Why is it So Hot in Here? Exploring Population Trends in Spitzer Thermal Emission Observations of Hot Jupiters Using Planet-specific, Self-consistent Atmospheric Models

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Published 2021 December 24 • © 2021. The American Astronomical Society. All rights reserved.
, , Citation Jayesh M. Goyal et al 2021 ApJ 923 242 DOI 10.3847/1538-4357/ac27b2

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jgoyal@astro.cornell.edu

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1 Department of Astronomy and Carl Sagan Institute, Cornell University, 122 Sciences Drive, Ithaca, NY 14853, USA; jgoyal@astro.cornell.edu

2 National Institute of Science Education and Research (NISER), HBNI, Jatni, Khurda-752050, Odisha, India

3 School of Physics, University of Bristol, HH Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, UK

4 Astrophysics Group, School of Physics and Astronomy, University of Exeter, Exeter EX4 4QL, UK

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  1. Received 2021 March 23
  2. Revised 2021 August 13
  3. Accepted 2021 August 31
  4. Published

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0004-637X/923/2/242

Abstract

Thermal emission has now been observed from dozens of exoplanet atmospheres, opening the gateway to population-level characterization. Here, we provide theoretical explanations for observed trends in Spitzer IRAC channel 1 (3.6 μm) and channel 2 (4.5 μm) photometric eclipse depths (EDs) across a population of 34 hot Jupiters. We apply planet-specific, self-consistent atmospheric models, spanning a range of recirculation factors, metallicities, and C/O ratios, to probe the information content of Spitzer secondary eclipse observations across the hot-Jupiter population. We show that most hot Jupiters are inconsistent with blackbodies from Spitzer observations alone. We demonstrate that the majority of hot Jupiters are consistent with low-energy redistribution between the dayside and nightside (hotter dayside than expected with efficient recirculation). We also see that high-equilibrium temperature planets (Teq ≥ 1800 K) favor inefficient recirculation in comparison to the low temperature planets. Our planet-specific models do not reveal any definitive population trends in metallicity and C/O ratio with current data precision, but more than 59% of our sample size is consistent with the C/O ratio ≤ 1 and 35% are consistent with whole range (0.35 ≤ C/O ≤ 1.5). We also find that for most of the planets in our sample, 3.6 and 4.5 μm model EDs lie within ±1σ of the observed EDs. Intriguingly, few hot Jupiters exhibit greater thermal emission than predicted by the hottest atmospheric models (lowest recirculation) in our grid. Future spectroscopic observations of thermal emission from hot Jupiters with the James Webb Space Telescope will be necessary to robustly identify population trends in chemical compositions with its increased spectral resolution, range, and data precision.

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1. Introduction

Spitzer observations of exoplanet thermal emission have proven fundamental to population studies of exoplanet atmospheres. To date, Spitzer (Werner et al. 2004) has been the only space-based observatory available for investigating exoplanets in close orbits to their host stars at infrared wavelengths longer than 2 μm. Spitzer's Infrared Array Camera (IRAC; Fazio et al.2004)photometric channels 1, 2, 3, and 4—centered at 3.6, 4.5, 5.8, and 8 μm, respectively—provided early insights into the atmospheres of close-in exoplanets (e.g., Charbonneau et al. 2005; Knutson et al. 2007; Beichman & Deming 2018). However, the cryogen exhaustion in 2009 May rendered IRAC channels 3 and 4 inoperative. Up until the end of the Spitzer mission in 2020, IRAC channels 1 (3.6 μm) and 2 (4.5 μm) were used extensively for exoplanet detection and atmospheric characterization.

A number of previous studies have computed/used and investigated thermal eclipse measurements for different populations of hot-Jupiter exoplanets (e.g., Cowan & Agol 2011; Triaud et al. 2014; Schwartz & Cowan 2015; Baxter et al. 2020; Garhart et al. 2020; Melville et al. 2020). Garhart et al. (2020) and Baxter et al. (2020) (hereafter G20 and B20, respectively) presented Spitzer IRAC channel 1 and 2 eclipse depth (ED) measurements for a population of planets. Both of these studies explored potential trends in hot-Jupiter dayside thermal emission as a function of the equilibrium temperature and the assumed atmospheric composition. G20 concluded that the ratio of 4.5 and 3.6 μm brightness temperatures (T b ), calculated using their EDs, increases with equilibrium temperature, indicating deviation from a planet that emits like a blackbody as found by Triaud et al. (2014). They also compared the observations presented in their paper with generic track models from Fortney (2005) and Burrows et al. (1997), instead of carrying out model simulations for each individual planet across a parameter space. B20 also find a similar deviation from blackbody emission spectra. Moreover, B20 also detect a statistically significant transition between hot-Jupiter emission observations above and below 1660 ±100 K, which they suggest as a natural boundary between hot and ultra-hot Jupiters. Again without carrying out model simulations for each individual planet, B20, using their generic grid of 1D radiative–convective models spanning a range of C/O ratio (C/O = 0.1, 0.54, 0.84) and metallicity ([M/H] = −1, 0, 1, 1.5) conclude that hot Jupiters statistically favor low C/O ratios (C/O ≤ 0.54), where ∼0.54 is the value of the solar C/O ratio. Cowan & Agol (2011) in their analysis that included both thermal (J, H, K, and Spitzer bands) as well as optical measurements, concluded that planets with no circulation and no albedo limit temperature of greater than 2400 K have uniformly low redistribution efficiencies and albedo. A subsequent study by Schwartz & Cowan (2015) conclusively showed that planets with high irradiation temperatures have low-heat transport efficiency.

Our investigation in this work builds on the previous works, where we apply a planet-specific, self-consistent grid of hot-Jupiter dayside emission spectra to explain the Spitzer IRAC channel 1 and 2 observations from Garhart et al. (2020) and Baxter et al. (2020). Self-consistent, planet-specific model simulations have an advantage of estimating a more accurate pressure–temperature (P–T) structure of a given planetary atmosphere compared to generic models. This enhanced accuracy arises from accounting for the host stellar energy deposited in the specific planet's atmosphere, alongside conservation of the energy in the atmosphere itself, when computing a self-consistent P–T profile. Consequently, the model emission spectra used to interpret observations, such as those in Spitzer IRAC channels 1 and 2, can attain higher accuracy. In the previous works (e.g., Baxter et al. 2020; Garhart et al. 2020) self-consistent generic model simulations were used without focusing on model simulations for specific planets (i.e., without using specific stellar/planetary parameters for model input). Whereas, in this work, we use self-consistent model simulations performed for the specific parameters of the target planets, spanning a wider parameter space. We use our planet-specific grid to explore population trends across the hot-Jupiter collective. The G20 and B20 studies show a few inconsistencies in their ED and Tb (and its uncertainty) values for same planets, due to differences in their data reduction techniques and methodology/assumption while computing them. Therefore, in this study we also revisit and compare these data sets.

We delve into the theoretical analysis of Spitzer IRAC ED and brightness temperature variations for each planet, thereby investigating any trends in them and any variation of these trends with planetary equilibrium temperature (Teq). We apply a grid of 1D self-consistent, planet-specific models across a wide parameter space, considering variations in their recirculation factor, metallicity, and C/O ratio (see Goyal et al. 2020, for further details). Our models incorporate horizontal advection by reducing the incoming flux in each 1D column of the atmosphere by a factor called the recirculation factor (Fortney & Marley 2007; Goyal et al. 2020), hereafter termed fc (see Section 2 for more details). Previous studies did not consider the full range of the variation of fc while computing self-consistent P–T profiles and the corresponding emission spectra, which we investigate in this work. It is important to note that fc alters the P–T profile drastically, therefore it is not just a proxy for temperature but also the pressure level probed using the emission spectra. We compare our theoretical EDs across the parameter space with observed EDs from G20 and B20. We find the best-fit parameters as well as those within 1σ of the best-fit model for each planet, with the motivation to identify trends and constraints in fc , metallicity, and the C/O ratio for the population of planets. We also show a detailed analysis for a few planets for which our models are not able to explain the observations and potential reasons for such anomalies.

