A global analysis of Spitzer and new HARPS data confirms the loneliness and metal-richness of GJ 436 b
A. A. Lanotte, M. Gillon, B.-O. Demory, J. J. Fortney, N. Astudillo, X. Bonfils, P. Magain, X. Delfosse, T. Forveille, C. Lovis, M. Mayor, V. Neves, F. Pepe, D. Queloz, N. Santos, S. Udry
AAstronomy & Astrophysics manuscript no. GJ436b-Lanotteetal c (cid:13)
ESO 2018September 5, 2018
A global analysis of
Spitzer and new HARPS data confirms theloneliness and metal-richness of GJ 436 b ∗ A. A. Lanotte , M. Gillon , B.-O. Demory , , J. J. Fortney , N. Astudillo , X. Bonfils , P. Magain , X. Delfosse , T.Forveille , C. Lovis , M. Mayor , V. Neves , , , F. Pepe , D. Queloz , , N. Santos , , and S. Udry Institut d’Astrophysique et de G´eophysique (Bˆat. B5c), Universit´e de Li`ege, All´ee du 6 Aoˆut, 17, B-4000 Li`ege, Belgium.e-mail: [email protected] Department of Earth, Atmospheric and Planetary Sciences, Department of Physics, Massachusetts Institute of Technology, 77Massachusetts Ave., Cambridge, MA 02139, USA Cavendish Laboratory, J J Thomson Avenue, Cambridge, CB3 0HE, UK Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA UJF-Grenoble 1 / CNRS-INSU, Institut de Plan´etologie et d’Astrophysique de Grenoble (IPAG) UMR 5274, 38041 Grenoble, France Observatoire de Gen`eve, 51 Ch. des Maillettes, 1290 Sauverny, Switzerland Departamento de F´ısica, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, RN, Brazil Centro de Astrof´ısica, Universidade do Porto, Rua das Estrelas, 4150-762 Porto, Portugal Departamento de F´ısica e Astronomia, Faculdade de Ciˆencias, Universidade do Porto, PortugalReceived ??, 2014; accepted ??, ??
ABSTRACT
Context.
GJ 436b is one of the few transiting warm Neptunes for which a detailed characterisation of the atmosphere is possible,whereas its non-negligible orbital eccentricity calls for further investigation. Independent analyses of several individual datasetsobtained with
Spitzer have led to contradicting results attributed to the di ff erent techniques used to treat the instrumental e ff ects. Aims.
We aim at investigating these previous controversial results and developing our knowledge of the system based on the full
Spitzer photometry dataset combined with new Doppler measurements obtained with the HARPS spectrograph. We also want tosearch for additional planets.
Methods.
We optimise aperture photometry techniques and the photometric deconvolution algorithm DECPHOT to improve the datareduction of the
Spitzer photometry spanning wavelengths from 3-24 µ m. Adding the high precision HARPS radial velocity data, weundertake a Bayesian global analysis of the system considering both instrumental and stellar e ff ects on the flux variation. Results.
We present a refined radius estimate of R P = ± ⊕ , mass M P = ± ⊕ and eccentricity e = ± µ m that led to divergent results on the occultation depthmeasurement is spurious. We obtain occultation depths at 3.6, 5.8, and 8.0 µ m that are shallower than in previous works, in particularat 3.6 µ m. However, these depths still appear consistent with a metal-rich atmosphere depleted in methane and enhanced in CO / CO2,although perhaps less than previously thought. We could not detect a significant orbital modulation in the 8 µ m phase curve. We findno evidence for a potential planetary companion, stellar activity, nor for a stellar spin-orbit misalignment. Conclusions.
Recent theoretical models invoking high metallicity atmospheres for warm Neptunes are a reasonable match to ourresults, but we encourage new modelling e ff orts based on our revised data. Future observations covering a wide wavelength range ofGJ 436b and other Neptune-class exoplanets will further illuminate their atmosphere properties, whilst future accurate radial velocitymeasurements might explain the eccentricity. Key words.
Techniques: photometric – techniques: radial velocities – stars: individual: GJ436 – planetary system - infrared: general
1. Introduction
More than one thousand extrasolar planets have been discoveredso far, most of them by the radial velocity (RV) and transit meth-ods. Transiting planets provide us with a wealth of informationon their structure and atmospheric properties (e.g., Winn 2010a;Seager & Deming 2010; Madhusudhan et al. 2014). During thetransit, the fraction of the stellar radiation transmitted throughthe planet’s atmospheric limb can be measured at di ff erent wave-lengths (Charbonneau et al. 2002) to deduce the absorption spec-trum of the planetary terminator. The occultation, i.e., the disap-pearance of the exoplanet behind its host star, enables the mea-surement of the dayside flux of the planet by spectroscopy and ∗ Based on observations made with the HARPS spectrograph on the3.6-m ESO telescope at the ESO La Silla Observatory, Chile. photometry (e.g., Deming et al. 2009). Because of signal-to-noise ratio (SNRs) limitations, most of the results in this fieldhave been obtained by the photometric monitoring of multi-ple occultations in di ff erent broadband filters (e.g., Charbonneauet al. 2005; Deming et al. 2005). Occultation spectrophotometryalso yields strong constraints on the planet’s orbit (e.g., Campoet al. 2011).The bulk of the first measurements concerning exoplane-tary atmospheres were gathered by the Spitzer Space Telescope (Werner et al. 2004).
Spitzer was equipped with an 85-cmdiameter telescope and three instruments to provide imagingand spectroscopic capabilities from 3.6 to 160 µ m. These in-struments are the Infrared Array Camera (IRAC, Fazio et al.2004), the Infrared Spectrograph (IRS, Houck et al. 2004), andthe Multiband Imaging Photometer (MIPS, Rieke et al. 2004). a r X i v : . [ a s t r o - ph . E P ] S e p anotte A. A. et al: Global analysis of GJ 436 Spitzer and new HARPS data
Spitzer data are unique thanks to their large infrared wavelengthrange. It was fully operational from 2003 to 2009. It has beenin the so-called Warm mission since its cryogen was exhaustedin May 2009, so that only two channels in the near-infrared (3.6and 4.5 µ m) are still operating. While ground-based facilities arenow able to measure the thermal emission of some highly irra-diated planets in the near-infrared (e.g., Gillon et al. 2009; Crollet al. 2011; Bean et al. 2013), we have to wait for future space-based facilities like the James Webb Space Telescope (Gardneret al. 2006) to complete these data at longer wavelengths.Among the transiting extrasolar planets, GJ 436b is one ofthe few low-mass planets orbiting a star which is small andnearby enough to allow an advanced characterisation. It is a ∼ ∼
10 pc) M2.5-type dwarf (Butler et al. 2004). Its transitwas originally detected by Gillon et al. (2007c) so that GJ 436bbecame the first confirmed warm Neptune.
Spitzer was then usedto accurately measure its radius. Its low density suggests an en-velope rich in H and He (Gillon et al. 2007a; Deming et al.2007). This exoplanet is even more interesting because it showsa significant eccentricity that appears to disagree with tidal cir-cularisation timescales and with the age of the system for anisolated planet (e.g. Demory et al. 2007). Di ff erent authors triedto explain this with di ff erent mechanisms, usually with the pres-ence of a companion (e.g., Maness et al. 2007; Deming et al.2007; Alonso et al. 2008; Ribas et al. 2008, 2009; C´aceres et al.2009). Beust et al. (2012) summarise those di ff erent explana-tions and propose an original solution based on a Kozai mecha-nism (Kozai 1962) assuming a distant disruptive body. More ob-servations of the system should make it possible to test their hy-pothesis and constrain their model. In the meantime, Stevensonet al. (2012b) (hereafter S12) announced their possible detec-tion of two new transiting Earth-sized companions to GJ 436bby means of Spitzer data.Di ff erent surveys have been performed to characteriseGJ 436b’s atmosphere. Pont et al. (2009) analysed two transmis-sion spectra acquired with the Near Infrared Camera and MultiObject Spectrograph (NICMOS, 1.1-1.9 µ m) on the HubbleSpace Telescope (HST) in 2007. Unfortunately, the strongNICMOS systematics led to inconclusive results. Recently, fourtransmission spectra were obtained by Knutson et al. (2014) withthe Wide Field Camera 3 (WFC3) instrument on board the HST.They are featureless between 1.14 and 1.65 µ m, ruling out cloud-free hydrogen-dominated atmosphere models. Besides, Kulowet al. (2014) showed through Lyman- α transit spectroscopy thatGJ 436b is probably trailed by a comet-like tail of neutral hy-drogen. Stevenson et al. (2010, hereafter S10) published theirphotometric observations ( Spitzer program 40685) of GJ 436boccultations in the 6 available bandpasses of the
Spitzer SpaceTelescope , i.e. IRAC at 3.6, 4.5, 5.8, and 8 µ m, IRS at 16 µ m,and MIPS at 24 µ m. They observed a high planetary flux at3.6 µ m, which they related to a possible depletion of methanein the atmosphere. In the meantime they could not detect theplanetary emission at 4.5 µ m, suggesting a high absorption com-ing most likely from CO and / or CO . This result was unex-pected, as methane, and not CO / CO , should be the main carbon-bearing molecule in the relatively cold atmosphere of GJ 436b( T eq =
770 K at periapsis assuming null albedo) according tothe Gibbs free energy (Burrows & Sharp 1999). These resultswere interpreted as the result of thermochemical disequilibriumby Madhusudhan & Seager (2011). Shortly after, Beaulieu et al.(2011, hereafter B11) analysed
Spitzer observations of GJ 436btransits obtained at 3.6, 4.5, and 8 µ m. They measured a di ff er-ent planetary radius at 4.5 µ m than at 3.6 and 8 µ m, what made them conclude a high abundance of methane. In addition, B11re-reduced the same occultation data as S10 at 3.6 and 4.5 µ mand obtained significantly di ff erent results. S10 and B11 thusstrongly di ff er in their interpretation, in particular on the IRAC3.6 and 4.5 µ m data during occultation. Both teams mentionedthe need of a new dataset at those wavelengths to check theirown theories. Later Knutson et al. (2011, hereafter K11) invokedevidence of stellar variability to explain their (and B11’s) plan-etary radius measurement discordance. They also improved thesystem parameter estimates, notably thanks to a larger Spitzer dataset.It is not the first time that di ff erent teams have obtained con-flicting results from the same Spitzer dataset. One can mentionthe detection (Tinetti et al. 2007; Beaulieu et al. 2008) or non-detection (D´esert et al. 2009) of water vapour in HD 189733b.In this context, we have decided to perform this new indepen-dent analysis of archived
Spitzer data. The main concept of thisproject is not only to perform global Bayesian analysis of theextensive
Spitzer datasets available for GJ 436b and to comparethem with the results previously obtained by di ff erent teamsfor subsets of the available data, but also to complement themwith our new HARPS RV measurements to derive stronger con-straints on the planetary properties. When combined with thestellar properties, RV measurements provide orbital parametersand the minimal planetary mass. When we add in the transit lightcurves we can derive the mass and the radius of the planet, sothat its mean density is known. Furthermore, the detection of ananomaly in the RV curve during the planetary transits, knownas the Rossiter-McLaughlin e ff ect, reveals the sky-projected an-gle between the stellar spin and planetary orbit axes (Quelozet al. 2000). The spin-orbit angle measurement may be helpfulin modelling the planetary orbital evolution. The High AccuracyRadial-velocity Planet Searcher (HARPS– Mayor et al. 2003),installed in 2002 on a 3.6-m telescope at the La Silla Observatory(Chile), has demonstrated a high e ffi ciency for detecting low-mass exoplanets and for constraining their masses and orbital pa-rameters, thanks to its sub-1 m / s RV stability (Pepe et al. 2011).Special attention is paid to the treatment of Spitzer system-atic noises and to their influence on the results. Our motivationis also to better understand the limitations of space IR observa-tions for the study of exoplanet atmospheres. Such an e ff ort isespecially important in the context of the future launch of JWST(Seager et al. 2009), in order to optimise the use of its capacitiesfor the studies of other worlds.In Sect. 2 we present all the observations obtained in the Spitzer programs targeting GJ 436b and the way we performedtheir data reduction. The new HARPS RVs are presented in thesame section. Section 3 summarises the analysis of the
Spitzer data and the RV measurements. Section 4 discusses the possibleevidence of companions, while Sect. 5 presents an atmosphericmodel based on our emission and transmission spectra. We dis-cuss our results in Sect. 6, before concluding in Sect. 7.
