The identification of solar wind waves at discrete frequencies and the role of the spectral analysis techniques

Abstract

The occurrence of waves at discrete frequencies in the solar wind (SW) parameters has been reported in the scientific literature with some controversial results, mostly concerning the existence (and stability) of favored sets of frequencies. On the other hand, the experimental results might be influenced by the analytical methods adopted for the spectral analysis. We focused attention on the fluctuations of the SW dynamic pressure (PSW) occurring in the leading edges of streams following interplanetary shocks and compared the results of the Welch method (WM) with those of the multitaper method (MTM). The results of a simulation analysis demonstrate that the identification of the wave occurrence and the frequency estimate might be strongly influenced by the signal characteristics and analytical methods, especially in the presence of multicomponent signals. In SW streams, PSW oscillations are routinely detected in the entire range f ≈ 1.2–5.0 mHz; nevertheless, the WM/MTM agreement in the identification and frequency estimate occurs in ≈50% of events and different sets of favored frequencies would be proposed for the same set of events by the WM and MTM analysis. The histogram of the frequency distribution of the events identified by both methods suggests more relevant percentages between f ≈ 1.7–1.9, f ≈ 2.7–3.4, and f ≈ 3.9–4.4 (with a most relevant peak at f ≈ 4.2 mHz). Extremely severe thresholds select a small number (14) of remarkable events, with a one‐to‐one correspondence between WM and MTM: interestingly, these events reveal a tendency for a favored occurrence in bins centered at f ≈ 2.9 and at f ≈ 4.2 mHz.

The Identification of Waves at Discrete Frequencies at the Geostationary Orbit: The Role of the Data Analysis Techniques and the Comparison With Solar Wind Observations

“…As discussed by Di Matteo and Villante (), in several cases a close WM/MTM agreement was achieved in the identification of the wave modes in the P SW spectra: obviously, in similar cases, the correspondence between SW and magnetospheric fluctuations can be more properly examined. We present in Figure d the event occurred on 12 February 2001.…”

“…The results in Figure also confirm that, in some cases, the MTM/WM results are not the same (Di Matteo & Villante, ); this aspect may determine the identification of different common events (e.g., those identified by WM and MTM in the same frequency bin) in different coordinate systems. In the present case, indeed, common events are identified in all coordinate systems in B μ , at f ≈ 1.5 and ≈4.7 mHz, and in B φ at f ≈ 3.9 mHz; however, an additional common peak appears in B φ , at f ≈ 1.9 mHz in MFA 11 while, in B ν , a common event is identified in MFA AVE at f ≈ 1.5 mHz.…”

“…In MFA 21 , the distribution profile is more pronounced (with peak‐to‐peak variation of ≈100%) and the spurious events attain peak values at the lowest frequency ( f ≈ 1.2 mHz) and high values in two other bands centered at f ≈ 2.7–2.9 and ≈4.2–4.7 mHz, respectively. Common events are ≈50% of those independently selected by WM and MTM (Di Matteo & Villante, ) and practically follow the same frequency distributions (Figures c and f).…”

“…According to previous conclusions, we conducted the statistical analysis of the wave events detected at the geostationary orbit in the MFA AVE coordinate system, which, although less precise in terms of the signal decomposition, is not contaminated by the occurrence of spurious events at favorite frequencies (see also Appendix ). Adopting the same selection criteria as for the SW fluctuations ( T = 25% and C = 92.5%; Di Matteo & Villante, ), we obtained the following results: Fluctuations along one or the other component were detected in all post‐SI structures: in particular, wave activity was identified in 107/124 “active” structures by both WM and MTM; 15 “active” structures were selected only by WM and 2 only by MTM. The global numbers of modes (366 for WM, 290 for MTM) reveals that, in general, two or three wave events (typically along different components) occur within “active” structures. As previously remarked, WM is unable to discriminate between modes with Δ f < ≈0.72 mHz; however, this aspect does not influence the WM/MTM comparison: indeed, the frequency separation between the selected MTM modes is generally greater than ≈1 mHz. Figures a, d, and g and b, e, and h (where we show the frequency distributions of the selected events) reveal that the WM and MTM events are distributed in the entire range f ≈ 1.2–4.9 mHz, with number of events exceeding only in few bins the “reference” threshold obtained from the analysis of the IGRF data plus noise (red dashed lines).…”

“…As an initial step toward a better understanding of these aspects, in a recent paper (Di Matteo & Villante, ), we analyzed the fluctuations of the SW dynamic pressure ( P SW ; f ≈ 1.2–5.0 mHz) observed by ACE in the leading edges of streams following interplanetary shocks (IS). Preliminarily, in that paper, we have analyzed, with various synthetic signals, the performance of two methods widely adopted in previous investigations, the Welch method (WM; Welch, ) and the multitaper windowing and F test (MTM; Thomson, ).…”