<figure><img src="image_1.png" /></figure>

# Solar Wind Anomalies at 1 au and Their Associations with Large-scale Structures

Yan Li¹ ID, Shaosui Xu² ID, Janet G. Luhmann² ID, and Benoit Lavraud³,⁴ ID

¹Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA; yanli@ssl.berkeley.edu

²Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA

³Laboratoire d'Astrophysique de Bordeaux, CNRS, Université de Bordeaux, Pessac, France

⁴Institut de Recherche en Astrophysique et Planétologie, CNRS, UPS, CNES, Université de Toulouse, Toulouse, France

Received 2021 March 5; revised 2021 September 23; accepted 2021 September 24; published 2021 December 14

## Abstract

We study solar wind anomalies and their associations with solar wind structures using the STEREO solar wind and suprathermal electron (STE) data from IMPACT and PLASTIC. We define solar wind anomalies as temporary and local excursions from the average solar wind state, regardless of their origins, for six anomalies: sunward strahls, counterstreaming suprathermal electrons, suprathermal electron depletions, nearly radial magnetic field episodes, anomalously low proton temperatures, and anomalously low proton beta. We first establish the solar wind synoptic contour displays, which show the expected variations in solar wind structure during the solar cycle: recurrent corotating heliospheric magnetic field (HMF) and stream structures are dominant during solar quiet times around the solar minimum (2008 December) preceding cycle 24, while complex structures characterize solar active times around the solar maximum (2014 April). During the declining phase of the cycle (2016–2019), the stream structures remain complex, but the HMF sectors show the structures of the solar minimum. We then systematically study the six anomalies by analyzing the STE data using automated procedures. All anomalies present some degree of dependence on the large-scale solar wind structure, especially around the solar minimum, implying that the solar wind structure plays a role in either the generation or transportation of these anomalies. One common feature of all of the anomalies is that the distributions of the durations of the anomalous episodes all peak at the 1 hr data resolution, but monotonically decrease over longer durations, which may arguably imply that solar anomalies occur on a continuum of temporal and spatial scales.

*Unified Astronomy Thesaurus concepts: Solar wind (1534); Interplanetary magnetic fields (824)*

## 1. Introduction

The solar wind consists of different types of plasma and magnetic field structures whose spatial distributions depend on the state of the solar coronal magnetic field at the time. In particular, the Ulysses observations have highlighted the role of the solar activity cycle phase in determining its global character (McComas et al. 2008). Around the solar minimum, the solar wind is roughly described by a dipolar coronal source. The main dipolar solar wind feature is the magnetic pole-to-equator, high-to-low-speed velocity gradients in each hemisphere. The interaction between the fast solar wind stream from the polar coronal holes and the low latitude slow wind belt gives rise to the next order of structural complication: the corotating interaction regions (CIRs). CIRs occur when the magnetic dipole axis is tilted with respect to the solar rotation axis (Pneuman & Kopp 1971; Pizzo 1990) or when higher-order moments in the solar magnetic field effectively warp the magnetic equator. Under these circumstances, solar rotation produces interactions between the radial outflows with different speeds coming from the different dipole latitudes (e.g., see Pizzo 1990). However, the solar coronal field is never perfectly dipolar, with images typically showing both polar coronal hole extensions to low latitudes and low latitude coronal holes throughout much of the solar cycle. The outflows from these various open field regions often have different speeds, producing CIRs/SIRs (stream interaction regions) even without the large-scale dipolar coronal structure. The solar wind structure for the more active phases of the solar cycle departs further still from this ideal, with the in situ observations suggesting a disorganized global wind with many transient sources and features. Its nature is related to the rapidly evolving and complex solar and coronal magnetic fields, coupled with more frequent coronal activity.

For the purpose of this study, we adopt the general concept that the global solar wind is generally composed of relatively steady high-speed solar winds from long-lived high latitude open coronal field regions. The high-speed solar winds from the northern and southern hemispheres are separated by a layer of—on average— slower, denser, more complicated, and variable outflows and structures (Gosling 1996; McComas et al. 2008). This boundary layer between the polar outflows has a latitudinal extent that is roughly defined by the heliospheric current sheet (HCS) maximum excursion. In the solar wind, there also exist various anomalous episodes, as consequences of transient and/or energetic activities that may be remote (in the corona) or heliospheric in origin. The following phenomena or transients relating to anomalous solar wind parameters have been studied and have inspired our study. (1) False magnetic field polarity reversals—evoking images of switchbacks—that have been argued as being interchange reconnection debris (Owens et al. 2013, 2017, 2020), and recently also observed much closer to the Sun by the Parker Solar Probe mission (Laker et al. 2021), and the origin is being debated. (2) Heliospheric magnetic field (HMF) departures from the Parker spiral to nearly radial field at 1 au (Murphy et al. 2002; Watari et al. 2005). The great majority of the initial mass function orientation statistics fall in the vicinity of Parker spiral fields for typical solar wind speeds. However, blocks of time occasionally stand out when the HMF is nearly radial. (3) Interplanetary coronal mass ejections (ICMEs), magnetic clouds (MCs), and other flux ropes, whose structures are foreign to the ambient solar wind and whose plasma differs from the background plasma, often bring anomalously low temperatures and plasma beta (Burlaga et al. 1981; Klein & Burlaga 1982; Burlaga 1988; Richardson & Cane 1995; Kilpua et al. 2009). (4) The intervals of counterstreaming suprathermal electrons (CSEs),
which are often interpreted as closed loops of magnetic fields with both ends being connected to a hot electron source within the corona (Bame et al. 1981; Gosling et al. 1987, 1992). (5) Heat flux dropouts, suggesting complete disconnection from hot electron sources (McComas et al. 1989). Many studies have been devoted to these phenomena, including their relationship to the location of the HCS/coronal streamer belt and their solar cycle variations (McComas et al. 1989; Fitzenreiter & Ogilvie 1992; Gosling et al. 1992, 1993; Shodhan et al. 2000; Murphy et al. 2002; Watari et al. 2005; Lavraud et al. 2010; Yu et al. 2014, 2016; Owens et al. 2017, 2020). Weaker solar cycles and advanced imaging and modeling capabilities have raised the profile of pseudostreamers and their boundaries as contributors to the outflows within this slow wind layer (Wang et al. 2012; Owens et al. 2013, 2014). Similarly, the density blobs that are released from the ends of the coronal streamers are another source of slow solar wind (Sheeley & Wang 2007; Rouillard et al. 2010a, 2010b) that belong to this collection of features. These have been associated with in situ observations of small flux rope-like structures in the solar wind at 1 au (Kilpua et al. 2009; Rouillard et al. 2010a, 2010b; Viall & Vourlidas 2015; Sanchez-Diaz et al. 2017; Lavraud et al. 2020). Clearly, there are many reasons and sources of evidence for the occurrence of anomalous characteristics that differ from the typical ambient solar wind. The question is whether they occur in organized ways that provide insights into their origins.

