Irradiated Planets Peter H. Hauschildt 1, Travis Barman 2 and E. Baron 3,4 1 Hamburger Sternwarte, Gojenbergsweg 112, 21029 Hamburg, Germany 2 Lowell Observatory, Hendricks Center for Planetary Studies, 1400 W. Mars Hill Rd., Flagstaff, AZ 86001, USA 3 Dept. of Physics and Astronomy, University of Oklahoma, 440 W. Brooks, Rm 100, Norman, OK 73019, USA 4 Computational Research Division, Lawrence Berkeley National Laboratory, MS 50F-1650, 1 Cyclotron Rd, Berkeley, CA 94720-8139, USA E-mail: yeti@hs.uni-hamburg.de Abstract. We present models for the spectra emitted by irradiated planets and discuss the numerical methods used in the modeling. In addition, we show results of simple 3D calculations that are designed as a first step towards detailled multidimensional models of irradiated planets 1. Introduction Most of the extrasolar planets discovered so far are very close to their parent stars. Therefore, the day-time hemispheres of such planets (which are very likely co-rotating with their orbit due to tidal locking) are strongly affected by the irradiation from the parent star, with incoming fluxes are often million times (for gas giants, the factor is even bigger for terrestrial planets) larger than the intrinsinc flux emitted by such planets if they would be left to their own. This also means that the spectra of the planets emitted by the day-time hemisphere will be very different from the night-time hemispheres, leading to strongly phase dependent specta of these planets. Of the more than 100 extrasolar planetary systems discovered so far, only very few have near edge-on orbits. These transiting planets are crucial for understanding giant planets in general since their masses and radii can easily be determined, and careful multi-wavelength observations can reveal some information about the planet s atmosphere. Recently, two transiting planets, HD209458b and TrES-1, were observed with the Spitzer Space Telescope, providing the first direct measurements of their thermal flux. These measurements provide the best constraints, so far, on the thermal structure and chemical composition of highly irradiated EGPs. Modeling the effects of irradiation on the structure of the day-side hemisphere is crucial for the interpretation of observed planetary spectra. It is also interesting to investigate the effects of horizontal energy transport by radiation and the leakage of radiation into the night-side of the planet. Treated correctly, irradiation is at least a
Irradiated Planets 2 Figure 1. Simple 1.5D modeling of irradiated planets. Each segment represents a ring of the planet s hemisphere with different irradiated angle (the zenith angle relative to the sub-stellar point). The segments are treated as 1D plane-parallel or spherical zones that are irradiated under different angles. Figure 2. Results of 1.5D modeling of irradiated planets. Each spectrum represents the sub-stellar point for different orbital separation between planet and parent star. 2D radiation transport problem in an atmosphere with strong temperature variations in both depth as well as distance from the sub-stellar point. In this contribution we describe some results of simple 1.5D modeling of irradiated planets and initial results of 3D radiation transport models for irradiated spheres. 2. 1.5D Modeling The basic idea of the 1.5D (or patchwork) models is illustrated in Figure 1, see (Barman et al. 2005) for details. Each surface element of the planet is treated as a 1D spherical shell with incident angles of irradiation varying according to the angular distance from
Irradiated Planets 3 Figure 3. Results of 1.5D modeling for HD 209458b. The (P, T ) structures are shown for different rings of the irradiated planets. Also indicated are the limits of formation of various solids. Figure 4. Example of a 2D temperature structure derived from the 1.5D models. Structures like this can be directly used in 2D or 3D radiative transfer calculations. the sub-stellar point. The night-side is treated approximately as a single atmosphere with no irradiation. This approach neglects horizontal energy transport, but models the variation of irradiation across the day-side hemisphere of the planet. Typically, the planetary atmospheres are modeled by dividing the day side into 10 concentric regions defined by µ = cos(θ), where θ is the angle between the surface normal and the direction to the star (see Figure 1). For these regions, µ typically ranges from 1.0 (at the sub-stellar point) to 0.1 (the model region closest to the terminator), in steps of µ = 0.1. The corresponding T-P profiles and emergent intensities were modeled using 1-D, spherically symmetric, atmospheres each receiving incident stellar flux along the appropriate angle for a given region. The incident fluxes can be expressed
