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SPECIAL FEATURE: PERSPECTIVE PERSPECTIVE SPECIAL FEATURE: Spectra as windows into atmospheres

Adam S. Burrows1 Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544

Edited by Neta A. Bahcall, Princeton University, Princeton, NJ, and approved December 2, 2013 (received for review April 11, 2013)

Understanding a ’s atmosphere is a necessary condition for understanding not only the planet itself, but also its formation, structure, evolution, and habitability. This requirement puts a premium on obtaining spectra and developing credible interpretative tools with which to retrieve vital planetary information. However, for , these twin goals are far from being realized. In this paper, I provide a personal perspective on exoplanet theory and remote sensing via and low-resolution spectroscopy. Although not a review in any sense, this paper highlights the limitations in our knowledge of compositions, thermal profiles, and the effects of stellar irradiation, focusing on, but not restricted to, transiting giant . I suggest that the true function of the recent past of exoplanet atmospheric research has been not to constrain planet properties for all time, but to train a new generation of scientists who, by rapid trial and error, are fast establishing a solid future foundation for a robust science of exoplanets.

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The study of exoplanets has increased expo- by no means commensurate with the effort , and this expectation is in part nentially since 1995, a trend that in the short expended. true. The has been a great, per- term shows no signs of abating. An important aspect of exoplanets that haps necessary, teacher. However, solar- have discovered and provisionally studied makes their characterization an extraordinary system spectra are angularly resolved with a more than a hundred times more planets challenge is that planets are not . They long time baseline and high signal-to-noise. outside the solar system than in it. Statistical have character and greater complexity. A Exoplanets will be point sources for the and orbital distributions of planets across ’s major properties are determined once foreseeable future, and signal-to-noise will their broad mass and radius continuum, in- its mass and are known. Most remain an issue. Perhaps more importantly, cluding terrestrial planets/Earths, “super- stars have atmospheres of atoms and their much solar-system research is conducted by Earths,”“,” and giants, are emerging ions. However, planets have molecular atmos- probes in situ or in close orbit, with an array of instruments for direct determination of, at a rapid pace. pheres with elemental compositions that be- for example, composition, surface morphol- However, understanding its atmosphere is speak their formation, accretional, and (where ogies, B-fields, charged-particle environments, a necessary condition for understanding not apt) geophysical histories. Anisotropic stellar and gravitational moments. Masses and radii only the planet itself, but also its formation, irradiation, clouds, and rotation can break planetary symmetry severely, with the clouds can be exquisitely measured. Orbits are evolution, and (where relevant) habitability, known to standard-setting precision. More- and this goal is far from being realized. themselves introducing multiple degrees of complexity, still unresolved even for our over, when comparing measured with - Despite multiple ground- and space-based retical spectra, the latter are often informed campaigns to characterize their thermal, com- Earth. Molecules have much more com- plicated spectra than atoms, with a hun- by direct compositional knowledge. positional, and circulation patterns (mostly dred to a thousand times more lines, and The exoplanet scientific landscape will be for transiting giant planets), the data gleaned irradiated objects experience complicated more challenging. Exoplanet science is an to date have (with very few exceptions) been photochemistry in their upper reaches. It observational science that must rely on the of marginal utility. The reason is that most astronomical tools of remote spectroscopic took stellar atmospheres ∼100 y to evolve of the data are low-resolution photometry at sensing to infer the physical properties of as a discipline, and it still is challenged by individual planets. Therefore, there is a pre- a few broad bands that retain major system- uncertainties in oscillator strengths and issues mium on obtaining spectra and developing atic uncertainties and large error bars. More- with Boltzmann and thermal equilibrium. interpretative toolkits in the tradition of clas- over, the theory of their atmospheres has yet Furthermore, the spectroscopic databases sical , without the luxury of direct, to converge to a robust and credible inter- for molecules (1), particularly at the high in situ probes. Therefore, although solar- pretive tool. The upshot of imperfect theory temperatures (500–3,500 K) experienced by in support of imprecise data has been system variety will continue to inform exopla- close-in transiting planets, are much more net thinking and motivate many calculations, ambiguity and, at times, dubious retrievals. incomplete than those for atoms, and the To be fair, (i) assets are being used relevant collisional excitation rates are all withgreateffortat(and,sometimes,beyond) but nonexistent. Therefore, it can reasonably Author contributions: A.S.B. wrote the paper. the limits of their designs; and (ii)most be suggested that the necessary theory for The author declares no conflict of interest. planet/star contrast ratios are dauntingly detailed studies of exoplanets is in its This article is a PNAS Direct Submission. small. As a consequence, the number of early infancy. 1E-mail: [email protected].

