Coupling of acoustic waves to clouds in the jovian troposphere
Introduction
Jupiter's internal structure is poorly known. The size of the planetary core, if any, remains unknown (Guillot, 1999), the high pressure hydrogen equation of state is still inaccurate, and the existence of a plasma phase transition at the metallic-molecular limit is still open (Saumon and Guillot, 2003). Seismology is a powerful tool to investigate the internal structure of planets and stars, by analyzing how acoustic waves propagate. Mosser (1997) and Gudkova and Zharkov (1999) showed that the detection and identification of non-radial modes up to the degree can constrain strongly the internal structure. The first theoretical studies of jovian oscillations were due to Vorontsov et al. (1976), whereas attempts to observe them began in the late 1980's (Schmider et al., 1991).
Different methods may be used to observe seismic waves which propagate through the interior and are trapped below the tropopause (Mosser, 1995). Doppler spectrometry is used to measure the velocity field in the upper troposphere. Infrared photometry is sensitive to the temperature fluctuations associated with the acoustic waves. Visible photometry is sensitive to the reflected solar flux changes related to wave displacements and their effects.
The main difficulty in detecting jovian oscillations is the weakness of the signal. The thermal infrared photometric measurements of Deming et al. (1989) yielded an upper limit to the velocity field amplitude around 1 m s−1. Mosser et al. (2000) reduced the upper limit to 0.6 m s−1 and proposed the identification of a typical oscillation signature: the removal of degeneracy due to the planet rotation. More recently, Vid'machenko (2002) detected brightness oscillations in the visible spectrum, whose frequencies could correspond to jovian modes. A new instrumental concept, dedicated to planetary seismology, was proposed by Schmider et al. (2002). The instrument, a Mach-Zehnder interferometer, can measure up to degree and was used in first campaign in 2003.
In contrast to a stellar target, whose photometric seismic signature in the visible is due to the brightness temperature change, the jovian visible flux depends mainly on how the solar flux is reflected in the planetary upper atmosphere. As a first approach, by considering only the geometrical distortions of Jupiter due to the seismic oscillations, Mosser (1995) showed that a velocity field characterized by an amplitude of about 50 cm s−1 and a period of 500 s induces relative variations of the reflected flux at the ppm level, what indicates that such weak photometric fluctuations are detectable only from space. The basic principle relies on the ability with high precision photometry to detect periodic oscillations in a noisy signal (Mosser et al., 2004). This is currently the most efficient method, according to the existing technology.
The present work focuses on photometry in the visible domain and the photometric signature of the acoustic waves. We calculate the response of the clouds subjected to acoustic waves. Two effects are studied: the albedo changes due to the displacement of the clouds without thermodynamics, and the albedo changes related to the thermodynamical evolution of the cloud. In this paper, we study the behavior of a single cloud layer. The generalization of this model to the whole planet, by taking into account all the spatial and temporal variations in the cloud decks will be presented in a future paper.
According to the standard model, three main cloud layers are present in the jovian troposphere: aqueous ammonia clouds around the 3-bar level, ammonium hydrosulfide layer in the pressure range [1.5, 2] bar and ammonia ice in the range [0.3, 0.7] bar (see, e.g., Atreya et al., 1999). Since our work focuses on the visible flux reflected in the troposphere, we consider only the ammonia ice layer. We first present a cloud model for the icy ammonia layer, in order to estimate the thermodynamical response of the cloud to a pressure perturbation (Section 2). The propagation of acoustic waves in the troposphere is revisited, taking into account the inclusion of a cloud layer, in order to analyze the motion of the clouds (Section 3). Then, the phase changes estimated from thermodynamics are analyzed in terms of microphysics and atmospheric kinetics (Section 4). After a presentation of the radiative transfer model (Section 5), we investigate the evolution of clouds in term of albedo variation (Section 6). The last section is devoted to conclusions (Section 7).
Section snippets
Temperature profile and clouds
The temperature pressure profile is obtained by fitting the Voyager data (Lindal et al., 1981) from the 1-bar level to the tropopause, with an adiabatic profile for the deeper layers. The atmosphere is assumed to be composed of an homogeneous mixture of molecular hydrogen (), helium (), and ammonia, where indicates the molar fraction. The ammonia molar fraction is usually estimated to have values between and at pressure levels greater than 5 bar, while it decreases
The propagation
The propagation of acoustic waves in the upper troposphere is treated in the same way as in Mosser (1995), with the addition of an ammonia ice cloud layer. The propagation model incorporates the same assumptions as in the atmospheric model: plane parallel atmosphere with an ammonia cloud layer. Furthermore, propagation is only vertical, which is valid for the modes with a degree ℓ less than a few thousand, and is adiabatic.
The linearized equations governing the evolution of the Eulerian
Microphysical aspects
The relations established previously according to the thermodynamics may be not hold if kinetics were too slow and equilibrium not valid. Saturation is defined as the ratio of the partial pressure of the condensable gas and its vapor pressure: Condensation occurs when the atmosphere is supersaturated (), while sublimation occurs when the atmosphere is subsaturated. Since the wave is a perturbation term, supersaturation is too weak to create new particles. Thus, we consider
Radiative transfer code
The calculation of the radiative transfer is composed of two steps: a Mie code (Mishchenko et al., 2002) that generates the particle optical properties and a two-stream code that calculates the radiative transfer through the cloud.
First, when cloud particles have a non-negligible size compared to the incident wavelength and are spherical, Maxwell's equations may be solved in spherical coordinates, Mie calculations, to retrieve the scattering properties (see, e.g., Hansen and Travis, 1974). Mie
Cloud albedo variations
The cloud albedo variations depend mostly on how the particle size varies with height and where the reflected light mainly originates. The answer to these questions is determined by a set of five parameters whose values are not precisely constrained: the ammonia abundance , the sedimentation parameter , the cloud optical depth , the mean particles size , and the subcloud reflectivity . The ranges of parameter space explored for these five parameters and the assumed default values
Conclusions
We have analyzed how the phases equilibrium in the jovian ammonia clouds is perturbed by acoustic waves. The coupling between the pressure modes and the cloud layers introduces albedo variations as large as the 70-ppm level for a velocity amplitude of 50 cm s−1 at the base of the cloud. Although this amplitude depends strongly on the subcloud conditions, on the particle size and on the latitudinal abundance variations, it is at least a few tens of ppm.
Therefore, assuming a photometric precision
Acknowledgements
We thank particularly Bruno Bézard for providing us with an efficient radiative transfer code and for his help in radiative transfer. We also thank Thierry Fouchet for his precious indications on the jovian cloud structure, Chantal Levasseur-Regourd for her suggestions about the Mie codes, and Darell Strobel for helpful discussion and careful reading of the paper.
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