Comment to the paper "Azimuthal Size Scales of Solar Wind Periodic Density Structures" by Di Ma eo et al. [2024]

Umberto Villante ^*

• Dipartimento scienze fisiche e chimiche - università dell'Aquila, L'Aquila, Italy

In a recent paper, Di Ma eo et al. [2024] proposed a sophis cated analysis of the quasiperiodic varia ons of the solar wind (SW) number density (NSW), referred to as Periodic Density Structures (PDSs; f≈0.45-4.65 mHz), which were observed by two spacecra (Wind and ARTEMIS-P1) in the interplanetary medium. They obtained results which, in my opinion, are important also in the context of the scien fic debate regarding the fluctua ons at discrete frequencies observed in the magnetosphere (mostly in range f≈1-5 mHz). Indeed, the occurrence, the origin and the characteris cs of these fluctua ons (which play an important role in the magnetospheric dynamics) have been examined, in the last decades, in a large number of papers, o en with controversial results mainly related to their rela onships with SW fluctua ons at similar frequencies and to the the possible existence (and stability) of sets of favorite magnetospheric frequencies (review by Di Ma eo and Villante, 2025 and papers therein referenced). On the other hand, in recent years, some papers highlighted some cri cal aspects of the data analysis which might have influenced the conclusions of several inves ga ons. In par cular, Di Ma eo and Villante [2017;2018] applied two different methods adopted in the scien fic literature (the Welch method, WM, and the Mul taper method and F-test, MTM) to the same data sets and showed that the WM/MTM agreement in the iden fica on of the wave occurrence and frequency es mate might occur only in ≈50% of cases, both in the SW and in the magnetosphere. In addi on, an analysis conducted by Villante et al. [2022] revealed different characteris cs in the fluctua ons of the SW dynamic pressure (PSW) when the same SW stream was observed by two spacecra at different places in front of the magnetosphere. All these aspects make ambiguous the analysis of the rela onships between the SW and the magnetospheric fluctua ons; as we discuss in this note, the results proposed by Di Ma eo et al. [2024] add other interes ng elements in this context.In their analysis, Di Ma eo et al.[2024] examined the characteris cs of PDS with periods ranging from a few minutes to a few hours (radial length scale of tens to several thousands of megameters). In par cular, they conducted a robust es mate of the spectral proper es of the NSW fluctua ons (they also examined the interplanetary magne c field's intensity, not considered in the present note) in the frequency range f≈0.45-4.65 mHz, that were associated with 68 PDSs observed by Wind and ARTEMIS-P1 in front of the magnetosphere over 9 years (2012-2020) and occurring during intervals of high density (maximum values above 15 cm -3 ), slow SW streams (below 450 km/s); they also determined the level of coherence between the events observed by the two spacecra , obtaining interes ng results. Namely, -79 out of 158 events of NSW fluctua ons iden fied by Wind occurred in the same frequency range (within +/-0.3 mHz) of the corresponding events detected by P1 (P1 iden fied 166 events). In prac ce, for the same SW parcels, comparable frequencies were es mated at the spacecra posi ons for about half of events; meanwhile, the frequency to be a ributed to the other half of the events that will impact the magnetosphere is uncertain. In this context it is interes ng to remind that Viall et al. [2009], who examined the frequencies of PDSs and dayside magnetospheric oscilla ons in the f=0.5-5.0 mHz range using 11 years of Wind andGOES observa ons (1995-2005), reported that in ≈54% of the SW segments with a spectral peak, at least one of the same discrete frequencies was sta s cally significant in the corresponding magnetospheric data segment. Eventually, according to the results of Di Ma eo et al. [2024], this percentage of correspondence between the frequencies of SW and magnetospheric fluctua ons might be related to SW events in which the es mated frequencies of fluctua ons would have been the same at different in front of the magnetosphere.