2. Observations and data reduction
Spitzer made the first transit and occultation observations ofGJ 436b in June 2007 at 8 µ m under the Target of Opportunity(ToO) program (ID : 30129) proposed by J. Harrington. After thepublication of several analyses of these data (Gillon et al. 2007a;Deming et al. 2007; Demory et al. 2007), the occultations ofthe planet were observed in the other Spitzer bandpasses in theframework of ToO program 40685 (PI J. Harrington). The result-ing emission spectrum was presented in S10. Later, the GeneralObserver (GO) program of H. Knutson was motivated to detect-
Spitzer and new HARPS data
Table 1.
Presentation of all the
Spitzer data of GJ 436 used in this paper. They are classified in ascending order of the bandpasswavelength and observing date. The first column gives the bandpass transmission centre of the instrument / channel, the second theeclipse nature of the event, the third the program ID and its corresponding Astronomical Observation Request (AOR) number incolumn 4. The content of the following columns results from our analysis and is mainly linked to the data analysed with aperturephotometry. Column 5 provides the chosen aperture photometry radii. In column 6 the “background contribution” indicates therelative sky background contribution in the chosen aperture photometry. Columns 7 and 8 give the horizontal and vertical averagecoordinates of the point-spread function (PSF) centre in fractional pixel units, considering the bottom left corner to have (0,0) forcoordinates. The centre is computed by fitting a 2D elliptical Gaussian for the bandpass ranging from 3.6 to 8 µ m. Otherwise, it isdone during the deconvolution process. Note that we do not give the PSF centre at 24 µ m since there are 14 di ff erent locations andthat they do not depend on the AOR. Each of the following columns respectively gives the baseline function selected for our globalmodelling (see Sect. 3.3), the β w and β r errors rescaling factors, the time interval used to compute β r , and the average total flux ofthe system. For the baseline function, p ( (cid:15) N ) respectively denotes a N -order polynomial function of the time ( (cid:15) = t ), of the logarithmof time ( (cid:15) = l ), and of the PSF x − and y − positions ( (cid:15) = [ xy ]) and widths ( (cid:15) = w x & (cid:15) = w y ). Bandpass Eclipse Program AOR Aperture Background PSF centre Baseline β w β r T β r Averagenature ID radius contribution x y model total flux( µ m) (pixels) (%) (pixels) (pixels) (min) (mJy)3.6 Occultation 40685 24882688 1.9 0.04 15.67 15.97 p ([ xy ] + w x + w y + t ) 0.95 1.24 15 1269.7 ± p ([ xy ] ) 1.00 1.60 60 1254.0 ± p ([ xy ] + w x + w y + l + t ) 0.97 1.00 5 1269.9 ± / A 60003 38807296 2.5 0.29 16.84 26.49 p ([ xy ] + w x + w y + l + t ) 1.25 2.87 40 1253.8 ± p ([ xy ] + w x + w y + l + t ) 1.12 2.88 35 1274.7 ± p ([ xy ] + w x + t ) 1.04 1.84 65 841.10 ± p ([ xy ] + w x + w y + l ) 1.10 1.36 40 848.50 ± p ([ xy ] + w y + l + t ) 1.06 1.17 25 841.91 ± / A 541 38702592 2.2 0.13 15.70 15.91 p ([ xy ] + w x + w y + l ) 1.09 1.20 120 857.20 ± / A 60003 38808064 3.5 0.21 15.92 26.36 p ([ xy ] + w x + w y + t ) 1.04 1.42 40 854.46 ± p ([ xy ] + w x + w y + l + t ) 1.12 1.00 5 847.55 ± / A 70084 42614016 2.4 0.14 15.70 16.01 p ([ xy ] + w x + w y ) 1.21 1.06 30 856.15 ± p ([ xy ] + t ) 1.26 1.00 5 374.57 ± p ([ xy ] + l ) 1.14 1.00 5 207.66 ± p ([ xy ] + l + t ) 1.15 1.14 60 205.31 ± p ([ xy ] + w y + l ) 1.03 1.00 5 205.44 ± p ([ xy ] + l ) 1.18 1.33 45 205.81 ± p ( l ) 1.17 1.37 15 205.58 ± p ([ xy ] + l ) 1.14 1.15 20 205.48 ± p ([ xy ] + l + t ) 1.30 1.07 20 205.90 ± p ([ xy ] + w x + w y ) 1.38 1.13 5 205.94 ± p ([ xy ] + t ) 1.30 1.02 5 205.99 ± / A 50056 27864064 2.8 3.24 15.52 15.24 p ([ xy ] ) 1.15 1.00 5 205.97 ± p ([ xy ] + l + t ) 1.16 1.00 10 205.36 ± p ( l ) 1.23 1.02 5 205.77 ± p ([ xy ] + w y + l + t ) 1.29 1.00 5 205.71 ± p ([ xy ] + l + t ) 1.15 1.00 5 205.73 ± p ([ xy ] + l + t ) 1.23 1.00 5 205.15 ± p ([ xy ] + l ) 1.22 1.00 5 205.60 ± p ([ xy ] + l + t ) 1.86 1.00 5 85.99 ± ± ing GJ 436b’s phase variation (ID : 50056). Afterwards, two setsof four consecutive occultations at 8 µ m were planned within G.Laughlin’s GO program (ID : 50734, K11) in order to analysethe tidal heating of the planet. Later, H. Knutson searched fortransit depth variations in the 3.6, 4.5, and 8.0 µ m IRAC bands(ID : 50051, B11, K11). Furthermore, the program 60003 at-tempted to observe occultations of GJ 436b at 3.6 and 4.5 µ m. Wrong ephemerides were used, and the occultation phase wasnot observed. Lately, S. Ballard (ID : 541, Ballard et al. 2010a)attempted to identify a third body in the system during an 18-hour observation at 4.5 µ m. Finally, J. Harrington et al. obtainedtwo more observations at 3.6 and 4.5 µ m with Warm Spitzer dur-ing two occultations of GJ 436b to try to confirm the conclu-sions given by S10 and S12. Table 1 summarises this extensive
Spitzer and new HARPS data
Spitzer dataset according to their scheduling units (called AOR = Astronomical Observation Request in
Spitzer terminology).In this section we present the photometric data with the dif-ferent tested data reduction strategies on each instrument and ourupdated HARPS RVs dataset. For all
Spitzer instruments, we usethe images calibrated by the standard
Spitzer pipeline and deliv-ered to the community as Basic Calibrated Data (BCD). Theirunits are converted from MJy / sr to electrons. We apply the rou-tine described by Eastman et al. (2010) to convert Julian daysinto BJD TT and we transform the IRAC data timestamps follow-ing K11 from BJD UTC to BJD TT at mid-exposure time. MIPS observations
On 2008 January 4, the 24 µ m channel of MIPS was used for6 hours to observe GJ 436. During every cycle, MIPS acquiredfive times the images of the source at 14 di ff erent locations ofthe detector distributed on 2 columns. At the beginning of everycycle one extra exposure of one second shorter than the specifiedexposure time was done for each column to obtain calibrationdata.We discard the two extra exposures of every cycle and onlyanalyse the science data, i.e. the 1680 9.96-second exposuresfrom the 1728 available BCD images (version S17.0.4). Thedithering scheme allows us to remove the sky background. Fora given frame, all frames having a maximum time di ff erence ofX min and a di ff erent dither position are combined to producea master sky frame. We test X = = s ( x ), instead of the total PSF t ( x ), whichcan then be represented as the convolution of the resulting PSFin the deconvolved image r ( x ) by the partial PSF : t ( x ) = s ( x ) ∗ r ( x ) (1)where ∗ stands for the convolution operator and x for the pixelposition in the array. r ( x ) is a Gaussian function chosen in sucha way that the final result is well sampled.DECPHOT relies on the minimisation of the following meritfunction: S = N (cid:88) i = σ i ( d i − b i − [ s ( x ) ∗ f ( x )] i ) + λ H ( s ) (2)where σ i is the standard deviation at pixel i . The values of d i , b i and f i respectively stand for the observed light, the sky andthe deconvolved light level at pixel i . The residual image back-ground is thus simultaneously retrieved during the deconvolution http: // astroutils.astronomy.ohio-state.edu / time / hjd2bjd.html see § MIPS instrument handbook process. It is represented by a 2-dimensional second order poly-nomial (6 free parameters). H ( s ) is a smoothing constraint onthe PSF that is introduced to regularise the solution and λ is aLagrange parameter. If the image is composed of point sources,the deconvolved light distribution f may be written: f ( x ) = M (cid:88) j = a j r ( x − c j ) (3)where a j and c j are free parameters corresponding to the inten-sity and position of the point source number j . A crucial pointin the deconvolution process is the partial PSF construction: themore accurate the partial PSF, the better the deconvolution (e.g.,Letawe et al. 2008). We derive the partial PSFs by deconvolv-ing the models made with the Spitzer
Tiny Tim Point SpreadFunction program (Krist 2002) available on the
Spitzer web-site for the di ff erent array locations. We compute the statisticalweight of every pixel for every image to discard cosmic hits andother deviant pixels during the deconvolution process. Finallywe deconvolve each image with its corresponding partial PSF,solving in the process for the star’s flux.In the context of this analysis, the main advantage ofDECPHOT is to optimally separate the light source fromthe (residual) complex background. This is crucial for high-precision infrared photometry in the high background regime(see Gillon et al. 2009). In addition to the preliminary sky sub-traction, we have to include an analytical model for the residualsky background (cf. b i in Eq. 2) in the modelling of the sky-subtracted images during the deconvolution process. A scalarplane fit is su ffi cient to model the background close to the stel-lar source. This highlights low frequency variations of the skystructure on short timescales. The raw and the fitted light curvesare presented in Fig. 1 and in the following section. As noticedby Knutson et al. (2009b), the flux appears constant at the be-ginning of the observation and does not sharply rise as would bethe case with the presence of the detector ‘ramp’ e ff ect (see Sect.3.3). IRS observations
On 2008 January 12, GJ 436 was monitored by IRS in the 16 µ mpeak-up imaging mode over a period of 6 hours with an expo-sure time of 6.29 seconds. This program was sequenced withoutany dithering in three parts of which the middle consisted in theobservation of GJ 436 while the two others targeted empty areason the sky in order to obtain a high-SNR map of the background.We discard the sky images because the photometric preci-sion is not improved using them. We perform aperture photome-try and partial deconvolution on the 1580 BCD images (versionS17.2) and conclude as Knutson et al. (2009a) and S10 that theuse of the PSF is to be preferred in the data reduction. Only de-convolution photometry is presented here.The partial PSF constructed from the over-sampled PSFmodel given on the Spitzer website does not satisfactorily fitthe data. We thus modify DECPHOT to simultaneously decon-volve a set of images. This technique attempts to find a uniquepartial PSF from the images themselves while it allows the po-sition of the point source, its intensity, and the background todi ff er from an image to another. We use the same images both todetermine the partial PSF and to perform deconvolution photom-etry. In a first step, we analyse twenty-five random images with http: // irsa.ipac.caltech.edu / data / SPITZER / docs / irs / calibrationfiles / peakuppsfPSF / Spitzer and new HARPS data
Fig. 1.
