atmospheric dynamics of hot exoplanetsea43ch17-heng ari 11 may 2015 10:4 remnant heat when the...

EA43CH17-Heng ARI 11 May 2015 10:4

Atmospheric Dynamics of HotExoplanetsKevin Heng1 and Adam P. Showman2

1Physics Institute, Center for Space and Habitability, University of Bern, CH-3012 Bern,Switzerland; email: [email protected] of Planetary Sciences and the Lunar and Planetary Laboratory, University ofArizona, Tucson, Arizona 85721; email: [email protected]

Annu. Rev. Earth Planet. Sci. 2015. 43:509–40

The Annual Review of Earth and Planetary Sciences isonline at earth.annualreviews.org

This article’s doi:10.1146/annurev-earth-060614-105146

Copyright c© 2015 by Annual Reviews.All rights reserved

Keywords

exoplanetary atmospheres, hot exoplanets, astronomical observations, fluiddynamics, radiation, clouds

Abstract

The characterization of exoplanetary atmospheres has come of age in thepast decade, as astronomical techniques now allow for albedos, chemicalabundances, temperature profiles and maps, rotation periods, and even windspeeds to be measured. Atmospheric dynamics sets the background state ofdensity, temperature, and velocity that determines or influences the spectraland temporal appearance of an exoplanetary atmosphere. Hot exoplanetsare most amenable to these characterization techniques. In this review, wefocus on highly irradiated, large exoplanets (the hot Jupiters), as astronom-ical data begin to confront theoretical questions. We summarize the basicatmospheric quantities inferred from the astronomical observations. We re-view the state of the art by addressing a series of current questions, andlook toward the future by considering a separate set of exploratory ques-tions. Attaining the next level of understanding requires a concerted effortof constructing multifaceted, multiwavelength datasets for benchmark ob-jects. Understanding clouds presents a formidable obstacle, as they introducedegeneracies into the interpretation of spectra, yet their properties and exis-tence are directly influenced by atmospheric dynamics. Confronting generalcirculation models with these multifaceted, multiwavelength datasets willhelp us understand these and other degeneracies.

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1. INTRODUCTION

1.1. Hot and/or Large Exoplanets Are Easiest to Characterize

For millennia, our understanding of worlds beyond Earth was confined to the Solar System. ThisSolar System– and Earth-centric perspective was shattered in the mid-1990s when astronomers be-gan finding planets orbiting other stars—first around pulsars (Wolszczan & Frail 1992), then lateraround a Sun-like star (Mayor & Queloz 1995). With an ever-expanding database of thousands ofexoplanets and exoplanet candidates, the discovery of planets beyond our Solar System is a firmlyestablished enterprise; exoplanet characterization is a nascent, flourishing field. Understandingexoplanets and their atmospheres may be the only path toward investigating the possibility of lifeelsewhere in the Universe. Among the several techniques available for exoplanet detection, theradial velocity and transit methods stand out as the workhorses, having been used to detect themajority of these exoplanets. The former measures the wobble of the star as it and its exoplanetsorbit around their common center of mass. The latter measures the diminution of light as exo-planets pass in front of (the transit) and behind (the secondary eclipse1) the star. Used in tandem,they yield the mass and radius of an exoplanet. Both methods require the star to be fairly quiescent,as stellar flares and star spots are sources of contamination and confusion.

Transits measured at multiple wavelengths also provide for a powerful way of characterizingthe atmospheres of exoplanets (Figure 1). Atoms and molecules present in the atmosphere absorbor scatter starlight to different degrees across wavelength, which translates into a variation inthe radius of an exoplanet with wavelength. By measuring the wavelength-dependent radius, oneobtains a transmission spectrum from which atmospheric composition may be inferred. However,to measure a transit in the first place requires that the exoplanet resides in a nearly edge-on orbit.Geometry dictates that this is more likely to occur for exoplanets residing closer (∼0.1 AU)2

to their stars because the transit probability is roughly the ratio of the stellar radius to theexoplanet-star separation. The variation in radius is also easier to measure for larger exoplanetsbecause the method actually measures the ratio of the exoplanetary to the stellar radius. Hot,close-in exoplanets also radiate higher heat fluxes than their cooler counterparts, implying largersecondary eclipse depths and phase curve variations in the infrared. For these reasons, hot, large3

exoplanets are the most amenable to atmospheric characterization via the transit method. One ofthe surprises of the exoplanet hunt was the discovery of hot Jupiters, Jupiter-like exoplanets located∼0.1 AU from their stars with atmospheric temperatures ∼1,000–3,000 K (Mayor & Queloz1995). Hot Jupiters provide unprecedented laboratories for the characterization of exoplanetaryatmospheres.

An emerging and complementary method is direct imaging, which—as the name suggests—obtains images of the exoplanet by isolating them from the accompanying starlight via corono-graphic methods and/or novel image reduction techniques. The most iconic examples are thefour directly imaged exoplanets in the HR 8799 system (Marois et al. 2008, 2010). As one mayexpect, this technique works best when the exoplanets are hot (and therefore brighter at shorterwavelengths, as dictated by Wien’s law) and located far away (∼10–100 AU) from their stars.Directly imaged exoplanets are hot not because of stellar irradiation (which is a negligible part oftheir energy budgets), but because of their remnant heat of formation. It is easier to detect this

1Some researchers use the terms eclipse or occultation.2The Earth-Sun distance is the astronomical unit, denoted by AU.3Once the transits of an exoplanet are detected, the quantification of spectral features is easier for exoplanets with lowerdensities (de Wit & Seager 2013).

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Exoplanet

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Figure 1Obtaining atmospheric information from transiting exoplanets via transits, eclipses, and phase curves.Courtesy of Tom Dunne (taken from Heng 2012b).

www.annualreviews.org • Atmospheric Dynamics of Hot Exoplanets 511

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remnant heat when the exoplanets are young, as it fades with time. For this reason, direct imagingtends to target young (�0.1 Gyr) stars. By contrast, hot Jupiters are hot because of the intenseflux of stellar irradiation they receive, rather than because of internal heat.

Although we are ultimately interested in detecting and characterizing Earth-like exoplanets,current astronomical techniques favor the atmospheric characterization of hot and/or large exo-planets. As technology advances, astronomy will deliver data on cooler and smaller objects. In themeantime, hot and/or large exoplanets present a unique opportunity for understanding unfamiliaratmospheric regimes and allow us to broaden the scope of our understanding (Burrows 2014a).This review focuses on the atmospheres of hot and/or large exoplanets discovered using transitsand the questions regarding their basic properties, which are not the traditional focus of the Earthand planetary science literature.

1.2. Complementarity and Conflict with Solar System Studies

A unique attribute of exoplanet science is its ability to simultaneously attract interest from theEarth atmosphere/climate, Solar System, and astronomy/astrophysics communities. A challengeis to unify the relevant bodies of knowledge within these fields toward understanding exoplane-tary atmospheres. The currently characterizable exoplanets (hot Earths/Neptunes/Jupiters4 anddirectly imaged exoplanets) reside in chemical and physical regimes for which there exists noprecedent in the Solar System. Well-established techniques in the Earth and Solar System com-munities may not carry over in a straightforward manner. Dynamical mechanisms that maintainthe circulations on Solar System planets will occur also on exoplanets, but may lead to differing de-tails of circulation because these mechanisms are operating in environments with different stellarflux, chemical composition, rotation rate, etc. For example, the ∼1 km s −1 wind speeds expectedin hot Jupiters—and measured, in one case (Snellen et al. 2010)—may imply that traditional ra-diative transfer methods, which do not consider the relative motion between parcels of gas, needto be revised (Menou & Rauscher 2010). However, some basic physics of atmospheric dynamicshave been established by these communities. For example, hydrostatic balance does not imply avertically static atmosphere; rather, it implies that vertical motion is so ponderous that hydrostaticbalance is quickly reestablished (via sound waves). We expect this insight to hold for hot Jupitersas well as Earth.

It is not for lack of trying that astronomers cannot obtain datasets to the same level of detail asfor a given Solar System object. After all, despite remarkable advances in our ability to spectrallyand temporally resolve them, distant exoplanets remain spatially unresolved point sources; wewill address this point further in Section 4.4. Astronomy will probably never allow us to knowintimate details about a given exoplanetary atmosphere (e.g., via spatially resolved imaging or insitu probes), but it can elucidate broad trends for dozens and perhaps hundreds of case studies, apoint we will address further in Section 4.5.

1.3. Structure of the Present Review

This review begins by summarizing the various astronomical observables from exoplanetary at-mospheres (Section 2), as motivation for addressing a series of key questions. These questionsare divided into two sections: Section 3 describes a series of questions that are well addressed inthe existing literature (up to the point of writing), whereas Section 4 lists questions that are onlybeginning to be addressed or are unaddressed.

4These exoplanets have approximately the mass and radius of Earth, Neptune, and Jupiter, respectively, but the nomenclaturedoes not imply that their atmospheric compositions, thermal profiles, etc., are the same.

