Periodic density structures in Solar Orbiter data: radial evolution and embedded helical structures

(Solar Orbiter Nugget #90 by C. Katsavrias^1,2, S. Di Matteo^3,2, L. Kepko², N. Viall², R. Chiiber^2,4 and A. Walsh⁵​^​​​​​​)

Introduction

The solar wind is traditionally viewed as bimodal, consisting of fast and slow components; however there is agreement on the need to move beyond the classic paradigm. A key ingredient is the notion of the time history of a solar wind parcel and the many pathways in which it can manifest and evolve. In this context, mesoscale structures have been suggested as a likely outcome [1]. One of the most studied mesoscale structures are the Periodic Density Structures (PDSs) which are quasi-periodic variations of the solar wind density ranging from a few minutes to a few hours (or roughly 0.1 – 5 mHz). They correspond to advected structures with radial length scales of tens to several thousand Mm (few to several hundred Earth Radii) as derived from statistical investigations and several cases studied at L1.

The mechanisms behind the generation of PDS remain a topic of ongoing debate. However, there is a prevailing agreement that many of these structures originate in the solar atmosphere, while others may form en route via processes such as turbulence. The solar corona origin of PDSs is supported by several remote-sensing observations of the Sun alongside MHD modelling and in situ measurements of the interplanetary magnetic field and elemental composition of the solar wind plasma, which have indicated that the solar wind is released through magnetic reconnection of previously closed magnetic fields [2].

Even though PDS at L1 and in the near-Earth region are extensively studied both through statistical and event analysis, their investigation at distances closer to the Sun, and therefore, their radial evolution is limited. In this work, we performed – for the first time to our knowledge – an extensive statistical study to identify PDSs in Solar Orbiter (SO) data spanning the 0.3 to 1 AU radial distance from the Sun and to investigate their evolution and propagation though the interplanetary medium.

Methods

We have used a well-established methodology combining the Multitaper method (MTM) and wavelet analysis (CWT) to accurately detect PDSs both in the frequency and time domains. The combination of MTM and CWT allows us to have a robust methodology by exploiting the major advantages of each method, while at the same time overcoming their limitations, namely:

• MTM provides a far more accurate detection of the PDS frequency compared to CWT, and
• CWT verifies the aforementioned detections by also overcoming the problem of nonstationarity of the solar wind, while further determining the duration of the PDS event.

An example of the aforementioned event detection procedure is shown in Figure 1 for an ≃0.74 mHz PDS event on April 24, 2021.

The aforementioned methodology produced a list of 29,891, 38,478 and 37,974 PDS events for six-, twelve- and eighteen-hour intervals, respectively, which is publicly available at https://zenodo.org/records/16038091. We note that the reason behind using 3 different time intervals is the fact that higher/lower frequency PDS are better identified with different analysis intervals, due to trade off between frequency resolution and PDS duration. Empirically, we find that 6-hr segments are better for identifying high frequency PDS, while the lower frequency PDS (<1 mHz) are best observed at longer window lengths.

Figure 1: Example of the April 24, 2021 PDS event detection using the MTM and CWT over a 6-hour window.
Panel a) Time series of the original and filtered total ion density, with black and red solid lines, respectively.
Panel b) Power spectral density, background normalized spectrum and 90% confidence level with the black solid, red solid and red dashed lines, respectively. The frequency that exceeds both thresholds (0.74 mHz) is shown as red solid circle.
Panel c)Wavelet spectrum of the total ion density, where the horizontal white dashed lines correspond to the frequency range of interest (f ∓0.15 mHz) and the solid black line depict the cone of influence, where edge effects in the processing become important.
Panel d) Time-series of the average wavelet power in the f∓ 0.15 mHz range. The horizontal red solid line corresponds to the 75th quantile of the power, within the same frequency range, over the entire time period (6 hours window for this case).

PDS radial evolution

Our statistical analysis shows that the solar wind is comprised by PDSs at approximately 22, 32 and 35%, which is in agreement with previous statistical studies at L1. Assuming PDSs are formed close to the Sun, via mechanisms that likely involve magnetic reconnection, the expected outcome would be the ejection of plasmoids (or flux ropes), which would propagate in the interplanetary space, embedded in the surrounding solar wind.

