1.3 Planets in Scattered Light

Research Collection

Doctoral Thesis

Characterization of planetary systems in scattered light with differential techniques

Author(s): Buenzli, Esther

Publication Date: 2011

Permanent Link: https://doi.org/10.3929/ethz-a-006838186

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ETH Library Diss ETH No. 19917

Characterization of Planetary Systems in Scattered Light with Differential Techniques

A dissertation submitted to

ETH Zurich¨

for the degree of DOCTOR OF SCIENCES

presented by

ESTHER BUENZLI Dipl. Phys. ETH

born May 22, 1983 citizen of Fehraltorf (ZH), Switzerland

accepted on the recommendation of

Prof. Dr. M. R. Meyer PD Dr. H. M. Schmid Dr. F. Menard´

Zurich,¨ 2011

— To Adrian —

Abstract

This thesis is devoted to the study of scattered optical and near-infrared light received from planetary system objects, in particular solar and extrasolar giant planets and debris disks. The light is originally emitted by the parent star and subsequently redis- tributed by the smaller bodies in a manner characteristic for their scattering particles. The measured scattered light therefore provides information on the size and composition of the individual particles, as well as on geometry and arrangement of an ensemble of particles. In this thesis, these are in particular gas and haze particles in planetary atmospheres, and dust particles in circumstellar debris rings. A challenge in measuring scattered light from exoplanetary systems is the brightness of the central star, whose halo outshines the much fainter, smaller objects at optical and near-IR wavelengths by many orders of magnitude. The stellar light must be removed to reveal the planets or dust, and a powerful method to achieve this is to use differential techniques. Differential polarimetry makes use of the fact that the emitted starlight is generally unpolarized, while scattering processes usually induce some amount of polarization. Subtraction of orthogonal polarization states therefore effectively removes unpolarized stellar light while preserving scattered polarized light. A second such technique is angular differential imaging, where the observed ﬁeld rotates around the star during the observations. The pupil plane, and therefore the stellar point spread function with its structure distortions introduced by the atmosphere and optics, remains ﬁxed. Subtraction of optimally chosen rotated frames removes the stellar point spread function while preserving the fainter objects’ signals.

PART ONE investigates in detail the diagnostic potential of polarimetry for the characterization of giant planet atmospheres. Models are calculated for the polarization depending on atmospheric parameters and constituents for extrasolar and solar system gas giants with a Monte Carlo multiple scattering code. First, a parameter study is performed with a large grid of simple models to determine the inﬂuence of scattering layer thickness, absorption and planet phase on intensity and polarization. Rayleigh scattering, isotropic scattering, and Henyey-Greenstein phase functions are considered. The disk-integrated polarization for phase angles typical for extrasolar planet observations, as well as the limb polarization effect observable for solar system objects near opposition, are discussed. The polarization as a function of wavelength is compared for a planet at quadrature and opposition, and predictions are made for broadband polarimetric observations.

v Abstract

In a second step, a detailed model of the atmosphere of Uranus is constructed to interpret spectropolarimetric observations of the limb polarization of Uranus for the wavelength range 530 to 930 nm. For the ﬁrst time, polarization properties of atmospheric constituents of Uranus are derived. The limb polarization is dominated by Rayleigh scattering on molecules. It is inﬂuenced by the polarization of a vertically extended tropospheric haze with wavelength dependent polarization properties, as well as a thin, highly polarizing stratospheric haze layer. From the limb polarization model, the polarization phase curve of Uranus and the spectropolarimetric signal at large phase angles is calculated in order to predict the polarization and detectability of an Uranus-like extrasolar planet. Finally, a model of Jupiter’s polar haze is made for spatially resolved spectropolarimetry, focusing on the polarimetric signal at 600 nm in a slit spanning from the North to the South pole. The strong radial polarization at the poles, with a seeing corrected maximum of more than 10%, is well explained by strongly polarizing and forward scattering fractal aggregate haze particles.

PART TWO describes observations of scattered light from the debris disk around the star HD 61005. Ground-based high-contrast imaging data in H-band are reduced with optimized angular differential imaging. The observations are of higher resolution than previous observations by the Hubble Space Telescope, and the disk is newly revealed to be a narrow, highly inclined ring. The ring center is found to be offset from the star by approximately 3 AU, which could be a result of a planetary companion that perturbs the remnant planetesimal belt. An upper mass limit for companions that excludes any object above the deuterium-burning limit for angular separations down to 0.35′′ is found. From a previously imaged swept-back outer feature, the likely result of interaction with the interstellar medium, we see two distinct streamers originating at the ansae of the ring. The ring shows a strong brightness asymmetry along both the major and minor axis. The brightness difference between the ring ansae can only partly be explained by the ring center offset, possibly suggesting density ﬂuctuations in the ring.

This thesis shows that scattered light observations with differential techniques are promising methods to detect and characterize planet atmospheres and debris disks as demonstrated on speciﬁc examples. These observations are very complementary to thermal light observations, and the sophisticated differential techniques make them feasible from large ground-based telescopes. In the outlook sections, ongoing observing programs are described that were initiated as a result of this thesis, in particular polarimetric observations of a hot Jupiter and follow-up observations of the HD 61005 debris disk for a characterization of the grain size distribution and a deeper planet search. Future prospects are discussed with a main emphasis on the upcoming 2nd generation instrument SPHERE for the Very Large Telescope.

vi Zusammenfassung

Diese Dissertation befasst sich mit dem Studium des optischen und nah- infraroten Streulichts von Objekten in Planetensystemen, insbesondere von so- laren und extrasolaren Riesenplaneten und Trummerscheiben.¨ Das Licht wird ursprunglich¨ vom Zentralstern ausgesendet und danach von den kleineren Objekten je nach Streueigenschaften ihrer Bestandteile weiterver- teilt. Das gemessene Streulicht enthalt¨ daher Informationen uber¨ die Grosse¨ und Zusammensetzung der einzelnen Teilchen und uber¨ die Geometrie und die An- ordnung der Ansammlung. In dieser Arbeit sind dies Gas- und Aerosolteilchen in Planetenatmospharen¨ und Staubteilchen in zirkumstellaren Trummerringen.¨ Eine Schwierigkeit beim Messen von Streulicht extrasolarer Planetensysteme ist die Helligkeit des Zentralsterns, dessen Halo das Streulicht der schwacheren¨ Objekte um ein Vielfaches uberstrahlt.¨ Differentielle Techniken sind wirksame Methoden, um das Sternenlicht zu entfernen und Planeten oder Staub sichtbar zu machen. Die differentielle Polarimetrie nutzt¨ aus, dass Sternenlicht im Allge- meinen unpolarisiert ist, wahrend¨ Streuprozesse meist einen Teil des Lichts po- larisieren. Subtrahiert man Messungen in orthogonalen Polarisationsrichtungen voneinander, verschwindet das unpolarisierte Sternlicht, wahrend¨ polarisiertes Streulicht erhalten bleibt. Eine zweite Technik ist “Angular differential imaging”. Dabei rotiert das beobachtete Bildfeld bei den Aufnahmen. Wahrenddessen¨ bleibt die Pupillenebene stabilisiert, und somit auch die stellare Abbildungsfunktion, welche durch die Atmosphare¨ und die Optik deformiert wird. Subtraktion von optimal ausgewahlten,¨ gegeneinander rotierten Bildern entfernt die Abbildung des Sterns, wahrend¨ die schwachen Objekte ubrig¨ bleiben.

DER ERSTE TEIL ist eine detaillierte Untersuchung des diagnostischen Potenti- als der Polarimetrie zur Charakterisierung der Atmospharen¨ von Riesenplaneten. Polarisationsmodelle in Abhangigkeit¨ von Atmospharenparametern¨ werden fur¨ solare und extrasolare Gasriesen mit einem Monte Carlo Streucode berechnet. Zuerst wird eine Parameterstudie mit einem grossen einfachen Modellgitter durchgefuhrt,¨ um den Einﬂuss von Streuschichtdicke, Absorption und Planeten- phase auf Intensitat¨ und Polarisation zu bestimmen. Rayleighstreuung, isotro- pe Streuung und Henyey-Greenstein-Phasenfunktionen werden betrachtet. Die scheibenintegrierte Polarisation fur¨ Phasenwinkel typisch fur¨ extrasolare Plane- ten sowie der Randpolarisationseffekt fur¨ raumlich¨ aufgeloste¨ Sonnensystempla- neten in Opposition werden diskutiert. Die Polarisation als Funktion der Wel- lenlange¨ wird fur¨ Planeten in Halbphase und Vollphase verglichen und Vorher- sagen fur¨ die Breitbandpolarisation werden gemacht.

vii Zusammenfassung

Im zweiten Schritt wird ein detailliertes Modell der Atmosphare¨ von Uranus erstellt, um spektropolarimetrische Beobachtungen der Randpolarisation von Uranus im Wellenlangenbereich¨ 530 bis 930 nm zu interpretieren. Zum ersten Mal werden polarimetrische Eigenschaften der Atmospharenbestandteile¨ von Uranus bestimmt. Die Randpolarisation wird durch Rayleighstreuung an Molekulen¨ do- miniert. Ausserdem wird sie durch eine vertikal ausgedehnte Aerosolschicht mit wellenlangenabh¨ angigen¨ Polarisationseigenschaften und eine dunne,¨ hochpolarisierende stratospharische¨ Aerosolschicht beeinﬂusst. Aus den Randpolarisati- onsmodellen wird die Polarisationsphasenkurve und das spektropolarimetrische Signal von Uranus bei grossen Phasenwinkeln berechnet, um die Polarisation und Beobachtbarkeit eines Uranus-ahnlichen¨ Exoplaneten vorherzusagen. Schliesslich wird ein Modell fur¨ die polaren Aerosole von Jupiter erstellt fur¨ raumlich¨ aufgeloste¨ Spektropolarimetrie, mit Fokus auf die Wellenlange¨ 600 nm in einem Spalt vom Nord- zum Sudpol.¨ Die hohe radiale Polarisation an den Polen, nach Seeingkorrektur hoher¨ als 10%, wird gut durch hochpolarisierende, vorwartsstreuende,¨ fraktal zusammengesetzte Aerosolteilchen erklart.¨

DER ZWEITE TEIL beschreibt Beobachtungen des Streulichts der Trummerscheibe¨ um den Stern HD 61005. Bodengestutzte¨ Hochkontrastbilder im H-Band werden mit optimiertem “Angular differential imaging” reduziert. Die Beobachtungen sind hoher¨ aufgelost¨ als fruhere¨ Bilder des Hubble Welt- raumteleskops, und die Scheibe wird neu als schmaler, stark inklinierter Ring gesehen. Das Ringzentrum ist vom Stern um ca. 3 AU versetzt, was auf einen planetaren Begleiter hinweisen konnte,¨ welcher den Ring von Planetesimalen stort.¨ Die obere Massengrenze fur¨ Begleiter mit einem Winkelabstand von mehr als 0.35′′ schliesst Objekte uber¨ der Deuteriumbrennlimite aus. Von einem schon fruher¨ abgebildeten, ausgedehnten, verformten Teil, welcher wohl durch Inter- aktion mit dem interstellaren Medium geformt wurde, sieht man zwei Bander,¨ welche von den Randern¨ des projizierten Rings ausgehen. Der Ring besitzt starke Helligkeitsasymmetrien entlang beider Halbachsen. Die Unterschiede zwischen den beiden Ringseiten konnen¨ nur teilweise durch das verschobene Ringzentrum erklart¨ werden, was zusatzlich¨ Dichteschwankungen im Ring vermuten lasst.¨

Diese Dissertation zeigt, dass Streulichtbeobachtungen mit differentiellen Techniken vielversprechend sind, um planetare Atmospharen¨ und Trummerscheiben¨ zu entdecken und zu charakterisieren, wie anhand mehrerer Beispiele demonstriert wird. Diese Beobachtungen sind komplementar¨ zu Mes- sungen der thermischen Strahlung. Die differentiellen Techniken ermoglichen¨ die Messung mit grossen erdgebundenen Teleskopen. Im Ausblick werden lau- fende Beobachtungsprogramme beschrieben, welche aufgrund der Resultate dieser Arbeit initiiert wurden. Dies sind polarimetrische Beobachtungen von heissen Jupitern und Nachfolge-Beobachtungen der HD 61005 Trummerscheibe¨ fur¨ die Bestimmung der Teilchengrossenverteilung¨ sowie eine tiefergehende Planetensuche. Zukunftsaussichten werden mit Hauptbezug auf das kommende Zweitgenerationeninstrument SPHERE fur¨ das Very Large Telescope diskutiert.

viii Contents

Abstract ...... v

Zusammenfassung ...... vii

1. Introduction ...... 1 1.1 The discovery of planetary systems ...... 2 1.1.1 Exoplanet detection techniques ...... 3 1.2 Scattering of light ...... 6 1.2.1 Physics of scattering ...... 7 1.2.2 Scattering on different particles types ...... 11 1.3 Planets in scattered light ...... 16 1.3.1 The structure of planetary atmospheres ...... 16 1.3.2 Observables ...... 18 1.4 Debris disks in scattered light ...... 23 1.4.1 Observables ...... 23 1.4.2 Current status of debris disks observations in scattered light 24 1.5 Differential techniques for high-contrast imaging of planetary systems ...... 25 1.5.1 Instruments for high contrast imaging ...... 25 1.5.2 Angular Differential Imaging ...... 26 1.5.3 Polarimetry ...... 27 1.6 Thesis overview ...... 29 Bibliography ...... 31

Part I Polarimetry of gaseous planets 35

2. A grid of polarization models for Rayleigh scattering planetary atmospheres ...... 37 2.1 Introduction ...... 38 2.2 Model description ...... 41 2.2.1 Intensity and polarization parameters ...... 42 2.2.2 Atmosphere parameters ...... 43 2.2.3 Geometric parameters ...... 43 2.2.4 Monte Carlo simulations ...... 45 2.3 Model results for a homogeneous Rayleigh-scattering atmosphere . 46

ix Contents

2.3.1 Phase curves ...... 47 2.3.2 Radial dependence for resolved planetary disks at opposition 50 2.3.3 Parameter study for quadrature phase and opposition . . . 53 2.4 Models beyond a Rayleigh scattering layer with a Lambert surface 59 2.4.1 Atmospheres with Rayleigh and isotropic scattering ..... 59 2.4.2 Forward-scattering phase functions ...... 60 2.4.3 Models with two polarizing layers ...... 63 2.5 Wavelength dependence ...... 64 2.6 Special cases and diagnostic diagrams ...... 67 2.6.1 Fractional polarization versus intensity ...... 68 2.6.2 Polarization near quadrature versus limb polarization . . . 70 2.6.3 Broadband polarized intensity ...... 70 2.7 Conclusions ...... 72 2.A Model grid tables ...... 75 Bibliography ...... 77

3. Polarization of Uranus: Constraints on haze properties and predictions for analog extrasolar planets ...... 79 3.1 Introduction ...... 80 3.2 Spectropolarimetric data ...... 81 3.3 Modeling ...... 83 3.3.1 Atmospheric structure and haze properties ...... 83 3.3.2 Radiative transfer code ...... 86 3.4 Results ...... 88 3.4.1 Rayleigh scattering and methane absorption ...... 88 3.4.2 Tropospheric haze ...... 89 3.4.3 Stratospheric haze ...... 92 3.5 Predictions for the polarimetric signal of Uranus at large phase angles ...... 93 3.6 Detectability of an Uranus analog around a nearby M dwarf . . . . 96 3.7 Conclusions ...... 97 3.7.1 Polarimetric properties of Uranus ...... 98 3.7.2 Limb polarization measurements for Uranus ...... 99 3.7.3 Prospects for exoplanet polarimetry ...... 99 Bibliography ...... 101

4. A polarimetric model for Jupiter’s polar haze ...... 103 4.1 Introduction ...... 103 4.2 Polarimetric data ...... 104 4.3 Polarization model for the poles of Jupiter ...... 107 4.4 Discussion and conclusions ...... 110 Bibliography ...... 113

x Contents

5. Outlook ...... 115 5.1 Prospects with SPHERE/ZIMPOL and beyond ...... 115 5.2 Hot Jupiter polarimetry ...... 118 5.2.1 Polarimetric search for WASP-18 b ...... 119 Bibliography ...... 122

Part II Angular differential imaging of a debris disk 123

6. Dissecting the ’Moth’: Discovery of an off-centered ring in the HD 61005 debris disk ...... 125 6.1 Introduction ...... 126 6.2 Observations ...... 127 6.3 Data reduction and PSF subtraction ...... 128 6.4 Results ...... 131 6.4.1 Surface brightness of ring and streamers ...... 131 6.4.2 Ring geometry and center offset ...... 132 6.4.3 Background objects and limits on companions to HD 61005 135 6.5 Discussion ...... 137 Bibliography ...... 141

7. Outlook ...... 143 7.1 Further observations of the Moth ...... 143 7.1.1 A search for companions inside the ring ...... 143 7.1.2 Resolved disk observations at different wavelengths . . . . 144 7.2 A detailed model for the Moth ...... 146 7.3 Future prospects for debris disks imaging ...... 147 Bibliography ...... 149

Acknowledgments ...... 151

List of Publications ...... 155

Chapter 1 Introduction

The question whether life is unique to Earth or ubiquitous in the universe has oc- cupied humankind for millennia. The astronomers’ task in answering this question is to determine whether planets around other stars are actually a common phenomenon, whether for such planets conditions for habitability are met, and how signs of life can be detected by remote observations. Taking a spectrum of a potentially habitable Earth-like planet is probably one of the greatest challenges of modern astronomy. Before we are capable of this endeavor, many subsequent smaller steps can be taken towards this ultimate goal. Giant planets are much easier to detect and characterize, and it is reasonable to develop the know-how for planet detection and characterization by studying large planets. At the same time, these studies can determine how diverse planetary systems are, provide clues to their formation and evolution, and help us establish the origin of our own solar system. During the past two decades it has been well established that planets around other stars exist with a wide range of masses and semi-major axes. Indeed, evidence points towards the fact that in particular smaller planets are quite common in the galaxy. Most planets have so far been found by indirect observing techniques, where the effect of the planet on the star is measured, rather than the light from the planet itself. This has the disadvantage that the planet’s atmosphere cannot be characterized. More recently, direct measurements have become feasible. There, the difﬁculty lies in separating the bright starlight from the much fainter planetary light. This is currently achieved with differential techniques, where the system is imaged in two ways, in which the star remains largely identical, but a planet property changes such that a subtraction removes the star and reveals the planet. The two techniques applied in this thesis are polarimetric differential imaging (PDI) and angular differential imaging (ADI). The planetary light has two components: a scattered light component that is reﬂected starlight, and a thermal light component, which is the radiation emitted by the planet itself. Young planets are quite warm and are therefore intrinsically bright, but the luminosity drops quickly with increasing age as the planet cools off. The amount of scattered light is independent of the planet age, rather it is inversely proportional to the squared distance between the star and the planet. Scattered light observations would constrain the planet albedo, the ratio between incoming and outgoing light, which is important for the energy balance of the atmosphere. Also, they would constrain particle properties, on which the scattering

1 Chapter 1. Introduction strongly depends. A scattered light search would target mainly nearby stars, because while the planet should be close to the star, it should also be well separated in angular distance. Also, many photons are required to have very low noise, because a high precision must be achieved to obtain the small star-planet contrast. The nearest brightest stars are therefore the ideal targets. Finding a planet in these systems would be extremely interesting for follow-up observations with future instruments. Not only planets can be imaged in scattered light. Debris rings, brighter Kuiper belt or asteroid belt analogs, are actually much easier targets. These observations directly reveal the dust geometry and can also show indirect evidence of planetary companions that sculpt the dust. The same differential techniques as for planet searches are applicable. In this thesis it is discussed how scattered light observations from planets and debris rings made with differential techniques can be interpreted. The introduction covers the fundamental background to this topic, starting from how planetary systems are discovered. The physics of light scattering and observables for planet atmospheres and debris disks are discussed, and the differential imaging techniques are introduced. Finally, a detailed overview over the content of the thesis is given.

1.1 The discovery of planetary systems

Before the development of optical instruments, five planets were known in addition to the Earth. Mercury, Venus, Mars, Jupiter and Saturn were easily visible by naked eye and recognizable as planets by their unusual motion with respect to the “fixed” stars. After the development of the telescope, two additional planets were discovered: Uranus in 1781 and Neptune in 1846. Many other objects were found to be a part of the Solar System that do not meet the currently accepted def- inition of a planet1. These include moons, asteroids, Kuiper belt objects, Comets, and small dust particles. While not planets, these objects still provide many clues towards the formation and evolution of our planetary system. The first evidence of circumstellar matter around a main sequence star without significant mass-loss was found in 1983, when the Infrared Astronomical Satellite (IRAS) discovered unexpectedly strong infrared radiation beyond 20 µm (Aumann et al. 1984) from Vega. The radiation was stronger than could be expected from the star alone, and this excess was quickly attributed to origin from small cool dust particles. The first scattered light image of such a dust disk was obtained when Smith & Terrile (1984) used a stellar coronagraph to block the light of the star β Pictoris, revealing an extended edge-on disk.

1 From the International Astronomical Union (IAU) resolution B5: A planet [in the solar Sys- tem] is a celestial body [excluding satellites] that is in orbit around the Sun, has sufﬁcient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and has cleared the neighborhood around its orbit.

2 1.1. The discovery of planetary systems

The discovery of an actual extrasolar planet happened in 1992, when Wol- szczan & Frail (1992) discovered three low-mass worlds orbiting the pulsar PSR B1257+12 by measuring the variation in the pulsar period induced by the planets. It is however likely that these planets accreted from ejected material after the supernova explosion that turned the star into a neutron star. The ﬁrst extrasolar planet orbiting a sun-like star was found around 51 Peg by Mayor & Queloz (1995). A big surprise was the fact that 51 Peg b is a Jupiter-mass planet orbiting its star with a period of only 4.2 days, much shorter than the orbital period of Mercury. This discovery led to a new era of planet detection using several different techniques, and today more than 500 extrasolar planets and more than 1000 additional planet candidates have been found. These discoveries show a huge diversity in planetary systems, with planet masses, separations and eccentricities often unlike those of the planets in the Solar System.

1.1.1 Exoplanet detection techniques The currently successful exoplanet detection techniques do not detect light scattered by the planet. Rather, most often they measure the effect the planet has on its host star. This effect can be the gravitational pull of the planet on the star (radial velocity and astrometry method), or the photometric dimming of the host star (transit method) or brightening (microlensing method) of a background source. Direct measurements have been made of the thermal emission of hot Jupiters (secondary eclipse measurements) and young self-luminous planets (direct imaging). Recent reviews of all techniques can be found e.g. in Seager (2011).

Radial Velocity In the radial velocity (RV) or Doppler spectroscopy method, a spectrum of the host star is measured at high resolution over the time of a planet’s orbit. The radial component of the motion of the star around the common center of gravity of star and planet can be detected through a periodic shift of the stellar absorption lines because of the Doppler effect. Today, radial velocity differences of less than 1 m/s can be measured for example with the HARPS instrument (Mayor et al. 2003), which has proven to be the most successful planet hunting instrument. The RV measurements do not deliver the true mass m of the planet, but only the projected mass m sin i, because only the line-of-sight component of the stellar motion produces a Doppler shift. Objects in a near face-on orbit will therefore have a true mass that is much higher than the measured minimum mass. However, this con- ﬁguration is statistically rare, assuming all planet orbits are randomly oriented in space. Therefore, most of the 500 planetary objects detected by the RV method will be true planets. Only for∼ 100 transiting planets the inclination is known, such that the true mass can be∼ found. The RV method additionally delivers the semi-major axis and eccentricity of the planet’s orbit. It is most suited for the detection of planets at small separations around quiet F to M-type stars with many absorption lines. Active and variable stars produce signiﬁcant noise in the radial

3 Chapter 1. Introduction velocity signal that makes the detection of low-mass planets difﬁcult. Planets at large separations, with periods of several years, need a long observing sequence until the planetary signal can be extracted. A long-term goal is to be able to measure radial velocities at precisions below 10 cm/s, which is required to ﬁnd an Earth-mass planet in the habitable zone of a solar type star.

Transits The transit method takes advantage of the fact that planets with an orbit that is well aligned with the line-of-sight will pass in front of the host star periodically, blocking a significant amount of stellar light, and thus dimming the star. The first discovered transiting planet, HD 209458, was found by Charbonneau et al. (2000). The transit method delivers the radius, and in conjunction with RV measurements the true mass and therefore density of the planet. A first characterization of the planet structure can thus be achieved, and has revealed a wide range of densities, from rocky planets (e.g. Kepler-10b, Batalha et al. 2011) to very puffy gas giants (e.g. Wasp-17b Anderson et al. 2010). During the transit, some stellar light passes through the atmosphere at the limb of the planet. Depending on the location of absorbers present in the atmosphere, the transit radius will vary with wavelength. Transit spectroscopy can therefore measure constituents of the planet’s atmosphere. Up to now, reliable detections were made for atomic sodium (Charbonneau et al. 2002), potassium (Sing et al. 2011) and hydrogen (Ly-α, Vidal-Madjar et al. 2003). When the planet passes behind the star in the secondary eclipse, the thermal light of the planet disappears and only the stellar light remains. Subtracting this light from a measurement made before the secondary eclipse leaves only the planetary light. Such a measurement can therefore be considered a direct detection of the planetary atmosphere (Charbonneau et al. 2005). If the planet is followed for the whole orbit, a thermal phase curve can be constructed (Fig. 1.1), and a basic longitudinal map of the planet temperature derived (Knutson et al. 2007). While a lot of information can be gleaned from a transiting planet, strict geometric requirements must be fulfilled for the planet to transit. The transit probability drops quickly for increasing planet separation from & 10% for hot jupiters to only 2% for a jupiter-sized planet in a 50-day orbit around a solar-type star (Kane &∼ von Braun 2009). Additionally, transits occur much less frequently for a long-period planet. A very large number of stars must therefore be continuously monitored. This is among others systematically done with the Kepler satellite (Borucki et al. 2003), which has in the first third of its mission already detected more than 1000 planet candidates (Borucki et al. 2011).

Microlensing The microlensing technique relies on the fact that an object can act as a lens that magniﬁes the light of a well-aligned background star, resulting in a well-deﬁned light curve. If a planet orbits the lens star, a secondary peak or lensing light curve

4 1.1. The discovery of planetary systems

Figure 1.1: Left: Schematic orbit of an eclipsing planet. Primary transit with transmit- ted light through the atmosphere, thermal phase variations and secondary eclipse. The planet size is not to scale. Right: Thermal phase curve with primary and secondary eclipse for HD 189733 b measured with Spitzer at 8 µm Knutson et al. (2007). distortions can be present in the light curve, giving the mass ratio between star and planet and the planet separation. These events are rare and unique, and cannot be followed-up. The method is sensitive to low-mass planets and planets at large separations. A large survey, monitoring millions of stars in the galactic bulge, can therefore provide unique statistical information about the occurrence of such planets. At this time, among others, a planet with a mass as low as 5 Mo plus (Beaulieu et al. 2006), a Jupiter-Saturn analog system (Gaudi et al. 2008) and a large number of giant planets at separations > 10 AU, some possibly even free-ﬂoating, (Sumi et al. 2011) have been detected.

Astrometry The astrometry method accurately measures the position of the star in the plane of the sky with respect to background stars, providing the projected orbit of the star around the center of mass of the star-planet system. The method is mainly sensitive to massive planets at large separations, for which long-term observations are necessary. At this time, no planet has been detected by astrometry, but several have been confirmed (e.g. GJ876 b, Benedict et al. 2002). The astrometric measurements then deliver the true mass and orbit of the planet. The space mission Gaia (Perryman et al. 2001) is expected to find thousands of giant planets at separations between 1 and 4 AU by measuring high-precision astrometry for 300,000 stars within 200 pc (Casertano et al. 2008). ∼ Direct imaging The most direct way of probing a planet’s atmosphere is through direct imaging, where an actual image of the planet is taken. This method is very difficult because the star is orders of magnitudes brighter than the planet and the planets are typically located at angular separations < 1′′. Even with the augmented resolution provided by an adaptive optics (AO) system and blocking the stellar light with

5 Chapter 1. Introduction a coronagraph, the stellar halo from the star’s PSF drowns the planetary signal. Sophisticated data reduction techniques are required to remove the stellar light. Such techniques are described in more detail in Sect. 1.5.2 and applied in Sect. 6. Favorable for direct detection are young planets that are still self-luminous because of gravitational contraction. In the near-infrared the star-planet contrast 5 6 for young massive planets is typically of order 10− 10− and therefore already in the range of today’s instruments at 8 m class telescopes− for separations & 20 AU. Older planets like in the Solar s System, that are barely self-luminous and 8 mainly shine from reflected starlight, show a contrast of only 10− and are much harder to discover. One method feasible for the detection∼ of such planets in the near future is polarimetry of scattered light. This technique is explained in Sect. 1.5.3 and its planet characterization potential discussed in Sect. 2 to 4. The first successful direct detection of a planetary system was achieved by Marois et al. (2008), who discovered three planetary mass objects (between 5 and 12 MJ) in wide orbits (24 to 68 AU) around the A-type star HR 8799 (Fig. 1.2). Further reasonably firm direct detections of planets are β Pic b ( 9MJ) at 8 AU Lagrange et al. 2010) and 1RXS J160929.1-210524 b, a planetary∼ mass object∼ at an unusually large orbit of 330 AU (Lafreniere` et al. 2010). Direct measurements in multiple filters allow a determination of the planet’s spectral type and thus a temperature, which together with the luminosity then provides a radius. Spectrophotometry or spectroscopy give a first indication of the composition of the planet’s atmosphere (e.g. Bowler et al. 2010; Currie et al. 2011, for HR 8799 b, indicating a cloudy atmosphere). The mass of the planets cannot be determined directly, but if the stellar (and thus planetary) age is known, evolutionary models (e.g. Baraffe et al. 2003) can give an estimate. Since the ages of stars are often not well known and the evolutionary models not yet well calibrated in the planetary mass range, the derived masses often have a relatively large uncertainty. Often enough, a potential planetary mass object is found to be a brown dwarf once the stellar age is determined more precisely (e.g. GJ 758 b, Thalmann et al. 2009; Currie et al. 2010).

1.2 Scattering of light

When an electromagnetic wave encounters a particle, be it a single electron, atom, molecule or a larger liquid or solid particle, the electric ﬁeld of the wave sets electric charges in the particle into oscillatory motion. The electric charges are accel- erated and therefore radiate electromagnetic energy (Fig. 1.3). This secondary radiation is commonly called “scattered light”. Even reﬂection and refraction on surfaces and interfaces and diffraction on slits, gratings or edges are actually scattering events on many coupled molecules. This thesis only treats elastic scattering, where the frequency of the scattered light remains constant. Inelastic scattering effects, e.g. Raman scattering, are not discussed. The excited charges may also convert part of the incident energy into other forms, for example thermal energy. This process is called “absorption”. A good

6 1.2. Scattering of light

Figure 1.2: The HR 8799 system with three directly imaged planets. The colorful pattern in the center are the speckle residuals after subtraction of the star’s PSF. Figure by Marois et al. (2008) review on the physics of scattering and absorption by particles is given in Bohren & Huffman (1983).

1.2.1 Physics of scattering In a single particle, the oscillating field induces a dipole moment in each region of the particle by perturbing the electron clouds of the atoms or molecules. Each dipole oscillates with the same applied frequency and emits light into all directions. At a distant point in some direction, the total scattered light is produced by a superposition of the single wavelets. Because dipole radiation is coherent, the phases have to be taken into account. The phase relations generally vary with scattering direction, depending on the size and shape of the particle. Both the amplitude and phase also depend on the particle material. Therefore, the final scattered intensity will strongly vary with direction, depending on the particle properties. For an incident monochromatic plane wave with an electric field

i(k x ωt) Ei = E0e · − , (1.1) the scattered field in the far-field region kr 1 is approximately transverse and can be written with respect to the incident field≫ as

ik(r z) E s e − S2 S3 E i k = k (1.2) E s ikr S4 S1. E i ⊥ − ⊥ E and E are the components parallel and perpendicular to the scattering plane k ⊥ deﬁned by the scattering direction er and the direction of the incident beam ez. S

7 Chapter 1. Introduction

Figure 1.3: Scattering of a light wave on a small particle, inducing dipole oscillations that reradiate energy at the same frequency. Figure by D. W. Hahn, Light Scattering Theory http://plaza.ufl.edu/dwhahn/RayleighandMieLightScattering.pdf. is the amplitude scattering matrix whose elements depend on the particle properties and scattering direction. A scattering process does not only influence the intensity of the light in a particular direction, but also its polarization. The polarization is the direction in which the electric field vector Ei(x, t) or Es(x, t) oscillates. Each wave has a certain polarization direction of its own, but the polarization of light, i.e. an ensemble of many waves, describes the degree to which the electric field vectors of these waves are aligned in a particular direction. If the orientation of the E-field vectors is randomly distributed, we speak of unpolarized light. There exist three types of polarization: linear, i.e. oscillation in a plane, circular, i.e. a rotating electric field vector at fixed z position, and elliptical polarization, which is a combination of the two. In this work, we focus solely on linear polarization, which is the dominant polarization for scattering from planetary atmospheres or dust grains in disks.

Stokes formalism Polarized light can be described with the four Stokes parameters, typically represented in the form of the Stokes vector I, where I is the intensity, Q and U the linear polarization in horizontal/vertical and diagonal direction, and V the circular polarization (Fig. 1.4).

2 2 E0 + E0 I x y I0◦ + I90◦ Q E2 E2 I I I =   =  0x − 0y  =  0◦ − 90◦  . (1.3) U 2E0 E0 cos (δx δy) I45◦ I135◦  x y −  −  V   2E E sin (δ δ )   IR IL     0x 0y x − y   −        x and y denote the components of the amplitude E0 and phase δ of the electric component of the wave in these directions, with the propagation direction being z. IX are the intensities measured through a polarization ﬁlter with throughput

8 1.2. Scattering of light

Figure 1.4: Left: Electric field vector evolution of elliptically polarized light, decomposed into circular polarization Ecirc (blue) and linear polarization components Ex (red) and Ey (green). Right: Stokes components for linear polarization Q and U. The direction of +Q is defined arbitrarily, but commonly in sky north direction. +U is defined as the direction rotated by 45◦ counter-clockwise. After rotation of 180◦ the polarization is back in the same state. for polarized light in direction X. R and L stand for right- and lefthand circular polarization. The Stokes vector is not actually a vector, but rather a one-column matrix. The following relation always holds:

I2 Q2 + U2 + V2 0, (1.4) ≥ ≥ where the ﬁrst equal sign holds for fully polarized light and the second for unpolarized light. Intermediate cases are called partially polarized. The degree of polarization is Q2 + U2 + V2 p = , (1.5) p I and the polarization angle θ for linear polarization is given by

U tan 2θ = , (1.6) Q counted in counter-clockwise direction with θ = 0◦ in positive Q direction. A scattering process modiﬁes the full Stokes vector of incoming light. Equa- tion 1.2 can be reformulated as

Is F11 F12 F13 F14 Ii Qs 1 F21 F22 F23 F24 Qi Is =   = 2 2     . (1.7) Us k r F31 F32 F33 F34 Ui  V  F F F F   V   s   41 42 43 44  i        with F the scattering matrix composed of the real components Fij that can be calculated from Sk in Eq. 1.2. For most scattering cases some degree of symmetry is present, and not all 16 matrix elements are independent.

9 Chapter 1. Introduction

For scattering on a sphere or on a group of randomly oriented particles which have a plane of symmetry, only six independent matrix elements remain:

F11 F12 0 0 F F 0 0 F =  12 22  (1.8) 0 0 F F 33 − 34  0 0 F F .   34 44    Neglecting circular polarization, i.e. setting any Fi4 component equal to 0, the remaining elements are given by: 1 F = ( S 2 + S 2 + S 2 + S 2), (1.9) 11 2 | 2| | 3| | 4| | 1| 1 F = ( S 2 S 2 + S 2 S 2), (1.10) 12 2 | 2| −| 3| | 4| −| 1| 1 F = ( S 2 S 2 S 2 + S 2), (1.11) 22 2 | 2| −| 3| −| 4| | 1| F = (S S∗ + S S∗). (1.12) 33 ℜ 2 1 3 4 These scattering matrix coefficients are discussed for different particle types in Sect. 1.2.2. F11 is usually referred to as the (single) scattering phase function, while F /F corresponds to the single scattering fractional polarization. − 12 11 Radiative transfer with scattering When electromagnetic radiation propagates through a medium, the Stokes vector I varies because of absorption, emission and scattering in the medium. Mathe- matically, this is expressed by the equation of radiative transfer: dI = αI + ǫ, (1.13) dS − where α = µa + µs is the extinction coefficient, the sum of absorption and scattering coefficient, and ǫ the emission coefficient that includes intrinsic emission and scattered radiation. Here the focus is only on absorption and scattering at a specific frequency ν, the intrinsic emission is neglected, which is reasonable in the short-wavelength limit. Then,

dIν µs,ν = (µa,ν σs,ν)Iν + F(θ)IνdΩ, (1.14) dS π Ω − − 4 Z where F is the scattering phase matrix and θ the scattering angle. There exist several methods for solving this equation to calculate the ﬂux and polarization scattered from an atmosphere into a particular direction. A few special cases can be calculated analytically, to be found for example in Chan- drasekhar (1950). For most cases however, numerical methods must be applied. A popular method to calculate the intensity and polarization of a multiply- scattering atmosphere is the “adding-doubling method” (Hovenier 1971). In this

10 1.2. Scattering of light technique, the reflection and transmission properties of a plane-parallel slab are calculated by starting from a thin homogeneous layer with known properties, doubling it to the desired thickness, or adding thin dissimilar slabs. Its disadvantage is that it is only suited for horizontally homogeneous planet atmospheres. A more flexible and straight-forward method is to use a Monte Carlo code. Pho- tons are followed on their path through the atmosphere, where they scatter or absorbe with some probability depending on the cross sections and abundances. Scattering directions are deduced from probability density functions constructed from the phase matrix. A detailed introduction to the specifics of the method applied to planet atmospheres in this thesis can be found in Schmid (1992), and a summary in Chapter 2.

