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Possible thermochemical disequilibrium in the atmosphere of the exoplanet GJ 436b

The nearby extrasolar planet GJ 436b--which has been labelled as a 'hot Neptune'--reveals itself by the dimming of light as it crosses in front of and behind its parent star as seen from Earth. Respectively known as the primary transit and secondary eclipse, the former constrains the planet's radius and mass, and the latter constrains the planet's temperature and, with measurements at multiple wavelengths, its atmospheric composition. Previous work using transmission spectroscopy failed to detect the 1.4-\mu m water vapour band, leaving the planet's atmospheric composition poorly constrained. Here we report the detection of planetary thermal emission from the dayside of GJ 436b at multiple infrared wavelengths during the secondary eclipse. The best-fit compositional models contain a high CO abundance and a substantial methane (CH4) deficiency relative to thermochemical equilibrium models for the predicted hydrogen-dominated atmosphere. Moreover, we report the presence of some H2O and traces of CO2. Because CH4 is expected to be the dominant carbon-bearing species, disequilibrium processes such as vertical mixing and polymerization of methane into substances such as ethylene may be required to explain the hot Neptune's small CH4-to-CO ratio, which is at least 10^5 times smaller than predicted.

. Figure 1 shows the observed secondary eclipses with best-fit models, and Table 1 presents the relevant eclipse parameters.
The phase of secondary eclipse imposes a tight constraint on the planet"s eccentricity, e, and argument of periapsis, . Using the secondary eclipse times listed in Table 1, in addition to published transit 16 and radial-velocity data 17 , a single-planet Keplerian orbit for GJ 436b has a period of 2.6438983 ± 0.0000016 days and an ephemeris time of Julian date 2,454,222.61587 ± 0.00012 (all errors are 1). These are nearly identical to the published results 16 , which do not consider secondary eclipses. Using either result, the weighted average of the five measured secondary eclipse phases is 0.5868 ± 0.0003. This significant improvement from previous analyses 3,4 is due to the more Our broadband observations constrain a one-dimensional atmospheric model, using a new temperature and abundance retrieval method 18 . This method searches over a wide parameter space using a functional form for the pressure-temperature profile (based on prior "hot Jupiter" and Solar System studies), a grid of abundance combinations, and energy conservation. We calculated ~10 6 models, which considered both inversion and noninversion temperature profiles and abundances that varied over several orders of magnitude per constituent. Figure 2 shows two representative models (the red and blue lines) that fit the data, and Table 2 compares them to seven other objects with hydrogen-dominated atmospheres. The red model has a dayside-to-nightside energy redistribution ratio of <0.04; the blue model favours a more efficient distribution ratio of <0.31. The red model fits the data better.
Chemical equilibrium predicts H 2 , H 2 O, CH 4 , CO and NH 3 to be the most abundant molecules in GJ 436b"s atmosphere (helium must also be present but contributes minimally to the spectrum and to active chemistry). Conventional chemical composition models predict 6 the major emission contributions to come from spectroscopically active H 2 O, CH 4 , and, to a lesser extent, CO, and possibly CO 2 . In a reduced, hydrogen-dominated atmosphere at ~700 K, CH 4 is thermochemically favoured to be the main carbon-bearing molecule. Assuming solar abundances for the elements and the pressure-temperature profile shown in Supplementary Fig. 5, chemical equilibrium predicts 6 a CH 4 -to-H 2 mixing ratio of 7 × 10 4 and an H 2 O mixing ratio of 2 × 10 3 . However, the strong planetary emission at 3.6 m, combined with the non-detection at 4.5 m, calls for a methane abundance that is depleted by a factor of ~7,000. The low H 2 O abundance favoured by our red model could, in principle, result from carbon and oxygen abundances that are ~0.01 times solar values; however, the resulting CH 4 mixing ratio would still be too high, by two orders of magnitude, to explain the data.
Methane absorbs strongly in the 3.6-m band. CO and CO 2 have absorption features at 4.5 m, CO 2 being the stronger absorber. The high flux at 3.6 m suggests very low absorption due to methane, while the low flux at 4.5 m implies high absorption due to CO and/or CO 2 . The degeneracy between the two molecules is solved by the low CO 2 concentration needed at 16 m. The absence of observed flux in the 4.5-m channel thus requires large amounts of CO, which is not expected in such a reduced atmosphere under thermochemical equilibrium, and makes a future detection at 4.5 m important.