Based on mass conservation, the ratio of solar wind speed (u) and radial length scale (L), and consequently the frequency (f = u/L), is expected to be constant, which is confirmed by remote sensing observations of PDSs in the solar corona [3]. Within these assumptions, it follows that the radial length scale of PDSs should evolve with distance as L = u(r)/f with u(r) being a solar wind speed profile.

The left panel of Figure 2 shows the comparison of the radial length scale of the twelve-hour interval PDS (black dotted line) with the characteristic length scale of the ambient/slow solar wind (red dotted line). The latter was inferred from the velocity distribution (divided by 1.18 mHz) given by Liu, Jia, and Liu (2024), who used data from Parker Solar Probe measurements during its first 15 encounters. For completion, we also include the radial length scale distribution inferred by a Sheeley-like empirical model (blue dotted line). As shown, the PDS and ambient solar wind radial length scale distributions are in good agreement, except for very low R (R<0.5). The latter could originate to the smaller amount of data available from SO at such low distances from the Sun and/or the fact that our dataset spans the Solar maximum and rising phase, only. On the other hand, PDSs detected in fast solar wind segments exhibit compression, similar to the one observed for the fast wind by PSP (black and red dotted line in the right panel of Figure 2, respectively).

Figure 2. Comparison of the radial length scale of PDS with the characteristic length scale of the ambient/slow solar wind (left panel) and fast solar wind (right panel) inferred from Parker Solar Probe measurements.

Helical structures in PDS

For the identification of helical structures in PDS we focused on the <1 mHz PDSs, which correspond to 1727, 2185, and 1895 events each, for the three window intervals. For these PDSs we derived the normalized reduced magnetic helicity (σ_m), the normalized cross helicity (σ_c), and the residual energy (σ_r), following the method by Zhao et al. [4]. Then, we searched for structures with | σ_m |>0.7, henceforth referred to as helical structures (HSs). We identified 751, 893, and 763 HS in 592, 738, and 607 PDS events for the window intervals of 6, 12, and 18 hours, respectively. Such an HS is illustrated in Figure 3. 

Figure 3. Example of a helical structure (HS) observed by Solar Orbiter on April 27, 2021.
From top to bottom: Total ion density and solar wind radial speed (VR) in black and blue, respectively; the transverse and normal component (VT and VN) of the solar wind speed; the Radial-Transverse-Normal (RTN) component of the interplanetary magnetic field along with |B|; the wavelet spectrum of the total ion density; spectrogram of the normalized reduced magnetic helicity, σ_m; spectrogram of the normalized cross helicity, σ_c; and spectrogram of the normalized residual energy, σ_r. The vertical black and the dashed horizontal white lines denote the PDS start and end time and the f_PDS ±0.15 mHz range, respectively. The black contour in the wavelet spectrum corresponds to the wavelet power threshold. The black contour in the σm, σ_c and σ_r panels corresponds to |σ_m|>0.7.

Moreover, we classified the aforementioned HS in three subcategories:

• HSs characterized by | σ_c |<0.4 and σ_r<-0.5 are candidate small flux ropes.
• HSs characterized by | σ_c |> 0.5 and | σ_r |< 0.1 suggest the coexistence of Alfvén waves within a magnetic flux rope, which our method cannot distinguish from stand-alone Alfvén waves. These events are categorized as Alfvénic HSs.
• Finally, complex HSs characterized by | σ_c |> 0.4 and σ_r<-0.5. Although this category contains magnetically dominated HSs, it also exhibits significant Alfvénic activity. A possible explanation for this category might be that the flux rope remains tethered to the Sun, and the spacecraft crosses one of the flux rope legs instead of the core. This category might also include small-scale magnetic flux ropes exhibiting field-aligned flows.

