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,Q7 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 δν_nl~(ν_nl)^α/E_nl to the data (where the E_nl are the mode inertias, and α is the power-law index to be extracted). Previous studies have suggested that a relation with α=0 provides an adequate description of the shifts up to ν~3500μHz. However, here we show that while nevertheless describing the shifts well up to ~2500μHz, the linear scaling breaks down conspicuously at higher frequencies. Above this threshold, the shifts follow a power-law dependence with α~2. Our analyses (for 1600<=ν<=4000μHz) make use of observations made by the ground-based GONG over the angular degree range 4<=l<=150 the ground-based BiSON over 0<=l<=2 and the VIRGO/LOI instrument on board the ESA/NASA SOHO satellite over 0<=l<=8. 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_nlQ1. 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.