HST SPECTRAL MAPPING OF L/T TRANSITION BROWN DWARFS REVEALS CLOUD THICKNESS VARIATIONS

We used the HST to obtain near-infrared grism spectroscopy of two L/T transition brown dwarfs as part of a larger campaign (Programs 12314, 12551 PI: Apai). The data were acquired with the sensitive Wide-Field Camera 3 instrument (MacKenty et al. 2010) by obtaining 256 × 256 pixel images of the targets' spectra dispersed by the G141 grism in six consecutive HST orbits. Table 1 provides a log of the observations. In short, we obtained 660 spectra for 2M2139, each with 22.34 s integration time; and 495 spectra for SIMP0136, each with 22.34 s integration time. In the analysis that follows we averaged sets of 10 spectra for 2M2139 and sets of 5 spectra for SIMP0136, giving us an effective temporal resolution of 223 s for 2M2139 and 112 s for SIMP0136. Our targets are relatively bright (J = 13.5 mag for SIMP0136 and J = 15.3 mag for 2M2139), resulting in very high signal-to-noise spectra (see Section 2.3 for a detailed assessment).

At the beginning of each orbit a direct image was obtained to accurately determine the position of the source on the detector, required for precise wavelength calibration. Cross-correlation of the images and centroid positions on source revealed positional differences less than 0.1 pixel (001) between images taken at different orbits. No dithering was applied to stabilize source positions and improve the accuracy of relative measurements.

The observations presented here focus on two L/T transition brown dwarfs. Target 2M2139 (or 2MASS J21392676+0220226) has been classified as a T0 dwarf based on red optical spectrum (Reid et al. 2008) and as a peculiar T2.5 ± 1 dwarf based on a 0.8–2.5 μm spectrum (Burgasser et al. 2006). More recently, Burgasser et al. (2010) found that the spectrum of 2M2139 is better fit by a composite spectrum of an earlier- (L8.5) and a later-type (T3.5) dwarf than any single template brown dwarf. It was recently found to show impressive periodic photometric variability with a peak-to-peak amplitude of ≃27% (Radigan et al. 2012). Ground-based photometry of variation 2M2139 argues for a period of 7.721 ± 0.005 hr, but also leaves open the possibility of a two times longer period (Radigan et al. 2012). Recent observations by Khandrika et al. (2013) confirm the variability and argue against a double-peak period. Based on JHK light curves and a fit to the spectrum by Burgasser et al. (2006), these authors argue that cloud thickness variations are likely responsible for the photometric variations seen in 2M2139. Target SIMP0136 (2MASS J0136565+093347), another T2 brown dwarf, has also been reported variable (Artigau et al. 2009). These targets are the first L/T transition sources observed in our two ongoing HST surveys; further results, including coordinated HST/Spitzer observations and sources with later spectral types, are discussed in Buenzli et al. (2012) and other upcoming papers.

Our reduction pipeline combined the standard aXe pipeline with a custom-made IDL script, which included corrections for different low-level detector systematics, critical for highly precise relative spectroscopy. We used two-dimensional spectral images from the standard WFC3 pipeline, which were bias and dark current-subtracted, and corrected for non-linearity and gain. Bad pixels were marked by a corresponding flag in the data quality plane. In order to correct for detector systematics we started with the .ima files, which contain all non-destructive sub-reads of each exposure, rather than the combined .flt images. Because our observations were not taken with a dithering pattern, we did not use the standard pipeline's MultiDrizzle routine.

We first extracted all sub-reads, discarded the first two zero-reads (0 s and 0.27 s), and compared the count rates of the individual pixels over the sub-reads of an exposure to identify and remove outliers by replacing them with the median value. We also corrected flagged bad pixels by interpolating over adjacent good pixels in the same row.

We identified a systematic nearly linear flux loss from the first to last sub-read of an exposure, with a steeper slope for the brighter pixels of a spectrum. We empirically determined a slope of −0.2% per 22.34 s (one sub-read) for pixels of brightness >60% of the maximum in the spectrum, and only −0.001% for pixels below that level (Figure 1). The uncertainties of the slopes are negligible, but a significant "zig-zag" pattern is present with a scatter of ∼0.1%. The standard deviation of the normalized fluxes measured at the same exposure but in different orbits is ⩽0.2%. This relation held for all of our objects, regardless of the absolute brightness of the spectra. Only the first sub-read had systematically higher flux than expected from the linear relation and had to be corrected individually for each source.