1.2.2 Scattering on different particles types Rayleigh scattering When the scattering particle is very small compared to the wavelength of the light, the Rayleigh scattering approximation holds. This type of scattering is very important in atmospheres, because all gas molecules fall in this regime. It is also valid for very small haze particles. The mathematical conditions for Rayleigh scattering are, 2πa x = 1, m α 1 (1.15) λ ≪ | | ≪ where x is the size parameter, a the particle radius, λ the incident wavelength in the surrounding medium (λ = λ0/m0 with λ0 the wavelength in vacuum and m0 the refractive index of the medium), and m = n iκ the complex refractive index of the particle. The real part n of the refractive index− indicates refraction of light, while the imaginary part corresponds to absorption. For a dielectric particle (κ = 0) there is only scattering, and no absorption. A Rayleigh scattering particle scatters light like an oscillating dipole. If the polarizability of the particle is isotropic, e.g. for a small sphere, the scattering matrix components (Eq. 1.9 to 1.12) are given by:

2 1 x6 m2 1 F = − 0.5(1 + cos2 θ), (1.16) k2r2 11 k2r2 m2 + 2 ·

2 1 x6 m2 1 F = − 0.5(cos2 θ 1), (1.17) k2r2 12 k2r2 m2 + 2 · −

2 1 x6 m2 1 F = − cos θ, (1.18) k2r2 33 k2r2 m2 + 2 ·

The angular distribution of scattered light depends on the incident polarization (Fig. 1.5). For incident unpolarized light, forward and backward scattering are enhanced with respect to right angle scattering. For scattering at an angle θ = 90 the polarization fraction p = F /F = 100% and the direction ◦ − 12 11

11 Chapter 1. Introduction

Figure 1.5: Angular distribution (normalized) of the light scattered by a sphere small compared to the wavelength for incident unpolarized light (solid), polarized parallel (dashed) and polarized perpendicular (dash-dot) to the scattering plane. Figure reprinted from Bohren & Huffman (1983). perpendicular to the scattering plane. For molecules the polarizability is generally not isotropic, and a small depolarisation is introduced, depending on the molecule shape and number of electrons. For the major ingredients of planet atmospheres, this effect is of order 1 2%. This small depolarization is neglected in the Rayleigh scattering calculations− in this thesis. Very typical for Rayleigh scattering is the wavelength dependence of the scattering cross section: if m is independent of λ, which nearly holds for molecules, ∝ x6 ∝ 4 then σ(λ) k2 λ− . Rayleigh scattering is therefore much stronger at shorter wavelengths than at longer wavelengths, which is the main reason why the Earth’s sky is blue. Rayleigh scattering in planet atmospheres is the main focus of Chapter 2.

Mie scattering on spherical particles Scattering on a spherical particle can be solved exactly using Mie theory (Mie 1908). The basis of the solution is the expansion of the plane wave in spherical harmonics. The lengthy calculation of incident and scattered ﬁeld is given in Bohren & Huffman (1983). The matrix components S1 to S4 (Eq. 1.2) are

∞ 2n + 1 S1(θ)= ∑ (anπn(cos θ)+ bnτn(cos θ)) (1.19) n=1 n(n + 1)

∞ 2n + 1 S2(θ)= ∑ (bnπn(cos θ)+ anτn(cos θ)) (1.20) n=1 n(n + 1)

S3(θ)= S4(θ)= 0 (1.21)

12 1.2. Scattering of light

Figure 1.6: Single scattering phase function and polarization of example Mie scattering particles as a function of scattering angle. F11 is normalized to the value at 0◦ scattering angle. Lines indicate: water droplets with effective size parameter xe f f = 23 and “standard” (Hansen & Travis 1974) size distribution (blue, Karalidi et al. 2011), haze particles (n = 1.66) with xe f f = 4.5 and standard size distribution (green, Stam et al. 2004), spheres with xe f f = 15 with refractive index m = 1.53 + 0.008i and power-law size distribution (red, Mishchenko & Travis 2003), and the Rayleigh scattering limit (black).

πn(cos θ) and τn(cos θ) are functions of Legendre polynomials. an and bn are expressed through Riccati-Bessel functions and also depend on the size parameter x (Eq. 1.15). From the coefficients follow also the scattering and extinction cross sections, ∞ 2π 2 2 Csca = 2 ∑ (2n + 1)( an + bn ), (1.22) k n=1 | | | | 2π ∞ Cext = 2 ∑ (2n + 1) (an + bn). (1.23) k n=1 ℜ For scattering on multiple particles a sum over all particles per unit volume must be performed to get the total scattering and extinction coefficients. The phase functions usually show a strong forward scattering peak, which increases with particle size. Phase functions of a collection of spherical particles of size similar to the wavelength often show strong ripples because of interference of multiply refracted rays. These disappear for larger particles, or are smoothed out if a wider size distribution of particles is present. The polarization can also be partly negative (parallel to scattering plane). Some spheres, such as water droplets, have one or more narrow peaks at large scattering angles, corresponding to a rainbow feature. The wavelength dependence of the scattering cross section is generally weak, which explains why clouds and fog are white. Numerical calculations are straightforward and many codes are available for the calculation of these coefficients from Mie theory, e.g. bhmie2 given in the Ap- pendix of Bohren & Huffman (1983). A sample of phase functions is shown in Fig. (1.6).

2 Code available in several programming languages at http://code.google.com/p/scatterlib/

13 Chapter 1. Introduction

Figure 1.7: An aggregate particle constructed by diffusion-limited aggregation seen from two different sides. The particle is made of 170 monomers with each monomer consisting of 22 dipoles. Each dipole is depicted as a small sphere. Figure from West (1991).

Scattering on fractal aggregate particles While Mie theory is only exact for spherical particles, e.g. water droplets, it is often used as a ﬁrst approximation for scattering on non-spherical particles, such as dust or aerosol particles. The phase function is often quite well reproduced, with a strong forward scattering peak and reduced back scattering compared to Rayleigh scattering. However, with more polarization measurements of planet atmospheres or dust disks available, it was soon found that the full phase matrix is often poorly reproduced by Mie theory. This was clearly demonstrated for the haze particles at the poles of Jupiter with Pioneer observations (West 1991). The polarization phase function resembles strongly the Rayleigh polarization phase function, with a peak of almost 100% near 90◦ phase angle, while the phase function is strongly forward scattering (Fig. 1.8). This combination cannot be reproduced by Mie theory. It was theorized that these particles are fractal aggregate particles (see Fig. 1.7 and Sect. 1.3.1 and 4), for which the forward scattering part is reproduced by the average projected area, while the high polarization arises from the smaller monomer components. The phase functions of such particles can only be calculated with approximations and the calculations are computa- tionally intensive. Two commonly used methods are the Discrete Dipole Approx- imation (DDA, e.g. Yurkin et al. 2007) and the T-matrix method (e.g. Mishchenko et al. 1996), for which a simpler approximate parametrization has been used by Tomasko et al. (2008).

Absorption The absorption along a beam of light penetrating an absorbing material generally follows the Beer-Lambert law, sometimes simply called Beer’s law,

µa(λ)z I(λ, z)= I0e− . (1.24)

The validity of the law breaks down at large abundances, in particular if the material is also highly scattering. In some instances, non-linear effects can also induce a deviation. In this thesis, the Beer-Lambert law is considered valid.

14 1.2. Scattering of light

Figure 1.8: Single scattering phase function and polarization of a sample fractal aggregate dust particle composed of silicate and graphite as a function of scattering angle for different wavelengths, calculated with the discrete dipole approximation. F11 is normalized to the value at 0◦ scattering angle. For the longest wavelength, the Rayleigh scattering limit holds. Figure adapted from Shen et al. (2009).

The absorption coefﬁcient of a particle is derived from the complex part κ of the index of refraction m = n iκ. Replacing the wave number in the propagation − direction kz in the electromagnetic wave (Eq. 1.1) with the relation kz = ωm/c,

ωκz i(kzz wt) E(z, t)= E0e− c e − (1.25)

This is therefore equivalent with a wave without a complex index of refraction and a damping factor. The absorption coefﬁcient is then,

ωk 4πκ µ = = . (1.26) a c λ If only the transmission of light into a particular direction is regarded, then light losses by scattering must also be taken into account. In that case,

(µa(λ)z+µs(λ)z) αz I(λ, z)= I0e− = I0e− , (1.27) where α is the extinction cross section. While dust, haze and cloud particles can be absorbing to some degree, the main absorbers in the solar system gas giant atmospheres are molecules with transitions in the optical or near-infrared. Absorption through dipole transitions which occur in the optical and infrared only work for polar molecules with a permanent dipole moment. For the cool gas giants, the dominant absorber at optical wavelengths is methane. No laboratory measurements exist for the methane absorption coefﬁcients at the temperature and pressure conditions of the gas giant planets. The best available absorption coefﬁcients were measured empirically

15 Chapter 1. Introduction from the Solar System gas giant’s albedo spectra by Karkoschka (1998) and improved by Karkoschka & Tomasko (2010) with in-situ measurements of Huygens on Titan. For hot atmospheres like hot Jupiters, pressure-broadened atomic features, such as Na or K can be very strong (e.g. Burrows et al. 2008). Another form of absorption that is significant especially in the cloud-free atmospheres like Uranus and Neptune is collision-induced absorption (CIA). This type of absorption occurs when the electron cloud of a molecule is displaced by collision with another molecule, thus forming a temporary dipole moment. The light wave can then modulate the dipole moment to shift the molecule between different rotovibrational (in the visible and near-infrared regions) or roto- translational (far-infrared and microwave regions) states. Then, part of the light is absorbed in some frequency bands. This mechanism works for non-polar molecules, and in gaseous atmospheres it is strongest for collisions between H2 molecules. The collision-induced absorption coefficients are proportional to the product of densities of the collision partners. Absorption profiles can be calculated by numerical integration of Schroedinger’s equation with the appropriate dipole and potential models. The calculated profiles can also be represented in simpler, analytical expressions that allow a faster evaluation for desired wavelengths, temperatures and gas densities and are reasonably accurate. Such calculations of absorption coefficients for all significant collision partners and frequency bands in planetary and stellar atmospheres were performed by A. Bo- rysow3, e.g. in Borysow (2002).

1.3 Planets in scattered light

1.3.1 The structure of planetary atmospheres The fundamental parameters of a planetary atmosphere are its pressure, temperature and composition. These vary strongly with height and often also with location on the planet. For simplicity we here assume only the 1D case where a single vertical pressure, temperature and abundance proﬁle describes each point on the planet sphere. The atmospheric structure has been investigated in detail for the Solar System planets, both remotely and in-situ, while ﬁrst observations of exoplanet atmospheres already provide insight into vastly different atmospheres. A review on Solar System gas giant atmospheres can be found in Irwin (2003), and on exoplanet atmospheres in Seager (2010), on both of which this chapter is based.

Pressure and Temperature If the vertical wind velocities are much smaller than the horizontal velocities, the assumption of hydrostatic equilibrium is very accurate. This is generally the case

3 Tables and codes for all calculations are publicly available at http://www.astro.ku.dk/ aborysow/programs/index.html

16 1.3. Planets in scattered light in planetary atmospheres. Then the pressure difference dp through a slab of air with density ρ and thickness dz subject to gravitational acceleration g is

dp = ρgdz. (1.28) − From the ideal gas law, which is adequate for planetary atmospheres,

ρkT P = nkT = (1.29) µmH with n the number density, k the Boltzmann constant, µ the mean molecular weight and mH the mass of a hydrogen atom. Inserting Eq. 1.29 into Eq. 1.28 and integrating under the assumption that the temperature is constant with height, it follows that z/H p = p0e− (1.30) where p0 is the pressure at z = 0 and

H = kT/µmH g (1.31) is the scale height. Because many giant planets rotate very rapidly and are therefore oblate, the gravitational acceleration g and thus the scale height H vary sig- niﬁcantly between equator and polar regions. Additionally, the mean molecular weight may vary with height if some species condense, and the temperature is generally not constant with height. In planetary atmospheres the competing modes of energy transport are mainly radiation and convection. If the optical depth is high, radiation cannot easily escape and the atmosphere is convective. This is generally the case in the lower troposphere. The temperature gradient is then adiabatic,

dT g = = Γd (1.32) dz −cp − with cp the speciﬁc heat capacity at constant pressure and Γd the dry adiabatic lapse rate. If clouds condense the temperature drop with height is a bit slower with the saturated adiabatic lapse rate Γs. At higher altitudes, the optical depth towards space becomes smaller and radiation can more easily penetrate and escape. The atmosphere becomes radiative and the temperature is determined by radiative equilibrium. In the upper troposphere the temperature decreases down to a certain level at the radiative-convective boundary (tropopause). In the stratosphere, the atmosphere is highly stable against convection, the air forms stratiﬁed layers and the temperature raises with height because of the absorption of sun- light (see e.g. Fig. 3.3 for the atmospheric structure of Uranus). For the giant planets, the temperature structure of the stratosphere and tropopause depends strongly on the photochemical processes.

17 Chapter 1. Introduction

Atmospheric composition The composition of atmospheres is mainly dominated by three components: gas, clouds and haze. The distinction between clouds and haze is not always clear in the literature. A simple distinction could be that clouds are formed through condensation of gaseous species, while haze is formed in the upper atmosphere layers through photochemical processes and may then gradually move lower through eddy transport. Gas abundances are usually given as the (volume) mixing ration fi = ni/ntot, with ni the number density of the ith gas and ntot the total number density of gases. For giant planets, the dominant gases are H2 and Helium, with the absorption features in the spectra of the Solar System gas giants dominated by methane. A gas condenses when its partial pressure equals the saturated vapor pressure and cloud condensation nuclei are present. The approximate condensation level of a cloud can be estimated from thermodynamics with the Clausius-Clapeyron equation, dp ∆S Lp = (1.33) dT ∆V ≈ RT2 with L the latent heat of vaporization per mole and R the molar gas constant. This equation can be integrated depending on the temperature dependence of L. Photochemistry is induced by UV radiation from the host star, which disso- ciates molecules in the upper layers of the atmosphere. The fragments can then recombine into different molecules. For example, dissociated methane may form ethane or other hydrocarbons, such as chains of polyacetylene that then assemble to aggregate particles. Another important dissociation mechanism are charged particles. For example at the poles of Jupiter, auroral activity is believed to play an important part in the formation of fractal aggregate particles. Figure 1.9 de- picts a plausible scheme for the formation, coagulation and settling of particles in the atmosphere at the poles of Jupiter (Friedson et al. 2002).

1.3.2 Observables When observing a planet inside or outside of the Solar System, we measure the flux received from the planet. Analyzing the flux variations with wavelength or polarization state and with respect to the incoming radiation from the star, many physical properties of the planet can be derived. The influence of different parameters on these observables is discussed extensively in Chapter 2 and applied to two specific cases in Chapters 3 and 4.

Reﬂectivity A key concept for scattered light observations from planets is the albedo, which is a measure of the reﬂectivity of the planet. It is given by the ratio of light scattered by the planet to that received. A high albedo indicates strong scattering, e.g. on gas or clouds, while for a low albedo the planet mainly absorbs light. The albedo

18 1.3. Planets in scattered light

Figure 1.9: Schematic view of production, coagulation and settling of aggregate haze at the poles of Jupiter through microphysical processes. Figure reprinted from Friedson et al. (2002). controls the energy balance of the planet and its effective temperature, because absorbed light contributes to the thermal pool of photons and is reemitted as heat at thermal wavelengths. There are different ways of specifying the planetary albedo, and it is important to clarify which albedo is meant in a specific situation. The spherical albedo AS is the reflectivity in all directions at a single wavelength. For AS = 1 all incoming radiation at that wavelength is scattered back into space. The bond albedo AB is the spherical albedo integrated over all wavelengths, and thus the total radiation scattered back into space over all directions and wavelengths. AB is weighted by the incoming radiation and therefore depends on the stellar spectrum. The Bond and Spherical albedos are not ideal quantities to describe extrasolar planets, since the radiation cannot generally be measured over all directions. It is favorable to express the reflectivity as a function of the phase angle α. The phase angle is the angle between the star, the planet, and the observer. At α = 0◦ the fully lit hemisphere of the planet is turned towards to the observer. Extrasolar planets are hidden behind their star at that point, while the outer Solar System planets are fully visible at opposition. At α = 180◦ only the dark side is visible and the planet is eclipsing the star. An extrasolar planet in a face-on system will

19 Chapter 1. Introduction

Figure 1.10: Schematic phase and polarization of a planet on an orbit with a moderate inclination. The solid lines indicate the orientation and strength of the polarization for a Rayleigh scattering atmosphere. The dotted circle approximately shows where the stellar halo will prevent planet detection. always be seen at a phase angle α = 90◦. More generally,

cos α =(sin i sin θ) (1.34) · where i is the inclination of the system and θ the angle of the planet with respect to the time t when the radial velocity is maximal. For circular orbits θ = 2π(t 0 − t0)/T with T the orbital period. The geometric albedo Ag(λ) is defined as the reflectivity at α = 0 at a particular wavelength λ, normalized to the reflectivity of a flat Lambert surface that sub- tends the same solid angle. A Lambert surface scatters all incoming radiation isotropically, and shows equal brightness when viewed from any direction. A Lambert sphere has an Ag = 2/3. In principle, an object can be more strongly reflecting into a particular direction than a Lambert surface, and therefore the geometric albedo can be larger than 1. This is for example the case for Saturn’s moon Enceladus for which Ag = 1.38 (Verbiscer et al. 2007). The phase function f (α) expresses the reflectivity at any phase angle. The relation between this reflectivity and the spherical albedo is then,

π As(λ)= 2 f (α) sin αdα (1.35) Z0 Polarization Not only the reﬂectivity changes with phase angle, but also the polarization fraction. If single scattering dominates, then the polarization phase function will basically follow the single scattering polarization function ( F12/F11 in Eq. 1.7). If multiple scattering occurs, the polarization directions of the− scattered photons will be more randomly oriented, and the resulting polarization is lower. Bumps in the single scattering polarization function (e.g. rainbows) are smoothed out. For Rayleigh scattering, the maximum polarization still occurs near 90◦, but it is only about 30% (see Chapter 2). Since the polarization is generally perpendicular to the scattering plane (and therefore positive), the orientation of the polarization also depends on phase angle (Fig. 1.10). If the system is seen near face-on,

20 1.3. Planets in scattered light

Figure 1.11: Illustration of the limb polarization effect for planets near opposition. Backscattered light from near the limb is either unpolarized (immediate backscattering) or polarized perpendicular to the limb after two or more scatterings. See text for explanation. Figure from Joos & Schmid (2007). the phase angle stays 90◦ and the polarization fraction p(α) will remain approximately constant. However, the polarization direction will vary and the polarization can still be measured differentially between different phases of the orbit in Stokes Q/I and U/I. If the orbit is near edge-on, the polarization direction will stay the same along the orbit, but the polarization fraction will vary between 0 at 0◦ phase angle and maximum near 90◦ (for Rayleigh scattering). At 0◦ phase angle, the polarization integrated over a planetary disk is zero if the planetary disk is uniform and/or symmetric. For extrasolar planet observations, this is not relevant. A planet is behind the star, and therefore not observable, in that situation. The outer Solar System gas giants are however always seen at very small phase angles from Earth and only a very small polarization is expected. However, a second order scattering effect, the limb polarization effect (van de Hulst 1980), produces a linear polarization near the limb of the planet that is measurable if the planet can be spatially resolved. Figure 1.11 illustrates why this effect occurs. An incoming unpolarized photon that is singly scattered backwards (at point 1) remains unpolarized. Photons that are scattered in a plane approximately tangential to the visible limb (at point 1) and, with one or more scatterings, back towards the observer (point 2) will have scattered predominantly perpendicular to the scattering plane and are therefore polarized perpendicular to the limb. Photons that are scattered perpendicular to the visible limb (at point 1) will have a higher chance of being absorbed if scattered downwards, or of escaping if scattered upwards because of the different densities. Therefore, a larger number of polarized photons scattered from the limb returns to the observer and a net radial polarization perpendicular to the limb is visible. Low spatial resolution degrades the polarization fraction, because overlapping areas of negative (horizontal) and positive (vertical) polarization cancel out.

21 Chapter 1. Introduction

Contrast When observing an extrasolar planet in scattered light, we cannot measure the albedo and polarization fraction directly. Rather, we measure the contrast between the star and the planet. This number depends also on the number of photons from the star incident on the planet, which directly depends on the distance of the planet to the star and the size of the planet. The intensity contrast, 2 2 Fp πR 4 f (α) R CI(α)= = 2 AS = 2 f (α) (1.36) Fs 4πa AS a where R is the planet radius, a its separation from the star, AS the spherical albedo, and f (α) the phase function with f (0◦) the geometric albedo. The factor of 4 f (α)/AS gives the solid angle into which the observed radiation is scattered at the planet surface with respect to 4π. From the intensity contrast, the polarization contrast is simply calculated by multiplying with the polarization fraction, R2 C (α)= C (α)p(α)= f (α)p(α) (1.37) p I a2 with p(α) the phase dependent polarization fraction. While the polarization contrast is lower than the intenstiy contrast because p 1, the liming contrast reached with polarimetry is signiﬁcantly better than only≤ in intensity thanks to the differential method. Effectively, a much fainter signal can be recovered.

Thermal emission All planets emit some amount of thermal radiation, mostly in the infrared, in addition to the reflected starlight. The thermal radiation is generally unpolarized. If the thermal contribution is significant with respect to the reflected light at a particular wavelength, the polarization degree of the planet at that wavelength will be lower than without thermal radiation. The wavelength range where significant thermal radiation is emitted depends strongly on temperature. For the cool Solar System gas giants, the thermal radiation is negligible with respect to the reflected light below 2 µm. For very young, hot self-luminous planets, or for strongly irradiated hot Jupiters, the thermal radiation can be significant even in the optical wavelength range. Reflected light searches therefore do not target very young planets. For hot Jupiters, the planet cannot be separated from the star, and additional contrast enhancing techniques like using a coronagraph or Angular Differential Imaging (cf. Sect. 1.5 are useless. The final contrast limit, that determines whether a planet of given contrast is measurabe, must therefore be established entirely from the polarimetrc accuracy of the instrument. The additional unpolarized thermal contribution of the planet is insignificant for polarization measurements, because only polarized reflected light is counted .For intensity searches of scattered light, e.g. phase curve measurements with CoRot (Snellen et al. 2009), it is however not possible to separate the scattered from the thermal light, making an albedo measurement more difficult.

22 1.4. Debris disks in scattered light

1.4 Debris disks in scattered light

Circumstellar dust in planetary systems holds a much smaller mass than planets, but because of the much larger surface area it produces strong observational signals in scattered light or from thermal reemission of photons. The easiest way to detect a dusty disk is by measuring the spectral energy distribution (SED) of the star in the thermal infrared. The thermal dust radiation provides an excess on top of the stellar spectrum. The IRAS satellite measured such excess for over a hun- dred nearby main-sequence stars (e.g. Backman & Gillett 1987) and the Spitzer satellite expanded the known sample (e.g. Hillenbrand et al. (2008)). The disk detections are sensitivity (or calibration) limited and only relatively bright debris disks can be detected with current instruments. An extrasolar analog of the So- lar System Kuiper belt or asteroid belt would remain yet undetected, therefore it can be reasonably assumed that circumstellar dust and planetesimals occur very frequently. From the shape of the SED excess some constraints on the dust temperature(s) and inner disk radius can be made. The geometry and grain properties of the dust are however quite degenerate. For example, depending on the dust properties one or multiple narrow rings can have a very similar infrared signature as more extended dust region. It is therefore crucial to additionally obtain resolved images of the disk which clearly constrain the geometry and give additional clues about the dust properties to break the degeneracies, either from scattered light observations or thermal infrared observations as performed by the Herschel satellite Matthews et al. (e.g. 2010). A detailed review on debris disks focusing on infrared observations and evolution is Wyatt (2008). More focus on direct imaging of disks in scattered light is given in Kalas (2010). The link of debris disks to planetesimals and planets is described in detail in Krivov (2010).

1.4.1 Observables The infrared brightness of a disk is usually expressed in terms of the fractional luminosity f = Lir/L , the ratio between disk and star infrared luminosity. For 2∗ debris disks f < 10− . Scattered light observations give the surface brightness of the disk as a function of separation from the star projected into 2 dimensions, usually expressed in Jy/arcsec2 or mag/arcsec2. With observations at multiple wavelengths and additional polarization measurements, grain properties such as size distribution or porosity can be much better constrained (e.g. Fitzgerald et al. 2007; Graham et al. 2007). Additionally, the geometry of the scattering disk is strongly constrained. The inclination with respect to the line of sight is immediately evident, which is of particular interest if an additional companion discovered with the radial velocity method is present that might have coplanar orbit with the disk. The system ar- chitecture in radial, vertical and/or azimuthal can also be assessed. Most often the debris disks were revealed to be quite narrow rings with large inner holes. The truncation slope of the inner or outer boundary or an offset of the disk center

23 Chapter 1. Introduction

Figure 1.12: The Fomalhaut debris ring (NASA press release for Kalas et al. 2005).

Figure 1.13: The edge-on AU Mic debris disk with polarization vectors on top of the Stokes I image (Graham et al. 2007). from the star may hint toward an unseen companion. This is discussed in detail for the Fomalhaut system in Kalas et al. (2005, see Fig. 1.12), and for the HD 61005 in Chapter 6 of this thesis. The scale height can be used to determine the vertical velocity dispersion. Azimuthal asymmetries are quite common, usually in the form of spiral arms or clumpy structures (e.g. Reche et al. 2008).

1.4.2 Current status of debris disks observations in scattered light More than 10 debris disks have currently been resolved in scattered light4 between 0.6 and 2 µm. Another 15 have been resolved with lower spatial resolution at longer, thermal wavelengths.∼ Most scattered light detections were made by HST coronagraphy with NICMOS in the near-infrared or ACS in the optical because the much more stable PSF in space was easier to remove than for ground-based observations. Only now, sophisticated reduction techniques for ground-based high-contrast imaging from large telescopes can deliver similar or even superior results as HST for special cases (see Sect. 1.5 and 6). For edge-on disks like AU Mic (Fig. 1.13) the geometry is less clear. In that case, polarimetric observations also made with HST could resolve degeneracies between disk geometry and scattering phase function, showing that the disk is also a ring with an inner hole (Graham et al. 2007).

4 Resolved circumstellar disk library: http://www.circumstellardisks.org

24 1.5. Differential techniques for high-contrast imaging of planetary systems

1.5 Differential techniques for high-contrast imaging of planetary systems

1.5.1 Instruments for high contrast imaging Current high-contrast imagers in operation that have successfully detected planetary companions and debris disks, or are capable of this, include VLT/NaCo, Sub- aru/HiCIAO, Keck/NIRC2, Gemini-N/NIRI, Gemini-S/NICI and MMT/CLIO. These systems all share a number of common features that are necessary to image an extrasolar planet. They are using a large telescope (6.5 10 m diameter) for a high resolution and a large photon collecting area. The instruments− are coupled to an adaptive optics (AO) system that corrects distortions by atmospheric turbulence in order to achieve a near diffraction-limited performance rather than a seeing limited image. A wavefront sensor measures the distortion of the incoming wavefront of a guide star (usually the target itself) by atmospheric turbulence, and a deformable mirror e.g. with piezo-elastic actuators is reshaped to remove the wavefront errors. Measurement and correction happen in a cycle with a duration of order 1 ms, faster than the typical characteristic speckle variation time scale (atmosphere coherence time scale τ0 of several ms). The cameras operate in the near infrared, typically from 1 5 µm (J to M band). Different types of coronagraphs, e.g. Lyot coronagraphs,− apodized Lyot coronagraphs, four quadrant phase masks (4QPM) or apodized phase plates (APP), are available to block the starlight as much as possible, or saturated imaging is possible by taking many images with very short exposure times at high efficiency. Some instruments also provide a low resolution spectroscopic mode to follow-up planetary candidates and provide a crude spectrum for a first characterization of the atmosphere. Two upcoming instruments with a primary goal of detecting extrasolar planets through direct imaging are SPHERE (Spectro-Polarimetric High-Contrast Ex- oplanet REsearch) for the VLT (Beuzit et al. 2006) and GPI (Gemini Planet Imager) for Gemini-S (Macintosh et al. 2008). They are extreme adaptive optics systems with more than 1000 actuators, providing a Strehl ratio of 90% in H-band. GPI consists of only one instrument, an Integral Field Spectrograph≈ (IFS) that takes a low resolution spectrum between 0.95 and 2.5 µm at any image point in the field of view (FoV) of 2.4”. It also features a polarimetric mode. The result is a 3D cube of images, with an image at each wavelength or polarization state. The PSF of the star can then be removed with differential methods, e.g. spectral differential imaging, angular differential imaging or polarimetry (see next section for last two). The system is due for first light in late 2011. SPHERE is a 2nd generation instrument for the VLT due for first light in the summer of 2012. It consists of three different parts: the near-infrared dual-beam spectral and polarimetric differential imager and low resolution spectrograph IRDIS (0.95-2.3 µm), an integral field spectrograph (IFS, 0.95-1.7 µm) and a differential polarimeter (ZIMPOL, 0.55-0.9 µm). IRDIS is well suited for the discovery of planets and imaging of disks with a large FoV of 11”. IRS can be used simulta-

25 Chapter 1. Introduction neously for atmospheric characterization of planets in the innermost region with a FoV of 1.77”. ZIMPOL is a fast-modulating polarimeter (see Sect. 1.5.3) with a FoV of about 3” optimized for the detection of polarized reﬂected light from planets around the most nearby stars.

1.5.2 Angular Differential Imaging For high-contrast observations, the PSF noise is a quasistatic speckle noise pattern caused by imperfect optics and slowly evolving optical alignments. To remove this pattern, a reference PSF must be subtracted. Conventionally, a reference star with similar properties and position angle was observed close in time to the target, and its PSF was used for the subtraction. While this procedure can attenuate the stelar PSF to some degree, the remaining residuals are still quasistatic. A better method is to use the target star’s own PSF as reference, by avoiding that the planetary companion is subtracted together with the PSF. This is achieved with a technique called Angular Differential Imaging (ADI, Marois et al. 2006). The observations are performed in pupil tracking mode, i.e. the field derotator of the alt-az telescope is switched off (for Cassegrain instruments) or adjusted (for Nasmyth instruments). The instrument and telescope optics remain aligned, but the field of view rotates on the detector. The field rotation rate in deg/min is given by

cos A cos φ ψ = 0.2596 (1.38) sin z with A the telescope azimuth, φ the telescope latitude and z the zenith angle of the object. It is most favorable to observe an object near meridian transit, where the field rotation is maximal. While the stellar PSF remains fixed, the companion slowly rotates around the star. For each short-exposure image, a reference PSF can be constructed by selecting images where the companion has rotated sufficiently. Removing this PSF will strongly reduce the quasistatic speckle noise and reveal faint companions after the residual images are derotated and combined (Fig. 1.14. The speckle noise at- tenuation is stronger for longer observing times, its main limitation is the amount of field rotation captured. There are a number of approaches on how to best select the images for the construction of the reference PSF. The simplest is to median-combine all images of the sequence. Advantages are that the same reference PSF is subtracted from all images and self-subtraction effects and pixel-to-pixel noise are minimized. But since the PSF evolves with time, this “simple” ADI method is usually not sufficient. The result is improved if for each image, a further, more optimized reference frame for subtraction is constructed. For each image a combination of only a few frames (typically 2-4) is used that were taken closely in time, but where the planet has rotated sufficiently (typically 1-2 FWHM) to avoid significant self- subtraction. Because the amount of field rotation needed to rotate away the signal differs with distance from the rotation center, the image is divided into annuli,

26 1.5. Differential techniques for high-contrast imaging of planetary systems

Figure 1.14: Schematic representation of the frame combination in the simple angular differential imaging method. The first row is a sequence of images taken in pupil-stabilized mode where the stellar PSF and speckles (gray) remain fixed while the companion (red) rotates around the center. The median of the images is subtracted, the images are derotated and combined to reveal the companion. Figure provided by C. Thalmann. and for each annuli different frames are chosen such that the separation criterion is met at that radial distance. An even more optimized PSF subtraction is provided by the LOCI (LOcalized Combination of Images, Lafreniere` et al. 2007) algorithm. Each image is divided into segments, and for each segment, frames that have sufficiently rotated are chosen and linearly combined in an optimized way to minimize the subtraction residuals in that segment, i.e.

2 2 T k k σ = ∑ Oi ∑ c Oi , (1.39) i − k !

T k with Oi the optimization segment of the ith image, and Oi the same segment in the kth image which has rotated sufﬁciently with respect to the ith image. Both the separation criterion and the segment size and geometry are adjustable parameters that can be chosen for a speciﬁc case, with a trade-off between subtraction residual noise and object self-subtraction.

1.5.3 Polarimetry The intrinsic polarization of stars is very small, at least integrated over their 7 whole surface. For the sun it is . 10− (Kemp et al. 1987). The measured polarization of stars is usually produced by interstellar dust in the line-of-sight. Starlight reﬂected by a planetary atmosphere however will generally be polarized to some degree, in particular if Rayleigh scattering or haze scattering dominate. This of-

27 Chapter 1. Introduction fers the possibility to discern the faint reﬂected and polarized light of the planet from the bright unpolarized halo of the star. Polarization cannot be measured directly. A polarimeter measures the intensity of the light in orthogonal polarization states, from which the polarization can then be calculated. The stellar PSF will look the same when measured in different polarization states, while the small planet dot will be stronger in one state. Sub- tracting an image of opposite polarization state will therefore suppress the PSF while bringing out the planet if the polarization is sufﬁcient. The most common setup in conventional instruments with a polarimetric mode (e.g. VLT/NaCo) is the combination of a half- or quarterwave plate with a Wollaston prism in dual-beam polarimeter. The halfwave plate selects the linear polarization state (Q, U) to be measured, the quarterwave plate selects the circular polarization V. The Wollaston prism then splits the incoming intensity into two beams of orthogonal polarization state, for example IQ, and IQ, , k ⊥ which are measured on separate parts of a detector. Then, I = IQ, + IQ, and k ⊥ Q = IQ, IQ, . To lessen the effects of irregularities on the detector, an ad- k − ⊥ ditional image is taken with the halfwave plate rotated by 45◦. For a halfwave plate rotation angle γ the polarization direction is rotated by 2γ, therefore a 45◦ switches the polarization direction of the two beams such that I′ = IQ, . The Q, ⊥ data are combined to obtain a polarization fraction Q/I with eitherk the difference method (see Fig. 1.15),

Q 1 I I I′ I′ = k − ⊥ + ⊥ − k , (1.40) I 2 I + I I′ + I′ ! k ⊥ ⊥ k or with the ratio method, Q R 1 I /I = − , with R2 = k ⊥ (1.41) I R + 1 I′ /I′ k ⊥ For high-precision polarimetry, the dual-beam method is not sufficiently precise. It is much more favorable to measure the two states on the same detector pixels. In that case, the orthogonal polarization states have to be measured se- quentially in time, and must therefore be taken more quickly than the typical time scales on which the atmospheric speckles change ( 10 ms). This poses a challenge because detector read-out times are generally slower.≈ ZIMPOL (Zurich Imaging POLarimeter, e.g. Povel 1995) uses a fast polarization modulation principle that circumvents this problem and has been successfully used to measure po- 5 larization to a precision better than 10− for solar applications (e.g. Stenflo 1996). The polarization of the incoming beam is modulated with a frequency in the kHz range by ferro-electric liquid crystal modulators. A polarizer selects a linear polarization state, which is measured on a chip that demodulates in real-time by shifting the measured charges to other, covered detector rows while the other state is measured, and then shifts them back. After many modulation periods, the signal is finally read out and the intensity and polarization can be constructed from the sum and difference of the two measured polarization states.

