Draft version October 29, 2018
Preprint typeset using LATEX style emulateapj v. 7/15/03
IDENTIFICATION OF ABSORPTION FEATURES IN AN EXTRASOLAR PLANET ATMOSPHERE
T. Barman
Lowell Observatory, 1400 W. Mars Hill Rd., Flagstaff, AZ 86001, barman@lowell.edu
Draft version October 29, 2018
ABSTRACT
Water absorption is identified in the atmosphere of HD209458b by comparing models for the planet’s
transmitted spectrum to recent, multi-wavelength, eclipse-depth measurements (from 0.3 to 1 µm)
published by Knutson et al. (2007). A cloud-free model which includes solar abundances, rainout
of condensates, and photoionization of sodium and potassium is in good agreement with the entire
set of eclipse-depth measurements from the ultraviolet to near-infrared. Constraints are placed on
condensate removal by gravitational settling, the bulk metallicity, and the redistribution of absorbed
stellar flux. Comparisons are also made to the Charbonneau et al. (2002) sodium measurements.
Subject headings: planetary atmospheres - extrasolar planets
1. INTRODUCTION
The discovery of transiting extrasolar planets has
opened the door to direct detections and characteriza-
tion of their atmospheres. Observations using the STIS
instrument on HST provided the first glimpse of what
the photospheric composition is like for a nearby EGP.
Charbonneau et al. (2002) measured the relative change
in eclipse depth for HD209458b across a sodium doublet
(5893Å) resulting in the first detection of atomic absorp-
tion in an EGP atmosphere. Following the Na detec-
tion, Vidal-Madjar et al. (2003) discovered an extended
hydrogen-rich atmosphere surrounding HD209458b using
a similar technique as Charbonneau et al., but in the UV.
At Lyman-α wavelengths, HD209458b is ∼ 3 times larger
than in the optical. These detections were made using a
technique called transit spectroscopy as the planet passes
in front of its star. Transit spectroscopy uses the fact that
the wavelength-dependent opacities in the planet’s atmo-
sphere obscure stellar light at different planet radii lead-
ing to a wavelength-dependent depth of the light-curve
during primary eclipse. Consequently, searching for rela-
tive changes in eclipse depth as a function of wavelength
directly probes the absorption properties of the planet’s
atmosphere with the potential to reveal the presence (or
absence) of specific chemical species.
In this paper, recent measurements of HD209458b’s
radius are combined in a multi-wavelength comparison to
model atmosphere predictions. Atmospheric molecular
and atomic absorption are identified and constraints are
placed on the basic atmospheric properties.
2. THE LIMB MODEL
Transit spectroscopy probes the limb of a planet which
is the transition region between the day and night sides.
One would, therefore, expect that, in the presence of
a horizontal temperature gradient between the heated
and non-heated hemispheres, the temperatures across
the limb would be cooler than the average dayside tem-
peratures (Barman et al. 2005; Iro et al. 2005). Re-
cent Spitzer observations of both transiting and non-
transiting hot-Jupiters showing large flux variations with
phase have provided strong evidence supporting such a
day-to-night temperature gradient (Charbonneau et al.
2005; Deming et al. 2005b, 2006; Harrington et al. 2006).
Describing the limb ultimately requires a multi-
dimensional model atmosphere solution; however, as is
common practice, a simpler one-dimensional model is
used here to represent the average properties of the limb,
in both a longitudinal and latitudinal sense. To explore
a variety of limb temperature structures, the incident
stellar flux has been scaled by a parameter α. A model
with α = 0.25 represents an average description of the
entire planet in the presence of very efficient horizontal
energy transport (Barman et al. 2005). Increasing α to
0.5 increases the heating of the model atmosphere mak-
ing it more appropriate for just the dayside which, in this
work, will represent an upper limit to the plausible mean
temperatures at the limb.
The basic chemistry across the limb is modeled assum-
ing chemical equilibrium, determined by minimizing the
free energy while including grain formation. To under-
stand the effects of gravitational settling of grains on the
chemistry and the transmission spectrum, the removal
of grains from the atmosphere is included via two simple
approximations that represent opposite extremes. The
first is the “cond” approximation used by Barman et al.
(2001) and Allard et al. (2001) which simply ignores the
grain opacity without altering the chemistry or abun-
dances. The second is the “rainout” approximation
which iteratively reduces, at each layer, the elemental
abundances (by the appropriate stoichiometric ratios)
involved in grain formation and recomputes the chem-
ical equilibrium with each new set of stratified elemen-
tal abundances. This approach is similar to other rain-
out models (Fegley & Lodders 1996; Burrows & Sharp
1999), except that the depletion of elements is contin-
ued until grains are no longer present.
