Revisiting Spitzer transit observations with Independent Component Analysis: new results for the GJ436 system

0.5 MB·English

by  G. Morello

Revisiting Spitzer transit observations with Independent
Component Analysis: new results for the GJ436 system
5 G. Morello, I. P. Waldmann, G. Tinetti, I. D. Howarth
1
Department of Physics & Astronomy, University College London, Gower Street, WC1E6BT, UK
0
2 [email protected]

n
a
G. Micela
J
3 INAF - Osservatorio Astronomico di Palermo, Piazza del Parlamento 1, 90134, Italy
2 and

]
P
F. Allard
E
Centre de Recherche Astrophysique de Lyon - E´cole Normale Sup´erieure de Lyon, 46 All´ee d’Italie, 69364
.
h
Lyon Cedex 07
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-
o
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a ABSTRACT
[
We analyzedfour Spitzer/IRAC observationsat 3.6 and 4.5 µm of the primary transit of the
1
exoplanet GJ436b, by using blind source separation techniques. These observations are impor-
v
tanttoinvestigatetheatmosphericcompositionoftheplanetGJ436b. Previousanalysesclaimed
6
6 strong inter-epoch variations of the transit parameters due to stellar variability, casting doubts
8 onthe possibility to extractconclusivelyan atmosphericsignal;those analysesalsoreporteddis-
5 crepantresults,hence the necessityofthis reanalysis. The methodweusedhasbeenproposedin
0
Morello et al.(2014)toanalyze3.6µmtransitlight-curvesofthehotJupiterHD189733b;itper-
.
1 formes an Independent Component Analysis (ICA) on a set of pixel-light-curves,i.e. time series
0
readbyindividualpixels,fromthe samephotometricobservation. Ourmethodonlyassumesthe
5
independenceofinstrumentalandastrophysicalsignals,andthereforeguaranteesahigherdegree
1
: of objectivity compared to parametric detrending techniques published in the literature. The
v
datasets we analyzed in this paper represent a more challenging test compared to the previous
i
X ones.
r Contrary to previous results reported in the literature, our results (1) do not support any de-
a tectable inter-epoch variations of orbital and stellar parameters, (2) are photometrically stable
atthe level 10−4 inthe IR,and(3)the transitdepthmeasurementsatthe twowavelengthsare
∼
consistentwithin 1σ. We also (4) detect a possible transit durationvariation (TDV) of 80 s (2
∼
σ significance level), that has not been pointed out in the literature, and (5) confirm no transit
timing variations (TTVs) &30 s.
Subjectheadings: methods: dataanalysis-techniques: photometric-planetsandsatellites: atmospheres
- planets and satellites: individual(GJ436b)
1. Introduction large majority of transiting exoplanets are “hot
Jupiters”, i.e. planets with size similar to Jupiter
Transit spectroscopy and differential photome-
orbitingverycloselyto their hoststar(semimajor
tryarelargelyusedtoinvestigatethecomposition
axis 0.01 0.5AU). Their typical surface tem-
and structure of exoplanetary atmospheres. The ∼ −
1
peratures are &1000K. transit observations, and their reanalysis of sec-
GJ436b is a Neptune-sized planet orbiting ondary eclipse data is consistent with this detec-
around an M dwarf with radius 0.46R⊙ at tion. Knutson et al. (2011) measured significant
a distance 0.03 AU. This planet∼is interest- time variations of the transit depths at the same
ing for seve∼ral reasons. It is one of the small- wavelengths, which strongly affect the inferred
est (radius 4.3R⊕) and coolest ( 700K) ex- transmission spectrum. They attributed such
oplanet for∼which optical-to-IR s∼pectra have variations to the stellar activity and found that
been measured (Gillon et al. 2007; Demory et al. different results are obtainable depending on the
2007; Alonso et al. 2008; Coughlin et al. 2008; observationsconsidered. Byrejectingthoseobser-
C´aceres et al.2009;Deming et al.2009;Pont et al. vations that they believe to be most strongly af-
2009; Ballard et al. 2010; Stevenson et al. 2010; fectedbystellaractivity,theirfinalresultssupport
Beaulieu et al. 2011; Knutson et al. 2011, 2014). CO as the dominant carbon molecule, with very
The primarytransitdepth is 0.7%. Another pe- little, if any, CH4. More recent Hubble/WFC3
culiarity of GJ436b is its high∼orbital eccentricity observations in the 1.2 1.6 µm wavelength inter-
−
(e 0.16), inferred from radial velocity measure- val, analyzed by Knutson et al. (2014), indicate a
me∼nts (Maness et al. 2007) and from secondary featureless transmission spectrum, which is con-
eclipse phasing (Deming et al. 2009). Both the sistent with relatively hydrogen-poor atmosphere
physical and dynamical properties of GJ436b are with a high cloud or haze layer.
