The Composition of Directly Imaged Giant Planets

On the Composition of Young, Directly Imaged Giant Planets

J. I. Moses Space Science Institute, 4750 Walnut Street, Suite 205, Boulder, CO 80301, USA M. S. Marley K. Zahnle NASA Ames Research Center, Moffett Field, CA 94035, USA M. R. Line J. J. Fortney Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064, USA T. S. Barman Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA C. Visscher Dordt College, Sioux Center, IA 51250, USA Space Science Institute, Boulder, CO 80301, USA N. K. Lewis Space Telescope Science Institute, Baltimore, MD 21218, USA M. J. Wolff Space Science Institute, Boulder, CO 80301, USA

The past decade has seen significant progress on the direct detection and characterization of young, self-luminous giant planets at wide orbital separations from their host stars. Some of these planets show evidence for disequilibrium processes like transport-induced quenching in their atmospheres; photochemistry may also be important, despite the large orbital distances. These disequilibrium chemical processes can alter the expected composition, spectral behavior, thermal structure, and cooling history of the planets, and can potentially confuse determinations of bulk elemental ratios, which provide important insights into planet-formation mechanisms. Using a thermo/photochemical kinetics and transport model, we investigate the extent to which disequilibrium chemistry affects the composition and spectra of directly imaged giant exoplanets. Results for specific “young Jupiters” such as HR 8799 b and 51 Eri b are presented, as are general trends as a function of planetary effective temperature, surface gravity, incident ultraviolet flux, and strength of deep atmospheric convection. We find that quenching is very important on young Jupiters, leading to CO/CH and N/NH ratios much greater than, and HO mixing ratios a factor of a few less than, chemical-equilibrium predictions. Photochemistry can also be important on such planets, with CO and HCN being key photochemical products. Carbon dioxide becomes a major constituent when stratospheric temperatures are low and recycling of water via the + OH reaction becomes kinetically stifled. Young Jupiters with effective temperatures 700 K are in a particularly interesting photochemical regime that differs from both transiting hot Jupiters and our own solar-system giant planets.

Subject headings:
planetary systems — planets and satellites: atmospheres — planets and satellites: composition — planets and satellites: individual (51 Erib, HR 8799b, HR 8799c) — stars: individual (51 Eri, HR 8799)
slugcomment: submitted to Astrophys. J.

1. Introduction

Most of the exoplanets discovered to date have been identified through transit observations or radial-velocity measurements — techniques that favor the detection of large planets orbiting close to their host stars. Direct detection of a planet within the overwhelmingly glare and non-negligible point-spread function of its brighter star is challenging and requires high-contrast observations, often with adaptive-optics techniques from large telescopes on the ground or in space. As a result of these observational challenges, direct imaging favors the detection of massive, self-luminous (i.e., young) giant planets at wide orbital separations from their host stars. These “young Jupiters” are hot at depth because the leftover accretional and gravitational potential energy from the planet’s formation has not had time to convect up through the atmosphere and be radiated away yet. Only 3% of the currently confirmed exoplanets111See, http://exoplanetarchive.ipac.caltech. edu, or have been detected through direct imaging, but these planetary systems have high intrinsic interest. For example, they serve as potential analogs to our own solar system in its formative years, when Jupiter and our other giant planets were born and evolved behind ice condensation fronts in the solar nebula but never migrated inward — unlike, apparently, many of the known close-in, transiting, extrasolar giant planets. Directly imaged planets therefore provide a window into our own past and provide important clues to our solar system’s origin and evolution (see, e.g., Madhusudhan et al., 2014). Wavelength-dependent photometry or spectra of directly imaged planets can also provide useful constraints on atmospheric properties such as composition, thermal structure, metallicity, bulk elemental ratios, and the presence or absence of clouds (see the reviews of Madhusudhan et al., 2014; Bailey, 2014; Crossfield, 2015; Madhusudhan et al., 2016).

Short-period, transiting “hot Jupiters” and directly imaged “young Jupiters” both have similar effective temperatures, often ranging from 500 to 2500 K. However, in terms of their thermal structure and spectral appearance, directly imaged planets have more in common with brown dwarfs than with hot Jupiters (e.g., Burrows et al., 2003; Fortney et al., 2008b; Bowler, 2016). In particular, the stratospheres (radiative regions) of directly imaged planets and brown dwarfs are much cooler than those of highly-irradiated hot Jupiters, and the cooler regions overlying hot continuum regions at depth can result in potentially deeper molecular absorption bands being present in emission spectra (Madhusudhan et al., 2014). It can therefore be easier to detect atmospheric molecules on young Jupiters and brown dwarfs, unless high clouds are present to obscure the absorption features.

One drawback of direct imaging is that the planet’s radius and mass cannot be well determined, unlike the situation with, respectively, transit observations and radial-velocity measurements. Instead, the mass and radius of directly imaged planets are more loosely constrained through atmospheric modeling and comparisons with the observed luminosity and spectral/photometric behavior, often in combination with estimates of the age of the system and constraints from evolutionary models. The theoretical modeling and model-data comparisons can result in degeneracies between the planet’s apparent size, surface gravity, effective temperature, and cloud properties (e.g., Marley et al., 2007, 2012; Barman et al., 2011a, b, 2015; Currie et al., 2011; Madhusudhan et al., 2011; Spiegel & Burrows, 2012; Bonnefoy et al., 2013, 2016; Lee et al., 2013; Skemer et al., 2014; Baudino et al., 2015; Morzinski et al., 2015; Zurlo et al., 2016).

On the other hand, the identification of molecular features in the observed spectra is typically unambiguous on young Jupiters (e.g., Konopacky et al., 2013; Barman et al., 2015), and HO, CO, and/or CH have been detected in in spectra from several directly imaged planets (Patience et al., 2010; Barman et al., 2011a, b, 2015; Oppenheimer et al., 2013; Konopacky et al., 2013; Janson et al., 2013; Snellen et al., 2014; Chilcote et al., 2015; Macintosh et al., 2015). The apparent deficiency of methane features on many cooler directly imaged planets, in conflict with chemical equilibrium expectations, has been argued as evidence for disequilibrium processes like transport-induced quenching on these planets (e.g., Bowler et al., 2010; Hinz et al., 2010; Janson et al., 2010, 2013; Barman et al., 2011a, b, 2015; Galicher et al., 2011; Marley et al., 2012; Skemer et al., 2012, 2014; Ingraham et al., 2014; Currie et al., 2014; Zahnle & Marley, 2014), and so many of the above groups included quenching in their theoretical modeling (see Visscher & Moses, 2011; Zahnle & Marley, 2014, for more details about CO CH quenching on directly imaged planets and brown dwarfs). Other disequilibrium chemical processes such as photochemistry have been assumed to be unimportant due to the large orbital distances of these planets (Crossfield, 2015); however, the young stellar hosts of directly imaged planets tend to be bright in the ultraviolet, making photochemistry potentially important (e.g., Zahnle et al., 2016).

The goal of the present investigation is to quantify the extent to which disequilibrium chemical processes like photochemistry and quenching affect the composition and spectra of young, directly imaged planets. Our main theoretical tool is a thermochemical-photochemical kinetics and transport model (e.g., Moses et al., 2011; Visscher & Moses, 2011; Moses et al., 2013a, b) that tracks the chemical production, loss, and transport of the most abundant gas-phase species in a hydrogen-dominated planetary atmosphere. We calculate the expected composition of specific directly imaged exoplanets such as 51 Eri b and HR 8799 b, for which observational spectra are available, as well as investigate how the composition of generic “young Jupiters” is affected by planetary parameters such as the effective temperature, surface gravity, incident ultraviolet flux, and the strength of atmospheric mixing. We also explore how disequilibrium chemistry affects the resulting spectra of directly imaged planets.