The flux modulation at 3.6 m is our strongest detection, with a signal-to-noise ratio of 12.1, and has been confirmed by an independent analysis. Using 2 error bars for this observation and the 3 upper limit at 4.5 m, the low-methane requirement cannot be lifted (this result is relatively insensitive to the remaining wavelengths). An increased methane mixing ratio of 10 6 would result in a higher blackbody continuum, thus requiring a CO 2 mixing ratio 10 3 in order to fit the flux constraint at 4.5 m (Figure 3). However, thermochemical equilibrium and photochemical models predict a CO 2 mixing ratio of ~10 7 in hydrogen-dominated atmospheres at solar abundance (~10 5 for 30 times solar metallicities) 19,20 .
We also explored other possibilities to explain the observations. A temperature inversion does not fit the data well, assuming thermochemical equilibrium, because H 2 O and CH 4 would emit much more strongly than we observe in the 5.8-and 8.0-m channels, respectively. Non-local thermodynamic equilibrium emission from the dayside of exoplanet HD 189733b is attributed 21 to CH 4 fluorescence near 3.25 m. However, our 3.6-m detection is too strong to be explained by fluorescence alone. Alternatively, the methane deficiency could be explained by a lack of hydrogen; however, mass and radius constraints placed by transit and radial-velocity observations call for a hydrogen-dominated The brown dwarf GJ 570D has an effective temperature similar to that of GJ 436b (800 K), but at atmospheric levels where T < 1,100 K, CH 4 is the dominant carbon-bearing molecule, with a CH 4 -to-CO ratio of ~10 2 (ref. 9). We estimate a ratio of 1 × 10 3 for GJ Information. We detect no eclipse at 4.5 m, but constrain the flux modulation at its 3 upper bound by fixing the secondary eclipse phase to the mean weighted value of the other channels. We use asymptotically constant exponential and linear functions to model the time-varying sensitivities at 8.0 and 16 m, respectively. Our 8.0-m analysis agrees with prior analyses 3,4 but we obtain a slightly higher brightness temperature (Table 1) due, in part, to a more recent Kurucz model 24 . No correction is necessary at 24 m. Page 10 of 42 860 K and 790 K, respectively. We need not invoke an internal heat source 3 . Assuming zero albedo and planet-wide redistribution of heat, GJ 436b has an equilibrium temperature (T eq , where emitted and absorbed radiation balance for an equivalent blackbody) of 770 K at periapse. For instantaneous reradiation of absorbed energy at secondary eclipse, the hemispheric effective temperature is 800 K and the peak temperature is 1,030 K. divided by the number of channels. We use the 3 upper limit for the 4.5-m observation.
The black surfaces show models with  2 < 1 and CH 4 /H 2 > 10 6 . The figure demonstrates that models with CH 4 mixing ratios close to 10 6 or above (panel a) require extremely large (>10 3 ) CO 2 mixing ratios (panel b), which are unphysical based on current understanding of CO 2 photochemistry. The parameter space was explored with ~10 6 models. The  2 parameter, which is related to the temperature gradient in the lower atmosphere 18 , was chosen arbitrarily for the abscissa. . A Monte Carlo method computes the uncertainty in brightness temperature by varying the flux modulation and stellar parameters. The differing brightness temperatures at 3.6 and 4.5 m suggest that these two wavelengths measure two different pressure levels; indeed Supplementary Fig. 5 shows that the 4.5-m channel has an additional contribution from higher up in the atmosphere. To explain the 400 K difference in brightness temperatures, the model requires a very low concentration of methane. *3 upper limit.
HD 189733b 26 (HST/NICMOS) Chemical equilibrium predicts a roughly increasing CH 4 -to-CO ratio. GJ 436b does not follow this general trend, as seen in the rightmost column. Its CH 4 -to-H 2 mixing ratio is >10 3 times less than that of a brown dwarf of similar temperature and its CH 4 -to-CO ratio is >10 5 times less. Excess CO may be the result of relatively strong vertical mixing 9 . A significant fraction of the methane may have polymerized into hydrocarbons 10 , resulting in a shortage in observed CH 4 . For comparison, GJ 436b's required methane mixing ratio of 10 7 is about 10 5 times less than that on Uranus and Neptune, 10 4 times less than that on Jupiter and Saturn, and ~20 times less than that on Earth, where methane is oxidized, not polymerized. NA, not available. *Above cloud.

Supplementary Information
At a relative flux level of just ~0.1% compared to the host star, exoplanet secondary eclipses are well below Spitzer's 2% relative photometric accuracy requirement 31 . This and their low intrinsic signal-to-noise ratios (SNR, often below 10) require that we attend closely to analysis details. Because different analysis approaches may obtain significantly different results, we also present more than the usual level of detail about our fits, so that future investigators who choose to analyze these data can compare their work to ours. This Supplementary Information (SI) presents how we determined the centres of the photometric apertures, adjusted for varying array sensitivity with respect to aperture centre location ("position sensitivity") and time ("ramp"), and fit models to the data. The final section presents the results of our fits in sufficient detail for evaluation of alternative analyses.
Many other methods appear in the SI to Ref. 14.

