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Accepted bytheAstrophysicalJournal,Jan24,2013 PreprinttypesetusingLATEXstyleemulateapjv.11/12/01 SPITZER TRANSITS OF THE SUPER-EARTH GJ1214B AND IMPLICATIONS FOR ITS ATMOSPHERE Jonathan D. Fraine1, Drake Deming1, Micha¨el Gillon2, Emmanu¨el Jehin2, Brice-Olivier Demory3, Bjoern Benneke3, Sara Seager3, Nikole K. Lewis4,5,6, Heather Knutson7, & Jean-Michel D´esert6,8,9 Accepted by the Astrophysical Journal, Jan 24, 2013 ABSTRACT 3 We observedthe transitingsuper-EarthexoplanetGJ1214busingWarmSpitzer at4.5µmwavelength 1 during a 20-day quasi-continuous sequence in May 2011. The goals of our long observation were to 0 accurately define the infrared transit radius of this nearby super-Earth, to search for the secondary 2 eclipse, and to search for other transiting planets in the habitable zone of GJ1214. We here report n results from the transit monitoring of GJ1214b, including a re-analysis of previous transit observations a by D´esert et al. (2011). In total, we analyse 14 transits of GJ1214b at 4.5µm, 3 transits at 3.6µm, J and 7 new ground-based transits in the I+z band. Our new Spitzer data by themselves eliminate 8 cloudless solar composition atmospheres for GJ1214b, and methane-rich models from Howe & Burrows 2 (2012). Using our new Spitzer measurements to anchor the observed transit radii of GJ1214b at long wavelengths, and adding new measurements in I+z, we evaluate models from Benneke & Seager (2012) ] P and Howe & Burrows(2012) using a χ2 analysis. We find that the best-fit model exhibits an increasein E transitradiusatshortwavelengthsduetoRayleighscattering. Purewateratmospheresarealsopossible. . However, a flat line (no atmosphere detected) remains among the best of the statistically acceptable h models, and better than pure water atmospheres. We explore the effect of systematic differences among p results from different observational groups, and we find that the Howe & Burrows (2012) tholin-haze - o model remains the best fit, even when systematic differences among observers are considered. r t Subject headings: Planets and satellites: atmospheres - Techniques: photometric - Infrared: planetary s a systems - Planets and satellites: composition [ 1. introduction IR water vapor opacity makeshydrogen-dominatedatmo- 1 spheresopaqueintheIRoverseveralscaleheights,inspite v The mass and radius of the nearby transiting super- of their relative paucity of heavy elements. Also, strong 3 Earth GJ1214b (Charbonneau et al. 2009) imply that bands of methane and carbon monoxide fall within the 6 it must have a significant atmosphere (Rogers & Seager WarmSpitzerbandpassesat3.6-and4.5µm,respectively. 7 2010). Thatinference motivatedanextensiveeffortto de- Considering that GJ1214b’s M-dwarf host star is bright 6 tect the atmosphere, by seeking wavelength variations of 1. the transitdepth. Awide varietyofcompositionsarepos- in the IR, transit observations of GJ1214b using Warm Spitzer become particularly relevant to the characteriza- 0 sibleforsuper-Earthatmospheres(Miller-Ricci & Fortney tion of its atmosphere. 3 2010; Benneke & Seager 2012; Howe & Burrows 2012), In May 2011, we observed the GJ1214 system quasi- 1 from hydrogen-dominated to heavy-element-rich. Most continuouslyfor20days,usingSpitzer’sIRACinstrument : current observations of the transits (Bean et al. 2010, v at 4.5µm. Our investigation had three goals: 1) to im- i 2011;Crossfield et al.2011;D´esert et al.2011;Berta et al. X 2011, 2012; de Mooij et al. 2012) have rejected hydrogen- prove the transit parameters of the system and constrain thepropertiesoftheplanet’stransmissionspectrum,2)to r dominated atmospheres for GJ1214b, but Croll et al. a searchforthe secondaryeclipse,and3)tosearchforother (2011) concluded in favor of a low molecular weight at- transiting planets in this system, to the outer edge of the mosphere. The infrared (IR) spectral region is partic- habitable zone. ularly important for such studies, because strong water Our observations included minor interruptions for data vapor bands increase the transit depth in the IR signifi- downloads. But, an unplanned 42-hour data loss also oc- cantly as compared to the optical. This is especially true curred during the 20-day sequence, caused by a combina- for hydrogen-dominated atmospheres, because of the in- tion of spacecraft and Deep Space Network (DSN) down- creased atmospheric scale height. The intrinsically strong 1 DepartmentofAstronomy,UniversityofMaryland,CollegePark,MD20742USA;[email protected] 2 Instituted’AstrophysiqueetdeGeophysique, UniversitedeLiege,Liege,Belgium 3 Department ofEarth, AtmosphericandPlanetarySciences, andDepartmentofPhysics,Massachusetts InstitureofTechnology, Cambridge, MA02139USA 4 DepartmentofPlanetarySciences andLunarandPlanetaryLaboratory,UniversityofArizona,Tucson,AZ85721USA 5 Present address: Department of Earth, Atmospheric and Planetary Sciences, and Department of Physics, Massachusetts Institure of Tech- nology, Cambridge,MA02139USA 6 SaganFellow 7 DivisionofGeologicalandPlanetarySciences,CaliforniaInstituteofTechnology, Pasadena,CA91125USA 8 Harvard-SmithsonianCenter forAstrophysics,60GardenSt.,Cambridge,MA02138USA 9 Presentaddress: DivisionofGeological andPlanetarySciences, CaliforniaInstitute ofTechnology, Pasadena, CA91125USA 1 2 Fraine et al. link anomalies. We therefore re-observed GJ1214 for an our analysis versus Gillon et al. (2012), and to add addi- additional 42-hours in November, 2011, using the IRAC tionalinformationrelevanttotheatmosphereofGJ1214b, 3.6µm band. Consequently, we have multiple transits at we observed 7 transits using the TRAPPIST facility both WarmSpitzer wavelengths,andthese data providea (Gillon et al.2011;Jehin et al.2011),overtheperiod2011 particularly powerful constraint on the IR transit depth. March 11 - May 18. The TRAPPIST observations and Moreover, since our 4.5µm transits were observed nearly photometry are described by Gillon et al. (2012), but we consecutively,wehaveanexcellentbasisforevaluatingthe summarize the data here. The observations were made degree to whichstellar activity (e.g.,star spots)affect the using the 60-cm robotic telescope in a slightly defocused inferred transit depth. mode. An I+z filter gave transmission from 750 to 1100 A global analysis of these GJ1214 data is being pub- nm. Differential photometry on the 25-sec exposure im- lished by Gillon et al. (2012), including a search for other ages was done (by M.G.) using IRAF/DAOPHOT.In our transiting planets in this system. In this paper, we focus analysis, we use the same version of the photometry as on the implications of our observations for understanding Gillon et al. (2012), but we perform an independent anal- the nature of GJ1214b’s atmosphere, and we investigate ysis and transit fitting. thewavelength-dependenttransitradiusofGJ1214binde- tail. Our analysis includes the degree to which star spots 3. spitzer photometry - even those not occulted by the planet - contribute to 3.1. Aperture Photometry possible bias in the measured radius of the planet. An- chored by our improved precision for these infrared tran- Our analysis utilizes the Basic Calibrated Data (BCD) sits of GJ1214b, we add 7 new ground-based transits in files produced by version S18.18.0 of the Spitzer pipeline. the I+z band, and we re-analyze the totality of pub- Two dimensional (2D) Gaussian centering produces the lished wavelength-dependent transit depths for GJ1214b, least scatter in our final photometry (Stevenson et al. exploiting recent advances in super-Earth model atmo- 2010; Agol et al. 2010). Knutson et al. (2012) found that spheres (Benneke & Seager 2012; Howe & Burrows 2012). flux-weighted centering gives superior results for Spitzer Sec. 2 describes the details of our observations, and datainstudiesofexoplanetaryphasecurvesoverlongtime Sec. 3 explains our procedure to extract precise photom- scales. We tried flux-weighted centering for our transit etry from the data. In Sec. 4 we fit to the photometry, analysis, but it did not result in significant improvement extracting the transit radius for the planet in the warm over our 2D Gaussian centering. Spitzer and I+z bands, and we derive improved system Inthecaseofthe4.5µmphotometrywecenteracircular parameters. Sec. 5 considers the possible effect of star aperture of constant radius on the star. We calculate the spots on our results. Sec. 6 discusses implications for the stellarfluxwithintheaperture,includinganalyticapprox- atmosphere of GJ1214b. imationsforthepartialcoverageofpixelsattheboundary of the aperture. We vary the radius of the aperture from 2. observations 2.0 to 5.0 pixels, in 0.5-pixelincrements, andthereby pro- 2.1. Spitzer ducesevenversionsofthephotometryateachwavelength. After decorrelation (see below), we chose to use an aper- We observed GJ1214 for 20 consecutive days using ture radius of 2.5 pixels for 4.5µm, based on the global WarmSpitzerat4.5µm,beginningonApril29,2011at03- scatter in the decorrelated photometry. 46UTC.Weusedsubarraymodewithanexposuretimeof Inthecaseofthe 3.6µmphotometry,weexaminedcon- 2secondsperframe. Theobservationscontainseveral 3- stant radius photometry– for the same seven radii as in ∼ hour interruptions for data download, and one unantici- the 4.5µm section– and variable radius aperture photom- pated42-hourgapwheredatawereirretrievablylost. The etry. The variable radius photometry improves the preci- data loss occurred because the DSN incurred anomalous sionby41%overconstantaperturephotometrybyvarying delaysindownloadingdataatthattime. WhentheSpitzer the aperture radius as a function of the ‘noise-pixel’ cal- observatory was designed, long observing campaigns of culations per frame (Mighell 2005; Knutson et al. 2012; exoplanet photometry were not envisioned. Spitzer’s on- Lewis et al. 2013). Therefore we adopt the noise pixel boardflightsoftwarewasdesignedtoautomaticallydelete method for our 3.6µm photometry, and subsequent intra- dataafteracertainperiodoftime, tomakeroominmem- pixel decorrelation (see below). oryfornewobservations. TheDSNanomalyconsequently The noise pixel method estimates the effective width of caused the onboard software to delete data before down- thepixelresponsefunction,accountingforundersampling, link (the flight software has now been corrected so that bycalculatingthevarianceofthefluxperframe,weighted this will not recur). by the square of the mean flux: To compensate for the data loss, we were awarded 42 hoursofcontinuousobservationsthatbeganonNovember (ΣI )2 6S,p2it0z1e1r’,sa3t.161µ-m54bUaTndCp.aWsse,teoleccotemdptloemaceqnutitrheeth4e.5seµdmatdaatina β˜i = Σ(Ijj)2, (1) from May 2011. We again used 2-second exposure times where β˜ is the noise pixel parameter for the stellar im- in subarray mode. In total, our data comprise 791,808 i ageinframei,I istheintensityofpixelj,andthesumma- exposures at 4.5µm, and 74,624 exposures at 3.6µm. j tions extend over all pixels wherein the stellar intensity is 2.2. TRAPPIST significant. Using the β˜ as the aperture radius collects i q In order to help define the possible effects of stellar an optimum amountof light for photometry. The average activity on the Spitzer transits, to further cross-check apertureradius fromusing this formulationonour3.6µm Spitzer transits of GJ1214b 3 data is 2.60 pixels. certainty estimates on the transit parameters, by 10%. ∼ Moreover,this phaserangecoincideswithsimilarsubdivi- 3.2. Decorrelation sions in the 4.5 µm data. After dividing by the results of the Gaussian weight- Upon producing photometry, we immediately see ing, we solve for and subtract an improved transit model, Spitzer’s well-known intra-pixel sensitivity effect, that and again apply a second stage weighting function decor- must be decorrelated and removed from the data. A relation. We experimented with a third iteration of this portion of the raw 4.5µm photometry (before decorrela- process, but it did not produce significant improvement. tion) is illustrated in Figure 1. Because the transits of Unlike the first (polynomial) stage of decorrelation, the GJ1214b are substantially larger than the intra-pixel sig- Gaussianweightingfunctionwasappliedto the totalityof nature,wefirstmaskoffthetransitsfromthefirststageof the data (i.e., all re-acquisitions) using a single Gaussian decorrelation. Our4.5µmdatacomprisesevendistinctre- kernel. The initial polynomial stage of the decorrelation acquisitions of GJ1214, with interruptions for data down- process may seem unnecessary, since the weighting func- load. Therefore our first stage of decorrelation is done