2. Theoretical Model

To calculate the vertical profiles of atmospheric species on directly imaged planets, we use the Caltech/JPL KINETICS code (Allen et al., 1981; Yung et al., 1984) to solve the coupled one-dimensional (1D) continuity equations for 92 neutral carbon-, oxygen-, nitrogen-, and hydrogen-bearing species that interact through 1650 kinetic reactions. Hydrocarbons with up to six carbon atoms are considered, although the reaction list becomes increasingly incomplete the heavier the molecule. We do not consider ion chemistry from photoionization (Lavvas et al., 2014) or galactic-cosmic-ray ionization (Rimmer et al., 2014). Ion chemistry is not expected to affect the mixing ratios of the dominant gas species, but it will likely augment the production of heavy organic molecules, just as on Titan (e.g., Waite et al., 2007; Vuitton et al., 2007). Lacking any definitive evidence to the contrary for directly imaged giant planets, we assume the atmospheres have a solar elemental composition.

The reaction list includes both “forward” (typically exothermic) reactions and their reverses, where the reverse reaction rate coefficient is calculated from the forward rate coefficient and equilibrium constant assuming thermodynamic reversibility (e.g., Visscher & Moses, 2011; Heng et al., 2016). All reactions except those involving photolysis are reversed. The fully reversed reaction mechanism ensures that thermochemical equilibrium is maintained kinetically in the hotter deep atmosphere, while disequilibrium photochemistry and transport processes can take over and dominate in the cooler upper atmosphere (e.g., Moses et al., 2011; Line et al., 2011; Venot et al., 2012; Kopparapu et al., 2012; Miller-Ricci Kempton et al., 2012; Agúndez et al., 2014a; Miguel & Kaltenegger, 2014; Hu & Seager, 2014; Benneke, 2015; Zahnle et al., 2016). The model automatically accounts for the transport-induced quenching of species, whereby mixing ratios are “frozen in” at a constant mixing ratio above some quench pressure as vertical transport processes start to dominate over the chemical reactions that are attempting to drive the atmosphere back toward thermochemical equilibrium (Prinn & Barshay, 1977; Lewis & Fegley, 1984; Fegley & Lodders, 1994).

The quenching process depends on the adopted reaction mechanism (cf. Visscher et al., 2010b; Moses et al., 2011; Visscher & Moses, 2011; Line et al., 2011; Venot et al., 2012; Moses, 2014; Zahnle & Marley, 2014; Wang et al., 2015; Rimmer & Helling, 2016). Our chemical reaction list is taken from Moses et al. (2013b) and includes a thorough review of the key reaction mechanisms of potential importance in the quenching of CO CH and N NH (Visscher et al., 2010b; Visscher & Moses, 2011; Moses et al., 2010, 2011, 2013a, 2013b; Moses, 2014); further details of the thermo/photochemical kinetics and transport model are provided in the above papers, and the reaction list is provided in the journal supplementary material. Note that we do not include the fast rate coefficient for H + CHOH CH + HO suggested by Hidaka et al. (1989) that is controlling CO-CH quenching in the Venot et al. (2012) mechanism. As discussed by Norton & Dryer (1990), Lendvay et al. (1997), and Moses et al. (2011), this reaction actually possesses a very high energy barrier ( 10,000 K) and is not expected to be important under either methanol-combustion conditions or in the deep atmospheres of hydrogen-rich exoplanets — in other words, the Hidaka et al. rate coefficient greatly overestimates the rate of this reaction. Zahnle & Marley (2014) adopt the upper limit for this reaction as suggested by Norton & Dryer (1989) and find it to be important but not typically dominant in CO–CH quenching, except for cooler brown dwarfs with weak mixing. We adopt the much smaller rate coefficient as calculated by Moses et al. (2011), and this reaction does not play a role in CO–CH quenching. Similarly, we do not adopt the relatively fast rate-coefficient expression for NH + NH NH + H estimated by Konnov & De Ruyck (2000) that is affecting N-NH quenching in the Venot et al. (2012) mechanism, as again, this reaction is expected to have a high-energy barrier and be slower under relevant conditions than the Konnov and De Ruyck estimate (e.g., Dean et al., 1984).

Our model grids consist of 198 vertical levels separated uniformly in log(pressure) (providing multiple grid levels per scale height to insure accurate diffusion calculations), with a bottom level defined where the deep atmospheric temperature on an adiabatic gradient is greater than 2700 K (to insure that the N-NH quench point is captured), and a top level residing at 10 mbar (to insure all the molecular absorbers are optically thin in the ultraviolet). The top region of our model grid extends through what would typically be the “thermosphere” of the planet; however, we neglect non-stellar sources of thermospheric heating (such as auroral and Joule heating), which are poorly understood but are important on our solar-system giant planets (e.g., Yelle & Miller, 2004; Nagy et al., 2009). Our results should therefore only be considered reliable from the deep troposphere on up to the homopause level at the base of the thermosphere (near 10 to 10 mbar, depending on the strength of atmospheric mixing), where molecular diffusion acts to limit the abundance of heavy molecular and atomic species in the lighter background hydrogen atmosphere.

Figure 1.— Theoretical temperature profiles for generic directly imaged planets from the radiative-convective equilibrium model of Marley et al. (2012), as a function of effective temperature for an assumed surface gravity (in cm s) of = 3.5 (colored solid lines) and = 4.0 (colored dashed lines) and assumed solar composition atmosphere in chemical equilibrium. Profiles are shown every 100 K from = 600 to 1400 K. The gray dot-dashed lines show the condensation curves for some important atmospheric cloud-forming species (as labeled) for an assumed solar-composition atmosphere. The thicker dotted black lines represent the boundaries where CH and CO have equal abundances and where N and NH have equal abundance in chemical equilibrium for solar-composition models. Methane and ammonia dominate to the lower left of these curves, while CO and N dominate to the upper right. Note that all the profiles remain within the CO-dominated regime at depth, whereas all except for the hottest planets transition to the CH-dominated regime at higher altitudes. A color version of this figure is available in the online journal.

The thermal structure itself is not calculated self-consistently but is adopted from two different atmospheric models: (1) the radiative-convective equilibrium models described in McKay et al. (1989), Marley et al. (1999), Marley et al. (2002), and Saumon & Marley (2008), with updates as described in Marley et al. (2012), and (2) the PHOENIX-based models described in Hauschildt et al. (1997), Allard et al. (2001), and Barman et al. (2011a), with updates as described in Barman et al. (2015). We add a smoothly varying, nearly isothermal profile at the top of the above-mentioned theoretical model profiles to extend our grids to lower pressures, except in isolated cases where we test the effects of a hotter (1000 K) thermosphere. Figure 1 shows the temperature profiles adopted for our cloud-free generic directly imaged planets, as a function of effective temperature for two different assumed 1-bar surface gravities, = 3.5 and 4.0 cgs. These profiles are calculated without considering stellar irradiation — for all directly imaged planets discovered to date, the external radiation field has little effect on the thermal profile due to the planets’ large orbital distance and strong internal heat flux. As such, the internal heat completely dominates the thermal structure, and temperatures on these planets are hotter at depth and colder in the stratospheric radiative region than for close-in transiting giant planets of the same effective temperature. The profiles from Fig. 1 were generated with the NASA Ames brown-dwarf and exoplanet structure models (e.g., Marley et al., 2012); tables with the individual pressure-temperature structure from these models can be found in the journal Supplementary Material. Disequilibrium processes like photochemistry and quenching are expected to have a relatively minor effect on the thermal structure (e.g., Agúndez et al., 2014b), unless these processes affect the HO abundance.