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Our review builds upon existing reviews of the atmospheric dynamics of hot Jupiters and Earth-like exoplanets (Showman et al. 2008b, 2010, 2013b). It complements a monograph (Seager 2010)and more observationally oriented reviews (Deming & Seager 2009, Seager & Deming 2010). Italso complements reviews focused on the chemistry and spectral signatures of exoplanets (Burrows2014a,b; Madhusudhan et al. 2014) and on what one can learn about atmospheric dynamics witha dedicated space mission (Parmentier et al. 2014). We do not discuss the upper atmosphere(thermosphere, exosphere) or atmospheric escape. We do not discuss the polarization signaturesof the atmosphere.

2. OBSERVATIONS OF EXOPLANETARY ATMOSPHERES

2.1. Transmission and Emission Spectra

Measuring spectra of exoplanetary atmospheres started with obtaining transits and eclipses of hotJupiters in several broadband channels (e.g., using the Spitzer Space Telescope at 3.6, 4.5, 5.8, and8.0 μm) and has evolved to include denser wavelength coverage. Over time, these techniques havebeen applied to smaller exoplanets, the so-called hot Neptunes (exoplanets of typically 3–5 Earthradii) and super Earths (exoplanets of typically 1–3 Earth radii), although the latter in particular willcontinue to provide a major observational challenge for the foreseeable future. In this subsection,we briefly summarize these techniques and recent results, and show how dynamical constraintsarise from them.

Transmission spectra show how the effective radius of a close-in exoplanet varies with wave-length (as seen during transit, when it is backlit by starlight) and therefore provide informationon how the atmospheric absorption and scattering vary with wavelength. At wavelengths wherethe atmosphere is opaque, stellar radiation directed toward Earth is absorbed or scatteredand the exoplanet appears bigger while seen in transit (Figure 1). At wavelengths where theatmosphere is transparent, the radiation passes through the atmosphere and the exoplanetappears smaller. From the early days of exoplanet science, there has been hope that this methodwill yield the atmospheric composition of exoplanets (Seager & Sasselov 2000, Brown 2001).The method has been most spectacularly and successfully applied to the alkali metals Na andK in medium-resolution spectra (Sing et al. 2011b, 2012; Nikolov et al. 2014); the widthsof these lines set an upper limit on the atmospheric pressure probed, via the weakness ofpressure broadening, and may in principle constrain the variation of scale height—and hencetemperature—with pressure (Huitson et al. 2012). Transmission spectroscopy may also be usedto constrain the mass of an exoplanet (de Wit & Seager 2013). These species are in the gasphase at the 1,000–2,000 K temperatures of typical hot Jupiters and are extremely absorbing atspecific absorption lines at visible wavelengths (Seager & Sasselov 2000). Confidently detectingthe existence of molecules such as water, methane, and carbon monoxide requires measurementsfrom 1–5 μm and has proved more challenging. For water, this has been recently accomplishedusing measurements from the Hubble Space Telescope (Deming et al. 2013, Mandell et al. 2013).Figure 2 shows an example of a transmission spectrum, where water was unambiguouslydetected.

Curiously, a number of exoplanets show relatively flat transmission spectra. Clouds tend to begrey and scatter broadly across a wide range of wavelengths, and thus the existence of clouds orhazes at high altitudes provides a likely explanation for such flat spectra (Pont et al. 2008, Singet al. 2011a, Knutson et al. 2014, Kreidberg et al. 2014). The existence of these cloud particlesrequires vertical mixing to be present and this places constraints on the dynamical mixing rates ofthe atmosphere (Heng & Demory 2013, Parmentier et al. 2013).


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Figure 2Example of a transmission spectrum of the hot Jupiter HD 209458b showing a clean detection of water. Thedetected feature would be stronger if the atmosphere was cloud-free, suggesting that clouds are present.Courtesy of Drake Deming (Deming et al. 2013).

Complementarily, emission spectra provide information on the flux of planetary emission asa function of wavelength, which can be converted to a spectrum of brightness temperature ver-sus wavelength. Typically, such spectra are obtained by subtracting the spectrum obtained justbefore/after secondary eclipse, when both the star and the planetary dayside are visible, from thespectrum obtained during secondary eclipse, when only the star is visible (Figure 1). Becausethe exoplanet’s dayside is oriented toward Earth immediately before and after secondary eclipse,such spectra are of its dayside. The structures of such emission spectra are affected not only bythe atmospheric composition but also by the vertical temperature profile in the exoplanet’s at-mosphere. Spectra exhibiting prominent absorption bands, e.g., from water, suggest atmosphereswhere temperatures decrease with altitude (Charbonneau et al. 2008), whereas spectra exhibitingprominent emission bands suggest atmospheres where temperatures increase with altitude (tem-perature inversions). Temperature inversions help maintain thermochemical equilibrium and thehigher temperatures also generally mitigate against disequilibrium due to photochemistry (Moseset al. 2011).

Most observations of secondary-eclipse spectra seem to indicate temperatures decreasing withaltitude in the layers probed. By contrast, several early analyses that suggested such thermalinversions on exoplanets (Knutson et al. 2008) are now being refined, and in some cases theevidence for inversions is weakening or disappearing (Hansen et al. 2014, Zellem et al. 2014).Regardless, atmospheric dynamics can affect the mean temperature of the dayside and hence themean depths of the secondary eclipses, and therefore these spectra contain information aboutthe strength of heat transport from the dayside to the nightside of these planets. In particular,hot Jupiters receiving unusually high stellar flux seem to have dayside temperatures close to local

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radiative equilibrium, implying inefficient transport of thermal energy from the dayside to thenightside (Cowan & Agol 2011b). By contrast, hot Jupiters receiving less stellar flux in manycases have dayside brightness temperatures significantly less than the local radiative equilibriumtemperature that would prevail in the absence of circulation, implying a more efficient transport ofheat from day to night. Circulation models of hot Jupiters naturally produce this type of behavior(Perna et al. 2012, Perez-Becker & Showman 2013).

2.2. Phase Curves and Brightness Maps

Often overlooked in favor of transmission or emission spectra—partly due to the time-consumingnature of obtaining them—phase curves contain a wealth of data that are multidimensional innature (Harrington et al. 2006, Knutson et al. 2007). A phase curve records the rise and ebb offlux at different orbital phases of the exoplanet (Figure 1). It is the longitudinal distribution offlux from the exoplanetary atmosphere convolved with its geometric projection to the observer(Cowan & Agol 2008). Deconvolving the phase curve yields a 1D brightness map, the most iconicexample of which is shown in Figure 3 for the hot Jupiter HD 189733b (Knutson et al. 2007).Infrared phase curves measured at different wavelengths probe different depths or pressure levelsof the atmosphere, allowing for the construction of 3D maps.

In special cases where the orbital planes of the exoplanet and its star do not coincide, high-cadence measurements before and after the secondary eclipse yield complementary, latitudinal(north-south) information on the exoplanetary atmosphere (Figure 4). This technique is knownas eclipse mapping. When combined with the phase curve, which contains purely longitudinal

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Figure 3Infrared phase curves of the hot Jupiters HD 189733b (left panel ) and HD 209458b (right panel ). Courtesy of Heather Knutson(Knutson et al. 2007, 2009a, 2012) and Robert Zellem (Zellem et al. 2014).


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Figure 4Combined eclipse and phase map of the hot Jupiter HD 189733b. Courtesy of Julien de Wit (de Wit et al. 2012).

(east-west) information, a 2D brightness map may be constructed, the first example of which wasreported for the hot Jupiter HD 189733b (de Wit et al. 2012; Majeau et al. 2012a,b).

High-quality light curves can be inverted to obtain the latitudinal-mean brightness temperatureversus longitude (Cowan & Agol 2008), a quantity that provides significant information about theatmospheric dynamics. In particular, exoplanets whose dynamics have equalized the temperaturesat all longitudes will exhibit flat lightcurves, whereas those with order-unity day-night temperaturedifferences will observe a high-amplitude phase variation throughout the orbit, comparable to thedepth of the secondary eclipse. Observations indicate that cooler planets such as HD 189733bhave modest phase-curve variations, suggesting modest brightness temperature variations fromdayside to nightside, whereas highly irradiated exoplanets have large phase variations, suggestingfractional brightness temperature differences from dayside to nightside of order unity (Perez-Becker & Showman 2013). This behavior complements similar findings from secondary-eclipsespectra alone (Cowan & Agol 2011b) and has been qualitatively explained with dynamical models(Perna et al. 2012, Perez-Becker & Showman 2013).

Moreover, the offsets of the flux minima and maxima in the lightcurves provide informationabout the longitudinal displacement of the hottest and coldest regions from the substellar andantistellar points, respectively. In Figure 3, for example, one can see that the flux extrema precedethe secondary eclipse and transit, indicating that the hot and cold regions are displaced to the east.First observed for HD 189733b (Knutson et al. 2007, 2009a, 2012), an eastward-shifted hot spothas also been detected for a variety of other hot Jupiters, including υ Andromedae b (Crossfieldet al. 2010), HAT-P-2b (Lewis et al. 2013), and HD 209458b (Zellem et al. 2014). Interestingly,this feature was predicted in 3D circulation models some years before its discovery (Showman& Guillot 2002), and has now been reproduced in a wide variety of general circulation models(GCMs) (Cooper & Showman 2005; Dobbs-Dixon & Lin 2008; Showman et al. 2009; Rauscher& Menou 2010; Heng et al. 2011a,b; Perna et al. 2012; Mayne et al. 2013). Section 3 discussesthese theoretical results in more detail.

