Studying the atmosphere of the exoplanet HAT-P-7b via secondary eclipse measurements with EPOXI, Spitzer and Kepler
Jessie L. Christiansen, Sarah Ballard, David Charbonneau, N. Madhusudhan, Sara Seager, Matthew J. Holman, Dennis D. Wellnitz, Drake Deming, Michael F. A'Hearn, EPOXI team
aa r X i v : . [ a s t r o - ph . E P ] D ec Studying the atmosphere of the exoplanet HAT-P-7b via secondary eclipsemeasurements with
EPOXI , Spitzer and
Kepler
Jessie L. Christiansen , Sarah Ballard , David Charbonneau , N. Madhusudhan , Sara Seager ,Matthew J. Holman , Dennis D. Wellnitz , Drake Deming , Michael F. A’Hearn and the EPOXI team
ABSTRACT
The highly irradiated transiting exoplanet, HAT-P-7b, currently provides one of thebest opportunities for studying planetary emission in the optical and infrared wave-lengths. We observe six near-consecutive secondary eclipses of HAT-P-7b at opticalwavelengths with the
EPOXI spacecraft. We place an upper limit on the relativeeclipse depth of 0.055% (95% confidence). We also analyze
Spitzer observations ofthe same target in the infrared, obtaining secondary eclipse depths of 0 . ± . . ± . . ± . . ± . Kepler secondary eclipse measurement, and generate atmospheric models for the day-side of the planet that are consistent with both the optical and infrared measurements.The data are best fit by models with a temperature inversion, as expected from the highincident flux. The models predict a low optical albedo of . .
13, with subsolar abun-dances of Na, K, TiO and VO. We also find that the best fitting models predict that10% of the absorbed stellar flux is redistributed to the night side of the planet, whichis qualitatively consistent with the inefficient day-night redistribution apparent in the
Kepler phase curve. Models without thermal inversions fit the data only at the 1.25- σ level, and also require an overabundance of methane, which is not expected in the veryhot atmosphere of HAT-P-7b. We also analyze the eight transits of HAT-P-7b presentin the EPOXI dataset and improve the constraints on the system parameters, finding aperiod of P = 2 . ± . R ⋆ = 1 . ± . R ⊙ , aplanetary radius of R p = 1 . ± . R Jup and an inclination of i = 85 . +3 . − . deg. Subject headings: planetary systems — eclipses — stars: individual (HAT-P-7) Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138; [email protected] Massachusetts Institute of Technology, Cambridge, MA 02159 University of Maryland, College Park, MD 20742
1. Introduction
The characterization of exoplanetary atmospheres is a quickly maturing field. Thus far, ob-servations have revealed an intriguing range of results that are in turn feeding back into a rapidlyevolving theoretical paradigm. The most fruitful method of investigation to date is the detec-tion of secondary eclipses of hot Jupiters—highly irradiated gas giant planets in short period (2–3day) orbits. By measuring the relative depths of the secondary eclipse of an exoplanet in multiplebandpasses, one can reconstruct a low-resolution emission spectrum from the dayside of the planet.The planet/star flux ratio is highest at infrared wavelengths, due to the thermal emissionfrom the planet. The
Spitzer Space Telescope has been used to measure the infrared secondaryeclipse depths for a growing list of extrasolar planets. These measurements reveal that the atmo-spheres span two distinct categories: those with temperature inversions in the upper atmospheres(HD 209458b, Knutson et al. 2008; XO-1b, Machalek et al. 2008; TrES-4, Knutson et al. 2009a; andXO-2b, Machalek et al. 2009), and those without (TrES-1, Charbonneau et al. 2005; HD 189733b,Charbonneau et al. 2008). It has been proposed that the distinguishing factor between the twoclasses is the incident flux on the planet, with higher incident flux resulting in gas-phase TiO/VO(Fortney et al. 2008; Burrows et al. 2008) or non-equilibrium products of photochemistry, as seenin solar system bodies (Burrows et al. 2008; Zahnle et al. 2009). The additional absorber in theupper atmosphere generates the temperature inversion. Orbiting an F6 star, with a large stel-lar radius and high stellar temperature, in a short orbital period, HAT-P-7b is one of the mosthighly irradiated hot Jupiters, receiving 4 . × erg s − cm − . It is therefore predicted to have atemperature inversion.At optical wavelengths, the planet/star flux ratio is an order of magnitude less favorable thanin the infrared, due to the much lower thermal emission from the planet at the shorter wavelengths,and also the low optical reflectance expected from cloud-free atmosphere models. Although ob-serving at optical wavelengths makes the detection of the secondary eclipse more difficult, it canprovide very useful information. For instance, in the case of HD 209458b, the observed tempera-ture inversion implies the presence of an unknown absorber high in the atmosphere, as mentionedabove (Burrows et al. 2007). Subsequently, Rowe et al. (2008) placed very stringent upper lim-its on the optical depth of the secondary eclipse using the Microvariablity and Oscillations ofStars ( MOST ) satellite, and concluded that the absorber must have low reflectance. Optical sec-ondary eclipses have been detected for CoRoT-1b (Snellen et al. 2009) and CoRoT-2b (Alonso et al.2009) with relatively low significance using the