Solar wind observations are usually made only at one point or a few points, and obtaining large-scale pictures of solar wind behavior is not straightforward. However, contour displays constructed from stacked time series data, where Carrington Rotations (CRs) are used as an organizing framework, provide a way of visualizing the large-scale structure in the ecliptic at 1 au and its evolution (Neugebauer 1975; Gazis 1995; Neugebauer et al. 1998). Although this view is spatially restricted, it gives a sense of the global behavior at this radial distance. We refer to this type of contour display as a solar wind synoptic display. In this paper, we study the characteristics of solar wind anomalies and their relationships with the large-scale solar wind structures observed in the ecliptic near 1 au using STEREO in situ data for more than a single solar cycle. We define solar wind anomalies as temporary and local excursions from the usual average solar wind state, regardless of their origins, for six solar wind anomalies: sunward strahls (Qs), CSEs, suprathermal electron depletions (SEDs), nearly radial field episodes (NRFs), anomalously low proton temperatures *Tp*, and anomalously low proton plasma beta. Plasma beta is the ratio of the plasma pressure to the magnetic pressure —see Equation (2) in the following methodology section. We carry out a systematic study of the anomalous solar wind parameters of these six anomalies. The specific criteria for each type of solar wind anomaly are described in the next section. We then construct synoptic displays in order to make comparisons and associations with the solar wind and field structures, which are also presented in synoptic contour displays using STEREO in situ data that span more than a single solar cycle. In addition, we carry out analysis of the statistical properties of all of the anomalies. For this purpose, we take advantage of the nearly continuous data of the STEREO-A suprathermal electron (STE), magnetic field, and plasma observations, from the beginning of its heliocentric prime mission in early 2007 until the end of 2019. A special advantage of these observations is that they are free from the

foreshock effects that sometimes influence observations at first Lagrange point L1. Further details of our data sets and analyses are to be found in following sections.

We describe our database and analysis methodology in Section 2. In Section 3, we establish the large-scale solar wind structures and the distributions of each solar wind anomaly in the same format of synoptic contour displays and their associations. In Section 4, we present the results of the statistical analysis of the solar wind parameters for each type of anomaly. In Section 5, we summarize and discuss our findings.

## 2. Methodology

### 2.1. *Description of the STEREO Heliospheric Data*

The twin STEREO spacecraft have been in heliocentric orbit since early 2007, for about 14 yr, encompassing the whole of cycle 24 and the long solar minimum preceding this cycle (Kaiser et al. 2008). The twin STEREO spacecraft Ahead (A) and Behind (B) are orbiting the Sun near 1 au and the ecliptic, and drifting away from the Earth at ~22° per year. The STEREO mission is the data source for this study, but only the STEREO-A data will be used, because the time span is important for this study and multipoint observations are not needed, and because the STEREO-B data ends in October 2014, when contact with the spacecraft was lost. We primarily use the STE data obtained by the Solar Wind Electron Analyzers (SWEAs; Sauvaud et al. 2008) and the magnetic field data obtained by the Magnetometer (MAG; Acuña et al. 2008) of the In-situ Measurements of Particles and CME Transients (IMPACT) instrument suite (Luhmann et al. 2008), complemented by the solar wind proton data from the PLasma And Supra-Thermal Ion Composition (PLASTIC) instrument (Galvin et al. 2008) on board STEREO-A. The SWEAs allow measurements of incoming particles up to angles of ±65 from the regular top-hat entrance (which faces the plane perpendicular to the Sun-spacecraft direction) in the energy range ~45 to ~2 keV. The SWEA instruments thus measure most of the electron distribution function (80% of the unit sphere), apart from two cones centered in the sunward and antisunward directions. When the magnetic field lies in these cones, the pitch angle coverage is limited and the data are not used. The data from the normal telemetry mode used here consist of 3D distribution functions, with 16 energy bins and a resolution of 22°.5 in azimuth and 21°.7 in polar angles. The primary SWEA data used for this study consist of the STE density Ne, Pitch Angle Distributions (PADs) for solar wind strahl and halo electrons, and heat fluxes (Q in units of erg s⁻¹ cm⁻²). The heat fluxes are computed by integrating the observed >50 eV electron distribution functions for the three directions specified by the standard Radial Tangential Normal (RTN) coordinate system (also used for interplanetary fields; e.g., Lavraud et al. 2010). The STEREO electron measurements have the advantage of not being contaminated by sunward electrons from the Earth’s bow shock, once the spacecraft had drifted away from the Earth’s longitude after the mission’s initial phase.

### 2.2. *Analysis Techniques*

Using the magnetic field vectors from IMPACT and the solar wind proton densities, temperatures, and bulk speeds from PLASTIC, we construct a series of maps in which the hourly data are sectioned in 28-day intervals, with the first day coinciding with the start date of each CR, and each interval as a
column then being stacked in time to form a 2D array. The contour maps of the 2D arrays are presented in Section 3, and show the large-scale structures revealed in the corresponding solar wind parameters. Contour maps of the SWEA STE number density, the total heat flux Q, the component of Q parallel to the magnetic field Qpar, and the radial component Qr in spacecraft (RTN) coordinates are also constructed in the same manner and are also presented in Section 3.

We have found a method to identify the sunward strahls that we name as Qs hereafter. The SWEA Q vector is given as Qr, Qt, and Qn in the spacecraft coordinates, and it is also given as Qpar and Qper, respectively, when it is parallel and perpendicular to the local magnetic field. We define a parameter, Qas, which is capable of separating the antisunward strahls from the sunward strahls by making the antisunward strahls positive and the sunward strahls negative. Qas can be obtained as the product of the absolute value of Qpar and the unit vector of the radial component Qr, i.e., $Qas = |Qpar|^{*}(Qr/|Qr|)$.

In this paper, the STE number density data provided by the SWEAs is used to study the anomalous STE depletions when the source of an STE is disconnected from a region, and these anomalies are referred to as STE depletions or SEDs hereafter. Historically, these anomalies have been termed high-frequency deflections (HFDs), and the heat flux vector Q has been used as the measurement in previous studies, but low Q values can be produced by CSEs and compromise the interpretations.

