STUDYING THE ATMOSPHERE OF THE EXOPLANET HAT-P-7b VIA SECONDARY ECLIPSE MEASUREMENTS WITH EPOXI, SPITZER, AND KEPLER

The characterization of exoplanetary atmospheres is a quickly maturing field. Thus far, observations have revealed an intriguing range of results that are in turn feeding back into a rapidly evolving theoretical paradigm. The most fruitful method of investigation to date is the detection of secondary eclipses of hot Jupiters—highly irradiated gas giant planets in short period (2–3 day) orbits. By measuring the relative depths of the secondary eclipse of an exoplanet in multiple bandpasses, 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 emission from the planet. The Spitzer Space Telescope has been used to measure the infrared secondary eclipse depths for a growing list of extrasolar planets. These measurements reveal that the atmospheres 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; and XO-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 two classes 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 seen in solar system bodies (Burrows et al. 2008; Zahnle et al. 2009). The additional absorber in the upper atmosphere generates the temperature inversion. Orbiting an F6 star, with a large stellar radius and high stellar temperature, in a short orbital period, HAT-P-7b is one of the most highly irradiated hot Jupiters, receiving 4.5 × 10⁹ erg s⁻¹ cm⁻². It is therefore predicted to have a temperature inversion.

At optical wavelengths, the planet/star flux ratio is an order of magnitude less favorable than in 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 observing at optical wavelengths makes the detection of the secondary eclipse more difficult, it can provide very useful information. For instance, in the case of HD 209458b, the observed temperature inversion implies the presence of an unknown absorber high in the atmosphere, as mentioned above (Burrows et al. 2007). Subsequently, Rowe et al. (2008) placed very stringent upper limits on the optical depth of the secondary eclipse using the Microvariablity and Oscillations of Stars (MOST) satellite, and concluded that the absorber must have low reflectance. Optical secondary 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 for HAT-P-7b (Borucki et al. 2009) using the Kepler spacecraft. The only detection of an optical secondary eclipse from the ground at the time of submission is for OGLE-TR-56b in the z' band (Sing & López-Morales 2009).

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The next step is to combine the optical and infrared secondary eclipse measurements to extend the planetary emission spectrum and refine statements about the atmospheric properties. Prior to the launch of Kepler, observations of HAT-P-7b were obtained with the Extrasolar Planet Observation and Characterization (EPOCh) component of the NASA EPOXI Mission of Opportunity. One of the science goals of this mission was to measure or place meaningful upper limits upon the geometric albedo of a small set of transiting extrasolar planets. The goal of this paper is to combine the HAT-P-7b secondary eclipse measurements made with the EPOXI, Kepler, and Spitzer spacecraft to generate a broadband spectrum covering 0.35–8 μm, and to identify a set of model planetary atmospheres that reproduce the observations. The paper is organized as follows. In Section 2, we describe the EPOXI observations and data analysis; in Section 3, we describe our analysis of the Spitzer observations of HAT-P-7; in Section 4, we combine the results of these two data sets with the published Kepler secondary eclipse measurement and describe the model fits to the final spectrum; and in Section 5 we discuss the conclusions of the paper and the extension of this analysis to additional EPOXI targets.

HAT-P-7b was the final transiting extrasolar planet target observed with EPOXI. We observed eight transits: the first in the "pre-look," an initial two day observation window (UT 2008 August 8 and 9) to refine the pointing, the latter seven observed consecutively in a 15 day observation run lasting from UT 2008 August 16 to August 31. Seven secondary eclipses were observed during the 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-board the EPOXI spacecraft. We used the 1024×1024 pixel CCD with a clear filter, providing wavelength coverage from 350 to 1000 nm. The instrument is significantly defocused, with the point-spread function(PSF) having an FWHM of 9.0 pixels (3.7 arcsec). Due to on-board memory limiting the number of full frame images that could be stored, we observed in two subarray modes: 128 × 128 pixels typically, and 256 × 256 pixels during times of select transits and eclipses to minimize pointing losses. Observations were taken nearly continuously, with gaps of approximately 7 hr every 2–3 days to download the data from the spacecraft.

