Theoretical Spectra and Light Curves of Close-in Extrasolar Giant Planets and Comparison with Data

1.2 MB·English

by  A. Burrows

Accepted to Ap.J.
PreprinttypesetusingLATEXstyleemulateapjv.10/09/06
THEORETICAL SPECTRA AND LIGHT CURVES OF CLOSE-IN EXTRASOLAR GIANT PLANETS AND
COMPARISON WITH DATA
A. Burrows1, J. Budaj1,2 & I. Hubeny1
Accepted toAp.J.
ABSTRACT
We present theoretical atmosphere, spectral, and light-curve models for extrasolar giant planets
(EGPs)undergoingstrongirradiationforwhichSpitzerplanet/starcontrastratiosorlightcurveshave
beenpublished(circaJune2007). TheseincludeHD209458b,HD189733b,TrES-1,HD149026b,HD
8
179949b,and υ And b. By comparing models with data, we find that a number of EGP atmospheres
0
0 experience thermal inversions and have stratospheres. This is particularly true for HD 209458b, HD
2 149026b, and υ And b. This finding translates into qualitative changes in the planet/star contrast
ratios at secondary eclipse and in close-in EGP orbital light curves. Moreover,the presence of atmo-
n
spheric water in abundance is fully consistent with all the Spitzer data for the measured planets. For
a
planets with stratospheres, water absorption features invert into emission features and mid-infrared
J
fluxescanbeenhancedbyafactoroftwo. Inaddition,thecharacterofnear-infraredplanetaryspectra
6
can be radically altered. We derive a correlation between the importance of such stratospheres and
2
the stellar flux on the planet, suggesting that close-in EGPs bifurcate into two groups: those with

and without stratospheres. From the finding that TrES-1 shows no signs of a stratosphere, while
]
h HD 209458b does, we estimate the magnitude of this stellar flux breakpoint. We find that the heat
p redistributionparameter,P , forthe familyofclose-inEGPsassumesvaluesfrom∼0.1to∼0.4. This
n
- paper provides a broad theoretical context for the future direct characterization of EGPs in tight
o
orbits around their illuminating stars.
r
t Subjectheadings: stars: individual(HD209458,HD189733,TrES-1,HD149026,υAnd,HD179949)—
s
a (stars:) planetary systems—planets and satellites: general
[

2
1. INTRODUCTION However,thetransitingEGPsyieldradiiaswell,andre-
v
solve the sini ambiguity to reveal the planets’ masses.
0 To date, more than 250 extrasolar planets have been
These data provide physical constraints with which de-
8 discoveredandmorethan29ofthemaretransitingtheir
0 primarystar3. Onetransitingplanetisa“Neptune”(GJ tailed evolutionary and structural models that incorpo-
rate irradiation and migration can be tested (see, e.g.,
4 436b),buttherestaregiantplanetswithanimpressively
Burrows et al. 2007a; Guillot et al. 2006). With su-
. wide rangeof masses and radiithat speak to the hetero-
9 geneityofthefamilyofclose-inEGPs(ExtrasolarGiant perb photometric accuracy, the wavelength-dependence
0
7 Planets). Table 1 lists these transiting EGPs and some of the transit radii can in principle provide a measure
of a planet’s atmospheric composition (Fortney et al.
0 of their relevant properties, along with many of the ref-
2003). In this way, sodium has been detected in HD
: erences to the observational and discovery papers from
v 209458b (Charbonneau et al. 2002) and water has been
whichthesedataweretaken. Table2listsusefuldatafor
i identified in both HD 189733b (Tinetti et al. 2007, but
X the correspondingprimary stars, including their masses,
see Ehrenreich et al. 2007) and HD 209458b (Barman
luminosities, radii, and approximate ages. Both tables
r 2007). Moreover, high-precision optical photometry has
a areinorderofincreasingplanetarysemi-majoraxisand,
constrained(perhaps,measured)thegeometricalbedoof
considering the pace of the field, both should be consid-
the close-in EGP HD 209458b(Rowe et al. 2006,2007).
eredprovisional. Notshownarethe eccentricities,which
HD 209458b’s optical albedo is very low (∼3.8±4.5%),
are generally small, but which for HAT-P-2b, GJ 436b,
inkeepingwith the predictionsofSudarskyetal. (2000)
and XO-3b are ∼0.507, ∼0.14, and ∼0.22, respectively.
when the alkali metals, and not clouds, dominate ab-
For these three close-in EGPs, significant tidal heating
sorptionintheatmosphereandRayleighscatteringdom-
and, perhaps, forcing by an unseen companion are im-
inates scattering.
plied.
Nevertheless, using current technology, transit mea-
Radial-velocity measurements for a non-transiting
surementshavelimitedutilityincharacterizingtheatmo-
EGP provide a lower limit to its mass, but little else.
spheres and compositions of these planets. Astronomers
1Department of Astronomy and Steward Observa- requiremoredirectdetectionsoftheplanet’sspectrumto
tory, The University of Arizona, Tucson, AZ 85721; probe its chemistry and atmospheric properties. This is
[email protected], [email protected], inthetraditionofremotesensinginthesolarsystemand
[email protected]
oftheEarth. Untilrecently,ithadbeenthoughtthatthe
2Astronomical Institute, Tatranska Lomnica, 05960 Slovak
lightfromanextrasolarplanethadto be separatedfrom
Republic
3 See J. Schneider’s Extrasolar Planet Encyclopaedia undertheglareofitsparentstarusinghigh-angularreso-
at http://exoplanet.eu, the Geneva Search Programme at lution, extremely high-contrastimaging. This is still the
http://exoplanets.eu, and the Carnegie/California compilation at case in the optical for the cool “wide-separation” EGPs
http://exoplanets.org
(Burrows et al. 2004; Sudarsky et al. 2005; Burrows
2
2005) and terrestrial planets, for which the planet-star interpretation. In fact, in Burrows et al. (2007b), we
contrastratiois∼10−9 to∼10−10,butsuchperformance speculate thatthermalinversionsandstratospheresmay
has not yet been demonstrated. play a role in the atmospheres of many close-in EGPs
However, for the hot close-in EGPs, the planet-star and are a new feature in the study of transiting plan-
contrast ratios in the mid-infrared are much more fa- ets. A similar conclusion was reached by Fortney et al.
vorable (Burrows, Sudarsky, & Hubeny 2003,2004), of- (2006), specifically in the context of HD 149026b.
timesexceeding10−3. Thiscapabilityhasledtoabreak- We find that we can fit all the secondary eclipse and
through in the study of exoplanets. With the infrared light-curve data, except for the nightside flux of HD
space telescope Spitzer (Werner & Fanson 1995), using 189733b and its day/night contrast. While we can fit
its IRAC and MIPS cameras and the IRS spectrome- its dayside secondary eclipse flux, we suspect that HD
ter,onecannowmeasurethesummedlightoftheplanet 189733b will require a more sophisticated day/night re-
andthestarinandoutofsecondaryeclipse,andthereby, distribution model than we now employ (§2). We note
from the difference, determine the planet’s spectrum at that Knutson et al. (2007b) conclude that the dimmest
superior conjunction. Moreover,for a subset of the clos- and brightest spots on HD 189733b reside on the same
est EGPs it is possible to use Spitzer to measure their hemisphere and that the dimmest spot is shifted from
fluxvariationswithplanetaryphasebetweentransitand the anti-stellar point by as much as ∼30◦. Our current
secondary eclipse. Hence, for the close-in EGPs in the light curve models are symmetric about the peak.