Secondary eclipses of GJ 436b observed with the IRS (top) and MIPS (bottom) instruments. Relative flux o ff sets are appliedto datasets for clarity. On the left , raw data are represented by cyan dots for the unbinned data, and by black dots for binned dataper interval of 7 min with their error bars. The superimposed red line is the best-fitting model and includes the transit model. Onthe middle , the same binned data divided by the best-fitting baseline model reveal the occultation shape. The eclipse model issuperposed in red. The right panel displays the binned residuals from the same dataset. The shaded green area of every panel showsthe eclipse event.our new version of DECPHOT to construct a satisfying partialPSF mode. In a second step, we deconvolve all images, one at atime and using as partial PSF model the result of the first step.The resulting normalised light curve is shown in Fig. 1. In the context of the
Spitzer programs 541, 30129, 40685, 50051,50056, 50734, 60003 and 70084, GJ 436 was monitored in thefour channels of the IRAC camera at 3.6, 4.5, 5.8 and 8 µ m.Those covered 16 occultations and 8 transits of GJ 436b, includ-ing a phase curve. In this work we perform for the first time auniform analysis of these 29 IRAC time-series. Our analysis isbased on the IRAC BCD images (version S18.18 for the two firstchannels and S18.25 for the last two). Because GJ 436 is a brighttarget for Spitzer with K ∼ × µ m, 0.08 and 0.32 s at 4.5 µ m, and 0.32 s for the twoother channels. For more details on these IRAC observations werefer the reader to Table 1, Gillon et al. (2007a), Deming et al.(2007), Demory et al. (2007), Ballard et al. (2010a), S10, K11,and S12.We reduce all the IRAC data with our EXOPHOT PyRAF pipeline to get raw light curves. We give a general overviewof its routines below. For every subarray image, a 2D ellipti-cal Gaussian profile fit is performed to determine the centreof the GJ 436 PSF. Aperture photometry is then accomplished PyRAF is a command language for running IRAF tasks based on thePython scripting language. with the
IRAF/DAOPHOT software (Stetson 1987). Other cen-tring approaches are tested (e.g., centroid fit and di ff erent double1D Gaussian adjustments ) but with lower performance (Fig. 2).The background level is measured in an annulus extending from12 to 15 pixels from the centre of aperture, and the resultingbackground flux in the aperture is subtracted from the measuredflux for every image. For every channel, we compute the stel-lar fluxes in aperture radii ranging from 1.5 to 6 pixels by in-crements of 0.1. We select the aperture radius minimising thescatter of the residuals and their time correlation on the lightcurves corrected for instrumental and astrophysical e ff ects (seeSect. 3). The chosen aperture sizes are all between 1.9 and 4.3pixels (Table 1). Larger apertures lead to larger background con-tributions while smaller apertures lead to pixelation problems and significantly smaller counts (the IRAC PSF full-width at halfmaximum ranges from 1.2 to 2 pixels, depending on the chan-nel).For every block of 64 subarray images, we reject the dis-crepant values for the measurements of the x - and y -position,and the stellar and background flux using a 3- σ median clipping.We generally discard up to 2 measurements from the 64 subar-ray images. Then the remaining measurements are averaged. Wetake the photometric error on the mean of the photometric error IRAF is distributed by the National Optical AstronomyObservatory, which is operated by the Association of Universitiesfor Research in Astronomy, Inc., under cooperative agreement with theNational Science Foundation. A 1-dimensional Gaussian of a given (fixed or pre-computed)FWHM is fitted to the marginal profiles in the x - and y -directions us-ing non-linear least square techniques. Contrary to a 2D Gaussian fit itadjusts the PSF profile in both directions separately. Because the fraction of the flux falling into a pixel at the edge ofthe aperture does not correspond to the fraction of the aperture withinthe same pixel, the measured flux on each pixel at the aperture border iswrongly evaluated. 5anotte A. A. et al: Global analysis of GJ 436
Spitzer and new HARPS data
Fig. 2.
Evolution of the photometric precision for raw data withthe aperture radius according to di ff erent centring techniques ina complete dataset (e.g., AOR : 42614016). The 2D Gaussianadjustment (green asterisks) provides the best photometric pre-cision for raw data in comparison to a centroid fit (magentacrosses), a double 1D Gaussian fit from the previously computed x -or y -FWHM (cyan boxes and red diamonds respectively), anda 1D Gaussian fit with a fixed FWHM (blue stars), in particularfor small aperture radii.for every BCD set. At this stage, the first measurements of eachlight curve are discarded if they correspond to deviant valuesfor all or some of the external parameters (detector or pointingstabilisation). In average ∼
10 min of data are rejected for eachdataset (Fig. 3). Finally we perform a slipping median filteringfor each light curve to discard outlier measurements due to, e.g.,cosmic hits.We also test a photometric reduction of the IRAC data withDECPHOT, without improving results. Still we use DECPHOTto assess the infrared variability of GJ 436. Indeed, aperture pho-tometry performed on deconvolved images reconvolved by thebest-fitting partial PSF model allows us to derive the aperturecorrections required for deriving the observed flux of the star F ∗ .For every dataset, we perform this procedure for a large range ofapertures. Then we average all the measurements and take theresulting value as the observed flux measurement for the dataset.The error on the mean is considered as its error bar. We apply thecolour and inter-pixel corrections . We do not correct the intra-pixel sensitivity as no complete correction map is available forthe Warm Spitzer mission at the time of our analysis. The intra-pixel behaviour of the InSb detectors for the Warm
Spitzer mis-sion substantially di ff ers from the one of the cryogenic phase ,making the correction map for the cryogenic phase unsuitablefor all our data. The observed stellar flux F ∗ is given in mJy foreach IRAC dataset in Table 1. Their temporal evolution is shownin Fig. 4. The standard deviations of the fluxes are 0.77, 0.78, and0.12 % at 3.6, 4.5, and 8 µ m, respectively. A fraction of the scat-ter in the shorter wavelengths should come from the absence ofintra-pixel correction. GJ 436 thus appears to be a stable star inthe IR. It is consistent with the nearly constant flux of the starin the optical over a period of five months as observed by K11with the Automatic Photoelectric Telescope. Finally we convert see § Spitzer Observer’s Manual andhttp: // irsa.ipac.caltech.edu / data / SPITZER / docs / irac / warmfeatures / see http: // irsa.ipac.caltech.edu / data / SPITZER / docs / irac / calibrationfiles / pixelphasecryo / and http: // irsa.ipac.caltech.edu / data / SPITZER / docs / irac / calibrationfiles / pixelphase / Fig. 3.
For illustration, evolution of the parameters measured byour reduction pipeline for a randomly chosen IRAC dataset (at3.6 µ m, 2009 January 9, AOR : 28894208). From top to bot-tom and left to right we display the evolutions of the normalisedstellar fluxes, the PSF x - and y -centres, the background values,and the PSF FWHMs in the x - and y -directions. The last threepanels display the correlation diagrams for several parameters,revealing a clear dependence on the FWHM with the positionfor both directions. The first values (large cyan coloured dots)are rejected, as the measured parameters (e.g., sky contribution)are not yet stabilised.the flux densities into Vega apparent magnitudes (presented inSect. 3.4.2 with the magnitude of the planet) using Reach et al.(2005) magnitude calibrations on the stellar flux measured as itwould be falling into a circular aperture radius of 10 pixels.We also test the noise pixel method of Lewis et al. (2013)to extract the fluxes of GJ 436. Based on the use of variable aper-ture radii, this method aims at minimising the correlation of thefluxes and the PSF centre positions. Our tests for the light curvesin the 3.6 and 4.5 µ m shows that this method leads up to 20%lower photometric precisions and larger time correlation of theresidual light curves in comparison to traditional fixed aperturephotometry and subsequent modelling of the position e ff ects. Itshows similar results only for a few datasets. Consequently, wedo not use its resulting light curves in our analysis. We used HARPS to record 171 spectra of GJ 436. AlthoughGJ 436 was not part of the nominal volume-limited sample ofM dwarfs (Bonfils et al. 2013) we used the same settings asfor the other M stars to record its spectra. We observed withoutthe simultaneous ThAr calibration and relied on the overnight http: // irsa.ipac.caltech.edu / data / SPITZER / docs / irac / iracinstrument-handbook / / Spitzer and new HARPS data
Fig. 4.
Stellar flux evolution in the 3.6- (top), 4.5- (middle), and8.0- µ m (bottom) IRAC channels. The stellar flux slightly fluctu-ates with time in the 3.6- and 4.5- µ m bandpasses and is constantat 8.0 µ m. A di ff erent inter-pixel map is used for the Warm mis-sion data. The Warm Spitzer phase is shaded in pale pink forclarity. The flux modulation is probably due to the uncorrectedintra-pixel e ff ect and to the calibration uncertainties, which arenot displayed here for clarity. (cid:46) / s stability of the instrument. This is a better mode for this V = . / s with exposure times of900 seconds.Between 2006 January 25 and 2010 April 6, we obtained 171measurements of which 44 were taken in a single night and therest (127) was spread over the whole period. The measurementsspread over the years generally have exposure times of 900 s,except some that were made with 1200 and 1800 s to compensatefor non-optimal meteorological conditions. They have a medianuncertainty of 1.0 m / s. The 44 observations taken on the samenight (2007 May 10) aim at measuring the possible Rossiter-McLaughlin e ff ect. They have exposure times of 300 secondseach and radial velocity uncertainties of 1.1 − / s. We notethat one of the 127 measurements coincidentally falls during atransit event.Extracted and wavelength calibrated spectra are delivered bythe standard HARPS pipeline, as well as di ff erential RVs ob-tained from the cross-correlation between the stellar spectra anda numerical template. To take full benefit of the many spectraof GJ 436 we merge them to derive a single high signal-to-noisetemplate. We then use this template to re-compute the di ff eren-tial RVs by minimising the χ of the di ff erence between thistemplate and each spectrum. Using a merged stellar spectrumis a common alternative to a numerical template (e.g., Howarthet al. 1997; Zucker & Mazeh 2006). It was already used onHARPS by a part of our group (e.g., when we derived the RVsof GJ 1214, Charbonneau et al. 2009) as well as by other groups(e.g., Anglada-Escud´e & Butler 2012; Anglada-Escud´e & Tuomi2012; Anglada-Escud´e et al. 2013). Before modelling the data,we subtract its 0.34 m / s / yr secular acceleration (K¨urster et al.2003). Our implementation of the algorithm will be presented ina forthcoming paper (Astudillo et al. in prep.) and the inferredRVs are given in Table 2.