28 1.6. Thesis overview

Figure 1.15: Illustration of the data reduction for polarimetric imaging taken with a dual- beam polarimeter using the difference method. Figure adapted from Hinkley et al. (2009).

Polarimetric Differential Imaging (PDI) can deliver a contrast enhancement of 4 5 8 10− to 10− . The planet polarization of typical SPHERE targets is only 10− . The∼ rest of the contrast is gained in intensity by the use of a coronagraph and∼ ADI, which can be combined with PDI at least in a simpliﬁed form with natural ﬁeld rotation. Pupil tracking is not foreseen for SPHERE/ZIMPOL.

1.6 Thesis overview

This thesis investigates which parameters can be derived from scattered light observations of planetary systems, i.e. planets and circumstellar material, with differential techniques, in particular polarimetry and angular differential imaging. These studies were executed in the broad context of the science case of SPHERE/ZIMPOL and SPHERE/IRDIS for scattered light observations of planetary systems. They make predictions and suggest interpretations for signals that may be detectable with SPHERE, and take advantage of similar observations already available or feasible with currently existing instruments that can already provide interesting scientific results in their own right. The first part of the thesis is dedicated to the study of planetary atmospheres in polarized light. In Chapter 2, a parameter study of polarimetric models for planet atmospheres is presented, that discusses the effects of the most important atmosphere parameters on the intensity and polarization phase curve and the limb polarization. The study is focused on Rayleigh scattering, but also considers scattering on haze particles. The connection between the limb polarization as measurable for the Solar System gas giants and the polarization at large phase angles as will be measured for extrasolar planets is discussed. Diagnostic diagrams are presented which could be useful for a first coarse analysis of broadband po- larimetic differential imaging observations of extrasolar planets in scattered light with SPHERE/ZIMPOL. Also, a large grid of models is provided for a homoge-

29 Chapter 1. Introduction neous Rayleigh scattering layer above a diffuse cloud layer that allows an easy calculation of polarization spectra. This work was presented in the paper “A grid of polarization models for Rayleigh scattering planetary atmospheres” by E. Buenzli & H. M. Schmid, published in 2009 in Astronomy & Astrophysics 504, 209. In Chapter 3 the polarization models are applied to the specific case of the atmosphere of Uranus. Spectropolarimetric observations of Uranus are modeled to derive polarimetric haze properties and atmospheric structure. The best-fit model is then used to predict the polarization signal of Uranus from an extrasolar view- point and the detection possibility for an ice giant around a nearby M-Dwarf is discussed. This work is presented in the paper “Polarization of Uranus: Constraints on haze properties and predictions for analog extrasolar planets” by E. Buenzli & H.M. Schmid, submitted for publication in Icarus, 2011. Chapter 4 is a brief investigation of the polar haze of Jupiter. A haze model is derived for observations at a single wavelength. This work is a modified verison of a part of the paper “Long slit spectropolarimetry of Jupiter and Saturn” by H.M. Schmid, F. Joos, E. Buenzli & D. Gisler, published in 2010 in Icarus 212, 701. The chapter focuses on my contribution to the paper, the haze modeling, after a short presentation of the data obtained and described by F. Joos and H. M. Schmid. The first part concludes with an outlook on the polarimetric search for reflected light from planets around the nearest stars with SPHERE/ZIMPOL, and in the more distant future with E-ELT/EPOL. Additionally, the application of polarimetry for hot Jupiter observations is discussed. The second part of the thesis investigates scattered light from circumstellar material by focusing on observations and analysis of a specific debris disk. In Chapter 6, ground-based high-contrast observation of the debris disk HD 61005, less formally known as ‘the Moth’, are presented at unprecedented angular resolution achieved through angular differential imaging. The disk is resolved as a debris ring with an outer faint component that appears to be interacting with the ambient interstellar medium. An analysis of the ring geometry and surface brightness is shown, which indicates that the ring center is offset from the star, and additional strong brightness asymmetries are present. Detection limits are given for potential planetary candidates that could be responsible for the ring perturbation, and detected point sources were confirmed to be background objects. This study was carried out in a collaboration within the framework of a large observing program searching for thermal emission from planetary mass companions around nearby young stars. Reduction and modeling codes were provided by several people. Detection limits and confirmation of background objects were done by collaborators. I led the study, performed the reduction, modeling and analysis of the disk and wrote the paper. Comments and suggestions were provided by co-authors. This work was presented in the letter “Dissecting the Moth: Discovery of an off-centered ring in the HD 61005 debris disk” by E. Buenzli et al., published in 2010 in Astronomy & Astrophysics 524, L1. The final chapter discusses ongoing and potential future follow-up observations of the HD 61005 debris disk as well as an idea for future modeling efforts, in particular for the faint outer component composed of particles blown-out from

30 BIBLIOGRAPHY the parent body ring. Additionally, some perspectives on disk observations in scattered light with other techniques and future instruments are given.

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Part I

Polarimetry of gaseous planets

35 36 Chapter 2 A grid of polarization models for Rayleigh scattering planetary atmospheres∗

E. Buenzli1 and H.M. Schmid1

Abstract

Context. Reflected light from giant planets is polarized by scattering, offering the possibility of investigating atmospheric properties with polarimetry. Polarimet- ric measurements are available for the atmospheres of solar system planets, and instruments are being developed to detect and study the polarimetric properties of extrasolar planets. Aims. We investigate the intensity and polarization of reflected light from planets in a systematic way with a grid of model calculations. Comparison of the results with existing and future observations can be used to constrain parameters of planetary atmospheres.. Methods. We present Monte Carlo simulations for planets with Rayleigh scattering atmospheres. We discuss the disk-integrated polarization for phase angles typical of extrasolar planet observations and for the limb polarization effect observable for solar system objects near opposition. The main parameters investigated are single scattering albedo, optical depth of the scattering layer, and albedo of an underlying Lambert surface for a homogeneous Rayleigh scattering atmosphere. We also investigate atmospheres with isotropic scattering and forward scattering aerosol particles, as well as models with two scattering layers. Results. The reflected intensity and polarization depend strongly on the phase angle, as well as on atmospheric properties, such as the presence of absorbers or aerosol particles, column density of Rayleigh scattering particles and cloud albedo. Most likely to be detected are planets that produce a strong polarization flux signal because of an optically thick Rayleigh scattering layer. Limb polarization depends on absorption in a different way than the polarization at large phase angles. It is especially sensitive to a vertical stratification of absorbers. From limb polarization measurements, one can set constraints on the polarization at large phase angles.

∗ This chapter has been published by Astronomy & Astrophysics (2009) 504, 209 1 Institute of Astronomy, ETH Zurich, CH-8093 Zurich, Switzerland

37 Chapter 2. Polarization models for planetary atmospheres

Conclusions. The model grid provides a tool for extracting quantitative results from polarimetric measurements of planetary atmospheres, in particular on the scattering properties and stratification of particles in the highest atmosphere layers. Spectropolarimetry of solar system planets offers complementary information to spectroscopy and polarization flux colors can be used for a first characterization of exoplanet atmospheres.

2.1 Introduction

Light reﬂected from planetary atmospheres is generally polarized. The reﬂection is the result of different types of scattering particles with characteristic polarization properties. Polarimetric observations therefore provide information on the atmospheric structure and on the nature of scattering particles that complements other observations. Systematic model calculations are required to interpret the available polarimetry from solar system planets and prepare for future polarimetric measurements of extrasolar planets.

Scattering processes. Rayleigh scattering occurs on particles much smaller than the wavelength of the scattered light. This process produces 100% polarization for a single right angle scattering. Rayleigh scattering is much stronger for short wavelengths because the cross section behaves like σ ∝ 1/λ4, and it favors forward and backward scattering, which are both equally strong. The blue sky in Earth’s atmosphere is a well known example of Rayleigh scattering by molecules. Aerosol haze particles with a size roughly comparable to the wavelength can produce strongly forward directed scatterings. Depending on the structure of the particle, a high (p > 90%) or low (p 20%) fractional polarization results for ≈ a scattering angle of 90◦. For example, the maximum polarization for scattering by optically thin zodiacal or cometary dust is not more than 30% (e.g. Leinert et al. 1981; Levasseur-Regourd et al. 1996), while a polarization≈ close to 100% is inferred for single scattering of haze particles in Saturn’s moon Titan (Tomasko et al. 2008)). Liquid droplets in clouds produce a polarization because of refraction and reflection, which can be particularly high (> 50%) for scattering angles of about 140◦ for spherical water droplets, corresponding to the primary rainbow (see e.g. Bailey 2007). Clouds made of ice crystals reflect and refract light in many different ways, and no distinct polarization features like rainbows are expected, except locally, where ice crystals may have very similar structures. Multiple scatterings in planetary atmospheres randomize the polarization direction of the single scatterings and lower the observable polarization significantly. Therefore the net polarization of the reflected light depends not only on the scattering angle and the properties of the scattering particles, but also on the atmospheric structure. For this reason it is not surprising that a large diversity of polarization properties exists for the solar system planets.

38 2.1. Introduction

Observations. Venus shows a low (< 5%) negative polarization, which is a polarization parallel to the scattering plane, for most phase angles . In the blue and UV, a rainbow feature with a positive polarization of several percent is present (e.g. Coffeen & Gehrels 1969; Dollfus & Coffeen 1970), indicating that the reflection occurs mainly from droplets in optically thick clouds (Hansen & Hovenier 1974). For the giant planets, only observations near opposition are possible with earth-bound observations. Near opposition the disk-integrated polarization is low because single back-scattering is unpolarized and multiple scattering polarization cancels for a symmetric planet. With disk-resolved observations of Jupiter, Lyot (1929) first detected that the Jovian poles show a strong limb polarization of order 5-10%. To understand this effect one has to consider a back-scattering situation at the limb of a sphere, where locally we have a configuration of grazing incidence and grazing emergence (for a plane parallel atmosphere) for the incoming and the back-scattered photons, respectively. Photons scattered upwards will mostly escape without a second scattering, and photons scattered down have a low probability of being reflected towards us after the second scattering, but a high probability of being absorbed or undergoing multiple scatterings. Thus photons that are reflected towards us by two scatterings travel predominantly parallel to the surface. Because the polarization angle induced in a single dipole-type scattering process, like Rayleigh scattering, is perpendicular to the propagation direction of the incoming photon, a polarization perpendicular to the limb is produced. Measurements at large phase angles ( 90◦) for Jupiter with spacecrafts detected a polarization of 50% for the poles≈ while the polarization is much lower (< 10%) for the equatorial≈ region (Smith & Tomasko 1984). The high polarization at the poles can be explained by reflection from a scattering aerosol haze layer, while the polarization at the equator is low because of reflection from clouds. To- wards short wavelengths (blue) the polarization at the equator increases strongly, indicating that also Rayleigh scattering contributes to the resulting polarization. For Saturn the polarization is qualitatively similar to Jupiter with an enhanced polarization at the poles at short wavelengths (blue). In the red the polarization level of the poles is lower than for Jupiter (Tomasko & Doose 1984). Uranus and Neptune display a strong limb polarization along the entire limb (Schmid et al. 2006b; Joos & Schmid 2007). Albedo spectra (e.g. Baines & Bergstralh 1986) and the polarization indicate that Rayleigh scattering is predominant in these atmospheres. An interesting case is Saturn’s moon Titan, which has a thick scattering layer of photochemical haze that produces a very high disk-integrated polarization of 50 % in the B and R band (Tomasko & Smith 1982). More recently the Huygens probe∼ measured the scattering and polarization properties of the aerosol particles in great detail during its descent through Titan’s atmosphere (Tomasko et al. 2008). The observations show that Rayleigh scattering is an important polarigeneric process in atmospheres of solar system objects, in particular for Uranus and Nep-

39 Chapter 2. Polarization models for planetary atmospheres tune, and for the equatorial regions of Jupiter and Saturn. Besides Rayleigh scattering one has to consider the reflection from haze particles (aerosols). Scattering by small aerosol particles (d < λ) may be approximated by Rayleigh scattering. For large particles, d & λ, the strong forward scattering effect and the reduced polarization for right angle scattering cause significant differences when compared to Rayleigh scattering. Clouds dominate in the atmosphere of Venus, and at longer wavelengths (red) also in Saturn and Jupiter. The reflection from clouds produces only a low positive or even negative polarization signal in Venus, Saturn or Jupiter, typically at a level p < 5 %. In a first approximation one may therefore treat clouds like a diffusely scattering layer producing no polarization. Polarimetric measurements of stellar systems with known extrasolar planets were attempted, but up to now no convincing detection of the polarized reflected light from an extrasolar planet has been made (Lucas et al. 2009; Wiktorowicz 2009). The deduced upper limits on the polarization flux from the close-in planet indicate that these objects are not covered with a well reflecting Rayleigh scattering layer.

Model calculations. The classical theory for the analytic solution of the multiple scattering problem is treated in the seminal work of Chandrasekhar (1950), from which the polarization of conservative (non-absorbing) Rayleigh scattering planets can be derived. van de Hulst (1980)) gives a comprehensive overview on theoretical work up to that time including many numerical model results. Schmid et al. (2006b) put together available model results useful for parameter studies of the polarization from Rayleigh scattering atmospheres. This includes the following model results:

Phase curves for the disk-integrated intensity and polarization for ﬁnite, • conservative (no absorption) Rayleigh scattering atmospheres for different optical thicknesses and ground albedos from Kattawar & Adams (1971),

the limb polarization at opposition for semi-inﬁnite Rayleigh scattering at- • mospheres with different single scattering albedos derived from formu- las and tabulated functions given in Abhyankar & Fymat (1970; 1971) and Chandrasekhar (1950),

the limb polarization at opposition for ﬁnite, conservative (no absorp- • tion) Rayleigh scattering atmospheres for different optical thicknesses and ground albedos from tabulations given in Coulson et al. (1960).

For Venus detailed models for the reﬂection from clouds were developed, which demonstrate nicely the diagnostic potential of polarimetric measurements (e.g. Hansen & Hovenier 1974)). More recent modeling of the polarization from planets was performed mainly to analyze and reproduce polarimetric observations of Jupiter and Titan from spacecrafts (e.g. Smith & Tomasko 1984; Braak et al. 2002; Tomasko et al. 2008)

40 2.2. Model description

Another line of investigation now concentrates on the expected polarization of extrasolar planets. The Rayleigh and Mie scattering polarization of close-in planets was investigated by Seager et al. (2000). These calculations consider planets which are unresolved from their central star and the polarization signal is strongly diluted by the unpolarized stellar light. Stam et al. (2004) modeled the polarization of a Jupiter-like extrasolar planet with methane absorption bands for three special cases and presented polarization spectra and wavelength integrated phase curves. Also monochromatic phase curves for a non-absorbing clear and a hazy atmosphere are available (Stam et al. 2006). Other studies determined the expected polarization from clouds of terres- trial planets (e.g. Bailey 2007) or the polarization of extrasolar analogs to Earth (Stam 2008). Despite all these models systematic model calculations are sparse in the literature. For finite Rayleigh scattering atmospheres, polarization phase curves have been calculated only for few selected cases. No results are available for the limb polarization of atmospheres with finite thickness and absorption. It is the goal of this paper to present a grid of model results for Rayleigh scattering models with absorption and to explore the model parameter space in a systematic way. The results should allow a comparison with observations and provide a tool for their interpretation. Additionally effects of selected deviations from simple Rayleigh scattering models will be discussed. In the next section the paper describes our scattering model and the Monte Carlo simulations. Section 2.3 presents the results from a comprehensive Rayleigh scattering model grid covering the three atmosphere parameters: single scattering albedo ω, optical thickness of the Rayleigh scattering layer τsc, and albedo of the underlying reflecting surface AS. In Sect. 2.4 we explore the effects of a mixture of isotropic and Rayleigh scattering, of particles with a forward scattering phase function, and of two polarizing layers. In Sect. 2.5 we discuss spectral dependences. Section 2.6 highlights some special cases and diagnostic diagrams which may be of particular interest for the interpretation of observational data. A discussion and conclusions are given in the final section. Appendix 2.7 describes the tables with the numerical results of our calculations of intensity and polarization phase curves for a grid of 333 model parameter combinations. These are available in electronic form at the CDS.

2.2 Model description

Our planet model consists of a spherical body of radius R, illuminated by a parallel beam. This geometry is appropriate for not rapidly rotating planets with a large separation, d R, from the parent star. Each surface element is approximated by a plane≫ parallel atmosphere. This simpliﬁcation is reasonable for planets without an extended, tenuous atmosphere.

41 Chapter 2. Polarization models for planetary atmospheres

2.2.1 Intensity and polarization parameters The intensity and polarization of the reflected light is described by the Stokes vector I = (I, Q, U, V). The linear polarized intensity or polarization flux is defined by the parameters Q = I0 I90 and U = I45 I135, where the indices stand for the polarization direction with− respect to a specified− direction in the selected coordinate system. In this paper only processes producing linear polarization are studied and therefore the Stokes parameter V for the circular polarization is omitted. We express the fractional polarization by the symbols

Q U Q2 + U2 q = , u = , p = , (2.1) I I p I and the polarized intensity

p I = Q2 + U2 . (2.2) · For the study of the limb polarizationp in resolved solar system planets at opposition we introduce the radial Stokes parameter Qr, which is positive for an orientation of the polarization parallel to the radius vector r (perpendicular to the limb) and negative for an orientation perpendicular to r. The Stokes Ur parameter is the polarization direction 45◦ to the radius vector (see e.g. Schmid et al. 2006b, for an illustrative description± of the radial polarization). The polarization fraction is represented by qr and ur. The radial polarization curves qr(r) and Qr(r) can only be observed if the planetary disk is well resolved. The measured radial profile depends strongly on the achieved spatial resolution. Because of the limited spatial resolution of most observations it is very hard to exactly measure the polarization near thelimb. It is much less difficult to evaluate a disk-integrated polarization or polarization flux and to estimate and correct the degradation of the observed value with respect to the intrinsic value with a simulation of the observational resolution or point spread function. This approach is described in detail in Schmid et al. (2006b) for seeing limited polarimetry of Uranus and Neptune. Therefore we mainly discuss the intensity weighted polarization qr = Q /I, which is the equivalent to the disk-integrated radial polarizatioh i n h ri Qr(r)2π r dr normalized to the geometric albedo. The geometric albedo Ag is the disk-integrated reflected intensity of a given model at opposition normal- R ized to the reflection of a white Lambertian disk. It corresponds to I(0◦) in our calculations. The radial polarization curves are qualitatively similar for most models. The shape of the intensity curve varies significantly from limb darkening to limb brightening for different model parameters and cannot solely be described by the geometric albedo. Additionally we choose the Minnaert law exponent k as fit parameter for the shape of the center-to-limb intensity curve. The Minnaert 2k 1 2 1/2 law for opposition is I(r) = Ir=0µ − , where µ(r)=(1 r ) . This yields the following one-parameter fit curve I(r)= I (1 r2)k 1/2−. r=0 − −

42 2.2. Model description

2.2.2 Atmosphere parameters The plane parallel atmosphere is assumed to consist of a homogeneous scattering layer that is either semi-infinite or finite with a reflecting (cloud or ground) Lambertian surface layer with a surface albedo. The basic model atmospheres are described by three parameters:

the single scattering albedo ω, • the (vertical) optical thickness for scattering, τ , of the scattering layer, • sc the albedo A of the surface below the scattering layer. • S The single scattering albedo ω is defined by the ratio between the scattering cross section σ and the sum of absorption cross section κ and scattering cross section σ, with the cross sections multiplied by the fractions of scattering or absorbing particles ( fsc or fabs) f σ ω = sc . (2.3) fabsκ + fscσ The value ω = 1 indicates pure scattering (no absorption) while ω = 0 is the other extreme of no scattering and just absorption (e.g. black dust). Similarly, a surface albedo of AS = 0 corresponds to a black surface, while a perfectly white Lambertian surface is defined by AS = 1. The optical depth for scattering τsc follows from the column density Z of the scattering layer: τ = Z σ, where σ is the scattering cross section per particle. sc · The semi-infinite case corresponds to τsc = ∞. We treat absorption like an addition of absorption optical depth to a layer with a given scattering optical depth τsc, which is equivalent to reducing the single scattering albedo. This approach is suited for discussing the reflected intensity and polarization inside and outside of absorption features like CH4 or H2O-bands, where κ differs dramatically while σ is essentially equal. Then the total optical thickness τ of the layer including absorption κ is given by τ τ =( f σ + f κ) Z = sc . (2.4) sc abs · ω

The basic model grid (Sect. 3) considers only Rayleigh scattering (σ = σRay, τsc = τRay) as scattering process and Lambert surfaces with an albedo AS below the scattering layer. Extensions, such as including non-polarizing isotropic scattering where σ = σRay + σiso, haze layers or more than one scattering layer are discussed in Sect. 4.

2.2.3 Geometric parameters The geometric parameters describe the location of the considered surface point P and the escape direction of the photons (Fig. 2.1). A global coordinate system

43 Chapter 2. Polarization models for planetary atmospheres

ϑ P δ +Q ϕ −Q δ

+Q ϑ 0

−Q S’

α S

E Figure 2.1: Model geometry. The dashed line represents the trajectory of a reﬂected photon. describes the orientation of the planet with respect to the star. Its polar axis is the surface normal at the sub-stellar point S′, and the location of each point P is described by polar angle δ and azimuthal angle θ (not drawn). δ is also the photon’s angle of incidence at point P. The escape direction, i.e. the location of the observer, is given by a polar angle α and azimuthal angle χ (not drawn). α is equivalent to the phase angle deﬁned by the three (central) points: star or sun S, planet 0, and observer E (Earth). For the description of the scattering processes, a local coordinate system is set up at point P for the plane parallel atmosphere with surface normal z perpendicular to the planet surface in P, polar angle ϑ and azimuthal angle ϕ. In general, each point P can have individual atmospheric properties. Then the model outputs, the Stokes vector components I, Q and U, depend each on seven parameters:

I(δ, θ, α, χ, τsc(δ, θ), ω(δ, θ), AS(δ, θ)) . This description allows calculation of the reflected intensity and polarization of each surface point on the illuminated hemisphere viewed from any direction. Obviously this large parameter space needs to be simplified for a first parameter analysis. If we adopt the same atmospheric structure everywhere on the planet, τsc, ω and AS are no longer functions of δ and θ and we obtain a rotationally

44 2.2. Model description symmetric model geometry with respect to the line S 0, which is independent of the azimuthal angle χ. − For extrasolar planets it will not be possible to resolve the disk in the near future. For disk-integrated results we can eliminate the dependence of the reﬂected intensity and polarization on the surface point parameters δ and ϑ. Because of the rotational symmetry of the geometric model, the intensity and the polarization then only depend on the polar viewing angle or phase angle α. Moreover the orientation of the polarization signal is either parallel or perpendicular to the scattering plane (the plane S-0-E), which we call the Q polarization direction. Q is deﬁned positive for a polarization perpendicular to the plane S-0-E and negative for a polarization parallel to this plane. The U-polarization is zero in this coordinate system for symmetry reasons. For the full disk the integrated intensity and polarization signals from a planet depend on the following parameters:

I(α, τsc, ω, AS) , Q(α, τsc, ω, AS) .

For solar system planets at opposition we obtain a rotationally symmetric scattering geometry (viewing direction is identical to the axis of symmetry of the geometric model). We then have a scattering model which depends only on δ or the normalized projected radius r = sin δ, and which is independent of θ. The resulting polarization will be in the radial direction either parallel or perpendicular to the radius vector r and therefore our model output is the radial Stokes parameter Qr (cf. Sect. 2.2.1). The Stokes Ur parameter again has to be zero for a spherically symmetric planet. For exact opposition the dependences of the scattering model results can be described by the following parameters:

I(r, τsc, ω, AS) , Qr(r, τsc, ω, AS) .

These are the center to limb intensity curve and the center to limb radial polarization curves which both depend only on the atmospheric parameters.

2.2.4 Monte Carlo simulations For our simulations we used the Monte Carlo code described in (Schmid 1992), which was slightly adapted for the case of light reflection from a planet. Basi- cally the code calculates the random walk histories of many photons in the planet model atmosphere until the photons have escaped or are destroyed by an absorption process. After a sufficiently large number have escaped, the scattering intensity and polarization of the reflected light can be established for different lines of sight. In our calculations we assume that despite multiple scatterings the escaping photons emerge at the same point where they penetrated into the planet. In each scattering process the photon undergoes a direction and polarization change calculated from the appropriate phase matrix. The linear polarization of the photons in the simulations is defined by the orientation γ of the electric vector for the

45 Chapter 2. Polarization models for planetary atmospheres photon’s electromagnetic wave. In a given coordinate system we can then evaluate the contribution to the Stokes intensity for each photon in Q ∝ cos 2γ and U ∝ sin 2γ direction. The escaping photons have to be collected in discrete direction bins (in our models phase angles α = 2.5◦, 7.5◦, . . . with a finite bin width ∆α = 5◦) to evaluate I(α) and Q(α). These are then a mean photon intensity and polarization for that bin. ∆α should be small to resolve any structure in I(α) and Q(α), but also sufficiently large to collect enough photons for results with small statistical errors. The aim of our simulations is to reach at least the expected precision of observational data. The rotational symmetry imposed on our models helps to increase the bin size for the phase curve interval αk, which behaves like αk ∝ sin α. This means that we have to divide the photon count per bin by the factor 2π sin α∆α. The intensity is obtained by normalizing with the reflectivity of a white Lamber- tian disk. For a given simulation the relative statistical errors (photon shot noise) are particularly good for α 90 , much less favorable for α = 2.5 and very bad ≈ ◦ ◦ for α = 177.5◦ where only a few photons will be collected, because the irradiated hemisphere of the planet is almost invisible for this phase angle. For the center- to-limb curves we bin uniformly in δ = arcsin(r) with a bin size of ∆δ = 5◦, which requires an additional normalization by 2π sin δ cos δ∆δ. The number of photons per model was chosen such that the number of reflected photons in phase angle bins relevant for observations (α 30◦ 120◦) are about N 2 106 when integrated over the whole disk. This corresponds≈ − to an error in polarization≈ · ∆p = √2/N = 0.1%. For the radial curves the total number of photons was increased such that the same precision was reached in most radial bins. No photons emerge at the exact phase angle α = 0◦. Therefore for the limb polarization calculations we count all photons that are in the bin 0◦ < α < 5◦, even though the calculation for the radial polarization includes the assumption that α = 0◦. The error induced by this measure is smaller than the statistical error. A general guideline for the Monte Carlo technique for random walk problems is given in Cashwell & Everett (1959) and many Monte Carlo simulations for the investigation of light scattering are described in the astronomical literature (see e.g. Witt 1977; Code & Whitney 1995; Wolf et al. 1999). In (Schmid 1992) a detailed description on many aspects of the employed Monte Carlo code are given; e.g. the general scheme of the code, the required transformations between the involved coordinate systems (star - planet, planet - plane parallel atmosphere, atmosphere - photon), the determination of the free path length, the treatment of isotropic scattering and Rayleigh scattering according to the Rayleigh phase matrix, an assessment of statistical errors, and a comparison with analytical calculations.

2.3 Model results for a homogeneous Rayleigh-scattering atmosphere

This section discusses the model grid results for simple homogeneous Rayleigh scattering atmospheres described by parameters ω, τsc and AS (cf. sec. 2.2.2) We

46 2.3. Model results for a homogeneous Rayleigh-scattering atmosphere

Figure 2.2: Left: Phase dependence of the intensity I, fractional polarization q and polarized intensity Q for Rayleigh scattering atmospheres. Right: Radial dependence of the intensity I, radial polarization qr and radial polarized intensity Qr at opposition. Line styles denote: Semi-infinite case τsc = ∞ (solid) for single scattering albedos ω = 1 (thick), 0.1 (thin) and finite atmosphere (τsc = 0.3) with ω =1 (dashed) and 0.6 (dash-dot) for surface albedos AS = 1 (thick) and 0 (thin). Also shown is the intensity curve for conservative semi-infinite isotropic scattering (dotted). discuss phase curves (Sect. 2.3.1) and radial profiles (Sect. 2.3.2) for selected cases and explore the full parameter space for disk-integrated results at α = 90◦ and α = 0◦ (Sect. 2.3.3). Many of the general dependences of these model results on atmospheric parameters were already discussed in previous studies mentioned in the introduction (Sect. 2.1). Compared to these our calculations are much more comprehensive and the extensive model grid results are provided in electronic form (see Appendix 2.7). An overview of the dependence of observable quantities, such as intensity, fractional polarization and polarized intensity, on atmosphere parameters is presented in diagrams which may be useful for the interpretation of observational data. The results presented in this section are in very good agreement with the previous calculations in Kattawar & Adams (1971); Stam et al. (2006) and Schmid et al. (2006b).

2.3.1 Phase curves For the investigation of extrasolar planets, the phase dependence of the disk- integrated polarization is of interest. We discuss the phase curve for selected

47 Chapter 2. Polarization models for planetary atmospheres model cases (Fig. 2.2, left): a semi-infinite and a finite scattering layer with different absorption properties of the scattering and surface layers. The semi-infinite, conservatively scattering layer is a good reference case for an illuminated sphere and is often used for scattering atmospheres. All irradiated light is reflected after one or several scatterings and the spherical albedo is equal to 1. An intensity phase curve for isotropic scattering is given in van de Hulst (1980), and Bhatia & Abhyankar (1982) published a polarization curve for Rayleigh scattering in graphical form, but no tabulated values could be found in the literature. In our Monte Carlo simulation we treat the semi-infinite atmosphere as τsc = 30 and AS = 1, which yields essentially the same results as an infinite layer but avoids infinite scattering of some photons. Our results of this case are tabulated in Table 2.1.

Intensity: The intensity phase curves I(α) have their maximum at α = 0◦, when the whole illuminated hemisphere is visible, and they decrease steadily to zero at α = 180◦, where only the dark side of the planet is seen. The intensity I(0◦) is equivalent to the geometric albedo. It is 0.7975 for the semi-infinite Rayleigh scattering atmosphere (Prather 1974), higher than for the semi-infinite isotropic scattering model, (Iiso(0◦) = 0.690 van de Hulst 1980) or a white Lambertian sphere (ILam(0◦) = 2/3), because the Rayleigh scattering phase matrix favors forward and backward scattering. On the other hand the Rayleigh scattering intensity curve is lower for the range α 52◦ 120◦. Of course, the reflected intensity decreases≈ − with absorption (with lower single scattering albedo ω) in the atmosphere and with the albedo AS of the underlying surface layer. The effect of absorption in the scattering atmosphere is important for thick layers, while the albedo of the underlying surface is important if the optical depths of the scattering region above is small. A quantitative description of these dependences is given in Dlugach & Yanovitskij (1974) and Sromovsky (2005b)).

Polarization fraction. The disk-integrated polarization fraction q(α) is always zero for phase angles α = 0◦ and α = 180◦ because of the imposed rotational symmetry. The polarization maximum is near the right-angle scattering configuration α 90◦. ≈The polarization for the semi-infinite, conservative Rayleigh scattering layer reaches a maximum of q = 32.6% for α = 95◦. For reduced scattering albedo, e.g. due to absorption in a molecular band, q(α) increases (see e.g. van de Hulst 1980). This happens because absorption strongly reduces the fraction of multiply scattered photons in the reflected light which have randomized polarization directions. If the absorption is very strong then the reflected light consists essentially only of photons that made one single Rayleigh scattering. The polarization phase curve then approaches the Rayleigh scattering polarization phase function p(α)=(1 cos2 α)/(1 + cos2 α) with a polarization close to 100 % at α = 90 . − ◦

48 2.3. Model results for a homogeneous Rayleigh-scattering atmosphere

Table 2.1: Reflectivity I(α), polarization fraction q(α) and polarized intensity Q(α) phase curves for a very deep (τ = 30) conservative (ω = 1) Rayleigh scattering atmosphere above a perfectly reflecting Lambert surface (surface albedo AS = 1). This model ap- proximates well a conservative, semi-infinite Rayleigh scattering atmosphere. Addition- ally the fit parameter a(α) for the parametrization of the polarized intensity Q(α) (Eq. 2.5) is given for relevant phase angles. α [◦] I(α) q(α) [%] Q(α) a(α) α [◦] I(α) q(α) [%] Q(α) a(α) 2.5 0.795 0.0 0.0000 92.5 0.174 32.5 0.0566 2.62 7.5 0.785 0.4 0.0031 97.5 0.150 32.5 0.0488 2.77 12.5 0.766 1.1 0.0084 102.5 0.130 31.8 0.0413 2.95 17.5 0.740 2.1 0.0155 107.5 0.111 30.5 0.0339 3.16 22.5 0.708 3.4 0.0241 1.85 112.5 0.094 28.6 0.0269 3.42 27.5 0.671 5.1 0.0342 1.86 117.5 0.079 26.2 0.0207 3.76 32.5 0.630 6.9 0.0435 1.87 122.5 0.066 23.4 0.0154 37.5 0.587 9.1 0.0534 1.89 127.5 0.054 20.3 0.0110 42.5 0.542 11.4 0.0618 1.91 132.5 0.043 17.0 0.0073 47.5 0.497 13.9 0.0691 1.94 137.5 0.033 13.7 0.0045 52.5 0.453 16.6 0.0752 1.98 142.5 0.025 10.4 0.0026 57.5 0.410 19.3 0.0791 2.03 147.5 0.018 7.3 0.0013 62.5 0.368 22.0 0.0810 2.08 152.5 0.013 4.4 0.0006 67.5 0.329 24.6 0.0809 2.14 157.5 0.008 2.0 0.0002 72.5 0.292 27.0 0.0788 2.21 162.5 0.005 0.0 0.0000 77.5 0.259 29.1 0.0754 2.29 167.5 0.002 -1.4 0.0000 82.5 0.228 30.7 0.0700 2.39 172.5 0.001 -1.9 0.0000 87.5 0.199 31.9 0.0635 2.49 177.5 0.000

The statistical error of the Monte Carlo calculation for I(α) is smaller than 0.001 for all α. The uncertainty of the polarization fraction is less than 0.1 % for phase angles between 5 and 165 degrees. Extrapolating the intensity I towards α = 0◦ with a quadratic least-squares ﬁt to the ﬁrst four points (α = 2.5◦, . . . , 17.5◦) yields a value I(0◦) = 0.7970. This agrees with the exact solution I(0◦)= 0.7975 from Prather (1974) to the third digit.

49 Chapter 2. Polarization models for planetary atmospheres

For finite scattering atmospheres the polarization fraction q also depends on the albedo of the surface layer. In the models discussed in this section the polarization is only produced in the Rayleigh scattering layer, while reflection from the surface layer is unpolarized. Therefore the resulting polarization is low for a high surface albedo and high for a low surface albedo (see e.g. Kattawar & Adams 1971; Stam 2008). This reflects the relative contribution of the polarized light from the scattering layer with respect to the unpolarized light reflected from the surface underneath. The peak of the polarization curve is shifted towards large phase angles (α 110 ) for models with thin scattering layers and high surface albedos, as pre- ≈ ◦ viously described by Kattawar & Adams (1971). At large phase angles (α > 90◦), when only a planet crescent is visible, the fraction of scattered photons hitting the planet initially under grazing incidence is relatively high. For a thin scattering layer grazing incidence helps to enhance the probability for a polarizing Rayleigh scattering. For this reason the polarized light from the Rayleigh scattering atmosphere is less diluted by unpolarized light reflected from the surface at large phase angles and the fractional polarization is higher.

Polarized intensity. The polarized intensity Q(α), which is the product of polarization q and intensity I, is zero at α = 0◦ and 180◦, while the maximum of the phase curve Q(α) is near α 65◦, depending slightly on the model parameters. The maximum value for the≈ polarized intensity, considering the entire parameters space, is Qmax = 0.0812 for the semi-infinite, conservative Rayleigh scattering atmosphere at α = 65◦. It seems unlikely that another type of scattering process and model atmosphere can produce a higher polarized intensity. The polarized intensity decreases with increasing absorption, because the drop in intensity is stronger than the increase in fractional polarization. The polarization flux is a rough measure for the number of reflected photons undergoing one single Rayleigh scattering. Second and higher order scatterings also add to the polarized intensity, but only at a much lower level. Adding absorption can only reduce the number of such scatterings and therefore diminishes the polarized intensity. A very important property of the polarization flux Q is that it does not depend on the albedo of the surface layer AS (assumed to produce no polarization) below the scattering region.

2.3.2 Radial dependence for resolved planetary disks at opposition For the interpretation of the limb polarization of solar system objects close to opposition, we discuss the radial or center-to-limb dependence of the intensity I(r), the radial polarization qr(r) and the radial polarized intensity Qr(r) (Fig. 2.2, right) for the same model parameters as for the phase curves in Sect. 2.3.1.