CoRoT spacecraft, and with high significance forHAT-P-7b (Borucki et al. 2009) using the
Kepler spacecraft. The only detection of an optical sec-ondary eclipse from the ground at the time of submission is for OGLE-TR-56b in the z ′ band(Sing & L´opez-Morales 2009).The next step is to combine the optical and infrared secondary eclipse measurements to extendthe planetary emission spectrum and refine statements about the atmospheric properties. Prior tothe launch of Kepler , observations of HAT-P-7b were obtained with the EPOCh (Extrasolar Planet 3 –Observation and Characterization) component of the NASA
EPOXI
Mission of Opportunity. Oneof the science goals of this mission was to measure or place meaningful upper limits upon thegeometric albedo of a small set of transiting extrasolar planets. The goal of this paper is tocombine the HAT-P-7b secondary eclipse measurements made with the
EPOXI , Kepler and
Spitzer spacecraft to generate a broadband spectrum covering 0 . − µ m, and to identify a set of modelplanetary atmospheres that reproduce the observations. The paper is organized as follows: InSection 2, we describe the EPOXI observations and data analysis; in Section 3, we describe ouranalysis of the
Spitzer observations of HAT-P-7; in Section 4 we combine the results of these twodata sets with the published
Kepler secondary eclipse measurement and describe the model fits tothe final spectrum; and in Section 5 we discuss the conclusions of the paper and the extension ofthis analysis to additional
EPOXI targets. EPOXI observations and analysis
HAT-P-7b was the final transiting extrasolar planet target observed with
EPOXI . We observedeight transits: the first in the ‘pre-look’, an initial two day observation window (UT 2008 August8 and 9) to refine the pointing, the latter seven observed consecutively in a fifteen day observationrun lasting from UT 2008 August 16 to August 31. Seven secondary eclipses were observed duringthe run. We obtained 26,781 observations of HAT-P-7 in total.We observed HAT-P-7 with the 30-cm diameter High Resolution Instrument (HRI) on-boardthe
EPOXI spacecraft. We used the 1024 × ×
128 pixels typically, and 256 × σ ) deviations from the model PSF, causedby readout smear or radiation events. We then apply several corrections based on our knowledgeof the CCD architecture, including scaling down the flux values in the two rows and two columnsthat form the internal boundaries at the center of the CCD, which has readout electronics in eachof the four corners. We also scale the counts in images taken in 256 ×
256 mode to those takenin 128 ×
128 mode, to account for a systematic flux offset between the two modes. Finally, wedivide the images by a flat field generated from a green LED stimulator lamp mounted beside the 4 –CCD, which corrects for changes in the position-dependent sensitivity that have occurred sincethe detector was characterized prior to launch. We obtained these calibration frames (‘stims’) insix short blocks, each of approximately 20 minutes duration, spaced every few days during theobservations of HAT-P-7. Each block contained 250 images, and in total we obtained 500 stims in128 ×
128 mode and 1000 in 256 ×
256 mode. We correct each science frame in a given mode withthe stims obtained in that mode.We perform aperture photometry on the resulting images, using a 10-pixel radius aperture. Atthis stage there is still considerable correlated noise in the data, shown as the lower light curve inFigure 1, due to the time-variable jitter in the spacecraft pointing. For the observations of HAT-P-7this jitter was on the order of 10 arcsec (40 pixels) hr − . We find that the monochromatic greenstims are a poor representation of the interpixel sensitivity, which seems to have a color-dependentcomponent, and as a result the pointing jitter introduces correlated noise that we are unable toremove with the calibration frames. We subsequently use the out-of-transit and out-of-eclipse datato map out the brightness variations with CCD position. For a small random subset (6% of the21684 points in the light curve) we find an iteratively sigma-clipped mean of the closest spatiallyneighbouring points, and use these values to generate a surface. We then fit a 2-dimensional spatialspline to the surface, and correct each point in the light curve by interpolating onto this surface.We discard an