CLOUDLESS ATMOSPHERES FOR L/T DWARFS AND EXTRASOLAR GIANT PLANETS

The role of clouds in brown dwarf (BD) and extrasolar giant planet (EGP) atmospheres has been an intense subject of research for the past 20 years since the first observations of these objects (e.g., Tsuji et al. 1996; Ackerman & Marley 2001; Allard et al. 2001; Burrows et al. 2006; Marley et al. 2010; Morley et al. 2014). While cloudy atmosphere models reproduce the observed reddening in infrared (IR) J–H and J–K colors (Allard et al. 2001; Burrows et al. 2006; Saumon & Marley 2008), several problems remain unsolved:

• 1.  
  The driving mechanism of the cloud dynamics remains poorly understood. Although convective overshooting has been proposed for such a mechanism (Freytag et al. 2010), the low variability of early L dwarfs (Metchev et al. 2015 and references therein), which points to a relatively steady process, seems incompatible with the transient nature of overshooting. Furthermore, the change of regime in this mechanism and the sharpness in effective temperature of the LT transition, in short, the very physical nature of this transition, remain so far unexplained.
• 2.  
  Neither the J-band brightening nor the FeH resurgence at the L/T transition are understood. Although holes in the cloud cover can reproduce these features (Ackerman & Marley 2001; Burgasser et al. 2002; Marley et al. 2010), Buenzli et al. (2015) recently showed that the variability of the spectrum is not compatible with holes but rather with height variations. The conclusion of Buenzli et al. (2015) is indeed that the explanation for the re-emergence of FeH still remains to be found.
• 3.  
  The absorption feature at 10 μm is not well reproduced with the current cloud models. Although some observations do suggest the presence of silicate dust (Cushing et al. 2006), the absorption feature is not present in all observed spectra, and for the ones that display it (e.g., 2M224, 2M0036, 2M1507, and 2M2244 in Stephens et al. 2009), cloud models cannot reproduce both the NIR reddening and the 10 μm absorption.
• 4.  
  Signatures of cloud polarization expected from cloud models remain undetected (Goldman et al. 2009). Even though L dwarfs might not rotate fast enough nor have low enough surface gravity to be sufficiently oblate to produce detectable polarization (Sengupta & Marley 2010), this lack of detection questions the cloud hypothesis.

In Tremblin et al. (2015), we showed that the spectra and near-IR colors of T and Y dwarfs can be reproduced without clouds if (i) non-equilibrium chemistry of NH₃ is taken into account, and (ii) the temperature gradient in the atmospheres of T dwarfs is reduced. In this Letter, we explore a similar mechanism for L dwarfs and hot EGPs, using Denis-P 0255 and HR8799c, respectively, as typical templates, and we show that these effects adequately reproduce both the FeH resurgence and the J-band brightening at the L/T transition. We show that a physical process responsible for the temperature gradient reduction in L and T dwarf atmospheres is the chemical or (compositional) convection triggered by a thermo-chemical instability at the CO/CH₄ and N₂/NH₃ transitions. Finally, we discuss the implications and the limitations of this scenario.

We use the same setup as described in Tremblin et al. (2015), i.e., a 1D spectral code ATMO with correlated-k coefficients for the radiative transfer, developed and tested in Amundsen et al. (2014), coupled to the CHNO-based chemical network of Venot et al. (2012). We improved our chemical and opacity database with the inclusion of the FeH molecule and used Wende et al. (2010) for the line list, Sharp & Burrows (2007) for the broadening coefficients, and Visscher et al. (2010) for the chemical equilibrium of FeH. In Tremblin et al. (2015), we applied the calculations to T dwarfs and showed that a reduced temperature gradient in the atmosphere, as reproduced with an effective adiabatic index ($\gamma \quad \sim$ 1.2–1.3) lower than the equilibrium value ($\gamma \quad \sim$ 1.3–1.4), correctly reproduces the observed spectra and the reddening in J–H colors, yielding a synthetic spectrum similar to the one with the inclusion of clouds (Morley et al. 2012). We have explored these effects on the EGP HR8799c (Figure 1) and the L dwarf Denis-P 0255 (Figure 2). As seen in Figures 1 and 2, the models reproduce the observed spectra very well provided that (i) we include non-equilibrium chemistry and quench CO/CH₄ (i.e., prevent the formation of CH₄),   and (ii) we decrease the adiabatic index to $\gamma \quad \sim$ 1.05 in the lower part of their atmospheres. The only difference with the T dwarf modeling of Tremblin et al. (2015) is that we modify the adiabatic index only within the layers corresponding to the emerging flux bands. The global effect of the modification of the adiabatic index along the L sequence and the L/T transition is shown in Figure 3, and the modified layers are indicated in the pressure/temperature (PT) profiles in Figure 4.