This work is structured as follows. We first detail our theoretical model calculations and grid, alongside techniques to compute model EDs and Tb (model derived and observed both), in Section 2. In Section 3, we benchmark and compare our model emission spectra with those presented in G20. In Section 4 we compare the observed EDs and derived Tb from G20 and B20. The results from our hot-Jupiter thermal emission population analysis are presented in Section 5, followed by a comparison to the observations of G20 and B20. Finally, we present our conclusions in Section 6.

2. Techniques and Model Details

In this work, we use a cloud-free planet-specific grid of emission spectra, generated using self-consistent simulated exoplanet atmospheres, building on the work of Goyal et al. (2020) using the ATMO, a 1D–2D radiative–convective equilibrium model for planetary atmospheres (Amundsen et al. 2014; Tremblin et al. 2015, 2016; Drummond et al. 2016; Goyal et al. 2018). Self-consistent here implies that the final computed P–T profiles (once they reach convergence) are in radiative–convective equilibrium consistent with equilibrium chemical abundances, under the constraints of hydrostatic equilibrium and the conservation of energy in each atmospheric layer and the atmosphere as a whole (see Goyal et al. 2020, for more details). Since the work of Goyal et al. (2020) did not contain model atmospheres for 14 of the exoplanets presented by both G20 and B20, we generated model atmospheres and spectra for these additional planets using exactly the same model and grid parameters as Goyal et al. (2020). The new planets considered here are: KELT-2b, KELT-3b, Qatar-1b, WASP-14b, WASP-18b, WASP-36b, WASP-46b, WASP-64b, WASP-65b, WASP-75b, WASP-77b, WASP-87b, WASP-100b, and WASP-104b. Observations of KELT-7 are present in G20 but not in B20. We note that while our analysis covers all the planets with observations presented by G20, it does not extend to all the planets considered by B20.

fc parameterizes the redistribution of input stellar energy in the planetary atmosphere, by the dynamics, where a value of 1 equates to no redistribution (hottest dayside temperature), while 0.5 represents efficient redistribution. The value of 0.5 fc indicates that 50% of the total incoming stellar energy is advected to the nightside (the side of the planet facing away from the star), while 0.25 fc indicates that 75% of the total incoming stellar energy is advected to the nightside. Given the short orbital periods, we assume that all the hot Jupiters in this study are tidally locked and therefore that the fc is a good description of the heat transport in the atmosphere. The model atmospheres and emission spectra for each planet are computed at four different recirculation factors (fc = 0.25, 0.5, 0.75, 1.0), six metallicities (0.1, 1, 10, 50, 100, 200; all in units of × solar), and six C/O ratios (0.35, 0.55, 0.7, 0.75, 1.0, 1.5), giving a total of 144 simulated model spectra per planet. For most planets, our 1D model atmospheres were generated spanning the full range of the parameter space. However, as noted in Goyal et al. (2020), in 5%–10% of the cases the combination of parameters for some of the planets failed to produce a realistic thermal structure (convergence not reached). We do not consider those models in this study.

We consider a wide range of opacity sources relevant to hot giant planets in our models. All model atmospheres include line opacity due to H2O, CO2, CO, CH4, NH3, Na, K, Li, Rb, Cs, TiO, VO, FeH, CrH, PH3, HCN, C2H2, H2S, SO2, H−, and Fe. The abundances of these species are determined via the assumption of thermochemical equilibrium, consistent with the radiative–convective equilibrium P–T profile. Besides these molecular, atomic, and ionic opacities, we also include collision-induced absorption due to H2–H2 and H2–He. The line-by-line cross-sections (resolution of 0.001 cm−1 evenly spaced in wavenumbers) of these opacities are used to generate correlated k-tables as a function of wavenumber, temperature, and pressure for each gaseous species. We use these correlated k-tables to generate P–T profiles and emission spectra for each model atmosphere, given the composition, deploying the random overlap technique (Amundsen et al. 2017) to combine k-tables of different gaseous species (see Goyal et al. 2018, 2020, for more details).

For the stellar spectra incident on each planet, we use models from the Phoenix BT-Settl 5 grid (Allard et al. 2012; Rajpurohit et al. 2013). For each planet, we choose the stellar model closest to the host star's observed temperature, gravity, and metallicity as listed in the TEPCat 6 database (Southworth 2011). We also adopt all of the other parameters required for model initialization (stellar radius, planetary radius, planetary equilibrium temperature, planetary surface gravity, and semimajor axis) from TEPCat—as shown in Table S3 of the online supplementary material in Goyal et al. (2020) and in Table 2 in Appendix C for the remaining 14 planets, for which the grid of model simulations have been developed in this work.

2.1. Model Eclipse Depth and Brightness Temperature Calculations

To compare ED observations in Spitzer IRAC channels 1 and 2 with simulated model emission spectra, we need to compute the model EDs in these channels. The ED is the product of the planet-to-star flux ratio and the transit depth ${({R}_{p}/{R}_{s})}^{2}$ of the planet. We compute planet-to-star flux ratio $\left(\tfrac{{F}_{\mathrm{int}(p)}}{{F}_{\mathrm{int}(s)}}\right)$ in Spitzer IRAC channels using

Equation (1)

and

Equation (2)

where Fp (λ) and Fs(λ) are the wavelength λ dependent planet and stellar flux from the models, respectively. These model planet and stellar fluxes are integrated in Equations (1) and (2) by convolving with the response function R(λ) of the given channel to obtain integrated planet (Fint(p)) and stellar (Fint(s)) fluxes. The transit depth obtained from the TEPcat (same database as our model input parameters) database when multiplied to this planet-to-star flux ratio in the given channel gives us the final model ED in that channel. We note that we employed EDs from G20 and not B20 while fitting to observations in Section 5.2, because G20 used an additional dilution correction in their data reduction to account for a stellar companion (see Section 4 for more details).

Brightness temperature (Tb) is a quantity commonly used in remote sensing, to quantify the blackbody temperature of the remotely sensed object. However, there is a subtle difference between the two approaches used to compute Tb for exoplanets. One approach is to compute theoretical Tb using model emission spectra. Alternatively, one may convert the observed EDs into an equivalent Tb . To highlight these differences, we demonstrate this computation using both model simulated emission spectra and observed EDs.

For this work we need to compute Tb in the Spitzer IRAC channel 1 centered at a wavelength (λ) of 3.6 μm and channel 2 centered at 4.5 μm.

We compute model Tb $\left({T}_{b(\mathrm{model})}\right)$ via a two-step procedure. First, we compute the integrated model planet flux in the required channel using Equation (1).

Second, we invert the Planck function to obtain the temperature with equivalent planet flux in the given channel using

Equation (3)

where h, c, and kb are Planck's constant, the speed of light, and Boltzmann's constant, respectively. We note that division by the factor of π converts the integrated planet flux (Fint(p)) to a specific intensity, required by the inverse Planck equation.

Alternatively, we derive observed Tb $\left({T}_{b(\mathrm{obs})}\right)$, using the EDs from G20, following a similar methodology as described by B20 using

Equation (4)

where Fint(s) is the integrated stellar flux (computed using Equation (2)), ED is the eclipse depth in the given channel from G20, and TD is the white light transit depth ${({R}_{p}/{R}_{s})}^{2}$. Since the TD values are not quoted in G20 or B20, we use the transit depth values from ExoMAST. 7 We note that the choice of database for TD values can lead to substantial variation in derived Tb of the planet. We use BT-Settl model stellar spectra, as described in the previous subsection, to compute Fint(s). The integrated stellar flux Fint(s) and TD is then removed from the ED to obtain the planetary flux, which is finally used to compute observed Tb of the planet. While solving Equation (4) we are integrating both the blackbody planetary and model stellar flux over the Spitzer bandpass and fitting them to obtain the observed Tb for a given value of ED, therefore this is iteratively solved to obtain a Tb value that closely matches the observed ED value. We note that we iterate between ±1000 K of the obtained Tb using an inverse Planck function while optimizing for the best-fit ED, as opposed to ±200 K used in B20. This was required because for some planets the ED fit with ±200 K was insufficient, due to the lower range of the explored temperature. The uncertainties on the observed Tb are computed using the minimum and maximum values of the EDs propagated through Equation (4) to obtain the minimum and maximum Tb . The 1σ uncertainty for the best-fit Tb is then taken as the mean of this minimum and maximum Tb , similar to the methodology adopted in B20. Our calculated Tb from observed EDs and their uncertainties for all the planets in this analysis are tabulated in Table 1 in Appendix A. Our uncertainties are very similar to that of B20 but very different from that in G20. To understand the uncertainties obtained by G20 we also computed the uncertainty in Tb by propagating the error in ED through Equation (4) (error propagation methodology). However, we were unable to obtain the uncertainties on Tb as in G20 (see Section 4 for more details).