hard facts obtained over the last 10 y con- One might have thought that the study This article contains supporting information online at www.pnas.org/ cerning exoplanet atmospheres is small and of our solar system had prepared us for lookup/suppl/doi:10.1073/pnas.1304208111/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1304208111 PNAS | September 2, 2014 | vol. 111 | no. 35 | 12601–12609 Downloaded by guest on September 27, 2021 the methodology of solar-system research is As direct imaging techniques mature, more no doubt involved in their formation, their not the best model for conducting exoplanet and smaller directly imaged planets will be elemental abundances should reflect the research. Rather, we must determine the most discovered. However, as articulated earlier, it most abundant elements in the . ‡ robust and informative methods with which is only with well-calibrated spectral meas- For giant exoplanets (like brown dwarfs ), to interpret remote spectra and perform urements at useful resolutions that we can this fact means H2,He,H2O, CO, CH4,NH3, credible spectral retrievals of physical prop- hope to characterize wide-separation exopla- PH3,H2S, Na, and K predominate, with most erties. Therefore, the science of exoplanet net atmospheres robustly. Polarization mea- of the metals sequestered in refractories at characterization is better viewed as a science surements will also have an important diagnos- depths not easily penetrated spectroscopi- of spectral diagnostics, and developing this tic role, particularly for cloudy atmospheres, cally. However, titanium and vanadium art should be our future focus. which at quadrature should be polarized in oxides (TiO and VO), identified in cool-star To date, planets that their stars due the optical to tens of percent. and hot-brown-dwarf atmospheres, have to the chance orientation of their orbit planes Currently, due to their larger size, the been suggested to reside in quantity in the have provided some of the best constraints photometric and spectroscopic techniques upper atmospheres of some hot to on hot exoplanet atmospheres. The variation mentioned above have been applied mostly heat them by absorption in the optical and † of transit depth and, thus, apparent planet to giant exoplanets. Earths are ten times create inversions (37). However, TiO and λ radius (Rp), with ( )isanersatz smaller in radius and one hundred times VO too are likely condensed out (38). Be- spectrum and can be used to infer the smaller in mass. Therefore, while astrono- cause such inversions require an optical ab- presence of chemical species with the cor- mers and theorists hone their skills on the sorber at altitude, what this absorber is, responding cross-sections.Water,sodium, giant exoplanets, fascinating in their own molecule or absorbing haze/cloud, remains and potassium have been unambiguously right, these giants are also serving as stepping a major mystery (39). stones to the smaller planets, in anticipation detected by this means. Approximately 180° For terrestrial planets, the molecules N2, of future routine campaigns to characterize out of phase with the primary transit, when CO2,O2,O3,N2O, and HNO3 must be added them as well. Therefore, I concentrate in this the same planet is eclipsed by its star, the to the list above, with O2,O3 (ozone), and article on the giant population, but all of the difference between the summed of N2O considered , along with the planet and star and that of the star alone basic methodologies used in their study can “chlorophyll red edge” (or its generalization). reveals the planet’s light. This is the second- be translated bodily to the investigation of Many other compounds could be envisioned, “ ” ary eclipse, and such measurements, when smaller exo-Neptunes, terrestrial planets/ and there is added complexity to terrestrial performed as a function of wavelength, ren- Earths, and super-Earths. planet atmospheres due to atmosphere–sur- der the planet’s emission spectrum; measure- A comprehensive review would necessitate face interactions that are so important, for ments taken between primary and secondary morepagesthanthismoresynopticand example, for our Earth. The major con- eclipse provide phase light curves. The sec- summary opinion piece can provide, but, for stituents of atmospheres are likely ondary eclipse planet/star flux ratio is lower those readers interested in an expanded closer to those of giants, but the relative 1=2 than the transit depth by ∼ Rp , where treatment, there are numerous archival papers abundances in any exoplanet atmosphere 2a from which to draw. They cover topics such a is the orbital semimajor axis and R* is the must be considered as yet poorly constrained. stellar radius. This ratio can be a factor of as the general theory of giant exoplanets (6), – Constraining these abundances is a goal, one tenth. atmospheres (7 9), analytic at- however, and one does so by identifying their The transit and radial-velocity techniques mosphere theory (10, 11), opacities (1, 12, unique signatures in measured atmospheric 13), thermochemistry and elemental abun- with which most exoplanets have been found spectra and comparing the observed spec- dances (14–17), the chemistry of hot Earth select for those in tight orbits. Tight orbits at trum in its totality with spectral models. This atmospheres (18), (19–22), giant the distances of stars in the solar neighbor- extraction is “retrieval,” which at a minimum planet models at wide separations (2, 4, 23), hood subtend very small angles (microarcsec- should also yield temperatures and temper- phase functions (24, 25), irradiated atmos- onds to 10s of milliarcseconds), and such ature profiles. Because many parameters pheres and inversions (10), basic transit the- angular proximity to a bright primary star characterize exoplanet atmospheres (e.g., ory (26, 27), transit spectra for Earths (28), mitigates against direct planet detection, im- species, abundances, temperatures, spatial emission spectra of Earth-like planets aging, or characterization. For wider separa- distributions, gravities, haze, and cloud lay- (29), transit spectra of Earth-like planets tions of tens of milliarcseconds to arcseconds, ers), the low information content of few- (30), habitable zones (31), theoretical exo- the resulting contrast ratios for terrestrial and band photometry is not adequate to avoid − − Neptune spectra (32), planet polarization giant planets in the optical of 10 10 − 10 6, the pitfalls of parameter degeneracy. With (20, 33), and clouds and hazes (34–36). In and in the near- to midinfrared of ∼ too few data points in pursuit of too many − − this paper, I refer preferentially to my own 10 8 − 10 4, are quite challenging (2). How- work but suggest that the general conclusions ever, such direct planet imaging is not only arrived at here have broad applicability. ‡ now conceivable, but has been accom- It is likely that the and giant planet mass functions overlap so that a tentative assignment is generally premature. A plished. Four giant exoplanets around HR Compositions and Opacities flexible and open-minded philosophy toward nomenclature is β 8799 (3, 4) and one around Pictoris (5), The variety of compositions found in the then best (8), which more data will progressively guide toward ∼ – a more reasonable classification scheme. I do note, however, that with masses of 5 15Jupitermasses(MJ) gaseous atmospheres of solar-system planets ∼ much recent data for giant planets has been for the close-in and angular separations between 0.3 and suggests that the corresponding variety for transiting subset. For this subset, the fact that these planets are ∼1.5 arcseconds, have recently been found. exoplanet atmospheres must be at least as irradiated, whereas free-floating brown dwarfs are not, signifi- cantly alters the colors and atmospheric characteristics of the broad. Generally lower in temperature than former, when they might otherwise have had spectra like isolated low-mass brown dwarfs (Fig. S1). One can speculate that, barring † 2 stellar atmospheres, planetary atmospheres Equal to the planet/star area ratio, Rp , where R and R are the the irradiation difference, differences in atmospheric abundances, R* p * planet and star radii, respectively—for giants, ∼1%; for Earths, are dominated by molecules. Although frac- rotation rates, and orbital regimes might eventually distinguish ∼0.01%. tionation and differentiation processes are brown dwarfs from giant planets (at least statistically).

