retrieval of atmosphere structure and composition of ...€¦ · retrieval of atmosphere structure...

Retrieval of Atmosphere Structure and Compositionof Exoplanets from Transit Spectroscopy

Jae-Min Lee

The confirmation report for the degree of Doctor of Philosophy

Wolfson College, University of Oxford

Trinity term, 2011(16,300 words)

Contents

1 Introduction 21.1 Beyond the first exoplanet observation . . . . . . . . . . . . . . . . . . . . 21.2 Transit spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Four close-in transiting exoplanets . . . . . . . . . . . . . . . . . . 51.3 Retrieval studies of exoplanetary atmospheres . . . . . . . . . . . . . . . . 10

2 Research objectives 12

3 Spectral modelling of a high temperature atmosphere 153.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1.1 Correlated-k approximation . . . . . . . . . . . . . . . . . . . . . 153.2 Line lists for k-distribution tables . . . . . . . . . . . . . . . . . . . . . . . 17

3.2.1 H2O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2.2 CO2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2.3 CO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2.4 CH4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.2.5 Alkali metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2.6 Metallic Oxides . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.3 Collision-induced absorption . . . . . . . . . . . . . . . . . . . . . . . . . 273.4 Current issues on spectral modelling . . . . . . . . . . . . . . . . . . . . . 28

4 Retrievals 294.1 NEMESIS – Non-linear optimisation retrieval algorithm . . . . . . . . . . 294.2 Secondary eclipse of HD 189733b . . . . . . . . . . . . . . . . . . . . . . 31

4.2.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.2.3 Best-fit dayside spectrum of HD 189733b . . . . . . . . . . . . . . 324.2.4 Contribution functions . . . . . . . . . . . . . . . . . . . . . . . . 344.2.5 Functional derivatives . . . . . . . . . . . . . . . . . . . . . . . . 354.2.6 Retrieval of P -T profile . . . . . . . . . . . . . . . . . . . . . . . 374.2.7 Retrieval of molecular abundances . . . . . . . . . . . . . . . . . . 424.2.8 Lapse rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464.2.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.3 Secondary eclipse of HD 209458b . . . . . . . . . . . . . . . . . . . . . . 494.3.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.3.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.3.3 Retrieval of P -T profile . . . . . . . . . . . . . . . . . . . . . . . 51

3

4.3.4 Case studies - Improved retrieval? . . . . . . . . . . . . . . . . . . 524.3.5 Retrieval of molecular abundances . . . . . . . . . . . . . . . . . . 534.3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.4 Primary transit of HD 189733b . . . . . . . . . . . . . . . . . . . . . . . . 574.4.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.4.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.4.3 Best-fit spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.4.4 Functional derivatives . . . . . . . . . . . . . . . . . . . . . . . . 594.4.5 Retrieval of molecular abundances . . . . . . . . . . . . . . . . . . 614.4.6 Aerosol scattering? : High transit depths at visible . . . . . . . . . 62

4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5 Future work 645.1 Retrieval studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.2 Thesis contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.3 Timeline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

A Available line lists for molecules and elements 68

B Partition function 70

C A manuscript for publication 72

4

Abstract

Recent spectroscopic observations of transiting exoplanets have permitted the derivation of

the thermal structure and molecular abundances of H2O, CO, CO2, CH4, metallic oxides

and alkali metals in these extreme atmospheres. Here, for the first time, a fully-fledged re-

trieval algorithm has been applied to exoplanet spectra to determine the thermal structure

and composition. The development of a suite of radiative transfer and retrieval tools for ex-

oplanet atmospheres is described, building upon an optimal estimation retrieval algorithm

extensively used in solar system studies. Firstly, the collection of molecular line lists and

the pre-tabulation of the absorption coefficients (k-distribution tables) for high temperature

application are discussed. Secondly, the best-fit spectra for a range of different exoplanet

classes, from hot Jupiters and hot Neptunes to a super Earth are demonstrated and discussed

case by case. Available sets of primary and secondary transit observations of exoplanets are

used to retrieve these spectra, quantifying the limits of our knowledge of exoplanetary atmo-

spheres based on the current quality of the data. The contribution functions and the vertical

sensitivity to the molecules are fully utilised to interpret these spectra, probing the structure

and composition of the atmosphere. Finally, the retrievals provide our best estimates of the

thermal and compositional structure to date, using the covariance matrices to properly assess

the degeneracy between different parameters and the uncertainties on derived quantities for

the first time. This sheds light on the range of diverse interpretations offered by other authors

so far, and allows us to scrutinise further atmospheric features by maximising the capability

of the current retrieval algorithm and to demonstrate the need for broadband spectroscopy

from future missions.

Chapter 1

Introduction

1.1 Beyond the first exoplanet observation

Since the first detection of a planet orbiting a Sun-like star (51 Pegasi) in 1995 (Mayor &

Queloz, 1995), more than 551 planets of various types have now been discovered around

main-sequence stars1. The detection of these exoplanets has revolutionised our understand-

ing of our solar system as one of many planetary systems in our galaxy. Encouragingly, the

rate of discovery of exoplanets has increased dramatically in recent years2 and detectable

masses and sizes are now comparable to Earth-mass (ME) and size (RE) (Mayor et al.,

2009). Recently, the Kepler telescope found >1200 exoplanet candidates, including six

Earth-sized planets orbiting in the habitable zone (Borucki et al., 2011). It is expected that

the next generation of telescopes being built within the few decades will successfully detect

tiny spectral signals from terrestrial exoplanets. In this sense, the implication for this study is

to provide the novel tool for characterising the atmospheres hosted by these remote obejcts,

and understanding the broad diversity of chemistry and thermal structure of planets.

A range of methodologies for discovering exoplanets have been established and advanced

in many ways. Although direct imaging, which requires very high contrast ratio and angular

resolution of instrument, is the most intuitive way, only a small number of exoplanets have

been directly imaged in this fashion (Chauvin et al., 2004; Marois et al., 2008). Instead,

indirect techniques have been more commonly used, including astrometry, gravitational mi-

crolensing, radial velocity, and transit spectroscopy. This is because most of the exoplanet

candidates orbit close to their parent star with rapid rotation rates, providing frequent oppor-

tunities to verify their existence within a short period.

1http://exoplanet.eu/index.php2http://exoplanet.eu/index.php;http://exoplanets.org/planets.shtml

2

Figure 1.1: A schematic diagram illustrating the geometry of a planetary system duringprimary and secondary transits.

1.2 Transit spectroscopy

The only indirect detection method that allows us to characterise exoplanet atmospheres is

transit spectroscopy, whereby a planet transits its host star, permitting the derivation of the

properties of exoplanet’s atmosphere. When a companion passes in front of (primary transit)

or behind (secondary transit) the parent star (Fig. 1.1), the combined light of the system is

slightly decreased for a time, if the orbital plane lies on the line of an observer’s sight. If

the dimming is deep enough to detect at regular intervals, it is deduced that there is a planet

spinning around the parent star. Even though an orbital inclination must be quasi-random,

a large number of transit light curves have been obtained from various planetary systems so

far (∼130). Spectroscopically, transit depths at multiple wavelengths are directly interpreted

as an atmospheric spectrum that includes a transmission spectrum (during primary transit

when light is filtered through the upper levels of a planet’s atmosphere) and a thermal emis-

sion spectrum (during secondary transit (or secondary eclipse) when the emission is directly

detected from a planet’s atmosphere). These two complimentary methods of spectroscopy

provide improved confidence in the derived atmospheric properties.

Transit depths during two phases are defined as a flux ratio between in- and out-of-

transits. For primary transit, its absorption depth is equivalent to the ratio of the cross sec-

tional areas of the parent star disk (πR2∗) and the optically thick disk of the exoplanet (AP )

including the atmospheric annulus (Aannulus). For secondary transit, the emission spectrum

is acquired by taking the ratio between the disk-averaged fluxes of the planet and star. The

area of the atmospheric annulus and the disk-averaged flux of the planet are basically a func-

3

tion of wavelength. Therefore, these would be

Absorption depth (Transmission) :AP + Aannulus,λ

πR2∗

, (1.1)

Flux ratio (Emission) :πR2

P σT 4P,λ

πR2∗ σT 4

∗,λ=

(RP

R∗

)2(TP,λ

T∗

)4

(1.2)

where TP , T∗, RP , and R∗ are the effective temperatures and radii of exoplanet and star,

respectively. For a typical Jupiter-size exoplanet, considered by Seager (2008), in which the

size of an atmosphere would be approximately 5 scale heights thick in theory, Eq. 1.1 can be

written as

AP + Aannulus,λ

πR2∗

=πR2

P +[π (RP + 5H)2 − πR2

P

]πR2

∗=

πR2P + [10HπRP + 25πH2]

πR2∗

' R2P

R2∗+

10HRP

R2∗

(∵ 25H2 � 10HRP ), (1.3)

where H is the scale height. The first term in Eq. 1.3 describes the transit depth by the

optically thick disk only and the second term describes the part of the transit depth due to the

atmospheric annulus of the planet. Due to the relation between temperature and scale height,

the temperature profile mainly determines the overall depth of the transmission spectrum

across the wavelengths, while compositional abundances play a critical role in the formation

of spectral features (Tinetti et al., 2007a). The planetary transmission spectra will therefore

be used as a tool to determine the molecular or atomic abundances in the upper atmospheres

of exoplanets. Moreover, the molecular features and contributions of cloud and hazes are

detectable via this method. On the other hand, the thermal emission spectrum during sec-

ondary transit can be obtained from a disk-averaged flux ratio between planet and star (Eq.

1.2). The flux ratio (Fplanet/Fstar) directly provides the brightness temperature of a plane-

tary atmosphere, which is a function of wavelength, and the thermal emission is therefore

strongly linked to the vertical structure of the temperature. The determinations of the dayside

temperature profile will be used to see whether specific thermal structures such as inverted,

isothermal, and adiabatic layers are present in the atmosphere.

Current research of exoplanet atmospheres is mostly based on transiting planets due to

their detectability. Among them, small orbital distances of close-in exoplanets make them

face strong radiation from the parent star so that the atmospheric temperatures reach to a few

thousand K. These high temperatures expand the atmosphere and stretches the atmospheric

scale height from a hundred to a few hundred kilometres. As a result, this combination of

large scale heights and high temperatures allows us to measure transmission and emission

spectra during transits for a small number of targets, some of which will be studied as part

of this work.

4

According to the theoretical chemistry models (Line et al., 2010, and references therein),

the atmospheres of close-in transiting exoplanets primarily consist of H2O, CO2, CO, and

CH4. These molecular transitions are widely distributed over the wavelengths (≥1µm) for

both transmission and emission spectra. The emission spectrum has only been measured in

the infrared (IR) region (1–30 µm), where the flux ratio between parent star and planet rises

appreciably. On the other hand, transmission spectra have also been measured at shorter

wavelengths where Rayleigh scattering and alkali metals are thought to be highly dominant

features in the visible wavelength (≤1µm). Therefore, for both primary and secondary tran-

sits, the atmospheric properties of exoplanets can be investigated in multiple wavelengths

using a small number of observations from space and ground-based telescopes.

1.2.1 Four close-in transiting exoplanets

There are a number of close-in exoplanets that have been intensively investigated since their

discovery. Each planet has diverse characteristics depending on its mass, orbital distance,

and the spectral type of the parent star. The range of exoplanets selected for this study were

chosen to be represent three different categories; two hot Jupiters, one hot Neptune, and one

super-Earth.

Commonly, previous attempts to characterise each atmosphere from spectroscopic data

have not solved inverse problem and not quantified the uncertainties caused by the composi-

tional degeneracy. Therefore, the following paragraphs describe the current understanding of

these four exoplanets based on their various forward modelling methods (see Chapter 1.3).

HD 189733b – hot Jupiter

A hot Jupiter type exoplanet, HD 189733b is one of the most extensively studied of all the

exoplanets observed. Tinetti et al. (2007b) and Swain et al. (2008a) deduced a high abun-

dance of H2O from transmission spectra of HD 189733b acquired during primary transits (∵transmission spectra are sensitive to terminator regions), which were observed by Spitzer

mid-IR (MIR) and far-IR (FIR) broadband photometry. Beaulieu et al. (2008), Agol et al.

(2009), Knutson et al. (2007), Knutson et al. (2009) and Desert et al. (2009) re-visited these

observations and obtained similar conclusions. (i.e. H2O is prevalent on this exoplanet). A

spectral feature of HD 189733b at 4.5 µm can be explained by either of the carbon bearing

molecules CO2 (Desert et al., 2009) or CO (Fortney et al., 2010), although it is still unclear

which due to the degeneracy of the solution. Swain et al. (2008a) reported strong absorp-

tion from CH4 in the near IR (NIR) using the HST/NICMOS spectrophotometry (Fig. 1.2).

However, Gibson et al. (2011) claimed that this measurement was not hard evidence for CH4

due to systematic errors of the instrument. At visible wavelengths, strong lines of the al-

5

kali metal, sodium, were reported using observations with the high resolution (R=60,000)

ground spectrograph of the Hobby–Eberly Telescope (Redfield et al., 2008), while a fea-

tureless spectrum detected by the HST/STIS is thought to be caused by thick atmospheric

hazes (Pont et al., 2008; Sing et al., 2009, 2011).

Observations of secondary transits of HD 189733b by Spitzer IRAC showed that H2O

is abundantly present in the dayside atmosphere (Charbonneau et al., 2008; Deming et al.,

2006), forming the main features of the emission spectrum and confirming some of the results

from the primary transits. Grillmair et al. (2008) confirmed a high abundance of H2O using

the Spitzer IRS spectrograph. In addition to H2O, the HST/NICMOS measurements showed

additional spectral features at NIR and indicated an existence of carbon bearing molecules

such as CO2, CO, and CH4(Madhusudhan & Seager, 2009; Swain et al., 2009a). Also, Swain

et al. (2009a) and Madhusudhan & Seager (2009) suggested that an atmosphere without a

thermal inversion layer best represents the atmospheric structure of HD 189733b, for which

a troposphere may be located between 0.01 and 1 bar pressure level. Therefore, one aim of

this study is to retrieve the vertical temperature structure of dayside HD 189733b for the first

time, and to quantify the true uncertainties on the compositional determinations proposed by

previous studies.

HD 209458b – hot Jupiter

The second hot Jupiter to be charactierised in this study, HD 209458b is the second-best

observed of transiting exoplanets. Charbonneau et al. (2002) reported a sodium doublet

feature at 589.6 and 589.9 nm from a transmission spectrum of HD 209458b. Knutson et

al. (2007) observed the transmission spectrum at the visible band between 300–770 nm,

showing possible absorption features due to H2 Rayleigh scattering (Sing et al., 2008) and

metallic oxides (TiO and VO) (Desert et al., 2008). In the ultraviolet (UV) region, Vidal-

Madjar et al. (2003, 2004) detected evaporating atmosphere of hydrogen, oxygen, and carbon

around HD 209458b using HST/STIS, which is due to strong heating from the parent star.

Beaulieu et al. (2010) analysed the Spitzer IRAC photometry of the primary transit of HD

209458b and suggested the best-fitted spectrum based on H2O transitions alone, showing

an agreement with the measurements in the visible (Barman, 2007) and FIR wavelengths

(Richardson et al., 2006). Snellen et al. (2010) discovered fast wind speeds at high altitude

by measuring doppler shifts of 56 CO lines at 2.291–2.349 µm during primary transit.

Burrows et al. (2007) discussed in-depth the structure of stratosphere and proposed the

possibility of a thermal inversion layer in HD 209458b. This has been generally accepted

through significant and successive observations of its dayside emission taken by various in-

struments on board Spitzer and HST (Burrows et al., 2007; Swain et al., 2010) but one

aim of this study is to test how robust such a conclusion actually is. Of all measurements of

6

Figure 1.2: Modelled (left) transmission and (right) emission spectra and measuredtransit depths of HD 189733b. These samples are taken by (left) the HST/NICMOSspectrophotometry (Swain et al., 2008b), and (right) the Spitzer photometry by IRACand MIPS (red), and IRS spectrograph (black) (courtesy of Grillmair et al. (2008)). Eachmodel is characterised by the heat distribution, Pn, which tells the fraction of the heattransport from dayside to nightside.

Figure 1.3: Modelled (left) transmission and (right) emission spectra, and measuredtransit depths of HD 209458b. These were obtained in (left) the MIR photometry offour Spitzer IRAC channels (Beaulieu et al., 2010), and (right) the compilation ofHST/NICMOS (black), and Spitzer IRAC (green) and IRS (red) (courtesy of Swain etal. (2009a)).

7

the secondary transit, the six Spitzer broadband photometry channels showed very high flux

ratios that require a thermal inversion layer during retrieval (Knutson et al., 2009; Madhusud-

han & Seager, 2009; Swain et al., 2009b). Although these studies commonly mentioned a

thermal inversion present in HD 209458b, the suggested pressure levels for the inversion are

entirely inconsistent with one another. In this sense, this study aims to quantify the uncer-

tainties in the temperature field based on the compositional degeneracy.

GJ 436b – hot Neptune

Recently, the M type stars have become a main target of transit spectroscopy because high

transit depths can be achieved with smaller and cooler planets, bringing us closer to the ter-

restrial regime. After discovery by Butler et al. (2004), GJ 436b, which is one of the hot

Neptune type (tens of times more massive than the Earth but smaller than hot Jupiters),

was reported to have diverse compositions such as H2O, and carbon bearing molecules,

which should be dominant constituents in the atmosphere with the effective temperature

cooler than a thousand K. In the visible, Ballard et al. (2010) detected the signature of alkali

metal lines over a visible band of 0.5–1.0 µm on the Deep Impact high-resolution instrument

(HRI) used for the EPOXI mission. For the NIR region, Alonso et al. (2008) and Caceres et

al. (2009) measured primary transits of GJ 436b in the H and K band on the VLT, respec-

tively, and Pont et al. (2008) presented a H2O feature between 1.35–1.85 µm based on the

HST/NICMOS observation. Beaulieu et al. (2011) explained all these transit depths by con-

sidering a CH4-rich atmosphere in GJ 436b, incorporating the Spitzer IRAC measurements

at 3.6, 4.5, and 8.0 µm. They also used the observation of the dayside emission to confirm a

CH4-rich atmosphere. On the other hand, Knutson et al. (2011) analysed the other set of the

Spitzer IRAC measurements and showed that the transmission spectrum of GJ 436b could

be modelled with less CH4 and more CO than the model atmosphere presented by Beaulieu

et al. (2011) (see the left plot in Figure 1.4). The CH4-rich scenario is consistent with the

conclusions made from the emission transit depths by the six different Spitzer broadbands

channels (Stevenson et al., 2010), including IRAC (3.6, 4.5, 5.8, and 8.0 µm), IRS (16 µm),

and MIPS (24 µm) (see the right plot in Figure 1.4).

The uncertainties over the composition of the hot Neptune will be the subject of studies

done in preparation for the thesis. The preliminary study for this exoplanet will not be

presented in this report.

GJ 1214b – super-Earth

The other transiting exoplanet near an M star, GJ 1214b, that will be considered in this study

has only been observed during primary transit. Its transmission spectrum in the visible has

been measured by Bean et al. (2010) in the 11 bands (0.78–1µm) of the FORS2 instrument on

8

Figure 1.4: Model (left) transmission and (right) emission spectra, and measured transitdepths of GJ 436b. In the left panel, the closed red circles from the shorter wavelengthsare taken by EPOXI (Ballard et al., 2010), the H (Alonso et al., 2008) and K (Caceres etal., 2009) bands of the VLT, the HST/NICMOS (Pont et al., 2008), and the three SpitzerIRAC channels at 3.6, 4.5, and 8 µm (courtesy of Knutson et al. (2011)). The open redcircles are the other measurements of Spitzer IRAC (Knutson et al., 2011). The crosses inthe right panel indicate the six Spitzer photometry measurements of the dayside emissionGJ 436b (Beaulieu et al., 2011; Stevenson et al., 2010).

Figure 1.5: Various model transmission spectra and measured transit depths of GJ 1214b.In order of wavelength, the measurements were obtained in the VLT (Bean et al., 2010),the J and K bands of CFHT (Croll et al., 2011), the 2.1–2.4 µm Keck/NIRSPEC (Cross-field et al., 2011), and the 3.6 and 4.5 µm Spitzer IRAC channels (Desert et al., 2011)(courtesy of Crossfield et al. (2011)). The blue and violet spectra, which are with lowcarbon and methane are the most plausible among the scenarios.

9

the VLT. It was found that its featureless spectrum is characterised by either a H2O abundant

atmosphere or a H2 dominant atmosphere including clouds or hazes. Desert et al. (2011) ob-

served transit depths in the 3.6 and 4.5 µm Spitzer IRAC bands, from which they concluded

that the atmosphere of GJ 1214b is consistent with the enhanced metallicity model, in which

the heavy elements may exist in the form of H2O. In contrast, Croll et al. (2011), whose mea-

surements are based on the J and K bands of the Canada−France−Hawaii−Telescope

(CFHT), claimed that the deeper spectral features at the NIR lead to a H2/He dominant and

optically thick layered atmosphere, otherwise non-equilibrium chemistry may play an impor-

tant role in this planet. Recently, Crossfield et al. (2011) analysed all available measurements

including their 2.1–2.4 µm Keck/NIRSPEC observations and noted that the high-metallicity

suggestions by Bean et al. (2010) and Desert et al. (2011) are the most agreeable model out

of candidate scenarios if the atmosphere of GJ 1214b is depleted in CH4 (i.e. blue spectrum

in Figure 1.5).

As GJ 1214b is only seven times more massive than the Earth, it is usually referred as

a super Earth. Its dayside emission spectrum should be available within 1–2 years with

current technology. This exoplanet also will be studied for the thesis but its preliminary

study is not included as part of this report.

1.3 Retrieval studies of exoplanetary atmospheres

The retrieval of atmospheric properties from remotely sensing measurements has been de-

veloped over many decades (Goody & Yung, 1989) and has become a common tool for the

study of planetary atmospheres. Measured radiances (either photometry or spectroscopy)

can be compared to synthetic spectra from radiative transfer modelling so as to determine

the atmospheric structure and composition. A retrieval model solves an ill-constrained in-

version problem, using an iterative approach to derive the most statistically-likely solution

for the available data.

Previous studies, such as those by Tinetti et al. (2007a) and Swain et al. (2008a, 2009a),

utilised forward modelling to determine a best-fit to the data, and constrained the range

of molecular abundances of transiting exoplanets by running forward models, which were

based on theoretical pressure-temperature (P -T ) profiles. An alternative forward modelling

approach used by a number of studies (Madhusudhan & Seager, 2009, 2010, 2011; Mad-

husudhan et al., 2011; Sing et al., 2008; Stevenson et al., 2010) applied freely roaming P -

T profiles and molecular abundances in a parameterised space, where calculated spectra

were again compared with observations in terms of the goodness-of-fit, and their numerous

runs enabled to constrain P -T profiles and atmospheric compositions. Although these for-

ward modelling techniques provide valuable insights, their methods are based on line-by-line

10

(LBL) radiative transfer models, which are slow when large numbers of synthetic spectra are

to be calculated over a wide wavelength range. Moreover, the huge degeneracies between

the different model parameters were not explored in detail.