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The spectral extraction was executed with aXe (Space Telescope-European Coordinating Facility, ESA 2011). First, the sub-array images were embedded in larger, full frame-sized images to allow aXe to use standard instrument calibration frames, which are full frame sized. The data quality flag was used to exclude the extra surrounding pixels of the extended frame from the actual data analysis. As a first step, the aXe pipeline subtracted a scaled master sky frame, with the scale factor determined individually for each images background level (i.e., excluding the observed spectra). Then, the location of the target spectrum and the wavelength calibration were determined from the direct (non-grism) images. For the source 2M2139, only one direct image was obtained at the beginning of the first orbit and this image was used for each subsequent spectra. For SIMP0136, a separate direct image was taken at the beginning of each orbit and used for all spectra in the given orbit. We fixed the spectral extraction width within each orbit, but allowed it to vary between subsequent orbits. The extraction width was determined by summing up all spectra in a single orbit and then collapsing the sum into a one-dimensional (1D) vertical profile. The extraction width was then chosen as three times the full width at half-maximum of a Gaussian fit to that profile. This resulted in an extraction width with mean and standard deviation for the six orbits of 6.50 ± 0.02 for SIMP0136 and 6.56 ± 0.01 pixels for 2M2139, respectively.

In the final step the spectra from each image were flat fielded, extracted, and collapsed using the standard pixel extraction tables of aXe and flux-calibrated with the latest instrument sensitivity curves. This led to 1D spectra with a spectral resolution of R = λ/Δλ ≃ 130 and highly reliable data over the wavelength range from 1.1 to 1.7 μm. We calculated the uncertainties as composed of photon shot noise, read noise, and sky noise. A second systematic detector effect became evident at this point. During each orbit, there was a small increase in flux in the form of an exponential ramp (Figure 1). Because the intrinsic variability of the sources prevented a direct quantification of this effect, we used the partial spectrum of a bright star visible in one of our target fields. The ramp was found to be independent of object brightness. We integrated the stellar spectrum over the full wavelength range and removed exposures where saturation had occurred. We fitted the exponential ramp C × (1 − Ae^−t/T) to the light curve, where t is the time since the beginning of an orbit. The ramp was very similar for all the orbits between the second and sixth, which we therefore averaged before fitting, but it was a different, stronger effect in the first orbit of a visit, which was fitted and corrected individually. In the final step, we corrected the spectra of all our objects by dividing the time-dependent data by the value of the analytical ramp function sampled at the times of the sub-reads. Figure 1 shows the ramp and its best-fit parameters. The latter are the following: for orbit 1: A = 0.0185 ± 0.0013, T = 5.95 ± 0.88, and C = 1.0005 ± 0.0005, while for orbits 2–6: A = 0.0077 ± 0.0009, T = 16.65 ± 6.02, and C = 1.0025 ± 0.0009. Note that these uncertainties include the propagated uncertainties from the slope correction described above. The combined uncertainties for the ramp correction lead to a 1σ uncertainty of ≃0.15%.

In the following, we briefly discuss the uncertainties of our measurements. We distinguish three different uncertainties that affect our data: random (white) noise emerging from photon noise and readout noise, systematic wavelength-dependent trends, and systematic time-dependent trends. As explained below, due to the fact that our targets are very bright by HST's standards the photon noise is very small (typically well below 0.1%) and the systematic wavelength-dependent trends are negligible, the residual time-dependent trends dominate the noise in our data. We characterize the amplitude of each of these three components based on our data.

2.3.1. White Noise

2.3.2. Time-dependent Trends

Both light curves contain distinct and prominent higher-frequency components. We interpret these variations as spots with different spectra rotating in and out of the visible hemispheres of the targets. We use the detailed data sets to identify the spectra and spatial distribution of these spots and contrast this information with predictions of state-of-the-art atmosphere models.

We identify the smallest set of independent spectra, over the mean spectrum, that account for the majority of the observed variance by applying a principal component analysis (PCA). We computed the covariance matrix of the spectral time series over wavelengths of 1.1–1.7 μm, cutting off lower signal-to-noise regions outside this range. Eigenvectors (E_i) and eigenvalues (Λ_i) of the covariance matrix were determined using the LA_PACK routine LA_EIGENQL in IDL. Components were sorted by eigenvalue, and the fractional contribution of each component to the overall variability is determined as Λ_i/(∑_iΛ_i), where the denominator is a sum over all eigenvalues.

