Spectra as Windows into Exoplanet Atmospheres
aa r X i v : . [ a s t r o - ph . E P ] D ec Spectra as Windows into ExoplanetAtmospheres
Adam Burrows ∗ ∗ Princeton University, Princeton, NJ 08544 USAAccepted to Proceedings of the National Academy of Sciences
Understanding a planet’s atmosphere is a necessary conditionfor understanding not only the planet itself, but also its forma-tion, structure, evolution, and habitability, This puts a premiumon obtaining spectra, and developing credible interpretative toolswith which to retrieve vital planetary information. However, forexoplanets these twin goals are far from being realized. In thispaper, I provide a personal perspective on exoplanet theory andremote sensing via photometry and low-resolution spectroscopy.Though not a review in any sense, this paper highlights the lim-itations in our knowledge of compositions, thermal profiles, andthe effects of stellar irradiation, focussing on, but not restrictedto, transiting giant planets. I suggest that the true function of therecent past of exoplanet atmospheric research has been not toconstrain planet properties for all time, but to train a new genera-tion of scientists that, by rapid trial and error, is fast establishinga solid future foundation for a robust science of exoplanets. exoplanets | atmospheres | planetary science | spectroscopy | charac-terization Introduction
The study of exoplanets has exponentiated since 1995, a trend thatin the short term shows no signs of abating. Astronomers have dis-covered and provisionally studied more than a hundred times moreplanets outside the solar system than in it. Statistical and orbital dis-tributions of planets across their broad mass and radius continuum,including terrestrial planets/Earths, “super-Earths," “Neptunes," andgiants, are emerging at a rapid pace.However, understanding its atmosphere is a necessary conditionfor understanding not only the planet itself, but also its formation,evolution, and (where relevant) habitability, and this goal is far frombeing realized. Despite multiple ground- and space-based campaignsto characterize their thermal, compositional, and circulation patterns(mostly for transiting giant planets), the data gleaned to date have(with very few exceptions) been of marginal utility. The reason forthis is that most of the data are low-resolution photometry at a fewbroad bands that retain major systematic uncertainties and large errorbars. Moreover, the theory of their atmospheres has yet to convergeto a robust and credible interpretive tool. The upshot of imperfecttheory in support of imprecise data has been ambiguity and, at times,dubious retrievals. To be fair, i) telescope assets are being employedwith great effort at (and, sometimes, beyond) the limits of their de-signs; and ii) most planet/star contrast ratios are dauntingly small.As a consequence, the number of hard facts obtained over the last tenyears concerning exoplanet atmospheres is small and by no meanscommensurate with the effort expended.An important aspect of exoplanets that makes their characteriza-tion an extraordinary challenge is that planets are not stars. They havecharacter and greater complexity. A star’s major properties are deter-mined once its mass and metallicity are known. Most stars have at-mospheres of atoms and their ions. However, planets have molecularatmospheres with elemental compositions that bespeak their forma-tion, accretional, and (where apt) geophysical histories. Anisotropicstellar irradiation, clouds, and rotation can break planetary symmetryseverely, with the clouds themselves introducing multiple degrees ofcomplexity, still unresolved even for our Earth. Molecules have muchmore complicated spectra than atoms, with a hundred to a thousand of times more lines, and irradiated objects experience complicated pho-tochemistry in their upper reaches. It took stellar atmospheres ∼ and,hence apparent planet radius (R p ), with wavelength ( λ ) is an ersatz Reserved for Publication Footnotes equal to the planet/star area ratio, (cid:16) RpR ∗ (cid:17) , where R p and R ∗ are the planet and star radii,respectively − for giants, ∼ ∼ Issue Date
Volume Issue Number 1 – pectrum and can be used to infer the presence of chemical specieswith the corresponding cross-sections. Water, sodium, and potassiumhave been unambiguously detected by this means. Approximately ◦ out of phase with the primary transit, when the same planet iseclipsed by its star, the difference between the summed light of planetand star and that of the star alone reveals the planet’s light. Thisis the secondary eclipse, and such measurements, when performedas a function of wavelength, render the planet’s emission spectrum;measurements taken between primary and secondary eclipse providephase light curves. The secondary eclipse planet/star flux ratio is Fig. 1.