The data reduction pipeline is detailed in Ballard et al. (2009) and summarized here. We receive calibrated data products from the existing Deep Impact pipeline (Klaasen et al. 2005), to which we apply an additional bias correction. We use PSF fitting to find the position of the target star in each image to within a hundredth of a pixel; we discard 4850 images at this stage due to the star falling out of the field of view or too close to the edge of the CCD for accurate photometry. We discard an additional 40 images due to significant (15σ) deviations from the model PSF, caused by readout smear or radiation events. We then apply several corrections based on our knowledge of the CCD architecture, including scaling down the flux values in the two rows and two columns that form the internal boundaries at the center of the CCD, which has readout electronics in each of the four corners. We also scale the counts in images taken in 256×256 mode to those taken in 128 × 128 mode to account for a systematic flux offset between the two modes. Finally, we divide the images by a flat field generated from a green LED stimulator lamp mounted beside the CCD, which corrects for changes in the position-dependent sensitivity that have occurred since the detector was characterized prior to launch. We obtained these calibration frames ("stims") in six short blocks, each of approximately 20 minutes duration, spaced every few days during the observations of HAT-P-7. Each block contained 250 images, and in total we obtained 500 stims in 128 × 128 mode and 1000 in 256 × 256 mode. We correct each science frame in a given mode with the stims obtained in that mode.

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We perform aperture photometry on the resulting images, using a 10-pixel radius aperture. At this stage, there is still considerable correlated noise in the data, shown as the lower light curve in Figure 1, due to the time-variable jitter in the spacecraft pointing. For the observations of HAT-P-7, this jitter was on the order of 10 arcsec (40 pixels) hr⁻¹. We find that the monochromatic green stims are a poor representation of the interpixel sensitivity, which seems to have a color-dependent component, and as a result the pointing jitter introduces correlated noise that we are unable to remove with the calibration frames. We subsequently use the out-of-transit and out-of-eclipse data to map out the brightness variations with CCD position. For a small random subset (6% of the 21684 points in the light curve), we find an iteratively sigma-clipped mean of the closest spatially neighboring points and use these values to generate a surface. We then fit a two-dimensional spatial spline 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 21,684 images. The full corrected light curve is shown as the upper light curve 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 is higher 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 of observations of GJ 436, and that these observations are distributed over a larger fraction of the CCD. Both of these effects decrease the robustness of the spatial spline and result in higher residual correlated noise.

There are two "flare"-type events visible in the light curve, both of which we believe to be instrumental artifacts. The first occurs during the pre-look, at which time one of the four CCD quadrants 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 not present, and therefore the data obtained during the pre-look in this particular quadrant are not well 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 in the 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.

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In order to determine the limb-darkening coefficients across the EPOXI bandpass, we use the four stellar model atmospheres (Kurucz 1994, 2005) that bracket the HAT-P-7 values of T_eff = 6350 K and log g = 4.07, with [M/H] =0.3 and v_turb = 2.0 km s⁻¹ (Pál et al. 2008). We found previously that for the wide EPOXI bandpass the choice of limb-darkening treatment did not systematically affect the results (Ballard et al. 2009). We fit the four coefficients of the nonlinear limb-darkening law of Claret (2000) to 17 positions across the stellar limb. We repeat this fit in 0.2 nm intervals across the 350–1000 nm bandpass, weighted for the total sensitivity (including filter, optics and CCD response) and photon count at each wavelength. We calculate the final set of coefficients as the average of the weighted sum across the bandpass, bi-linearly interpolated between the four models, for which we find c₁ = 0.43, c₂ = 0.14, c₃ = 0.46, and c₄ = −0.25.

2.1. Transits

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 remove any residual instrumental linear trend. We use the analytic algorithms of Mandel & Agol (2002) to fit the transit parameters, using χ² 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 the planetary 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 8 times of transit center for a total of 11 free parameters. We initially fix the period to the value from the discovery paper (Pál et al. 2008), 2.2047299 days. We find R_p /R_⋆ = 0.0756 ±  0.0013, R_⋆/a = 0.2249 ±  0.0116, and cos i = 0.0754^+0.0374 _−0.0608. 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), with 2000 permutations. The quoted 1σ errors encompass 68% of the permutations. The light curve is shown in Figure 2, phased and binned in 5 minute intervals, with the best-fit model transit overplotted. Using the stellar mass value derived by Pál et al. (2008), M_* = 1.47 ± 0.08 M_☉, we find R_⋆ = 1.824 ± 0.089 R_☉, R_p = 1.342 ± 0.068 R_Jup and i = 85.7^+3.5 _−2.6 deg, which are consistent with and an improvement over the values in the discovery paper. However, they are moderately inconsistent with the parameters presented in the recently posted Winn et al. (2009) paper; a rigorous comparison of the results is not undertaken here. The new EPOXI values and the best-fit times of transit center are given in Table 1. For the transit times, shown in Figure 3, we see no evidence for transit timing variations on the order of 1–2 minutes, and we use a weighted linear fit to derive a new ephemeris combining the discovery ephemeris and the 8 times listed here: $T_c \rm {(BJD)} = 2454700.81308\pm 0.00100$, P = 2.2047308 ± 0.0000025 days.