3. Benchmarking

Before presenting the results of our analysis, we first benchmark our emission spectrum model against G20. While model emission spectra from ATMO have previously been benchmarked against various published model spectra (Baudino et al. 2017; Malik et al. 2019), here we compare our ATMO model to Figure 19 of G20 (hereafter, the G20 Fortney model), with exact same planet parameters. Figure 1 (top panel) shows the planet flux from ATMO and the G20 Fortney model spectra, using their respective P–T profiles and chemical abundances. Figure 1 (bottom panel) shows residuals (differences) between both the model spectra. The agreement between both the model spectra is quite good, especially in Spitzer IRAC channels 1 and 2, where the differences are within +5%. This +5% (rather than ±5%) difference is because the overall spectral flux in the G20 Fortney model spectra is greater than in our ATMO model spectra, since the P–T profile for the G20 Fortney model spectra is ∼100–200 K hotter than the ATMO P–T profile between the ∼0.1 and 1 bar pressure levels. We note that, for a fair comparison in this benchmarking test, we removed TiO, VO, Li, Rb, Cs, FeH, HCN, SO2, and C2H2 opacities while computing the P–T profiles and spectra in ATMO (as these opacities are not included, or these species have very low abundances, in the G20 Fortney model). However, all these opacities are included in our other simulations used throughout this work. Therefore, when using a similar model setup as in G20, the agreement between both models is very good. The differences in the P–T profiles and chemical abundances drive the discrepancies between the model spectra. To illustrate this, Figure 1 (top panel) shows that the ATMO model spectra with all opacities is substantially different from the G20 Fortney model spectra, due to the inclusion of TiO/VO in our simulation leading to the formation of a temperature inversion.

Figure 1.

Figure 1. Top panel: comparison between our ATMO emission spectrum model and a reference model from G20. Four model spectra are shown: the planetary emission spectra from ATMO (blue) using the exact same opacities as in G20, the G20 Fortney model spectra (red), an ATMO model using the same P–T profile and chemical abundances as the G20 Fortney model spectra (black), and ATMO model spectra with all opacities (yellow). In all cases, the planet parameters are the same as those described in caption of Figure 19 in G20. Spitzer IRAC channels 1 and 2 are shaded in blue and green, respectively. Bottom panel: flux difference (residuals) in percentage between the G20 Fortney model spectra and ATMO model emission spectra are shown in the top panel in blue and black. The ATMO model spectra with all opacities being too different from the G20 Fortney model spectra is not shown here.

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The larger differences in residuals that we see for λ < 1 μm can be attributed to different model choices: in particular, the species included in the equilibrium chemistry computation, the rainout condensation methodology, line-list sources, and the pressure broadening prescription for alkali resonance lines. Optical absorbers such as Na and K are especially affected by these model choices, leading to larger differences for λ < 1 μm. However, we do not focus on this region of the spectrum in this study. Therefore, a detailed benchmarking exercise for optical wavelengths is beyond the scope of this work. In Figure 1 (top panel) we also show the ATMO model planet flux derived using input P–T profiles and chemical abundances from the G20 Fortney model, resulting in excellent agreement between the two models, especially in the Spitzer IRAC channels. The residuals for this model can also be seen in the bottom panel, where the differences are within ±2% in Spitzer IRAC channels 1 and 2. The differences in this case can be directly attributed to differences in line lists and cross-section computations. The details of line-list sources can be found in Goyal et al. (2020) for the ATMO model and in Marley et al. (2021) for the G20 Fortney model.

In addition, we benchmarked our model Tb calculations by using an isothermal emission spectrum with a known temperature as its input. In this case, the accuracy of the Tb computed from our simulations was within 2 K of the assumed isothermal temperature.

4. Observational Comparison between G20 and B20

Recently B20 and G20 presented independent population-level studies of available Spitzer eclipses. Before comparing predictions from our planet-specific, self-consistent grid of model simulations to the observed values, it is important to understand the possible inconsistencies in those observed values that might arise due to choices in data reduction techniques and assumptions made in the Tb calculation. Here we compare the observations and results of G20 and B20. Figure 2 (top panels) compares the EDs from G20 (left) and B20 (right) for all the planets in G20. We see that the agreement is quite good for most planets. However, some of the planets display key differences, e.g., WASP-103b in both the 3.6 and 4.5 μm channels (∼600 and 450 ppm, respectively), WASP-12b at 3.6 μm (∼500 ppm), and WASP-19b at 4.5 μm (∼700 ppm). It is important to note that the EDs for both WASP-103b and WASP-12b from G20 include a dilution correction due to a companion star (see Section 3.5 in G20 for more details), which is not included in B20.

Figure 2.

Figure 2. Top: observed EDs from G20 and B20 in the Spitzer IRAC 3.6 and 4.5 μm channels. Planets for which a dilution correction has been applied (as detailed in G20) are shown in red. Planets WASP-12b, WASP-19b, and WASP-103b labeled in these plots are examples of planets with quite large differences in ED between G20 and B20. Bottom: same, but comparing the brightness temperature Tb from G20 and B20. The differences in Tb are quite large for many of the planets, especially the uncertainties in G20 are substantially larger than B20.

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We compare the Tb from G20 and B20 in the lower panels of Figure 2. Unlike the EDs, we see that the Tb display more notable differences. In particular, the Tb error bars from G20 are much larger than from B20. As shown in Table 1, and described earlier in Section 2.1, we also calculate our own Tb from observed EDs, for which the error bars (see Section 2.1 for more detail) are in close agreement with that of B20. It is unclear why the Tb error bars from G20 are so large. We used different methodologies to compute uncertainty in Tb (see Section 2.1 for more details), but we could not reproduce uncertainties as high as those obtained by G20. We need to inflate our uncertainties by more than 100% for many of the planets to match the Tb uncertainties in G20. The differences in the Tb values between the different studies are mainly because of the assumed planetary/stellar parameters and the methodology used in the calculation of Tb itself. While G20 used ATLAS stellar models (Kurucz 1979), B20 performed tests using a range of stellar models before ultimately adopting PHOENIX models for their final Tb calculations. We also use PHOENIX models for our calculations, with a similar methodology to compute Tb as that used in B20.

In summary, we conclude that the differences in EDs from G20 and B20 are negligible, except for some planets with high Teq and the systems that require dilution correction. However, the differences in Tb , and especially their uncertainties, are quite substantial. Moreover, the computation of Tb involves assumptions about the stellar spectra and transit depth (see Equation (4)). Therefore, in what follows we present our analysis and comparison between Spitzer IRAC observations and our theoretical models in terms of EDs instead of Tb .

5. Results and Discussion

We computed the model Tb and EDs in Spitzer IRAC channels 1 and 2, as described in Section 2.1, for all the model simulations in our grid for a given planet. These model simulations for each planet span a wide range of recirculation factors, metallicities, and C/O ratios (see Section 2). In this section, we first show the theoretical trends in the 3.6 and 4.5 μm EDs using examples of certain planets in Section 5.1. The interpretation of the Spitzer observations from G20 for the full population of planets is detailed in Section 5.2. Finally, we highlight a few interesting cases where large anomalies exist between the predictions from the model atmospheres and Spitzer observations in Section 5.3.