debated in the literature. In this paper we reanalyze four transit light-
Maness et al. (2007) and Demory et al. (2007) curves obtained with Spitzer/IRAC at 3.6 and
investigated the origin of the high orbital ec- 4.5 µm passbands (channels 1 and 2 of IRAC).
centricity of GJ436b, concluding that the cir- We adopt a non-parametricdata detrending tech-
cularization timescale ( 108 yr) is significantly nique,basedonIndependentComponentAnalysis
smaller than the age o∼f the system (&6 109). (ICA) applied to single pixel-light-curves, to en-
Maness et al. (2007) also found a long tre×nd in sure a higher degree of objectivity. This method
radial velocity measurements; they suggested the has proven to give robust results, when applied
presenceofanexternalperturber onawider orbit to the transits of the hot-Jupiter HD189733b
to explain both the high eccentricity of GJ436b observed with IRAC at 3.6 µm (Morello et al.
and the long trend in radial velocity measure- 2014). We further test here the performance of
ments. Ribas et al. (2008) hypothesized a Super- this detrending technique with the morechalleng-
Earth on a close orbit to explain those evidences, ing datasets of the Neptune-sized planet GJ436b,
later retracted. Transit timing variations (TTVs) forwhichthetransitdepthiscomparablewiththe
reported by Alonso et al. (2008); C´aceres et al. amplitude of the instrumental pixel-phase signal,
(2009) do not support any evidence of external and the transit duration is very similar to the pe-
perturbers. Stevenson et al. (2012) claimed the riod of that signal. Additionally, we discuss the
possible detection of two nearby sub-Earth-sized stellar and orbital stability of the GJ436 system,
exoplanets transiting in GJ436 system; accord- the repeatability of transit measurements, poten-
ing to the authors, the dynamic of the proposed tially affected by stellar, planet, and instrument
system is consistent with the current non-TTV- variability, and the atmospheric contribution. We
detections. discussthereliabilityofourresultsinlightofother
observations reported in the literature, in partic-
Basedonmultiwavelengthinfraredeclipsemea-
ular Beaulieu et al. (2011); Knutson et al. (2011,
surements, Stevenson et al. (2010) proposed a
2014).
high CO-to-CH4 ratio compared to thermochem-
ical equilibrium models for hydrogen-dominated
2. Data Analysis
atmospheres. Their atmospheric model includes
disequilibrium processes, such as vertical mixing
2.1. Observations
and polymerization of methan to explain the ob-
served deficiency of CH4. Beaulieu et al. (2011) We analyze four photometric observations of
suggested strong CH4 absorption at 3.6, 4.5, and GJ436b, which are part of the Spitzer program
8.0 µm Spitzer/IRAC passbands from primary ID 50051. They include two 3.6 and two 4.5 µm
2
Table 1: Spitzer observations of primary transits of GJ436b.
Obs. Number Detector Wavelength (µm) UT Date Orbit Number
1a IRAC, ch1 3.6 2009 Jan 9 234
1b IRAC, ch1 3.6 2009 Jan 28 241
2a IRAC, ch2 4.5 2009 Jan 17 237
2b IRAC, ch2 4.5 2009 Jan 31 242
primary transits as detailed in Tab. 1. Each ob- including all the non-transit components plus a
servationconsists of1829exposures using IRAC’s constantterm. Thedetrendedtransitsignalisob-
sub-array mode, taken over 4.3 hr: 0.8 hr on the tained by subtracting all the non-transit compo-
primary transit of the planet, the remaining 3.5 nents, properly scaled by their fitting coefficients,
hr before and after transit. The interval between from the integral light-curve. It is renormalized
consecutive exposures is 8.4 s. Each exposure in- by the mean value on the out-of-transit, so that
cludes 64 consecutive frames integrated over 0.1 the out-of-transit level is unity.
s. We replaced the single frames of each exposure After the extractionsofthe detrendedandnor-
with their averages to reduce the random scatter, malized transit time series, we modelled them by
1
and the computational time . During an observa- using the Mandel & Agol (2002) analytical for-
tion, the centroid of the star GJ436 is stable to mulae. We originally assumed the orbital period,
within one pixel. P, and the epoch of the first transit, E , re-
tr
ported by C´aceres et al. (2009); the eccentricity,
2.2. Detrending method, light-curve fit-
e, and the argument of periastron, ω, reported
ting and error bars
by Maness et al. (2007); they are consistent with
those reported by previous papers (Butler et al.