Anomally low solar wind proton temperatures have previously been found and associated with heliospheric plasma sheets (HPSs) and ICMEs (Richardson & Cane 1995, 2010; Cane & Richardson 2003). The anomalously low $Tp$ occurs when the observed $Tp$ is much lower than the expected proton temperature $T_{ex}$, estimated from the empirical relationship with the proton bulk speed $Vp$. The empirical formula is given in the equation below (Lopez & Freeman 1986). The low $Tp$ anomaly is selected by $Tp/Tex \le 0.5$, following Richardson & Cane (1995):

$$ 
\begin{aligned}
T_{ex} &= (0.031Vp - 5.1)^2 \text{ V} < 500 \text{ km s}^{-1} \\
T_{ex} &= (0.51Vp - 142) \text{ V} \ge 500 \text{ km s}^{-1}.
\end{aligned} 
\quad (1) $$

The proton plasma beta is also analyzed in the study. The plasma beta, symbolized as $\beta$, is the ratio of the plasma pressure ($p=n_p k_B T_p$) to the magnetic pressure ($p_{mag} = B^2/2 \mu_0$), as below:

$$ \beta = (n_p k_B T_p)/(B^2/2\mu_0), \quad (2) $$

where $k_B = 1.3806e^{-23} (\text{JK}^{-1})$ and $\mu_0 = 1.257e^{-6} (\text{N/A}^2)$ in SI units.

In the next sections, we investigate the solar wind anomalies of sunward strahls (Qs), CSEs, and SEDs, using the SWEA electron data, as well as nearly radial magnetic fields or NRFs, anomalously low proton temperatures, and plasma beta episodes, using the IMPACT magnetic field data and the PLASTIC solar wind proton data for more than one solar cycle.

# 3. Solar Wind Anomalies in Large-scale Structures

## 3.1. Solar Wind Synoptic Structures

Synoptic contour maps of the solar wind parameters for the years 2007–2019 are presented in Figure 1, where panel (a) shows the proton bulk speed, $Vp$; panel (b) shows the temperature, $Tp$; panel (c) shows the density, $Np$; panel (d)

shows the HMF magnitude, $|B|$; and panel (e) shows the radial magnetic field, Br. Figure 1(f) then gives the smoothed monthly sunspot numbers (SSNs) over the same time span, covering solar cycle 24 (2009 January–2019 December) and the preceding solar minimum. In all of the contour maps, the solid black lines overlaid on the filled contours are the neutral Br contour (i.e., Br = 0), where the radial field switches sign between sunward and antisunward directions. The Br field is heavily smoothed (by 12 hr), before the neutral Br contour is found, preserving only the large-scale field reversals to represent the sector boundary crossings or HCSs. In the synoptic contour maps, the colors from blue to red indicate the speed, from slow to fast wind; the temperature, from low to high; the density, from low to high; the magnetic magnitude, from weak to strong; and the radial field, Br, from sunward to antisunward, as indicated by the color bars to the right of the contour maps.

In panel (a), two major fast solar wind streams in the sunward and antisunward HMF sectors, separated by the neutral Br contour (dark curves), maintain the recurrent corotating structure in the interval that is bracketed by the dashed magenta lines between 2007 February (at the start of the plot) and 2009 October, around the time of the minimum smoothed sunspot number (2008 December), as indicated by the black dashed line and seen in the SSN time series in panel (f). As the solar activity rises, the recurrent corotating stream structure disappears, being replaced with a more complex structure from 2010. From 2014 August to 2016 January, STEREO-A was in solar conjunction on the far side of the Sun relative to Earth, and the data are incomplete, resulting in the gaps shown in white in Figure 1. When STEREO-A reemerges with adequate data in 2016, the solar cycle has just passed the maximum phase and is entering the declining phase. The recent solar minimum occurs in 2019 December, as per NOAA.<fnref n="5" /> For four years (from CR 2172 in 2015 December to CR2224 in 2019 December), the solar wind structure in the declining phase becomes better organized than it was in the previous four years around the solar maximum, and it appears to have a character differing from both the minimum and maximum phases.

The solar wind proton temperature shows a structure similar to the speed, due to the known correlation between the two parameters (Lopez & Freeman 1986; Lopez 1987). The proton density during the first interval around the solar minimum shows two recurrent corotating high-density structures along the neutral Br contour, where compressions associated with stream interactions are expected. In fact, the high proton density regions are generally coincident with the sector boundaries or compression regions throughout the observed solar cycle phases, with a few exceptions. The HMF magnitude shows a structure similar to the proton density, i.e., the stronger magnetic fields occur in the compression regions. The transient strong fields known to be in ICMEs are not readily distinguishable in these synoptic displays, even though ICMEs may last for a day to a few days. The radial magnetic field component magnitude also shows a similar solar cycle dependence, being well-ordered near the solar minimum and complex away from the solar minimum. Over the declining phase from 2016–2019, the structure of the radial component Br appears to be more organized or show a less complex structure than the other parameters.

<footnote n="5">⁵ https://www.weather.gov/news/201509-solar-cycle</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Maps of (a) solar wind speed, *Vp*; (b) proton temperature, *Tp*; (c) density, *Np*; (d) magnetic field magnitude, |*B*|; and (e) radial magnetic field, *Br*. All maps are overlaid with the *Br* = 0 contour as sector boundary (dark lines). Panel (f) shows the SSNs. The black dashed lines mark the solar minimum and maximum, and the magenta dashed lines bracket the interval between 2007 February and 2009 October around the solar minimum, with two long-lived high-speed streams of opposite magnetic field polarity. (All of the in situ solar wind data in this paper are taken from STEREO-A.)</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Maps of (a) the STE number density; (b) the energy flux density; (c) the energy flux density parallel to the B vector Qpar; and (d) the energy flux in radial direction Qr, in spacecraft coordinates (r, t, n). All are overlaid with the Br = 0 contour as the sector boundary (dark lines). Panel (e) shows the SSNs.</figcaption></figure>

Solar wind electrons in the suprathermal energy range are analyzed in this study. Contour maps of the STE parameters are constructed in the same manner as shown in Figure 2, where panels (a) to (d) show the STE number density, Ne; the total STE energy flux, Q (or heat flux); the component Qpar, along the magnetic field lines; and the radial component Qr, in spacecraft coordinates (r, t, n). Figure 2(e) again shows the SSNs over the same time span. The map of the STE number density Ne in Figure 2(a) displays a very similar structure and solar cycle variation to the solar wind proton and magnetic field parameters in Figure 1, especially the proton density *Np* and the magnetic field magnitude |*B*|. The highest values of the STE number density Ne are coincident with the stream interaction regions and HCS on a large scale. This is the first time that

solar wind STE parameters have been shown in this large-scale format and that associations with the proton parameters have been made. It is interesting, and it may provide observational bases for relevant theoretical work. The map of the total STE energy flux Q in Figure 2(b) also shows a similar structure to the other solar wind parameters described earlier. Figure 2(c) shows the structure of the STE strahls Qpar at 1 au, where the parallel Qpar is shown on the red side of the contours and the antiparallel flux is shown on the blue side of the contours. The structure of Qpar is ordered by the solar wind magnetic sector, and it essentially follows the structure of the radial field Br in Figure 1(e). The radial component Qr holds information about the sunward or antisunward directions of the STE strahls. In the map of Qr in Figure 2(d), the red sides of the contours show the
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Maps of the constructed parameters as the bases for finding solar wind anomalies: (a) Qas; (b) the ratio of the STE flux (246 eV) at pitch angles 0° and 180°; (c) the ratio of Br over $|B|$; (d) the ratio of $Tp$ over $Tex$; and (e) the solar wind plasma beta. All are overlaid with the $Br = 0$ contour as the sector boundary (dark lines).</figcaption></figure>

antisunward Qr and the blue sides of the contours show the sunward Qr. The map is obviously biased to the red contours, as expected.