5.1. Theoretical Trends in Hot-Jupiter Emission Spectra

Model emission spectra for different planets change as a function of fc , metallicity, and the C/O ratio. This can lead to a range of different values for the Spitzer channel 1 and 2 EDs, i.e., their ratios can be strongly influenced by these three atmospheric parameters. In this section, we discuss the variation in these EDs and note some important trends.

We illustrate these trends for three planets in Figure 3. In the top panels, we show model EDs in Spitzer channel 1 (3.6 μm) and channel 2 (4.5 μm) for WASP-101b (Teq = 1559 K), WASP-14b (Teq = 1893 K), and WASP-103b (Teq = 2513 K), spanning a range of fc values (different markers) and C/O ratios (different colors). The observed EDs from G20 and B20 are overlaid for comparison. In the panels on the second row from the top, we show the corresponding P–T profiles for a range of C/O ratios, assuming a solar metallicity and efficient recirculation (fc = 0.5). In the panels on the third row, we show chemical abundances at C/O ratios of 0.55 (solar) and 1.0. Finally, in the last row we show the 3.6 and 4.5 μm contribution functions for these three planets, at C/O ratios of 0.55 (solar) and 1.0. As an example, we include an ED plot for WASP-101b, similar to that in the top panel in Figure 3, in Appendix B, but with different colors representing models with different metallicities.

Figure 3.

Figure 3. First row: model EDs in the 3.6 and 4.5 μm Spitzer bands for WASP-101b, WASP-14b, and WASP-103b. The markers correspond to different fc values, while the colors correspond to different C/O ratios (see the legend). The observed EDs for each planet from G20 (gray circle with uncertainties) and B20 (gray star with uncertainties) are overlaid for comparison. The observed EDs for WASP-101b from G20 and B20 overlap. Second row: the self-consistent P–T profiles for each planet, for fc = 0.5 and solar metallicity, as C/O varies. Third row: chemical abundances at different atmospheric (pressure) layers for certain important chemical species with strong opacities in either the 3.6 and 4.5 μm Spitzer bands, at C/O ratios of 0.55 (solid line) and 1.0 (dashed line), with the corresponding consistent P–T profiles shown in the second row. Fourth row: contribution functions at 3.6 and 4.5 μm for C/O ratios of 0.55 (red) and 1.0 (cyan), for the P–T profiles and chemical abundances shown in the second and third row, respectively.

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We see a clear structural change in how the 3.6 versus 4.5 μm EDs cluster for different atmospheric parameters between the lowest Teq planet (WASP-101b) and the highest temperature planet (WASP-103b). Namely, the spread of points decreases as Teq increases, indicating that the change in percentage ED between 3.6 and 4.5 μm decreases with increasing Teq for the variations in model C/O ratio and metallicity. For the extremely high Teq planets, like WASP-103b, the 3.6 and 4.5 μm EDs follow a strongly linear correlation across a wide range of our model grid parameters. However, the 4.5 μm ED is consistently larger (by ∼500 ppm) than the 3.6 μm ED for WASP-103b. We also notice that model simulations with the same C/O ratio (same color in Figure 3) have an almost vertical structure, indicating a constant ED in the 3.6 μm channel while it varies substantially in the 4.5 μm channel. This trend is especially strong for WASP-103b in the vertical branch close to ∼2000 ppm in the 3.6 μm channel. This trend results from the change in metallicity affecting primarily the 4.5 μm channel ED, as explained in detail later in this section for WASP-101b. In contrast, the model simulations with the same metallicity (same color in the left side of Figure 9 shown in Appendix B) show horizontal structure indicating constant ED in the 4.5 μm band. This trend results from the change in the C/O ratio primarily effecting the 3.6 μm channel ED, as explained in detail below for each planet.

The P–T and chemical abundance profiles for the three planets and their contribution functions (all shown in Figure 3) can shed more light into differences between 3.6 μm versus 4.5 μm model EDs. For WASP-101b, greater atmospheric depths are probed at 3.6 μm compared to 4.5 μm for a solar C/O ratio, since there is no dominant source of opacity at 3.6 μm while at 4.5 μm CO strongly absorbs. The absorption cross-section of CO2 is almost an order of magnitude greater than CO at 4.5 μm (see Figure 2(b) in Goyal et al. 2020), but it has a lower abundance (see the chemical abundances in the third row from the top in Figure 3). Therefore, the impact of CO2 on the ED is less than that for CO in this band. At a C/O ratio of 1.0 (cyan color) the trend is reversed, with low pressures being probed at 3.6 μm and comparatively deeper pressures being probed at 4.5 μm. This leads to lower EDs at 3.6 μm for a C/O ratio of 1.0 as compared to a solar C/O ratio, as seen in the top panel showing variation in EDs due to the C/O ratio. Fundamentally, this is a result of the change in chemical abundances (see the chemical abundance plots in the third panel from the top in Figure 3), especially the increase in HCN and CH4 at a C/O ratio of 1.0. HCN and CH4 have strong opacity in the 3.6 μm band, and thus the increase in the abundance of these species makes the atmosphere optically thick, therefore allowing only comparatively lower pressure layers with lower temperatures to be probed (see the P–T profiles in the middle panel). The change in the atmospheric layers being probed in 4.5 μm due to a change in C/O ratio is very small, as seen in the contribution functions. Moreover, the change in the CO abundance with the C/O ratio is also small. Therefore, for WASP-101b the change in the 4.5 μm ED with the change in the C/O ratio is smaller compared to the 3.6 μm ED. In contrast, the change in the 4.5 μm ED with metallicity is larger compared to 3.6 μm (see Figure 9 in Appendix B). This is driven by the increase in the abundances of CO and CO2 as metallicity increases, making the atmosphere optically thicker at 4.5 μm, thereby probing comparatively low pressures (and hence low temperatures), and finally leading to a lower 4.5 μm ED at higher metallicities compared to that at solar metallicity.

For WASP-14b, a similar pattern of change in the layers being probed with a change in that C/O ratio (and therefore the EDs) can be seen in the contribution function plots, albeit to a lesser degree. Similar to WASP-101b, at a solar C/O ratio deeper pressures are probed at 3.6 μm compared to 4.5 μm. However, unlike WASP-101b, at a C/O ratio of 1.0 there is a small change in the pressure levels being probed (toward shallower pressures) at 3.6 μm. The change is such that in both of the channels almost same atmospheric layers are probed. This is mainly due to the lower CH4 abundance in the upper atmosphere, as seen in the chemical abundance plots, thereby allowing deeper layers to be probed at 3.6 μm (compared to WASP-101b). Therefore, the percentage differences in EDs between both the channels due to the change in the C/O ratio is smaller for a recirculation factor of 0.5 compared to WASP-101b. However, at lower recirculation factors (cooler P–T profiles) the differences in EDs are similar to that of WASP-101b. This decrease in the differences between the 3.6 and 4.5 μm channel model EDs due to the change in the C/O ratio, with an increase in the recirculation factor (hotter P–T profiles), highlights the temperature dependence of ED differences due to variation in the C/O ratio.

For WASP-103b, the P–T profiles as well as the chemical abundance profiles of the atmosphere are very different compared to WASP-101b and WASP-14b. The presence of temperature inversion in the P–T profile being the major difference. At a solar C/O ratio similar atmospheric layers are probed in both the 3.6 and 4.5 μm channels. While emission due to CO from the inversion layer contributes to the 4.5 μm channel, VO from the inversion layer also contributes to the 3.6 μm channel (see the chemical abundance plot in the third row of Figure 3 and the absorption cross-section Figure 2(b) in Goyal et al. 2020). However, the lower abundance of VO, combined with the differences in the absorption cross-sections of VO and CO, lead to consistently lower EDs in the 3.6 μm band compared to the 4.5 μm band across a wide range of parameter space (as seen in the ED plot in the first row of Figure 3). The only exception is the vertical branch at ∼2000 ppm in the 3.6 μm channel, where the change in metallicity at a recirculation factor of 0.25 alters the CO abundances (similar to WASP-101b) and therefore the 4.5 μm band ED. At a C/O ratio of 1.0, deeper pressures are probed in both of the channels due to the change in the P–T profile, however, much deeper pressures are probed in the 3.6 μm channel (unlike WASP-101b and WASP-14b) since the abundance of VO decreases while that of CO approximately remains the same. The increase in the abundances of species, such as CH4 and HCN, for higher C/O ratios is lower for WASP-103b compared to WASP-101b and WASP-14b, leading to smaller percentage variations in the 3.6 μm ED with the C/O ratio.

