Helios Observations of Quasiperiodic Density Structures in the Slow Solar Wind at 0.3, 0.4, and 0.6 AU

Abstract

Following previous investigations of quasiperiodic plasma density structures in the solar wind at 1 AU, we show using the Helios1 and Helios2 data their first identification in situ in the inner heliosphere at 0.3, 0.4, and 0.6 AU. We present five events of quasiperiodic density structures with time scales ranging from a few minutes to a couple of hours in slow solar wind streams. Where possible, we locate the solar source region of these events using photospheric field maps from the Mount Wilson Observatory as input for the Wang-Sheeley-Arge model. The detailed study of the plasma properties of these structures is fundamental to understanding the physical processes occurring at the origin of the release of solar wind plasma. Temperature changes associated with the density structures are consistent with these periodic structures developing in the solar atmosphere as the solar wind is formed. One event contains a flux rope, suggesting that the solar wind was formed as magnetic reconnection opened up a previously closed flux tube at the Sun. This study highlights the types of structures that Parker Solar Probe and the upcoming Solar Orbiter mission will observe, and the types of data analyses these missions will enable. The data from these spacecrafts will provide additional in situ measurements of the solar wind properties in the inner heliosphere allowing, together with the information of the other interplanetary probes, a more comprehensive study of solar wind formation.

1. Introduction

The outflow of coronal plasma from the Sun, the solar wind, has been historically classified by its velocity into fast and slow streams. However, the use of speed alone is often not the best way to discriminate different kinds of solar wind plasma due to dynamics that reduce velocity differences between the fast and slow wind (Burlaga, 1995), particularly by the time the wind reaches L1. For example, Sanchez-Diaz et al. (2016) identified near the Sun (inside 0.7 AU) very slow solar wind streams (<300 km/s), rarely observed at 1 AU, with properties that were different from both the slow and fast wind. Due to the dynamic processing solar wind plasma undergoes during transit to 1 AU, neither temperature nor speed at these heliospheric distances are good proxies for solar source. Instead, the source region of the different solar wind streams is more clearly distinguished with the plasma charge state ratios, which is a proxy for the electron temperature at the source in the solar corona, and the elemental abundances (Stakhiv et al., 2015, 2016; Zurbuchen et al., 2002), as these do not evolve during the transit to 1 AU (Zhao & Fisk, 2011).

The fast wind plasma has element abundances similar to those of the photosphere and to the coronal plasma of open-field regions and charge state ratios consistent with the temperature of open-field regions. The combined observations of solar wind velocity and composition from Ulysses showed that the high-speed solar wind originates from open coronal holes (McComas et al., 2008; Zurbuchen, 2007), in particular to radially expanding flux tubes rooted in the intergranular lane of the photosphere (Cranmer, 2009; Cranmer & van Ballegooijen, 2005).

In contrast, the slow solar wind (SSW) is highly variable, exhibiting large fluctuations in density and composition (Gosling, 1997), and containing plasma with abundances and charge state ratios similar to the closed field regions of the solar corona (Gosling, 1997; von Steiger & Zurbuchen, 2016). In addition, the slow-speed streams always contain the heliospheric current sheet (HCS), which maps to the streamer belt region on the Sun (Burlaga & Ness, 2012) and the boundary between open and closed fields in the solar corona (Antiochos et al., 2011). Consequently, the SSW has been associated with several different sources near the boundaries between coronal holes and streamers, including rapidly expanding open fields near the streamer (Cranmer et al., 2007), the heliospheric current sheet near the top of helmet streamers cusps (Sheeley et al., 1997; Suess et al., 1996), and low-latitude active regions (AR) in the rising phase of solar activity (Luhmann et al., 2002; Kasper et al., 2007; Wang, Ko, et al., 2009). Therefore, the SSW could form through continuous release of structures (Antiochos et al., 2011; Einaudi et al., 2001; Lapenta & Knoll, 2005) or it could be made of two components, one structured and one continuous, the latter originated in similar way as the fast wind (Stakhiv et al., 2015, 2016; Wang, Robbrecht, et al., 2009; Wang, 2010).

Three general models have been proposed to explain the release of the SSW plasma. Briefly, in the expansion factor model (Cranmer et al., 2007; Wang & Sheeley, 1990), the coronal plasma flows along superradially expanding magnetic flux tubes along the boundary of open and close field lines. In the interchange model (Fisk, 2003; Fisk et al., 1998; Fisk & Zhao, 2009), plasma from closed-field loops throughout the solar corona is continually released into the solar wind via continuous reconnection with field lines that are open to the heliosphere. The Separatrix-web (S-web; Antiochos et al., 2011) model is a hybrid of the other two models: interchange reconnection occurs, but only along the boundary between open and closed field lines. This open-closed boundary is composed of a web of separatrices, and observations show that it can be highly complex. All three models reproduce the observed characteristics of the slow and fast solar wind at long time scales, and therefore, further observational constraints are required to test them. In particular, knowledge of the fundamental time scale over which the properties of the SSW change would improve our understanding of the release processes of solar wind plasma by providing better constraints for these models. An important way to provide this much-needed constraint on models of the SSW is by investigating mesoscale structures (with time scales of tens of minutes to several hours) in the solar wind, such as the quasiperiodic density structures that we examine here.

