BROADBAND TRANSMISSION SPECTROSCOPY OF THE SUPER-EARTH GJ 1214b SUGGESTS A LOW MEAN MOLECULAR WEIGHT ATMOSPHERE^*

We also ensured that any difference in the transit depth from the J to K_s bands was not due to an ineffective nonlinearity correction. During the I'iwi preprocessing step, a nonlinearity correction is applied to correct the count levels for pixels that approach saturation. Near saturation this nonlinearity correction can be as large as 10%. At the maximum count levels recorded in a pixel of the aperture of our target star, GJ 1214, during our observations, the detector is well below its saturation level, and the WIRCam detector is approximately 3%–5% nonlinear at these count levels. The vast majority of the pixels in our target star and reference star apertures are illuminated to much lower levels and are expected to be nonlinear at the 1%–3% level. If this nonlinearity correction was applied ineffectively then this could cause a systematic offset in our measured transit depths; although this discrepancy was expected to be much smaller than the difference in the transit depth from J to K_s that we measure, we nonetheless demonstrated this was the case by reprocessing and reanalyzing our 2010 September 22 transit data in the J and K_s bands without applying the nonlinearity correction. Any deviations in the pixel count values from the current nonlinearity correction will be more than an order of magnitude smaller than the effect induced by not applying the nonlinearity correction whatsoever. Not employing the nonlinearity corrections, as expected, leads to shallower transit depths than when the nonlinearity correction is applied. However, the ratio of the transit depths from K_s to J is near identical whether the nonlinearity correction is, or is not, applied. Overall, as this test should create a variation much larger than one due to an ineffective nonlinearity correction, it is safe to conclude that the greater K_s-band than J-band transit depth does not arise from the nonlinearity correction.

We display our best-fit transit depths in Figure 3 and Table 1. The J-band transit depths are largely consistent with one another and also with, or at most insignificantly shallower than, the depths reported by (Charbonneau et al. 2009) and Bean et al. (2010) in the optical and very near-infrared. The K_s-band transits also display similar depths to one another. However, the K_s-band transits appear to be deeper than the J-band transits; this is a small effect, but is clearly visible in the bottom panel of Figure 2 where we present the residuals of our observations from the best-fit J-band transit depths observed nearly simultaneously.

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The CH₄On transit depth, on the other hand, appears to have a similar transit depth to the J-band transit observed simultaneously on 2011 August 7. As this is a partial transit only, and as much of the transit and the egress of transit occurs at very high airmass, caution is warranted in any robust comparison of the J to CH₄On transit depth and to other wavelengths.

By combining all the K_s-band and J-band transits, we find the weighted means and the associated errors on the transit depths are (R_pJ/R_*)² = 1.338 ± 0.013% for the J band, and (R_pKs/R_*)² = 1.438 ± 0.019% for the K_s band. As we only have one partial transit of GJ 1214 in the CH₄On filter, the depth in that band is simply the value from the 2010 August 7 transit: ($R_{p{\rm CH_4On}}/R_{*}$)² = 1.290^+0.050_{− 0.043}%. We determine the error on the weighted mean of our J-band and K_s-band points by determining the weighted error of all our observations in that particular band and then scaling that error upward by a factor of ζ. To determine ζ we calculate the χ² of all our data in a single band compared to a model with a consistent transit depth equal to the weighted mean of the transit depths in that band; we then scale-up the errors to ensure the reduced χ² is equal to one.¹¹ The K_s-band data points are consistent with one another, so only the J-band errors are scaled upward. The resulting value is ζ_J = 1.02 for the J-band photometry, so this suggests that both the K_s- and J-band weighted errors are already appropriately sized, or close to it. Overall, this analysis suggests that our K_s-band and J-band transit depths are inconsistent with one another; the K_s-band transit depth is deeper than the J-band depth with 5σ confidence.

Charbonneau et al. (2009) reported that GJ 1214 is an active star and displays longer-term variability with a period of several weeks at the 2% level in the MEarth bandpass. More recently, Berta et al. (2010) presented and analyzed MEarth photometry of GJ 1214 from 2008 to 2010 and observed long-term photometric variability at the 1% level with a period of approximately 50 days. This variability is presumably due to rotational modulation from spots rotating in and out of view. As the long-term photometric monitoring presented in Berta et al. (2010) ends in 2010 July (in the midst of the observations we present here), we assume the more conservative limit of 2% variability for our calculations henceforth.