tionalonecouldremovestructureinthedataonbothlarge separately for each of the seven re-acquisitions. That ini- and small spatial scales. However, we find that the poly- tal decorelation fits two polynomials to the data for each nomials speed up the iterative process by providing a fast re-acquisition. (There are seven sections of the data de- start to the iteration. Our final photometry has a stan- fined by the data downloads and re-acquisitions.) One dard deviation of 3.7 10−3, which is only 15% greater polynomial fit is applied to those data points wherein the × than the photon noise. Moreover, red noise is minimal imagecentroidliesatY-coordinategreaterthanthecenter and the precision for binned data improves nearly as the ofthepixel,andanotherpolynomialfitisappliedtothose square-rootof the bin size, as we demonstrate below. data wherein the image lies at Y-coordinate less than the Figure 2 shows an overview of our 4.5µm photometry, center of the pixel. Our rationale for this two-parameter after decorrelation;moredetaileddepictions arediscussed fit is based on visual inspection of the photometry, that and shown below. showsdifferentbehaviorabovethecenter-of-pixelthanbe- low center (see lower panel of Figure 1). The polynomi- 4. model fitting for transit parameters als are fourth order in Y and second order in X, because We analyzeallavailableSptizer transits,including are- the photometric variations as a function of Y are more analysis of the transits reported by D´esert et al. (2011), pronounced than with X. Also, visual examination of the andTRAPPIST transitsusing the I+z filter (Gillon et al. variation with Y indicated that lower order polynomials 2012). We usethree methodologiesto determine the best- (e.g., quadratic) would not represent the variations opti- fittransitparametersforeachdatasetandwavelength. All mally. After finding the best fit polynomials, we divide three methods use only the data within a phase interval themintothedata,includingthein-transitdata. Weonly of 0.05 around the center of eachtransit– except for the used this step to determine initial conditions for an itera- ± TRAPPIST transits, which used all of the available data tive weighting function method (see below). from Gillon et al. (2012). We follow the polynomial decorrelation with a sec- The first method solves for the best-fit transit parame- ond procedure that is itself a two-pass iterative pro- tersofalltransitssimultaneouslyateachwavelength. The cess. We first remove a preliminary transit model from second method fits each transit individually and indepen- the polynomial-decorrelated data, and apply a Gaussian dently, then calculates the average of the transit param- weighting function (Ballard et al. 2010; Lewis et al. 2013; eters at each wavelength, weighting the individual results Knutson et al. 2012) to correct the intra-pixel signatures. by the inverseof their variance. The third method phases The kernel of the Gaussian weighting uses a σ of 0.005 and bins all of the transits at each wavelength into a sin- pixels in Y, and 0.01 pixels in X for the 4.5µm data, that gle transit, and fits to those phased & binned data. All 3 we determined by trial and error - evaluating the noise methods included a total of 3 transits at 3.6µm, 14 tran- level of the final decorrelated photometry. A separate sits at4.5µm, and7 transits inthe I+z band. Comparing Gaussianweightingwasappliedtoeachsectionofthedata these threemethods givesanindicationofthe consistency between downloads,but the same kernel size was used for of our results, and we do indeed find good consistency, as all data sections at 4.5µm. noted below. For the 3.6µm data, we applied a noise-pixel, Gaus- We now describe the details of those fitting procedures. sian weighting function that uses a variable σ in Y, X, and β˜ (noise-pixel value). This varied the weights in the 4.1. Spitzer 4.5µm Transits Gaussiankernelto accommodate the necessarynumber of neighboring points that influence the strength of the cor- WeusetheformulationofMandel & Agol(2002)togen- relation between center position and flux, as discussed in erate transit curves and fit them to the observed data, Lewis et al. (2013) and Knutson et al. (2012). thereby extracting the essential parameters of the tran- Because of effects near the pixel boundary, we chose to sit. The 14 Spitzer transits at 4.5µm comprise our most subdivide the 3.6 µm data into 2 sections, encompassing extensive and highest quality data. Our simultaneous the 2 transits in the data. The pixel boundary effects oc- fit holds the orbital period fixed at the value measured cured well out of phase of both transits. After examining by Bean et al. (2011) 1.58040481 1.210−7 , and uses a the globalscatter and σ vs. N−0.5 (bin size) slope residu- Levenberg-Marquardt(cid:0)algorithm to±minimiz(cid:1)e the χ2 for als, we found that decorrelating after subdividing the 3.6 each transit. Although we are minimizing χ2, we do not µm data set to within 0.05 of each transit produced the acceptthatparticularsetoftransitparametersasourbest- ± best noise levels, and resulted in more conservative un- fit values. Instead, we explore parameter space using a 4 Fraine et al. Markov Chain Monte Carlo (MCMC) method, and also aroundthecenterofeachtransitminimizedtheRMSscat- usingaresidual-permutation(‘prayer-bead’)method. Our ter and the residual of the σ vs. N−0.5 slope, which mini- best-fit valuesaretakenfromthe mediansofthe posterior mizedtherednoiseforthesetransits;andwasfortuitously distributions generated in this exploration of parameter the same range as the 0.05in phase that we adopted for ± space (see Sec. 4.4). our 4.5µm fits. Our fit extracts a correction to the transit center time Werepeatedallofthemethodologydescribedinthissec- (asmightbecausedbyephemeriserror),aswellasa/R∗,i, tion on the D´esert et al. (2011) 3.6µm transit data, and Rp/R∗, and a linear limb-darkening coefficient. We hold we found that the slope of σ vs. N−0.5 was insensitive to the quadratic limb darkening coefficient at zero because the range of data analyzed. As a result, we use the entire BayesianInformationCriterion(Liddle2007)analysissup- D´esert et al. (2011) 3.6µm data set. ports a linearlaw, whichgivesanadequateaccountof the Asinthe4.5µmcase,wefittoall3ofthe3.6µmtransits minimal limb darkening that is characteristic of infrared using3methods: simultaneously,individually,andphased transits. Moreover, our derived linear limb darkening co- & binned. Figure 6 shows all 3 of the 3.6µm transits efficients at 3.6 and 4.5 microns (c0 =0.158 and 0.128 re- phased & binned, overlaid with a best-fit curve. Figure 7 spectively, see Table 4)are reasonablyconsistent with the illustrates the standard deviation of the 3.6µm residuals values predicted by Claret & Bloemen (2011) (c0= 0.147 as a function of bin size for our fits to the simultaneous and0.155)foramodelatmospherehavingT=3500K(that transit parameters. temperature being their closest match to GJ1214). Figure 3 zooms in on a portion of the simultaneous fit 4.3. TRAPPIST I+z Transits for the first two 4.5µm transits, and Figure 4 shows the For the TRAPPIST data set, we used all 7 distinct standard deviation of residuals (data minus simultaneous epochs of the GJ1214b transiting system provided by fit) when binned over different time intervals. Note that Gillon et al. (2012). Three of these epochs overlapped we find very little red noise in these data, indicating the withthe Spitzer4.5µmdataset. Gillon et al.(2012)used success of our multi-stage intra-pixel decorrelation. Note the I+zfilter onthe TRAPPISTtelescope becauseit sup- alsothatourdecorrelationprocesswilltendtoremoveslow plied a near uniform filter profile from 0.7 - 1.0 µm. variations in the stellar brightness. Hence the apparently We determined the physical parameters using all three constant flux seen in Figure 2 should not be interpreted methods discussed above: a simultanous fit, individual as evidence for stellar quiesence. (The possible effects of fits, and a fit to phased & binned data. Similar to the stellar activity on our results are discussed in Sec. 5). Spitzer data sets, we fit a Mandel & Agol (2002) transit In addition, we bin all 14 4.5 µm transits, including model using a Levenberg-Marquardt routine. In contrast that of D´esert et al. (2011), into bins of width 0.001 in to the Spitzer data sets,we fit the TRAPPIST data using phase, using a running standard deviation for the weights a Mandel & Agol (2002) model that included quadratic ina weightedmean–phasingthemallto acommonepoch limb darkening, which accounted for the excess stellar determined from the simultaneous fit. As before, we in- limb-darkening observed in the shorter wavelength tran- clude only data within a phase range 0.05 of transit ± sitdata. The fittothephased&binnedTRAPPISTdata center, and we fit to the phased & binned transit us- is shown as Figure 8. To analyze the quality of the fit, ing the same Levenberg-Marquardt algorithm described Figure 9 showsthe σ vs. N−0.5 for the simultaneous fit of above. Figure 5 shows the resulting fit in comparison to the TRAPPIST data set. the phased & binned data. The results for the planet-to-star radius ratios, and re- The best-fit Spitzer transit parameters for each 4.5µm lated errorbars, in the I+z band are plotted on Figure 10 transit fitted individually are given in Table 1; the indi- for comparison to our 13 Spitzer transits at 4.5µm, and vidual 3.6µm transits (Sec. 4.2) are given in Table 2, and listedinTables3&4. Furtherinformationaboutthedata the individual TRAPPIST results (Sec. 4.3) are given in reduction process for the TRAPPIST data set is included Table 3. Results using the combining methods are sum- in Gillon et al. (2012). marized in Sec. 4.5. 4.4. Errors 4.2. Spitzer 3.6µm Transits We used two methods to estimate uncertainties for our Our 42-hour ‘replacement’ observations contain two derived transit parameters: MCMC and prayer-bead. In transits at 3.6µm, one near the beginning of these data both methods the errors - as well as the best-fit values and one near the end. The photometry for these transits - follow from the posterior distributions. We adopted was decorrelated using the same methodology described the prayer-bead method for our quoted results because above for 4.5µm. In contrast to the 4.5µm case, our it explicitly includes the effect of red noise (D´esert et al. 3.6µm photometry exhibits noticeable red noise. Fortu- 2011b). Figure 11 shows the distributions for Rp/R∗ for nately, this red noise is most significant in the long in- oneofour4.5µmindividualfits,showingabroaderdistri- terval between the two transits. We limited the effect of bution for the prayer-beadmethod. this red noise by limiting the range of the data included In implementing the prayer-bead method, we permute in our decorrelations and fits. The omitted data did not the residuals only within the adopted phase range of the occur near the transits, nevertheless we tried to develop fit ( 0.05 in phase). At each permutation, we find the ± objective criteria for the range of data that were used. best-fittransitparametersusingtheLevenberg-Marquardt After comparing the σ vs. N−0.5 and global σ, or RMS method, and we add those best-fit values to the posterior scatter, of various sized data slices, we determined that distributions of each parameter. We adopt the median of trimming the 3.6 µm data set into a phase range of 0.05 the posterior distribution as the best fit value, following ± Spitzer transits of GJ1214b 5 D´esert et al. (2011b). resultantretrievalsfor Rp/R∗ areincluded inTable5. On A potentialadditionalsourceof erroris associatedwith average, constraining our orbital parameters to have the thedecorrelation,thatisnotexplicitlypropagatedintothe values found by either Bean et al. (2011) or Berta et al. stage of fitting the photometry. However,we are not con- (2012) results indecreasingourRp/R∗ value at4.5µm by cerned about this for two reasons. First, the 4.5µm data about 0.0010, but with less difference at 3.6µm or I+z. are so extensive, and the intra-pixel effect is so modest at Arguably, we should adopt these constrained values as thatwavelength,thatwebelievethoseerrorsindecorrela- ourprincipalresult. However,thelowlimbdarkeningthat tionhavenegligibleeffect. Second,ourprocedureaccounts prevails at Spitzer wavelengths, in combination with the forimperfectdecorrelationatbothSpitzerwavelengths,in high precision we achieve from our large dataset, moti- an implicit fashion. Imperfections in decorrelation create vates us to rely primarily on our own orbital parameters. red noise, and that red noise contributes to errors on the Nevertheless, we explore the implications of adopting the derivedtransitparametersusing the prayer-beadmethod. Bean et al.