On the other hand, the NEMESIS optimal estimation retrieval algorithm (Irwin et al.,

2008) used in this study solves the inverse problem, rather than calculating forward models,

and uses the correlated-k technique (Lacis & Oinas, 1991) in its radiative transfer model,

which rapidly integrates synthetic spectra using k-distribution tables pre-calculated from

line databases (Goody & Yung, 1989). The combination of the correlated-k forward model,

which is orders of magnitude faster than a standard LBL model, with an optimal estimation

retrieval scheme has been used to successfully investigate planetary atmospheres in our own

solar system. In this study, this rapid retrieval architecture is applied for exoplanets, for-

mally addressing the uncertainties and degeneracies inherent in previous studies. Moreover,

understanding of the detailed correlations between the derived P -T profile and atmospheric

compositions can be achieved from the covariance matrices which are calculated using this

method, and which quantify the correlations between the retrieved values of different prop-

erties. Consequently, this study will show that how the characteristics of these extreme

exoplanet atmospheres can be deduced from spectroscopic measurements, and, finally, the

limitations of the datasets available today will be highlighted.

11

Chapter 2

Research objectives

The transmission and emission spectra of exoplanets have been extensively studied since

the first spectroscopic discovery of HD 209458b (Charbonneau et al., 2002). Currently, the

increasing sampling at various wavelengths is becoming significant, permitting meaningful

estimation of atmospheric properties of exoplanets. Various studies have characterised these

extreme atmospheres based on their own observation techniques and atmospheric models,

and have interpreted temperature profiles and composition abundances in many ways. Of the

models, theoretical chemistry and dynamic models provide a general view of atmospheric

states that allow us to understand the initial impression of chemical and thermal structure

of an exoplanet. On the basis of these results, radiative transfer models compare modelled

spectra with measured transit depths in order to identify any previously suggested features.

However, it has been shown that their results, in some cases, are inconsistent due to ei-

ther insufficient knowledge for theoretical models or noisy measurements. Also, inefficient

modelling methods such as LBL calculations and iterations of forward model in a param-

eterised space (i.e. not solving inverse problem) limit a full understanding of exoplanetary

atmospheres.

Hence the final goal of this study is to quantify the best estimates for the temperature

and composition of the atmospheres of close-in transiting exoplanets by solving the inverse

problem and quantifying the errors on properties from all currently available measurements

for the first time. By using full retrieval theory, we are able to quantify the uncertainties

on the characterisations that have been presented in the literature so far in order to answer

the question of what can we learn from the exoplanet spectra available to date?. This

study will focus on examining the atmospheres of transiting exoplanets via a conventional

retrieval architecture that has been successfully used in studies of our own solar system. This

includes re-analysis of the various sets of measurements to investigate the diverse scenarios

made to date, and to deduce further feasible aspects of atmospheric systems. Finally, this

study will conclude with a discussion of which characteristics it may be possible to retrieve

12

from a small number of measurements. This is, of course, a synthesis of all the measurements

within the retrieval framework, providing a comprehensive atmospheric characterisation of

exoplanets considered here. In this perspective, the research items can be listed as follows.

• Setting up the high-temperature line database for the molecules (H2O, CO2, CO,CH4, TiO, and VO) and alkali metals (Na and K). This includes the conversion of

various line lists into a typical HITRAN format, the estimation of partition functions,

and line strength calculations for various compositions (see Section 3.2). Collisional

induced absorption data for high temperatures will be also calculated (see Section 3.3).

• Creating k -distribution tables for molecules and metals based on the line liststabulated in the HITRAN format. This includes a comparison study of transmissions

integrated by both LBL and correlated-k distribution methods in order to confirm the

accuracy of pre-calculated k-distribution tables (also see Section 3.2).

• Retrieving the atmospheric properties that enable an explanation of the transmis-sion and emission transit depths of exoplanets. This includes the retrievals of two

hot Jupiters of HD 189733b (see Section 4.2 and 4.4) and HD 209458b (see Section

4.3), a hot Neptune of GJ 436b (see Section 5.1), and a super Earth of GJ 1214b (see

Section 5.1). For all cases, the atmospheric characteristics (temperature profile and

molecular abundances) will be investigated. This includes extensive explanation of

resultant retrieval matrices such as contribution functions and functional derivatives.

Variable uncertainties and degeneracy between the properties will be explored by us-

ing correlation and covariance matrices. All available measurements are listed in Table

2.1.

• Suggest interpretations for the measurements which may either support or pro-vide evidence against characteristics inferred in previous studies. In addition,

unique features of exoplanets that have not yet been identified will be also provided

(e.g. see Section 4.3.8).

13

Table2.1:A

vailablem

easurements

ofHD

189733b,HD

209458b,GJ

436b,andG

J1214b

HST

SpitzerE

POX

IM

Earth

Ground

TelescopeR

eferencesN

umberof

availablem

easurements

STIS

NIC

MO

SIR

AC

IRS

MIPS

PlanetIDV

ISN

IR3.6

4.55.6

8.0M

IR16

240.5-1.0

0.8-0.9

SecondaryE

clipse

HD

189733b(hotJupiter)

AB

BB

BC

BB

A.

Swain

etal.

(2009a);B

.C

harbon-neau

etal.

(2008);C

.G

rillmairetal.(2008)

69

HD

209458b(hotJupiter)

DE

EE

EF

ZE

,H

D.

Swain

etal.

(2009b);E

.K

nutsonetal.(2007);F.Sw

ainet

al.(2008a)

;H.

Dem

inget

al.(2006)

;Z.

Dem

ing(2009)from

Madhusudhan

&Seager(2009)

35

GJ

436b(hotN

eptune)I,J

I,JI

I,JI

II.

Stevensonet

al.(2010)

;J.Beaulieu

etal.(2011)

6

GJ

1214b(superE

arth)

Primary

Transit

HD

189733bK

L,M

,NO

,PO

,PO

,PO

,PQ

R(H

obby-Eberly)

K.

Pontet

al.(2008)

;L.

Swain

etal.

(2008b);M

.Sing

etal.

(2009);N

.G

ibsonet

al.(2011)

;O.

Tinettiet

al.(2007b)

;P.Desertetal.(2009)

;Q.

Knutson

etal.

(2007);R

.Redfield

etal.(2008)

35

HD

209458bT

UU

UU

V

T.K

nutsonet

al.(2007)

;U.

Beaulieu

etal.

(2010);V.

Richardson

etal.

(2006)

15

GJ

436bA

BA

E,A

FA

E,A

FA

E,A

FA

AA

C,A

D

AA

.B

allardet

al.(2010);A

B.Pontetal.

(2008);AC

.Alonso

etal.

(2008);A

D.

Cac-

eresetal.(2009);A

E.

Beaulieu

etal.(2011)

;AF.

Knutson

etal.

(2011)

7

GJ

1214bA

HA

HA

IA

G,A

J,AK

AG

.Bean

etal.(2010);A

H.

Desert

etal.

(2011);A

I.C

harbon-neau

etal.(2009);AJ.

Croll

etal.

(2011);A

K.

Crossfield

etal.

(2011)

16+

14

Chapter 3

Spectral modelling of a high temperatureatmosphere

3.1 Theory

3.1.1 Correlated-k approximation

If only the averaged spectral intensity in given wavelength bins (of a given resolution) is re-

quired, the position and strength of every line in each bin need not necessarily be considered

during the iteration of radiative transfer. Thus a pre-calculated absorption coefficient, k, for

each bin could be used instead. This fact allows a reduction in the resource demand for the

iterative process. As one approximation method, a band model takes advantage of the mean

absorption coefficient by simply adding up all the line strengths in the interval. Due to its

fast integration, band models are suitable for computations which need only low resolution

and low accuracy. Band models, however, cannot include scattering calculations due to the

limitation of the Curtis-Godson approximation (Curtis, 1952; Godson, 1955), which cannnot

concern the transmission of an inhomogeneous atmospheric path.

On the other hand, the correlated-k approximation model (Goody & Yung, 1989) can

consider single and multiple scattering atmospheres, has a high computational speed com-

parable to the band model, and has been shown to be reliable, fast and sufficiently accurate.

Unlike band models, correlated-k models use spectral frequency space re-distributed into a

fraction of the frequency domain containing absorption coefficients between k and k+dk.

The mean transmission of the absorber amount m, T (m), over interval ∆ν from ν0, is ex-

pressed as

T (m) =1

∆ν

∫ ν0+∆ν

ν0

exp (−kνm) dν. (3.1)

15

Using fraction of the frequency space, f (k) dk, this is now re-written as

T (m) =

∫ ∞

0

f (k) exp (−km) dk, where f (k) =1

∆ν

∑∣∣∣∣dνdk∣∣∣∣ . (3.2)

Here a cumulative function of the fraction of the frequency interval, g (k), is defined as,

g (k) =

∫ k

0

f (k) dk. (3.3)

Due to characteristics of the cumulative function, g (k) has an inverse function k (g) called a

k-distribution function, and g (k) approaches unity when k goes to infinity. Therefore, T (m)

in Eq. 3.2 becomes a function of g:

T (m) =

∫ 1

0

exp (−k (g)m) dg. (3.4)

From the above equation, it is known that a well-defined k (g) with sufficient intervals of g

can precisely calculate the mean transmission. With discrete quadrature points, N , Eq. 3.4

is written as

T (m) =N∑i=1

exp (−kim) ∆gi (3.5)

where ki and ∆gi are the k-coefficients and quadrature weights at each quadrature points.

The number of quadrature points N determines the performance of the approximation form,

and N=20 is applied in this study. Therefore, k-distributions are calculated from line databases

for a range of temperatures and pressures expected in the exoplanet atmospheres and tabu-

lated in advance of the retrieval so that a fast forward model calculation is possible during the

iteration. In this study, 18 temperature points between 400–2950 K and 12 pressure points

between 1.388×10−11 (e−25) –20.085 (e3) bar are chosen in order that the large range of tem-

peratures in known exoplanets are fully covered. Parameters required for k-coefficient calcu-

lation are also determined as 5 cm−1 in wavenumber and 5 nm in wavelength for resolution

and 1.5 cm−1 for bin width (WING), in which line data is stored during calculation, 10 cm−1

for FWHM of each bin (FWHM), 25 cm−1 for extra intervals to include wing contribution

of lines outside initially given interval (VREL), and 25 cm−1 for wing cut-off (CUTOFF),

respectively. In the next section, the k-distribution tables calculated for the molecules and

metals will be demonstrated and extensively compared with LBL calculations.

16

3.2 Line lists for k-distribution tables

3.2.1 H2O

H2O, which shows strong absorptions throughout the exoplanet spectra, is one of the most

important gases in the atmospheres of exoplanets. It has been predicted that H2O opacity is

the most dominant feature in atmospheres of close-in exoplanets (Liang et al., 2003, 2004(;

Line et al., 2010; Seager & Sasselov, 2000). Of well-known H2O line lists, the latest edition

of HITRAN (Rothman et al., 2008) considers transitions between rotational quanta less than

J ′′=32, excluding line strengths weaker than 10−32 cm molecule−1. Only less than 70,000

lines are available in total, hence radiative transfer with this HITRAN version may be suitable

only for low temperatures (less than a few hundred K). One of the most complete lists for

H2O, a line list by Barber et al. (2006) (hereafter BT2), is selected in this study. This line

list covers wavelengths between 0–30000 cm−1 and includes most of the transitions between

roto-vibrational quantum numbers (J ′′ ≤ 50). The list uses 221,097 energy levels, containing

over half a billion transitions, a size 7,000 times greater than the latest HITRAN. In general,

lots of weak lines in BT2 certainly show no contribution at room temperature because the line

strength cutoff in BT2 goes down to ∼10−100. Their features, however, become noticeable

at temperatures larger than 1000 K (Figure 3.1). The BT2 list has been recently chosen for

the latest HITRAN compilation for high temperature calculation (HITEMP) (Rothman et al.,

2010) and tabulated in the typical format of HITRAN, in which line broadening widths are

also included. In Figure 3.1, transmission spectra created by LBL calculation and correlated-

k approximation are compared using the 43 layered hot exoplanet atmospheres in which

temperatures are distributed from 1800 K at 10 bar to 800 K at 10−10 bar. Mean difference

between LBL and correlated-k methods is less than 5 % over 1–30 µm, which is considerably

smaller than the range of uncertainties on available exoplanet measurements.

3.2.2 CO2

One complete version for CO2 available at high temperatures is the Carbon Dioxide Spectro-

scopic Databank (CDSD) (Tashkun et al., 2003). There are several versions of CDSD which

are suitable for different temperature levels: CDSD-296, -1000 and -4000. Here each number

refers to a reference temperature applied to calculate line strengths. Recently, a new CDSD

version (CDSD-HITEMP) that is mostly based on CDSD-1000 version has been released

and the lines are converted into the HITEMP format (Rothman et al., 2010). The 11,193,608

lines are distributed between 0 cm−1 and 12500 cm−1. The CDSD version of HITEMP is

available to download via ftp://ftp.iao.ru/pub/CDSD-HITEMP. The top plot of Figure 3.2

shows the absorption coefficient difference between the HITRAN and CDSD-1000. It is

17

1 10Wavenumber (cm-1)

-24

-23

-22

-21

-20

-19

-18

log 1

0(κ)

(cm

2 /mol

ecul

e)

h2o - LBL(Black) and Corre.-k(Blue)


0.0

0.2

0.4

0.6

0.8

1.0

Tra

nsm

issi

on

Figure 3.1: (Top) The latest HITRAN (grey) and Barber et al.(2007)[BT2] (black) versionof H2O line opacity at 1 atm and 1500 K. H2O of HITRAN version underestimates ab-sorption coefficients at some wavelength ranges (e.g. 4–5 µm due to lack of weak lines).(Bottom) H2O transmission spectra of 43 hot atmospheric layers calculated by LBL (black)and correlated-k approximation (blue). The difference between LBL and correlated-k meth-ods is small (< 5 %)

18


-24

-22

-20

-18

-16lo

g 10(

κ) (

cm2 /m

olec

ule)

co2 - LBL(Black) and Corre.-k(Blue)


0.0

0.2

0.4

0.6

0.8

1.0

Tra

nsm

issi

on

Figure 3.2: (Top) The latest HITRAN (grey) and CDSD (black) version of CO2 line opac-ity at 1 atm and 1000 K. CO2 in HITRAN underestimates absorption coefficients at somewavelength ranges (e.g. 20–30 µm) due to lack of weak lines. (Bottom) CO2 transmissionspectra of 43 hot atmospheric layers calculated by LBL (black) and correlated-k approxi-mation (blue). For CO2 case, transmission spectra calculated by the LBL and correlated-kmethods are nearly identical.

19


-24

-22

-20

-18

-16

log 1

0(κ)

(cm

2 /mol

ecul

e)

co - LBL(Black) and Corre.-k(Blue)


0.0

0.2

0.4

0.6

0.8

1.0

Tra

nsm

issi

on

Figure 3.3: (Top) CO opacity from old HITEMP (1995) (blue) and new HITEMP (2010)(purple) at 1 atm and 1000 K. CO lines in recent HITEMP version highly underestimateabsorption coefficients at 2.5 and 5 µm. (Bottom) CO transmission spectra of 43 hot at-mospheric layers calculated by LBL (black) and correlated-k approximation (blue). For COcase, transmission spectra calculated by the LBL and correlated-k methods are nearly iden-tical except few wavelengths (e.g. 5.3 µm).

20

found here that weak CO2 lines of HITRAN are not enough to estimate of absorption co-

efficients at some wavelengths (e.g. 20-30 µm). The bottom of Figure 3.2 demonstrates

transmission spectra in the hot atmosphere used in the previous section, which are calculated

by LBL and correlated-k methods, and mean difference between the methods is less than 1

%.

3.2.3 CO

As the next most abundant molecule after H2O in the atmospheres of hot Jupiters, CO plays

an important role in chemistry between carbon bearing molecules (Liang et al., 2003, 2004().

Commonly used line lists for CO are versions of HITRAN, GEISA (Jacquinet-Husson et al.,

2009), and HITEMP (Rothman et al., 1995). A CO line list from new HITEMP compilation

(Rothman et al., 2010) originates from the old HITEMP version (Rothman et al., 1995).

Its wavelength range covers from 3 to 8465 cm−1 and this range is much broader than the

previous version. However, it is found that the line strengths in the new version in the 4.6

µm region are seemingly a factor of 4 weaker than in the old one (top plot in Figure 3.3) so

that there will be a significant change in calculation of the spectrum. For this reason, the old

version of HITEMP (Rothman et al., 1995) is selected in this study. The bottom of Figure

3.3 also shows a comparison of transmission spectra integrated by LBL and correlated-k

models. The difference between LBL and correlated-k models is small (<5 %) only except

few wavelengths ranges (e.g. 5.3 µm)

3.2.4 CH4

The CH4 lines are widely distributed and distinct between the NIR and FIR. In particular, a

database suitable for high temperatures ranging over the entire IR (<1µm) is not yet avail-

able. As the most complete line list, Sharp & Burrows (2007) stitched together four databases

from diverse sources (Brown et al., 1997; Borysow et al., 2003; Karkoschka, 1994; Strong

et al., 1993) so as to make up a single list of CH4, and Nassar and Bernath (2003) experi-

mentally measured CH4 line strengths between 2000–6400 cm−1 at high temperatures (800,

1000, and 1273 K). In this study, a theoretical line list by the University of Bourgogne for

spherical top molecules, called Spherical Top Data System (STDS) (Wenger & Champion,

1998), is selected for CH4 due to its wide spectral coverage (0–6500 cm−1) and large num-

ber of weak lines included. The line list is delivered from laborious runs of calculation, and

is converted into the HITRAN format. As a result, the list contains approximately 9 mil-

lion CH4 lines up to 6500 cm−1 (J ≤ 50) and the line strength cutoff is less than 10−79 cm

molecule−1. Figure 3.5 shows CH4 opacity at 1 atm and 1000 K calculated from STDS and

the latest HITRAN. Large differences are shown throughout the wavelengths.

21

Figure 3.4: The (left) air- and (right) self-broadening widths of 12CH4 (blue) and 13CH4

(red).


-24

-23

-22

-21

-20

-19

-18

log 1

0(κ)

(cm

2 /mol

ecul

e)

Figure 3.5: CH4 opacity at 1 atm and 1000 K are calculated from STDS (black) and HITRAN(grey) database. Significant difference between STDS and HITRAN are shown throughoutthe wavelengths.

22

ch4 - LBL(Black) and Corre.-k(Blue)


0.0

0.2

0.4

0.6

0.8

1.0

Tra

nsm

issi

on

Figure 3.6: CH4 transmission spectra of 43 hot atmospheric layers calculated by LBL(black) and correlated-k approximation (blue). Transmission spectra calculated by LBL andcorrelated-k are nearly identical.

Due to the absence of broadening widths in the STDS line list, air- and self-broadening

widths for CH4 are directly extracted from the HITRAN database, in which the widths are

available for transitions up to J=31. These widths are extrapolated extensively to estimate

the rest of the widths having transitions up to J=50 (Figure 3.4). The CH4 transmissions in

the hot atmosphere calculated by LBL and correlated-k methods are shown in Figure 3.6 and

it is found that the mean difference between two methods is quite small (<1 %).

3.2.5 Alkali metals

The low ionisation energy makes the alkali metals dominant absorbers in the visible and

NIR. A few alkali metal lines can overwhelm any spectral features here such as H2O due

to their extreme broadening at the far wings, which is caused by the collisions with H2 and

He. In the case of atmospheres with hot temperatures, sodium doublet lines at 589.0 nm and

589.6 nm and potassium doublet lines at 766.5 nm and 769.9 nm are considered as dominant

features over the whole visible and NIR regions. Unlike molecules, the alkali line properties

can be taken from an elements line database such as either The Opacity Project database

(TOPbase) (Cunto and Mendoza, 1992; Cunto et al., 1993), NIST Atomic Spectroscopy

Database (Fuhr and Wiese, 1998) or Vienna Atomic Line Database (VALD) (Kupta et al.,

2000). Of known line lists, VALD is used in this study. With the provided properties, the line

strength is calculated in the unit used in the HITRAN format (cm−1/molecule cm−2). The

air-broadening width of alkali metals by a perturber (e.g. other species) in the atmosphere is

23

na - LBL(Black) and Corre.-k(Blue)

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2Wavenumber (cm-1)

0.0

0.2

0.4

0.6

0.8

1.0

Tra

nsm

issi

on

k - LBL(Black) and Corre.-k(Blue)

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2Wavenumber (cm-1)

0.0

0.2

0.4

0.6

0.8

1.0

Tra

nsm

issi

on

Figure 3.7: Comparison of (Top) Na and (Bottom) K transmissions in the 43-layered hotatmosphere. The difference between LBL and correlated-k models are evident. The reasonfor the difference is under investigation.

24

obtained from

γair = 1.664461

[kT

NA

(1

m+

1

mp

)]0.3C0.4

6 Np/c, (3.6)

where NA is the Avogadro’s number, m and mp are the mass of the atom and the perturb-

ing components such as H2 and He in the atmosphere, and C6 and Np are the interaction

coefficient and the number density of the perturbing components (Sharp & Burrows, 2007).

Although various studies proposed theoretical treatments of broad line wings, no unique

solution is available yet. In this study, the Lorentzian shape, which is assumed to be an

adequate line shape for low abundance (Lodders, 1999), is used to explain the line wings.

Sauval and Tatum (1984) provided the polynomial coefficients for the partition functions

of alkali metals. Its polynomial form is slightly different from the polynomials used in

molecular cases, and, as provided in Sauval and Tatum (1984), thus can be expressed as

log10Q (T ) =4∑

i=0

ailiθ, (3.7)

where lθ is log10(5040T

). Derived polynomial coefficients for Na and K are tabulated in

Appendix B. Figure 3.7 shows the transmission spectra of Na and K in the hot atmosphere

calculated by LBL and correlated-k models. The line wings of Na and K doublet at 589.0–

589.6 nm and 766.5–769.9 nm are dominant and broadly extened throughout the visible

wavelengths. The reason for the difference between LBL and correlated-k models is under

investigation.

3.2.6 Metallic Oxides

At T ≥ 1000K, metallic oxides such as TiO and VO are expected to be strong candidates

for a thermal inversion in HD 209458b by absorbing the light at the visible wavelengths

and heating the stratosphere up (Fortney et al., 2008). For TiO and VO, there exists no

commonly available line list. Hence these have been acquired from R. S. Freedman for TiO

(private communication) and Plez (1998) for VO. The databases were listed in the HITRAN

format and the broadening widths were reasonably guessed by the provider. The wavelength

coverage for TiO ranges from 0 to 20000 cm−1 while the VO lines cover between 3850–

25950 cm−1. The partition functions for both molecules are also obtained from Sauval and

Tatum (1984). Figure 3.8 shows TiO and VO transmission spectra in a single atmosphere at 1

atm and 1000 K. For both TiO and VO cases, mean differences between LBL and correlated-

k models are < 5 %.

The k-distribution tables are calculated in both wavelength and wavenumber spaces. Ta-

ble 3.1 lists the current status of the k-distribution table calculation for the molecules and

metals described in this section.

25

TiO (Single atmos.) lbl(black) vs. correlated-k(blue) @ 1 atm and 1000 K

0.5 1.0 1.5 2.0Wavelength (um)

0.0

0.2

0.4

0.6

0.8

1.0

Tra

nsm

issi

on

VO (Single atmos.) lbl(black) vs. correlated-k(blue) @ 1 atm and 1000 K

0.5 1.0 1.5 2.0Wavelength (um)

0.0

0.2

0.4

0.6

0.8

1.0

Tra

nsm

issi

on

Figure 3.8: (Top) TiO and (Bottom) VO of a single atmosphere transmission comparisonsat 1 atm and 1000 K. Mean difference for both cases is less than 5 %.