Transit observations obtained at different epochs may show small differences in the transit depth due to rotational modulation arising from both occulted and unocculted spots (Czesla et al. 2009; Berta et al. 2010; Carter et al. 2011). In the case of unocculted spots, if the 2% observed rotational modulation represents the full range from a spotted to unspotted photosphere¹² then we may expect measurements of the transit depth of GJ 1214b will vary by as much as 0.03% of the stellar signal in the MEarth bandpass (assuming an unspotted transit depth of 1.35%) from observations taken at epochs spanning the maximum and the minimum of the observed rotational modulation. On the other hand, occulted spots will cause small brightening events during the transit that may lead one to underestimate the true transit depth. Thus, for transit-depth measurements obtained at different epochs, such as our own, it is possible that the variability caused by rotational modulation creates small differences in the measured depths for observations taken at different epochs.

However, for our data obtained nearly simultaneously in two different bands, the effect of spots should be reduced for the following reasons. First of all, as the stellar rotation period of GJ 1214 appears to be much longer (Charbonneau et al. 2009; Berta et al. 2010) than the ∼1 hr duration of the transit, the spot pattern should be essentially static during a single transit. Secondly, even if the star is very spotted during our own observations, the difference between the transit depths measured nearly simultaneously in our two bands will be minute. This small difference will arise due to the differing ratio of the Planck function of the spot and the star due to their different temperatures; however, this difference will be muted as we move into the near-infrared. For instance, assuming that GJ 1214 has spots 500 K cooler—a value supposedly consistent with another M4.5 dwarf (Zboril et al. 2003)—than GJ 1214's ∼3000 K effective temperature (Charbonneau et al. 2009), the 2.0% variability due to rotational modulation in the MEarth bandpass (∼780 nm), will translate into 1.5%, and 1.0% variability in the J band and K_s band, respectively. Assuming the unspotted transit depth is 1.350% in these bands then the maximum transit depths from unocculted spots, which would result from measurements at the minimum flux of the observed rotational modulation, would be 1.369% in the J and 1.364% in the K_s band. The variation in the transit depth between the J and K_s bands that we observe is both much larger than this predicted effect due to starspots, and also would serve to create a deeper transit in J band rather than K_s band; we, of course, observe the opposite phenomenon.

A deeper K_s-band than J-band transit could arise from spots along the transit chord that are occulted during the observations. Occultation of spots by a planet will create anomalous brightenings during transit, as has been observed for the transiting planets HD 189733b (Pont et al. 2007), TrES-1b (Rabus et al. 2009; Dittmann et al. 2010), and more recently for GJ 1214b (Bean et al. 2010; Berta et al. 2010; Carter et al. 2011). However, due to the near-simultaneous nature of our photometry, it is unlikely that occulting spots could account for the variation in K_s- to J-band transit depth that we observe, again due to the small difference in the Planck functions of the spot relative to the star between our two bands. For instance, occulting a spot 500 K cooler than the surrounding photosphere that is 30% of the planetary size will lead to transits that are 0.07% shallower for the duration of the occultation than the presumed 1.35% transit depth in the J band. However the K_s-band transit depth will also be 0.05% shallower; the 0.02% relative difference between the two bands expected from a spot occultation is much less than the observed transit-depth difference we observe. Lastly, as spot occultations will lead to overall shallower transit depths, one would require the true transit depth of GJ 1214b to be deeper than that observed in our own J-band observations and in the optical and very near-infrared (Charbonneau et al. 2009; Bean et al. 2010). For these reasons we find it unlikely that the transit-depth difference we observe arises from occulted or unocculted spots.

Due to the aforementioned possible variations in the transit depths from epoch to epoch induced by spots, a more straightforward method to compare the depths of transits in our bands is to directly compare the depth of the transit in one band to the depth obtained simultaneously in another—that is (R_PKs/R_PJ)² for each one of our transits observed simultaneously in the K_s and J bands. We ignore our data observed on 2010 August 7 for this analysis, as GJ 1214 was observed in the J band and the CH₄On filter rather than in J and K_s.