Every observed spectrum at a given time, S(t), can then be approximated by a linear combination of the principal components,

$$\begin{equation} {\bf S}(t) \approx \langle {\bf S}\rangle + c_0(t){\bf E}_0 + c_1(t){\bf E}_1 + \cdots, \end{equation} \tag{ 1 }$$

where the series is truncated to include only components that contribute significantly above the noise level. The coefficients c_i(t) are given by projections of the principal components onto the observed S(t) − 〈S〉.

Perhaps surprisingly, variations of a single principal component account for 99.6% and 99.7% of the observed variability for 2M2139 and SIMP0136, respectively, with second components contributing at the 0.1% and 0.4% levels. In Figure 3, the mean spectrum and first two principal components (〈S〉, E₀, and E₁), as well as the time variability of the principal components (c_i(t)) are shown for both targets. In both cases, variations are given by S(t) ≈ 〈S〉 + c₀(t)E₀, where only a single principal component is required to account for most of the observed variability. This implies that only two dominant spectra contribute to the observed variations (e.g., take E₀ to represent the difference between two types of time-independent spectra S₂ − S₁), with the appearance of one "surface type" completely correlated with the disappearance of the other.

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Thus, our major conclusion is that only two types of "surface" patches (e.g., cloudy and clear, or thick and thin clouds) are required to explain the observations in both of these sources. This finding validates a simple light curve model, applied below, in which the photosphere is describe by a linear combination of two 1D model atmospheres differing in cloud thickness and/or temperature.

Next we search for the simplest physically plausible surface brightness model that explains the observed light curve. We model the surface brightness distributions using the self-developed genetic algorithm-optimized mapping routine Stratos (described in the Appendix in detail). The only assumption of the model is that it describes surface features as elliptical spots with their major axes parallel to the rotational direction, an assumption that is motivated by the common outcome of simulations of hydrodynamical turbulent flows in shallow water approximation (e.g., Cho & Polvani 1996). (We note here that our two targets, just like all solar system giant planets, will be rotationally dominated with a Rossby number R ≪ 1; Showman & Kaspi 2012). The input parameters of the model are the number of spots (i) and the number of different surface types allowed (2 in our case, as given by the PCA); the optimized parameters are the inclination and limb darkening of the brown dwarf, the surface brightness of each surface type, as well as five values for each spot (longitude, latitude, aspect ratio, area, and surface type). Possible solutions are ranked and optimized on the basis of their fitness, which we define as the reduced chi-square difference between the observed and predicted light curves.

Interestingly, for both 2M2139 and SIMP0136 we find that models with at least three spots are required to explain the structured light curves: models with only one or two elliptical spots failed to reproduce the observed light curves. In Figure 8, we show the best-fit model, a non-unique, but representative solution for 2M2139. Additional models with somewhat different surface distributions are shown in Figure 9. Although the solutions are somewhat degenerate (as discussed in the Appendix) the best solutions for 2M2139 all agree in the following: (1) the overall longitudinal spot covering fraction distribution is similar (between 20% and 30%); (2) at least three spots are required; (3) the surface brightness of the spots typically differ by a factor of two to three (either brighter or fainter) from the surface, corresponding to approximately ≃300 K difference in brightness temperature; and (4) the size of the largest spot extends about 60° in diameter. We note that more complex solutions with a higher number of spots are also possible, but these replace the larger spots with groups of smaller spots, without changing the general properties identified above.

An important property of all solutions is the presence of very extended spots or spot groups in the photosphere, which raises the question whether such large structures can exist in the fast-rotating, warm brown dwarfs. As for Jupiter, the gradient of the Coriolis force on our rotating targets is expected to break the atmospheric circulation into parallel jet systems (belts), which will limit the maximum size of continuous atmospheric structures. Here, we use the Rhines scale (e.g., Showman et al. 2011) to estimate the relative number of jet systems between our fast-rotating and slowly rotating sources: N_jet ≃ (2Ω × a/U)^1/2, where Ω is the angular velocity, a is the brown dwarf radius, and U is the wind speed. If the maximum size of a feature (s_i) is limited by the jet width, the relative maximum spot sizes for two sources will be given by

$$\begin{equation} \frac{s_1}{s_2} = \frac{ \pi / N_{{\rm jet},1}}{ \pi / N_{{\rm jet},2} } = \left(\frac{\Omega _1 a_1 U_2}{\Omega _2 a_2 U_1} \right)^{1/2}. \end{equation} \tag{ 2 }$$