50 2.3. Model results for a homogeneous Rayleigh-scattering atmosphere

Intensity: The radial intensity curve I(r) shows a pronounced limb darkening in the semi-infinite conservative case. For a strongly absorbing atmosphere, e.g. within an absorption band, the I(r)-curve becomes essentially flat. Thus for an absorbing (and homogeneous) semi-infinite atmosphere limb brightening cannot be produced. For comparison the center-to-limb intensity curve I(r) for isotropic scattering and for a Lambert sphere (I(r)= 1/π(1 r2)1/2) are also shown. For finite scattering atmospheres with an optically− thin layer the center-to- limb intensity curve can show a limb brightening effect. Limb brightening occurs for a highly reflective scattering layer (high ω) located above a dark surface (low AS), e.g. a thin aerosol layer or a methane-poor layer above the methane-rich absorbing layer (e.g. Price 1978). Limb brightening is observed in solar system planets in deep absorption band (e.g. Karkoschka 2001; Sromovsky & Fry 2007). Limb brightening is investigated in more detail in Sect. 2.3.2.

Radial polarization fraction: The radial polarization fraction qr(r) is always zero in the disk center because of the symmetry of the scattering situation. For all cases the polarization increases steadily towards the limb and reaches a maximum value close to the limb between r = 0.95 and 1.0. The polarization qr(r) is always positive, which means a radial polarization direction or limb polarization perpendicular to the limb. It is important to note that the limb polarization decreases with decreasing single scattering albedo ω (more absorption) in contrast to the situation at large phase angles. This indicates that the photons producing the limb polarization are more strongly reduced by absorption than the reflected “unpolarized” photons. The explanation is that singly scattered (i.e. backscattered) photons do not contribute to the limb polarization, while reflected photons scattered twice or a few times are responsible for the largest part of the limb polarization. Absorp- tion implies that a larger fraction of escaping photons are singly-scattered and therefore unpolarized at opposition. Note however that for the semi-infinite atmosphere, the maximum radial polarization is not reached in the conservative case. A slightly lower scattering albedo (ω 0.95) mostly reduces the amount of highest order scatterings and thus the polarization≈ fraction is somewhat enhanced when compared to the conservative case (see Schmid et al. 2006b), and Fig. 2.5 in Sect. 2.3.3). The fractional limb polarization qr(r) for finite scattering layers depends strongly on the albedo of the underlying surface AS: qr(r) is high for low AS and low for high AS like for large phase angles. A low surface albedo decreases the photons with multiple scatterings in the plane perpendicular to the limb, which are polarized parallel to the limb, thus enhancing the polarization in perpendicular direction. Therefore the limb polarization of a bright layer over a dark one can be even higher than for a semi-infinite atmosphere. This is discussed in more detail in Sect. 2.3.3.

51 Chapter 2. Polarization models for planetary atmospheres

Figure 2.3: Radial intensity curves for different model parameters normalized to the central disk intensity, showing examples of limb darkening and limb brightening. The solid line is the calculated model and the dotted line the best ﬁt with the Minnaert law. (a), (b) and (c) are for conservatively (ω = 1) scattering layers above black surfaces (AS = 0) with scattering layer thickness τsc = 0.1 (a), 1 (b) and ∞ (c). (d)isathin(τsc = 0.2), highly absorbing ω = 0.2 scattering layer above a white surface (AS = 0).

Radial polarized intensity: The radial polarized intensity Qr(r) = qr(r) I(r) increases with r from zero in the disk center to a maximum at r > 0.9 and· then drops at the very limb. For semi-infinite atmospheres, Q just decreases at all radii with decreasing single scattering albedo ω. For finite atmospheres, the limb polarization flux Qr(r) depends only slightly on the surface albedo. Decreasing AS from 1 to 0 can increase Qr(r) at most 0.002 for some models, while for most models Qr(r) is virtually constant. This is∼ similar to the case for large phase angles.

Limb darkening and limb brightening vs. limb polarization

For a surface with a low albedo AS below a thin scattering layer the limb can be brighter than the disk center, an effect that is generally called limb brightening. In principle this effect should be called “a central disk darkening”, because the low surface albedo AS does not brighten the limb. It only absorbs more light in the center of the disk, where a higher fraction of photons reach the absorbing surface because of their perpendicular incidence when compared to the situation of grazing incidence at the limb. Despite this fact we will retain the term “limb brightening” and consider the limb brightness on a relative scale compared to the brightness of the disk center. The limb darkening and limb brightening effect can be parametrized to a ﬁrst 2 k 1/2 order using the Minnaert law I(r) = Ir=0(1 r ) − . The Minnaert parameter k determines the shape of the curve, k = 1 corresponds− to Lambert’s law, k = 0.5

52 2.3. Model results for a homogeneous Rayleigh-scattering atmosphere

to a flat intensity distribution I(r) = I0 and k < 0.5 to limb brightening. The k parameter was determined by fitting Minnaert’s law to all modeled intensity profiles, fixing the intensity at the center and excluding the outermost point where the formula diverges for k < 0.5. With the exception of some cases mentioned below, most profiles can be fitted adequately. In Fig. 2.3 different examples of limb darkening and limb brightening are shown along with the best fit of the Minnaert law. Intensities are normalized to the central disk intensity. There are two types of limb brightening curves. For very thin atmospheres the maximal brightness is measured at the very edge of the planet, while for a moderate optical depth the intensity raises slightly up to a certain radius (e.g. 0.9Rp) and then drops very close to the limb. This second case cannot be fitted with the one-parameter Minnaert law and is approximated here by a relatively flat curve k 0.5. The limiting case of a conservative≈ semi-infinite atmosphere yields a Minnaert parameter of k 0.9. For ω going towards 0, k tends to a flat intensity distribution k = 0.5. For finite≈ atmospheres there is a strong dependence on the surface albedo AS. For a strongly absorbing atmosphere over a bright surface (ω low, AS high) absorption is more likely towards the limb (k > 1), for a bright atmosphere over a dark surface the opposite is true (k < 0.5). In the latter case the central disk intensity is very low. Similar to limb brightening, the limb polarization is also enhanced for a bright scattering layer over a dark surface. However, there are fundamental differences between these two effects. Limb polarization arises only for a polarizing process like Rayleigh scattering, while limb brightening occurs also for non-polarizing scattering processes like isotropic scattering. Additionally limb brightening is the stronger the thinner the upper bright layer, while limb polarization requires a sufficiently thick scattering layer above the dark surface. Finally, limb polarization can also occur for cases of limb darkening, e.g. the semi-infinite, conservative atmosphere. Therefore, the two effects provide complementary diagnostics of the vertical structure of the atmosphere.

2.3.3 Parameter study for quadrature phase α = 90◦ and opposition α = 0◦ This section explores the full parameter space for simple Rayleigh scattering atmospheres. We explore the parameter space by varying one of the three parameters ω, τsc and AS (cf. sec. 2.2.2) while ﬁxing the other two. We study the resulting intensity I(90◦), polarization fraction q(90◦), and polarized intensity Q(90◦) (Figs. 2.4 to 2.8). The shapes of the model phase curves for the intensity I(α), fractional polarization q(α), and polarized intensity Q(α) look very similar for different model parameters (see Fig. 2.2). Therefore it is reasonable for a model parameter study to select the results for the phase angle α = 90◦, considering them as representative (qualitatively) for all phase angles. A phase angle α = 90◦ is ideal for

53 Chapter 2. Polarization models for planetary atmospheres extrasolar planets because all planets will pass through this conﬁguration twice during an orbit, regardless of inclination. The same type of parameter study is presented for the limb polarization of planets at opposition (α = 0◦). For this we determine disk-integrated (averaged) quantities for the intensity and radial polarization from the model results (Figs. 2.5 to 2.9). The integrated intensity I(0◦) is equivalent to the geometric albedo, qr is the intensity weighted average of the fractional polarization, and Qr the integratedh i polarized intensity on the same scale as the integrated intensity.h Thesei quantities are determined as described in Sect. 2.2.1. Figures 2.4 and 2.5 show the dependence on the single scattering albedo ω. For a given scattering optical depth τsc a reduction in ω is equivalent to an enhancement of the absorption κ in the scattering layer. Strong differences in κ(λ) occur in planetary atmospheres for molecular absorptions (e.g. due to CH4 or H2O) inside and outside the band while σ is essentially equal. In Figs. 2.6 and 2.7 the Rayleigh scattering optical depths from τsc = 10.0 to 0.01 are plotted. This illustrates quite well the possible spectral dependence from short to long wavelengths (left to right) for a Rayleigh scattering atmosphere. Since the Rayleigh scattering cross sections is proportional to 1/λ4, it is possible that a planet has τsc = 4 at 400 nm and τsc = 1/4 at 800 nm. The effect of the albedo AS of the surface below the Rayleigh scattering layer is shown in Figs. 2.8 and 2.9. General results from the Figures 2.4 to 2.9 are:

lowering the Rayleigh scattering albedo ω always results in a lower inten- • sity I, and lower polarized intensity Q or Qr, lowering the Rayleigh scattering albedo ω results in a higher polarization q • at large phase angles. Contrary to this the fractional limb polarization qr is reduced for lower ω,

lowering the Rayleigh scattering optical depth τ produces a strong reduc- • sc tion in the polarized intensity Q or Qr in the optically thin case τ . 2 and causes essentially no change in Q or Qr in the optical thick case τ & 2, lowering the surface albedo A lowers the intensity I and enhances the frac- • S tional polarization q or qr, changing the surface albedo A does not change the polarized ﬂux Q and • S hardly Qr. The most important difference between the limb polarization q and the h ri disk-averaged polarization q(90◦) is their opposite dependence on the Rayleigh scattering albedo ω (see e.g. the middle panels of Figs. 2.8 and 2.9). This occurs because the limb polarization at opposition is mainly caused by photons undergoing two to about six scatterings rather than just one. Another difference is the inﬂuence of τsc on the fractional polarization: q drops with τsc for bright non-polarizing surfaces and increases for dark surfaces. It

54 2.3. Model results for a homogeneous Rayleigh-scattering atmosphere

Figure 2.4: Intensity, polarization and polarized intensity at quadrature as function of single scattering albedo ω for optical depths τsc = ∞ (solid), 0.6 (dashed), 0.1 (dash-dot) and surface albedos AS = 1 (left), 0.3 (middle), 0 (right).

Figure 2.5: Geometric albedo, disk-integrated radial polarization and polarized intensity at opposition as function of single scattering albedo ω for optical depths τsc = ∞ (solid), 0.6 (dashed), 0.1 (dash-dot) and surface albedos AS = 1 (left), 0.3 (middle), 0 (right).

55 Chapter 2. Polarization models for planetary atmospheres

Figure 2.6: Intensity, polarization and polarized intensity at quadrature as function of optical depth τsc for single scattering albedos ω = 1 (solid), 0.8 (dashed), 0.4 (dash-dot) and surface albedos AS = 1 (left), 0.3 (middle), 0 (right).

Figure 2.7: Geometric albedo, disk-integrated radial polarization and polarized intensity at opposition as function of optical depth τsc for single scattering albedos ω = 1 (solid), 0.8 (dashed), 0.4 (dash-dot) and surface albedos AS = 1 (left), 0.3 (middle), 0 (right).

56 2.3. Model results for a homogeneous Rayleigh-scattering atmosphere

Figure 2.8: Intensity, polarization and polarized intensity at quadrature as function of surface albedo AS for optical depths τsc = ∞ (solid), 0.6 (dashed), 0.1 (dash-dot) and single scattering albedos ω = ωRay = 1 (left), 0.8 (middle), 0.4 (right).

Figure 2.9: Geometric albedo, disk-integrated radial polarization and polarized intensity at opposition as function of surface albedo AS for optical depths τsc = ∞ (solid), 1 (dotted), 0.6 (dashed), 0.1 (dash-dot) and single scattering albedos ω = ωRay = 1 (left), 0.8 (middle), 0.4 (right).

57 Chapter 2. Polarization models for planetary atmospheres

Table 2.2: Best ﬁt parameter b(α, τsc) for the parametrization of the polarized intensity Q (Eq. 2.5). τsc b(30◦, τsc) b(60◦, τsc) b(90◦, τsc) b(120◦, τsc) 0.1 0.38 0.39 0.39 0.44 0.2 0.63 0.65 0.66 0.75 0.3 0.77 0.80 0.82 0.90 0.5 0.99 1.02 1.04 1.10 0.8 1.23 1.22 1.26 1.23 1.0 1.32 1.33 1.32 1.25 2.0 1.52 1.48 1.42 1.27 10.0 1.59 1.59 1.45 1.28 is more complicated at opposition: the limb polarization is highest if the dark ground eliminates photons that would otherwise scatter twice perpendicular to the limb, but the atmosphere is still thick enough to produce many photons that escape having scattered twice parallel to the limb. The maximum possible limb polarization q = 5.25% is reached for τ = 0.8, A = 0 and ω = 1. h ri r S From the variation of τsc shown in Fig. 2.6 it can be seen that the polarized intensity Q(90◦) saturates above τ = τsc ω & 2. Therefore Q(90◦) cannot probe deep atmospheric layers. For the intensity· and fractional polarization, an absorbing ground under a conservatively scattering layer can be noticed even at τ & 10. The polarized intensity Q(α) consists mostly of photons undergoing just one single Rayleigh scattering. Therefore, Q is not changed by processes which happen deep in the atmosphere or by diffuse scattering on the surface. Q is only reduced if the number of single Rayleigh scatterings are reduced, e.g. because there is only a thin Rayleigh scattering layer, or because photons are efﬁciently absorbed high in the atmosphere. We can approximate the polarized intensity Q by the following parametrization:

a(α)τ b(α,τ ) Q(α, τ , ω)= Q(α, ∞, 1) (1 e− sc ) ω sc , (2.5) sc · − · where a(α) and b(α, τsc) are ﬁt parameters. Table 2.2 shows the best ﬁt parameter b(α, τsc), while Q(α, ∞, 1) and a(α) are listed in Table 2.1. For optically thick Rayleigh scattering atmospheres the polarized intensity Q depends only on the single scattering albedo ω, and the parametrization reduces to: Q(α, ω, τ & 2) Q(α, ∞, 1) ωb(α,τsc&2) . (2.6) sc ≈ · At quadrature this is

1.45 Q(90◦, ω, τ & 2) 0.060 ω ( 0.002) . (2.7) sc ≈ · ± For the limb polarization ﬂux Q (0 ) the dependence on ω is much steeper h r ◦ i because both I and qr drop with decreasing ω, as can be seen from the bottom

58 2.4. Models beyond a Rayleigh scattering layer with a Lambert surface panels of Fig. 2.5. For thick Rayleigh scattering layers, τ & 2, the ω-dependence of the limb polarization ﬂux is

Q (τ & 2) 0.022 ω4.23 ( 0.001) . (2.8) r sc ≈ · ± 2.4 Models beyond a Rayleigh scattering layer with a Lambert surface

The three parameter model grid discussed in Sect. 2.3.3 provides an overview on basic dependences of simple Rayleigh scattering models. In this section we describe a few results for particle scattering properties different from pure Rayleigh scattering, or models with more than one polarizing scattering layer.

2.4.1 Atmospheres with Rayleigh and isotropic scattering Pure Rayleigh scattering is a simplification for planetary atmospheres. Already for Rayleigh scattering by molecular hydrogen one needs to account for a weak depolarization effect, because the diatomic molecule is non-spherical. Another depolarization effect for scattered radiation occurs in dense gas because collisions with other particles take place frequently during the scattering process. In addition aerosols and dust particles can also be efficient scatterers in planetary atmospheres and the net scattering phase matrix differs from Rayleigh scattering and should be evaluated, e.g. by using the more general Mie theory. A simple way for taking such effects into account in a first approximation is to use a linear combination of the Rayleigh scattering and isotropic scattering phase matrices S = w R +(1 w) I , (2.9) · − · where w = σRay/σ and 1 w = σiso/σ are the relative contributions of the Rayleigh scattering and isotropic− scattering to the total scattering cross section σ = σRay + σiso. Note that the single scattering albedo ω and the scattering optical depth τsc now include both the Rayleigh and the isotropic scattering cross section (cf. Sect. 2.2.2). Isotropic scattering is non-polarizing. If the scattering in the atmosphere is composed of both isotropic and Rayleigh scattering, then the fractional polarization and the polarized intensity are reduced by isotropic scattering, while the intensity is comparable (cf. Fig. 2.2). Figure 2.10 shows the fractional polarization p(90◦) at quadrature as a function of σiso/σ for a few representative cases. In the single scattering limit the decrease is linear, the strongest deviation from a linear law is found for the semi- infinite atmosphere because of the large amount of multiple scatterings. A similar behavior is found for other phase angles, as well as for the radial limb polarization at opposition.

59 Chapter 2. Polarization models for planetary atmospheres

Figure 2.10: Polarization of atmospheres with Rayleigh and isotropic scattering at 90◦ as a function of isotropic single scattering albedo ωi, normalized to the case of pure Rayleigh scattering ωr = 1 or ωi = 0. Plotted models are: semi-inﬁnite atmosphere (thick solid), τsc = 0.3, AS = 1 (dashed), τsc = 0.3, AS = 0 (dash-dotted), and τsc = 0.05 (thin solid). All models are without absorption, i.e. ωi + ωr = 1.

2.4.2 Forward-scattering phase functions The high polarization of Jupiter’s poles and the disk-integrated polarization of Titan (e.g. Tomasko & Smith 1982; Smith & Tomasko 1984) has been explained by the presence of a thick layer of polarizing haze particles. The derived single scattering properties indicate strong forward scattering and Rayleigh-like linear polarization with maximal polarization close to 100% at about 90◦ scattering angle. Particles that satisfy this behavior are thought to be aggregates that are non- spherical and with a projected area smaller than optical wavelengths (e.g. West 1991). We investigate the polarization properties of a planet with such a haze layer. The particle scattering properties are implemented as described in Braak et al. (2002) using a simple parametrized scattering matrix of the form

F11(ϑ) F12(ϑ) 0 0 F (ϑ) F (ϑ) 0 0 F(#)=  12 11  , (2.10) 0 0 F33(ϑ) 0  0 0 0 F (ϑ)   44  where ϑ is the scattering angle and 

1 g2 F11(ϑ)= PHG(g, ϑ)= − , (2.11) (1 + g2 2g cos ϑ)(3/2) − 2 F12(ϑ) cos ϑ 1 = pm 2 − , (2.12) F11(ϑ) cos ϑ + 1

60 2.4. Models beyond a Rayleigh scattering layer with a Lambert surface

Figure 2.11: Probability density function ρ(ϑ) for Rayleigh scattering (solid), Henyey- Greenstein function with asymmetry parameter g = 0.6 (dashed) and g = 0.9 (dotted).

F33(ϑ) 2 cos ϑ = 2 , (2.13) F11(ϑ) cos ϑ + 1

F44 = 0 . (2.14)

F11(ϑ) or PHG(ϑ) is the Henyey-Greenstein phase function with the asymmetry parameter g (see e.g. van de Hulst 1980). g = 0 corresponds to isotropic scattering, g = 1 to pure forward scattering, g < 0 to enhanced backscattering. Since haze particles have been shown to be strongly forward scattering, we limit our discussion to the two cases g = 0.6 and g = 0.9. Figure 2.11 shows the probability density function ρ(ϑ) for PHG(ϑ) in comparison with Rayleigh scattering. The probability density function for the scattering angle ϑ is the phase function F11(ϑ) weighted by sin(ϑ) and normalized such that the integral over ρ(ϑ) equals 1. From this function the probability of the scattering angle within a certain interval is calculated by integrating ρ(ϑ) over this interval. One can see that for the haze models small scattering angles (forward scattering) are greatly enhanced in comparison to Rayleigh scattering, while the probability for backscattering is much lower. F12(ϑ)/F11(ϑ) describes the fractional polarization of the scattered radiation as a function of the scattering angle. For scattering on haze particles it can be similar to Rayleigh scattering scaled by a factor pm, the maximal single scattering polarization at 90◦ scattering angle. For a ﬁrst qualitative analysis we set pm = 1 which is an upper limit that may slightly overestimate the resulting polarization. The other matrix elements are identical to Rayleigh scattering. Figures 2.12 and 2.13 show the phase and radial dependences for the haze models similar to the Rayleigh scattering case in Sect. 2.3.1 and 2.3.2.

61 Chapter 2. Polarization models for planetary atmospheres

Figure 2.12: Phase dependence of the intensity I, fractional polarization q and polarized intensity Q for a haze layer. Left: Semi-inﬁnite case τsc = ∞ for single scattering albedos ω = 1 (thick), 0.6 (thin) and g = 0.6 (solid), 0.9 (dashed). The dotted line is the Rayleigh scattering case for comparison. Right: Finite atmosphere τsc = 0.3 with ω = 1 for surface albedos AS = 1 (thick), 0 (thin) and line styles as for the left plot.

Figure 2.13: Radial dependence of the intensity I, radial polarization qr and radial polarized intensity Qr at opposition for a haze layer. Left: Semi-inﬁnite case τsc = ∞ for single scattering albedos ω = 1 (thick), 0.6 (thin) and g = 0.6 (solid), 0.9 (dashed). The dotted line is the Rayleigh scattering case for comparison. Right: Finite atmosphere τsc = 0.3 with ω = 1 for surface albedos AS = 1 (thick), 0 (thin) and line styles as for the left plot.

62 2.4. Models beyond a Rayleigh scattering layer with a Lambert surface

Intensity: The phase curves of the haze models differ from the Rayleigh scattering models mainly at small phase angles. The geometric albedo is lower for the haze models because backscattering is strongly suppressed compared to Rayleigh scattering. This is already discussed by Dlugach & Yanovitskij (1974), who calculated albedos for semi-infinite hazy atmospheres. Our calculations result in slightly higher albedos because of the inclusion of polarization. At phase angles around 90◦ the intensities are very similar for all models for non-absorbing atmospheres. An absorber greatly reduces the albedo of a planet with enhanced forward scattering, because many photons penetrate deeply into the atmosphere after the first scattering and then have a high probability of being absorbed. The radial intensity curves mainly reflect the lower geometric albedo, while the shape of the curve is similar for all models.

Polarization fraction: The angle of maximal polarization is generally larger for the haze models than for Rayleigh scattering. In the semi-inﬁnite conservative case it is 110◦ for haze as opposed to 95◦ for Rayleigh scattering. The shift to larger angles≈ is particularly enhanced for≈ a ﬁnite haze layer over a bright Lam- bert surface. However the maximal polarization decreases with increasing g. For strong absorption, both in or below the scattering layer, the polarization phase curve tends toward the single scattering function like in the Rayleigh case. The fractional limb polarization of haze layers can be much higher than for Rayleigh scattering layers, with disk-integrated values reaching q 11% and peak max- h ri≈ ima qr(r) 20%. This is understandable because the singly scattered (backscattered) photons≈ which are unpolarized are strongly reduced for foward scattering particles.

Polarized intensity: The polarized intensity Q(α) is signiﬁcantly lower for forward scattering phase functions than for Rayleigh scattering in the phase angle range α = 30◦ 90◦ and for the limb polarization effect at opposition. It drops strongly with increasing− g or increasing absorption. Like for Rayleigh scattering the polarized intensity is independent of the surface albedo AS. The phase curves Q(α) show a shift of the maximum towards larger phase angles when compared to Rayleigh scattering, in particular for models with thin scattering layers.

2.4.3 Models with two polarizing layers Up to now we have treated the region below the scattering layer simply as a Lambert surface with an albedo AS, which produces no polarization. In this section we explore model results for two polarizing layers with different absorption properties, where the lower layer can be a semi-inﬁnite Rayleigh scattering atmosphere as described in Sect. 2.3.1. We focus on the question at what depth of the upper scattering layer τsc the polarization properties of the underlying layer are washed out by multiple scattering and are no longer recognizable in the reﬂected radiation.

63 Chapter 2. Polarization models for planetary atmospheres

Figure 2.14: Fractional polarization q as function of τsc of the upper layer at quadrature for models with Rayleigh scattering (solid) or isotropic (dotted) upper layer, and semi- inﬁnite Rayleigh scattering lower layer with ω = 0.6 (thick) or Lambertian lower layer with A = 0.2 (thin), which provides the same reﬂectivity.

Figure 2.14 compares the fractional polarization q(90◦) for three cases as a function of scattering optical depth of the upper layer, τsc,u: a non-absorbing Rayleigh scattering layer above a semi-infinite, low albedo Rayleigh scattering atmosphere, the same scattering layer above a low albedo Lambertian surface, and an isotropic, non-polarizing scattering layer above the semi-infinite, low albedo Rayleigh scattering atmosphere. The reflected polarization shows no dependence on the polarization properties of the underlying surface for deep scattering layers with τsc > 2. There are too many multiple scatterings to preserve this type of information from deeper layers in the escaping photons. An imprint from the polarization of the lower layer becomes visible for thin scattering layers with τsc . 2. Particularly well visible is the polarization dependence on τsc for the case where a polarizing layer is located below an isotropically scattering layer. The polarizing lower layer only becomes apparent for τiso < 1. The same is true for the polarized intensity, because the reflected intensity only shows a very weak dependence on the phase function of the scattering layer. The effects are also very similar for the limb polarization at opposition.

2.5 Wavelength dependence

The wavelength dependence of the reﬂected intensity and polarization of a model planet can be calculated using wavelength dependent parameters τsc(λ), ω(λ), and AS(λ) or ωl(λ) for single or double layer models respectively. These param-

64 2.5. Wavelength dependence eters must be derived from a model with a given column density of scattering particles and mixing ratios for Rayleigh-scattering and absorbing particles. As an example we selected parameters which approximate very roughly an Uranus-like atmosphere Trafton (e.g. Trafton 1976) considering only Rayleigh scattering by H2 and He and absorption by CH4. In our first example we look at a homogeneous scattering layer with methane absorption above a reflecting cloud layer with a wavelength independent surface albedo AS = 1. This is a strong simplification for Uranus because the methane mixing ratio is of order 100 lower in the stratosphere than in the troposphere (Sromovsky & Fry 2007). Nevertheless it is a useful example for discussing basic effects of the wavelength dependence. In a second example we make a first approximation for a methane mixing ratio that is varying with height, by having an upper layer of finite thickness without methane and a lower semi-infinite layer that includes methane. The Rayleigh scattering cross section of molecular hydrogen is given by Dal- garno & Williams (1962) as

8.14 10 13 1.28 10 6 1.61 σ (λ)= · − + · − + , (2.15) Ray,H2 λ4 λ6 λ8 ˚ 2 where λ is in A and σRay,H2 in cm /molecule. The total Rayleigh scattering optical depth is

(n 1)2 τ = σ ∑ Z i − , (2.16) Ray ray,H2 i (n 1)2 i H2 − where Zi is the column density and ni the index of refraction of the i-th con- 2 stituent . We use the same wavelength dependence as for the H2 cross section for all constituents. Our upper scattering layer has a column density Z = ∑i Zi = 500 km-am.3 For the atmospheric composition we adopt particle fractions of 0.5% CH4 in the single layer case, and a methane free upper layer with 1 % CH4 in the lower layer in the two layer case. In all layers the He fraction is 15% and the rest is H2. Because of the strong wavelength dependence of the Rayleigh scattering cross section, τsc(λ) changes signiﬁcantly from the UV to the near-IR (Fig. 2.15, top panel). Keeping ω and AS ﬁxed (no absorber) yields the intensity and polarization results given in Figs. 2.6 and 2.7 as function of τsc, which are in this case equivalent to results as function of λ. The wavelength dependent single scattering albedo ω(λ) follows from the

CH4 absorption optical depth τCH4 = ZCH4 κCH4 (λ) and the Rayleigh scattering optical depth according to

τ (λ) ω(λ)= sc . (2.17) τsc(λ)+ τCH4 (λ)

2 nH2 = 1.0001384, nHe = 1.000035, nCH4 = 1.000441 3 1 km-am = 2.687 1024 molecules cm 2 · −

65 Chapter 2. Polarization models for planetary atmospheres

Figure 2.15: Wavelength dependences of the model parameters total optical depth

τ(λ) = τsc + τCH4 of the upper layer, single scattering albedo ω(λ) or ωu(λ) of the upper layer, surface albedo AS or single scattering albedo ωl(λ) of the lower layer. Two cases are considered: A layer of Rayleigh scattering with CH4 absorption above a white (AS = 1) Lambert surface (solid), Rayleigh scattering layer without absorption ωu = 1 above a deep clear atmosphere with methane absorption (dotted).

The absorption cross sections κCH4 (λ) were taken from Karkoschka (1994) and the resulting ω(λ) is shown in Fig. 2.15. The intensity I(λ), fractional polarization q(λ), and polarized intensity Q(λ) is determined from the wavelength dependent model parameters for our two cases at quadrature and opposition (Fig. 2.16). At quadrature both examples show similar results. In both cases the polarization is enhanced and the polarized intensity is reduced within methane absorption bands, only the changes are less pronounced for a non-absorbing upper layer. The polarized intensity Q(λ) also drops with wavelength, but it is overall higher in the second case because the polarizing Rayleigh scattering extends to deeper layers. The biggest qualitative difference is seen in the continuum polarization q(λ). In the case of an underlying reﬂecting cloud, q(λ) drops towards longer wavelengths because of the smaller scattering optical depth above the diffusely scattering cloud. In the second case there is only polarizing Rayleigh scattering and no depolarization effect, so that the increasing absorption with wavelength in the lower layer results in a higher polarization. Similar spectropolarimetric models but with a Jupiter-like homogeneous atmosphere (higher column density, less methane than in our example) above both

66 2.6. Special cases and diagnostic diagrams

Figure 2.16: Model spectra for the intensity, polarization, and polarized intensity at quadrature (left) and intensity, radial polarization, and radial polarized intensity at opposition (right). Lines as in Figure 2.15.

a dark surface AS = 0 and a reflecting extended cloud were discussed by Stam et al. (2004) for α = 90◦. The qualitative behavior of intensity and polarization with wavelength is quite similar to our example. However, for the same column density and methane fraction we find a significantly lower intensity and higher polarization within methane bands. The origin of this discrepancy is unclear. A further comparison with intensity calculations for a Neptune-like atmosphere by Sromovsky (2005a) shows a very good agreement at all wavelengths. Based on this we conclude that our model spectra should be correct. Intensity and polarized intensity at opposition behave qualitatively similar to the large phase angle case. However the fractional polarization qr(λ) is completely different. Absorbing particles in the upper layer tend to reduce the fractional limb polarization, while absorption in the lower layer enhances it. Obser- vations of the limb polarization of Uranus and Neptune (Joos & Schmid 2007) show that the fractional polarization is indeed enhanced within methane bands. Clearly for modeling limb polarization of these planets in absorption bands it is important to take into account the proper vertical stratification of the absorbing component. A detailed model accounting for methane saturation and freeze-out to fit the observations is beyond the scope of this paper.

2.6 Special cases and diagnostic diagrams

We explore some special and extreme model cases in diagnostic diagrams of observational parameters for phase angle α = 90◦ and opposition.

67 Chapter 2. Polarization models for planetary atmospheres

2.6.1 Fractional polarization versus intensity

Figure 2.17 displays the diagnostic diagram for the reflectivity I(90◦) and the relative polarization q(90◦) at phase angle α = 90◦. Also indicated are the iso- contours for the polarization flux Q(90◦). The diagram shows points for special model cases and curves for the dependence on specific model parameters. The shaded area defines the area of observational parameters covered by our 3-parameter model grid for Rayleigh scattering (Sect. 2.3). Including isotropic scattering (Sect. 2.4.1) or having a vertically inhomogeneous atmosphere (Sect. 2.4.3) does not expand the covered area. Figure 2.17 emphasizes that it is not possible to have a Rayleigh scattering planet with both very high albedo and polarization. A high albedo implies either a lot of multiple or isotropic scattering, which both reduce the fractional polarization. On the other hand a high polarization implies mainly single scattering and therefore strong absorption and a low reflectivity. The maximal polarization at a fixed intensity is given by the model with a conservative (ω = 1) scattering layer over a dark (AS = 0) surface and appropriate τsc. The semi-infinite atmosphere with varying ω gives only slightly lower results than the former models. The maximum of the product Q = q I = 0.060 is reached for the conservative · semi-infinite atmosphere (τsc = ∞). Since the polarized intensity Q is independent of the surface albedo AS, a change in AS is equivalent to a shift along the Q iso-contours in the diagram. The diagram also indicates the location of the haze models discussed in Sect. 2.4.2. Most of the haze models lie within the same area as Rayleigh scattering. Only for very thick haze layers with high single-scattering albedo is it theoretically possible to get somewhat higher fractional polarization for a given intensity. Figure 2.18 is the same diagram at opposition for the geometric albedo I(0◦), the disk-integrated limb polarization q and iso-contours for the radial polar- h ri ized intensity Qr . Like for large phase angles, the limb polarization for fixed intensity is highesth i for the conservative Rayleigh scattering layers over a dark surface. However, for τ 0 the polarization drops to 0%, while at large phase sc → angles with AS = 0 it raises towards 100% when the few reflected photons are mainly singly scattered. The semi-infinite models provide a distinctly lower fractional polarization signal than a finite conservatively scattering atmosphere over a dark surface. The fractional limb polarization for very low albedos can be significantly higher for atmospheres with haze than for Rayleigh scattering, because the unpolarized backscattering is greatly reduced. For models with two polarizing layers with different absorption properties, the results are located in the same area as for one layer above a surface. The limiting cases are models with a completely dark lower layer (equivalent to a dark surface), and two identical layers (equivalent to a single semi-infinite layer). For atmospheres that contain also isotropically scattering particles the polarization is always lower and the intensity either slightly enhanced or reduced depending on α because of the different scattering phase functions.

68 2.6. Special cases and diagnostic diagrams

Figure 2.17: Intensity vs. polarization at quadrature for the grid models. The shaded area indicates the possible range for Rayleigh and isotropic models. The symbols and lines indicate: semi-infinite conservative Rayleigh scattering (square), Lambert sphere (round), and black planet (diamond). The dash-dotted line shows semi-infinite models, the dashed and full line finite models without absorption (ω = 1) with surface albedo AS = 1 and 0 respectively. The haze models shown in Fig. 2.12 are indicated by crosses (high albedo) and plusses (low albedo).

Figure 2.18: Geometric albedo vs. disk-integrated radial polarization at opposition for the grid models. The models are the same as in Fig. 2.17.

69 Chapter 2. Polarization models for planetary atmospheres

2.6.2 Polarization near quadrature versus limb polarization For the prediction or the future interpretation of the polarization of extrasolar planets it is of interest to compare the polarization at phase angles near quadrature with the limb polarization at opposition. Figure 2.19 shows a diagram for the fractional polarization q(90◦) and the fractional limb polarization qr(0◦) . Again the special models are indicated with black symbols and lines as inh Figs. i2.17 and 2.18. A lower limit for the polarization fraction at phase angles α 90◦ can be set from the limb polarization at opposition q for Rayleigh scattering≈ or partly h ri isotropic scattering atmospheres. For example a limb polarization of qr 2% implies a minimal polarization of q(90 ) 20%. The upper limit for theh polariza-i ≈ ◦ ≈ tion fraction q(90◦) is not well constrained by qr . The lower limit for Rayleigh or isotropic scattering may overestimate the polarizationh i at large phase angles only for very thick and bright haze layers. A tighter correlation is obtained for the polarization flux Q(90◦) and the limb polarization flux Qr , which is shown in Fig. 2.20. All Rayleigh scattering models are located inh a narrowi area along a line from the origin (Lambert sphere / black planet) to the semi-infinite, conservative Rayleigh scattering model. Thus, for Rayleigh scattering atmospheres, one can predict the large phase angle polarization flux Q(α) from the limb polarization flux Qr and vice versa. The area is slightly broadened if isotropic scattering is includedh i in the models, but the relation still holds quite well. Only very thick and high albedo haze layers show a significantly lower Q(90 ) for a given Q (0 ) . ◦ h r ◦ i 2.6.3 Broadband polarized intensity Color indices of observational parameters are often relatively easy to measure and they are helpful for the characterization of atmospheres. From the atmosphere models they are obtained by averaging spectral results (Sect. 2.5) over the filter bandwidths. Here we discuss the colors for a Rayleigh scattering atmosphere with methane as a main absorber. It is investigated how the polarized intensity color changes as a function of methane mixing ratio and column density above a cloud or surface. Color indices are calculated by integrating Q(λ) over the wavelength range foreseen for filters in the SPHERE/ZIMPOL instrument (Beuzit et al. 2006). The filters are assumed to have flat transmission curves with cut offs at 555 and 700 nm (R-band) and 715 and 865 nm (I-band). We concentrate on the color index of the polarized intensity QI/QR (Fig. 2.21). The polarized intensity is higher at shorter wavelengths, and QI/QR < 1 for all models because of the decrease of the Rayleigh scattering cross section with wavelength and the general increase of the absorption cross section of methane with wavelength. QI/QR is near 1 only for very thick atmospheres with very little methane or very thin atmospheres above a surface with wavelength independent scattering properties. In the former case QR and QI are very high, in the latter

70 2.6. Special cases and diagnostic diagrams

Figure 2.19: Disk-integrated radial polarization at opposition vs. polarization at quadrature for the grid. The models are the same as in Fig. 2.17. All Rayleigh scattering models lie in the dark shaded area, (partly) isotropic models also in the light shaded area.

