The phenomenology of solar-cycle-induced acoustic eigenfrequency variations: a comparative and complementary analysis of GONG, BiSON and VIRGO/LOI data

We use high-quality helioseismic data collected by three different observational programmes during the declining phase of activity cycle 22, and a substantial portion of the rising phase of the current cycle (23), to study the phenomenological nature of the cycle-induced (centroid) eigenfrequency variations. We have analysed the frequency dependence of the shifts by fitting a power law of the form delta nu (nl) proportional to (nu (nl))(alpha)/E-nl to the data (where the E-nl are the mode inertias, and alpha is the power-law index to be extracted). Previous studies have suggested that a relation with alpha = 0 provides an adequate description of the shifts up to nu approximate to 3500 mu Hz. However, here we show that while nevertheless describing the shifts well up to similar to 2500 mu Hz, the linear scaling breaks down conspicuously at higher frequencies. Above this threshold, the shifts follow a power-law dependence with alpha similar to2. Our analyses (for 1600 less than or equal to nu less than or equal to 4000 mu Hz) make use of observations made by the ground-based GONG over the angular degree range 4 less than or equal tol less than or equal to 150; the ground-based BiSON over 0 less than or equal tol less than or equal to2; and the VIRGO/LOI instrument on board the ESA/NASA SOHO satellite over 0 less than or equal tol less than or equal to8. We show that GONG shifts averaged over different ranges in l, together with the BiSON and LOI data averaged over their full quoted ranges, all scale at fixed frequency with the normalized mode inertia ratio Q(nl). This is to be expected if the solar-cycle perturbation affecting the modes is confined in the surface layers; the excellent agreement also reflects favourably on the external consistency of the different observations.