A&a Manuscript No. 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 c) to obtain the observed radius, we cannot discriminate non-seismically between diierent convective theories, regardless of how low-eeciency convection is treated. In this paper we consider how the additional information provided by global p-mode frequencies can be used to investigate low-eeciency convection at the top of the solar convec-tive envelope and discriminate between diierent theories. We consider a parametrization which in addition to the mixing length has two further parameters: one (c) which regulates the relative degree of overadiabaticity (or inef-ciency) of convection, and a second (m) that aaects the transition between the regimes of eecient and ineecient convection. Our parametrization includes traditional MLT and the theory of Canuto & Mazzitelli as particular cases. We study the eeect 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.