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Optical phase curves record the reflectivity of the atmosphere across longitude and set con-straints on the size and relative abundances of condensates or aerosols (Demory et al. 2013, Heng& Demory 2013). For the very hottest Jupiters, their thermal emission extends into the opticalrange of wavelengths—their phase curve thus contains both reflected light and thermal emission.Examples include the optical phase curves of HAT-P-7b by the Kepler Space Telescope (Boruckiet al. 2009) and CoRoT-1b by CoRoT (Snellen et al. 2009).

For rare cases of exoplanets that reside very close to their stars, such that they become gravi-tationally distorted, regular flux modulations known as ellipsoidal variations are produced in thephase curve (Welsh et al. 2010, Cowan et al. 2012). In the case of Kepler-76b, relativistic beaminghas been detected (Faigler et al. 2013).

2.3. Ultra-High-Resolution Cross-Correlation Techniques

A complementary technique to using space-based telescopes is the use of ultra-high-resolution(spectral resolution ∼105) spectrographs, mounted on 8-meter-class telescopes, to record trans-mission spectra, albeit over a narrow wavelength range (Figure 5). The measured spectra arecross-correlated with a theoretical template of a specific molecule to determine (or rule out) itspresence. For example, 56 absorption lines of carbon monoxide were analyzed and an overallblueshift of 2 ± 1 km s −1 was reported relative to the expected motion of the hot Jupiter HD209458b, which was interpreted to be a signature of global atmospheric winds (Snellen et al.2010). (Such an analysis also allows for the orbital motion of the exoplanet to be directly mea-sured, leading to an accurate estimation of its mass.) The interpretation of these measurementshas been challenged as being an artefact of a mildly eccentric orbit (Montalto et al. 2011), due toa misunderstanding of the orbital properties being measured, and subsequent work has demon-strated that the orbital motion of HD 209458b produces a blueshift of ∼0.1 km s −1, insufficientto solely account for the reported blueshift (Crossfield et al. 2012, Showman et al. 2013a).

The same method has been used to detect carbon monoxide in the nontransiting hot Jupiters τ

Bootis b (Brogi et al. 2012, Rodler et al. 2012) and HD 179949b (Brogi et al. 2014), which allowedtheir orbital inclinations to be measured, and water (Birkby et al. 2013) and carbon monoxide(de Kok et al. 2013) in HD 189733b. The ability to characterize nontransiting exoplanets greatlyincreases the potential sample size of exoplanets to be studied. Improvements in the data qualitywill eventually allow for the procurement of phase curves.

2.4. The Inflated Hot Jupiter Problem

A puzzling observed phenomenon is that hot Jupiters appear to have larger radii when theyare more irradiated, with some objects having radii twice that of Jupiter’s (Baraffe et al. 2010)(Figure 6). Keeping hot Jupiters inflated is nontrivial because Jupiter-mass objects are expected tobe partially degenerate.5 A plausible mechanism for inflation has to deposit a sufficient amount ofenergy deep within the interior of the exoplanet. Proposed mechanisms include the dynamical de-position of heat via vertical mixing (Guillot & Showman 2002, Showman & Guillot 2002), Ohmicdissipation (Batygin & Stevenson 2010; Perna et al. 2010a,b) and semiconvection (Chabrier &Baraffe 2007), although we note that semiconvection does not depend on the strength of stellarirradiation. Both vertical mixing and Ohmic dissipation are mechanisms that are intimately

5Matter becomes degenerate when it is packed so closely together that its pressure no longer depends on temperature and isdetermined by quantum mechanical effects.


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Figure 5Example of ultra-high-resolution spectroscopy for studying exoplanet atmospheres. The top panel shows452 spectra of the system τ Bootis observed with CRIRES at the VLT, after removing telluric and stellarlines, and contains the absorption signatures of various molecules as well as noise. For clarity, only 1/4 of thecovered spectral range is shown. The spectra are shifted to the rest frame of the exoplanet τ Bootis b andcoadded. The expected exoplanet spectrum, containing molecular absorption from carbon monoxide, isshown by the model plotted in the same panel. After cross-correlating the data with the model, the exoplanetsignal appears at a signal-to-noise ratio of about 6, at the known systemic velocity of τ Bootis (−16.4 km s−1).Courtesy of Matteo Brogi and Ignas Snellen.

related to atmospheric dynamics. Furthermore, the location of the radiative-convective boundaryin hot Jupiters is influenced by atmospheric dynamics, which enhances the long-term contractionand exacerbates the inflated hot Jupiter problem (Rauscher & Showman 2014).

2.5. Albedos and Albedo Spectra

Optical measurements of the secondary eclipse directly yield the geometric albedo—the albedo atzero phase angle—of either the atmosphere or surface of an exoplanet (Seager 2010), provided theexoplanet is not so hot that its thermal emission leaks into the optical range of wavelengths (Heng& Demory 2013). When corrected for contamination by thermal emission, surveys of hot Jupitersreveal that the geometric albedo is uncorrelated, or weakly correlated at best, with the incidentstellar flux (Heng & Demory 2013), stellar metallicity, and various properties (surface gravity,mass, radius, and density) of the exoplanets (Angerhausen et al. 2014). Curiously, the geometric

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0105

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Figure 6Measured radii of hot Jupiters versus the incident stellar flux upon them. Hot Jupiters appear to be more“inflated” when they are more irradiated. For comparison, the solar constant at Earth is ∼106 erg cm−2 s−1.Courtesy of Brice-Olivier Demory (Demory & Seager 2011).

albedos of super Earths appear to be statistically higher, as a population, compared to hot Jupiters(Demory 2014), implying either that their atmospheric properties are fundamentally different orthat these albedos might be associated with their surfaces.

Measuring both the dayside and nightside brightness temperatures, in the infrared, allows forthe albedo and the circulation efficiency to be simultaneously constrained; applied to a sample ofhot Jupiters, this has demonstrated that a range of albedos and circulation efficiencies exist (Cowan& Agol 2011a). In the case of the hot Jupiter HD 189733b, its relatively bright star allows for thealbedo spectrum of the exoplanet to be measured and demonstrates that its atmosphere is morereflective at shorter/bluer optical wavelengths (Evans et al. 2013). The measured albedo spectrumis consistent with an atmosphere dominated by Rayleigh scattering (either by condensates orhydrogen molecules) and absorption by sodium atoms (Heng & Demory 2013) or unusually smallcondensates (Heng et al. 2014).

2.6. Temporal Variability

For spatially unresolved exoplanets, measurements of the temporal variability of their atmospheresoffer an unprecedented opportunity to probe their atmospheric dynamics. As an example, if Earthwere an exoplanet, measuring its temporal power spectrum would reveal a broad peak at 30 to60 days associated with the Madden-Julian oscillation (Peixoto & Oort 1992). To date, temporal


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variability has not been detected for any exoplanetary atmosphere. An upper limit of 2.7% has beenset on the dayside variability of HD 189733b (Agol et al. 2010, Knutson et al. 2012), thus rulingout 2D shallow-water simulations that neglect thermal forcing and predict ∼10% variability (Choet al. 2003, 2008), although it remains consistent with the ∼1% predictions of 3D simulations(Showman et al. 2009). Attempts have been made to detect temporal variability from HD 149026b(Knutson et al. 2009b), HD 209458b (Crossfield et al. 2012), and υ Andromedae b (Crossfieldet al. 2010).

3. CURRENT QUESTIONS CONCERNING THE DYNAMICSOF EXOPLANETARY ATMOSPHERES

The rotation rate of an exoplanet is a fundamental property that affects all aspects of the atmo-spheric dynamics and therefore the thermal structure. It is an important input in general circulationmodels. Generally, this quantity is not easily obtained from astronomical observations. However,for hot Jupiters/Neptunes/Earths residing on close-in, circular orbits, the orbital and rotationperiods are expected to be equal; the orbital period is easily measured using the transit and radialvelocity techniques.

The lowest-energy orbital state of an exoplanet occurs when it resides on a spin-synchronized,circular orbit. The timescale for spin synchronization is (Bodenheimer et al. 2001)

tsyn = 8Q�M a6

45GM 2∗ R3, (1)

where � is the rotation rate, M is the mass of the exoplanet, G is Newton’s gravitational constant,and M ∗ is the stellar mass. The timescale for circularization takes a different form (Goldreich &Soter 1966),

tcirc = 4QM a13/2

63G1/2 M 3/2∗ R5

. (2)

The tidal quality factor Q is the reciprocal of the fraction of tidal energy dissipated per orbit. Itsvalue has been experimentally estimated to be Q ∼ 10–100 for Earth (Knopoff 1964). For Jupiter, itis estimated that Q ∼ 104–105 (Lainey et al. 2010). Generally, because tcirc has a steeper dependenceon a than tsyn, it is expected that circularized orbits are also spin-synchronized. (The converse isnot true: tidally de-spun but eccentric orbits may exist, where the simple permanent dayside andnightside picture does not hold.) Astronomical measurements of the orbital eccentricity of hotJupiters show that their orbits are consistent with being circularized for orbital periods of �2 days(Figure 7) (Pont et al. 2011). Thus, for hot Jupiters at least, the rotation period may be indirectlyinferred.