Given a temperature-pressure profile, the NASA CEA code of Gordon & McBride (1994) is then used to determine the chemical-equilibrium abundances, which are used as initial conditions in the photochemical model. We use the protosolar abundances listed in Table 10 of Lodders (2010) to define our “solar” composition. The mean molecular mass profile from the chemical-equilibrium solution, the pressure-temperature profile, and the assumed physical parameters of the planet become inputs to the hydrostatic equilibrium equation, whose solution sets the altitude scale and other atmospheric parameters along the vertical model grid. For a surface (1-bar) gravity of = 10 cm s, the planet mass M is , and for = 10 cm s, M = . For boundary conditions, we assume the fluxes of the species are zero at the top and bottom of the model. The models are run until steady state, with a convergence criterion of 1 part in 1000. For the photochemical calculations, the atmospheric extinction is calculated from the absorption and multiple Rayleigh scattering of gases only — aerosol extinction is ignored due to a lack of current predictive capability regarding the hazes. The atmospheric radiation field for the photochemical model is calculated for diurnally averaged conditions for an assumed (arbitrary) 24-hour rotation period at 30 latitude at vernal equinox, with an assumed zero axial tilt for the planet. These assumptions should provide acceptable “global average” conditions for most young Jupiters.

As is standard in 1D photochemical models, we assume that vertical transport occurs through molecular and “eddy” diffusion, with the eddy diffusion coefficient profile being a free parameter. The molecular diffusion coefficients assumed in the model are described in Moses et al. (2000). Although vertical transport of constituents in real atmospheres occurs through convection, large-scale advection, atmospheric waves, and turbulent “eddies” of all scales, this constituent transport often mimics diffusion (Lindzen, 1981; Strobel, 1981; Brasseur et al., 1999), and the concept of eddy diffusion has proven to be a useful one for atmospheric models. The eddy diffusion coefficient profile for an atmosphere cannot typically be derived accurately from first principles. Instead, observations of chemically long-lived species are used to empirically constrain (e.g., Allen et al., 1981; Atreya et al., 1984; Moses et al., 2005). On H-dominated planets and brown dwarfs, the relative abundance of CO and CH can be used to constrain  at the quench point (see Prinn & Barshay, 1977; Fegley & Lodders, 1994; Griffith & Yelle, 1999; Visscher & Moses, 2011). For most directly imaged planets planets, the CO-CH quench point will reside in the deep, convective portion of the atmosphere, where free-convection and mixing-length theories (e.g., Stone, 1976) predict relatively large eddy diffusion coefficients and rapid mixing (e.g.,   10 for most young Jupiters, assuming the atmospheric scale height as the mixing length). However, the mixing length to use for these expressions is not obvious (Smith, 1998; Freytag et al., 2010), and the quench point for some planets may approach the radiative region, where  is expected to drop off significantly before increasing roughly with the inverse square root of atmospheric pressure due to the action of atmospheric waves (e.g., Lindzen, 1981; Strobel, 1981; Parmentier et al., 2013).

Figure 2.— Eddy diffusion coefficient profiles (colored solid lines) adopted in our thermo/photochemical kinetics and transport models. The  profiles are assumed to vary as 10 cm s in the radiative region, with different models having different cutoff values () at depth. Profiles derived for Jupiter (Moses et al., 2005) and the hot Jupiter HD 209458b (Parmentier et al., 2013) are shown for comparison (dashed lines). A color version of this figure is available in the online journal.

We therefore explore a range of possible  profiles, with roughly constant values at depth, trending to values that vary as 1/ as the pressure decreases. In particular, we assume that  (cm s) = 10 in the radiative region above 300 mbar (hereafter called the stratosphere), but we do not let  drop below some value “” that varies with the different models considered (see Fig. 2). This convention allows the different models for a given  to have a similar homopause pressure level in the upper atmosphere (i.e., the pressure level to which the molecular species can be mixed before molecular diffusion starts to limit their abundance), while still testing the effect of variations in  at the quench point.

Note from Fig. 2 that we have chosen stratospheric  profiles that are intermediate between those derived empirically from chemical tracers for our own solar-system (cold) Jupiter (Moses et al., 2005) and those derived from tracer transport in 3D dynamical models of the hot transiting exoplanet HD 209458b (Parmentier et al., 2013), which seems reasonable given that atmospheric temperatures for directly imaged planets are intermediate between the two. Eddy diffusion coefficients scale directly with vertical velocities and atmospheric length scales, and both tend to be larger for higher temperatures. Young Jupiters are very hot and convective at depth, but their stratospheres are relatively cold and statically stable.

When estimating  profiles for exoplanetary atmospheres, we keep in mind that atmospheric waves are typically responsible for mixing in the stratosphere (e.g., Lindzen, 1981), and wave activity could be correlated with both the strength of stellar insolation and internal heat, as the main drivers for these waves. In the troposphere, convection dominates, and mixing is stronger for higher internal heat fluxes. For example, in the Freytag et al. (2010) hydrodynamic models of cool dwarfs, the maximum effective tropospheric diffusion coefficient (analogous to our “”) increases with increasing  over the whole 900   2800 K model range examined. Freytag et al. (2010) also find that the effective diffusion coefficients in the stratosphere, where convectively excited gravity waves are responsible for atmospheric mixing, also increase with increasing  for   1500 K and   2000 K, but the behavior at intermediate 1500   2000 K becomes more complicated due to the effects of clouds, which alter atmospheric stability. At the base of the stratosphere in the Freytag et al. (2010) models, the effective diffusion coefficient goes through a minimum. The  profiles are also sensitive to gravity and the overall static stability in the atmosphere. Without running realistic dynamical models for the planets in question, we cannot reliably estimate  profiles a priori, and we caution that our empirical profiles may have different magnitudes or functional forms than those of the real young-Jupiter atmospheres. In particular, our profiles do not have the very weak  minimum that might be expected at the base of the stratosphere on young Jupiters. Because this minimum  results in maximum column abundances for photochemical species produced at high altitudes (e.g., Bézard et al., 2002), our convention may cause us to underestimate the abundances of photochemical products, but not as severely as if we assumed that  were constant throughout the atmosphere.

Figure 3.— The ultraviolet stellar irradiance adopted in the models: (Top) The irradiance of 51 Eri (blue) and HR 8799 (red) as received at 1 AU, in comparison with that the Sun (black); (Bottom) the irradiance at the top of the planet’s atmosphere for 51 Eri b (blue) and HR 8799 b (red) in comparison with Jupiter (black). Note from the top panel that both 51 Eri and HR 8799 are brighter than the Sun in the ultraviolet, but 51 Eri b and HR 8799 b are farther away from their host stars than Jupiter, so in terms of the H Lyman alpha flux received, which drives much of the interesting photochemistry, Jupiter receives a flux intermediate between 51 Eri b and HR 8799 b (bottom panel). A color version of this figure is available in the online journal.