Top:
The figure on the top depicts the logarithm base 10 of the crosssection per molecule or atom (in cm ) versus wavelength (in microns) from 0.4to 5.0 µ m for various important species thought to be prominent in the atmo-spheres of exoplanets, in particular giant exoplanets. They are H (gray), H O(blue), CH (green), NH (orange), TiO (cyan), Na (red; leftmost, with strongpeak at 0.589 µ m), and K (red; rightmost, with strong peak at 0.77 µ m). Othermolecules of note (not depicted) are CO , N O, O , and O . For presentationpurposes, these cross sections have been calculated at 1500 K and 100 bars.The latter is far too high a pressure to be representative of regions in exoplanetatmospheres that can be probed, but was employed to more clearly distinguishindividual features. Importantly, the wavelengths of the major bands and lines arenot significantly temperature- or pressure-dependent, though their strengths are. Bottom:
The figure on the bottom is the same plot, but extended to 16 µ m tohighlight the mid-infrared and to include CO (brown) at 296 K and atmosphericpressure [40]. Note the prominent CO feature at ∼ µ m. The spectral fea-tures for each chemical species are crucial discriminating diagnostics for remoteexoplanetary sensing and characterization. See text for a discussion. lower than the transit depth by approximately ∼ (cid:0) R ∗ a (cid:1) / , where a isthe orbital semi-major axis and R ∗ is the stellar radius. This can be afactor of one tenth.The transit and radial-velocity techniques with which most exo-planets have been found select for those in tight orbits. Tight orbitsat the distances of stars in the solar neighborhood subtend very smallangles (micro-arseconds to 10’s of milli-arcseconds), and such angu-lar proximity to a bright primary star mitigates against direct planetdetection, imaging, or characterization. For wider separations of tensof milliarseconds to arcseconds, the resulting contrast ratios for ter-restrial and giant planets in the optical of − − − , and in thenear- to mid-infrared of ∼ − − − , are quite challenging[2].However, such direct planet imaging is not only now conceivable,but has been accomplished. Four giant exoplanets around HR 8799[3, 4] and one around β Pictoris [5], with masses of ∼ −
15 Jupitermasses (M J ) and angular separations between ∼ ∼ Compositions and Opacities
The variety of compositions found in the gaseous atmospheres ofsolar-system planets suggests that that for exoplanet atmospheresmust be at least as broad. Generally lower in temperature than stel-lar atmospheres, planetary atmospheres are dominated by molecules. It is likely that the brown dwarf and giant planet mass functions overlap, so that a tentativeassignment is generally premature. A flexible and open-minded philosophy towards nomen-clature is then best[8], which more data will progressively guide towards a more reasonableclassification scheme. I do note, however, that much recent data for giant planets has been forthe close-in transiting subset. For these, the fact that these are irradiated, while free-floatingbrown dwarfs are not, significantly alters the colors and atmospheric characteristics of theformer, when they might otherwise have had spectra like isolated low-mass brown dwarfs(see figures in the Supplement). One can speculate that, barring the irradiation difference,differences in atmospheric abundances, rotation rates, and orbital regimes might eventuallydistinguish brown dwarfs from giant planets (at least statistically). hough fractionation and differentiation processes are no doubt in-volved in their formation, their elemental abundances should reflectthe most abundant elements in the Universe. For giant exoplanets(like brown dwarfs ), this means H , He, H O, CO, CH , NH , PH ,H S, Na, K predominate, with most of the metals sequestered in re-fractories at depths not easily penetrated spectroscopically. However,titanium and vanadium oxides (TiO and VO), identified in cool-starand hot-brown-dwarf atmospheres, have been suggested to reside inquantity in the upper atmospheres of some hot Jupiters to heat themby absorption in the optical and create inversions[37]. However, TiOand VO too are likely condensed out [38]. Since such inversions re-quire an optical absorber at altitude, what this absorber is, moleculeor absorbing haze/cloud, remains a major mystery[39].For terrestrial planets, the molecules N , CO , O , O , N O,and HNO must be added to the list above, with O , O (ozone), andN O considered biosignatures, along with the “chlorophyll red edge"(or its generalization). Many other compounds could be envisioned,and there is added complexity to terrestrial planet atmospheres dueto atmosphere-surface interactions that are so important, for exam-ple, for our Earth. The major constituents of “Neptune" atmospheresare likely closer to those of giants, but the relative abundances in anyexoplanet atmosphere must be considered as yet poorly constrained.Constraining these abundances is a goal, however, and one does soby identifying their unique signatures in measured atmospheric spec-tra and comparing the observed spectrum in its totality with spectralmodels. This extraction is “retrieval," which at a minimum shouldalso yield temperatures and temperature profiles. Since many param-eters characterize exoplanet atmospheres (e.g., species, abundances,temperatures, spatial distributions, gravities, haze and cloud layers),the low information content of few-band photometry is not adequateto avoid the pitfalls of parameter degeneracy. This, however, withvery few exceptions, is the current situation in exoplanet research.With too few data points in pursuit of too many quantities, interpreta-tion is thereby severely compromised and error-prone. It is only withgood-resolution spectra, with small and credible error bars, that wecan establish robust conclusions about exoplanets and build a solidfuture for the subject. This is a challenge, but a necessity.Helium and N have weak spectral features. A prominent O fea-ture is the Fraunhofer A-band at 0.76 µ m, and the signal feature forO is the band at 9.6 µ m. Rayleigh scattering off molecules roughlyfollows a λ − dependence, is proportional to the summed product ofmolecular polarizability and abundance, and is most relevant only inthe blue and UV in reflection.Figure 1 depicts example gas-phase absorption cross sections permolecule (or atom) versus wavelength [13, 1] for H , H O, CH , CO,Na, K, and CO [40]. These species are expected to be important ingiant exoplanet atmospheres (for which we currently have the mostdata), but are also likely important (to varying degrees) in terrestrial,super-Earth, and exo-Neptune atmospheres. In the top plot, we focuson the 1.0 − µ m range and include the TiO, Na, and K opacitiesso prominant in the optical, while the bottom plot extends to 15 µ mto reveal the behavior in the mid-infrared and the signature feature ofCO at ∼ µ m.As indicated in Figure 1, strong water features are ubiquitous andare found at (roughly) 0.94, 1.0, 1.2, 1.4, 1.9, 2.6, and 5 − I , Z , J , H , K , and M bands throughwhich much of ground-based near-infrared astronomy is conducted.Methane has important features at 0.89, 1.0, 1.17, 1.4, 1.7, 2.2, 3.3,and 7.8 microns. Carbon monoxide stands out at 2.3 and 4.5 microns,while CO has diagnostic features near 2.1, 4.3, and 15 microns.Ammonia has many features, but the one at 10.5 microns is mostnoteworthy. Molecular hydrogen (H ) has no permanent dipole, butone can be induced by collisions (“collision-induced absorption") athigh pressure, and the result is a family of undulations from ∼ ∼
20 microns that has been seen in Jupiter, Saturn, and brown dwarfs.A central goal of transit, reflection, or emission spectroscopy of ex- oplanets is to identify these species (and perhaps infer their abun-dances) by these distinctive features.
