DETECTION OF THERMAL EMISSION FROM A SUPER-EARTH

The aim of this step is to perform an exhaustive model comparison to determine the optimal baseline model for each AOR. The baseline model accounts for the time- and position-dependent systematic effects relevant to the IRAC 4.5 μm observations (see D11; G12 and references therein). For this purpose, we individually analyze each AOR by employing our adaptative Markov Chain Monte Carlo (MCMC) implementation described in Gillon et al. (2010). We set the occultation depth as a jump parameter and fix the orbital period P, transit duration W, time of minimum light T₀, and impact parameter b = acos i/R_⋆ to the values obtained from the global analysis of the system (G12). We further impose a Gaussian prior on the orbital eccentricity (e = 0.06 ± 0.05; D11), allowing the eclipse phase and duration to float in the MCMC. For each model, we run two chains of 10⁴ steps each. Throughout this work, we assess the convergence and good mixing of the Markov chains using the statistical test from Gelman & Rubin (1992).

We first assume a baseline model based on a classical second-order x–y position polynomial (D11, Equation (1)) to correct the "pixel-phase" effect, added to a time-dependent linear trend. We then increase this basic baseline complexity by trying combinations of up to third- and fourth-order x–y position polynomials, second-order logarithmic ramp models, and second-order time-dependent polynomials. The baseline models tested are therefore characterized by 7–20 free parameters, well constrained by the ∼6200 measurements of each AOR. We finally compute the Bayesian information criterion (BIC; e.g., Gelman et al. 2003) for all combinations and choose, from the MCMC output, the baseline model that yields the highest marginal likelihood. We show the resulting individual light curves on Figure 2 and the selected model along with the occultation depth for each AOR in Table 1.

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The correlated noise affecting each light curve is taken into account following Gillon et al. (2010). A scaling factor β from the comparison of the standard deviation of binned and unbinned flux residuals is determined during a preliminary MCMC run. This factor is then applied to the individual uncertainties of the flux time series. The β values for each AOR are shown in Table 1. To obtain an additional estimation of the residual correlated noise, we conduct a residual-permutation bootstrap analysis on each light curve corrected from the baseline model, similar to D11. This part of the analysis yields parameters in good agreement with the results from our MCMC analyses, albeit with significantly smaller error bars, suggesting that the error budget is dominated by the uncertainties on the coefficients of the complex baseline model and not by the residual correlated noise contribution.

The examination of the individual light curves obtained with more complex models leads to similar results to the light curves shown on Figure 2, which are obtained with the baseline models selected in the previous step (Table 1). The resulting occultation depths are compatible within 1σ, securing both our detection and the insensitivity of the occultation signal to our adopted method for systematics correction.

As in D11 and G12, we perform a Lomb–Scargle periodogram analysis (Scargle 1982) on the residuals of our selected model for each AOR. Peaks with marginal significance are found at 69 minutes in the second AOR and at 51 minutes in the third AOR, while neither of the first nor fourth AOR's residuals reveal a periodic signal. We include these sinusoidal modulations in the baseline models of our second and third AORs and perform a new MCMC that yields a higher BIC value than our model selected during the previous step of the analysis. We therefore neglect the sinusoidal term in both AORs. No hint of a ∼50 minutes and ∼100 ppm amplitude modulation similar to the one reported in D11 and G12 is found in the four data sets.