additional 207 frames affected by readout smear or radiation events at this stage,resulting in a final set of 21684 images. The full corrected light curve is shown as the upper lightcurve in Figure 1, with an out-of-transit scatter that is 91% above that expected from Poisson noise.The excess is due to the remaining correlated noise that we have been unable to calibrate, and ishigher than the 56% value we attained for the EPOXI observations of GJ 436 (Ballard et al. 2009).This is due to the fact that the HAT-P-7 light curve has approximately two-thirds the number ofobservations of GJ 436, and that these observations are distributed over a larger fraction of theCCD. Both of these effects decrease the robustness of the spatial spline and result in higher residualcorrelated noise.There are two ‘flare’-type events visible in the light curve, both of which we believe to beinstrumental artifacts. The first occurs during the pre-look, at which time one of the four CCDquadrants was affected by a particular systematic flux correlation that was observed for other
EPOXI targets. For the remainder of the HAT-P-7 observations this systematic effect was notpresent, and therefore the data obtained during the pre-look in this particular quadrant are notwell calibrated by the spline. The second, which can be seen at approximately 18.6 days in Figure 1,occurs at a time when the star was illuminating a part of the CCD to which it does not return inthe course of the HAT-P-7 observations. The spline procedure we describe above therefore fails,since it relies on multiple visits to the same parts of the detector.In order to determine the limb-darkening coefficients across the
EPOXI bandpass, we use thefour stellar model atmospheres (Kurucz 1994, 2005) that bracket the HAT-P-7 values of T eff =6350K and log g = 4 .
07, with [M/H] = 0 . v turb = 2 . EPOXI bandpass the choice of limb-darkening treatment did not 5 –Fig. 1.—
Upper panel : The full HAT-P-7
EPOXI light curve. The first transit was observed duringthe two day ‘pre-look’ that established the pointing; a further seven were observed consecutivelyover the following 15 day observation run. The lower light curve has not had the surface splinecorrection applied; the upper light curve includes the correction and is the final light curve used inthe analysis. The two brightening events are instrumental in origin (see text). The vertical dashedlines indicate the expected secondary eclipses.
Lower panel : The scatter in the out-of-transit data(shown as diamonds) does not decrease with increasing bin size as expected for Gaussian noise(1 / √ N , where N is the number of points in the bin, shown as the solid line normalized to theunbinned value of the scatter), indicating that there is a component of correlated noise remainingin the light curve.systematically affect the results (Ballard et al. 2009). We fit the four coefficients of the non-linearlimb-darkening law of Claret (2000) to 17 positions across the stellar limb. We repeat this fit in0.2 nm intervals across the 350–1000 nm bandpass, weighted for the total sensitivity (includingfilter, optics and CCD response) and photon count at each wavelength. We calculate the finalset of coefficients as the average of the weighted sum across the bandpass, bi-linearly interpolatedbetween the four models, for which we find c = 0 . c = 0 . c = 0 .
46, and c = − . We first consider the transits observed by
EPOXI . We fit each transit with a linear, time-dependent slope using four hours of data before and four hours of data after the transit, to removeany residual instrumental linear trend. We use the analytic algorithms of Mandel & Agol (2002) 6 –to fit the transit parameters, using χ as the goodness-of-fit estimator. Using the Levenberg-Marquardt algorithm, we fit for three geometric parameters: R p /R ⋆ , where R p and R ⋆ are theplanetary and stellar radii respectively; R ⋆ /a , where a is the semi-major axis; and cos i , where i is the inclination of the orbit. We also fit for eight times of transit center for a total of elevenfree parameters. We initially fix the period to the value from the discovery paper (P´al et al.2008), 2.2047299 days. We find R p /R ⋆ = 0 . ± . R ⋆ /a = 0 . ± . i =0 . +0 . − . . In order to account for the effects of the remaining systematics in the error budget,we use the “rosary bead” residual permutation method described by Winn et al. (2008), with2000 permutations. The quoted 1- σ errors encompass 68% of the permutations. The light curveis shown in Figure 2, phased and binned in 5 minute intervals, with the best fit model transitoverplotted. Using the stellar mass value derived by P´al et al. (2008), M ∗ = 1 . ± . M ⊙ , wefind R ⋆ = 1 . ± . R ⊙ , R p = 1 . ± . R Jup and i = 85 . +3 . − . deg, which are consistentwith and an improvement over the values in the discovery paper. However, they are moderatelyinconsistent with the parameters presented in the recently posted Winn et al. (2009) paper; arigorous comparison of the results is not undertaken here. The new EPOXI values and the best fittimes of transit center are given in Table 1. For the transit times, shown in Figure 3, we see noevidence for transit timing variations on the order of 1–2 minutes, and we use a weighted linearfit to derive a new ephemeris combining the discovery ephemeris and the eight times listed here: T c (BJD) = 2454700 . ± . P = 2 . ± . We monitored eight secondary eclipses of HAT-P-7b with
