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

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

May 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988apj...328..879k&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 328, May 15, 1988, p. 879-887.

Statistics

Computation

49

Boltzmann Distribution, Harmonic Oscillators, Solar Interior, Solar Oscillations, Solar Rotation, Stochastic Processes, Computational Astrophysics, Differential Equations, Eigenvalues, Statistical Distributions

Scientific paper

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.

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