A UNIFIED THEORY FOR THE ATMOSPHERES OF THE HOT AND VERY HOT JUPITERS:
TWO CLASSES OF IRRADIATED ATMOSPHERES
J. J. Fortney
1,2,3
Space Science and Astrobiology Division, Mail Stop 245-3, NASA Ames Research Center, Moffett Field, CA 94035; jfortney@ucolick.org
K. Lodders
Planetary Chemistry Laboratory, Department of Earth and Planetary Sciences, Washington University, St. Louis, MO 63130
and
M. S. Marley and R. S. Freedman
2
Space Science and Astrobiology Division, Mail Stop 245-3, NASA Ames Research Center, Moffett Field, CA 94035
Received 2007 September 4; accepted 2007 December 7
ABSTRACT
We highlight the importance of gaseous TiO and VO opacity on the highly irradiated close-in giant planets. The day-
side a tmospheres of these planets naturally fall into two classes that are somewhat analogous to the M- and L-type
dwarfs. Those that are warm enough to have appreciable opacity due to TiO and VO gases we term ‘‘pM class’’ planets,
and those that are cooler we term ‘‘pL class’’ planets. We calculate model atmospheres for these planets, including
pressure-temperature profiles, spectra, and characteristic radiative time constants. We show that pM class planets have
temperature inversions (hot stratospheres), appear ‘‘anomalously’’ bright in the mid-infrared secondary eclipse, and
feature molecular bands in emission rather than absorption. From simple physical arguments, we show that they will
have large day/night temperature contrasts and negligible phase shifts between orbital phase and thermal emission
light curves, because radiative timescales are much shorter than possible dynamical timescales. The pL class planets
absorb incident flux deeper in the atmosphere where atmospheric dynamics will more readily redistribute absorbed
energy. This will lead to cooler day sides, warmer night sides, and larger phase shifts in thermal emission light curves.
The boundary between these classes (0.04Y 0.05 AU from a Sun-like primary for solar composition) is particularly
dependent on the incident flux from the parent star, and less so on other factors. We apply these results to several
planets and note that the eccentric transiting planets HD 147506b and HD 17156b alternate between the classes. Ther-
mal emission in the optical from pM class planets is significant redward of 400 nm, making these planets attractive
targets for optic al detection. The difference in the obse rved day/night contrast between And b (pM class) and
HD 189733b (pL class) is naturally explained in this scenario.
Subject headinggs: planetary systems — radiative transfer
1. INTRODUCTION
The blank et term ‘‘hot Jupiter’’ or even the additional term
‘‘very hot Jupiter’’ belies the diversity of these highly irradiated
planets. Each planet likely has its own unique atmosphere, in-
terior structure, and accretion history. The relative a mounts of
refractory and volatile compounds i n a planet will reflect the
parent star abundances, nebula temperature, total disk mass, lo-
cation of the planet’s formation within the disk, duration of its
formation, and its subsequent migration (if any). This accretion
history will give rise to differences in core masses, total heavy
elements abundances, and atmospheric abundance ratios. Given
this incredible complexity, it is worthwhile to first look for phys-
ical processes that may be common to groups of planets.
In add ition to a mass a nd radius, o ne can fu rther characterize
a planet by studyin g its atmosphere. The visible atmosphere is a
window into the composition o f a p lanet and contains clues to
its formation history (e.g., Marley et al. 2007). Of premier im-
portance in this class of highly irrad iated p lanets is how stellar
insolation affects the atmosphere, as this irradiation directly af-
fects the atmospheric structure, temperatures, and chemistry, the
planet’s cooling and contraction history, and even its stability
against evaporation .
Since irradiation is perhaps the most important factor in de-
termining the atmospheric properties of these planets, we exam-
ine the insolation levels of the 23 known transiting planets. We
restrict ourselves to those planets more massive than Saturn, and
hence for now exclude treatment of the ‘‘hot Neptune’’ GJ 436b,
which is by far the coolest known transiting planet. Figure 1 il-
lustrates the stellar flux incident on the planets as a function of
both planet mass (Fig. 1a) and planet surface gravity (Fig. 1b). In
these plots diamonds indicate transiting planets and triangles
indicate other intere sting hot Jupiters for which Spitzer Space
Telescope data exist, but which do not transit.