We further build a "pixel map" to characterize the intrapixel variability on a fine grid. This approach has been already demonstrated by Ballard et al. (2010) and Stevenson et al. (2011) as an efficient method to remove the flux modulation due to the "pixel-phase" effect. The improved tracking accuracy brought by the new PCRS peak-up mode is indeed expected to increase the resolution of the pixel map, hence motivating this step of the analysis for our observations. More specifically, our implementation divides the area covered by the PRF in a grid made of 30 × 30 boxes and counts the number of out-of-eclipse data points that fall in each box. If a given box has at least four data points spanning at least 50% of the AOR duration, the individual fluxes are divided by their mean, otherwise the corresponding measurements are rejected. As this method could average out an eclipse signal located in the designated out-of-eclipse parts of the light curve, we repeat this procedure by gradually shifting the out-of-eclipse data points in time. On average, as compared to the first AOR (obtained without the PCRS peak-up mode), the measurements sample 24% more time per box in the second AOR, 57% in the third AOR, and 48% in the fourth AOR. The occultation depth and duration obtained using the pixel-map-corrected light curves are in good agreement with the ones employing a polynomial baseline model.

The different analysis techniques applied above yield detrended time series in which the occultation signal is visible by eye with consistent phase and duration in three out of the four AORs (Figure 2). The second AOR is the only one in which the detection is marginal (68 ± 52 ppm). The different approaches used to correct the photometry from the "pixel-phase" effect show that the intrapixel sensitivity does not explain this discrepancy. We notice that the β factor for this second AOR is ∼50% larger than for the other AORs (see Table 1), suggesting a larger amount of correlated noise of instrumental or astrophysical origin. Examination of the onboard temperature sensors readings and other external parameters in the FITS files do not reveal any unusual patterns. While an actual variability of the planet's emission cannot be ruled out, the marginal disagreement (1.2σ) of the second occultation's amplitude relative to the three others is probably caused by this larger correlated noise.

The final step of our analysis consists of performing a global analysis, including all four light curves in the same MCMC framework, to constrain both the occultation depth and orbital eccentricity. For this purpose, we assume Gaussian priors on b, W, T₀, $\sqrt{e} \cos \omega$, $\sqrt{e} \sin \omega$ and the stellar parameters based on the posterior distributions derived in D11, G12, and in von Braun et al. (2011). We first run two MCMC (one with the occultation model and one without) to assess the robustness of our detection, using as input the four raw light curves. We employ the baseline models selected in the previous step and shown in Table 1. These two runs are composed of three chains of 10⁴ steps each.

We find an occultation depth of 131 ± 28 ppm, and an eccentricity e < 0.06 (3σ upper limit). The odds ratio computed using the BIC between the two models (with versus without occultation) is ∼10⁴ in favor of the occultation model. The thermal emission from 55 Cnc e is therefore firmly detected.

To test the robustness of the eccentricity signal, we then perform an identical MCMC run but with the assumption of a circular orbit. The odds ratio between the circular and non-circular orbits is ∼10³ in favor of the circular case. The resulting occultation depth in this case is 122 ± 21 ppm, in excellent agreement with the value obtained for the non-circular case. The phase-folded occultation lightcurve with the best-fit circular model is shown in Figure 3.

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From the measured secondary eclipse depth we obtain a brightness temperature estimate of 2360  ±  300 K, using a stellar blackbody emission spectrum, with T_eff = 5196  ±  24 K (von Braun et al. 2011). At face value, the high brightness temperature suggests that either 55 Cnc e has both a low Bond albedo and an inefficient heat transportation from the day side to the night side, or the observations in the IRAC 4.5 μm bandpass probe layers in the atmosphere that are at temperatures higher than the equilibrium temperature (Figure 4). Either scenario may explain why the brightness temperature is observed to be higher than the zero Bond albedo equilibrium temperature, T_eq = 1950 K, for a uniformly re-radiating planet.

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One interpretation could be that the planet is a rock with only a minimal atmosphere established through vaporization (Schaefer & Fegley 2009; Léger et al. 2009; Castan & Menou 2011). Rocky objects in the solar system, e.g., Mercury and the Moon, have low Bond albedos between 0.07 and 0.12. Lacking a thick atmosphere, a rocky super-Earth also does not have any efficient means of transporting heat from the day side to the night side. We disfavor the bare rock scenario, however, because the 55 Cnc e mass and radius measurements (D11; G12) exclude a rocky composition similar to Mercury and Earth; to be a rocky planet with minimal atmosphere 55 Cnc e would have to have the unlikely bulk composition of pure silicate.