The photochemical model results also depend on the host star’s ultraviolet flux and spectral energy distribution (e.g., Venot et al., 2013; Miguel & Kaltenegger, 2014; Miguel et al., 2015). For our specific exoplanet models, both 51 Eri (spectral type F0) and HR 8799 (spectral type A5) are expected to be brighter than the Sun at UV wavelengths (see Fig. 3). However, the only direct ultraviolet spectral observations we could find for either star are derived from International Ultraviolet Explorer (IUE) satellite observations of 51 Eri in the MAST archive ( Therefore, except for these IUE observations, our assumed stellar spectra are assembled from a variety of theoretical sources. For wavelengths greater than 1979 Å, the 51 Eri spectrum is taken from the Heap & Lindler (2011) NextGen model for 51 Eri (HD 29391); for wavelengths between 1200 and 1978.72 Å — except right at H Lyman — we use IUE observations of 51 Eri from the MAST IUE archive; for wavelengths less than 1150 Å, we adopt the theoretical spectrum of HR 8799 (as the closest analog star) from the Sanz-Forcada et al. (2011) X-exoplanets archive; and for Lyman at 1215.7 Å, we adopt the reconstructed intrinsic H Lyman alpha flux for 51 Eri from Landsman & Simon (1993). The HR 8799 spectrum is a composite of several theoretical models. At wavelengths less than 1150 Å and in the wavelength bin at 1190 Å, the HR 8799 spectrum is from the aforementioned Sanz-Forcada et al. (2011) model of HR 8799; at wavelengths greater than 1150 Å — except for the wavelength bins at 1190 and 1215.7 Å — we use a Castelli & Kurucz (2004) model with assumed parameters of = 7500 K, log() = 4.5 (cgs), log[Fe/H] = , radius = 1.44; and for 1215.7 Å, we estimate the flux as the average of four stars ( Tau [A7V], HR 1507 [F0V], 30 LMi [F0V], Hyi [F0V]) from the Landsman & Simon (1993) database of reconstructed intrinsic H Lyman alpha fluxes, after scaling appropriately for stellar distance. For the spectral irradiance of the Sun shown in Fig. 3, we adopt the solar-cycle minimum spectrum of Woods & Rottman (2002).

Note from Fig. 3 that 51 Eri and HR 8799 are intrinsically brighter than the Sun in the ultraviolet. Despite the great orbital distances of the HR 8799 planets (b at 68 AU, c at 43 AU, d at 27 AU; cf. Marois et al. 2008 & Maire et al. 2015) and 51 Eri b (14 AU according to De Rosa et al. 2015, although we used 13.2 AU for the calculations based on the earlier report by Macintosh et al. 2015), these planets — like the giant planets within our own solar system — receive sufficient ultraviolet flux that photochemistry should be effective. In fact, 51 Eri b receives a greater H Lyman alpha flux than any of our solar-system giant planets, including Jupiter (see Fig. 3), while the most distant HR 8799 b receives a greater H Ly flux than either Uranus or Neptune, which both have rich stratospheric hydrocarbon photochemistry (Summers & Strobel, 1989; Romani et al., 1993; Moses et al., 1995; Dobrijevic et al., 2010; Orton et al., 2014). Indeed, the first investigation into the photochemistry of 51 Eri b (Zahnle et al., 2016) suggests that photochemical production of complex hydrocarbons and sulfur species will be important on this young Jupiter and may lead to the formation of sulfur and hydrocarbon hazes.

3. Results

Results from our thermo/photochemical kinetics and transport model are presented below. We first discuss the results for generic directly-imaged planets, including trends as a function of , log(), , and distance from the host star (see also Zahnle & Marley, 2014). The relevant disequilibrium chemistry that could potentially affect the spectral appearance of young Jupiters is described. Then, we present specific models for HR 8799 b and 51 Eri b and compare to observations. Note that the model abundance profiles for both the generic and specific planets discussed below are included in the journal supplementary material.

Figure 4.— The vertical mixing-ratio profiles of CH (purple) and CO (green) for planets with a surface gravity log() = 4 (cgs), a moderate eddy mixing = 10 cm s, and = 600 K (Left), 800 K (Middle), 1000 K (Right). Results for chemical equilibrium are shown with dashed lines, and results from our thermo/photochemical kinetics and transport model are shown as solid lines. Note that CH dominates in the observable portion of the atmosphere in chemical equilibrium, whereas CO dominates in the disequilibrium models. The CH/CO ratio is strongly dependent on temperature for both types of chemistry, with a higher CH/CO ratio being favored for cooler planets. A color version of this figure is available in the online journal.

3.1. Generic Directly Imaged Planets: Chemistry

For our “generic” young Jupiters, we generate a suite of models for nine different effective temperatures ( ranging from 600 K to 1400 K, at 100-K intervals), seven different eddy diffusion coefficient profiles (see Fig. 2), and two different surface gravities ( = 10 and 10 cm s). The thermal profiles of these models are shown in Fig. 1. Note from Fig. 1 that all the models have deep atmospheres that lie within the CO stability field, whereas all but the hottest models switch over to the CH stability field in the upper atmosphere. Therefore, if the atmosphere were to remain in chemical equilibrium, CH would be the dominant carbon constituent at “photospheric” pressures in the 10–0.1 mbar range for most of these planets, and methane absorption would be prominent in the near-infrared emission spectra. However, CO CH chemical equilibrium cannot be maintained at temperatures 1300 K for any reasonable assumption about the eddy diffusion coefficient profile (e.g., Visscher & Moses, 2011), and quenching will occur in the deep, convective regions of these planets. For all the thermal profiles investigated, the CO-CH quench point occurs within the CO stability field, and the quenched abundance of CO will be greater than that of CH.

The dominant kinetic reaction scheme converting CO to CH near the quench point in our models is


with M representing any third atmospheric molecule or atom. This scheme is identical to the dominant scheme (15) that Visscher & Moses (2011) propose is controlling the conversion of CO into CH on brown dwarfs and is just the reverse of the scheme (3) that Moses et al. (2011) propose is controlling CO quenching on hot Jupiters. The rate-limiting step in the above scheme is the reaction + M + OH + M, where the rate coefficient is derived from the reverse reaction from Jasper et al. (2007). Our chemical model differs from some others in the literature (e.g., Venot et al., 2012; Zahnle & Marley, 2014) in that we adopt a slower rate coefficient for H + + based on the ab initio transition-state theory calculations of Moses et al. (2011) & Lendvay et al. (1997), and the discussion of relevant experimental data in Norton & Dryer (1990). However, the rate coefficient for this reaction adopted by Zahnle & Marley (2014) and Zahnle et al. (2016) is slow enough that + M + OH + M is usually faster, and hence their quench results are not greatly different from those described here. In any case, quenching is very effective in all the generic young-Jupiter models we investigated, and CO replaces CH as the dominant carbon species in the photospheres of these planets.

Figure 5.— Quenched mixing ratios of CH (top) and CO (bottom) for models with surface gravities of = 10 (left) and 10 cm s (right) as a function of  and . High CH abundances and low CO abundances are favored by small , small , and large , although the CO abundance is relatively insensitive to these factors over the range of models investigated. A color version of this figure is available in the online journal.

3.1.1 - quenching as a function of  and

Figure 4 shows how the methane and carbon monoxide abundance vary with the planet’s effective temperature (for  = 600, 800, 1000 K), for both the assumption of chemical equilibrium and from our thermo/photochemical kinetics and transport modeling, for  = 10 cm s and log() = 4 (cgs). Figure 4 emphasizes just how significantly thermochemical equilibrium fails in its predictions for the composition of directly imaged planets, underpredicting the CO abundance by many orders of magnitude, and overpredicting the CH abundance. The CO-CH quench point is discernible in the plot — it is the pressure at which the CH and CO mixing ratios stop following the equilibrium profiles and become constant with altitude. For the = 600 K planet, the quench point is near the CO = CH equal-abundance curve shown in Fig. 1, and carbon monoxide and methane quench at nearly equal abundances. Warmer planets have quench points more solidly within the CO stability field, and so the CO abundance then exceeds that of methane at high altitudes. The quenched CH abundance depends strongly on , decreasing with increasing , when other factors like  and are kept identical. The depletion in both the CO and CH mixing ratios at high altitudes in the disequilibrium models in Fig. 4 is due to molecular diffusion, which is dependent on temperature. Planets with a higher  have warmer upper atmospheres, causing molecular diffusion to take over at deeper levels. Therefore, warmer planets have homopause levels at higher pressures (lower altitudes), all other things being equal.