Here we outline the main steps of the analysis,
i.e. data detrending, light-curve fitting and esti- 2004; Gillon et al. 2007; Deming et al. 2009), and
more accurate. We tested two different sets of
mating parameter error bars. Further details are
quadratic limb darkening coefficients for the star
reported in Morello et al. (2014).
(Howarth 2011b), γ1 and γ2, derived by an At-
To detrend the transit signals from single ob-
las (Kurucz 1970; Howarth 2011) and a Phoenix
servations, we performed an ICA decomposition
(Allard & Hauschildt 1995; Allard et al. 2001)
over selected pixel-light-curves, i.e. time series
models (see Sec. 2.3.1). With these settings, we
from individual pixels. We considered 5 5 ar-
× estimated the planet-to-star radii ratio, p = rp,
rays of pixels with the stellar centroids at their Rs
the orbitalsemimajoraxisinunits ofstellarradii,
centers. In this way, we obtain a set of maxi-
a0 = a , and inclination, i. First estimates were
mally independent components: one of them is Rs
obtained through a Nelder-Mead optimization al-
thetransitsignal,othersmaybeinstrumentalsys-
gorithm (Lagarias et al. 1998); they were used as
tematics and/or astrophysical signals. Observed
optimal starting points for an Adaptive Metropo-
light-curvesare linear combinations of these inde-
lis algorithm with delayed rejection (Haario et al.
pendent components, the coefficients of the linear
2006), generating chains of 20,000 values. Up-
combinationscanbe calculatedbyfitting the out-
datedbestestimatesand(partial)errorbarsofthe
of-transit parts. To estimate the transit signal in
a robust way, the fit is performed on the out-of- parameters, σpar,0, are the means and standard
deviations of the relevant (gaussian distributed)
transitofthe relevantintegrallight-curve,i.e. the
sampled chains, respectively. The final parameter
sum of the pixel-light-curves from the array used,
error bars are:
1Computational time is dominated by the time for transit σ2+σ2
fititntgins)g,uwsehdi.chInstorounrgclaysed,eptreanndssitofinttthinegatlgimoreitwhmasso(fansedvesreat-l σpar =σpar,0s 0 σ02ICA (1)
hours, and it scales as O(dN), being d the number of free σ2 is the sampled likelihood variance, approxi-
transitparameters,andN thedatapoints. 0
mately equal to the variance of the residuals for
3
the best transit model; σI2CA is a term estimating 3.3x 104 Obs 1a 3.3x 104 Obs 1b
the uncertainty associated to the ICA extraction
(seFeoArpcpo.mApl.e3tefonresfsu,rtahnedrfdoertacoilms)p.arisonwith the Photon counts333..12.255 333..12.255
literature,wealsocalculatedthetransitdepth,p2,
3.10 5000 10000 15000 3.10 5000 10000 15000
theimpactparameter,b,andthetransitduration, Time (s) Time (s)
T, where (see Ford et al. (2008)): 2.2x 104 Obs 2a 2.2x 104 Obs 2b
b=a0cosi1+1−esein2ω (2) Photon counts2.15 2.15
P√1 b2 √1 e2 2.10 5000Time (1s0)000 15000 2.10 5000Time (1s0)000 15000
T = − − (3)
πa0 1+esinω Fig. 1.—Rawintegrallight-curvesofthefourpri-
For a more thorough analysis, we performed marytransitobservations. Datapoints ontheleft
other fits with different choices of the free param- of black vertical lines have been discarded for the
eters, introducing a phase-shift parameter to con- analysis. Note that the transit depth is compara-
sider possible timing error/variations, and simul- ble with the amplitude of systematics.