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Table 1. HAT-P-7 System Parameters

Parameter	Value
Adopted values a
M*(M☉)	1.47 ± 0.08
Mp (MJup)	1.776 ± 0.077
Derived values
P (days)	2.2047308 ± 0.0000025
Tc (BJD)	2, 454, 700.81308 ± 0.00100
R⋆(R☉)	1.824 ± 0.089
Rp (RJup)	1.342 ± 0.068
i (deg)	85.7+3.5 −2.2
Transit times (BJD)	2, 454, 687.5815 ± 0.0012
	2, 454, 696.40413 ± 0.00075
	2, 454, 698.6064 ± 0.0012
	2, 454, 700.8139 ± 0.0011
	2, 454, 703.01513 ± 0.00099
	2, 454, 705.22219 ± 0.00086
	2, 454, 707.43077 ± 0.00074
	2, 454, 709.63062 ± 0.00092

Note. ^aMasses are from Pál et al. (2008).

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2.2. Secondary Eclipses

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. Observations 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 μm channels for 9.1 hr, the second on UT 2008 October 30 in the 4.5 and 8.0 μm channels for 8.1 hr. The latter 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), and Machalek et al. (2009). We summarize the procedure here, with particular care taken to describe any ways in which our analysis differs from earlier work.

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For each channel, we perform aperture photometry on the Basic Calibrated Data (BCD) products, using an aperture radius of 2.0 pixels for the 3.6 and 5.8 μm channels, 2.5 pixels for the 4.5 μm channel, and 3.0 pixels for the 8.0 μm channel. We determine the centers of the apertures by calculating the weighted sum of the flux in a circle of radius of 3 pixels positioned at the approximate location of the star. We choose the aperture size to minimize the scatter in the out-of-eclipse data. From this point, we treat the two shorter wavelength channels in a different manner to the two longer wavelengths, and the analyses are described separately.

3.1. 3.6 and 4.5 μm Channels

For each image, the position of the aperture was compared to the median of the preceding 10 and following 10 images. Where the position deviated by more than 3 times the rms of these values from the median, the estimate of the centroid was corrupted and the image discarded. For the 3.6 μm channel, 26 (0.53%) of 4906 images were discarded; for the 4.5 μm channel, 11 (0.25%) of 4370 images were discarded. For both channels, the sky background was calculated in an annulus centered on the aperture with inner and outer radii of 10 and 15 pixels, respectively, and subtracted.

Observations in these shorter wavelength channels are characterized by a position-dependent flux sensitivity (Reach et al. 2005; Charbonneau et al. 2005; Knutson et al. 2008, 2009a); we fit for this sensitivity and the eclipse light curve simultaneously. We generate the light curve with the analytic 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 both channels with linear and quadratic coefficients in the x and y positions, as shown in Equation (1), where the measured flux f' is a function of the incident flux f and position; adding higher order position terms or time-dependent terms did not significantly improve the final fit:

$$\begin{equation} f^{\prime } = f(b_1 + b_2(x - \bar{x}) + b_3(x - \bar{x})^2 + b_4(y - \bar{y}) + b_5(y - \bar{y})^2). \end{equation} \tag{ 1 }$$