near-tomid-infrared,andwithouttheneedtoseparately We find that the degree of longitudinal heat redistri-
image planet and star, the direct detection of planetary bution(P )mayvaryfromplanettoplanet,hintingata
n
atmospheres via low-resolution spectroscopy and preci- variety of meteorological conditions and day/night con-
sion infrared (IR) photometry is now a reality. trasts within the family of close-in EGPs. Moreover, as
The secondary eclipse fluxes have now been measured also concluded in Burrows et al. (2005), we can not ob-
for five transiting EGPs (HD 189733b, TrES-1, HD tain good fits at secondary eclipse without the presence
209458b, HD 149026b, GJ 436b), but not yet in all of water in abundance in the atmospheres of these irra-
Spitzer bands. In addition, using the IRS spectrome- diated EGPs. This is particularly true for TrES-1 and
ter, spectra between ∼7.5 µm and ∼15 µm of two tran- HD 209458b. Though we will not dwell in this paper
siting EGPs at secondary eclipse have been obtained on metallicity, we find that the metallicity dependence
(HD 189733b [Grillmair et al. 2007] and HD 209458b of the secondary-eclipse fluxes is not strong, but that
[Richardson et al. 2007]). Though at very low resolu- it is in principle measurable, and that the metallicity
tion, these arethe firstmeasuredspectra ofanyextraso- dependence of the variation of the planetary flux with
larplanet. Furthermore,lightcurveshavebeenmeasured phaseisonlymodest. Importantly,wealsoconcludethat
for three EGPs (υ And b [Harrington et al. 2006: at 24 upper-atmosphereabsorptionin the optical by anas-yet
µm], HD179949b[Cowanetal. 2007: at8µm], andHD unknown molecule, and the concommitent thermal in-
189733b [Knutson et al. 2007b: at 8 µm]). Only one versionsandstratospheres,providebetterfits tosomeof
of these (HD 189733b)is transiting and has an absolute the data.
calibration. For none of the latter three are there ex- In §2, we describe our numerical techniques, the new
tantlight-curvemeasurementsformorethanoneSpitzer heat redistribution model, and how we generate strato-
band; for some of these EGPs only upper limits in a few spheres. This section is supported with Appendices §A,
of the other bands have been determined. Table 3 sum- §B, §C, and §D, in which we provide details concern-
marizes all the direct detection data for the EGP family ing the heat redistribution model and derive some ana-
obtained to date (circa June 1, 2007),along with associ- lytic formulae concerning atmospheric physics with day-
ated references, comments, and table notes. Clearly, in night coupling. In particular, in §D, we address the en-
thenextyearortwowecanexpectagreatdealmoresec- hancement at secondary eclipse in the integrated plan-
ondaryeclipseandlight-curvedatainthevariousSpitzer etary flux at Earth over and above what would be ex-
IRACandMIPSbands. However,therehasalreadybeen pected if the planet emitted isotropically. For a radar
significant progress in measuring EGP atmospheres. antenna, this would be its “gain” factor. In §3, we dis-
This paper is a continuation of our series of interpre- cussthederivedtemperature-pressureprofilesontheday
tative studies (e.g., Burrows et al. 2005,2006,2007b)of and the night sides for all six EGPs highlighted in this
the direct measurements of close-in EGPs. Here, we an- investigation. We show that the τ = 2/3 decoupling
alyzethe secondaryeclipse andlight-curvedata summa- layers for the Spitzer IRAC and MIPS (24-µm) band
rizedinTable3fortheEGPsHD189733b,HD209456b, fluxes are all above the isothermal region of an irradi-
TrES-1, HD 149026b, HD 179949b, and υ And b and ated EGP’s atmosphere and, hence, that Spitzer does
make theoreticalpredictions in support offuture Spitzer not probe these deeper regions. For the same reasons,
planet measurement campaigns. Importantly, by fitting we find that the presence of a thermal inversion at al-
thecurrentdataweextractphysicalinformationconcern- titude and of a stratosphere in some EGP atmospheres
ing the atmospheres, compositions, and thermal profiles can significantly alter these Spitzer fluxes and their rel-
of these first six objects listed in Table 3. We have ex- ative strengths. In §3, we also provide representative
ploredthe dependence ofthe spectraandlightcurveson planet spectra to demonstrate that most of the planet’s
the heat redistribution factor P (Burrows et al. 2006), flux emerges at shorter wavelengths than are accessible
n
on atmospheric metallicity, and onthe possible presence to Spitzer, and, hence, that Spitzer probes only a small
of a stratospheric absorber. The recent analysis by Bur- tail of the emergent flux distribution. This may be of
rows et al. (2007b) of the IRAC data of Knutson et al. relevance when JWST is available to follow up on the
(2007c) indicates that HD 209458bboasts a thermal in- Spitzer EGP data and, even earlier, as the JWST exo-
version that radically alters the Spitzer fluxes and their planet campaign is being designed.
3
In §4, we present the best-fit planet-star contrast ra- low a prescribed value, generally take to be 0.03 bars.
tios at secondary eclipse for four of the transiting EGPs Hence, κ is the most important parameter to be ad-
e
forwhichthesehavebeenmeasured(allbutGJ436b,for justed. We could easily introduce a specified frequency
whichseeDemingetal. 2007andDemoryetal. 2007),as and/or depth dependence, but this would add free pa-
wellasvariouscomparisonmodelstogaugeafewparam- rameters which we feel are not justified at this stage.
eter dependences. Then, in §5 we match our theoretical We have also generated models in which TiO and VO
phase light curves with the three measured light curves are allowed to assume their chemical-equilibrium upper-
and derive approximate planetary parameters. The pa- atmosphereabundances(Sharp&Burrows2007),uncor-
per is brought to a close in §6 with a synopsis of our rectedforthecold-trapeffect(§6;Burrowsetal. 2007b),
results and a general discussion of the issues raised. and to generate a stratosphere. These TiO/VO models
produce qualitatively the same effects as do our ad hoc
2. NUMERICALTECHNIQUES models. However, in this paper we prefer the flexibility
Our model atmospheres are computed using the up- of the κe prescription.
datedcodeCoolTLUSTY,describedinSudarsky,Bur- In Burrows et al. (2006), once the day- and night-
rows, & Hubeny (2003), Hubeny, Burrows, & Sudarsky side atmospheres were calculated, we used a 2D radia-
(2003),andBurrows,Sudarsky,&Hubeny(2006),which tive transfer code to determine the integrated emissions
is a variant of the universal spectrum/atmosphere code “at infinity” at a given viewing angle from the planet-
TLUSTY (Hubeny 1988; Hubeny & Lanz 1995). The star axis for the day- and night-side hemispheres. These
molecular and atomic opacities are taken from Sharp & numbers were then transformed into a light curve as a
Burrows (2007) and the chemical abundances, which in- function of wavelength and planetary phase angle using
clude condensate rainout, are derived using the thermo- the methods described in Sudarsky et al. (2000, 2005).
chemical model of Burrows & Sharp (1999), updated as However,we have found that since the detailed shape of
described in Sharp & Burrows (2007) and in Burrows et the light curve connecting the day- and the night-side
al. (2001). fluxesislikelytobe onlypoorlyconstrainedforthe fore-
To handle convection, we use standard mixing-length seeable future and since our model is symmetric about
theory, with a mixing length equal to the pressure scale secondary eclipse, it is inappropriate to invest a dispro-
height. Thestellarirradiationboundaryconditionisnu- portionate amount of effort in performing expensive 2D
mericallychallenging,andhasnotbeendoneproperlyby transfercalculations. Rather,weinvestoureffortsinob-
some workersin the past. To ensure an accurate numer- taining state-of-the-art day- and the night-side fluxes at
ical solution with a non-zero incoming specific intensity, secondary and primary eclipse and then connect them
we use the formalism discussed in Hubeny, Burrows, & with a simple, though well-motivated, curve. Therefore,
Sudarsky (2003). The stellar spectral models are taken our light curve model is:
fromKurucz(1994)forthesixstarslistedinTable2that
D+N D−N
are the primaries of the EGPs upon which we focus in
C = + cosαsini, (1)
this paper. The day and night sides are approached dif- 2 2
ferently,withthenightside,quitenaturally,experiencing
where C is the planet/star flux ratio, D is the dayside
no incident flux, but receiving heat from the irradiated
flux (see Fig. 4), N is the nightside flux, α is the phase
dayside using the new algorithm described in Appendix
angle,and i is the inclination angle (∼90◦ if in transit).