The first known tran siting planet, HD 209458b, is seen to be
fairly representative of these planets in terms of incident flux.
Planets OGLE-TR-56b and OGLE-TR-132b are somewhat sep-
arate from the rest of the group be caus e they receive the highest
stellar irradiation. Both orbit their parent stars in less than 2 days
and are prototypes of what has been called the class of ‘‘very hot
Jupiters’’ ( Konacki et al. 2003; Bouchy et al. 2004) with orbital
periods less than 3 days. However, orbital period is a poor discrim-
inator between ‘‘very hot’’ and merely ‘‘hot,’’ as HD 189733b
clearly shows. Labeled a very hot Jupiter on its discovery, due
to its short 2.2 day period ( Bouchy et al. 2005), HD 189733b
1
Spitzer Fellow.
2
Carl Sagan Center, SETI Institute, 515 North Whisman Road, Mountain
View, CA 94043.
3
Department of Astronomy and Astrophysics, UCO/Lick Observatory, Uni-
versity of California, Santa Cruz, CA 95064.
1419
The Astrophysical Journal, 678:1419Y1435, 2008 May 10
# 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.
actually receives a comparatively modest amount of irradia-
tion due to its relatively cool parent star. Therefore, perhaps a
classification based on incident flux, equilibrium temperature,
or other attributes would be more appropriate. In this paper we
argue that based on the examination of few physical processes
that two classes of hot Jupiter atmospheres emerge with dra-
matically different spectra and day/night contrasts. Equilibrium
chemistry, the depth to which incident flux will penetrate into a
planet’s atmosphere, and the radiative time constant as a function
of pressure and temperature in the atmosphere all naturally de-
fine two classes these irradiated planets.
Our work naturally builds on the previous work of Hubeny
et al. (2003), who first investigated the effects of TiO and VO
opacity on close-in giant planet atmospheres as a function of
stellar irradiation. These authors computed optical and near-
infrared spectra of models with and without TiO/VO opacity. In
general, they found that models with TiO/VO opacity feature
temperature in versions and molecu lar bands a re seen in emis-
sion, rather than absorption. Two key questions from the initial
Hubeny e t al. (2003 ) investigation were addressed but cou ld not
be definitely answered were (1) whether a relatively cold plan-
etary interior would lead to Ti/ V condensing out deep in the at-
mosphere regardless of incident flux, thereby removing gaseous
TiO and VO; and (2) if this condensation did not occur, at what
irradiation level would TiO/VO indeed be lost at the lower at-
mospheric temperatures found at smaller incident fluxes.
Later Fortney et al. (2 006b) investigated model atmosphe res
of planet HD 1 49026b, includ ing TiO/VO opacity a t various
metallicities. Particular attention was paid to the temperature
of the deep atmosphere pressure-temperature (P-T ) pr ofiles (as
derived from an evolution mo del) in relation to the Ti/ V c on-
densation boun dary. Similar to Hubeny et al. (200 3), they found
a temperature inversion due to absorption by TiO/VO and com-
puted near- and mid-infrared spectra that featured emission bands.
Using the Spitzer Infrared Array Camera (IRAC) Harrington et al.