Clouds and Hazes
Condensates can form and reside in exoplanet atmospheres as cloudsor hazes [21, 35] and can have a disproportionate influence on spec-tra. This is because, assembled in a grain, such aggregations can re-spond coherently to light (depending upon the particle size and wave-length). So, very little areal mass density can translate into a largeoptical depth and a trace species can loom large. In addition, with aspectrum of particle sizes and enhanced line broadening in the grain,their absorption and scattering cross sections can have a continuumcharacter and veil a wide spectral range. The result can be partial (orcomplete) muting of the gas-phase spectral features, making under-standing condensates and incorporating their effects into models asimportant as it is difficult. To properly handle the effects of cloudswe need to know the condensate species, grain size and shape distri-butions, the complex index of refraction, and the spatial distributionin the atmosphere. Such knowledge is generally in short supply.The possibility of water clouds in terrestrial atmospheres is un-controversial, the presence of ammonia clouds in the atmospheresof Jupiter and Saturn has been observed in detail, and the centralrole of silicate and iron clouds in brown dwarf L dwarfs is reason-ably inferred by their very red infrared colors. These situations arein part informed by known thermochemistry. However, water cloudsare expected in cold giant exoplanet and brown dwarf atmospheres[24, 41]; Na S and KCl clouds are thought to reside in late T dwarfbrown dwarfs; an extra absorber in the optical and at altitude hasbeen invoked to explain the inversions and over-hot atmospheres in-ferred from the spectra at secondary eclipse of some transiting hotJupiters[39]; a thick haze envelopes the atmosphere of Saturn’s Ti-tan; and there is a trace absorber in the blue that makes Jupiter andSaturn redder than Neptune or Uranus. None of the causative speciesin these situations is either known, or if known, well-modeled. Thecase of Jupiter’s color is a cautionary tale. The factor of two sup-presion in its reflected blue flux could be due to traces at the part in level of either polyacetylenes, sulfur or phorphorus compounds,tholins, or something else [19]. Such leverage by a small (and un-known) “actor" in the interpreation of such a large effect should giveone pause, and emphasizes the potential complexity of the task of ex-oplanet characterization. Photolytic chemistry is likely a cause in Ti-tan’s atmosphere, as in many other contexts, but this is small comfortwhen designing a modeling effort aimed at anticipating all reasonablepossibilities.Scattering in general is important only in reflection and transitspectra, not in emission, and is most prominent for hazes and clouds.In fact, longward of the ultraviolet (UV), clouds are necessary to givea planet any appreciable reflection albedo above ∼
1% [19]. Also, inreflection, as a general rule, cloud or UV/blue Rayleigh scattering canyield highly polarized fluxes [20]. The polarized fraction is higherwhen the absorption fraction is higher and the scattering albedo islow, but in this case the overall reflected flux is low. This suggests thatpolarization might in some circumstances be a useful ancillary diag-nostic of exoplanet atmospheres. Unlike for gas species, for manyrealizations of likely hazes or clouds in exoplanet atmospheres, thescattering albedo can be either high or low, depending upon speciesand wavelength range, and is frequently high. This suggests that re-flection spectra can be dominated by the effects of such layers, and,moreover, that transit spectra can be affected by particulate scattering(as opposed to only absorption). Clearly, one must be aware of thepossible presence of clouds and hazes when performing exoplanetspectral retrievals. the ratio of the scattering cross section to the total cross section Footline Author PNAS
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Volume Issue Number .5 1 1.50.0190.020.0210.022 1 2 3 4 50.0190.020.0210.0220.023 Fig. 2.
