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Seismic properties of the Sun's superadiabatic layer. I. Theoretical modelling and parametrization of the uncertainties.

Some alternatives to the traditional mixing-length theory (MLT) have recently been proposed for modelling convective heat transport inside stars. The ideal formulation is one that does not involve any free parameters. However, in our present state of ignorance we still need at least one free parameter in order to build solar models with the correct radius. Having adjusted this parameter (e.g. the mixing-length parameter α_c_) to obtain the observed radius, we cannot discriminate non-seismically between different convective theories, regardless of how low-efficiency convection is treated. In this paper we consider how the additional information provided by global p-mode frequencies can be used to investigate low-efficiency convection at the top of the solar convective envelope and discriminate between different theories. We consider a parametrization which in addition to the mixing length has two further parameters: one (β_c_) which regulates the relative degree of overadiabaticity (or inefficiency) of convection, and a second (m) that affects the transition between the regimes of efficient and inefficient convection. Our parametrization includes traditional MLT__ and the theory of Canuto & Mazzitelli as particular cases. We study the effect of varying these parameters by constructing a series of envelope models with the same depth of the convection zone and computing their oscillation frequencies. We discuss our results in terms of kernels relating frequency changes to changes in the structure of the superadiabatic region.