The quenched species abundances also depend strongly on  and on surface gravity. Figure 5 illustrates this relationship for CO (top row) and CH (bottom row) for a suite of generic young Jupiter models, with the lower-gravity (log() = 3.5) case being plotted in the left column and the higher-gravity case (log() = 4.0) in the right column. Note from Fig. 5 that the quenched CH abundance is highly sensitive to both  and , and is greatest for low temperatures and weak deep vertical mixing. Higher-gravity planets with the same  are cooler at any particular pressure level, so higher favors increased CH abundance, all other factors being equal. In contrast, high , low , and low  favor smaller quenched CO abundances. Note, however, the nearly constant quenched CO mixing ratio over a large swath of parameter space in Fig. 5 for these two relatively low surface gravities. The quenched CO mixing ratio is less sensitive than CH to variations in , , and in this range because CO is dominant at the quench point, and the equilibrium CO mixing ratio is more constant with height through the quench region, whereas the equilibrium CH mixing-ratio profile in this region has a significant vertical gradient.

This is an important point. Disequilibrium chemistry from transport-induced quenching will cause CO — not CH — to dominate in the photospheres of virtually all directly imaged young planetary-mass (and planetary-gravity) companions, despite the equilibrium predictions for the predominance of ; in addition, the CO abundance should be similar for directly imaged planets with the same metallicity. Spectral signatures of CO should therefore be common for young Jupiters, and derived CO abundances can help constrain the planet’s metallicity. Note that this conclusion changes for higher-gravity ( 10 cm s) T dwarfs in this temperature range (Hubeny & Burrows, 2007; Zahnle & Marley, 2014), where CH can dominate and CO is the minor species.

Figure 6.— Vertical profiles of several important species in our thermo/photochemical kinetics and transport models (solid colored lines) and in chemical equilibrium (dashed gray and black lines) for a planet with  = 1000 K and = 10 cm s, at a distance of 68 AU from a star with properties like HR 8799 (Fig. 3), as a function of  (see the legend in the top left panel, and the  profiles shown in Fig. 2). Note that the atmosphere is far out of equilibrium for all the eddy diffusion coefficient profiles considered. The quenched CH mixing ratio increases with decreasing . The mixing ratios of methane photochemical products such as CH, CH, and H also increase with decreasing . Water quenches at the same time as CO and CH, remaining in disequilibrium in the photosphere. Species like HCN and CO are affected both by photochemistry and by quenching of the major carbon, oxygen, and nitrogen species. A color version of this figure is available in the online journal.

3.1.2 Sensitivity of disequilibrium chemistry to

Figure 6 illustrates how the abundances of several constituents change with the different eddy diffusion coefficient profiles shown in Fig. 2, for a model with  = 1000 K, log() = 4.0, and an orbital distance of 68 AU from a star with the properties of HR 8799. As the eddy diffusion coefficient at depth, , is increased, vertical transport begins to dominate at greater and greater depths over the chemical kinetic reactions that act to maintain equilibrium. Smaller  values lead to mixing ratio profiles that follow the equilibrium profiles to higher altitudes before quenching occurs. The quenched methane abundance therefore increases with decreasing , and species that are produced through the photochemical destruction of methane, like CH and CH, also have mixing ratios that increase with decreasing . Conversely, the quenched CO abundance decreases with decreasing , but because the chemical equilibrium abundance of CO is only slightly decreasing with altitude over the range of quench points for the different  values investigated, the quenched CO mixing ratio is relatively insensitive to .

Water quenches via reaction scheme (1) above at the same point as that of CO and CH. Since the equilibrium mixing ratio for HO is increasing with increasing altitude very slightly over the pressure range of the quench points, the quenched HO abundance very slightly increases with decreasing . Water is a key opacity source in young Jupiters that affects how efficiently heat is lost from the planet, so it is important to keep in mind that the resulting quenched water mixing ratio on directly imaged planets can be a factor of a few below that of chemical-equilibrium predictions in the photosphere. This quenching of HO becomes more important for higher , larger , and lower surface gravities. Quenching of water should therefore be considered in models that calculate the thermal evolution of brown dwarfs and directly imaged planets, particularly for young, small, hot objects.

The NH-N quench point is deeper than that of CO-CH-HO. For all the planets considered, this major nitrogen-species quench point is well within the N-dominated regime, so N dominates in the photosphere, and NH is less abundant. The equilibrium profiles are not strongly sloped in the quench region, so the quenched abundances of NH — and N in particular — are not very sensitive to  (see Fig. 6). The dominant quenching scheme for N NH in our generic young-Jupiter models is


which is simply the reverse of reaction scheme (5) for quenching discussed in Moses et al. (2011). The rate-limiting step in the above scheme is the reaction H + NH + , where the rate coefficient derives from the reverse reaction, as determined by Klippenstein et al. (2009).

Constituents such as HCN and CO are affected both by photochemistry and by quenching of the dominant carbon, nitrogen, and oxygen carriers (HO, CO, CH, NH, and N) and thus exhibit complicated vertical profiles in Fig. 6. For large values of , transport controls the HCN and CO profiles throughout the atmospheric column. The quenched abundance of HCN increases with increasing  because the equilibrium profile decreases with height within the quench region. Conversely, the quenched abundance of CO decreases with increasing  because the equilibrium profile increases with height near the quench point; moreover, the photochemically produced CO takes longer to diffuse downward when the stratospheric  is smaller, so a larger column abundance can build up. In fact, at higher altitudes with the smaller  models, photochemical production of HCN and CO can dominate over transport from below, and the resulting mixing-ratio “bulges” in the stratosphere represent the signatures of that photochemical production. In general, the column-integrated CO abundance increases with decreasing , while that of HCN decreases with decreasing . However, this latter result also depends on the planet’s thermal structure and incident ultraviolet flux.

Note that the sharp drop off in the species profiles at high altitudes in Fig. 6 is due to molecular diffusion. Because the molecular diffusion coefficient profiles for this thermal structure cross the  profiles at relatively high altitudes where the  profiles have already transitioned to the sloped region, the homopause levels for most of the models for any particular species are the same for the different  models. However, the CH homopause level is at 3 mbar for the sloped  case, and Fig. 2 shows that the  = 10 cm s  profile does not reached the sloped  portion until pressures less than a few 10 mbar. Therefore, the CH molecular diffusion coefficient crosses the  = 10 cm s  profile at a higher altitude (lower pressure) than the other models, leading to a higher-altitude homopause and CH being carried to higher altitudes in that model than the others. Similarly, the HO, NH, CO, and N molecular diffusion coefficients cross the sloped  profile at pressures between where the  = 10 and 10 cm s models transition to the sloped case, so both the  = 10 and 10 cm s cases have higher-altitude HO, NH, CO, and N homopauses than the other models.

Figure 7.— The vertical mixing-ratio profiles of several atmospheric species as a function of orbital distance for a planet with  = 1000 K, = 10 cm s, and  = 10 cm s, that is being irradiated by an HR 8799-like star at a distance of 10 AU (dashed lines), 32 AU (solid lines), and 100 AU (dotted lines). The greater UV flux received by the closest-in planet leads to increased destruction of photochemically active “parent” molecules such as CH, NH, HO, CO, and N, and increased production of photochemical “daughter” products such as HCN, CO, complex hydrocarbons, complex nitriles, and atomic species and small radicals. A color version of this figure is available in the online journal.