Top:
Shown are model fractional transit depths versus wavelength (inmicrons) between 0.4 and 1.8 µ m for a WASP-19b-like planet. The blue curveis a dayside model with TiO in its atmosphere and a redistribution parameter,P n , of 0.3[39], that is irradiated by a stellar model of WASP-19 at the distance ofWASP-19b. The black curve (“SE Fit") is a dayside model with a P n = 0.3 andan “extra absorber" at altitude with an opacity of 0.05 cm g − from 0.4 to 1.0 µ m, configured to fit the measured Spitzer/IRAC secondary eclipse data. Thered and green models have isothermal atmospheres at 2500 K, with the flattergreen model having a uniform haze with an opacity of 0.01 cm g − . Bottom:
The bottom plot is the same, but extended to 5.0 microns. In all models shown,water features (see Figures 1) are the most prominent, while TiO features arein evidence in the TiO model and the effect of a veiling haze is manifest in thatmodel. Note that for this exoplanet the magnitude of the variation with wavelengthis generally less than or equal to a part in a thousand. See text for details.
Transit Spectra
Transit spectra are direct probes of atmospheric scale heights andatmospheric abundances near the terminator(s). However, if the at-mosphere is optically thick and overlays a rocky core there is no obvi-ous way to determine the core’s contribution to the measured radius.Therefore, it is standard practice to analyze transit spectra with re-spect to an arbitrarily determined reference radius, often taken to bethe inferred discovery radius in the optical. When the solid surfaceof a terrestrial or super-Earth planet is not a priori known, or is inac-cessible by measurement, then there will be ambiguity with respectto its contribution to the transit depth. This will not be the case withan airless planet, and is moot for a gaseous planet, but is an issue toconsider when falsifying theory.The measured fractional diminution in the stellar light at a givenwavelength is the transit depth [27, 42]. The stellar beams pointed at the Earth probe the planet’s atmosphere transversely along a chordperpendicular to the impact radius. Hence, the relevant optical depth, τ , is not the depth in the radial direction associated with emission,but much larger. The contribution of the annulus, or partial annulusin the case of the ingress or egress phases, to the blocking of stellarlight is 1 - e − τ times the annular area. The sum of such terms overthe entire atmosphere provides the integrated blocking fraction due tothe atmosphere. That this τ is larger than the radial τ allows transitdepth to be more sensitive to trace chemical species than emission orsecondary eclipse spectra and amplifies their effect. This may be par-ticularly true of atmospheric hazes that may be too thin in the radialdirection to affect emission, but are thick along the chord[43], andmay be why Pont et al. [44] see an almost featureless transit spectrumfor HD 189733b and infer a veiling haze, while the associated IRACand IRS data at secondary eclipse clearly reveal water signatures[45].Another reason may be that since transit spectra probe the termina-tor, the transition region between day and night, a condensate is morelikely to form as the temperature transitions to lower values. Be thatas it may, the terminator is a complicated region that introduces spe-cial challenges for the theory of transit spectra.Despite this, a simple analytic model[43, 46, 8] can be developedthat captures the basic elements of general transit theory. Integratingalong a chord at a given impact parameter and assuming an exponen-tial atmosphere with a pressure scale height, H , yields an approxi-mate amplification factor for the chord optical depth ( τ chord ) over theradial optical depth of p πR p /H , which can be − . This meansthat the τ chord = 2 / condition that approximately defines the ap-parent planet radius at a given wavelength is pushed to larger impactparameters (radii) and that the fractional transit depth is increased bya factor ∝ H/R p . Moreover, it is straightforward to show that dR p d ln λ ≈ H d ln σd ln λ , [1] where σ is the total species-weighted interaction cross section (thesum of absorption and scattering). Note that, whereas emission spec-tra (ignoring reflection) depend upon only absorption, transit spec-tra depend upon both scattering and absorption processes. In fact,the haze inferred for HD 189733b could be purely scattering, andas such would make no contribution to the emission at secondaryeclipse. However, it is likely that any haze has a non-unity scatteringfraction/albedo, introducing flexibility, but also further complexity,into the simultaneous interpretation of transit and emission spectra.Equation 1 suggests that significant wavelength variations incross section, as across an absorption band, translate into a changein the apparent radius of order H . This is the essence of the use oftransit measurements as a function of wavelength to determine com-positions. Since R p depends upon the logarithm of σ , eq. 1 alsoindicates that the dependence upon abundance is logarithmic and,hence, weak. While it is “easy" to discern a molecular feature, itis not easy with transit spectra to determine its abundance. Note thatsince H = kT /µg , a low (high) temperature, high (low) gravity,or high (low) mean molecular