Scientists have already successfully used mesoscale structures to study the source of the SSW. Yet progress has been limited by the enormous observational gap between the remote observations of the high corona and 1 AU in situ measurements, which makes it difficult to directly relate in situ structures to their coronal source. Some successful examples are the studies of plasma blobs filling the SSW surrounding the HCS that have been tracked from their coronal source to their Earth impact (Rouillard, Davies, et al., 2010; Rouillard, Lavraud, et al., 2010). These plasma blobs are periodically released from the top of helmet streamers on time scales of many hours down to the resolution of the imagers (many minutes; DeForest et al., 2016, 2018; Sheeley et al., 1997; Sanchez-Diaz, Rouillard, Davies, Lavraud, Sheeley, 2017a; Sanchez-Diaz, Rouillard, Davies, Lavraud, Pinto, 2017b; Viall et al., 2010; Viall & Vourlidas, 2015; Wang et al., 2000). Simulations show that these blobs could be formed by coronal plasma released by magnetic reconnection as result of thermal instability at the tip of streamers (Rappazzo et al., 2005; Suess et al., 1996) in a periodic nature (Allred & MacNeice, 2015; Endeve et al., 2004). Allred and MacNeice (2015) showed that the periodicity ranges between 2 and 13 hr and is dependent on the heating factor of the corona.

Observational evidence shows that magnetic reconnection is fundamental to the release of streamer blobs. Sanchez-Diaz, Rouillard, Davies, Lavraud, Sheeley, et al. (2017a) observed in the outer coronagraph (field of view between 2.5 R_⊙ and 15 R_⊙) of the SECCHI package onboard the STEREO spacecraft signatures of inwardly collapsing magnetic arcs associated with the outflow of loops and twisted magnetic field lines happening simultaneous to the outward streamer blobs every 19.5 hr. In situ plasma data also indicate that quasiperiodic plasma structures are created through magnetic reconnection (Kepko et al., 2016; Rouillard et al., 2011; Sanchez-Diaz, Rouillard, Davies, Lavraud, Pinto, et al., 2017b; Suess et al., 2009), in particular by the appearance of flux ropes and counterstreaming electrons. Some studies show that streamer blobs at the HCS may only comprise 15% of the SSW mass at solar maximum (Sanchez-Diaz, Rouillard, Davies, Lavraud, Pinto, et al., 2017b). However, the SSW encompasses more than just the HCS, and spans a large latitude far above and below the HCS (e.g., ±40° latitude; Crooker et al., 2012). Hence, it is important to examine the SSW inside of and outside of the HCS as their origins may have some similarities and some differences (Higginson & Lynch, 2018; Stakhiv et al., 2016).

For example, Borovsky (2012) examined plasma and magnetic field in the SSW between 0.31 and 0.98 AU in Helios data, and found a wealth of mesoscale solar wind structures throughout the slow wind in the heliosphere. Borovsky (2008) identified characteristic flux tube sized in the solar wind at 1 AU, which interestingly, when accounting for expansion, correspond to the size scales of granules and supergranules on the Sun suggesting some relation to the photosphere dynamics, although a direct mapping is unlikely. Using Helios data, Roberts et al. (2005) found that the solar wind associated with the HCS was highly structured. The density structures were associated with entropy changes, indicating that their source was the solar atmosphere. Stansby and Horbury (2018) also examined Helios data and showed density structures in the inner heliosphere with temperature increases consistent with the release of hotter closed field plasma through interchange reconnection. Viall et al. (2008) examined quasiperiodic mesoscale density structures at 1 AU and showed that they are a major constituent of the SSW, occurring in up to 80% of the SSW. Unlike in the Helios data, temperature measurements at 1 AU do not maintain variations imposed by the solar source; instead, composition must be used. During periodic density structure events observed at 1 AU, composition measurements demonstrate that they are formed in the solar atmosphere as part of solar wind origin or acceleration (Kepko et al., 2016; Viall, Spence, et al., 2009). Studies of coronagraph images (Viall et al., 2010; Viall & Vourlidas, 2015) identified periodic density structures emanating from coronal streamers with periodicities on the same time scales as often observed in situ, with ≈90 min being one characteristic time scale. A unique deep field exposure campaign revealed that periodic density structures also are released from the Sun into the solar wind on even smaller time scales (DeForest et al., 2018).