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The data for HR8799c are taken from Oppenheimer et al. (2013), Ingraham et al. (2014), and Skemer et al. (2014). In Figure 1, the blue spectrum is the out-of-equilibrium model obtained with a value of the turbulent diffusion coefficient K_zz = 10¹¹ cm² s⁻¹. Such a high value is consistent with the convective velocities computed in the model for these low gravities. The 3.78 μm flux is higher in our model, but PH₃ opacity could be significant around 4 μm and is not included in our models (see Morley et al. 2014). Our out-of-equilibrium cloudless model with a modified adiabatic index provides a better fit to the NIR data between 1 and 2 μm compared to the cloud models (Ingraham et al. 2014). The effective temperature, surface gravity, and radius we derive are compatible with evolutionary models (Baraffe et al. 2003) and suggest a lower-mass, younger object (3 M_Jup at 10 M_years) than previous studies. Since we used a higher metallicity, however, different C/O ratios could also lead to a good fit with slightly different values of effective temperature, surface gravity, and radius. These effects need to be investigated in greater detail in follow-up studies.

The spectrum of Denis-P 0255 was obtained from Cushing et al. (2005). This object is a typical late-type L dwarf (L8) that has a characteristic reddening in J–H and J–K. The model we used includes a zone with a modified adiabatic index γ = 1.05 in the deep atmosphere. As a result, the atmospheric profile has cooler deep layers and hotter upper ones than the equilibrium atmosphere (see Figure 4). As a consequence, the fluxes in the Y and J bands are reduced and the ones in the H and K bands are enhanced. The modeled spectrum shows that this effect adequately reproduces the main characteristics of the data, provided CH₄ is still reduced compared to the equilibrium value (now with a value of K_zz = 10${}^{7.5}$ cm² s⁻¹, consistent, again, with the convective velocities computed in the model for these gravities). The effect is similar to what was inferred in Tremblin et al. (2015) for T dwarfs at the N₂/NH₃ transition. L dwarfs just require a lower value of the adiabatic index in order to produce a stronger reddening.

From our T dwarf modeling in Tremblin et al. (2015), it was unclear whether the need to use cooler deep atmospheric layers was due to a real effect (fingering convection) or was rather a way to mimic the effect of clouds. The left panel of Figure 3 displays the evolution of the spectrum along the L sequence (from T_eff = 1600–1400 K). As expected, we clearly see a weakening of the FeH spectral signature as a function of decreasing effective temperature. The right panel of Figure 3 illustrates the evolution of the spectrum at constant T_eff (=1400 K) along the L/T transition when varying the modified adiabatic index from a value of γ = 1.05 for L dwarfs, to γ = 1.2–1.3 for early T dwarfs. Observations (Golimowski et al. 2004) indeed suggest that the L/T transition occurs at a relatively constant effective temperature. Figure 3 clearly shows that along this transition our models naturally yield a resurgence of the FeH absorption feature and a brightening of the J-band flux similar to what was found in observations.

The L dwarf reddening is due to cooler deep atmospheric layers than the ones corresponding to a radiatively stable atmosphere, a consequence, as detailed in the next section, of the enhanced energy transport due to local chemical turbulence, triggered by the thermo-chemical instability. As one moves toward cooler atmospheres when transitioning toward T dwarfs, the instability vanishes. Turbulent dissipation warms up the deep atmosphere, steepening the temperature gradient (yielding a larger effective adiabatic index) and increasing the FeH abundance and the flux in these hotter layers, compared to the L dwarf profile. This global effect is illustrated in Figure 4. Along the L sequence, the atmospheric profiles keep cooling down, notably in the deeper layers (P ≥ 1 bar), due to the smaller thermal gradient (i.e., the smaller effective adiabatic index). Along the L/T transition, the deep layers warm up, yielding a steeper temperature gradient, while the upper layers keep cooling down. An alternative suggested scenario to explain the resurgence of FeH and the J-band brightening is holes in the cloud cover (Ackerman & Marley 2001; Burgasser et al. 2002; Marley et al. 2010), although it appears to be partly excluded by Buenzli et al. (2015). We suggest, rather, that the proper explanation for these puzzling spectral behaviors is (i) cooler deep atmospheres for L dwarfs than obtained with cloudy atmospheres, the conventional explanation for the past 20 years, yielding the J–H and J–K reddening, and (ii) a warming up of the deep layers at the L–T transition, due to small-scale turbulent dissipation, which explains both the FeH resurgence and the J-band brightening.