taneousfitsonmorethanonemultiplelight-curves
with some common free parameters. 1.5x 104 Obs 1a 1.5x 104 Obs 1b
1.4 1.4
2.3F.ig.A1pprelpicoarttisotnhetoraowbs“einrtveagtriaolnlsight-curves” Photon counts111...1123 111...1123
0.9 0.9
observed. The main systematic effect for IRAC 0.80 5000 10000 15000 0.80 5000 10000 15000
Time (s) Time (s)
channels1and2observationsisanalmostregular
Obs 2a Obs 2b
undulation with period 3000 s, so-called pixel- 12000 12000
∼ 11000 11000
psciehtniaotseneroe(fffFteahcztei,osboeeutcracauel.sce2ei0nt0tdr4oe;ipdMenwodritsahloernse-tsChpaeelcdrte´eltraootniaveeptipxaoel-.l Photon counts17890000000000000 17890000000000000
6000 6000
2006). This effect is particularly difficult to de-
50000 5000 10000 15000 50000 5000 10000 15000
trend from these datasets because its timescale is Time (s) Time (s)
similar to the transit duration, and its amplitude
Fig. 2.—Centralpixel-light-curvesofthefourpri-
is comparable to the transit depth. Recently, a
marytransitobservations. Datapoints ontheleft
timedependenceofthepixel-phaseeffecthasbeen
of black vertical lines have been discarded for the
suggested (Stevenson et al. 2010; Beaulieu et al.
analysis. Note that pixel-light-curves are domi-
2011).
natedbysystematics,andthe transitsignalis not
If considering the whole datasets for detrend-
visible by eye (but it is present, as provenby ICA
ing, our ICA algorithm is able to remove most of
retrieval).
the non-flatness on the out-of-transits, and visi-
bly improve the in-transit shapes, but some vis-
ible issues remain (see Fig. 16). We noted that 450 exposures from each observation, correspond-
results improve significantly if rejecting a number ing to 3780 s, for which the ICA performances
∼
of data points from the beginning of each obser- areoptimal. Itisworthtopointoutthatdifferent
vation. It is discussed on a statistical basis in choices (including no data rejections) give consis-
Sec. 3.1. A possible explanation is that first data tent results (within 1 σ), with larger or similar
points containa long-tailvariationuntil stabiliza- error bars.
tion of the instruments (Fazio et al. (2004), see
also App. A.1); this is not a crucial point for the 2.3.1. Limb darkening coefficients
data analysis. In the rest of this paper we dis-
Tab. 2reportsthequadraticlimbdarkeningco-
cuss the results obtained after rejecting the first
efficientsusedat3.6and4.5µmIRACpassbands.
4
BoththeAtlasandPhoenixmodelsarecomputed PCC -0.7 for channel 2. After the ICA detrend-
∼
with T = 3680 K, logg = 4.78 (Torres 2009), ing including all the data, these correlations are
eff
and solar abundances (Asplund et al. 2009). significativelyreduced(PCC <0.3). Ifweremove
| |
the first450data points, the ICA detrending gen-
erallyperformssignificantlybetter(PCC 10−3-
Table 2: Quadratic limb darkening coefficients 7 10−2). Fig. 5 reports the level o|f sign|i∼ficance
computedbyAtlasandPhoenixstellarmodelsfor ×
of the residual correlationsin the detrended data,
IRAC 3.6 and 4.5 µm bands.
calculated with a permutation test. When we re-
Atlas 3.6 µm 4.5 µm
ject the first 450data points, the residualcorrela-
γ1 5.489 10−2 1.331 10−2 tionsinthedetrendeddataarebelow1.5σ,except
γ2 3.0653× 10−1 2.8396× 10−1 for Obs. 2a, for which the residual correlation is
× ×
Phoenix 3.6 µm 4.5 µm
higherinanycase. Theresidualcorrelationswith-
γ1 3.87 10−3 3.27 10−3 out the cut of the first 450 data points are larger,
γ2 2.3615× 10−1 1.8193× 10−1 i.e. >4 σ in the post transit, with the exception
× ×
of Obs. 1b,for whichthe residualcorrelationsare
below 1 σ in any case.
3. Results 1.5x 104 Obs 1a 1.5x 104 Obs 1b
1.4 1.4
3.1T.o iTnveessttsigoafteptihxeele-ffpehcatisveenceosrsroeflatthieondasta de- Photon counts111...1123 111...1123
trending we measure the correlations of the sig- 0.9 0.9
nalswiththepixel-phaseposition,beforeandafter 0.80 5000 10000 15000 0.80 5000 10000 15000
Time (s) Time (s)
the corrections. We refer to the Pearsonproduct- Obs 2a Obs 2b
12000 12000
moment correlationcoefficient (PCC), defined as: 11000 11000
PCC = coσv(Xσ,Y) (4) Photon counts17890000000000000 17890000000000000
X Y 6000 6000
50000 5000 10000 15000 50000 5000 10000 15000
wherecov(X,Y)isthecovarianceofthesignalsX Time (s) Time (s)
and Y, σ and σ are the standard deviations.