§A. An importantadditionalfeature ofour new heatre-
This is the form adopted in Cowan et al. (2007). Using
distributionformalismis the capacitytomatchboth the
thissimplerapproach,onedoesnotimplymoreprecision
entropyandthe gravityatthebaseofboththe day-and
than is warrantedat this preliminary stage of inquiry.
the night-side atmospheres. Since the inner convective
We have revisited the question of what type of av-
zone, which constitutes most of the planet, is isentropic,
eraging of the incoming radiation from the star over
this is the physically correct procedure. For a dayside
the surface of the planet is best suited to describe the
calculation, we can assume a given interior flux effec-
planetary spectrum close to the secondary eclipse. We
tive temperature, T (a standard number could be 75
int had demonstrated earlier (Sudarsky et al. 2005) that
K).Foragivengravityandirradiationregime,thisleads
detailed 2D phase-dependent spectra averaged over the
to an atmosphere solution on the dayside. This solu-
phase are equal, within a few percent, to the spectrum
tion incorporatesan entropy in the convective zone. For
computed for a representative model atmosphere that
the nightside atmosphere, we can adjust the nightside
is constructed assuming that the incoming flux is dis-
T until the entropy in its convective interior matches
int tributed evenly over the surface of the dayside. In the
that found in the dayside convective zone. One prod-
usual terminology, this corresponds to the flux distribu-
uct of this procedure is a connection between dayside
tion factor f =1/2 (Burrows et al. 2000)4.
and nightside T that has a bearing on overall planet
int However, the spectrum of a planet observed close to
cooling and shrinkage (Burrows et al. 2007a). However,
the secondary eclipse should be biased toward a higher
since for a given measured planet radius, this mapping
flux than that obtained using the f = 1/2 model. This
does not have a significant effect on the close-inplanet’s
is because the hottest part of the planet, the substellar
spectrum, we do this here only approximately and leave
point, is seen as emerging from the planet perpendicu-
to a later paper a general discussion of this topic.
larly to the surface, and, thus, with the lowest amount
The simple parametrization we use to simulate the
of limb darkening. Therefore, the contribution of the
effects of an extra stratospheric absorber entails plac-
ing an absorber with constant opacity, κ , in the opti-
e 4 We allow the planet to be irradiated by the full flux received
cal frequency range (ν ,ν ) = (3 × 1014 Hz, 7 × 1014
0 1 fromthestar;itisonlydeeperintheatmospherewheretheenergy
Hz) and high up at altitude, where the pressure is be- istransportedtothenightside. SeeAppendixA.
4
hottest part of the planet is maximized. To study this P ranges from 0.1 to 0.5. For all models, the radiative-
n
effect, we have computed a series of model atmospheres convective boundaries are identified and are quite deep
corresponding to a number of distances from the sub- (on the far right of each panel). When κ 6=0, the T/P
e
stellar point, and have integrated the individual contri- profiles show distinct thermal inversions.
butions to get the flux received by an external observer There are quite a few generic features in evidence on
at a phase close to superior conjunction. It turns out these panels. The firstis thatthe atmospheresarenever
that the flux is very close to that computed for f =2/3, isothermal. Since the opacities in the optical, where
whichis the value we subsequentlyuse inallsimulations mostofthestellarirradiationoccurs,andintheinfrared,
presentedhere. Thereisasimpleanalyticargumentwhy where most of the reradiation occurs, are very different,
f shouldbeapproximatelyequalto2/3whichwepresent a quasi-isothermal inner region interior to ∼1 bar is al-
in Appendix §D. ways bounded by an outer region in which the tempera-
TheformalismforD andN isthe bestwehavefielded turedecreases(Hubeny, Burrows,& Sudarsky2003). As
to date. Nevertheless, a 3D general circulation model Fig. 1 indicates, the magnitude of the temperature de-
(GCM)thatincorporatesstate-of-the-artopacities,com- creasefromtheplateautothe∼10−5barlevelfordayside
positions, and radiative transfer will be needed to prop- modelswithoutstratospheresis∼1000K.Withastrato-
erly address day-night heat redistribution, the vortical sphere,theoutwardincreasefromapressureof∼0.1bars
and zonal mass motions, and the positions of the hot can be correspondingly large. For our nightside models,
and cold spots. Such a model is not yet within reach, the monotonic decrease is ∼500−1000 K. Models with
but there have been preliminary attempts to treat this temperature inversions due to a strong absorber at alti-
physics (Showman & Guillot 2002; Cho et al. 2003; tude clearly stand out in the panels of Fig. 1 and may
Menouetal.2003;Williamsetal. 2006;Cooper&Show- result from the presence of a trace species, TiO/VO, or
man 2005; Lunine & Lorenz 2002). The proper GCM a non-equilibrium species (Burrows et al. 2007b). The
physics remains the major uncertainty in current plane- possible effect of such upper-atmosphere absorbers on
tary secondary eclipse and light-curve modeling. the T/P profiles and the resultant dayside spectra are
exciting new features of the emerging theory of irradi-
3. TEMPERATURE−PRESSUREPROFILES ated EGPs.
We haveusedthe techniquesoutlinedin§2andinAp- The discussion above is made more germane when we
pendix§AandthedatainTables1and2tocreatemod- notethatthedecouplingsurfacesfortheIRACandMIPS
els of six ofthe close-inEGPsin Table 3 for whichthere (24-µm)channels,the effective photosphereswhereτλ ∼
are Spitzer secondary eclipse or phase light curve data. 2/3,areallintheouterzone. Figure1indicatestheirpo-
These planets are HD 209458b, HD 189733b, TrES-1, sitions for the dayside Pn = 0.3 model of TrES-1. They
HD 179949b, HD 149026b, and υ And b. The product are at similar pressuresfor all other models. The photo-
of our investigation is an extensive collection of atmo- spheres for shorter wavelengths not accessible to Spitzer
sphere models, with associated spectra, for many com- are deeper in. Figure 2 portrays these “formation,”
binations of planet, P , metallicity, and values of P /P “brightness,”orphotospherictemperaturesasafunction
n 0 1
(§A). Wehave,however,settledonpresentinginthispa- of wavelength for three models of TrES-1 with different
peronlythe centralandessentialresultsforeachplanet, valuesofPn,andforboththedaysideandnightside,and
in the knowledge that the data are not yet exquisitely illustrates this fact. The approximate wavelength inter-
constraining. vals of the Spitzer bands are superposed. Though the
We focus on models with solar-metallicity (Asplund, IRAC1fluxcandecoupleatinterestingdepths,thepho-
Grevesse,&Sauval2006)opacities,(P ,P )=(0.05,0.5) tospheres for the Y, J, H, and K bands are generally
0 1
bars, and an interior flux T of 75 K. These are our deeper. The photospheres in the far-IR beyond ∼10 µm
int
baselinemodelparameters. For agivenmeasuredplanet are high up at altitude and we repeat that Spitzer pho-
radius,thedependenceofthemodelsonT isextremely tometry does not probe the isothermalregionso charac-
int
weak. We find that the specific pressure range (P ,P ) teristic of theoretical close-in EGP atmospheres. More-
0 1
inwhichmostoftheheatcarriedfromthedaysidetothe over,sincetheSpitzerobservationsareprobingtheouter
nightside is conveyed plays a role in the planet-star flux regionsoftheatmospheremostaffectedbystellarirradia-
ratios, but a subtle one. Therefore, in lieu of a compre- tionandwhichcanhave inversions,the treatmentof the
hensive, and credible, 3D climate model, we prefer not outer boundary condition due to incoming stellar flux
to claim too much concerning the details of atmospheric must be accurate. Slight errors or uncertainties in the
circulation and heat redistribution. We also explore the outer boundary condition of the transfer solution, or in
effectsofastratosphericabsorberwithanopticalopacity the upper-atmosphere opacities, can translate into sig-
of κ (see also Burrows et al. 2007b). We find that such nificant errors in the predicted Spitzer fluxes. This is
e
models will be most important for close-in EGPs with particularlytrue longwardof ∼10µm. As a result, mea-
the greatest stellar insolation and guided by this princi- sured fluxes in both the near-IR and mid-IR are useful
ple, particularly relevant for HD 209458b, HD 149026b, diagnostics of upper-atmosphere absorbers and thermal
and υ And b, we explore the consequences. inversions(Hubeny,Burrows,&Sudarsky2003;Burrows
Figure 1 portrays in six panels the temperature- etal. 2006;Burrowsetal. 2007b;Knutsonetal. 2007c).
pressure (T/P) profiles of a representative collection of Allthesecaveatsandpointsmustbeborneinmindwhen
dayside and nightside models of the six close-in EGPs interpreting the Spitzer EGP data.
of this study. For the dayside, the different curves cor- As a prelude to our discussions in §4 and §5 of the
respond to different values of P from 0.0 (no redistri- Spitzer planet-star flux ratios at secondary eclipse and
n
bution) to 0.5 (full redistribution) and to models with duringanorbitaltraverse,andtoemphasizethefactthat
and without stratospheric absorbers. For the nightside, Spitzer does not comprehensively probe the irradiated
5
planet’satmosphere,weplotinFig. 3theoreticaldayside of Spitzer/IRS. Hence, fluxes at the longer IR wave-
spectra(λF versuslog (λ))forthreemodelsofTrES-1 lengths might be good diagnostics of thermal inversions.