For each channel, there are seven free parameters in the fit: a constant, a linear and a quadratic coefficient in the x position, a linear and quadratic coefficient in the y position, an eclipse depth, and a time 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 of the five parameters at each step, and discarding the first 20% of each chain. The best-fit value of each parameter is taken as the median of the distribution, and the error as the range centered on the median that encompasses 68% of the total points. We find depths of 0.098% ± 0.017% and 0.159% ± 0.022% in the 3.6 and 4.5 μm bands, respectively. The results are shown in Figures 5 and 6: the former shows the uncorrected data in 6 minute bins, with the model of intra-pixel sensitivity overplotted, the latter shows the binned data with the sensitivity divided out, and the best-fit eclipse model overplotted. In order to assess the effect of any remaining correlated noise in the data, we also use the rosary bead method described in Section 2.1. In each case, the number of permutations of the residuals is set to the number of points in the light curve (4880 points and 4359 points in the 3.6 and 4.5 μm bands, respectively) and the eclipse fit performed with the seven free parameters described above. We measure nearly identical eclipse depths and errors for the rosary bead method as for the MCMC method, finding 0.099% ± 0.014% in the 3.6 μm band and 0.162% ± 0.016% in the 4.5 μm band. For the remainder of the paper, we adopt the MCMC eclipse depths and errors.

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3.2. 5.8 and 8.0 μm Channels

The 5.8 and 8.0 μm channels show a long timescale time-dependent (as compared to position-dependent) flux sensitivity. The correlation is strongest in the 8.0 μm channel, where an increase in the flux during the course of the observations, referred to as the "detector ramp" is evident. One interpretation of this is an increase in the effective gain of the pixels with time in the 8.0 μm 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 of the target observations in order to pre-emptively increase the effective gain of the pixels. For the 8.0 μm observations of HAT-P-7, a 30 minute set of preflash observations, 3648 images in total, were obtained from the H ii region GAL 075.83+00.40 (α= 20 21 39.5, δ= +37 31 04). The median flux in the pixels in the aperture used for the HAT-P-7 observations ranges from 3500 to 4500 MJy sr⁻¹. After the pre-flash a time-dependent correlation is evident in the data, albeit significantly attenuated 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 find that removing the most significantly affected data, in this case the first 18 minutes (79 of 2185 images, 3.6% of the total), removes the need for higher order terms in the fit to the correlation described below. We also perform an iterative 3σ flux cut over the running median to discard outliers, possibly caused by radiation events, which removes 47 (1.9%) of 2453 images in the 5.8 μm channel, and 51 (2.4%) of the remaining 2106 images in the 8.0 μm channels.

We chose the time-dependent function that minimized the out-of-eclipse scatter, which was a linear function of ln(dt) in both channels, where dt is the time elapsed from the center of the first observed transit, shown in Equation (2). Previous analyses have used quadratic functions of ln(dt) (Charbonneau et al. 2008; Knutson et al. 2008, 2009a; Machalek et al. 2008, 2009); however, by comparison the ramp is attenuated in both channels in these data, and adding higher order functions of time or position-dependent functions did not improve the fit:

$$\begin{equation} f^{\prime } = f (c_1 + c_2({\rm ln}(dt + 0.02))). \end{equation} \tag{ 2 }$$

The additional factor of 0.02 prevents the singularity at dt = 0, and similar 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: a constant, a coefficient in time, and an eclipse depth. We found that when the time of eclipse was included as a free parameter there was a correlation between the time of eclipse and the coefficient in time. Since the measured times of eclipses in the shorter wavelengths do not deviate significantly from the predicted times for e = 0, we do not allow the time of eclipse to vary in the final fit for the 5.8 and 8.0 μm channels. We instead fix them to the values predicted by the EPOXI ephemeris for zero eccentricity. We calculate the values and errors in the same fashion as for the 3.6 and 4.5 μm channels, finding 0.245% ± 0.031% and 0.262% ± 0.027% in the 5.8 and 8.0 μm channels, respectively. In order to confirm the validity of fixing the time of eclipse, we repeated the analysis, this time drawing the time of eclipse from a Gaussian distribution defined by the times of eclipses and errors measured in the simultaneously observed channels, using the 3.6 μm values for the 5.8 μm channel and the 4.5 μm values for the 8.0 μm channel. We find near-identical results using this analysis. The results are shown in Figures 5 and 6. Again, we performed a rosary bead analysis to measure the effect of remaining correlated noise on the eclipse parameters. We find that a depth of 0.256% ± 0.029% in the 5.8 μm band, consistent with the depth measuring using the MCMC method. In the 8.0 μm band, the depth is 0.225% ± 0.052%, approximately 1σ shallower and with a larger error than that produced by the MCMC method, indicating that correlated noise represents the dominant contribution to the error budget for this channel. Therefore, we adopt the rosary bead method eclipse depth and error for the 8.0 μm band for the following analysis.