weight atmosphere will yield weaker(stronger) indications of composition. Hence, as long as spectro-scopically interesting species reside in the atmosphere in reasonableabundances, a hot, H -rich atmosphere (without a veiling haze/cloud)yields the largest, most diagnostic, radius variations with wavelength.If there are differences in the compositions and scale heights atthe east and west limbs of a planet, such differences are in princi-ple discernible as differences in ingress and egress transit spectra.Though difficult even for a giant exoplanet, such measurements might Often referred to imprecisely as “transmission spectra." What one is actually measuring isthe transit depth, which reflects what is not transmitted. In addition, the implication of the term“transmission" is that we are imaging the planet’s limb region and measuring the variation in τ or e − τ . However, we are actually probing 1 - e − τ , its complement. H = kT/µg , where g is the gravity, µ is the mean molecular weight, T is an averageatmospheric temperature, and k is Boltzmann’s constant. e doable in the future and could shed light on atmospheric dynamicsand any pronounced zonal flow asymmeties.In addition, narrow-band, very-high-resolution spectroscopy be-fore and during transit has great potential to reveal planetary orbital,spin, and wind speeds, as well as compositions (cf. the measurementof CO lines by [47]). Though giant exoplanets are the most studiedpopulation to date via multi-band transit photometry and spectropho-tometry (as opposed to wide single-band observations à la Kepler [48]), such data around small M dwarfs for terrestrial planets andsuper-Earths (such as GJ 1214b − see [43], and references therein)have great promise to probe the atmospheres of these smaller, butlikely more numerous, planets. Measuring the emission spectra ofEarths around solar-like stars will be much more challenging.Figures 2 portray the general character of representative theoret-ical exoplanet transit spectra from 0.4 to 5.0 microns. The modelsare for the giant WASP-19b and include isothermal atmospheres at T = 2500 K, with and without a uniform gray haze with an opac-ity of 0.01 cm g − , a model that attempts to fit its IRAC data atsecondary eclipse [49] with an unknown “extra absorber" at altitudeof constant optical opacity 0.05 cm g − (from 0.4 to 1.0 micron),and a similar model employing TiO as the extra absorber. For clarity,the latter two are shifted arbitrarily from the former two. We notethat the transit depth is of order ∼
2% and that the variation due to thepresence of water bands is approximately one part in a thousand. Thedepths for other hot Jupiters could vary with wavelength by as littleas a few parts in ten thousand.One sees immediately that the extra optical absorber, whateverits nature, increases the ratio of the optical to infrared radii, that theTiO hypothesis can readily be falsified, that the spectral features of(here) water should be readily detected , that the radius variationsin the mid-infrared can be of larger amplitude, and that even low-opacity hazes can mute these variations substantially. The diagnosticpotential of transit spectra is manifest in plots such as these. It isequally clear that the interpretation of but a few photometric pointswith significant error bars are ambiguous. Good spectra are the key. Secondary Eclipse
For a circular orbit, when 180 ◦ out of phase with the transit, theplanet is occulted by the star and is in secondary eclipse. Duringthe eclipse, the summed light of the planet and star being monitoredshifts to that of the star alone, and by the difference the planet’s emis-sions are determined. The Spitzer space telescope [51] has been par-ticularly productive in this mode, providing near- and mid-infraredphotometric points for ∼
30 nearby transiting planets (mostly giants).For close-in planets, for which the transit probability is largest, theplanet is emitting mostly reprocessed stellar light [52, 53]. Stellar ir-radiation and zonal atmospheric winds and dynamics break the sim-ple spherical symmetry, so that 3D models would seem most appro-priate. However, such models have yet to prove themselves and sim-pler 1D hemisphere-averaged models have been employed, howeverprofitably, to compare with data. Issues with such a prescription in-clude what average flux to employ to derive a representative daysideT/P profile, how to incorporate longitudinal and latitudinal surfaceflows into the energy budget, non-equilibrium chemistry[56], photo-chemistry, and day-night differences when interested in total phasecurves[53, 54, 55]. Nevertheless, such simple models are still com-mensurate with the information content of the extant observations.The various quantities and topics that influence secondary eclipsespectra and have exercised the community include 1) the presenceor absence of an extra absorber of currently unknown origin in theupper atmosphere that could heat those regions, at times produc-ing thermal inversions over a restricted pressure range[39, 57]; 2)the temperatures and temperature profiles of the atmosphere; 3) thephase shifts from the orbital ephemeris of the light curves at variouswavelengths and spectral bands due to zonal winds that redistributeheat[58]; 4) the compositions and elemental abundances of the atmo-
Fig. 3.