(2011)andBerta et al.(2012) orbitalparame- Inadditiontorandomerror,systematicdifferencesmay ters in Sec. 6. exist between our results and other investigators. We dis- cussonesourceofpossiblesystematicdifferenceinSec.4.5; 5. transit-to-transit variability and star spots the implications of these differences for the nature of GJ1214b’s atmosphere is discussed in Sec. 6. A star spot crossing during transit appears as an anomalous spike or bump in the transit light curve (e.g., Deming et al. 2011). Our photometry shows no evidence 4.5. System Parameters that the planet crossed even one significant star spot Asnotedabove,weestimatedthesystemparametersus- during our thirteen 4.5µm transits. Nevertheless, spots ingthreemethods: 1)simultaneousfittingofalltransitsat are common on M-dwarf stars, and uncrossed star spots a given wavelength, 2) averaging system parameters from couldstillaffectthe transit(Sing et al.2009;D´esert et al. the individual fits to each transit at a given wavelength, 2011b). and3)fittingtophased&binnedcombinationsoftransits TRAPPIST photometery of GJ1214 out of transit, but at a given wavelength. We included the transits observed over the same time period as our 4.5µm Spitzer ob- byD´esert et al.(2011)inallthreemethods. Wealsofitthe servations, shows essentially no variation in the I-band TRAPPISTtransitsusingallthreemethods(seeTable4). (Gillon et al. 2012), to a limit of about 0.2%. Neverthe- Table1liststheindividualfitstothe4.5µmdata;Table2 less,other investigationshavefound that GJ1214exhibits gives the individual fit results at 3.6µm and Table 3 lists rotationally-modulatedsignaturesofstarspots,sowecon- theindividualfitresultsfortheTRAPPISTtransitsinthe siderthe potentialimpactofsuchvariationonourresults. I+z band. Aswewilldemonstratebelow,evenallowingformorepho- Since our different fitting methods (summarized in Ta- tometric variationthan Gillon et al.(2012) observed,star ble4)aresimplydifferentwaysofaccountingforthesame spots have negligible effect on our results. data,theyshouldgiveconsistentresultsasfarasthebest- Berta et al. (2011) found that GJ1214 shows a photo- fit parametersareconcerned. Beyondbest-fit consistency, metricvariationof1%amplitude(2%peak-to-peak)inthe we find that comparison of these methods can provide a I-band(0.715-1.0µm)witharotationperiodof 53days, ∼ basis for caution concerning the errors on the derived pa- based on MEarth data (Nutzman & Charbonneau 2008), rameters. Forexample, our4.5µmresultsfromthe simul- spanning three years of observations. Using PHOENIX taneousfitgiveRp/R∗ =0.11710 0.00017,whereasaver- model atmospheres (Allard & Hauschildt 1995), we cal- ± aging the individual fits, weighted by the inverse of their culate that the Berta et al. (2011) amplitude of variation variances,givesRp/R∗ =0.11699 0.00026. Althoughthe could be produced by two star spots, each covering as ± best-fit values agree well, the larger error from averaging much as 2% of the sky-projectedstellar disk, separatedin ◦ the individual fits may indicate potential variations from longitude by 180 . Based on Doppler imaging studies of transit-to-transit. active dwarf stars (Rice & Strassmeier 1998), we adopt a Table5summarizesourresultsfortheRp/R∗parameter temperaturecontrast(spotvs. photosphere)∆T/T =0.1, thatpotentiallyrevealsinformationabouttheatmosphere thusT 2700K. Notethatthisisthesameasadopted spot ∼ ofGJ1214bintooneconciseTable. Forthediscussionthat by Berta et al. (2011). We use limb darkening coefficients follows, we adopt the results from the phased & binned forboththephotosphereandthestarspot,calculatedfrom method, because we feel that the high precision of these our transitfitting at 4.5µm (c =0.11, c =0.0). On this 0 1 combined transit curves allows the most reliable solution. basis, we determined that a 1% variation of the stellar We explored further comparison with two other pre- light curve in the I-band translates to 0.42% variation in cise measurements of Rp/R∗: Bean et al. (2011) and Spitzer photometry at 4.5µm. Berta et al. (2012). We choose these investigations for We developed a numerical tile-the-star model to calcu- more in-depth comparisonbecause the former is the high- latetheeffectofunoccultedstarspotsonthetransitdepth. est precision ground-basedmeasurement of GJ1214b,and Wecreatedasynthetictime-seriesof2DimagesofGJ1214, thelatterisaprecisespace-bornemeasurement. Weinves- at4.5µm,andprojectedtwocircularstarspotsonitssur- ◦ tigatedtowhatextentdifferencesinRp/R∗ arisefromthe face at the equator, separated by 180 of longitude. This different transit solutions, with different values for orbital arrangementofspotsinoppositehemispheresproducesan transit parameters such as a/R∗ and orbital inclination. appropriatequasi-sinusoidaleffectinthetotalstellarlight. Because these orbital parameters should not vary with We accounted for variation in the spots projected area wavelength, we force our solutions to adopt the values as as the star rotates, but we ignored the Wilson depres- derivedbyBean et al.(2011)andBerta et al.(2012). Our sion effect. The PHOENIX model with T = 3000K, 6 Fraine et al. [M/H] = +0.3, log(g) = 5.0 and α = 0.0 represented our conclusions concerning the atmosphere of GJ1214bin GJ1214; and, the PHOENIX model with T = 2700K, Sec. 6.5. [M/H] = +0.3, log(g) = 5.0, α = 0.0 represented the 6.1. Comparing Models to Observations star spot. We multiplied Spitzer’s 4.5µm filter profile by thespectralmodelsandintegratedoverwavelengthtocal- To compare transmission models for GJ1214b with the culate the expected 4.5µm flux variations due to stellar observations,we need to integrate the models– multiplied rotation with the spots fixed in longitude. Both the star by the filter profiles– over the observed bandpasses. Let andspotsareaffectedbylimbdarkeningasdeterminedby F (λ) be the out of transit flux measured from the star ot our fitted Mandel & Agol (2002) model parameters. as a function of wavelength. Similarly let F (λ) be the it Itiseasytoshowthattheeffectofunoccultedstarspots in-transit flux as a function of wavelength. Consider the on the planetary radius derived from the transit is given simplifiedcasewherelimbdarkeningcanbeneglected(ar- as: guably applicable in the infrared), and include the fact that there is a wavelength-dependent observational sensi- Rp 2 = Fot−Fit = (cid:16)RRp∗(cid:17)2spotlessIph (2) tivity, S(λ). In that case: (cid:18)R∗(cid:19)spotted Fot (1−ǫ)Iph+ǫIspot Fit(λ)=S(λ)I∗(λ)(πR∗2−πRp(λ)2), (3) with ǫ = Aspot, and where ot indexes out of transit, it where I∗(λ) is the intensity emergent from the stellar πR2∗ atmosphere at wavelength λ. The out of transit flux is: indexes in transit. I indicates the intensity of the stellar disk, I being the intensity of the photosphere, and I being tphhe intensity of the spot. spot Fot(λ)=S(λ)I∗(λ)πR∗2. (4) Using this equation together with flux variations from With realistic spectral resolution, the observed quanti- our tile-the-star model, we calculated the potential vari- tiesareintegralsoverthe observationalbandpass,andthe ation in transit depth as a function of time. This quasi- transit depth d is: sinusoidal variation has an unknown phase because we do not know the longitudes of anyrealstar spots onGJ1214. d= [F (λ) F (λ)]dλ/ F (λ)dλ, (5) ot it ot Nevertheless, the amplitude of variation in Rp/R∗ from Z − Z this model is 9.6 10−5, which is negligible compared Thus: × to the observed scatter in our measurements (see Fig- ure 11). Moreover, as noted above, the photometric vari- d= S(λ)I∗(λ)Rp(λ)2dλ/ S(λ)I∗(λ)R∗2dλ. (6) ations of GJ1214, observed concurrently with our tran- Z Z sit data (Gillon et al. 2012), were much less than from Whenweseektoevaluateamodeloftheplanet’stransit Berta et al. (2011). We therefore conclude that star spots radius as a function of wavelength(Rp(λ)), it is necessary play a negligible role on the observed variations and/or to include the wavelengthdependence of the stellar inten- possible bias of our inferred radii for GJ1214b. However, sity as well as the observational sensitivity. The latter is wecannotexcludethepossibilitythatincreasedstarspots commonlyincorporatedinnumerousstudies ofbothtran- during Bean et al.(2011) andBerta et al.(2012) observa- sits and secondary eclipses, but the necessity of including tions are responsible for some of the differences between the stellar intensity is less widely appreciated, especially our results. thepossibleeffectoflinestructureinthestellarspectrum. For example, if the stellar spectrum contains water vapor 6. the atmosphere of gj1214b absorption that overlaps to some degree with planetary There are numerous transit observations in the watervapor features,then the apparenttransitdepth will literature that bear on the nature of the atmo- be reduced compared to the case where the star is purely sphere of GJ1214b (Charbonneau et al. 2009; Bean et al. a continuum source. Stellar intensity weighting is par- 2010, 2011; D´esert et al. 2011; Berta et al. 2011, 2012; ticularly important for M-dwarf host stars like GJ1214, Croll et al. 2011; Sada et al. 2010; Carter et al. 2011; becausetheir spectrumvariesstronglywithwavelengthin Kundurthy et al.2011;de Mooij et al.2012;Murgas et al. the optical and near-IR. Unfortunately, that weighting is 2012; Narita et al. 2012). Nevertheless,the improvedpre- alsoconsiderablyuncertainforM-dwarfstars,particularly cision we have been able to achieve in the Spitzer bands, at the very interesting blue wavelengths where the planet together with the new TRAPPIST results in the I+z- mayexhibitscatteringfromhaze(Benneke & Seager2012; band, and recent advances in modeling the atmosphere Howe & Burrows 2012). of GJ1214b (Benneke & Seager 2012; Howe & Burrows TocomparemodelsofRp(λ)/R∗ toobservations,wecal- 2012),motivateustore-examinethenatureofGJ1214b’s culate the value of d using Eq. (6), and infer Rp/R∗ as atmosphere. √d. This procedure is valid even at wavelengths where In the following sub-sections we review the methodol- appreciable limb darkening prevails. ogy for comparing observations and models (Sec. 6.1), we AlthoughweuseaPHOENIXmodelatmospheretoper- brieflypreviewwhatourSpitzerobservationsalonecanre- formtheweightingovertheobservedbandpass,thismodel vealconcerningtheatmosphereofGJ1214b(Sec.6.2),and is not ultimately satisfactory for this purpose. For ex- we thencomparethe totality ofallpublished observations ample, in the green bandpass (0.46 µm) where a tran- to existing models, using a χ2 analysis (Sec. 6.3). Since sitwasobservedbyde Mooij et al.(2012),the PHOENIX planetary radii derived by different observational groups model has essentially no flux (many orders of magnitude can differ systematically, we discuss the effect of one par- below the peak flux), whereas the real star has suffi- ticularsystematicdifferenceinSec.6.4,andwesummarize cientflux to produce a transit havinggoodsignal-to-noise Spitzer transits of GJ1214b 7 (de Mooij et al. 2012). The reason is that the model in- alent to increasing (or decreasing) the size of the opaque cludes only LTE thermalemissionfromthe star,anddoes (i.e., solid)portionofthe planetbyasmallamount. That not incorporate the various emission signatures of mag- effectively varies the surface gravity of the planet, and netic activity. Thereforewe canuse the PHOENIXmodel would strictly speaking be inconsistent with the model onlyinthered-opticalandinfrared. Ourdefaultprocedure thatisbeingadjusted. However,the planetaryradiusata is to hold the stellar intensity constant for wavelengths givenatmosphericpressurelevelis notknownata levelof shortward of 1000 nm (i.e., we set I∗(λ) = I∗(1000) for accuracy comparable to the adjustments we are making. λ 1000nm), but we verified that using other prescrip- Moreover, the requisite adjustments in the model output ≤ tions shortward of this limit (e.g., blackbody spectra) do (typically, 0.0005 in Rp/R∗), correspond to less than 1% not greatly influence our present results. However, as the differencesinsurfacegravity. Wethereforefindthisproce- precision of observations improves, it will eventually be duretobeavalidandusefultoolfortestingmodelsversus necessary to have an accurate spectrum for the host star theobservations,andwenotethatasimilarprocedurewas at all wavelengths. usedbyBerta et al.