Distribution functions for the time-averaged energies of stochastically excited solar p-modes

The excitation of a damped harmonic oscillator by a random force is studied as a model for the stochastic excitation of a solar p-mode by turbulent convection. An extended sequence of observations is required to separate different p-modes and thus determine the energies of individual modes. Therefore, the observations yield time-averaged values of the energy. The theory of random differential equations is applied to calculate distribution functions for the time-averaged energy of the oscillator. The instantaneous energy satisfies a Boltzmann distribution. With increasing averaging time, the distribution function narrows and its peak shifts toward the mean energy. Numerical integrations are performed to generate finite sequences of time-averaged energies. These are treated as simulated data from which approximate probability distributions for the time-averaged energy are obtained. 7 references