3. Data Analysis
We choose to perform a global analysis of our extensive datasetto take full advantage of its observational constraints on the sys-tem parameters. Our Bayesian approach of the analysis is basedon the use of the Markov Chain Monte Carlo algorithm (MCMC;e.g., Ford 2006).
In addition to the
Spitzer photometry and the HARPS radialvelocity measurements detailed in section 2, we used the 59Keck / HIRES RVs presented in Maness et al. (2007) as input datain our global analysis to add further constraints on GJ 436b’s or-bital and physical parameters. We also extend this analysis with atotal of 29 transit times acquired with the Euler telescope (Gillonet al. 2007a), the Carlos Sanchez telescope (Alonso et al. 2008),the VLT (C´aceres et al. 2009), WISE and FWLO (Shporer et al.2009), telescopes at the Apache Point Observatory (Coughlinet al. 2008), the HST (Pont et al. 2009; Bean et al. 2008), andthe EPOXI mission (Ballard et al. 2010b).An exhaustive description of the MCMC adaptive algorithmapplied in this study can be found in Gillon et al. (2010, 2012).We use a model based on a star and a transiting planet ona Keplerian orbit about their centre of mass. For the RVs, aKeplerian 1-planet model is assumed. A model of the Rossiter-McLaughlin e ff ect is also implemented following Gim´enez’ pre-scription (2006). We apply the model of Mandel & Agol (2002)to represent the eclipse photometry, assuming a quadratic limb-darkening law for GJ 436 and neglecting limb darkening for itsplanet. For each light curve, an analytical baseline model rep-resenting the flux variations of instrumental and stellar originmultiplies the eclipse model (see Sect. 3.3). Thanks to the interferometric measurement from von Braun et al.(2012), we have a strong constraint on the stellar radius valueof 0.455 ± (cid:12) . Deriving the mass of an M dwarf froma stellar evolution model is not as reliable as for higher massstars (e.g., Torres 2013). To best benefit from this high-precisionmeasurement and deduce a posterior distribution for the stellarmass independently from any stellar evolution model, we use thenormal distribution N (0 . , . ) as prior distribution for thestellar radius. At each step of the MCMC, the stellar mass is di-rectly computed from the stellar radius value (constrained by theinterferometric prior) and from the stellar density value, which isconstrained by the transit light curves (Seager & Mall´en-Ornelas2003).For the atmospheric stellar parameters (e ff ective temperature T e ff , metallicity [Fe / H], projected rotational velocity V sin i , andsurface gravity log g ), normal prior distributions are assumedbased on the following arguments: we take a value of 3416 Kfor the e ff ective temperature (von Braun et al. 2012) derivedfrom spectral energy distribution fitting and adopt a typical errorvalue of 100 K for the case of low-mass stars (e.g., Casagrandeet al. 2008); we use log g = ± / H]of + ∆ ( V − K s )value into Neves et al. (2012) empiric photometry-metallicityrelation, which is in good agreement with [Fe / H] = -0.03 fromBonfils et al. (2005) and [Fe / H] = + ± Spitzer and new HARPS data finally, we impose V sin i < − (Delfosse et al. 1998) inthe MCMC.For the limb darkening, the two quadratic coe ffi cients u and u are allowed to float in the MCMC. To minimise the cor-relations of these model parameters, those coe ffi cients them-selves are not used as jump parameters , only their combina-tions c = × u + u and c = u − × u (Holman et al. 2006).For each transit, c and c are thus constrained by priors underthe control of the normal prior probability distribution functionsdeduced from Claret & Bloemen’s tables (2011). A baseline model aiming at representing systematic e ff ects orig-inating from several sources multiplies each transit / occultationmodel. It depends on the instrument and wavelength. In addi-tion we include a thermal phase variation model to represent the8- µ m data. We describe the selection of our baseline model forevery AOR in the next subsections. The main source of correlated noise in the IRAC InSb (3.6 and4.5 µ m) arrays is the dependence on the observed flux on thestellar centroid location on the pixel. These detectors show in-deed an inhomogeneous intra-pixel sensitivity, which, combinedwith the jitter of the telescope and to the poor sampling of thePSF, leads to strong correlation of the measured fluxes with theposition of the targets PSF on the array (e.g., Knutson et al. 2008,and references therein). It is known as the ‘pixel-phase’ e ff ect.Our baseline models include two types of low-order polyno-mials to deal with the pixel-phase e ff ect. The first one uses theprescription of D´esert et al. (2009). It considers the dependenceon the fluxes to the x - and y -positions of the PSF centre with thehelp of a polynomial that depends on the shift of the centroidcentre on the array: F ( dx , dy ) = a + a dx + a dx + a dx + a dy + a dy + a dy + a dxdy + a dxdy + a dx dy (4)where dx and dy are the relative distance of the centroid fromthe pixel centre and a to a are free parameters in the fit.The second one is motivated by the correlation of the FWHMwith the PSF centroid location and with the stellar flux variation(Fig. 3). The following polynomial represents the dependenceon the fluxes to the PSF FWHMs in the x - and / or y -directions: F ( f x , f y ) = a + a w x + a w x + a w x + a w y + a w y + a w y (5)where w x and w y respectively stand for the PSF FWHM in the x -and y -directions measured by our centring algorithm and a to a are free parameters in the fit. Modelling this dependence isrequired for most IRAC InSb light curves.Only the lowest frequencies of the pixel-phase e ff ect can bemodelled with the polynomial approach. For an improved mod-elling of the e ff ect, Ballard et al. (2010a) and Stevenson et al.(2012a) demonstrated the e ffi ciency of building a “pixel map”to characterise the intra-pixel variability on a fine grid. Herewe combine the Bi-Linearly-Interpolated Sub-pixel Sensitivity(BLISS) mapping method presented by Stevenson et al. (2012a)with the position / FWHM polynomial models. The BLISS map-ping is performed at every step of the chain after the modelling Jump parameters are the model parameters that are randomly per-turbed at each step of the MCMC. of the polynomial models. This method maps the intra-pixel sen-sitivity at high resolution at every step of the MCMC from thedata themselves. In our implementation of the method, a sub-pixel-scale grid of N knots along the x - and y -directions slicesthe sensibility map. We empirically set N in such a way that oneaverage knot is never associated to less than 5 measurements toe ffi ciently constrain the sensibility map. In most cases, we obtaina smaller scatter in the residuals using both parametric modelsand the sensitivity map. Another well-documented detector e ff ect, especially impor-tant for the Arsenic-doped Silicon (Si:As) material instruments(IRAC 5.8 and 8 µ m, IRS 16 µ m), but also present in the InSbones, is the increase of the detector response at the start of AORs.The so-called “ramp” is attributed to a charge-trapping mech-anism resulting in a dependence on the gain of the pixels totheir illumination history (e.g., Knutson et al. 2008). FollowingCharbonneau et al. (2008), we model this ramp with a polyno-mial of the logarithm of time.Besides, we also test linear and quadratic functions of timein our baseline models to check time-dependent trends of instru-mental and / or stellar origin. As thermal emission is isotropic, the emission of an atmosphericlayer is analogous to the scattering of incident light by a Lambertsurface (Seager 2010). Assuming that one specific atmosphericlayer dominates the emission at a given wavelength, the thermalphase curve of a pseudo-synchronised planet on an eccentric or-bit can be modelled by the following function: F r = A (cid:18) r m r (cid:19) ( π − α ) cos( α ) + sin( α ) π (6)where A is the thermal day-night contrast for a circular orbit, r isthe distance between the star and the planet, and r m is its average.The last fraction models the phase variation of a Lambert sphere(Russell 1916), with α being the phase angle. It can be easilyfound with the relation cos( α ) = sin( ω + f ) sin( i ) (e.g. Sudarskyet al. 2005), where i is the orbital inclination, ω is the argumentat periapsis, and f is the true anomaly. This baseline model alonesupposes a constant stellar flux during the observation time buttakes into account the received stellar radiation variation withtime according to the planet-star distance (e.g. Kane & Gelino2010; Cowan & Agol 2011). The phase curve modelling impliesthe insertion of A and the phase o ff set in the phase angle as jumpparameters. A preliminary evaluation of all the necessary input parametersin our MCMC code is done before performing a global analy-sis of the GJ 436 dataset. Furthermore, the multiple observationswithin the same filters allow us to search for variability in theeclipse parameters.
For each light curve (corresponding to a specific AOR), we testa large range of baseline models and look for the minimisationof the Bayesian Information Criterion (BIC; e.g., Gideon 1978)
Spitzer and new HARPS data to select the simplest model that best fits the data (Occam’s ra-zor). We aim at detecting the thermal phase curve at 8 µ m priorto the global analysis. However its amplitude is not significantat a 3- σ level and the baseline model for the phase curve mod-elling (Eq. 6) does not minimise the BIC, making it useless inthe global analysis. Afterwards we test it again with prior con-straints from the global analysis without better success (Sect. 5).The MIPS light curves corresponding to the 14 di ff erent ditheredpositions are treated separately to take into account the spatialinhomogeneity of the detector response. Apart from a rescal-ing normalisation no baseline model is applied to the individualMIPS light curves.Once we have selected the baseline models for all AORs, weperform a preliminary MCMC analysis (two chains of 80,000steps) to assess the need for rescaling the photometric errors.For each AOR, the ratio of the residuals’ standard deviation andmean photometric error is stored as β w . This factor approximatesthe required rescaling of the white noise of each measurement.To take into account the correlation of the noise, a scaling fac-tor β r is determined through the ‘time-averaging’ method (Pontet al. 2006) in which the scatter of individual points and the scat-ter of binned data with di ff erent time intervals are compared withthe expected scatter of the corresponding binned data without thepresence of correlated noise. The largest values of β r are kept. Atthe end, the error bars are multiplied by the corresponding cor-rection factor CF = β w × β r . The values of β w and β r derivedfor each AOR are given in Table 1. The β w values are gener-ally higher than unity, indicating the undervaluation of photo-metric errors, e.g. the photometric IRAC errors on the mean arelower than the real photometric errors. Besides, light curves with β r > / or astrophysical e ff ects).For the RVs, both our minimal baseline models correspond toa scalar representing the systemic velocity of the star. To com-pensate both instrumental and astrophysical e ff ects that are notincluded in the initial error calculation, the ‘jitter’ noises of 3.8(Keck / HIRES) and 1.7 m.s − (HARPS) are quadratically addedto the error bars to equal the mean error to the standard deviationof the best-fit residuals. Once the models selected and the errors rescaled, we performa global MCMC analysis of our dataset to probe the posteriorprobability distributions of the jump and physical parameters.Two chains of 240,000 steps compose this analysis. We success-fully check their good convergence and mixing with the statisti-cal test of Gelman & Rubin (1992), all jump parameters showingindeed a value close to 1 at the 0.01 level. The resulting medianvalues and 68.3% probability interval for the jump and physicalparameters are given in Table 3. The fitted light curves are com-pared with the data in Figs. 1, 5, 6, and 7. Note that the lightcurves are not binned prior to the analysis (except for the sub-array images, see Sect. 2.3). The fitted radial velocities are dis-played in Fig. 8. Unfortunately, the Rossiter-McLaughlin e ff ectis not detected. We also try to model the Rossiter-McLaughline ff ect with the implementation of Bou´e et al. (2013) but resultsare not conclusive either. According to Winn (2010b), we canexpect to observe a maximum amplitude of the RV anomaly ∆ V RM ∼ − × V sin i ∼
12 m.s − considering a maximum pro-jected rotational velocity of 3 km.s − . However one should betterexpect ∆ V RM ∼ − assuming a stellar rotation of 48 days(see Sect. 4.3). Table 3.
