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

Kumar, Pawan and Franklin, Joel and Goldreich, Peter (1988) Distribution functions for the time-averaged energies of stochastically excited solar p-modes. Astrophysical Journal, 328 (2). pp. 879-887. ISSN 0004-637X. doi:10.1086/166345.

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We study the excitation of a damped harmonic oscillator by a random force 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. We apply the theory of random differential equations 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. We also perform numerical integrations to generate finite sequences of time-averaged energies. These are treated as simulated data from which we obtain approximate probability distributions for the time-averaged energy. A comparison of our calculated distributions with those determined observationally should help to resolve whether the solar p-modes are stochastically excited. If they are, modes of the same frequency with degree l ≾ 200 should have identical values for the products of their mean energies, line-widths, and masses. If, in addition, turbulence or radiative dissipation provides the principal damping mechanism, the mean energies should be independent of angular order, l.

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Additional Information:© 1988 American Astronomical Society. Received 1987 August 12; accepted 1987 November 9. P. K. is grateful to Ken Libbrecht for many useful discussions. The research reported in this paper was supported by NSF through grant AST-861299
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Subject Keywords:convection, Sun: interior, Sun: oscillations, turbulence
Issue or Number:2
Record Number:CaltechAUTHORS:20130312-145928531
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Official Citation:Distribution functions for the time-averaged energies of stochastically excited solar p-modes Kumar, P., Franklin, J., & Goldreich, P. Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 328, May 15, 1988, p. 879-887.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:37478
Deposited By: Ruth Sustaita
Deposited On:12 Mar 2013 22:22
Last Modified:09 Nov 2021 23:29

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