λ 10
at zero phase angle (superior conjunction). Superposed The models in Fig. 4 for HD 209458b and HD 149026b
on the plot are the positions of the near-IR, IRAC, and demonstrate this feature best.
MIPS bands. Such a figure allows one to determine at No attempt has been made to achieve refined fits, but
a glance the wavelengths at which most of the flux is the correspondence between theory and measurement,
radiated (at least, theoretically). As Fig. 3 suggests, whilenotperfect,israthergoodforalltheplanets. More-
most of the planet’s flux emerges in the near-IR, not in over, different EGPs seem to call for different values of
the IRAC or MIPS channels. In fact, depending on the P and κ , and, hence, perhaps, different climates, de-
n e
planet,nomorethanonefifthtoonethirdoftheplanet’s grees of heat redistribution, compositions, and upper-
flux comes out longwardof∼3.6 µm (IRAC 1), while no atmospheric physics. The light-curve analyses in §5 also
more than one twentieth to one tenth emerges longward suggest this. A goal is to relate these measured differ-
of∼6.5µm,the“left”edgeoftheIRAC4channel. Since ences with the physicalproperties of the star and planet
much of the best EGP data have been derived in IRAC andthese infraredsecondaryeclipse dataallowus to be-
channel4,onemustacknowledgethattheymayrepresent gin this programin earnest.
very little of the total planetary emissions. We note that comparisons between model and data
Finally, we call the reader’s attention to the slight must actually be made after the band-averaged flux-
bumps (on the nightside) and depressions (on the day- density ratios of the detected electrons are calculated.
side) between 0.05 and 1.0 bars in the T/P profiles de- Performing this calculation slightly mutes the predicted
picted in Fig. 1. This region is near where we imposed variation from channel to channel in the IRAC regime.
heat redistribution using the formalism described in §A. This is particularly true when comparing IRAC 1 and
Theactualshapesoftheseprofilesaredeterminedbythis IRAC2,evenifapronouncedspectralbumpatandnear
mathematical procedure and other algorithms will pro- ∼3.6 µm obtains, as it does for models with modest or
duce different localthermalprofiles. Note that with this no thermal inversion. However, to avoid the resultant
formalismitispossibleatthehigherP s(≥0.35)forthe clutter and confusion, we do not plot these bandpass-
n
nightsidetobehotterthanthedaysideatthesamepres- averaged predictions on Figs. 4 and 5. We now turn
sure levels in the redistribution region. While this may to case-by-casediscussions ofthe secondaryeclipse mea-
seem at odds with thermodynamics, what is essential is surements and models.
that energy is conserved and is redistributed at optical
depths that are not either too low or too high. If the 4.1. HD 209458b
former, the absorbed stellar heat would be reradiated The first transiting EGP discovered was HD 209458b
before it can be carried to the nightside. If the latter, (Henry et al. 2000;Charbonneauet al. 2000)and it has
then the stellar radiation can not penetrate to the con- sincebeenintensivelystudied. Thedirect-detectiondata
veyorbelt. Forourdefault choiceofP0 andP1, τRossland ofrelevancetothispaperaresummarizedinTable3. The
is generallybetween ∼0.3 and ∼6. These depths are not most relevant data are the geometric albedo constraints
unreasonable,but our redistribution algorithmis clearly in the optical from MOST (Rowe et al. 2006,2007), a
onlyastopgapuntilabetterGCMcanbedevelopedand K-band upper limit using IRTF/SpeX from Richard-
justified. son, Deming, & Seager (2003), a MIPS/24-µm photo-
metric point from Deming et al. (2005) (and its possi-
4. PLANET-STARFLUXRATIOS−COMPARISONWITH bleupdate),alow-resolutionSpitzer/IRSspectrumfrom
DATA Richardson et al. (2007), and, importantly, photomet-
We discuss below and in turn model fits for each ric points in IRAC channels 1 through 4 from Knutson
transiting EGP at secondary eclipse. However, first we et al. (2007c). These data collectively provide useful
present our results collectively and in summary fashion. information on the atmosphere of HD 209458b.
Figure 4 in four panels portrays for the four transiting MotivatedbytherecentdataofKnutsonetal. (2007c),
EGPs the correspondencebetween the secondaryeclipse Burrows et al. (2007b) provide partial theoretical ex-
data and representative models of the planet-star flux planations for HD 209458b’s atmosphere. Much of the
ratio as a function of wavelengthfrom 1.5 µm to 30 µm. discussion in the current paper concerning HD 209458b
This figure summarizes our major results. The models is taken from Burrows et al. (2007b), so we refer the
areforvaluesofP of0.1,0.3,and0.5andvariousvalues readertoboththeBurrowsetal. (2007b)andKnutsonet
n
of κ . The data include 1-σ error bars and can be found al. (2007c) papers for details. However, here we expand
e
in Table 3. As Fig. 4 indicates, we can fit all the pub- upon the discussion in those works where it is necessary
lished data. The P dependence for both stratospheric to put the HD 209458b findings in the broader context
n
modelsandmodelswithoutinversionsisstrongestinthe of the EGPs listed in Table 3. The major conclusion of
K band and in IRAC 1. In fact, in the near-IR, models Burrows et al. (2007b) is that the atmosphere of HD
with inversions depend very strongly on P . Fig. 5 for 209458bhasathermalinversionandastratosphere,cre-
n
HD 209458b in the near-IR indicates this most clearly. ated by the absorptionof optical stellar flux by a strong
This finding implies that measurements at these shorter absorberat altitude, whose originis currently unknown.
IR wavelengths are good diagnostics of P , particularly This convertsabsorptionfeatures into emissionfeatures,
n
if inversions are present. while still being consistent with the presence of water in
Importantly, including a non-zero κ and generating a abundance.
e
stratosphere results in a pronounced enhancement long- All relevant data, save the albedo constraint in the
ward of IRAC 1, particularly in IRAC 2 and 3, but optical, are displayed in the upper-left panel of Fig. 4.
also at MIPS/24 µm and at the 16-µm peak-up point Figure 5 includes the Knutson et al. (2007c) IRAC 1
6
point and the Richardson,Deming, & Seager (2003)up- sit spectroscopy (Charbonneau et al. 2002). Both these
perlimitinK andfocusesonthenear-IR.Alsoprovided datasetssuggestthatanycloudsthatmightresideinthe
on both figures are models for P = 0.1, 0.3, and 0.5, atmosphereof HD 209458bare thin. A thick cloud layer
n
without and with an extra stratospheric absorber. The wouldreflectlightefficiently,leadingtoahighalbedo. If
latter is implemented using the formalism in outlined in the extra stratosphericabsorber is in the gas phase, and
§2 and a κ of 0.1 cm2/g. there is no cloud, then our new thermal inversion mod-
e
Figure 4 shows that the low upper limit of Richard- els are easily consistent with the low albedo derived by
son, Deming, & Seager (2003) in the K band that Roweetal. (2006,2007). Iftheextraabsorberisacloud,
was problematic in the old default theory (Burrows, thecloudparticlesmusthavealowscatteringalbedoand
Hubeny, &Sudarsky2005;Fortney etal. 2005;Barman, cannotbe veryreflecting. Thisrulesoutpure forsterite,
Hauschildt, & Allard 2005; Seager et al. 2005; Burrows enstatite, and iron clouds.