26

Table 3.1: Currently available k-distribution tablesa

Molecule/Element Wavelengthb Coverage (µm) Wavenumberc Coverage (cm−1)

H2O •d 0.3–30 • 300–20000

CO2 • 1–30 • 300–10000

CO • 1–10 • 1000-10000

CH4 • 1.55–30 • 300–6500

Na • 0.4–1.4 • 7000–22000

K • 0.4–1.4 • 7000-22000

TiO • 0.3–30 ◦e 300–30000

VO • 0.4–2.5 ◦ 4000–25000a 400 K ≤ T ≤ 2950 K, 1.39×10−11 bar ≤ P ≤ 20.09 barb Resolution=0.005 µm, FWHM=0.01 µmc Resolution=5 cm−1, FWHM=10 cm−1

d • calculation completee ◦ calculation on-going

3.3 Collision-induced absorption

Collisions between the nonpolar molecules of H2 and He induce a temporary dipole moment

so that numerous transitions arise at wavelengths >1 µm. Here pairs of H2-H2, H2-He, and

even H2-CH4 are dominant sources of collision. In general, the metallicities of exoplanets

are thought to be similar to their parent stars, hence the atmospheres may consist of large

fractions of H2 and He gases. Therefore collision-induced absorption (CIA) certainly forms

a continuum in giant exoplanets.

The database of CIA can be obtained from Borysow & Frommhold (1990), Zheng &

Borysow (1995), Borysow et al. (1997) for H2-H2 and Borysow et al. (1989), Borysow &

Frommhold (1989) for H2-He. Transitions of all bands for H2-H2 and H2-He including

roto-transitional and roto-vibrational band are computed using the provided routines by A.

Borysow1. Collisions between H2-CH4 are not regarded here due to the small abundance of

CH4. For a typical hot Jupiter atmosphere, the CIA shows the largest absorption at 2.3 µm

and decreases from 6∼7 µm to longer wavelengths. Figure 3.9 demonstrates the CIA transit

depths in the reference atmosphere of the terminators in HD 189733b. The opacity peaks at

2.3 µm and propagates towards longer wavelengths up to FIR (∼30 µm).

1http://www.astro.ku.dk/ aborysow/programs/index.html

27

Collisional Induced Absorption during primary transit of HD 189733b

1 10Wavelength (um)

2.30

2.35

2.40

2.45

2.50A

bsor

ptio

n (%

) (R

P/R

S)2

Figure 3.9: Combined transit depths of the collisional induced absorption between H2–H2

and H2–He are calculated in the reference atmosphere of HD 189733b and their opacities aretaken from Borysow & Frommhold (1990), Zheng & Borysow (1995), Borysow et al. (1997)for H2-H2 and Borysow et al. (1989), Borysow & Frommhold (1989) for H2-He. Measuredtransit depths using HST/NICMOS (Swain et al., 2008b) are displayed in red crosses. TheCIA opacity increases gradually and propagates smoothly longward of 2.3 µm.

3.4 Current issues on spectral modelling

Spectral modelling for atmospheres of close-in exoplanets evidently relies on the line lists

available for hot temperatures. This means that the retrievals are limited by the availability of

these line data, broadening widths, or partition functions for molecules and atoms. Therefore,

the reliability of any findings for close-in exoplanets will ultimately improve when new line

lists become available for high temperatures. In addition, the inclusion of other molecules

such as NH3, H2S, or other carbon bearing molecules will be very important for the future

development in this field.

28

Chapter 4

Retrievals

4.1 NEMESIS – Non-linear optimisation retrieval algorithm

NEMESIS (Irwin et al., 2008) solves the inverse problem using a method based on a Bayesian

and maximum-likelihood approach with the addition of a priori information (Rodgers,

2000). The optimal state in the algorithm is accomplished after a moderate number of it-

erations (Approximately 10-20), whose scheme is based on the Marquardt-Levenberg prin-

ciple (Levenberg, 1944; Marquardt, 1963). The algorithm calculates synthetic spectra us-

ing the correlated-k approximation method, which has been shown to be fast, reliable, and

sufficiently accurate compared to a LBL calculation as given in Chapter 3.2. The NEME-

SIS algorithm uses two novel tools for an efficient retrieval of the atmospheric properties:

a non-linear optimal estimation scheme and a fast forward model taking advantage of the

correlated-k approximation and k-distribution look-up tables. Moreover, the optimal estima-

tion retrievals permit an extension of previous results and formal quantification of errors and

uncertainties. In addition, the functional derivatives that are analytically-computed partial

derivatives allow analysing the vertical contribution of the constituents in each observation

channel.

The NEMESIS retrieval algorithm uses the non-linear optimal estimation technique,

which finds the optimal solutions numerically and iteratively (Rodgers, 2000), to minimise

the deviation between the measurements and the model spectrum and this process can be

made by minimising the cost function,

φ = (ym − yn)T S−1

ε (ym − yn) + (xn − x0)T S−1

x (xn − x0),

where ym and yn are the measurement and the calculated spectrum, Sε and Sx are the co-

variance matrices for the measurement and the a priori, and xn and x0 are the state vectors

of the nth calculation and a priori. Here, the measurement covariance matrix, Sε includes

the sum of measurement errors and forward model errors (i.e. being caused by incorrect

29

physics (Rodgers, 2000)) to consider both effects into the output together. The first term of

the cost function represents the minimisation of the residual between model and data, whilst

the second term constrains the solution xn to lie close to the a priori value x0.

During the iterations, the state vector, xn is updated from non-linear optimal equation

(Rodgers, 2000),

xn+1 = x0 + SxKTn

(KnSxK

Tn + Sε

)−1(ym − yn −Kn (x0 − xn))

Here, the a priori vector x0 always participates in each calculation so that derived state

vector xn+1 remains close to a priori profile. To achieve fast convergence to the minimum

cost function in NEMESIS, xn+1 is tested before the subsequent iteration whether it needs

to be modified to x′n+1, which yields closer spectrum to the measured vector ym than xn+1

does. Based on the Marquardt-Levenberg scheme, x′n+1 is defined as

x′n+1 = xn +

xn+1 − xn

1+ λ, (4.1)

where λ is an adjustable parameter for each iteration, which determines convergence speed

and pattern of retrieval. Therefore, the state vector xn+1 becomes x′n+1 when λ approaches

to zero, which means the optimal estimation state is now achieved.

For the cases where the expected solution is not very well known, there is not enough

information to be used as a priori, and there may exist only the predicted model profile from

theoretical studies. In addition, if given measurements are insufficient for strong constraints

and have large errors, a priori errors should be carefully determined in order to prevent

the retrieval from becoming ill-conditioned or over-constrained. Therefore a prioris in this

context are used to provide a smoothing constrain, keeping the solutions physically realistic

whilst not over-constraining them. Also, smoothed profiles with reasonable errors can be

achieved by making a balance between a priori error and the measurement covariance error

Sε. As described in Irwin et al. (2008), this balance can be found via test retrievals with

various constraint degrees and choosing the best constraint between the results, which is

weighted equally by the a priori and the measurement.

In the following sections the retrieval model will be applied to the study of hot Jupiters

(Section 4.2), a hot Neptune and, finally, a super earth, which will be studied for the final

thesis, to demonstrate the limitations of our knowledge based on currently-available mea-

surements.

30

4.2 Secondary eclipse of HD 189733b

4.2.1 Model

The a priori dayside atmosphere of HD 189733b extends from 10−9 to 10 bar. For initial

modelling it is assumed that all species were well-mixed throughout the atmosphere and the

molecular abundance was defined in terms of a single scaling parameter. This is because the

retrieval of a continuous profile of composition would be under-constrained, leading to non-

physical oscillations in the retrieved profile. The a priori estimate for the abundance scaling

parameter is assumed to have a large uncertainty so that retrieved values are not weighted by

initial guesses since a simple scaling parameter already includes vertical smoothing. The a

priori for the temperature is assumed to have a continuous profile and its error, however, had

to be adjusted to achieve the optimal balance between the quality of the fit to the measured

data and the vertical smoothing. This will be further discussed in Section 4.2.6. The mole

fractions of H2 and He are assumed to be as same as the fractions of atomic H and He, which

are close to the typical solar value as 0.91 and 0.0887 each (Burrows et al., 1999)

4.2.2 Data

To retrieve the P -T profile and compositional abundances, three measurement sets of the

secondary eclipse for HD 189733b, only available dayside emission data at the present

time, are used, ranging over a wide IR wavelength from 1.45 µm to 24 µm: 1) sixteen

HST/NICMOS (Swain et al., 2009a, hearafter S09a) channels covering the range 1.45–2.5

µm (excluding the 1.476 and 1.525 µm channels, which have unrealistic planet–stellar flux

ratios (FPlanet/FStar) less than zero); 2) forty seven Spitzer IRS (Grillmair et al., 2008)

channels covering the range 5–14.5 µm and one IRS photometry (Deming et al., 2006) chan-

nel at 16 µm; and 3) five Spitzer IRAC/MIPS (Charbonneau et al., 2008) photometry chan-

nels at 3.6, 4.5, 5.8, 8.0, and 24 µm. As a result, only The reference stellar spectrum for HD

189733 is taken from the Kurucz grid model1.

Despite the efforts towards finding and reducing the errors from the data, the uncertainties

on given datasets still remain and are widely distributed over the wavelengths due to its

various error sources. First of all, techniques to decorrelate a transit light curve from the

combined light of a planetary system are not consistent each other (e.g. Swain et al. (2008b)

vs. Gibson et al. (2011)). Also, systematic errors inherent in the observations itself can be a

strong error source. These two facts may cause the planet–stellar flux ratio to be dependent

on the data reduction process. Nonconcurrent observations for different wavelengths can

deliver a large gap between measurements, which may be caused by significant temporal

1http://kurucz.harvard.edu/stars/HD189733/

31

Table 4.1: The system properties for HD 189733, HD 209458, GJ 436, and GJ 1214

HD 189733 HD 209458 GJ 436 GJ 1214

Spectral Type K1.5V G0V M2.5V M4.5

Teff (K) 5050 6100 3350 3026

log(g) 4.53 4.38 4.84 4.15

log[Fe/H] -0.03 +0.00 -0.03

Rp/R∗ 0.155 0.121 0.083

variability in the atmosphere of HD 189733b. Therefore, all these sources of potential error

could lead to substantial inconsistencies between the datasets taken from different studies,

instruments, and observation times.

4.2.3 Best-fit dayside spectrum of HD 189733b

Using the NEMESIS algorithm, the best-fit dayside spectrum of HD 189733b is retrieved,

incorporating both the Spitzer and HST observations. Figure 4.1 shows the best-fit spec-

trum, in addition to the contributions from the four main gases (H2O, CO2, CO, and CH4)

included in the model. This figure also shows the wavelength ranges where the molecular

contributions are distributed by co-plotting the computed synthetic spectra with high and low

abundances for each molecule. Spectral features of H2O and CO2 affect the spectrum at all

wavelengths. CO has absorption features at 1.6, 2.3–2.5, and 5.0–5.5 µm, while CH4 fea-

tures can be seen at 1.7, 2.1–2.5, 3–4, and 5–9 µm. A striking feature of the best-fit spectrum

is a deep IR absorption by CO2 at 9–24 µm as shown in Figure 4.1(c), which is rather differ-

ent from the fitting by the other studies (Charbonneau et al., 2008; Fortney & Marley, 2007;

Grillmair et al., 2008; Madhusudhan & Seager, 2009, hearafter MS09), who concluded that

the features at the longer wavelengths of IRS are caused mainly by H2O, of which absorption

is also dominant at the shorter wavelengths of 5–9 µm. The low CO2 hypothesis might give

a good reproduction of the long-wave Spitzer data, however, it fails to reproduce the shorter

wavelengths covered by HST. As seen here, one of the benefits of the model in this study is

that the use of a broad range of IR wavelengths allows us to break some of the degeneracies

inherent in modelling a small number of data points. (cf. Section 4.2.4).

In this study, the high CO2 abundance causes a sharp drop at 9 µm and then a flat and

featureless spectrum between 9–24 µm. H2O still contributes to the spectrum at 5–9 µm and

>20 µm as well as a small feature from a vibrational transition at 6–6.5 µm, which is one

of the H2O features highlighted by Grillmair et al. (2008). In particular, the spectrum fits a

32

(a) H2O (1-30 µm)

HST NICMOS (Swain et al. 2009)

Spitzer IRS (Grillmair et al. 2008)

Spitzer IRAC/MIPS (Charbonneau et al. 2008)

Spitzer IRS broadband (Deming et al. 2006)

x 0.1x 0.2x 1x 5x 10

1 10Wavelength (µm)

0

2

4

6

8

Fpl

anet/F

star (

x10-3

)

(b) H2O (1.5-2.5 µm)

1.6 1.8 2.0 2.2 2.4Wavelength (µm)

0

0.2

0.4

0.6

0.8

1.0

Fpl

anet/F

star (

x10-3

)

(c) CO2 (1-30 µm)

x 0.01x 0.05x 1x 20x 100


0

2

4

6

8

Fpl

anet/F

star (

x10-3

)

(d) CO2 (1.5-2.5 µm)

1.6 1.8 2.0 2.2 2.4Wavelength (µm)

0

0.2

0.4

0.6

0.8

1.0

Fpl

anet/F

star (

x10-3

)

(e) CO(1-30 µm)

x 0.01x 0.05x 1x 20x 100


0

2

4

6

8

Fpl

anet/F

star (

x10-3

)

(f) CO(1.5-2.5 µm)

1.6 1.8 2.0 2.2 2.4Wavelength (µm)

0

0.2

0.4

0.6

0.8

1.0

Fpl

anet/F

star (

x10-3

)

(g) CH4 (1-30 µm)

x 0.01x 0.05x 1x 20x 100


0

2

4

6

8

Fpl

anet/F

star (

x10-3

)

(h) CH4 (1.5-2.5 µm)

1.6 1.8 2.0 2.2 2.4Wavelength (µm)

0

0.2

0.4

0.6

0.8

1.0

Fpl

anet/F

star (

x10-3

)

Figure 4.1: Fitted dayside emission spectra of HD 189733b. The orange, purple with red,and green symbols are the measured planet-star flux ratio from the HST/NICMOS (Swainet al., 2009a) spectrophotometry, the Spitzer IRS spectroscopy (Grillmair et al., 2008), andthe Spitzer broadband photometry (Charbonneau et al., 2008; Deming et al., 2006). Thebest-fit spectrum retrieved by the NEMESIS algorithm is displayed as a black line in all fig-ures. We also show calculated spectra with various molecular abundances to understand thecontributions of different molecules to the best-fit spectrum. For H2O, molecular abundancesare varied 0.1, 0.2, 5.0, and 10.0 times from the abundance leading to the best-fit spectrum,and, 0.01, 0.02, 20.0, and 100.0 times for the other molecules.

33

Spitzer photometry

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0Normalised Contribution Functions

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

Spitzer IRS

0.0 0.2 0.4 0.6 0.8 1.0


100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

HST NICMOS

0.0 0.2 0.4 0.6 0.8 1.0


100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

Figure 4.2: Contribution functions for the Spitzer broadband photometry (left), IRS spec-troscopy (middle), and the HST/NICMOS spectrophotometry (right) channels. For theSpitzer photometry channels, each line pattern means MIPS 24 µm (solid), IRS 16 µm(solid-black), IRAC 8.0 µm (dotted), 5.8 µm (dashed), 4.5 µm (dot-dashed), and 3.6 µm(triple dot-dashed). For the Spitzer IRS and the HST/NICMOS channels, the brightercolours denote the channels at the shorter wavelength. For all cases, emission from thelower atmosphere tends to dominate the shorter wavelength channels.

planet-star flux ratio for the Spitzer IRAC 3.6 µm channel, a feature which has been previ-

ously explained by the large 3.25 µm emission of CH4 in non-local thermodynamic equilib-

rium (NLTE) conditions (Swain et al., 2010; Thatte et al., 2010). Unfortunately, the current

retrieval algorithm is unable to model radiative transfer in NLTE and thus a detailed anal-

ysis will be left for future studies. For the HST/NICMOS channels between 1.45–2.5 µm,

the measurements are fitted using a high amount of CO2 as suggested in MS09 (∼7×10−4)

rather than in S09a whose model suggested low CO2 mixing ratio (10−7–10−6). This dis-

crepancy is not yet fully resolved, but, as Shabram et al. (2011) stated, this may come from

the difference in the forward models used for each study. In our spectrum, the channels at

1.584, 1.869, 2.159–2.216 µm, however, are underestimated with the high CO2 abundance,

leading to a decrease in the quality of the fit to the data. The sharp edge present at 9 µm,

where a sudden CO2 line weakening is shown, is caused by a strong CO2 absorption and is a

real feature of this exoplanet’s spectrum.

4.2.4 Contribution functions

The radiance measured in each channel originates from different pressure levels within the

atmosphere. This is generally described using a contribution function, which is the prod-

34

uct of the Planck function at the local temperature in the atmosphere and the transmission

weighting function, which describes the rate of change of atmospheric transmission with

height. The contribution functions are dependent on a prioris, which are assumed for the

atmospheric structure and abundances. Thus the calculated contribution functions indicate

the pressure levels at which thermal emission from the atmosphere contributes most to the

radiance observed in each channel. The Figure 4.2 shows the contribution functions for all

channels of the Spitzer IRS, IRAC, and MIPS, and HST/NICMOS.

The six Spitzer broadband photometry channels in the range 3.6–24 µm have broadly-

distributed contribution functions whose peak pressures range from 2 to 400 mbar. The

contribution functions for the IRAC channels (3.6, 4.5, 5.8, and 8 µm) and MIPS (24 µm) are

located in the deeper atmosphere and provide strong constraints for the temperature between

30–400 mbar. The contribution function of the IRAC 4.5 µm channel has a second peak at

high altitude (3–4 mbar), being close to the peak of the IRS 16 µm channel at 2 mbar. Hence,

the temperature at pressures as low as 2 mbar can be retrieved from the IRAC channels only

if the temperature of the deep atmosphere is well constrained from the other measurements.

The 47 Spitzer IRS spectroscopy channels between 5 and 14.5 µm have closely spaced

overlapping contribution functions, with peaks ranging from 1 to 200 mbar. The radiance

from the lower atmosphere (∼100 mbar) contributes to the channels in the range 5–9 µm,

whereas radiance from the upper atmosphere (&10 mbar) contributes longward of 9 µm.

Unlike the MIR and FIR channels on Spitzer, the HST/NICMOS NIR 1.45–2.5 µm channels

can measure the emission from the deeper atmosphere at 10–700 mbar and their contribution

functions are partly distributed over the pressure levels that are not covered by the Spitzer

measurements.

In summary, the contribution functions show that the P -T profile over a broad range of

pressures from 1 to 700 mbar can be constrained by retrieving from the Spitzer and HST

measurements together. On the other hand, studies that focus on a single narrow wavelength

range are sensitive to only a narrow altitude range. Thus, by considering all available datasets

simultaneously, better constraints on retrieved properties can be provided.

4.2.5 Functional derivatives

The functional derivatives are defined to be the partial derivatives of the radiance (or any

spectral output in the forward model) with respect to any given atmospheric parameters. By

calculating the functional derivatives for molecular abundances, we can understand which

measurements are sensitive to the abundance of which molecules and at which pressure lev-

els. Figure 4.3 shows the functional derivatives for the 4 molecules considered in this study.

For ease of comparison, these are normalized to the peak of the functional derivatives for

each measurement set. Using Figure 4.3 the sensitivity can be interpreted in two directions:

35

Spitzer photometry

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

Spitzer IRS

HST NICMOS

H2O

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

CO

2

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

CO

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

-1.0 -0.5 0.0 0.5 1.0d[flux ratio]/d[VMR]

-1.0 -0.5 0.0 0.5 1.0d[flux ratio]/d[VMR]

CH

4

-1.0 -0.5 0.0 0.5 1.0d[flux ratio]/d[VMR]

Figure 4.3: Normalised functional derivatives of molecules in all channels of Spitzer andHST. The applied colours are described in Figure 4.2. Each row shows the vertical sensitivityof radiance with respect to the abundance of the molecules H2O, CO2, CO, and CH4 (fromtop to bottom). This figure shows the pressure levels at which molecular abundance can beretrieved (row direction) from which channel (column direction).

36

Each row indicates which pressure levels show high sensitivity to a given molecule in each

channel, and each column indicates how molecular sensitivity is distributed through pressure

levels in a given set of measurements. In all cases, the derivatives are negative because the

output of the forward model here is regarded as a disk-averaged flux ratio between the planet

and star.

High sensitivity to the abundance of H2O is seen in all channels, with the exception of the

1.93–2.16 µm channels of HST/NICMOS, 4.5 µm channel of Spitzer IRAC, 9–14.5 µm and

16 µm channels of the Spitzer IRS, in which regions the modelled radiance is dominated by

CO2 absorption, as explained below. The H2O functional derivatives all peak in the ∼100–

500 mbar region, showing that the measurements can only constrain the H2O abundance in

this altitude range. In contrast, the CO2 functional derivatives are divided into two separate

pressure levels (peaks between 0.1–1 bar and 0.1–1 mbar) as is clearly shown in the second

row of Figure 4.3. The HST/NICMOS channels between 1.45–2.15 µm are only sensitive to

the CO2 abundance in altitudes below 100 mbar whereas the Spitzer broadband photometry

and IRS spectroscopy are sensitive to the CO2 at the 0.1–10 mbar region as well. Despite this

sensitivity to a range of altitudes for CO2, a combination of these channels, however, may

not determine CO2 abundance at both levels due to small sensitivity in the upper atmosphere

(cf. Section 4.2.7). For CO, this molecule can only be detected in three HST/NICMOS

channels in the range 2.33–2.45 µm at 100 mbar. The absorption features of CO seen in

these HST/NICMOS channels have been extensively used to constrain its mixing ratio (S09a

and MS09). The contribution functions for CH4 again all peak at ∼100 mbar and have a

detectable influence on a number of channels (i.e. Spitzer IRAC at 3.6 and 8 µm, IRS 5–9

µm, and HST/NICMOS 2.2–2.5 µm).

In summary, the functional derivatives indicate the altitudes showing sensitivities which

help to constrain each molecular abundance. The sensitivities of the molecules are mostly

clustered in the lower atmosphere (∼100 mbar), and, in particular, CO2 shows an additional

peak at ∼1 mbar. Therefore the molecular abundances can be constrained from the deep

pressure levels. Also, the spectrum is sensitive to the H2O abundance over the broadest

range and in the most channels. This implies that there is an inherent degeneracy between

temperatures and H2 abundances in these datasets.

4.2.6 Retrieval of P -T profile

Best-fit P -T profile

Previously P -T profiles of HD 189733b have been estimated based on theoretical models to

generate model spectra, which are to be compared with observations. However, such models

do not explicitly solve the inverse problem during the constraining process and thus it is

37

(a) T(p) - a priori shape

500 2000 Temperature (K)

100

10-2

10-4

10-6

Pre

ssur

e (b

ar)

(b) T(p) - a priori root temp.


Figure 4.4: (a) Retrieved P -T profiles from a range of diverse a priori profiles. Each linepattern used means: a priori P -T profiles (dashed), retrieved P -T profiles (solid) and theirerrors (dot-dashed and dotted). This plot shows the pressure range over which the P -Tprofile is retrievable from these measurements. (b) Retrieved P -T profiles from the same apriori profile shape, but offset from each other with root temperatures at 1600 K, 2000 K,and 2400 K at 10 bar.

