Atmospheric Circulation and Tides Of" 51Peg B-Like" Planets
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A&A manuscript no. ASTRONOMY (will be inserted by hand later) AND Your thesaurus codes are: ASTROPHYSICS 08 Atmospheric Circulation and Tides of “51Pegb-like” Planets Adam P. Showman1 and Tristan Guillot2 1 University of Arizona, Department of Planetary Sciences and Lunar and Planetary Laboratory, Tucson, AZ 85721; show- [email protected] 2 Observatoire de la Cˆote d’Azur, Laboratoire Cassini, CNRS UMR 6529, 06304 Nice Cedex 4, France; [email protected] Submitted 23 March 2001; Accepted 18 January 2002 Abstract. We examine the properties of the atmo- the similar brown dwarfs, for which theoretical models spheres of extrasolar giant planets at orbital distances now reproduce the observations well, even in the case of smaller than 0.1 AU from their stars. We show that these low-temperature objects (Teff ∼ 1000K or less) (e.g. Mar- “51 Peg b-like” planets are rapidly synchronized by tidal ley et al. 1996; Allard et al. 1997; Liebert et al. 2000; interactions, but that small departures from synchronous Geballe et al. 2001; Schweitzer et al. 2001 to cite only a rotation can occur because of fluid-dynamical torques few). However, an important feature of extrasolar plan- within these planets. Previous radiative-transfer and evo- ets is their proximity to a star: The irradiation that they lution models of such planets assume a homogeneous at- endure can make their atmospheres significantly different mosphere. Nevertheless, we show using simple arguments than those of isolated brown dwarfs with the same ef- that, at the photosphere, the day-night temperature dif- fective temperature. This has been shown to profoundly ference and characteristic wind speeds may reach ∼ 500K alter the atmospheric vertical temperature profile (Sea- and ∼ 2kmsec−1, respectively. Substantial departures ger and Sasselov 1998; Goukenleuque et al. 2000; Barman from chemical equilibrium are expected. The cloud cov- et al. 2001). We will show that most importantly, it also erage depends sensitively on the dynamics; clouds could affects the horizontal temperature distribution and atmo- exist predominantly either on the dayside or nightside, spheric chemistry so that the models calculated thus far depending on the circulation regime. Radiative-transfer may fail to provide an adequate description of the atmo- models that assume homogeneous conditions are there- spheres of the most intensely irradiated planets. Advec- fore inadequate in describing the atmospheric properties tion has never previously been considered, but it can play of 51 Peg b-like planets. We present preliminary three- a major role for the composition, temperature, spectral dimensional, nonlinear simulations of the atmospheric cir- appearance and evolution of extrasolar planets. culation of HD209458b that indicate plausible patterns for We will focus on the extrasolar planets for which irra- arXiv:astro-ph/0202236v1 12 Feb 2002 the circulation and generally agree with our simpler esti- diation is the most important: 51 Peg b-like planets, which mates. Furthermore, we show that kinetic energy produc- we henceforth dub “Pegasi planets” and define as gas gi- tion in the atmosphere can lead to the deposition of sub- ants orbiting solar-type stars at less than 0.1 AU. Their stantial energy in the interior, with crucial consequences importance is demonstrated by the fact that they orbit for the evolution of these planets. Future measurements nearly 1% of stars surveyed so far and constitute 27% of of reflected and thermally-emitted radiation from these currently-known extrasolar giant planets. They are also planets will help test our ideas. more easily characterized by the transit method than are other planets, as indicated by the discovery of the transit- Key words: extrasolar planets, 51 Peg, HD209458, tides, ing gas giant HD209458b (Charbonneau et al. 2000; Henry atmospheric dynamics, interior structure, giant planets et al. 2000). In the preceeding paper (Guillot and Show- man 2001, hereafter Paper I), we showed how the atmo- spheric boundary condition governs the evolution of Pe- 1. Introduction gasi planets. We also advocated that an additional source of energy is needed to explain the radius HD209458b, and The discovery of extrasolar planets has led to a growing that this would most likely be provided by the down- list of work devoted to modeling their atmospheres (Bur- ward transport and subsequent dissipation of kinetic en- rows et al. 1997; Seager and Sasselov 1998, 2000; Gouken- ergy with a flux of ∼ 1% of the absorbed stellar energy. leuque et al. 2000; Barman et al. 2001). While no spec- In this paper, we use the temperature profiles obtained tra of these objects have yet been measured, one might in Paper I to evaluate the dynamical state of Pegasi- be encouraged by the successes obtained in the case of planet atmospheres, and discuss how dynamics may in- 2 A.P. Showman and T. Guillot: Dynamics of Pegasi-planet Atmospheres fluence the cloud abundance, chemical composition, and thermal state (all of which will be amenable to