Top:
The top figure portrays model temperature-pressure curves for acollection of transiting giant exoplanets. These models were constrcuted in anattempt to fit respective Spitzer/IRAC data at secondary eclipse and demonstratethe span of temperatures expected in giant exoplanet atmospheres. This spanreflects, among other things, the range of sub-stellar fluxes at these given planets,as well as the extra heating of the upper atmosphere by an absorber in the opticalthat, at times, has been invoked to explain Spitzer/IRAC data, in particular at 5.8microns. Note that the XO-1b model is the black line at the left, while the blackline at the right is for WASP-12b with an inversion ( κ = 0 . cm g − ), with P n = 0.1, and in chemical and radiative equilibrium at solar elemental abundances.The gray curve is also a model for WASP-12b, but without an inversion, depletedin water by a factor of 100, and enhanced in CH and CO to uniform fractionalabundances of × − . Each model was used to address the WASP-12b IRACand near-infrared secondary eclipse data. Bottom:
The planet/star flux ratiosfrom 0.4 to 10 microns for the models on the top. The “predicted" range in values,even for a class of solely giants, is very wide. Note also that comparison betweenthe two WASP-12b models (black and gray) is a cautionary tale against relyingtoo heavily on error-prone photometry to characterize exoplanet atmospheres,and a clarion call for accurate spectra over a wide wavelength range. See textfor a discussion. spheres; 5) the presence of hazes and clouds; 6) the day/night fluxcontrast; 7) Doppler signatures of atmospheric motions; 8) reflectionalbedos [59]; and 9) the presence and role of evaporative planetarymass loss. I mention these challenges only to indicate the range ofcomplex problems to be addressed, but will focus in this paper ononly the simplest of approaches taken to extract information fromsecondary-eclipse data.A few conceptual points are worth noting in passing: 1) An at-mosphere calculation with external incident flux will automatically In fact, water has alreadybeen detectedin severalgiantplanet atmospheresvia transitspectra(e.g., [50]). f = 1/4 for isotropic models. Footline Author PNAS
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Volume Issue Number enerate a reflection albedo and is not extra physics. 2) For a givenelemental ratio set, the metallicity dependence of the emergent spec-trum is quite weak. Most relevant species (such as water) have one“metal" and incident and emergent integral fluxes must almost bal-ance. 3) The difference between incident and emergent total fluxesis due to the true effective temperature ( T eff ), which for giant ex-oplanets of Gigayear ages ranges from 50 to 500 K, and results ina very small contribution to the emergent flux for a strongly irradi-ated planet. T eff is important only when the stellar irradiation flux issmall, and this obtains only for wide-separation planets. 4) The so-called equilibrium temperature, T eq , is defined as the surface black-body temperature for which the incident stellar flux is balanced andis given by T eq = T ∗ (cid:18) R ∗ a (cid:19) / ( f (1 − A B )) / , [2] where T ∗ is the stellar effective temperature, f is the heat redistribu-tion factor , and A B is the Bond albedo[8, 19]. While providing ameasure of the mean temperature achieved in a planet’s atmosphere,assuming this can be used as the inner boundary condition T eff hasintroduced quite a lot of confusion. Very different T/P profiles canyield the same total flux, but very different flux spectra. Figures 4in the Supplement show two models with the same emergent flux,and, hence, T eq . One consistently incorporates stellar irradiation,while the other puts a flux with T eff = T eq at the base of the at-mosphere. Both are in radiative and chemical equilibrium. As thesefigures demonstrate, despite the fact that the emergent fluxes are thesame, the corresponding T/P profiles are hugely different and the fluxdensities at a given wavelength can be off by factors of 2 −
4! Irradi-ated atmospheres are different from isolated atmospheres.Lastly, 5) if an atmosphere is in fact isothermal, there must be anextra absorber in the optical at altitude. Even under irradiation, thetemperature gradient must otherwise be negative from base to height,with characteristic temperature changes of ∼ − T = 34 T κ J κ B (cid:20) τ R + 1 √ (cid:21) + κ J κ B W T ∗ , [3] where W is the dilution factor, ( R ∗ /a ) , τ R is the Rossleand depth, κ J is the photon energy-density weighted opacity, κ B is the corre-sponding local black-body-weighted opacity, and we have used theEddington approximation for the angular moments. For an isolatedatmosphere, κ J κ B is close to one, but for an irradiated atmosphere κ J and κ B can differ appreciably. The former at altitude is dominatedby the stellar spectrum, while the latter reflects the local atmosphericblack-body spectral distribution. If this difference is an interestingfunction of altitude, an inversion can result[10]. We note that T eff is generally small for close-in hot Jupiters. In this case, the tem-peratures at depth are determined by the second term, which yieldssomething like eq. (2). In reality, gas giants are convective at highoptical depths ( ∼ ∼
100 bars. The atmospheres of close-in giants can vary in temperature, depending upon W and T ∗ , by ∼ − ∼ − ∼ − and CO,depleted H O, and no inversion (gray) attest, mid-infrared planetaryspectra can vary significantly for the same stellar irradiation regimeand gravity. Figure 3, together with Figure 1, demonstrate the greatdiagnostic potential of multi-frequency spectra to extract composi-tions. One can also determine the presence or absence of extra heat-ing by enhanced absorption of stellar light that leads to inversions, butalso hotter upper atmospheres and elevated fluxes of features formedin the heated zone. The pronounced bump at ∼ − .Though inversions have been inferred from enhanced Spitzer