(2007) observed HD 149026b in secondary eclipse with Spitzer
at 8 m and derived a planet-to-star flux ratio consistent with a
Fortney et al. (2006b) model with a temperature inversion due
to TiO/VO opacity. At that point, looking at the work of Fortney
et al. (2006b) and especially Hubeny et al. (2003), Harrington
et al. (2007) could have postulated that all objects more irradi-
ated than HD 149026b may possess inversions due to TiO/VO
opacity, but given the single-band detection of HD 149026b, cau-
tion was in order. More recently, based on the four-band detec-
tion of flux from HD 209458b by Knutson et al. (2008), Burrows
et al. (2007b) found that a temperature inversion, potentially due
to TiO/VO opacity, is necessary to explain this planet’s mi d-
infrared photometric data. Based on their new HD 209458b model
and the previous mode ling inves tigations, these authors posit
that planets warmer than HD 209458b may feature inversions,
while less irradiated objects such as HD 189733b do not, and dis-
cuss photochemical products and gaseous TiO/VO as potential
absorbers that may lead to this dichotomy.
We find, as has been previously shown, that those planets that
are warmer than required for condensation of titanium (Ti)- and
vanadium ( V )-b earing compounds will possess a tempera ture
Fig. 1.— Flux incident on a collection of hot Jupiter planets. At left is incident flux as a function of planet mass, and at right as a function of planet surface gravity. In
both figures the labeled dotted lines indicate the distance from the Sun that a planet would have to be to intercept this same flux. Diamonds indicate the transiting planets
while triangles indicate nontransiting systems (with minimum masses plotted but unknown surface gravities). Red indicates that Spitzer phase curve data are published,
while blue indicates there is no phase data. The error bars for HD 147506 ( HAT-P-2b) and HD 17156 indicate the variation in incident flux that the planets receive over their
eccentric orbits. Flux levels for pM class and pL class planets are shown, with the shaded region around 0.04Y 0.05 AU indicating the a possible transition region between
the classes. ‘‘Hot Neptune’’ GJ 436b experiences less intense insolation and is off the bottom of this plot at 3:2 ; 10
7
ergs s
1
cm
2
.
FORTNEY ET AL.1420 Vol. 678
inversion at low pressure due to absorption of incident flux by
TiO and VO, and will appear ‘‘anomalously’’ bright in se cond-
ary eclipse at mid-infrared wavelengths. Thermal emission in the
optical will be significant ( Hubeny et al. 2003; Lo
´
pez-Morales
& Seager 2007). Furthermore, here we propose that these plan-
ets will have large day/night effective temperature contrasts. We
term these very hot Jupiters the pM class, meaning that gaseous
TiO and VO are the prominent absorbers of optical flux. The pre-
dictions of equilibrium chemistry for these atmospheres are sim-
ilar to dM stars, where absorption by TiO, VO, H
2
O, and CO is
prominent (Lodders 2002). Planets with temperatures below the
condensation curve of Ti and V bearing compounds will have a
gradually smaller mixing ratio of TiO and VO, leaving Na and K
as the major optical opacity sources ( Burrows et al. 2000), along
with H
2
O, and CO. We term these planets the pL class, similar to
the dL class of ultracool dwarfs. These planets will have rela-
tively smaller secondary eclipse depths in the mid-infrared and
significantly smaller d ay/night effective temperature contrasts.
As discussed below, published Spitzer data are con sistent with
this picture. The boundary between these classes, at irradiation
levels (and atmospheric temperatures) where Ti and V may be
partially condensed is not yet well defined.
In this paper we begin by discussing the observations to date.
We then give an overv iew of our modeling meth ods and th e
predicted che mistry of Ti and V. We calculate P-T profiles and
spectra for models planets. For these model atmospheres we then
analyze in detail the deposition of incident stellar flux and the
emission of thermal flux, and go on to calculate characteristic ra-
diative time constants for these atmospheres. We briefly exam-
ine transmission spectra before we apply our models to known
highly irradiated giant planets. Before our discussion and con-
clusions we address issues of planetary classification.
2. REVIEW OF SPITZER OBSERVATIONS
2.1. Secondary Eclipses
The Spitzer Space Teles cope allows astronomers to measure
the thermal emission from 3Y30 m from the highly irradiated
atmospheres of these extra-solar giant planets (EGPs). This field
has progressed quickly from the first observat ions of second-
ary eclipses (when the planet passes behind its parent star) by
Charbonneau et al. (2005) for TrES-1 and by Deming et al.