The transmission of stellar fluxes through the limb of
HD209458b is determined by solving the spherically sym-
metric radiative transfer equation while fully accounting
for scattering and absorption of both intrinsic and ex-
trinsic radiation (Hauschildt 1992; Barman et al. 2001,
2002). Spherical, instead of the more traditional plane-
parallel geometry, naturally accounts for the curvature of
the atmospheric layers and changes in chemistry along
the slant paths through the upper atmosphere. The
planet radius at a given wavelength (Rλ) is obtained by
determining the radial depth at which the transmitted
http://arxiv.org/abs/0704.1114v1
Fig. 1.— Monochromatic transit radii over the STIS spectral range for the baseline rainout model with (red) and without (blue)
photoionization of Na and K. The solid and dotted red lines are the same, except H2O line opacity is excluded in the latter. Horizontal
bars correspond to mean radii across bins with λ-ranges indicated by the width of each bar. STIS measurements by Knutson et al. (2007)
are shown in green with 1 σ error bars. Vertical dashed lines mark the narrow λ-range used by Charbonneau et al. (2002).
flux is equal to e−1 times the incident starlight along
that same path.
3. RESULTS
A cloud-free atmosphere with rainout, α = 0.25, and
solar abundances is adopted as the baseline model. This
model, along with others, is compared to the relative
Rλ measurements of Knutson et al. (2007) which have
a reported precision high enough to constrain many of
the basic atmospheric properties. Since a comparison is
being made to relative Rλ values, the model results were
uniformly scaled to match the observations in the 4580
to 5120Å wavelength bin; this scaling was always less
than 0.005RJup. Overall, the baseline model (red solid
line in Fig. 1) reproduces the observed rise in Rλ toward
shorter wavelengths, the increase across the Na doublet,
and the increase at the far red wavelengths. The baseline
model comparison to the data has a χ2 that is 3 times
smaller than a constant Rλ.
3.1. Water Absorption
Water is predicted to be one of the most abundant
species in an EGP atmosphere and, given its broad ab-
sorption features in the infrared, plays a crucial role in
regulating the temperature-pressure (T-P) profile. The
first major H2O absorption band appears between 0.8
and 1 µm, a region covered by the last two wavelength
bins of Knutson et al. (2007). As illustrated in Fig. 1,
there is excellent agreement between the baseline model
and the observations in this part of the spectrum espe-
cially across the longest wavelength bin that sits on top
of the H2O band. Qualitatively similar water features are
seen in the models of Brown (2001) and Hubbard et al.
(2001); however these models fall many σ below the ob-
servations. The baseline model also predicts mean Rλ-
peaks equal to 1.330, 1.343, and 1.341 RJup for the next
three water bands (at λ ∼ 1.15, 1.4, and 1.9 µm).
A model that excludes H2O line opacity is also shown
in Fig. 1 and is greater than 10 σ below both the observa-
tions and the baseline model prediction. Removing H2O
opacity also produces a significant drop in Rλ near 0.9
µm that further increases the discrepancy between the
model and overall red/near-IR observations. No other
opacity source could be responsible for the observed rise
in Rλ across this part of the spectrum.
3.2. Photoionization
After the reported sodium detection in the atmosphere
of HD209458b (Charbonneau et al. 2002), there were
several attempts to explain why the strength of this fea-
ture was much lower than expected based on earlier mod-
els (e.g., by Seager & Sasselov, 2000). Barman et al.
(2002) explored departures from local thermodynamic
equilibrium (LTE) which are capable of producing an in-
version in the cores of the Na doublet line profiles. How-
ever, the earlier models of Barman et al. (2001, 2002)
were constructed under the cond approximation and,
consequently, contained a larger number of free met-
als along with TiO and VO molecular absorption com-
pared to a rainout model. These additional sources of
optical/UV opacity lead to a hotter upper atmosphere
and a very shallow photoionization depth for Na (only
a 5% reduction of Na across the region probed by tran-
sit spectroscopy). Fortney et al. (2003) also explored Na
photoionization and found that their atmosphere model
(which included rainout) could be brought into reason-
able agreement with the Na observations. The models
presented here account for the angular dependence of
ionziation on the limb’s dayside, but not on the night
side. However, Fortney et al. (2003) have shown that Na
ionization is still present at ∼ 5◦ past the terminator for
pressures relevant to the transit spectrum modeled here.
