All Figures

$\begin{figure} \par\resizebox{7cm}{!}{\includegraphics[clip]{3698fig1.eps}}\end{figure}$ Figure 1: Sketch of the geometry: $\Theta$ is the total scattering angle, and $\alpha$ is the planetary phase angle, i.e. the angle between the star and the observer as seen from the center of the planet.
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{8.25cm}{!}{\includegraphics[clip]{3698fig2.eps}}\end{figure}$ Figure 2: The phase functions of a planet with a non-absorbing molecular model atmosphere of (scattering) optical thickness 0.575 (solid lines), 5.75 (dashed lines), 57.5 (dotted lines), and 575.0 (dot-dashed lines) calculated neglecting polarization, thus using $1 \times 1$ matrices (thick lines), and taking polarization into account, thus using $3 \times 3$ matrices (thin lines).
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{18cm}{!}{\includegraphics[clip]{3698fi3a.eps} \hspace*{1.5cm} \includegraphics[clip]{3698fi3b.eps}}\end{figure}$ Figure 3: The errors in the phase functions of Fig. 2 when polarization is neglected, thus when $1 \times 1$ matrices are used instead of $3 \times 3$ matrices: a) the absolute errors, and b) the relative errors. The errors are shown for atmospheric (scattering) optical thicknesses b of 0.575 (solid line), 5.75 (dashed line), 57.5 (dotted line), and 575.0 (dot-dashed line). There is no absorption in the atmosphere. Note that the absolute errors for $b \geq 5.75$ and the relative errors for $b \geq 57.5$ are virtually indistinguishable.
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{8.25cm}{!}{\includegraphics[clip]{3698fig4.eps}}\end{figure}$ Figure 4: The geometric albedos, $A_{\rm G}$ , and the Bond albedos, $A_{\rm B}$ , of a planet with non-absorbing molecular model atmosphere as functions of the atmospheric (scattering) optical thickness b, calculated neglecting polarization (thick lines), and taking polarization into account (thin lines). The thick and thin lines pertaining to the Bond albedo are indistinguishable. The vertical dotted lines indicate the values of b that were used in Figs. 2 and 3.
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{18cm}{!}{\includegraphics[clip]{3698fi5a.eps} \hspace*{1.5cm} \includegraphics[clip]{3698fi5b.eps} }\end{figure}$ Figure 5: The absolute a) and relative b) errors in $A_{\rm G}$ and $A_{\rm B}$ of Fig. 4 that are due to neglecting polarization. Both the absolute and the relative error in the Bond albedo $A_{\rm B}$ have been multiplied with 100. The maximum absolute error in $A_{\rm B}$ is thus about 0.0001, and the maximum relative error is about 0.017 $\%$ .
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{8.25cm}{!}{\includegraphics[clip]{3698fig6.eps}}\end{figure}$ Figure 6: The geometric albedo, $A_{\rm G}$ , and the Bond albedo, $A_{\rm B}$ , of a clear (i.e. without aerosol/cloud layers), Jupiter-like planet as functions of the wavelength, for $1 \times 1$ matrices (thick line) and $3 \times 3$ matrices (thin line). The thick and thin lines pertaining to the Bond albedo are indistinguishable. The vertical dotted line indicates the wavelength at which the atmospheric scattering optical thickness equals 5.75, the value used in Figs. 2 and 3.
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{8cm}{!}{\includegraphics[clip]{3698fig7.eps}}\end{figure}$ Figure 7: Similar to Fig. 6, except with a cloud layer of scattering optical thickness 6.0 at $\lambda=0.55~\mu$ m added to the deepest layers of the planetary model atmosphere.
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{18cm}{!}{\includegraphics[clip]{3698fi8a.eps} \hspace*{1.5cm} \includegraphics[clip]{3698fi8b.eps} }\end{figure}$ Figure 8: The absolute a) and relative b) errors in $A_{\rm G}$ that are due to neglecting polarization. The thin lines pertain to the clear atmosphere (Fig. 6) and the thick lines to the cloudy atmosphere (Fig. 7).
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{18cm}{!}{\includegraphics[clip]{3698fi9a.eps} \hspace*{1.5cm} \includegraphics[clip]{3698fi9b.eps} }\end{figure}$ Figure 9: The absolute a) and relative b) errors in $A_{\rm B}$ that are due to neglecting polarization. The thin lines pertain to the clear atmosphere (Fig. 6) and the thick lines to the cloudy atmosphere (Fig. 7). Both the absolute and the relative error in the Bond albedo $A_{\rm B}$ have been multiplied with 100. The maximum absolute error in $A_{\rm B}$ is thus about 0.0007 for the clear atmosphere, and 0.00015 for the cloudy atmosphere. The maximum relative error is about 0.3 $\%$ for the clear atmosphere and about 0.08 $\%$ for the cloudy atmosphere.
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{18cm}{!}{\includegraphics[clip]{3698f10a.eps} \hspace*{1.5cm} \includegraphics[clip]{3698f10b.eps} }\end{figure}$ Figure 10: The errors in the phase functions of the cloudy model planet when polarization is neglected: a) the absolute errors, and b) the relative errors. The errors are shown at the following wavelengths: 0.55 $\mu$ m (solid line), 0.75 $\mu$ m (dashed line), and 0.95 $\mu$ m (dotted line).
Open with DEXTER

