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Pulsation Frequencies and Modes of Giant Exoplanets

We calculate the eigenfrequencies and eigenfunctions of the acoustic oscillations of giant exoplanets and explore the dependence of the characteristic frequency and the eigenfrequencies on several parameters: the planet mass, the planet radius, the core mass, and the heavy element mass fraction in the envelope. We provide the eigenvalues for degree $l$ up to 8 and radial order n up to 12. For the selected values of l and n, we find that the pulsation eigenfrequencies depend strongly on the planet mass and radius, especially at high frequency. We quantify this dependence through the calculation of the characteristic frequency which gives us an estimate of the scale of the eigenvalue spectrum at high frequency. For the mass range 0.5 < M_P < 15 M_J, and fixing the planet radius to the Jovian value, we find that the characteristic frequency is ~164.0 * (M_P/M_J)^(0.48) microHz, where M_P is the planet mass and M_J is Jupiter's mass. For the radius range from 0.9 to 2.0 R_J, and fixing the planet's mass to the Jovian value, we find that the characteristic frequency is ~164.0 * (R_P/R_J)^(-2.09) microHz, where R_P is the planet radius and R_J is Jupiter's radius. We explore the influence of the presence of a dense core on the pulsation frequencies and on the characteristic frequency of giant exoplanets. We find that the presence of heavy elements in the envelope affects the eigenvalue distribution in ways similar to the presence of a dense core. Additionally, we apply our formalism to Jupiter and Saturn and find results consistent with both the observationnal data of Gaulme et al. (2011) and previous theoretical work.