Figure 1 compares cloud-free solar abundance rainout
models with and without photoionization of Na and K.
While these models include photoionization, the LTE ap-
proximation on the atomic level populations and line
source function is maintained. Ionization (radially) at
the limb reaches 50% at P ∼ 0.1 and 1.2 mbar for Na
and K, respectively, and stops at P ∼ 2 and 7 mbar, re-
spectively, resulting in a reduction of the Rλ-peaks across
Fig. 2.— Relative flux differences (with time from center of
eclipse) between a wavelength band centered on the Na doublet and
the mean of two wavelength bands on either side of the Na doublet.
The total wavelength range is indicated by vertical lines in Fig. 1.
Each model is cloud-free with solar abundances and α = 0.25. See
Figure legend and text for the distinguishing characteristics of each
model. Symbols are the observations of Charbonneau et al. (2002)
with 1 σ error bars.
the Na and K lines. For K, this reduction extends out to
the line-wings resulting in a significantly smaller mean
Rλ, bringing the model into ∼ 3σ agreement with the
Knutson et al. measurement. The impact of Na pho-
toionization is mostly confined to the core of the doublet
leading to only a small reduction of the mean Rλ, but suf-
ficient to bring the model into ∼ 1σ agreement with the
observations at these wavelengths. Though not included
here, ionization past the terminator onto the night side
should further improve the agreement across the Na and
K doublets. The two narrow features on the red wing
of the K doublet are due to Rb, which should also be
affected by photoionization due to its very low first ion-
ization potential. Photoionization of Rb resulted in a
near complete removal of these features, but reduced the
mean Rλ for this bin by less than 0.002 RJup.
The broad wavelength bins allowed Knutson et al. to
obtain very precise relative Rλ measurements; however,
as illustrated by the Na doublet, such broad bins lim-
its the constraints that can be placed on atomic absorp-
tion features. In contrast, the narrow range analyzed
by Charbonneau et al. (2002) resulted in much larger
Rλ error-bars, but still precise enough to easily distin-
guish between the various models shown in Fig. 1. The
flux differences across the Na doublet as a function of
time (measured from the transit center) were computed
for each model using the same narrow wavelength bins
as Charbonneau et al. (2002), indicated in Fig. 1 by
vertical dashed lines. Fig. 2 compares model transit
curves to the 2002 Na measurements and shows a large
discrepancy between the observations and solar abun-
dance models with pure equilibrium chemistry (cond or
rainout). Including photoionization brings the baseline
rainout model into rough agreement with the observa-
tions. Note the cond model shown in Fig. 2 does not
include photoionization (similar to the LTE model from
Barman et al. (2002)) and illustrates how far off the pre-
dicted Rλ can be across the Na doublet under simplified
assumptions.
3.3. Rainout, Metallicity, and Temperature
The rainout model used here reduces the individual
metal abundances with depth iteratively until clouds do
not form, thus mimicking efficient gravitational settling.
However, the removal of metals is not 100% efficient,
leaving behind a variety of atoms (in addition to Na and
K) to contribute to the line opacity. The impact of rain-
out on the planet’s atmosphere is made apparent by com-
paring rainout and cond models (Fig. 3). In the cond
model grain opacities are simply ignored in the transfer
equation while the chemistry remains that of a pure equi-
librium model without any actual removal of refractory
elements. Thus, the cond model represents the minimum
impact of grain formation on the stratified abundances
and leaves behind a considerable amount of free metals
along with molecules like TiO and VO. This leads to
much stronger atomic lines, including Na and K along
with TiO and VO bands.
Apart from a very minor contribution from molecules,
the Rλ features at λ < 0.8µm are all due to atomic line
opacity 1. These narrow features are due to blended lines
from metals like Ca, Al, Fe, Ni, Mn, and Cr. Note that,
while Rayleigh scattering does contribute to the opacity
in the blue/UV, a removal of atomic line opacity would
drop Rλ by∼ 0.02RJup for λ < 0.45µm. The top panel of
Fig. 3 compares the solar abundance rainout model with
photoionization (shown in Fig. 1) to a rainout model
with 10× solar abundances. Since the metal abundances
were uniformly scaled, the grain formation and corre-
sponding removal of refractory elements were also uni-
formly enhanced. The additional opacity altered the T-P
profile as well as the total atmospheric extension. These
factors contribute to a similar Rλ pattern in the opti-
cal but enhanced molecular absorption features in the
red/near-IR. The increase in metals increases the H2O
absorption feature along with the wings of the Na and
K doublets (which form deeper in the atmosphere where
photoionization is less important). Also, FeH and CrH
absorption is larger in the metal-rich atmosphere leading
to an increase in Rλ on both sides of the K doublet. The
metal-enhanced Rλ spectrum is in good agreement with
the observations near 0.9µm, but is noticeably too high
across both the K doublet and the H2O band.