38

unclear if the solutions are biased more towards theoretical expectations than being driven

by the measurements themselves. For this reason, temperature is retrieved using several

differently shaped a priori profiles to show that the retrieved temperature converges to a

unique profile in the altitude range covered by the contribution functions. Because a retrieved

P -T profile may vary with the a priori, if it is biased, an appropriate a priori error and its

vertical shape are found in order that a P -T profile can be retrieved with a static shape,

irrespective of the shape of the a priori profile. Figure 4.4(a) presents the retrieved P -T

profile and its error for a range of selected temperature a priori. For all cases, the P -T

profiles share a common shape between 0.1 mbar and 1 bar, demonstrating the validity of

the temperature retrieval. It is shown that even with the simplest possible assumption such

as an isothermal temperature (blue line in Figure 4.4(a)), the measurements still produce

a similar thermal profile with the other retrievals. As a further test, an a priori structure

from the retrieved profile is taken in the previous step, offset by a temperature 400 K, and

the temperature retrieval is repeated again. Figure 4.4(b) shows that the P -T profile is still

sufficiently constrained by the measurements, even if there are large shifts of a priori at

levels not covered by the contribution functions, and, at these altitudes, the solutions relax

back to their different a prioris.

As a result, it is found that the temperature decreases adiabatically from 1900 K at 700

mbar to ∼1000 K at 100 mbar, then becomes isothermal up to the upper atmosphere (∼1

mbar). These adiabatic and isothermal layers in the thermal structure are dominant fea-

tures of heat transfer by convection and radiative cooling, respectively. In comparison S09a

claimed a decreasing temperature layer between 0.01 and 1 bar to model the HST/NICMOS

measurements, making an adiabatic layer ∼10 times thicker than our estimation, and theoret-

ical models also considered adiabatic layers for a troposphere model (Burrows et al., 2008;

Fortney et al., 2006; Showman et al., 2008). For the isothermal structure, Charbonneau et

al. (2008) and Knutson et al. (2007) suggested that the warmed temperature (1000–1200 K)

of the dayside hemisphere may be maintained by an efficient energy re-distribution through

the whole planet system, leading to a quasi-isothermal structure in the upper atmosphere

(Showman et al., 2008).

In summary, the broad wavelength range on available measurements has provided a

strong constraint on the vertical P -T profile (an adiabatic troposphere and isothermal strato-

sphere) without excessive sensitivity to the a priori assumptions.

Temperature degeneracy

In general, the best-fit P -T profile from the retrieval is a non-unique solution. This means

that there is potentially a large family of solutions for the P -T profile that could fit the mea-

sured spectrum equally well within the same error range. In many retrievals, there may also

39

(a)cross-correlation

-0.5 0.0 0.5c(i,j)

100

10-1

10-2

10-3

Pre

ssur

e (b

ar)

(b)Retrieved T(p)-All


(c)Retrieved T(p)-H2O


100

10-1

10-2

10-3

Pre

ssur

e (b

ar)

(d)Retrieved T(p)-CO2


(e)Retrieved T(p)-CO


100

10-1

10-2

10-3

Pre

ssur

e (b

ar)

(f)Retrieved T(p)-CH4


Figure 4.5: (a) The vertical structure of the cross-correlation functions. The high correla-tion by H2O and CO2 dominates the degeneracy of temperature at most pressures. (b-f) Theretrieved P -T profiles of the dayside HD 189733b with various mixing ratios are presentedwith ∆χ2 and the colors demonstrate ∆χ2 <0.5 (red), <1.0 (green), and <2.0 (blue), respec-tively. As a result, the large uncertainties of P -T profile are broadly distributed at the low-and mid-atmosphere. On the other hand, narrow uncertainty at 3 mbar implies an isothermalstructure in the upper atmosphere of the dayside HD 189733b.

40

exist cross-correlation, an index to find alikeness between retrieval variables, with other fitted

quantities, indicated by covariances that are larger than zero. As the set of the correlation,

the covariance matrix is advantageous because the matrix is computed as a part of the re-

trieval process and can be used in assessing the results at the end of retrieval. Therefore, the

uncertainties can be estimated by considering the degeneracy between the variables, which

is based on the cross-correlation analysis.

For the dayside spectrum of HD 189733b, the degeneracy between the molecular abun-

dances and the P -T profile is thought to be significant at some pressure levels and bandpasses

(S09a and MS09), however, a detailed analysis of these correlations has not previously been

discussed. Here, the cross-correlation functions c(i , j ) (i.e. the off-diagonal elements of the

covariance matrix) are examined that determine the degree of degeneracy between elements i

and j of the measurement vector. By definition, |c(i , j )|=1.0 represents a perfect correlation

between variable i and j, and according to the general practice it is considered that |c|=0.5

is a limitation for independent retrievals of different variables. The profiles in Figure 4.5(a)

show the vertical structure of cross-correlation functions between the molecular abundances

and the temperature at different pressure levels. It can be seen that the P -T profile is sig-

nificantly correlated with molecular abundances at some levels, being most correlated with

the H2O abundance between 200–400 mbar and with CO2 for altitudes above the 30 mbar

pressure level.

To determine the degeneracy of temperature from Figure 4.5(a), multiple retrievals were

performed where individual molecular abundances were fixed at a particular value and all

other variables retrieved. Then the goodness-of-fit (χ2) of the solution was assessed as

a function of the set molecular abundance, compared with the minimum goodness-of-fit

(χ2min) of the best-fit retrieval, and determined the range of temperatures for which the change

∆χ2 = χ2 − χ2min was less than 0.5, 1.0, and 2.0, respectively.

Figure 4.5(b) shows the ranges in the retrieved P -T profile for different values of ∆χ2

due to the molecular degeneracy. At each pressure level, allowed temperature ranges are

determined by varying the molecular abundance with which temperature is most strongly

correlated. The temperature uncertainties for ∆χ2 < 1.0 calculated in this way are 590 K

at 700 mbar, 600 K at 200 mbar, and 80 K at 3 mbar. As described on the basis of cross-

correlation, the temperature uncertainties at altitudes below 10 mbar are caused mainly due

to the degeneracy with the H2O abundance and those at altitudes above 10 mbar are degen-

erate with the CO2 abundance. On the other hand, the degeneracies between temperature

and the abundances for CO and CH4 are small. Therefore it can be seen that although some

uncertainty in the P -T profile exists due to degeneracy, the small degree of degeneracy at

lower pressures confirms our conclusion that the atmosphere of HD 189733b has an isother-

mal structure at the upper atmosphere.

41

4.2.7 Retrieval of molecular abundances

In addition to the temperature retrieval, molecular abundances may also be retrieved from

secondary eclipse measurements of HD 189733b. As stated earlier, each gas considered is

assumed to be well-mixed in our forward model atmosphere giving a constant mole fraction

with height. However, it is known that the functional derivatives are only sensitive to a

limited pressure range and thus the retrieved abundances represent the mean concentrations

at the pressure levels which show the highest sensitivity. The best-fit molecular abundances

are determined from the retrieval accompanying the best-fit P -T profile given in Section

4.2.6 and it is found that those are 4.3×10−4 (H2O), 2.5×10−3 (CO2), 2.0×10−3 (CO), and

1.6×10−6 (CH4), respectively. Additionally, the C/O ratio of HD 189733b is constrained as

close as the solar value (∼0.6).

By looking at the covariance of current retrieved solution it is found that the cross-

correlation between the different molecular abundances is rather small (c < 0.1) for all the

combinations of the molecules. However, there remains some degeneracy due to the main

correlation with temperature and to quantify this ∆χ2 was calculated for each gas by chang-

ing the abundance of a molecule and retrieving all other parameters including temperature.

The variation of ∆χ2 with abundance for all four gases is shown in Figure 4.6. It is found that

the following range of abundances have ∆χ2 < 0.5: (3–100)×10−5 for H2O, (3–200)×10−4

for CO2, <2×10−1 for CO, and <3×10−5 for CH4, respectively. The constrained abun-

dances for ∆χ2 < 1.0 and 2.0 are also shown in Table 4.2 and are compared with the results

of a thermo- and photo-chemistry model (Line et al., 2010), and previous studies (S09a and

MS09). It is found that only the upper bound of the mixing ratio is constrained for CO and

CH4. This is because CO and CH4 contributions to the emission spectrum appears in only

few bandpasses, and their abundances show low sensitivity over planet-stellar flux ratio as

shown in Figure 4.3. Variation of these two gases leads to a tiny change in ∆χ2 where the

abundances are lower than the best-fit estimation and, consequently, it is not possible to con-

strain the abundances of CO and CH4 based on given datasets alone as previous studies have

attmepted.

All channels of Spitzer and HST are capable of constraining the H2O mixing ratio as

presented in the functional derivatives, and the constrained H2O is consistent with other

estimations. For CO, the strongest constraints are taken from the HST/NICMOS data as

previously mentioned before (MS09) and the high upper limit of the CO abundance in this

study can include all other estimations. Relatively low abundance of CH4 is estimated in all

model atmospheres in Table 4.2 except for a large amount (10−2) model derived from the

Spitzer IRS spectroscopy at 7.6 µm (MS09), which is not consistent with this study. The

derived abundance of CO2 (3–150×10−4) is 2–3 orders of magnitude larger than previous

studies by Line et al. (2010) (∼10−7–∼10−5), S09a (10−7–10−6), and MS09 (using Spitzer

42

Tabl

e4.

2:E

stim

ated

and

retr

ieve

dm

ixin

gra

tios

and

the

C/O

inth

eda

ysid

eof

HD

1897

33b.

H2O

(10−

4)

CO

2(1

0−4)

CO

(10−

4)

CH

4(1

0−4)

C/O

Dat

aSo

urce

Lin

eet

al.2

010

6–13

0.00

47–0

.016

2–9

0.00

26–6

.758

The

rmos

chem

istr

y

∼6.

360.

004–

∼0.

1∼

8.4

∼0.

4Ph

otoc

hem

istr

y

Swai

net

al.2

009

0.1–

10.

001–

0.01

1–3

<0.

001

0.5–

1H

ST/N

ICM

OS

Mad

husu

dhan

&Se

ager

2009

0.01

–100

0...

...<

100

...Spitzer

IRS

0.1–

100.

007–

0.7

...<

0.02

0.00

7–1

Spitzer

phot

omet

ry

∼1

∼7

2–20

0<

0.06

0.5–

1H

ST/N

ICM

OS

Thi

sst

udy

Bes

t-fit

valu

e

4.3

2520

0.01

60.

6A

llm

easu

rem

ents

Poss

ible

fitra

nge

0.3–

303–

150

<20

00<

0.3

0.5–

1∆χ2<

0.5

0.07

–70

1–30

0...

<0.

70.

4–1

∆χ2<

1.0

0.01

–300

0.3–

800

...<

20.

2–1

∆χ2<

2.0

43

Molecular Degeneracy

0

0.5

1

2

10-7 10-6 10-5 10-4 10-3 10-2 10-1

Volume Mixing Ratio

H2O

CO2

CO

CH4

Figure 4.6: The degeneracy ranges of the molecular mixing ratios for H2O, CO2, CO, andCH4. Each line shows resultant reduced χ2 with respect to given abundances. The ∆χ2 con-strains the uncertainties of the molecular abundances which are ranged around the best-fittedabundance of H2O (4.3×10−4), CO2 (2.5×10−3), CO (2.0×10−3), and CH4(1.6×10−6), re-spectively. Lower bounds of CO and CH4 uncertainties are unconstrained because of theirlow contribution to the spectrum.

photometry, 7–700×10−7) for all ∆χ2 ranges and thus our retrieved CO2 abundance is only

consistent with the HST/NICMOS estimation by MS09. Although the flux ratios at the

IRAC 4.5 and 16 µm channels can be explained by either high or low CO2 abundance,

and, however, the HST/NICMOS channels constrain this to be a higher abundance of CO2

(∼10−3).

Here, the contribution of CO2 in the upper atmosphere of HD 189733b is tested by com-

paring the best-fit spectra, each retrieved from low and high CO2 abundances in the upper

atmosphere. Instead of using a well-mixed abundance of CO2 with altitude, the abundance

is allowed to vary with height. The CO2 mixing ratio is fixed at a certain mixing ratio up

to a pre-defined deep pressure level, and declines linearly into the upper atmosphere with a

slope being determined by the fractional scale height (the ratio of the scale height of the gas

to the scale height of the atmosphere). This allows us to demonstrate the effect of differ-

ent mixing ratios with height, but avoiding the need to introduce a complete vertical profile

of CO2 (and hence a large number of additional parameters in state vector). In Figure 4.7,

the retrieval with the new CO2 vertical profile that decreases from 2.5×10−3 at 100 mbar to

3.3×10−7 at 0.1 mbar, produces a very similar spectrum to the well-mixed high-CO2 case,

44

Synthetic Spectra of Day-side HD 189733b - CO2

best-fit with q[CO2]=2.5X10-3

best-fit with q[CO2]=1X10-7

best-fit with q[CO2]=2.5X10-3 @ 100 mbarq[CO2]=3.3X10-7 @ 0.1 mbar

1 10Wavelength (um)

0

2

4

6

8F

plan

et/F

star (

X10

-3)

1.6 1.8 2.0 2.2 2.4Wavelength (um)

0.0

0.2

0.4

0.6

0.8

1.0

Fpl

anet/F

star (

X10

-3)

Figure 4.7: Synthetic emission spectra of the dayside HD 189733b with different CO2 abun-dances. The spectrum in black, orange, and cyan color represents the best-fit spectrum withfixed CO2 amount of 2.5×10−3 and 1×10−7, and different CO2 amount of 2.5×10−3 at 100mbar and 3.3×10−7 at 0.1 mbar, respectively. High and low CO2 abundances at 100 and 0.1mbar retrieve a consistent spectrum with the best-fit one.

45

leading to an insignificant improvement in terms of the χ2. This is because the CO2 sensitiv-

ity at the Spitzer bandpasses is too low to adequately constrain its abundance in the upper

atmosphere (0.1–1 mbar) despite having sensitivity here whereas the strong constraints of the

HST/NICMOS and Spitzer IRS channels between 9–16 µm enable constraining the abun-

dance in the lower atmosphere (∼100 mbar). In contrast, a low abundance of CO2 (10−7)

with a well-mixed vertical profile is unable to produce a spectrum that fits with better χ2.

Therefore it is clear that a high amount of CO2 (∼10−3) exists at ∼100 mbar but that the

abundance at 0.1–1 mbar is unconstrained by current measurements. In other words, the

proposed abundance of CO2 in this study represents only the value at ∼100 mbar, where

the highest sensitivity is shown. As suggested in MS09, if only the mean mixing ratio of

CO2 is considered over the entire pressure levels rather than only few layers holding high

concentrations, the CO2 profile with its low abundance at high altitude and a high abundance

at low altitude would then give a consistent amount of CO2 (∼10−7–∼10−6) as suggested by

the chemistry models and S09a.

4.2.8 Lapse rate

The retrieved thermal structure is a useful tool for further understanding of dynamic pro-

cesses in the atmosphere. As a description of atmospheric stability, the lapse rate (Γ =

dT/dz), the rate of change of temperature with respect to the height, is directly evaluated

from the P -T profile by taking its first derivative (Figure 4.8). An increase in the lapse rate

indicates that there is an adiabatic layer up to ∼100 mbar (∼1500 km above from the level

of 10 bar), and the lapse rate tends to remain at zero above ∼40 mbar (∼1700 km) where

this pressure level indicates the boundary of an isothermal expansion condition. Moreover,

the dry adiabatic lapse rate (DALR) indicates both the stability of the atmosphere higher

altitudes than ∼350 mbar (∼1200 km) and a sub-adiabatic layer, being extended up to 40

mbar.

4.2.9 Conclusion

Using the optimal estimation retrieval algorithm retrieval, it was shown that the current set

of observations of the dayside spectrum of HD 189733b are enough to constrain the ther-

mal structure at some pressure levels and the mixing ratios for H2O, CO2, CO, and CH4.

Furthermore, the ability to calculate the cross-correlation function allows us to assess the

degeneracies between the various modelled parameters in our state vector.

With the retrieval method presented here, three major findings are derived from the avail-

able measurements given in this study. Firstly, the retrieved thermal structure of the dayside

HD 189733b shows that the constraints in the NIR and MIR lead to an adiabatically decreas-

46

T(p)

500 1000 1500 2000Temperature (K)

100

10-1

10-2

10-3

Pre

ssur

e (b

ar)

Lapse Rate

-2.0 -1.5 -1.0 -0.5 0.0 0.5Lapse Rate (K/km)

100

10-1

10-2

10-3

Pre

ssur

e (b

ar)

Figure 4.8: Disk-averaged dayside lapse rate of HD 189733b (right) is demonstrated bycalculating the derivatives of P -T profile. The given pressures correspond to the levelscovered by the contribution functions. Dry adiabatic lapse rate (DALR) that displayed ingray colour is assumed to be constant over the given temperature range.

ing temperature between 0.1–1 bar. In addition, strong constraints from the Spitzer IRS

measurements in the 9–16 µm range suggest that the temperature structure in the mid and

upper atmosphere (1–100 mbar) seems to be isothermal with a uniform temperature (∼1000

K). One explanation for the isothermal layer is that super-rotating jets blowing from night- to

dayside play a critical role of an efficient energy re-distribution over the whole planet and it

may be responsible for maintaining the high temperature in the upper atmosphere (Knutson

et al., 2007; Showman et al., 2008).

Secondly, the functional derivatives for the molecules show that the measurements at

the NIR (1.45–2.1 µm), MIR (4.5 µm), and FIR (9–16 µm) spectral ranges independently

constrain CO2 abundance at ∼100 mbar and 0.1–10 mbar. Its abundance in the lower atmo-

sphere is responsible for the spectral flatness at 9–16 µm, where previous studies assumed

H2O to be the dominant consituent. The vertical sensitivity of CO2 abundance is deter-

mined by comparing the retrievals with abundant (2.5×10−3) and scarce CO2 (10−7), and

height-dependant CO2 profile. The functional derivatives for CO2 show low sensitivity at

0.1–1 mbar, which means that, at the upper atmosphere, the mixing ratio of CO2 remains

unconstrained and the spectrum looks the same irrespective of the chosen value of CO2 at

this pressure level. In contrast, high sensitivity of CO2 at the lower atmosphere (100 mbar)

47

indicates high abundance of CO2 at this pressure level.

Thirdly, the degeneracies between the atmospheric properties are quantified using the

cross-correlation functions. The correlations between molecular abundances and tempera-

ture exhibit sizable degeneracies, in particular, between temperature and H2O abundance at

300 mbar. The temperature uncertainty at different pressure levels is determined by calculat-

ing the statistics of the retrievals with the variation of each molecular mixing ratio and, as a

result, this confirms the isothermal structure in the stratosphere. In same way, the molecular

abundances are also constrained by demonstrating that the uncertainty on retrieved parame-

ters, based on the available measurements and the degeneracy with the temperature profile

is much larger than previous studies have suggested. Therefore, additional data is clearly

required to break the degeneracy between temperature and compositions, particularly H2O.

As long as the number of retrieval variables for the molecular abundance are kept to a small

number, the cross-correlation functions are not significant between molecules. If we were

forced to use a more detailed representation of the vertical distributions of the gases, then the

degeneracies would grow more substantial.

This study has shown the benefit of considering a wide spectral range for breaking the

degeneracy between different atmospheric parameters. By constraining the overall shape of

the infrared spectrum, the HST and Spitzer secondary eclipse data of HD 189733b allow us

to evaluate the vertical temperature structure and molecular abundances. Studies that focus

on smaller wavelength ranges or fewer data points are subject to broader uncertainties than

are currently being presented in the literature. Further work in Section 4.4 will permit an

extension of this technique into cross-comparison with transmission spectroscopy, including

the visible range (alkali metals, metallic oxides, and clouds and hazes), at the terminator

regions of this planet.

48

4.3 Secondary eclipse of HD 209458b

Despite the other hot Jupiter, HD 209458b has been second best observed of transiting exo-

planet next to HD 189733b, the results for its dayside emission that will be presented in the

following sections are still not quite as mature as the case of HD 189733b. Therefore, points

of the debate on this exoplanet such as the presence of the inversion in the atmosphere are

need to be further tested.

4.3.1 Model

The a priori and the atmosphere model for HD 209458b are very similar to those applied for

HD 189733b. This is because they are physically alike, commonly having Jupiter-like mass

and radius, high effective temperature, small orbital distance, and similar chemistry. As used

in the atmosphere of HD 189733b, the a priori for P -T profile of dayside atmosphere of HD

209458b is also fully covered over a range from 10−9 to 10 bar. All constituents are assumed

to be well-mixed and each abundance is simply explained by a single scaling parameter. In

the same manner, the fraction of H2 and He are determined to be the solar value (0.91 and

0.0887). One major difference between the two hot Jupiters is that the metallic oxides such

as TiO and VO may play an important role for a thermal inversion at a pressure level of

HD 209458b (Burrows et al., 2008; Fortney et al., 2008). However, these molecules will

not be involved for current retrievals due to their low absorption coefficients at >1 µm, but

k-distributions have been computed to aid in future investigations. The physical properties

of HD 209458b used here are displayed in Table. 4.1.

4.3.2 Data

Unlike the dayside of HD 189733b, fewer measurements are only available for the dayside

emission of HD 209458b. The secondary eclipse of HD 209458b has been measured in

the four channels of Spitzer IRAC (3.6, 4.5, 5.8, 8 µm) (Knutson et al., 2007), the 16 µm

Spitzer IRS channel (taken from MS09), the 24 µm Spitzer MIPS channel (Deming et al.,

2006), and the fifteen Spitzer IRS (7.5–14 µm) channels (Swain et al., 2008a). Addition-

ally, the NIR dayside spectrum was obtained using the HST/NICMOS (Swain et al., 2009b)

spectroscopy and they provided the sixteen binned NICMOS measurements. All available

measurements will be used for the retrieval here, only excluding two measurements of NIC-

MOS at 2.1–2.2 µm, which show negative planet-star flux ratios. The HD 209458 spectrum

is directly downloaded from the Kurucz grid model 2.

2http://kurucz.harvard.edu/stars/HD209458/

49

500 1000 1500 2000 2500Temperature (K)

101

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

Figure 4.9: Retrieved P -T profiles of the dayside HD2009458b using diverse a prioris. All profiles commonlyconverge to an unique P -T structure between 10−4 to 1 bar.Thick-black line indicates the best estimation.

500 1000 1500 2000 2500Temperature (K)

101

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

1 10Wavelength (um)

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Fp/

F*

Figure 4.10: (left) Retrieved best-fit P -T profile of the dayside HD 209458b explicitlydemonstrates an adiabatic troposphere and a weak thermal inversion in the stratosphere.The retrieval error range is displayed in grey colour. (right) The best-fit spectrum is con-strained from 34 channels of all measurements except the 5.8 µm Spitzer IRAC channelwhich provides no contribution at all. A spectrum in red colour demonstrates best-fitspectrum using the P -T profile with no inversion in stratosphere, which is red-colouredin the left plot.

50

Spitzer photometry

0.0 0.2 0.4 0.6 0.8 1.0


100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

Spitzer IRS

0.0 0.2 0.4 0.6 0.8 1.0


100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

HST NICMOS

0.0 0.2 0.4 0.6 0.8 1.0


100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

Figure 4.11: Contribution functions for the channels used for the HD 209458b dayside emis-sion retrieval. For the Spitzer broadband photometry channels, the solid, solid-black, dotted,dashed, dot-dashed lines correspond to MIPS 24 µm, IRS 16 µm, IRAC 8.0 µm, 4.5 µm, and3.6 µm. The brighter colours for the Spitzer IRS and the HST/NICMOS channels denotechannels at the shorter wavelength.

