Helioseismic measurements in the solar envelope using group velocities of surface waves

Abstract

At intermediate and high degree l, solar p-and f modes can be considered as surface waves. Using variational principle, we derive an integral expression for the group velocities of the surface waves in terms of adiabatic eigenfunctions of normal modes, and address the benefits of using group-velocity measurements as a supplementary diagnostic tool in solar seismology. The principal advantage of using group velocities, when compared with direct analysis of the oscillation frequencies, comes from their smaller sensitivity to the uncertainties in the near-photospheric layers. We address some numerical examples where group velocities are used to reveal inconsistencies between the solar models and the seismic data. Further, we implement the group-velocity measurements to the calibration of the specific entropy, helium abundance Y and heavy-element abundance Z in the adiabatically-stratified part of the solar convective envelope, using different recent versions of the equation of state. The results are in close agreement with our earlier measurements based on more sophisticated analysis of the solar oscillation frequencies , MNRAS 430, 1636. These results bring further support to the downward revision of the solar heavy-element abundances in recent spectroscopic measurements.

Determining the metallicity of the solar envelope using seismic inversion techniques

“…The results presented in section 4.1 have significant consequences for solar modelling since they confirm the low metallicity values found by Vorontsov et al (2014). This result implies that the observed discrepancies found in sound speed inversions (e.g.…”

“…The first result is that a very large majority of inversions favour a low metallicity, as presented in Vorontsov et al (2014). Only one small region of the parameter space, for the inversion of Model 4, built with the CEFF equation of state, gives a high metallicity as a solution.…”

“…Antia & Basu (2006) determined its value as 0.0172 ± 0.002 using an analysis of the dimensionless sound-speed gradient, denoted W(r). In contrast, Vorontsov et al (2014) determined that it should lie within 0.008 and 0.013 using a detailed analysis of the adia-batic exponent of solar envelope models for various equations of state.…”

Seismic inversion of the solar entropy

“…Simultaneously, other studies used seismology to estimate the solar metallicity. Some confirmed the GS98 values (Basu & Antia 2006), while others agreed with the AGSS09 values (Vorontsov et al 2014), illustrating the current stalemate regarding this question.…”

Solar structure and evolution

“…It is evident that the use of C 1 as a composition diagnostics depends critically on the assumed equation of state, probably even more for the heavy-element abundance than in the case of the determination of the helium abundance. Careful analyses were carried out by Vorontsov et al (2013Vorontsov et al ( , 2014, fitting helioseismic observations to solar convectiveenvelope models based on a variety of equations of state, including the so-called SAHA-S implementation (Baturin et al 2013). They found that SAHA-S provided a substantially better fit to the observations than other formulations, with a heavyelement abundance in the range Z ¼ 0:008 À 0:013, i.e., strongly supporting the revised low values of Z, while acknowledging that a complete solar model with this abundance would be inconsistent with seismic inferences of the radiative interior.…”