Figure 7 shows the four Spitzer secondary eclipse depth measurements, the 95% confidence EPOXI upper limit at 0.65 μm, and the recently published Kepler eclipse depth of 0.0130% ± 0.0011% at 0.63 μm (Borucki et al. 2009). This latter measurement was derived from the initial 10 days of Kepler calibration data and is expected to be refined in the future. We use these eclipse depths to calculate the brightness temperature in each bandpass. Assuming the planet emits as a blackbody, this is a measure of the dayside temperature of the planet required to generate sufficient flux in the bandpass to reproduce the measured planet-to-star flux ratio. In each bandpass, we integrate the ratio of a black body spectrum to a model stellar atmosphere of HAT-P-7, with T_eff = 6500 K, log g = 4.0, [M/H] =0.3 and v_turb = 2.0 km s⁻¹ (Kurucz 1994, 2005), weighted for the instrument throughput, and solve for the temperature required to match the measured eclipse depth. As expected, the highly irradiated HAT-P-7b has the hottest dayside brightness temperatures measured for any exoplanet, with temperatures in the four bands ranging from 2250 K to 3190 K. These values are given in Table 3. We also calculate this value for the Kepler secondary eclipse depth measurement (Borucki et al. 2009) and find T_b = 3175 ± 40 K.

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We fit the Kepler and Spitzer data using the model described in Madhusudhan & Seager (2009) but extended to visible wavelengths (N. Madhusudhan & S. Seager 2010, in preparation), using a photosphere radius of 1.363 R_Jup (Pál et al. 2008). The model assumes global energy balance between the incident and emergent radiation. The HAT-P-7b atmosphere is too hot for condensates; the visible-wavelength opacities include TiO and VO, Na and K, and Rayleigh scattering. We include additional molecular opacities of H₂O, CO, CH₄, and H₂–H₂ collision-induced opacities (CO₂ and NH₃ are included in the model but are not required by the current data). Our H₂O, CH₄, CO, and NH₃ molecular line data are from (Freedman et al. 2008, and references therein). Our CO₂ data are from R. Freedman (2009, private communication) and Rothman et al. (2005), and we obtain the H₂–H₂ collision-induced opacities from Borysow et al. (1997) and Borysow (2002).

Our model has 15 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 nominally define "best-fit" models as those that fit the data to within the 1σ errors shown in Figure 7. An exhaustive exploration of the fifteen-dimensional model parameter space is beyond the scope of the present study. Nevertheless, based on strategies outlined in Madhusudhan & Seager (2009), we have been able to empirically assess the region in the parameter space that best explains the data. Figure 7 shows one representative model that provides a best fit to the observations. The red circles with error bars are the data and the green circles are the bandpass integrated model points. The red dotted lines show the Kepler and Spitzer bandpasses. The black curve is the model fit. The blue dashed curves show two black-body spectra corresponding to 2029 K and 2974 K. The orange dashed curve shows a a black-body spectrum at 2600 K, for reference. The inset shows a zoom-in of the Kepler point and the model in the 0.4–1.0 μm range. The cyan and purple curves in the inset show the thermal emission and scattered light, respectively. Figure 8 shows 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 thermal inversion is strongly suggested by the high flux ratio in the 4.5 μm channel of Spitzer compared to the 3.6 μm channel, in addition to the high flux ratios in the 5.8 and 8 μm channels. The emission features in the 4.5 μm and 5.8 μm channels are due to CO and H₂O, respectively. The features in the 3.6 μm and 8 μm channels are predominantly due to CH₄. The molecular mixing ratios (with respect to H₂) for the model shown in Figure 7 are H₂O = 1.0⁻³, CO = 1.0⁻³, CH₄ = 1.0⁻⁶, and no CO₂. If we relax the model assumption of thermochemical equilibrium and allow a "best fit" to the data to be defined by 1.25σ errors, it is possible to generate suitable models that do not have a thermal inversion. However, these models require an overabundance of CH₄ in the atmosphere. Given the very hot atmosphere of HAT-P-7b, thermochemical equilibrium favors a high abundance of CO and low CH₄. Therefore, a non-inversion model fit to data would imply signs of extreme non-equilibrium chemistry (Madhusudhan & Seager 2010).