Figure 2.20: Disk-integrated radial polarized ﬂux at opposition vs. polarized ﬂux at quadrature for the grid models. The indicated models are the same as in Fig. 2.17. All Rayleigh scattering models lie in the dark shaded area, (partly) isotropic models also in the light shaded area.

71 Chapter 2. Polarization models for planetary atmospheres

Figure 2.21: Polarized intensity QR as a function of color QI/QR where QR is the broadband R signal (555 to 700 nm) and QI the broad-band I signal (715 to 865 nm) for Rayleigh scattering planets with methane at 90◦ phase angle. Indicated are models with constant methane mixing ratios f (dashed) or constant atmosphere column density Z in km-am (dotted) above a Lambert surface. very low. For intermediately thick atmospheres the color index QI/QR mainly depends on the methane mixing ratio, while QR mainly depends on the column density. From this diagram we may predict that a color index of QI/QR 0.25 0.5 could be typical for Rayleigh scattering atmospheres with methane≈ absorption.− Aerosol particles and absorbers other than methane are expected to have a different spectral dependence of the scattering and absorption cross sections.

2.7 Conclusions

This paper presents a grid of model results for the intensity and polarization of Rayleigh scattering planetary atmospheres, covering the model parameter space in a systematic way. The model parameters considered are the single scattering albedo ω, which describes absorption, the scattering optical depth of the layer τsc, and the albedo of a Lambert surface AS. The results of these model calculations are available in electronic form at CDS (see Appendix 2.7). In addition we explore models which combine Rayleigh and isotropic scattering, as well as particles with strong forward scattering and atmospheres with vertical stratification. Simple Rayleigh scattering models are a good first approximation to the polarization of light reflected from planetary atmospheres because some amount of Rayleigh-like scattering by molecules or very small aerosol particles can be

72 2.7. Conclusions expected in any atmosphere. From the model grid, which basically provides monochromatic results, the spectropolarimetric signal can be calculated. This is done by considering the wavelength dependence of Rayleigh scattering and absorption in an atmosphere with given column density and particle abundance (see Sect. 2.5). The phase curves for the reflected intensity and polarization show a strong dependence on phase but they always have similar shapes (see Fig. 2.2). However, the absolute level of the phase curve is a strong function of atmospheric parameters such as the abundance of absorbers or aerosol particles, the optical thickness of the Rayleigh scattering layer, or the albedo of the surface layer underneath (Sect. 2.3 and 2.4, see also Kattawar & Adams (1971)). The model calculations demonstrate that polarimetric observations would provide strong constraints on the atmospheric properties of the planetary atmospheres. An example is the polarization flux Q(α) of the reflected light which for optically thick atmospheres is a simple function of the single scattering albedo roughly according to Q(α) ∝ ωb (b 1.5). If both polarization and intensity can be measured, then one can distinguish≈ between highly reflective and absorbing planets with or without substantial layers of Rayleigh-like scattering particles. According to the models a similar diagnostic is possible with observations of the geometric albedo, center-to-limb polarization profile, and limb polarization for solar system planets near opposition. The limb polarization is in addition particularly sensitive to the vertical stratification of scattering or absorbing particles located high in the atmosphere. The diagnostic potential is further enhanced if data for different spectral features, e.g. inside and outside of absorption bands, or from different spectral wavelength regions can be combined (Sect. 2.5, see also Stam et al. (2004)). The calculations presented in this work are based on simple atmosphere models and they are therefore mainly useful for a first interpretation of data. For spectropolarimetric data of high quality, which are already available for solar system planets, one should use more sophisticated atmospheric models including a more detailed geometric structure, accurate abundances, and better scattering models for aerosol particles. With such models it might be possible for polarimetric studies to make a contribution to our knowledge on the rather well known atmospheres of solar system objects. Nonetheless the simple limb polarization models are of interest because they link the model results for large phase angles, suitable for extrasolar planet research, to models which can be easily compared with observations of solar system objects. Thus it may be possible to associate polarimetric observations of extrasolar planets to solar system objects. On the other hand it is possible to predict the expected polarization for quadrature phase of Uranus- and Neptune-like extrasolar planets with this simple model grid based on the existing limb polarization measurements of Uranus and Neptune (Fig. 2.20). Polarimetric measurements for extrasolar planets are expected in the near future from high precision polarimeters. The measurements will first provide the polarimetric contrast, which is the ratio of the polarization flux from the planet

73 Chapter 2. Polarization models for planetary atmospheres

Q(α) to the ﬂux of the central star according to

R2 R2 C(α)= q(α) I(α)= Q(α) , (2.18) D2 · · D2 · where R is the radius of the planet and D the distance from its central star. Very sensitive polarimetric measurements of stars with known close-in planets already exist, taken e.g. with the PLANETPOL instrument (Hough et al. 2006; Lucas et al. 2009). This instrument measures the polarized intensity Q(α) of the planet diluted by the unpolarized flux of the central star. It is then difficult to separate the fractional polarization q and the reflected intensity I. D is known from the radial velocity curve, but already the radius of the planet R may be hard to derive if the system shows no transits. For photometrically very stable stars the reflected intensity I(α) R2/D2 may be measurable with photometry of the · phase curve with high precision instruments like MOST (e.g. Rowe et al. 2008). An uncertainty in the planet radius will affect the precision of the estimation of the normalized reflected intensity I(α) (or reflectivity) of the planet. SPHERE, the future “VLT planet finder”, which includes the high precision imaging polarimeter ZIMPOL, could provide successful polarimetric detections (Beuzit et al. 2006; Schmid et al. 2006a). This instrument will be able to spatially resolve nearby (d < 10 pc) star-planet systems and allow a polarimetric search for faint companions to stars. In a first step only the differential polarization signal, i.e. the polarization flux Q(α), can be measured in the residual halo of the central star. The measurement of the intensity signal I(α) might be possible if further progress in techniques like angular differential imaging is achieved. Even if a determination of I(α) R2/D2 is possible, an uncertainty remains in the translation to normalized intensity· I(α) if the radius of the planet is not known. Thus it may initially be quite difficult to measure intensity and radius. For this reason it is important to investigate the diagnostic potential of the wavelength dependence in the polarization flux in more detail. For example the R-band and I-band yield a polarization color index QI/QR from which it should be possible to infer constraints on the Rayleigh scattering optical depth or the strength of absorption bands (see Sect. 2.6.3). Another route of investigation for atmospheres of extrasolar planets are measurements of the phase dependence of the polarization flux. For example the location of the maximum of Q along the phase curve is sensitive to the presence of aerosol particles, as discussed in Sect. 2.4.2. For planets in eccentric orbits the dependence of the polarization flux on the separation from the host star can be determined. One can hope that the current rapid progress in extrasolar planet observations continues, so that intensity measurements and accurate radius estimates for extrasolar planets become available soon after the first polarization flux detections, using the next generation of ground based telescopes and space instruments. Such instruments, if equipped with a polarimetric observing mode, would allow a broad range of observational programs on the reflected intensity and polarization from planets.

74 2.7. Conclusions

Acknowledgements. This work is supported by the Swiss National Science Foun- dation (SNF). We thank Harry Nussbaumer and Franco Joos for carefully reading the manuscript.

2.A Model grid tables

Our extensive model grid of intensity and polarization phase curves for homogeneous Rayleigh scattering atmospheres (Sect. 2.3) is available in electronic form at CDS. Table 2.3 shows a sample of the first few lines and columns. The table is structured as follows: Model parameters: Column 1: scattering optical thickness τsc, Column 2: single scattering albedo ω, Column 3: surface albedo AS, Model results: Column 4: spherical albedo Asp, Column 5: geometric albedo I(0◦), Col- umn 6: limb polarization flux Q (0 ) , Column 7: I(7.5 ), Column 8: I(12.5 ),. . . , h r ◦ i ◦ ◦ Column 40: I(172.5◦) Column 41: Q(7.5◦),. . . , Column 74: Q(172.5◦). Columns 7 to 74 are I(α) and Q(α) spaced in 5 degree intervals. I(0◦) is equivalent to I(2.5◦) in our calculations. Q(2.5◦), I(177.5◦) and Q(177.5◦) are very close to zero for all models and are not listed. All results are disk-integrated. Binning, normalization and errors are described in Sect. 2.2.4. For all calculations the number of photons was chosen such that ∆(Q/I) < 0.1% for phase angles α = 0◦ 130◦, and therefore (∆I)/I < 0.07% . − The model grid spans the following parameters: τsc = 99, 10, 5, 2, 1, 0.8, 0.6, 0.4, 0.3, 0.2, 0.1, 0.05, 0.01, ω = 1, 0.99, 0.95, 0.9, 0.8, 0.6, 0.4, 0.2, 0.1, AS = 1, 0.3, 0. Models for only three values of AS are given because the polarized intensity is independent of AS and the intensity drops nearly linearly with increasing AS. Models with τsc = 99 were calculated only for AS = 1 since the results are independent of AS. Instead of a model with ω = 1 and τsc = 99, we calculated the model with τsc = 30 to reduce computation time, but the results are equivalent. The spherical albedo Asp in column 4 is the ratio of reflected photons in any direction to total incoming photons, while the geometric albedo I(0◦) in column 5 is the disk-integrated reflected intensity at opposition normalized to the reflection of a white Lambertian disk. For our sample of Rayleigh scattering models, typically I(0 )=(0.80 0.06)A . ◦ ± sp

75 Chapter 2. Polarization models for planetary atmospheres ) ◦ 172.5 ( Q . . . ) ◦ 7.5 ( Q ) ◦ 87 0.003347 . 0.00331 .6 . . 0.00304 . -0.00001 6 . . 0.00278 . -0.00001 4 . . 0.00229 . -0.00001 3 . . 0.00146 . -0.00001 1 . . 0.00084 . -0.00001 1 . . 0.00039 . -0.00000 8 . . 0.00018 . 0.00000 8 . . 0.00338 . 0.00000 8 . . 0.00338 . 0.00000 8 . . 0.00336 . -0.00001 7 . . 0.00310 . -0.00002 7 . . 0.00342 . -0.00002 . . 0.00344 . -0.00001 . . . -0.00003 . -0.00002 172.5 ( I . . . ) ◦ 12.5 ( I ) ◦ 7.5 ( I Extract of model grid results. ) ◦ 0 ( r Q Table 2.3: ) ◦ 0 ( I sp A S A ω sc τ 99.00 0.9999.00 1.0 0.9599.00 0.7947 1.0 0.9099.00 0.6378 0.5975 1.0 0.8099.00 0.02108 0.4884 0.4794 1.0 0.60 0.629099.00 0.01686 0.3980 0.3438 1.0 0.40 0.481399.00 0.6130 0.01316 0.2912 0.1966 1.0 0.20 0.391899.00 0.4681 0.00837 0.1707 . 0.1087 . 1.0 . 0.10 0.286610.00 0.3807 0.00341 0.0958 . 0.0470 . 1.0 0.000 . 1.00 0.167610.00 0.2779 0.00118 0.0418 . 0.0221 . 1.0 0.000 . 1.00 0.094010.00 0.1623 0.00024 0.0197 . 1.0000 . 0.3 0.000 . 1.00 0.041010.00 0.0908 0.00006 0.7949 . 0.8889 . 0.0 0.000 . 0.99 0.019310.00 0.0396 0.02141 0.7085 . 0.8833 . 1.0 0.000 . 0.99 0.784810.00 0.0186 0.02227 0.7042 . 0.8057 . 0.3 0.000 . 0.99 0.6992. 0.7662 . 0.02236 . 0.6453 . 0.7875 . 0.0 0.000 . 0.6950 0.6820 0.02111 0.6326 . 0.7858 . 0.000 . 0.6378 0.6779 0.02112 0.6312 . . 0.000 . 0.6238 0.6214 0.02107 . . 0.000 . 0.6225 0.6076 . . 0.000 . 0.6064 . . 0.000 . . . 0.000 . 0.000 30.00 1.00 1.0 1.0000 0.7947 0.02161 0.7846 0.7661 . . . 0.000

76 BIBLIOGRAPHY

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78 Chapter 3 Polarization of Uranus: Constraints on haze properties and predictions for analog extrasolar planets∗

E. Buenzli1 and H.M. Schmid1

Abstract

We model spectropolarimetric observations of the limb polarization of Uranus for the wavelength range 530 to 930 nm using a Monte Carlo scattering code, and derive for the first time polarization properties of atmospheric constituents of Uranus. We find that the limb polarization is dominated by Rayleigh scattering on molecules. The observed enhancement of the fractional polarization in the methane bands can be naturally explained by a methane depletion in the stratosphere. We obtain a very good fit to the full spectropolarimetric observations by including tropospheric aerosols with a wavelength dependent single scattering polarization, dropping from pm 0.25 at 630 nm to 0.25 at 840 nm at 90◦ scattering angle, and constant at smaller≈ and larger wavelengths.− Additionally a thin (τ 0.01 0.03), positively polarizing stratospheric haze layer is required to reproduce≈ the− limb polarization in the strong methane bands at 790 and 890 nm. The distribution and optical depth of the haze particles agrees well with the extended haze layer model proposed by Karkoschka & Tomasko (2009), with most of the haze continuously intermixed with gas below 1.2 bar. From the limb polarization model we derive the polarization phase curve of Uranus and the spectropolarimetric signal at large phase angles in order to predict the polarization and detectability of an Uranus-like extrasolar planet. At 90◦ phase angle, the polarization fraction is predicted to be 30% averaged over the wavelength range 555 to 865 nm. Within deep absorption≈ bands the polarization fraction can reach as high as 75%. We show that the direct detection of an Uranus-analog around a nearby M-dwarf could be feasible with a polarimetric instrument as proposed for the E-ELT 42 m telescope.

∗ This chapter has been submitted for publication in Icarus 1 Institute of Astronomy, ETH Zurich, CH-8093 Zurich, Switzerland

79 Chapter 3. Polarization of Uranus

3.1 Introduction

Strong limb polarization signals have been detected for Uranus and Neptune with ground based observations (Schmid et al. 2006b; Joos & Schmid 2007). These data for the first time provide an observational assessment of the scattering polarization for the atmospheres of these two planets. In this work we present scattering atmosphere models for the polarization of Uranus, compare the results to the observations and predict the polarization of Uranus for large phase angles. The structure and scattering properties of the troposphere and stratosphere of Uranus have been studied in detail through imaging and spectroscopic observations (e.g. Rages et al. 1991; Baines et al. 1995). Most recently, Karkoschka & Tomasko (2009) (hereafter K09) presented comprehensive HST-STIS spectroscopy covering the wavelength range 300 to 1000 nm at high spatial resolution. One of their most important findings was that the methane mixing ratio appears to vary with latitude. In addition they present evidence for vertically extended haze with an altitude dependent specific optical depth, as opposed to clouds at or below the methane condensation level (e.g. as inferred from Keck infrared imaging and spectroscopy by Sromovsky & Fry 2007; 2008). A complementary approach to studying properties of the upper atmosphere is given by polarimetry. Light scattered by gas, aerosols or clouds is generally polarized to some degree, depending on size, shape and distribution of the scattering particles (see e.g. Buenzli & Schmid 2009, and references therein). Polarimetric observations of planetary atmospheres are especially powerful if a large range of phase angles can be covered. From Earth this is possible for Venus, where Hansen & Hovenier (1974) derived detailed properties of cloud droplets from polarimetriy. For the giant planets, the phase angles seen from Earth are always small, for Uranus less than 3 degrees. Because of symmetry reasons the disk integrated polarization is essentially≈ zero. A larger phase angle coverage can only be obtained from space crafts. This has been achived for Jupiter, Saturn and Titan from the Pioneer 10 and 11 missions (see e.g. Smith & Tomasko 1984; Tomasko & Doose 1984; Tomasko & Smith 1982), Voyager (e.g. West et al. 1983b;a), and more recently by Galileo for Jupiter (Braak et al. 2002) and Cassini for Saturn (West et al. 2009, for preliminary results) and Titan (not yet published). In situ measurements of the haze polarization were performed by Cassini-Huygens for Titan (Tomasko et al. 2008). The only spacecraft to visit Uranus and obtain a large phase angle coverage was Voyager 2 in 1986. But while Voyager 2 carried a photopolarimeter, to our knowledge no polarimetric observations of Uranus for large phase angles were published. The only polarimetric information obtainable for Uranus from the ground is through measurement of the limb polarization effect with disk resolved polarimetry. Limb polarization is a higher order scattering effect that produces a radial polarization signal of up to several percent near the planetary limb because of symmetry breaking (see e.g. Schmid et al. 2006b; van de Hulst 1980, for more detailed descriptions of this effect).

80 3.2. Spectropolarimetric data

An advantage of the ground based measurements is that they allow for more versatile observing modes than usually possible from a spacecraft. Spectropolari- metric observations provide the detailed dependence of polarization with wavelength, and differences inside and outside of strong absorption bands. Addi- tionally, ground based measurements are easily repeatable and could be used to monitor temporal variability of the haze properties. The limb polarization of Uranus was measured for the ﬁrst time by Schmid et al. (2006b) from imaging polarimetry, and by Joos & Schmid (2007) from spectropolarimetry, in the wavelength range of 530 to 930 nm. The observations showed a polarization of 1 3% along the entire limb, dropping with wavelength, but enhanced within∼ methane− absorption bands. The observations were discussed qualitatively and compared to simple analytic models, but no detailed modeling considering the atmospheric structure was done. A parameter study for the limb polarization effect for scattering atmospheres was made in Buenzli & Schmid (2009). Up to now, no detailed modeling of the limb polarization effect for any solar system planet has been published. It is the goal of this paper to model the spectropolarimetric observations of Uranus with a radiative transfer scattering code, considering the atmospheric properties derived by K09. The spatial resolution of the available polarimetric observations is seeing limited and cannot compete with the spatial resolution and wavelength coverage of the HST-STIS observations. Therefore it is not possible to investigate latitudinal or longitudinal structures. But because of the additional polarimetric information they provide an independent test of the extended haze layer model, while at the same time constraining the polarimetric properties of the aerosols. Additionally, from this model the full polarization phase curve can be predicted, which is of interest for future polarimetric observations of extrasolar planets, e.g. with the VLT/SPHERE instrument (Beuzit et al. 2006; Schmid et al. 2006a), and in particular for the follow-up instruments planned for the E-ELT or space-based coronagraphic missions. In Sect. 3.2 we summarize the spectopolarimetric limb polarization observations that we model. Section 3.3 outlines our modeling approach, describing the adapted atmospheric structure and particle scattering properties, and the radiative transfer code. In Sect. 3.4 we discuss the results of the model ﬁt to the observations. In Sect. 3.5 we predict the polarization signal of Uranus at large phase angles, and in Sect. 3.6 we assess the detectability of an Uranus-like planet around a nearby M-dwarf. We conclude in Sect. 3.7.

3.2 Spectropolarimetric data

The spectropolarimetric observations of Uranus were obtained on November 29, 2003 with the EFOSC2 instrument at the ESO 3.6 m telescope in La Silla, Chile. The data are described in detail in Joos & Schmid (2007). In this section we summarize the most important points. The diameter of Uranus at the time of observations was 3.51”, the sub-earth

81 Chapter 3. Polarization of Uranus

Figure 3.1: Orientation of the slit shown on an image of Uranus in radial Qr limb polarization flux. Data from Schmid et al. (2006b). latitude 19 , the position angle of the south pole was 78 , and the phase angle − ◦ ◦ 2.8◦. Long slit spectropolarimetry was taken with an 0.5” wide slit oriented in N-S and E-W direction in the celestial coordinate system. The slit in N-S direction covers roughly the equatorial region (see Fig. 3.1), while the slit in E-W direction spans from near the South pole towards northern latitudes. The data cover the wavelength range 520-935 nm, with a wavelength scale of 0.206 nm per pixel, and a spatial scale of 0.157” per pixel. The seeing was about 1” during the observations. The data were spectrally averaged into 3 nm bins, in order to improve the S/N ratio and to remove a fringe pattern at λ > 700 nm. The instrumental polarization was found to be less than 0.2 %, and the polarization angle calibration was accurate to θ 2◦. In this work we≈ focus on the equatorial data, for which the atmospheric properties are not expected to vary a lot over the slit, whereas the northern latitudes differ considerably from the southern parts of the planet because of strong sea- sonal effects (K09). No absolute intensity calibration using standard stars was performed. In- stead, an average intensity spectrum was calculated from the two slit integrated spectra, which was then normalized to the full disk albedo spectrum of Karkoschka (1998). The resulting albedo spectrum is therefore essentially identical to Karkoschka (1998). The fractional polarization shows a strong dependence along the slit, with a high radial polarization at the limbs and essentially no polarization in the center (see Fig. 3.1). The spectropolarimetric signal was determined for the limb regions, the central region, and the flux weighted average over the total slit. It is important to consider that the polarization is degraded due to the seeing and the finite slit width, while the model assumes basically infinite resolution and an infinites-

82 3.3. Modeling imally thin slit. The degradation of the polarization by the seeing can only be corrected accurately if the signal from the entire slit is considered. Therefore we concentrate our modeling efforts on the ﬂux weighted, slit averaged spectropolarimetry for the equatorial slit orientation indicated in Fig. 3.1. From the seeing of about 1” and a slit width of 0.5”, a “seeing”-correction factor of 1.37 0.15 was derived by Joos & Schmid (2007) for the integrated polarization signal.± The relatively large uncertainty is due to the typical but not well known seeing variations during the observations. The slit averaged fractional polarization is deﬁned as

Qr(r)dr Qr/I = , (3.1) h islit I(r) r R d where Qr is the radial polarization, i.e. theR polarization measured in radial direction from the planet center, corresponding here simply to the direction of the slit. A polarization parallel to the slit (perpendicular to the planetary limb) is defined as +Q , while perpendicular to the slit (parallel to the planetary limb) is Q . The r − r Ur component is zero within the errors of the observations, which is expected because of symmetry reasons. The radial polarization is described in more detail in Schmid et al. (2006b). Figure 3.2 shows the albedo spectrum and the seeing corrected slit averaged spectropolarimetry that we will model in the following sections. Considering only slit averaged data is reasonable because there is no obvious longitudinal asymmetry present, neither in the used spectropolarimetry nor in contemporary HST imaging (Karkoschka 2001). In any case the dependence of the polarimetric center-to-limb profile on atmospheric parameters is rather subtle and can not be investigated with the seeing limited spatial resolution of our data. The uncertainty in the polarization data is indicated in the panel and is mainly due to the not accurately known seeing correction factor. In addition strong photon noise is present in the deep (low flux) absorption bands around 790 nm and between 850 nm and 920 nm. The spectral features in the fractional polarization spectrum are anti-correlated to the features in the intensity spectrum. However, the polarization flux Q ∝ Q/I slit Ageo still shows the methane absorptions, but much less pronounced thanh thei intensity· spectrum.

3.3 Modeling

3.3.1 Atmospheric structure and haze properties As a base for our models we adopt the atmospheric structure given by model D of Lindal et al. (1987), their most plausible model, which was derived from radio occultation measurements of Voyager 2 in the equatorial region of Uranus. The model provides temperature, pressure, total number density of gas molecules, 4 and methane fraction as a function of height for 111 layers between 2.5 10− and 2.3 bar. The helium abundance is assumed to be 15% by number dens· ity,

83 Chapter 3. Polarization of Uranus

Figure 3.2: Geometric albedo, slit averaged limb polarization corrected for polarization dilution due to seeing and slit width and radial polarization ﬂux. Dotted lines in the polarization fraction indicate the uncertainty of the seeing correction. constant with altitude. The methane fraction reaches a maximum of 2.26% at the 1.3 bar level and is assumed constant deeper in the atmosphere. Above this level the relative humidity of methane is constant at 30% and above 660 mbar the atmosphere is completely free of methane. The remaining gas is H2. We extend the atmosphere downwards to 30 bar to ensure a large enough optical depth at all wavelengths of the model. The temperature is extrapolated linearly in log p. The full temperature-pressure diagram is shown in Fig. 3.3. It is in good agreement with the model by Marley & McKay (1999) who provide a T-p proﬁle down to 10 bars. The total molecular number density is calculated from the ideal gas law. The atmosphere then consists of 150 layers and is bound below by a Lambertian surface with an albedo of 0.8, accounting for the small chance of absorption for photons that could penetrate below this deep level. To

84 3.3. Modeling

Figure 3.3: Temperature-pressure diagram for Uranus used in our model calculations. Dotted lines separate the regions of constant haze optical depth per bar. speed up the calculations we reduce the number of layers by combining adjacent layers with very similar single scattering albedos by adding up the optical depth contribution of the different components, resulting in model atmospheres with 15 to 40 layers depending on wavelength. Following K09 we distribute the haze into four atmospheric zones with different haze optical depths τh per bar. These are the stratosphere (p < 0.1 bar), the upper troposphere (0.1 < p < 1.2 bar), the mid-troposphere (1.2 < p < 2 bar) and the low troposphere (p > 2 bar). For the tropospheric haze particles, we adopt K09’s scattering properties that have provided a good ﬁt to their spectroscopic observations. These are a double Henyey-Greenstein phase function for F (ϑ) (cf. Sect. 3.3.2, eq. 3.6) with asymmetry parameters g = 0.7, g = 0.3 11 1 2 − and wavelength dependent weighting factor f , and single scattering albedo ωh,t:

1000 λ f = 0.94 0.47 sin4 − , (3.2) − 445 1 ωh,t = 1 λ 290 , (3.3) − 2 + e −37 with λ in nm. In our wavelength range ωh,t > 0.998. Where ωh,t = 1 we set the value to 0.9999 to avoid inﬁnite scatterings. Since K09 did not model the polarization, we set the other arguments Fxy of the phase matrix (eq. 3.5) as described in Sect. 3.3.2, with the maximum single scattering polarization pm in eq. 3.7 as a free paramter. For the stratospheric particles, K09 adopt Mie theory, but they state that their observations cannot distinguish between spherical and aggregate particles. A high single scattering polarization together with strong forward scattering would

85 Chapter 3. Polarization of Uranus be indicative of aggregate particles, like on Jupiter or Titan (e.g. West 1991). Therefore, for the stratospheric haze, we explore different particle types using a parametrized phase matrix (Eq. 3.5) with a one-term Henyey-Greenstein phase function (Eq. 3.6 with f = 1), where the asymmetry parameter g and the maximum single scattering polarization pm are free parameters. The single scattering albedo is set to 365 λ ω = 1 0.25e 150− , (3.4) h,s − which was obtained from a ﬁt to the values calculated by K09 from Mie theory, and accounts for the darker haze at shorter wavelengths. It is ωh,s = 0.92 at 534.4 nm and ωh,s = 0.994 at 924.4 nm.

3.3.2 Radiative transfer code We use an extended version of the Monte Carlo scattering code described in Buenzli & Schmid (2009). The code calculates the random walk histories of many photons in the atmosphere from incidence to escape or absorption, and follows the direction and polarization change because of scattering processes. The intensity and polarization are then established as a function of radial distance from the disk center for the backscattering situation (phase angle α 0◦) as needed to compare to the Uranus data. For all other phase angles, the disk≈ integrated signals are calculated assuming a homogeneous planet (no latitudinal structures) to provide the full intensity and polarization phase curve. The code fully includes multiple scattering, which is essential because the photons mainly contributing to limb polarization have been scattered twice or more. The incoming radiation is assumed to be a parallel beam of unpolarized photons incident on the spherical planet. The model atmosphere consists of multiple, locally plane parallel layers, and photons emerge at the same point where they entered into the atmosphere, despite multiple scatterings. These simpliﬁcations are reasonable for Uranus because of its optically thick atmosphere and small scale height with respect to the radius. The direction and polarization changes are calculated from probability density functions derived from the appropriate phase matrices of the scattering particles. This approach is described in detail for Rayleigh scattering in Schmid (1992). For scattering on haze and cloud particles, our code allows for scattering matrices of the form

F11(ϑ) F12(ϑ) 0 0 F (ϑ) F (ϑ) 0 0 F(#)=  12 11  , (3.5) 0 0 F33(ϑ) 0  0 0 0 F (ϑ)   44  where ϑ is the scattering angle. For simplicity we use the approach of parametrized functions, as introduced by Braak et al. (2002), because the exact shape of the phase functions is not very signiﬁcant for limb polarization calculations. We choose the two-term Henyey Greenstein function as the intensity phase

86 3.3. Modeling function

F11(ϑ) = PHG(g1, g2, f , ϑ) 1 g2 = f − 1 (3.6) · (1 + g2 2g cos ϑ)3/2 1 − 1 1 g2 +(1 f ) − 2 , − · (1 + g2 2g cos ϑ)3/2 2 − 2 and scaled Rayleigh-like single scattering polarization dependence with positive or negative maximum pm as variable parameter:

2 F12(ϑ) cos ϑ 1 = pm 2 − . (3.7) F11(ϑ) cos ϑ + 1

F12/F11 is the single scattering polarization fraction. A positive (negative) single scattering− polarization means a polarization orthogonal to the scattering plane (parallel). F33 is the same as for Rayleigh scattering,

F33(ϑ) 2 cos ϑ = 2 , (3.8) F11(ϑ) cos ϑ + 1 and we neglect circular polarization by setting F44 = 0. We also neglect Raman scattering, which beyond 500 nm has an effect smaller than 4% on the reflectivities (Sromovsky 2005). The Rayleigh scattering optical depth is computed from the gas column density for each layer as described by Buenzli & Schmid (2009). We include absorption by methane and collision-induced absorption for H2-H2 and H2-He, although H2-He was found to be negligible. Methane absorption coefficients are taken from Karkoschka (1998). The coefficients provided by Karkoschka are not temperature and pressure dependent but are an average derived directly from observations of the Jovian planets and Titan. K09 found that for Uranus some minor modification for the methane windows allow for simpler models. We adopt their corrections and find much better fits to the geometric albedo spectrum. Recently, Karkoschka & Tomasko (2010) published new methane absorption coefficients derived from additional newer data including temperature and pressure dependences. For wavelengths shorter than 1000 nm the changes are small and therefore we did not recalculate our models with the new coefficients. Coefficients for collision induced absorption were calculated from Fortran programs which are available online from A. Borysow2 and are documented in Borysow (1991; 1993) for the H2-H2 fundamental band, Zheng & Borysow (1995) for the first overtone band, Borysow et al. (2000) for the second overtone band, and for H2-He in Borysow & Frommhold (1989) and Borysow et al. (1989). We made the calculations at temperature steps of 10 K, and linearly interpolated for temperatures in between.

2 http://www.astro.ku.dk/ aborysow/programs/index.html

87 Chapter 3. Polarization of Uranus

For each layer and wavelength we set or calculate the optical depth and the single scattering albedo for the gas and haze particles, which are the input to our Monte Carlo code. Models are run with 109 5 1010 photons depending on wavelength, such that at each wavelength point− the· statistical error of the fractional polarization ∆ Q/I 0.07% . h islit ≤|± | 3.4 Results

In this section we discuss our model fit and the parameter space explored with our calculations. Our best model compared to the observations is shown in Fig. 3.4. The derived values for the parameters of this model are listed in Tab. 3.1. The modeled polarization agrees with the observations within ∆ Q/I slit 0.2% for almost all wavelengths, and the agreement is generallyh betteri than≈ 0.1%.± This lies within the uncertainty of the observations and the statistical errors of the Monte Carlo simulation. The residuals are largest within some methane bands, and arise most likely from observational errors or possibly the uncertainties in the methane coefficients and in the methane abundance distribution. The derivation and discussion of the best-fit parameters are addressed in more detail in the following subsections. Because the full spectropolarimetric calculations take up a significant amount of computation time, we could not perform a full exploration of the large parameter space. The uncertainties and limitations of our model fit are therefore also discussed.

3.4.1 Rayleigh scattering and methane absorption

InourmodelwedonotfittheCH4 gas abundances. Therefore we discuss their influence on the polarization in this section. Rayleigh scattering on H2 and He is the main contributor to the polarization on Uranus. A semi-infinite, non-absorbing atmosphere would produce a slit integrated limb polarization Q/I slit = 1.64% (Schmid et al. 2006b), more than is seen for Uranus at continuumh wavelengths.i In the case of absorption, this value can rise up to a maximum of 3.8% if the predominant absorption occurs below the main scattering layer, and it is smaller than the contimuum value if the absorber is well mixed with the scattering gas (Buenzli & Schmid 2009). For Uranus, the inhomogeneous vertical methane mixing ratio, with a much larger methane fraction at higher pressures, naturally leads to the enhancement of the limb polarization seen in methane bands. A purely gaseous atmosphere with the gas mixing ratios of Uranus would overestimate the observed limb polarization by a factor of 2 or more in the continuum at all observed wavelengths, and in absorption bands for wavelengths shorter than 750 nm. Additionally, the absorptions in the albedo spectrum would be overestimated. Therefore the polarization of Uranus can be explained as mainly arising from Rayleigh scattering on gas, but reduced in strength by scattering from intermixed weakly- or non-polarizing tropospheric cloud or haze particles. In the strongest methane bands, at λ = 790 and 890 nm, the observed limb

88 3.4. Results

Table 3.1: Best-ﬁt model parameters of the haze particlesa Param. pres. [bar] Value τh < 0.1 0.15 / bar pm < 0.1 1 g < 0.1 0.6 ωh,s < 0.1 (see eq. 3.4)

τh 0.1 1.2 (0.03 / bar) τ 1.2− 2 1/bar h − τh > 2 0.3 / bar pm > 0.1 see Fig. 3.5 g1 > 0.1 (0.7) g2 > 0.1 ( 0.3) f > 0.1 (see eq.−3.2) ωh,t > 0.1 (see eq. 3.3)

a Parameter values of the haze are given for different pressure regions. The top four parameters are for the stratospheric haze, the others for the tropospheric haze. Listed are the optical depth per bar τh, single scattering polarization pm (cf. eq. 3.7), parameters of the single or double Henyey- Greenstein function (g, or g1, g2 and f, cf. eq. 3.6), and single scattering albedo ωh,s or ωh,t. Values in brackets were not determined but set following K09. polarization is underestimated and requires an additional thin, highly polarizing stratospheric haze layer to augment the polarization.

3.4.2 Tropospheric haze The tropospheric haze was investigated by K09, who found a strong increase in haze optical depth at a pressure p = 1.2 bar, corresponding to the condensation level of methane. Their best-fit model to the HST-STIS spectroscopy for latitudes 1 near the equator had optical depths τh 1.0 1.1 bar− at 1.2 < p < 2 bar, and 1 ≈ − τh 0.1 0.6 bar− at p > 2 bar, with τh constant with wavelength. We use their findings≈ − as a starting point for our models and vary the optical depth together with the polarization properties of the haze. In a first step we assume a wavelength independent polarization to keep the numbers of free parameters as low as possible. Calculating the spectropolarimetric signal for a grid of haze optical depths and polarization, we cannot find a model that correctly reflects the slope of the polarization fraction with wavelength. For any fixed 1 < pm < 1, and τh(1.2 < p < 2 bar) and τh(p > 2 bar) , either the polarization− at wavelengths λ < 700 nm is underestimated, or overestimated at λ > 700 nm. Keeping pm fixed but introducing a decreasing τh with wavelength similarly does not provide a good solution, because a lower τh results

89 Chapter 3. Polarization of Uranus

Figure 3.4: Best model ﬁt (red) to the observed (black dotted) geometric albedo and radial slit averaged polarization.

in a higher polarization in methane bands. An increase in τh with wavelength on the other hand seems implausible because for hazes and dust the optical depth is typically larger for short wavelengths. Also a change in optical depth would influence the intensity. We therefore keep τh constant with wavelength, consistent with K09, but vary pm with wavelength. 1 Indeed, we can now find a good fit for τh = 1 bar− at 1.2 < p < 2 bar, and τh 1 = 0.3 bar− at p > 2 bar, consistent with K09, with the polarization as discussed below. Our observations therefore support the extended haze layer model. There are some degeneracies in the optical depth parameters. The results are almost as good for a more equal haze distribution in the two tropospheric pres- 1 sure regions, e.g. for τh = 0.65 bar− in both regions. We therefore cannot clearly distinguish whether the haze is equally distributed in pressure, or if there is a clear drop in haze opacity below some pressure level. However, without haze in one of the two regions, the fits are clearly worse, and the models also indicate that the haze optical depth in the upper region cannot be much lower than in the lower region. The optical depth of the thin haze layer in the upper troposphere (0.1 < p <

90 3.4. Results

Figure 3.5: Wavelength dependence of the single scattering polarization parameter pm (Eq. 3.7) for our best model.