Centring and Photometry
Spitzer"s instrumental point-spread functions (PSFs) are stable in time and vary little with the normal pointing wander (<1") over a few-hour staring observation. Since zodiacal light and instrumental effects contribute significant noise, we use a small aperture plus an aperture correction at short wavelengths and optimal photometry 15,32 at longer wavelengths. In either case, mismatching the aperture or PSF model to the data produces additional error, so one must determine PSF centres accurately. Here we compare three methods. The first 33 computes the centre of light of pixels within a circular aperture and above the frame's median value by at least 0.1% of the median-subtracted peak value. The second fits a two-dimensional (2D) Gaussian with free position parameters. The third, called least asymmetry, optimizes the stellar radial profile by calculating: where (x, y) is the current pixel location and σ r is the standard deviation of the n r pixels at the radial distance r i in pixels from the current central pixel. The first few discrete values for r i are 1, √2, 2, √5, 2√2, 3, etc. We find using i max = 5 provides comparable precision and computes faster than larger values. An inverted 2D Gaussian with free position parameters finds the minimum in asymmetry space, which defines the centre of the object.
Tests using real datasets show that the 2D Gaussian and least-asymmetry methods are more precise than the centre-of-light method (see Supplementary Figure 1). For the example data, the Gaussian method is the most precise, but this is not always true. We The IRS and MIPS channels typically achieve their best results using optimal photometry, but 5-interpolated aperture photometry 14 is best for the IRAC channels.
Supplementary Table 1 gives the best aperture sizes, found by varying the size and minimizing the standard deviation of the normalized residuals. Changing the aperture size by 0.25 pixels from the best value increases this standard deviation by <0.4% and typically by much less, so smaller pixel increments are unnecessary.

Position Sensitivity
In the 3.6-and 4.5-m Spitzer channels, sensitivity varies up to 3.5% with centroid position. We detect for the first time much smaller variations at 5.8 m, which may be due to intra-pixel sensitivity variations or residual flat-field errors. Polynomial models in the two position variables fit the position sensitivity: where ' and  are the measured and corrected fluxes, respectively, x and y denote the PSF centre relative to the pixel centre, and a -i are (potential) free parameters. In general (but not for these particular datasets), if many of the PSF centres fall on two or more pixels, the sensitivity difference between pixels (uncorrected flat field) becomes important. In this case, each of the visited pixels has its own correction.

Time-Varying Sensitivity
Two functions model the time-varying sensitivity: an asymptotically constant exponential 14 where, in Eqn. 4, the positive and negative signs are used for exponentially decreasing and increasing variability, t is the observation time, and the free parameters are a, b, and t 0 . If both intra-pixel and time-varying sensitivities apply, their multiplied corrections use only one . Although ' in Eqn. 5 tends toward infinity at large t, this physical impossibility is not a problem for observations of a few hours. Eqn. 4 curves more, so it generally produces slightly deeper eclipses than Eqn. 5. Without any physical reason to prefer either funct ion, we test both and report the one with the lowest Bayesian Information Criterion value (described below). in" of at least 10 5 iterations to forget the starting conditions, we rescale the uncertainties to give a reduced χ 2 of ~ 1. After 10 6 or more iterations, the best-fit parameters are those with the least χ 2 value. We calculate the 34 th percentile in both directions from the median value to obtain uncertainties (averaged if close, quoted separately otherwise).

Determining the Best Model
The Bayesian Information Criterion (BIC) 37,38 compares models with differing numbers of free parameters, heavily penalizing those with more, relative to the least χ 2 method. The preferred model has the lowest BIC value: where  i and is the residual of the i th data point, σ 2 is the error variance, n is the number of data points, and k is the number of free parameters. Supplementary Table 2

Supplementary Discussion
The short-lived spike that occurred after the eclipse at 3.6 m may be the result of stellar activity 30,39 . If this sharp increase in observed flux had affected the eclipse, the flux ratio would have been larger and the duration longer, thus requiring even lower levels of methane in the models and an inexplicably long duration. We contend that this is not the case and do not fit the affected points. The high interest in M-dwarf planets calls for observational study of M-dwarf activity, notably flares, across the spectrum. The residuals are normalized to the stellar flux.

Supplementary Figures
Supplementary Figure 5 presents the contribution functions 41  However, strong correlations do occur between the star flux and certain intra-pixel terms