Linear r-Modes below the Sun’s Convective Envelope

Theoretical properties of linear r-modes in a standard solar interior are computed, and the excitation of some by convective overshoot is estimated. The modes oscillate in a resonant cavity usually occupying most of the nonconvecting interior. Most modes concentrate their kinetic energy toward the center of the Sun. Over half the energy usually lies below 0.15 R☉ with an asymptotic limit of 0.11 R☉ for high radial harmonics (R☉ is the solar radius). The oscillation frequencies are very close to the well-known toroidal frequency, σt = 2Ωm[l(l + 1)]-1, deviating by fractional amounts ~ 10-6±1 which are roughly 3 orders of magnitude smaller than deviations found earlier for r-modes in convective layers. An explicit formula for the ratio of divergent motion to curl motion is derived. It shows how rapidly the compressible component changes as a function of r. Compressibility is only ~ 10-6 of the total motion for low l-modes and declines proportionally to ml-3 for high l. A small subset of modes (the lowest radial harmonic of angular states |m| = l) avoid the core which makes them sensitive to convective overshoot. Just one of the giant convection cells detected by Beck et al. can excite such modes to kilometer-size amplitudes with the possibility that far larger displacement amplitudes can accumulate in the mode over time if the interaction between cells and r-modes is found to be strong.