System parameters derived from our global analysis ofthe
Spitzer data and radial velocities.
Parameter Value
Stellar parameters ρ ∗ /ρ (cid:12) . + . − . M ∗ (M (cid:12) ) 0 . + . − . Orbital parametersb = a cos iR ∗ . + . − . Duration (day) 0 . + . − . T (BJD TT ) 4865 . + . − . P (days) 2 . + . − . K (m / s) 17 . + . − . e . + . − . ω ( ◦ ) 327 . + . − . a (AU) 0 . + . − . a / R ∗ . + . − . i ( ◦ ) 86 . + . − . √ V sin( i ) cos β ( √ m / s ) − . + . − . √ V sin( i ) sin β ( √ m / s ) − . + . − . β ( ◦ ) 181 + − V sin( i ) (km / s) 0 . + . − . Planetary parametersdF (%) 0 . + . − . R p ( R ⊕ ) 4 . + . − . M p ( M ⊕ ) 25 . + . − . Occultation depths (ppm)3.6 µ m 177 . + . − . µ m 28 . + . − . µ m 229 . + . − . µ m 362 . + . − . µ m 1260 . + . − . µ m 1690 . + . − . From the inferred planet-star flux ratios we retrieve thebrightness temperature T bright of the planet assuming the planetemits as a blackbody in the di ff erent Spitzer bandpasses and us-ing a
Phoenix stellar atmosphere model (Hauschildt et al. 1999)(with T e ff = g = .
0, and solar metallicity, Table 4).We warn the reader that the error bars do not take into accountthe error of the model. We finally derive the magnitude of theplanet in the di ff erent IRAC bandpasses. Our global analysis assumes a constant transit depth and dura-tion, orbital period, and occultation depth at every wavelength.Even if the resulting model fits very well our data, some vari-ations may indicate diverse physical phenomena which are rel-evant enough to be verified. For this purpose, we conduct newMCMC analyses, benefiting from the strong constraints broughtby the global analyses to attain the highest sensitivity.First we check if the transit depth dF varies with wavelength. dF provides the apparent radius of the planet, which gives inreturn a piece of the transmission spectrum of the terminator ofthe planet. We thus perform three separate additional MCMC Spitzer and new HARPS data
Fig. 8.
On the top , radial velocities measured with the HIRESand HARPS spectrographs. The data are period-folded on thebest-fit transit ephemeris, the 0 of the x- axis corresponding tothe inferior conjunction time. The fit is superimposed on red andthe respective residuals are shown on the bottom panel. The leftpanels display those corresponding data during the whole plan-etary orbit and the right ones are a zoom on the box to high-light the (undetected) Rossiter-McLaughlin e ff ect. The HARPSbinned data are added in black diamonds filled white for clarity Table 4.
Planetary brightness temperatures evaluated for ev-ery instrument / bandpass. The second column gives the planetarydayside temperature assuming a Phoenix stellar atmospheremodel with T e ff = Wavelength T bright ( µ m) (K)3.6 922 + − ≤ + − + − + − + − Table 5.
Apparent and absolute magnitudes of GJ 436 and itsplanet. We estimate the errors of the apparent and absolute mag-nitude around 0.07 mag and 0.12 mag respectively, taking intoaccount the uncertainty in the absolute calibration, the photo-metric error, the uncertainty of the zero magnitude flux, and theerror on the parallax.
Wavelength Magnitudes( µ m) Star PlanetApparent Absolute Apparent Absolute3.6 5.88 5.85 15.26 15.234.5 5.84 5.81 - -5.8 6.28 6.25 15.38 15.358.0 6.27 6.24 14.87 14.84 Table 6.
Transit depth variation with wavelength.
Wavelength Transit depth( µ m) (ppm)3.6 6770 ± ± ± Table 7.
Individual measurements of the occultation depths forthe di ff erent AORs (Sec. 3.4.3). Wavelength AOR Depth( µ m ) (ppm)3 . . − . + . . . − . + . . . − . + . . . − . + . . . − . + . . . − . + . . . − . + . . . − . + . . . − . + . . . − . + . . . − . + . . . − . + . . . − . + . . . − . + . . . − . + . analyses for each of the three relevant IRAC channels (3.6, 4.5and 8 µ m) considering only the light curves including a transit.We use a uniform prior distribution for dF and assume normalprior distributions for the other jump parameters based on theposterior distributions resulting from our main global analysis(Table 3). We cannot detect any significant chromaticity of thetransit depth (Table 6, Fig. 9, and Sect. 5).Then we test the transit and occultation depth variations asa function of time within a given instrument. Such transit depthvariations could reveal a physical change of the radius with time(for e.g. due to the thermal expansion of the atmosphere or thepresence of variable clouds) or stellar activity (see K11 for allthose aspects). Besides, the occultation depth fluctuation shouldprovide constraints on general circulation models. We separateall light curves including an eclipse event in groups accordingto their channel origin and perform new MCMC analyses foreach group separately. We set the transit and occultation depthsas jump parameters for each individual eclipse and keep theother parameters as normal prior distributions based again onour global analysis (Table 3). We find no significant occultationdepth variation (Table 7 and Fig. 10 for the data at 8 µ m), and notransit depth variation contrary to B11 and K11 studies (Fig. 11and Table 8).The transit duration variation, which might be due to thepresence of another orbiting body such as a moon (e.g., Kipping2009), is the third parameter we examine. Because it might belinked to a transit depth variation, we set those two parametersas jump parameters in our MCMC analyses and maintain normal Spitzer and new HARPS data
Fig. 9.
Detrended
Spitzer µ m ( left ), 4.5- µ m ( middle ), and 8- µ m ( right ) photometry folded on the best-fit transit ephemerisobtained in our analysis per channel for the transits ( top , Sect. 3.4.3) and in our global analysis for the occultations ( bottom ). Thebest-fit eclipse models are superimposed. Fig. 10.
Occultation depth variation at 8 µ m as function of time.Brown diamonds with their 1- σ -error bar represents occultationdepths. The dashed blue lines indicate temporal caesura in the x- axis. The red horizontal line displays the eclipse depth valueobtained during the global analysis and the shaded region sur-rounding it is its 1- σ -error bar.prior distributions for the other parameters. We perform individ-ual MCMC analyses on each time-series recording a transit. Wedo not detect any significant transit duration variation (Fig. 11and Table 8).Finally, we search for transit timing variations (TTV), whichmay disclose the presence of another orbiting body in the sys- tem (Holman & Murray 2005; Agol et al. 2005, and referencestherein). We perform a new individual analysis of the transitlight curves, keeping all the parameters except the mid-transittimes under the control of Bayesian penalties based on the re-sults of our global analysis. The measured timings are given inTable 8. When compared with the transit ephemeris deducedin our global analysis, they do not reveal any significant TTV(Fig. 11, bottom panel). Previous studies of GJ 436
Spitzer datasets reported structuresthat could potentially be attributed to stellar flares. The first onewas signalled just after an occultation at 3.6 µ m (2008 January30, AOR : 24882688) by S10 and B11 and led to contradictoryresults. Their opinions diverged on how to take care of the postoccultation spike they both identified. On our side, we noticethat the amplitude of the structure highly depends on the chosenaperture radius, and disappears for aperture radii below 2.1 pix-els (Fig. 12). The insertion of Eq. 5 in the baseline model leadsto a significantly decreased occultation depth ( ∼
170 ppm insteadof ∼
535 ppm) and to a higher photometric accuracy (mean pho-tometric error ∼ − instead of 10.30 10 − , Fig. 12), whichwe assign to the strong evolution of the FWHMs during the oc-cultation. Thanks to the inclusion in our modelling of the impactof the FWHM variations, a series of tests reveal that our mea-sured occultation depth of 169 ±
48 ppm is not dependent on theselected aperture radius or on the rejection of a fraction of thepost-occultation data, demonstrating its robustness.
Spitzer and new HARPS data
Table 8.
Individual transit parameters. Columns 3 to 5 derive from our analysis. Our transit depths are compared with formerstudies in the last two columns.
Wavelength AOR Depth Duration Timing Depth from B11 Depth from K11( µ m ) (%) (day) BJD TT − . (%) (%)3.6 28894208 0 . − . + . . − . + . . − . + . . ± . . . − . + . . − . + . . − . + . . ± .
006 0 . ± . . . − . + . . − . + . . − . + . . ± .
018 0 . ± . . . − . + . . − . + . . − . + . . ± . . . − . + . . − . + . . − . + . . ± .
012 0 . ± . . . − . + . . − . + . . − . + . . ± .
012 0 . ± . . . − . + . . − . + . . − . + . . ± .
013 0 . ± . . . − . + . . − . + . . − . + . . ± . Fig. 11.
Transit parameter variations. From top to bottom, theplots respectively show the transit depth, the transit duration,and the transit timing variation with their error bars accordingto time for the di ff erent IRAC channels. The pink dots stand forthe 3.6- µ m channel, the green crosses for the 4.5- µ m channel andthe brown diamonds for the 8- µ m channel. The vertical dashedblue lines indicate temporal caesura in the x- axis. The horizontalred lines present in the two top panels respectively indicate thetransit depth and duration derived from the global analysis. Theshaded surrounding area is its 1- σ error bar.The second occultation time-series at 3.6 µ m was supposedto confirm or infirm S10 and B11 interpretations but anotherflare-like structure was recorded during the occultation by S12(see Fig. 6, second light curve from the top, 2011 February 1,AOR : 40848384). In this case, we cannot identify any sharpvariation of an external parameter able to explain it. We tryto measure the occultation depth when discarding (or setting azero-weight on) the last flux measurements that show a net dis-crepancy but the occultation depth cannot be constrained. So wecannot discuss the influence of this flare-like structure on theoccultation depth measurement. The addition of this light curve Fig. 12.