(2012). Wefitthethreemodelsshown in Figure 12 (Benneke & Seager 2012), together with all 6.2. Implications from Spitzer of the models from Howe & Burrows (2012), and we cal- culate χ2 values for each fit. We also fit a flat line to Prior to an exhaustive analysis of all data versus all the data, i.e., a planetary radius that does not vary with models, we mention what our new Spitzer data alone wavelength - indicating no signature of the atmosphere. immediately reveal and/or constrain concerning the at- SeveralofthebestfittingmodelsareshowninFigure13, mosphere of GJ1214b. We (BB & SS) generated three comparedtotheentiretyofpublishedradiiforthisplanet. new model atmospheres for GJ1214b at an equilibrium temperature of 546 K, based on the methodology of In total, there are 97 observations of Rp/R∗ versus wave- length on Figure 13. The water atmosphere from Fig- Benneke & Seager (2012). The models are: 1) a H- ure 12,andtwo models fromHowe & Burrows(2012), are rich solar abundance model, 2) a ‘Hot-Halley’ composi- alsoincludedonFigure13. FortheFigure,themodelsare tion model which begins with solar composition and adds overplotted monochromatically, without integrating over minor molecular constituents from accreted icy material the bandpass. However, the χ2 values are calculated by (Benneke & Seager 2012), and 3) a pure water vapor at- integrating the model over the bandpass of each obser- mosphere. Figure 12 shows the result of integrating these vation as described above, and adopting the observed er- three models over the Spitzer observational bandpasses, rors from each source. In the case of multi-band analyses and including the stellar intensity using a PHOENIX (Kundurthy et al. 2011), we use the total bandpass from modelhavingTeff/log(g)/[M/H]=3000K/5.0/0.3. Based multiple filters. For the three overplotted models we also on this comparison, the solar composition model is elim- show the values for the integrals over the Spitzer band- inated based on the Spitzer data alone. The water va- passes, as open symbols. por model is preferred over the hot Halley model, based on the χ2 analysis described below. Moreover, we expect With96degreesoffreedom,modelscanonlyberejected at the 99.9% confidence level if they have a χ2 exceeding that methane-rich models having large scale heights (not 144.6. Among the possible models, The pure water atmo- illustrated)willberejectedbytheSpitzerdata,duetothe sphere from Benneke & Seager (2012) yields χ2 = 142.7 relative lack of an enhanced radius in the 3.6µm band - for 96 degrees of freedom. The hot Halley and solar com- that contains the strong ν band of methane. 3 position models from Benneke & Seager (2012) have χ2 6.3. A χ2 Analysis values of 167.9 and 1054.7 respectively, and are unlikely descriptions of GJ1214b’s atmosphere. The solar compo- To gain further quantitative insight, we weighted sition model in particular is strongly rejected unless high the three models from Benneke & Seager (2012) dis- clouds are included (see below). In this respect, we note cussed above, as well as all of the models given by that some discussion of a solar composition atmosphere Howe & Burrows (2012) over the observed bandpasses of hasoccurredwithrespecttotransitobservationsnear2µm all extant transit observations of GJ1214, including the (Croll et al. 2011; Bean et al. 2011). We here emphasize TRAPPIST and warm Spitzer data reported here. We fit that a cloudless solar composition model is incompatible the models to the data using a χ2 analysis, as described with the Spitzer data alone, as well as with the totality below. Berta et al. (2012) applied a similar χ2 analysis of the observations over all wavelengths. The issue of the to data from Hubble/WFC3, but not to the complete set transit depth near 2µm - while an important datum - is of data that we do here, and in particular not including not crucial to rejecting a solar composition atmosphere. our new and precise results in the warm Spitzer bands. Our improvement in the observed Spitzer precision at The utility of χ2 is well known to be problematic when 3.6µm - overlapping the strong ν band of methane, 3 combiningdatafromdifferentobservationalgroups. How- promptsustoinvestigatethemethane-compositionmodels ever, χ2 is at least an objective way to compare different of Howe & Burrows (2012). All of their methane compo- models, and we explicitly consider one cause of observer- sitions have χ2 above 184.6 (the value for 1% methane). to-observer systematic differences in Sec. 6.4. However, a solar composition model having high clouds To evaluate and compare possible models of the plane- (down to pressures of 0.1 mbars) produces an accept- tary atmosphere, we fit eachmodel to the data by adding able χ2 = 145.5. This model is plotted as the red line an adjustable constant (i.e., wavelength-independent off- on Figure 13; it predicts an increase in radius in the set) to the modeled values of Rp/R∗. We choose the con- difficult-to-observe regions near 2.7 and 3.3µm. The best stantto minimize the χ2 ofthe difference betweenthe ad- fit to the data is the yellow line on Figure 13, having justed modelandthe data. Adding this constantis equiv- 8 Fraine et al. χ2 = 119.8. This model, from Howe & Burrows (2012), systematic error. Hence we also conclude that the null contains a dense haze of small (0.1µm) tholin particles, hypothesis (no atmosphere detected) remains among the extending to very high altitudes (1µbar). It was disfa- mostfavoredmodels,especiallywhensystematicerrorsare voredbyHowe & Burrows(2012),butourmethodologyis considered. differentinthatweincorporateamarginallyadditivecon- stantwhenfittingthemodels. However,wepointoutthat 6.5. Summary of Implications for the Atmosphere of also among the acceptable models is a flat line (not illus- GJ1214b tratedonFigure13). Thisnullhypothesis(noatmosphere detected) yields χ2 =137.0. We have obtained new radii for GJ1214b in the I+z band using TRAPPIST, and very precise radii at 3.6- 6.4. Systematic Differences Between Observers and 4.5µm using Warm Spitzer in a long series of new One further check on the acceptable models is to fo- observations. Our χ2 analysis indicates that the best-fit cusonthedifferencebetweenourpreciseSpitzerradiiand model for the atmosphere of GJ1214b contains a haze of very precise radii derived at other wavelengths, i.e., by small particles extending to high altitudes, although pure Bean et al. (2011) and Berta et al. (2012). As noted at water vapor models remain a possibility. However, a flat the end of Sec. 4.5, we fix the variable orbital param- line is among the best-fitting models, particularly when eters (a/R∗ and i) at the values derived by Bean et al. observer-to-observersystematicdifferencesareconsidered. (2011) and Berta et al. (2012) and derive a lower value of Therefore we extend the conclusion of Berta et al. (2012) Rp/R∗ at 4.5µm by about 0.001 (Table 5). Using that concerningthe flatness of the transmisisonspectrum from alternative value in our χ2 analysis is one way of evaluat- 1.1- to 1.7µm to include our new high-precision Spitzer ing the possible effect of observer-to-observer differences measurements at 3.6- and 4.5µm. The atmosphere of in radii. This procedure increases the χ2 values of most GJ1214b is not unequivocally detected at this point in models, but by varying amounts. Interestingly, the two time. least affected models are the flat line, whose χ2 increases by δχ2 = +1.6, and the tholin-haze model. The water modelfromBenneke & Seager(2012)hasδχ2 =+8.4,and This work is based on observations made with the their hot Halley model has δχ2 = +19.8. The scattering Spitzer Space Telescope, which is operated by the Jet tholin-haze model from Howe & Burrows (2012) remains Propulsion Laboratory, California Institute of Technol- as the lowest absolute χ2, and has δχ2 = 2.3, i.e. it be- ogy under a contract with NASA. Support for this work − comes more likely, not less likely. We conclude that, even was provided by NASA through an award issued by when systematic differences among observational groups JPL/Caltech. We thank the Spitzer staff for their hard are considered, a scattering atmosphere is currently the workanddedicationinimplementingthesedifficultobser- best estimate for GJ1214b. However, we are unable to vations, andthe anonymousreferee for a carefulreview of explore the vast phase space of other possible sources of this paper. REFERENCES Agol,E.,Cowan,N.B.,Knutson,H.A.,Deming,D.,Steffen, J.H., Gillon, M., Demory, B.-O., Barman, T., Bonfils, X., Mazeh, T., Henry,G.W.,&Charbonneau, D.,2010,ApJ,721,1861. Pont, F., Udry, S., Mayor, M., & Queloz, D., 2007, A&A, 471, Allard,F.,&Hauschildt,P.H.,1995, ApJ,445,433. L51. Ballard, S., Charbonneau, D., Deming, D., Knutson, H. A., Gillon, M., Jehin E., Magain, P., Chantry, V., Hutsemekers, D., Christiansen, J. L., Holman, M. J., Fabrycky, D., Seager, S., & Manfroid, J., Queloz, D., & Udry, S., 2011, in ‘Detection and A’Hearn,M.F.,2010, PASP,122,1341. DynamicsofTransitingExoplanets,’EPJWebofConferences,eds. Bean,J.L.,Miller-RicciKempton,E.,&Homeier,D.,2010,Nature, F.Bouchy, R.Diaz,&C.Moutou,Vol.11,id.06002. 468,669. Gillon, M., Demory, B.-O., Deming, D., Seager, S., et al., 2012, in Bean,J.L.,and9co-authors,2011,ApJ,743,id.92. preparationforA&A. Benneke, B., & Seager, S., 2012, submitted to ApJ, astro- Howe,A.R.,&Burrows,A.S.,2012,ApJ,756,176. ph/1203.4018. Jehin,E.,Gillon,M.,Queloz,D.,etal.,TheMessenger,145,2. Berta, Z. K., Charbonneau, D., Bean, J., Irwin, J., Burke, C. J., Knutson,H.A.,&13co-authors,2012,ApJ,754,22. D¨esert,J.-M.,Nutzman,P.&Falco,E.E.,2011,ApJ,736,id.12. Kundurthy,P.,Agol,E.,Becker,A.C.,Barnes,R.,Williams,B.,& Berta,Z.K.,&9co-authors,2012,ApJ,747,id.35. Mukadam,A.,2011,ApJ,731,123. Carter,J.A.,Winn,J.N.,Holman,M.J.,Fabrycky,D.,Berta,Z.K., Lewis,N.K.,&23co-authors,2013,submittedtoApJ. Burke,C.J.,&Nutzman,P.,2011,ApJ,730,id.82. Liddle,A.R.,2007,MNRAS,377,L74. Charbonneau, D.,and18co-authors,2009,Nature,462,891. Mandel,K.,&Agol,E.,2002,ApJ,580,L171. Claret,A.,&Bloemen,S.,2011, A&A,529,id.A75 Mighell,K.J.,2005,MNRAS,361,861. Croll, B., Albert, L., Jayawardhana, R., Miller-Ricci Kempton, E., Miller-RicciKempton,E.,&Fortney, J.J.,2010,ApJ,716,L74. Fortney, J. J., Murray, N., & Neilson, Hilding, 2011, ApJ, 736, Murgas,F.,Pall´e,E.,Cabrera-Lawers,A.,Colo´n,K.D.,Mart´ın,E.L., id.78. Parviainen,H.,2012, A&A,554,id.A41. Crossfield,I.J.M.,Barman,T.,&Hansen,B.M.S.,2011,ApJ,736, Narita, N., Nagayama, T., Suenaga, T., Fukui, A., Ikoma, M., id.132. Nakajima, Y., Nishiyama, S., Tamura, M., submitted to PASJ, Deming,D.,and11co-authors,2009,PASP,121,883. astro-ph/1210.3169. Deming, D., Sada, P. V., Jackson, B., Peterson, S. W., Agol ,E., Nutzman,P.,&Charbonneau, D.,2008,PASP,120,317. Knutson, H. A., Jennings, D. E., Haase, F., & Bays, K., 2011, deMooij,E.J.W.,and10co-authors,2012, A&A,538,id.A46. ApJ,740,id.33. Rice,J.B.,Strassmeier,K.G.,1998,A&A,336,972. D¨esert, J. M., Bean, J., Miller-Ricci Kempton, E., Berta, Z. K., Rogers,L.,&Seager,S.,2010, ApJ,716,1208. Charbonneau, D., Irwin, J., Fortney, J. J., Burke, C. J., & Sada, P. V., Deming, D., Jackson, B., Jennings, D. E., Nutzman,P.,2011,ApJ,731,id.L40. Peterson, S. W., Haase, F., Bays, K., O’Gorman, E., & D¨esert, J. M., Sing, D., Vidal-Madjar, A., Hebrard, G., Lundsford,A.,2010,ApJ,720,L215. Ehrenreich, D., Lecavelier Des Estangs, A., Parmentier, V., Sing, D., D¨esert, J.-M., Des Estangs, L., Ballester, G. E., Vidal- Ferlet,R.,&Henry,G.W.,2011,A&A,526,id.A12. Madjar, A., Parmentier, V., Hebrard, G., & Henry, G. W., 2009, Ford,E.B.,2005, AJ,129,1706. A&A,505,891. Stevenson, K.B.,&9co-authors,2010,Nature,464,1161. Spitzer transits of GJ1214b 9 Fig. 1.—Thetoppanelillustratesrawdataforthefirst2.9-dayportionofour4.5µmphotometry,containingtwotransits. Eachdatapoint is aperture photometry before decorrelation, binned by every 10 data points. The middle panel shows the Y-center position as a function time;thatwhichwecorrelatewiththefluxtoremovetheintra-pixeleffect, andrelatedsystematicnoisesources. Thelowerpanel showsthe samephotometricvalues,exceptwiththetransitregionsexcluded,plottedversustheY-pixelpositionofthestellarimage. Notethedifferent spatial dependence of the photometry on each side of pixel center. The red curves are the 4th order polynomial fits that we use to initiate thedecorrelationprocess(seetext). 10 Fraine et al. Fig. 2.— Overview of our 4.5µm photometry, after decorrelation andbinned in100 two-second exposures per plotted point. Thedashed lineshowsthe transitdepth thatcorresponds to oneEarthradius. The13transits ofGJ1214b areapparent. SeeGillonetal.(2012)foran analysisofother possibletransitingplanetsinthissystem.