In summary, the emission spectra in Spitzer IRAC channel 2 (4.5 μm) is dominated by CO across the parameter space for all of the planets. This leads to minor variations in the ED as the C/O ratio changes. However, larger ED variations occur when metallicity changes, due to the sensitivity of the CO abundance to metallicity. In Spitzer IRAC channel 1 (3.6 μm) many other species (e.g., CH4, HCN, and VO) can shape the spectrum, depending on the C/O ratio, thus leading to a large spread in the 3.6 μm band ED with the C/O ratio for all of the planets (see Figure 3). The percentage variations in ED in both of the bands strongly depends on the temperature (via the recirculation factor and the P–T profile), such that planets with lower equilibrium temperatures show increased percentage variations with C/O ratio and metallicity, while the percentage variations are smaller for planets with higher equilibrium temperatures (e.g., WASP-103b).

The observations from G20 and B20 are also shown in Figure 3 for each of the planets. For WASP-101b the observations are consistent with the fc value of 1 (no heat redistribution) with the lower 1σ range extending to fc = 0.75 (see Figures 4 and 5). For the metallicity we do not obtain any constraints and a large range is possible all the way from solar to 200 times solar metallicity. However, the C/O ratio is constrained between a subsolar value of 0.35 to a slightly super-solar value of 0.75. For WASP-14b the observations are consistent with the fc value of 0.75 (no heat redistribution) with the upper 1σ range extending to fc = 1.0. The metallicity and C/O ratio are totally unconstrained for WASP-14b. For WASP-103b the observations are also consistent with the fc value of 1 (no heat redistribution) with the lower 1σ range extending to fc = 0.75. The metallicity and C/O ratio are totally unconstrained even for WASP-103b. These constraints for the population of planets are discussed in Section 5.2. We provide ED plots for all of the planets in our analysis, similar to top panel of the Figure 3, in the figure set of Figure 10 in Appendix D.

5.2. Comparison of Observations with Model Spectra

We now compare our self-consistent, planet-specific grid of models to all the planets with ED observations in G20. As an example, Figure 6 (top panel) shows the Spitzer observations of WASP-101b, WASP-14b, and WASP-103b (the same set of planets as in Figure 3) and all the models within 1σ of the minimum χ2 (i.e., best-fitting) model. We show in Figure 6 (bottom panel) the corresponding χ2 map of each grid parameter for the observations from G20, fitted to all of the model simulated spectra from the planet-specific grid for each planet with 1–4σ contours (see Goyal et al. 2020 for more details). The χ2 map reveals that the Spitzer observations of all three planets favor models with high recirculation factors (fc ≥ 0.75 within the 1σ contour). Moreover, WASP-101b exhibits a preference for low C/O ratios (i.e., less than 0.75 within 1σ and less than 1.0 within 3σ of the best-fit model). However, we are unable to place any tight constraints on the metallicity or the C/O ratio for these three planets, given the precision and wavelength coverage of these Spitzer observations. This can also be noticed in Figure 4, where many models with different metallicities and C/O ratios lie within 1σ of the best-fitting model.

We conducted a similar analysis for the full hot-Jupiter population covered in G20. A compendium of our best-fitting, self-consistent model emission spectra to the Spitzer IRAC channel 1 and 2 data for this population in shown in Figure 5. For comparison, we also show the equivalent blackbody curve derived from the observed Tb of channel 1 alone (via Equation (4)). We conclude that our self-consistent models generally achieve much better fits to the Spitzer IRAC observations than blackbodies; that is, hot Jupiters do not emit like blackbodies, in agreement with previous works (Triaud et al. 2014; Garhart et al. 2020; Baxter et al. 2020). Moreover, the CO feature at 4.5 μm can be clearly identified for many of the planets either in emission or absorption. Going from high to low temperature planets (high to low Tb ) a general trend is seen where CO is seen as an emission feature for high temperature planets due to the presence of temperature inversion in their P–T profile, while CO/CO2 is seen as an absorption feature in many of the low temperature planets without the temperature inversions. However, there are some exceptions depending on the best-fitting model parameters. For example, even though WASP-19b is a high temperature planet, with the potential to form a temperature inversion with an associated CO emission feature, our model fit to the data suggests that CO is seen as an absorption feature. Indeed, the best-fit model parameters for WASP-19b lead to a self-consistent P–T profile without a temperature inversion. Due to such exceptions caused by the dependence on metallicity and the C/O ratio, we do not see any clear transition with Teq as in B20.

Figure 4.

Figure 4. Atmospheric parameter trends derived from Spitzer EDs of hot Jupiters. Each planet is uniquely represented by its Teq on the x-axis. The best-fitting (filled points) model parameters (minimum χ2), and their 1σ error bars (model parameters within the 1σ χ2 of the best-fit model) with increments of grid spacing for each parameter (gray horizontal lines), are shown for the recirculation factor (top panel), log10 of metallicity with respect to solar metallicity (middle panel), and the C/O ratio (bottom panel) as a function of Teq. Planet names are annotated in the top panel which can be used to read their constraints of all three model parameters. The associated best-fitting spectra are shown in Figure 5. The large population of planets generally favor high fc (fc ≥ 0.75) values and C/O ratios ≤ 1. A broad range of metallicities are possible, without any population-level trends. A broader range of fc is able to match the data for planets with Teq below ∼1800 K.

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Figure 5.

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Figure 5.

Figure 5. The best-fit emission spectra (black) for 34 planets from our planet-specific, self-consistent grid are compared to the Spitzer IRAC channel 1 and 2 EDs from G20. The red filled curve shows the blackbody emission spectrum for each planet using their observed channel 1 (3.6 μm) brightness temperature calculated in this work as described in Section 2.1. The planets are arranged in decreasing order of their brightness temperature from top to bottom and left to right. We conclude that most hot Jupiters are inconsistent with blackbodies, in agreement with previous works (Baxter et al. 2020; Garhart et al. 2020). The best-fitting model parameters for each planet—recirculation factor (fc ), metallicity (Z), and C/O ratio—are annotated at the top of each panel.

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For model fits of all the planets shown in Figure 5 we also compute the 1σ value of the model parameters with respect to the best-fit model, as done for WASP-101b, WASP-14b, and WASP-103b in Figure 6. Our constraints on the model parameters, i.e., atmospheric recirculation factor (fc ), metallicity, and C/O ratios, for this population of planets are summarized in Figure 4. Note that each planet is uniquely represented by its Teq on the x-axis. The error bars indicate a 1σ parameter value of the model with respect to the best-fit model. The observations of 62% of the planets from the sample are consistent with fc ≥ 0.75, while 91% of the planets from the sample are consistent with fc ≥ 0.5. Thus, a preference for inefficient recirculation of energy from the dayside to nightside of the planet (high fc values) can be inferred for the population of planets from this figure (top panel). Above ∼1800 K, the range of allowed fc is much more narrow and skewed toward inefficient recirculation of energy (high fc values). Below ∼1800 K the range of allowed fc values increases, with some of the lowest values for fc (more efficient recirculation of the energy from the dayside to the nightside) allowed at low Teq s. This trend is consistent with theoretical expectations from the relative magnitudes of the radiative and advective timescales as one progresses from higher to lower Teq planets (e.g., see Cowan & Agol 2011; Perez-Becker & Showman 2013; Schwartz & Cowan 2015). It is important to note that the points in Figure 4 with no error bars are not infinitely well constrained parameters, it is just that the neighboring values of those parameters in the grid are not within the 1σ χ2 of the best-fit model.

