Overstability of acoustic modes and the solar five-minute oscillations

Abstract

The stability of linear convective and acoustic modes in solar envelope models is investigated by incorporating the thermal and mechanical effects of turbulence through the eddy transport coefficients. With a reasonable value of the turbulent Prandtl number it is possible to obtain the scales of motion corresponding to granulation, supergranulation and the five-minute oscillations. Several of the acoustic modes trapped in the solar convection zone are found to be overstable and the most unstable modes, spread over a region centred predominantly around a period of 300 s with a wide range of horizontal length scales, are in reasonable accord with the observed power-spectrum of the five-minute oscillations. It is demonstrated that these oscillations are driven by a simultaneous action of the -mechanism and the radiative and turbulent conduction mechanisms operating in the strongly superadiabatic region in the hydrogen ionization zone, the turbulent transport being the dominant process in overstabilizing the acoustic modes.