Irradiated Planets 4 Figure 5. Example of a 3D radiation transfer modeling of a perfectly absorbing irradiated sphere. Contour lines of the mean intensity J are shown. The red circle shows the size of the planet (outer boundary). The left panel is for an isolated, non irradiated sphere, the right panel shows the results for a sphere that is irradiated with 1 million times its internal luminosity. Figure 6. Example of a 3D radiation transfer modeling of a irradiated sphere with a thermalization parameter ɛ = 10 2 (in 99 out of 100 interactions, photons are scattered). Contour lines of the mean intensity J are shown. The red circle shows the size of the planet (outer boundary). The left panel is for an isolated, non irradiated sphere, the right panel shows the results for a sphere that is irradiated with 1 million times its internal luminosity. as ( ) 2 R F inc,λ (µ) = µi,λ = µ F,λ, (1) d where F,λ are the monochromatic fluxes from the star s surface, R is the stellar radius, and d is the distance from the stellar surface to the planet s atmosphere. For the night side, a single, non-irradiated, model was used. All models have to be calculated self-consistently so that each µ-region has a chemistry characterized by its local T-P profile. By having chemical equilibria consistent with the T-P profiles across the planet s atmosphere, this approach naturally leads to variations in the important photospheric
Irradiated Planets 5 opacity sources from the day to night side an important aspect when computing the synthetic spectra. Since giant planets are believed to have fully convective interiors, the intrinsic effective temperature (T int ). Here, T int characterizes the intrinsic luminosity of an irradiated model atmosphere, defined by 4πR 2 p σt int 4. For non-irradiated models, the normal T eff is used to describe the flux and luminosity. For irradiated models, each modeled region was adjusted so that, after convergence, all T-P profiles reached the same adiabat below the photosphere. The region referred to as the photosphere lies roughly between P = 0.01 and 1 bar, corresponding to where the optical depth at IR wavelengths is near unity. The adiabat was selected based on planetary interior and evolution calculations for a given mass, age, metallicity, and irradiation. This entropy matching technique has also been used for irradiated binary stars and allows one to assign models with different intrinsic luminosities to different regions of the same star or planet, see Barman et al. (2005) for details. In Figure 2 we show the structures and emitted spectra of irradiated planets for the sub-stellar point at different orbital distances from the parent star. The effect of the irradiation increases rapidly with smaller separation. The variation of the temperature structure across the day-side hemisphere of a planet is shown for HD 209458b in Figure 3. The difference between the sub-stellar point and the limb of the planet is very obvious, the horizontal temperature gradients are very significant. 3. 3D Modeling Figure 4 shows the combined results of the 1.5D modeling as a 2D temperature plot. Such models can be used as input to calculate spectra (and later on structures) with 3D radiative transfer codes. In Figure 5 and Figure 6 we show the results of 3D radiative transfer calculations (Hauschildt & Baron 2006, Baron & Hauschildt 2007) for test cases with and without irradiation (the x-z plane is shown in the figures). The irradiation is set to 1 million times stronger than the intrinsic luminosity of the planet (typical for giant planets) and the planet s atmosphere is set to either perfectly absorbing (ɛ = 1) or moderately scattering (ɛ = 10 2 ). The effects of irradiation are large and increase for stronger scattering. This will introduce horizontal radiative energy transport and also affect the night-side hemisphere. In addition, the phase dependent spectra will likely be affected, in particular transit spectra. We will investigate this in later work. 4. Conclusions In this contribution we briefly discussed the methodology and results of 1.5D modeling of irradiated planets and the extension of this approach to true 2D or 3D modeling, which becomes feasible now.
Irradiated Planets 6 Acknowledgments PHH s work on this project was supported in part by the DFG via Graduiertenkolleg 1351. EB was supported in part by by NASA grant NNG04GD368, and NSF grant AST- 0307323. Some of the calculations presented here were performed at the Höchstleistungs Rechenzentrum Nord (HLRN); at the NASA s Advanced Supercomputing Division s Project Columbia, at the Hamburger Sternwarte Apple G5 and Delta Opteron clusters financially supported by the DFG and the State of Hamburg; and at the National Energy Research Supercomputer Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098. We thank all these institutions for a generous allocation of computer time. References Barman T S, Hauschildt P H & Allard F 2005 ApJ 632, 1132 1139. Baron E & Hauschildt P H 2007 A&A 468, 255 261. Hauschildt P H & Baron E 2006 A&A 451, 273 284.