We were unable to obtain any population-level trends for the metallicity of the planetary atmospheres (middle panel in Figure 4). A broad range of metallicities is possible for planets, from 0.1 times solar all the way up to 200 times the solar value. For the C/O ratio also a wide range from subsolar values (0.35) to super-solar values (1.5) is possible for the population of planets shown in Figure 4. However, about 59% of the planets tend to favor C/O ratio ≤ 1.0, while 35% of the planets span a broad range of a C/O ratio anywhere between 0.35 and 1.5.

We are not able to identify any definitive population-level trends for metallicity and the C/O ratio, and also trends in these parameters with respect to planetary Teq solely from Spitzer observations. One of the main reasons for this being the larger error bars in current observations, in comparison to the change in the 3.6 and 4.5 μm EDs due to metallicity and the C/O ratio. The other reason being the lack of spectral resolution and range. Our results for the C/O ratio are in line with the findings of B20, where they conclude that hot Jupiters with high C/O ratios (C/O ≥ 0.85) are rare. However, it is difficult to make a definitive statement with the precision, spectral resolution, and range of the current data set. We note the our sample size for this analysis is from G20 (34 planets with positive ED values), which is smaller than the sample size of B20.

5.3. Discrepancies between Models and Observations

For most of the planets in G20, we find at least a subset of our models provide a good fit (any of the model simulations from the grid lie within the error bars of the observations) to the observations. In Figure 7, we show the deviations of model EDs from the observed EDs in each of the Spitzer IRAC channels for all of the planets from G20 considered in this work. It can be noticed that for most of the planets 3.6 and 4.5 μm model EDs lie within ±1σ of the observed EDs. However, there are some planets for which the model spectrum is not a good fit (see Figure 5) and the model EDs lie outside the 1σ error bar of the observations in either of the channels. Many of these fits are not good because the model grid has its own resolution (spacing) between each parameter (e.g., 0.25 in fc ). Therefore, by increasing the model grid resolution of each parameter one can provide a better fit. For example, the observations of WASP-94b could be possibly explained by a model simulation with fc between 0.25 and 0.5, as seen in Figure 8. However, the Spitzer IRAC observations for some of the planets cannot be fit by our models, even at the extreme edges of our grid parameter space. This effect is particularly strong for HAT-P-40b, WASP-62b, and WASP-12b as shown in Figures 8(b)–(d), respectively. These anomalies also exist, but to a lesser extent, for a few other planets in our analysis, particularly, WASP-65b and WASP-87b. We provide ED plots, similar to Figure 8, for all of the planets included in our analysis in the figure set of Figure 10 in Appendix D.

Figure 6.

Figure 6. Top: figures showing all of the model emission spectra for WASP-101b, WASP-14b, and WASP-103b (same planets as in Figure 3) within 1σ of the best-fit model spectra when compared with observations (red points with error bars) from G20. Bottom: χ2 map of each grid parameter (fc , metallicity, and C/O ratio) for the WASP-101b, WASP-14b, and WASP-103b observations from G20, fitted to all the model simulated spectra from the planet-specific grids for each planet. 1–4σ contours with respect to the best-fit model parameters are shown.

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Figure 7.

Figure 7. Figure showing the deviation (in sigma units) of model EDs in comparison to the observed EDs in Spitzer 3.6 μm IRAC 1 band (top panel) and 4.5 μm IRAC 2 band (bottom panel) for all of the planets considered. Each planet is uniquely represented by its Teq on the x-axis, while also alternately annotated on the upper and lower edge of each panel from low to high Teq. The gray shaded area shows the ±1σ deviation.

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Figure 8.

Figure 8. (a) The Spitzer channel 1 and 2 model EDs for WASP-94b across the entire planet-specific grid, compared to the observed EDs from G20 and B20 (they are overlapping). A model with 0.25 ≥ fc ≤ 0.5 should be able to explain the observations. (b) Similar to (a), but for HAT-P-40b. The observed ED is substantially higher that the hottest (largest ED) model in our grid for this planet in both of the channels. (c) Similar to (a), but for WASP-62b. Here, the observed channel 1 ED is much higher than the model with largest channel 1 ED. (d) Similar to (a), but for WASP-12b. Here, the observed EDs for both of the channels lie outside the theoretical trend structure of all the model simulations in the grid.

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As shown in Figure 8(b) for HAT-P-40b (and WASP-87b), the observed EDs in both of the Spitzer channels are larger than the prediction of the simulated model spectra with the largest ED (hottest models with fc = 1) across the entire planet-specific grid. This indicates that the atmosphere of HAT-P-40b is substantially hotter than the models for which the entire host star energy is dumped on the dayside of the planet. For WASP-62b shown in Figure 8(c) (and WASP-65b), the observed ED only in channel 1 (3.6 μm) is larger than the largest channel 1 model ED (hottest model in channel 1) across the entire planet-specific grid. For WASP-12b observed channel 1 and 2 ED is not higher than the largest model ED, but lies outside the theoretical trends of all of the model simulations in the grid, as shown in Figure 8(d). The discrepancy in the observations between G20 and B20 can also be noted for WASP-12b in Figure 2 and Appendix A. For the planets where we see anomalies between observations and models, most commonly the observed channel 1 ED (3.6 μm) is larger (hotter) than the model ED. This happens for fewer planets in channel 2 (4.5 μm). This motivates us to investigate the mechanisms that could cause such anomalies, especially in channel 1.

We first assessed the potential role of an unknown opacity source in causing these anomalies by adding/removing a gray absorbing opacity in either or both Spitzer channels 1 and 2. We find that for planets with low Teq (and hence without inversions), such as WASP-62b, removing (decreasing) opacity in a given band tends to increase the model ED. This is due to deeper, higher temperature, layers of the atmosphere being probed, thus taking the model ED closer to observed ED shown in Figure 8(c). However, for planets with a temperature inversion in their P–T profile such as WASP-12b, adding gray opacity in a given band tends to increase the ED in that band, thus bringing our model EDs closer to the observed value. Therefore, the presence/absence of some opacity source in our models that may or may not be present in the atmosphere of the planet could be one of the potential reasons for the anomalies we see for some planets. The opacity in a given band is also a function of the abundance of the species that has strong absorption cross-section in that band. Therefore, another reason for the anomaly could be that some of the chemical species that are important in either of the bands, such as CH4 in channel 1 and CO in channel 2, may have disequilibrium abundances leading to higher/lower EDs. For example, we tested increasing the CH4 abundance to ∼10−4, that is ∼ 105 times its solar value for WASP-12b at 1 bar, in which case the model simulation was able to explain the anomalously high channel 1 (3.6 μm) ED seen in the observations. The detailed analysis of these anomalies is beyond the scope of this study and will be addressed in our future work considering nonequilibrium chemistry. As we noted earlier, the model simulations in this grid are cloud-free, however, the presence of clouds leads to emission from lower pressures within an atmosphere and hence lower temperature. This will only lead to a decrease in the ED. Therefore, even the presence of clouds cannot explain this enhanced observed ED (hotter temperatures) for certain planets. We also note that we do not include opacity due to many of the refractory species such as Fe ii, Ti i, Ni i, Mn i, Ca i, Ca ii, etc. in our model. These species can substantially increase transit depths in the optical part of the spectrum (due to their strong UV–optical opacities), especially for ultra-hot Jupiters (Lothringer et al. 2020, 2021). Therefore, these species have the potential to effect the P–T profile, and thereby the emission spectrum in the Spitzer IRAC channels. These atomic and ionic metallic species could therefore be one source of the anomaly we identify in this work for ultra-hot Jupiters.

6. Conclusions

In this study, we considered theoretical explanations for thermal emission observations of 34 hot Jupiters via Spitzer IRAC channel 1 (3.6 μm) and channel 2 (4.5 μm). We first benchmarked our emission spectra model with a published model in the literature. We highlighted subtle differences in computing Tb using observed EDs compared to computing EDs directly from a model spectrum. We conclude that Tb and their uncertainties are highly influenced by modeler choices, which can lead to large variations where assumptions differ. We therefore advocate using EDs to directly compare observations with models. Our main results are as follows.