We attempt to measure the fraction that the K_s-band transits are deeper than the J-band transits, (R_PKs/R_PJ)², by two methods. In the first method, we display the best-fit MCMC transit depth of our K_s-band photometry divided by the J-band transit depth from our individual analysis ("Ind.") in Figure 4. The associated errors displayed in this figure are generated by propagating through the associated errors on the individual best-fit MCMC transit depths as displayed in Table 1. The weighted mean and error of these data indicates that the K_s-band transits are deeper than the J-band transits by a factor of (R_PKs/R_PJ)² = 1.072 ± 0.018. The associated errors do not need to be scaled up, as the reduced χ² is near one for a comparison of our three (R_PKs/R_PJ)² data points as compared to the weighted mean of these observations; specifically χ² = 1.92, which is reasonable given the two degrees of freedom.¹³ By analyzing the individual transits, our K_s-band photometry displays a deeper transit depth than our J-band photometry observed nearly simultaneously with a confidence in excess of 4σ.

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In the second method we use the "Joint" MCMC analysis described above where we simultaneously fit the three data sets that observe in the K_s band and J band simultaneously. We fit each J-band transit with an independent transit depth, but assume that all the K_s-band transits were a consistent factor deeper (or shallower) than the J-band transits observed nearly simultaneously (R_PKs/R_PJ)². We also fit the limb-darkening parameters after applying a Gaussian a priori assumption as described in Section 3. We display this ratio for our "Joint" analysis in Figure 5; we measured this fraction as (R_PKs/R_PJ)² = 1.063^+0.019_{− 0.021}. This distribution is not a perfect Gaussian, and therefore, according to this method our K_s-band transits are deeper than our J-band transits with greater than 3σ confidence.

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Both methods return reasonably similar results, and argue for a deeper K_s-band transit depth than J-band transit depth with a confidence in excess of 3σ. We quote the value of (R_PKs/R_PJ)² from our "Ind." results henceforth.

The transit depths from our CFHT/WIRCam photometry suggests that GJ 1214b should have a large-scale height, low mean molecular weight and thus a hydrogen/helium-dominated atmosphere. These conclusions arise from the fact that our K_s-band transit depths are deeper than our J-band transit depths by a factor of (R_PKs/R_PJ)² = 1.072 ± 0.018. This corresponds to a relative change in the radius of GJ 1214b from the K_s band to the J band of 1.04%, or ∼610 km compared to GJ 1214b's radius of ∼17070 km. Using its equilibrium temperature of T_eq ∼ 560 K (the value obtained assuming zero bond albedo) this amounts to absorption increasing the radius of GJ 1214b by ∼2 atmospheric scale heights for a hydrogen gas envelope (H₂). As the molecular weight of H₂O is approximately nine times greater than hydrogen gas, a spectral feature this prominent assuming a water-world composition would require an increase in the planetary radius of ∼20 atmospheric scale heights. This suggests that an atmosphere dominated by light elements is much more probable than one composed of heavier elements.

The change in transit depth due to a change in planetary radius between the line, R_PL, and the continuum, R_PC, can be related to the scale height, H, and the opacities in the absorption line, κ_l, and the continuum, κ_c; this value can be approximated by the ratio of the opacities multiplied by the area of an annulus one scale height thick relative to that of the stellar disk:

$$\begin{equation} (R_{{\rm PL}}/R_{*})^2-(R_{{\rm PC}}/R_{*})^2 = \frac{2 \pi R_{P} H}{\pi R_*^2} \ln (\kappa _{l}/\kappa _{c}) \end{equation} \tag{ 2 }$$

(Brown et al. 2001). To cause the observed transit-depth difference in a hydrogen gas atmosphere would require line opacity marginally greater than that of the continuum (κ_l/κ_c ∼ 8); the water-world composition would require an opacity that is unrealistically larger than that of the continuum (κ_l/κ_c ∼ 2 × 10⁸). Therefore from our CFHT/WIRCam observations, one would expect that the atmosphere of GJ 1214b must have a low mean molecular weight, a large-scale height, and thus an atmosphere dominated by hydrogen and/or helium.