The knowledge of the periodicities of these density fluctuations is a good constraint for models that try to explain the origin of the related structures. For example, Kepko et al. (2016) showed quasiperiodic SSW structures, with a period of ≈90 min, that had large concomitant composition, charge state, and density enhancements, without a change in velocity. The steady state expansion factor model is unable to reproduce the observed composition and charge state changes at time scales less than a few hours with no concurrent velocity change. Therefore, events such as this support a model with time dynamics such as the S-web model in which the interchange reconnection releasing coronal plasma of closed-field regions generates solar wind structures.

While at 1 AU we have direct in situ measurements of this process (Kepko et al., 2002, 2016; Kepko & Spence, 2003; Rouillard, Lavraud, et al., 2010; Rouillard et al., 2011), in the inner heliosphere such events have only been identified in coronagraph images (Rouillard, Davies, et al., 2010; Sanchez-Diaz, Rouillard, Davies, Lavraud, Sheeley, et al., 2017a; Sanchez-Diaz, Rouillard, Davies, Lavraud, Pinto, et al., 2017b; Viall et al., 2010; Viall & Vourlidas, 2015). Here we present the first in situ measurement of periodic solar wind density fluctuations at 0.3, 0.4, and 0.6 AU observed by the Helios1 and Helios2 spacecrafts. Their unique position allows the study of the density periodicities and of the properties of the related solar wind structures only a short time after their release from the Sun, therefore close to their pristine state, bringing us closer to linking in situ measurements with remote sensing.

2. Data, Models, and Techniques

The solar probes Helios1 and Helios2 were launched in December 1974 and January 1976, respectively, in highly eccentric, elliptical orbits around the Sun that ranged from 0.3 and 1 AU heliocentric distance. For this study, we use the reanalyzed plasma measurements obtained from http://helios-data.ssl.berkeley.edu, where the original 3-D ion distribution functions were fitted with a bi-Maxwellian function (Stansby, 2017; Stansby, Salem, et al., 2018). This procedure provides better estimates of proton number density, velocity, and temperature, discriminating the proton core and the proton beam populations unlike the original approach based on reduced 1-D distribution functions (Schwenn et al., 1975). The velocity components are expressed in the Heliographic Radial-Tangential-Normal (HGRTN or RTN) coordinate system: R is along the Sun-observer line pointing toward the observer, N is perpendicular to R and in the plane containing both R and the solar north pole, and T completes the set satisfying R × T = N (Fränz & Harper, 2002; Thompson, 2006). The plasma measurements were sampled every 40.5 s. The magnetic field measurements were obtained at a higher cadence, and were averaged over the 40.5-s plasma measurement, which we use here (Scearce et al., 1975). The magnetic field components are expressed in the Spacecraft Solar Ecliptic (SSE) coordinate system: X is the projection of the spacecraft-Sun vector onto the XY plane (Earth mean ecliptic of date), Z is positive toward the Sun north pole, and Y completes the set satisfying X × Y = Z (Fränz & Harper, 2002). In the following, we will express the interplanetary magnetic field in terms of its intensity (B) and its direction through θ_B = asin (B_Z/B), the angle formed by the magnetic field vector ($\overrightarrow{B}$) and the XY plane, and ϕ_B = atan (B_Y/B_X), the angle formed by the projection of $\overrightarrow{B}$ on the XY plane and the X axis (positive toward the Y axis). To identify the magnetic sector in which the spacecraft was located, we compare the ϕ_B angle with the Parker spiral angle ϕ_P = atan(−Ωrsinθ/v_R), where Ω is the Sun’s angular rotation rate and r and θ are the radial distance and colatitude of the spacecraft in heliographic Carrington coordinates (Thompson, 2006), respectively, and v_R is the radial solar wind speed.

We selected the time intervals in which the spacecraft's distance from the Sun was less than 0.6 AU, the proton number density measurements were continuous for at least 6 hr, and the data segments had data coverage higher than 90% with the maximum allowable continuous data gap of ≈5 min. Due to the elliptical orbit and the large amount of missing data in the Helios measurements, these requirements eliminated a large portion of the Helios data set, precluding a large statistical study of quasiperiodic density structures. The start date and the end date of the time intervals satisfying these criteria are available in Tables S1 and S2 in the supporting information for Helios1 and Helios2, respectively. The adoption of different requirements for the data selection changes the list of the selected intervals. Due to the high number of missing data in the Helios mission, the most critical choice regards the length of the interval. Maintaining the other parameters fixed, while the number of accepted intervals drops drastically for longer lengths, it increases for shorter ones. However, for this investigation continuous data for less than 6 hr do not provide the necessary frequency resolution to investigate the periodic density structure of interest. On the other hand, lowering the data coverage (less than 90%) and extending the allowable data gap (more than ≈5 min) would increase the list of the selected intervals, but their use in statistical analysis for the identification of periodic fluctuations would give unreliable results, in particular on time scales similar to or shorter than the length of the data gap.