12602 | www.pnas.org/cgi/doi/10.1073/pnas.1304208111 Burrows Downloaded by guest on September 27, 2021 A expected to be important in giant exoplanet and has been observed in de- PERSPECTIVE -16 atmospheres (for which we currently have tail, and the central role of silicate and iron SPECIAL FEATURE: the most data) but are also likely important clouds in brown dwarf L dwarfs is reasonably -18 (to varying degrees) in terrestrial, super- inferred by their very red colors. Earth, and exo-Neptune atmospheres. In Fig. These situations are in part informed by -20 1A, we focus on the 1.0- to 5.0-μmrange known thermochemistry. However, water and include the TiO, Na, and K opacities clouds are expected in cold giant exoplanet -22 so prominant in the optical whereas the and brown dwarf atmospheres (24, 41); Na2S plot in Fig. 1B extends to 15 μm to reveal and KCl clouds are thought to reside in late T -24 the behavior in the midinfrared and the sig- dwarf brown dwarfs; an extra absorber in the ∼ μ 1 2 3 4 5 nature feature of CO2 at 15 m. optical and at altitude has been invoked to As indicated in Fig. 1, strong water features explain the inversions and over-hot atmos- B -16 are ubiquitous and are found at (roughly) pheres inferred from the spectra at secondary 0.94, 1.0, 1.2, 1.4, 1.9, 2.6, and 5–7 μm, de- eclipse of some transiting hot Jupiters (39);

-18 fining between them the I, Z, J, H, K,andM a thick haze envelopes the atmosphere of bands through which much of ground-based Saturn’sTitan;andthereisatraceabsorberin

-20 near-infrared astronomy is conducted. Meth- the blue that makes Jupiter and Saturn redder ane has important features at 0.89, 1.0, 1.17, than Neptune or . None of the causa- 1.4, 1.7, 2.2, 3.3, and 7.8 μm. Carbon mon- tive species in these situations is either known, -22 oxide stands out at 2.3 and 4.5 μmwhereas or if known, well-modeled. The case of Jupiter’s CO2 has diagnostic features near 2.1, 4.3, and color is a cautionary tale. The factor of two -24 15 μm. Ammonia has many features, but suppresion in its reflected blue flux could be μ 10 5 01 51 the one at 10.5 m is most noteworthy. due to traces at the part in 10 level of either Molecular (H2) has no permanent polyacetylenes, sulfur or phorphorus com- Fig. 1. (A) The base 10 of the cross-section per dipole but one can be induced by collisions pounds, , or something else (19). Such molecule or atom (in cm2) versus wavelength (in μm) from (“collision-induced absorption”)athigh leverage by a small (and unknown) “actor” μ 0.4to5.0 m for various important species thought to be pressure, and the result is a family of undu- in the interpretation of such a large effect prominent in the atmospheres of exoplanets, in particular lations from ∼2.2 to ∼20 μm that has been should give one pause and emphasizes the giant exoplanets. They are H2 (gray), H2O(blue),CH4 (green), NH3 (orange),TiO(cyan),Na(red;leftmost,withstrongpeak seen in Jupiter, Saturn, and brown dwarfs. potential complexity of the task of exopla- at 0.589 μm), and K (red; rightmost, with strong peak at A central goal of transit, reflection, or emis- net characterization. Photolytic chemistry μ 0.77 m). Other molecules of note (not depicted) are CO2, sion spectroscopy of exoplanets is to identify is likely a cause in ’s atmosphere, as in N2O, O2,andO3. For presentation purposes, these cross- sections have been calculated at 1,500 K and 100 bars. The these species (and perhaps infer their abun- many other contexts, but this explanation latter is far too high a pressure to be representative of dances) by these distinctive features. is small comfort when designing a modeling regions in exoplanet atmospheres that can be probed but effort aimed at anticipating all reasonable was used to more clearly distinguish individual features. Clouds and Hazes possibilities. Importantly, the of the major bands and lines Condensates can form and reside in exopla- Scattering in general is important only in are not significantly temperature- or pressure-dependent al- net atmospheres as clouds or hazes (21, 35) though their strengths are. (B) The same plot, but extended reflection and transit spectra, not in emission, and can have a disproportionate influence on to 16 μm to highlight the midinfrared and to include CO2 and is most prominent for hazes and clouds. (brown) at 296 K and atmospheric pressure (40). Note the spectra. This influence is because, assembled In fact, longward of the UV, clouds are ∼ μ prominent CO2 feature at 15 m. The spectral features for in a grain, such aggregations can respond necessary to give a planet any appreciable each chemical species are crucial discriminating diagnostics coherently to light (depending upon the ∼ for remote exoplanetary sensing and characterization. reflection above 1% (19). Also, in particle size and wavelength). So, very little reflection, as a general rule, cloud or UV/blue areal mass can translate into a large Rayleigh scattering can yield highly polarized quantities, interpretation is thereby severely optical depth, and a trace species can loom fluxes (20). The polarized fraction is higher compromised and error-prone. It is only large. In addition, with a spectrum of particle when the absorption fraction is higher and with good-resolution spectra, with small sizes and enhanced line broadening in the the scattering albedo§ is low, but in this and credible error bars, that we can establish grain, their absorption and scattering cross- case the overall reflected flux is low. This robust conclusions about exoplanets and sections can have a continuum character and reasoning suggests that polarization might in build a solid future for the subject. veil a wide spectral range. The result can be some circumstances be a useful ancillary di- and N2 have weak spectral features. partial (or complete) muting of the gas-phase agnostic of exoplanet atmospheres. Unlike A prominent O2 feature is the Fraunhofer spectral features, making understanding con- for gas species, for many realizations of likely μ A-band at 0.76 m, and the signal feature densates and incorporating their effects into hazes or clouds in exoplanet atmospheres, μ for O3 is the band at 9.6 m. Rayleigh modelsasimportantasitisdifficult.To the scattering albedo can be either high or scattering off molecules roughly follows a properly handle the effects of clouds, we need low, depending upon species and wavelength λ−4 dependence, is proportional to the sum- to know the condensate species, grain size range, and is frequently high. This fact sug- med product of molecular polarizability and and shape distributions, the complex index gests that reflection spectra can be dominated abundance, and is most relevant only in the of refraction, and the spatial distribution in by the effects of such layers and, moreover, blue and UV in reflection. the atmosphere. Such knowledge is gener- that transit spectra can be affected by Fig. 1 depicts example gas-phase absorp- ally in short supply. particulate scattering (as opposed to only tion cross-sections per molecule (or atom) The possibility of water clouds in terrestrial versus wavelength (1, 13) for H2,H2O, CH4, atmospheres is uncontroversial, the presence § CO, Na, K, and CO2 (40). These species are of ammonia clouds in the atmospheres of The ratio of the scattering cross-section to the total cross-section.