Influence of the chosen aperture radius and the baselinemodelling. We present the same light curve (at 3.6 µ m, 2008January 30, AOR: 24882688) four times, however showing dif-ferent noise level and a di ff erent occultation depth due to thedata reduction and analysis. On the left , the aperture photometryis centred by a 2D elliptical Gaussian fit with an aperture radiusof 1.9 pixels, while on the right the aperture radius equals 3.5pixels. They all proceed to the same MCMC analysis with theinferred parameters from Table 3, except that the top ones con-tain a baseline model dealing with the measured PSF FWHM,while the bottom ones do not.to our global analysis cannot give a strong confirmation (217 ±
140 ppm) of our first 3.6 µ m occultation depth measurement butagrees with it.We finally report another flare-like structure during an obser-vation of GJ 436 at 3.6 µ m. This one happened outside a sched-uled eclipse (2010 June 23, AOR : 38807296, Fig. 13). We can-not remove this peak with any of our baseline models. However,for that AOR we notice a surprising absence of correlation be-tween the noise pixel parameter and the measured PSF FWHM(Fig. 14), suggesting again an instrumental origin of the photo-metric structure. In the end, we can only identify one flare-likestructure of which the origin is probably instrumental (cosmichit in the PSF core), considering the absence of other similarstructures in our extensive data set and the extreme quietness of Spitzer and new HARPS data
Fig. 13.
Flux modulations present in the 2010 June 6
Spitzer light curve (AOR : 38807296) during GJ 436 monitoring.
Fig. 14.
Lack of correlation on the PSF FWHM of GJ 436 (AOR: 38807296) with the square root of the pixel noise parameter( √ β ) on the left. For comparison, the same graph correspondingto a light curve from the same bandpass (AOR : 28894464) isdisplayed on the right. The mean FWHM is clearly proportionalto the square root of the pixel noise parameter, as expected.GJ 436. Indeed, the S HK index, a proxy for stellar activity, mea-sured from the HARPS spectra is weak in comparison to the Ca ii H&K emission of similar type stars and does not significantlyvary on short time scales (Astudillo et al. in prep).
4. Planetary companion
In this section, we present the search for a second planet orbit-ing GJ 436, which we perform on the residual light curves andthe HARPS RVs. We also discuss the two potential transitingcompanions found recently by S12 in some
Spitzer datasets.
We analyse the best-fit residual light curves resulting from ourglobal MCMC analysis in order to be detached from GJ 436beclipses and from any instrumental systematics. We use our ownversion of the algorithm MISS MarPLE (Berta et al. 2012) onthe residual light curves.We can identify only two potential transit-like events. Thestrongest one corresponds to a transit depth of ∼
150 ppm last-ing for 0.5 hour at BJD = ∼ σ signif-icance. The second one recovers a signal of only a 3.1- σ sig-nificance at BJD = ∼
100 ppm. It should be noted that the correlated noiseis not fully taken into account when estimating those signifi-cance levels. The actual significance of both structures is clearlymarginal, as can be judged by eye in Fig. 15. With 1475 mea-surements from both light curves and 4 more degrees of free-dom for the transit model, a ∆ χ = -6 between the transitingand non-transiting companion model corresponds to a ∆ BIC = -6 + = + ∆ BIC results in
Fig. 15.
Transit-like structures detected in two residual lightcurves by our own version of the code MISS MarPLE (Bertaet al. 2012). For both structures, a box-like model illustrates atransit depth of 120 ppm and a duration of 0.6 h.an approximated Bayes factor of e ∆ BIC / ∼
28 in favour of thenon-transiting companion model.These two transit-like features (Fig. 15) were also detectedby S12 although with a higher depth and longer duration. Theseauthors attributed them to their planet candidate UCF-1.01.Assuming that both structures correspond to two transits ofthe same and still undetected planet, the elapsed time betweenthe two signals gives a maximum period of ∼ Spitzer data. Injecting faketransits at the corresponding phases, we check our ability to re-cover them in the
Spitzer data with MISS MarPLE for each pe-riod and each expected transit. Fig. 16 shows the period rangesthat we can keep from these tests. In this figure, the periods tooclose to GJ 436b’s one are also discarded to allow the dynamicalstability of the system (from ∼ ∼ . + N × .
98 days. For thesake of completeness, we also analyse the residual light curveswith two versions of the algorithm BLS (Kov´acs et al. 2002)(the Optimal BLS from Ofir (2014) and the BLS available onthe NASA Exoplanet Archive website ), which searches for pe-riodic box-shaped structures in photometric time-series. We failto detect any significant signal. S12 proposed two planetary candidates in the GJ 436’s stellarsystem and named them temporarily UCF-1.01 and UCF-1.02until their confirmation. They observed UCF-1.01 transits during2008 July 14, 2010 January 28, 2010 June 29, 2011 January 24and July 30 datasets. UCF-1.02 potential transits occurred duringboth of those 2010 datasets. http: // exoplanetarchive.ipac.caltech.edu 13anotte A. A. et al: Global analysis of GJ 436 Spitzer and new HARPS data
Fig. 16. Top:
Timing of GJ 436 observations with the 3.6 and4.5 µ m IRAC channels. The two vertical lines indicate thedatasets having the transit-like features. Bottom:
Distributionof the possible period range for the putative additive transitingplanet. The observational coverage discards all periods below1.18 days.
Fig. 17.
Atypical behaviour of measured parameters during twoof S12’s UCF-1.01 transits. The figure on the left shows a back-ground contribution discontinuity around BJD 2,455,225.09.The one on the right points out a strong fluctuation of the x -FWHM around BJD 2,454,662.32. UCF-1.01 transit events areshaded in green.In our analysis we pay particular attention to the behaviourof the measured external parameters. The following two exam-ples may cast doubt on some observations of S12’s candidatetransits. A change of the background contribution (Fig. 17) in-deed a ff ects the 2010 January 28 dataset just at the end of theobservation of UCF-1.01 transit, while a larger x -FWHM altersthe 2008 July 14 light curve during another UCF-1.01 transit.Ballard et al. (2010a) also discarded the latter example becauseonly small photometric apertures reveal a transit-like shape.The signal-to-noise quality of our residual light curves be-ing su ffi cient to identify transit shapes similar to S12, we mustalso verify that our adopted baseline models are not responsi-ble for the subtraction of the transit signals. We thus insert thetransit signals observed by S12 in our original light curves andperform individual MCMC to get new residual light curves. Welook for transit-box shapes on the individual residual light curveswith the previous manner and identify the injected transits with Fig. 18.
Highlight on the impact of the data reduction / analysisdetails on the presence of low-amplitude transit-shaped struc-tures in the Spitzer photometry (2010 Jan 28, AOR: 38702848).We apply relative flux o ff sets in the above two plots for clarity.The upper dataset is the result of aperture photometry with a 2Delliptical Gaussian centring while the lower one is done with adouble 1D Gaussian fit. The upper is corrected with a baselineinvolving the measured FWHM while the lower is not. Blackdots are the binned data per interval of 5 min with 1- σ errorbars. The supposed UCF-1.01 (right) and UCF-1.02 (left) transitevents are shaded in green.more than 4- σ confidence. Our models correcting for instrumen-tal systematics do not destroy transit signals.We wonder why our results diverge. We both opted for a sim-ilar aperture radius (S12 : 2.25 px; our study : 2.2 px) and for aBLISS mapping in the 2010 January 28 dataset, but we di ff er inthe choice of the centring technique. S12 employed their time-series image de-noising for this purpose before centring with aGaussian whereas we use a 2D elliptical Gaussian fit. We can ob-tain a similar structure to S12 (Fig. 18), if we centre the PSF witha double 1D Gaussian having the computed x- FWHM and do notmodel the light curve with the FWHMs (Eq. 5), but the UCF-1.01 transit signal-to-noise ratio remains very low. Likewise, asimilar transit-like shape in the 2011 July 30 light curve is foundusing the same aperture radius as S12 (5 px) with a PSF centringobtained by a double 1D Gaussian fit (Fig. 19) and with the samebaseline as the one from our analysis. However, the transit is notsignificant ( ∼ σ ). The standard deviation for the RV residuals around a Kepleriansolution composed of a single planet is 1.53 m / s, its mean errorof 0.02 m / s, and the resulting χ of 2.0 ± + drift model (Fig. 20), we iden-tify several peaks although none shows a significant power ex-cess. Eight peaks have power excess above the 1- σ -significancelevel (which corresponds to a power p = ff ers from the rotational periodidentified by photometry by K11, P ∼
57 days) based on spec-
Spitzer and new HARPS data
Fig. 19.
Same as Fig. 18 for the 2011 Jul 30 data (AOR:42614016). The upper dataset is the result of aperture photome-try with a 2D elliptical Gaussian centring and is corrected for allsystematics minimising the BIC. The lower dataset is producedfrom a double 1D Gaussian fit of the computed x- FWHM andcorrected in the same way. The shaded green area correspondsto UCF-1.01 transit event.
Fig. 20.
GJ 436 periodogram of the residuals for the model com-posed of 1 planet on a Keplerian orbit plus 1 drift. The horizontalyellow line represents the 1% false alarm probability. No peakshows a significant power excess.tral indices for a sub-sample of our HARPS spectra, and an-other power excess around 23 days, i.e. about half the 48-dayperiod and thus possibly a harmonic. Nevertheless, they all havea power much below the power threshold for the 3- σ -confidencelevel ( P = ∼ ⊕ ) should correspond to masses lower than our upper-limit mass. Fig. 21.
Conservative detection limits on M p sin i applied toGJ 436 residual RV time-series around a chosen model (com-posed of planets, linear drifts, and / or a simple sine function).Planets above the limit are excluded, with a 99% confidencelevel, for all 12 trial phases. The vertical dashed yellow linemarks the duration of the survey.
5. Atmospheric analysis
In order to use our new measurements to draw inferences onthe atmospheric properties of GJ 436b we employ a number ofatmospheric modelling tools. We first derive planetary pressure-temperature
P–T profiles using the 1D plane-parallel model at-mosphere code described in Fortney et al. (2005, 2008). Theopacity database is described in Freedman et al. (2008) and theequilibrium chemistry calculations in Lodders & Fegley (2002).We use the base solar abundances of Lodders (2003).We first generate thermal emission spectra for models rep-resentative of conditions on the dayside of the planet. Withinthe framework of the thermal emission calculations, we are con-strained to pre-tabulated equilibrium chemistry abundances. InFig. 22 we plot two models. One uses solar abundances andthe other 50 × -solar, broadly similar to the carbon abundance inUranus and Neptune (Baines et al. 1995). At higher metallicity,hydrogen-poor molecules such as CO and CO become moreabundant (Lodders & Fegley 2002), with the mixing ratio of COrising linearly, and CO2 quadratically, with metallicity. Whilethis metal-enhanced model certainly goes in the right directiontowards reproducing the large measured flux ratio di ff erences be-tween the 3.6 and 4.5 µ m IRAC bandpasses, the fit is not satis-factory and our occultation depth at 3.6 µ m, which is smallerthan S10’s, is still too high to be explained by a CH fluores-cence with only stellar photons (Waldmann et al. 2012). S10 andMadhusudhan & Seager (2011) have previously shown that ex-traordinarily low CH mixing ratios, along with high CO and / orCO abundances are needed to reproduce the previous S10 ob-servations. We concur on this point based on our measurements.Inversion techniques could be used on to better constrain the at-mospheric abundances (e.g., Madhusudhan & Seager 2011; Lineet al. 2012).In Figure 23 we compare our Spitzer depths to two modelsfrom Moses et al. (2013) that were created to better fit the pre-vious
Spitzer depths derived by S10. The model labelled “best-fit retrieval” used the Bayesian inversion methods of Line et al.(2013, 2014) to find a best-fit spectrum, with free parametersthat include the P − T profile and chemical mixing ratios. The Spitzer and new HARPS data
Fig. 22.