To identify periodic fluctuations in the proton number density, we performed a spectral analysis by means of the multitaper windowing and F test using four tapers (K = 4) with time-half bandwidth product NW = 3 (Thomson, 1982; see also Di Matteo & Villante, 2017; Viall et al., 2008; Viall, Kepko, et al., 2009). A signal is considered significant when it passes both the F test and the narrow band test, which tests for enhancements in the power spectral density relative to the background spectra evaluated by fitting a power law to the median smoothed spectra (Mann & Lees, 1996), at the 95% confidence level. However, attention must be paid in the identification of signals in the Helios data because, in the phase of the perihelion, the plasma instrument I1a switched for 10 min to the instrument I3 every hour (research report BMFT-FB-W 81–015; Rosenbauer et al., 1981). This operation introduced a spurious, instrumental periodicity in the solar wind plasma parameters that could be easily misunderstood as periodic fluctuations in the actual plasma.

We also estimated the source region at 1 solar radius (R_⊙) for the solar wind streams observed by the Helios spacecraft using the Wang-Sheeley-Arge (WSA) model (Arge & Pizzo, 2000; Arge et al., 2003, 2004). First, we used the photospheric field Carrington maps from the Mount Wilson Observatory (MWO) as input for the coupled magnetostatic potential field source surface and Schatten Current Sheet (Schatten, 1971) model to reconstruct the Sun's coronal field from 1 to 5 R_⊙. We use a source surface height of 2.5 R_⊙ (Hoeksema et al., 1983) which has been shown in recent work to obtain good agreement between WSA-derived open flux and that obtained from helium and EUV coronal hole observations over nearly two solar cycles (Wallace et al., 2019). Then, after mapping the solar wind streams onto the 5 R_⊙ (or outer boundary) surface by ballistic propagation, we map down to the surface of the Sun by tracing field lines from 5 R_⊙ to the photosphere at 1 R_⊙ using the WSA coronal field solution. We sought to identify clean cases where the Helios observations of IMF polarity and HCS crossings agreed well with the WSA-derived back mapping (constrained by the resolution of the model and input photospheric field maps). We make use of MWO maps, with the appropriate correction factor (Wang & Sheeley, 1995) when available, due to their higher resolution and range of availability that overlapped with our events. When there were not enough magnetogram observations to assemble a Carrington map, coronal field solutions derived from Wilcox Solar Observatory (WSO) were used (http://wso.stanford.edu/synsourcel.html). Both MWO and WSO observations are very similar because they use the same Fe I 5250 Å line to derive the magnetic field, and for the time period in this study, MWO and WSO total (open) fluxes at the source surface are in reasonably good agreement (Arge et al., 2002). Beyond 1981–1982, there is a consistent offset between the two maps that would need to be addressed (Arge et al., 2002).

3. Event Studies

Within the set of data intervals shown in the supplemental document, we identified instances of quasiperiodic structures in the proton number density of the SSW. In the following, we discuss the details of five events that occurred between 1975 and 1981, during the rising phase of the 21st solar cycle. In each event, whose properties are summarized in Table 1, we first visually identified structures that appear to have significant changes both in the density and in the magnetic field. Then, we estimated rigorously the corresponding density periodicities following the methods described in section 2.

Table 1.

Periodicities and Frequencies Identified in the Five Events by Visual Inspection of the Data and by Means of the Multitaper Method

Event (Δf	Periodicity (Frequency) Visual Inspection	Frequency (Periodicity) MTM	<νr> ± σr (km/s)	L ± ΔL (RE)	Source Region	HCS Crossing/ Mapped to HCS	Temperature	Other
1 (0.06 mHz)	≈31 min (≈0.54 mHz)	≈0.53 mHz (≈31.5 min)	410 ± 10	120 ± 10	AR and CH extension	No/near	Hotter (T∥)	/
2 (0.04 mHz)	≈120 min (≈0.14 mHz) ≈33 min (≈0.51 mHz)	≈0.16 mHz (≈104 min) ≈1.47 mHz (≈11 min) ≈3.58 mHz (≈4.7 min)	360 ± 20	350 ± 60 38 ± 3 16 ± 1	CH	Yes/yes	Hotter (both)	/
3 (0.04 mHz)	≈112 min (≈0.15 mHz)	≈0.13 mHz (≈128 min) ≈1.83 mHz (≈9 min)	380 ± 10	460 ± 80 33 ± 1	AR and CH extension	No/near	Hotter (T∥)	/
4 (0.04 mHz)	≈74 min (≈0.23 mHz) ≈15 min (≈1.11 mHz)	≈0.20 mHz (≈83 min) ≈0.57 mHz (≈29 min) ≈1.55 mHz (≈11 min)	310 ± 10	240 ± 30 85 ± 6 31 ± 1	Lacking source data	Yes/yes	Hotter (both)	Flux rope
5	≈5.8 ± 0.4 hr (≈0.05 mHz) ≈128 ± 26 min (≈0.13 mHz)	Lacking continuous data	330 ± 20 300 ± 20	1080 ± 140 360 ± 95	AR and CH extension	No/far	Hotter (both)	/

Note. For each event we report the mean and the standard deviation of the radial velocity and the consequent size scales of the observed structures, the kind of solar wind stream source region at 1 R_⊙, the position respective to the HCS, the temperature features of the quasiperiodic structures respective to the surrounding plasma, and additional properties.