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Preview Spitzer Transits of the Super-Earth GJ1214b and Implications for Its Atmosphere

Accepted bytheAstrophysicalJournal,Jan24,2013 PreprinttypesetusingLATEXstyleemulateapjv.11/12/01 SPITZER TRANSITS OF THE SUPER-EARTH GJ1214B AND IMPLICATIONS FOR ITS ATMOSPHERE Jonathan D. Fraine1, Drake Deming1, Micha¨el Gillon2, Emmanu¨el Jehin2, Brice-Olivier Demory3, Bjoern Benneke3, Sara Seager3, Nikole K. Lewis4,5,6, Heather Knutson7, & Jean-Michel D´esert6,8,9 Accepted by the Astrophysical Journal, Jan 24, 2013 ABSTRACT 3 We observedthe transitingsuper-EarthexoplanetGJ1214busingWarmSpitzer at4.5µmwavelength 1 during a 20-day quasi-continuous sequence in May 2011. The goals of our long observation were to 0 accurately define the infrared transit radius of this nearby super-Earth, to search for the secondary 2 eclipse, and to search for other transiting planets in the habitable zone of GJ1214. We here report n results from the transit monitoring of GJ1214b, including a re-analysis of previous transit observations a by D´esert et al. (2011). In total, we analyse 14 transits of GJ1214b at 4.5µm, 3 transits at 3.6µm, J and 7 new ground-based transits in the I+z band. Our new Spitzer data by themselves eliminate 8 cloudless solar composition atmospheres for GJ1214b, and methane-rich models from Howe & Burrows 2 (2012). Using our new Spitzer measurements to anchor the observed transit radii of GJ1214b at long wavelengths, and adding new measurements in I+z, we evaluate models from Benneke & Seager (2012) ] P and Howe & Burrows(2012) using a χ2 analysis. We find that the best-fit model exhibits an increasein E transitradiusatshortwavelengthsduetoRayleighscattering. Purewateratmospheresarealsopossible. . However, a flat line (no atmosphere detected) remains among the best of the statistically acceptable h models, and better than pure water atmospheres. We explore the effect of systematic differences among p results from different observational groups, and we find that the Howe & Burrows (2012) tholin-haze - o model remains the best fit, even when systematic differences among observers are considered. r t Subject headings: Planets and satellites: atmospheres - Techniques: photometric - Infrared: planetary s a systems - Planets and satellites: composition [ 1. introduction IR water vapor opacity makeshydrogen-dominatedatmo- 1 spheresopaqueintheIRoverseveralscaleheights,inspite v The mass and radius of the nearby transiting super- of their relative paucity of heavy elements. Also, strong 3 Earth GJ1214b (Charbonneau et al. 2009) imply that bands of methane and carbon monoxide fall within the 6 it must have a significant atmosphere (Rogers & Seager WarmSpitzerbandpassesat3.6-and4.5µm,respectively. 7 2010). Thatinference motivatedanextensiveeffortto de- Considering that GJ1214b’s M-dwarf host star is bright 6 tect the atmosphere, by seeking wavelength variations of 1. the transitdepth. Awide varietyofcompositionsarepos- in the IR, transit observations of GJ1214b using Warm Spitzer become particularly relevant to the characteriza- 0 sibleforsuper-Earthatmospheres(Miller-Ricci & Fortney tion of its atmosphere. 3 2010; Benneke & Seager 2012; Howe & Burrows 2012), In May 2011, we observed the GJ1214 system quasi- 1 from hydrogen-dominated to heavy-element-rich. Most continuouslyfor20days,usingSpitzer’sIRACinstrument : current observations of the transits (Bean et al. 2010, v at 4.5µm. Our investigation had three goals: 1) to im- i 2011;Crossfield et al.2011;D´esert et al.2011;Berta et al. X 2011, 2012; de Mooij et al. 2012) have rejected hydrogen- prove the transit parameters of the system and constrain thepropertiesoftheplanet’stransmissionspectrum,2)to r dominated atmospheres for GJ1214b, but Croll et al. a searchforthe secondaryeclipse,and3)tosearchforother (2011) concluded in favor of a low molecular weight at- transiting planets in this system, to the outer edge of the mosphere. The infrared (IR) spectral region is partic- habitable zone. ularly important for such studies, because strong water Our observations included minor interruptions for data vapor bands increase the transit depth in the IR signifi- downloads. But, an unplanned 42-hour data loss also oc- cantly as compared to the optical. This is especially true curred during the 20-day sequence, caused by a combina- for hydrogen-dominated atmospheres, because of the in- tion of spacecraft and Deep Space Network (DSN) down- creased atmospheric scale height. The intrinsically strong 1 DepartmentofAstronomy,UniversityofMaryland,CollegePark,MD20742USA;[email protected] 2 Instituted’AstrophysiqueetdeGeophysique, UniversitedeLiege,Liege,Belgium 3 Department ofEarth, AtmosphericandPlanetarySciences, andDepartmentofPhysics,Massachusetts InstitureofTechnology, Cambridge, MA02139USA 4 DepartmentofPlanetarySciences andLunarandPlanetaryLaboratory,UniversityofArizona,Tucson,AZ85721USA 5 Present address: Department of Earth, Atmospheric and Planetary Sciences, and Department of Physics, Massachusetts Institure of Tech- nology, Cambridge,MA02139USA 6 SaganFellow 7 DivisionofGeologicalandPlanetarySciences,CaliforniaInstituteofTechnology, Pasadena,CA91125USA 8 Harvard-SmithsonianCenter forAstrophysics,60GardenSt.,Cambridge,MA02138USA 9 Presentaddress: DivisionofGeological andPlanetarySciences, CaliforniaInstitute ofTechnology, Pasadena, CA91125USA 1 2 Fraine et al. link anomalies. We therefore re-observed GJ1214 for an our analysis versus Gillon et al. (2012), and to add addi- additional 42-hours in November, 2011, using the IRAC tionalinformationrelevanttotheatmosphereofGJ1214b, 3.6µm band. Consequently, we have multiple transits at we observed 7 transits using the TRAPPIST facility both WarmSpitzer wavelengths,andthese data providea (Gillon et al.2011;Jehin et al.2011),overtheperiod2011 particularly powerful constraint on the IR transit depth. March 11 - May 18. The TRAPPIST observations and Moreover, since our 4.5µm transits were observed nearly photometry are described by Gillon et al. (2012), but we consecutively,wehaveanexcellentbasisforevaluatingthe summarize the data here. The observations were made degree to whichstellar activity (e.g.,star spots)affect the using the 60-cm robotic telescope in a slightly defocused inferred transit depth. mode. An I+z filter gave transmission from 750 to 1100 A global analysis of these GJ1214 data is being pub- nm. Differential photometry on the 25-sec exposure im- lished by Gillon et al. (2012), including a search for other ages was done (by M.G.) using IRAF/DAOPHOT.In our transiting planets in this system. In this paper, we focus analysis, we use the same version of the photometry as on the implications of our observations for understanding Gillon et al. (2012), but we perform an independent anal- the nature of GJ1214b’s atmosphere, and we investigate ysis and transit fitting. thewavelength-dependenttransitradiusofGJ1214binde- tail. Our analysis includes the degree to which star spots 3. spitzer photometry - even those not occulted by the planet - contribute to 3.1. Aperture Photometry possible bias in the measured radius of the planet. An- chored by our improved precision for these infrared tran- Our analysis utilizes the Basic Calibrated Data (BCD) sits of GJ1214b, we add 7 new ground-based transits in files produced by version S18.18.0 of the Spitzer pipeline. the I+z band, and we re-analyze the totality of pub- Two dimensional (2D) Gaussian centering produces the lished wavelength-dependent transit depths for GJ1214b, least scatter in our final photometry (Stevenson et al. exploiting recent advances in super-Earth model atmo- 2010; Agol et al. 2010). Knutson et al. (2012) found that spheres (Benneke & Seager 2012; Howe & Burrows 2012). flux-weighted centering gives superior results for Spitzer Sec. 2 describes the details of our observations, and datainstudiesofexoplanetaryphasecurvesoverlongtime Sec. 3 explains our procedure to extract precise photom- scales. We tried flux-weighted centering for our transit etry from the data. In Sec. 4 we fit to the photometry, analysis, but it did not result in significant improvement extracting the transit radius for the planet in the warm over our 2D Gaussian centering. Spitzer and I+z bands, and we derive improved system Inthecaseofthe4.5µmphotometrywecenteracircular parameters. Sec. 5 considers the possible effect of star aperture of constant radius on the star. We calculate the spots on our results. Sec. 6 discusses implications for the stellarfluxwithintheaperture,includinganalyticapprox- atmosphere of GJ1214b. imationsforthepartialcoverageofpixelsattheboundary of the aperture. We vary the radius of the aperture from 2. observations 2.0 to 5.0 pixels, in 0.5-pixelincrements, andthereby pro- 2.1. Spitzer ducesevenversionsofthephotometryateachwavelength. After decorrelation (see below), we chose to use an aper- We observed GJ1214 for 20 consecutive days using ture radius of 2.5 pixels for 4.5µm, based on the global WarmSpitzerat4.5µm,beginningonApril29,2011at03- scatter in the decorrelated photometry. 46UTC.Weusedsubarraymodewithanexposuretimeof Inthecaseofthe 3.6µmphotometry,weexaminedcon- 2secondsperframe. Theobservationscontainseveral 3- stant radius photometry– for the same seven radii as in ∼ hour interruptions for data download, and one unantici- the 4.5µm section– and variable radius aperture photom- pated42-hourgapwheredatawereirretrievablylost. The etry. The variable radius photometry improves the preci- data loss occurred because the DSN incurred anomalous sionby41%overconstantaperturephotometrybyvarying delaysindownloadingdataatthattime. WhentheSpitzer the aperture radius as a function of the ‘noise-pixel’ cal- observatory was designed, long observing campaigns of culations per frame (Mighell 2005; Knutson et al. 2012; exoplanet photometry were not envisioned. Spitzer’s on- Lewis et al. 2013). Therefore we adopt the noise pixel boardflightsoftwarewasdesignedtoautomaticallydelete method for our 3.6µm photometry, and subsequent intra- dataafteracertainperiodoftime, tomakeroominmem- pixel decorrelation (see below). oryfornewobservations. TheDSNanomalyconsequently The noise pixel method estimates the effective width of caused the onboard software to delete data before down- thepixelresponsefunction,accountingforundersampling, link (the flight software has now been corrected so that bycalculatingthevarianceofthefluxperframe,weighted this will not recur). by the square of the mean flux: To compensate for the data loss, we were awarded 42 hoursofcontinuousobservationsthatbeganonNovember (ΣI )2 6S,p2it0z1e1r’,sa3t.161µ-m54bUaTndCp.aWsse,teoleccotemdptloemaceqnutitrheeth4e.5seµdmatdaatina β˜i = Σ(Ijj)2, (1) from May 2011. We again used 2-second exposure times where β˜ is the noise pixel parameter for the stellar im- in subarray mode. In total, our data comprise 791,808 i ageinframei,I istheintensityofpixelj,andthesumma- exposures at 4.5µm, and 74,624 exposures at 3.6µm. j tions extend over all pixels wherein the stellar intensity is 2.2. TRAPPIST significant. Using the β˜ as the aperture radius collects i q In order to help define the possible effects of stellar an optimum amountof light for photometry. The average activity on the Spitzer transits, to further cross-check apertureradius fromusing this formulationonour3.6µm Spitzer transits of GJ1214b 3 data is 2.60 pixels. certainty estimates on the transit parameters, by 10%. ∼ Moreover,this phaserangecoincideswithsimilarsubdivi- 3.2. Decorrelation sions in the 4.5 µm data. After dividing by the results of the Gaussian weight- Upon producing photometry, we immediately see ing, we solve for and subtract an improved transit model, Spitzer’s well-known intra-pixel sensitivity effect, that and again apply a second stage weighting function decor- must be decorrelated and removed from the data. A relation. We experimented with a third iteration of this portion of the raw 4.5µm photometry (before decorrela- process, but it did not produce significant improvement. tion) is illustrated in Figure 1. Because the transits of Unlike the first (polynomial) stage of decorrelation, the GJ1214b are substantially larger than the intra-pixel sig- Gaussianweightingfunctionwasappliedto the totalityof nature,wefirstmaskoffthetransitsfromthefirststageof the data (i.e., all re-acquisitions) using a single Gaussian decorrelation. Our4.5µmdatacomprisesevendistinctre- kernel. The initial polynomial stage of the decorrelation acquisitions of GJ1214, with interruptions for data down- process may seem unnecessary, since the weighting func- load. Therefore our first stage of