For the purpose of finding solar wind anomalies, we have defined or calculated the following parameters, which are shown in the synoptic displays of the entire time span presented in Figure 3. Panel (a) provides the maps of Qas, as defined

earlier in Section 2; panel (b) shows the ratio of the STE flux at pitch angles 0° and 180° for energy 246 eV; panel (c) shows the ratio of Br over $|B|$; panel (d) shows the ratio of $Tp$ over $Tex$, as defined earlier in Section 2; and panel (e) shows the solar wind plasma proton beta. Based on these parameters, we will further isolate and analyze the anomalous solar wind episodes in the following sections.
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Maps of (a) the sunward strahl episodes Qs; (b) the Qs (black contours) overlaid on the solar wind speed, $V_p$; (c) the Qs overlaid on the proton density, Ne; and (d) the Qs overlaid on the magnetic field All are overlaid with the $Br = 0$ contour as the sector boundary (orange lines). Panel (e) shows the SSNs. (Note: a different color map is used for the background solar wind parameter contours to better show the overlaid Qs.)</figcaption></figure>

## 3.2. Solar Wind Anomalies with Sunward Suprathermal Electron Strahls

In undisturbed solar wind, the STEs flow out of the solar corona, and subsequently form STE strahls that beam along the magnetic field lines in the antisunward direction. However, episodes of sunward strahls also occur at times. Sunward strahls have been associated with false polarity reversals of the HMF or switchbacks (Owens & Forsyth 2013) and IP shock-heated electron sources beyond 1 au or reflected STEs from solar wind stream compression regions (Gosling et al. 1993; Levraud et al. 2010). In this section, we study these sunward

strahl episodes in general. At 1 au, the average Parker spiral HMF is angled at approximately 45° to the solar radial direction, which is also the direction of the electron strahl Qpar. In order to identify the sunward Qpar, we define the parameter Qas, as described in the previous section and shown in Figure 3(a). The negative Qas represents all of the sunward STE episodes, named Qs, including those given by false polarity reversals and any other causes, including sunward STEs from interplanetary shock heating sources. We then isolate the sunward strahl episodes Qs, and the resulting contour map of Qs is presented in Figure 4(a). In order to examine the associations of the sunward strahls Qs with
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Maps of (a) CSEs represented by $-0.5 < Rp < 0.5$ (where $Rp$ is the ratio between the STE parallel (PA 0°) and antiparallel (PA 180°) strahl flux without isotropic cases); (b) CSEs (black contours) overlaid on the solar wind speed, $Vp$; (c) CSEs overlaid on the proton density, $Np$; and (d) CSEs overlaid on the B field. All are overlaid with the $Br = 0$ contour as the sector boundary (orange lines). Panel (e) shows the SSNs. (Note: a different color map is used for the background solar wind parameter contours to better show the overlaid Qs.)</figcaption></figure>

large-scale structures and features, we overlay the Qs contours (in black lines) on the solar wind speed map in panel (b); on the solar wind proton density map in panel (c); and on the HMF magnitude map in panel (d). The Qs appears to have a slight tendency to cluster around the sector boundary or HCS (the orange lines overlaid on the contour displays) during solar activity minimum periods, but not during solar active times, and it appears to be located in slow solar wind and low magnetic magnitude regions regardless of the solar activity level.

### 3.3. Solar Wind Anomalies with CSEs and SEDs

To identify CSE episodes, the SWEA STE PAD data are used to calculate the ratio between the parallel and antiparallel streaming strahls. Figure 3(b) provides the contour map of the ratio for STEs at energy 246 eV. We isolate the CSE episodes by removing the isotropic and unidirectional distributions. The isotropic distribution is defined as a case where the ratio of parallel to perpendicular STE fluxes and the ratio of antiparallel to perpendicular fluxes are both greater than 0.8 and less than 1.2. The unidirectional distribution is defined as a case where
<figure><img src="image_7.png" /><figcaption>**Figure 6.** Maps of (a) anomalous low STE density Ne, with the heliospheric current sheet loci shown by orange lines; (b) low Ne episodes (black contours) overlaid on the solar wind speed map; (c) low Ne overlaid on the density $N_p$ map; and (d) low Ne overlaid on the HMF magnitude map. All are overlaid with the $Br = 0$ contour as the sector boundary (orange lines). Panel (e) shows the SSNs. (Note: a different color map is used for the background solar wind parameter contours to better show the overlaid Qs.)</figcaption></figure>

the ratio between parallel and antiparallel STE fluxes is less than 0.3 or greater than 3. These thresholds are subjective, and one may keep in mind that when the ratio is closer to 1, CSEs are closer to being symmetric, and the greater the departure from 1 the less symmetric the CSEs are. Figure 5(a) provides the contour maps of the CSE episodes. Panels (b) to (d) of Figure 5 show the contours of the CSE episodes (in black) overlaid on the solar wind proton speed, the proton density, and the HMF magnitude maps. Figure 5(e) shows the SSNs. It is clearly evident from Figure 5(a) that the occurrence frequency of the CSEs has a positive solar cycle dependence with solar activity, and this will be further discussed later in Section 3.6,

together with other statistical properties. The CSEs appear to have a tendency to cluster around the sector boundaries (or HCS or compression regions) during all phases of solar activity levels. Along with this association, CSEs appear to prefer slower solar wind regions, as seen in Figure 5(b); higher density regions, as seen in Figure 5(c); and stronger magnetic field regions.