In order to investigate the relative occurrence of each HS type in our sample, we calculated the probability of occurrence, with respect to the total HS number, for the various HS types detected within and outside the PDS start and end time limits. As shown (Figure 4), ~30% of the HSs within the PDS start and end time limits (regardless of the window interval) have flux ropes properties (green bars). This means that at least 10% (~30% of the flux ropes of ~30% of the HS) of the <1 mHz PDSs contain flux ropes. In contrast, flux ropes detected outside the PDS start and end time limits have an occurrence probability lower than 2%. Alfvénic HSs, on the other hand, exhibit a very different occurrence. The percentage of Alfvénic HSs observed within the PDS start and end time limits (yellow bars) is ~10% of all HSs, which corresponds to ~2-3% of the PDS events. Moreover, we identified ~25-30% Alfvénic HSs outside the PDS start and end time limits, which also corresponds to ~2-3% of the PDS events.

Figure 4. Occurrence probability with respect to the total HS number for the various HS types detected inside (left panel) and outside (right panel) of the PDS start and end time limits. The HS are colored with green, magenta and yellow bars corresponding to flux ropes, complex events, and Alfvénic HSs, respectively.

Conclusions & Discussion

Using 3.5 years of Solar Orbiter measurements that span the rising phase and maximum of solar cycle 25 (2021–2024), we compiled and made publicly available an extensive list of PDS events between radial distances of 0.3 to 1 AU. The list includes 29,891, 38,478 and 37,974 individual PDS events for the six-, twelve- and eighteen-hour analysis interval, respectively.

Our results indicate that PDS expand as they advect with the ambient/slow solar wind. On the other hand, PDSs detected in fast solar wind segments exhibit compression, similar to the one observed for the fast wind by PSP. This is consistent with the scenario in which PDSs are formed close to the Sun, via mechanisms that likely involve magnetic reconnection.

By further exploiting the normalized cross helicity and residual energy of the identified HSs, we classified them as small flux ropes and Alfvénic structures. Our results indicate that small flux ropes are a particular constituent of PDS events, since the percentage of low frequency PDS that have embedded flux ropes was 10% at least (for the three window intervals), while flux ropes detected in the vicinity of the PDS (outside the PDS start and end time limits) exhibited an occurrence probability lower than 2%. In contrast, Alfvénic HSs exhibited a similar occurrence probability (2-3%) within and outside the PDS. This is an important addition to the scenario in which PDSs are formed by processes involving magnetic reconnection in the solar corona.

This nugget is based on the following papers:

• Katsavrias et al., Sol Phys 301, 30 (2026).
• Katsavrias et al., A&A, 708, A240 (2026).

Acknowledgements

This material is based upon work supported by the National Aeronautics and Space Administration through the completed Heliophysics Internal Scientist Funding Model Program. The authors thank the Solar Orbiter team for the use permission of the data and the ESA Solar Orbiter archive for making these data available (https://soar.esac.esa.int/soar/). CK received support from the ESA Archival Research Visitor Programme. S.D. was also supported by NASA Grant 80NSSC21K0459.

Affiliations

(1) Department of Physics, National and Kapodistrian University of Athens, Athens, Greece

(2) NASA-Goddard Space Flight Center, Greenbelt, MD, USA

(3) Physics Department, The Catholic University of America, Washington, DC, USA

(4) Department of Physics and Astronomy, University of Delaware, Newark, DE, USA

(5) ESA/ESAC, Madrid, Spain

References

[1] Viall N.M., DeForest C.E. and Kepko L. (2021) Front. Astron. Space Sci. 8:735034, https://www.frontiersin.org/journals/astronomy-and-space-sciences/articles/10.3389/fspas.2021.735034

[2] Kepko, L., Viall, N. M., & DiMatteo, S. (2024) JGR: Space Physics, 129, e2023JA031403, https://doi.org/10.1029/2023JA031403

[3] Viall N. and Vourlidas A. (2015) ApJ, 807, 176, https://iopscience.iop.org/article/10.1088/0004-637X/807/2/176

[4] Zhao et al. (2020) ApJS, 246, 2613, https://iopscience.iop.org/article/10.3847/1538-4365/ab4ff1