(2005) for HD 209458b. Once it was clear what Spitzer ’s ca-
pabilities were for these planets, additional observations came
quickly. These included secondary eclipses for HD 189733b
(Deming et al. 2006), HD 1 49026b (Harrington et al. 200 7),
GJ 436b (Deming et al. 2007; Demory et al. 2007), and a wealth
of new (yet to be published) data for 10 other systems. In ad-
dition, mid-infrared spectra were obtained for HD 209458b
(Richardson et al. 2007; Swain et al. 2008) and HD 189733b
(Grillmair et al. 2007). In particular, Richardson et al. (2007)
claim evidence for emission features in the mid-infrared spec-
trum. Very recently, Knutson et al. (2008) observed the sec-
ondary eclipse of HD 209458b in all four IRAC bands.
One can now begin to examine the secondary eclipse data for
trends in planetary brightness temperatures. The brightness tem-
perature, T
B
is defined as the temperature necessary for a black-
body planet to emit the flux observed in the given observational
wavelength or band (Chamberlain & Hunten 1987). For the pub-
lished secondary eclipse data as of 2007 June, Harrington et al.
(2007) show that the observed dayside brightness temperatures
for most transiting planets (TrES-1, HD 189733b, HD 209458b)
vary by 20% from calculated p lanetary equilibrium temper-
atures (when making a uniform assumption for all planets re-
garding albedo and flux redistribution). These diffe rences ar e
presumably d ue to w avelen gth dep endent o pacit y and vary -
ing dynamical redistribution of the absorbed flux. However,
HD 149026b has a 45% higher brightness temperature than pre-
dicted from this relation, meaning that the temperature one mea-
sures at 8 m is significantly higher than the planet’s equilibrium
temperature. This level of infrared emission was predicted by
Fortney et al. (2006b) for models of HD 149026b that included
a hot stratosphere induced by absorption of stellar flux by TiO
and VO. More recent Knutson e t al. (2008) observations of
HD 209458b are broadly similar to the one-band detection for
HD 149026b. Relatively high brightness temperatures of 1500Y
1900 K were observed from 3.6 to 8 m, compared to the
Harrington et al. (2007) predic ted equilibrium temperature of
1330 K. These observations have also been interpreted by Burrows
et al. (2007b) as being caused by a temperature inversion (hot
stratosphere). As we discuss in x 5.1, HD 209458b is in a temper-
ature regime that is difficult to model, where Ti and V are ex-
pected to be partially condensed.
2.2. Phase Cur
ves
The observations that b est allow us to understand the atmo-
spheric dynamics of these presumably tidally locked planets are
those made as a function of orbital phase. Two approaches have
been used to measure the thermal emission of these planets away
from secondary eclipse. The first is to periodically observe the
infrared flux from the combined planet+star system at several
times in the planet’s orbit. The advantage of periodic short ob-
servations is that little telescope time is used. The disadvantage is
that since the system is not monitored continuously, systematic
uncertainties could be important and may be hard to correct for.
There are published data for four planets that have been observed
in this way: detections of phase variation for And b (Harrington
et al. 2006) and HD 179949b (Cowan et al. 2007), and upper
limits for HD 209458b, 51 Peg b (Cowan et al. 2007). Alterna-
tively, one could monitor a system continuously over a significant
fraction of a planet’s orbital period to eliminate any uncertainties
induced by having to revisit the target. This method was employed
by Knutson et al. (2007) to observe HD 189733b continuously for
33 hr, including the transit and secondary eclipse. Large day/night
contrasts were found for pM class planets Andb(whichis
consistent with a dark night side) and HD 179949b, wherea s
pL class p lanet HD 189733b has a day/night 8 mbrightness
temperature difference of only 240 K. We return to the Cowan
et al. (2007) upper limit for HD 209458b in x 8.