Burrows PNAS | September 2, 2014 | vol. 111 | no. 35 | 12603 Downloaded by guest on September 27, 2021 absorption). Clearly, one must be aware of the temperature transitions to lower values. Be teresting species reside in the atmosphere in possible presence of clouds and hazes when that as it may, the terminator is a compli- reasonable abundances, a hot, H2-rich atmo- performing exoplanet spectral retrievals. cated region that introduces special chal- sphere (without a veiling haze/cloud) yields lenges for the theory of transit spectra. the largest, most diagnostic radius variations Transit Spectra { Despite this challenge, a simple analytic with wavelength. Transit spectra are direct probes of atmo- model (8, 43, 46) can be developed that If there are differences in the compositions spheric scale heights and atmospheric abun- captures the basic elements of general transit and scale heights at the east and west limbs dances near the terminator(s). However, if the theory. Integrating along a chord at a given of a planet, such differences are in principle atmosphere is optically thick and overlays impact parameter and assuming an expo- discernible as differences in ingress and egress a rocky core, there is no obvious way to de- nential atmosphere with a pressure scale transit spectra. Although difficult even for a ’ jj termine the core s contribution to the mea- height, H, yields an approximate ampli- giant exoplanet, such measurements might sured radius. Therefore, it is standard practice fication factor for the chord optical depth be doable in the future and could shed light to analyze transit spectra with respect to an (pτchordffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi) over the radial optical depth of on atmospheric dynamics and any pro- arbitrarily determined reference radius, often 2πRp=H, which can be 5 − 10. This fact nounced zonal flow asymmeties. taken to be the inferred discovery radius in the means that the τchord = 2=3 condition that In addition, narrow-band, very-high-reso- optical. When the solid surface of a terrestrial approximately defines the apparent planet lution spectroscopy before and during transit or super-Earth planet is not a priori known, or radius at a given wavelength is pushed to hasgreatpotentialtorevealplanetaryorbital, is inaccessible by measurement, then there will larger impact parameters (radii) and that spin, and wind speeds, as well as composi- be ambiguity with respect to its contribution the fractional transit depth is increased by a tions (compare the measurement of CO lines to the transit depth. Interpretation will not be factor ∝ 2H=Rp. Moreover, it is straight- by ref. 47). Although giant exoplanets are the ambiguous with an airless planet, and is moot forward to show that most studied population to date via multi- foragaseousplanet,butisanissuetoconsider band transit photometry and spectropho- σ when falsifying theory. dRp dln tometry [as opposed to wide single-band ≈ H ; [1] The measured fractional diminution in the dlnλ dlnλ observations à la Kepler (48)], such data stellar light at a given wavelength is the tran- around small M dwarfs for terrestrial planets sit depth (27, 42). The stellar beams pointed where σ is the total species-weighted interac- andsuper-Earths(suchasGJ1214b)(seeref. ’ at the Earth probe the planet satmosphere tion cross-section (the sum of absorption and 43 and references therein) have great promise transversely along a chord perpendicular to scattering). Note that, whereas emission spec- to probe the atmospheres of these smaller, but the impact radius. Therefore, the relevant tra (ignoring reflection) depend upon only likely more numerous, planets. Measuring the optical depth, τ, is not the depth in the radial emission spectra of Earths around solar-like absorption, transit spectra depend upon both direction associated with emission, but much stars will be much more challenging. scattering and absorption processes. In fact, larger. The contribution of the annulus, or Fig. 2 portrays the general character of partial annulus in the case of the ingress or the haze inferred for HD 189733b could be representative theoretical exoplanet transit egress phases, to the blocking of stellar light purely scattering and, as such, would make no spectra from 0.4 to 5.0 μm. The models are −τ is 1 − e times the annular area. The sum contribution to the emission at secondary for the giant WASP-19b and include iso- of such terms over the entire atmosphere eclipse. However, it is likely that any haze thermal atmospheres at T = 2500 K, with and provides the integrated blocking fraction has a nonunity scattering fraction/albedo, in- without a uniform gray haze with an opacity − due to the atmosphere. That this τ is larger troducing flexibility, but also further com- of 0.01 cm2·g 1, a model that attempts to fit than the radial τ allows transit depth to be plexity, into the simultaneous interpretation its IRAC data at secondary eclipse (49) with more sensitive to trace chemical species than of transit and emission spectra. an unknown “extra absorber” at altitude of 2 −1 emission or secondary eclipse spectra and Eq. 1 suggests that significant wavelength constant optical opacity 0.05 cm ·g (from amplifies their effect. This effect may be variations in cross-section, as across an ab- 0.4 to 1.0 μm), and a similar model using TiO particularly relevant of atmospheric hazes sorption band, translate into a change in the as the extra absorber. For clarity, the latter that may be too thin in the radial direction to apparent radius of order H. This fact is the two are shifted arbitrarily from the former affect emission, but are thick along the chord essenceoftheuseoftransitmeasurementsas two. We note that the transit depth is of (43), and may be why Pont et al. (44) see an a function of wavelength to determine com- order ∼2% and that the variation due to the almost featureless transit spectrum for HD positions. Because Rp depends upon the presence of water bands is approximately one 189733b and infer a veiling haze whereas the logarithm of σ,Eq.1 also indicates that the part in a thousand. The depths for other hot associated InfraRed Array Camera (IRAC) dependence upon abundance is logarithmic Jupiters could vary with wavelength by as and Infrared Spectrometer (IRS) data at sec- and, thus, weak. Although it is “easy” to little as a few parts in ten thousand. ondary eclipse clearly reveal water signatures discern a molecular feature, it is not easy with One sees immediately that the extra optical (45). Another reason may be that, because transit spectra to determine its abundance. absorber, whatever its nature, increases the transit spectra probe the terminator, the Note that, because H = kT=μg,alow(high) ratio of the optical to infrared radii, that the transition region between day and night, temperature, high (low) gravity, or high (low) TiO hypothesis can readily be falsified, that a condensate is more likely to form as the mean molecular weight atmosphere will yield the spectral features of (here) water should be weaker (stronger) indications of composition. readily detected,** that the radius variations in the midinfrared can be of larger amplitude, { Therefore, as long as spectroscopically in- Often referred to imprecisely as “transmission spectra.” What one and that even low-opacity hazes can mute is actually measuring is the transit depth, which reflects what is not transmitted. In addition, the implication of the term “trans- jj mission” is that we are imaging the planet’s limb region and H = kT=μg ,whereg is the gravity, μ is the mean molecular measuring the variation in τ or e−τ. However, we are actually weight, T is an average atmospheric temperature, and k is **In fact, water has already been detected in several giant planet probing 1 − e−τ , its complement. Boltzmann’s constant. atmospheres via transit spectra (50).