Brown dwarfs typically have rotation periods of about 1 to 12 h (Reiners & Basri 2008) andthe first observational estimate of rotation for a directly imaged exoplanet shows that its rotationperiod is likewise short—close to 8 h (Snellen et al. 2014). These rapid rotations place browndwarfs and directly imaged gas giants in a different dynamical regime than close-in exoplanets thatare synchronously—and therefore more slowly—rotating (Showman & Kaspi 2013).

3.1. What Are the Basic Thermal Structures of Highly Irradiated Atmospheres(as Predicted by Theory)? How Is Heat Transported from the PermanentDayside to the Nightside?

The zeroth order way of describing an atmosphere is to state its equilibrium temperature (assuminga vanishing albedo), Teq = T∗(R∗/2a)1/2, where T∗ is the effective stellar temperature, R∗ is the

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Ecc

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Figure 7Orbital eccentricity of a sample of exoplanets, with measured masses and radii, as a function of the orbitalperiod (in units of Earth days) (Pont et al. 2011). To obtain more accurate estimations of the eccentricitiesand their uncertainties, a Markov Chain Monte Carlo (MCMC) analysis is used to correct for the effect thatthe orbital eccentricity is bounded from below by zero. Data points consistent with zero eccentricity arerepresented by the green circles, whereas the blue squares are measurements of nonzero eccentricity.Exoplanets that are located close enough to their host stars (i.e., with orbital periods less than about 2 days)appear to reside on circular orbits. Courtesy of Nawal Husnoo and Frederic Pont (Pont et al. 2011).

stellar radius, and a is the spatial separation between the exoplanet and the star. The stellar fluxincident upon the exoplanet is 2σSBT 4

eq (the stellar constant), where σSB is the Stefan-Boltzmannconstant. Favored by astronomers, the stellar constant is an atmosphere-independent quantity,which is convenient to compute and state. Unsurprisingly, a survey of the Solar System planetsand moons reveals that such a description is inadequate for describing the actual atmospherictemperatures. Additionally, there is theoretical interest to understand the thermal structures ofexoplanetary atmospheres both vertically and horizontally, as observations are starting to constrainthese quantities.

The temperature on exoplanets in general, and especially on synchronously rotating exoplanetswith permanent daysides and nightsides, will depend significantly on latitude and longitude. Fortidally locked exoplanets, intense stellar irradiation on the permanent dayside produces a hori-zontal temperature gradient, which drives zonal and meridional winds. The extent to which thesewinds redistribute heat from the dayside to the nightside, and the resulting day-night temperaturecontrast, is one of the outstanding questions in current exoplanet science. Several authors havesuggested that whether the day-night temperature difference is small or large can be understoodby a comparison of the characteristic timescale over which air advects horizontally from day tonight, tadv, with the characteristic timescale over which air gains or loses energy by absorption ofstarlight and radiation of infrared energy, trad (Showman & Guillot 2002; Cooper & Showman2005; Showman et al. 2008a; Heng et al. 2011a,b; Cowan & Agol 2011b; Perna et al. 2012). Ac-cording to this scenario, the fractional day-night temperature difference is small when trad � tadv

and large when trad � tadv. Under conditions typical of hot Jupiters, both timescales span therange ∼104–10 5 s, suggesting that hot Jupiters reside in the regime where day-night temperaturedifferences may be large (unlike on Earth). Comparisons of these two timescales in 3D numericalsimulations of hot Jupiters, with each timescale evaluated a posteriori from the simulation results,


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suggest that the transition from small to large fractional day-night temperature difference doesoccur approximately where trad ∼ tadv (Perna et al. 2012). Moreover, it was predicted that whentrad ∼ tadv, the winds can distort the temperature pattern, leading to hot spots that are displacedfrom the substellar point (Showman & Guillot 2002). In particular, they predicted a fast, broadeastward jet stream at the equator (see Section 3.2), which causes a displacement of the hottestregions to the east. As summarized in Section 2, this phenomenon has now been observed onseveral hot Jupiters and has been reproduced in a wide range of 3D circulation models.

Nevertheless, this timescale comparison is not predictive, as tadv—which is simply a mannerof expressing the wind speeds—is unknown a priori and depends on many atmospheric parame-ters (Perez-Becker & Showman 2013). Unfortunately, it is therefore not possible to predictivelyevaluate the criterion; one can only estimate after the fact whether it is consistent with a givennumerical simulation. Moreover, this timescale comparison neglects a role for other importanttimescales in the problem, including those for planetary rotation, friction, vertical advection, andpropagation of various types of waves both horizontally and vertically. These almost certainlyaffect various aspects of the dynamics, including the day-night temperature differences. Using anidealized, analytical model for the wind speeds and fractional day-night temperature differences,it was demonstrated that, under certain conditions, the trad versus tadv comparison breaks down(Perez-Becker & Showman 2013). This occurs under conditions of weak day-night forcing, whenthe horizontal advection term is small relative to vertical advection in the thermodynamic en-ergy equation. Generally, a comparison between the vertical advection timescale and the radiativetimescale provides a better description of the regime transition between small and large fractionalday-night temperature differences (Perez-Becker & Showman 2013). Furthermore, the advectiontimescales can be represented in terms of the timescales for planetary rotation, friction, wavepropagation, and radiation (Perez-Becker & Showman 2013).

A crucial question concerns whether the mean temperature profile, on both the dayside andnightside, decreases or increases with height; as described in Section 2, this question is directlyamenable to observational characterization using secondary eclipses and lightcurves at a varietyof wavelengths. Simple atmospheric theory (Guillot 2010, Pierrehumbert 2010) shows that, inthe absence of scattering, one expects temperature to decrease with altitude near photosphericlevels when the visible opacity is less than the infrared opacity, whereas temperature increaseswith height when the visible opacity exceeds the infrared opacity (Figure 8). On hot Jupiters, thepresence of a visible absorber can lead to such a stratosphere confined to the dayside alone, withthe nightside temperature decreasing strongly with altitude (Showman et al. 2009, Heng et al.2011a).

If the advection timescale is less than the chemical timescale of a given transition (e.g., carbonmonoxide to methane), then chemical disequilibrium may be induced by atmospheric dynamics(Cooper & Showman 2006, Burrows et al. 2010). In the case of HD 189733b, examining its color-magnitude diagram at different orbital phases of the exoplanet reveals both a temperature andchemical transition from the dayside to the nightside (Triaud 2014) and allows the data to beginto address this question.

3.2. What Are the Global Circulation Structures of Highly Irradiated,Tidally Locked Exoplanets?

The dominant dynamical feature emerging from 3D circulation models of hot Jupiters is theexistence of a fast, broad eastward-flowing equatorial jet at and near the photosphere (Figure 9)(Showman & Guillot 2002; Cooper & Showman 2005, 2006; Dobbs-Dixon & Lin 2008; Dobbs-Dixon et al. 2010, 2012; Showman et al. 2008a, 2009; Lewis et al. 2010; Heng et al. 2011a,b;

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10–4

10–3

10–2

10–1

102

800 1,000 1,200 1,400

100

101

P (b

ar)

T (K)

Figure 8Examples of temperature-pressure profiles. The families of solid, dotted, and dashed curves correspond tomodel atmospheres with pure absorption, shortwave scattering present, and longwave scattering present,respectively. Each family of curves keeps the shortwave opacity fixed at κS = 0.01 cm2g−1 and performs asweep of the longwave opacity (κL = 0.001–0.02 cm 2 g−1). Stellar irradiation determines the thermalstructure down to ∼10 bar, where internal heat takes over. For illustration, we have adopted a surface gravityof g = 103 cm s−1, an equilibrium temperature of Teq = 850 K, and an internal temperature ofT int = 200 K. Models are taken from Guillot (2010), Heng et al. (2012), and Heng et al. (2014).