For a planet as hot as HAT-P-7, both scattered starlight and planet thermal emission could contribute to the planet flux in the Kepler bandpass (López-Morales & Seager 2007). The relative amount of scattered starlight and thermal emission depends on the absorbers and scatterers at visible wavelengths: molecular opacities due to TiO and VO, atomic opacities due to Na and K, and Rayleigh scattering mostly from H₂. HAT-P-7b is too hot for condensates, and without a reflective condensate layer, visible-wavelength photons will be absorbed before they can be scattered, except at very blue wavelengths. Even without a rigorous quantitative model, therefore, we can infer that the albedo of HAT-P-7b is likely to be low.

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Our best-fit models show a low albedo and include the prominent sources of opacity in the optical. The model shown gives a geometric albedo of about 0.13 in the Kepler bandpass, and has scattered light dominating at wavelengths blueward of approximately 0.6 microns and the planet's thermal emission dominating redward of approximately 0.6 microns. The abundances of Na and K are free parameters in the model and are found to be 0.01 solar; similarly the TiO/VO abundances are found to be 10⁻⁴ of their solar abundances. We note that even though TiO and VO are expected to contribute to the visible and IR opacity, whether they are responsible for the thermal inversion is not known (see Spiegel et al. 2009).

We emphasize that the Kepler data point for HAT-P-7b was instrumental in constraining the P–T profile, beyond the constraints placed by the Spitzer data alone. This is particularly true because of the high planet–star flux ratio of HAT-P-7b; in general, a visible-wavelength observation with 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 framework of a one-dimensional averaged dayside 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 atmospheric structure, 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 redistribution of absorbed stellar energy. Although energy redistribution is not a focus of this paper, we emphasize that a relatively inefficient day–night redistribution is consistent with, and even required by, our best-fit models. We find that approximately 10% of the incident stellar flux is redistributed to the nightside, under the assumption that the visible and infrared thermal phase curves will be similar.

We have assembled a broadband emission spectrum of the highly irradiated dayside of HAT-P-7b, extending from 0.35 to 8.0 μm. We find that this spectrum is best reproduced using an atmospheric model with a temperature inversion, supporting the hypothesis that the presence of an inversion layer is related to the absorbed stellar radiation. A census of exoplanet atmospheres at 3.6 and 4.5 μm that is being undertaken as part of the Warm Spitzer program will shed more light on the parameter space between where temperature inversions are present in the atmospheres of the most highly irradiated planets and absent in the less irradiated planets. This will include full phase curves of HAT-P-7 at 3.6 and 4.5 microns, which will further constrain the redistribution 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 only provide higher constraints on the secondary eclipse and phase curve measurements, but will allow investigation into the variability of the planetary emission properties.

At optical wavelengths, we find that the best-fit models predict a low geometric albedo of ≲0.13, which is far less reflective than gas giants in our solar system (e.g., 0.52 for Jupiter). The extremely hot atmosphere precludes the condensation of a reflective layer (i.e., clouds), and our predicted 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 confirm the Kepler measurement, given that the relative depth of the signal at visible wavelengths is on the order of 10⁻⁴. We observed a second transiting exoplanet target in the Kepler field of view with EPOXI, TrES-2, obtaining similar phase coverage to HAT-P-7, and will present those results in a forthcoming paper. Spitzer observations of TrES-2 have been obtained in the four IRAC bandpasses, and we envision that an analysis of the extended broadband emission spectrum such as that described in this paper will be similarly fruitful in terms of constraining the properties of the planetary atmosphere. Further EPOXI targets for which we will provide constraints on the geometric albedo are WASP-3, TrES-3, and HAT-P-4, all of which will have Spitzer IRAC measurements of the infrared secondary eclipse depths in at least the 3.6 and 4.5 μm channels.

We are extremely grateful to the EPOXI Flight and Spacecraft Teams that made these difficult observations possible. At the Jet Propulsion Laboratory, the Flight Team has included M. Abrahamson, 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 Cornell University.

Support for this work was provided by the EPOXI Project of the National Aeronautics and Space Administration's Discovery Program via funding to the Goddard Space Flight Center, and to Harvard University via Cooperative Agreement NNX08AB64A, and to the Smithsonian Astrophysical Observatory via Cooperative Agreement NNX08AD05A. This work is also based on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract to NASA. The authors acknowledge and are grateful for the use of publicly available transit modeling routines by Eric Agol and Kaisey Mandel, and also the Levenberg–Marquardt least-squares minimization routine MPFITFUN by Craig Markwardt. The authors also thank H. Knutson and F. Fressin for several useful discussions about Spitzer data analysis.