decorrelation is done tionalonecouldremovestructureinthedataonbothlarge separately for each of the seven re-acquisitions. That ini- and small spatial scales. However, we find that the poly- tal decorelation fits two polynomials to the data for each nomials speed up the iterative process by providing a fast re-acquisition. (There are seven sections of the data de- start to the iteration. Our final photometry has a stan- fined by the data downloads and re-acquisitions.) One dard deviation of 3.7 10−3, which is only 15% greater polynomial fit is applied to those data points wherein the × than the photon noise. Moreover, red noise is minimal imagecentroidliesatY-coordinategreaterthanthecenter and the precision for binned data improves nearly as the ofthepixel,andanotherpolynomialfitisappliedtothose square-rootof the bin size, as we demonstrate below. data wherein the image lies at Y-coordinate less than the Figure 2 shows an overview of our 4.5µm photometry, center of the pixel. Our rationale for this two-parameter after decorrelation;moredetaileddepictions arediscussed fit is based on visual inspection of the photometry, that and shown below. showsdifferentbehaviorabovethecenter-of-pixelthanbe- low center (see lower panel of Figure 1). The polynomi- 4. model fitting for transit parameters als are fourth order in Y and second order in X, because We analyzeallavailableSptizer transits,including are- the photometric variations as a function of Y are more analysis of the transits reported by D´esert et al. (2011), pronounced than with X. Also, visual examination of the andTRAPPIST transitsusing the I+z filter (Gillon et al. variation with Y indicated that lower order polynomials 2012). We usethree methodologiesto determine the best- (e.g., quadratic) would not represent the variations opti- fittransitparametersforeachdatasetandwavelength. All mally. After finding the best fit polynomials, we divide three methods use only the data within a phase interval themintothedata,includingthein-transitdata. Weonly of 0.05 around the center of eachtransit– except for the used this step to determine initial conditions for an itera- ± TRAPPIST transits, which used all of the available data tive weighting function method (see below). from Gillon et al. (2012). We follow the polynomial decorrelation with a sec- The first method solves for the best-fit transit parame- ond procedure that is itself a two-pass iterative pro- tersofalltransitssimultaneouslyateachwavelength. The cess. We first remove a preliminary transit model from second method fits each transit individually and indepen- the polynomial-decorrelated data, and apply a Gaussian dently, then calculates the average of the transit param- weighting function (Ballard et al. 2010; Lewis et al. 2013; eters at each wavelength, weighting the individual results Knutson et al. 2012) to correct the intra-pixel signatures. by the inverseof their variance. The third method phases The kernel of the Gaussian weighting uses a σ of 0.005 and bins all of the transits at each wavelength into a sin- pixels in Y, and 0.01 pixels in X for the 4.5µm data, that gle transit, and fits to those phased & binned data. All 3 we determined by trial and error - evaluating the noise methods included a total of 3 transits at 3.6µm, 14 tran- level of the final decorrelated photometry. A separate sits at4.5µm, and7 transits inthe I+z band. Comparing Gaussianweightingwasappliedtoeachsectionofthedata these threemethods givesanindicationofthe consistency between downloads,but the same kernel size was used for of our results, and we do indeed find good consistency, as all data sections at 4.5µm. noted below. For the 3.6µm data, we applied a noise-pixel, Gaus- We now describe the details of those fitting procedures. sian weighting function that uses a variable σ in Y, X, and β˜ (noise-pixel value). This varied the weights in the 4.1. Spitzer 4.5µm Transits Gaussiankernelto accommodate the necessarynumber of neighboring points that influence the strength of the cor- WeusetheformulationofMandel & Agol(2002)togen- relation between center position and flux, as discussed in erate transit curves and fit them to the observed data, Lewis et al. (2013) and Knutson et al. (2012). thereby extracting the essential parameters of the tran- Because of effects near the pixel boundary, we chose to sit. The 14 Spitzer transits at 4.5µm comprise our most subdivide the 3.6 µm data into 2 sections, encompassing extensive and highest quality data. Our simultaneous the 2 transits in the data. The pixel boundary effects oc- fit holds the orbital period fixed at the value measured cured well out of phase of both transits. After examining by Bean et al. (2011) 1.58040481 1.210−7 , and uses a the globalscatter and σ vs. N−0.5 (bin size) slope residu- Levenberg-Marquardt(cid:0)algorithm to±minimiz(cid:1)e the χ2 for als, we found that decorrelating after subdividing the 3.6 each transit. Although we are minimizing χ2, we do not µm data set to within 0.05 of each transit produced the acceptthatparticularsetoftransitparametersasourbest- ± best noise levels, and resulted in more conservative un- fit values. Instead, we explore parameter space using a 4 Fraine et al. Markov Chain Monte Carlo (MCMC) method, and also aroundthecenterofeachtransitminimizedtheRMSscat- usingaresidual-permutation(‘prayer-bead’)method. Our ter and the residual of the σ vs. N−0.5 slope, which mini- best-fit valuesaretakenfromthe mediansofthe posterior mizedtherednoiseforthesetransits;andwasfortuitously distributions generated in this exploration of parameter the same range as the 0.05in phase that we adopted for ± space (see Sec. 4.4). our 4.5µm fits. Our fit extracts a correction to the transit center time Werepeatedallofthemethodologydescribedinthissec- (asmightbecausedbyephemeriserror),aswellasa/R∗,i, tion on the D´esert et al. (2011) 3.6µm transit data, and Rp/R∗, and a linear limb-darkening coefficient. We hold we found that the slope of σ vs. N−0.5 was insensitive to the quadratic limb darkening coefficient at zero because the range of data analyzed. As a result, we use the entire BayesianInformationCriterion(Liddle2007)analysissup- D´esert et al. (2011) 3.6µm data set. ports a linearlaw, whichgivesanadequateaccountof the Asinthe4.5µmcase,wefittoall3ofthe3.6µmtransits minimal limb darkening that is characteristic of infrared using3methods: simultaneously,individually,andphased transits. Moreover, our derived linear limb darkening co- & binned. Figure 6 shows all 3 of the 3.6µm transits efficients at 3.6 and 4.5 microns (c0 =0.158 and 0.128 re- phased & binned, overlaid with a best-fit curve. Figure 7 spectively, see Table 4)are reasonablyconsistent with the illustrates the standard deviation of the 3.6µm residuals values predicted by Claret & Bloemen (2011) (c0= 0.147 as a function of bin size for our fits to the simultaneous and0.155)foramodelatmospherehavingT=3500K(that transit parameters. temperature being their closest match to GJ1214). Figure 3 zooms in on a portion of the simultaneous fit 4.3. TRAPPIST I+z Transits for the first two 4.5µm transits, and Figure 4 shows the For the TRAPPIST data set, we used all 7 distinct standard deviation of residuals (data minus simultaneous epochs of the GJ1214b transiting system provided by fit) when binned over different time intervals. Note that Gillon et al. (2012). Three of these epochs overlapped we find very little red noise in these data, indicating the withthe Spitzer4.5µmdataset. Gillon et al.(2012)used success of our multi-stage intra-pixel decorrelation. Note the I+zfilter onthe TRAPPISTtelescope becauseit sup- alsothatourdecorrelationprocesswilltendtoremoveslow plied a near uniform filter profile from 0.7 - 1.0 µm. variations in the stellar brightness. Hence the apparently We determined the physical parameters using all three constant flux seen in Figure 2 should not be interpreted methods discussed above: a simultanous fit, individual as evidence for stellar quiesence. (The possible effects of fits, and a fit to phased & binned data. Similar to the stellar activity on our results are discussed in Sec. 5). Spitzer data sets, we fit a Mandel & Agol (2002) transit In addition, we bin all 14 4.5 µm transits, including model using a Levenberg-Marquardt routine. In contrast that of D´esert et al. (2011), into bins of width 0.001 in to the Spitzer data sets,we fit the TRAPPIST data using phase, using a running standard deviation for the weights a Mandel & Agol (2002) model that included quadratic ina weightedmean–phasingthemallto acommonepoch limb darkening, which accounted for the excess stellar determined from the simultaneous fit. As before, we in- limb-darkening observed in the shorter wavelength tran- clude only data within a phase range 0.05 of transit ± sitdata. The fittothephased&binnedTRAPPISTdata center, and we fit to the phased & binned transit us- is shown as Figure 8. To analyze the quality of the fit, ing the same Levenberg-Marquardt algorithm described Figure 9 showsthe σ vs. N−0.5 for the simultaneous fit of above. Figure 5 shows the resulting fit in comparison to the TRAPPIST data set. the phased & binned data. The results for the planet-to-star radius ratios, and re- The best-fit Spitzer transit parameters for each 4.5µm lated errorbars, in the I+z band are plotted on Figure 10 transit fitted individually are given in Table 1; the indi- for comparison to our 13 Spitzer transits at 4.5µm, and vidual 3.6µm transits (Sec. 4.2) are given in Table 2, and listedinTables3&4. Furtherinformationaboutthedata the individual TRAPPIST results (Sec. 4.3) are given in reduction process for the TRAPPIST data set is included Table 3. Results using the combining methods are sum- in Gillon et al. (2012). marized in Sec. 4.5. 4.4. Errors 4.2. Spitzer 3.6µm Transits We used two methods to estimate uncertainties for our Our 42-hour ‘replacement’ observations contain two derived transit parameters: MCMC and prayer-bead. In transits at 3.6µm, one near the beginning of these data both methods the errors - as well as the best-fit values and one near the end. The photometry for these transits - follow from the posterior distributions. We adopted was decorrelated using the same methodology described the prayer-bead method for our quoted results because above for 4.5µm. In contrast to the 4.5µm case, our it explicitly includes the effect of red noise (D´esert et al. 3.6µm photometry exhibits noticeable red noise. Fortu- 2011b). Figure 11 shows the distributions for Rp/R∗ for nately, this red noise is most significant in the long in- oneofour4.5µmindividualfits,showingabroaderdistri- terval between the two transits. We limited the effect of bution for the prayer-beadmethod. this red noise by limiting the range of the data included In implementing the prayer-bead method, we permute in our decorrelations and fits. The omitted data did not the residuals only within the adopted phase range of the occur near the transits, nevertheless we tried to develop fit ( 0.05 in phase). At each permutation, we find the ± objective criteria for the range of data that were used. best-fittransitparametersusingtheLevenberg-Marquardt After comparing the σ vs. N−0.5 and global σ, or RMS method, and we add those best-fit values to the posterior scatter, of various sized data slices, we determined that distributions of each parameter. We adopt the median of trimming the 3.6 µm data set into a phase range of 0.05 the posterior distribution as the best fit value, following ± Spitzer transits of GJ1214b 5 D´esert et al. (2011b). resultantretrievalsfor Rp/R∗ areincluded inTable5. On A potentialadditionalsourceof erroris associatedwith average, constraining our orbital parameters to have the thedecorrelation,thatisnotexplicitlypropagatedintothe values found by either Bean et al. (2011) or Berta et al. stage of fitting the photometry. However,we are not con- (2012) results indecreasingourRp/R∗ value at4.5µm by cerned about this for two reasons. First, the 4.5µm data about 0.0010, but with less difference at 3.6µm or I+z. are so extensive, and the intra-pixel effect is so modest at Arguably, we should adopt these constrained values as thatwavelength,thatwebelievethoseerrorsindecorrela- ourprincipalresult. However,thelowlimbdarkeningthat tionhavenegligibleeffect. Second,ourprocedureaccounts prevails at Spitzer wavelengths, in combination with the forimperfectdecorrelationatbothSpitzerwavelengths,in high precision we achieve from our large dataset, moti- an implicit fashion. Imperfections in decorrelation create vates us to rely primarily on our own orbital parameters. red noise, and that red noise contributes to errors on the Nevertheless, we explore the implications of adopting the derivedtransitparametersusing the prayer-beadmethod. Bean et al.