Although we have a model that can reproduce all the observed effects, we need an explanation for the change in the modified adiabatic index and the transition from γ = 1.05 to 1.2–1.3. In Tremblin et al. (2015), we proposed that small-scale "diffusive" turbulence, more efficient than radiative transport, induced by fingering convection triggered by thin dust condensation, would be responsible for the decrease of the temperature gradient. We revisit this scenario and suggest that the real culprit is the instability of carbon and nitrogen chemistry in BD and EGP atmospheres. Within the temperature range of interest, carbon is preferentially in the form of CO at high temperature and of CH₄ at low temperature. Similarly, nitrogen changes from N₂ at high temperature to NH₃ at low temperature. The net reactions for these transitions are

$$\begin{eqnarray}\mathrm{CO}+3{{\rm{H}}}_{2} & \to & {\mathrm{CH}}_{4}+{{\rm{H}}}_{2}{\rm{O}}\\ {{\rm{N}}}_{2}+3{{\rm{H}}}_{2} & \to & 2{\mathrm{NH}}_{3}.\end{eqnarray} \tag{ 1 }$$

It is quite clear that the part of the atmosphere in the methane or ammonia dominant state will have a higher mean molecular weight than the corresponding CO- or N₂-dominated one since there are globally fewer molecules in these latter states. On the other hand, it is well known from chemical network studies that the chemistry for these transitions can be very slow (Moses et al. 2011; Venot et al. 2012). Therefore, atmospheres with these chemical transitions can develop an instability similar in nature to fingering double diffusive convection, but with the chemical reactions themselves now playing the role played otherwise by molecular diffusion, leading to a thermo-chemical instability. The analogy is as follows: at the CH₄/CO transition, if a perturbation drives some "CH₄+H₂O" mixture down in the "CO+3 H₂" (warmer) deeper layers, and if we are in the stable radiative part of the atmosphere because of the slowness of the chemical reaction, the mixture will stay in its methane-rich state and sink because of its higher molecular weight. The same process can happen at the N₂/NH₃ transition. The extent of the unstable zone can be estimated by using an extension of the Ledoux criterion (Rosenblum et al. 2011):

$$\begin{eqnarray}&&{R}_{0}=\displaystyle \frac{{{\rm{\nabla }}}_{T}-{{\rm{\nabla }}}_{\mathrm{ad}}}{{{\rm{\nabla }}}_{\mu }}\lt \displaystyle \frac{1}{\tau }=\displaystyle \frac{{\kappa }_{T}}{{l}^{2}/{\tau }_{\mathrm{chem}}}.\end{eqnarray} \tag{ 2 }$$

We have replaced the usual molecular diffusion coefficient by ${l}^{2}/{\tau }_{\mathrm{chem}}$ with ${\tau }_{\mathrm{chem}}$, the timescale of the chemical reaction and l, the typical size of the unstable structures. We have computed the timescales for the reactions using the equations given by Zahnle & Marley (2014), and we assumed that the typical size of the unstable structures is 1% of the scale height (see Traxler et al. 2011 for a discussion on the size of the fingers expected in the stellar context). In order to be conservative, we use an upper limit for R₀, given by ${R}_{\mathrm{max}}={{\rm{\nabla }}}_{\mathrm{ad}}/| {{\rm{\nabla }}}_{\mu }|$. The unstable regions are portrayed in the top panel of Figure 5 for the CO/CH₄ chemistry in an L dwarf at T_eff = 1400 K and for the N₂/NH₃ chemistry for a T dwarf at T_eff = 600 K. For simplicity, we derived the mean molecular weight gradient ${{\rm{\nabla }}}_{\mu }$ from the difference between a full ammonia or methane state and a full CO or N₂ state over one scale height H, reduced by a factor l/H (i.e., ${{\rm{\nabla }}}_{\mu }\quad \sim$ –10⁻⁵ for CO/CH₄ and ${{\rm{\nabla }}}_{\mu }\quad \sim$ –10⁻⁶ for N₂/NH₃). The top panel of Figure 5 shows that the chemical transitions in all the upper atmosphere of a L or T dwarf are unstable because of the slow chemistry. In the bottom panel of Figure 5, we compare the color–magnitude diagram (CMD) M_J versus J–H obtained with the equilibrium models and with the models with out-of-equilibrium chemistry and a modified adiabatic index. As for the T dwarfs in Tremblin et al. (2015), the L dwarf reddening is well reproduced in the CMD with the temperature gradient reduction. Other CMDs with the NIR bands Y, J, H, and K give a similar good match between our models and the observations since, as shown in Figure 2, the NIR spectra are well reproduced. We also illustrate the transition from L to T with a model at constant effective temperature and an adiabatic index varying from 1.05 (L) to 1.25 (T) (orange line in Figure 5). This highlights the occurrence of the J-band brightening in our (cloudless) 1D models, even though a detailed sequence based on consistent evolutionary models is needed to properly take into account the evolution of gravity, effective temperature, and modified adiabatic index. This will be explored in a forthcoming paper. We indicate the domains where the CO/CH₄ and N₂/NH₃ transitions are predicted to be unstable. The sharpness of the limits corresponding to the instability, according to the above modified Ledoux criterion, naturally explains the sharpness of the L/T transition. Indeed, as temperature decreases, reaching the later T dwarf regime, the CO/CH₄ transition will lie at deeper levels than the ones subject to the instability, so that the now CH₄-dominated atmosphere will become stable again, as the chemical reaction timescale ${\tau }_{\mathrm{chem}}$ becomes shorter than the radiative timescale. This does not preclude, however, the presence of some (quenched) CH₄ in the upper layers of L dwarf atmospheres.