Further, for both sources a₁ and a₂ should closely approach 1 R_Jup. If we assume that the wind speeds (U₁ and U₂) are similar in these two T2 dwarfs, the relative spot sizes in Equation (2) will be simply approximated by s₁/s₂ = (P₂/P₁)², arguing for ∼3.2× larger maximum spot surfaces on 2M2139 than on SIMP0136, in line with the larger amplitudes observed.

Based on the above considerations, we can also estimate the physical spot sizes. Although wind speeds are not known for brown dwarfs, in the following we explore the possible range. In estimating wind speeds only a few reference points are available: while the highest wind speeds (U ≃ 2 km s⁻¹) yet have been observed in the upper atmospheres of heavily irradiated hot Jupiters (e.g., Snellen et al. 2010), much lower wind speeds are typical for the cooler and only weakly irradiated atmospheres of solar system planets (typically 40–100 m s⁻¹, but up to ≃300 m s⁻¹ in Saturn). For a discussion on how brown dwarf circulation may fit in this picture we refer the reader to Showman & Kaspi (2012). We will now assume two bracketing cases: U = 100 m s⁻¹ (Jupiter-like) and U = 1000 m s⁻¹ (hot Jupiter-like). Our simple approximation with the low and high wind speeds would suggest N_jet ≃ 17 and N_jet ≃ 5, respectively, for the slowly rotating 2M2139 and N_jet ≃ 32 and N_jet ≃ 10, respectively, for the rapidly rotating SIMP0136. These values correspond to maximum latitudinal spot diameters of ≃ 10° and ≃ 36° for 2M2139, and ≃ 6° and ≃ 18° for SIMP0136. Thus, slower, Jupiter-like wind speeds would lead in small maximum features sizes (6°–10°), while high speeds would allow larger features (18°–36°). While we cannot accurately determine the wind speeds in our targets, the fact that these sources show large-amplitude variations emerging from large regions across their photospheres argues for wind speeds that are higher than those typical to Jupiter.

The simple predictions described above are consistent with the much larger variation seen in the slowly rotating 2M2139 than in its faster-rotating sibling and the predicted maximum spot sizes are similar to the size of the largest spots predicted by the best-fit light curve models of 2M2139 (Figure 2). With more data on varying brown dwarfs, a realistic treatment of the atmospheric circulation will be possible, replacing the simple argument introduced above.

Even the most capable state-of-the-art ultracool model atmospheres provide only imperfect fits to the fine structure of brown dwarf spectra; therefore, the full interpretation of our very high signal-to-noise spectral series is constrained by the fact that no existing model can accurately describe atmospheres at sub-percent accuracy. Nevertheless, the existing models can be used to explore the types of changes required to account for the observed color/magnitude variations. We proceed by identifying the best-fit atmosphere models for our two targets with the assumption that these models would well describe the dominant surface type on the targets. Then we explore what secondary surface types have to be added to account for the observed color–magnitude variations by adding a second model atmosphere.

We base our analysis on the state-of-the-art radiative–convective model atmospheres in and out of chemical equilibrium described in Burrows et al. (2006) and Madhusudhan et al. (2011), but also used an independent set of models by Allard et al. (2011) to verify that our conclusions are model-independent. The Burrows models include different empirical descriptions of the vertical structures of clouds of different condensates (Burrows et al. 2006). For each condensate, the vertical particle distribution is approximated by a combination of a flat cloud shape function and exponential falloffs at the high- and low-pressure ends. The cloud altitudes are defined by the intersects of the temperature–pressure profile and the condensation curves. The tested models included cloud shape functions with constant vertical distribution of particles above the cloud base (B-clouds, qualitatively consistent with the DUSTY models described in Allard et al. 2001), and different parameterizations of the generic cloud shape function (A, C, D, E in Burrows et al. 2006). Of particular interest is cloud type E, a generic cloud with very steep exponential falloffs corresponding to thin clouds thought to be typical to clouds composed of a single refractory condensate's large grains.