12604 | www.pnas.org/cgi/doi/10.1073/pnas.1304208111 Burrows Downloaded by guest on September 27, 2021 A reprocessed stellar light (52, 53). Stellar irra- planets. (iv) The so-called equilibrium tem- PERSPECTIVE SPECIAL FEATURE: 0.022 diation and zonal atmospheric winds and perature, Teq, is defined as the surface black- dynamics break the simple spherical sym- body temperature for which the incident metry, so that 3D models would seem most stellar flux is balanced and is given by 0.021 appropriate. However, such models have yet   to prove themselves, and simpler 1D hemi- 1=2 R p 1=4 T = T p ðf ð1 − A ÞÞ ; [2] sphere-averaged models have been used, eq a B 0.02 however profitably, to compare with data. Issues with such a prescription include what where Tp is the stellar effective temperature, f average flux to use to derive a representative †† 0.019 0.5 1 1.5 dayside temperature/pressure (T/P) profile, is the heat redistribution factor , and AB is how to incorporate longitudinal and lat- the Bond albedo (8, 19). While providing a B itudinal surface flows into the energy budget, measure of the mean temperature achieved in 0.023 nonequilibrium chemistry (54), photochem- a planet’s atmosphere, assuming this can be – istry, and day night differences when in- used as the inner boundary condition, Teff has 0.022 terested in total phase curves (53, 55, 56). introduced quite a lot of confusion. Very dif- Nevertheless, such simple models are still ferent T/P profiles can yield the same total 0.021 commensurate with the information con- flux but very different flux spectra. Fig. S1 shows tent of the extant observations. two models with the same emergent flux, and, 0.02 The various quantities and topics that in- fluence secondary eclipse spectra and have thus, Teq. One consistently incorporates stellar irradiation whereas the other puts a flux with 0.019 exercised the community include (i)the 1 2 3 4 5 = presence or absence of an extra absorber of Teff Teq at the base of the atmosphere. Both are in radiative and chemical equilibrium. As Fig. 2. (A) Model fractional transit depths versus currently unknown origin in the upper at- wavelength (in μm) between 0.4 and 1.8 μm for a WASP- mosphere that could heat those regions, at Fig. S1 demonstrates, despite the fact that the 19b–like planet. The blue curve is a dayside model with times producing thermal inversions over a emergent fluxes are the same, the correspond- TiO in its atmosphere and a redistribution parameter, Pn, restricted pressure range (39, 57); (ii)the ing T/P profiles are hugely different and the of 0.3 (39), that is irradiated by a stellar model of WASP- temperatures and temperature profiles of 19 at the distance of WASP-19b. The black curve (SE Fit) is flux at a given wavelength can be off = “ ” the atmosphere; (iii) the phase shifts from a dayside model with a Pn 0.3 and an extra absorber by factors of 2−4! Irradiated atmospheres are 2· −1 at altitude with an opacity of 0.05 cm g from 0.4 to the orbital ephemeris of the light curves at different from isolated atmospheres. 1.0 μm, configured to fit the measured Spitzer/IRAC various wavelengths and spectral bands due Lastly, (v)ifanatmosphereisinfactiso- secondary eclipse data. The red and green models have to zonal winds that redistribute heat (58); thermal, there must be an extra absorber in isothermal atmospheres at 2,500 K, with the flatter green (iv) the compositions and elemental abun- model having a uniform haze with an opacity of 0.01 the optical at altitude. Even under irradiation, 2· −1 μ dances of the atmospheres; (v) the presence cm g .(B) The same, but extended to 5.0 m. In all the temperature gradient must otherwise be models shown, water features (Fig. 1) are the most of hazes and clouds; (vi) the day/night flux prominent whereas TiO features are in evidence in the contrast; (vii) Doppler signatures of atmo- negative from base to height, with charac- ∼ − TiO model and the effect of a veiling haze is manifest in spheric motions; (viii) reflection albedos (59); teristic temperature changes of 500 1,500 K that model. Note that, for this exoplanet, the magnitude for close-in giant exoplanets. Therefore, of the variation with wavelength is generally less than or and (ix) the presence and role of evaporative equal to a part in a thousand. planetary mass loss. I mention these chal- inferences of isothermality are not as content- lenges only to indicate the range of complex neutralasisoftenimplied(60). problems to be addressed but will focus in One can derive an average temperature these variations substantially. The diagnostic this paper on only the simplest of approaches profile in a radiative-equilibrium exoplanet potential of transit spectra is manifest in plots taken to extract information from secondary- atmosphere under stellar irradiation by gen- such as these. It is equally clear that the in- eclipse data. eralizing the classical Milne atmosphere (10, terpretation of but a few photometric points A few conceptual points are worth noting 11). One obtains: with significant error bars are ambiguous. in passing: (i) An atmosphere calculation   Good spectra are the key. with external incident flux will automatically 3 κ 1 κ T4 = T4 J τ + pffiffiffi + J WT4 ; [3] generate a reflection albedo and is not extra eff κ R κ p Secondary Eclipse 4 B 3 B . (ii) For a given elemental ratio set, For a circular orbit, when 180° out of phase the metallicity dependence of the emergent ð = Þ2 τ with the transit, the planet is occulted by the where W is the dilution factor Rp a , R is spectrum is quite weak. Most relevant species κ star and is in secondary eclipse. During the (such as water) have one “metal” and in- the Rossleand depth, J is the photon energy- κ eclipse, the summed light of the planet and cident and emergent integral fluxes must al- density weighted opacity, B is the corre- star being monitored shifts to that of the star most balance. (iii) The difference between sponding local black-body-weighted opacity, ’ alone and by the difference the planet s incident and emergent total fluxes is due to and we have used the approxima- emissions are determined. The Spitzer space the true effective temperature (Teff ), which, tion for the angular moments. For an isolated κ telescope (51) has been particularly pro- for giant exoplanets of gigayear ages, ranges atmosphere, J is close to one, but, for an κB ductive in this mode, providing near- and from 50 to 500 K and results in a very small irradiated atmosphere, κ and κ can differ ap- ∼ J B midinfrared photometric points for 30 contribution to the emergent flux for a preciably. The former at altitude is dominated nearby transiting planets (mostly giants). For strongly irradiated planet. Teff is important close-in planets, for which the transit proba- only when the stellar irradiation flux is small, †† bility is largest, the planet is emitting mostly and this flux is small only for wide-separation f = 1/4 for isotropic models.