Perna et al. 2012; Rauscher & Menou 2010, 2012b). This so-called equatorial superrotation isinteresting because such an eastward equatorial jet corresponds to a local maximum of angularmomentum per unit mass with respect to the planetary rotation axis; waves or eddies are requiredto maintain such a feature. (For example, the atmospheres of Titan and Venus superrotate.) Inmany cases, the jet is accompanied by an obvious chevron-shaped feature, with a preferentialtendency for northwest-southeast tilts in the northern hemisphere and southwest-northeast tiltsin the southern hemisphere. Analytical theory and idealized numerical models suggest that theequatorial superrotation results from standing, planetary-scale Rossby and Kelvin wave modesthat result from the strong day-night thermal forcing (Showman & Polvani 2010, 2011; Tsai et al.2014). The resulting Matsuno-Gill pattern (Matsuno 1966, Gill 1980) also causes the chevronpattern in at least some cases (Heng & Workman 2014). The jet width is controlled by theequatorial Rossby deformation radius (Showman & Polvani 2011),

Ro ∼(

NHR2�

)1/2

, (3)

where N is the Brunt-Vaisala frequency, H is the scale height, R is the planetary radius,and � is the rotation rate. Thus, faster rotation leads to a narrower equatorial jet, and


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a

–135 –90 –45 0 45 95 135 180–180

60

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–60

–30

Longitude (°)

c

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1,062

1,124

1,186

1,248

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1,372

1,434

1,496

1,558

1,6201,683

T (K)

470

630

780

930

1,100

1,200

1,400

Figure 9Examples of calculations from general circulation models of hot Jupiters. Despite the use of different input parameters, techniques totreat radiation and numerical schemes for atmospheric dynamics, the chevron-shaped feature appears to be a generic outcome of thehot exoplanet regime. Courtesy of Kevin Heng ( panel a, using the FMS GCM), Emily Rauscher ( panel b, using the IGCM), IanDobbs-Dixon ( panel c, using a customized code), Nathan Mayne ( panel d, using the U.K. Met Office GCM), and Adam Showman( panel e, using the MITgcm). Panel f shows an analytical model from Heng & Workman (2014), generalized from the work of Matsuno(1966), Gill (1980), and Showman & Polvani (2010, 2011).

in some cases the emergence of additional eastward jets at high latitudes (Showman et al.2008a, 2009; Kataria et al. 2013). The circulation in 3D models is also accompanied bystrong mean-meridional circulation cells; the strength and depth of these cells are sensi-tive to the stellar irradiation, becoming stronger and deeper for more irradiated atmospheres

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(Perna et al. 2012). The equatorial jet strengthens as the metallicity6 increases (Lewis et al.2010).

Despite the overall tendency toward equatorial superrotation, theory and idealized simulationspredict distinct circulation regimes for synchronously rotating hot Jupiters depending on theincident stellar flux and other parameters. Using idealized models, it is suggested that when thestellar irradiation is particularly large (Showman et al. 2013a)—perhaps on hot Jupiters withmean temperatures exceeding ∼2,000 K—the atmospheric radiative time constant is so shortthat radiation damps the large-scale Rossby and Kelvin waves that drive superrotation, leading toan atmosphere dominated at low pressures by day-night flow. However, when the radiative timeconstant is very long, the day-night thermal forcing gradient becomes less important, and the meanequator-pole heating gradient instead should become dominant; such a circulation would exhibitstrong zonal (east-west) banding. These two dynamical regimes have very different predictionsfor the wind behavior as observed with high-resolution spectroscopy during transit (Kempton &Rauscher 2012, Showman et al. 2013a). They also lead to a transition from large to small fractionalday-night temperature differences (Perna et al. 2012, Showman et al. 2013a, Perez-Becker &Showman 2013). Hot Jupiters such as HD 189733b and HD 209458b lie at an intermediate pointalong this continuum. Nevertheless, magnetic effects may significantly influence the dynamics forparticularly hot exoplanets (see Section 3.4), a phenomenon whose effects are still being workedout.

The basic global circulation structure appears to be robust to the presence of a nonzero orbitaleccentricity (Kataria et al. 2013). A key difference is that spin-synchronized exoplanets on eccentricorbits are flash-heated at periastron, compared to the constant stellar flux received by exoplanetson circular orbits. If the radiative timescale is sufficiently long, this flash heating remains imprintedfor several rotational periods and manifests as ringing in the infrared phase curves (Cowan & Agol2011a, Kataria et al. 2013). To date, this ringing has not been detected.

The dynamical mechanisms that maintain the circulation in Solar System atmospheres such asthose of Earth and Jupiter differ in detail from those operating in hot Jupiters, but they share asimilar foundation. On most Solar System planets (with Mars being an exception), the solar dayis less than the atmospheric radiative time constant, such that (at least deep in the atmosphere)longitudinal day-night thermal forcing is subdominant relative to the equator-to-pole thermalforcing. On Earth, the poleward heat transport occurs via the Hadley circulation at low latitudesand baroclinic instabilities at high latitudes (Vallis 2006). Coriolis forces in the poleward-flowingupper branch of the Hadley circulation lead to so-called subtropical jets near the poleward edges ofthe Hadley cells. Baroclinic instabilities cause radiation of Rossby waves in the midlatitudes, and thepropagation and breaking of these waves produce the eddy-driven jet streams in the midlatitudes.Similar mechanisms may be important in maintaining the zonal jets on Jupiter and Saturn. Inslowly rotating atmospheres such as those of Venus and Titan, by contrast, the Hadley circulation isnearly global, with the subtropical jets at high latitudes, and equatorial superrotation emerges frominstabilities that transport angular momentum to the equator. In contrast to these Solar Systemexamples, the day-night forcing seems to play the overriding role for the typical hot Jupiter. Thisforcing induces global-scale waves, including Rossby waves, that cause equatorial superrotationand help maintain the overall thermal structure. Despite the differences in detail, all of theseatmospheres share fundamental similarities in the importance of heat and angular momentumtransports in shaping the circulation, and in the importance of wave-mean-flow interactions incontrolling the structure of the jet streams.

6In astronomy, one refers to the elements heavier than hydrogen and helium as metals. Atmospheres with higher metallicitieseffectively have higher mean molecular weights and thus smaller scale heights.


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3.3. Is There a Continuum of Thermal and Circulation Structures andDynamical Mechanisms? Do We Expect the Atmospheres of HighlyIrradiated Exoplanets to be Fundamentally Different from Thoseof the Solar System Objects or Brown Dwarfs?

An argument that is often made is, “If we do not understand the atmospheres of Earth and the SolarSystem bodies, what chance do we have of understanding the atmospheres of exoplanets?” Theanswer is that it depends on the question one is asking. In Earth climate studies, one is interestedin predicting temperature variations on fine scales: a warming of 2 K is significant for terrestrialclimate change, but of little consequence for interpreting the global properties of an exoplanetaryatmosphere.

Despite sharing the term Jupiter in their names, Jupiter and hot Jupiters have little in common,dynamically, besides both being gas giants. Jupiter is a fast rotator, whereas hot Jupiters areexpected to be tidally locked and slow rotators. Internal heat and solar irradiation are comparablefor Jupiter. In hot Jupiters, the stellar irradiation flux is ∼104 times stronger than if their internalheat fluxes were to be comparable to Jupiter’s, and the tidal forces experienced are ∼106 timesstronger. Based on estimations of the Rossby and Rhines numbers, Jupiter is expected to possesssmall vortices and a large number of narrow zonal jets, whereas the vortices and jets on hot Jupitersare expected to be global in scale. Atmospheric circulation in hot Jupiters is believed to be bothstrong and deep, implying that measured properties may be representative of the entire atmosphere(and not just confined to the cloud-top level as for Jupiter). Because the temperatures on Jupiterare ∼100 K, whereas those on hot Jupiters are ∼1,000–3,000 K, there is little reason to believethat their atmospheric chemistries and aerosol properties will resemble each other, although thisremains an active topic of research.

However, Jupiter might bear more resemblance to brown dwarfs, substellar objects that aremassive enough to ignite deuterium and lithium burning within their cores, but not massiveenough to sustain full-blown nuclear fusion like in stars. Dynamically, brown dwarfs and Jupitermay be similar if rotation is fast (Showman & Kaspi 2013). Chemically, because brown dwarfscover a temperature range ∼100–3,000 K (termed the sequence of Y, T, and L dwarfs), theyexhibit a continuum of spectral signatures that may link smoothly to Jupiter’s (Burrows et al.2003). Characterizing the coolest Y dwarfs is a work in progress. There are currently no empiricalconstraints on the atmospheric dynamics of directly imaged exoplanets, but the analysis of spectrasuggests that their chemical and aerosol properties are similar to brown dwarfs (Barman et al.2011).

It is interesting to note a source of confusion arising from a misnomer. In stars, there exists anatmospheric layer known as the radiative zone, where energy is transported outward by radiativediffusion rather than by convection. It typically sits below a convective zone. In hot Jupiters,the intense stellar irradiation forms a deep radiative zone that sits above a convective zone; thedeepness comes from the stellar flux diminishing the vertical temperature gradient and stabilizingit against convection. However, unlike for stars, atmospheric circulation exists in the radiativezone of hot Jupiters due to stellar heating.

3.4. What Are the Effects of Magnetic Fields on the Atmospheric Circulation?

In highly irradiated atmospheres, the ∼1,000–3,000 K temperatures allow for collisional ioniza-tion to act upon the alkali metals such as sodium and potassium. This source of free electronscreates a partially ionized atmosphere. If the exoplanet possesses a magnetic field, then it willresist the partially ionized atmosphere being advected across it—a global manifestation of Lenz’s

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law (Batygin & Stevenson 2010, Perna et al. 2010a). This magnetic drag slows down the atmo-spheric winds and converts kinetic energy into heat (Ohmic heating) (Perna et al. 2010b), althoughthis effect is expected to saturate (Menou 2012b). When magnetic drag becomes significant, theatmosphere may transition from being dominated by zonal flows to substellar-to-antistellar flow(Showman et al. 2013a), although the conditions under which this transition is expected to occurremain under debate (Batygin et al. 2013). Ohmic dissipation is a plausible mechanism for keepinghot Jupiters inflated and is qualitatively consistent with the observational trends (Perna et al. 2012,Wu & Lithwick 2013), but it remains a matter of debate if it works out in the details (Rauscher &Menou 2013, Rogers & Showman 2014). The presence of clouds is expected to further complicatethis issue (Heng 2012a).