  • 1.  
    We presented theoretical trends in EDs in Spitzer channels 1 and 2 for a population of hot Jupiters, spanning a range of recirculation factors, metallicities, and C/O ratios. We find that the emission spectrum in Spitzer IRAC channel 2 (4.5 μm) is dominated by CO across the parameter space, leading to minor variations in the ED due to the C/O ratio. However, changes in metallicity lead to large variations in the ED in this channel, driven by changes in the abundance of CO with metallicity. In contrast, many other species (e.g., CH4, HCN, and VO) can shape the spectrum in Spitzer IRAC channel 1 (3.6 μm band), depending on the C/O ratio and P–T profile, thus leading to a large spread in ED in this band with the C/O ratio. The percentage variations in ED in both of the bands has a strong dependence on temperature (via recirculation factor and consistent P–T profiles), such that planets with lower equilibrium temperatures show a higher percentage of variations with the C/O ratio and metallicity, while the percentage of variations is smaller for planets with higher equilibrium temperatures.
  • 2.  
    Our best-fitting model spectra for each of the planets demonstrate that Spitzer observations of hot Jupiters are poorly described by blackbodies. This is consistent with the findings of the previous studies (Triaud et al. 2014; Baxter et al. 2020; Garhart et al. 2020). The spectral fits for a population of planets show that the planets with high-equilibrium temperatures tend to show CO emission features (in Spitzer channel 2) indicating temperature inversions, while planets with low equilibrium temperatures show CO/CO2 absorption features indicating a P–T profile without a temperature inversion. However, there are many exceptions governed by the metallicity and C/O ratio of the best-fit model atmosphere. Therefore, we do not see any clear transition with equilibrium temperature as concluded in Baxter et al. (2020).
  • 3.  
    By comparing our self-consistent models with the Spitzer observations from Garhart et al. (2020), we find a trend in the recirculation factor (fc ) across the hot-Jupiter population. The majority of hot Jupiters favor higher values of fc , indicating inefficient recirculation of energy from their dayside to nightside (hotter dayside than expected with efficient recirculation) in agreement with previous findings for different populations of planets (Cowan & Agol 2011; Schwartz & Cowan 2015). Specifically, for equilibrium temperatures above ∼1800 K the range of allowed fc is much more narrow and skewed toward inefficient recirculation (fc > 0.5). We also see that 59% of our sample size of hot Jupiters are consistent with a C/O ratio of less than 1 and 35% are consistent with the whole range of C/O ratio (0.35 ≤ C/O ≤ 1.5). We do not see any definitive population-level trend for metallicity and the C/O ratio. This is because the variation in EDs caused by metallicity and C/O ratio variations is smaller than the Spitzer data precision, making them indistinguishable. The lack of spectral coverage and resolution in Spitzer also make it difficult to place strong constraints on metallicity and the C/O ratio. We also do not see any trend in metallicity or C/O ratio with equilibrium temperature, most likely due to poor constraints. We also find that, for most of the planets in our sample, 3.6 and 4.5 μm model EDs lie within ±1σ of the observed EDs.
  • 4.  
    Some hot Jupiters, such as HAT-P-40b and WASP-62b, display substantially larger EDs than the maximum theoretical value predicted by our planet-specific grid. That is, some of the planets are significantly hotter than expected in one or both of the Spitzer channels. Such anomalies could arise from the disequilibrium abundance of the species whose opacity dominate in that specific channel or due to opacity of any atomic/ionic species not included in our current model. This will be addressed in more detail in our future work.

In the near future, the James Webb Space Telescope (JWST) will provide thermal emission spectra for many of these hot Jupiters with much higher spectral resolution and precision. The planet-specific grid of self-consistent atmospheres presented in this work may then be used to precisely constrain atmospheric metallicities and C/O ratios. We eagerly await the improved data quality from JWST emission spectra, which may illuminate the underlying cause of the anomalously high EDs of some of the hot Jupiters and give more stronger constraints on their atmospheric recirculation, metallicity, and C/O ratio.

We thank Professor Jonathan Fortney for providing us with the relevant model spectrum from G20 for comparison with the ATMO models utilized in this study. J.M.G, N.K.L, and R.J.M acknowledge funding from NASA grant 80NSSC20K0586 from JWST GTO program. N.J.M. would like to acknowledge funding from a Science and Technology Facilities Council Consolidated grant (ST/R000395/1), the Leverhulme Trust through a research project grant RPG-2020-82, and the UKRI Future Leaders Scheme: MR/T040866/1.

Appendix A: Table of Observed and Derived Quantities for Each Planet

Table 1 summarizes the equilibrium temperature, Spitzer IRAC channel 1 and 2 EDs and Tb from G20 and B20, and Tb derived in this work (JG21), for all of the hot-Jupiter exoplanets with positive values of EDs from G20.

Table 1. Observed Eclipse Depth (ED) and Derived Brightness Temperature (Tb ) for Each Planet from Different Works

PlanetEquilibrium G20 3.6 ED G20 4.5 ED B20 3.6 ED B20 4.5 ED G20 3.6 Tb G20 4.5 Tb B20 3.6 Tb B20 4.5 Tb JG21 3.6 Tb JG21 4.5 Tb
NameTemperature (K)(ppm)(ppm)(ppm)(ppm)(K)(K)(K)(K)(K)(K)
HAT-P-131653 ±50851 ±1071090 ±124851 ±1071090 ±1241810 ±2291754 ±2001775 ±871728 ±891788 ±891735 ±89
HAT-P-301718 ±341603 ±1081783 ±1491584 ±1071825 ±1472087 ±1401938 ±1601868 ±511763 ±651894 ±521753 ±67
HAT-P-331855 ±1481663 ±1321896 ±2061603 ±1271835 ±1992112 ±1621990 ±2092000 ±671901 ±982034 ±701926 ±101
HAT-P-401771 ±38988 ±1681057 ±145988 ±1681057 ±1452074 ±3541887 ±2592005 ±1461840 ±1192022 ±1481848 ±119
HAT-P-411685 ±581842 ±3212303 ±1791829 ±3192278 ±1771694 ±2941622 ±1252173 ±1722179 ±882196 ±1742199 ±90
KELT-021721 ±36739 ±43761 ±53650 ±38678 ±471994 ±1041782 ±1111862 ±441679 ±521979 ±481777 ±57
KELT-031829 ±421788 ±981677 ±1051766 ±971656 ±1042445 ±1332132 ±1332300 ±592006 ±622320 ±602017 ±63
KELT-072056 ±311688 ±461896 ±57N/AN/A2512 ±692415 ±73N/AN/A2431 ±322340 ±38
Qatar-11422 ±361511 ±4552907 ±4151490 ±5102730 ±4901410 ±4251532 ±2191374 ±1531470 ±1081391 ±1361512 ±89
WASP-0122546 ±824715 ±2704389 ±1884210 ±1104280 ±1203329 ±1722934 ±1142872 ±402649 ±433077 ±2172698 ±167
WASP-0141893 ±601816 ±672161 ±881870 ±702240 ±1802302 ±852256 ±922248 ±392221 ±932229 ±372180 ±46
WASP-0182416 ±583037 ±624033 ±973000 ±2003900 ±2003057 ±633323 ±802990 ±1093231 ±1042903 ±454756 ±249
WASP-0192099 ±395016 ±2595081 ±3924830 ±2505720 ±3002451 ±1272191 ±1692326 ±572270 ±632388 ±592140 ±84
WASP-0361705 ±44914 ±5791953 ±545913 ±5781948 ±5441336 ±8441506 ±4201300 ±2671475 ±1681306 ±2701472 ±168
WASP-0431444 ±403773 ±1383866 ±1953460 ±1303820 ±1501781 ±651537 ±781664 ±241497 ±241751 ±241521 ±32
WASP-0461663 ±541360 ±7014446 ±5891360 ±7014446 ±5891435 ±7402014 ±2671394 ±2411968 ±1291449 ±2572074 ±139
WASP-0621432 ±331616 ±1461359 ±1301616 ±1461359 ±1301955 ±1771593 ±1531906 ±711568 ±631924 ±721575 ±64
WASP-0631536 ±37486 ±96560 ±130552 ±95533 ±1281547 ±3081395 ±3241573 ±971347 ±1231534 ±1061395 ±127
WASP-0641674 ±1692859 ±2702071 ±4712859 ±2702071 ±4712135 ±2021607 ±3662102 ±871610 ±1592133 ±901628 ±162
WASP-0651490 ±451587 ±245724 ±3181587 ±245724 ±3181833 ±2841179 ±5181781 ±1081160 ±1771791 ±1091162 ±177
WASP-0741922 ±461446 ±662075 ±1001446 ±662075 ±1002049 ±942161 ±1051997 ±392106 ±511989 ±392089 ±51
WASP-0762190 ±432979 ±723762 ±922645 ±633345 ±822669 ±572747 ±602411 ±282471 ±332576 ±322799 ±110
WASP-0771677 ±282016 ±1032487 ±1341845 ±942362 ±1271786 ±841696 ±871685 ±321628 ±371763 ±361682 ±41
WASP-0782200 ±412001 ±2182013 ±3512001 ±2182013 ±3513034 ±3312763 ±4832787 ±1602565 ±2552813 ±2052594 ±534
WASP-0791760 ±511394 ±881783 ±1061394 ±881783 ±1061959 ±1251948 ±1171893 ±491882 ±541899 ±501884 ±53
WASP-0872320 ±622080 ±1272708 ±1372077 ±1272705 ±1372802 ±1722988 ±1522687 ±852863 ±872714 ±853589 ±334
WASP-0941508 ±75867 ±59995 ±93867 ±59995 ±931385 ±951249 ±1181527 ±361398 ±501525 ±361392 ±50
WASP-0971545 ±401359 ±841534 ±1011359 ±841534 ±1011772 ±1111615 ±1071727 ±401590 ±441759 ±421613 ±46
WASP-1002207 ±1701267 ±981720 ±1191267 ±981720 ±1192306 ±1802429 ±1682216 ±792337 ±882228 ±782344 ±89
WASP-1011559 ±381161 ±1111194 ±1131161 ±1111194 ±1131723 ±1661524 ±1451680 ±611492 ±581692 ±611498 ±58
WASP-1032513 ±493854 ±2265230 ±4244458 ±3835686 ±1382993 ±1503268 ±2313114 ±1493337 ±522900 ±1484905 ±895
WASP-1041501 ±1891709 ±1952643 ±3031709 ±1952643 ±3031716 ±1971783 ±2051734 ±761828 ±981720 ±751802 ±96
WASP-1212366 ±573685 ±1144684 ±1213150 ±1034510 ±1072490 ±772562 ±662358 ±362591 ±352428 ±362497 ±36
WASP-1311463 ±32364 ±96289 ±80364 ±97282 ±781397 ±3691114 ±3091361 ±1151077 ±961369 ±1161090 ±97

