Variation of acoustic mode centroid frequencies over the solar cycle

Abstract

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 ≤ ν ≤ 4000 μHz) 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 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 δν _nl ∝ (ν _nl/ 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 ≈ 3500 μHz. However, here we show that while nevertheless describing the shifts well up to ∼ 2500 μHz, the linear scaling breaks down conspicuously at higher frequencies. Above this threshold, the shifts follow a power-law dependence with α ∼ 2.