et al. 2006) is consistent with the models with an extra TheIRSdataarenoisy,buttheirflattishshapeiscon-
upper-atmosphere absorber in the optical, particularly sistent with our model(s) with thermal inversions and a
for higher values of P . This is more clearly seen in Fig. stratosphere. Richardsonetal. (2007)suggestthatthere
n
5. Moreover,thetheoreticalpeakneartheIRAC1chan- isevidenceintheIRSdatafortwospectralfeatures: one
nel (∼3.6 µm) in the old model without an inversion is near 7.78 µm and one near 9.67 µm. However, we think
reversed with the extra absorber into a deficit that fits the data are too noisy to draw this conclusion. Richard-
the Knutson et al. (2007c) point. The theory without son et al. (2007) also suggest that the flatness and ex-
an extra absorber at altitude predicts that the planet- tension of their data to shorter wavelengths implies the
star flux ratio in the IRAC 2 channel should be lower near absence of water, since previous theoretical mod-
than the corresponding ratio at IRAC 1. However, with els predicted a spectral trough between ∼4 µm and ∼8
the extra absorber the relative strengths in these bands µm. However, if there is an outer thermal inversion, as
are reversed, as are the Knutson et al. (2007c) points. we here and in Burrows et al (2007b) argue is the case
This reversalis a direct signature of a thermal inversion for HD 209458b, a trough is flipped into a peak for the
in the low-pressure regions of the atmosphere, and an samewaterabundance. Thisrendersmoottheuseofthe
indirect signature of the placement of the heat redistri- spectral slope at the edge of the IRS spectrum to deter-
bution band (see Appendix §A). The top-left panel of minethepresenceorabsenceofwater. Oneofourmajor
Fig. 1 depicts the corresponding temperature-pressure conclusions, implicit in Figs. 4 and 5, is that water is
profilesandthe thermalinversionatlowpressuresintro- not depleted at all in the atmosphere of HD 209458b.
ducedbythepresenceofanextraabsorberintheoptical Therecentcontroversiessurroundingsuchaninterpre-
that is indicated by the data. tationoccasionthefollowingremarks. Onethingtobear
As Fig. 4 also demonstrates, there is a significant dif- in mind concerning the use of these IRS spectra to infer
ference in the IRAC planet-star flux ratios between the compositions is that they are very low resolution. The
olddefaultmodelwithoutaninversionandthenewmod- useofclassicalastronomicalspectroscopytoidentifycon-
els with a stratospheric absorber, and that the models stituentsstemsfromtheabilityatmuchhigherresolution
with a stratosphere fit the IRAC channel 1, 2 and 4 flux to see characteristic features at precise wavelengths and
points much better. However, the height of the IRAC 3 patternsofabsorptionoremissionlinestohighaccuracy.
pointnear5.8µmis noteasilyfit, while maintaining the This allows one to make element and molecule identifi-
goodfitsattheotherIRACwavelengthsandconsistency cations in a narrow wavelength range without a global
withtheK-bandlimit. Theoretically,thepositionsofthe view across the whole spectrum. However, at the low
IRAC3andIRAC4photospheresshouldbeclosetoone resolution of the IRS, no individual water features are
another, so this discrepancy is surprising. Nevertheless, accessible. There are water features near ∼10 µm, but
the IRAC 2, 3, and 4 data together constitute a peak, theywouldrequireaλ/∆λisexcessof∼2000toidentify.
whereas in the default theory an absorption trough was Otherwise, all one sees is the collective effect of millions
expected. of lines and the resulting pseudo-continuum (the band
The 24-µm MIPS point obtained by Deming et al. structure). Clearly, when the data are low-resolution,
(2005)is lowerthanthe predictionofour best-fit model. a global photometric and spectral fit is necessary to ad-
However, the flux at this point is being reevaluated and dress the issue of composition. The signature of water’s
may be closer to ∼0.0033±0.0003 (D. Deming, private presencecomesfromthegoodnessoftheglobalfitacross
communication). If the new number supercedes the old the entire spectrum from the optical to the mid-IR. The
published value, then our best-fit model(s) with inver- good fit we obtain in Fig. 4, lead us to conclude that
sions fit at this mid-IR point as well (Fig. 4). Higher the IRS, IRAC 4, and MIPS data for HD 209458b are
planetaryfluxeslongwardof∼10µmaregenericfeatures consistent with the presence of water in abundance.
of stratospheric inversions. Note that if the T/P profile were entirely flat (but
The 1-σ optical albedo limit from Rowe et al. (2007) see Fig. 1), whatever the opacity and molecular abun-
is a very low 8.0%. For comparison, the geometric albe- dances the emergent spectrum would be a perfect black
dos of Jupiter and Saturn are ∼40%. However, such body and would give no hint concerning composition.
a low number was predicted due to the prominence in Transit spectra would then be our only reliable means
theopticalofbroadbandabsorptionsbythealkalimetals of determining atmospheric composition (Fortney et al.
sodium and potassium in the hot atmospheres of irradi- 2003; Barman 2007; Tinetti et al. 2007; Ehrenreich et
atedEGPs(Sudarskyetal. 2000;their“ClassIV”). The al. 2007). However, as we have argued, there is every
associatedplanet-starflux ratiosare ∼10−5−10−6. This indication that the T/P profiles of strongly irradiated
lowalbedoisconsistentwiththeidentificationofsodium EGPs are not flat (Fig. 1). As a result, spectral mea-
intheatmosphereofHD209458busingHST/STIStran- surements of irradiated EGPs can be usefully diagnostic
7
of both composition and non-trivial thermal profiles. 2,and3dataforHD189733bprovetodecreasemonoton-
ically with wavelength shortward of IRAC 4, this would
4.2. HD 189733b be fully consistent with the presence of the water band
ModelsforHD189733batsecondaryeclipse,withand between ∼4 µm and ∼8 µm in absorption.
without an extra upper-atmosphere absorber, are por-
4.3. TrES-1
trayed in the upper right-hand panel of Fig. 4. They
include κ = 0.0 cm2/g models with P = 0.1, 0.3, and Charbonneau et al. (2005) obtained IRAC 2 (∼4.5
e n
0.5, and one κ = 0.04 cm2/g model with P = 0.3. µm) and IRAC 4 (∼8.0 µm) data for TrES-1 and these
e n
The IRAC 4 data at 8 µm from Knutson et al. (2007b) data were analyzed by Burrows et al. (2005). A major
[brown], the IRS peak-up point at 16 µm obtained by conclusionofthatpaperwasthatwaterisindeedseenin
Deming et al. (2006) [gray], and the IRS spectrum absorption. Ournewmodels,depictedinthebottom-left
between ∼7.5 µm and ∼13.5 µm from Grillmair et al. panel of Fig. 4 with the two IRAC data points super-
(2007)[gold] are superposed on the figure. Though data posed, reinforce this finding. As can be seen in the fig-
in the other IRAC channels and at 24 µm have been ure,themodelswithdifferentvaluesofP (here,allwith
n
taken and reduced, they have yet to be published. κ = 0) can not easily be distinguished using these two
e
As this panel indicates, the IRAC 4 point can be fit IRAC points. This fact emphasizes the need to obtain
by models that include most values of P , with a very more Spitzer photometric data to help better constrain
n
slight preference for lower values from 0.1 to 0.3. The the properties of the atmosphere of TrES-1. However,it
IRS data are not well-calibrated, but evince the slight isclearfromthesignificantdropinplanet/starfluxratio
turndownattheshorterwavelengthscharacteristicofat- from IRAC 4 to IRAC 2 that the atmosphere of TrES-1
mospheres with weak or no stratosphericabsorber. This is qualitatively different from that of HD 209458b. In
turndownisincontrastwiththebehavioroftheRichard- particular, this behavior is a signature of a strong water
sonetal. (2007)IRSdataforHD209458b,andreinforces absorptiontrough. There are no signatures of a thermal
the conclusionthata thermalinversion,if presentinHD inversion in the atmosphere of TrES-1, or of water in
189733b,is very slight (see the upper-right panel of Fig. emission, and the old, default models with a monotonic
1). However, the 16-µm point of Deming et al. (2006) temperature profile (see left-middle panel of Fig. 1) are
is a bit higher than models with κ = 0, whatever the perfectly suitable. Given this, we predictthat the IRAC
e
value of P . This suggests that there may be some ex- 1 point (when obtained) will be slightly higher than the
n
traheatingintheupperatmosphereofHD189733b,but IRAC 2 point.
thatitis weakerthaninthe atmosphereofHD 209458b.