(2011)andBerta et al.(2012) orbitalparame- Inadditiontorandomerror,systematicdifferencesmay ters in Sec. 6. exist between our results and other investigators. We dis- cussonesourceofpossiblesystematicdifferenceinSec.4.5; 5. transit-to-transit variability and star spots the implications of these differences for the nature of GJ1214b’s atmosphere is discussed in Sec. 6. A star spot crossing during transit appears as an anomalous spike or bump in the transit light curve (e.g., Deming et al. 2011). Our photometry shows no evidence 4.5. System Parameters that the planet crossed even one significant star spot Asnotedabove,weestimatedthesystemparametersus- during our thirteen 4.5µm transits. Nevertheless, spots ingthreemethods: 1)simultaneousfittingofalltransitsat are common on M-dwarf stars, and uncrossed star spots a given wavelength, 2) averaging system parameters from couldstillaffectthe transit(Sing et al.2009;D´esert et al. the individual fits to each transit at a given wavelength, 2011b). and3)fittingtophased&binnedcombinationsoftransits TRAPPIST photometery of GJ1214 out of transit, but at a given wavelength. We included the transits observed over the same time period as our 4.5µm Spitzer ob- byD´esert et al.(2011)inallthreemethods. Wealsofitthe servations, shows essentially no variation in the I-band TRAPPISTtransitsusingallthreemethods(seeTable4). (Gillon et al. 2012), to a limit of about 0.2%. Neverthe- Table1liststheindividualfitstothe4.5µmdata;Table2 less,other investigationshavefound that GJ1214exhibits gives the individual fit results at 3.6µm and Table 3 lists rotationally-modulatedsignaturesofstarspots,sowecon- theindividualfitresultsfortheTRAPPISTtransitsinthe siderthe potentialimpactofsuchvariationonourresults. I+z band. Aswewilldemonstratebelow,evenallowingformorepho- Since our different fitting methods (summarized in Ta- tometric variationthan Gillon et al.(2012) observed,star ble4)aresimplydifferentwaysofaccountingforthesame spots have negligible effect on our results. data,theyshouldgiveconsistentresultsasfarasthebest- Berta et al. (2011) found that GJ1214 shows a photo- fit parametersareconcerned. Beyondbest-fit consistency, metricvariationof1%amplitude(2%peak-to-peak)inthe we find that comparison of these methods can provide a I-band(0.715-1.0µm)witharotationperiodof 53days, ∼ basis for caution concerning the errors on the derived pa- based on MEarth data (Nutzman & Charbonneau 2008), rameters. Forexample, our4.5µmresultsfromthe simul- spanning three years of observations. Using PHOENIX taneousfitgiveRp/R∗ =0.11710 0.00017,whereasaver- model atmospheres (Allard & Hauschildt 1995), we cal- ± aging the individual fits, weighted by the inverse of their culate that the Berta et al. (2011) amplitude of variation variances,givesRp/R∗ =0.11699 0.00026. Althoughthe could be produced by two star spots, each covering as ± best-fit values agree well, the larger error from averaging much as 2% of the sky-projectedstellar disk, separatedin ◦ the individual fits may indicate potential variations from longitude by 180 . Based on Doppler imaging studies of transit-to-transit. active dwarf stars (Rice & Strassmeier 1998), we adopt a Table5summarizesourresultsfortheRp/R∗parameter temperaturecontrast(spotvs. photosphere)∆T/T =0.1, thatpotentiallyrevealsinformationabouttheatmosphere thusT 2700K. Notethatthisisthesameasadopted spot ∼ ofGJ1214bintooneconciseTable. Forthediscussionthat by Berta et al. (2011). We use limb darkening coefficients follows, we adopt the results from the phased & binned forboththephotosphereandthestarspot,calculatedfrom method, because we feel that the high precision of these our transitfitting at 4.5µm (c =0.11, c =0.0). On this 0 1 combined transit curves allows the most reliable solution. basis, we determined that a 1% variation of the stellar We explored further comparison with two other pre- light curve in the I-band translates to 0.42% variation in cise measurements of Rp/R∗: Bean et al. (2011) and Spitzer photometry at 4.5µm. Berta et al. (2012). We choose these investigations for We developed a numerical tile-the-star model to calcu- more in-depth comparisonbecause the former is the high- latetheeffectofunoccultedstarspotsonthetransitdepth. est precision ground-basedmeasurement of GJ1214b,and Wecreatedasynthetictime-seriesof2DimagesofGJ1214, thelatterisaprecisespace-bornemeasurement. Weinves- at4.5µm,andprojectedtwocircularstarspotsonitssur- ◦ tigatedtowhatextentdifferencesinRp/R∗ arisefromthe face at the equator, separated by 180 of longitude. This different transit solutions, with different values for orbital arrangementofspotsinoppositehemispheresproducesan transit parameters such as a/R∗ and orbital inclination. appropriatequasi-sinusoidaleffectinthetotalstellarlight. Because these orbital parameters should not vary with We accounted for variation in the spots projected area wavelength, we force our solutions to adopt the values as as the star rotates, but we ignored the Wilson depres- derivedbyBean et al.(2011)andBerta et al.(2012). Our sion effect. The PHOENIX model with T = 3000K, 6 Fraine et al. [M/H] = +0.3, log(g) = 5.0 and α = 0.0 represented our conclusions concerning the atmosphere of GJ1214bin GJ1214; and, the PHOENIX model with T = 2700K, Sec. 6.5. [M/H] = +0.3, log(g) = 5.0, α = 0.0 represented the 6.1. Comparing Models to Observations star spot. We multiplied Spitzer’s 4.5µm filter profile by thespectralmodelsandintegratedoverwavelengthtocal- To compare transmission models for GJ1214b with the culate the expected 4.5µm flux variations due to stellar observations,we need to integrate the models– multiplied rotation with the spots fixed in longitude. Both the star by the filter profiles– over the observed bandpasses. Let andspotsareaffectedbylimbdarkeningasdeterminedby F (λ) be the out of transit flux measured from the star ot our fitted Mandel & Agol (2002) model parameters. as a function of wavelength. Similarly let F (λ) be the it Itiseasytoshowthattheeffectofunoccultedstarspots in-transit flux as a function of wavelength. Consider the on the planetary radius derived from the transit is given simplifiedcasewherelimbdarkeningcanbeneglected(ar- as: guably applicable in the infrared), and include the fact that there is a wavelength-dependent observational sensi- Rp 2 = Fot−Fit = (cid:16)RRp∗(cid:17)2spotlessIph (2) tivity, S(λ). In that case: (cid:18)R∗(cid:19)spotted Fot (1−ǫ)Iph+ǫIspot Fit(λ)=S(λ)I∗(λ)(πR∗2−πRp(λ)2), (3) with ǫ = Aspot, and where ot indexes out of transit, it where I∗(λ) is the intensity emergent from the stellar πR2∗ atmosphere at wavelength λ. The out of transit flux is: indexes in transit. I indicates the intensity of the stellar disk, I being the intensity of the photosphere, and I being tphhe intensity of the spot. spot Fot(λ)=S(λ)I∗(λ)πR∗2. (4) Using this equation together with flux variations from With realistic spectral resolution, the observed quanti- our tile-the-star model, we calculated the potential vari- tiesareintegralsoverthe observationalbandpass,andthe ation in transit depth as a function of time. This quasi- transit depth d is: sinusoidal variation has an unknown phase because we do not know the longitudes of anyrealstar spots onGJ1214. d= [F (λ) F (λ)]dλ/ F (λ)dλ, (5) ot it ot Nevertheless, the amplitude of variation in Rp/R∗ from Z − Z this model is 9.6 10−5, which is negligible compared Thus: × to the observed scatter in our measurements (see Fig- ure 11). Moreover, as noted above, the photometric vari- d= S(λ)I∗(λ)Rp(λ)2dλ/ S(λ)I∗(λ)R∗2dλ. (6) ations of GJ1214, observed concurrently with our tran- Z Z sit data (Gillon et al. 2012), were much less than from Whenweseektoevaluateamodeloftheplanet’stransit Berta et al. (2011). We therefore conclude that star spots radius as a function of wavelength(Rp(λ)), it is necessary play a negligible role on the observed variations and/or to include the wavelengthdependence of the stellar inten- possible bias of our inferred radii for GJ1214b. However, sity as well as the observational sensitivity. The latter is wecannotexcludethepossibilitythatincreasedstarspots commonlyincorporatedinnumerousstudies ofbothtran- during Bean et al.(2011) andBerta et al.(2012) observa- sits and secondary eclipses, but the necessity of including tions are responsible for some of the differences between the stellar intensity is less widely appreciated, especially our results. thepossibleeffectoflinestructureinthestellarspectrum. For example, if the stellar spectrum contains water vapor 6. the atmosphere of gj1214b absorption that overlaps to some degree with planetary There are numerous transit observations in the watervapor features,then the apparenttransitdepth will literature that bear on the nature of the atmo- be reduced compared to the case where the star is purely sphere of GJ1214b (Charbonneau et al. 2009; Bean et al. a continuum source. Stellar intensity weighting is par- 2010, 2011; D´esert et al. 2011; Berta et al. 2011, 2012; ticularly important for M-dwarf host stars like GJ1214, Croll et al. 2011; Sada et al. 2010; Carter et al. 2011; becausetheir spectrumvariesstronglywithwavelengthin Kundurthy et al.2011;de Mooij et al.2012;Murgas et al. the optical and near-IR. Unfortunately, that weighting is 2012; Narita et al. 2012). Nevertheless,the improvedpre- alsoconsiderablyuncertainforM-dwarfstars,particularly cision we have been able to achieve in the Spitzer bands, at the very interesting blue wavelengths where the planet together with the new TRAPPIST results in the I+z- mayexhibitscatteringfromhaze(Benneke & Seager2012; band, and recent advances in modeling the atmosphere Howe & Burrows 2012). of GJ1214b (Benneke & Seager 2012; Howe & Burrows TocomparemodelsofRp(λ)/R∗ toobservations,wecal- 2012),motivateustore-examinethenatureofGJ1214b’s culate the value of d using Eq. (6), and infer Rp/R∗ as atmosphere. √d. This procedure is valid even at wavelengths where In the following sub-sections we review the methodol- appreciable limb darkening prevails. ogy for comparing observations and models (Sec. 6.1), we AlthoughweuseaPHOENIXmodelatmospheretoper- brieflypreviewwhatourSpitzerobservationsalonecanre- formtheweightingovertheobservedbandpass,thismodel vealconcerningtheatmosphereofGJ1214b(Sec.6.2),and is not ultimately satisfactory for this purpose. For ex- we thencomparethe totality ofallpublished observations ample, in the green bandpass (0.46 µm) where a tran- to existing models, using a χ2 analysis (Sec. 6.3). Since sitwasobservedbyde Mooij et al.(2012),the PHOENIX planetary radii derived by different observational groups model has essentially no flux (many orders of magnitude can differ systematically, we discuss the effect of one par- below the peak flux), whereas the real star has suffi- ticularsystematicdifferenceinSec.6.4,andwesummarize cientflux to produce a transit havinggoodsignal-to-noise Spitzer transits of GJ1214b 7 (de Mooij et al. 2012). The reason is that the model in- alent to increasing (or decreasing) the size of the opaque cludes only LTE thermalemissionfromthe star,anddoes (i.e., solid)portionofthe planetbyasmallamount. That not incorporate the various emission signatures of mag- effectively varies the surface gravity of the planet, and netic activity. Thereforewe canuse the PHOENIXmodel would strictly speaking be inconsistent with the model onlyinthered-opticalandinfrared. Ourdefaultprocedure thatisbeingadjusted. However,the planetaryradiusata is to hold the stellar intensity constant for wavelengths givenatmosphericpressurelevelis notknownata levelof shortward of 1000 nm (i.e., we set I∗(λ) = I∗(1000) for accuracy comparable to the adjustments we are making. λ 1000nm), but we verified that using other prescrip- Moreover, the requisite adjustments in the model output ≤ tions shortward of this limit (e.g., blackbody spectra) do (typically, 0.0005 in Rp/R∗), correspond to less than 1% not greatly influence our present results. However, as the differencesinsurfacegravity. Wethereforefindthisproce- precision of observations improves, it will eventually be duretobeavalidandusefultoolfortestingmodelsversus necessary to have an accurate spectrum for the host star theobservations,andwenotethatasimilarprocedurewas at all wavelengths. usedbyBerta et al.