EPOXI . Two of the eclipses areinterrupted by the systematic effects described earlier, and for the final analysis, we remove thesetwo eclipses and use the remaining six, shown in Figure 4. For this analysis, we perform anadditional calibration step. When producing the full HAT-P-7 light curve, we use only 6% of thedata points to create the 2-dimensional spatial spline, in order to minimize suppression of anyadditional astrophysical signals in the data, such as transits of additional planets in the system.However, when trying to extract the shallow signal of the eclipses of HAT-P-7b, we can make useof all of the data points that are not obtained during those events to increase the robustness ofthe calibration. For each event, we consider the points that occur within ± . σ outliers within eachbin. As with the transit analysis, we fit the data on either side of the eclipse with a linear slope 7 –Fig. 2.— The EPOXI
HAT-P-7 light curve, phase-folded and binned in five minute intervals. Thesolid line shows the best fit transit model, and the lower panel shows the residuals after this modelis subtracted from the data.with time to remove longer timescale trends. We generate a model using the geometric parametersderived from the transit fitting and with no limb-darkening, and scale the model depth to thatwhich minimizes the χ of the fit to the binned data. We do not allow the time of secondary eclipseto vary, fixing it at the expected phase value of 0.5, since there is no evidence of eccentricity forHAT-P-7b (see Section 3). We use the rosary bead method to determine the 1- σ error bars, shiftingthe residuals and re-binning each time, with approximately 820 permutations per eclipse. The sixeclipse depths are given in Table 2, where a negative eclipse depth corresponds to an increase influx at the predicted time of secondary eclipse. The best fit eclipse models are overplotted inFigure 4. The error bars in the figure are calculated from the scatter in each bin normalized bythe square-root of the number of points in that bin. For the final value we take the mean of the 8 –Fig. 3.— Observed transit times of HAT-P-7b minus the best fit linear ephemeris. Upper panel :The solid data point is from P´al et al. (2008), the hollow points are the
EPOXI transit times.
Lower panel : An expanded view of the
EPOXI transit times.six measurements; the systematics preclude us from scaling down the individual error bars whencombining the measurements, resulting in a best fit depth of 0 . ± . σ (0.048%) encompasses the six points. Spitzer observations and analysis
Secondary eclipses of HAT-P-7b were observed with the
Spitzer Space Telescope (Werner et al.2004) under a Target of Opportunity program (program 40685) led by Joseph Harrington. Observa-tions of two consecutive eclipses were obtained with the InfraRed Array Camera (IRAC; Fazio et al.2004): the first was observed on UT 2008 October 28 in the 3.6 and 5.8 micron channels for 9.1hours, the second on UT 2008 October 30 in the 4.5 and 8.0 micron channels for 8.1 hours. Thelatter were preceded by a 30 minute preflash set of observations, described further in Section 3.2.We treat the data in the same fashion as Charbonneau et al. (2008); Knutson et al. (2008, 2009a);Machalek et al. (2008, 2009). We summarize the procedure here, with particular care taken todescribe any ways in which our analysis differs from earlier work.For each channel, we perform aperture photometry on the BCD (Basic Calibrated Data) prod-ucts, using an aperture radius of 2.0 pixels for the 3.6 and 5.8 micron channels, 2.5 pixels for the4.5 micron channel, and 3.0 pixels for the 8.0 micron channel. We determine the centers of theapertures by calculating the weighted sum of the flux in a circle of radius 3 pixels positioned at 9 –Table 1. HAT-P-7 system parameters
Parameter ValueAdopted values a M ∗ ( M ⊙ ) 1 . ± . M p ( M Jup ) 1 . ± . P (days) 2 . ± . T c (BJD) 2 , , . ± . R ⋆ ( R ⊙ ) 1 . ± . R p ( R Jup ) 1 . ± . i (deg) 85 . +3 . − . Transit times (BJD) 2 , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . , , . ± . a Masses are from P´al et al. (2008).
Table 2. HAT-P-7b
EPOXI secondary eclipse measurements. Negative values imply increases influx at the predicted time of eclipse.
