Solar Oscillations and Convection. I. Formalism for Radial Oscillations

Abstract

Solar p-mode oscillations are excited by the work of stochastic, nonadiabatic, pressure fluctuations on the compressive modes. We evaluate the expression for the radial mode excitation rate derived by Nordlund & Stein using numerical simulations of near-surface solar convection. We first apply this expression to the three radial modes of the simulation and obtain good agreement between the predicted excitation rate and the actual mode damping rates as determined from their energies and the widths of their resolved spectral profiles. These radial simulation modes are essentially the same as the solar modes at the resonant frequencies, where the solar modes have a node at the depth of the bottom of the simulation domain. We then apply this expression for the mode excitation rate to the solar modes and obtain excellent agreement with the low l damping rates determined from data obtained by the ``global oscillations at low frequencies'' (GOLF) instrument on SOHO. Excitation occurs close to the surface, mainly in the intergranular lanes and near the boundaries of granules (where turbulence and radiative cooling are large). The nonadiabatic pressure fluctuations near the surface are produced by small instantaneous local imbalances between the divergence of the radiative and convective fluxes near the solar surface. Below the surface, the nonadiabatic pressure fluctuations are produced primarily by turbulent-pressure fluctuations (Reynolds stresses). The frequency dependence of the mode excitation is due to effects of the mode structure and the pressure fluctuation spectrum. Excitation is small at low frequencies because of mode properties-the mode compression decreases and the mode mass increases at low frequency. Excitation is small at high frequencies because of the pressure fluctuation spectrum-pressure fluctuations become small at high frequencies because they are due to convection, which is a long-timescale phenomenon compared with the dominant p-mode periods.