Seismology of the solar envelope: measuring the acoustic phase shift generated in the outer layers

Partial reflection of acoustic waves by regions of rapid spatial variation modulates the solar p-mode frequencies, in a manner that is often described in terms of an acoustic phase α. At low degree, α is a function of frequency alone. At higher degrees, the inclination of the acoustic ray paths from the normal to the reflecting layers becomes significant, and gives rise to a degree dependence. With the current accuracy of frequency measurements, this phenomenon is significant for all the p modes trapped in the convection zone. We describe a technique capable of separating the degree-dependent component from the leading term α0(ω). We determine the leading-order contribution to the degree dependence of α from the solar p-mode frequencies reported by Libbrecht, Woodard & Kaufman, and compare the results with direct computations from a solar model based on the formalism described by Brodsky & Vorontsov. The dominant contribution comes from the second helium ionization zone, and can be used as a new source of information relevant to the helioseismic calibration of the equation of state of the solar plasma and to the determination of the solar helium abundance.