The STE number density Ne is analyzed to study the SEDs, as previously described in Section 2.2. We isolate the intervals that satisfy $Ne \le 0.3 \text{ cm}^{-3}$, but exclude those where $|B| < 4 \text{ nT}$, as Ne is naturally low in weak magnetic field regions, and not necessarily due to the same physics causing the anomaly, such
<figure><img src="image_8.png" /><figcaption>**Figure 7.** Maps of (a) anomalous NRFs nearly radial B field episodes with $|Br/B| \ge 0.9$; (b) NRFs (black contours) overlaid on the solar wind speed, $Vp$; (c) NRFs overlaid on the proton density, $Np$; and (d) NRFs overlaid on the B field. All are overlaid with the $Br = 0$ contour as the sector boundary (orange lines). Panel (e) shows the SSNs. (Note: a different color map is used for the background solar wind parameter contours to better show the overlaid Qs.)</figcaption></figure>

as magnetic disconnection from the solar corona. Therefore, we only consider the low Ne episodes where the total magnetic magnitude satisfies $|B| \ge 4$ nT for SEDs. The contour map of the SED episodes is given in Figure 6(a). The SEDs are also overlaid on the solar wind speed, density, and $|B|$ in panels (b), (c), and (d) of Figure 6, respectively. For reference, the SSNs are in the bottom panel (e) again. From the synoptic displays, it can be seen that the SEDs appear slightly more frequently during the solar active time than the quiet time, and a quantitative analysis is given later (Section 3.6, Figure 10). We also see that the SEDs have a simpler structure during the solar minimum and the declining phase, and a complex structure during the solar maximum, similar to the background solar wind stream structure. We do not see

clear associations of the SEDs with the sector boundaries or compression regions.

### 3.4. Solar Wind Anomalies with NRFs at 1 au

The well-established observation that the HMF is typically in the direction of the Parker spiral, at about a 45° angle from the solar radial line at 1 au, has been found to be violated (Neugebauer et al. 1997; Gosling & Skoug 2002; Murphy et al. 2002; Watari et al. 2005) when the B vector is in the nearly radial direction. We here analyze the ratio between the radial field $Br$ and the B magnitude in order to obtain the general behavior of this anomalous behavior over about one solar cycle. The synoptic
<figure><img src="image_9.png" /><figcaption>**Figure 8.** Maps of (a) the low proton temperature *Tp* episodes; (b) the low *Tp* episodes (black contours) overlaid on the solar wind speed, *Vp*; (c) the low *Tp* episodes overlaid on the proton density, *Np*; and (d) the low *Tp* episodes overlaid on the magnetic field magnitude. All are overlaid with the Br = 0 contour as the sector boundary (orange lines). Panel (e) shows the SSNs. (Note: a different color map is used for the background solar wind parameter contours to better show the overlaid Qs.)</figcaption></figure>

display of the ratio of Br over |B| was previously given in Figure 3(d). We now isolate the episodes where |Br/B| ≥ 0.9, and provide the contour map in Figure 7(a). These high ratio episodes of NRFs are also overlaid on the maps of solar wind speed, density, and |B| in panels (b), (c), and (d) of Figure 7, respectively. Panel (e) gives the SSNs. The most obvious trend from these maps is that the NRF episodes occur more frequently around the solar minimum and during the declining phase of the solar cycle than the solar activity maximum phase, displaying an anticorrelation with solar activity. No associations between the NRFs and the large-scale solar wind structure, sector boundaries, or solar wind streams are observed in the synoptic displays.

### 3.5. Solar Wind Anomalies with Low *Tp* and Low Plasma Beta

We investigate the distribution and characteristics of anomalous low proton temperature episodes in general. The synoptic display of the ratio between the observed and expected *Tp*, *R*<sub>T</sub>=*Tp*/*T*<sub>ex</sub>, was previously shown in Figure 3(e). We now isolate the low *Tp* episodes using the threshold of *R*<sub>T</sub>≤0.5, as described in Section 2.2, and provide the contour map in Figure 8(a), then overlay these episodes on the map of the solar wind speed in Figure 8(b), the map of the density in Figure 8(c), and the map of the HMF magnitude |*B*| in Figure 8(d). The occurrence of the low *Tp* episodes shows a clear solar cycle dependence, with a positive correlation with solar activity. Low *Tp* episodes follow the solar
<figure><img src="image_10.png" /><figcaption>**Figure 9.** Maps of (a) the low plasma beta episodes; (b) the low beta episodes (black contours) overlaid on the solar wind speed, $V_p$; (c) the low beta episodes overlaid on the proton density, $N_p$; and (d) the low beta episodes overlaid on the magnetic field magnitude. All are overlaid with the $Br = 0$ contour as the sector boundary (orange lines). Panel (e) shows the SSNs. (Note: a different color map is used for the background solar wind parameter contours to better show the overlaid Qs.)</figcaption></figure>

wind stream structure pattern during the low solar activity period between the two magenta dashed lines, but they do not appear to be ordered by the large-scale solar wind and HMF structure during other phases of the solar cycle.

The ratio between the plasma pressure and the magnetic pressure gives the plasma beta, as defined in Equation (2). We investigate anomalously low proton beta in general. The contour map of the logarithm of the plasma beta was previously shown in Figure 3(e). The low beta episodes, satisfying the threshold of beta $\le 0.1$, are shown as the contour map in Figure 9(a) below, and they are overlaid on the solar wind speed, density, and HMF $|B|$ in panels (b), (c), and (d), respectively. The low beta episodes are seen to occur predominantly during solar active times, with more

frequent occurrences and often longer durations. The low beta episodes show a tendency to cluster around the sector boundary or HSC around the solar minimum time and during the declining phase, but not during solar active times. It is also notable that the low beta episodes are clearly less frequent during the declining phase than they are around the solar minimum time.

### 3.6. Statistical Properties of Solar Wind Anomalies

Here we present the statistical studies of the solar wind anomalies shown in the synoptic displays above. Specifically, we investigate the occurrence frequencies and their solar cycle dependence, the distributions of the timescales or durations of
<figure><img src="image_11.png" /><figcaption>**Figure 10.** Annual %Hours as a function of years for (a) sunward strahls (Qs); (b) CSEs; (c) anomalous low STE Ne (≤0.3 cm⁻³) or SEDs; (d) NRFs (Br/B ≥ 0.9); (e) low *Tp* (*R*<sub>T</sub> ≤ 0.5); (f) low proton beta (≤0.1); and (g) the SSNs.</figcaption></figure>

the anomalous episodes, and the distributions of each of the anomalies against the solar wind parameters.

Figure 10 provides the annual percentage (ANL%) of occurrences of solar wind anomalies of each year over one solar cycle. To obtain the ANL%, we first calculate the sum of the occurrence hours of a solar wind anomaly in each year, then divide the total occurrence hours by the total observation hours in the corresponding year, and name it ANL%. The occurrence ANL% of the solar wind anomalies as functions of years are presented in Figure 10 for: (a) sunward strahls (Qs); (b) CSEs; (c) low STE Ne anomaly SEDs; (d) NRF anomalies; (e) low *Tp*; and (f) low beta; with panel (g) showing the SSNs. The occurrence ANL% of the Qs, SEDs, low *Tp*, and low beta show clear positive solar cycle correlations. The occurrence ANL% of the CSEs appears to have a weak positive solar cycle dependence. The occurrence ANL% of the NRFs has a clear anticorrelation with the solar activity. These measures confirm and reinforce what has been observed in the synoptic displays and pointed out in the previous sections.