The spectra we explored ranged in temperature from 600 K to 1800 K with steps of 100 K, included solar and 10× sub-solar metallicities, and log g = 4.0 and 5.0 for the Burrows et al. (2006) models and log g = 4.0, 4.5, and 5.0 for the Allard et al. (2001) models. Figure 4 shows our two targets and the best-fit spectra and templates. The upper models are from the BT-SETTL series from Allard et al. (2011), which we plot for comparison, while the lower curves are model calculations based on models described in Madhusudhan et al. (2011). The field brown dwarf spectral templates are from Leggett et al. (2000) and Chiu et al. (2006). We find that for 2M2139 the best-matching spectral template is a T2-type template, while for SIMP0136 a T2.5 provides a good match.

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Both sources can be fit well with a BT-SETTL model in local thermodynamical equilibrium and an effective temperature of 1200 K, but fitting the spectrum of 2M2139 requires a lower surface gravity (log g = 4.5) than SIMP0136, which is better matched by a higher surface gravity model (log g = 5.0). Fits with the Burrows models suggest slightly lower temperatures. Given the coarser spacing of the surface gravity grid of the Burrows models we used log g = 4.0 for 2M2139 and log g = 5.0 for SIMP0136. Although the lower surface gravity fits better our spectra, due to its limited wavelength coverage we take these log g values as comparative but do not argue that they represent accurate characterization of the surface gravity (see also, e.g., Cushing et al. 2008 for the difficulty of determining precise atmospheric parameters from single-band spectroscopy). The modal grain sizes are an adjustable parameter in the Burrows models and models with large grains provided the best match for 2M2139. We note that this model comparison is based on peak-to-valley normalized spectra, i.e., it focuses on the spectral shape rather than the absolute J, H brightnesses—we do so because our sources show strong J-, H-band variations and only weak variations in the spectral shape.

After establishing the best-fit starting model for the two sources, we explore what secondary surface type is required to explain the observed color–magnitude variations. Our tool for this step is the near-infrared color–magnitude diagram (CMD) shown in Figure 5. Here, we plotted a full sequence of L/T dwarfs using the parallax and near-infrared photometric database by Dupuy & Liu (2012). Fully cloudy L-type brown dwarfs typically appear bright and red, while the dust-free atmospheres of T-type brown dwarfs are blue and faint. Transition objects are seen to show brighter J-band magnitudes with later spectral types before an eventual turn to the clear T-dwarf sequence (Dahn et al. 2002; Tinney et al. 2003; Vrba et al. 2004).

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Next, we tried to vary each model parameter separately to assess its effect with the observed variations. We found that no combination of models with a difference only in a single parameter (temperature, cloud scale height, and the presence or the absence of cloud layer) can introduce the observed changes (see dashed black lines lower right panel in Figure 5): the tracks along which the source would vary on the CMD if such a secondary surface type would be added is clearly inconsistent with the actual variations. The same conclusion was reached by Artigau et al. (2009) for SIMP0136 based on comparison of models by Allard et al. (2003) and Tsuji (2005) to their ground-based ΔJ/ΔK observations and by Radigan et al. (2012) for 2M2139 through comparison to models by Saumon & Marley (2008).

We next explored correlated changes in parameter pairs. We found that correlated changes in cloud scale height and temperature are required (green dashed lines in Figure 5). By allowing these two model parameters to vary together we find that thin clouds in combination with large patches of cold and thick clouds (i.e., T_eff = 1100 K models with E-type clouds and 800 K B-type clouds, green dashed lines) can explain well the observed color–magnitude variations (blue and red crosses).

This solution requires about 300 K temperature difference between the spots and the surface, fully consistent with the factor of three surface brightness change predicted by our light curve shape model. Our models also predict the relative surface covering fraction for the thin and thick clouds (given as percentages in Figure 5), which are also consistent with the surface model shown in Figure 8.

We note that qualitatively similar results were obtained for 2M2139 using a ground-based photometric data set and models of Saumon & Marley (2008) by Radigan et al. (2012).