3.1.3 Sensitivity of disequilibrium chemistry to orbital distance

Figure 7 illustrates how the disequilibrium composition changes as a function of distance from the host star, for planets with  = 1000 K, log() = 4.0 (cgs),  = 10 cm s, orbiting at 10, 32, and 100 AU from a star with the properties of HR 8799. Because the strong interior heat dominates the energy transport on these young planets, the thermal structures are virtually identical in these cases, so the main differences in the models are due to the incoming ultraviolet flux. The closer a planet is to its star, the greater the UV irradiation received, leading to greater destruction rates of key molecules such as CH, NH, HO, CO, and N. That in turn leads to greater production rates of photochemical products such as HCN, CO, CH, CH, complex hydrocarbons such as methylacetylene (an isomer of CH) and benzene (an isomer of CH), complex nitriles such as HCN, small oxygen-bearing species such as NO and O, and small radicals and atoms such as C, N. O, OH, NH, and CH.

The dominant photochemical product on young Jupiters is atomic hydrogen. The atomic H is derived largely from water photolysis (producing OH + H), and the subsequent reaction of OH + H HO + H — a two-step process that catalytically destroys H to produce two H atoms. In this regard, young Jupiters have more in common with close-in transiting giant planets (e.g., Liang et al., 2003) than our solar-system giant planets, and the copious amount of atomic H produced from this photochemistry (see Fig. 7) affects much of the subsequent stratospheric chemistry on young Jupiters.

Another key photochemical product is CO. Carbon dioxide is produced overwhelmingly from the reaction OH + CO CO + H, with the OH deriving from water photolysis. If the stratosphere is relatively warm, as in the example shown in Fig. 7 (with a 1 bar temperature of 377 K), the OH + H HO + H reaction occurs at a much faster rate than OH + CO CO + H, but the latter reaction provides a slow but steady stream of oxygen away from water and CO into CO. Loss of CO occurs through the reverse of the main production reaction (i.e., H + CO CO + OH), provided that the upper-atmospheric temperature is warm enough to overcome the substantial energy barrier for this reaction, as well as through photolysis, through reaction of atomic N to produce NO + CO, and through reaction of CH to produce HCO + CO. Note that all the main loss processes for CO end up recycling the CO. For our generic young Jupiter models, the column-integrated CO production rate exceeds the loss rate, and the photochemically produced CO diffuses down through the atmosphere until it reaches higher-temperature regions where it can once again reach a chemical balance with CO and HO. The greater the incident ultraviolet flux, the greater the net photochemical production rate of CO (see Fig. 7).

Molecular oxygen becomes a notable high-altitude photochemical product on more highly-irradiated young Jupiters. It is produced as a byproduct of the water photochemistry, where photolysis of HO produces OH + H and O + 2H, and the OH and O react to form O + H. The O is lost through photolysis (which primarily leads back to HO eventually) and through reactions with atomic carbon (which leads to CO).

Some of the CH in the upper atmospheres of young Jupiters will be oxidized to produce CO and eventually CO. In our generic young Jupiter models, this process occurs through schemes such as:


with representing an ultraviolet photon. Methane oxidation schemes such as the one above are more effective the higher the incident stellar ultraviolet flux.

As on the giant planets in our own solar system (e.g., Strobel, 1983; Atreya & Romani, 1985; Yung & DeMore, 1999; Moses et al., 2004; Fouchet et al., 2009), the reduced hydrocarbon photochemistry in the atmospheres of young Jupiters will be efficacious and complex. However, the overall column abundance of the hydrocarbon species produced by neutral photochemistry (as opposed to ion chemistry) on young Jupiters will typically be smaller than on our own giant planets, as a result of the greater stratospheric temperatures, greater stratospheric water abundance, and different dominant and/or competing kinetic reactions, including methane recycling and oxidation. The typically smaller CH mixing ratio on young Jupiters (due to quenching) also contributes to the differences, as does a potentially larger stratospheric eddy  coefficient (due to upwardly propagating atmospheric waves generated in the rapidly convecting deep atmospheres of young Jupiters), which allows the high-altitude hydrocarbon photochemical products to be transported more rapidly to the deeper, high-temperature regions, where they become unstable. However, the larger stratospheric temperatures and resulting decreased stability of the complex hydrocarbons play a larger role.

As an example, the column abundance of ethane (CH) above 100 mbar on Saturn (Moses et al., 2015), which is 10 AU from the Sun, is five orders of magnitude larger than that of the generic 10-AU young Jupiter shown in Fig. 7, despite the greater H Lyman alpha and overall UV flux received by the 10-AU generic young Jupiter around its brighter star. The main source of the ethane is still the same on both planets — the three-body reaction CH + CH + M CH + M — but the CH on the 10-AU young Jupiter goes back to recycle the CH more than 99.9% of the time, because the higher atmospheric temperatures lead to a more efficient reaction of CH with H to form CH + H. Still, the total stratospheric column production rate of CH is larger on the 10-AU young Jupiter than on Saturn due to the brightness of the star and the larger UV flux; however, CH is also more readily destroyed on the warmer young Jupiter through H + CH CH + H, with a much larger percentage of the carbon ending up back in CH rather than in CH and other higher-order hydrocarbons. On Saturn, the photochemically produced CH is much more chemically stable in the colder stratosphere, so the net production rate minus loss rate is greater on Saturn than on the generic 10-AU young Jupiter. It is also interesting to note that the direct photolysis of CH on our warmer generic young Jupiters is less important to the production of complex hydrocarbons than the reaction of atomic H with CH to form CH + H, with the H deriving from HO photolysis (see discussion above).

Acetylene (CH) is also an important photochemical product on our 10-AU generic young Jupiter shown in Fig. 7 that is produced through reaction schemes such as the following that first go through CH and CH:


Acetylene is lost (a) through insertion reactions with atomic C and CH radicals to form CH and CH, (b) through reactions with atomic H to form CH, with subsequent reactions leading to other CH species and eventual methane recycling, and (c) by photolysis, which leads predominantly to recycling of the CH. As on transiting hot Jupiters (Moses et al., 2011), the atomic carbon from loss process (a) here derives both from photolysis of CO and from methane photodestruction to form CH, CH, and CH, which can react with H to eventually form C.

The relative efficiency of CH and CH production in some of our more highly irradiated young-Jupiter models (e.g, the 10-AU case) is interesting and suggests that complex carbon-rich species like PAHs could potentially form on some directly imaged planets, and might even lead to the condensation of organic hazes in these atmospheres, as enthusiastically advocated by Zahnle et al. (2009, 2016). However, in general, the efficiency of production of refractory organics from simple precursors like CH, CH, and CH in an H-dominated atmosphere seems to have been overestimated by Zahnle et al. (2009), Miller-Ricci Kempton et al. (2012), and Morley et al. (2013) — their arguments would suggest that Jupiter, Saturn, and Neptune should be completely enshrouded in optically thick stratospheric hydrocarbon hazes, yet that is not the case. Because of a lack of laboratory or theoretical kinetic information on reactions of CH and CH with other hydrocarbon radicals under relevant low-pressure, reducing conditions, the fate of these CH species is not obvious (see also Moses et al., 2011; Hébrard et al., 2013). Three-body addition reactions of CH and CH with abundant ambient H atoms can lead to CH and CH, respectively, and the CH can react with CH to form CH (Fahr & Nayak, 2000; Knyazev & Slagle, 2001) or self-react to form various CH isomers (Atkinson & Hudgens, 1999; Fahr & Nayak, 2000), but these three-body reactions are not particularly effective at low pressures. Therefore, CH and CH build up to mixing ratios of a few 10 at high altitudes in our 10-AU young-Jupiter model. The comparatively large abundance of CH and CH radicals here is likely an artifact of having insufficient knowledge of other possible loss mechanisms for these species, and we make a plea for future laboratory experiments or theoretical modeling to rectify this situation.