Model planet-to-star flux ratios compared to the ob-served
Spitzer occultation data. Both models assume a hot dayside, with absorbed energy redistributed over the dayside only.The blue model uses solar metallicity, while the red model uses50 × -solar. The Spitzer data are orange circle while the modelband averages in the six bands are shown as coloured squares.The location of prominent absorption features that di ff er be-tween the models (where CO and CO absorb strongly) are la-belled. The planet-to-star flux ratios of 500, 700, and 900 Kblackbodies are shown in dashed black.“300 × -solar” model uses a Line et al. P − T profile, but mixingratios from a detailed non-equilibrium chemistry calculation foran atmosphere enriched in metals by a factor of 300 over solarabundances. It is clear that reduced secondary eclipse depths at3.6, 5.8, and 8.0 µ m from our analysis lead to a poor fit fromthese models. Given these lower fluxes, it appears plausible thata cooler atmospheric P − T profile would better fit these data, andalso yield a lower flux in the 4.5 µ m band, which has always beenproblematic to fit (S10; Madhusudhan & Seager 2011; Moseset al. 2013). It does appear that some CH depletion and CO / CO enhancement will still be needed to match 3.6 and 4.5 µ m banddepths, given our models presented in the previous plot (Fig. 22).Also, cooler day-side temperatures may allow for a fit with alower metallicity, and hence less CO , and a better fit at 16 µ m,which includes a strong CO band.We next turn to the transmission spectrum of the planet toexamine whether a large abundance of CO and CO , and cor-responding small mixing ratio of CH , are also consistent withthis dataset. For this purpose, we complete our Spitzer transitdepths with those from EPOXI (Ballard et al. 2010b, 0.35-1.0 µ m), HST WFC3 (Knutson et al. 2014, 1.14-1.65 µ m), HSTNICMOS (Pont et al. 2009, 1.1-1.9 µ m), and from the groundin the H and K bands (Alonso et al. 2008; C´aceres et al. 2009)on Fig. 24. Here we model the planetary transit radius, which isinferred from the transit depth and von Braun et al. (2012) stellarradius (0.455 R (cid:12) ), as a function of wavelength, using the trans-mission spectrum code described in Fortney et al. (2003, 2010).The transmission spectrum of the planet GJ 436b was previouslymodelled in some detail with this code by Shabram et al. (2011).An advantage of these calculations is that we are able to modelarbitrary chemical mixing ratios, rather than equilibrium chem-istry.We first compute the transmission spectrum of the 50 × -solarmodel, shown on Fig. 24 in orange. We compare to the two best-fit chemical models of S10 in red and blue, which use low CH Fig. 23.
Comparison of our observed
Spitzer occultation datawith synthetic emission spectra for GJ 436b from Moses et al.(2013). The green and blue curves correspond respectively tothe best fit retrieved model, given S10 data, using the method ofLine et al. and the 300 × -solar model. The model band averagesin the six bands are shown as coloured squares. Our Spitzer dataare shown as orange circles.and high CO and CO mixing ratios. The models di ff er dramati-cally in the optical only because it is unclear if the neutral atomicalkalis Na and K are still present in the planetary atmosphere, orhave condensed into clouds. The equilibrium chemistry model isstrongly disfavoured by the Spitzer data, as it yields the wrongplanetary radius ratio between the 3.6 and 4.5 µ m bands. Theblue and red curves reproduce the Spitzer data better. This isconsistent with the dayside occultation data, where models withstrongly enhanced CO and CO and strongly depleted CH arepreferred.We also note that deviations from a constant radius model arenot particularly significant. This could suggest that cloud ma-terial obscures the transmission spectrum (e.g., Fortney 2005).Alternatively, the atmospheric mean molecular weight couldbe higher that assumed. A very metal-rich atmosphere wouldshrink the scale height as well as produce abundant ‘metal-metal’ species such as CO and CO , which is certainly neededto explain the dayside spectrum.Our phase curve fit (Fig. 25) presents a phase o ff set of − − + ◦ , a day-night contrast parameter A = − + ppm,which is not significant at a 3- σ level, and a peak-to-peakflux di ff erence of 268 ppm. Those latter two values should beidentical for a circular orbit model being perpendicular to thesky plane. We compare our phase curve fit with the 3D cou-pled radiative transfer and general circulation model adaptedto GJ 436b by Lewis et al. (2010) (Fig. 25). It takes into ac-count the pseudo-synchronous rotation of GJ 436b and the at-mosphere metallicity. The 1x-solar atmospheric metallicity caseof GJ 436b (represented by green stars) does not fit the obser-vations while the 50x-solar case (magenta circles) gets closerto them. If revealed significant, the amplitude disparity betweenthe 3 light curves would require a (very) metal-rich atmosphere( > / night temperature contrasts.Indeed, at higher metallicity, photons are absorbed and emit-ted from lower pressures, where the radiative timescale is short,making temperature homogenisation more di ffi cult. This resultwould be in good qualitative agreement with our transmissionand emission spectra analysis. Spitzer and new HARPS data
Fig. 24.
Model transit radius as function ofwavelength compared with published tran-sit depths and our
Spitzer results. From leftto right, the radii are derived from EPOXI(Ballard et al. 2010b), HST WFC3 (Knutsonet al. 2014, represented by empty diamondswith thinner error bars in the 1.14-1.65 µ mwavelength range), HST NICMOS (Pont et al.2009), the H and K bands from the ground(Alonso et al. 2008; C´aceres et al. 2009), andIRAC (ours) studies. Three models are shown.In orange is the 50 × -solar model from Fig. 22.In red and blue are transmission spectra takenfrom Shabram et al. (2011), who used mixingratios suggested for the planetary dayside byS10. Band-average calculations are shown assquares for the three models, across the Spitzer bandpasses. The dramatic di ff erences betweenthe models at optical wavelength are only dueto di ff erent assumptions about the abundancesof alkali metals. The blue and red models,which have depleted CH and enhanced COand CO , are generally preferred. Fig. 25. Top : the observed phase curve of GJ 436 at 8 µ m (2008July 12, AORs: 27863296, 27863552, 27863808) superimposedto a model for a Lambert sphere (red line). The adopted baselinemodels are respectively p ([ xy ] + w x + w y + l ), p ([ xy ] + w x + w y ),and p ([ xy ] + w x + w y ) to exclude temporal models. The blackcrosses are binned data with their 1- σ error bars. The peak-to-peak flux di ff erence equals 268 ppm while A = ±
100 ppm.Our model for a Lambert sphere is compared with Lewis et al.(2010) models shifted vertically. The models correspond to 1x-solar (green stars) and 50x-solar (magenta circles) metallicitycases. The observed day-night temperature contrast indicates ametal-rich atmosphere.
Bottom : the residual light curve.
6. Discussion
We could not find any hint of stellar activity (large amplitudetrend, convincing flare-like structure) in our photometric time-series for GJ 436. A low stellar activity for GJ 436 is supportedby the stable stellar flux (Fig. 4), and by the temporal stability ofthe transit depths. In our light curves, we detect no occultation of stellar spots by the planet during its transits. Neither do Knutsonet al. (2014) in their HST WFC3 data. This is in good agreementwith the advanced age of the star deduced from its kinematics(Leggett 1992) and weak chromospheric Ca ii H and K emissionlines (Butler et al. 2004).Our global analysis gives a stellar mass of 0 . + . − . M (cid:12) .This value is higher than what Delfosse et al. (2000) obtain frommass-luminosity relations partly calibrated with eclipsing bina-ries (0.44 ± (cid:12) ). Our error on the stellar mass strongly de-pends on the stellar radius error. Multiplying by a factor two thestellar radius error almost doubles our uncertainty on the stellarmass ( ∆ M ∗ = (cid:12) ). The fact that GJ 436 appears as a M2.5star despite its somewhat high mass might reflect an e ff ect ofthe metallicity. Indeed, the stellar spectral type depends both onthe mass and metallicity : for a given mass, the more metal-rich astar is, the lower its e ff ective temperature is. For instance, GJ 436mass and temperature agree with Spada et al. (2013) models fora solar or supersolar metallicity (Fig. 26) as supported by our de-rived metallicity, and by e.g. Johnson & Apps (2009) and Neveset al. (2013) with [Fe / H] = + + Our findings fit in reasonably well with recent theoretical ad-vances. Motivated by previous observational work on GJ 436b,there have been recent suggestions along multiple theoreticallines that Neptune-class exoplanet atmospheres may commonlyhave extremely high metallicities, perhaps several hundred timessolar, or higher. Fortney et al. (2013) have suggested, based onatmospheric accretion of planetesimals in population synthesisformation models, that high atmospheric metallicities may be acommon outcome of the planet formation process. Moses et al.(2013), in a detailed chemical study of GJ 436b, suggest thatlow CH abundances, and high CO and CO abundance can bea natural outcome in an atmosphere where metals are so abun-dant that H is no longer the dominant atmospheric constituent,by number. Independently, Ag´undez et al. (2014) favour modelswith an e ffi cient tidal heating and also a high metallicity. Finally, Spitzer and new HARPS data
Fig. 26.
Theoretical e ff ective temperature-mass relations fromthe stellar evolution model of Spada et al. (2013), with the mix-ing length parameter α set to 0.5. Theoretical 4 Gyr isochronesare plotted for di ff erent metallicities indicated by legend. Themagenta filled box shows the GJ 436 position on the diagram ac-cording to von Braun et al. (2012)’s stellar temperature and ourinferred stellar mass.the featureless transmission spectrum extracted by Knutson et al.(2014) leads to an atmospheric metallicity of 1,900 times solaror to a cloud layer at pressure below 10 mbar. It is not clear ifsuch high envelope metallicity is consistent with the radius andbulk density of the planet. We suggest continuing chemical stud-ies of the atmosphere of GJ 436b with our revised occultationand transit depths. It may possibly favour a high cloud seen intransmission without such a high atmospheric metallicity. Futurecomparisons with GJ 3470b (Bonfils et al. 2012; Crossfield et al.2013; Venot et al. 2014; Demory et al. 2013) will also be illumi-nating.
7. Conclusion
We performed an independent and global analysis of all avail-able
Spitzer data for GJ 436 combined with our new HARPSRV measurements. In this analysis, we optimised the data reduc-tion procedure for each
Spitzer instrument with the adaptationof partial deconvolution photometry or aperture photometry, andwe paid a particular attention to the modelling of the system-atic e ff ects. We recommend the use of the FWHM of the PSF inboth directions as parameters to model the instrumental system-atics. The insertion of the HARPS RVs complements well thephotometric data. Our results are globally consistent with previ-ous studies (e.g., S10; B11; K11; S12) but some discrepanciesdisclose another facet of GJ 436b. In particular we obtained con-stant values of the transit depth with time, a flat transmissionspectrum and a significantly lower 3.6 µ m emission.GJ 436b is a warm Neptune with a mass of 25.4 ± ⊕ and a radius of 4.096 ± ⊕ . It is in an eccentric orbit( e = . ± . . ± .