The κ = 0.04 cm2/g model shown in the HD 189733b 4.4. HD 149026b
e
panels of Figs. 1 and 4 indicates the possible magnitude AsissuggestedbytherelativevaluesofF foundinTa-
p
ofsuch stratosphericheating, if present. Note that to fit ble 1 for HD 209458b,HD 189733b,and TrES-1 and the
the 16-µm point we require a smaller value of κ than different thermal profiles inferred for their atmospheres,
e
usedtofittheIRACchanneldataforHD209458b(κ = there appears to be a correlation between the charac-
e
0.1 cm2/g). This may not be surprising, since, as Table ter of a planet’s atmosphere and its value of F , or a
p
1 indicates, the stellar flux atthe substellar point of HD related quantity (UV insolation?). This possibility is in-
189733b is lower by more than a factor of two than the triguing, but not yet explained. In particular, we have
correspondingnumber for HD209458b. Perhaps,this in- yet to identify the extra stratospheric absorber in that
dicatesasystematictrendforthefamilyofstronglyirra- subsetofclose-inEGPs“clearly”manifestingthermalin-
diatedtransitingEGPs(seeTables1and3),withplanets versions. However, 1) HD 149026b’s F is almost twice
p
withthehighervaluesofF possessingstratospheresand that of HD 209458b, 2) it has one of the hottest atmo-
p
atmospheres with pronounced inversions. spheres among those listed in Table 1 (see middle-left
Be that as it may, we can predict, using the logic em- panel of Fig. 1), and 3) we can not fit the IRAC 4
ployedin §4.1, that if the IRAC 1 to IRAC 2 ratio turns data point obtainedby Harringtonet al. (2007)without
out to be greater than or close to one, any thermal in- a strong temperature inversion. The latter conclusion
version in the atmosphere of HD 189733b is either not agrees with that of Fortney et al. (2006), who predicted
pronounced,orisabsent. Underthesecircumstances,we a mid-infrared flux for HD 149026bnear the value actu-
certainly would then expect the “brightness” tempera- ally measured by Harrington et al. (2007) by allowing
ture at IRAC 1 to be demonstrably higher than that at TiO/VO to reside at low pressures for the hottest at-
IRAC 2 (see, e.g., Fig. 2). Conversely, if the IRAC mospheres (Hubeny et al. 2003). The lower-right panel
1 to IRAC 2 ratio is much less than one (as for HD of Fig. 4 depicts three models for HD 149026b, one of
209458b),then a thermal inversionin the atmosphere of which has κ = 0.64 cm2/g. This is much larger than
e
HD189733bwouldbe stronglysuggested. Thesamecan the κ employed to fit HD 209458b. The stratospheric
e
besaidoftheIRAC4toIRAC3ratio. IftheIRACchan- modelshownhasP =0.0,whichminimizesthevalueof
n
nel 3 planet-to-star flux ratio is higher than the Knut- κ necessarytofitthe loneHarringtonetal. (2007)data
e
son et al. (2007b) point at 8 µm, then a stratosphere point,anditisthe onlymodelamongthe threedepicted
would be indicated for HD 189733b. Since the irradi- in Fig. 4 that does fit. Therefore, the trend in “inver-
ation regime of HD 189733b is a bit more benign than sion”strength”withF ,seeninthesequenceTrES-1,HD
p
thatofHD209458b,andgiventhe contrastintheshort- 189733b,and HD 209458b, continues with HD 149026b.
wavelength behavior of the IRS data for each EGP, we Not only do the EGP atmospheres grow hotter with F
p
hypothesize that HD 189733b does not boast much of a (a not unexpected result), but the importance of a ther-
stratosphere. NotethatourHD189733bmodelsallhave malinversionandastratosphereinexplainingtheextant
waterinabundanceandthatiftheunpublishedIRAC1, data increaseswith it as well. Given the currentpaucity
8
of data for HD 149026b, we urge that HD 149026b be at the lower temperatures (∼1000−2000 K) of the re-
a priority target so as to help discriminate the various sulting planetary atmospheres. The ratio between the
models only partially represented on the HD 149026b opticalandIRcomponents,andthus the relativeadvan-
panel of Fig. 4. We predict that the pattern of the four tage of IR measurements, is roughly the square of the
IRAC flux ratios for HD 149026bwill mimic that found ratiobetween the orbitaldistance andthe stellar radius,
forHD209458b,andthatits fluxratiosfrom∼10µmto a number near ∼102 for most of the planets listed in
∼30µmwillcomfortablyexceedthoseofmodelswithout Table 1.
obvious thermal inversions, perhaps by large margins.
5.1. υ And b
5. LIGHTCURVES−COMPARISONWITHDATA Harringtonetal. (2006)havemeasuredthephasevari-
Measuring the infrared planet-star contrast ratio as a ationat24µmoftheplanet-starcontrastfortheclose-in
function of orbital phase, i.e., the planet’s light curve, EGP υ And b (Butler et al. 1997). Since this planet is
provides the best constraints on the longitudinal dis- not transiting, we know neither Mp nor sin(i), but only
tribution of planetary emissions. In principle, phase- thecombinationMpsin(i)(=0.69MJ). Moreover,with-
dependent light curves at different wavelengths can be outatransitwedon’thaveameasurementofRp. Infact,
inverted to determine the “brightness” temperature and themodelsusedtofitthefive(!) datapointsobtainedby
composition distributions over the surface of the planet, Harrington et al. (2006), which are not anchored by ab-
includingitsnightside. Contrastratiosobtainednotjust solutecalibration,dependonPn,κe,Rp,andsin(i)(see
at secondary eclipse (α = 0◦), but also at other phase eq. 1). In addition, all interpretations hinge upon only
angles, help reveal and quantify zonal winds and estab- the two extreme points in the Harrington et al. (2006)
lish their role in redistributing stellar energy (i.e., P ) dataset. Therefore, we have too many degrees of free-
n
and matter around the planet. They can help identify dom to allow us to draw strong conclusions concerning
transitions at the terminator (Guillot & Showman 2002; planetary and atmospheric parameters and must make
Showman & Guillot 2002), shifts in the substellar hot do with limits and general correlations.
spot (Cooper & Showman 2005; Williams et al. 2006), Figure 6 portrays in eight panels comparisons of theo-
asymmetriesinthethermaldistributions(Knutsonetal. retical 24-µm phase curves with the υ And b data. The
2007b), and persistent atmospheric structures. In sum, left panels contain models with κe = 0, and the right
light curve measurements probe both atmospheric dy- panelscontainmodels withκe = 0.2cm2/g. The models
namics and the planet’s climate and are the key to the in the top four panels have Pn = 0.0, and those in the
bona fide remote sensing of exoplanets. bottom four panels have Pn = 0.3. Inclinations of both
Having said this, since full light curves require many 45◦ and80◦ (near eclipse)are employed. Oneachpanel,
morepointings andmuchmoretelescope time to obtain, we provide models with a wide range of planetary radii.
and mostly address the dimmer phases of a planet’s or- Since the data have no absolute calibration, we are free
bitaltraverse,obtainingthemismuchmoredifficultthan to move the data points up and down, as long as their
measuring the contrast ratio at secondary eclipse. As a relative values are maintained, and we have done so in
result,todatethereareonlythreepublishedlightcurves an attempt to provide on each panel the best fit to the
for irradiatedEGPs (for υ And b, HD 179949b,and HD overall shape and the day/night difference. The corre-
189733b), despite numerous observational forays. All of sponding T/P profiles at α = 0◦ (day) and α = 180◦
these are for only one Spitzer waveband each and none (night) are displayed in the lower-left panel of Fig. 1.