Benzene (CH) itself is produced in our models through CH–CH recombination, which first goes through a linear CH isomer before eventual production of benzene (Fahr & Nayak, 2000). The benzene mixing ratio reaches 1 ppb in our 10-AU model (see Fig. 7), but neither benzene nor any of the other relatively light hydrocarbons considered by our model become abundant enough to achieve saturation and condense. Similarly, the coupled carbon-nitrogen photochemistry in our model leads to non-trivial amounts of complex nitriles such as HCN being produced (see Fig. 7), but again, these relatively light nitriles never reach saturation. Our neutral chemistry alone does not lead to hazes on these planets. However, we know from Titan that organic hazes can readily form from ion chemistry in a N-dominated atmosphere (Waite et al., 2007; Vuitton et al., 2007; Imanaka & Smith, 2007; Hörst et al., 2012), and the presence of 10 ppm N in the upper atmospheres of young Jupiters may augment the production of refractory condensable hydrocarbons through Titan-like ion chemistry. This possibility deserves further investigation, both experimentally and theoretically.

The dominant product of the coupled carbon-nitrogen photochemistry is HCN, which forms through hypothesized schemes such as the following:


Note that N, not NH, is the source of the nitrogen in this scheme, which is effective at high altitudes. That is why the HCN abundance can exceed the NH abundance at high altitudes in the 10-AU model shown in Fig. 7. However, NH can also contribute to HCN formation through schemes such as the following that are more effective at lower stratospheric altitudes:


As shown in Fig. 7, the coupled nitrogen-carbon photochemistry is more efficient with a greater UV flux from the host star.

Molecular nitrogen is fairly stable on young Jupiters. Photodissociation is only effective at wavelengths shorter than 1000 Å, so N can be shielded to some extent by the more abundant H, CO, and HO. In addition, the atomic N produced from N photolysis can go back to recycle the N, through reactions such as N + OH NO + H, followed by N + NO N + O. The production rate of NO through this process exceeds the loss rate, and NO appears as a minor high-altitude photochemical product on young Jupiters (Fig. 7), especially for higher UV irradiation levels.

Ammonia, on the other hand, is much less stable than N because of weaker bonds, photolysis out to longer wavelengths ( 2300 Å), efficient reaction with atomic H, and relatively inefficient recycling. The NH photolysis products can end up in N through reactions such as N + NH NNH + H, followed by NNH N + H, or by NH + H NH + H, followed by NH + H N + H, and N + NO N + O. The nitrogen in the ammonia can also end up in HCN, through reaction pathways such as scheme (6) above. As is apparent from Fig. 7, the NH in the upper stratosphere of young Jupiters becomes more depleted the higher the incident UV flux.

One other nitrogen-bearing photochemical product worth mentioning is HCN, which is produced in the model through reaction of atomic N with CH and CH (e.g., Millar et al., 1991) — speculative reactions that may not be as efficient if we had more information about additional loss processes for these CH species — and by CN + HCN + H (with the CN from HCN photolysis), which at least has a more convincing pedigree (e.g., Sims et al., 1993). Again, more HCN (and CHCN) are produced with higher incident UV fluxes. We have not included in the model reactions from the coupled photochemistry of CH and NH, which can produce a host of complex organic molecules (e.g., Keane et al., 1996; Moses et al., 2010), due to a lack of published thermodynamic properties for these molecules. However, heavier species such as acetaldazine, acetaldehyde hydrazone, and ethylamine may also form on young Jupiters due to this coupled chemistry, particularly on cooler, more highly UV irradiated planets. Unlike on our own solar-system gas giants, hydrazine (NH) is not a major product of the ammonia photochemistry in our young-Jupiter models because the NH from ammonia photolysis preferentially reacts with the copious amounts of atomic H to produce NH, and eventually N and N, or with CH to form CHNH and eventually HCN. On Jupiter and Saturn, the coupled ammonia-methane photochemistry is less efficient due to the lack of CH present in the tropospheric region where NH is photolyzed (e.g., Kaye & Strobel, 1983; Moses et al., 2010). However, the hydrazine abundance is very sensitive to temperature and increases significantly as  decreases.

Figure 8.— The vertical mixing-ratio profiles of several atmospheric species as a function of  for a planet with = 10 cm s and  = 10 cm s, that is being irradiated by an HR 8799-like star at a distance of 68 AU (dashed lines), for  = 1200 K (dotted lines), 900 K (dashed lines), and 600 K (solid lines). Most disequilibrium photochemical products are synthesized more effectively in low- atmospheres, but some photochemical products (most notably HCN and CH) become more abundant at higher . A color version of this figure is available in the online journal.

3.1.4 Sensitivity of disequilibrium chemistry to temperatures

Finally, many photochemical products on directly imaged planets tend to be very sensitive to temperature — both the effective temperature of the planet,  (which on young Jupiters is controlled by the internal heat flux rather than radiation from the host star), and the temperature in the planet’s stratosphere (i.e., the radiative region above the convecting troposphere). Note that because irradiation from the host star has less of an effect than internal heat flow on the upper-atmospheric temperatures of these distant, young, hot, directly imaged planets, our generic young-Jupiter models with larger  have larger stratospheric temperatures, too (see Fig. 1). As discussed previously,  affects the quenched abundances of the photochemically active parent molecules, which can in turn influence the production rate of disequilibrium photochemical “daughter” products. More importantly, the stratospheric temperatures affect the subsequent reaction rates of the photochemically produced molecules and radicals, as well as affect the height to which the photochemically active parent molecules are carried before molecular diffusion takes over and severely limits their abundance. The altitude variation of this homopause level can change the pressure at which photolysis occurs, thereby affecting subsequent pressure-dependent reactions. Figure 8 shows how the vertical profiles of some of the major photochemically active molecules in our models vary with temperature, for planets with  = 600, 900, or 1200 K, and log() = 3.5 (cgs),  = 10 cm s, orbiting at 68 AU from a star with the properties of HR 8799. Although variations in  have a relatively straightforward influence on the quenched species’ abundances, the response to upper atmospheric temperatures is more complicated.

Smaller  results in larger quenched abundances of CH, NH, and HO (all other factors being equal), and allows these molecules to be carried to higher homopause altitudes, so one might naively assume that these factors lead to greater abundances of photochemical products on cooler planets. However, photolysis in these young-Jupiter models is photon-limited rather than species-limited, and the column-integrated photolysis rate of water — which produces H, as well as OH, and thus drives much of the subsequent photochemistry for carbon, nitrogen, and oxygen species — is only slightly different for all three different  models shown in Fig. 8. Instead, the critical factor is the efficiency of recycling of the parent species versus competing reactions to form other products. When temperatures are larger, recycling of water is more prevalent through reactions such as OH + H HO + H, which has a high energy barrier and operates more effectively at high temperatures. Therefore, fewer reactive OH and O radicals are available to form oxygen-rich photochemical products such as CO, HCO, CHOH, or O when temperatures are higher (see also Zahnle et al., 2016). Moreover, the H atom abundance increases as the upper-atmospheric temperature increases (due to the more efficient catalytic destruction of H following water photolysis), and the increased H atom abundance decreases the stability of some photochemical products such as CO and CH.

On the other hand, the more efficient atomic H production at high temperatures leads to an overall increase in the production rate of reactive CH and NH radicals as the temperature increases, as a result of reactions like H + + H and H + NH NH + H, and even though the reverse recycling reactions are also more effective at high temperatures, the nitrogen- and carbon-bearing products can still form at any temperature. The result is that some photochemical products, like HCN and CH that have strong bonds and are more stable at high temperatures, are produced more efficiently at higher , while other species like CH, CH, and NH are produced more efficiently at lower . The peak production altitude and overall shape of the mixing-ratio profiles can vary with , as well (see Fig. 8).