4.3.3 Retrieval of P -T profile

Of various studies considering a thermal inversion in the atmosphere of this planet, Knutson

et al. (2007) and Burrows et al. (2008) proposed a possible steep temperature inversion at

high altitude by showing a high flux ratio at 5.8 µm of Spitzer IRAC, which has not fitted

reasonably using a non-inversion atmosphere. Sing et al. (2008) indicated that a tempera-

ture increase over the pressure levels can be explained by the UV observations. Using the

Spitzer IRAC, IRS, and MIPS, and HST/NICMOS observations, Swain et al. (2009b) sug-

gested some plausible scenarios, and concluded that a temperature increase of 500–700 K

occurs somewhere between 0.1–100 mbar. On the other hand, MS09 and Madhusudhan &

Seager (2010) demonstrated using only the six Spitzer photometry channels, that a thermal

inversion is more likely to explain the observations within smaller uncertainties on the mea-

surements, and found that a constrained inversion layer can be placed at ∼30–500 mbar. As

predicted by various studies, one strong candidate for this inversion is strong UV or visible

absorption by TiO and VO at some pressures, which might be detectable during primary

transit (Burrows et al., 2007, 2008; Fortney et al., 2008). However, this has not been clearly

observed yet (Desert et al., 2008) and is still debated. Since a thermal inversion in the atmo-

sphere of HD 209458b has been of current interest, the robustness of the thermal inversion

hypothesis will be tested with our retrieval approach.

As considered in the previous retrieval, various a prioris for temperatures are used to

51

constrain a unique shaped profile and, at the same time, molecular abundances for H2O, CO2,

and CH4 are given with large uncertainties. The CO amount is retrieved with unrealistic mole

fraction for all retrieval cases (q[CO]>1), with which the retrievals show a tiny improvement

in the fitting to the channels of HST/NICMOS and Spitzer IRAC. Moreover, CO sensitivity

on these channels are negligible, hence, the CO opacity is excluded in the forward model

during the retrieval. In Figure 4.9, it is indicated that all the retrieved P -T profiles commonly

show a decreasing adiabatic layer up to 100 mbar and an inversion above a quasi-isothermal

layer at 1–100 mbar. It is more clearly shown in Figure 4.10 that the temperatures beneath

1 bar and above ∼10−4 relax back to the a priori, where the contribution functions are not

sufficiently distributed. As given in Figure 4.11, the Spitzer IRAC and IRS channels have

contribution functions which peak at pressures from 0.3 to ∼100 mbar. In particular, the

3.6 and 8.0 µm IRAC and two IRS channels at 7.7 and 8.0 µm constrain the temperatures at

highest altitude (∼1 mbar), where a strong CH4 emission is explicitly turned up. The shorter

wavelength channels in HST/NICMOS constrain the temperature in the lower atmosphere

(0.2–1 bar) whereas the channels in the longer wavelengths are responsible for the upper

atmosphere at 10–40 mbar.

Figure 4.10 also shows that the best-fit spectrum of dayside HD 209458b is characterised

by both absorption at NIR (<2.5 µm) and emission at MIR and FIR (>2.5 µm). In NIR,

a strong CH4 feature shows a deep absorption at 1.6–1.9 µm and a broad emission at 1.9–

2.4 µm with CO2 absorption. In contrast, a large amount of CO2 and CH4 at high altitude,

where the thermal inversion is placed, shows strong emission features at 4.5 and 16 µm (by

CO2), and 3.6 and 8.0 µm (by CH4). On the other hand, the flux ratio at 5.8 µm shows

substantially high that seems not to be fitted with any available atmospheric models in this

study. Burrows et al. (2008); Knutson et al. (2007) suggested that this high flux ratio at

5.8 µm would be rather indicate a possible thermal inversion at high altitude. However,

its contribution function shown in Figure 4.11 seems not to be involved significantly in the

retrieval. Therefore, it is noted that the 5.8 µm Spitzer IRAC observation is exempted during

the retrieval.

4.3.4 Case studies - Improved retrieval?

The retrieval of the dayside HD 209458b emission spectrum is more challenging than HD

189733b because of the difficulty in fitting all available measurements simutaneously. As

reported previously, there are some reasons for this problem: there may exist 1) atmospheric

variability in HD 209458b (Swain et al., 2009b), leading to a large fluctuation between differ-

ent measurements, 2) data reduction diversity among the groups (MS09), or 3) complications

in the calculation of disk-averaged spectrum in which a single P -T profile may not represent

the whole dayside hemisphere. Here retrieval studies are carried out on a case-by-case basis

52

in order that different combinations of the measurements may deliver enhanced or consistent

retrieval results for selected features. Four cases among various measurement combinations

are displayed in Figure 4.12.

Case A. The Spitzer/IRS Figure 4.12(a) shows that the selected fifteen IRS channels can

be fitted with a flat spectrum by H2O rather than emissions by CH4 and CO2. These channels

do not provide enough constraints for a temperature retrieval and thus show no evidence for

a thermal inversion.

Case B. The Spitzer/IRAC, MIPS and IRS In Figure 4.12(b), all Spitzer channels con-

strain the temperatures between 0.1 and 100 mbar, where an inversion is located. Here the

CO2 emission departs from the H2O continuum to fit the 4.5 µm IRAC and 14.5 µm IRS

channels. The 5.8 µm IRAC channel is still not explained by any molecular feature.

Case C. The HST/NICMOS A retrieved P -T profile from the HST/NICMOS channels

in Figure 4.12(c) display two constrained layers at the lower (0.01–1 bar) and upper (0.1–1

mbar) atmospheres. The channels at 2.2–2.5 µm, where CH4 absorption is shown, provide

strong constraints for the temperatures at the upper atmosphere. No thermal inversion is

suggested.

Case D. The HST/NICMOS and Spitzer IRAC (3.6 and 4.5 µm) Emission features of

CH4 and CO2 fit the 3.6 and 4.5 µm IRAC channels, leading to a temperature inversion layer

placed between 0.01–1 mbar. At this time, the HST/NICMOS channels at 2.2–2.5 µm are

characterised by emission of CH4.

Consequently, it is found that the Spitzer IRAC channels at 3.6 and 4.5 µm seem to pro-

vide strong constraints for a thermal inversion between 0.1–10 mbar in the dayside of HD

209458b. Also, the HST/NICMOS channels constrain an adiabatically degreasing temper-

aures at low altitude (∼100 mbar). However, the Spitzer IRS spectroscopy itself is unable

to offer constraints for the P -T profile at any pressure level.


The best estimation for the three volume mixing ratios corresponding to the best-fit model

in Section 4.3.3 are reported in Table 4.3, along with previous retrievals. As seen in Table

4.3, there are a few orders of magnitude difference in mixing ratios between the retrievals. In

particular, the mixing ratios for CH4 and CO2 estimated previously are considerably lower

than in this study. In this retrieval, these two molecules struggle to fit the measurements and,

53

500 1000 1500 2000 2500

101

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

(a)

8 10 12 14Wavelength (um)

0.001

0.002

0.003

0.004

0.005

Fp/

F*

Spitzer/IRS

500 1000 1500 2000 2500

101

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

(b)

10Wavelength (um)

0.000

0.001

0.002

0.003

0.004

0.005

0.006

Fp/

F*

Spitzer/IRAC, MIPS, and IRS

500 1000 1500 2000 2500

101

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

(c)

1.6 1.8 2.0 2.2 2.4Wavelength (um)

0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

Fp/

F*

HST/NICMOS

500 1000 1500 2000 2500

101

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

(d)

1 2 3 4 5Wavelength (um)

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

Fp/

F*

NICMOS and IRAC (3.6 and 4.5 um)

Figure 4.12: Retrieved P -T profiles (left column) and the best-fit spectra (right column) ofthe dayside HD 209458b using four different measurement combinations. Diverse combina-tions are used: (a)Spitzer IRS; (b)Spitzer/IRAC, MIPS, and IRS; (c)HST/NICMOS; and(d)HST/NICMOS and Spitzer IRAC (3.6, 4.5 µm only).

54

Table 4.3: Best estimated mixing ratios (ppm) for the dayside emission of HD 209458b.

H2O CO2 CO CH4 Inversion layer data source

Swain et al.(2009)

100 10 ... 200 1 mbarHST/NICMOSSpitzer/IRSSpitzer/IRAC

10 5 ... 60 10 mbar

10 5 ... 60 No Inv.

0.8 1 ... 10 100 mbar

Madhusudhan& Seager (2010)

6 0.006 30000 0.04 100 mbar SpitzerPhotometry40 0.00005 8 9 No Inv.

This study

HST/NICMOSSpitzer/IRSSpitzer

photomtery

8.8 120 ... 1800 1 mbar

as a result, strong emission leads to the large mixing ratio, whereas previous retrievals show

either a weak emission of CH4 and CO2 (Swain et al., 2009b), or a very high emission by

CO (Madhusudhan & Seager, 2010).

In Table 4.3, it is commonly shown that the chemistry in the dayside of HD 209458b is

predominantly carbon-rich, irrespective of CO, except for the no-inversion case by Mad-

husudhan & Seager (2010). This implies that, for some reason, the metallicity of HD

209458b appears to be very enhanced (C/O�1) unlike the result for HD 189733b.

4.3.6 Conclusion

Various studies have suggested evidence for a temperature inversion layer in a stratosphere

of the dayside atmosphere of HD 209458b (Burrows et al., 2008; Knutson et al., 2007; Mad-

husudhan & Seager, 2009, 2010; Swain et al., 2009a). In this context, the best-fit P -T profile

and molecular abundances were retrieved within the NEMESIS architecture. The retrieved

temperatures show that a weak inversion layer lies at ∼0.1 mbar, causing emission features

of CO2 at 4.5 and 16 µm, and CH4 at 3.3 and 7.7 µm. These features were the evidence for an

inversion as indicated in Swain et al. (2009b). However, the retrieved spectrum in this study

is rather flat and the deep absorptions in Swain et al. (2009b) (cf. the right plot in Figure 1.3

in Chapter 1) have not appeared at any wavelength. As stated in Section 4.2.4, this may be

because of the different forward models used for each study.

The additional retrievals for four different cases were carried out with diverse combi-

nations of the measurements. The Spitzer IRS channels require a featureless spectrum,

55

giving an unconstrained P -T profile, while the entire Spitzer channels yield a broad inver-

sion layer. A thermal inversion is also constrained when high planet-star flux ratios in the

Spitzer IRAC channels (i.e. 3.6 and 4.0 µm) are involved in the retrieval.

The estimated mixing ratio for H2O agrees with the retrieval models including an inver-

sion layer in the atmosphere, however, the mixing ratios for CO2 and CH4 are significantly

enhanced compared to previous studies, showing strong emission at the Spitzer MIR and

FIR channels. Evidence for a high amount of CO (Madhusudhan & Seager, 2010) was not

discovered in this study.

Obviously, current data allow fitting to the data with various solutions, leading to extreme

degeneracies between retrieval variables. Therefore, it is clear that the used data here for

emission spectrum of dayside HD 209458b are still in their infancy, which need of significant

improvement in the near future in order to characterise the atmospheric features with high

reliability.

56

4.4 Primary transit of HD 189733b

Now the first hot Jupiter, HD 189733b will be studied again by considering the additional

constraints offered by primary transit spectroscopy of the day/night terminator region. The

study being present in the following sections is preliminary before the arrival at clear con-

clusions later.

4.4.1 Model

Due to a low sensitivity to temperature variation with height (Tinetti et al., 2007a), the trans-

mission spectrum may not provide strong constraints for a P -T profile retrieval. Hence it is

assumed here that the terminator of HD 189733b has a similar thermal structure to the day-

side of the atmosphere, therefore, a priori for P -T profile is directly taken from the retrieved

P -T profile of the secondary eclipse of HD 189733b. The atmospheres in a forward model

cover a pressure range between 10−9–10 bar. The a prioris for molecular volume mixing

ratios for H2O, CO2, CO, and CH4 are investigated with diverse profile patterns in order to

find the best fitting profile. The collisional induced absorption opacity contributes at >1 µm,

based on the interactions of H2–H2 and H2–He.

4.4.2 Data

Many measurement sets are available for the transmission spectrum of HD 189733b. Ab-

sorption depths (defined as R2p/R

2s) at the MIR wavelengths were measured in the Spitzer

IRAC channels (Agol et al., 2009; Beaulieu et al., 2008; Desert et al., 2009), and, in FIR,

Knutson et al. (2007) obtained an absorption depth in the 24 µm MIPS channel. In NIR,

the fifteen HST/NICMOS data points (Swain et al., 2008a) in addition to two re-measured

data (1.66 and 1.87 µm) by Sing et al. (2009) are currently available. In the visible range at

0.55–1.05 µm, Pont et al. (2008) acquired continuous absorption depths using HST/STIS. In

particular, there is an disagreement between the Spitzer IRAC measurements by Beaulieu

et al. (2008) and Desert et al. (2009) due to their different data reduction processes (Fortney

et al., 2010). Therefore these data sets will remain out of scope here in order to avoid a

high degree of discrepancy between various observations. Here, sixteen HST/NICMOS data

(Swain et al., 2008a) are initially used for the retrieval of the transmission spectrum.

4.4.3 Best-fit spectrum

Figure 4.14 shows the best-fitted transmission spectrum of HD 189733b at the terminator.

The HST/NICMOS channels at 1.657, 2.060, and 2.175 µm cannot be fitted well, which are

also not explained in MS09 whereas Swain et al. (2008a) showed a fitted spectrum including

57

Temperature

500 1000 1500 2000 2500Temperature (K)

101

100

10-1

10-2

10-3

10-4

10-5

10-6

Pre

ssur

e (b

ar)

H2O

10-6 10-5 10-4 10-3 10-2 10-1 100

VMR

101

100

10-1

10-2

10-3

10-4

10-5

10-6

Pre

ssur

e (b

ar)

CH4

10-8 10-6 10-4 10-2 100 102

VMR

101

100

10-1

10-2

10-3

10-4

10-5

10-6

Pre

ssur

e (b

ar)

Figure 4.13: Retrieved profiles of P -T (left) and H2O (middle) and CH4 (right) abundancesat the terminator of HD 189733b. The a priori shape of P -T profile was taken from the re-trieved P -T profile of the dayside HD 189733b. For CH4, each line displays a priori (dashed),retrieved CH4 (solid), and their errors (dot-dashed and dotted).

1.6 1.8 2.0 2.2 2.4Wavelength (um)

2.34

2.36

2.38

2.40

2.42

2.44

Abs

orpt

ion

(%)

(RP

2 /RS

2 )

Figure 4.14: Best-fit transmission spectrum of the HD 189733b for thesixteen HST/NICMOS channels (Swain et al., 2008a). Binned absorp-tion depths at each channel are displayed in grey dots.

58

these channels with abundant CH4. This discrepancy is possibly due to the CH4 line list used

for each study.

As proposed in Swain et al. (2008a) and MS09, the eighteen measurements of the HST/

NICMOS channels implied that a high H2O absorption are clearly shown and, addition-

ally, transit depths between 2.15–2.5 µm can be explained via a high amount of CH4. The

abundances of CO, CO2, and even NH3 in the spectrum model enable to improve fitting the

measurements at some channels (Swain et al., 2008a) and, however, their contributions are

shown at few channels only, which are unable to provide strong constraints for a P -T profile

retrieval.

Here various profiles of a prioris are tested for retrieval of molecular mixing ratios and

a P -T profile. Unlike retrievals in previous sections, the primary transit measurements only

provide very weak constraints for retrieval of a P -T profile (i.e. low temperature sensitivity

of transmission spectrum) so that a scale factor is applied to retrieve the most plausible

profile which has same shape as the dayside thermal profile. Moreover, it is found that well-

mixed abundances of H2O and CH4 are unable to fit the measurement with reasonable χ2.

The HST/NICMOS transit depths seem to require different abundances for H2O and CH4

in different altitudes. For this reason, state vectors for H2O are defined in terms of a deep

pressure level (P0 level) and a fractional scale height (fsh) whose definitions are described

in Section 4.2.7. Here a new parameter, a low pressure level (P1 level), where the abundance

is fixed at the higher altitudes above, is added to avoid unrealistic abundance larger than

>1 at the upper atmosphere. On the other hand, a 43-layered profile is used for the CH4

state vectors because retrievals with simple profiles failed to fit the observations. Figure 4.13

demonstrates the retrieved profiles for temperatures, H2O, and CH4. It is shown that a higher

H2O abundance is required at high altitude than at low altitude, and that an increase-and-

decrease shape between 0.1–100 mbar seems to be essential for the CH4 abundance profile.

As performed in Section 4.2.7, a test for the CH4 sensitivity using a range of models and

∆χ2 is currently in progress.

4.4.4 Functional derivatives

As seen in Figure 4.15, the functional derivatives can be displayed in a 2-dimensional plot

(pressure vs. wavelength). These figures show the corresponding pressures where the sen-

sitivity of each retrieval variable is shown in the given wavelengths. Temperature and H2O

abundance are extremely correlated over the wavelengths so that care must be taken to derive

their values. A more detailed study for this subject will be done in future investigation. The

temperature sensitivity also shows somewhat large correlation with other molecules at the

wavelengths where each molecule has a high sensitivity.

59

Tem

pera

ture

1.6

1.8

2.0

2.2

2.4

Wav

elen

gths

(um

)

100

10-2

10-4

10-6

Pressure (bar)

H2O

1.6

1.8

2.0

2.2

2.4

Wav

elen

gths

(um

)

100

10-2

10-4

10-6

Pressure (bar)

CO

2

1.6

1.8

2.0

2.2

2.4

Wav

elen

gths

(um

)

100

10-2

10-4

10-6

Pressure (bar)

CO

1.6

1.8

2.0

2.2

2.4

Wav

elen

gths

(um

)

100

10-2

10-4

10-6

Pressure (bar)

CH

4

1.6

1.8

2.0

2.2

2.4

Wav

elen

gths

(um

)

100

10-2

10-4

10-6

Pressure (bar)

Figu

re4.

15:S

ensi

tivity

fort

empe

ratu

re,H

2O

,CO

2,C

O,a

ndC

H4.E

ach

sens

itivi

tyis

plot

ted

agai

nstp

ress

ure.

60

Table 4.4: Best estimated mixing ratios for the transmission spectrum of HD 189733b usingthe eighteen HST/NICMOS channels (Swain et al., 2008a)

H2O CO2 CO CH4 Notes

Swain et al.(2008a) 5×10−4 ... ... 5×10−5 inc. NH3 (∼10−5)

Madhusudhan& Seager (2009) 5×10−4–0.1 ... ... 10−5–0.3

Secondary transit(Section 4.2)

4.3×10−4 2.5×10−3 2×10−3 1.6×10−6

This study ∼10−3 5.7×10−7 5.6×10−5 ∼10−4


In Table 4.4, the retrieved abundances for each molecule are compared with the previous

studies of the HST/NICMOS observations. It can be seen that the H2O and CH4 abundances

are consistent with the results suggested in Swain et al. (2008a) and MS09. However, the

amounts of CO2 and CO were not reported in the earlier studies. One of number available

for direct comparison, the CO mixing ratio in equilibrium chemistry model by Fortney et al.

(2010) is determined as 5×10−4 which is a factor of ∼10 higher than the estimation here. As

mentioned in previous section, the CO sensitivity only appears in narrow wavelengths (1.55–

1.65 µm and 2.3–2.5 µm) and is too small to be constrained with high reliability. Therefore,

the mixing ratio retrievals of CO and CO2 should be performed using further measurements

with either very high resolution spectroscopy or by including a broader range of wavelengths

in the retrievals.

The retrieved abundances of carbon bearing molecules from the dayside emission of HD

189733b in Section 4.2 differ from those from tranmission spectrum. As demonstrated in

Figure 4.15, the molecules of CO2 and CO are sensitive to few HST/NICMOS channels only

and contribute to the fitting quite small, probably leading to large degeneracy ranges (see

Section 4.2.7). Thus their abundances may have broad ranges of uncertainty, which limit the

direct comparison to the secondary eclipse results. The CH4 abundance (∼10−4) that shows

a high contribution over the wavelength range are two factors of higher than the one from the

secondary emission spectrum (1.6×10−6). However, this high CH4 is clearly consistent with

the degeneracy range (∆χ2) larger than 1.0 for CH4 in Figure 4.2.6. A detailed degeneracy

study for these molecules is in progress and will be added in the final thesis.

61

Transmission spectrum of HD 189733b

0.5 1.0 1.5 2.0 2.5Wavelength (um)

2.30

2.35

2.40

2.45

2.50A

bsor

ptio

n (%

) (R

P/R

S)2

Figure 4.16: Transmission spectrum fitting to the NIR measurements of HD 189733b inte-grated from the visible region. Broad spectral features by Na and K each centred at 589 nmand 766 nm are dominant at < 0.8 µm. The opacities by the Rayleigh scattering (< 1.0 µm)and collisonal induced absoprtion (> 1.0 µm) are displayed in grey colour. Continuous tran-sit depths between 0.55–1.05 µm (Pont et al., 2008) are shown in green crosses. This tellsthat high transit depths in the visible require a thick and smoothed opacity by an absorber.

4.4.6 Aerosol scattering? : High transit depths at visible

Pont et al. (2008) reported linearly decreasing transit depths at visible wavelengths (0.55–

1.05 µm), thought to be due to scattering by thick hazes. However, there is a debate on

the wavelength region affected by the scattering (Beaulieu et al., 2008; Desert et al., 2009;

Gibson et al., 2011; Pont et al., 2008; Sing et al., 2008). Figure 4.16 shows the best-fit

spectrum of the HST/NICMOS observations sampled from as short as 0.5 µm. As predicted

in a theoretical model (Sharp & Burrows, 2007), the opacity at wavelengths <1.0 µm is

dominated by absorption by alkali metal lines and the Rayleigh scattering by H2 and He.

However, scattering by additional high amount of aerosol may blanket these low opacities

(grey curve in Figure 4.16) and fit the high transit depths as mentioned in various studies

(Desert et al., 2009; Gibson et al., 2011; Pont et al., 2008; Sing et al., 2008). Currently, an

improvement is on going in the forward model of NEMESIS so as to calculate scattering

by any size and any amount of aerosol. The improved retrieval should reveal the various

characteristics of aerosol in the atmosphere of HD 189733b.

62

4.5 Summary

It is presented here that the analysis of hot Jupiters’ two secondary emission spectra and

a transmission spectrum have showed the possibility of the retrieval of P -T profiles and

moleuclar abundances by using current limited datasets. The studies for the hot Jupiters will

be updated continuously in the coming months as well as looking at a hot Neptune (GJ 436b)

and a super earth (GJ 1214b). In the next chapter, the future investigations of these planets

will be described in detail.

63

Chapter 5

Future work

5.1 Retrieval studies

Further retrieval analysis to constrain uncertainties of molecular abundances and P -T pro-

file will be carried out for the emission spectrum of HD 209458b (Section 4.3) and the

transmission spectrum of HD 189733b (Section 4.4). Additionally, the retrieval studies for

the transmission spectrum of HD 209458b, a hot Neptune (GJ 436b), and a super Earth (GJ

1214b), and the emission spectrum of GJ 436b will be completed and retrieved results will

be included in the thesis.