X Y Fig. 3.— Time series of the pixel-phase values
In this context, X and Y are temporal series of
for the four observations. Data points on the
fluxes and pixel-phases. The PCCs are measured
left of black vertical lines have been discarded
overthreeintervals,i.e. pre-,in-,andpost-transit,
for the analysis; dashed green lines delimit the
wherethe astrophysicalsignalsareexpectedto be
endsofpre-transitsandthebeginsofpost-transits;
almost flat 2. In general -1 PCC +1, where +1
≤ ≤ dashed red lines delimit the in-transits.
is total positive correlation, -1 is total negative
correlation,and0is nocorrelation. Fig. 3reports
the temporalseriesofpixel-phases. Fig. 4reports 3.2. Fitting p, a0 and i
the values of the PCCs measured on the pre-, in-,
andpost-transitforeachobservation,uncorrected, Fig. 6 reports the detrended light-curves,
correctedwithoutandwithpre-transittruncation. binnedover7points,withtherelativebesttransit
The originaldata are strongly anticorrelatedwith models, and the residuals. The transit models in
thepixel-phase,withPCC.-0.9forchannel1,and Fig. 6arecomputedwithγ1 andγ2 Phoenixcoef-
ficients. Analogoustransit models computed with
2We used the following definitions: pre-transit (φ < - γ1 and γ2 Atlas coefficients are very similar, with
0.0082); in-transit (-0.00433 < φ <0.00416); post-transit averagestandarddeviations.1.9 10−5,andmax-
(φ>0.0082). Thesehavebeendecidedsothatallthetran- imum discrepacies .10−4. Discre×pancies between
sit models obtained during the analysis, modified with no
the transit models and the detrended light-curves
limbdarkening,areflatinthesethreeintervals. Wechecked are at the level 2.0 10−4 for IRAC channel 1,
thatotherreasonablechoicesofthelimitsdonotaffectthis
analysis. and 2.6 2.9 1∼0−4×for IRAC channel 2, there-
∼ − ×
5
Obs 1a Obs 1b 3.2.1. Combining observations
1 1 raw curve
detrended (no rej.)
0.5 0.5 detrended (w rej.) We performed two couples of simultaneos fits,
PCC 0 0 one for the 3.6 µm and one for the 4.5 µm light-
−0.5 −0.5 curves, with Atlas and Phoenix limb darkening
−1 pre in post −1 pre in post coefficients, assuming common orbitalparameters
1 Obs 2a 1 Obs 2b (a0 andi),andpotentiallydifferenttransitdepths
0.5 0.5 (p), in order to cancel the effects of parameter in-
PCC 0 0 tercorrelations. The assumption that orbital pa-
rameters are the same during each observation
−0.5 −0.5
is very reliable, because they are sparse over a
−1 pre in post −1 pre in post
short period of time (less than 1 month, 9 plan-
Fig. 4.— PCCs between fluxes and pixel-phases etary orbital periods), so that variations due to
for pre-, in-, and post-transits of the four light- relativistic effects, external perturbers or tidal ef-
curves; (blu circles) raw data, (green rightwards fects, would be very small compared to the error
triangles) ICA detrended data with no rejections, bars (Alonso et al. 2008; Jord´an & Bakos 2008;
(red upwards triangles) ICA detrended data after Pa´l & Kocsis 2008).
rejecting the first 450 points. The results of these combined fits are reported
in Fig. 8, 9, in Tab. 6 and 7. The 4.5 µm tran-
Obs 1a Obs 1b sit depths become identical, with an intermedi-
6 6 no rej.
σC significance ()2345 2345 w rej. aavetreargtveeasfi,lutbesu;bttehtthewee3ier.6nseµtphmaerattrwtaioonnsditiestdesretmpiltlihnlseedsssliwgthihtathlnys1edσpi--.