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In this paper, we show that:

• 1.  
  Conditions characteristic of the atmospheres of L dwarfs favor the onset of a thermo-chemical instability at the CO/CH₄ transition, while conditions typical of T dwarf atmospheres yield the same instability at the N₂/NH₃ transition. The instability is due to the development of a destabilizing molecular weight gradient induced by the slowness of these chemical equilibrium reactions. This gradient generates local chemical (compositional) convection, which decreases the temperature gradient in the atmosphere.
• 2.  
  The spectra of L dwarfs and hot EGPs is well reproduced if (i) the temperature gradient in the atmosphere is decreased because of the aforementioned instability, and (ii) if the quenching of CH₄ at the CO/CH₄ transition is taken into account. The same picture applies to T dwarfs, with quenching of NH₃ at the N₂/NH₃ transition.
• 3.  
  As the instability vanishes along the L/T transition, small-scale turbulent dissipation warms up the deep layers and thus increases the temperature gradient in the atmosphere. This naturally explains the so far unexplained FeH resurgence and J-band brightening in early T dwarfs.

A detailed numerical analysis of the instability is certainly needed to determine the growth rate and the size of the most unstable mode and thus the typical time and space scales of the instability. The efficiency of the induced small-scale turbulent energy transport and dissipation also need to be determined in order to properly quantify (i) the modified adiabatic index, and (ii) the amount of turbulent heating that yields an increase of temperature in the deep atmospheric layers at the L/T transition. Such studies require non-trivial numerical explorations.

Although by no means providing a proof, several features bring support to the reality of this instability. First, its disappearance when the atmosphere becomes stable again (according to condition 2) could explain the sharpness in effective temperature of the L/T transition. Second, turbulent energy transport, triggered by the instability of the CO/CH₄ and N₂/NH₃ transitions, decreases the temperature gradient in the atmosphere, leading to the reddening of L and T dwarfs, respectively. Third, the strength of the instability being intrinsically linked to the magnitude of the mean molecular weight gradient and the fact that the gradient associated with the CO/CH₄ transition is larger than the one at the N₂/NH₃ transition (because of the C/N ∼ 4 abundance ratio Asplund et al. 2009) explains the stronger reddening for L dwarfs than for T dwarfs. Fourth, the turbulence induced by CO or temperature fluctuations in the atmosphere during the transition from CO to CH4 at the L/T transition could explain the observed variability. Thus, the fluctuations observed by Doppler imaging reflect the ones in CO abundances or in temperature (Crossfield et al. 2014).

Given the coherence of this global picture, we conclude that clouds are not needed to explain the main characteristics of the emission spectra of BDs and directly imaged EGPs. We emphasize that this does not imply an absence of clouds. Given the possibility of many stable condensates and the presence, according to the present scenario, of turbulent layers, these atmospheres very likely present some cloud cycles. Furthermore, some observations, such as the absorption in the 10 μm window (e.g., Cushing et al. 2006), suggest the presence of condensates. Current cloud models, however, do not well reproduce this signature (see Stephens et al. 2009), requiring a revision of the models in order to reproduce both this signature and the NIR color reddening.

Not only does the present scenario completely change our present understanding (and non-understanding) of BD and EGP atmospheres, but, if correct, it shows that the same physical mechanism, namely, chemical or fingering convection induced by a thermo-chemical instability, would take place in environments as different as Earth's oceans (Rahmstorf 2003), the Earth core-mantle boundary (Hansen & Yuen 1988), and exoplanet and brown dwarf atmospheres, nicely illustrating the universality of physical processes in nature.

We thank Patrick Ingraham and Rebecca Oppenheimer for providing their data. This work is partly supported by the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013 Grant Agreement No. 247060 and FP7/2007-2013 Grant Agreement No. 247060-PEPS and grant No. 320478-TOFU). Part of this work is supported by the Royal Society award WM090065. O.V. acknowledges support from the K. U. Leuven IDO project IDO/10/2013 and from the FWO Postdoctoral Fellowship programme.