Predicted time of eclipse (BJD) Eclipse depth2,454,695.30127 0 . ± . − . ± . . ± . . ± . . ± . . ± . . ± .
10 –Fig. 4.— The relative flux versus orbital phase for the six HAT-P-7b eclipses observed with
EPOXI ,binned in 20 minute intervals, and offset by a constant for clarity. The solid line shows the best fiteclipse model in each case.the approximate location of the star. We choose the aperture size to minimize the scatter in theout-of-eclipse data. From this point, we treat the two shorter wavelength channels in a differentmanner to the two longer wavelengths and the analyses are described separately.
For each image, the position of the aperture was compared to the median of the preceding10 and following 10 images. Where the position deviated by more than 3 times the rms of thesevalues from the median, the estimate of the centroid was corrupted and the image discarded. For 11 –the 3.6 micron channel, 26 (0.53%) of 4906 images were discarded; for the 4.5 micron channel, 11(0.25%) of 4370 images were discarded. For both channels, the sky background was calculated inan annulus centered on the aperture with inner and outer radii of 10 and 15 pixels respectively andsubtracted.Observations in these shorter wavelength channels are characterized by a position-dependentflux sensitivity (Reach et al. 2005; Charbonneau et al. 2005; Knutson et al. 2008, 2009a); we fit forthis sensitivity and the eclipse light curve simultaneously. We generate the light curve with theanalytic equations from Mandel & Agol (2002) with no limb darkening, using the revised HAT-P-7b parameters from the
EPOXI analysis. We model the intra-pixel flux sensitivity for bothchannels with linear and quadratic coefficients in x and y position, as shown in Equation 1, wherethe measured flux f ′ is a function of the incident flux f and position; adding higher order positionterms or time-dependent terms did not significantly improve the final fit. f ′ = f ( b + b ( x − ¯ x ) + b ( x − ¯ x ) + b ( y − ¯ y ) + b ( y − ¯ y ) ) (1)For each channel, there are seven free parameters in the fit: a constant, a linear and a quadraticcoefficient in x position, a linear and quadratic coefficient in y position, an eclipse depth, and atime of center of eclipse. For the fitting, we use the Monte Carlo Markov Chain (MCMC) method(Ford 2005; Holman et al. 2006): in each case we run four chains of 500,000 steps, varying one ofthe five parameters at each step, and discarding the first 20% of each chain. The best fit valueof each parameter is taken as the median of the distribution, and the error as the range centeredon the median that encompasses 68% of the total points. We find depths of 0 . ± . . ± . . ± . . ± . The 5.8 and 8.0 micron channels show a long timescale time-dependent (as compared toposition-dependent) flux sensitivity. The correlation is strongest in the 8.0 micron channel, wherean increase in the flux during the course of the observations, referred to as the ‘detector ramp’ isevident. One interpretation of this is an increase in the effective gain of the pixels with time in 12 –the 8.0 micron detector. One successful method for mitigating this ramp is the preflash technique(Knutson et al. 2009b), where a bright diffuse region is observed immediately prior to the start ofthe target observations in order to pre-emptively increase the effective gain of the pixels. For the8.0 micron observations of HAT-P-7, a 30 minute set of preflash observations, 3648 images in total,were obtained of the HII region GAL 075.83+00.40 ( α = 20 21 39.5, δ = +37 31 04). The medianflux in the pixels in the aperture used for the HAT-P-7 observations ranges from 3500-4500 MJysr −
1. After the pre-flash a time-dependent correlation is evident in the data, albeit significantlyattenuated when compared with similar time series analysis performed in this channel (for example,Deming et al. (2007)). As noted by Charbonneau et al. (2008) and Knutson et al. (2008) we findthat removing the most significantly affected data, in this case the first 18 minutes (79 of 2185images, 3.6% of the total), removes the need for higher order terms in the fit to the correlationdescribed below. We also perform an iterative 3- σ flux cut over the running median to discardoutliers, possibly caused by radiation events, which removes 47 (1.9%) of 2453 images in the 5.8micron channel, and 51 (2.4%) of the remaining 2106 images in the 8.0 micron channels.We chose the time-dependent function that minimized the out-of-eclipse scatter, which wasa linear function of ln( dt ) in both channels, where dt is the time elapsed from the center of thefirst observed transit, shown in Equation 2. Previous analyses have used quadratic functions ofln( dt ) (Charbonneau et al. 2008; Knutson et al. 2008, 2009a; Machalek et al. 2008, 2009), howeverby comparison the ramp is attenuated in both channels in these data, and adding higher orderfunctions of time or position-dependent functions did not improve the fit. f ′ = f ( c + c (ln( dt + 0 . dt = 0, and similarly to Knutson et al.