We compare our data to the Miller-Ricci & Fortney (2010) atmospheric models of GJ 1214b in Figure 3. We first employ the most conservative scenario and assume that due to rotational modulation, or other systematic errors, that we cannot directly compare our measured transit depths to the Charbonneau et al. (2009) or Bean et al. (2010) depths. We thus scale-up or scale-down the predicted absorption of the Miller-Ricci & Fortney (2010) models by a multiplicative factor, analogous to an increase or decrease of the squared ratio of the planetary to stellar radius, to produce the best-fit (minimum χ²) compared to our observations. We display the Miller-Ricci & Fortney (2010) water-world model (an H₂O-dominated world) in the dotted gray line. We compare to two hydrogen/helium-dominated atmospheres; the first has solar-metallicity (orange dot-dashed line) while the second has solar metallicity but does not feature methane (cyan dot-dashed line). We integrate these models over the WIRCam response functions and calculate the associated χ² of our data compared to the model. Although we cannot strongly differentiate between hydrogen–helium envelopes with solar metallicity (χ²_solar = 9) from those without methane (χ²_no-methane = 7), the water-world composition is disfavored ($\chi ^2_{{\rm H_2O}}$ = 26) by greater than 2σ for our seven degrees of freedom. Other high mean molecular weight models (e.g., the Miller-Ricci & Fortney (2010) CO₂-dominated or H₂O/CO₂-mixture atmospheres) are disfavored with similar confidence. The support for the hydrogen/helium composition arises from the observed increased absorption in K_s-band as opposed to our J-band observations. The CH₄On filter is nominally 1σ discrepant from the observed models; it is unclear at this present time whether this discrepancy is physical or simply due to low signal-to-noise.

Arguably, completely excluding the constraints imposed by transit-depth observations at other wavelengths, because of the effects of spots or systematic effects, is unnecessarily conservative. Therefore, we also compare the weighted means of our transit-depth measurements and the Miller-Ricci & Fortney (2010) models to the Charbonneau et al. (2009) depth measurement in the MEarth bandpass, the J-band measurement of Sada et al. (2010), and the Bean et al. (2010) measurements from 0.78–1.0 μm in Figure 6. We do not attempt to make a correction for the possibly variable spot activity between the various epochs at which the data were obtained; as discussed above in Section 4.2 rotational modulation can be expected to induce spurious transit-depth variations as large as 0.03% of the ∼1.35% transit depth of GJ 1214b near 1 μm and will cause smaller variations at longer wavelengths. Also, a small discrepancy will be induced by the fact that the Sada et al. (2010) and Charbonneau et al. (2009) transit-depth measurements were produced with the original Charbonneau et al. (2009) estimates of the inclination and other parameters for this system, rather than the values derived from the Bean et al. (2010) white light photometry that we use here and that have been applied to the Bean et al. (2010) spectrophotometry. For these reasons, we caution that this comparison should be considered illustrative rather than definitive.

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Of the original Miller-Ricci & Fortney (2010) atmospheric models the heavy mean molecular weight models, such as the water-world composition model ($\chi ^2_{{\rm H_2O}}$ = 40), are highly favored over the low mean molecular weight compositions (χ²_solar = 101 for the solar metallicity hydrogen/helium-dominated envelope).¹⁴ The water-world composition is favored over the solar metallicity hydrogen/helium-dominated model with more than 5σ confidence. This is unsurprising, as it is largely the conclusion of the Bean et al. (2010) paper, and results from the high pre- cision of the VLT/FORS2 spectrophotometry and the lack of observed spectral features in the very near-infrared. The Bean et al. (2010) paper excludes the expected methane and water spectral absorption features from a hydrogen/helium-dominated atmosphere from 0.78 to 1.0 μm with high confidence.

Another possibility to explain the lack of observed spectral features are high-altitude hazes (Fortney 2005) in the atmosphere of GJ 1214b that could mute the spectral features at shorter wavelengths. We discuss this possibility further below (Section 4.6). We thus also compare our observations to a no-methane model where we cut off the absorption below 1 μm and set it equal to a nominal value of 1.35%. At wavelengths greater than 1 μm, the values are identical to the no-methane model. This abrupt transition is not intended to be physical, but simply illustrative of the impact hazes could have on the expected transmission spectrum at shorter wavelengths.¹⁵ This model has the lowest χ² (χ²_{hazy-hydrogen} = 34) of any of the models as it is able to address the lack of observed spectral features in the Bean et al. (2010) spectrophotometry, and our deeper K_s-band depth compared to our J-band depth. We note that the improvement in the χ² of this haze model to the water-world model is not significant, and both remain leading candidates to explain all the observations of GJ 1214 to date, as discussed below.

All the transmission spectroscopy observations of GJ 1214b to date could be explained by a high mean molecular weight atmosphere if our deeper K_s-band transit is simply an outlier. If GJ 1214b's atmosphere does have a high mean molecular weight, a water-vapor atmosphere is a leading possibility. This water-world scenario will remain a viable candidate until observations are performed to confirm that either our K_s-band transit depths are indeed deeper or spectral features are detected at other wavelengths.