IRAC band fluxes (in particular at 5.8 microns), the nature of theabsorber is still unknown. It is suggested that TiO could do it, butthere are good reasons to believe this compound would be rainedout to depth by various cold traps[38]. There may be a photochemi-cal hazes with the right optical absorbing properties, but this has notbeen demonstrated. Still, it is tantalizing to hypothesize that the hazeinferred by Pont et al.[44] in the atmosphere of HD 189733b andthat inferred by Deming et al.[50] in the atmosphere of HD 209458bmight in some way be implicated, or at least be of similar composi-tion.Though the interpretative and diagnostic promise of good spectrais suggested in Figure 3, the current reality is depicted in Figures 5(in the Supplement). Here, I plot representative measured planet/starflux ratios for 17 transiting giant exoplanets. Most of the data are
Spitzer
IRAC photometry in four bands, while some of the data arefrom the ground and the Hubble Space Telescope. For HD 189733b,we have
Spitzer /IRS spectra from ∼ σ error bars generally rangefrom ∼
10% to 30%. In an attempt to divide out universal expecta-tions and to focus on what may distinguish one planet from another,I have normalized the planet/star flux ratio with the correspondingblack-body value First, we see from Figures 5 that the normalized ratio is ratherflat over a broad range of wavelengths and close to one, perhaps a bithigher. However, the mean level could just reflect the crudeness ofthe T p employed for the comparison. We see undulations, but theyhave little information content, aside from the possible suggestion ofenhanced or reduced flux in particular broad spectral regions. TheIRS data near 6.2 microns for HD 189733b do imply the presence ofwater, but what is the feature near 12.5 microns? There is a system-atic increase in the ratios to shorter wavelengths, and this is probablyreal. As supplementary figures 4 imply, fluxes from irradiated planetsare expected to be mostly in the near infrared.The comparison of Figures 3 and 5 starkly emphasizes that wehave a long way to go before comparative exoplanetology becomesa richly diagnostic science. At times, data such as are depicted inFigure 5 have been used to find temperatures, compositions, albedos,inversions, carbon-to-oxygen ratios [61], metallicities, and day-nightheat redistribution factors, etc. Clearly, these data, and the still prim-itive state of exoplanet atmosphere theory, do not justify attempts Emission features won’t always be seen when the extra absorber is active − this depends onwhere in the atmosphere the band is “formed." Dividing by the factor fbbpfbb ∗ ( λ ) = (cid:16) RpR ∗ (cid:17) e hcλkT ∗ − e hcλkTp − , where T p has been set equalto T ∗ q R ∗ a . o constrain such quantities simultaneously, or perhaps at all. Un-til high-quality transit and emission spectra across a wide range ofwavelengths are routinely available, only the most primitive and con-servative conclusions will be justified. I reiterate that the data in Fig-ures 5 are for giant exoplanets. Smaller Neptunes, super-Earths, andterrestrial planets around similar stars will be much more difficulttargets. Systematic Uncertainties in the Data and Theory
Theorists and observers alike, anxious to extract all the conclusionsthey can from this first generation of measurements of exoplanet at-mospheres, have tended to overinterpret them. A comparison be-tween Figures 3 and 5 is a sober indication of the current limitationsof the science. The telescopes being used were not designed with ex-oplanets in mind. For example,
Spitzer was designed for photometryat the ∼
1% level, yet it is being used (however heroically) to ob-tain numbers at the ∼ − ∼
2, and such afactor can completely alter the conclusions drawn about abundances,C/O ratios, inversions, etc.Given this list of limitations, one should be highly sceptical ofextraordinary claims based on imperfect data with low intrinsic infor-mation content. Many published model fits have been highly under-constrained. This is all the more important given the gross imperfec-tions in current exoplanet atmosphere theory. With a few photometricpoints, one can not simultaneously determine with any confidence,or credibly incorporate into the fitting procedures, chemical and ele-mental abundances, wind dynamics, longitudinal heat redistribution,thermal profiles, albedos, the potential influence of hazes and clouds,non-equilibrium chemistry and photochemistry, and magnetic fields.Furthermore, the opacities for many chemical species are only im-perfectly known, convection at depth is frequently handled with amixing-length approach, and emissions over a planetary hemisphereare never calculated with correct, multi-dimensional radiative trans-fer. Moreover, most of the current generation of 3D general circu-lation models (GCMs) filter out sound waves, but derive transonicflows speeds with Mach numbers at and above one without a meansto handle shock waves. Many of these codes have also inherited fromEarth GCM practice various ad hoc “Rayleigh drag" and hyperdiffu-sivity terms with arbitrary coefficients calibrated on the Earth thatcompromise the wind dynamics on strongly irradiated gas giants,even if magnetic torques are sub-dominant. Importantly, GCMs wereconfigured to look at winds and pressures, not spectral emissions,highlighting the mismatch between the traditional goals of planetaryand Earth scientists and exoplanet astronomers.At times, basic atmosphere practice has been shunted aside inattempts to retrieve thermal and compositional information from afew (though precious) data points. Examples are 1) using unphysi-cal, parametrized T/P profiles and arbitrary compositions, while notaddressing local energy and chemical balance; 2) using 1D averagedmodels for what is a 3D planet; 3) using T eq as if it were a real physi-cal quantity of relevance to spectra; 4) defining and deriving a reflec-tion albedo when the planet is mostly emitting thermally; or 5) fittingphotometric points with T eq and a Bond albedo. Such approachesmight seem right-sized to the data at hand, but are likely to gener-ate an erroneous sense of confidence in the conclusions derived. Forexample, it is long been known that small errors in ∆ T can translateinto large spectral flux errors, even if the total reprocessed emittedflux is ostensibly addressed.