1.2 bar) has very little effect on our disk- or slit-integrated model results, and is therefore not constrained by our observations. K09 derived the optical depth of this haze layer from UV observations and limb-darkening. We simply adopt a 1 value of τh = 0.03 bar− , which is an average of the haze optical depth derived by K09 for latitudes near the equator. The wavelength dependence of the polarization parameter pm is mainly determined by the observed level and slope of the polarization outside of the methane bands. For a constant, non-polarizing haze, the polarization is too low at short, and too high at long wavelengths, both in the continuum and methane absorption bands. This suggests a higher single scattering polarization at shorter and a lower one at longer wavelengths, with some decrease in between. We therefore describe pm(λ) as a single analytic function which levels off at some wavelength at both the high and low end. We find a good match for pm with a value of +0.25 below 630 nm, a value of 0.25 above 840 nm, and a constant gradient in between as shown in Fig. 3.5. − The derived function for pm(λ) can be considered an approximation for a more realistic, smoother function. The function simply illustrates the general behavior of the polarization: a positive single scattering polarization near 90◦ scattering angle at λ < 700 nm and a negative at λ > 700 nm. Such a dependence might be explained by droplets or ice crystals with sizes of a few µm (see e.g. Karalidi et al. 2011, for spherical water droplets), but detailed calculations for particles to be expected at the temperatures of Uranus are lacking. Also, for such particles the used Rayleigh-like scattering angle dependence is an oversimplifi- cation. The exact scattering properties of the tropospheric haze particles is not well constrained by our measurements, because the limb polarization arises from multiply scattered photons. However, scattering particles with generally positive (orthogonal to scattering plane) polarization pm . 0.25 at wavelengths between 530 and 730 nm and negative (parallel) polarization pm & 0.25 between 730 and 930 nm seems robust because we cannot find a haze in good− agreement with

91 Chapter 3. Polarization of Uranus

K09 with different polarization properties that can fit both the intensity and the limb polarization spectra. Another option might be a change in haze scattering properties with altitude, which we did not consider here. We tested a number of models with localized, geometrically thin clouds at fixed pressure levels. A coarse grid spanning different optical depths, pressure levels and single scattering polarization of particles for the cloud indicates that the slope of the continuum polarization and/or ratios of polarization in methane bands to continuum fit systematically worse than for the extendend haze layer model. Our data therefore indicate that the extended haze layer model proposed by K09, which also fits better for the HST/STIS data, is more likely than a localized cloud model. Because the parameter space is large, we cannot exclude combinations of multiple cloud levels.

3.4.3 Stratospheric haze All models without a stratospheric haze that fit the wavelengths shorter than 750 nm underestimate the polarization in the strong absorption bands at wavelengths longer than 750 nm, for our best model by 0.2-0.3%. This discrepancy does not occur outside of the deep bands. Only a polarizing haze layer situated in the stratosphere, such that the scattering occurs above the absorbing methane, can increase the polarization in these bands sufficiently. This thin layer does not significantly affect the model fit a shorter wavelengths. Evidence for a thin stratospheric haze layer was also found by K09 in intensity measurements. 1 K09 derived an optical depth of about 0.05 bar− at the equator for the stratospheric haze. If we adopt the same optical depth, the resulting methane band polarization is not increased sufficiently, even if the haze particles are set to be very highly polarizing (pm = 1) and reduced in backscttering (g = 0.6). 1 A better match is achieved for τh 0.15 bar− (and thus a total optical depth of 0.015 for the stratospheric haze above≈ a pressure level of 0.1 bar), for afore mentioned scattering properties, even though the polarization is still 0.1% too low in the absorption band around 790 nm. The fit is degenerate in op∼tical depth τh and maximum single scattering polarization pm. A higher optical depth com- 1 bined with a lower single scattering polarization (e.g. τh = 0.3 bar− , pm = 0.5) also provide good fits for the polarization. Much higher optical depths for the stratospheric haze are unlikely because the intensity signal would be too strongly affected. The uncertainties of the polarization measurements is larger in the deep methane bands because of the low photon counts. However, the polarization in the absorption bands between 750 and 900 nm does give strong evidence for a thin, positively polarizing stratospheric haze layer. Our observations unfortunately cannot constrain the particle type of the stratospheric haze. If the particles are highly polarizing, they may either be forward scattering aggregate aerosol particles like at the poles of Jupiter, or they are very small particles which can be described by a Rayleigh-like phase function. For the case of moderate polariza-

92 3.5. Predictions for the polarimetric signal of Uranus at large phase angles

tion, pm 0.5, larger spherical particles as described by Mie-theory are also a possibility.≤

3.5 Predictions for the polarimetric signal of Uranus at large phase angles

Our best fit model to the limb polarization data, with the parameters summarized in Tab. 3.1, now allows for predictions for the intensity and polarization spectra of Uranus at different phase angles. This is mainly of interest for future programs aimed at the detection and characterization of reflected light from extrasolar planets, in particular using polarimetry. While in the solar system the outer gas giants are always seen at small phase angles from Earth, an extrasolar planet circling another star will cover the phase angle interval [90 i, 90 + i], where i is the inclination of its orbit. − We calculate the disk integrated spectropolarimetric signal over the full phase curve, assuming for the whole planet the same atmospheric structure as for the equatorial region of Uranus. This is a simplification, because methane abundance and haze optical depths probably vary with latitude (K09). However, the main deviations in methane abundance occur at high southern latitudes and for the haze at pressures > 2 bar, where the influence on the disk integrated value is relatively small. Also, discrete cloud features are small and of low optical depth. Figure 3.6 shows the intensity and polarization spectra of our best fit model at quadrature phase angle (α = 90◦) and at the angle of maximum polarization flux (α 70◦). The intensity spectrum is very similar to the geometric albedo spectrum,≈ but reduced in flux because only a part of the visible planetary disk is illuminated. The polarization fraction varies strongly with wavelength. The polarization is greatly enhanced within methane bands, and reaches maximum values of up to 75% at quadrature. Because of the strong absorption most photons are singly ≈ scattered and therefore have a high polarization if scattered at 90◦ angle. If the thin stratospheric haze is not highly polarizing, the maximum value can be 10- 20% lower. Outside methane bands multiple scatterings lower the polarization fraction because the scatterings occur in differently oriented planes. The polarization fraction drops with wavelength outside methane bands, from 25% at ≈ 550 nm (20% at 70◦), to 10% at 830 nm. This happens because the optical ≈ 4 depth of the highly polarizing Rayleigh scattering gas drops as λ− , meaning that the tropospheric haze has a stronger influence on the polarizati∼ on signal at longer wavelengths. Even if the single scattering polarization of the haze did not decrease with wavelength, the polarization would drop. The polarized intensity, which is the product of intensity and polarization fraction, drops strongly with wavelength, with additional dips in methane bands. If differential polarimetry is used as a contrast enhancing tool for the detection

93 Chapter 3. Polarization of Uranus

Figure 3.6: Predicted disk integrated ﬂux I, polarization fraction Q/I and polarized intensity Q as a function of wavelength at 90◦ phase angle (red) and at 70◦ phase angle (blue) for our best ﬁt model. of extrasolar planets, the measured signal is the contrast

R2 C(α)= p(α) F(α) (3.9) D2 · · where R is the planet’s radius and D its distance to the central star. It is proportional to the polarized intensity. Therefore it is favorable to perfom these observations at short wavelengths and outside of strong absorption bands. First polarimetric detections of extrasolar planets will not deliver the spectropolarimetric signal, but an average polarization for broadband filters. There- fore, we have also calculated the full phase curve averaged over three filters foreseen in the SPHERE/ZIMPOL instrument. The filters are assumed as having flat transmission curves between 555 and 700 nm (R-band), 715 and 865 nm (I-band), and 555 and 865 nm (RI-band). Figure 3.7 displays the intensity, polarization fraction and polarized intensity as a function of phase angle. Before the integration

94 3.5. Predictions for the polarimetric signal of Uranus at large phase angles

Figure 3.7: Predicted disk integrated flux I, polarization fraction Q/I and polarized intensity Q as a function of phase angle for our best fit model, integrated over a broadband RI filter (555 to 865 nm, green), R filter (555 to 700 nm, blue), and I filter (715 to 865 nm, red) and weighted with the photon spectrum of a G2V star. Addtionally, the broadband RI curve weighted with the photon spectrum of a M4V star is shown (black). over the spectral region, the albedo and polarization spectra at each phase angle were weighted with a template photon spectrum of a G2V star (Pickles 1998). The intensity phase curve obviously drops with phase angle, because smaller fractions of the visible hemisphere are illuminated at larger phase angles. From the spectrum it is also clear that the integrated intensity is larger at shorter wavelengths because methane absorption is weaker. The polarization fraction however shows only little color dependence integrated over the selected filter bands. The maximum is 28% at 90 95◦ for both the shorter and longer wavelength filter. This occurs despite≈ the−strongly increased polarization in the absorption bands in the longer wavelength filter, because the flux in these bands is very low and therefore they do not contribute strongly to the integrated polarization. The maximal polarized intensity is found at 70 , and the FWHM is about ≈ ◦ ≈ 80◦. Therefore polarimetric observations should be taken at phase angles between 30◦ and 110◦.

95 Chapter 3. Polarization of Uranus

As obvious from the spectrum the polarized intensity is much larger in the shorter wavelength ﬁlter.

3.6 Detectability of an Uranus analog around a nearby M dwarf

An upcoming instrument to search for polarized reflected light from extrasolar planets resolved from its central star will be SPHERE at the VLT (Beuzit et al. 2006). The main targets of SPHERE are planets closer than 1 AU to the central star, and these are generally much warmer than Uranus. Nevertheless, for a successful interpretation of a future polarization signal of an exoplanet, it is helpful to understand the signature of a planet such as Uranus. This case would be characteristic for a planet with a relatively clear troposphere mixed with haze particles, a vertically inhomogeneous distribution of methane, an overabundance of C with respect to the solar values, and strong CH4 absorption bands. The detection of an Uranus-analog around a solar-type star is very challenging and beyond the capacities of the currently planned EPICS/E-ELT instrument (Kasper et al. 2010), because the large separation of 20 AU will result in a very low contrast. However, around cooler stars, a planet of a similar temperature can be found much closer in. Here we estimate if a planet of the size and temperature of Uranus could be detectable with the proposed polarimeter in the EPICS instrument for the E-ELT (Kasper et al. 2010) around a nearby M-dwarf. We dis- regard for our estimation that the lower energetic stellar radiation could result in a significantly different atmospheric structure. One of the prime targets could be Barnard’s star, a very low luminosity M dwarf at a distance of only 1.8 pc. With a bolometric luminosity of L = 0.0035L , a planet would receive the same amount of radiation as Uranus around the sun⊙ at a separation of 1.18 AU, or 0.64”, corresponding to an orbital period of about 3.2 years. At this separation, the current upper mass limit for a planetary companion from radial velocity measurements is M sin i 30 M (Zechmeister et al. 2009), more than twice as massive as Uranus. ≈ ⊕ The predicted phase curve weighted with the photon spectrum of an M4V dwarf compared to a G2V dwarf is also depicted in Fig. 3.7. For an M4V star, the photon flux rises strongly towards redder wavelengths, unlike for a G2V star, where the photon flux decreases slightly. Therefore, the spectral regions where the reflected flux is smaller are weighted more strongly, making the intensity and polarization flux phase curve significantly lower for the broadband RI filter. The effect is much smaller for the R and I filter because of the narrower filter pass- bands. The polarization fraction is not affected, because it is nearly constant with wavelength outside of absorption bands. In Fig. 3.8 we show the polarization constrast of an Uranus-analog derived from our best-fit model for one period of a circular orbit around Barnard’s star at 1.18 AU for four inclinations, using the RI phase curve shown in Fig. 3.7. The maximum contrast reached is about 6 10 10, which lies approximately at the de- · −

96 3.7. Conclusions

Figure 3.8: Predicted polarization contrast of an Uranus analog around Barnard’s star for our best ﬁt model, integrated over a broadband RI ﬁlter (555 to 865 nm), weighted with the photon spectrum of an M4V star, for four inclinations: i = 90◦ (blue), i = 60◦ (green), i = 30◦ (red), i = 0◦ (black) tection limit that is currently planned to be achieved with an imaging polarimeter at the E-ELT (Kasper et al. 2010). In the face-on case (i = 0◦), the phase angle is always equal to 90◦ and therefore the polarization contrast remains constant at a relatively high level. In the edge-on case (i = 90◦) the contrast varies strongly because of the large phase angle variation, with two relatively short duration peaks, and diminishing to zero during transit and secondary eclipse. For an inclination of 30◦ the contrast remains very high for half the orbital period, during which the phase angles are in the favorable range of 60 - 90 degrees. Even though only few low luminosity M-dwarfs will be suitable for observations with EPICS, this estimation shows that with differential polarimetry a direct observation of a cool, Uranus-like extrasolar ice-giant could be feasible within the next 10-15 years. Somewhat closer-in or larger planets with a similar atmospheric structure as Uranus could be observed and characterized quite easily with the E- ELT around many nearby stars. A big advantage would be if the orbital phase of the planet is already known, for example from radial velocity measurements, allowing to perform the polarization observations when the planet’s polarization signal is expected to be strong.

3.7 Conclusions

We have modeled the polarization signal of the reflected light from Uranus. We compared our model with spectropolarimetric limb polarization observations of Uranus between 530 and 930 nm. It is the first full spectropolarimetric model fit

97 Chapter 3. Polarization of Uranus to observations of a solar system planet. We simulated in detail the polarimetric structure of spectral features and derived for the ﬁrst time polarimetric parameters of scattering particles on Uranus, in particular the scattering haze. We were able to obtain a very good ﬁt to the slit-integrated limb polarization in the whole wavelength range. For the vertical distribution of the haze, our model also supports the extended haze layer model derived by K09.

3.7.1 Polarimetric properties of Uranus Our model is the first to determine polarimetric properties of scattering particles in the atmosphere of Uranus. Constraints on the haze distribution and scattering properties of the haze particles could be derived. The limb polarization spectrum is especially sensitive to the altitude level of absorption with respect to that of scattering. The increase of fractional polarization within methane bands strongly supports a decrease in CH4 abundance towards high altitudes as determined e.g. from radio occultation observations (Lindal et al. 1987). The absolute level of polarization, which decreases quickly with wavelength, and the relative difference between continuum and CH4 bands require besides Rayleigh scattering on H2 a tropospheric haze that is extended and intermixed with the gas and whose polarization properties change significantly with wavelength, from positive to negative single scattering polarization like for scattering by certain types of droplets. 1 The optical depth of this haze is of order 1 bar− below 1.2 bar, and most likely lower below 2 bar, in good agreement with values derived by K09. The extended haze layer model performs better at fitting the limb polarization than more localized clouds. The derived single scattering polarization function of the tropospheric haze must be regarded as a first order approximation because its scattering angle dependence is not well defined for limb polarization measurements. Regardless, we can say that for a haze in accordance with K09 the haze polarizes positively at wavelengths below 730 nm, and negatively beyond, if uniform scattering properties are assumed throughout the troposphere. A next step would be to calculate effective scattering matrices for different size distributions and compositions as a function of wavelength to determine which physical haze properties match the determined scattering properties. The measured limb polarization in the deep CH bands requires a thin (τ 4 h ≈ 0.015 0.03), positively polarizing (pm 0.5 1 depending on τh) stratospheric haze at− pressures p < 0.1 bar. The nature≈ of the− particles, whether they are small molecules that essentially act as additional Rayleigh scatterers, larger spherical particles, or whether forward scattering fractal aggregates as found on Jupiter’s poles and Titan are required, cannot be determined with certainty from our observations. Their properties could be better constrained with additional high- precision limb polarization measurements in strong near-infrared methane bands (e.g at 1.7 µm), where practically no limb polarization is expected from Rayleigh scattering.

98 3.7. Conclusions

3.7.2 Limb polarization measurements for Uranus Limb polarization measurements provide the opportunity to investigate observationally the polarimetric properties of the atmosphere of Uranus with Earth- based polarimetry, despite the small phase angle. This work demonstrates that an excellent model fit to the spectropolarimetric data can be achieved. Since this is the first detailed spectropolarimetric modeling of the limb polarization of a planet, the full diagnostic potential of such observations still needs to be investigated. The interpretation of limb polarization measurements alone is ambiguous and therefore we have based our model analysis strongly on previous modeling, in particular on the modeling of the HST/STIS spectrometry. In this way the limb polarization spectrum confirms previous results and provides new constraints on the vertical distribution and the polarimetric properties of the scattering particles in the atmosphere as summarized in the previous section. For an interpretation of these results with respect to particle properties such as size and structure, a significant amount of calculations of wavelength dependent scattering matrices of haze particles must be made. Some effort into this direction was taken by Tomasko et al. (2008) to determine the haze properties on Titan. Limb polarization measurements should be considered as one useful tool for future studies of Uranus. High precision spectropolarimeters are readily available for the community at several observatories, providing access to wavelength regions from the near-UV to the near-IR, far beyond the range explored in this work. High spatial resolution polarimetry is possible with ground-based AO systems (see Perrin et al. 2008) and HST which allow detailed studies on the latitude dependence of the limb polarization, or of differences between the morning and the evening limb. Variations of the limb polarizaton on a large range of time scales can also be investigated. Considering all these possibilities it seems very likely that limb polarization data can play a crucial role in future investigations of Uranus. It will be important to obtain well-calibrated intensity measurements together with high-precision limb polarization measurements. While the polarization fraction is a differential measurement independent of the intensity calibration, only a precise measurement of both parameters together over a wide spectral range will allow some degeneracies in optical depth and polarization properties in the models to be resolved. In addition, a code that can calculate both the polarization and intensity combined with an algorithm for an efficient parameter space search will be required to determine meaningful uncertainties in the large parameter space.

3.7.3 Prospects for exoplanet polarimetry Differential polarimetry is a very promising contrast enhancing technique for detecting and characterizing extrasolar planets through their reﬂected light. Planets with a similar atmospheric structure as Uranus are particularly well suited for polarimetric detection because of the relatively thick, strongly polarizing gas layer, and strong absorption occuring only below 1 bar. In our own solar system, ∼

99 Chapter 3. Polarization of Uranus equally well suited is only Neptune (with a quite similar atmosphere as Uranus). Additionally, planets with a thick photochemical haze layer would be promising targets. For example, Titan is the most strongly polarizing solar system object because of a very thick, highly polarizing haze layer (Tomasko & Smith 1982; Tomasko et al. 2008). Jupiter shows a high polarization in the polar regions because of a similar thick photochemical haze layer, while the polarization of the equatorial region is much lower (Smith & Tomasko 1984; Schmid et al. 2011). The near-future polarimetric searches for extra-solar planets will only be able to target planets at much smaller separations than the giant planets in our solar system. Only around M-dwarfs planets at similar temperatures as our solar system giants may be found, but because of the faintness of these stars only a very limited sample will be accessible even with a 40 m class telecope. For planets around earlier-type stars, the targeted planets will be warmer. Because no observations and only very few and rather basic models without polarization (Su- darsky et al. 2000; 2003; 2005; Cahoy et al. 2010) exist for such atmospheres, the polarimetric signal to be expected from these planets is still very unclear. Fur- ther modeling efforts in this direction should be undertaken, with an emphasis on highly polarizing photochemical haze particles. For ground based observations, the lower limit of observable wavelengths is currently set by the performance of the adaptive optics systems. With the current generation of extreme AO-systems, seeing correction for wavelengths shorter than 600 nm is difficult. Observations at shorter wavelengths would be very attractive because of the strong increase of the Rayleigh scattering cross section towards shorter wavelengths, thus an increase of the polarization flux can be expected for most planets. This is seen e.g. in the equatorial regions of Jupiter (Smith & Tomasko 1984), and the same is of course true for Earth (the blue sky is a direct result of Rayleigh scattering). Therefore, an advancement in AO-technology towards shorter wavelengths, or a high precision polarimeter on a space mission, could significantly improve detection prospects of planets through polarimetry and provide a unique window into atmospheres of planets reflecting similarly as the planets in the solar system. Acknowledgements. We are grateful to Franco Joos for providing the reduced polarimetric observations of Uranus in electronic form. We thank Michael R. Meyer and François Menard´ for reading the manuscript and providing comments.

100 BIBLIOGRAPHY

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Baines, K. H., Mickelson, M. E., Larson, L. E., & Ferguson, D. W. 1995, Icarus, 114, 328 Beuzit, J., Feldt, M., Dohlen, K., et al. 2006, The Messenger, 125, 29 Borysow, A. 1991, Icarus, 92, 273 Borysow, A. 1993, Icarus, 106, 614 Borysow, A., Borysow, J., & Fu, Y. 2000, Icarus, 145, 601 Borysow, A. & Frommhold, L. 1989, ApJ, 341, 549 Borysow, A., Frommhold, L., & Moraldi, M. 1989, ApJ, 336, 495 Braak, C. J., de Haan, J. F., Hovenier, J. W., & Travis, L. D. 2002, Icarus, 157, 401 Buenzli, E. & Schmid, H. M. 2009, A&A, 504, 259 Cahoy, K. L., Marley, M. S., & Fortney, J. J. 2010, ApJ, 724, 189 Hansen, J. E. & Hovenier, J. W. 1974, Journal of Atmospheric Sciences, 31, 1137 Joos, F. & Schmid, H. M. 2007, A&A, 463, 1201 Karalidi, T., Stam, D. M., & Hovenier, J. W. 2011, A&A, 530, A69 Karkoschka, E. 1998, Icarus, 133, 134 Karkoschka, E. 2001, Icarus, 151, 84 Karkoschka, E. & Tomasko, M. 2009, Icarus, 202, 287 Karkoschka, E. & Tomasko, M. G. 2010, Icarus, 205, 674 Kasper, M., Beuzit, J., Verinaud, C., et al. 2010, in Adaptative Optics for Extremely Large Telescopes Lindal, G. F., Lyons, J. R., Sweetnam, D. N., Eshleman, V. R., & Hinson, D. P. 1987, J. Geo- phys. Res., 92, 14987 Marley, M. S. & McKay, C. P. 1999, Icarus, 138, 268 Perrin, M. D., Graham, J. R., & Lloyd, J. P. 2008, PASP, 120, 555 Pickles, A. J. 1998, PASP, 110, 863 Rages, K., Pollack, J. B., Tomasko, M. G., & Doose, L. R. 1991, Icarus, 89, 359 Schmid, H. M. 1992, A&A, 254, 224 Schmid, H. M., Beuzit, J., Feldt, M., et al. 2006a, in IAU Colloq. 200: Direct Imaging of Exoplanets: Science & Techniques, ed. C. Aime & F. Vakili, 165–170 Schmid, H. M., Joos, F., Buenzli, E., & Gisler, D. 2011, Icarus, 212, 701 Schmid, H. M., Joos, F., & Tschan, D. 2006b, A&A, 452, 657 Smith, P. H. & Tomasko, M. G. 1984, Icarus, 58, 35 Sromovsky, L. A. 2005, Icarus, 173, 254 Sromovsky, L. A. & Fry, P. M. 2007, Icarus, 192, 527 Sromovsky, L. A. & Fry, P. M. 2008, Icarus, 193, 252 Sudarsky, D., Burrows, A., & Hubeny, I. 2003, ApJ, 588, 1121 Sudarsky, D., Burrows, A., Hubeny, I., & Li, A. 2005, ApJ, 627, 520 Sudarsky, D., Burrows, A., & Pinto, P. 2000, ApJ, 538, 885 Tomasko, M. G., Doose, L., Engel, S., et al. 2008, Planet. Space Sci., 56, 669

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102 Chapter 4 A polarimetric model for Jupiter’s polar haze∗

E. Buenzli1, H.M.Schmid1,F.Joos1 & D. Gisler1

Abstract

We present models of ground-based limb polarization observations of Jupiter for spatially resolved (long slit) spectropolarimetry, focusing on the polarimetric signal at λ = 6000 A˚ in a slit spanning from the North to the South pole. For the polar region we ﬁnd a very strong radial (perpendicular to the limb) fractional polarization with a seeing corrected maximum of about +11.5 % in the South and +10.0 % in the North. This indicates that the polarizing haze layer is thicker at the South pole. The polar haze layers extend down to 58◦ in latitude. The derived polarization values are much higher than reported in previous studies because of the better spatial resolution of our data and an appropriate considera- tion of the atmospheric seeing. The model calculations demonstrate that the high limb polarization can be explained by strongly polarizing (p 1.0), high albedo (ω 0.98) haze particles with a scattering asymmetry parameter≈ of g 0.6 as expected≈ for aggregate particles of the type described by West (1991). The≈ deduced particle parameters are distinctively different when compared to lower latitude regions.

4.1 Introduction

Solar system planets have frequently been observed polarimetrically until 1990 with instruments using single channel (aperture) detectors (e.g. Leroy 2000). However, almost no data were taken with “modern”, ground-based imaging polarimeters and spectropolarimeters using array detectors. Therefore the polarimetric properties of solar system planets are still not well characterized. As part

∗ This chapter is a modiﬁed excerpt of the paper ‘Long slit spectropolarimetry of Jupiter and Saturn’ by H.M. Schmid, F. Joos, E. Buenzli & D. Gisler, published in Icarus 212, 701 (2011), focusing on my contribution to this work. 1 Institute for Astronomy, ETH Zurich, CH-8093 Zurich, Switzerland

103 Chapter 4. Jupiter’s polar haze of a program of “modern” ground-based polarimetric observations of solar system planets, Schmid et al. (2006) and Joos & Schmid (2007) described polarimetric data for Uranus and Neptune, for which strong limb polarization was detected. Modeling for the data of Uranus was presented in Chapter 3 of this thesis. In this chapter we present models for polarimetry of Jupiter taken with the EFOSC2 instrument attached to the ESO 3.6 m telescope. Polarimetric data of Jupiter was first published in the pioneering paper of Lyot (1929), who detected a strong positive polarization of p 5 8 % at the poles with an orientation perpendicular to the limb. In the disk≈ center− he measured a phase angle dependent polarization, which is essentially zero near opposition and slightly negative (parallel to the scattering plane), p 0.4 %, for phase ≈ − angles around α = 10◦. These measurements were confirmed and improved in many later observations using single aperture polarimeters (e.g. Dollfus 1957; Gehrels et al. 1969; Morozhenko 1973; Hall & Riley 1976) and some imaging polarimetry by Carlson & Lutz (1989). Important results on the polarization of Jupiter were achieved with the Pio- neer 10 and 11 spacecrafts, which obtained polarization maps for phase angles larger than α = 12◦. The data show that the polarization in the B- and R-band for α 90◦ reaches a level of about p 50 % at the poles, while the polarization is rather≈ low (< 10 %) in the equatorial≈ region (e.g. Smith & Tomasko 1984). Here we present models for spatially resolved long slit spectropolarimetry of Jupiter, focusing on the wavelength 6000 A˚ in a North-South oriented slit. In the next section a description of the observational data, including the observations and data reduction, is given. In section 4.3 the observations are compared with haze model simulations. The results are discussed in the final section.

4.2 Polarimetric data

Spectropolarimetric observations of Jupiter were taken during the nights of November 29 and 30, 2003 with EFOSC2 at the ESO 3.6m telescope at La Silla. These data originate from the same run and instrument setup as the spectropolarimetry of Uranus and Neptune from Joos & Schmid (2007), where descriptions of the measuring strategy and the data reduction are given. Here we provide only a brief outline and highlight some special points. Observational parameters for Jupiter were taken or derived from data given in U. S. Naval Observatory & Royal Greenwich Observatory (2001) and are summarized in Table 4.1. The position angle (PA) of the scattering plane θ is given with respect to the central meridian (North-South direction) of the planet. The bright limb is on the East for θ close to 90◦. If the scattering plane is tilted with respect to the East-West direction, a perpendicular or parallel polarization with respect to the scattering plane will not only produce a Q-polarization (in N-S orientation), but also a signiﬁcant U-polarization component. For a tilt angle of ∆θ = 2 as in the case of our Jupiter observations this factor is U = 0.07 Q. − ◦ − The apparent diameters dN S and dE W are used to convert locations x from the − −

104 4.2. Polarimetric data

Table 4.1: Parameters for the Jupiter observations. θ is the orientation of the scattering plane, and rCM are distances from the sub-earth point on the central meridian. parameter Jupiter date (2003) Nov. 29 Phase angle α 10.4◦ θ 88◦ polar axis incl. 1.5◦ lat. sub-earth point −1.6 − ◦ diameter (E-W) 35.91′′ r limbs 16.79 CM ± ′′ rCM south pole 16.78′′ r equator − 0.5 CM − ′′ disk center (= sub-earth point) along the central meridian (CM) to radial distances rCM = x dN S/2 which can be converted to planetographic latitudes considering the ellipsoidal· − shape and the inclination of the planet (Table 4.1). The EFOSC2 instrument provides long slit spectropolarimetry. A special slit mask is placed in the focal plane. It consists of a series of 19.7′′ long slitlets with a period of 42.2′′ to avoid overlapping of the two beams produced by the Wollaston prism. The width of the slitlets used was 0.5′′. The spatial scale was 0.157′′ and the spectral scale 2.06 A˚ per pixel. The spatial resolution (given by the effective seeing) of our data is about 1′′, as derived from the width of the spectra of the standard stars. The spectral resolution was 6.4 A˚ for a 0.5′′ wide slit. We focus here on the observations in N-S direction since we are mostly interested in the polarization properties of the polar haze. The instrumental polarization was found to be less than 0.2 % in the central region of the field. The polarization angle calibration should be accurate to about ∆θ 2◦. Solar and telluric spectral features in the intensity spectra were corrected≈ ± with the help of Mars observations taken with the same instrument configuration. The overall slope of the intensity spectrum was adjusted to the albedo spectrum from Karkoschka (1998). We define the Q parameter of the Stokes vector as positive for a polarization parallel to the slit (N-S direction), and thus perpendicular to the limb. In this case Q is equivalent to the radial polarization Qr. The orientation of +Ur is rotated by 45◦ in counter-clock wise direction (North over East). The long-slit spectropolarimetric measurements provide polarimetrically well calibrated profiles for the central meridian for all wavelengths between 5300 and 9300 A.˚ Figure 4.2 shows profiles for the continuum at 6000 A,˚ spectrally averaged from 5900 to 6100 A,˚ (solid line). Spectral averaging was done to enhance the signal to noise ratio. The intensity profile shows belt and zones in good agreement with previous studies (e.g. Moreno et al. 1991; Chanover et al. 1996). The Qr/I and Qr polarization profiles in Fig. 4.2 show Q /I 10 % at the south pole. At the north pole, r ≈ Qr/I reaches a maximum value just above 8 %. The peak polarization at the limb

105 Chapter 4. Jupiter’s polar haze

Figure 4.1: Slit positions for the spectropolarimetric observations with EFOSC2 on a Q (left) polarization flux image of Jupiter from Gisler (2005). North is up and East is left. The gray scale is normalized to the central intensity and spans the range from 1.0 % − (black) to +1.0 % (white). depends significantly on the spatial resolution (or the effective seeing). It is interesting to note that the South pole shows not only a stronger polarization than the North pole, but also a stronger limb brightening in the methane absorption λ8870. The polarization is negative in the center of the disk. The sign change occurs at about 12.5 arcsec, corresponding to a Jovian latitude of about 59◦. The polarization in± the disk center depends on phase and it varies from Q/±I 0.0 % ≈ for α = 0◦ to about Q/I 0.5 % for α = 12◦ as described in detail in Mo- rozhenko (1973). The measurements≈ − are qualitatively in good agreement with earlier studies for the visual-red spectral region, e.g. from Lyot (1929), Dollfus (1957), or Hall & Riley (1968). The fractional intensity I/Islit can be converted into reflectivity f . If the average reflectivity along the central meridian fslit is known, then the reflectivity in a bin is h i I/Islit f = fslit . h i x/xslit From the full disk image the ratio Λ = f / f between the average re- h diski h sliti flectivity for the full planetary disk ( = the geometric albedo Ag) and fslit can be derived. With the geometric albedo from the literature

Ag f = . h sliti Λ We derive Λ = 0.92 from a ZIMPOL image (Gisler 2005) for the “continuum” filter centered at 6010 A˚ (width 180 A).˚ This value does not differ much from ΛLam = 0.85 for a perfectly white Lambert sphere. Karkoschka (1998) gives a geometric albedo of Ag = 0.59 for data taken in 1995 at this wavelength. This value can be used for our calibration because the global reflectivity variations of Jupiter are small (. 5 %) and the phase dependence of the reflectivity ( 1.5 % for α 0 10 ) can be neglected. ≈ ≈ ◦ − ◦

106 4.3. Polarization model for the poles of Jupiter

The flux weighted fractional polarization Qr/I for the wavelength 6000 A˚ does not depend on uncertainties in the absolute flux calibration. The uncertainties are mainly due to systematic errors like instrument calibration or inaccuracies in the slit positioning. The derived Qr/I profile (Fig. 4.2) should be accurate to ∆(Q /I) 0.1 % 0.2 %. r ≈± − 4.3 Polarization model for the poles of Jupiter

Our polarimetry of Jupiter has revealed a surprisingly high limb polarization. We explore whether these observational results are compatible with simple haze scattering models. For a detailed characterization of the scattering particles in Jupiter extensive modeling would be required. Unfortunately up to now there are only few limb polarization models available – the model grid presented in Chapter 2 and polarization model of Uranus in Chapter 3, as well as a few previous, mostly analytic results as summarized in Schmid et al. (2006). It is not yet well explored how the limb polarization depends on the scattering phase matrix of the haze particles, the stratification of the atmosphere, and the optical depth of absorbers. Therefore, our model fitting remains ambiguous without extensive model simulations which are beyond the scope of this work. The goal of these model calculations is to explain the observed peak limb polarization of more than 9.5 % in the V-band at the South pole. Considering that the seeing degrades this polarization, the maximum limb polarization must be well above 10 %. Rayleigh scattering models yield up to 10 % limb polarization (e.g. Schmid et al. 2006), but only for highly absorbing atmosphere models, which are not appropriate for the reflected intensity seen on the poles of Jupiter. Detailed scattering models for the polarization of Jupiter were presented by Smith & Tomasko (1984) and Braak et al. (2002), but only for mid and low latitudes. No detailed scattering models exist for the polarization at the poles. Smith & Tomasko (1984) made a simple fit to the polarization measured in the red with the Pioneer spacecraft near quadrature phase for a Rayleigh scattering layer with single-scattering albedo of ω = 0.983, optical thickness τ = 0.5, and a surface albedo of AS = 0.67. However, this Rayleigh scattering model yields a maximum limb polarization of only 7.3 %, or 6.5 % if the degradation by the seeing is considered, whereas our measurements≈ show a much higher fractional polarization. We calculate the polarization along the central meridian of Jupiter, considering three zones: the N and S polar zones where the polarization is positive (S+ and N+), and a central zone where the polarization is negative. For the S+ and N+ zones we use the Monte Carlo multiple scattering code described in Chapter 2. The chosen atmosphere structure is very similar to the haze model presented by Smith & Tomasko (1984) for low latitudes. They determined haze and gas properties for the South Tropical Zone and South Equatorial Band with an atmosphere consisting of a top gas layer G1, a scattering haze layer H, a lower gas layer G2, and an optically thick surface layer S at the bottom. We fit the polar regions S+ and N+ with this model. For the wavelength 6000 A˚ the optical depths

107 Chapter 4. Jupiter’s polar haze

for the two Rayleigh scattering gas layers are τG1 = 0.011 and τG2 = 0.018, and the single scattering albedo is ωG = 0.976, calculated for a methane abundance of 0.18 %. Thus, the haze layer is geometrically thin and located at a pressure level of 290 mbar, while the opaque surface layer is at 760 mbar. The continuum polarization at 6000 A˚ does not depend much on the exact height of the haze and cloud surface layers. Having the haze layer at 10 mbar, as suggested by near-IR observations by Banfield et al. (1998), and the≈ cloud layer at 1.3 bar, as measured by the Galileo probe at a different location (Ragent et al. 1998≈ ), would not notably change the intensity and polarization. The situation is different for the polarization in the CH4 bands which depends in various ways on the pressure level of the different layers. The full spectropolarimetry should therefore strongly constrain the vertical distribution of the haze and cloud particles. The free parameters of our model are: the cloud layer albedo AS assumed to be a gray Lambert surface, the optical thickness of the haze layer τh, and the haze parameters, which are single scattering albedo ωh, single term Henyey-Greenstein asymmetry parameter gh, and maximum polarization for right angle scattering ph (see Braak et al. 2002). The polar model is independent of latitude, but the incidence and viewing angles produce a latitude dependence in the reflected polarization and intensity. For the reflected intensity at lower latitudes the same model is used, but for the fractional polarization an “artificial” constant value of Qr/I = 0.7 % is adopted. The negative polarization is introduced to fit the transition between− the positively polarized polar zones and the negative central zone. The borders rS and rN are free parameters which are determined in the data fitting process. In order to describe the smearing of the signal due to atmospheric seeing and instrumental light scattering, the “discrete” three zone model is convolved with a Moffat (Moffat 1969) point spread function (PSF). In the formalism of Trujillo et al. (2001) this PSF includes a β-parameter which describes the scattering wing. A small β implies strong wings, a Gaussian is obtained for β ∞, while atmospheric turbulence theory predicts β = 4.76. For our observations→ we derive β = 1 from the residual light outside the nominal limb, indicating significant scattering in the instrument. In Fig. 4.2 the observed intensity and polarization profiles for the central meridian for 6000 A˚ are compared with the model fit. At the poles for r > 0.8 the match is satisfactory except for the fractional polarization outside| the| limb r > 1, where the statistical errors are large because I 0. At low latitudes there are| | some discrepancies because we did not try to fit→ the band structure for the intensity, and instead adopted a constant value for the fractional polarization. A good fit for the limb polarization at λ = 6000 A˚ for both poles is obtained for strongly polarizing ph = 1 haze with low absorption ωh = 0.99 and an asymmetry parameter gh = 0.6. Such scattering parameters are typical for (randomly oriented) aggregate particles as proposed to be present in Jupiter and Titan by West (1991). Small Mie scatterers with diameters much smaller than the wavelength of the scattered light have similar scattering parameters. But the scattering cross section for small spheres is much higher in the blue and one would expect a

108 4.3. Polarization model for the poles of Jupiter

Figure 4.2: Observations of Jupiter (dotted line) from November 2003 compared to model calculations (dashed). Intensity I, fractional polarization Qr/I, and polarization flux Qr profiles through the central meridian (N-S) are given for the continuum at 6000 A.˚ fractional limb polarization which decreases rapidly with wavelength. The scattering cross section and therefore the scattering optical depths of the haze layer are expected to decrease only slowly with wavelength for aggregate particles and they can therefore explain the rather gentle decrease in the Q/I and Q-spectra towards longer wavelengths observed for the poles of Jupiter (see Fig. 4.3), which are not discussed here in detail. The measured limb polarization at the poles for r = 0.96 is about 9.8 % in the South and 8.4 % in the North. The North-South differences± can be explained by different optical depths τh(N+) = 0.72, τh(S+) = 1.1 for the haze layers. Our model fit includes the smearing due to seeing and the modeling indicates that the intrinsic limb polarization reaches maxima of about 11.5 % in the South and 10.0 % in the North. Such a high limb polarization is probably only possible with particles having a scattering phase function with reduced backscattering, with an asymmetry parameter comparable to g 0.6 as used in our model. Our model fit is not unique. However, many parameters≈ are already well constrained. From the parameter space explored by us it seems very likely that the asymmetry

109 Chapter 4. Jupiter’s polar haze

parameter lies in the range 0.5 < gh < 0.8 and the single scattering polarization is ph > 0.8. The locations of the transitions rS and rN between the highly polarized poles and the negatively polarized central zone are at r = 0.82 0.01, identical for ± ± both hemispheres. This corresponds to a planetographic latitude of 58◦ 3◦. In the South the transition between the S+ and the central region is compatib± ±le with an unresolved discontinuity. In the North the transition is more gradual, with a weak wing of positive polarization towards lower latitude. This is in qualitative agreement with Fig. 14 in Smith & Tomasko (1984), who measured the latitudinal polarization dependence with Pioneer for large phase angles (82◦ and 98◦). Their red filter data show a steep increase in the polarization in the South from about 10 % at a latitude of 55 to about 33 % at 65 and a more gradual increase from − ◦ − ◦ 13 % at +55◦ to about 25 % at +65◦ in the North. The surface albedo AS = 0.75 is also quite well constrained, since a high value AS > 0.9 would significantly reduce the resulting fractional polarization and a low value AS < 0.6 would underpredict the reflectivity at the poles. It also seems quite safe to explain the North-South asymmetry in the polar polarization with a difference in the optical thickness of the polarizing haze layer. Finally, it is interesting to note that the haze model for low latitudes with ωh = 0.95, ph = 0.9 and gh = 0.75 from Smith & Tomasko (1984), which was also adopted by Braak et al. (2002), cannot fit the high limb polarization at the poles. This points to distinct differences between the haze particles at the poles and at lower latitudes.