For each event we show the measured solar wind parameters: the proton number density (n_p); the interplanetary magnetic field intensity (B), and direction (θ_B and ϕ_B); the three components of the solar wind velocity in the RTN system; the parallel (T_∥), perpendicular (T_⊥), and total (T_p = (2 T_⊥ + T_∥)/3) proton temperatures; the ratio between parallel and perpendicular temperatures (T_∥/T_⊥); the quantity log (T_p/n_p^{(γ – 1)}) proportional to the entropy per proton (Burton et al., 1999; Pagel et al., 2004; Siscoe & Intriligator, 1993); the proton thermal pressure (p_p = n_pk_BT_p); the magnetic pressure (p_B=B²/2μ₀); and the proton beta value (β_p = p_p/p_B). We follow the approach of Stansby and Horbury (2018) to estimate the total pressure p_tot = (p_T + p_B), where p_T is the thermal pressure. We estimate the contribution of electrons and alpha particles to the pressure by using their typical temperatures in SSW streams, T_e ≈ 0.2–0.4 MK (Štverák et al., 2015) and T_α ≈ 0.2–1 MK (Marsch, Mühlhäuser, Rosenbauer, et al., 1982). Considering the alpha to proton density ratio n_α/n_p ≈ 0.01–0.05 (Kasper et al., 2007) and assuming plasma neutrality (n_e = n_p + 2n_α), the total pressure is given by

$${\mathrm{p}}_{{}_{\mathrm{T}}}={\mathrm{p}}_{\mathrm{p}}+{\mathrm{p}}_{\alpha }+{\mathrm{p}}_{\mathrm{e}}={\mathrm{n}}_{\mathrm{p}}{\mathrm{k}}_{\mathrm{B}}\left[{\mathrm{T}}_{\mathrm{p}}+\frac{{\mathrm{n}}_{\alpha }}{{\mathrm{n}}_{\mathrm{p}}}{\mathrm{T}}_{\alpha }+\left(1+\frac{2{\mathrm{n}}_{\alpha }}{{\mathrm{n}}_{\mathrm{p}}}\right){\mathrm{T}}_{\mathrm{e}}\right].$$

Following the approximations listed above, we obtain a minimum and a maximum value for the thermal pressure, namely, p_T,min = n_pk_B (T_p + 2 × 10⁵ K) and p_T,max = n_pk_B (T_p + 5 × 10⁵ K), and consequently also for the total pressure.

3.1. 18 October 1975

The Helios1 spacecraft was located at ≈0.59 AU from the Sun (Carrington latitude λ_C ≈ 6.5°) between ≈16:30 UT and ≈22:40 UT on 18 October 1975 during Carrington rotation (CR) 1633. In Figure 1, we show the measured solar wind parameters. We visually identify six enhancements in the proton number density that we associate with the transit of six structures. We identify their boundaries (red vertical lines in Figure 1a) as the local minima in n_p and the simultaneous variations of the magnetic field strength or direction, as these will be boundaries of flux tubes (Borovsky, 2008). The first four structures have durations of ≈26, ≈35, ≈64, and ≈35 min, respectively, and have radial velocity between 405 and 432 km/s. The fifth one (≈65 min) manifests two substructures (vertical black line): the first of ≈35 min, in which the speed slowly decrease to ≈390 km/s, and the second of ≈30 min. The last structure (≈57 min) can be separated in three substructures, respectively, of ≈15, ≈20, and ≈22 min whose boundaries (vertical black lines) delimit three enhancements in T∥, T_⊥, and more clearly in the ratio T_∥/T_⊥. Interestingly, the third structure contains three fluctuations of T_∥ and T_∥/T_⊥ of durations ≈24, ≈18, and ≈23 min, not seen in the SW number density. The temperature changes are likely remnants of details of the formation of the structure. The β_p value and the entropy per proton, useful to identify different solar wind plasma conditions, manifest small enhancements inside the structures strengthening the idea that they are related to the release of plasma from different region on the Sun. In addition, the anticorrelation between n_p and B (correlation coefficients, respectively, of −0.32, −0.88, −0.69, −0.61, 0.10, and −0.91 for each structure), and p_p and p_B (correlation coefficients, respectively, of −0.13, −0.88, −0.68, −0.40, 0.18, and −0.87 for each structure) in concomitance with a roughly constant range for the total pressure, suggest that some of these structures are pressure balance structures (Burlaga & Ogilvie, 1970; Tu & Marsch, 1994; Bavassano et al., 2004).

Figure 1.

