Variation of acoustic mode centroid frequencies over the solar cycle

Together with a brief historical overview, 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) eigenfrequencies. Our analyses (for 1600 less than or equal to nu less than or equal to 4000 muHz) make use of observations made by the ground-based GONG over the angular degree range 4 less than or equal to l less than or equal to 150; the ground-based BiSON over 0 less than or equal to l less than or equal to 2; and the VIRGO/LOI instrument on board the ESA/NASA SOHO satellite over 0 less than or equal to l less than or equal to 8. We show that GONG shifts averaged over different ranges in 1, together with the BiSON and LOI data averaged over their full quoted ranges, all scale at a given frequency with the normalized mode inertia ratio Q(nl) (Christensen-Dalsgaard & Berthomieu 1991). This is to be expected if the time-dependent perturbation affecting the modes is confined in the surface layers; the excellent agreement also reflects favourably on the external consistency of the different observations. We have also analyzed the frequency dependence of the shifts by fitting a power-law of the form deltanu(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 muHz. However, here we show that while nevertheless describing the shifts well up to similar to 2500 muHz, the linear scaling breaks down conspicuously at higher frequencies. Above this threshold, the shifts follow a power-law dependence with alpha similar to 2. (C) 2002 COSPAR. Published by Elsevier Science Ltd. All rights reserved.