A scenario that would qualitatively explain all the observations to date, is a hydrogen/helium-dominated atmosphere with thick hazes that would mute the presence of spectral features arising from shorter wavelengths due to scattering. This haze layer would have to be at high altitudes, and low pressures (<200 mbar), to effectively mute the expected spectral features that would arise from being able to stare deep into the atmosphere of the planet in opacity windows in the very near-infrared. The efficiency of scattering diminishes for wavelengths longer than the approximate particle size (Hansen & Travis 1974). The haze particles could not be much smaller than sub-micron size to account for the lack of observed spectral features in the Bean et al. (2010) spectrophotometry in the very near-infrared. Due to the expected size of these putative haze particles, shorter wavelength optical observations would not be expected to show simply the monotonic increase in planetary radius expected from a Rayleigh scattering signal, but instead the more complicated transmission spectrum signal of Mie scattering (see, for example, Lecavelier des Etangs et al. 2008).

Such a haze or cloud layer is certainly not inconceivable. A cloud deck or haze has been reported to mute the optical transmission spectrum from 0.29 to 1.05 μm of the hot Jupiter HD 189733b (Pont et al. 2008; Sing et al. 2011); in the infrared HD 189733b may have absorption features with an opacity even greater than those that result from the haze at those wavelengths (Desert et al. 2011). The hazes of Jupiter and Titan may be other suitable analogies. Titan has a haze layer that is optically thick in the optical, but has transparent windows as one moves into the near-infrared (Tomasko et al. 2008; Griffith et al. 1993). The opacity of hazes on Jupiter are high at short optical wavelengths, but are much smaller as one moves into longer optical wavelengths and into the near-infrared (Rages et al. 1999).

A potential culprit for the particle causing this haze is a hydrocarbon derived from the photochemical destruction of methane (Moses et al. 2005; Zahnle et al. 2009). Methane is found in the atmospheres of all the solar system's giant planets, as well as that of Titan. The end products of the breakdown of methane are higher-order hydrocarbons that condense as solids (Rages et al. 1999). Since GJ1214b should be relatively cool (T_eq ∼ 500 K) its atmospheric carbon inventory could feature abundant methane, like that of Jupiter. Particulates with a relatively small mixing ratio can have important effects at the slant viewing geometry appropriate for transits (Fortney 2005), and thus hydrocarbons in a high-altitude haze are one possible explanation the lack of observed features in the Bean et al. (2010) spectrophotometry.

We finally note that the actual spectral features of GJ 1214b, whether its atmosphere is hydrogen/helium dominated or not, could be more complicated and thus very different from what the Miller-Ricci & Fortney (2010) models predict. One such reason could be the impact of non-equilibrium chemistry (Miller-Ricci Kempton et al. 2011).

Clearly further observations are required to differentiate between these scenarios and determine the true atmospheric makeup of GJ 1214b.

4.6.1. An Opacity Source at ∼2.15 μm

A hydrogen/helium-dominated atmosphere on GJ 1214b would be expected to undergo significant hydrodynamic escape. Therefore, if GJ 1214b is hydrogen/helium dominated then it may have lost, or is losing, a significant fraction of its gaseous envelope. Charbonneau et al. (2009) and Rogers & Seager (2010) predicted that if GJ 1214b's atmosphere is dominated by hydrogen gas then it will lose on the order of ∼10⁹ g s⁻¹, or ∼0.02 M_⊕ on a 4 Gyr timescale.¹⁶ As its host star may have been more active earlier in its life, and thus brighter in the ultraviolet, its cumulative mass loss may be higher. Thus, either if GJ 1214b's hydrogen/helium envelope is primordial or due to outgassing we may expect it to have lost, and will be losing, a non-negligible fraction of its atmosphere.

Also, Carter et al. (2011) have pointed out that the radius of the star, GJ 1214, that one obtains from stellar evolutionary models is very different from the radius one obtains from an analysis of the light curve. As a result the density of GJ 1214b varies accordingly, from one where a significant gaseous atmosphere is likely, to a much higher density where one would only expect a thin gaseous atmosphere on top of a solid terrestrial planet. Our increased K_s-band transit depth argues in favor of the lighter density and the stellar radius suggested by fits to light-curve parameters.

4.7.1. Constraints on GJ 1214b's Bulk Composition