Transit spectroscopy can also help constrain the tem-
peratures across the limb. The lower panel of Fig. 3
compares an α = 0.5 model (i.e. a model with a hotter
dayside-like T-P profile) to the cooler α = 0.25 base-
line model. In the hotter model, grain formation is less
pronounced resulting in a greater concentration of most
free metals and, thus, stronger UV/blue absorption lines
than in the α = 0.25 model. Higher temperatures at
depth also result in equilibrium concentrations of Na
and K that are several times lower than found at the
cooler temperatures of the α = 0.25 model. The net re-
sults are two distinctively different Rλ spectra with the
α = 0.25 model being more consistent with the Knutson
et al. measurements.
4. SUMMARY
1 Ballester et al. (2007) claim the Rλ rise in the blue/UV is due
to the Blamer edge of hot hydrogen in an extended atmosphere.
While the present model does not support this explanation, if ver-
ified, it could indicate that rainout is more efficient than predicted
here.
Fig. 3.— Monochromatic transit radii over the STIS spectral range. Top panel: solar abundance models, cond (black) and rainout(red),
are compared to a model with 10× solar metal abundances including rainout (blue). Lower panel: solar abundances baseline rainout model
with α = 0.25 (red) compared to a similar model with α = 0.5 (blue). Horizontal bars have the same meaning as in Fig. 1.
Photoionziation plays an important role for both Na
and K, and potentially many other species. No evidence
is found to support a large metal enhancement (e.g., 10×
solar), though smaller Jupiter-like enhancements are not
ruled out. Furthermore, the agreement between model
and observations demonstrated here alleviates the need
for substantial cloud coverage along the limb between
0.05 and 0.001 bars, which would otherwise truncate and
flatten the Rλ spectrum (Brown 2001). In the baseline
model, the predicted location of clouds (e.g., MgSiO3)
lies just below the minimum Rλ(∼ 1.315RJup) across the
STIS wavelength range, consequently deep clouds (and
also very high clouds) remain a possibility.
The models presented here also predict Rλ variations
(∼ 0.02 RJup) across the 2-0 R-branch of CO in the K-
band. This is inconsistent (at 2.5σ) with a non-detection
of CO based on Keck-NIRSPEC transit spectra taken
in 2002 (Deming et al. 2005a). It is likely that using a
single T-P profile to represent the horizontal and pole-
to-pole variations across the limb averages out too much
of the upper atmospheric structure; this simplification
might explain the K-band discrepancy. High clouds may
also be involved. In addition, the Keck and HST obser-
vations were taken between 1 and 2 years apart and time-
dependent atmospheric variations along the limb cannot
be ruled out (Menou et al. 2003).
While Knutson et al. (2007) did not attribute their
measured Rλ variations to any absorption features (this
was not the focus of their paper), the models presented
above clearly show that these measurements are consis-
tent with strong water absorption near 1 µm. A detection
of water in the limb of HD209458b is nominally at odds
with a recent Spitzer IRS spectrum that shows no H2O
features for this planet(Richardson et al. 2007). These
data were taken during secondary eclipse and directly
probe the planet’s dayside with negligible contribution
from the limb. It is possible that the dayside atmosphere
is nearly isothermal (Fortney et al. 2006) which would re-
sult in a spectrum with no detectable water absorption
features, despite a copious water supply. The transmis-
sion spectrum, however, would contain absorption fea-
tures independent of an isothermal dayside or limb.
The author thanks B. Hansen and the referees for their
comments. This research was supported by NASA Ori-
gins and Spitzer Theory Grants and made use of NASA’s
Project Columbia computer system.
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  Water absorption is identified in the atmosphere of HD209458b by comparing
models for the planet's transmitted spectrum to recent, multi-wavelength,
eclipse-depth measurements (from 0.3 to 1 microns) published by Knutson et al.