Two additional factors that affect these observations are the
brightness of the parent star and the inclination of the planetary
orbit. While the brightest p lanet-hosting stars allow for the larg-
est flux measurements (e.g., And b), the brightest hot Jupiter
systems do not transit. A measure ment of the secondary eclipse
depth while obtaining a lig ht curve is e xtremely valuable, be-
cause the planet-to-star flux ratio at full planet illumination is
thus known, as is the p lanet’s radius from transit observations.
The interpretation is then much more straightforward for the tran-
siting systems.
Among the current published data there appear to be two
planets that are bright in secondary eclipse, HD 149026b and
HD 209458b, compared to other transiting planet s, and two
planets that appear to have large day/night temperature differ-
ences, And b and HD 179949b. We show that these planets,
HD 149026b, HD 209458b, And b, and HD 179949b, are
pM class planets, while the less irradiated hot Jupiters (such as
HD 189733b and TrES-1) are pL class. We now turn to models
TWO CLASSES OF HOT JUPITER ATMOSPHERES 1421No. 2, 2008
of these classes of planets to examine how and why their atmo-
spheres differ so strikingly.
3. MODEL ATMOSPHERES
3.1. Methods
We have compu ted atmospheric PYT profiles and spectra for
several planets with a plane-parallel model atmosphere code that
has been used for a variety of planetary and substellar objects.
The code was first used to generate profiles and spectra for Titan’s
atmosphere by McKay et al. (1989). It was significantly revised
to model the atmospheres of brown dwarfs (Marley et al. 1996,
2002; Burrows et al. 1997) and irradiated giant planets (Marley
& McKay 1999, for Uranus). Recently, it has been applied to
L- and T-type brown dwarfs (Saumon et al. 2006, 2007; Cushing
et al. 2008) and hot Jupiters (Fortney et al. 2005, 2006b, 2007). It
explicitly accounts for both incident radiation from the parent
star and thermal radiation from the planet’s atmosphere and in-
terior. The radiative transfer solution algorithm was developed
by Toon et al. (1989). We model the impinging stellar flux from
0.26 to 6.0 m and the emitted thermal flux from 0.26 to 325 m.
We use the elemental abundance data of Lodd ers (2003)
and chemical equilibri um compositions are computed with the
CONDOR code, following Lodders & Fegley (2002, 2006) and
Lodders (1999, 2002). We maintain a large and constantly up-
dated opacity database, which is described in Freedman et al.
(2008). When including the opacity of clouds, such as Fe-metal
and Mg-silicates, we use the cloud model of Ackerman & Marley
(2001). However, in our past work we have found only weak
effects on P-T profiles and spectra due to cloud opacity (Fortney
et al. 2005), so we ignore cloud opacity here. However, the se-
questering of elements into condensates, and their removal from
the gas phase (‘‘rainout’’) is always accounted for in the chem-
istry calculations. We note that day sides of the strongly irradi-
ated pM class planets are too warm for Fe-metal and Mg-silicates
condensates to form.
3.2. Very Hot Jupiters and TiO/VO Chemistry
It is clear that the abundances to TiO and VO gases is impor-
tant in these atmospheres. Hubeny et al. (2003) first discussed
how u nder standing the ‘‘cold trap’’ phenomenon may be signif-
icant in under standin g these abundances. If a gi ven P-T profile
crosses a condensation curve in two corresponding altitude levels,
the condensed species is expected to eventually mix down to the
highest pressure condensation point, where the cloud remains
confined due to the planet ’s gravitational field. This process is
responsible for the extremely low water abundance in the Earth’s
stratosphere. It can also be seen in the atmospheres Jupiter and
Saturn, where the ammonia ice clouds are confined to a pressure
of several bars, although both these planets exhibit stratospheres,
such that their warm upper atmospheres pass the ammonia con-
densation curve again at millibar pressures. For the highly irra-
diated planets, the relevant c ondensa tes are those that remov e
gaseous TiO and VO, and sequester Ti and V into sol id con-
densates at pressures of tens to hundreds of bar s, f ar bel ow the
visible atmosphere.