observation in the near future). We then present preliminary numer- ical simulations of the circulation that indicate plausible circulation patterns and show how downward propagation of kinetic energy from the atmosphere to the interior can occur. After reviewing the expected interior structure (Sec- tion 2), we begin in Section 3 with the problem of tides: Pe- gasi planets have been predicted to rotate synchronously (Guillot et al. 1996), implying that they always present the same face toward the star. We argue however that dynamical torques may maintain the interior in a non- synchronous rotation state, which has important impli- cations for understanding atmospheric processes. In sec- tion 4, we discuss the probable wind speeds, day-night Fig. 1. Left: Temperature profiles for the “hot” model temperature differences, and flow geometries, including (thin line) and “cold” model (thick grey line) at times both order-of-magnitude arguments and our numerical (5.37 and 0.18 Ga, respectively) when the models match simulations. A summary of the results is provided in sec- HD209458b’s measured radius. The diamonds indicate tion 5. the radiative/convective boundary. The terms “hot” and “cold” are chosen to indicate the models’ relative tem- 2. Interior structure peratures in the region from ∼ 1–300 bars, which is the important region of the atmosphere for affecting the evo- Fully self-consistent models including both the atmo- lution. See Paper I for details. The discontinuity in the spheres and interiors of Pegasi planets do not yet exist. profiles’ slopes is unphysical; it results from the fact that To obtain first-cut estimates of the expected tempera- atmospheric models assume a much higher intrinsic lumi- ture profiles, we therefore use the same approach as in nosity than predicted by evolution models. Right: Dimen- Paper I: we choose two extreme evolution models (“hot” sionless mean specific heat per particle in the atmosphere. and “cold”) that match the radius of HD209458b (but at The local maxima in c are due to the dissociation of the different ages and hence intrinsic luminosities). These evo- p H molecule. lution calculations only pertain to pressures larger than 3 2 to 10 bars (depending on the boundary condition), and so we extend the profiles to lower pressure using radiative- transfer calculations for intensely-irradiated planets from the planet is about 10,000 times smaller than the energy Marley (personal communication) and Barman (2001). absorbed from the star. If energy dissipation in the outer The calculations are not strictly appropriate to the case of layers is large (see Paper I), another convective zone can HD209458b, but provide us with reasonable estimates of appear at the levels where dissipation is the largest. This the expected structure (and as we will see our qualitative however requires a very high dissipation of ∼ 10% of the conclusions are not sensitive to the type of profile chosen). incoming heat flux. We therefore chose to only consider The resulting “hot” and “cold” models that we will use the simple radiative/convective scenario, as depicted in hereafter are depicted in Figure 1. Interestingly, Paper I Fig. 2. shows that these two models are representative of a rel- We split the planet into an “atmosphere” dominated atively wide variety of models of HD209458b, including by stellar heating, with possible horizontal temperature those with energy dissipation. inhomogeneities, and an “interior” including the con- It should be noted that the high temperatures can trig- vective core, for which inhomogeneities should be much ger the dissociation of the hydrogen molecule, which is in- smaller. The crux of the problem is to understand how dicated in Fig. 1 by a local maximum of the heat capacity the heat absorbed on the day side and near the equator is cp. This effect is important for our purposes because it redistributed by winds and/or rotation to the night side implies that stellar heat can be stored in hot regions and and to the poles. reclaimed in colder regions by molecular recombination. Other molecules (e.g. H O) can undergo dissociation, but 2 3. Synchronization of Pegasi planets this will be neglected due to their small abundances. Evolution models of Pegasi planets show that two in- It has been shown that the tides raised by the star on terior regions exist: a radiative zone (including the atmo- Pegasi planets should rapidly drive them into synchronous sphere) that extends down to pressures of 100 to 800bar, rotation (Guillot et al. 1996; Marcy et al. 1997; Lubow and a deeper convective core. The intrinsic luminosity of et al. 1997). This can be seen by considering the time A.P. Showman and T. Guillot: Dynamics of Pegasi-planet Atmospheres 3 3.1. Spindown energies Angular momentum conservation requires that as the planet spins down, the orbit expands. The energy dissi- pated during the spindown process is the difference be- tween the loss in spin kinetic energy and the gain in orbital energy: d 1 1 E˙ = − k2MR2ω2 − Ma2ω2 , (2) dt 2 2 s where k is the dimensionless radius of gyration (k2 = I/MR2, I being the planet’s moment of inertia).