(2009a) we find no significant change in the measured depth of the eclipse on varying this value.The MCMC fit was performed as described previously, with three free parameters in each case: aconstant, a coefficient in time, and an eclipse depth. We found that when the time of eclipse wasincluded as a free parameter there was a correlation between the time of eclipse and the coefficientin time. Since the measured times of eclipses in the shorter wavelengths do not deviate significantlyfrom the predicted times for e = 0, we do not allow the time of eclipse to vary in the final fit for the5.8 and 8.0 micron channels. We instead fix them to the values predicted by the EPOXI ephemerisfor zero eccentricity. We calculate the values and errors in the same fashion as for the 3.6 and 4.5micron channels, finding 0 . ± . . ± . . ± . . ± . σ shallowerand with a larger error than that produced by the MCMC method, indicating that correlated noiserepresents the dominant contribution to the error budget for this channel. Therefore we adopt therosary bead method eclipse depth and error for the 8.0 micron band for the following analysis.Fig. 5.— Secondary eclipses of HAT-P-7b observed in the four Spitzer
IRAC bands. The data arebinned in 6 minute intervals and offset in flux for clarity. The solid line is the best fit model of theposition- and time-dependent instrument effects in each case, described in Section 3.
4. Discussion
Figure 7 shows the four
Spitzer secondary eclipse depth measurements, the 95% confidence
EPOXI upper limit at 0.65 micron, and the recently published
Kepler eclipse depth of 0 . ± . Kepler calibration data and is expected to be refined in the future. We use these eclipsedepths to calculate the brightness temperature in each bandpass. Assuming the planet emits as ablackbody, this is a measure of the dayside temperature of the planet required to generate sufficientflux in the bandpass to reproduce the measured planet-to-star flux ratio. In each bandpass, weintegrate the ratio of a black body spectrum to a model stellar atmosphere of HAT-P-7, with T eff = 6500K, log g = 4 .
0, [M/H] = 0 . v turb = 2 . Kepler secondary 15 –eclipse depth measurement (Borucki et al. 2009) and find T b = 3175 ± Kepler and
Spitzer data using the model described in Madhusudhan & Seager(2009a) but extended to visible wavelengths (Madhusudhan & Seager, in prep.), using a photo-sphere radius of 1 . R Jup (P´al et al. 2008). The model assumes global energy balance betweenthe incident and emergent radiation. The HAT-P-7b atmosphere is too hot for condensates; thevisible-wavelength opacities include TiO and VO, Na and K, and Rayleigh scattering. We includeadditional molecular opacities of H O, CO, CH , and H -H collision-induced opacities (CO andNH are included in the model but are not required by the current data). Our H O, CH , CO andNH molecular line data are from (Freedman et al. 2008, and references therein). Our CO dataare from R. Freedman (personal communication) and Rothman et al. (2005), and we obtain theH -H collision-induced opacities from Borysow et al. (1997), and Borysow (2002).Our model has fifteen free parameters, and we have at hand only five observational constraints.Consequently, the data allow a large number of solutions at any level of fit. Therefore, we nominallydefine ‘best fit’ models as those that fit the data to within the 1- σ errors shown in Figure 7. Anexhaustive exploration of the fifteen dimensional model parameter space is beyond the scope ofthe present study. Nevertheless, based on strategies outlined in Madhusudhan & Seager (2009a),we have been able to empirically assess the region in the parameter space that best explains thedata. Figure 7 shows one representative model that provides a best fit to the observations. Thered circles with error bars are the data and the green circles are the bandpass integrated modelpoints. The red dotted lines show the Kepler and
Spitzer bandpasses. The black curve is themodel fit. The blue dashed curves show two black-body spectra corresponding to 2029 K and2974 K. The orange dashed curve shows a a black-body spectrum at 2600 K, for reference. Theinset shows a zoom-in of the
Kepler point and the model in the 0.4-1.0 µ m range. The cyan andpurple curves in the inset show the thermal emission and scattered light, respectively. Figure 8shows the pressure-temperature (P-T) profile of the model atmosphere.We find that all of our best fit models require a thermal inversion to fit the data. A thermalinversion is strongly suggested by the high flux ratio in the 4.5 micron channel of Spitzer comparedto the 3.6 micron channel, in addition to the high flux ratios in the 5.8 and 8 micron channels. Theemission features in the 4.5 micron and 5.8 micron channels are due to CO and H O, respectively.The features in the 3.6 micron and 8 micron channels are predominantly due to CH . The molecularTable 3. HAT-P-7b Spitzer
IRAC secondary eclipse measurements
Wavelength ( µ m) Depth (MCMC) Depth (Rosary) Time (BJD) O-C (minutes) T b (K)3.6 0 . ± . . ± . , , . ± . . ± .