Because of the richness of possible condensates in brown dwarf atmospheres one may expect a complex mix of cloud properties, composition, and cloud scale height to be represented even within a single brown dwarf atmosphere. The observational fingerprint of such surface complexity in a rotating brown dwarf would be multi-component, complex changes in the spectra, brightness, and color. In stark contrast, the two sources observed show a single distinct type of simple change. This is reflected, for example, in the single-direction track in the CMD (Figure 5). The PCA analysis (see Section 3.1) reveals that all the observed variance in the two sources can be reproduced with the combination of only two different spectra. This surprising result shows that all major features in the visible photosphere, although distributed across both hemispheres of each target, share the same spectra (i.e., same deviation from the mean spectrum).

We note that based on spectral fits from composite near-infrared spectra Burgasser et al. (2010) has identified 2M2139 as a strong candidate for being an unresolved binary brown dwarf. These authors argue that 2M2139 could be matched better, although imperfectly, by a blend of an L7–L9.5 and a T3.5–T4.0 binary than by any single template brown dwarf. It is tempting to consider the possibility that the fit by two blended spectra in this case is not the sign of an unresolved binary, but instead emerges from the blend of two different surface types on the source (as also proposed by Khandrika et al. 2013; Radigan et al. 2012)—one with a spectrum of an L8.5 ± 0.7 dwarf, the other with a spectrum of a T3.5 ± 1.0 dwarf. However, this explanation is unlikely to be correct. A composite spectrum of two such dwarfs with time-varying weights due to the rotation would introduce J versus J–H color variations in the direction of the L–T transition, very different from what we observed (see Figure 5).

The fact that flux density in the observed molecular bands—with the exception of the less-changing water band—varies together and at the same rate as the continuum shows that the opacity variations in the targets cannot originate from changes in the abundances of the common gas-phase absorbers, such as methane. Based on comparison to atmosphere models we argue that these spots are patches of very thick clouds. The fact that any two such cloud patches would share the same spectra, different from the dominant spectrum of the sources, argues for the presence of a single mechanism to form these thick cloud patches. Possibilities, as explored below, include circulation and large-scale vertical mixing.

With our surface mapping tools (see Section 3.2) we find that both sources have relatively complex surface brightness distributions: assuming elliptical spots, no one- or two-spot model can reproduce the structure of the light curves. While our model is not able to deduce the precise appearance of the photosphere, it provides useful insights into the complexity and overall distribution of the thick cloud patches observed. Specifically, the light curve and our models reveal that a large fraction of the surface of both targets is covered by the cloud patches. These patches may be very large single structures (corresponding to our simplest model) or they may be super-structures, consisting of dozens or even hundreds of smaller cloud patches with the same surface covering fractions. Whether single or complex structures, however, any mechanism that explains the spectral appearance and high cloud scale height, needs to account for the concentration of these patches on the surface of the targeted brown dwarfs.

We note here that the light curve modeling is only sensitive to the varying surface components, because homogeneously distributed features will not introduce brightness variations. Thus, it is likely that the large patches deduced from the light curve are not the only features present in the photosphere. Reinforcing this possibility is the fact that color–magnitude modeling based on model atmospheres (Section 3.3) suggests similar level of asymmetry but on top of a more symmetric component. According to the best-fit model atmosphere combination, the fraction of surface covered by thick clouds varies from about 50%–63% on the visible 2M2139, while it occupies only 25%–29% of the surface of SIMP0136 (see Figure 5). Thus, the modeling suggests that most of 2M2139's surface is covered by thick clouds with large thin patches (that are brighter and contribute most of the observed emission), while SIMP0136 has an overall thin cloud layer with large patches of thick clouds. Although the covering fractions are different, based on the overall similarity of the spectra and the spectral variations these two sources have very similar thin and thick cloud layers.

The complex distribution of otherwise similar or identical thick cloud patches also offers opportunity for further exploration of the dynamics of brown dwarf atmospheres. Cloud structures are subject to multiple dynamical processes and are likely to evolve on a broad range of timescales. For example, the structure of the light curves may evolve due to differential rotation, an effect that should be observable with high-precision data set covering sufficient baselines. Other processes, such as thick cloud formation (i.e., rapid increase of the cloud scale height) or the reverse of this process, rain out of the condensate grains, may also result in changes over relatively short timescales.

