not to be confused with the Chapter 9. Summary & Discussion 188 phase curves presented in this thesis) was completed. This will be used in conjunction with the atmospheric models presented in the radiative transfer portions of this thesis to obtain a more complete description of the effects expected from the better characterised planetary systems.

9.2.2 Context

Let’s return to the question in the introduction of why we study exoplanets, and how the research presented in this thesis fits into that picture. The three reasons I referred to in the introduction to this thesis were:

Astrobiology drives us; we seek to pin down the numbers in Drake’s equa- tion, to tell us how prevalent life and intelligent life are in the universe.

Understanding our own solar system and planet formation drives us; we seek to know why our solar system looks different from other solar systems.

Personally, I am delighted by the strangness of the “inhospitable” places we find... If we are made of star stuff, so are planets.

The precursor to what will (hopefully) be very precise measurements of the deuterium isotope ratio of Uranus relates directly to planet formation. The preliminary cloud models presented here are novel in their attempt to fit the contiguous H-band observation for two different lattitudinal regions of the planet. They will aid in providing a better determination, with the highest resolution spectra yet used, of the D/H ratio for the planet. Uranus is a great diagnostic for the migration processes that took place in our early solar system, processes which seem to bring about a great variety of exoplanetary systems.

The radiative transfer models I’ve presented here are novel in their simultaneous treat- ment of the reflected, emitted and transmitted light with a single atmospheric model. They also use some of the most robust line-by-line modelling software available in the form of HIPPI. The confirmations and refinements to these radiative transfer models pre- sented here relate to the characterisation of wonderfully strange worlds. Furthermore, Chapter 9. Summary & Discussion 189 although these planets are certainly inhospitable to life as we know it, the continuing improvement of VSTAR and similar modelling software, congruent with improvements in the spectral data collection of planets, is already lending itself to astrobiology. We characterise hot Jupiters to learn about how strange they are and how they formed, but also to improve our abilities to characterise smaller, more “habitable” planets.

Finally the polarimetric measurements taken with HIPPI and presented in this thesis are among the most sensitive polarised light measurements yet taken of exoplanetary systems. Although this thesis does not report any certain detections, it converys the promise of further observations with HIPPI (and POLISH2). The findings presented here show the usefulness of polarimetry while simultaneously highlighting some additional considerations in determining the source of polarised light in exoplanetary systems.

In the very near future polarimeters may report the first (saving that reported in Berdyugina et al. [169]) detections of polarised light from the atmospheres of exoplan- ets. With moderatly detailed phase curve data astronomers would be able to dertermine some orbital parameters and basic physical characteristics (e.g. inclination, geometric albedo, presence of Rayleigh scattering) of the systems, which helps us understand the migration and formation of these strange systems.

More detailed polarimetry data in multiple photometric bands can provide even more detailed information about the constituents of the atmosphere. This contributes not only to the characterisation of the variety of planets, but with ever increasing sensi- tivities, may pave the way for the future characterisation of possible habitable worlds. Polarimetry could theoretically also aid astrobiology in the detection of glint from oceans and (for circularly polarised light) chiral molecules if capabilities continue to improve.

So, not only is the characterisation of planets a logical next step in learning about these three driving questions, but polarimetry in particular may be among the most valuable tools in moving forward with that characterisation.

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