Technically, one needs to solve the governing equations of fluid dynamics in conjunction withthe magnetic induction equation,

∂ �B∂t

= ∇ ×(�v × �B

)− ∇ ×

(η∇ × �B

), (4)

where �B is the magnetic field strength, t represents time, �v is the velocity, and η is the magneticdiffusivity; η is expected to vary by orders of magnitude within a highly irradiated atmosphere.The term involving η behaves like a diffusion term and accounts for departures from ideal mag-netohydrodynamics (MHD). There exist other terms (Hall, ambipolar diffusion) in the magneticinduction equation, but they are believed to be subdominant (Perna et al. 2010a). To date, mostpublished work invokes the kinematic approximation—the simplification that the magnetic fieldaffects the velocity field of the atmosphere, but not vice versa (Menou 2012a; Perna et al. 2010a,b,2012; Rauscher & Menou 2013). This allows for the effects of magnetic drag and Ohmic dissipa-tion to be studied via postprocessing of hydrodynamic simulations. More recent work has startedto formally include MHD, albeit with other simplifying assumptions (Batygin et al. 2013, Rogers& Showman 2014). This technical challenge remains open.

3.5. What Are the Effects of Aerosols/Clouds/Hazes on the Thermal Structureand Atmospheric Circulation (and Vice Versa)?

An inversion occurs in temperature-pressure profiles when the optical opacity exceeds the infraredone (Hubeny et al. 2003, Hansen 2008, Guillot 2010). When clouds or hazes are present, theycomplicate this simple description by introducing both greenhouse and anti-greenhouse effects,depending on their relative strength of absorption versus scattering (Heng et al. 2012). Scattering inthe optical generally introduces an anti-greenhouse effect—it warms and cools the upper and loweratmosphere, respectively, by shifting the photon deposition depth to higher altitudes (Heng et al.2012, 2014). Scattering in the infrared always warms the atmosphere (Heng et al. 2014). Examplesof model temperature-pressure profiles displaying these basic trends are shown in Figure 8.

Clouds exert both radiative and dynamical effects on the atmospheric circulation, whereastheir ability to be kept aloft depends on the local conditions set by the circulation. Even whenthey are negligible by mass, clouds may alter the temperature-pressure profile via scattering andabsorption (Heng & Demory 2013). If they form a nonnegligible part of the mass budget ofthe atmosphere, they may alter the flow if they are sufficiently coupled to it. The extent of thecoupling depends on the size of the cloud particles relative to the local flow conditions and alsodetermines if the particles see the local vertical flows that keep them aloft (Spiegel et al. 2009,Heng & Demory 2013, Parmentier et al. 2013). Both scaling arguments and 3D simulations ofatmospheric circulation suggest that micron-sized particles (or smaller) should be ubiquitous inhot Jupiters (Heng & Demory 2013, Parmentier et al. 2013). This may help to explain the flat


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spectra seen in transmission spectra (Section 2) and will exert a strong influence on atmosphericchemistry and radiation if the particles can sublimate on the dayside.

Given the expected diversity of flow and temperature conditions throughout the atmosphereof a tidally locked, highly irradiated exoplanet, the abundances and sizes of cloud particles are notexpected to be uniform. The rich structure contained within the optical phase curve of Kepler-7b,which probes the abundances and sizes of clouds within its atmosphere, is consistent with thisexpectation (Demory et al. 2013, Heng & Demory 2013).

4. FUTURE QUESTIONS

4.1. What Are the Structures of Atmospheric Winds(as Probed by Observations)?

Ultra-high-resolution, ground-based transit observations have led to a tentative measurement ofwind speeds in one object (Snellen et al. 2010), but the potential of this technique to measurecirculation structures remains largely untapped. Measurements of wind speeds will help constrainmodels of magnetic drag and Ohmic dissipation (Batygin & Stevenson 2010; Perna et al. 2010a,b)and bracket numerical uncertainties (Heng et al. 2011b). The Doppler profile of the winds—whether they are blue- or redshifted—indicates the dynamical regime they are in, whether theatmosphere is dominated by zonal winds or substellar-to-antistellar flow (Kempton & Rauscher2012, Showman et al. 2013a). Quantifying the circulation regime of an exoplanet places con-straints on the importance of various dynamical mechanisms operating within the atmosphere(e.g., magnetic drag).

These efforts will be significantly advanced with the next generation of giant, ground-basedtelescopes: the European Extremely Large Telescope (E-ELT), with a 39-m mirror; the GiantMagellan Telescope (GMT), with a collecting area equivalent to having a 22-m mirror; and theThirty Meter Telescope (TMT).

4.2. Why Do Only Some Exoplanets Appear to Be Cloudy/Hazy (as Inferredfrom Transmission Spectra)? What Observations Do We Need to Breakthe Degeneracies Associated with Aerosols/Clouds/Hazes and ConstrainTheir Properties?

To date, there is no straightforward explanation as to why some exoplanetary atmospheres appearto be cloudy, whereas others do not. The presence of clouds renders the interpretation of spectradegenerate, as the chemical abundances inferred are degenerate with the cloud model assumed(Burrows et al. 2011, Deming et al. 2013, Lee et al. 2013). The degeneracy arises because cloudsdiminish the strength of spectral features, but this may also be caused by reduced abundances.

Breaking the degeneracies associated with aerosols/clouds/hazes requires a coordinated effort ofobtaining albedos, phase curves, and ultra-high-resolution transit and secondary-eclipse spectrafor a given exoplanet. Measuring the albedo and phase curve will only constrain a degeneratecombination of the sizes and abundances of the cloud particles, the total optical depth of thecloud, and the altitude and vertical extent of the cloud (Heng & Demory 2013). If the infraredphase curve is also obtained, it provides a powerful way of diagnosing the relative abundancesof the cloud particles across longitude because one now has information on the thermal profileof the atmosphere and thus its lofting properties due to dynamics. If the exoplanet possesses aflat transmission spectrum, then ultra-high-resolution spectra may be able to set constraints onthe pressure levels of the cloud deck because the cores of atomic or molecular lines may still be

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detected given sufficient spectral resolution (Pont et al. 2013, Kempton et al. 2014). Furthermore,obtaining transmission and emission spectra shortward of 1 μm and longward of 8 μm, along withmeasurements of the mass and radius of the exoplanet, will set constraints on the size, opticaldepth and composition of the cloud particles (Lee et al. 2014).

4.3. What Technical Advances Do We Need to Make in OurSimulation Techniques?

Exploring the atmospheric dynamics of exoplanets started with adapting GCMs designed for thestudy of Earth. Although these GCMs provide a reasonable starting point for initial investigations,they have a number of shortcomings that need to be remedied to address several outstandingquestions. Standard, Earth-based GCMs do not include a treatment of shocks, which are expectedto exist in highly irradiated atmospheres and will convert a significant fraction of the kinetic energyinto heat (Dobbs-Dixon & Lin 2008, Li & Goodman 2010, Heng 2012c). Standard GCMs also donot include the dynamical effects of magnetic fields. Instead, several studies have added a Rayleighdrag term into the momentum equation (−�v/tdrag) to mimic magnetic drag (Perna et al. 2010a,b,2012), even though hydrodynamic and magnetic drag are expected to possess qualitatively differentdamping behavior (Heng & Workman 2014, Rogers & Showman 2014). Given the interest inclouds as motivated by the astronomical observations, there is a need to develop non-Earth-centriccloud schemes for GCMs.

Table 1 lists and summarizes the GCM studies of exoplanetary atmospheres to date, includingthe governing equations solved (see Appendix A for details), the approximations taken, and if keyproperties are being modeled. GCMs that formally include magnetic fields are starting to emerge,albeit with their own technical limitations (Batygin et al. 2013, Rogers & Showman 2014). SomeGCMs do not solve the pole problem, where meridians converging at the poles of a sphere leadto a vanishing computational time step (Stanisforth & Thuburn 2012), and thus have 3D butnonglobal grids (Dobbs-Dixon & Lin 2008; Dobbs-Dixon et al. 2010, 2012; Dobbs-Dixon &Agol 2013). Several of the listed studies do not explicitly demonstrate if they are able to reproducethe standard benchmark test for Earth (Held & Suarez 1994).

Ultimately, to understand highly irradiated exoplanetary atmospheres and predict their emer-gent properties, we need a GCM that does some combination of the following: solves the Navier-Stokes equation in tandem with the magnetic induction equation; employs a numerical schemethat conserves mass, energy, and angular momentum simultaneously; treats shocks (or at leastallows for the possibility of shocks emerging); performs multiwavelength radiative transfer; andconsiders the effects of disequilibrium chemistry.