(2007). A cloud-free model which includes solar abundances, rainout of
condensates, and photoionization of sodium and potassium is in good agreement
with the entire set of eclipse-depth measurements from the ultraviolet to
near-infrared. Constraints are placed on condensate removal by gravitational
settling, the bulk metallicity, and the redistribution of absorbed stellar
flux. Comparisons are also made to the Charbonneau et al. (2002) sodium
measurements.

Draft version October 29, 2018
Preprint typeset using LATEX style emulateapj v. 7/15/03
IDENTIFICATION OF ABSORPTION FEATURES IN AN EXTRASOLAR PLANET ATMOSPHERE
T. Barman
Lowell Observatory, 1400 W. Mars Hill Rd., Flagstaff, AZ 86001, barman@lowell.edu
Draft version October 29, 2018
ABSTRACT
Water absorption is identified in the atmosphere of HD209458b by comparing models for the planet’s
transmitted spectrum to recent, multi-wavelength, eclipse-depth measurements (from 0.3 to 1 µm)
published by Knutson et al. (2007). A cloud-free model which includes solar abundances, rainout
of condensates, and photoionization of sodium and potassium is in good agreement with the entire
set of eclipse-depth measurements from the ultraviolet to near-infrared. Constraints are placed on
condensate removal by gravitational settling, the bulk metallicity, and the redistribution of absorbed
stellar flux. Comparisons are also made to the Charbonneau et al. (2002) sodium measurements.
Subject headings: planetary atmospheres - extrasolar planets
1. INTRODUCTION
The discovery of transiting extrasolar planets has
opened the door to direct detections and characteriza-
tion of their atmospheres. Observations using the STIS
instrument on HST provided the first glimpse of what
the photospheric composition is like for a nearby EGP.
Charbonneau et al. (2002) measured the relative change
in eclipse depth for HD209458b across a sodium doublet
(5893Å) resulting in the first detection of atomic absorp-
tion in an EGP atmosphere. Following the Na detec-
tion, Vidal-Madjar et al. (2003) discovered an extended
hydrogen-rich atmosphere surrounding HD209458b using
a similar technique as Charbonneau et al., but in the UV.
At Lyman-α wavelengths, HD209458b is ∼ 3 times larger
than in the optical. These detections were made using a
technique called transit spectroscopy as the planet passes
in front of its star. Transit spectroscopy uses the fact that
the wavelength-dependent opacities in the planet’s atmo-
sphere obscure stellar light at different planet radii lead-
ing to a wavelength-dependent depth of the light-curve
during primary eclipse. Consequently, searching for rela-
tive changes in eclipse depth as a function of wavelength
directly probes the absorption properties of the planet’s
atmosphere with the potential to reveal the presence (or
absence) of specific chemical species.
In this paper, recent measurements of HD209458b’s
radius are combined in a multi-wavelength comparison to
model atmosphere predictions. Atmospheric molecular
and atomic absorption are identified and constraints are
placed on the basic atmospheric properties.
2. THE LIMB MODEL
Transit spectroscopy probes the limb of a planet which
is the transition region between the day and night sides.
One would, therefore, expect that, in the presence of
a horizontal temperature gradient between the heated
and non-heated hemispheres, the temperatures across
the limb would be cooler than the average dayside tem-
peratures (Barman et al. 2005; Iro et al. 2005). Re-
cent Spitzer observations of both transiting and non-
transiting hot-Jupiters showing large flux variations with
phase have provided strong evidence supporting such a
day-to-night temperature gradient (Charbonneau et al.
2005; Deming et al. 2005b, 2006; Harrington et al. 2006).
Describing the limb ultimately requires a multi-
dimensional model atmosphere solution; however, as is
common practice, a simpler one-dimensional model is
used here to represent the average properties of the limb,
in both a longitudinal and latitudinal sense. To explore
a variety of limb temperature structures, the incident
stellar flux has been scaled by a parameter α. A model
with α = 0.25 represents an average description of the
entire planet in the presence of very efficient horizontal
energy transport (Barman et al. 2005). Increasing α to
0.5 increases the heating of the model atmosphere mak-
ing it more appropriate for just the dayside which, in this
work, will represent an upper limit to the plausible mean
temperatures at the limb.
The basic chemistry across the limb is modeled assum-
ing chemical equilibrium, determined by minimizing the
free energy while including grain formation. To under-
stand the effects of gravitational settling of grains on the
chemistry and the transmission spectrum, the removal
of grains from the atmosphere is included via two simple
approximations that represent opposite extremes. The
first is the “cond” approximation used by Barman et al.