04 2250 ± . ± . . ± . , , . ± . − . ± .
62 2600 ± . ± . . ± . ± . ± . . ± . ±
16 –mixing ratios (with respect to H ) for the model shown in Figure 7, are H O = 1.0 − , CO = 1.0 − ,CH = 1.0 − , and no CO . If we relax the model assumption of thermochemical equilibrium, andallow a ‘best fit’ to the data to be defined by 1.25- σ errors, it is possible to generate suitable modelsthat do not have a thermal inversion. However, these models require an overabundance of CH inthe atmosphere. Given the very hot atmosphere of HAT-P-7b, thermochemical equilibrium favorsa high abundance of CO and low CH . Therefore, a non-inversion model fit to data would implysigns of extreme non-equilibrium chemistry (Madhusudhan & Seager 2009b).For a planet as hot as HAT-P-7, both scattered starlight and planet thermal emission couldcontribute to the planet flux in the Kepler bandpass (L´opez-Morales & Seager 2007). The relativeamount of scattered starlight and thermal emission depends on the absorbers and scatterers atvisible wavelengths: molecular opacities due to TiO and VO, atomic opacities due to Na and K, andRayleigh scattering mostly from H . HAT-P-7b is too hot for condensates, and without a reflectivecondensate layer, visible-wavelength photons will be absorbed before they can be scattered, exceptat very blue wavelengths. Even without a rigorous quantitative model, therefore, we can infer thatthe albedo of HAT-P-7b is likely to be low.Our best fit models show a low albedo and include the prominent sources of opacity in theoptical. The model shown gives a geometric albedo of about 0.13 in the Kepler bandpass, and hasscattered light dominating at wavelengths blueward of approximately 0.6 microns and the planet’sthermal emission dominating redward of approximately 0.6 microns. The abundances of Na and Kare free parameters in the model and are found to be 0.01 solar; similarly the TiO/VO abundancesare found to be 10 − of their solar abundances. We note that even though TiO and VO are expectedto contribute to the visible and IR opacity, whether they are responsible for the thermal inversionis not known (see Spiegel et al. 2009).We emphasize that the Kepler data point for HAT-P-7b was instrumental in constraining theP-T profile, beyond the constraints placed by the Spitzer data alone. This is particularly truebecause of the high planet-star flux ratio of HAT-P-7b; in general, a visible-wavelength observationwith a lower contrast may not be as useful for constraining P-T profile.The values of atomic and molecular abundances present in our models are valid in the frame-work of a 1D averaged day-side atmosphere. The true values of atomic and molecular abundances,and hence the resulting albedo, in the atmosphere of HAT-P-7b depend on the 3D atmosphericstructure, and in 3D are degenerate at the resolution of the
Kepler data point.The
Kepler phase curve (Borucki et al. 2009) shows a very inefficient day-night redistributionof absorbed stellar energy. Although energy redistribution is not a focus of this paper, we emphasizethat a relatively inefficient day-night redistribution is consistent with, and even required by, ourbest fit models. We find that approximately 10% of the incident stellar flux is redistributed to thenight side, under the assumption that the visible and infrared thermal phase curves will be similar. 17 –Fig. 7.— The
EPOXI , Spitzer and
Kepler secondary eclipse measurements of HAT-P-7b. The solidline is a representative best fit model, with a temperature inversion. The points with error barsare the observed measurements; the points without are the bandpass-integrated model values. Thedashed lines show black-body spectra corresponding to 2029 K, 2600 K and 2974 K, for reference.The dotted lines are the instrument response curves. The inset is an expansion of the optical regionof the spectrum, showing the
Kepler measurement and response curve. The cyan and purple linesare the thermal and scattered components of the model respectively.