Figure 11 provides the distributions of the durations of the solar wind anomalous episodes of (a) sunward strahls (Qs); (b) STE CSEs; (c) anomalous low STE number density Ne; (d) radial field Br/B ≥ 0.9; (e) anomalous low *Tp*; and (f) low

plasma beta. The durations of the Qs, CSE, low Ne, NRF, low *Tp*, and low beta episodes range from 1–24 hr, 1–32 hr, 1–28 hr, 1–17 hr, 1–42 hr, and 1–31 hr, respectively. The occurrence peaks for all of the anomalies appear to be at 1 hr intervals, and decrease in number over longer durations without secondary peaks. 1 hr is the resolution of the data sets that were used for the analyses, which suggests that these anomalous episodes occur frequently in durations shorter than 1 hr. The distribution curves of each anomaly have their own forms, and are different from one another. As pointed out earlier, this paper is focused on the study of the general overall properties of the anomalies. Each anomaly could be the result of multiple sources and processes. Detailed scrutiny and interpretations are beyond the scope of the current investigation, and are deferred to future follow-up studies.

Figure 12 presents the normalized distribution of each anomaly's occurrence against the basic solar wind parameters; the proton bulk speed, *Vp*; the temperature, *Tp*; the density, *Np*; the HMF magnitude, |*B*|; and the proton beta; overplotted with the distribution of the corresponding base parameter of each anomaly (previously defined in Figure 3) for comparison. In panel (a), the normalized distributions of Qs (red dotted lines) and the absolute values of the strahls, |*Qpar*| or |*Qas*| (black
<figure><img src="image_12.png" /><figcaption>**Figure 11.** The distributions of the durations of the solar wind anomalous episodes as (a) sunward strahls (Qs); (b) STE CSEs; (c) anomalous low Ne (≤0.3 cm⁻³); (d) radial field Br/B ≥ 0.9; (e) anomalous low Tp (R<sub>T</sub> ≤ 0.5); and (f) low proton beta (≤0.1).</figcaption></figure>

lines), are presented. From left to right, it is observed that the peak distribution of Qs shifts slightly to the slower bin of the *Vp* at ~360 km s⁻¹, as opposed to at ~400 km s⁻¹ for |Qpar|; that Qs quite clearly shifts to a lower *Tp* than |Qpar|; that Qs overall slightly favors a lower density *Np* as compared to |Qpar|; that there is no difference against |B|; and that Qs overall slightly favors a higher plasma beta than |Qpar|. In panel (b), the normalized distributions of the CSE fluxes (red dotted lines) and general STE fluxes (black lines) are presented. From left to right, the distribution of the CSEs spreads over a wider speed range, to the slower bins of *Vp* versus a peak at ~400 km s⁻¹ for all STEs; it overall favors a slower solar wind than the general STEs; and the distribution of the CSEs also favors lower temperatures, higher densities, weaker |B|, and higher plasma beta than the general STEs. In panel (c), the distributions of the SEDs (red dotted lines) do not much differ from those of all of the STEs (black lines) against *Vp*, *Np*, and |B|, but they favor a lower *Tp*, and display a clear shift to a lower beta. A small bump at ~600 km s⁻¹ is seen on the tail of the SED distribution against the *Vp* (red dotted line). In panel (d), the NRFs slightly favor a higher *Vp* and a higher *Tp*, but a lower *Np*. In panel (e), the low *Tp* episodes favor a higher *Vp*, a lower *Np*, and a lower beta. In panel (f), the distribution of the low beta episodes against the *Vp* only differs from the overall beta distribution in its medium speed, while the low beta distribution favors a lower *Tp*, a lower *Np* and a higher |B|. These results are consistent with the associations between

anomalies and solar wind parameters that were observed in the synoptic contour displays in the previous sections.

## 4. Summary and Discussion

The global solar wind has a solar cycle-dependent structure that reflects its variety of sources as the cycle progresses. To better understand its sources and how it evolves in response to solar conditions would require a dense global network of heliospheric spacecraft observations. However, heliospheric in situ observations of the solar wind are sparse, and usually only include one to several points of measurements. We must currently rely on these to learn as much as we can about its global structure, and how it changes with time, using mainly ecliptic plane observations, which sample only a “slice” of the heliosphere. Part of the problem is understanding how the shorter small-scale structures relate to the large-scale structure. In order to study the associations between solar wind anomalies and the large-scale solar wind structure, we constructed sets of synoptic displays of the solar wind over one solar cycle, using STEREO IMPACT data. The synoptic displays of the basic solar wind parameters show pictures that are consistent with the expected solar wind structure variations over the solar cycle, with a recurrent corotating stream structure in an ordered appearance during low solar activity or the minimum phase, and a complex stream structure during high solar activity or the maximum phase. It has been reported that the corona structure
STA IMPACT-SWEA 2007-2019

<figure><img src="image_13.png" /><figcaption>**Figure 12.** Normalized distributions of (a) the parallel heat flux Qpar (black line) and sunward head flux Qs (red dotted line); (b) the STE strahls (black line) and CSEs (red dotted line); (c) the STE density Ne (black line) and the anomalous low Ne (red dotted line); (d) the ratio between the radial magnetic field over the total field (black line) and NRFs, when the ratio ≥ 0.9; (e) the ratio between *Tp* and the expected proton temperature *T*ex (black line) and the low *Tp* or low value of the ratio (red dotted line); and (f) the proton beta (black line) and low beta (red dotted line); all against solar wind speed, proton temperature, proton density, HMF magnitude, and solar wind plasma beta, from left to right.</figcaption></figure>

was not as dipolar during the deep solar minimum between
cycles 23 and 14, due to the weak polar fields, and that it often
included low latitude coronal holes that are unusual for the
solar minimum (Abramenko et al. 2010; de Toma et al. 2010).
Our synoptic displays, however, suggest the presence of two
dominant streams, as might be expected for a simpler dipolar
corona source. This reminds us that the relationship between
the solar wind structure at 1 au and the coronal field is not
always straightforward. During the declining phase between
2016 and 2019, the solar wind streams (with contours of *Vp*,
*Np*, Ne, etc.) continue to exhibit a complex structure, much like
that during the solar maximum phase, but the HMF sectors are

now similar to those around the solar minimum phase, as
presented in Figure 1(e). The different behaviors of the HMF
structure (simple) and the plasma stream structure (complex) in
the solar wind during this declining phase are interesting. We
can only postulate that the solar dipole field has begun to form,
in order for the HMF to approach a two-sector structure, but
multiple solar wind stream structures have also formed within
sectors of the same magnetic polarity, meaning that a credible
explanation will only be possible with further investigations
and evidence.