As emphasized by Zahnle et al. (2016), the oxygen-bearing photochemical products are particularly sensitive to the upper-atmospheric temperature, and the abundance of the oxygen species increases significantly when stratospheric temperatures fall below 250 K. The rate coefficient for the water recycling reaction OH + H HO + H drops by almost three orders of magnitude with a reduction in temperature from 500 K to 200 K (Baulch et al., 2005). The reduced efficiency of OH + H HO + H at low temperatures opens the door for efficient carbon oxidation, and CO + OH CO + H becomes a competitive loss process for the OH. As a result, neither HO nor CO are as efficiently recycled in the colder atmospheres, and the OH + CO reaction will proceed effectively until it depletes enough CO that the OH + H reaction can again compete as a loss process for the OH. One then sees a depletion of HO and CO at high altitudes in the coldest models, with a concomitant increase in CO and other oxygen products like O and CHOH that can form when OH does not effectively recycle back to water. Carbon dioxide becomes a spectroscopically significant photochemical product on colder young Jupiters (see section 3.2), and the effect is further magnified the greater the incident UV flux.

Figure 9.— Integrated column abundance of CO (top left), HCN (top right), CH (bottom left), and CH (bottom right) above 1 mbar as a function of  and  for planets with a surface gravity of = 10 located at 68 AU from a star with the properties of HR 8799. Photochemistry dominates in this region of the atmosphere, and different species exhibit a complicated sensitivity to both  and . A color version of this figure is available in the online journal.

Figure 9 provides further details showing how the photochemical products CO (top left), HCN (top right), CH (bottom left), and CH (bottom right) vary with changes in both  and , for planets with log() = 3.5 cgs located 68 AU from a star like HR 8799. For the shape of the vertical  profiles we have assumed (see Fig. 2), smaller  values also correspond to weaker eddy mixing in the lower stratosphere, which increases the residence time for photochemical products synthesized at higher altitudes, allowing them to build up to larger abundances. Therefore, most photochemical products exhibit increased abundances for smaller  values. One exception is HCN, which has a more complicated dependence because larger  values favor larger quenched abundances of HCN; i.e., quenching, not just photochemistry, contributes to the overall abundance of HCN. For any particular  value, the temperature dependence can be complicated, with CO exhibiting a major increase at the lowest temperatures for the reasons discussed above, CH being favored at moderately low temperatures, and CH and HCN being favored at   1200 K.

In general, hydrocarbons such as CH and CH are not expected to become abundant enough to be observable on young Jupiters, except potentially for closer-in planets (i.e., those receiving a large UV flux) in combination with a more stagnant (lower ) lower stratosphere and an increasingly well-mixed and colder (250 K) upper stratosphere, in which water recycling is less effective and the resulting H production is reduced. Low upper-atmospheric temperatures favor CH over CH, while higher temperatures favor CH. The quenched HCN abundance reaches potentially observable abundances of a few 10 cm above 100 mbar for large  ( 10 cm s), and a high UV flux combined with moderate  of 1100–1300 K would provide an increased photochemical component on top of that that quenched HCN. Carbon dioxide is the big winner from a disequilibrium-chemistry standpoint, with observable quantities (see section 3.2) of greater than 10 cm above 100 mbar being produced through both quenching and photochemistry in all the models studied, with a column abundance greater than 10 cm above 100 mbar forming in the planets with cooler, more stagnant lower stratospheres.

Figure 10.— Synthetic spectra from our photochemical models of generic young Jupiters orbiting at 68 AU from a star with the properties of HR 8799, with planetary properties of log() = 4.0 cgs, = 1.2, a global gray absorbing cloud (no patchiness), at a distance of 39 pc from Earth, for (Left)  = 600 K and  = 10 cm s and (Right)  = 1000 K and  = 10 cm s. The cloud base is assumed to be located at the pressure where the MgSiO condensation curve crosses the temperature profile, and the cloud is assumed to extend to the top of the atmosphere, with the opacity adjusted such that the optical depth is unity between 1 and 10 bars. The plots show how various photochemical products affect the spectra, through the removal of CO (blue), HCN (red), and CH (green) from the spectral calculations. Of these photochemical products, only CO affects the spectra significantly at near-IR wavelengths. A color version of this figure is presented in the online journal.
Figure 11.— Synthetic spectra from our photochemical models of generic young Jupiters orbiting 68 AU from a star with the properties of HR 8799, with surface gravities = 3200 cm s, eddy  = 10 cm s, and effective temperatures  = 600 K (blue), 900 K (orange), and 1200 K (red). These models correspond to the ones shown in Fig. 8. For the purpose of the spectral calculations, we have assumed that the planets have radii = 1.0, are located 39 pc from Earth, and possess uniform gray absorbing clouds with optical depths of one between the base of the MgSiO condensation region and the top of the atmosphere. Note that the absorption in most of the molecular bands (e.g., HO, CH, NH, and CO) increases as  decreases (cf. Fig. 8). A color version of this figure is available in the online journal.
Figure 12.— Synthetic spectra from our photochemical models of generic young Jupiters with  = 1000 K, = 10 cm s,  = 10 cm s, orbiting a star with the properties of HR 8799 at 10 AU (red), 32 AU (green), and 100 AU (blue). These models correspond to the ones shown in Fig. 7. For the purpose of the spectral calculations, we have assumed that the planets have radii = 1.2, are located 39 pc from Earth, and possess uniform gray absorbing clouds with optical depths of one between 1 and 10 mbar. Note that at this relatively high  and  the photochemical products have little impact on the spectrum, except for the minor increase in CO absorption at 4.2-4.3 m in the shorter-period model, due to its greater photochemical production and correspondingly larger CO abundance. A color version of this figure is available in the online journal.

3.2. Generic Directly Imaged Planets: Spectra

We show selected spectra from our directly imaged planets in Figs. 10 & 11. These synthetic spectra were generated from the forward radiative-transfer model described in Line et al. (2013, 2014, 2015). First, Fig. 10 shows results from two generic models with different quenched abundances of CH and CO. Both planets are assumed to be 39 pc from Earth, with surface gravities of 10 cm s, a radius of 1.2, and a uniform gray absorbing aerosol layer with a base located where the thermal profile crosses the MgSiO condensation curve and a total optical depth of unity between 1 bar and 10 bars. Both planets are assumed to orbit 68 AU from a star with properties of HR 8799. The planet shown in the left panel has  = 600 K and  = 10 cm s, for which the quenched CH mixing ratio is 2.4 times that of CO (see Fig. 5). The planet in the right panel has  = 1000 K and  = 10 cm s, such that the quenched CO mixing ratio is 18 times that of CH. Absorption features of HO are readily apparent in the spectra of both planets in bands near 1.4, 1.8-1.9, 2.6-2.8, and the 5.5-7.5 m region, and CO absorption features are apparent in both plots in the 4.5-4.8 m region. Although CH absorption features are also obvious in both plots, the bands at 2.3, 3.3, and 7.7 m are deeper for the cooler planet, with its larger quenched methane abundance. The cooler planet also has a larger column of photochemically produced CO, which shows up most distinctly in the 4.2-4.3 m absorption bands on both planets, as well as more subtlely in the 2.7-2.8-m region on the warmer planet and the 14-16 m region on the cooler planet. Absorption in the 4.2–4.3-m CO bands should be particularly apparent on young Jupiters, trending toward greater absorption for lower . HCN is abundant enough on the warmer, more rapidly mixed planet (see Fig. 9) to have a minor effect on the spectrum at 3 m, while other photochemical products such as CH are not abundant enough to notably affect the spectra for either of these generic young Jupiters considered.

Figure 11 further illustrates how the spectra of our generic young Jupiters changes as a function of . In this figure, we plot the synthetic spectra from the photochemical models shown in Fig. 8 — these planets are assumed to orbit 68 AU from a star with properties similar to HR 8799, and have = 3200 cm s,