4.4. Is There a Fundamental Limit to What We Can Learn About SpatiallyUnresolved (but Spectrally and Temporally Resolved) Exoplanets?

Astronomy has come a long way since the first exoplanet detections in the 1990s. The promiseof using transits, eclipses, and direct imaging to measure basic, bulk properties of exoplanetaryatmospheres has largely been fulfilled. Mass-radius diagrams of exoplanets allow a rich set ofproperties to be inferred, from whether an exoplanet is likely to be rocky or possesses an extendedatmosphere to whether its radius is anomalously large as expected by standard physics. Detailedtransit spectroscopy (or spectrophotometry) allows for the presence of molecules to be identified,using space- or ground-based telescopes. The next generation of telescopes will allow for evenmore detailed inferences to be made, including the global structures and speeds of winds, therotation period, the vertical structure of chemical abundances, and 3D maps over a broad range


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Table 1 Atmospheric circulation studies of hot exoplanets using general circulation models (GCMs)

Study (alphabetical)Approx.

usedGlobalgrid?

Irradiateda

atmosphere?Radiativea

transfer?Treatsshocks?

Magneticfields?

PassesEarthb

benchmark?Batygin et al. (2013)c BQ (3D) Y Y N N Y NBending et al. (2012) PE (3D) Y Y N N N YBurkert et al. (2005)c,d EE (2D) N Y Y N N NBurrows et al. (2010) PE (3D) Y Y N N N YCho et al. (2003) EB (2D) Y N N N N NCho et al. (2008) EB (2D) Y N N N N NCooper & Showman(2005)

PE (3D) Y Y N N N Y

Cooper & Showman(2006)

PE (3D) Y Y N N N Y

Dobbs-Dixon & Lin(2008)c

EE (3D) N Y Y N N N

Dobbs-Dixon et al.(2010)c

NS (3D) N Y Y Y N N

Dobbs-Dixon et al.(2012)c

NS (3D) N Y Y Y N N

Dobbs-Dixon & Agol(2013)

NS (3D) N Y Y Y N N

Heng et al. (2011b) PE (3D) Y Y N N N YHeng et al. (2011a) PE (3D) Y Y Y N N YKataria et al. (2013) PE (3D) Y Y Y N N YLangton & Laughlin(2008)

EE (2D) Y Y Y N N N

Lewis et al. (2010) PE (3D) Y Y Y N N YLi & Goodman (2010) NS (2D) N Y N Y N NLiu & Showman (2013) PE (3D) Y Y N N N YMayne et al. (2013) EE (3D) Y Y N N N YMayne et al. (2014)e EE (3D) Y Y N N N YMenou & Rauscher (2009) PE (3D) Y Y N N N YMenou (2012a) PE (3D) Y Y Y N N YParmentier et al. (2013) PE (3D) Y Y Y N N YPerna et al. (2010a) PE (3D) Y Y N N N YPerna et al. (2010b) PE (3D) Y Y N N N YPerna et al. (2012) PE (3D) Y Y Y N N YPolichtchouk & Cho(2012)

PE (3D) Y N N N N Y

Rauscher & Menou (2010) PE (3D) Y Y N N N YRauscher & Menou(2012a)

PE (3D) Y Y N N N Y

Rauscher & Menou(2012b)

PE (3D) Y Y Y N N Y

Rauscher & Menou (2013) PE (3D) Y Y Y N N Y(Continued )

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Table 1 (Continued )

Study (alphabetical)Approx.

usedGlobalgrid?

Irradiateda

atmosphere?Radiativea

transfer?Treatsshocks?

Magneticfields?

PassesEarthb

benchmark?Rogers & Showman(2014)

AN (3D) Y Y N N Y N

Showman & Guillot(2002)

PE (3D) Y Y N N N Y

Showman et al. (2008a) PE (3D) Y Y N N N YShowman et al. (2009) PE (3D) Y Y Y N N YThrastarson & Cho (2010) PE (3D) Y Y N N N YThrastarson & Cho (2011) PE (3D) Y Y N N N Y

aIrradiated refers specifically to whether the model atmosphere is being forced by stellar irradiation, i.e., whether the irradiation is doing work on theatmosphere. Simulations that are unforced by irradiation are sometimes termed adiabatic. It is possible for the effects of radiation in irradiated atmospheresto be mimicked without explicitly performing radiative transfer, by adopting a Newtonian relaxation or cooling term in the thermodynamic equation.bOnly marked “Y” if there is either an explicit demonstration in the publication or a clear citation to previous publications describing that the simulationcode used is able to reproduce the Held-Suarez benchmark test for Earth (Held & Suarez 1994). Because it is a 3D test, 2D simulations, by definition, areunable to reproduce it.cEmploys flux-limited diffusion in the region encompassing the photosphere, an approximation that is strictly valid only in optically thin or thick situations.dRotation of the exoplanet is not included.eNonhydrostatic.Abbreviations: Boussinesq (BQ), anelastic (AN), equivalent barotropic (EB), primitive equations (PE), Euler equation (EE), Navier-Stokes equation (NS).

of pressure levels. That all of these accomplishments will come without being able to spatiallyresolve these exoplanets is in itself a remarkable feat.

Nevertheless, the lack of spatial resolution will ultimately introduce inescapable degeneraciesinto our interpretations of even next-generation data. At the day-night (and night-day) terminatorsof exoplanetary atmospheres, a rich variety of conditions are expected to be present, and departuresfrom chemical and radiative equilibrium are expected (Cooper & Showman 2006, Rauscher &Menou 2010, Heng et al. 2011a). Transmission spectroscopy probes some global average of theseterminator regions, which may not reflect local conditions. Similarly, the daysides of exoplanetaryatmospheres are expected to exhibit a diverse range of circulations, chemistry, and temperatures.Emission spectroscopy again probes some global average of these conditions. In breaking thesedegeneracies, GCMs have a key role to play (once they overcome the technical challenges describedin Section 4.3). By combining a comprehensive dataset consisting of transmission and emissionspectra, phase curves, and eclipse maps obtained at multiple wavelengths, one can begin to iteratewith GCMs to obtain self-consistent solutions and study degeneracies. If the data are good enough,one may even assess the time dependence of 3D structure in exoplanetary atmospheres.

4.5. What Are the Pros and Cons of Investing Resources into a Few BenchmarkExoplanets Versus Spreading Them Over Many Exoplanets to Study StatisticalTrends? What May We Expect from Future Instruments/Missions?

A strength of astronomical observations is the ability to measure basic quantities (mass, radius,density, incident stellar flux, albedo, bulk chemistry) for a large sample of exoplanets, much morethan for the eight planets in our Solar System. By making these measurements for a diverse sampleof stars with different ages, metallicities, and stellar types, a catalogue of properties may be built


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up and may yield important clues on how these exoplanets and their atmospheres formed. Suchan approach is orthogonal to collecting and analyzing samples or sending in situ probes, as is donefor the Solar System.

However, a decisive way to advance our understanding of exoplanetary atmospheres is to focuson a handful of exoplanets around nearby, bright stars, which serve as benchmarks for testingboth observational and theoretical techniques. Although the heavy investment of telescope timein these objects carries a certain amount of risk (Knutson et al. 2014, Kreidberg et al. 2014), suchmeasurements must be allowed to continue as the rewards will be immense (e.g., identification ofmolecules in an Earth-like exoplanet) (Seager 2012).

Not all exoplanets are equally characterizable—it is no accident that HD 189733b and HD209458b, two of the most studied exoplanetary atmospheres, orbit nearby, bright stars. Thereare three exoplanet detection missions on the horizon designed to greatly increase the sampleof exoplanets around bright stars: TESS (Ricker et al. 2014), CHEOPS (Broeg et al. 2013), andPLATO (Rauer et al. 2014), all approved by NASA or ESA and to be launched between 2017and 2024. The discoveries made by these missions will enable a significantly larger sample ofcharacterizable exoplanets to be constructed across a broader range of stellar types and atmospherictemperatures, which will inspire more detailed questions regarding their atmospheric dynamicsand chemistry.

The James Webb Space Telescope ( JWST) will be equipped with three instruments covering 0.6to 29 μm at spectral resolutions of 100–3,000. While this is insufficient to resolve individual ro-vibrational lines, it will definitively identify line complexes and thus molecules (Line et al. 2013).The JWST is capable of obtaining multifaceted datasets of exoplanetary atmospheres, includingtransmission and emission spectra and multiwavelength phase curves. The hope is that physical ef-fects such as shock heating or Ohmic dissipation may produce unique signatures of their existencewhen examined collectively across transmission, emission, and phase-curve data. Multiwavelengthphase curves will provide a wealth of data for constraining atmospheric dynamics, as they measuretemperatures across longitude and depth (Burrows et al. 2010). Combined with eclipse maps,there is the potential to obtain 2D maps at different altitudes within an exoplanetary atmosphere,enabling the data to decisively confront general circulation models. For the brightest objects, itwill be complemented by the E-ELT, GMT, and TMT from the ground, where the identifica-tion of molecules will be corroborated. Complementary, ground-based optical data (shortward of0.6 μm) will set additional constraints on cloud or aerosol properties in the atmosphere.