PC1 1 The standard deviations of residuals between the
0 pre in post 0 pre in post detrended light-curves and the transit models in-
Obs 2a Obs 2b crease of 2 3 10−6 for Obs 2a and 2b (neg-
σC significance ()23456 23456 s(licugomibmplept)ia,ornaabn∼oldef c−woofimt×h∼m7to−hne8o×σr01b0iut−an6lcepfroatrraaiOnmtbieestse)1r.as TfaonhrdeOa1bsbs-
PC1 1 2a and 2b may be valid, being the consequent
0 pre in post 0 pre in post transit models as good as the individually fitted
ones. Being the transit depths also identical, the
Fig. 5.— Significance level of correlation between twolight-curvesareverywellapproximatedbythe
fluxes and pixel-phases for the four observations; same transit model. The original discrepancies
(green rightwards triangles) ICA detrended data between the two sets of transit parameters were
with no rejections, (red upwards triangles) ICA enlarged by their intercorrelations. The same as-
detrendeddataafterrejectingthefirst450points. sumption for Obs 1a and 1b lead to worse transit
models andmore divergenttransitdepths, but, in
both cases, not dramatically.
foreitis notpossibleto distinguishbetweenAtlas
3.3. Timing variations
and Phoenix models from the data. Best param-
eter results and error bars are reported in Fig. 7, We performed transit model-fits with a free
in Tab. 4 and 5. Atlas and Phoenix stellar mod- phase-shift in addition to p, a0, and i, in order
els lead to two systematically different parameter to investigate the effect of possible timing varia-
sets,butwithintheerrorbars. Alltheparameters tions. Fig. 10reportsthetime-shiftsobtained. No
fromdifferent observationsarecomparablewithin evidence of timing variation have been detected,
1σ, even neglecting the detrending errors (σ ), with upper limits <30 s. Both Atlas and Phoenix
ICA
except the transit durations for Obs 1a and 1b. stellar models lead to the same shifts. Other pa-
This is discussed in the following sections. rameter estimates are not affected.
6
0.0880 This paper (Atlas)
This paper (Phoenix)
0.0860 Knutson et al. 2011
Beaulieu et al. 2011
0.0840
p
0.0820
0.0800
0.0780 1a 1b 2a 2b
7.5x 10−3 This paper (Atlas)
Obs 1a 1x 10−3 TKhniust spoanp eert (aPl.h 2o0e1n1ix)
1 7 Beaulieu et al. 2011
malized flux00..99996800 0.05 2p6.5
Nor0.9940 −0.5
0.99−200.03−0.02−0.01 Φ0 0.01 0.02 0.03 −−01.03−0.02−0.01 Φ0 0.01 0.02 0.03 6 1a 1b 2a 2b
1 Obs 1b 1x 10−3 17 This paper (Atlas)
This paper (Phoenix)
Normalized flux000...999999468000 −00..055 a0111456 KBneuatusloienu eett aal.l. 22001111
0.99−200.03−0.02−0.01 Φ0 0.01 0.02 0.03 −−01.03−0.02−0.01 Φ0 0.01 0.02 0.03 13
1 Obs 2a 1x 10−3 12 1a 1b 2a 2b
Normaiized flux000...999999468000 −00..055 00.9.95 TTBhheiiassu ppliaaeppuee err t(( aAPlth.l ao2se0)n1i1x)
0.99−200.03−0.02−0.01 Φ0 0.01 0.02 0.03 −−01.03−0.02−0.01 Φ0 0.01 0.02 0.03 b0.85
Obs 2b 1x 10−3 0.8
1
Normalized flux000...999999468000 −00..055 08.77.50 1a 1b 2a 2b TThhiiss ppaappeerr ((APthlaose)nix)
0.99−200.03−0.02−0.01 Φ0 0.01 0.02 0.03 −−01.03−0.02−0.01 Φ0 0.01 0.02 0.03 8866..68 Knutson et al. 2011
i
Fig. 6.— Left panels: (blue) detrended light- 86.4
curves for the four observations with (red) best 86.2
transit models overplotted, binned over 7 points; 86.0 1a 1b 2a 2b
best transit models are calculated with p, a0, and
i as free parameters, and Phoenix quadratic limb 3000 This paper (Atlas)
This paper (Phoenix)
darkening coefficients (see Sec. 2.3.1). Right pan- 2950 Beaulieu et al. 2011
els: Residuals betweendetrendedlight-curvesand 2900
best transit models; black horizontal dashed lines T (s)2850
indicate the standard deviations of residuals.
2800
2750 1a 1b 2a 2b
Fig. 7.— From top to bottom: Comparisons of
the parameters p, a0, and i (left side), p2, b, and
T (right side), obtained in this paper with Atlas
stellarmodel(cyan,emptycircles),Phoenixstellar
model (blue, full circles), in Knutson et al. (2011)
(red triangles), and in Beaulieu et al. (2011) (yel-
low squares).