A leading hypothesis to explain the dramatic spectral changes observed to occur at the L/T transition invokes a breaking apart of the cloud cover (e.g., Ackerman & Marley 2001; Burgasser et al. 2002). This idea provided motivation for our initial observations, and predicts surfaces consisting of clouds and holes that act as windows into the deeper photosphere. The most simple picture, and the one that has been explored by models (Burgasser et al. 2002; Marley et al. 2010), is one where holes in the cloud layer represent pure clearings, 100% free of condensate opacity. In contrast to this assumption, our observations of two of the most variable brown dwarfs suggest that dark and bright regions of the photosphere represent thick and thin cloud regions rather than cloudy and cloud-free regions (Section 3.3). This may reflect holes in a thick cloud layer that look down into a thinner cloud layer. More generally, our observations argue for a more complex picture of cloud heterogeneities than envisioned with simple cloudy and cloud-free models. A similar conclusion was arrived at by Radigan et al. (2012), who found that JHK photometric monitoring of 2M2139 was inconsistent with the presence of cloud-free regions, based on models of Saumon & Marley (2008). Thus, both photometric observations out to the K band and spectroscopic observations from 1 to 1.7 μm argue against the existence of cloud-free regions.

We also found that the cloud thickness variations are correlated with changes in the effective temperature of the secondary model. This correlation is not surprising: the higher the dust scale height, the shallower the pressures and the lower the temperatures visible to the external observer (see Figure 6). This correlation, thus, argues for patches of thick clouds towering over the otherwise thinner cloud layer covering most of the hemispheres of the targets.

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The vertical structure and composition of these thick clouds is an exciting question, albeit one our current data do not constrain well. Recently, Buenzli et al. (2012) have shown that by combining data over a broad wavelength range—where different wavelengths probe different atmospheric depths—the vertical structures of the clouds can be explored. In their study five atmospheric layers of a T6.5 dwarf's were sampled by obtaining five complete light curves at depths ranging from 0.1 to ∼10 bar. An important and surprising result of their study was a significant and pressure-dependent phase difference in the atmosphere with the largest phase shift observed at the deepest level exceeding 180°. While a full analysis like that carried out by Buenzli et al. (2012) is beyond the scope of this paper, we show in Figure 7 that the same narrowband light curves as used by those authors, when extracted from our spectral series, show no significant phase shift. Thus, while the results of the T6.5 brown dwarf suggest correlated large-scale vertical–horizontal structures, the two early-T dwarfs studied here show similar cloud structures at different layers without phase differences.

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The remarkable cloud scale height variations in our targets demonstrate how this parameter affects the brightness of ultracool atmospheres. Thick clouds persisting at temperatures lower than typical for brown dwarfs have been proposed as one of the processes that may explain the apparent underluminosity of directly imaged giant exoplanets compared to brown dwarfs with similar spectral morphology (magenta crosses in Figure 5; see also Skemer et al. 2012; Barman et al. 2011a, 2011b; Currie et al. 2011; Madhusudhan et al. 2011; Marley et al. 2012). Several authors propose that such unusually thick clouds would be present in directly imaged exoplanets due to the low surface gravities of these sources, which provides an attractive and self-consistent explanation for the appearance and low occurrence rate of these sources. However, the effects of thick clouds remained difficult to verify, as multiple parameters (metallicity, surface gravity, age, mass, chemistry, and cloud structure) vary simultaneously between any two ultracool atmosphere. The novelty of our observations is that they are comparing different cloud structures within the same atmospheres, i.e., keeping metallicity, surface gravity, age, mass, and bulk composition constant. This allows the effects of cloud structure to be isolated. We note that a minor caveat here is that the pressure–temperature profile of atmospheres with large spots may differ from those with only thick or thin clouds; thus, the thick clouds' impact must be evaluated keeping this possible difference in mind.

We can explore the effect the thick clouds would have by extending their surface covering fraction in our model beyond that observed in our targets, i.e., by increasing the surface covering fractions of the thick cloud patches to values approaching 100%. The resulting green dashed line in Figure 5 shows that increasing thick cloud coverage will produce color–magnitude tracks crossing the positions of the directly imaged planets (magenta crosses). Thus, if the thick cloud patches we observed in the atmospheres of our T2 targets would cover their complete or near-complete atmospheres, their near-infrared brightness and colors would provide a good match to the directly imaged exoplanets. These results lend support to the models in which the peculiar color and brightness of exoplanets is introduced by thick clouds, but we note that in this work no attempt was made to match the spectra predicted by our simple models to those observed by exoplanets. While our observations cannot identify the cause for the thick clouds in exoplanets, we expect that any successful model for the thick clouds in faint and red exoplanet atmospheres will also provide an explanation for the coexistence of thin and thick clouds in L/T transition brown dwarfs.