Transmission spectrum of HD 209458b For the transmission spectrum of HD 209458b,

it has been shown that the alkali metals and the Rayleigh scattering are dominant absorbers

in the UV/visible wavelengths. Recently, Desert et al. (2009) showed plausible absorption

features of gaseous TiO/VO in the visible region. In this sense, the further retrieval study

will include a work investigating these absorbers, which may cause a thermal inversion in

the atmosphere, using the HST observations made at the visible range. Finally, the validity

of the themal inversion hypothesis will be tested.

Transmission and Emission spectra of a hot Neptune, GJ 436b For GJ 436b, the chem-

istry of CH4 and H2O still remains unclear. The small number of observations may cause

strong degeneracy between molecules and thus the estimation of abundances can be inter-

preted in many ways. Here, the retrievals will be carried out with several case studies, consid-

ering different molecular abundances and P -T profiles in the atmosphere, in order to suggest

the most plausible scenarios for each controversial measurement.

Transmission spectrum of a super Earth, GJ 1214b For the transmission spectrum of

GJ 1214b, various interpretations come with its featureless and flat spectra which have been

64

measured in the fifteen channels at NIR and MIR. Its degeneracy problem is mostly linked to

the metallicity of the atmosphere, and, in particular, the depletion of CH4 seems to be a key

issue to solve the degeneracy. The retrieval study here will propose the answer whether cur-

rent observations can provide enough constraints for the retrieval of molecular abundances

mentioned above.

Even though plenty of studies remain to be done, it is clearly shown that the application

of the optimal estimation retrieval architecture to a broad range of measured wavelengths

can provide new constraints on the atmospheric structure and composition of exoplanets.

Highlights in this study to date include the first retrieval of atmospheric P -T profile and

assessments of the degeneracies between composition and temperature on HD 189733b, the

testing of the thermal inversion hypothesis for HD 209458b, and comparing the results from

the secondary emission spectrum to those from the transmission spectum of the day/night

terminator in HD 189733b.

5.2 Thesis contents

The final thesis contents will be as follows in the perspective of this study as presented above.

1. Exoplanet1.1 Discovery and detection

1.2 Atmospheric chemistry

2. Transit spectroscopy2.1 Primary transit

2.1.1 Theoretical background

2.1.2 Current issues

2.2 Secondary transit

2.2.1 Theoretical background

2.2.2 Current issues

3. Spectral modelling3.1 Radiative transfer

3.1.1 Line-by-line calculation

3.1.2 Correlated-k approximation

3.2 Line lists

3.2.1 H2O

3.2.2 CO2

3.2.3 CO

3.2.4 CH4

65

3.2.5 Alkali metals – Na and K

3.2.6 Metalic oxides – TiO and VO

3.2.7 Partition functions

3.2.8 Collisional Induced Absorption

3.3 k-distribution tables

3.3.1 k-coefficient claculation

3.3.2 comparision with lbl calculation

4. Non-linear optimisation retrieval4.1 Theory

4.2 Forward model calculation

5. Retrieval of a hot Jupiter, HD 189733b5.1 Primary transit

5.1.1 Introduction

5.1.2 Model

5.1.3 Data

5.1.4 Results

5.1.5 Conclusion


5.2.1 Introduction

5.2.2 Model

5.2.3 Data

5.2.4 Results

5.2.5 Conclusion

6. Retrieval of a hot Jupiter, HD 209458b6.1 Primary transit


7. Retrieval of a hot Neptune, GJ 436b7.1 Primary transit


8. Retrieval of a super Earth, GJ 1214b8.1 Primary transit

9. Conclusion9.1 Summary

9.2 Future prospect

66

5.3

Tim

elin

e

Afo

llow

ing

Gan

ttch

arts

how

sho

wto

inte

ndto

com

plet

eD

Phil

cour

se.N

otic

eabl

eda

tes

are

liste

dbe

low

→by

30/J

UN

/201

1–k

-dis

trib

utio

nca

lcul

atio

n

→by

31/J

UL

/201

1–

seco

ndar

yem

issi

onfo

rHD

2094

58b

&tr

ansm

issi

onfo

rHD

1897

33b

→by

31/J

UL

/201

1–

subm

issi

onof

the

first

pape

r

→by

31/A

UG

/201

1–

tran

smis

sion

forH

D20

9458

b&

seco

ndar

yem

issi

onfo

rGJ

436b

→by

30/S

EP/

2011

–tr

ansm

issi

onan

dem

issi

onfo

rGJ

436b

and

tran

smis

sion

forG

J12

14b

→by

31/D

EC

/201

1–

Com

plet

eth

eth

esis

wri

ting

67

App

endi

xA

Avai

labl

elin

elis

tsfo

rm

olec

ules

and

elem

ents

68

Tabl

eA

.1:A

vaila

ble

line

lists

form

olec

ule,

elem

enta

ndco

ntin

uum

abso

rptio

n.H

ITR

AN

08G

EIS

A09

HIT

EM

P10

indi

vidu

allis

t

H2O

XX

XPa

trid

ge&

Schw

enke

(199

7)B

arbe

reta

l.(2

007)

AM

ES

SCA

NC

O2

XX

XC

DSD

-Tas

hkun

etal

.(200

3)C

OX

XX

-

CH

4X

XX

Stro

nget

al.(1

993)

Bro

wn

etal

.(199

7)K

arko

schk

a(1

994)

STD

S-W

enge

r&C

ham

pion

(199

8)N

assa

r&B

erna

th(2

003)

Thi

evin

etal

.(200

8)

TiO

--

-A

llard

etal

.(200

0)Pl

ez(1

998)

VO

--

-Pl

ez(1

998)

alka

lim

etal

VAL

DN

IST

Ato

mic

Spec

tra

Dat

abas

eTO

Pbas

e

Col

lisio

n-In

duce

dA

bsop

rtio

n

Bor

ysow

&Fr

omm

hold

(199

0),

Zhe

ng&

Bor

ysow

(199

5),

Bor

ysow

etal

.(199

7)fo

rH2-H

2

Bor

ysow

etal

.(198

9),

Bor

ysow

&Fr

omm

hold

(198

9)fo

rH2-H

e

69

App

endi

xB

Part

ition

func

tion

70

Tabl

eB

.1:P

olyn

omia

lfor

mof

part

ition

func

tion

and

coef

ficie

nts

Spec

ies

poly

.for

mis

otop

eno

.po

lyno

mia

lcoe

ffici

ents

a 0a 1

a 2a 3

a 4H

2O

∑ 3 i=0aiT

i

161

-1.6

9592

e+2

1.29

367e

+0-5

.210

98e-

46.

2488

7e-7

CO

2

626

-2.4

9458

e+3

1.38

585e

+1-1

.654

51e-

28.

1438

5e-6

636

-5.4

6924

e+3

3.02

257e

+1-3

.626

77e-

21.

7705

1e-5

628

-5.4

7892

e+3

3.03

745e

+1-3

.634

34e-

21.

7828

6e-5

627

-3.1

4590

e+4

1.74

564e

+2-2

.086

53e-

11.

0250

4e-4

638

-1.2

0742

e+4

6.65

827e

+1-8

.008

06e-

23.

8945

6e-5

637

-6.9

1181

e+4

3.81

536e

+2-4

.538

35e-

12.

2332

3e-4

828

-3.0

0858

e+3

1.66

473e

+1-1

.995

91e-

29.

7599

4e-6

CO

261.

1713

3e+1

3.01

374e

-15.

6859

2e-5

1.10

085e

-836

2.52

449e

+16.

2527

1e-1

1.26

461e

-42.

2811

0e-8

281.

2703

7e+1

3.13

604e

-16.

3793

0e-5

1.14

406e

-827

7.33

570e

+11.

8463

6e+0

3.62

534e

-46.

7393

7e-8

382.

7435

0e+1

6.51

846e

-11.

4224

8e-4

2.37

446e

-838

1.50

771e

+23.

8859

3e+0

7.33

075e

-41.

4175

8e-7

CH

4(<

1000

K)

211

-3.1

4109

e+2

4.59

494e

+0-8

.399

81e-

31.

1989

5e-5

-6.2

8187

e+2

9.18

943e

+0-1

.679

91e-

22.

3977

9e-5

-2.5

4542

e+3

3.71

886e

+1-6

.799

55e-

29.

7062

6e-5

CH

4(1

000∼

2000

K)

311

-2.6

0101

e+5

6.48

085e

+2-5

.451

39e-

11.

6491

6e-4

-5.2

0196

e+5

1.29

615e

+3-1

.090

25e+

03.

2782

1e-4

-2.1

0531

e+6

5.24

595e

+3-4

.412

87e+

01.

3269

6e-3

CH

4(>

2000

K)

212

-1.1

9710

e+7

1.68

635e

+4-8

.076

04e+

01.

3385

6e-3

-2.3

9334

e+7

3.37

157e

+4-1

.614

71e+

12.

6763

7e-3

-9.6

8816

e+7

1.36

480e

+5-6

.536

34e+

11.

0834

1e-2

TiO

log 1

0Q(T

)=

∑ 4 i=0aili θ

5.30

51-2

.373

90.

8940

-0.3

641

VO

5.06

87-2

.218

60.

9545

-0.4

592

Na

log 1

0Q(T

)=

∑ 4 i=0aili θ

0.30

955

-0.1

7778

1.10

594

-2.4

2847

1.70

721

K0.

3441

9-0

.048

157

1.92

563

-3.1

7826

1.83

211

71

Appendix C

A manuscript for publication

Title :

Retrieval of atmospheric structure and composition of

HD 189733b from secondary eclipse spectroscopy

To be submitted to the Astrophysical Journal

72

TO BE SUBMITTED TO ASTROPHYS. J.Preprint typeset using LATEX style emulateapj v. 11/10/09

RETRIEVAL OF ATMOSPHERIC STRUCTURE AND COMPOSITION OFHD 189733b FROM SECONDARY ECLIPSE SPECTROSCOPY

J.-M. LEE1 , L. N. FLETCHER1 , AND P. G. J. IRWIN1

Atmospheric, Oceanic, and Planetary Physics, University of Oxford, Oxford, UKTo be submitted to Astrophys. J.

ABSTRACTRecent spectroscopic observations of transiting hot Jupiters have permitted the derivation of the thermal struc-ture and molecular abundances of H2O, CO2, CO, and CH4 in these extreme atmospheres. Here, for the firsttime, a fully-fledged retrieval algorithm has been applied to exoplanet spectra to determine the thermal structureand composition. The development of a suite of radiative transfer and retrieval tools for exoplanet atmospheresis described, building upon an optimal estimation retrieval algorithm which is extensively used in the study ofour own solar system. We discuss the best-fit spectrum retrieved from all available sets of secondary eclipseobservations of HD 189733b. Additionally, we use the contribution functions and the vertical sensitivity to themolecules to interpret this spectrum, probing the structure and composition of the atmosphere. Our retrievalsuggests that there exist an isothermal layer above an adiabatically decreasing shape of temperature-pressureprofile over the vertical range covered by the contribution functions and the resultant structure shows goodconsistency with dynamical and observational results previously reported. Constraining the uncertainties ofthe parameters is accomplished by investigating the cross-correlation functions and degeneracy between theparameters. The formal solution of the inverse problem suggests that the uncertainties on retrieved parametersare larger than suggested in previous studies. Nevertheless, by including as broad a wavelength range as pos-sible in the retrieval, we demonstrate that available spectra of HD189733b can constrain a family of potentialsolutions for the atmospheric structure.Subject headings: exoplanet: general — planetary systems: individual(HD 189733b)

1. INTRODUCTION

The vertical structure of an exoplanetary atmosphere can bederived from transmission and emission spectroscopy whena planet transits its host star. The atmospheric propertiesof HD 189733b have been extensively investigated using asmall number of observations from both space and ground-based telescopes. Transmission spectra acquired during pri-mary transits, where light from the host star is filtered throughthe upper layers of an exoplanetary atmosphere, which wereobserved by Spitzer mid- and far-infrared (MIR and FIR)broadband photometry, were used to deduce a high abundanceof H2O in the terminator region of this planet (Tinetti et al.2007a; Swain et al. 2008; Beaulieu et al. 2008; Desert et al.2009). In addition, a strong absorption due to CH4 was re-ported in the near-infrared (NIR) using the HST/NICMOSspectrophotometry (Swain et al. 2008). However, the accu-racy of transit spectroscopy and photometry has been calledinto question (see the review by Seager and Deming (2010)),and most recently Gibson et al. (2011) claimed that instru-mental systematics limit our ability to constrain atmosphericCH4 from these HST/NICMOS data. A spectral feature at4.5 µm can be explained by either of the carbon bearingmolecules CO2 or CO, although it is still unclear which dueto the degeneracy of the solution (Desert et al. 2009; Fort-ney et al. 2010). At visible wavelengths, strong lines of thealkali metal, sodium, were reported using observations withthe high resolution ground spectrograph of the Hobby–EberlyTelescope (Redfield et al. 2008), while a featureless spectrumdetected by the HST/STIS is thought to be caused by thickatmospheric hazes (Pont et al. 2008; Sing et al. 2011).

Observations of secondary transit spectra, when emission

[email protected]

spectra from the planet’s dayside is detected before and afterthe planet is eclipsed, of HD 189733b by Spitzer broadbandphotometry have shown that H2O is also abundantly presentin the dayside atmosphere (Charbonneau et al. 2008; Deminget al. 2006), forming the main features of the emission spec-trum. The H2O-rich atmosphere was confirmed via SpitzerIRS spectroscopy (Grillmair et al. 2008). HST/NICMOS day-side observations indicated a high abundance of CO2, CO,and CH4 (Swain et al. 2009, hearafter S09), supporting theconclusions of their primary transit spectrophotometry. Withall measurements, each of these studies suggested that an at-mospheric thermal profile lacking a thermal inversion (i.e.,without a warm stratosphere) could best explain their obser-vations. A decreasing temperature with altitude between 0.01-1.0 bar suggested the presence of a troposphere. (S09; Mad-husudhan & Seager 2009, hearafter MS09).

Various techniques have been used to investigate the atmo-spheric constituents and structure from transit spectroscopy.Infrared dayside spectra during secondary eclipses measurethe thermal emission of the dayside of the exoplanet, whichdepends mostly on the vertical temperature structure, whileprimary eclipse observations are more sensitive to the abso-lute temperature at the terminator due to its scale height de-pendence (Brown 2001; Tinetti et al. 2007b). The retrieval ofatmospheric properties from remotely sensing measurementshas been developed over many decades (Goody & Yung 1989)and has become a common tool for the study of planetary at-mospheres. Measured radiances (either photometry or spec-troscopy) can be compared to synthetic spectra from radia-tive transfer modelling so as to determine the atmosphericstructure and composition. A retrieval model solves an ill-constrained inversion problem, using an iterative approachto derive the most statistically-likely solution for the avail-able data. Previous studies, such as those by Tinetti et al.

2 LEE, FLETCHER, & IRWIN

(2007a), Swain et al. (2008), and S09, have utilised forwardmodelling to determine a best-fit to the data, and have con-strained the range of molecular abundances of transiting ex-oplanets by running forward models which were based ontheoretical pressure-temperature (P-T ) profiles. An alterna-tive forward modelling approach used by a number of studies(Sing et al. 2007; Madhusudhan & Seager 2010; Stevenson etal. 2010; Madhusudhan & Seager 2011; Madhusudhan et al.2011, ;MS09) used freely roaming P-T profiles and molecularabundances in a parameterised space, where calculated spec-tra were again compared with observations in terms of thegoodness-of-fit, and their numerous runs enabled to constrainP-T profiles and atmospheric compositions. Although theseforward modelling techniques provide valuable insights, theirmethods are based on line-by-line radiative transfer models,which are slow when large numbers of synthetic spectra areto be calculated over a wide wavelength range. Moreover,the huge degeneracies between the different model parame-ters was not explored in detail.

The NEMESIS optimal estimation retrieval algorithm (Ir-win et al. 2008) uses the correlated-k technique (Lacis &Oinas 1991) in its radiative transfer model, which rapidlyintegrates synthetic spectra using k-distribution tables pre-calculated from line databases (Goody & Yung 1989). Thecombination of the correlated-k forward model, which is or-ders of magnitude faster than a standard line-by-line model,with an optimal estimation retrieval scheme has been used tosuccessfully investigate planetary atmospheres in our own so-lar system. In this study we apply this rapid retrieval archi-tecture to exoplanets, formally addressing the uncertaintiesand degeneracies inherent in previous studies. Moreover, un-derstanding of the detailed correlations between the derivedP-T profile and atmospheric compositions can be achievedfrom the covariance matrices which are calculated using thismethod, and which quantify the correlations between the re-trieved values of different properties. Consequently, this studywill show that how the characteristics of these extreme exo-planet atmospheres can be deduced from spectroscopic mea-surements, and, finally, we will highlight the limitations of thedatasets available today.

In this report, the modelling method used to retrieve the at-mospheric properties from the dayside spectroscopy and pho-tometry of HD 189733b is described in Section 2. All avail-able measurements used to constrain atmospheric propertiesare described in Section 3 and the best-fit spectrum to thesemeasurements is discussed in Section 4. Section 5 demon-strates the validity of the retrieval scheme, and quantifies thedegeneracy of the solution. In Section 6 we discuss the ap-proach and implications, and arrive at our conclusions.

2. MODELLING

We used a non-linear optimal estimation program for the re-trieval of atmospheric variables, NEMESIS, which solves theinverse problem, the question of investigating the best estima-tion of the variables, using a method based on a Bayesian andmaximum-likelihood approach with the addition of a prioriinformation (Rodgers 2000). The optimal state in the al-gorithm is accomplished after a moderate number of itera-tions (approximately 10–20), whose scheme is based on theMarquardt-Levenberg principle (Levenberg 1944; Marquardt1963). The algorithm calculates synthetic spectra using thecorrelated-k approximation method, which has been shownto be fast, reliable, and sufficiently accurate compared to aline-by-line calculation. We compared spectra calculated by

line-by-line and correlated-k models, and found that mean dif-ference between two techniques are less than 5 %, which isconsiderably smaller than the range of uncertainties on avail-able exoplanet measurements. In the k-distribution method,the absorption spectrum over an interval is sorted in order ofincreasing absorption and the fraction of the interval with ab-sorption less than a certain value k(g) is represented in termsof the fraction of interval g. Since k(g) is a smoothly varyingfunction of g, it may be integrated with relatively few quadra-ture points N to determine the mean transmission over the in-terval as:

T (m) 'N∑

i=1

e−kim∆gi, (1)

where m is the amount of a molecule; and ki and ∆gi are the k-coefficients and quadrature weights at each quadrature points(Irwin et al. 2008). The k-coefficients are calculated from linedata for a range of temperatures and pressures expected in theatmosphere in advance of the retrieval so that the fast forwardmodel calculation is possible during the iteration. The molec-ular line lists used in this study were taken from HITEMP2010(Rothman et al. 2010) for H2O, the Carbon Dioxide Spec-troscopic Databank (CDSD-1000) (Tashkun et al. 2003) (alsoused for HITEMP2010) for CO2, HITEMP1995 (Rothman etal. 1995) for CO, and the Spherical Top Data System (STDS)(Wenger & Champion 1998) for CH4, respectively. As a re-sult, the combination of the two characteristics of the op-timal estimation and correlated-k method enhances the effi-ciency of the retrieval process in terms of time and computa-tional resources. Furthermore, NEMESIS calculates the ma-trix of the partial derivatives of radiances at each wavelengthwith respect to each retrieved variable, which are called thef unctional derivatives, in order that the contribution of dif-ferent atmospheric parameters at each wavelength can be eas-ily interpreted by comparing the elements of this matrix.

The a priori dayside atmosphere of HD 189733b extendsfrom 10−9 to 10 bar. For initial modelling we assumed that allspecies were well-mixed throughout the atmosphere and themolecular abundance was defined in terms of a single scalingparameter. This is because the retrieval of a continuous profileof composition would be under-constrained, leading to non-physical oscillations in the retrieved profile. The a priori esti-mate for the abundance scaling parameter is assumed to havea large uncertainty so that retrieved values are not weightedby initial guesses since a simple scaling parameter already in-cludes vertical smoothing. The a priori for temperature isassumed to have a continuous profile and its error, however,had to be adjusted to achieve the optimal balance between thequality of the fit to the measured data and the vertical smooth-ing. This will be further discussed in Section 5.3.1. As animportant source of absorption in exoplanetary atmospheres,collisional-induced absorption (CIA) between principle gasesare included in the model atmosphere. We consider the in-teractions between H2–H2 and H2–He and the coefficients aretaken from Borysow et al. (1989), Borysow and Frommhold(1989), Borysow and Frommhold (1990), Zhang and Borysow(1995), Borysow et al. (1997), and Borysow (2002). The molefractions of H2 and He are assumed to be as same as the frac-tions of atomic H and He, which are close to the typical solarvalue as 0.91 and 0.0887 each (Burrows & Sharp 1999).

3. DATA

RETRIEVAL OF ATMOSPHERIC STRUCTURE AND COMPOSITION 3

To retrieve the P-T profile and compositional abundances,we use three measurement sets of the secondary eclipse forHD 189733b, only available dayside emission data at thepresent time, are used, ranging over a wide IR wavelengthfrom 1.45 µm to 24 µm: 1) sixteen HST/NICMOS (Swain etal. 2009) channels covering the range 1.45–2.5 µm (exclud-ing the 1.476 and 1.525 µm channels, which have unrealisticplanet-stellar flux ratios (FPlanet/FStar) less than zero); 2) fortyseven Spitzer IRS (Grillmair et al. 2008) channels coveringthe range 5–14.5 µm and one IRS photometry (Deming etal. 2006) channel at 16 µm; and 3) five Spitzer IRAC/MIPS(Charbonneau et al. 2008) photometry channels at 3.6, 4.5,5.8, 8.0, and 24 µm. The reference stellar spectrum for HD189733 is taken from the Kurucz grid model1.

Despite the efforts towards finding and reducing the errorsfrom the data, the uncertainties on given datasets still remainand are widely distributed over the wavelengths due to its var-ious error sources. First of all, techniques to decorrelate atransit light curve from the combined light of a planetary sys-tem are not consistent each other (e.g. Swain et al. (2008)vs. Gibson et al. (2011)). Also, systematic errors inherentin the observations itself can be a strong error source. Thesetwo facts may cause the planet–stellar flux ratio to be depen-dent on the data reduction process. Nonconcurrent observa-tions for different wavelengths can deliver a large gap betweenmeasurements, which may be caused by significant temporalvariability in the atmosphere of HD 189733b. Therefore, allthese sources of potential error could lead to substantial in-consistencies between the datasets taken from different stud-ies, instruments, and observation times.

4. BEST-FIT DAYSIDE SPECTRUM OF HD 189733b

Using the NEMESIS algorithm, we retrieve the best-fit day-side spectrum of HD 189733b, incorporating both the Spitzerand HST observations. Figure 1 shows the best-fit spec-trum, in addition to the contributions from the four main gases(H2O, CO2, CO, and CH4) included in our model. This figurealso shows the wavelength ranges where the molecular contri-butions are distributed by co-plotting the computed syntheticspectra with high and low abundances for each molecule.Spectral features of H2O and CO2 affect the spectrum at allwavelengths. CO has absorption features at 1.6, 2.3–2.5, and5.0–5.5 µm, while CH4 features can be seen at 1.7, 2.1–2.5,3–4, and 5–9 µm. A striking feature of the best-fit spectrum isa deep IR absorption by CO2 at 9–24 µm as shown in Figure1(c), which is rather different from the fitting by the otherstudies (Fortney & Marley (2007); Grillmair et al. (2008);Charbonneau et al. (2008); MS09), who concluded that thefeatures at the longer wavelengths of IRS are caused mainlyby H2O, of which absorption is also dominant at the shorterwavelengths of 5–9 µm. The low CO2 hypothesis might givea good reproduction of the long-wave Spitzer data, however,it fails to reproduce the shorter wavelengths covered by HST.As seen here, one of the benefits of our model is that the useof a broad range of IR wavelengths allows us to break someof the degeneracies inherent in modelling a small number ofdata points. (cf. Section 5.4).