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Appendix B: Eclipse Depth Variation with Metallicity

This section shows variation of Spitzer IRAC channel 1 and 2 model EDs with metallicity and the recirculation factor (fc ) for WASP-101b on the left side of Figure 9. Additionally, the chemical abundance profiles of important species at solar and 100 times solar metallicity are also shown on the right side of Figure 9.

Figure 9.

Figure 9. Left: model EDs in the 3.6 and 4.5 μm Spitzer bands for WASP-101b. The markers correspond to different fc values, while the colors correspond to different metallicities (see the legends). The observed EDs from G20 and B20 are overlaid for comparison, which overlap for WASP-101b from G20 and B20. Right: chemical abundances at different atmospheric (pressure) layers for certain important chemical species with strong opacities in either of the 3.6 and 4.5 μm Spitzer bands, at solar metallicity (solid line) and 100 times solar metallicity (dashed line).

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Appendix C: Table of System Parameters

All of the stellar and planetary parameters adopted from TEPCat (Southworth 2011) database, for the model simulations of extra 14 exoplanets developed for this work are tabulated in Table 2. The stellar and planetary parameters for the other 20 planets used in this work can be found in Goyal et al. (2020). First column shows planet names with "b" omitted indicating first planet of the stellar system as in TEPCat database. Subsequent columns show stellar temperature (Tstar) in Kelvin, stellar metallicity (${\left[\mathrm{Fe}/{\rm{H}}\right]}_{\mathrm{star}}$), stellar mass (Mstar) in units of solar mass, stellar radius (Rstar) in units of solar radius, logarithmic (base 10) stellar gravity (log gstar) in m s−2, semimajor axis (a) in astronomical units, planetary mass (Mp ) in units of Jupiter mass, planetary radius (Rp ) in units of Jupiter radius, planetary surface gravity (gp ) in m s−2, planetary equilibrium temperature (Teqp ) in Kelvin assuming zero albedo and efficient redistribution, V magnitude (Vmag) of the host star, discovery paper reference (Discovery Paper), and finally the most updated reference.

Table 2. System Parameters

System Tstar ${\left(\mathrm{Fe}/{\rm{H}}\right)}_{\mathrm{star}}$ Mstar Rstar log gstar a Mp Rp gp Teqp Vmag Discovery PaperUpdated Reference
 (K) (MSun)(RSun)(m s−2)(au)(Mjup)(Rjup)(m s−2)(K)   
KELT-0261510.0341.3141.8364.030.055041.5241.2922.717128.7Beatty et al. (2012)Beatty et al. (2012)
KELT-0363060.0441.2781.4724.2090.041221.4771.34520.218119.82Pepper et al. (2013)Pepper et al. (2013)
Qatar-149100.20.8380.8034.5520.023321.2941.14324.55141812.84Alsubai et al. (2011)Collins et al. (2017)
WASP-014646201.31.3184.3120.0377.591.2412318729.75Joshi et al. (2009)Raetz et al. (2015)
WASP-01864000.11.2951.2554.3530.0205510.521.204179.924119.27Hellier et al. (2009)Maxted et al. (2013)
WASP-0365928−0.011.0810.9854.4860.026772.3611.32733.2173312.7Smith et al. (2012)Mancini et al. (2016)
WASP-0465600−0.370.8280.8584.4890.023351.911.17434.3163612.93Anderson et al. (2012)Ciceri et al. (2016)
WASP-0645550−0.081.0041.0584.3920.026481.2711.27119.6168912.29Gillon et al. (2013)Gillon et al. (2013)
WASP-0655600−0.070.931.014.40.03341.551.11228.7148011.9Chew et al. (2013)Chew et al. (2013)
WASP-07561000.071.141.264.290.03751.071.2715.1171011.45Chew et al. (2013)Chew et al. (2013)
WASP-07756050.071.0020.9554.330.0241.761.2127.61167710.3Maxted et al. (2013)Maxted et al. (2013)
WASP-0876450−0.411.2041.6274.0960.029462.181.38526.1232210.74Anderson et al. (2014)Anderson et al. (2014)
WASP-1006900−0.031.5724.040.04572.031.6916.2219010.8Hellier et al. (2014)Hellier et al. (2014)
WASP-10454500.321.0760.9634.5030.029181.2721.13722.5151611.79Smith et al. (2014)Smith et al. (2014)

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Appendix D: Eclipse Depth Plots

For the reader's convenience, the figure set of Figure 10 contains four panels showing the variation of Spitzer IRAC channel 1 and 2 model EDs for all of the models, models with different recirculation factors (fc ), models with different fc and metallicity, and the models with different fc and C/O ratios for all of the systems. The Spitzer observed EDs in these channels from Garhart et al. (2020) and Baxter et al. (2020) are also shown for each planet in each of the panels. These 34 component figures are similar to the top panels of Figures 3 and 8.

Figure 10.

Figure 10.

The variation of Spitzer IRAC channel 1 and 2 model EDs for all models (upper left), the recirculation factors (upper right), metallicity (lower left), and C/O ratios (lower right). The complete figure set (34 images) is available in the online journal. (The complete figure set (34 images) is available.)

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    Footnotes

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    10.3847/1538-4357/ac27b2