Using the STEREO-A IMPACT magnetic field and STE
data, we studied six solar wind anomalies, namely: sunward
STE strahls, measured by Qs; CSEs, using the STE PAD measurements; SEDs (HFDs), measured by anomalously low STE Ne; nearly radial HMFs or NRFs, measured by the ratio of Br over $|B|$ (≥0.9); anomalously low proton temperatures, $Tp$, normalized by the expected Tex from the proton speed $Vp$; and low plasma beta. We summarize and discuss our major findings relating to their statistical properties and their associations with the large-scale solar wind structure as follows.

**Sunward strahls (Qs).** Qs represent all sunward strahls, without discriminating their origins. Two known origins of sunward strahls are magnetic field false polarity reversals (e.g., Owens et al. 2014) and IP shock electron heating (e.g., Lavraud et al. 2010). From the comparison with the solar wind structure in the synoptic displays, we can see that the sunward strahls (Qs) have a weak tendency to cluster around the sector boundary or HCS during solar activity minimum times, but not during solar active times. The sunward strahls also appear to favor regions with slower solar wind, lower $Tp$, and lower HMF, regardless of the solar activity level. Owens et al. (2017) pointed out that sunward strahls related to magnetic field switchbacks tend to cluster around HCSs, in partial agreement with the results found here. Owens et al. (2017) also found that their sunward strahls favored lower $Tp$, which they interpreted as greater expansion and quasi-adiabatic cooling. The occurrence ANL% of Qs shows a clear positive solar cycle dependence. The durations of the Qs episodes range between 1–24 hr, with the peak of occurrence at the 1 hr interval, before monotonically decreasing over longer durations. Overall, these results point to the need to better interpret the occurrences of sunward-directed strahls at 1 au. Further analysis identifying the contributions to sunward strahls (Qs) from different origins will require substantial further efforts, such as the inclusion of energy spectra and strahl widths.

**Counterstreaming suprathermal electrons (CSEs).** Occurrences of CSEs have a tendency to cluster around the sector boundaries (or HCS or compression regions) during all phases of solar activity. Along with this association, CSEs appear to prefer slower solar wind regions, as seen in Figure 5(b); higher density regions, as seen in Figure 5(c); and stronger magnetic field regions. The occurrence frequency of CSEs has a weak positive solar cycle dependence. The durations of the CSE episodes range between 1–2 hr (as shown in Figure 11). Similarly, the CSEs identified include all cases, without discriminating their origins. Previous studies have discussed CSEs on closed magnetic field lines, with both ends anchored to the Sun, leading to coronal hot electron streaming in both directions. It is also possible for CSEs to be on open field lines, with one end connected to the Sun and the other connected to an IP shock, producing heated electrons streaming sunward, or toward a compressed region that simply reflects the solar strahl electrons. Many previous studies of CSEs relate to coronal mass ejections (CMEs)/ICMEs (Gosling et al. 1992; Larson et al. 1997; Shodhan et al. 2000). In fact, CSEs have been listed as one of the identifiers of ICMEs, although they do not always occur during ICMEs. CSEs are often found only in part of the ICME structure, occurring randomly, in patches, rather than continuously (Shodhan et al. 2000). The durations of the general CSEs in Figure 11 are mostly shorter than those of typical ICMEs. The results of the CSE characteristics in this study, both the positive solar cycle dependence and the duration, are consistent with those of previous studies (Shodhan et al. 2000). Further detailed studies, to understand the contributors to the behavior of the overall CSEs found in this study, and their associations with solar wind structures, are again deferred to future efforts.

**Suprathermal electron depletions (SEDs).** HFDs have been attributed to the disconnection of the magnetic field from the solar corona (McComas et al. 1989) and the enhanced Coulomb scattering of STE strahls in transit from the Sun (Fitzenreiter & Ogilvie 1992). In this paper, we have used the STE number density to study these anomalies, and have termed them SEDs. We found that the SEDs have structures similar to the corotating structure/pattern of the background solar wind around the solar minimum, that they display no particular patterns during the solar maximum, and that they display a corotating pattern in part of the declining phase (see Figure 6). We do not see clear associations between the SEDs and the sector boundaries or compression regions. Our statistical results in Figure 12(c) show that the SED distributions favor lower temperatures, lower plasma beta, and that they display no biases regarding solar wind proton speed or density, in comparison with all of the STEs. Our findings are in partial disagreement with previous results using smaller data samples in McComas et al. (1989) and Fitzenreiter & Ogilvie (1992), where HFDs were found in regions of increased plasma density and decreased electron temperature, and associated with sector boundaries. The occurrence ANL% of the SEDs shows a positive solar cycle dependence, but the occurrences during the declining phase appear to be obviously lower than those during the solar minimum times, which is interesting and calls for further studies. The durations of the SED episodes are 1–28 hr in Figure 11(c). McComas et al. (1989) identified 25 HFDs ranging from 20 minutes to over 11 hr in duration, which fall in the range of our findings.

**Nearly radial fields (NRFs).** We found that the NRF episodes occur more frequently around the solar minimum and during the declining phase of the solar cycle than around the solar activity maximum phase. The occurrence ANL% of the NRFs shows a clear anticorrelation with solar activity. Previous studies found that long-duration NRF events often occur in the rarefraction regions behind high-speed solar wind streams (Gosling & Skoug 2002; Murphy et al. 2002). Solar wind streams are indeed better defined when solar activity is low, and CIRs and SIRs are clearly the dominant structures. But we see no clear associations of NRFs with sector boundaries or solar wind streams. Previously, NRF events have also been reported in post-ICME flows (Neugebauer et al. 1997), while ICMEs occur more frequently during the solar maximum, in contrast to the solar cycle variation of the NRFs. The durations of the NRF episodes are 1–17 hr (Figure 11). Previous studies usually begin by selecting NRF events longer than several hours. Watari et al. (2005) found that the occurrence of their long-duration events showed an anticorrelation with sunspot numbers, and this is consistent with our current finding of their primary association with a low activity solar wind structure.