The solar wind parameters as measured by Helios1 on 18 October 1975: (a) proton number density; (b) magnetic field strength; (c and d) θ_B and ϕ_B angle, the green and blue dashed lines represent, respectively, the outward and inward directions of the Parker spiral angle relative to the Sun; and (e–g) the velocity component in RTN coordinate system. The overlapping red lines are the corresponding 11 points running averages. (n) The parallel (blue), perpendicular (red), and total (black) proton temperature. (o) The parallel and perpendicular temperature ratio; the green dashed line indicates isotropic plasma. (p) The β_p value (black) and entropy per proton with γ = 1.5 (red). (q) The proton thermal (blue), magnetic (red), and total (gray shaded region between its minimum and the maximum value) pressure. (h and i) The power spectral density and the F test relative to the proton number density; the vertical dashed line indicates the frequency of the relevant signal. (l and m) The same as before for the entire frequency range.

We performed spectral analysis on the number density of the solar wind between ≈17:24 UT and ≈22:06 UT, in the time interval where we identified the structures (number of data points N = 418, corresponding to frequency resolution Δf = 0.06 mHz), by means of the multitaper method. We show the power spectral density in Figure 1h, and we approximate the background spectra as a power law (solid red line) fitted in the 0–10-mHz range to the running median of the spectra over bandwidths of ≈1.5 mHz (green line). Imposing a 95% confidence level (horizontal red dashed lines in Figures 1h and 1i) for the narrow band test and the F test, we identified a signal at f ≈ 0.53 mHz that passes both the tests. This corresponds to ≈32 min, close to the average periodicity derived by visual inspection of the data (≈31 min).

Analyzing the WSA model output based on the photospheric field maps obtained from the Mount Wilson Observatory (Figure 2a), we identified the source region of the solar wind stream containing the quasiperiodic density structures. Once the trajectory of the spacecraft is ballistically mapped back to 5 R_⊙ (red line, Figure 2b), we compare the polarity of the coronal field at 5 R_⊙ with the direction of the magnetic field observed by Helios1 (ϕ_B; Figure 2c). In Figure 2b, the gray and black areas correspond to the outward and the inward direction of the coronal field, respectively. In Figure 2c, the green circles (ϕ_P,+) and the blue crosses (ϕ_P,−) are the possible Parker spiral angles at the spacecraft position for positive and negative polarity. Comparing Figures 2b and 2c, we found a good agreement for the first half of the CR. The red line in Figures 2b and 2e represents the trajectory mapped ballistically to 5 R_⊙. The position of the solar wind stream that transit through the spacecraft on 18 October 1975 (bigger red dot in Figure 2f) is mapped at 1 R_⊙ (Figures 2a and 2d) and 5 R_⊙ (Figures 2b and 2e) to the red dots. After ≈19 UT on 10 October 1975 (Carrington longitude lower than ≈163°), contrary to the prediction, ϕ_B remained inward directed except for a short period which correspond to our event (red vertical line), suggesting that the source region is very close to the HCS. Looking at the coronal holes derived by the WSA model, the solar wind stream maps to a small coronal hole close to two active regions visible in the photospheric field map (red dot in Figure 2d and Figure 2a, respectively). The model-derived solar wind speed at 5 R_⊙ is reported in Figure 2e and for our event it is ≈550 km/s.

Figure 2.

The WSA model output based on the photospheric field map (a) from the Mount Wilson Observatory for CR 1633. (b) The coronal field derived at 5 R_⊙: the gray (black) region indicates the outward (inward) direction of the magnetic field. (c) The ϕ_B observed by Helios1 (black dots) as compared to the expected outward (green circles) and inward (blue crosses) direction respective to the Sun of the Parker spiral angle. The red dashed line marks the 18 October 1975 event date. (d) Colored areas represent the coronal holes; the color scale indicates the corresponding solar wind velocity derived by the model. The light (dark) gray areas represent the outward (inward) direction of the magnetic field at 1 R_⊙. (e) Model-derived solar wind velocity. (f) Schematic representation of the trajectory of the spacecraft for the entire CR (red line starting from the smaller dot) relative to the source surface (black dot).