The Future
Therefore, I suggest that once high-quality, well-calibrated, stablespectra across a broad range of wavelengths from the optical to themid-infrared are finally available many conclusions reached recentlyabout exoplanet atmospheres will be overturned. The current inter-pretations and theories are just not robust enough to survive intactinto the future. However, despite the generally cautionary tone ofmuch of this paper, I see an exciting future. The past ∼
20 years hasbeen but a training period for a new generation of exoplanet scientists,forged by trial and error and educated in the new questions posed byexoplanets. Its growing membership is testing its tools − new tech-nologies, concepts, theories, and techniques − that will serve to es-tablish a solid foundation for a true science of planets not tetheredto the solar system. Informed by the latter, but optimized to addressits unique challenges as a remote-sensing science, comparative plan-etology’s youth is rapidly maturing.The near- and mid-term future of exoplanet atmosphere charac-terization will include the James Webb Space Telescope (JWST)[62,63], ground-based Extremely-Large/Giant-Segmented-Mirror Tele-scopes (ELTs/GSMTs)[64], and perhaps dedicated Explorer, M-Class (e.g., EchO[65]), or Probe-Class space missions. The contin-ued creative use of existing ground-based telescopes is assured, andnew high-contrast coronagraphic imaging programs now coming online (such as GPI[66] and SPHERE[67]) show great promise. Impor-tantly, there is the exciting possibility of putting a coronagraph onWFIRST/AFTA [68]. In the farther future, once a cost-effective plancan be articulated, a major dedicated space mission of exoplanetaryatmosphere characterization, such as was envisioned with the TPFsand Darwin, should be possible. Currently, giant planets and Nep-tunes pose the most realistic targets, but terrestrial planets and thepossibility of discerning signatures of life are majors goal of many.Soon, the spectra of terrestrial planet atmospheres around small M-dwarf stars may be within reach.Given this, it is clear that, for the field to remain vibrant and grow,it needs a heterogeneous and balanced program of ground-based andspace-based facilities and programs. If anything has been demon-strated by the first ∼
20 years of exoplanet research, it is that some ofthe best techniques for studying them are unanticipated. The transittechnique for close-in planets has been a game-changer, but was notenvisioned in previous planning documents. High-contrast imaging,only now coming of age, was to inaugurate the era of atmosphericcharacterization. It is also clear that large, expensive missions arecounterproductive until they are demanded by the science, in fact un-til the science indicates that further progress demands them. Precur-sor technologies for such missions should certainly be pursued andallowed to compete. But overlarge and expensive missions withoutthe requisite credibility and technological heritage in place can fatallysqueeze the smaller programs that have proven so fruitful. This im-plies that an international Roadmap should be crafted for exoplanet’snext ∼
20 years. Its guiding principle should be a balanced approachof small, medium, and large initiatives that encourages flexibility andscientific return, and does not presume (or proscribe) a specific fu-ture. The clear goal is to understand in rich detail the planets that wenow know exist in profusion in the galaxy and Universe. One is onlyleft to ask: Are we ready to assume the challenge?
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Left:
Shown are the temperature-pressure profiles for two models of HD 209458b. The black curve was generated including the stellar irradiation flux at theorbital distance of the planet and a token effective temperature (T eff ) of 200 K at the base. Note that T eff for such a model reflects the net flux, not the emergentflux. The red curve is for an isolated model with roughly the same total emergent flux at an effective temperature T eff of 1700 K. Despite having the same emergentflux, these temperature-pressure profiles are profoundly different.
Right:
The bottom panel depicts the corresponding normalized spectra, F ν , versus wavelength (inmicrons). These spectra are vastly different, though the total emergent fluxes are the same, and demonstrate that one cannot assume that an equal emergent fluxconstraint will translate into useful spectra or colors. They also demonstrate that one must be careful when quoting an effective temperature, and not confute T eff with an “equilibrium temperature," T eq . See text for a discussion.
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Fig. 5.
Left:
Planet/Star flux ratio data points at secondary eclipse for eight giant planets (WASP-19b, HD 149026b, HAT-P-7b, HAT-P-2b, CoRoT-2b, CoRoT-1b,HD 189733b, and HD 209458b), normalized to the corresponding ratio if both star and planet were black bodies at the corresponding measured stellar T eff = T ∗ and zero-albedo equilibrium temperature, T eq (cid:18) = T ∗ q R ∗ a (cid:19) , respectively. The lines connect points for the same object. Most of the data are Spitzer/IRAC points,but points at shorter wavelengths, where available, are also included. For HD 209458b and HD 189733b, points at 16 and/or 24 microns are also given, along withpoints (unconnected and for comparison) derived from other reductions. To avoid further clutter, quoted error bars are given only for the IRS spectrometer data for HD189733b and the Spitzer data for HD 209458b. Right:
The same as on the top, but for XO-3b, XO-2b, XO-1b, WASP-18b, WASP-12b, TrES-4, TrES-3, TrES-2, andTrES-1. Error bars for only WASP-12b are given. The normalization provided helps to rationalize the interpretation potential of such photometric and low-resolutiondata and to facilitate planet-planet comparison. The data were taken from [69, 70, 71, 72, 73, 74, 75, 45, 76, 77, 57, 78, 79, 80, 81, 82, 83, 84, 60, 85, 86, 87, 88, 89,90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 49]. See text for a discussion.10