Alternatively, if 55 Cnc e has a substantial gas atmosphere or envelope, the scenario of inefficient heat redistribution is still supported by the T = 2360 K brightness temperature, as long as the radiation at 4.5 μm is not coming from a very hot layer, such as a deep layer or a thermal inversion layer. The interpretation of 55 Cnc e having a supercritical water envelope above a solid nucleus (D11) fits with the inferred high temperature; the absence of clouds at such a high temperature results in a water envelope with a naturally low albedo. Although we cannot fully exclude the case of heat redistribution, for the water planet or even a gas atmosphere over a rocky core, the probe to deep hot layers or the thermal inversion would have to be extreme. A probe of extremely deep, hot atmosphere layers is unlikely because many of the gases likely to be present in the atmosphere, in particular CO₂ and CO, have high absorption cross sections in the spectral region of the IRAC bandpass between 4 and 5 μm. A thermal inversion, while present in solar system planet atmospheres and suggested to be present in many similarly highly irradiated hot Jupiters (e.g., Burrows et al. 2007; Knutson et al. 2008), is also an extreme explanation because the temperature would have to be ∼500 K above most of the rest of the atmosphere. In general, while we know the total amount of energy re-radiated by the planet, it is the interplay between absorption of stellar radiation at short wavelength, the opacities at wavelengths at which the bulk radiation is emitted (∼1–5 μm for a body at T ∼ 2000 K), and the opacity in our IRAC 4.5 μm bandpass that sets the observed brightness temperature.

Considering the observational uncertainty, the observed brightness temperature in the IRAC bandpass could be as low as 1830 K at the 2σ level. At this level of uncertainty, we can say that at least one or more of the following statements are true: (1) the planet's Bond albedo is low; (2) the planet has an inefficient heat transport from the day side to night side; and/or (3) the IRAC 4.5 μm bandpass probes at atmospheric levels that are considerably hotter than the dayside equilibrium temperature.

Our global MCMC analysis improves the 3σ upper limit on 55 Cnc e's orbital eccentricity from 0.25 (D11) to 0.06. However, even such a small eccentricity is unlikely because tidal interactions between the planet and star would probably damp an initial eccentricity that large in a few Myr. Much larger initial eccentricities would be damped on similar timescales. However, high-order dynamical interactions among the planets in the system may maintain an eccentricity for 55 Cnc e of a few parts per million, by comparison with theoretical studies of multi-planet systems having close-in super-Earths (Barnes et al. 2010). Strong observational constraints on 55 Cnc e's eccentricity may even provide information about the planet's tidal response and internal structure (Batygin et al. 2009). While a small eccentricity might have little direct influence on observation, the concomitant tidal dissipation within the planet can have dramatic geophysical consequences, perhaps powering vigorous volcanism and resupplying the planet's atmosphere (Jackson et al. 2008). The planet's proximity to its host star suggests, in fact, it may be shedding its atmosphere, and so active resupply may be necessary for long-term atmospheric retention.

From the first landmark detection of infrared light from a hot Jupiter (Charbonneau et al. 2005; Deming et al. 2005) and further occultation observations of more than two-dozen Neptune- and Jupiter-sized planets (see Deming & Seager 2009), Spitzer remains today the best instrument for exoplanet high-precision near-infrared photometry. At the dawn of the super-Earth-sized planet discovery era (see, e.g., Batalha et al. 2012), Spitzer's continued legacy shows the need for keeping this observatory operational. With the future launch of the James Webb Space Telescope, the exoplanet community anticipates thermal emissions measurements for a number of different super-Earths (see, e.g., Deming et al. 2009), hence improving our knowledge of this class of planets in a way similar to the achievements made by Spitzer for hot Jupiters.