Comparison between solar activity and planetary torque corresponding to case 1 in both frequency and time domain. a) Solar activity φ reconstructed from cosmogenic radionuclides (Steinhilber et al. 2012). b) Wavelet coherence between observation (φ) and torque (| N(t)|). Arrows indicate the relative phase between both series (Grinsted et al. 2004) (pointing to left, anti-phase; to right in phase). The constant phase between φ and the torque for the bands centered at 208 yr and 506 yr are an indication of phase locking. The black contours show the 5% significance regions (95% confidence level). c) Band-pass-filtered annually averaged torque (green curve) along with φ (blue curve – inverted scale-) around the 208 yr periodicity (de Vries). Note that the intervals where forcing (torque) and the response (φ) are in anti-phase correspond to time periods when Grand Minima are more frequent, which is also evident in the wavelet analysis, supporting the assumption of a physical coupling between the planets and the Sun.
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