7
0.90 Atlas
Phoenix
0.88
0.86
b
0.84
0.82
0.80 2a 2b 2a+2b
0.0850 Atlas 0.90 APthlaosenix
Atlas (common a, i) 0.88
0
0.0840 Phoenix
Phoenix (common a, i) 0.86
0
b
p0.0830 0.84
0.0820 0.82
0.0810 1a 1b 0.80 2a 2b 2a+2b
0.0850 Atlas 2950 APthlaosenix
Atlas (common a, i)
0 2900
0.0840 Phoenix
Phoenix (common a, i)
p0.0830 0 T (s)2850
2800
0.0820
0.0810 2a 2b 2750 2a 2b 2a+2b
7.3x 10−3 Atlas 2950 APthlaosenix
7.2 Atlas (common a0, i) 2900
Phoenix
2p7.71 Phoenix (common a0, i) T (s)2850
6.9 2800
6.8
6.7 1a 1b 2750 2a 2b 2a+2b
7.3x 10−3 Atlas Fig. 9.—Comparisonsofthe parametersbandT,
7.2 Atlas (common a0, i) obtained in this paper, with common orbital pa-
Phoenix
7.1 Phoenix (common a0, i) rametersforobservationsatthe samewavelength,
2p 7 and Atlas or Phoenix stellar models.
6.9
6.8
6.7 2a 2b 30 Atlas
20 Phoenix
oFbigt.ai8n.e—d Cinomthpisarpisaopnesr,ofwtihthepcaormammeotnerosrpbiatnaldppa2-, TTV (s)−11000
rametersforobservationsatthe samewavelength, −20
and Atlas or Phoenix stellar models. −30 1a 1b 2a 2b
Fig. 10.— Best fitted time-shifts of the mid-
transit with respect to the periodically predicted
mid-transit times, assuming Atlas or Phoenix
stellar models. Note that results are model-
independent, because mid-transit time will not
correlate with limb darkening parameters, or any
other physical parameters.
8
4. Discussion 3.2.1. Simultaneousfitsoverthefourobservations
with common orbital parameters do not add any
4.1. Comparing observations
information.
Fig. 11 and 12 report the superpositions of 3.6
4.2. Comparisonwith previousanalyses of
and4.5µmlight-curvesrespectively,andtheresid-
the same observations
uals. Inbothcasesthemeanvalueofthein-transit
residuals is small (.5 10−5), but the transit 1b Fig. 7 reports the parameter values obtained
×
is clearly longer than transit 1a, as measured by in this paper for the individual observations with
transitduration (T)parameters. As T is function the analogues reported by Beaulieu et al. (2011);
of the orbital parameters and stellar model, this Knutson et al. (2011). Our results suggest a con-
is the reason why simultaneous fits with common stantvalueofthetransitdepth(largelywithin1σ)
orbital parameters and stellar model do not be- bothbetweenthe3.6and4.5µmobservations,and
have very well. We also note that the ingresses of forthetwowavelengths. Knutson et al.(2011)re-
transits 2a and 2b have different slopes. port variations of the transit depth with a 3.4σ
significance between the two epochs at 3.6 µm,
Obs 1a & 1b
1.002 and2.1σ at4.5µm, whichthey attributedtostel-
1
0.998 lar activity. Beaulieu et al. (2011) also obtained
Normalized flux000...999−99901246.0 x3 10−3 −0.02 −0.01 0 0.01 0.02 0.03 sthigenisfiacmanetwdaiffveerleenngceths,bebtuwteetnhedyiffaetrternibtuetpeodchssucaht
0 discrepanciestoanunfavorabletransit-systematic
−−01.03 −0.02 −0.01 Φ0 0.01 0.02 0.03 phasing, then they discarded those epochs from
the analysis. Our error bars are generally compa-
Fig. 11.— Top panel: detrended light-curves for rabletotheonesreportedinbothpreviouspapers,
Obs 1a (blue), and for Obs 1b (green). Bottom butinsomecasestheyarelargeruptoafactor 2.
∼
panel: Residuals between the two observations. This is not surprising, because we are not making
Black dotted lines delimit the out-of-transit, red any prior assumptions about the signals, to guar-
dotted lines delimit the in-transit (as defined in antee a high degree of objectivity (Morello et al.
Sec. 3.1). 2014; Waldmann 2012; Waldmann et al. 2013).