In this study, the high CO2 abundance causes a sharp dropat 9 µm and then a flat and featureless spectrum between 9–24µm. H2O still contributes to the spectrum at 5–9 µm and >20µm as well as a small feature from a vibrational transitionat 6–6.5 µm, which is one of the H2O features highlighted

1 http://kurucz.harvard.edu/stars/HD189733/

by Grillmair et al. (2008). In particular, the spectrum fits aplanet-star flux ratio for the Spitzer IRAC 3.6 µm channel,a feature which has been previously explained by the large3.25 µm emission of CH4 in non-local thermodynamic equi-librium (NLTE) conditions (Swain et al. 2010; Thatte et al.2010). Unfortunately, the current retrieval algorithm is un-able to model radiative transfer in NLTE and thus we leavea detailed analysis for future studies. For the HST/NICMOSchannels between 1.45–2.5 µm, we fit to the measurementsusing a high amount of CO2 as suggested in MS09 (∼7×10−4)rather than in S09 whose model suggested low CO2 mixingratio (10−7–10−6). This discrepancy is not yet fully resolved,but, as Shabram et al. (2011) stated, this may come fromthe difference in the forward models used for each study. Inour spectrum, the channels at 1.584, 1.869, 2.159–2.216 µm,however, are underestimated with the high CO2 abundance,leading to a decrease in the quality of the fit to the data. Thesharp edge present at 9 µm, where a sudden CO2 line weak-ening is shown, is caused by a strong CO2 absorption and is areal feature of this exoplanet’s spectrum.

5. RETRIEVAL OF ATMOSPHERIC PROPERTIES

On the basis of the best-fitted spectrum stated in theprevious section, we here validate the retrieval method byanalysing the temperature contribution functions and thefunctional derivatives for the molecular abundances. Thesesensitivity analyses then allow plausible interpretations fortemperature and composition structure of the dayside HD189733b.

5.1. Contribution functionsThe radiance measured in each channel originates from dif-

ferent pressure levels within the atmosphere. This is generallydescribed using a contribution function, which is the productof the Planck function at the local temperature in the atmo-sphere and the transmission weighting function, which de-scribes the rate of change of atmospheric transmission withheight. The contribution functions are dependent on a prioriswe assume for the atmospheric structure and abundances.Thus the calculated contribution functions indicate the pres-sure levels at which thermal emission from the atmospherecontributes most to the radiance observed in each channel.Figure 2 shows the contribution functions for all channels ofthe Spitzer IRS, IRAC, and MIPS, and HST/NICMOS.

The six Spitzer broadband photometry channels in therange 3.6–24 µm have broadly-distributed contribution func-tions whose peak pressures range from 2 to 400 mbar. Thecontribution functions for the IRAC channels (3.6, 4.5, 5.8,and 8 µm) and MIPS (24 µm) are located in the deeper at-mosphere and provide strong constraints for the temperaturebetween 30–400 mbar. The contribution function of the IRAC4.5 µm channel has a second peak at high altitude (3–4 mbar),being close to the peak of the IRS 16 µm channel at 2 mbar.Hence, the temperature at pressures as low as 2 mbar can beretrieved from the IRAC channels only if the temperature ofthe deep atmosphere is well constrained from the other mea-surements. The 47 Spitzer IRS spectroscopy channels be-tween 5 and 14.5 µm have closely spaced overlapping con-tribution functions, with peaks ranging from 1 to 200 mbar.The radiance from the lower atmosphere (∼100 mbar) con-tributes to the channels in the range 5–9 µm, whereas ra-diance from the upper atmosphere (&10 mbar) contributeslongward of 9 µm. Unlike the MIR and FIR channels onSpitzer, the HST/NICMOS NIR 1.45–2.5 µm channels can


(a) H2O (1-30 µm)

HST NICMOS (Swain et al. 2009)

Spitzer IRS (Grillmair et al. 2008)

Spitzer IRAC/MIPS (Charbonneau et al. 2008)

Spitzer IRS broadband (Deming et al. 2006)

x 0.1x 0.2x 1x 5x 10


0

2

4

6

8F

plan

et/F

star (

x10-3

)

(b) H2O (1.5-2.5 µm)

1.6 1.8 2.0 2.2 2.4Wavelength (µm)

0

0.2

0.4

0.6

0.8

1.0

Fpl

anet/F

star (

x10-3

)

(c) CO2 (1-30 µm)

x 0.01x 0.05x 1x 20x 100


0

2

4

6

8

Fpl

anet/F

star (

x10-3

)

(d) CO2 (1.5-2.5 µm)

1.6 1.8 2.0 2.2 2.4Wavelength (µm)

0

0.2

0.4

0.6

0.8

1.0

Fpl

anet/F

star (

x10-3

)

(e) CO(1-30 µm)

x 0.01x 0.05x 1x 20x 100


0

2

4

6

8

Fpl

anet/F

star (

x10-3

)

(f) CO(1.5-2.5 µm)

1.6 1.8 2.0 2.2 2.4Wavelength (µm)

0

0.2

0.4

0.6

0.8

1.0

Fpl

anet/F

star (

x10-3

)

(g) CH4 (1-30 µm)

x 0.01x 0.05x 1x 20x 100


0

2

4

6

8

Fpl

anet/F

star (

x10-3

)

(h) CH4 (1.5-2.5 µm)

1.6 1.8 2.0 2.2 2.4Wavelength (µm)

0

0.2

0.4

0.6

0.8

1.0

Fpl

anet/F

star (

x10-3

)

Figure 1. Fitted dayside emission spectra of HD 189733b. The orange, purple with red, and green symbols are the measured planet-star flux ratio from theHST/NICMOS (Swain et al. 2009) spectrophotometry, the Spitzer IRS spectroscopy (Grillmair et al. 2008), and the Spitzer broadband photometry (Charbonneauet al. 2008; Deming et al. 2006). The best-fit spectrum retrieved by the NEMESIS algorithm is displayed as a black line in all figures. We also show calculatedspectra with various molecular abundances to understand the contributions of different molecules to the best-fit spectrum. For H2O, molecular abundances arevaried 0.1, 0.2, 5.0, and 10.0 times from the abundance leading to the best-fit spectrum, and, 0.01, 0.02, 20.0, and 100.0 times for the other molecules.


Spitzer photometry

0.0 0.2 0.4 0.6 0.8 1.0


100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

Spitzer IRS

0.0 0.2 0.4 0.6 0.8 1.0


100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

HST NICMOS

0.0 0.2 0.4 0.6 0.8 1.0


100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

Figure 2. Contribution functions for the Spitzer broadband photometry (left), IRS spectroscopy (middle), and the HST/NICMOS spectrophotometry (right)channels. For the Spitzer photometry channels, each line pattern means MIPS 24 µm (solid), IRS 16 µm (solid-black), IRAC 8.0 µm (dotted), 5.8 µm (dashed),4.5 µm (dot-dashed), and 3.6 µm (triple dot-dashed). For the Spitzer IRS and the HST/NICMOS channels, the brighter colours denote the channels at the shorterwavelength. For all cases, emission from the lower atmosphere tends to dominate the shorter wavelength channels.

Spitzer photometry

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

Spitzer IRS

HST NICMOS

H2O

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

CO

2

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

CO

100

10-1

10-2

10-3

10-4

10-5

Pre

ssur

e (b

ar)

-1.0 -0.5 0.0 0.5 1.0d[flux ratio]/d[VMR]

-1.0 -0.5 0.0 0.5 1.0d[flux ratio]/d[VMR]

CH

4

-1.0 -0.5 0.0 0.5 1.0d[flux ratio]/d[VMR]

Figure 3. Normalised functional derivatives of molecules in Spitzer and HST channels. The applied colours are described in Figure 2. Each row shows thevertical sensitivity of radiance with respect to the abundance of the molecules H2O, CO2, CO, and CH4 (from top to bottom). This figure shows the pressurelevels at which molecular abundance can be retrieved (row direction) from which channel (column direction).


measure the emission from the deeper atmosphere at 10–700mbar and their contribution functions are partly distributedover the pressure levels that are not covered by the Spitzermeasurements.

In summary, the contribution functions show that the P-Tprofile over a broad range of pressures from 1 to 700 mbarcan be constrained by retrieving from the Spitzer and HSTmeasurements together. On the other hand, studies that fo-cus on a single narrow wavelength range are sensitive to onlya narrow altitude range. Thus, by considering all availabledatasets simultaneously, we provided better constraints on re-trieved properties.

5.2. Functional derivativesThe functional derivatives are defined to be the partial

derivatives of the radiance (or any spectral output in the for-ward model) with respect to any given atmospheric parame-ters. By calculating the functional derivatives for molecularabundances, we can understand which measurements are sen-sitive to the abundance of which molecules and at which pres-sure levels. Figure 3 shows the functional derivatives for the4 molecules considered in this study. For ease of comparison,these are normalised to the peak of the functional derivativesfor each measurement set. Using Figure 3 the sensitivity canbe interpreted in two directions: Each row indicates whichpressure levels show high sensitivity to a given molecule ineach channel, and each column indicates how molecular sen-sitivity is distributed through pressure levels in a given set ofmeasurements. In all cases, the derivatives are negative be-cause the output of the forward model here is regarded as adisk-averaged flux ratio between the planet and star.

High sensitivity to the abundance of H2O is seen in allchannels, with the exception of the 1.93–2.16 µm channelsof HST/NICMOS, 4.5 µm channel of Spitzer IRAC, 9–14.5µm and 16 µm channels of the Spitzer IRS, in which regionsthe modelled radiance is dominated by CO2 absorption, asexplained below. The H2O functional derivatives all peak inthe ∼100–500 mbar region, showing that the measurementscan only constrain the H2O abundance in this altitude range.In contrast, the CO2 functional derivatives are divided intotwo separate pressure levels (peaks between 0.1–1 bar and0.1–1 mbar) as is clearly shown in the second row of Fig-ure 3. The HST/NICMOS channels between 1.45–2.15 µmare only sensitive to the CO2 abundance at altitudes below100 mbar whereas the Spitzer broadband photometry and IRSspectroscopy are sensitive to the CO2 in the 0.1–10 mbar re-gion as well. Despite this sensitivity to a range of altitudesfor CO2, a combination of these channels, however, may notdetermine CO2 abundance at both levels due to small sensi-tivity in the upper atmosphere (cf. Section 5.4). For CO, thismolecule can only be detected in three HST/NICMOS chan-nels in the range 2.33–2.45 µm at 100 mbar. The absorptionfeatures of CO seen in these HST/NICMOS channels havebeen extensively used to constrain its mixing ratio (S09 andMS09). The contribution functions for CH4 again all peak at∼100 mbar and have a detectable influence on a number ofchannels (i.e. Spitzer IRAC at 3.6 and 8 µm, IRS 5–9 µm,and HST/NICMOS 2.2–2.5 µm).

In summary, the functional derivatives indicate the altitudesshowing sensitivities, which help to constrain each molecu-lar abundance. The sensitivities of the molecules are mostlyclustered in the lower atmosphere (∼100 mbar), and, in par-ticular, CO2 shows an additional peak at ∼1 mbar. Thereforethe molecular abundances can be constrained from the deep

(a) T(p) - a priori shape


100

10-2

10-4

10-6

Pre

ssur

e (b

ar)

(b) T(p) - a priori root temp.


Figure 4. (a) Retrieved P-T profiles of the dayside HD 189733b from a rangeof diverse a priori profiles. Each line pattern used means: a priori P-Tprofiles (dashed), retrieved P-T profiles (solid) and their errors (dot-dashedand dotted). This plot shows the pressure range over which the P-T profileis retrievable from these measurements. (b) Retrieved P-T profiles from thesame a priori profile shape, but offset from each other with root temperaturesat 1600 K, 2000 K, and 2400 K at 10 bar.

pressure levels. Also, the spectrum is sensitive to the H2Oabundance over the broadest range and in the most channels.This implies that there is an inherent degeneracy between tem-peratures and H2O abundance in these datasets.

5.3. Retrieval of P-T profile5.3.1. The best-fit P-T profile

Previously P-T profiles of HD 189733b have been esti-mated based on theoretical models to generate model spec-tra, which are to be compared with observations. However,such models do not explicitly solve the inverse problem dur-ing the constraining process and thus it is unclear if the so-lutions are biased more towards theoretical expectations thanbeing driven by the measurements themselves. For this rea-son, we retrieve temperature using several differently shapeda priori profiles to show that the retrieved temperature con-verges to a unique profile in the altitude range covered by thecontribution functions. Because a retrieved P-T profile mayvary with the a priori, if it is biased, we look for an appro-priate a priori error and its vertical shape in order that a P-Tprofile can be retrieved with a static shape, irrespective of theshape of the a priori profile. Figure 4(a) presents the retrievedP-T profile and its error for a range of selected temperature apriori. For all cases, the P-T profiles share a common shapebetween 0.1 mbar and 1 bar, demonstrating the validity of thetemperature retrieval. It is shown that even with the simplestpossible assumption such as an isothermal temperature (blueline in Figure 4(a)), the measurements still produce a similarthermal profile with the other retrievals. As a further test, wetake an a priori structure from the retrieved profile in the pre-vious step, offset it by a temperature 400 K, and repeat thetemperature retrieval again. Figure 4(b) shows that the P-Tprofile is still sufficiently constrained by the measurements,even if there are large shifts of a priori at levels not coveredby the contribution functions, and, at these altitudes, the solu-tions relax back to their different a prioris.

As a result, we find that the temperature decreases adiabati-cally from 1900 K at 700 mbar to ∼1000 K at 100 mbar, then


becomes isothermal up to the upper atmosphere (∼1 mbar).These adiabatic and isothermal layers in the thermal struc-ture are dominant features of heat transfer by convection andradiative cooling, respectively. In comparison S09 claimed adecreasing temperature layer between 0.01 and 1 bar to modelthe HST/NICMOS measurements, making an adiabatic layer∼10 times thicker than our estimation, and theoretical mod-els also considered adiabatic layers for a troposphere model(Fortney et al. 2006; Burrows et al. 2008; Showman et al.2008). For the isothermal structure, Charbonneau et al. (2008)and Knutson et al. (2007) suggested that the warmed temper-ature (1000–1200 K) of the dayside hemisphere may be main-tained by an efficient energy re-distribution through the wholeplanet system, leading to a quasi-isothermal structure in theupper atmosphere (Showman et al. 2008).

In summary, the broad wavelength range on available mea-surements has provided a strong constraint on the vertical P-Tprofile (an adiabatic troposphere and isothermal stratosphere)without excessive sensitivity to the a priori assumptions.

5.3.2. Temperature degeneracy

In general, the best-fit P-T profile from the retrieval is anon-unique solution. This means that there is potentially alarge family of solutions for the P-T profile that could fit themeasured spectrum equally well within the same error range.In many retrievals, there may also exist cross-correlation, anindex to find alikeness between retrieval variables, with otherfitted quantities, indicated by covariances that are larger thanzero. As the set of the correlation, the covariance matrix isadvantageous because the matrix is computed as a part of theretrieval process and can be used in assessing the results at theend of retrieval. Therefore, the uncertainties can be estimatedby considering the degeneracy between the variables, whichis based on the cross-correlation analysis.

For the dayside spectrum of HD 189733b, the degener-acy between the molecular abundances and the P-T profileis thought to be significant at some pressure levels and band-passes (S09 and MS09), however, a detailed analysis of thesecorrelations has not previously been discussed. Here, weexamined the cross-correlation functions c(i, j) (i.e. the off-diagonal elements of the covariance matrix) that determinethe degree of degeneracy between elements i and j of themeasurement vector. By definition, |c(i, j)|=1.0 represents aperfect correlation between variable i and j, and according tothe general practice we consider that |c|=0.5 is a limitationfor independent retrievals of different variables. The profilesin Figure 5(a) show the vertical structure of cross-correlationfunctions between the molecular abundances and the temper-ature at different pressure levels. It can be seen that the P-Tprofile is significantly correlated with molecular abundancesat some levels, being most correlated with the H2O abundancebetween 200–400 mbar and with CO2 for altitudes above the30 mbar pressure level.

To determine the degeneracy of temperature from Fig-ure 5(a), we performed multiple retrievals where individualmolecular abundances were fixed at a particular value and allother variables retrieved. We then assessed the goodness-of-fit (χ2) of the solution as a function of the set molecular abun-dance, compared with the minimum goodness-of-fit (χ2

min) ofthe best-fit retrieval, and determined the range of temperaturesfor which the change ∆χ2 = χ2 −χ2

min was less than 0.5, 1.0,and 2.0, respectively.

Figure 5(b) shows the ranges in the retrieved P-T profile

(a)cross-correlation

-0.5 0.0 0.5c(i,j)

100

10-1

10-2

10-3

Pre

ssur

e (b

ar)

(b)Retrieved T(p)-All


(c)Retrieved T(p)-H2O


100

10-1

10-2

10-3

Pre

ssur

e (b

ar)

(d)Retrieved T(p)-CO2


(e)Retrieved T(p)-CO


100

10-1

10-2

10-3

Pre

ssur

e (b

ar)

(f)Retrieved T(p)-CH4


Figure 5. (a) The vertical structure of the cross-correlation functions. Thehigh correlation by H2O and CO2 dominates the degeneracy of temperature atmost pressures. (b-f) The retrieved P-T profiles of the dayside HD 189733vwith various mixing ratios are presented with ∆χ2 and the colours demon-strate ∆χ2 <0.5 (red), <1.0 (green), and <2.0 (blue), respectively. As aresult, the large uncertainties of P-T profile are broadly distributed at thelow- and mid-atmosphere. On the other hand, narrow uncertainty at 3 mbarimplies an isothermal structure in the upper atmosphere of the dayside HD189733b.


for different values of ∆χ2 due to the molecular degener-acy. At each pressure level, allowed temperature ranges aredetermined by varying the molecular abundance with whichtemperature is most strongly correlated. The temperature un-certainties for ∆χ2 < 1.0 calculated in this way are 590 K at700 mbar, 600 K at 200 mbar, and 80 K at 3 mbar. As de-scribed on the basis of cross-correlation, the temperature un-certainties at altitudes below 10 mbar are caused mainly dueto the degeneracy with the H2O abundance and those at alti-tudes above 10 mbar are degenerate with the CO2 abundance.On the other hand, the degeneracies between temperature andthe abundances for CO and CH4 are small. Therefore it can beseen that although some uncertainty in the P-T profile existsdue to degeneracy, the small degree of degeneracy at lowerpressures supports our conclusion that the atmosphere of HD189733b has an isothermal structure at the upper atmosphere.

5.4. Retrieval of molecular abundancesIn addition to the temperature retrieval, molecular abun-

dances may also be retrieved from secondary eclipse mea-surements of HD 189733b. As stated earlier, each gas con-sidered is assumed to be well-mixed in our forward modelatmosphere giving a constant mole fraction with height. How-ever, we know that the functional derivatives are only sensi-tive to a limited pressure range and thus our retrieved abun-dances represent the mean concentrations at the pressure lev-els which show the highest sensitivity. The best-fit molecularabundances are determined from the retrieval accompanyingthe best-fit P-T profile given in Section 5.3 and we find thatthose are 4.3×10−4 (H2O), 2.5×10−3 (CO2), 2.0×10−3 (CO),and 1.6×10−6 (CH4), respectively. Additionally, the C/O ra-tio of HD 189733b is constrained as close as the solar value(∼0.6).

By looking at the covariance of our retrieved solution wefind that the cross-correlation between the different molecularabundances is rather small (c < 0.1) for all the combinationsof the molecules. However, there remains some degeneracydue to the main correlation with temperature and to quantifythis we calculated ∆χ2 for each gas by changing the abun-dance of a molecule and retrieving all other parameters in-cluding temperature. The variation of ∆χ2 with abundancefor all four gases is shown in Figure 6. We find that the follow-ing range of abundances have ∆χ2 < 0.5: (3–100)×10−5 forH2O, (3–200)×10−4 for CO2, <2×10−1 for CO, and <3×10−5

for CH4, respectively. The constrained abundances for ∆χ2 <1.0 and 2.0 are also shown in Table 1 and are compared withthe results of a thermo- and photo-chemistry model (Line etal. 2010), and previous retrievals (S09 and MS09). It is foundthat we constrain only the upper bound of the mixing ratio forCO and CH4. This is because CO and CH4 contributions tothe emission spectrum appears in only few bandpasses, andtheir abundances show low sensitivity over planet-stellar fluxratio as shown in Figure 3. Consequently, variation of thesetwo gases leads to a tiny change in ∆χ2 where the abundancesare lower than the best-fit estimation. We conclude that it isnot possible to constrain the abundances of CO and CH4 basedon given datasets alone as previous studies have attmepted.

All channels of Spitzer and HST are capable of constrain-ing the H2O mixing ratio as presented in the functional deriva-tives, and the constrained H2O is consistent with other esti-mations. For CO, the strongest constraints are taken from theHST/NICMOS data as previously mentioned before (MS09)and the high upper limit of the CO abundance in this study

Molecular Degeneracy

0

0.5

1

2

10-7 10-6 10-5 10-4 10-3 10-2 10-1

Volume Mixing Ratio

H2O

CO2

CO

CH4

Figure 6. The degeneracy ranges of the molecular mixing ratios for H2O,CO2, CO, and CH4. Each line shows resultant reduced χ2 with respectto given abundances. The ∆χ2 constrains the uncertainties of the molecu-lar abundances which are ranged around the best-fitted abundance of H2O(4.3×10−4), CO2 (2.5×10−3), CO (2.0×10−3), and CH4(1.6×10−6), respec-tively. Lower bounds of CO and CH4 uncertainties are unconstrained becauseof their low contribution to the spectrum.

can include all other estimations. Relatively low abundance ofCH4 is estimated in all model atmospheres in Table 4.2 exceptfor a large amount (10−2) model derived from the Spitzer IRSspectroscopy at 7.6 µm (MS09), which is not consistent withthis study. The derived abundance of CO2 (3–150×10−4) is2–3 orders of magnitude larger than previous studies by Lineet al. (2010) (∼10−7–∼10−5), S09 (10−7–10−6), and MS09 (us-ing Spitzer photometry, 7–700×10−7) for all ∆χ2 ranges andthus our retrieved CO2 abundance is only consistent with theHST/NICMOS estimation by MS09. Although the flux ra-tios at the IRAC 4.5 and 16 µm channels can be explainedby either high or low CO2 abundance, and, however, theHST/NICMOS channels constrain this to be a higher abun-dance of CO2 (∼10−3).