The coming decade holds the promise of ground-breaking advances in the study of exoplan-etary atmospheres and will witness the decisive confrontation of theory and simulation by theobservations.

APPENDIX

A. THE GOVERNING EQUATIONS OF ATMOSPHERIC DYNAMICS

A.1. General Form: Navier-Stokes Equation. The general, governing equation of fluid dy-namics is known as the Navier-Stokes equation (Vallis 2006),

D�vDt

= −2 �� × �v − ∇ Pρ

+ ν∇2�v + ν

3∇ (∇.�v) + �g + �Fdrag, (5)

where �v is the velocity vector, t represents the time, �� is the rotation rate vector, P is the pressure,ρ is the mass density, ν is the (constant) molecular viscosity, �g = −gz is the surface gravity oracceleration due to gravity, z is the unit vector of the vertical spatial coordinate, and �Fdrag represents

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the various drag forces per unit mass. Equation 5 formally expresses the linear conservation ofmomentum in a fluid. In atmospheric applications, either the assumption of an inviscid (v = 0)or an incompressible (∇.�v = 0) fluid is often made. Enforcing the former and latter assumptionsyield the Euler and the incompressible Navier-Stokes equations, respectively.

The Navier-Stokes equation has three scalar components and five variables. To close the setof equations, we need three equations and one more variable. One of them is the mass continuityequation,

∂ρ

∂t+ ∇. (ρ�v) = 0, (6)

which formally expresses the conservation of mass. The thermodynamic equation introducestemperature (T ) into the system and enforces the conservation of energy,

DTDt

= κTP

DPDt

+ Q, (7)

where κ is the adiabatic coefficient and the term Q represents sources of heating (including fromstellar irradiation). Finally, the assumption of an equation of state, usually that of an ideal gas,ensures an equal number of equations and variables,

P = ρRT , (8)

where R is the specific gas constant. The assumption of an ideal gas breaks down in the deepinterior of an exoplanet, where pressures are high and degeneracy starts to become important.

A.2. Boussinesq Approximation. An approach that is seldom adopted in studies of exoplanetaryatmospheres is to apply the Boussinesq approximation, which assumes that density variations arenegligible (i.e., incompressibility) except when they are induced by gravity.

A.3. Anelastic Approximation. The anelastic approximation is a slight generalization of theBoussinesq approximation in that we now have the background state of density varying withheight.

A.4. Shallow-Water Approximation. The shallow-water system of equations governs the dy-namics of a single, vertically uniform, hydrostatically balanced layer of constant-density fluid underthe assumption that the structures being modeled have wavelengths long compared to the fluidthickness. By definition, the Boussinesq, anelastic, and shallow-water approximations preclude thetreatment of acoustic waves (and thus shocks).

A.5. Equivalent Barotropic Approximation. The equivalent barotropic approximation (Salbyet al. 1990) is similar to the shallow-water one as the layer thickness is also a variable of thesystem, but it is more general in the sense that it allows for a direct calculation of the temperature.The lower boundary of the system is generalized to an isentropic surface, with constant potentialtemperature, of arbitrary physical shape.

A.6. Hydrostatic Primitive Equations. Originally designed for the study of Earth, there is areduced form of the set of equations in Equations 5, 6, 7, and 8 that is commonly utilized in thestudy of atmospheric dynamics and is known as the primitive equations. It involves three sets ofapproximations.

� Hydrostatic balance: The assumption that the vertical component of the velocity is muchless than the sound speed. It does not mean that the atmosphere is vertically static, i.e., thatthe vertical velocity is zero.

� Shallow atmosphere: Let the radial coordinate be represented by r. The lower boundaryof the model atmosphere is set to be r = R and the vertical spatial coordinate is z. Thus,


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we have r = R + z. The shallow-atmosphere approximation simply asserts that r ≈ R (butretains dr = dz).

� Traditional approximation: The set of governing equations is first written out in sphericalcoordinates. It is then assumed that the Coriolis and curvature terms involving the verticalvelocity vz are subdominant. However, the term involving vz in the D/Dt operator is retained.

DISCLOSURE STATEMENT

The authors are not aware of any affiliations, memberships, funding, or financial holdings thatmight be perceived as affecting the objectivity of this review.

ACKNOWLEDGMENTS

K.H. acknowledges financial, logistical, and secretarial support from the University of Bern andthe University of Zurich, as well as grants from the Swiss National Science Foundation (SNSF)and the Swiss-based MERAC Foundation and participation in the Swiss-wide PlanetS framework(PI: W. Benz). A.P.S. acknowledges support from the NASA Origins program. We thank Juliende Wit, Brice-Olivier Demory, Drake Deming, Jonathan Fortney, Robert Zellem, and DidierQueloz for constructive feedback following their reading of an earlier version of the manuscript.K.H. thanks Sara Seager, Scott Tremaine, Didier Queloz, Willy Benz, and Dick McCray forencouragement.

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EA43-FrontMatter ARI 11 May 2015 13:12

Annual Reviewof Earth andPlanetary Sciences

Volume 43, 2015 Contents

A Conversation with James J. MorganJames J. Morgan and Dianne K. Newman � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1

Global Monsoon Dynamics and Climate ChangeAn Zhisheng, Wu Guoxiong, Li Jianping, Sun Youbin, Liu Yimin, Zhou Weijian,

Cai Yanjun, Duan Anmin, Li Li, Mao Jiangyu, Cheng Hai, Shi Zhengguo,Tan Liangcheng, Yan Hong, Ao Hong, Chang Hong, and Feng Juan � � � � � � � � � � � � � � � � � �29

Conservation Paleobiology: Leveraging Knowledge of the Pastto Inform Conservation and RestorationGregory P. Dietl, Susan M. Kidwell, Mark Brenner, David A. Burney,

Karl W. Flessa, Stephen T. Jackson, and Paul L. Koch � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �79

Jadeitites and Plate TectonicsGeorge E. Harlow, Tatsuki Tsujimori, and Sorena S. Sorensen � � � � � � � � � � � � � � � � � � � � � � � � � � 105

Macroevolutionary History of the Planktic ForaminiferaAndrew J. Fraass, D. Clay Kelly, and Shanan E. Peters � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 139

Continental Lower CrustBradley R. Hacker, Peter B. Kelemen, and Mark D. Behn � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 167

Oceanic Forcing of Ice-Sheet Retreat: West Antarctica and MoreRichard B. Alley, Sridhar Anandakrishnan, Knut Christianson, Huw J. Horgan,

Atsu Muto, Byron R. Parizek, David Pollard, and Ryan T. Walker � � � � � � � � � � � � � � � � � 207

From Geodetic Imaging of Seismic and Aseismic Fault Slipto Dynamic Modeling of the Seismic CycleJean-Philippe Avouac � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 233

The Pyrogenic Carbon CycleMichael I. Bird, Jonathan G. Wynn, Gustavo Saiz, Christopher M. Wurster,

and Anna McBeath � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 273

The Architecture, Chemistry, and Evolution of ContinentalMagmatic ArcsMihai N. Ducea, Jason B. Saleeby, and George Bergantz � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 299

Paleosols as Indicators of Paleoenvironment and PaleoclimateNeil J. Tabor and Timothy S. Myers � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 333

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Role of Arc Processes in the Formation of Continental CrustOliver Jagoutz and Peter B. Kelemen � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 363

Environment and Climate of Early Human EvolutionNaomi E. Levin � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 405

Magma FragmentationHelge M. Gonnermann � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 431

Atmospheric Escape from Solar System TerrestrialPlanets and ExoplanetsFeng Tian � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 459

A Tale of Amalgamation of Three Permo-Triassic Collage Systems inCentral Asia: Oroclines, Sutures, and Terminal AccretionWenjiao Xiao, Brian F. Windley, Shu Sun, Jiliang Li, Baochun Huang,

Chunming Han, Chao Yuan, Min Sun, and Hanlin Chen � � � � � � � � � � � � � � � � � � � � � � � � � � � � 477

Atmospheric Dynamics of Hot ExoplanetsKevin Heng and Adam P. Showman � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 509

Transient Creep and Strain Energy Dissipation: An ExperimentalPerspectiveUlrich Faul and Ian Jackson � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 541

Rapid Plate Motion Variations Through Geological Time:Observations Serving Geodynamic InterpretationGiampiero Iaffaldano and Hans-Peter Bunge � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 571

Rethinking the Ancient Sulfur CycleDavid A. Fike, Alexander S. Bradley, and Catherine V. Rose � � � � � � � � � � � � � � � � � � � � � � � � � � � � 593

Indexes

Cumulative Index of Contributing Authors, Volumes 34–43 � � � � � � � � � � � � � � � � � � � � � � � � � � � 623

Cumulative Index of Article Titles, Volumes 34–43 � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 628

Errata

An online log of corrections to Annual Review of Earth and Planetary Sciences articlesmay be found at http://www.annualreviews.org/errata/earth

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