The cold trap phenomenon constitutes a departure from chem-
ical equilibrium that cannot be easily accounted for in the pre-
tabulated ch emica l eq uilibri um ab unda nces used by Hub eny
et al. (2003), Fortney et al. (2006b), Burrows et al. (2007b), and
here as well. Our chemical abundances and opacities are pre-
tabulated in P-T spaceandtheatmospherecodeinterpolatesin
these abundances as it converges to a solution. The abundances
determined for any one pressure level of the P-T profile are not
cognizant of abundances of other levels of the profile, al-
though condensation and settling of species is always properly
accounted for. In th is case a tabu lated TiO abundance at a g iven
P-T point at which, in equilibrium, TiO would be in the gas-
eous state (warmer th an required for Ti con densatio n), may not
be corr ect. If the atmospher ic P-T profile int ersects the c onden-
sation curve, the atmosphere becomes depleted in TiO above
the cloud. We do not treat the cold trap here. In practice, we use
two different opacity dat abases: one with TiO and VO removed
at P < 10 bars, which simulates the removal of Ti and V into
clouds, and one in which gases TiO and VO remain as calculated
by equilibrium chemistry (which does not include depletion from
a cold trap).
A full discussion of titanium and vanadium chemistry in the
context of M- and L-dwarf atmospheres can be found in Lodders
(2002). Much of that discussion pertains to the atmospheres of
highly irradiated planets as well. The chemistry is complex. For
instance Lodders & Fegley (2006) (using the updated Lodders
2003 abundances) find that the first Ti condensate will not nec-
essarily be CaTiO
3
. For sol ar metallici ty, the first condensate
is TiN if P bars k 30 bars, Ca
3
Ti
2
O
7
if 5 b ars P P P 30 bars,
Ca
4
Ti
3
O
10
if 0:03 bars P P P 5 bars, and CaTiO
3
if P P 0:03
bars. T hese four condensa tes are the ini tial condensatesasa
function of total pressure and their condensation temperatures
define the Ti-condensation curve in Figure 2. Another important
point is that, following Lodders (2002), we assume that vana-
dium condenses into solid solution with Ti-bearing condensates,
as is found in meteorites ( Kornacki & Fegley 1986). Lodders
(2002) find this condensation sequence is also consistent with
observed spectra at the M- to L-dwarf transition ( Kirkpatrick
et al. 1999). In the abse nce of this e ffect V woul d not cond ense
until 200 K cooler temperatures are reached and solid VO forms,
as in the chemistry calculations of Burrows & Sharp (1999), Allard
Fig. 2.— Model P-T profiles for planets with g ¼ 15 m s
2
and T
int
¼ 200 K at
various distances (0.025Y 0.055 AU ) from the Sun. This T
int
value is roughly con-
sistent with that expected for a 1 M
J
planet with a radius of 1.2 R
J
. Condensation
curves are dotted lines and the curve where CO and CH
4
have equal abundances is
dashed. The 0.1X Ti-Cond curve shows where 90% of the Ti has condensed out.
However, even then TiO is a major opacity source. For none of these profiles has
TiO/VO been artificially removed. The kinks in the 0.035 AU profile are due to
interpolation difficulties, as the opacity drops significantly over a small tempera-
ture range.
FORTNEY ET AL.1422 Vol. 678
et al. (2001), and Sharp & Burrows (2007). Choices made in the
calculation of the Ti condensation curve (e.g., number of potential
T i-bearing compounds included in the calculations) and the V con-
densation curve (e.g., whether V enters into Ti-bearing conden-
sates or condenses as solid VO) will cause some shift in the
position of these condensation curves, important boundaries be-
tween the pL and pM classes.
3.3. Calculatin
g Pressure-Temperature Profiles
When modeling the atmospheres o f irra diated objects with a
one-dimensional, plane parallel atmosphere code it is necessar y
to weigh the stellar flux by a geometric factor if one is comput-
ing a profile for dayside avera ge or planet-wide average con-
ditions. Descriptions of this issue in solar system atmosphere
modeling can be found in Appleby & Hogan (1984) and McKay
et al. (1989). In the context of highly irradiated EGPs, Burrows
et al. (2004, 2006, 2007a), Barman et al. (2005), Seager et al.