(2001) and Allard et al. (2001) which simply ignores the
grain opacity without altering the chemistry or abun-
dances. The second is the “rainout” approximation
which iteratively reduces, at each layer, the elemental
abundances (by the appropriate stoichiometric ratios)
involved in grain formation and recomputes the chem-
ical equilibrium with each new set of stratified elemen-
tal abundances. This approach is similar to other rain-
out models (Fegley & Lodders 1996; Burrows & Sharp
1999), except that the depletion of elements is contin-
ued until grains are no longer present.
The transmission of stellar fluxes through the limb of
HD209458b is determined by solving the spherically sym-
metric radiative transfer equation while fully accounting
for scattering and absorption of both intrinsic and ex-
trinsic radiation (Hauschildt 1992; Barman et al. 2001,
2002). Spherical, instead of the more traditional plane-
parallel geometry, naturally accounts for the curvature of
the atmospheric layers and changes in chemistry along
the slant paths through the upper atmosphere. The
planet radius at a given wavelength (Rλ) is obtained by
determining the radial depth at which the transmitted
http://arxiv.org/abs/0704.1114v1
Fig. 1.— Monochromatic transit radii over the STIS spectral range for the baseline rainout model with (red) and without (blue)
photoionization of Na and K. The solid and dotted red lines are the same, except H2O line opacity is excluded in the latter. Horizontal
bars correspond to mean radii across bins with λ-ranges indicated by the width of each bar. STIS measurements by Knutson et al. (2007)
are shown in green with 1 σ error bars. Vertical dashed lines mark the narrow λ-range used by Charbonneau et al. (2002).
flux is equal to e−1 times the incident starlight along
that same path.
3. RESULTS
A cloud-free atmosphere with rainout, α = 0.25, and
solar abundances is adopted as the baseline model. This
model, along with others, is compared to the relative
Rλ measurements of Knutson et al. (2007) which have
a reported precision high enough to constrain many of
the basic atmospheric properties. Since a comparison is
being made to relative Rλ values, the model results were
uniformly scaled to match the observations in the 4580
to 5120Å wavelength bin; this scaling was always less
than 0.005RJup. Overall, the baseline model (red solid
line in Fig. 1) reproduces the observed rise in Rλ toward
shorter wavelengths, the increase across the Na doublet,
and the increase at the far red wavelengths. The baseline
model comparison to the data has a χ2 that is 3 times
smaller than a constant Rλ.
3.1. Water Absorption
Water is predicted to be one of the most abundant
species in an EGP atmosphere and, given its broad ab-
sorption features in the infrared, plays a crucial role in
regulating the temperature-pressure (T-P) profile. The
first major H2O absorption band appears between 0.8
and 1 µm, a region covered by the last two wavelength
bins of Knutson et al. (2007). As illustrated in Fig. 1,
there is excellent agreement between the baseline model
and the observations in this part of the spectrum espe-
cially across the longest wavelength bin that sits on top
of the H2O band. Qualitatively similar water features are
seen in the models of Brown (2001) and Hubbard et al.
(2001); however these models fall many σ below the ob-
servations. The baseline model also predicts mean Rλ-
peaks equal to 1.330, 1.343, and 1.341 RJup for the next
three water bands (at λ ∼ 1.15, 1.4, and 1.9 µm).
A model that excludes H2O line opacity is also shown
in Fig. 1 and is greater than 10 σ below both the observa-
tions and the baseline model prediction. Removing H2O
opacity also produces a significant drop in Rλ near 0.9
µm that further increases the discrepancy between the
model and overall red/near-IR observations. No other
opacity source could be responsible for the observed rise
in Rλ across this part of the spectrum.
3.2. Photoionization
After the reported sodium detection in the atmosphere
of HD209458b (Charbonneau et al. 2002), there were
several attempts to explain why the strength of this fea-
ture was much lower than expected based on earlier mod-
els (e.g., by Seager & Sasselov, 2000). Barman et al.
(2002) explored departures from local thermodynamic
equilibrium (LTE) which are capable of producing an in-
version in the cores of the Na doublet line profiles. How-
ever, the earlier models of Barman et al. (2001, 2002)
were constructed under the cond approximation and,
consequently, contained a larger number of free met-
als along with TiO and VO molecular absorption com-
pared to a rainout model. These additional sources of
optical/UV opacity lead to a hotter upper atmosphere
and a very shallow photoionization depth for Na (only
a 5% reduction of Na across the region probed by tran-
sit spectroscopy). Fortney et al. (2003) also explored Na
photoionization and found that their atmosphere model
(which included rainout) could be brought into reason-
able agreement with the Na observations. The models
presented here account for the angular dependence of
ionziation on the limb’s dayside, but not on the night
side. However, Fortney et al. (2003) have shown that Na
ionization is still present at ∼ 5◦ past the terminator for
pressures relevant to the transit spectrum modeled here.