5. Conclusions and future work
We have assembled a broadband emission spectrum of the highly irradiated dayside of HAT-P-7b, extending from 0.35–8.0 micron. We find that this spectrum is best reproduced using anatmospheric model with a temperature inversion, supporting the hypothesis that the presence ofan inversion layer is related to the absorbed stellar radiation. A census of exoplanet atmospheresat 3.6 and 4.5 micron that is being undertaken as part of the Warm
Spitzer program will shed morelight on the parameter space between where temperature inversions are present in the atmospheresof the most highly irradiated planets and absent in the less irradiated planets. This will includefull phase curves of HAT-P-7 at 3.6 and 4.5 microns, which will further constrain the redistribution 18 –Fig. 8.— The temperature-pressure profile of HAT-P-7b corresponding to the atmosphere modelshown in Figure 7, showing a temperature inversion.and energy budget of the planetary atmosphere. In addition, as the
Kepler observations of HAT-P-7 accumulate, the quality of the resulting light curve will be exquisite. This will not onlyprovide higher constraints on the secondary eclipse and phase curve measurements, but will allowinvestigation into the variability of the planetary emission properties.At optical wavelengths, we find that the best fit models predict a low geometric albedo of . .
13, which is far less reflective than gas giants in our solar system (e.g. 0.52 for Jupiter). Theextremely hot atmosphere precludes the condensation of a reflective layer (i.e. clouds), and ourpredicted albedo is consistent with those measured for other hot Jupiters (Rowe et al. 2008).The
EPOXI
HAT-P-7 secondary eclipse constraint is one of the few opportunities to confirmthe
Kepler measurement, given that the relative depth of the signal at visible wavelengths is onthe order of 10 − . We observed a second transiting exoplanet target in the Kepler field of viewwith
EPOXI , TrES-2, obtaining similar phase coverage to HAT-P-7, and will present those resultsin a forthcoming paper.
Spitzer observations of TrES-2 have been obtained in the four IRACbandpasses, and we envision that an analysis of the extended broadband emission spectrum suchas that described in this paper will be similarly fruitful in terms of constraining the propertiesof the planetary atmosphere. Further
EPOXI targets for which we will provide constraints on 19 –the geometric albedo are WASP-3, TrES-3 and HAT-P-4, all of which will have
Spitzer
IRACmeasurements of the infrared secondary eclipse depths in at least the 3.6 and 4.5 micron channels.We are extremely grateful to the
EPOXI
Flight and Spacecraft Teams that made these difficultobservations possible. At the Jet Propulsion Laboratory, the Flight Team has included M. Abra-hamson, B. Abu-Ata, A.-R. Behrozi, S. Bhaskaran, W. Blume, M. Carmichael, S. Collins, J. Diehl,T. Duxbury, K. Ellers, J. Fleener, K. Fong, A. Hewitt, D. Isla, J. Jai, B. Kennedy, K. Klassen, G.LaBorde, T. Larson, Y. Lee, T. Lungu, N. Mainland, E. Martinez, L. Montanez, P. Morgan, R.Mukai, A. Nakata, J. Neelon, W. Owen, J. Pinner, G. Razo Jr., R. Rieber, K. Rockwell, A. Romero,B. Semenov, R. Sharrow, B. Smith, R. Smith, L. Su, P. Tay, J. Taylor, R. Torres, B. Toyoshima,H. Uffelman, G. Vernon, T. Wahl, V. Wang, S. Waydo, R. Wing, S. Wissler, G. Yang, K. Yetter,and S. Zadourian. At Ball Aerospace, the Spacecraft Systems Team has included L. Andreozzi,T. Bank, T. Golden, H. Hallowell, M. Huisjen, R. Lapthorne, T. Quigley, T. Ryan, C. Schira, E.Sholes, J. Valdez, and A. Walsh. We also thank the remainder of the
EPOXI team, including R. K.Barry, M. J. Kuchner, T. A. Livengood and T. Hewagama at the Goddard Space Flight Center,J. M. Sunshine at the University of Maryland, D. Hampton at the University of Alaska Fairbanks,C. Lisse at the Johns Hopkins University Applied Physics Laboratory, and J. Veverka at CornellUniversity.Support for this work was provided by the
EPOXI
Project of the National Aeronautics andSpace Administration’s Discovery Program via funding to the Goddard Space Flight Center, andto Harvard University via Co-operative Agreement NNX08AB64A, and to the Smithsonian As-trophysical Observatory via Co-operative Agreement NNX08AD05A. This work is also based onobservations made with the
Spitzer Space Telescope , which is operated by the Jet Propulsion Labo-ratory, California Institute of Technology, under contract to NASA. The authors acknowledge andare grateful for the use of publicly available transit modeling routines by Eric Agol and KaiseyMandel, and also the Levenberg-Marquardt least-squares minimization routine MPFITFUN byCraig Markwardt. The authors also thank H. Knutson and F. Fressin for several useful discussionsabout
Spitzer data analysis. 20 –
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