We conclude that our detrending method lead to
more robust results than the previous ones in the
Obs 2a & 2b
1.002 literature,andtheyshownoevidenceofstellarac-
0.9918 tivity variations at 10−4 photometric level. Re-
Normalized flux 000...999−999001246.0 x3 10−3 −0.02 −0.01 0 0.01 0.02 0.03 sc1ie.g2nn−tifi1rc.e6asunµtltmstrfa(rnKosmnituHtds∼euopnbtbheltev/aaWlr.iFa2tC0i1o34n)osbaoslveserovrasfthoiuoownrsonabot-
−1
−0.03 −0.02 −0.01 Φ0 0.01 0.02 0.03 servations in about 2 months.
Fig. 12.— Top panel: detrended light-curves for 4.3. Comparison with other observations
Obs 2a (blue), and for Obs 2b (green). Bottom
Fig. 13 compares our estimated transit depth
panel: Residuals between the two observations.
valuesat3.6and4.5µm(averagedovertheobser-
Black dotted lines delimit the out-of-transit, red
vationsatthesamewavelength)withthemostre-
dotted lines delimit the in-transit (as defined in
cent results at 1.2 1.6 µm (Knutson et al. 2014).
Sec. 3.1).
−
Theresultingspectrumisfeaturelesswithintheer-
ror bars. However,when comparing transit depth
The difference between p2 values at the two
measurementsat differentwavelengths,we should
wavelengths is (on average) 5 10−5, then there
∼ × ensure that the GJ436 system is uniformly mod-
is no evidence of differences in planetary atmo-
elled, i.e. same stellar model and orbital parame-
sphere’s absorption at the two wavelengths.
ters. A uniform multiwavelength reanalysis is re-
The orbital parameters at the two wavelengths
quired to confirm this result, and investigate po-
are also comparable, as detailed in Sec. 3.2 and
tential small features.
9
7.2x 10−3 This paper nificance level), but no significant TTVs; more
Knutson et al. 2014 measurements arerequiredto investigatethe pos-
7.1
siblepresenceofaperturber,anditsnature. Also,
2p 7 more uniform analyses at other wavelengths are
required to get a more reliable transmission spec-
6.9
trum.
6.180 0 101
λ (µm)
G. Morello is funded by UCL Perren/Impact
Fig. 13.— Transit depth values obtained in this scholarship (CJ4M/CJ0T). I. P. Waldmann is
paper at 3.6 and 4.5 µm (blue circles); values at funded by the European Research Council Grant
1.2 1.6µmreportedbyKnutson et al.(2014)(red “Exolights”. G. Tinetti is funded by the Royal
−
triangles). Society. G.Micelaissupportedby“ProgettoPre-
miale-AWaytoOtherWorlds”,fundedbyItalian
Minister for University and Scientific Research”.
Our non-detection of TTVs higher than 30 s
∼
(see Sec. 3.3) is consistent with previous analyses
in the infrared (Alonso et al. 2008; C´aceres et al.
2009;Pont et al.2009;Ballard et al.2010;Knutson et al.
2011,2014). WemeasuredasignificantTDV( 80
∼
s) between Obs 1a and 1b; we did not find any
study of TDVs for GJ436b in the literature, but
injecting parameters from Knutson et al. (2011)
into our Eq. 3 we obtain a similar trend for
the same observations. More observations are
required to investigate the cause of the apparent
TDVbetweenObs1aand1b,whether itisdue to
a perturber (as currently required to explain the
high orbital eccentricity), a stellar phenomenon,
or something else.
5. Conclusions
We have applied a blind signal-source sepa-
ration method, firstly proposed by Morello et al.
(2014), to analyze other photometric data of pri-
mary transits of an exoplanet, and extending its
validity to the Spitzer/IRAC 4.5 µm band. These
datasets were more challenging to analyze, be-
cause of the lower transit depth, comparable with
the amplitude ofthe instrumentalpixel-phasesig-
nal,thetransitduration,verysimilartotheperiod
of said signal, and possible stellar variability.
We obtain consistent results between transits
atdifferentepochs,rulingoutstellaractivityvari-
ations within 10−4 photometric level. We do
∼
notdetectanysignificantdifferenceforthetransit
depth at 3.6 and 4.5 µm, neither with the re-
centmeasurementsat1.2 1.6µm(Knutson et al.
−
2014), supporting the hypothesis of a flat trans-
mission spectrum. We measure a TDV of 80 s
between transits separated by 7 orbits (2 σ sig-
10