Figure 1 compares cloud-free solar abundance rainout
models with and without photoionization of Na and K.
While these models include photoionization, the LTE ap-
proximation on the atomic level populations and line
source function is maintained. Ionization (radially) at
the limb reaches 50% at P ∼ 0.1 and 1.2 mbar for Na
and K, respectively, and stops at P ∼ 2 and 7 mbar, re-
spectively, resulting in a reduction of the Rλ-peaks across
Fig. 2.— Relative flux differences (with time from center of
eclipse) between a wavelength band centered on the Na doublet and
the mean of two wavelength bands on either side of the Na doublet.
The total wavelength range is indicated by vertical lines in Fig. 1.
Each model is cloud-free with solar abundances and α = 0.25. See
Figure legend and text for the distinguishing characteristics of each
model. Symbols are the observations of Charbonneau et al. (2002)
with 1 σ error bars.
the Na and K lines. For K, this reduction extends out to
the line-wings resulting in a significantly smaller mean
Rλ, bringing the model into ∼ 3σ agreement with the
Knutson et al. measurement. The impact of Na pho-
toionization is mostly confined to the core of the doublet
leading to only a small reduction of the mean Rλ, but suf-
ficient to bring the model into ∼ 1σ agreement with the
observations at these wavelengths. Though not included
here, ionization past the terminator onto the night side
should further improve the agreement across the Na and
K doublets. The two narrow features on the red wing
of the K doublet are due to Rb, which should also be
affected by photoionization due to its very low first ion-
ization potential. Photoionization of Rb resulted in a
near complete removal of these features, but reduced the
mean Rλ for this bin by less than 0.002 RJup.
The broad wavelength bins allowed Knutson et al. to
obtain very precise relative Rλ measurements; however,
as illustrated by the Na doublet, such broad bins lim-
its the constraints that can be placed on atomic absorp-
tion features. In contrast, the narrow range analyzed
by Charbonneau et al. (2002) resulted in much larger
Rλ error-bars, but still precise enough to easily distin-
guish between the various models shown in Fig. 1. The
flux differences across the Na doublet as a function of
time (measured from the transit center) were computed
for each model using the same narrow wavelength bins
as Charbonneau et al. (2002), indicated in Fig. 1 by
vertical dashed lines. Fig. 2 compares model transit
curves to the 2002 Na measurements and shows a large
discrepancy between the observations and solar abun-
dance models with pure equilibrium chemistry (cond or
rainout). Including photoionization brings the baseline
rainout model into rough agreement with the observa-
tions. Note the cond model shown in Fig. 2 does not
include photoionization (similar to the LTE model from
Barman et al. (2002)) and illustrates how far off the pre-
dicted Rλ can be across the Na doublet under simplified
assumptions.
3.3. Rainout, Metallicity, and Temperature
The rainout model used here reduces the individual
metal abundances with depth iteratively until clouds do
not form, thus mimicking efficient gravitational settling.
However, the removal of metals is not 100% efficient,
leaving behind a variety of atoms (in addition to Na and
K) to contribute to the line opacity. The impact of rain-
out on the planet’s atmosphere is made apparent by com-
paring rainout and cond models (Fig. 3). In the cond
model grain opacities are simply ignored in the transfer
equation while the chemistry remains that of a pure equi-
librium model without any actual removal of refractory
elements. Thus, the cond model represents the minimum
impact of grain formation on the stratified abundances
and leaves behind a considerable amount of free metals
along with molecules like TiO and VO. This leads to
much stronger atomic lines, including Na and K along
with TiO and VO bands.