Here, we test the contribution of CO2 abundance in theupper atmosphere of HD 189733b by comparing the best-fitspectra, each retrieved from low and high CO2 abundances inthe upper atmosphere. Instead of using a well-mixed abun-dance of CO2 with altitude, we allowed the abundance to varywith height. The CO2 mixing ratio is fixed at a certain mixingratio up to a pre-defined deep pressure level, and declines lin-early into the upper atmosphere with a slope being determinedby the fractional scale height (the ratio of the scale height ofthe gas to the scale height of the atmosphere). This allowsus to demonstrate the effect of different mixing ratios withheight, but avoiding the need to introduce a complete verticalprofile of CO2 (and hence a large number of additional param-eters in our state vector). In Figure 7, the retrieval with thenew CO2 vertical profile that decreases from 2.5×10−3 at 100mbar to 3.3×10−7 at 0.1 mbar, produces a very similar spec-trum to the well-mixed high-CO2 case, leading to an insignifi-cant improvement in terms of the χ2. This is because the CO2sensitivity at the Spitzer bandpasses is too low to adequatelyconstrain its abundance in the upper atmosphere (0.1–1 mbar)despite having sensitivity here whereas the strong constraintsof the HST/NICMOS and Spitzer IRS channels between 9–


Table 1Estimated and retrieved mixing ratios and C/O in the dayside of HD 189733b.

H2O (10−4) CO2 (10−4) CO (10−4) CH4 (10−4) C/O Data Source

Line et al. 20106–13 0.0047–0.016 2–9 0.0026–6.758 Thermoschemistry

∼6.36 0.004–∼0.1 ∼8.4 ∼0.4 Photochemistry

Swain et al. 2009 0.1–1 0.001–0.01 1–3 <0.001 0.5–1 HST/NICMOS

Madhusudhan& Seager 2009

0.01–1000 ... ... <100 ... Spitzer IRS

0.1–10 0.007–0.7 ... <0.02 0.007–1 Spitzer photometry

∼1 ∼7 2–200 <0.06 0.5–1 HST/NICMOS

This study

Best-fit value

4.3 25 20 0.016 0.6 All measurements

Possible fit range

0.3–30 3–150 <2000 <0.3 0.5–1 ∆χ2 <0.5

0.07–70 1–300 ... <0.7 0.4–1 ∆χ2 <1.0

0.01–300 0.3–800 ... <2 0.2–1 ∆χ2 <2.0

16 µm enable constraining the abundance in the lower atmo-sphere (∼100 mbar). In contrast, a low abundance of CO2(10−7) with a well-mixed vertical profile is unable to producea spectrum that fits with better χ2. Therefore it is clear thata high amount of CO2 (∼10−3) exists at ∼100 mbar but thatthe abundance at 0.1–1 mbar is unconstrained by current mea-surements. In other words, the proposed abundance of CO2 inthis study represents only the value at ∼100 mbar, where thehighest sensitivity is shown. As suggested in MS09, if weonly consider the mean mixing ratio of CO2 over the entirepressure levels rather than only few layers holding high con-centrations, the CO2 profile with its low abundance at highaltitude and a high abundance at low altitude would then givea consistent amount of CO2 (∼10−7–∼10−6) as suggested bythe chemistry models and S09.

6. DISCUSSION AND CONCLUSIONS

The retrieved thermal structure is a useful tool for fur-ther understanding of dynamic processes in the atmosphere.As a description of atmospheric stability, the lapse rate (Γ =dT/dz), the rate of change of temperature with respect to theheight, is directly evaluated from the P-T profile by taking itsfirst derivative (Figure 8). An increase in the lapse rate indi-cates that there is an adiabatic layer up to ∼100 mbar (∼1500km above from the level of 10 bar), and the lapse rate tends toremain at zero above ∼40 mbar (∼1700 km) where this pres-sure level indicates the boundary of an isothermal expansioncondition. Moreover, the dry adiabatic lapse rate (DALR) in-dicates both the stability of the atmosphere higher altitudesthan ∼350 mbar (∼1200 km) and a sub-adiabatic layer, beingextended up to 40 mbar.

The NEMESIS algorithm uses two novel tools for an effi-cient retrieval of the atmospheric properties: a non-linear op-timal estimation scheme and a fast forward model taking ad-vantage of the correlated-k approximation and k-distributiontables. The optimal estimation retrievals permit an exten-

sion of previous results and the formal quantification of er-rors and uncertainties. The functional derivatives, which areanalytically computed, enable us to analyse the vertical con-tribution of the constituents in each channel. We have shownthat the current set of observations of the dayside spectrumof HD 189733b are enough to constrain the thermal struc-ture at some pressure levels and the mixing ratios for H2O,CO2, CO, and CH4. Furthermore, the ability to calculate thecross-correlation function allows us to assess the degeneraciesbetween the various modelled parameters in our state vector.

With the retrieval method presented here, we derive threemajor findings from the measurements of the dayside of HD189733b. Firstly, the retrieved thermal structure of the day-side HD 189733b shows that the constraints in the NIR andMIR lead to an adiabatically decreasing temperature between0.1–1 bar. In addition, strong constraints from the SpitzerIRS measurements in the 9–16 µm range suggest that thetemperature structure in the mid and upper atmosphere (1–100 mbar) seems to be isothermal with a uniform temperature(∼1000 K). One explanation for the isothermal layer is thatsuper-rotating jets blowing from night- to dayside play an crit-ical role of an efficient energy re-distribution over the wholeplanet and it may be responsible for maintaining the high tem-perature in the upper atmosphere (Knutson et al. 2007; Show-man et al. 2008).

Secondly, the functional derivatives for the molecules showthat the measurements at the NIR (1.45–2.1 µm), MIR (4.5µm), and FIR (9–16 µm) spectral ranges independently con-strain CO2 abundance at ∼100 mbar and 0.1–10 mbar. Itsabundance in the lower atmosphere is responsible for thespectral flatness at 9–16 µm, where previous studies assumedH2O to be the dominant consituent. We determine the verti-cal sensitivity of CO2 abundance by comparing the retrievalswith abundant (2.5×10−3) and scarce CO2 (10−7), and height-dependant CO2 profile. The functional derivatives for CO2show low sensitivity at 0.1–1 mbar, which means that, at the


Synthetic Spectra of Day-side HD 189733b - CO2

best-fit with q[CO2]=2.5X10-3

best-fit with q[CO2]=1X10-7

best-fit with q[CO2]=2.5X10-3 @ 100 mbarq[CO2]=3.3X10-7 @ 0.1 mbar

1 10Wavelength (um)

0

2

4

6

8

Fpl

anet/F

star (

X10

-3)

1.6 1.8 2.0 2.2 2.4Wavelength (um)

0.0

0.2

0.4

0.6

0.8

1.0

Fpl

anet/F

star (

X10

-3)

Figure 7. Synthetic emission spectra of the dayside HD 189733b with differ-ent CO2 abundances. The spectrum in black, orange, and cyan colour repre-sents the best-fit spectrum with fixed CO2 amount of 2.5×10−3 and 1×10−7,and different CO2 amount of 2.5×10−3 at 100 mbar and 3.3×10−7 at 0.1mbar, respectively. High and low CO2 abundances at 100 and 0.1 mbar re-trieve a consistent spectrum with the best-fit one.

T(p)

500 1000 1500 2000Temperature (K)

100

10-1

10-2

10-3

Pre

ssur

e (b

ar)

Lapse Rate

-2.0 -1.5 -1.0 -0.5 0.0 0.5Lapse Rate (K/km)

100

10-1

10-2

10-3

Pre

ssur

e (b

ar)

Figure 8. Disk-averaged dayside lapse rate of HD 189733b (right) is demon-strated by calculating the derivatives of P-T profile. The given pressures cor-respond to the levels covered by the contribution functions. Dry adiabaticlapse rate (DALR) that displayed in grey colour is assumed to be constantover the given temperature range.

upper atmosphere, the mixing ratio of CO2 remains uncon-strained and the spectrum looks the same irrespective of thechosen value of CO2 at this pressure level. In contrast, highsensitivity of CO2 at the lower atmosphere (100 mbar) indi-cates high abundance of CO2 at this pressure level.

Thirdly, we quantify the degeneracies between the atmo-spheric properties using the cross-correlation functions. Thecorrelations between molecular abundances and temperatureexhibit sizable degeneracies, in particular, between tempera-ture and H2O abundance at 300 mbar. We determine the tem-perature uncertainty at different pressure levels by calculatingthe statistics of the retrievals with the variation of each molec-ular mixing ratio and, as a result, this confirms the isother-mal structure in the stratosphere. In same way, the molecularabundances are also constrained by demonstrating that the un-certainty on retrieved parameters, based on the available mea-surements and the degeneracy with the temperature profile ismuch larger than previous studies have suggested. Therefore,additional data is clearly required to break the degeneracy be-tween temperature and compositions, particularly H2O. Aslong as the number of retrieval variables for the molecularabundance are kept to a small number, the cross-correlationfunctions are not significant between molecules. If we wereforced to use a more detailed representation of the verticaldistributions of the gases, then the degeneracies would growmore substantial.

This study has shown the benefit of considering a widespectral range for breaking the degeneracy between differentatmospheric parameters. By constraining the overall shape ofthe infrared spectrum, the HST and Spitzer secondary eclipsedata allow us to evaluate the vertical temperature structure andmolecular abundances. Studies that focus on smaller wave-length ranges or fewer data points are subject to broader un-certainties than are currently being presented in the literature.Future work will permit an extension of this technique intocross-comparison with transmission spectroscopy, includingthe visible range (alkali metals, metal oxides, and clouds andhazes), at the terminator regions of this planet.

We are grateful to James Cho, Giovanna Tinetti, SuzanneAigrain for a discussion. This study is conducted as ... .

REFERENCES

Beaulieu, J.P., Carey, S., Ribas, I. & Tinetti, G. 2008, ApJ, 677, 1343Borysow, A., Frommhold, L., & Moraldi, M. 1989, ApJ, 336, 495Borysow, A. and Frommhold, L. 1989, ApJ, 341, 549Borysow, A. and Frommhold, L. 1990, ApJ, 348, L41Borysow, A., Jorgensen, U.G., & Zheng, C. 1997, A&A, 324, 185Borysow, A. 2002, A&A, 390, 779Brown, T. M. 2001, ApJ, 553, 1006Burrows, A., Budaj, J., & Hubeny, I. 2008, ApJ, 678, 1436Burrows, A. & Sharp, C. M. 1999, ApJ, 512, 843Charbonneau, D., Knutson, H.A., Barman, T., Allen, L.E., Mayor, M.,

Megeath, S.T., Queloz, D., & Udry, S. 2008, ApJ, 686, 1341Deming, D., Harrington, J., Seager, S., & Richardson, L.J. 2006, ApJ, 644,

560Desert, J.-M., Lecavelier des Etangs, A., Hebrard, G., Sing, D. K.,

Ehrenreich, D., Ferlet, R., & Vidal-Madjar, A. 2009, ApJ, 699, 478Fortney, J.J., Saumon, D., Marley, M.S., Looders, K., & Freedman, R.S.

2006, ApJ, 642, 495Fortney, J.J., & Marley, M.S. 2007, ApJ, 666, L45Fortney, J.J., Shabram, M., Showman, A.P., Lian, Y., Freedman, R.S.,

Marley, M.S., & Lewis, N.K. 2010, ApJ, 709, 1396Gibson, N.P., Pont, F., & Aigrain, S. 2011,MNRAS, 411, 2199Goody, R.M., & Yung, Y.L. 1989, Atmospheric radiation : theoretical basis,

2nd ed., by Richard M. Goody and Y.L. Yung. New York, NY: OxfordUniversity Press, 1989,


Grillmair, C.J., et al. 2008, Nature, 456, 767Irwin, P.G.J., et al. 2008, J. Quant. Spec. Radiat. Transf., 109, 1136Knutson, H.A., et al. 2007, Nature, 447, 183Knutson, H.A., Charbonneau, D., Allen, L. E., Burrows, A., & Megeath,

S.T. 2008, ApJ, 673, 526Knutson, H.A., et al. 2009, ApJ, 690, 822Lacis, A.A., & Oinas, V. 1991, J. Geophys. Res., 96, 9027Levenberg, K. 1944, Quart. Appl. Math. 2, 164Line, M.R., Liang, M.C., & Yung, Y.L. 2010, ApJ, 717, 496Madhusudhan, N., and Seager, S. 2009, ApJ, 707, 24Madhusudhan, N., and Seager, S. 2010, ApJ, 725, 261Madhusudhan, N., and Seager, S. 2011, arXiv:1004.5121Madhusudhan, N., et al. 2011, Nature, 469, 64Marquardt, D. 1963, SIAM J. Appl. Math., 11, 431Pont, F., Knutson, H., Gilliland, R.L., Moutou, C., & Charbonneau, D. 2008,

MNRAS, 385, 109Redfield, S., Endl, M., Cochran, W.D., & Koesterke, L. 2008, ApJ, 673, L87C. D. Rodgers, 2000, Inverse Methods for Atmospheric Sounding: theory

and practice. Singapore: World ScientificRothman, L.S., Wattson, R.B., Gamache, R., Schroeder, J.W., & McCann,

A. 1995, Proc. SPIE, 2471, 105Rothman, L.S., et al. 2010, J. Quant. Spec. Radiat. Transf., 111, 2139Seager, S and Deming, D. 2010, ARA&A, 48, 631Shabram, M., Fortney, J.J., Greene, T.P., Freedman, R.S. 2011, ApJ, 727, 65

Showman, A.P., Cooper, C.S., Fortney, J.J. & Marley, M.S. 2008, ApJ, 682,559

Sing, D.K., Desert, J.-M., Lecavelier Des Etangs, A., Ballester, G.E.,Vidal-Madjar, A., Parmentier, V., Hebrard, G.a , & Henry, G.W., (2009),A&A 505, 891

Sing, D.K., Pont, F., Aigrain, S., Charbonneau, D., Desert, J.-M., Gibson,N., Gilliland, R., Hayek, W., Henry, G., Knutson, H., Lecavelier desEtangs, A., Mazeh, T., & Tal-Or, L. 2011, arXiv:1103.0026

Stevenson, K. et al. 2010. Nature, 464, 1161Swain, M.R., Vasisht, G., & Tinetti, G. 2008, Nature, 452, 329Swain, M.R., Vasisht, G., Tinetti, G., Bouwman, J., Chen, P., Yung, Y.,

Deming, D., & Deroo, P. 2009, ApJ, 690, L114Swain, M.R., et al. 2010, Nature, 463, 637Tashkun, S.A., Perevalov, V.I., Teffo, J.-L., Bykov, A. D., & Lavrentieva,

N.N. 2003, J. Quant. Spec. Radiat. Transf., 82, 165Thatte, A., Deroo, P., & Swain, M.R. 2010, A&A, 523, A35Tinetti, G., et al. 2007, Nature, 448, 169Tinetti, G., et al. 2007, ApJ, 654, L99Wenger, C., and Champion, J.P. 1998, J. Quant. Spec. Radiat. Transf., 59,

471Zheng. C. and Borysow, A. 1995, ApJ, 441, 960

Bibliography

Agol, E., et al. 2009, Proceedings of the International Astronomical Union, IAU Symposium, 253, 209

Alonso, R., et al. 2008, A&A, 487, L5

Ballard, S., et al. 2010, PASP , 122, 1341

Barber, R. J., et al. 2006, MNRAS, 368, 1087

Barman, T. 2007, ApJ , 661, L191

Bean, J. L., et al. 2010, Nature, 731, 16

Beaulieu, J. P., et al. 2008, ApJ , 677, 1343

Beaulieu, J. P., et al. 2010, MNRAS, 409, 963

Beaulieu, J. P., et al. 2011, ApJ , 731, 16

Brown, T. M. 2001, ApJ , 553, 1006

Brown, L. R., et al. 1997, BAAS, 29, 1010

Borysow, A., et al. 1989, ApJ , 336, 495

Borysow, A. and Frommhold, L. 1989, ApJ , 341, 549

Borysow, A. and Frommhold, L. 1990, ApJ , 348, L41

Borysow, A., Jorgensen, U.G., & Zheng, C. 1997, A&A, 324, 185

Borysow, A. 2002, A&A, 390, 779

Borysow, A., et al. 2003, in ASP Conf. Ser. 288, Stellar Atmosphere Modeling, ed. I. Hubeny, D. Mihalas, &

K. Werner (San Fransisco: ASP), 352

Borucki, W. J., et al. 2011, ApJ , submitted (arXiv:1102.0541)

Bouchy, F., et al. 2005, A&A, 444, L15

Burrows, A. and Sharp, C. M. 1999, ApJ , 512, 843

Burrows, A. 2007, ApJ , 668, L171

Burrows, A., Budaj, J., & Hubeny, I. 2008, ApJ , 678, 1436

73

Burrows, A., et al., 2010, ApJ , 719, 341

Butler, R. P., et al. 2004, ApJ , 617, 580

Caceres, C., et al. 2009, A&A, 507, 481

Charbonneau, D., et al. 2002, ApJ , 568, 377



Charbonneau, D., et al. 2009, Nature, 462, 891

Chauvin, G., et al. 2004, A&A, 425, L29

Croll, B. 2010, ApJ , 718, 920

Croll, B. 2011, ApJ , in press, arXiv:1104.1011

Crossfield, I. J. M., et al. 2010, ApJ , 723, 1436

Cunto, W. and Mendoza, C. 1992, Rev. Mex. Astron. Astrofis., 23, 107

Cunto, W., et al. 1993, A&A, 275, L5

Curtis, A. R. 1952, QJRMS, 78, 165

Deming, D., Harrington, J., Seager S. & Richardson, L.J. 2006, ApJ , 644, 560

Desert, J. -M., et al. 2008, A&A, 492, 585

Desert, J. -M., et al. 2009, ApJ , 699, 478

Desert, J. -M., et al. 2011, ApJ , 731, L40

Fortney, J. J., Saumon, D., Marley, M. S., Looders, K., & Freedman, R. S. 2006, ApJ , 642, 495

Fortney, J. J., and Marley, M. S. 2007, ApJL, 666, L45

Fortney, J. J., et al. 2008, ApJ , 678, 1419

Fortney, J. J., et al. 2010, ApJ , 709, 1396

Fuhr, J. R. and Wiese, W. L. Improved transition probabilities were taken for Na through Ca, when available,

from, Atomic Transition Probabilities, published in the CRC Handbook of Chemistry and Physics, 79th

Edition, edited by D.R. Lide (CRC Press, Inc., Boca Raton, FL, 1998).

Gibson, N. P., Pont, F., & Aigrain, S. 2011, MNRAS, 411, 2199

Godson, W. L. 1955, J. Meteorol., 12, 123

Goody, R. M., and Yung, Y. L. 1989, Atmospheric radiation : theoretical basis, 2nd ed., by Richard M. Goody

and Y.L. Yung. New York, NY: Oxford University Press, 1989,

74

Grillmair, C. J., et al. 2008, Nature, 456, 767

Huber and Herzberg, 1979, Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules

(New York: Van Nostrand Reinhold)

Irwin, P. G. J., et al. 2008, JQSRT , 109, 1136

Jacquinet-Husson, N., et al. GEISA-08 Spectroscopic Database New Edition : Evaluation for IASI Hyperspec-

tral Remote Sensing Applications. ASSFTS14 IFAC-CNR, Sesto, Fiorentino, Italia, 6-8 may 2009.

Jørgensen, 1996, IAU Symp. 178, Molecules in Astrophysics: Probes and Processes, ed. E. F. Van Dishoeck

(Dordrecht: Kluwer), 441

Karkoschka, E. 1994, Icarus, 111, 174

Knutson, H. A., et al. 2007, Nature, 447, 183

Knutson, H. A., et al. 2008, ApJ , 673, 526

Knutson, H. A., et al. 2009, ApJ , 690, 822

Knutson, H. A., et al. 2011, ApJ , submitted (arXiv:1104.2901)

Kupka, F. G., et al. 2000, BalticAstronomy, 9, 590

Kurucz, R. 2006, Stellar Model and Associated Spectra (http://kurucz.harvard.edu/grids.html)

Lacis, A. A., and Oinas, V. 1991, JGR, 96, 9027

Levenberg, K. 1944, Quart. Appl. Math. 2, 164

Liang, M. -C., Parkinson, C. D., Lee, A. Y.-T., Yung, Y. L., and Seager, S. 2003, ApJ , 596, L247

Liang, M. -C., Seager, S., Parkinson, C. D., Lee, A. Y.-T., and Yung, Y. L. 2004, ApJ , 605, L61

Line, M. R., Liang, M. C., & Yung, Y. L. 2010, ApJ , 717, 496

Lodders, K. 1999, ApJ , 519, 793

Madhusudhan, N., and Seager, S. 2009, ApJ , 707, 24

Madhusudhan, N., and Seager, S. 2010, ApJ , 725, 261

Madhusudhan, N., and Seager, S. 2011, arXiv:1004.5121

Madhusudhan, N., et al. 2011, Nature, 469, 64

Marois, C., et al. 2008, Science, 322, 1348

Marquardt, D. 1963, SIAM J . Appl. Math., 11, 431

Mayor, M. and Queloz, D. 1995, Nature, 378, 355

Mayor, M., et al. 2009, A&A, accepted

75

Plez, B. 1998, A&A, 337, 495

Pont, F., et al. 2008, MNRAS, 385, 109

Pont, F., et al. 2008, MNRAS, 393, L6

Nassar, R. and Bernath, P. 2003, JQSRT , 82, 279

Redfield, S., et al. 2008, ApJ , 673, 87

Richardson, L. J., et al. 2006, ApJ , 649, 1043

Rodgers, C. D. 2000, Inverse Methods for Atmospheric Sounding: theory and practice. Singapore: World

Scientific

Rothman, L. S., et al. 1995, Proc. Soc. Photo Optical Instrumentation Engineers, 2471, 105-111

Rothman, L. S., et al. 2008, JQSRT , 110, 533

Rothman, L. S., et al. 2010, JQSRT , 111, 2139

Sauval, A. J. and Tatum, J. B. 1984, ApJS, 56, 193

Seager, S. and Sasselov, D. D. 2000, ApJ , 537, 916

S. Seager, 2008, Exoplanet Transit Spectroscopy and Photometry, Space Sci. Rev., 135, 345

Shabram, M., Fortney, J. J., Greene, T. P., Freedman, R. S. 2011, ApJ , 727, 65

Sharp, C. M. and Burrows, A. 2007, ApJS, 168, 140

Showman, A. P., Cooper, C. S., Fortney, J. J. & Marley, M. S. 2008, ApJ , 682, 559

Sing, D. K., et al. 2009, A&A, 505, 891

Sing, D. K., et al. 2009, A&A, 505, 2

Sing, D. K., et al. 2011, arXiv:1103.0026

Snellen I. A. G., et al. 2010, Nature, 465, 1049

Stevenson, K., et al. 2010. Nature, 464, 1161

Strong, K., et al. 1993, J . Quant. Spectrosc. Radiat. Transfer, 50, 363

Swain, M. R., Vasisht, G., & Tinetti, G. 2008, Nature, 452, 329

Swain, M. R., et al. 2008, ApJ , 674, 482

Swain, M. R., et al. 2009, ApJ , 690, L114

Swain, M. R., et al. 2009, ApJ , 704, 1616

Swain, M. R., et al. 2010, Nature, 463, 637

76

Tashkun, S. A., Perevalov, V. I., Teffo, J. -L., Bykov, A. -D., & Lavrentieva, N. N. 2003, JQSRT , 82, 165

Thatte, A., Deroo, P., & Swain, M.R. 2010, AAP , 523, A35

Tinetti, G., et al. 2007, Nature, 448, 169

Tinetti, G., et al. 2007, ApJ , 654, L99

Vidal-Madjar, A., et al. 2003, Nature, 6928, 143

Vidal-Madjar, A., et al. 2004, ApJ , 604, L69

Wenger, C., and Champion, J.P. 1998, JQSRT , 59, 471

Zheng, C. and Borysow, A. 1995, ApJ , 441, 960

77

retrieval of atmosphere structure and composition of ...€¦ · retrieval of atmosphere structure...

Documents