coversacompleteorbit. Theredoexistrecentupperlim- Fromfigures like Fig. 6, we can extractgeneraltrends
its (e.g., Cowan et al. 2007), but these are not usefully and limits. In their discovery paper, the authors noted
constraining and we will not address them here5. that the shift of the hot spot away from the substel-
Below, we discuss the three systems for which light lar point was small. They also remarked on the large
curves,howeversparse,havebeenobtainedandtrytoex- difference from peak to trough (∼0.002). Both observa-
tractphysicalinformationby comparisonwithour light- tionssuggestedthatthereisnotmuchheatredistribution
curve models (eq. 1). Before we do so, we note the from the dayside to the nightside and that Pn is small,
following. Classic light curve studies are in the opti- perhaps near zero. While at this stage this conclusion
calandmeasuregeometricalbedos,phase functions (Su- can not be refuted, our models suggest that there is a
darsky et al. 2005), and polarizations, i.e. they mea- broader range of possible interpretations. Importantly,
surereflectedstellarlight. Albedosandpolarizationsare as we have noted in §4, the presence of a stratosphere
significantly affected by the presence of clouds, and so canenhance dayside planetaryfluxes in the mid-IR, and
these traditional optical campaigns focus on reflection certainlynear24µm,evenformodestvaluesofPnwhich
by condensates or surfaces. The planet-star flux ratios would otherwise decrease D/N (eq. 1). υ And b expe-
in the optical range from ∼10−10 for EGPs at AU dis- riences a substellar flux, Fp, of ∼1.3×109 erg cm−2 s−1,
tancesto ∼10−5−10−6 for the close-inEGPsnear∼0.05 andthisislargerthanthatimpinginguponHD209458b.
AU (Table 1). However, in the near- and mid-IR, the Therefore, we expect that the atmosphere of υ And b
planet-star contrasts are around ∼10−3 (see Figs. 4 and will have a thermal inversion as well, thereby enhanc-
5). These larger numbers are why Spitzer IR measure- ingthe mid-IRday/nightcontrastsevenforvaluesofPn
ments, rather than optical measurements, have assumed near0.36. Whatismore,largevaluesofRparebecoming
center stage in the direct study of EGPs. The light seen
is not reflected stellar light, but reprocessed stellar flux, 6Itispossiblethatsin(i)issmall,and,therefore,thatthegrav-
emitted predominantly in the near- and mid-IR (Fig. 3) ity and Mp are large. It is also possible that a large gravity can
shiftthe breakpoint between EGP atmospheres withand without
inversions. However,wesuspectthatFp,morethangravity,isthe
5 However,afewoftheselimitsarelistedinTable3. crucialparameterindeterminingthisbifurcation.
9
commonplace, and we can not eliminate this possibility 7),whilea(P ,κ ,i)=(0.0,0.08,80◦)modelrequiresa
n e
forυ Andb. Alargevalue ofR increasesthe amplitude radiusof∼1.0R (top-rightpanelofFig. 7). Whereasa
p J
swing from day to night. Therefore, many parameter (P , κ , i) = (0.3, 0, 80◦) model requires an R of ∼1.6
n e p
combinations can fit these data. R , one with κ = 0.08 cm2/g requires a much smaller
J e
We summarize the lessons of Fig. 6 as follows. All radius, ∼1.1 R . These radii are unexceptional, and
J
else remaining the same, a change of Pn from 0.0 to 0.3 in general the presence of a stratosphere substantially
resultsinanincreaseintheRprequiredof∼0.3−0.5RJ . decreasesthevaluesrequiredtofitthesedata. Therefore,
Substituting κ = 0.2 cm2/g for κ = 0.0 decreases the for HD 179949b we can fit the light-curve data with a
e e
R necessary by ∼0.4−0.5 R . Replacing models with i quite reasonable combination of parameters, though the
p J
= 45◦ by those with i = 80◦ decreases the R required various degeneracies still need to be broken.
p
by ∼0.2−0.3 R . Specifically, a (P , κ , i) = (0.0, 0, Finally,Fig. 7suggeststhattheshiftbetweenthetran-
J n e
80◦) model has a required radius of ∼2.0 R (top-left sit ephemeris and the light curve phases is not large, so
J
panel of Fig. 6), while a (P , κ , i) = (0.0, 0.2, 80◦) we don’t see any obvious advection downstream of the
n e
model has a required radius of ∼1.5 R (top-right panel hot spot. This is consistent with the interpretation by
J
of Fig. 6). And while a (P , κ , i) = (0.3, 0, 80◦) model Harrington et al. (2007) of the υ And b phase curve
n e
requires an R of ∼2.5 R , one with κ = 0.2 cm2/g (Fig. 6) and may be a feature of EGPs with strato-
p J e
requiresaradiusof“only”∼1.8R . Clearly,introducing spheres and/or hot upper atmospheres. While very ten-
J
stratospheres into the mix allows P to assume a range tative, this suggestion is reinforced by the observation
n
of non-zero values for which heat redistribution would that there is a definite displacement of the hot spot of
notbe consideredsmall. However,theimpliedplanetary HD 189733b, which seems to have a cooler upper atmo-
radiuswouldnotbesmalleither,thoughitwouldstillbe sphere (Fig. 1). However, the perception of meaningful
within the currently measured range. differences in the displacements of hot spots could just
Some of this degeneracy might be broken with light- as easily be false and be a consequence of having better
curve measurements at many wavelengths and with a data for HD 189733b. Moreover, we don’t yet have a
more rapid cadence. Furthermore, astrometric mea- good model for the origin of such differences and possi-
surements of the stellar wobble can provide sin(i) and ble correlations with P . Clearly, better sampled phase
n
the planet’s mass, eliminating one important ambiguity. curve data would be very useful.
Spitzer canstill be usedto providethe former,while the
latter is well within reach of ground-based astronomy. 5.3. HD 189733b
Finally, we would be remiss if we did not mention that Currently, the only light curve we have for a transit-
JWST will inaugurate an era of stunning photometric ing EGP was obtained in IRAC 4 at ∼8 µm by Knutson
improvement (by a factor of at least ∼102) over current et al. (2007b)7. Not only do we have HD 189733b’s
IR platforms for the study of the light curves of both radius (Table 1), but these light-curve data have abso-
transiting and non-transiting EGPs. lute calibrations. In addition, there is dense coverage
overa bit more than half the orbit, from just before sec-
5.2. HD 179949b ondary eclipse to just after primary transit. Knutson et
al. (2007b) derive the longitudinal dependence of the
Cowan et al. (2007) obtained a light curve in IRAC
surface brightness and find a hot spot shifted by 16±6◦
channel 4 (∼8 µm) of another non-transiting giant
east of the substellar point, while the coolest region is
planet, HD 179949b (Santos, Israelian & Mayor 2004;
shifted about 30◦ west of the anti-stellar point. Curi-
Wittenmyer, Endl & Cochran2007). It has an M sin(i)
p ously, both the hot spot and the coolest spot are in the
of ∼0.95 M and a value of F of ∼1.32×109 erg cm−2
J p same hemisphere. Nevertheless, this is the first “map”
s−1). This makes it similar to the υ And system, both
of the surface of an exoplanet (Burrows 2007). The au-
in its general properties and in the limitations on what
thors also found an indication of a nonzero, but small,
can be uncovered.
eccentricity with ecosω = 0.0010±0.0002, where ω is
The lowerright-handpanel of Fig. 1 displays the day-
the longitude of periastron, a transit radius at 8 µm of
sideandnightsideT/P profilesofthelight-curvemodels
1.137±0.006R (slightlysmallerthantheopticalradius),
J
used to model these data. Figure 7 portrays the cor- astellarradiusof0.757±0.003R⊙,andaninclinationof
responding eight-panel figure comparing our theoretical 85.61±0.04 degrees.
models for various combinations of P , κ , sin(i), and
n e These data are clearly the best of their kind and we
R with the eight data points of Cowan et al. (2007).
p have attempted to fit them with our techniques and eq.