3.2. 14 April 1977

The Helios2 spacecraft was located at about ≈0.37 AU (Carrington latitude λ_C ≈ −2.9°) from the Sun between ≈5:00 UT and ≈13:00 UT on 14 April 1977 during CR 1653. In Figure 3, similarly to the previous event, we show the measured solar wind parameters and structure/substructure boundaries (red/black vertical lines) visually identified at the local minima in n_p, concomitant to the variations of the magnetic field strength or direction. In this case we identify the boundaries of three structures. The first two, of ≈132 and ≈116 min, have, respectively, five (≈23, ≈20, ≈31, ≈39, and ≈19 min) and three (≈39, ≈41, and ≈36 min) substructures. Together with a preceding region of ≈11 min, they seem to be part of a single stream whose radial velocity slowly raise from ≈350 to ≈390 km/s. In the third structure of ≈113 min, composed of three substructures, respectively, of ≈39, ≈47, and ≈27 min, the solar wind speed fluctuates around ≈340 km/s. The selected boundaries correspond to sharp variations in the profile of temperatures, β_p, entropy per proton, and pressures (Figures 3n-3q). In particular, the β_p value increases inside each subinterval of the first two structures, while in the third show a single broad enhancement. Moreover, β_p is highly variable spanning 2 orders of magnitude from ≈0.08 to ≈6.5. The average periodicities of the density fluctuations identified by visual inspection correspond to ≈120 min (f ≈ 0.14 mHz) and ≈33 min (f ≈ 0.51 mHz). The spectral analysis (Figures 3h-3m) is performed on the whole interval (number of points N = 621 and a frequency resolution Δf = 0.04 mHz); we assumed the background spectra as a power law (solid red line) fitted in the 0–10-mHz range to the running median of the spectra over bandwidths of ≈1.5 mHz (green line). We confirmed at the 95% confidence level (horizontal red dashed lines) the occurrence of an oscillation at f ≈ 0.16 mHz (≈104 min) accompanied by other two signals at f ≈ 1.47 mHz (≈11 min) and f ≈ 3.58 mHz (≈4.7 min). As a matter of fact, the anticorrelation between n_p and B (correlation coefficients, respectively, of −0.82, −0.45, and −0.78 for each structure) and between p_p and p_B (correlation coefficients, respectively, of −0.93, −0.65, and −0.81 for each structure), together with the roughly constant range for the total pressure inside each substructure, suggest that the density oscillations are also related to the transit of pressure balance structures, as in the first event.

Figure 3.

The solar wind parameters as measured by Helios2 on 14 April 1977: (a) proton number density; (b) magnetic field strength; (c and d) θ_B and ϕ_B angle, the green and blue dashed lines represent, respectively, the outward and inward directions of the Parker spiral angle relative to the Sun; and (e–g) the velocity component in RTN coordinate system. The overlapping red lines are the corresponding 11 points running averages. (n) The parallel (blue), perpendicular (red), and total (black) proton temperature. (o) The parallel and perpendicular temperature ratio, the green dashed line indicates isotropic plasma. (p) The β_p value (black) and entropy per proton with γ = 1.5 (red). (q) The proton thermal (blue), magnetic (red), and total (gray shaded region between its minimum and the maximum value) pressure. (h and i) The power spectral density and the F test relative to the proton number density; the vertical dashed lines indicate the frequencies of the relevant signals. (l and m) The same as before for the entire frequency range.

As in the previous event, we compare the observed ϕ_B angle with the expected Parker spiral angles (Figure 3d). The magnetic field angle is in good agreement with the outward orientation for the first two structures; in the third the ϕ_B angle switches to that expected for the opposite polarity, consistent with the spacecraft crossing the HCS. Unfortunately, we lack data for later times to confirm that this was not a local kink in the magnetic field. The back mapping of this event to the Sun is consistent with a HCS crossing. The position of Helios2, during the transit of this stream mapped at 5 R_⊙ (red dot in Figure 4b), is close to the HCS position predicted using the WSA model. Moreover, at longer times, the observed ϕ_B (Figure 4c) changes direction from outward (green circles) to inward (blue crosses). The source region of the observed solar wind stream back to 1 R_⊙ is far from active regions (red dot in Figure 4a) and lies on the edge of the southern polar coronal hole (red dot in Figure 4d). The model-derived solar wind speed at 5 R_⊙ is reported in Figure 4e and for our event it is ≈534 km/s.

Figure 4.

The WSA model output based on the photospheric field map (a) from the Mount Wilson Observatory for CR 1653. (b) The coronal field derived at 5 R_⊙: the gray (black) region indicates the outward (inward) direction of the magnetic field. (c) The ϕ_B observed by Helios1 (black dots) as compared to the expected outward (green circles) and inward (blue crosses) direction respective to the Sun of the Parker spiral angle. The red dashed line marks the 14 April 1977 event date. (d) Colored areas represent the coronal holes; the color scale indicates the corresponding solar wind velocity derived by the model. The light (dark) gray areas represent the outward (inward) direction of the magnetic field at 1 R_⊙. (e) Model-derived solar wind velocity. (f) Schematic representation of the trajectory of the spacecraft for the entire CR (red line starting from the smaller dot) relative to the source surface (black dot).

