Characteristic frequencies of giant exoplanets

We calculate the eigenfrequencies and eigenfunctions of the acoustic oscillations of giant exoplanets and explore the dependence of the characteristic frequency {nu}_0_ 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 {nu}_0_ which gives us an estimate of the scale of the eigenvalue spectrum at high frequency. For the mass range 0.5M_J_<=M_P_<=15M_J_, and fixing the planet radius to the Jovian value, we find that {nu}_0_~164.0x(M_P_/M_J_)^0.48^{mu}Hz, where M_P_ is the planet mass and M_J_ is Jupiter's mass. For the radius range from 0.9 to 2.0R_J_, and fixing the planet's mass to the Jovian value, we find that {nu}_0_~164.0x(R_P_/R_J_)^-2.09^{mu}Hz, where R_P_ is the planet radius and R_J_ is Jupiter's radius.