Burrows PNAS | September 2, 2014 | vol. 111 | no. 35 | 12605 Downloaded by guest on September 27, 2021 A These profiles are provided to communicate Although the interpretative and diagnostic -6 the range of atmospheric temperatures en- promise of good spectra is suggested in Fig. countered for hot Jupiters and the matching -4 3B, the current reality is depicted in Fig. 4. to adiabats at depth above ∼100 bars. The Here, I plot representative measured planet/

-2 atmospheres of close-in giants can vary in star flux ratios for 17 transiting giant exo- temperature, depending upon W and Tp,by planets. Most of the data are Spitzer IRAC 0 ∼1,000−2,000 K. Importantly, the difference photometry in four bands whereas some of in upper-atmosphere temperatures between the data are from the ground and the Hubble 2 “inverted” and noninverted situations can be . For HD 189733b, we have ∼ − ∼ – μ 4 1,000 1,500 K, a huge difference that can Spitzer/IRS spectra from 5 15 maswell 1000 2000 3000 Temperature (in K) translate into flux spectrum differences of (45). To keep the plots from being any more B factors of ∼2−4 for ostensibly the same ob- cluttered, error bars for only a few measure-

0.006 ject.ThisfactisdepictedinFig.3B,which ments are shown. The quoted 1 − σ error provides the corresponding planet/star flux bars generally range from ∼10–30%. In an ratios versus wavelength. Among this set of attempt to divide out universal expectations 0.004 exoplanets, the theoretical flux ratios vary at and to focus on what may distinguish one a given wavelength by an order of magnitude. planet from another, I have normalized the Moreover, as the comparison between (i)the planet/star flux ratio with the corresponding 0.002 model for WASP-12b with solar abundances, black-body value.§§ chemical equilibrium, and an extra upper First, we see from Fig. 4 that the normal-