Our observations provide exceptionally high signal-to-noise spectra that probe spectral variations within the photospheres of brown dwarfs. The accuracy of this data set is high enough that finding a perfect match (<1%) with existing atmosphere models was not possible, demonstrating the limitations of the existing models. Although the best-fit spectra match the mean spectrum to typically within 5%–10% in the spectral range studied, which are typically considered to be good fits for brown dwarf atmospheres, these differences are comparable to or larger than the amplitude of changes we observe in our spectral series. Therefore, the accuracy of the existing models used in this paper did not allow meaningful modeling of the entire spectral series yet. Instead, in our modeling procedure we started from atmosphere models that provided best fits to the mean spectra of the targets and then explored their color variations. Our approach to model a patchy cloud cover with a linear combination of independent 1D models is imperfect and it is likely not physically self-consistent due to the somewhat different pressure–temperature profiles of these models (e.g., Marley et al. 2010, 2012).

It is worthwhile to briefly explore the limitations of current models and potential pathways to improve them. Arguably, the key limitations are the incomplete molecular opacity databases and the fundamentally 1D nature of most atmosphere models. Expanding and refining the opacity databases relies on the continuation of ongoing laboratory and theoretical efforts and not limited by the observations of ultracool atmospheres. In contrast, constraining and further developing two- or three-dimensional models (e.g., Freytag et al. 2010) will require more accurate data sets and, in particular, data sets that provide spectrally and spatially resolved information. We anticipate that the brown dwarf spectral mapping technique introduced in this paper will lead to a major step in testing and refining physically realistic models of cloud formation and cloud structure (e.g., Helling et al. 2008a, 2008b) and atmospheric dynamics (Freytag et al. 2010; Showman & Kaspi 2012)

In this paper we also applied a method, spectral mapping, to a new class of objects, ultracool atmospheres. As a new method for this field we now briefly discuss its potential and future uses. Photometric phase mapping has been proposed early on to reach spatial information beyond the diffraction limit (e.g., Russell 1906). Since then, different variants of this idea have been used successfully to derive asteroid shapes from photometry (e.g., Kaasalainen et al. 2001; Kaasalainen & Viikinkoski 2012), to map their surface composition from spectral mapping (e.g., Binzel et al. 1995), to map starspots via photometry and Doppler imaging (e.g., Budding 1977; Vogt et al. 1987; Lüftinger et al. 2010), and to translate precision Spitzer photometry to one-dimensional and two-dimensional brightness distributions for hot Jupiters (e.g., Knutson et al. 2007; Cowan et al. 2012; Majeau et al. 2012). Similarly to the hot Jupiter studies, in an upcoming study, Heinze et al. (2013) use precision Spitzer photometry complemented by ground-based near-infrared light curve to explore cloud properties on an early L-dwarf. Most recently, Buenzli et al. (2012) have found pressure-dependent phase shifts in multi-band light curves extracted from the HST spectral series and a Spitzer 4.5 μm light curve of a T6.5 brown dwarf, revealing vertical structure in an ultracool atmosphere for the first time.

The method used here is a logical next step in these brown dwarf studies, where a large time-resolved spectral set is used to identify the diversity, spatial distribution, and spectra of the key photospheric features. Further similar studies with space-based instruments on HST and Spitzer, complemented by sensitive ground-based photometric observations, will allow obtaining data similar to those presented here on brown dwarfs covering a much broader range of atmospheric parameters. Such a data set will allow the exploration of the properties of cloud cover with spectral type, surface gravity, and rotation period, an important step toward establishing a physically consistent picture of condensate clouds. Next-generation adaptive optics systems will also be capable of measuring relatively small photometric variations in directly imaged giant exoplanets, allowing comparative studies of brown dwarfs and extrasolar giant planets (Kostov & Apai 2012).

The changes observed in SIMP0136, first reported in Artigau et al. (2009) and also seen in our Figure 2, also highlight another exciting question. Cloud covers in some brown dwarfs clearly change on very short timescales on very significant levels, offering an opportunity to study the atmospheric dynamics of ultracool atmospheres via multi-epoch, multi-timescale, and multi-wavelength observations.

Spectral mapping is set to be a powerful new method not only to characterize brown dwarf atmospheres, but also extrasolar planets.