Free Access
Issue
A&A
Volume 574, February 2015
Article Number A35
Number of page(s) 22
Section Planets and planetary systems
DOI https://doi.org/10.1051/0004-6361/201323127
Published online 20 January 2015

Online material

Appendix A: Additional material

The opacities in the form of k-coefficients used in the numerical model and discussed in Sect. 5.2 are presented in Fig. A.1.

The analytical model adjusted to match the temperature/pressure profile of an atmosphere without TiO, discussed in Sect. 6 is presented in Fig. A.2 and Table A.1.

The effect of a strong internal luminosity on the analytical model, discussed in Sect. 5.5 is presented if Fig. A.3.

thumbnail Fig. A.1

Opacities from Freedman et al. (2008) organized as k-coefficient inside each bin of wavelength atmospheres with different irradiation. The first five panels are for solar-composition atmospheres whereas the bottom right panel is for an atmospheres depleted in TiO/VO. The different colors are for different temperature and pressure taken along the corresponding numerical P-T profile. The thick bars on top represents the wavelength range where 90% of the thermal flux is emitted, the thin bars where 99% of the thermal flux is emitted. We used Tint = 100K, and g = 25m/s2.

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thumbnail Fig. A.2

Top panel: coefficients obtained for the six different models described in Sect. 5.2 as a function of the irradiation temperature for planets with different gravities and an internal temperature of 100 K. TiO and VO have been artificially removed from the atmosphere. Bottom panel: mean relative difference between the numerical and the analytical model for the six different models described in Sect. 5.2. The first line is the mean difference for 10-4bar <P< 10-2bar, the second line for 10-2bar <P< 100bar and the third line for 100bar <P< 102bar. In terms of Rosseland optical depth, the low pressure zone corresponds to the optically thin part of the atmosphere with 10-8 (25 ms-2/ g) ≲ τR ≲ 10-2 (25 ms-2/ g). The medium pressure zone corresponds to the transition from optically thin to optically thick with 10-4 (25 ms-2/ g) ≲ τR ≲ 10 (25 ms-2/ g). The high pressure zone corresponds to the optically thick part of the atmosphere with (25 ms-2/ g) ≲ τR ≲ 104 (25 ms-2/ g).

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Table A.1

Functional form of the coefficients of the analytical model of Paper I valid for atmospheres where TiO and VO have been removed. We use X = log 10(Teff).

thumbnail Fig. A.3

Top panel: coefficients obtained for the six different models described in Sect. 5.2 as a function of the irradiation temperature for planets with a solar composition atmosphere with different gravities and an internal temperature of 100 K, 300 K and 1000 K. The model of Col. D uses the functional form of the coefficients derived in the case Tint = 100 K only. Bottom panel: mean relative difference between the numerical and the analytical model for the six different models described in Sect. 5.2. The first line is the mean difference for 10-4bar <P< 10-2bar, the second line for 10-2bar <P< 100bar and the third line for 100bar <P< 102bar. In terms of Rosseland optical depth, the low pressure zone corresponds to the optically thin part of the atmosphere with 10-8 (25 ms-2/ g) ≲ τR ≲ 10-2 (25 ms-2/ g). The medium pressure zone corresponds to the transition from optically thin to optically thick with 10-4 (25 ms-2/ g) ≲ τR ≲ 10 (25 ms-2/ g). The high pressure zone corresponds to the optically thick part of the atmosphere with (25 ms-2/ g) ≲ τR ≲ 104 (25 ms-2/ g) When TeffTint the low pressures are not properly represented by our model (see Sect. 5.5 for more details).

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© ESO, 2015

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