Apart from a very minor contribution from molecules,
the Rλ features at λ < 0.8µm are all due to atomic line
opacity 1. These narrow features are due to blended lines
from metals like Ca, Al, Fe, Ni, Mn, and Cr. Note that,
while Rayleigh scattering does contribute to the opacity
in the blue/UV, a removal of atomic line opacity would
drop Rλ by∼ 0.02RJup for λ < 0.45µm. The top panel of
Fig. 3 compares the solar abundance rainout model with
photoionization (shown in Fig. 1) to a rainout model
with 10× solar abundances. Since the metal abundances
were uniformly scaled, the grain formation and corre-
sponding removal of refractory elements were also uni-
formly enhanced. The additional opacity altered the T-P
profile as well as the total atmospheric extension. These
factors contribute to a similar Rλ pattern in the opti-
cal but enhanced molecular absorption features in the
red/near-IR. The increase in metals increases the H2O
absorption feature along with the wings of the Na and
K doublets (which form deeper in the atmosphere where
photoionization is less important). Also, FeH and CrH
absorption is larger in the metal-rich atmosphere leading
to an increase in Rλ on both sides of the K doublet. The
metal-enhanced Rλ spectrum is in good agreement with
the observations near 0.9µm, but is noticeably too high
across both the K doublet and the H2O band.
Transit spectroscopy can also help constrain the tem-
peratures across the limb. The lower panel of Fig. 3
compares an α = 0.5 model (i.e. a model with a hotter
dayside-like T-P profile) to the cooler α = 0.25 base-
line model. In the hotter model, grain formation is less
pronounced resulting in a greater concentration of most
free metals and, thus, stronger UV/blue absorption lines
than in the α = 0.25 model. Higher temperatures at
depth also result in equilibrium concentrations of Na
and K that are several times lower than found at the
cooler temperatures of the α = 0.25 model. The net re-
sults are two distinctively different Rλ spectra with the
α = 0.25 model being more consistent with the Knutson
et al. measurements.
4. SUMMARY
1 Ballester et al. (2007) claim the Rλ rise in the blue/UV is due
to the Blamer edge of hot hydrogen in an extended atmosphere.
While the present model does not support this explanation, if ver-
ified, it could indicate that rainout is more efficient than predicted
here.
Fig. 3.— Monochromatic transit radii over the STIS spectral range. Top panel: solar abundance models, cond (black) and rainout(red),
are compared to a model with 10× solar metal abundances including rainout (blue). Lower panel: solar abundances baseline rainout model
with α = 0.25 (red) compared to a similar model with α = 0.5 (blue). Horizontal bars have the same meaning as in Fig. 1.
Photoionziation plays an important role for both Na
and K, and potentially many other species. No evidence
is found to support a large metal enhancement (e.g., 10×
solar), though smaller Jupiter-like enhancements are not
ruled out. Furthermore, the agreement between model
and observations demonstrated here alleviates the need
for substantial cloud coverage along the limb between
0.05 and 0.001 bars, which would otherwise truncate and
flatten the Rλ spectrum (Brown 2001). In the baseline
model, the predicted location of clouds (e.g., MgSiO3)
lies just below the minimum Rλ(∼ 1.315RJup) across the
STIS wavelength range, consequently deep clouds (and
also very high clouds) remain a possibility.
The models presented here also predict Rλ variations
(∼ 0.02 RJup) across the 2-0 R-branch of CO in the K-
band. This is inconsistent (at 2.5σ) with a non-detection
of CO based on Keck-NIRSPEC transit spectra taken
in 2002 (Deming et al. 2005a). It is likely that using a
single T-P profile to represent the horizontal and pole-
to-pole variations across the limb averages out too much
of the upper atmospheric structure; this simplification
might explain the K-band discrepancy. High clouds may
also be involved. In addition, the Keck and HST obser-
vations were taken between 1 and 2 years apart and time-
dependent atmospheric variations along the limb cannot
be ruled out (Menou et al. 2003).
While Knutson et al. (2007) did not attribute their
measured Rλ variations to any absorption features (this
was not the focus of their paper), the models presented
above clearly show that these measurements are consis-
tent with strong water absorption near 1 µm. A detection
of water in the limb of HD209458b is nominally at odds
with a recent Spitzer IRS spectrum that shows no H2O
features for this planet(Richardson et al. 2007). These
data were taken during secondary eclipse and directly
probe the planet’s dayside with negligible contribution
from the limb. It is possible that the dayside atmosphere
is nearly isothermal (Fortney et al. 2006) which would re-
sult in a spectrum with no detectable water absorption
features, despite a copious water supply. The transmis-
sion spectrum, however, would contain absorption fea-
tures independent of an isothermal dayside or limb.
The author thanks B. Hansen and the referees for their
comments. This research was supported by NASA Ori-
gins and Spitzer Theory Grants and made use of NASA’s
Project Columbia computer system.
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