Helioseismic inferences on the stratification and dynamics of the solar interior

Small amplitude oscillations at the surface of the sun have been first observed more than 30 years ago, with amplitudes around 300 m/s and periods around five minutes. In contrast to classical variable stars where only a few set of pulsation modes are excited (like for instant Cepheids), the solar oscillation spectrum is a rich set where millions of modes are simultaneously excited and observed. This huge amount of information forms the observational basis of helioseismology which allow us to infer the properties of the sun's interior from the characteristics of its oscillations. The five-minute oscillations observed on the sun are acoustic resonant modes, namely pressure waves that propagate through the interior of the sun and are reflected near the surface by the strong density gradient, where they are observed. The frequency of any given mode is directly related to the precise stratification of the medium it samples, namely the pressure, density, temperature and chemical composition of the fraction of the solar interior where the mode amplitude is significant. Dynamical effects also modify the observed frequency, e.g. advection by rotation. Accurate measurements of a large ensemble of mode frequencies allow us to derive the internal conditions of our star. In this paper we describe the methodologies that allow us to infer the internal structure and rotation rate from helioseismic observations. We also present examples of such inferences, whose unprecedent precision imposes strong constrains on modern theoretical models of stellar structure and evolution.