06 M (cid:12) ). Wedetect no stellar variability (no stellar flux variation on a largescale and no transit depth variation with time) in the whole setof
Spitzer light curves. No occulted star spots were observed inthe transit light curves. K11 observed very weak photometric ac-tivity in the optical. In addition, Astudillo et al. (in prep) measurea S HK index in the HARPS spectra that is consistent with a weakstellar activity and does not show a detectable periodicity. Wethus confirm GJ 436’s weak activity. Neither the amplitude of the phase curve nor its shape can beconstrained with the current data set. We recommend new obser-vations with future facilities at multiple wavelengths longer than8 µ m combined with stellar monitoring at shorter wavelengths,such as 4.5 µ m or in the visible to discern the planetary phasecurve from stellar variability. Such observations should constrainlongitudinal properties of the atmosphere at di ff erent depths.Despite our shallower occultation depths at 3.6, 4.5, and8 µ m compared to previous works, all the photometric Spitzer time-series are still in good agreement with a metal-rich atmo-sphere depleted in methane and enhanced in CO / CO . Howeverthe metallicity of the atmosphere may not be as high than previ-ously thought. A cooler atmospheric model with disequilibriumchemical abundance profiles should better fit our data, and alsoyield a lower flux in the 4.5 µ m band, which has always beenproblematic to fit. We encourage an entirely new modelling anal-ysis based on our revised data for firm conclusions on the jointconstraint from the emission and transmission spectra.We found no significant evidence for a second planet andconstrained a maximum mass for a potential companion of 10Earth masses up to few-hundred days period and of 3-5 Earthmasses in GJ 436’s habitable zone. Acknowledgements.
This work is based in part on observations made with theSpitzer Space Telescope, which is operated by the Jet Propulsion Laboratory,California Institute of Technology under a contract with NASA. Support for thiswork was provided by NASA through an award issued by JPL / Caltech. M. Gillonis FNRS Research Associate. N. Astudillo acknowledges support from“Becas deDoctorado en el Extranjero, Becas Chile” (grant 72120460). V. Neves and N. C.Santos acknowledge the support by the European Research Council / EuropeanCommunity under the FP7 through Starting Grant agreement number 239953.NCS was also supported by FCT through the Investigador FCT contract refer-ence IF / / / FSE (EC) by FEDER funding through the pro-gram“Programa Operacional de Factores de Competitividade - COMPETE”. Wethank the anonymous referee for his helpful comments and suggestions as well asPierre Drossart for helpful discussion about the methane fluorescence, Gwena¨elBou´e for information about ARoME use, Michael Line for providing his mod-els from Moses et al. (2013) and Heather Knutson. We are grateful to JosefinaMontalban for highlights on the stellar parameters and Thierry Morel for dis-cussions about errors on inferred parameters for low mass stars. We thank EvaEulaers, Alice Decock, and Sebastien Salmon for their helpful comments on theredaction. A special thank to Sandrine Sohy for her help and commitment inprogramming part of this work.
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Spitzer and new HARPS data , Online Material p 1
Table 2.
Radial velocities of GJ 436. BJD TT - 2 450 000.0 RV (km s − ) σ RV (km s − )3760.83575 9.774490 0.0011103761.84061 9.807520 0.0011103762.82805 9.782330 0.0009003763.84203 9.780590 0.0008903765.80411 9.775230 0.0009403785.76121 9.809860 0.0009303788.77940 9.800960 0.0009004122.84306 9.776460 0.0009104135.83242 9.781010 0.0009204140.82196 9.788840 0.0010304142.83025 9.808690 0.0009104166.75093 9.806690 0.0011404172.74297 9.782380 0.0010004194.70900 9.777700 0.0012304197.67745 9.791090 0.0010904199.67093 9.774910 0.0009704202.66419 9.777130 0.0009504228.58285 9.778490 0.0010404230.48575 9.797180 0.0011704230.49514 9.796850 0.0012804230.50134 9.794220 0.0018004230.50510 9.793220 0.0017604230.50900 9.796050 0.0016104230.51279 9.795530 0.0015504230.51650 9.798750 0.0016904230.52037 9.796760 0.0016804230.52431 9.794440 0.0025204230.52814 9.795850 0.0019704230.53201 9.796930 0.0017004230.53564 9.794730 0.0015404230.53947 9.791850 0.0015104230.54345 9.793580 0.0015004230.54718 9.792180 0.0015104230.55108 9.793940 0.0014904230.55499 9.792370 0.0015304230.55882 9.793830 0.0014104230.56257 9.793770 0.0013704230.56648 9.793990 0.0014404230.57016 9.795420 0.0014504230.57410 9.793690 0.0012904230.57783 9.795000 0.0012904230.58159 9.794400 0.0014704230.58552 9.793470 0.0013204230.58943 9.794290 0.0013104230.59315 9.793000 0.0014404230.59713 9.792140 0.0013904230.60078 9.790910 0.0016204230.60464 9.793860 0.0015704230.60854 9.793070 0.0017604230.61237 9.792890 0.0017804230.61624 9.792660 0.0019904230.61995 9.792060 0.0019304230.62385 9.797390 0.0018904230.62773 9.790550 0.0015404230.63151 9.791650 0.0015004230.63534 9.794210 0.0013804230.63951 9.792870 0.0013704230.64327 9.791080 0.0013404230.64710 9.792050 0.0013604230.65100 9.791110 0.0013204230.65472 9.791060 0.0013604230.65863 9.790150 0.0014004234.55338 9.787160 0.0011804253.54525 9.805840 0.0010604254.51133 9.785900 0.0011804255.51652 9.776930 0.001160anotte A. A. et al: Global analysis of GJ 436 Spitzer and new HARPS data , Online Material p 2
Table 2. continued. BJD TT - 2 450 000.0 RV (km s − ) σ RV (km s − )4259.48729 9.794650 0.0008604291.48864 9.786670 0.0017704292.47496 9.776630 0.0009704293.45165 9.807350 0.0008404294.45008 9.780610 0.0010204296.47679 9.797980 0.0013004297.45381 9.773530 0.0009704478.85281 9.800580 0.0009504478.87832 9.800520 0.0009404479.86544 9.774800 0.0010604479.87612 9.776220 0.0010204480.85907 9.802150 0.0009704480.87048 9.803650 0.0010804481.86319 9.787750 0.0009804481.87376 9.787880 0.0009404482.85401 9.779690 0.0010604482.86479 9.777000 0.0010404483.85232 9.810150 0.0010004483.86342 9.810410 0.0009404485.85751 9.791110 0.0010004485.86862 9.791410 0.0010004486.85432 9.797240 0.0010504486.86446 9.797920 0.0011304487.85213 9.776690 0.0012004487.86293 9.776470 0.0010604488.85500 9.808410 0.0011004522.83874 9.790160 0.0012304523.78988 9.801300 0.0010704524.79013 9.774390 0.0009004525.81324 9.805200 0.0011104526.76364 9.789100 0.0009004527.75196 9.775780 0.0009604528.71729 9.809030 0.0009304529.81240 9.781870 0.0009904530.77746 9.788820 0.0009704548.70327 9.775930 0.0008804549.69758 9.807770 0.0011504551.71918 9.780560 0.0009504553.69816 9.777170 0.0008004557.65838 9.809100 0.0011104562.64495 9.797950 0.0009904564.64742 9.777990 0.0012204567.56615 9.779660 0.0008204567.73507 9.787220 0.0008604568.57079 9.807880 0.0008904568.69152 9.805640 0.0009404569.62883 9.775720 0.0008604570.63780 9.799210 0.0009204571.60962 9.792680 0.0010204593.55210 9.774620 0.0009604610.47902 9.809060 0.0011204610.56287 9.812700 0.0010804611.55737 9.784050 0.0010304616.47724 9.796650 0.0014104832.87687 9.807660 0.0011904848.87131 9.805790 0.0010204854.84706 9.782360 0.0010504878.78979 9.778840 0.0009404879.79209 9.790510 0.0013804880.79826 9.795860 0.0016904880.81312 9.797910 0.0012404881.78795 9.775030 0.0009904882.78434 9.806450 0.0011004883.79460 9.787100 0.0009204884.77339 9.777030 0.0014004885.79300 9.807700 0.000920anotte A. A. et al: Global analysis of GJ 436 Spitzer and new HARPS data , Online Material p 3
Table 2. continued. BJD TT - 2 450 000.0 RV (km s − ) σ RV (km s − )4886.77008 9.777430 0.0010804913.68867 9.777280 0.0009404914.70871 9.813120 0.0010004915.68788 9.783630 0.0010604916.69305 9.786200 0.0009504917.68034 9.805840 0.0010204918.72808 9.777910 0.0009904919.66311 9.801600 0.0010304920.70757 9.793540 0.0009604932.64335 9.788420 0.0013004933.63867 9.799470 0.0010704934.62726 9.776640 0.0010104936.63242 9.791100 0.0015004937.61224 9.780310 0.0012004938.62352 9.810220 0.0009604939.64008 9.781560 0.0014304940.61510 9.793920 0.0013704941.62296 9.799100 0.0009804946.60518 9.807600 0.0008904949.58281 9.797480 0.0009804950.58399 9.775750 0.0009404953.58922 9.784570 0.0010404954.58379 9.808130 0.0009604955.58240 9.779020 0.0009904956.58363 9.801020 0.0012104990.49882 9.778470 0.0011204991.51076 9.810730 0.0010304993.46558 9.788340 0.0009804998.46541 9.779650 0.0013204999.45630 9.807500 0.0012305272.70295 9.780040 0.0011105275.70795 9.773080 0.0013205277.71133 9.789610 0.0012605278.70343 9.779770 0.0016905279.68465 9.807250 0.0011705280.70084 9.777020 0.0011905283.67801 9.775340 0.0009805287.65616 9.811220 0.0010805292.65024 9.812290 0.002210anotte A. A. et al: Global analysis of GJ 436 Spitzer and new HARPS data , Online Material p 4
Fig. 5.
Eight transit light curves of GJ 436b. The two upper panels are the data at 3.6 µ m from 2009 January 9 and 28. The followingtwo were taken at 4.5 µ m on 2009 January 17 and 30. The lower four were obtained at 8 µ m on 2007 June 29, 2008 July 12, 2009January 25 and February 2. The left plot displays the raw binned and unbinned data, the middle one the binned data corrected forinstrumental systematics, and the right one the binned residuals. Measurements are binned per interval of 7 min. The light curvesare shifted along the y -axis for the sake of clarity. The shaded green areas show the transit events. anotte A. A. et al: Global analysis of GJ 436 Spitzer and new HARPS data , Online Material p 5
Fig. 6.
Eight occultation light curves of GJ 436b. The two upper plots are the data at 3.6 µ m from 2008 January 30 and 2011February 1. The following two were obtained with the 4.5 µ m channel on 2008 February 2 and 2011 January 24. The fifth is thelight curve at 5.8 µ m from 2008 February 5. The last three were taken at 8 µ m on 2007 June 30, 2008 June 11, and 13. The left plotdisplays the raw data, the middle one the corrected data, and the right one the residuals. The shaded green areas show the eclipseevents. anotte A. A. et al: Global analysis of GJ 436 Spitzer and new HARPS data , Online Material p 6
Fig. 7.
Same as Fig. 6 with eight occultation light curves of GJ 436b at 8 µµ