4.4 Discussion and conclusions

We present the first polar haze model for Jupiter based on polarimetric data, focusing on the wavelength region around 6000 A,˚ where the limb polarization is exceptionally strong. The new data are of unprecedented quality and well calibrated for seeing effects to allow for detailed comparisons with model calculations of the scattering layers in Jupiter. Stratospheric haze is responsible for the strong polar polarization, and the sharp transition near 60◦ is pointing to a well defined border in the stratospheric circulation. We measure a resolution-corrected peak polarization of about +11.5 %. All previous studies reported lower values (p 6 8 %) for the maximum polarization at the poles of Jupiter. This difference≈ is− easily explained by the better spatial resolution (seeing 1′′) of our data and the appropriate seeing correction. ≈ Comparison of the polarization flux of the entire positively polarized polar hoods with previous and future observations for long term studies would be interesting for investigations of the haze production, destruction and transport in the polar stratosphere of Jupiter. Such long term polarization changes were reported e.g. by Starodubtseva et al. (2002) and Starodubtseva (2009). Since we found no limb polarization models with a limb polarization higher

110 4.4. Discussion and conclusions than 10 % in the literature, we carried out exploratory model calculations. These indicate that a polar haze layer consisting of forward scattering and highly polarizing aggregate particles as proposed by West (1991) is compatible with our observations. Similar haze particles, but with much lower optical depth, were proposed to exist above the negatively polarizing clouds in Jupiter’s equatorial region (Smith & Tomasko 1984; Braak et al. 2002) This work shows that modern polarimetric measurements from the ground can provide accurate quantitative results which strongly constrain the scattering properties of the atmospheres. More observations, e.g. for other wavelengths, and a lot of limb polarization modeling still needs to be done. Further models should investigate the dependence of the limb polarization signal on the scattering phase matrix of different populations of haze particles. In addition one needs to take into account the spectropolarimetric structure in the methane bands in order to derive the vertical stratification of the scattering layers. Figure 4.3 shows the measured spectropolarimetric signal of Jupiter that we did not discuss in detail in this chapter. Like on Uranus (cf. Chapter 3), the polarization is enhanced in the methane bands. The reason for this enhancement however is different. On Uranus, the enhancement is primarily because of the methane depletion at low pressures, resulting in stronger absorption below the main scattering layer and thus an increase in limb polarization. The very thin, highly polarizing stratospheric haze layer only has a small effect in the deepest methane bands. On Jupiter, the methane mixing ratio is essentially constant with pressure. The enhanced polarization in methane bands then results from the thick, highly polarizing stratospheric haze layer which is not well mixed with the gas. Again, the main polarizing scattering layer is then located above the main absorber. Scattering layers, reflecting the solar light, are an intriguing aspect of solar system planets. They affect the radiative transfer in these objects. For the investigation of the reflected light from extra-solar planets a comprehensive under- standing of the physics of the high altitude haze layers is very important. For this reason it is essential to carry out detailed investigations of the reflecting layers in solar system planets. Investigations based on modern polarimetric observations, as presented here for Jupiter, are therefore very valuable for progress in this direction. Acknowledgments. We are indebted to the ESO La Silla support team at the 3.6m telescope who were most helpful with our very special EFOSC2 instrument setup. We are particularly grateful to Oliver Hainaut. We thank Harry Nussbaumer for carefully reading the Icarus manuscript. We also acknowledge the many useful comments from the referees of the Icarus paper. This work was supported by a grant from the Swiss National Science Foundation.

111 Chapter 4. Jupiter’s polar haze

Figure 4.3: Spectropolarimetry of Jupiter for southern (solid) and northern (dotted) polar (positively polarized, S+ and N+) and equatorial (negatively polarized, S and N ) − − regions. The intensity I(λ) for the polar regions S+ and N+ are multiplied by a factor of 3 with respect to S and N for visibility reasons. The middle panel gives Q /I(λ) and − − r the bottom panel the polarization ﬂux Qr.

112 BIBLIOGRAPHY

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113

Chapter 5 Outlook

5.1 Prospects with SPHERE/ZIMPOL and beyond

Polarimetric detection of extrasolar planets will only really begin once SPHERE/ZIMPOL has gone on sky, currently expected in 2012. Even then, a detection will be very difficult. The largest limitation is the small target sample. Only for the very nearest, brightest stars the necessary contrast for a detection can be achieved. In the photon-noise limit, the noise scales with the inverse 2 square root of the photon flux. The photon flux goes as d− , where d is the target distance in pc. The noise is therefore proportional to the stellar distance. The planet polarization signal is in principle independent from stellar distance for fixed physical separation from the star. However, the angular separation of the planet scales inversely proportional with the stellar distance. At the same angular separation, even if the same noise limit is reached, the signal of the planet is by a 2 factor d− smaller. The S/N ratio of a planet at fixed angular separation therefore 2 3 scales either with d− in the speckle-noise limit, or even d− in the photon-noise limit (see also Thalmann 2008). This strong distance dependence leaves only a handful of feasible targets. α Centauri A and B, with their distance of only 1.3 pc, are by far the best targets. They are followed by Sirius, Altair, Procyon, ε Eridani, τ Ceti and ε Indi. For α Cen A and B, there are detection limits down to M sin i 1 MJ for a < 2 AU from radial velocity measurements (Endl et al. 2004), and≈ much deeper limits with more recent measurements (yet unpublished, M. Endl, X. Dumusque, private communication). These exclude objects down to a few Earth masses in the separation range best probed by SPHERE/ZIMPOL. A Jupiter around τ Ceti and ε Indi should likely also have been detected already. Sirius, Altair and Procyon are earlier-type stars with broad lines, and ε Eri a younger, more active star, therefore high-precision RV measurements are more difficult for these targets. With the occurrence rate of planets with masses between 0.3 and 13 MJ at separations of 0.1 1 AU estimated from radial velocity data (Cumming et al. 2008; Heinze et al. 2010−), to 5%, the target sample is however not large enough to expect a detection statistically.≈ It should be noted that the statistics is determined mainly from FGK-stars, rather than earlier-type stars. A further difficulty is the fact that most of the target stars are actually binaries, where planet occurence, while possisble, is not statistically determined but expected to be even lower than for single stars.

115 Chapter 5. Outlook

Assuming that a planet of appropriate size is present at a suitable separation around a bright nearby star, it is still not necessarily detectable. Two other parameters are crucial for a detection: the phase angle and the atmospheric properties (see Eq. 1.37). Only for phase angles between 30 110◦ (ideal: 50 90◦) the polarization signal is high enough for typical≈ polarizing− atmospheres,− and the planet is separated enough from the star (see Sect. 1.3.2, 2.3.1, 3.5). Because in any orbit with inclination i & 20◦ detection will be impossible for parts of the orbit, a better chance of detection is obtained by making multiple observations spaced by fractions of an orbital interval. The observing strategy must be set for each target individually, depending on the typical orbital period of a planet in the SPHERE/ZIMPOL detection range. The atmospheric properties of a planet are even harder to estimate than the planet phase angle. SPHERE/ZIMPOL will pioneer direct imaging of a completely new type of planet: Jupiters at separations of tenths of an AU. No comparable planets exist in the solar system, and for extra solar planets only atmospheres of hot Jupiters and young planets at far separations have been measured. A few theoretical models that calculate albedo spectra or phase curves of Jupiters with temperatures of a few 100 K have been made (Sudarsky et al. 2000; 2003; 2005; Cahoy et al. 2010). These suggest that such planets are either cloudless planets that are dark because of strong absorption by sodium and potassium, or that they are bright because of condensed water clouds, which then are not expected to show a strong polarization. It must however be noted that these atmosphere models are quite simple and neglect any photochemistry, which may be responsible for production of bright, polarizing haze as seen on the poles of Jupiter and on Titan. Additionally, cloud condensation is generally more complicated than assumed. On Uranus no signiﬁcant clouds have been found where expected at the condensation level of methane. This could mean that atmospheres with a thick Rayleigh scattering layer similar to that of Uranus and Neptune cannot be excluded. If SPHERE/ZIMPOL should detect a polarization signature of a planet, these models must be reﬁned to include more realistic physical and chemical processes. The only star in the SPHERE/ZIMPOL target list for which a planet has been published is ε Eridani. Radial velocity and astrometry measurements suggested a highly eccentric, Jupiter-mass planet with a periastron of 0.3′′(Hatzes et al. 2000; Benedict et al. 2006). At that point it would lie just at≈ the edge of the AO control radius and could be detectable if the atmospheric properties are favorable. From the orbit proposed by astrometry, we have constructed a curve for the expected planet contrast for a 1.2 RJ planet with an optimistic Rayleigh scattering atmosphere as a function of orbital separation (Fig. 5.1). Because of the high eccentricity, the planet will only spend a very short time of its 7-year period at close separations where it is detectable. Good timing of the observations is therefore crucial. The 5σ-detection limit for a planet around ε Eri at 0.3′′separation was es- 8 timated by Thalmann (2008) to 3 10− for a 4 hour observation. The photon noise limit is reached with angular≈ · differential imaging for this source. There- fore, a longer integration may result in a sensitivity low enough for the detection

116 5.1. Prospects with SPHERE/ZIMPOL and beyond

Figure 5.1: Polarization contrast versus angular separation of the proposed planet around ε Eridani from an orbit provided by astrometry, assuming a radius of 1.2 RJ. of the planet if its polarization properties are favorable. ε Eri is therefore a promising candidate for the first polarimetric detection of an atmosphere. However, it should be noted that recently, doubts about the reality of the planet have risen from new radial velocity data (A. Hatzes, private communication). Because the astrometric measurements require the RV measurements to constrain parameters, they cannot be viewed as an independent confirmation. This example shows the importance of confirmation of planets through completely independent methods. Thermal high-contrast imaging excludes planets at a mass M > 3MJ (Janson et al. 2008), with the proposed planet having M = 1.55 MJ. SPHERE/ZIMPOL can largely be seen as a test-case for the potential of planet detection through polarimetry. If all goes well, and deep contrast limits are reached, even if there are no detections, it can be considered a success that opens the door for a more ambitious instrument. A follow-up instrument of SPHERE is already planned for the European Extremely Large Telescope (E-ELT) with a planned mirror diameter of 42 m. The high contrast imager EPICS (Exo-Planets Imaging Camera and Spectrograph, Kasper et al. 2010) could also incorporate a polarimetric arm called EPOL (Keller et al. 2010). With the much larger photon collecting area and the smaller inner working angle than SPHERE, a much larger number of targets will be available. Several already known radial-velocity planets will be within reach, simplifying a detection because the optimal phase is already known. It can be expected that several Jupiter and Neptune-sized planets could be detected. For the closest, brightest stars, even Super-Earths could be found and characterized, providing their polarization is high enough. Unfortu- nately, Earth-like planets would still be out of reach even for α Cen A and B. The

117 Chapter 5. Outlook

E-ELT could go online in 2020, but EPICS would most likely not be a first-light instrument. Therefore, the≈ first large survey for polarization from planets will have to wait for another few years. A future upgrade to SPHERE/ZIMPOL with improved AO and new coronagraphic methods (e.g. an APP, see Sect. 7.1.1) could improve the chances for a detection already before the EPICS is ready. Space- based high-contrast imagers with polarimeters are not currently foreseen. Differential polarimetry is a unique but very challenging method for direct imaging of extrasolar planets. Clearly, observations in the near-infrared will be more successful at imaging planets. These observations are however limited to relatively young planets outside of the vicinity of the sun. A direct image of a planet in the nearest solar neighborhood would be an important step in our quest towards the ultimate goal of characterizing an Earth analog. Therefore the potential of differential polarimetry should be fully explored, and SPHERE/ZIMPOL can be seen as the first step in this direction.

5.2 Hot Jupiter polarimetry

Hot Jupiters are the planets with the smallest separations from the star, orbiting with a period of less than a few days at a distance of a few percent of an AU. Be- cause of the inverse square dependence of the polarization signal of the planet on separation from the star, these planets can in principle show a high polarization signal, about 2 orders of magnitude higher than the SPHERE targets. However, they cannot be observationally separated from the star, and methods like coronagraphy and angular differential imaging cannot be applied to improve the contrast. Polarimetry can disentangle the scattered (partially polarized) light of the planet from the (unpolarized) direct light of the star as well as the (unpolarized) thermal light of the planet. Other methods that target the scattered light signal are high resolution spectroscopy (Charbonneau et al. 1999) and transit measurements at short wavelengths (Rowe et al. 2008, e.g.). The former method has a much lower efﬁciency than polarimetry, the latter works only for transiting planets and requires the stability of a space mission. Also, it cannot distinguish the thermal light from very hot planets from scattered light. 6 5 For these observations, a polarimetric sensitivity of 10− to 10− must be achieved. This requires very high stability and calibration≈ of the instrument and is generally only possible with a dedicated, optimized instrument. Attempts to detect polarization from hot Jupiters have already been made. The ﬁrst was Lu- cas et al. (2009) who searched for the known planets around τ Boo and 55 Cnc with the PLANETPOL instrument (Hough et al. 2006) at wavelengths between 500 900 µm. They could show that τ Boo b cannot be covered by a bright, Rayleigh≈ − scattering atmosphere. The idea that hot Jupiters are dark was supported by an albedo measurement by the MOST satellite for HD 209458 b, which provided a 3σ upper limit of Ag < 0.17 for λ between 400 700 nm (Rowe et al. 2008). Model calculations for HD 209458b are in agreement≈ − with the low upper limits for the albedo. Burrows et al. (2008) and Fortney et al. (2008) obtain a geo-

118 5.2. Hot Jupiter polarimetry

Figure 5.2: Theoretical ﬂux spectrum of HD 209458 compared to Uranus, Jupiter, a Rayleigh sphere and a Lambert sphere (Fortney 2009).

metric albedo Ag < 0.1 beyond 500 nm. However, they predict a strong increase towards the blue and near-UV (see Fig. 5.2) because of Rayleigh scattering by H2, H and He. Berdyugina et al. (2008) and Berdyugina et al. (2011) reported a polari- 4 metric detection of HD 189733 b at the 2 10− level in the UV and blue. This un- physically high polarization (higher than· for a semi-inﬁnite Rayleigh scattering atmosphere) was contradicted by higher-precision measurements by Wiktorow- icz (2009). Their POLISH instrument (Wiktorowicz & Matthews 2008) is the only instrument with demonstrated capabilities to achieve a polarimetric contrast of 6 . 10− at blue wavelengths (Wiktorowicz & Graham 2011) after recent improve- ments. HD 189733 b remains an interesting target for scattered light searches because HST transmission spectroscopy showed evidence of a Rayleigh scattering haze layer (Sing et al. 2011). Once a detection is made, it would be interesting to compare with polarization models for hot Jupiter atmospheres. A few generic examples with Mie scattering condensates were calculated by Seager et al. (2000) before atmospheric properties were actually measured. Polarization could be added to current hot Jupiter intensity models. However, these models do not yet properly treat photochemical haze layers. A ﬁrst interpretation could already be made with simple Rayleigh scattering models as presented in Chapter 2.

5.2.1 Polarimetric search for WASP-18 b We have developed our own observing program to polarimetrically search for polarized light from a hot Jupiter, which was granted time by ESO and observations were successfully carried out in October 2010. Our goal was to achieve a 5 polarimetric contrast of . 10− on the VLT/FORS2 instrument to detect the po-

119 Chapter 5. Outlook larization of the transiting hot Jupiter WASP-18 b, or set a meaningful upper limit on it’s albedo. FORS2 is an imaging and spectropolarimeter at the Cassegrain focus with an absolute instrumental polarization of 0.1% and a detector that is particularly sensitive in the UV/blue. The key issue≈ is the polarimetric calibration of the data to a level of 0.001%. With FORS2 this can only be achieved with a “calibration trick”. Models≈ and observations indicate that we can assume no (significant) polarization signal for hot Jupiters at long wavelengths (say & 500 nm). Thus we use the long wavelengths as zero polarization reference and search for a polarization signal in the blue/near- UV relative to this reference. In this way the instrument and telescope polarization can be monitored in the red and accurately subtracted for all wavelengths. This method requires simultaneous measurement of the full wavelength range between 350 600 nm. We therefore use spectropolarimetry, which has the additional advantage≈ − of smaller read-out overheads than imaging polarimetry. The observations are strongly limited by the read-out time for the bright (V 10) sources, but spreading the photons over a large detector area increases the≈ efficiency. In addition to the wavelength differential, we also take observations during several phases, where the expected planet signal is strong and weak and differentiate the two. This gets rid of potential interstellar polarization. This calibration technique is new, and to check its feasibility we analyzed re- peated standard star spectropolarimetry from a previous FORS1 program. The results show that the (instrumental) polarization for a zero polarization star changes continuously during the night (with parallactic angle) by up to 0.08%. With the 600 nm region as zero polarization reference, the polarization∼ in the UV/blue is constant within the photon noise limit of 0.02 %. A higher precision can only be reached by accumulating more photons.∼ For hot Jupiter polarimetry the photon noise should be improved by at least another factor of 10. It cannot be tested in advance whether calibration to the photon-noise limit is still possible at that level. The transiting planet WASP-18b (Hellier et al. 2009) is large, Rp = 1.17 RJ and in a very tight orbit with a = 0.02 AU, having a period of only 0.94 days. There- fore, its ratio R2/a2 is one of the highest of the currently known hot jupiters. The maximum possible polarization contrast (for a semi-infinite Rayleigh scattering 5 atmosphere) is 6 10− . Also, the system is bright enough (V= 9.3) to reach a pho- · 5 ton noise limit of < 10− thanks to the photon collecting power of the VLT and the high efficiency of the spectropolarimetric mode of FORS2, using all photons between 350 and 620 nm and applying a wide spectral binning. Targeting brighter systems would not reduce the required telescope time with FORS because of detector read-out overheads. With twenty hours of observing time, covering high polarization phases and zero-point phases (secondary eclipse), as well as some intermediate phases, at least twice each, the necessary amount of photons can be 6 reached for a photon noise limit of 6 10− . Comparison between equal phases taken at different times can be used as· a calibration check. The observations were carried out in good conditions in October 2010. A 4 preliminary analysis shows that a polarimetric precision of 10− can easily be

120 5.2. Hot Jupiter polarimetry reached with simple data reduction, as suggested by the previous calibration test. To gain an additional order of magnitude of precision, a sophisticated reduction, e.g. with more precise spectral extraction and accounting for irregularities in individual frames, is required and currently ongoing. Successful polarization observations of hot Jupiters would have great potential for a very complementary atmospheric characterization than provided by the transit technique. The polarization yields strong constraints on the albedo, while a comparison of different spectral bins allows an estimate on the abundance of Rayleigh scatterers, gray scatterers (e.g. haze or dust particles), and of absorbing particles in the high altitude layers of the atmosphere. Most importantly, even the atmospheres of non-transiting planets like τ Boo could be investigated, and inclination and orbital parameters be determined. Systems seen from polar directions could be compared with those seen in the orbital plane. The very high accuracy of polarimeters required to make such detailed measurements of hot Jupiters is still a challenge to overcome, in particular if the planets are predominantly dark in scattered light.

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122 Part II

Angular differential imaging of a debris disk

123 124 Chapter 6 Dissecting the ’Moth’: Discovery of an off-centered ring in the HD 61005 debris disk∗

E. Buenzli1, C. Thalmann2, A. Vigan3, A. Boccaletti4, G. Chauvin5, J.- C. Augereau5, M.R. Meyer1, F. M´enard5, S. Desidera6, S. Messina7, T. Hen- ning2, J. Carson8,,2, G. Montagnier 9, J.-L. Beuzit5, M. Bonavita10, A. Eggen- berger5, A.M. Lagrange5, D. Mesa6, D. Mouillet5, and S.P. Quanz1,

Abstract

The debris disk known as “The Moth” is named after its unusually asymmetric surface brightness distribution. It is located around the 90 Myr old G8V star HD 61005 at 35 pc and has previously been imaged by the∼ HST at 1.1 and 0.6 µm. Polarimetric observations suggested that the circumstellar material consists of two distinct components, a nearly edge-on disk or ring, and a swept- back feature, the result of interaction with the interstellar medium. We resolve both components at unprecedented resolution with VLT/NACO H-band imaging. Using optimized angular differential imaging techniques to remove the light of the star, we reveal the disk component as a distinct narrow ring at inclination i = 84.3 1.0◦. We determine a semi-major axis of a = 61.25 0.85 AU and an eccentricity± of e = 0.045 0.015, assuming that periastron is located± along the apparent disk major axis. Therefore,± the ring center is offset from the star by at least

∗ A shorter version of this chapter is published in Astronomy & Astrophysics 524, L1 (2010) 1 Institute of Astronomy, ETH Zurich, CH-8093 Zurich, Switzerland 2 Max Planck Institute for Astronomy, Heidelberg, Germany 3 Laboratoire d’Astrophysique de Marseille, UMR 6110, CNRS, Universite´ de Provence, 13388 Marseille, France 4 LESIA, Observatoire de Paris-Meudon, 92195 Meudon, France 5 Laboratoire d’Astrophysique de Grenoble, UMR 5571, CNRS, Universite´ Joseph Fourier, 38041 Grenoble, France 6 INAF - Osservatorio Astronomico di Padova, Padova, Italy 7 INAF - Osservatorio Astroﬁsico di Catania, Italy 8 College of Charleston, Department of Physics & Astronomy, Charleston, South Carolina, USA 9 European Southern Observatory: Casilla 19001, Santiago 19, Chile 10 University of Toronto, Toronto, Canada

125 Chapter 6. An off-centered ring in the HD 61005 debris disk

2.75 0.85 AU. The offset, together with a relatively steep inner rim, could indicate± a planetary companion that perturbs the remnant planetesimal belt. From our imaging data we set upper mass limits for companions that exclude any object above the deuterium-burning limit for separations down to 0.35”. The ring shows a strong brightness asymmetry along both the major and minor axis. A brighter front side could indicate forward-scattering grains, while the brightness difference between the NE and SW components can be only partly explained by the ring center offset, suggesting additional density enhancements on one side of the ring. The swept-back component appears as two streamers originating near the NE and SW edges of the debris ring.

6.1 Introduction

Dust in planetary systems is most likely produced by collisions of planetesimals that are frequently arranged in a ring-like structure (Wyatt 2008). These debris disks are therefore thought to be brighter analogs of our solar system’s Kuiper belt or asteroid belt. Previous studies found no correlation between the presence of known massive planets and infrared dust emission from debris disks (Moro- Mart´ın et al. 2007; Bryden et al. 2009; Kosp´ al´ et al. 2009), but several systems are known to host both (e.g. HR 8799, HD 69830). Scattered light imaging of debris disks has revealed numerous structures thought to be shaped by planets. Warps in the β Pic debris disks (Mouillet et al. 1997; Augereau et al. 2001) are caused by a directly confirmed 9 3 MJ planet (Lagrange et al. 2009; 2010; Quanz et al. 2010). Fomalhaut hosts a debris± ring with a sharp inner edge and an offset between ring center and star (Kalas et al. 2005), for which dynamical models suggest the presence of a planet (Quillen 2006). A planetary candidate was indeed imaged (Kalas et al. 2008). Other larger scale asymmetric structures, e.g. around HD 32297 (Kalas 2005), are thought to result from interaction with the ambient interstellar medium (ISM), such as movement through a dense interstellar cloud (Debes et al. 2009). Alternatively, they might be perturbed by a nearby star (e.g. HD 15115, Kalas et al. 2007). The source HD 61005 was first discovered to host a debris disk by the Spitzer/FEPS program (formation and evolution of planetary systems, Meyer et al. 2006). The star properties are summarized in Tab. 6.1. It has the largest 24 µm infrared excess with regard to the photosphere ( 110%, Meyer et al. 2008) of any star observed in FEPS . The star’s age was estimated∼ to be 90 40Myr (Hines et al. 2007), although a more recent analysis suggests that HD 61005± could be a member of the 40 Myr old Argus association (Desidera et al. 2011). This significantly younger age would better match the very strong infrared excess. The disk was resolved with HST/NICMOS coronagraphic imaging at 1.1 µm (Hines et al. 2007, Fig. 6.1 a) that revealed asymmetric circumstellar material with two wing-shaped edges, that is the reason for in the nickname “the Moth”. The disk was also resolved at 0.6 µm with HST/ACS imaging and polarimetry (Maness et al. 2009, Fig. 6.1 b). The polarization suggests two distinct components, a

126 6.2. Observations

Figure 6.1: (a): HD 61005 imaged at 1.1 µm with HST/NICMOS (Hines et al. 2007). (b): HD 61005 imaged at 0.6 µm with HST/ACS with polarization vectors overlaid (Maness et al. 2009). nearly edge-on disk or ring and a swept-back component that interacts with the ISM. Both papers focused on the properties and origin of the swept-back component. In this work, we present high-contrast ground-based imaging with unprecedented angular resolution. We discover and characterize a distinct asymmetric ring in the inner disk component and discuss the probability of a planetary companion.

6.2 Observations

We observed HD 61005 on February 17, 2010 with the NACO instrument (Rous- set et al. 2003; Lenzen et al. 2003) at the VLT. The observations were obtained in the framework of the NaCo Large Program Collaboration for Giant Planet Imag- ing (ESO program 184.C0567). The images were taken in the H-band (1.65 µm) in pupil-tracking mode (Kasper et al. 2009) to allow for angular differential imaging (ADI, Marois et al. 2006). The field of view was 14′′ 14′′ and the plate scale 13.25 mas/pixel. We performed the disk observations× without a coronagraph, and used the cube-mode of NACO to take 12 data cubes. Each cube consisted of 117 saturated exposures of 1.7927 s, yielding a total integration time of 41.95 min. The saturation radius was 0.15”. A total of 112 of field rotation was captured ∼ ◦ while the pupil remained fixed. Additionally, the star drifted by 2.4′′on the detector during the observations, but the drift during single exposures is negligible and can be compensated by proper re-centering of each frame. Before and after the saturated observations we took unsaturated images with a neutral density filter to measure the photometry for the central star. The adaptive optics system provided a point spread function (PSF) with a full-width at half-maximum (FWHM) of 60 mas with 0.8” natural seeing in H-band (22% Strehl ratio). A single exposure raw frame∼ is shown in Fig. 6.2.

127 Chapter 6. An off-centered ring in the HD 61005 debris disk

Table 6.1: Stellar properties of HD 61005, from SIMBAD or Desidera et al. (2011).

Parameter Value Error RA 07 h 35 m 47.46 s DEC -32◦ 12’ 13.044” Distance 35.3 pc 1.1 Spectral type G8V V mag 8.22 0.01 H mag 6.578 L/L 0.583 0.046 R/R⊙ 0.84 0.038 ⊙ Te f f 5500 K 50 log g 4.2 0.2 Fe/H 0.01 0. v sin i 8.2 km/s 0.5 Rotation period 5.04 d 0.04 istar 77◦ +13, 15 age 40Myr 10, +−80 −

6.3 Data reduction and PSF subtraction

The data were flat-field corrected with twilight flats and bad-pixel corrected with a 10σ filter, replacing the bad pixels by the median of surrounding pixels. All frames were centered on the star by manually determining the center for the frame in the middle of the full time-series from the diffraction spikes and align- ing the others through cross-correlation. We removed 3 bad-quality frames where the AO loop was open and averaged the remaining images in groups of three for a total of 467 frames. This binning significantly speeds up the subsequent PSF subtraction, but does not significantly affect its quality because very little movement has taken place during this time because of the very short exposure times of single frames. A more limiting factor to the reduction quality is the accuracy of the centering, which we estimate to 0.5 pixels. We then used LOCI (locally optimized≈ combination of images, Lafreniere` et al. 2007) and customized ADI to subtract the stellar PSF to search for point sources and extended non-circular structures. In our customized ADI reduction, each image is divided into annuli of 2 FWHM width. For each frame and each annulus, an average of the two frames where the field object is rotated by 2 FWHM in either direction is subtracted to remove the stellar halo. Frames too close to the beginning and end of the time-series to have two corresponding subtraction frames are excluded from the process. Fi- nally, all images are derotated and median combined. In LOCI, each annulus is further divided into segments, and for each seg-

128 6.4. Results

Figure 6.2: Raw NaCo H-band observation of HD 61005. The star center is saturated and the diffraction spikes are visible. The images is displayed in log scale. The image size is 14x14′′. ment an optimized PSF is constructed from a linear combination of sufﬁciently rotated frames. A minimum rotation of 0.75 FWHM is optimal for point source detection and has led to several detections around other targets (Marois et al. 2008; Thalmann et al. 2009; Lafreniere` et al. 2010). To reveal the extended neb- ulosity around LkCa 15, Thalmann et al. (2010) used a much larger minimum separation of 3 FWHM. For the nearly edge-on and therefore very narrow debris disk around HD 61005, we obtain an optimal result for a minimum separation of 1 FWHM, but using large optimization areas of 10000 PSF footprints to lessen the self-subtraction of the disk. We also reduced the data with LOCI with a separation criterion of 0.75 FWHM and small optimization segments of 300 PSF footprints to set hard detection limits on companions. To check that the revealed structures are not artifacts of the ADI methods, a classical PSF subtraction was applied to HD 61005 using the unresolved star TYC-7188-571-1, observed 3 hours after HD 61005 in the same observing mode. A total of 400 frames matching the same parallactic angle variation for HD 61005 and the reference star were considered. After shift-and-add, a scaling factor was derived from the ratio of the azimuthal average of the HD 61005 median image to the azimuthal average of the recentered median image of the PSF. The median of the PSF sequence was then subtracted from all individual frames of HD 61005. The resulting cube was derotated and collapsed to obtain the PSF-subtracted image. Additional azimuthal and low-pass ﬁltering was applied to improve the disk detection.

129 Chapter 6. An off-centered ring in the HD 61005 debris disk

Figure 6.3: High-contrast NACO H-band images of HD 61005, (a) reduced with LOCI, (b) reduced with ADI. In (b) The slits used for photometry are overlaid. The curved slit traces the maximum surface brightness of the lower ring arc, while the rectangular boxes enclose the streamers. In all images the scaling is linear, and 1′′corresponds to a projected separation of 35.3 AU. The arc-like structures in the background are artifacts of the observation and reduction techniques, and are asymmetric because the field rotation center was offset from the star. The region with insufficient field rotation is masked out. The yellow plus marks the position of the star, the green cross the ring center.

130 6.4. Results

6.4 Results

The NACO H-band images obtained by reduction with LOCI, ADI and reference PSF subtraction are shown in Fig. 6.3 and Fig. 6.4. The circumstellar material is resolved to an off-centered, nearly edge-on debris ring with a clear inner gap and two narrow streamers originating at the NE and SW edges of the ring. A strong brightness asymmetry is seen between the NE and SW side and between the lower and upper arc of the ring. The inner gap has not been previously resolved by HST, where only the direction of the polarization vectors hinted at a disk-like component separate from the extended material that interacts with the ISM. LOCI provides the cleanest view of the ring geometry with respect to the background because it effectively removes the stellar PSF while bringing out sharp brightness gradients. The negative areas near the ring result from oversubtrac- tion of the rotated disk signal embedded in the subtracted PSF constructed by LOCI. In particular, the ring’s inner hole is enhanced. However, tests with artificial flat disks showed that while self-subtraction can depress the central regions, the resulting spurious gradients are shallow and different from the steep gradients obtained from the edge of a ring. Because of significant variable flux loss, photometry is unreliable in the LOCI image. In the ADI reduction, the self- subtraction is deterministic and can be accounted for, while the stellar PSF is subtracted adequately enough to allow photometric measurements. In the image produced by reference PSF subtraction (Fig. 6.4) the stellar PSF is not effectively removed. The image is unsuitable for a quantitative analysis, but it confirms the streamers and the strong brightness asymmetry, and also suggests the presence of a gap on the SW side.

6.4.1 Surface brightness of ring and streamers The surface brightness of the ring and streamers (Fig. 6.5) is obtained from the ADI image. We measure the mean intensity of the bright ring arc as a function of angular separation from the star in a curved slit of 5 pixels width ( 65 mas, see Fig. 6.3b) following the maximum brightness determined in Sect. ≈6.4.2. For the streamers the slit is rectangular and of the same width. We calculate the mean intensity in the intersection of the slit with annuli of 9 pixels width. To estimate the self-subtraction because of ADI, we apply our ADI method to a model ring (Sect. 6.4.2). The measured ﬂux loss in our slit is 24 5%, where the error includes variations with radius and between the two sides.± For the true ring this value might differ by a few percent. For lack of a good model for the swept material, we apply the same correction factor for the streamers, though the systematic error is likely larger. The dominant source of error are subtraction residuals, which we measure as the dispersion in wider slits rotated by 45◦. To obtain absolute photometry we use the observations of HD 61005 taken± in the neutral density ﬁlter as reference. The NE arc is about 1 mag/arcsec2 or a factor of 2–3 brighter than the SW arc, consistent with the factor of 2 brightness asymmetry seen by

131 Chapter 6. An off-centered ring in the HD 61005 debris disk

Figure 6.4: NaCo image of HD 61005 after reference PSF subtraction using the star TYC- 7188-571-1, observed 3 hours after HD 61005 in the same observing mode.