**Anomalous low $Tp$.** Low $Tp$ episodes show a similar corotating occurrence pattern with the solar wind stream structure during the low solar activity time between the two magenta dashed lines, but they do not appear to be ordered by the large-scale solar wind and HMF structure during other phases of the solar cycle. Richardson & Cane (1995) identified low $Tp$ intervals using OMNI solar wind data between 1965 and 1991, as well as some Helios 1 and 2 spacecraft data. Around a third of their intervals were found to be encounters with the “quiet” HPS, and these intervals occurred mostly at low solar activity times, when the HPS lies closer to the ecliptic. They argued that these HPS-associated anomalously low $Tp$ intervals might be intrinsic to the HPS, or they might
provide support to the proposal that the coronal streamer belt underlying the HPS is a frequent source of ejecta. They found a solar cycle dependence of the occurrences of the low *Tp* intervals. Their non-HPS low *Tp* intervals had even better correlations with the solar cycle and with ICMEs. They then further argued that these anomalously low *Tp* intervals could be a good indicator of ICMEs. The occurrence frequency of the anomalously low *Tp* episodes that we found by applying the same criteria to the STEREO solar wind data shows a similar positive solar cycle dependence. But we defer detailed investigations, such as separating the episodes from different sources, to future follow-up studies that will focus on the low *Tp* anomaly. The durations of our low *Tp* episodes are 1–42 hr, but the majority of the low *Tp* episodes occur at short timescales of less than, e.g., 6 hr, well below the typical duration of ICMEs. The low *Tp* episodes with the longest durations agree with and do not exceed the durations of typical ICMEs. Recent studies on both coronagraph CMEs and in situ ICMEs found ubiquitous narrow CMEs or small flux ropes, which have similar eruptive scenarios or mechanisms as larger CMEs, and these authors argue that CMEs arise at large and small scales in a continuous spectra (Lamy et al. 2019; Huang et al. 2020). Our findings relating to the low *Tp* characteristics are not inconsistent with these findings and suggestions.

*Low plasma beta.* While solar wind plasma beta is one of the fundamental parameters and plays an essential role in the dynamic processes of the solar wind, anomalies in the solar wind are the focus of this study. Anomalously low beta episodes are seen to occur predominantly during solar active times, with more frequent occurrences and more episodes of longer durations. The low beta episodes show a tendency of clustering around the sector boundary or HCS around the solar minimum time and during the declining phase, but not during solar active times. The durations of the low beta episodes here range between 1–31 hr, again peaking at 1 hr and then monotonically decreasing. The low beta intervals have been one of the identifiers of MCs, the type of flux rope of ICMEs. The occurrence of MCs has been found to have no clear solar cycle dependence (Li et al. 2011). The low beta episodes of the longest durations agree with and do not exceed the durations of typical MCs. Shorter low beta episodes represent a large fraction of the total occurrences. A similar argument that flux ropes arise on both large and small scales in continuous spectra (Lamy et al. 2019; Huang et al. 2020) may also apply here, while the contributors to low beta anomalies may not be limited to flux ropes, and further studies are needed in this respect.

Although we believe that the distributions of the durations of these anomalies are consistent with the concept that they occur on both small and large scales in continuous spectra, we note that a few other factors could contribute to the behavior of such distributions that peak at short intervals, including random data points that happen to cross the thresholds; part of a cluster of short intervals being associated with a larger structure where the observations intermittently cross the thresholds; bad data points; or incomplete observations. After selecting the anomalously low *Tp* intervals with *Tp*/Tex ≤ 0.5 using OMNI and HELIOS data in a 1 hr resolution, Richardson & Cane (1995) grouped together the intervals that were separated by less than 3 hr on the assumption that they formed part of the same event. They also grouped together the intervals that were part of the same temperature depression. Following the above process, they gave the distributions of the durations of their events. Their distributions also peak at durations of 1 hr, then decrease monotonically, similar to the

results presented in our Figure 11. Therefore, we believe that this characteristic of the distribution of the duration is real, at least for the low *Tp* anomalies, and that it supports the argument that such anomalies occur in continuous scales. Further detailed investigations into each of the anomalies are not the intention of this paper, but will be carried out in future follow-up studies, as pointed out elsewhere in this paper.

## 5. Concluding Remarks

The structure of the solar wind in the synoptic displays over 13 yr is consistent with current knowledge in terms of solar cycle variation in general. The solar minimum structure shows clear corotating or recurrent behavior, despite the apparent departure from the dipolar geometry of the coronal magnetic field around the solar minimum (2008 December). The solar wind structure around the solar maximum (2014 April) is complex, and over the declining phase (2016–2019) it is interesting, in that the HMF sectors suggest a simple two-sector structure similar to the solar minimum, while the plasma stream structure is more complex. The basic solar wind parameters and structure serve as the basis of our study of solar wind anomalies.

All six of the solar wind anomalies in our study show some degree of association with the large-scale solar wind structure, especially at low solar activity times, implying that the solar wind structure plays a role in either the generation or the transport of each anomaly. One common feature is that the distributions of the occurrence counts versus the durations of the anomalies all peak at 1 hr episodes, then monotonically decrease over longer durations. 1 hr is the resolution of the data sets that were used for the analyses, which may imply that these anomalous episodes occur frequently over shorter timescales and smaller spatial scales than 1 hr in observations at ~1 au. This result may support the concept that solar anomalies generally occur in continuous spectra across temporal and spatial scales, but further investigations will be needed in order to confirm this argument (or not). As pointed out earlier, this paper has focused on providing a general overall picture of the properties and large-scale contexts of the six anomalies. Each anomaly could be the result of multiple sources/ processes, including those occurring at remote sites. Further detailed scrutiny, studies of the contributors to each anomaly, and interpretations of the sources, causes, and processes will be the topics of follow-up studies.

We are grateful to NASA’s STEREO Project for its overall management of the mission, and for operations and data analysis support, via contract 80NSSC18K1446 P00003 to the University of California. Dr. S. Xu gratefully acknowledges support from NASA’s Heliophysics Guest Investigator Program, grant #80NSSC21K0731.

We also acknowledge the contributions to the archived data used here by the IMPACT investigation instrument and data providers at IRAP (SWEA), NASA GSFC, and UCLA (MAG), and the PLASTIC plasma analyzer team (A.B. Galvin, PI) at the University of New Hampshire. The data used are publicly available through the STEREO Science Center (SSC) at NASA GSFC (https://stereo-ssc.nascom.nasa.gov/) and through the NASA Space Physics Data Facility Coordinated Data Analysis Web (CDAWeb, https://cdaweb.gsfc.nasa.gov/index.html/) of the NSSDC.
ORCID iDs

Yan Li https://orcid.org/0000-0003-4112-3122

Shaosui Xu https://orcid.org/0000-0002-5121-600X

Janet G. Luhmann https://orcid.org/0000-0003-0626-9353

Benoit Lavraud https://orcid.org/0000-0001-6807-8494

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