(2005), and Fortney & Marley (2007) have all discussed this
issue in some detail. All are approximations for atmospheric
structures that are surely complex for these highly irradiated
atmospheres. In this paper we make a straightforward choice to
multiply the incident flux by a factor f ¼ 0:5foradaysideav-
erage (since the atmosphere radiates over 2 sr but intercepts
flux over only radians) and assume normal incidence of flux,
¼ 1. This differs slightly from choices in our previous papers
(see Fortney & Marley 2007). All profiles shown in this paper
are relevant for the irradiated planetary day side.
In Figure 2 we show P-T profiles as a function of distance
from t he Sun. At 0.025 and 0.03 AU the profiles are everywhere
warmer that the condensation curve for a solar abundance of
Ti and V. Essentially all Ti and V is expected to be in TiO and
VO. By 0.035 AU, where the incident flux is weaker, the profile
crosses this conde nsation curve, labeled ‘‘1X Ti/ V-Cond .’’ To
the left o f this curve, the TiO/ VO abundances fall exponentially
with decreasin g temper ature. To the right, the TiO/VO abun-
dances are essentially constant. This particular P-T profile is
oddly s haped, since it samples a re gion of P -T space in which
the opacity drops rapidly with temperature. It crosses back to
the right of the condensation curve, where it again finds the
‘‘full’’ abundance of TiO/VO. This is an example of a profile
that violates the cold-trap (which we do not model), as at lower
pressures, TiO/VO abundances should be reduced, given the
condensation of Ti and V below. The dotted curve labeled ‘‘90%
Ti-Cond’’ shows where 90% of Ti has been lost to a solid con-
densate (A. S. Lee & K. Lodders 2008, in preparation). Figure 3
is a plot of optical and near-infrared opacity at 1 mbar and shows
that TiO/VO are still major optical opacity sour ces even after
condensation has begun. At 1700 K, before Ti/V condensa-
tion, opacity [here log ()incm
2
g
1
]inV -band is 0.5. By
1600 K, 33 K cooler than the 90% Ti-Cond curve, this opacity
is still an order of magnitude larger than the opacity at 1400 K,
by which point the strong TiO/VO bands have given way to
alkali lines and water bands.
That TiO/VO gradually wane in importance is consistent with
observations of dwarfs at the MYL transition (Lodders 2002).
The mixing ratios of these species do not drop to zero at the solar
abundances condensation curve. For model atmospheres more
distant from the parent star (0.05 AU and beyond), the abun-
dance of TiO/VO continues to fall exponentially with tempera-
ture, such that in the upper atmosphere it is no longer a major
opacity source.
We can examine how the derived P-T profiles for the pM class
planets vary as a function of T
int
, a planet’s intrinsic effective
temperature in the absence of irradiation, and as a function of
surface gravity. This is shown in Figure 4. Lower gravity planets
have lower pressure photospheres and consequently have warmer
Fig. 3.— Total abundance-weighted atmospheric opacity at P ¼ 1 mbar and T ¼ 1700 (blue), 1600 ( green), and 1400 (red ) K. The hottest temperature, 1700 K, is
warmer than the temperature for Ti and V condensation, which begins to occur at 1670 K. The intermediate temperature, 1600 K, is 33 K cooler than temperature at which
Ti is 90% condensed. The optical opacity drops due to the removal of gaseous TiO and VO into Ti- and V-bearing solid condensates. By 1400 K TiO and VO bands have
given way to prominent water bands and alkali lines. A strong water vapor band at 1.4 m is readily seen at all three of these temperatures, and indicates the relatively
modest change in absorption by water vapor with a 300 K drop in temperature.
TWO CLASSES OF HOT JUPITER ATMOSPHERES 1423No. 2, 2008