HST at shorter wavelengths. The surface brightness of the inner 1.1” of the SW arc is of the same order as the residuals, making a power-law ﬁt unreliable. The two streamers are tilted by an angle of 23◦ with respect to the ring’s semi-major axis. We detect material out to a projected∼ distance of 140 AU (4”) ∼ from the star. Beyond 2.8′′ the S/N ratio is too low to perform a meaningful power-law ﬁt. Closer, the power-law slopes agree with those by Maness et al. (2009) within errors. We do not detect the fainter, more homogeneously distributed swept material seen by HST because such structures are subtracted by ADI. However, the streamers are also seen in the reference PSF subtracted image and thus are the most visible component of the swept material. They may represent the limb-brightened edges of the total scattering material.

6.4.2 Ring geometry and center offset We convolve the LOCI image with the PSF and measure the ring’s inclination and position angle by ellipse fitting through points of maximum intensity in selected regions. Assuming that the ring is intrinsically circular, the fit yields an inclination of 84.3◦ and position angle 70.3◦, with systematic errors of 1◦. The position angle agrees well with the position angle of the disk-component∼ determined by HST, while we find the inclination to be 4◦ closer to edge-on. To determine the separation of the ring ansae, we create inclined∼ ring annuli and find for each side the ring with maximum intensity at and close to the ansa. The error of the semi- major axis and offset is assessed by measuring the 1σ background of an equally large region away from the ring at equal angular separation. All values for a and o for which the corresponding ansa has an intensity within 1σ from the maximum

132 6.4. Results

Figure 6.5: H-band surface brightness of the brighter ring arc and the streamers measured from the ADI image and corrected for self-subtraction. Dotted lines indicate the error. The dotted dark line is the 1 σ sky background. Solid dark lines are power-law fits with the obtained slope indicated. The transition regions between ring and streamers are not fitted. are considered solutions within a 1σ error. This fit yields a radius of 61.25 0.85 AU, and a ring center offset from the star by 2.75 0.85 AU toward SW along± the apparent disk major axis. The radial extension of± the ring agrees with the location of the power-law break seen by HST at 0.6 µm. To assess the effect of our PSF subtraction method and determine additional ring parameters, we create synthetic scattered light images of inclined rings with the GRaTer code for optically thin disks (Augereau et al. 1999). The models are inserted into the data of our PSF reference star (cf. 6.3) and the LOCI algorithm is applied to allow direct comparison with the observations. We let the (unprojected) ring be intrinsically elliptical with the periastron located along the apparent disk major axis, because our data cannot constrain an offset along the minor axis. The ring’s surface density as a function of radial distance r to the star (corrected for eccentricity) is described as r σ(r)= σ R(r) , (6.1) 0 × a with the radial structure R(r) a smooth combination of two power laws, such that the profile rises to a peak position and then fades with distance from the star:

1 r 2αin r 2αout − 2 R(r)= − + − , (6.2) a a where a is the semi-major axis, αin > 0 and αout < 0. Directionally preferential scattering is represented by a Henyey-Greenstein (HG) phase function with an asymmetry parameter g.

133 Chapter 6. An off-centered ring in the HD 61005 debris disk

Figure 6.6: Comparison of a radial cut averaged over 5 pixels through the midplane for the observation reduced with LOCI and two model disk implanted into the reference star and reduced in the same way. a Best ﬁt model, b Model without an offset. The intensity of the SW-side of the model is scaled down by a factor 1.3.

Figure 6.7: As ﬁg. 6.6 but for a model without an offset.

We compare the model constructed from the parameters derived above, as well as a similar model without an offset, with the observation. An inclination of i = 84.3 1.0◦ is also a good match for an intrinsically elliptical ring. While the center offset± leads to a small increase (factor of 1.2) in surface brightness on the NE side with respect to the SW side, models that∼ are identical on the two sides except for the offset still underestimate the extent of the enhancement by a factor of 1.3. That the brightness asymmetry is visible after all reduction methods and in∼ the HST 0.6 µm image suggests a physical asymmetry in the density or grain properties. Because asymmetric dust models that include the ISM interaction go beyond the scope of this study, we focus on validating the ring geometry. We compare a radial cut along the midplane averaged over 5 pixels (Fig. 6.6), artiﬁcially lowering the model intensity on the faint side by a factor of 1.3. Indeed, models with an offset o = a e of 2.75 0.85 AU, where a is the semi-major axis for the peak density (61.25 · 0.85 AU)± and e the eccentricity (0.045 0.015), still provide a decent match after± reduction with LOCI. Models without± offset are

134 6.4. Results

Table 6.2: Properties of the debris ring derived from the NaCo observations reduced with LOCI

Inclination 84.3 1 ± ◦ Position angle 70.3 1◦ Semi-major axis 61.25 0.85± AU Eccentricity 0.045± 0.015 Star center offset 2.75 0.85± AU ±

worse particularly out to 63 AU for each ring side because the shift in peak intensity is missing (see Fig.∼ 6.7). Therefore the offset does not appear to be an artifact of the data reduction. Model comparison suggests an inner surface density power-law slope of 7, but a fit is difficult because reduction artifacts differ for models and observations.∼ The outer slope (fixed to 4) is uncertain because we do not model the ISM interaction. In any case, the inner− rim appears to be significantly steeper than the outer rim. From the brightness asymmetry between the upper and lower arc we estimate the HG asymmetry parameter to g 0.3. This value is uncertain because the weak arc is strongly contaminated by| | reduction ∼ residuals. Additionally, the HG phase function is a simplistic model for scattering in debris disks. A positive g-value, assuming that the brighter side is the front, would indicate forward scattering grains. This may not always be the case (see e.g. Min et al. 2010).

6.4.3 Background objects and limits on companions to HD 61005

In our full VLT/NaCo ﬁeld image (Fig. 6.8) we detect six faint sources at r > 3′′, marked as fs-1 to fs-6. In addition to our VLT data, we used the HST/NICMOS observations of Hines et al. (2007) (program 10527) obtained in November 20, 2005 and June 18, 2006, to determine whether these are bound or background objects. The relative positions recorded at different epochs can be compared to the expected evolution of the position measured at the ﬁrst epoch under the assumption that the sources are either stationary background objects or comoving companions. For the range of explored semi-major axes, any orbital motion can be considered to be of lower order compared with the primary proper and parallactic motions. Considering a proper motion of (µα, µδ)=( 56.09 0.70, 74.53 0.65) mas/yr and a parallax of π = 28.95 0.92 mas for HD− 61005± as well as the± relative positions of all faint sources at each± epoch (see Table 6.3), a χ2 probability test of 2 N degrees of freedom (corresponding to the measurements: × epochs separations in the ∆α and ∆δ directions for the number Nepochs of epochs) was applied. None of the six sources are comoving with HD 61005 with a probability higher than 99.99%. They are found to be background stationary objects with a

135 Chapter 6. An off-centered ring in the HD 61005 debris disk

Figure 6.8: Full field of view of our NACO H band data reduced by derotating, adding − and spatially filtering. Six background sources are identified.

Table 6.3: Relative positions of the faint sources 1 to 6 (Fig. 6.8). A conservative astrometric error of 1 pixel has been considered for the relative position measurements obtained with HST/NICMOS and VLT/NaCo observations (i.e 75.8 mas and 13.25 mas).

Name UT Date ∆RA ∆DEC UT Date ∆RA ∆DEC NICMOS (mas) (mas) VLT (mas) (mas) fs-1 2006-06-18 -1929 2918 2010-02-17 -2189 3080 fs-2 2005-11-20 -4672 4669 2010-02-17 -4449 4441 fs-3 2005-11-20 -2326 9321 2010-02-17 -2068 9034 fs-4 2005-11-20 -8487 -15 2010-02-17 -8222 -370 fs-5 2006-06-18 -1586 -6848 2010-02-17 -1358 -7123 fs-6 2006-06-18 -1148 -7671 2010-02-17 -1336 -8024

136 6.5. Discussion probability higher than 60%. We can therefore fully exclude the possibility that these sources are physically bound companions of HD 61005. Maness et al. (2009) had already determined that four sources visible in their image were background sources. Two of these correspond to fs-3 and fs-4, and we here confirm their result. Their other two sources are outside of our field of view. We therefore provide a new result for the four sources fs-1, fs-2, fs-5 and fs-6. In the LOCI image reduced with the smaller minimum rotation (Fig. 6.9) we search for closer companions. After convolving the resulting image with an aperture of 5 pixels diameter, we calculate the noise level at a given separation as the standard deviation in a concentric annulus. To determine the flux loss from partial self-subtraction we implant artificial sources in the raw data and measure their brightness after the reduction process. The measured contrast curve is corrected for this flux loss to yield the final 5σ detectable contrast curve (Fig. 6.10). We translate the contrast to a mass limit using the COND evolutionary models by Baraffe et al. (2003) for ages 40 Myr, 90 Myr and 140 Myr. We do not detect any companion candidates, but are able to set limits well below the deuterium burning limit.

6.5 Discussion

The high-resolution image enables us to distinguish the actual debris ring from the material that appears to be streaming away from the system. The results reveal a ring center offset of 3 AU and an additional brightness asymmetry suggesting density variations.∼ The eccentricity of the debris ring could be shaped by gravitational interaction with a companion on an eccentric orbit. A similar system is Fomalhaut with a belt eccentricity of 0.11 (Kalas et al. 2005). Mass constraints were discussed for Fomalhaut b by Chiang et al. (2009) with disk stability arguments. A planet will disrupt the disk more strongly the more massive and the closer to the ring it is. For the planet to secularly force the ring planetesimals on eccentric orbits without completely disrupting the debris ring, it is thought that the inner boundary of the ring should lie at the edge of the chaotic zone of the planet, in which overlapping ﬁrst-order mean-motion resonances are responsible for sending particles on chaotic, short-lived orbits. A universal empiric relation between planet mass and it’s distance from the inner ring edge was found by both Quillen (2006) and Chiang et al. (2009):

achaotic apl Mpl 2 ∆a = | − | = b ( ) 7 , (6.3) apl · M⋆ where b is a scaling factor determined to b = 1.5 by Quillen (2006) purely from models, and to b = 2 by Chiang et al. (2009) for an actual ﬁt to the HST data of the Fomalhaut ring. This equation is translatable to other planetary systems, even though the exact scaling factor may depend on the shape of the ring, in particular on the sharpness

137 Chapter 6. An off-centered ring in the HD 61005 debris disk

Figure 6.9: NaCo high contrast imaging data reduced with LOCI with a minimum separation of 0.75 FWHM to search for close point sources. The debris ring is still faintly visible. The image size is 3′′x 3′′

Figure 6.10: Contrast for companions around HD 61005 detectable at the 5σ level, and corresponding mass limits determined from the COND models by Baraffe et al. (2003) for ages 90 Myr (solid), 40 Myr (dotted), 140 Myr (dashed). One arcsec corresponds to a projected separation of 35.3 AU.

138 6.5. Discussion

Figure 6.11: Mass of a planet as function of separation from the star that would secularly force the debris disk’s planetesimals into elliptical orbits. We assume the semi-major axis of the inner ring edge to be at 52 AU. The mass is compared to the mass limits derived from high-contrast imaging for various ages, assuming a potential planet to be at maximum angular separation. The mass contrast curves as function of separation are thus only a lower limit. Red: scaling factor by Quillen (2006), blue: scaling factor by Chiang et al. (2009). Solid: Detection limit age of 90 Myr, dotted: 40 Myr, dashed: 140 Myr. of the inner edge. It is still a reasonable ﬁrst approximation to determine the allowed planet masses depending on the location of the planet. Figure 6.11 shows this relation for HD 61005, assuming an inner ring edge of 52 AU and a star mass of 1 M . The curve is compared to the detection limits from the high-contrast imaging⊙ data, assuming the planet to be a maximum angular separation along it’s orbit. A planet well below our detection limit of 2-5 MJ located beyond 37 AU at maximum angular separation could easily perturb∼ the ring. Because of the∼ high inclination a planet of higher mass and lower semi-major axis could also hide within the residuals at smaller projected separation from the star. Multiple epoch data taken several years apart would be required to cover the full orbital parameter space for massive planets. The dynamical arguments therefore currently do not provide a planet mass limit. Additionally, it must be remembered that these models only assume perturbations by a single planet, while multiple smaller planets may induce the same effect. Models of the spectral energy distribution by Hillenbrand et al. (2008) suggested the debris with multiple temperature components provided a better ﬁt than models with a single-temperature blackbody. This could be understood as either an extended debris model (Rinner < 10 AU and Router >40 AU), or an inner warm ring and an outer cool ring. The outer cool ring could coincide with the dust detected in the scattered light images. Additionally, a preliminary resolved

139 Chapter 6. An off-centered ring in the HD 61005 debris disk detection of an inner warm component at 10µm was made by Fitzgerald et al. (2010). Interestingly, the suggested inclination of this ring does not match the inclination of the outer, cooler ring. The detection is however still very tentative. To explain the structure of the interacting material, Maness et al. (2009) explored several scenarios, and proposed that a low-density cloud is perturbing grain orbits because of ram pressure. The streamers would be barely bound, sub- micron sized grains on highly eccentric orbits, consistent with the observed blue color and the brightness proﬁle. Their model currently cannot reproduce the sharpness of the streamers, but the observed geometry of the parent body ring might help improve the models to validate this theory. These might then answer whether the ring offset could also be caused by the ISM interaction rather than a planet. Obtaining colors of the ring through high-resolution imaging at other wavelengths could indicate if a grain size difference exists between parent body ring and swept material. As a solar-type star, and with a debris ring at a radius not much larger than that of the Kuiper belt, the HD 61005 system provides an interesting comparison to models of the young solar system. Booth et al. (2009) calculate the infrared excess of the solar system as a function of time based on strong assumptions consistent with the Nice model (Gomes et al. 2005). This model of the early solar system’s history proposes that a dynamical rearrangement of the outer giant planets through migration resulted in a planetesimal clearing event. This event then led to the so called Late Heavy Bombardment (LHB) at an age of the solar system of 880 Myr, a period of time where a strongly increased amount of impacts was registered in the inner solar system, visible e.g. on the surface of the moon. This event also dramatically changed the luminosity evolution of the solar system’s debris. At an age between 30-100 Myr, HD 61005 has an excess ratio at 24 µm and 70 µm that is about 4 times∼ higher (Hillenbrand et al. 2008) than the ratios calculated for the solar system at comparable age for the assumption of a single- phase size distribution. For more realistic grain size distributions, the solar system might have been similarly bright. In any case, HD 61005 is one of the most luminous debris disks known. Its other obvious unusual feature is the morphol- ogy of the swept component. Perhaps further modeling will provide a causal connection between its high observed dust generation rate and this apparent interaction with the ISM. It is also an interesting target for future deeper searches for planetary mass companions as well as remnant gas that could be associated with the debris. Acknowledgments. We thank David Lafreniere` for providing the source code for his LOCI algorithm. We thank J. Alcala, E. Brugaletta, E. Covino and A. Lan- zafame for discussions on the stellar properties and H.M. Schmid for comments. EB acknowledges funding from the Swiss National Science Foundation (SNSF). AE is supported by a fellowship for advanced researchers from the SNSF (grant PA00P2 126150/1)

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142 Chapter 7 Outlook

The HD 61005 system is a highly interesting system that encompasses several features and lies at a distance from Earth that allows for well-resolved images already with current telescopes. The debris disk itself shows a very strong infrared excess and an unusual asymmetric structure in scattered light. Its parent planetesimal ring at 60 AU appears to be slightly off-centered, which may be due to gravitational forcing≈ by one or multiple companions inside the belt. The outer thin disk component is swept-up by interaction with the ISM and therefore well visible. There also exists preliminary evidence for a second, inner belt of warm dust. All these features make HD 61005 a highly interesting target for follow- up studies at multiple wavelengths. The following section describes some of the ongoing and planned follow-up observations of this debris disk and its potential planetary mass companions. With additional data, it will also be possible to more strongly constrain models on grain properties, dynamics of the disk/ISM interaction and disk/planet interaction. Finally, this section will discuss future prospects for debris disk imaging with upcoming extreme adaptive optics instruments.

7.1 Further observations of the Moth

7.1.1 A search for companions inside the ring Our H-band observations did not yield any planet candidates at the 5σ-level inside the debris ring. The derived mass limits within the ring are of order 2 5M − J at projected separations beyond 0.7”, and rising up to a limit of 10 MJ at the inner working angle of 0.3 . However, we see three candidate≈ signals at a ≈ ′′ 2 4σ-level inside the ring, with hypothetical masses of 4 10 MJ at projected separation− of 10 20 AU. While chances are high that these− sources are artifacts, if any of≈ these− were conﬁrmed as real, it would be a very valuable object of study because of the strong similarities of this system with our own solar system and its disk-planet interaction. The NaCo Large Program collaboration has therefore initiated new observations of the HD 61005 system in the L’-band at 4 µm (led by C. Thalmann), where the Strehl ratio and PSF stability are better than at shorter wavelengths and should render the PSF removal with ADI particularly effective. Also, the brightness contrast between planet and star, as well as planet and disk, is ex-

143 Chapter 7. Outlook pected to be more favorable than in the H-band. The recent update of NaCo with an apodizing phase plate (APP) additionally provides the opportunity to reach significantly lower masses at small separations from the star. The APP modifies the wavefront phase in the pupil plane, suppressing the airy diffraction rings on one half of the field of view, while producing a much more distorted PSF on the other half. Making two observations with the APP rotated by 180◦ in between, a full image at or near the background limit can be obtained towards small ( 0.2′′) separations from the central star (Kenworthy et al. 2010). Quanz et al. (2010≈) successfully detected the companion around βPic using the APP. The observations were performed in early 2011. Preliminary analysis suggests that, unfortunately, the predicted background limited performance could not be reached (C. Thalmann, private communication). In fact, the obtained planet mass limit surprisingly appears to be very similar to that in H-band, except for reaching a slightly smaller inner working angle. No point sources are detected, thus making the low-sigma H-band signals unlikely planetary candidates. It is possible that further refinement of the reduction procedure may yet result in better detection limits or detection of point sources. No traces of the debris disk are seen.

7.1.2 Resolved disk observations at different wavelengths Prior to our NaCo observations of HD 61005, the only resolved scattered light images of this debris disk had been obtained by HST. Images at 0.6 µm and 1.1µ allowed a first color determination of the disk, although limited to the spatial resolution of the 1.1µ NICMOS data. This data set had resolved only the outer, swept component. While for the shorter wavelength ACS observations additional polarimetric data hinted towards a highly inclined disk or ring component, the ring was not directly resolved. A color determination could therefore only be made for the outer, swept-back component. It was found that this component appears predominantly blue at these wavelengths, indicating small grains with amin < 0.3µm and a steep size distribution (Maness et al. 2009). With the resolution of the dust within the parent-body planetesimal belt, the question opens whether the grain size distribution differs in the belt with respect to the outer component. The standard scenario for dust replenishment in debris disks involves the grinding down of planetesimals to smaller and smaller sizes in a collisional cascade. Smaller grains are forced onto orbits of much higher eccentricity than that of the parent planetesimal belt by radiation pressure, and the smallest grains are entirely removed from the cascade by blow-out onto hyper- bolic orbits. Observational evidence of a cascade around an intermediate mass star where dust production and removal are in steady-state is seen for the Vega debris disk (Muller¨ et al. 2010) from resolved images at mid-infrared to mm- wavelengths. The collisional evolution is thought to be similar for bright debris disks around solar-type stars (e.g. Kains et al. 2011). However, this remains observationally unconfirmed. The HD 61005 disk is an ideal target to directly confirm the blow-out scenario

144 7.1. Further observations of the Moth for a solar-type star. The outer, usually very faint component, is well visible for this disk in scattered light because it is swept-up by the ISM, while the parent- body ring is resolvable with large telescopes from the ground because its nearly edge-on inclination make it well suitable for the effective ADI method for PSF removal. We have therefore submitted a proposal (for which I am the PI) to ESO which has been accepted to obtain observations of HD 61005 in J- and Ks-band with the same observing setup as used for our H-band observations. The surface brightness of the ring and streamers will be measured with conservative ADI analogous to Sect. 6.4.1. We will obtain color information for both the ring and the faint outer component. While the uncertainty of absolute photometry is relatively high for these observations, we are mainly interested in relative differences that can be obtained conﬁdently. Also, the J-band observations of the outer component can be calibrated with the available HST data. A radial color dependence will be good evidence for a change in grain size distribution, with the bluer component being depleted in large grains (cf. next section), thus directly conﬁrming the blow-out scenario. Additionally, the new data will determine whether the previously measured 3σ-offset between the stellar position and ring center is indeed real and reveal whether the disk asymmetries show a dependence on wavelength in geometry or brightness. Further resolved scattered-light observations at various wavelengths have been obtained or are scheduled by several different groups. Fitzgerald et al. (2010) reported H- and K-band observations of HD 61005 obtained with Keck/NIRC2 at the “In the Spirit of Lyot” conference in the fall 2010. Their H-band result, obtained through removal of a reference PSF, appears to be very similar to our image reduced with conservative ADI, at least in terms of geometry. It will be interesting to compare the surface brightness distribution to determine the true uncertainty of the ADI observations. Their K-band data is ap- parently of poor quality. Interestingly, they also obtained thermal imaging 10 µm observations using Gemini-S/T-ReCS, a mid-infrared imager and spectrograph at an 8 m class telescope. After a preliminary analysis, the data show a small blob of 0.2” diameter which is consistent with a ring of warm dust that is strongly inclined≈ with respect to the outer cool ring. It is unclear whether this feature is indeed real, but its presence would be in accordance with SED models that indicate an inner warm dust component. The strong inclination with respect to the second belt could point towards planetary companions strongly disturbing the dust. Other ongoing projects include HST/STIS observations (PI: G. Schneider) which are obtaining high-resolution scattered light images at optical wavelengths towards a small inner working angle. Finally, Herschel observations (PI: V. Geers) are scheduled to search for remnant gas associated with the debris disk by looking for O[I] line emission.

145 Chapter 7. Outlook

7.2 A detailed model for the Moth

Combining the multi-wavelength HST and above described additional ground- based observations with the SED available from Spitzer/FEPS and long wavelength observations (Roccatagliata et al. 2009), we will construct a detailed disk model using the radiative transfer code GraTer by Augereau et al. (1999). The code calculates scattered light images and SED for various debris disk geometries, grain compositions and grain size distributions. A color difference in scattered light images will indicate if a difference in grain size distribution exists between parent body ring and swept material. This is expected when collisional equilibrium is reached in the birth ring, leading to a grain size distributiondn(a) ∝ aκ da with a the grain radius. The theoretical power-law exponent in the birth ring is κ = 3.5. Small grains are forced outward onto large, eccentric orbits, down to − a critical size amin = ablow below which they are blown out of the system on hy- perbolic orbits. Larger grains stay bound in the birth ring. Thus, in our scenario the grain size distribution gets steeper (p smaller), meaning the color bluer, with increasing distance to the star due to pressure forces (Augereau et al. 2001). The flux scattered for a given grain distribution and chemical composition and stellar irradiation field is proportional to the mean scattering cross section σsca. Figure 7.1 shows the theoretical ratio of σsca in J- and Ks- bands, which is directly proportional to the color index J-Ks, as a function of κ = κ(d). We considered several chemical compositions, and for each we fixed amin according to a best-fit value for the mid- and far-IR SED or to the theoretical blowout size. It shows that color differences between the inner and outer disk will provided strong constraints on the chemical composition of the grains and their size distribution. We would therefore obtain a direct confirmation of the blow-out scenario for a solar-type star and thus the main mechanism of dust removal for most known systems. Dynamical modeling will most likely present a challenge, both to explain the shape of the material that is interacting with the ISM and the eccentric shape and brightness asymmetry of the birth ring. The currently favored model for the ISM interaction (Maness et al. 2009) suggests that a warm, low-density cloud is perturbing orbits of the small grains. These models are only a crude approximation to the data and may be missing fundamental processes. However, at least the previously proposed cold dense cloud has been ruled out by observations of the Na I column density towards the object (Maness et al. 2009), which can be translated into an total hydrogen (H I+H2) column density. A new program of spectroscopic observations with HST/STIS is searching for evidence of the low-density cloud, but so far the results have been inconclusive (J. Graham, private communication) except for confirming the ruling out of a dense cloud. Dynamical models for the potential planetary perturber are also tricky in particular because the inner boundary of the ring is not well defined by the LOCI observations. In the case of Fomalhaut, the ring shows a very sharp edge, which does not appear to be the case for HD 61005. While the inner rim seems to be steeper than the outer rim, it is unclear how much LOCI smoothes or steepens

146 7.3. Future prospects for debris disks imaging

8 8 Si (amin = 2.03) Si (amin = 0.203) Si+ice (amin = 0.202) Si+ice (amin = 0.224) Si+C+ice+P (amin = 1.23) Si+C+ice+P (amin = 1.11) 6 6 (K)> (K)> sca sca σ σ 4 4 (J)> / < (J)> / < sca sca σ σ < < 2 2

0 0 −20 −15 −10 −5 −20 −15 −10 −5 κ = κ(d) κ = κ(d)

Figure 7.1: Theoretical ratios of scattering cross sections in J- to Ks-bands as function of the size distribution power-law (proxy for distance from the star, larger distances having smaller κ values, from right to left) for different grain compositions, including silicates (Si), ice, amorphous carbon (C) and porosity (P). Cross sections are normalized such that σ (κ = 3.5) = 1 (i.e. in the birth ring). A larger ratio means a bluer color. Left: min. sca − grain size amin derived from SED model-ﬁtting. Right: amin = ablowout. amin is given in µm. Calculations made by J. Lebreton. the slope and more studies on the effect of LOCI on extended structures would be required. The HST/STIS imaging observations may provide a better constraint for this material. Also, it is at this time unclear if the ISM interaction also has an effect on the birth ring. The strong brightness asymmetry, which cannot be explained simply by the eccentric shape of the ring, hints towards a more complicated phenomenon. A model encompassing both the ISM interaction and a planetary perturber may be required to ﬁt all the geometric properties of this system.

7.3 Future prospects for debris disks imaging

Possibilities for space-based observations of debris disks in scattered light have taken a serious set-back with the failure of both NICMOS and the High Reso- lution Channel (HRC) of the ACS camera on HST. The new WFC3 instrument does not include a coronagraph. The only remaining instrument for debris disk imaging on HST is STIS, which has imaged the disk around HR 4796A (Schneider et al. 2009), and has an ongoing program to image several known debris disks to small inner working angles (PI: G. Schneider). The disadvantages of STIS are its non-optimal coronagraphic mode (occulting bar and wedges) and the fact that coronagraphy cannot be combined with ﬁlters. The images are taken simply in the range of the detector sensitivity between 200 1030 nm. With no further service missions to HST planned, it is therefore≈ unlikely− that HST can continue to make a signiﬁcant contribution to debris disk imaging. Unless a small space mission dedicated to direct imaging, such as EXCEDE (PI: G. Schneider), is launched in the near future, no space-based imaging will be possible until the launch of

147 Chapter 7. Outlook the James Webb Space Telescope (JWST), currently expected in approximately 2018. The future of debris disk imaging must therefore lie with ground-based telescopes. Already today, ground-based imaging of debris-disks is feasible with angular differential imaging techniques, as evidenced in Chapter 6 of this thesis for HD 61005. The ansae of HR 4796A have been imaged with polarimetric differential imaging (Hinkley et al. 2009) on a 3.6 m telescope, and high quality images have been taken with SDI and ADI on Gemini-S/NICI (Liu et al., Lyot Confer- ence). The NaCo/PDI mode has been successfully used on the disk of the Her- big Ae/Be star HD 100456 (Quanz et al. 2011) and should be sufficient to also characterize some of the brightest known debris disks in polarization. The ADI technique should be applicable to all reasonably bright disks that are sufficiently inclined towards the line of sight and therefore do not show strong angular symmetry. In the next 1-2 years, two ground-based instruments with strong imaging capabilities will go online: SPHERE and GPI (cf. Sect. 1.5.1). For both instruments, a science case for debris disk imaging has been established and dedicated programs are expected to be conducted by the instrument teams. GPI is optimized to measure both intensity and polarization. Debris disks with infrared fractional 5 luminosities of a few 10− should be within reach (Perrin et al. 2010). SPHERE will mainly be able to measure the polarized intensity, but over a larger wavelength range and with more filters. Studies for both instruments could focus on the detailed characterization of disk geometry and sub-structures and particle properties for previously imaged disks towards small inner working angles of 0.1′′, also revealing warm dust closer to the star than currently accessible. This≈ could for example be done for the Moth, to confirm the inner ring suggested by Fitzgerald et al. (2010). A survey of bright Spitzer-detected sources could resolve additional disks in scattered light to expand the sample and achieve better statistics on debris disk grain properties and geometries. Additionally, more planets within the inner gaps of debris rings could be found, showing direct evidence of disk/planet interactions and thereby constraining planet formation theory. With the next generation of extremely large telescopes, it could be expected to reach the innermost part of solar system analogs where Earth-like planets may form.

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149

Acknowledgments

This thesis would not have been possible without the support and help of many people to whom I am most grateful. First and foremost, I would like to thank Hans Martin Schmid, my primary advisor, for offering me the PhD position in the exciting field of exoplanet research, even before the funding was fully secured. During the course of the thesis, he always had an open door and useful advice on many problems I encountered. He managed to keep me enthusiastic about the ‘diagnostic potential’ of polarimetric observations, but also supported my venturing off into a related field of my own choosing. He always encouraged me to attend schools and conferences, to write papers, submit my own observing proposals, and develop my own ideas. Thank you for the always very positive and pleasant atmosphere within our small group. Secondly, I am very grateful to Michael Meyer, who also served as my advisor and main referee of this thesis. With his arrival at ETH he brought a lot of fresh ideas and a vibrant new group with related research interests that resulted in many interesting discussions. Thank you for giving me a home in your group and for being an inspiration on how to do exciting and careful scientific research. Without your support I might not have dared to take on ‘the Moth’. Thank you for your guidance towards a scientific career without forgetting to listen to concerns and problems and always trying to find constructive solutions. I would like to thank Francois Menard for agreeing to be the external examiner of this thesis, providing useful comments and traveling to Zurich to attend the defense. I also thank Simon Lilly and Jan Stenflo for providing financial support for my position and travel during the first half of my PhD. This PhD was also supported by a grant from the Swiss National Science Foundation (SNSF). I was fortunate to have two wonderful friends at the institute, Lucia Kleint and Susanne Wampfler, who shared my passion for astronomy throughout our Physics studies and PhD theses. It was always fun to exchange the most recent gossip, solve problems together related to IDL or general science, do public out- reach together or spend nights at the observatory hunting every barely visible deep sky object just for fun. Lucia, we were a great team on Diavolezza during the Astrowoche in 2009. Thanks also for providing the template for this dissertation. Susanne, you were a terrific office mate. I am very grateful for the help with many little day-to-day problems an astronomer encounters, and even more so for your support and open ear when things did not go smoothly. Many other people at the institute were responsible for a productive and friendly atmosphere. Sascha Quanz often had useful tips, be it for proposals,

151 Acknowledgments papers, data reduction or job applications. Franco Joos took me along to an observing run in La Silla, Chile, only 3 months into my thesis, where I learned a lot about polarimetric observations. Peter Steiner always provided swift help with any computer related problems, while Barbara Codoni, Rajni Malhotra and Marianne Chiesi took care of administrative matters very efficiently. I had interesting conversations over lunch, coffee or cake about life, the universe and ev- erything, about science, teaching duties or Dungeons and Dragons, with Andreas Bazzon, Daniel Gisler, Christian Monstein, Rene´ Holzreuter, Christian Thalmann, Marina Battaglia, Simon Bruderer, Richard Wenzel, Dominique Fluri, Nadine Afram, Kevin Heng, Maddalena Reggiani, Carolin Dedes, Vincent Geers, Richard Parker, Andrea Banzatti, Henning Avenhaus, Michiel Cottar, Udo Wehmeier, Alex Feller, Svetlana Berdyugina, Jan Stenflo, Harry Nussbaumer, Julien Carron, Adam Amara, Thomas Bschorr, Katharina Kovac and Monique Aller. I am also very grateful to my external collaborators, in particular the members of the SPHERE science team. I was readily welcomed into the team and could often take part in meetings all over Europe. Most importantly, they allowed me to participate in the related NaCo Large program which lead to an important result of this thesis. I am indebted to Christian Thalmann for suggesting my application for NaCo observations one fine evening in the midst of a D&D session, once again showing that important steps in scientific careers usually happen at unex- pected times. I thank Jean-Luc Beuzit and Gael Chauvin for selecting me as an observer to the VLT, and Gael for teaching me about high-contrast imaging observations in Paranal. The whole team gave me their confidence for taking on the exciting data of ‘the Moth’ and I am thankful to all my co-authors for the contributions and helpful suggestions, in particular Christian, Gael, Arthur Vigan, Anthony Boccaletti, Jean-Charles Augereau, and David Mouillet. I also thank Jer´ emy´ Lebreton for his modeling efforts and input for the future observations for the Moth. I was fortunate to be able to travel to many beautiful places for observing runs, conferences and work-shops, where I met a lot of interesting people, both for scientific conversations but also to have fun with like-minded people. In particular I had a great time at the ESA summer school in Alpbach designing an Astrobi- ology space mission, and hanging out and climbing Arecibo with a fun group of grad students and post-docs at the DPS meeting in Puerto Rico. I am happy to be a part of the (exo)planetary community, which consists of mostly very pleasant people. I also want to thank Daniel Apai for providing me the opportunity to continue pursuing a career in astronomy for the next couple of years beyond my PhD, so that maybe I will find my own exoplanet at some point, after all. I am looking forward to working with you in Arizona. While a PhD thesis is a lot of work and a rewarding way to spend four years, there fortunately also exists a life outside of astronomy. I always enjoyed the weekly lunch with the good friends and former physics student colleagues, Ros- marie, Lukas, Dominik and Patrick. A welcome diversion were also my weekly choir rehearsals in the ACZ, which also gave me the opportunity to perform beau-

152 Acknowledgments tiful and difficult choral works in two of the greatest concert halls in Switzerland. I particularly thank Hiu, Tamara, Stefan, Christoph and Catherine for fun times during and after singing. I also spent many evenings in fun D&D sessions with Christian, Rene,´ Marina, Carolin, Leonidas and Tobias that were always exciting and challenging, in particular thanks to the expert dungeon mastering by Ath- man. A big thank you goes to my family and friends. My parents always supported and encouraged me. Without them, I would not have got to where I am now. My sister, my brother and my close friends were also a great support during a particularly difficult phase. Last, but definitely not least, I want to thank Adrian, my love. You have been with me from the start to the end of this thesis and went through all the highs and lows with me, constantly providing love and encouragement. Thank you for always believing in me more than I did. And thank you for supporting my dreams. I am happy that we will face our next and probably yet biggest adventure together.

Esther Buenzli, Institute for Astronomy, ETH Zurich August 2011

153

List of Publications

Publications in refereed journals

Buenzli, E. & Schmid, H.M. • A grid of polarization models for Rayleigh scattering planetary atmospheres 2009, A&A 504, 259

Buenzli, E., Thalmann, C., Vigan, A., Boccaletti, A., Chauvin, G., Augereau, • J.C., Meyer, M.R., Menard,´ F., Desidera, S., Messina, S., Henning, T., Carson, J., Montagnier, G., Beuzit, J.L., Bonavita, M., Eggenberger, A., Lagrange, A.M., Mesa, D., Mouillet, D., & Quanz, S.P. Dissecting the Moth: Discovery of an off-centered ring in the HD 61005 debris disk 2010, A&A 524, L1

Buenzli, E. & Schmid, H.M. • Polarization of Uranus: Constraints on haze properties and predictions for analog extrasolar planets 2011, submitted to Icarus

Schmid, H.M., Joos, F., Buenzli, E., & Gisler, D. • Long slit spectropolarimetry of Jupiter and Saturn 2011, Icarus 212, 701

Thalmann, C., Janson, M., Buenzli, E., Brandt, T.D., Wisniewski, J.P., Moro- • Martin, A., Usuda, T., Schneider, G., Carson, J., McElwain, M.W., Grady, C.A., Goto, M., and the SEEDS collaboration, Images of the extended out regions of the debris ring around HR 4796 A 2011, ApJL in press

Publications in conference proceedings

Buenzli, E., Schmid, H.M & Joos, F. • Polarization models for Rayleigh scattering planetary atmospheres 2009, Earth, Moon, and Planets, 105, 153 Conference proceedings of ’Future ground based solar system research’

155 List of Publications

Joos, F.,Buenzli, E., Schmid, H.M & Thalmann, C. • Reduction of polarimetric data using Mueller calculus applied to Nasmyth instruments 2008, Proc. of SPIE, Vol. 7016, 2008

156