Seismic analysis of the second ionization region of helium in the Sun: I. Sensitivity study and methodology

The region of the second ionization of helium in the Sun is a narrow layer near the surface. Ionization induces a local change of the adiabatic exponent $\Gamma_1$, which produces a characteristic signature in the frequencies of p-modes. By adapting the method developed by (Monteiro et al. 1994), we propose a methodology for determining the properties of this region by studying such a signature in the frequencies of oscillation. Using solar data we illustrate how the signal from the helium ionization zone can be isolated. Using solar models with different physics -- theory of convection, equation of state and low temperature opacities -- we establish how the characteristics of the signal depend on the different aspects contributing to the structure in the ionization layer. We further discuss how the method can be used to measure the solar helium abundance in the envelope and to constrain the physics affecting this region of the Sun. The potential usefulness of the method we propose is shown. It may complement other inversion methods developed to study the solar structure and to determine the envelope helium abundance.