-Considering only the events characterized by high level of coherence (43) between Wind and P1, the percentage of agreement is higher below f≈1 (≈59%), progressively decreasing and prac cally vanishing at higher frequencies. Reinforcing previous arguments, these conclusions are important in this context in that the frequencies below ≈1 mHz have been rarely explored in the magnetosphere; consequently, the analysis of the rela onship between SW and magnetospheric fluctua ons could likely have been inves gated mostly in a frequency range (f≈1-5 mHz) in which the agreement between the frequencies of SW fluctua ons observed at two different places might be poor.-In extreme cases, moreover, Wind and P1 provided, for the same PDS, very different results: for example, for a parcel observed on Jan. 1, 2014, Wind iden fied a single fluctua on event (f≈1.8 mHz; Table 1 in Di Ma eo et al., 2024) while four peaks emerged in the power spectra at P1 (f≈0.7, ≈1.5, ≈2.2, ≈3.7 mHz). It confirms that the aspects of the SW fluctua ons o en differ significantly between the observa ons of the same SW parcel at different places (Villante et al., 2022; Figure 2). All these arguments suggest cau on before assuming a definite iden fica on of the characteris cs of the compressive fluctua ons impinging the magnetosphere when the event is observed by a single spacecra (Di Ma eo and Sivadas, 2022).-Obviously, the global frequency distribu of events at Wind and P1 are not the same (Fig. 5 in Di Ma eo et al., 2024). Nevertheless, in both cases, they manifest the highest occurrence at f≈0.5-0.8 mHz (a frequency range rarely explored in magnetospheric inves ga ons, as previously remarked), with some evidence for enhancements around f≈1.9 mHz, and, less explicit, around f≈2.7-2.9 mHz and f≈3.2-3.8 mHz. Interes ngly, in the last 30 years, several papers, proposed the possible existence of frequencies more common than others for magnetospheric fluctua ons, in par cular f1≈1.3, f2≈1.9 (most common), f3≈2.6-2.7, and f4≈3.2 -3.4 mHz [e. g., Samson et al., 1991Samson et al., , 1992;;Ruohoniemi et al., 1991;Walker et al., 1992;Francia and Villante, 1997;Villante et al., 2001]. In this sense, corrobora ng the conclusions of several analysis in favor of magnetospheric fluctua ons directly driven by compressional SW modes approximately at the same frequencies [Kepko et al., 2002;Kepko and Spence, 2003;Villante et al., 2013Villante et al., , 2016;;Viall et al., 2009], the results of Di Ma eo et al. [2024] might confirm, at least in a sta s cal sense, that several magnetospheric fluctua ons at discrete frequencies might be associated with the interac on of PDSs with the magnetosphere.As discussed in the previous paragraph, several results obtained for PDS by Di Ma eo et al.[2024] might find correspondence in those obtained, over many years, in the analysis of the magnetospheric fluctua ons at discrete frequencies (such as the enhancements of the event occurrence at given discrete frequencies, more evident around f≈1.9 mHz…; review by Di Ma eo and Villante, 2025 and papers therein referenced). On the other hand, other aspects such as the general ≈50% of (dis)agreement between the frequencies of fluctua ons observed by the two spacecra (Di Ma eo and Villante, 2017Villante, , 2018) ) as well as the strong disagreement in the fluctua ons content occasionally obtained when the same SW parcel is observed at different places confirm that, as underlined by Di Ma eo and Villante [2025], further inves ga ons of the rela onship between SW and magnetospheric fluctua ons should pay careful a en on to several cri cal aspects which may strongly influence the results of the data analysis (i.e. the method of data processing which may be cri cal for the iden fica on of events; the unambiguous iden fica on of the characteris cs of the SW fluctua ons impinging the magnetosphere); in addi on, it is useful to remind that the magnetospheric response is expected to be different in different regions (and intermixed with concurring local genera on and strongly influenced, at least in terms of the frequency of fluctua ons, by the daily, seasonal and solar cycle varia on of the local resonant frequency.