In the text

$\begin{figure} \par\resizebox{7cm}{!}{\includegraphics[clip]{3698fig1.eps}}\end{figure}$	Figure 1: Sketch of the geometry: $\Theta$ is the total scattering angle, and $\alpha$ is the planetary phase angle, i.e. the angle between the star and the observer as seen from the center of the planet.
Open with DEXTER

$\begin{figure} \par\resizebox{8.25cm}{!}{\includegraphics[clip]{3698fig2.eps}}\end{figure}$	Figure 2: The phase functions of a planet with a non-absorbing molecular model atmosphere of (scattering) optical thickness 0.575 (solid lines), 5.75 (dashed lines), 57.5 (dotted lines), and 575.0 (dot-dashed lines) calculated neglecting polarization, thus using $1 \times 1$ matrices (thick lines), and taking polarization into account, thus using $3 \times 3$ matrices (thin lines).
Open with DEXTER

$\begin{figure} \par\resizebox{18cm}{!}{\includegraphics[clip]{3698fi5a.eps} \hspace*{1.5cm} \includegraphics[clip]{3698fi5b.eps} }\end{figure}$	Figure 5: The absolute a) and relative b) errors in $A_{\rm G}$ and $A_{\rm B}$ of Fig. 4 that are due to neglecting polarization. Both the absolute and the relative error in the Bond albedo $A_{\rm B}$ have been multiplied with 100. The maximum absolute error in $A_{\rm B}$ is thus about 0.0001, and the maximum relative error is about 0.017 $\%$ .
Open with DEXTER

$\begin{figure} \par\resizebox{8cm}{!}{\includegraphics[clip]{3698fig7.eps}}\end{figure}$	Figure 7: Similar to Fig. 6, except with a cloud layer of scattering optical thickness 6.0 at $\lambda=0.55~\mu$ m added to the deepest layers of the planetary model atmosphere.
Open with DEXTER

$\begin{figure} \par\resizebox{18cm}{!}{\includegraphics[clip]{3698fi8a.eps} \hspace*{1.5cm} \includegraphics[clip]{3698fi8b.eps} }\end{figure}$	Figure 8: The absolute a) and relative b) errors in $A_{\rm G}$ that are due to neglecting polarization. The thin lines pertain to the clear atmosphere (Fig. 6) and the thick lines to the cloudy atmosphere (Fig. 7).
Open with DEXTER

$\begin{figure} \par\resizebox{18cm}{!}{\includegraphics[clip]{3698f10a.eps} \hspace*{1.5cm} \includegraphics[clip]{3698f10b.eps} }\end{figure}$	Figure 10: The errors in the phase functions of the cloudy model planet when polarization is neglected: a) the absolute errors, and b) the relative errors. The errors are shown at the following wavelengths: 0.55 $\mu$ m (solid line), 0.75 $\mu$ m (dashed line), and 0.95 $\mu$ m (dotted line).
Open with DEXTER