(2012). Wefitthethreemodelsshown in Figure 12 (Benneke & Seager 2012), together with all 6.2. Implications from Spitzer of the models from Howe & Burrows (2012), and we cal- culate χ2 values for each fit. We also fit a flat line to Prior to an exhaustive analysis of all data versus all the data, i.e., a planetary radius that does not vary with models, we mention what our new Spitzer data alone wavelength - indicating no signature of the atmosphere. immediately reveal and/or constrain concerning the at- SeveralofthebestfittingmodelsareshowninFigure13, mosphere of GJ1214b. We (BB & SS) generated three comparedtotheentiretyofpublishedradiiforthisplanet. new model atmospheres for GJ1214b at an equilibrium temperature of 546 K, based on the methodology of In total, there are 97 observations of Rp/R∗ versus wave- length on Figure 13. The water atmosphere from Fig- Benneke & Seager (2012). The models are: 1) a H- ure 12,andtwo models fromHowe & Burrows(2012), are rich solar abundance model, 2) a ‘Hot-Halley’ composi- alsoincludedonFigure13. FortheFigure,themodelsare tion model which begins with solar composition and adds overplotted monochromatically, without integrating over minor molecular constituents from accreted icy material the bandpass. However, the χ2 values are calculated by (Benneke & Seager 2012), and 3) a pure water vapor at- integrating the model over the bandpass of each obser- mosphere. Figure 12 shows the result of integrating these vation as described above, and adopting the observed er- three models over the Spitzer observational bandpasses, rors from each source. In the case of multi-band analyses and including the stellar intensity using a PHOENIX (Kundurthy et al. 2011), we use the total bandpass from modelhavingTeff/log(g)/[M/H]=3000K/5.0/0.3. Based multiple filters. For the three overplotted models we also on this comparison, the solar composition model is elim- show the values for the integrals over the Spitzer band- inated based on the Spitzer data alone. The water va- passes, as open symbols. por model is preferred over the hot Halley model, based on the χ2 analysis described below. Moreover, we expect With96degreesoffreedom,modelscanonlyberejected at the 99.9% confidence level if they have a χ2 exceeding that methane-rich models having large scale heights (not 144.6. Among the possible models, The pure water atmo- illustrated)willberejectedbytheSpitzerdata,duetothe sphere from Benneke & Seager (2012) yields χ2 = 142.7 relative lack of an enhanced radius in the 3.6µm band - for 96 degrees of freedom. The hot Halley and solar com- that contains the strong ν band of methane. 3 position models from Benneke & Seager (2012) have χ2 6.3. A χ2 Analysis values of 167.9 and 1054.7 respectively, and are unlikely descriptions of GJ1214b’s atmosphere. The solar compo- To gain further quantitative insight, we weighted sition model in particular is strongly rejected unless high the three models from Benneke & Seager (2012) dis- clouds are included (see below). In this respect, we note cussed above, as well as all of the models given by that some discussion of a solar composition atmosphere Howe & Burrows (2012) over the observed bandpasses of hasoccurredwithrespecttotransitobservationsnear2µm all extant transit observations of GJ1214, including the (Croll et al. 2011; Bean et al. 2011). We here emphasize TRAPPIST and warm Spitzer data reported here. We fit that a cloudless solar composition model is incompatible the models to the data using a χ2 analysis, as described with the Spitzer data alone, as well as with the totality below. Berta et al. (2012) applied a similar χ2 analysis of the observations over all wavelengths. The issue of the to data from Hubble/WFC3, but not to the complete set transit depth near 2µm - while an important datum - is of data that we do here, and in particular not including not crucial to rejecting a solar composition atmosphere. our new and precise results in the warm Spitzer bands. Our improvement in the observed Spitzer precision at The utility of χ2 is well known to be problematic when 3.6µm - overlapping the strong ν band of methane, 3 combiningdatafromdifferentobservationalgroups. How- promptsustoinvestigatethemethane-compositionmodels ever, χ2 is at least an objective way to compare different of Howe & Burrows (2012). All of their methane compo- models, and we explicitly consider one cause of observer- sitions have χ2 above 184.6 (the value for 1% methane). to-observer systematic differences in Sec. 6.4. However, a solar composition model having high clouds To evaluate and compare possible models of the plane- (down to pressures of 0.1 mbars) produces an accept- tary atmosphere, we fit eachmodel to the data by adding able χ2 = 145.5. This model is plotted as the red line an adjustable constant (i.e., wavelength-independent off- on Figure 13; it predicts an increase in radius in the set) to the modeled values of Rp/R∗. We choose the con- difficult-to-observe regions near 2.7 and 3.3µm. The best stantto minimize the χ2 ofthe difference betweenthe ad- fit to the data is the yellow line on Figure 13, having justed modelandthe data. Adding this constantis equiv- 8 Fraine et al. χ2 = 119.8. This model, from Howe & Burrows (2012), systematic error. Hence we also conclude that the null contains a dense haze of small (0.1µm) tholin particles, hypothesis (no atmosphere detected) remains among the extending to very high altitudes (1µbar). It was disfa- mostfavoredmodels,especiallywhensystematicerrorsare voredbyHowe & Burrows(2012),butourmethodologyis considered. differentinthatweincorporateamarginallyadditivecon- stantwhenfittingthemodels. However,wepointoutthat 6.5. Summary of Implications for the Atmosphere of also among the acceptable models is a flat line (not illus- GJ1214b tratedonFigure13). Thisnullhypothesis(noatmosphere detected) yields χ2 =137.0. We have obtained new radii for GJ1214b in the I+z band using TRAPPIST, and very precise radii at 3.6- 6.4. Systematic Differences Between Observers and 4.5µm using Warm Spitzer in a long series of new One further check on the acceptable models is to fo- observations. Our χ2 analysis indicates that the best-fit cusonthedifferencebetweenourpreciseSpitzerradiiand model for the atmosphere of GJ1214b contains a haze of very precise radii derived at other wavelengths, i.e., by small particles extending to high altitudes, although pure Bean et al. (2011) and Berta et al. (2012). As noted at water vapor models remain a possibility. However, a flat the end of Sec. 4.5, we fix the variable orbital param- line is among the best-fitting models, particularly when eters (a/R∗ and i) at the values derived by Bean et al. observer-to-observersystematicdifferencesareconsidered. (2011) and Berta et al. (2012) and derive a lower value of Therefore we extend the conclusion of Berta et al. (2012) Rp/R∗ at 4.5µm by about 0.001 (Table 5). Using that concerningthe flatness of the transmisisonspectrum from alternative value in our χ2 analysis is one way of evaluat- 1.1- to 1.7µm to include our new high-precision Spitzer ing the possible effect of observer-to-observer differences measurements at 3.6- and 4.5µm. The atmosphere of in radii. This procedure increases the χ2 values of most GJ1214b is not unequivocally detected at this point in models, but by varying amounts. Interestingly, the two time. least affected models are the flat line, whose χ2 increases by δχ2 = +1.6, and the tholin-haze model. The water modelfromBenneke & Seager(2012)hasδχ2 =+8.4,and This work is based on observations made with the their hot Halley model has δχ2 = +19.8. The scattering Spitzer Space Telescope, which is operated by the Jet tholin-haze model from Howe & Burrows (2012) remains Propulsion Laboratory, California Institute of Technol- as the lowest absolute χ2, and has δχ2 = 2.3, i.e. it be- ogy under a contract with NASA. Support for this work − comes more likely, not less likely. We conclude that, even was provided by NASA through an award issued by when systematic differences among observational groups JPL/Caltech. We thank the Spitzer staff for their hard are considered, a scattering atmosphere is currently the workanddedicationinimplementingthesedifficultobser- best estimate for GJ1214b. However, we are unable to vations, andthe anonymousreferee for a carefulreview of explore the vast phase space of other possible sources of this paper. REFERENCES Agol,E.,Cowan,N.B.,Knutson,H.A.,Deming,D.,Steffen, J.H., Gillon, M., Demory, B.-O., Barman, T., Bonfils, X., Mazeh, T., Henry,G.W.,&Charbonneau, D.,2010,ApJ,721,1861. Pont, F., Udry, S., Mayor, M., & Queloz, D., 2007, A&A, 471, Allard,F.,&Hauschildt,P.H.,1995, ApJ,445,433. L51. Ballard, S., Charbonneau, D., Deming, D., Knutson, H. A., Gillon, M., Jehin E., Magain, P., Chantry, V., Hutsemekers, D., Christiansen, J. L., Holman, M. J., Fabrycky, D., Seager, S., & Manfroid, J., Queloz, D., & Udry, S., 2011, in ‘Detection and A’Hearn,M.F.,2010, PASP,122,1341. DynamicsofTransitingExoplanets,’EPJWebofConferences,eds. Bean,J.L.,Miller-RicciKempton,E.,&Homeier,D.,2010,Nature, F.Bouchy, R.Diaz,&C.Moutou,Vol.11,id.06002. 468,669. Gillon, M., Demory, B.-O., Deming, D., Seager, S., et al., 2012, in Bean,J.L.,and9co-authors,2011,ApJ,743,id.92. preparationforA&A. Benneke, B., & Seager, S., 2012, submitted to ApJ, astro- Howe,A.R.,&Burrows,A.S.,2012,ApJ,756,176. ph/1203.4018. Jehin,E.,Gillon,M.,Queloz,D.,etal.,TheMessenger,145,2. Berta, Z. K., Charbonneau, D., Bean, J., Irwin, J., Burke, C. J., Knutson,H.A.,&13co-authors,2012,ApJ,754,22. D¨esert,J.-M.,Nutzman,P.&Falco,E.E.,2011,ApJ,736,id.12. Kundurthy,P.,Agol,E.,Becker,A.C.,Barnes,R.,Williams,B.,& Berta,Z.K.,&9co-authors,2012,ApJ,747,id.35. Mukadam,A.,2011,ApJ,731,123. Carter,J.A.,Winn,J.N.,Holman,M.J.,Fabrycky,D.,Berta,Z.K., Lewis,N.K.,&23co-authors,2013,submittedtoApJ. Burke,C.J.,&Nutzman,P.,2011,ApJ,730,id.82. Liddle,A.R.,2007,MNRAS,377,L74. Charbonneau, D.,and18co-authors,2009,Nature,462,891. Mandel,K.,&Agol,E.,2002,ApJ,580,L171. Claret,A.,&Bloemen,S.,2011, A&A,529,id.A75 Mighell,K.J.,2005,MNRAS,361,861. Croll, B., Albert, L., Jayawardhana, R., Miller-Ricci Kempton, E., Miller-RicciKempton,E.,&Fortney, J.J.,2010,ApJ,716,L74. Fortney, J. J., Murray, N., & Neilson, Hilding, 2011, ApJ, 736, Murgas,F.,Pall´e,E.,Cabrera-Lawers,A.,Colo´n,K.D.,Mart´ın,E.L., id.78. Parviainen,H.,2012, A&A,554,id.A41. Crossfield,I.J.M.,Barman,T.,&Hansen,B.M.S.,2011,ApJ,736, Narita, N., Nagayama, T., Suenaga, T., Fukui, A., Ikoma, M., id.132. Nakajima, Y., Nishiyama, S., Tamura, M., submitted to PASJ, Deming,D.,and11co-authors,2009,PASP,121,883. astro-ph/1210.3169. Deming, D., Sada, P. V., Jackson, B., Peterson, S. W., Agol ,E., Nutzman,P.,&Charbonneau, D.,2008,PASP,120,317. Knutson, H. A., Jennings, D. E., Haase, F., & Bays, K., 2011, deMooij,E.J.W.,and10co-authors,2012, A&A,538,id.A46. ApJ,740,id.33. Rice,J.B.,Strassmeier,K.G.,1998,A&A,336,972. D¨esert, J. M., Bean, J., Miller-Ricci Kempton, E., Berta, Z. K., Rogers,L.,&Seager,S.,2010, ApJ,716,1208. Charbonneau, D., Irwin, J., Fortney, J. J., Burke, C. J., & Sada, P. V., Deming, D., Jackson, B., Jennings, D. E., Nutzman,P.,2011,ApJ,731,id.L40. Peterson, S. W., Haase, F., Bays, K., O’Gorman, E., & D¨esert, J. M., Sing, D., Vidal-Madjar, A., Hebrard, G., Lundsford,A.,2010,ApJ,720,L215. Ehrenreich, D., Lecavelier Des Estangs, A., Parmentier, V., Sing, D., D¨esert, J.-M., Des Estangs, L., Ballester, G. E., Vidal- Ferlet,R.,&Henry,G.W.,2011,A&A,526,id.A12. Madjar, A., Parmentier, V., Hebrard, G., & Henry, G. W., 2009, Ford,E.B.,2005, AJ,129,1706. A&A,505,891. Stevenson, K.B.,&9co-authors,2010,Nature,464,1161. Spitzer transits of GJ1214b 9 Fig. 1.—Thetoppanelillustratesrawdataforthefirst2.9-dayportionofour4.5µmphotometry,containingtwotransits. Eachdatapoint is aperture photometry before decorrelation, binned by every 10 data points. The middle panel shows the Y-center position as a function time;thatwhichwecorrelatewiththefluxtoremovetheintra-pixeleffect, andrelatedsystematicnoisesources. Thelowerpanel showsthe samephotometricvalues,exceptwiththetransitregionsexcluded,plottedversustheY-pixelpositionofthestellarimage. Notethedifferent spatial dependence of the photometry on each side of pixel center. The red curves are the 4th order polynomial fits that we use to initiate thedecorrelationprocess(seetext). 10 Fraine et al. Fig. 2.— Overview of our 4.5µm photometry, after decorrelation andbinned in100 two-second exposures per plotted point. Thedashed lineshowsthe transitdepth thatcorresponds to oneEarthradius. The13transits ofGJ1214b areapparent. SeeGillonetal.(2012)foran analysisofother possibletransitingplanetsinthissystem.

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