Signatures relevant to wave modulation. (a) Gyrophase distribution of 4.3 keV, 45° PA proton’s count rates in the solar wind frame, derived from STEP data. (b) Gyrophase distribution of 4.3 keV, 45° PA proton’s differential fluxes. The horizontal dashed black lines refer to the gyrophase range of 0°–60°. (c) Residual gyrophase distribution corresponding to (b). The residual flux is defined as: $j_{\mathrm{res}}=\frac{j_{\mathrm{diff}}-j_0}{j_0}$, where j₀ is a 30 s running average of j_diff. The plus signs give the gyrophase of the magnetic wave (processed with a 0.08–0.12 Hz band-pass filter) field (B_w) between −30°–120°, which is defined as $arctan\frac{B_{\perp ,2}}{B_{\perp ,1}}$. (d) Two perpendicular magnetic field components in the mean (30 s) field-aligned coordinates. Data presented in (c–d) are smoothed with a 5 s moving-window. (e–f) The squared wavelet coherence between 0°–60° gyrophase, 45° PA proton differential flux and (e) B_⊥, 1, (f) B_⊥, 2 in the mean-field-aligned coordinates. The “cross-hatched” areas mark the regions where the PSD of the corresponding magnetic field component is lower than 10 nT²/Hz. The dashed lines mark the frequency of 0.09 Hz.