0 atmosphere absorber in the optical (upper ized ratio is rather flat over a broad range of 02468 10 black) and (ii) the model for WASP-12b with wavelengths and close to one, perhaps a bit Fig. 3. (A) Model temperature-pressure curves for a enhanced CH4 and CO, depleted H2O, and higher. However, the mean level could just collection of transiting giant exoplanets. These models no inversion (gray) attest, midinfrared reflect the crudeness of the Tp used for the were constructed in an attempt to fit respective Spitzer/ planetary spectra can vary significantly for comparison. We see undulations, but they IRAC data at secondary eclipse and demonstrate the span thesamestellarirradiationregimeandgrav- have little information content, aside from of temperatures expected in giant exoplanet atmos- pheres. This span reflects, among other things, the range ity. Fig. 3B, together with Fig. 1, demonstrates the possible suggestion of enhanced or re- of substellar fluxes at these given planets, as well as the the great diagnostic potential of multifre- duced flux in particular broad spectral extra heating of the upper atmosphere by an absorber in quency spectra to extract compositions. One regions. The IRS data near 6.2 μmforHD the optical that, at times, has been invoked to explain can also determine the presence or absence Spitzer/IRAC data, in particular at 5.8 μm. Note that the 189733b do imply the presence of water, but XO-1b model is the black line at the left whereas the of extra heating by enhanced absorption what is the feature near 12.5 μm? There is black line at the right is for WASP-12b with an inversion of stellar light that leads to inversions, but a systematic increase in the ratios to shorter κ = : 2· −1 = ( 0 1 cm g ), with Pn 0.1, and in chemical and also hotter upper atmospheres and ele- wavelengths, and this increase is probably radiative equilibrium at solar elemental abundances. The vated fluxes of features formed in the heated real. As Fig. S1 implies, fluxes from irradi- gray curve is also a model for WASP-12b, but without an ∼ − μ inversion, depleted in water by a factor of 100, and en- zone. The pronounced bump at 4.5 5.5 m ated planets are expected to be mostly in the hanced in CH4 and CO to uniform fractional abundances on the inverted spectrum for WASP-12b is near infrared. × −4 of 2 10 . Each model was used to address the WASP- due to water in emission and the fact that The comparison of Figs. 3B and 4 starkly 12b IRAC and near-infrared secondary eclipse data. (B) this band forms where the corresponding The planet/star flux ratios from 0.4 to 10 μm for the emphasizes that we have a long way to go models in A.The“predicted” range in values, even for temperature profile has a positive (inverted) ‡‡ before comparative exoplanetology becomes a class of solely giants, is very wide. Note also that slope. a richly diagnostic science. At times, data comparison between the two WASP-12b models (black Although inversions have been inferred such as are depicted in Fig. 4 have been used and gray) is a cautionary tale against relying too heavily from enhanced Spitzer IRAC band fluxes (in to find temperatures, compositions, albedos, on error-prone photometry to characterize exoplanet μ atmospheres, and a clarion call for accurate spectra over particular at 5.8 m), the nature of the ab- inversions, carbon-to-oxygen ratios (91), me- a wide wavelength range. sorber is still unknown. It is suggested that tallicities, and day–night heat redistribution TiO could do it, but there are good reasons to factors, etc. Clearly, these data, and the still believe this compound would be rained out by the stellar spectrum whereas the latter re- primitive state of exoplanet atmosphere the- to depth by various cold traps (38). There flects the local atmospheric black-body spectral ory, do not justify attempts to constrain such may be photochemical hazes with the right distribution. If this difference is an interesting quantities simultaneously, or perhaps at all. optical absorbing properties, but this possi- function of altitude, an inversion can result Until high-quality transit and emission spec- bility has not been demonstrated. Still, it is tra across a wide range of wavelengths are (10).WenotethatT is generally small for eff tantalizing to hypothesize that the haze in- routinely available, only the most primitive close-in hot Jupiters. In this case, the temper- ferred by Pont et al. (44) in the atmosphere and conservative conclusions will be justi- atures at depth are determined by the second of HD 189733b and that inferred by Deming fied. I reiterate that the data in Fig. 4 are for term, which yields something like Eq. 2.In et al. (50) in the atmosphere of HD 209458b giant exoplanets. Smaller Neptunes, super- reality, gas giants are convective at high optical might in some way be implicated, or at least Earths, and terrestrial planets around similar ∼ – depths ( 100 1,000) and the T/P profile be- be of similar composition. stars will be much more difficult targets. comes an adiabat. Otherwise, it would be flat. Representative theoretical average day-side   ‡‡ hc ’ f bb 2 λkT Emission features won t always be seen when the extra absorber §§ p ðλÞ = Rp e * − 1 Dividing by the factor bb hc , where Tp has temperature-pressure profiles for a subset of qffiffiffiffif R* is active—this circumstance depends on where in the atmo- * eλkTp − 1 been set equal to T R* . transiting gas giants are given in Fig. 3A. sphere the band is “formed.” * 2a

12606 | www.pnas.org/cgi/doi/10.1073/pnas.1304208111 Burrows Downloaded by guest on September 27, 2021 3 A perfectly corrected for, there frequently is thermally; or (v) fitting photometric points PERSPECTIVE SPECIAL FEATURE: no absolute calibration across disparate with Teq and a Bond albedo. Such approaches 2.5 wavelength regions, stellar spots are diffi- might seem right-sized to the data at hand cult to account for, and corrections for the but are likely to generate an erroneous sense ’ 2 Earth s atmosphere for ground-based ob- of confidence in the conclusions derived. For servations have been problematic. Data for example, it is long been known that small

1.5 the same object at the same wavelength, but errors in ΔT can translate into large spec- taken by different teams, have varied by up tral flux errors, even if the total reprocessed ∼ 1 to factors of 2, and such a factor can com- emitted flux is ostensibly addressed. pletely alter the conclusions drawn about The Future 510152025abundances, C/O ratios, inversions, etc. Given this list of limitations, one should be Therefore, I suggest that once high-quality, 3 B highly skeptical of extraordinary claims based well-calibrated, stable spectra across a broad on imperfect data with low intrinsic in- range of wavelengths from the optical to the formation content. Many published model midinfrared are finally available, many con- 2 fits have been highly underconstrained. This clusions reached recently about exoplanet observation is all the more important given atmospheres will be overturned. The current the gross imperfections in current exoplanet interpretations and theories are just not ro-