Figure 7 is similar to Fig. 6, but the thermal inversion
1. The results are displayed in Fig. 8. The data are
models are for κ = 0.08 cm2/g and the range of model
e plotted as black hexagons, while the models are for var-
radii are different. The data for HD 179949bare impor-
ious values of P . One model (dashed green) assumes
n
tant, but no less ratty than those for υ And b. Never- 10×solarmetallicity. All these models, save one, assume
theless, the values of R required to fit HD 179949b are
p (P : P ) = (0.1, 1.0) bars, not our default pair, but this
0 1
systematically lower. makes little difference. As indicated in §4.2, we can fit
We summarize our conclusions from Fig. 7 as follows.
the contrast ratio in IRAC 4 at secondary eclipse rather
AchangeofP from0.0to0.3requiresR toincreaseby
n p easily,withaslightpreferenceforasmallnon-zeroκ . As
e
∼0.1−0.2 RJ . Replacing κe = 0.0 cm2/g by κe = 0.08 Fig. 8 suggests, a super-solar metallicity might also do
decreasesRpby∼0.2−0.4RJ . Substitutingmodelswith the trick, but the metallicity dependence is rather weak.
i = 45◦ for those with i = 80◦ decreasesRpby ∼0.1−0.2 Data in other bandpasses should break the degeneracy.
R . A (P , κ , i) = (0.0, 0, 80◦) model that fits the
J n e
data requires a radius of ∼1.2 RJ (top-left panel of Fig. 7 However,thisisonlythefirstofmanyanticipated.
10
However,we cannot fit the small day/nightdifference & Sudarsky (2003) and Burrows, Sudarsky, & Hubeny
with any of our models. The data seem to imply a se- (2006),aswellasintheprescientpaperbyFortneyetal.
vere degree of heat redistribution, one that is still not (2006), the absorber was gas-phase TiO/VO, which for
captured even with our P = 0.5 model. We note in hotatmospheresinchemicalequilibriumcanexistatlow
n
passingthatmodelswithP =0.5donotimplythatthe pressures at altitude and not just at high temperatures
n
dayside and nightside should look the same, only that at depth. The upper-atmosphere absorber that is pro-
the integral fluxes over the entire spectrum should be ducing stratospheres for the higher values of F might
p
comparable. Since the dayside is irradiated, while the indeed be TiO/VO, but a “cold-trap” effect can operate
nightside emits into the blackness of space, as the upper to deplete the upper atmosphere of TiO/VO. However,
right-hand panel of Fig. 1 indicates, the T/P profiles whenmasslossis ongoing,aswe knowto be the casefor
at α = 0◦ and α = 180◦ are different. This translates HD 209458b(Vidal-Madjar et al. 2003,2004),the atmo-
quitenaturallyintodifferentday-nightcontrastratiodif- sphere is constantly being replenished and TiO/VO at
ferences for different wavelengths,even for P =0.5. some non-zero abundance remains a viable option. Such
n
What we seem to be seeing in the Knutson et al. vigorousmassloss is expected for those planets with the
(2007b) data are atmospheric inhomogeneities, thermal highest values of F , and in this paper we have discov-
p
structures (vortices?), on the surface of HD 189733b. ereda possible correlationbetween F and the existence
p
That the hot spot and the coolest spot are in the same ofthermal inversionsand stratospheres. Hence, the pos-
hemisphere, separated by only ∼45◦, suggests our sym- sible mass-loss/stratosphere connection may make for a
metricmodelsareinadequatetofitthisphasecurve. Itis compelling scientific narrative.
of paramount importance that a full light curve over all Thetholins,polyacetylenes,orvariousnon-equilibrium
phase angles be taken in a variety of wavebands. Well- compoundsdiscussedinthecontextofsolar-systembod-
sampled data at longer wavelengths would be particu- ies could also be the necessary upper-atmosphere op-
larly welcome. Moreover, model phase curves need to tical absorber. Given the stellar UV and integral-flux
besophisticatedenoughtoincorporatetemporaland3D regimes experienced by strongly-irradiated EGPs, such
spatial variations. The light curves and night-side heat- species might be photolytically produced with sufficient
ingandthermalprofilesdependcentrallyonjetstreams, abundance (Burrows et al. 2007b; Marley et al. 2007).
winds, and general thermal redistribution. This puts a However, to study these molecules requires a full non-
premium on developing GCMs with reasonable global equilibriumchemicalnetworkandwewon’tattemptthis
dynamics coupled to realistic radiative transfer models. here. Clearly, what the high-altitude absorber actually
Such models do not yet exist for the study of EGPs. is, TiO/VO or some other compounds, awaits investi-
gation and is the primary reason we parametrized its
6. DISCUSSIONANDCONCLUSIONS opacity with κ 8.
e
In this paper, we have constructed atmosphere and The trend with Fp we have uncovered suggests, how-
spectralmodels for allthe close-inextrasolargiantplan- ever crudely, that those EGPs with values of Fp higher
ets for which direct-detection data from Spitzer have than HD 209458b’s (∼109 erg cm−2 s−1) may well have
been published (except for the “Neptune” GJ 436b). stratospheres. Table 1 provides the needed numbers.
These models incorporate the effects of external stel- WhatthistablesuggestsisthatTrES-2,TrES-3,TrES-4,
larirradiation,detailedatmospheres,heatredistribution, HAT-P-2b, HAT-P-4b, HAT-P-5b, HAT-P-6b, OGLE-
and, for some, a model for stratospheric heating. Com- TR-10b, WASP-1b, WASP-3b, XO-3b, OGLE-TR-56b,
paring the resulting suite of models with the data for OGLE-TR-211b,andOGLE-TR-132b,inadditiontoHD
these six EGPs, we have derivedconstraints on their at- 149026b,are strong candidates for having stratospheres,
mospheric properties. We find, as did Burrows et al. with all the consequences implied for their spectra and
(2007b), that many severely irradiated EGPs can have light curves (§4; §5). Close-in, though non-transiting,
thermal inversions at altitude which translate into qual- EGPs with high values of F (such as τ Boo b, to name
p
itative changes in 1) the planet/star contrast ratios at only one of many) are also likely to have thermal inver-
secondary eclipse, 2) their wavelength dependences, and sions. They too should manifest the spectral discrimi-
3)day-nightfluxcontrastsduringaplanetaryorbit. Ab- nants identified in Figs. 4 and 5 and the changes in the
sorption features can flip into emission features, plane- phase curves discussed in §5 and suggested by Figs. 6
taryfluxesatlongwavelengthscanbeenhanced,andthe and 7. Note that by including in the above list HAT-
secondary-eclipse spectra in the near-IR can be altered P-2b, which has ∼10× the mass of the average close-in
significantly. What is more, we find a correlation be- EGP, we have not addressed the possible role of grav-
tween the importance of such stratospheres and the flux ity in these systematics. Though we suspect gravity is
at the substellar point on the planet. sub-dominant when compared with F , the dependence
p
Hubeny, Burrows, & Sudarsky (2003) and Burrows, ofupper-atmospherephysicsandchemistryupongravity
Sudarsky,& Hubeny (2006)showedthatstrongly irradi- should prove worth exploring.
atedatmospherescanexperienceasolutionbifurcationto Itisunlikelythatwewillsoonobtainspectraldatafor
anatmospherewithaninversionforwhichwaterspectral theOGLEplanets. However,itisdistinctlypossiblethat
features arereversedfromtroughs(absorption)to peaks EGPs listed in Table 1 with F s slightly lower than HD
p
(emission). Thispossibilityissupportedbythegoodfits 208459b’s will have “weak” stratospheres, as we specu-
obtained by Burrows et al. (2007b) to the HD 209458b
IRAC data (Knutson et al. 2007c)andby our models in 8 However, for some of the models in Burrows et al. (2007b)
thispaperforthesubsetofirradiatedEGPsforwhichthe we used equilibrium TiO/VO abundances and the corresponding
molecularopacities(Sharp&Burrows2007). Thesemodelsrepro-
presence of stratospheres is suggested (in particular HD
ducedtheHD209458b IRACdatareasonablywell.
149026b and, perhaps, υ And b). In Hubeny, Burrows,