1 atmosphere theory. With a few photometric bust enough to survive intact into the future. points, one cannot simultaneously determine However, despite the generally caution- with any confidence, or credibly incorporate arytoneofmuchofthispaper,Iseean into the fitting procedures, chemical and el- exciting future. The past ∼20 y has been 0 2 4 6 8 emental abundances, wind dynamics, longi- but a training period for a new generation tudinal heat redistribution, thermal profiles, of exoplanet scientists, forged by trial and Fig. 4. (A) Planet/star flux ratio data points at second- albedos, the potential influence of hazes and ary eclipse for eight giant planets (WASP-19b, HD error and educated in the new questions 149026b, HAT-P-7b, HAT-P-2b, CoRoT-2b, CoRoT-1b, HD clouds, nonequilibrium chemistry and pho- posed by exoplanets. Its growing member- 189733b, and HD 209458b), normalized to the corre- tochemistry, and magnetic fields. Further- ship is testing its tools—new technologies, sponding ratio if both star and planet were black bodies more, the opacities for many chemical species concepts, theories, and techniques—that at the corresponding measured stellar T = T and zero- eff *qffiffiffiffi are only imperfectly known, convection at will serve to establish a solid foundation for albedo equilibrium temperature, T = T R* , re- eq * 2a depth is frequently handled with a mixing- a true science of planets not tethered to the spectively. The lines connect points for the same object. length approach, and emissions over a plan- solar system. Informed by the latter, but op- Most of the data are Spitzer/IRAC points, but points at etary hemisphere are never calculated with shorter wavelengths, where available, are also included. timized to address its unique challenges as a correct, multidimensional radiative transfer. For HD 209458b and HD 189733b, points at 16 and/or remote-sensing science, comparative plan- 24 μm are also given, along with points (unconnected Moreover, most of the current generation of etology’s youth is rapidly maturing. and for comparison) derived from other reductions. To 3D general circulation models (GCMs) filter avoid further clutter, quoted error bars are given only for The near- and midterm future of exopla- out sound waves but derive transonic flow net atmosphere characterization will include the IRS spectrometer data for HD 189733b and the speeds with Mach numbers at and above one Spitzer data for HD 209458b. (B) The same as in A, but the James Webb Space Telescope (JWST) (92, without a means to handle shock waves. for XO-3b, XO-2b, XO-1b, WASP-18b, WASP-12b, TrES-4, 93), ground-based Extremely-Large/Giant- TrES-3, TrES-2, and TrES-1. Error bars for only WASP-12b Many of these codes have also inherited from Segmented- (ELTs/GSMTs) are given. The normalization provided helps to rationalize Earth GCM practice various ad hoc “Ray- (94), and perhaps dedicated Explorer, the interpretation potential of such photometric and low- leigh drag” and hyperdiffusivity terms with resolution data and to facilitate planet–planet compari- M-Class (e.g., EchO) (95), or Probe-Class arbitrary coefficients calibrated on the Earth son. The data were taken from refs. 45, 49, 57, 60, and space missions. The continued creative use of 61–90. that compromise the wind dynamics on strongly irradiated gas giants, even if mag- existing ground-based telescopes is assured, and new high-contrast coronagraphic im- Systematic Uncertainties in the Data and netic torques are subdominant. Importantly, GCMs were configured to look at winds and aging programs now coming on line [such Theory pressures, not spectral emissions, highlighting as (96) and SPHERE Theorists and observers alike, anxious to the mismatch between the traditional goals of (97)] show great promise. Importantly, there extract all of the conclusions they can from planetary and Earth scientists and exoplanet is the exciting possibility of putting a co- this first generation of measurements of exo- astronomers. ronagraph on Wide-Field Infrared Survey planet atmospheres, have tended to over- Attimes,basicatmospherepracticehas Telescope (WFIRST)/ Focused interpret them. A comparison between been shunted aside in attempts to retrieve Telescope Assets (AFTA) (98). In the farther Figs. 3B and 4 is a sober indication of the thermal and compositional information from future, once a cost-effective plan can be current limitations of the science. The tele- a few (although precious) data points. Exam- articulated, a major dedicated space mission scopes being used were not designed with ples are (i) using unphysical, parametrized of exoplanetary atmosphere characterization, exoplanets in mind. For example, Spitzer T/P profiles and arbitrary compositions, while such as was envisioned with the Terrestrial was designed for photometry at the ∼1% not addressing local energy and chemical Planet Finder (TPF) and , should level, yet it is being used (however heroically) balance; (ii) using 1D averaged models for be possible. Currently, giant planets and ∼ − to obtain numbers at the 0.1 0.01% level. what is a 3D planet; (iii) using Teq as if it Neptunes pose the most realistic targets, Generally, the space-based and ground-based were a real physical quantity of relevance to but terrestrial planets and the possibility data have limited signal-to-noise, the sys- spectra; (iv) defining and deriving a reflection of discerning signatures of are major tematic effects/errors are variously and im- albedo when the planet is mostly emitting goals of many. Soon, the spectra of terrestrial

Burrows PNAS | September 2, 2014 | vol. 111 | no. 35 | 12607 Downloaded by guest on September 27, 2021 planet atmospheres around small M-dwarf also clear that large, expensive missions are scientific return and does not presume (or stars may be within reach. counterproductive until they are demanded proscribe) a specific future. The clear goal is Given this landscape, it is clear that, for the by the science, in fact until the science indi- to understand in rich detail the planets that field to remain vibrant and grow, it needs cates that further progress demands them. we now know exist in profusion in the a heterogeneous and balanced program of Precursor technologies for such missions and universe. One is only left to ask: Are we ground-based and space-based facilities and should certainly be pursued and allowed to ready to assume the challenge? programs. If anything has been demonstrated compete. However, overlarge and expensive by the first ∼20 y of exoplanet research, it is missions without the requisite credibility and ACKNOWLEDGMENTS. A diverse suite of exoplanetary spectral and evolutionary models for a range of masses that some of the best techniques for studying technological heritage in place can fatally and compositions is available at www.astro.princeton. them are unanticipated. The transit tech- squeeze the smaller programs that have edu/∼burrows and from the author upon request. The author acknowledges support in part under National nique for close-in planets has been a game proven so fruitful. Implied is an international Aeronautics and Space Administration/Astrophysics Theory changer but was not envisioned in previous roadmap crafted for exoplanet’snext∼20 y Program Grant NNX07AG80G, planning documents. High-contrast imaging, This roadmap’s guiding principle should be Grants HST-GO-12181.04-A, HST-GO-12314.03-A, HST- GO-12473.06-A, and HST-GO-12550.02, and Jet Propul- only now coming of age, was to inaugurate a balanced approach of small, medium, and sion Laboratory/Spitzer Agreements 1417122, 1348668, the era of atmospheric characterization. It is large initiatives that encourages flexibility and 1371432, 1377197, and 1439064.

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