3.3. 3 May 1980

The Helios1 spacecraft was located at ≈0.58 AU from the Sun (Carrington latitude λ_C ≈ −6.9°) between ≈8:30 UT and ≈16:15 UT on 3 May 1980 during CR 1694. In Figure 5 we show the corresponding SW parameters as in the previous events. We observe three main enhancements in the SW number density corresponding to three subintervals of ≈95, ≈131, and ≈110 min, respectively (delimited by red vertical lines). In the first subinterval, the magnetic field decreases and smoothly rotates from θ_B ≈ 20° to θ_B ≈ −40° while the radial speed fluctuates around ≈375 km/s. The second subinterval can be divided in three parts (black vertical lines). The first part (≈57 min) corresponds to an increase of B and to a high variability of the radial velocity, which reaches ≈430 km/s. The second part (≈36 min) has a sharp increase in speed, up to ≈440 km/s, concomitant to a temperature enhancement whose boundaries can be seen clearly in β_p and in the entropy per proton. The third part (≈39 min) manifests a dip in B corresponding to an enhancement in β_p and entropy per proton. The third subinterval is characterized by the increase of T∥ and the decrease of T_⊥ which leads to a strong anisotropy (T_∥/T_⊥ up to ≈10). In addition, the sharp increase of the magnetic field intensity and of the radial velocity (black vertical line) divides this subinterval in two different parts of ≈66 and ≈44 min. The three subintervals constitute quasiperiodic density structures with an average period ≈112 min (f ≈ 0.15 mHz). The spectral analysis of n_p (Figures 5h-5m) is performed by means of the multitaper method (number of points N = 595 and step in frequency Δf ≈ 0.04 mHz). As in the previous events, we assumed the background spectra as a power law (solid red line) fitted in the 0–10-mHz range to the running median of the spectra over bandwidths of ≈1.5 mHz (green line). The clear enhancement in the power spectra at f ≈ 0.13 mHz (≈128 min) confirms the periodicity identified by visual inspection. A second signal at f ≈ 1.83 mHz (≈9 min) is also significant. In contrast to the previous events, the number density and the magnetic field strength (the proton thermal and magnetic pressure) are poorly correlated inside the three subintervals, with correlation coefficients −0.36, −0.56, and 0.26 (−0.05, −0.64, and 0.18), respectively, and this event is not an example of a pressure balance structures.

Figure 5.

The solar wind parameters as measured by Helios1 on 3 May 1980: (a) proton number density; (b) magnetic field strength; (c and d) θ_B and ϕ_B angle, the green and blue dashed lines represent, respectively, the outward and inward directions of the Parker spiral angle relative to the Sun; and (e-g) the velocity component in RTN coordinate system. The overlapping red lines are the corresponding 11 points running averages. (n) The parallel (blue), perpendicular (red), and total (black) proton temperature. (o) The parallel and perpendicular temperature ratio, the green dashed line indicates isotropic plasma. (p) The β_p value (black) and entropy per proton with γ = 1.5 (red). (q) The proton thermal (blue), magnetic (red), and total (gray shaded region between its minimum and the maximum value) pressure. (h and i) The power spectral density and the F test relative to the proton number density; the vertical dashed lines indicate the frequencies of the relevant signals. (l and m) The same as before for the entire frequency range.

The red line in Figures 6b and 6e represents the trajectory mapped ballistically to 5 R_⊙. The position of the solar wind stream that transit through the spacecraft on 3 May 1980 (bigger red dot in Figure 6f) is mapped at 1 R_⊙ (Figures 6a and 6d) and 5 R_⊙ (Figures 6b and 6e) to the red dots. The solar wind stream is mapped at 5 R_⊙ in a region close to the HCS (red dots in Figure 6b) with an inward directed coronal field. The orientation of the magnetic field agrees with the one observed in the interplanetary medium (ϕ_B in Figure 5c). Looking at the whole CR in Figures 6b and 6c, there is a good agreement between the predicted and the observed direction of the magnetic field above ≈180° of Carrington longitude. Below ≈180° we expected a clear interval of outward directed magnetic field before a crossing of the HCS toward inward directed field. Instead, the observed ϕ_B shows a mostly inward direction with some short outward intervals suggesting a different HCS profile. This disagreement is likely due to the significant amount of solar activity in this Carrington rotation, and the inability of the Carrington map to represent the dynamic of the corresponding photospheric field. The source region of the observed solar wind stream back to 1 R_⊙ (red dot in Figures 6a and 6d) is close to an active region and correspond to a small coronal hole near the Sun equator. The model-derived solar wind speed is reported in Figure 6e and for our event it is ≈327 km/s.

Figure 6.

The WSA model output based on the photospheric field map (a) from the Mount Wilson Observatory for CR 1694. (b) The coronal field derived at 5 R_⊙: the gray (black) region indicates the outward (inward) direction of the magnetic field. (c) The ϕ_B observed by Helios1 (black dots) as compared to the expected outward (green circles) and inward (blue crosses) direction respective to the Sun of the Parker spiral angle. The red dashed line marks the 3 May 1980 event date. (d) Colored areas represent the coronal holes; the color scale indicates the corresponding solar wind velocity derived by the model. The light (dark) gray areas represent the outward (inward) direction of the magnetic field at 1 R_⊙. (e) Model-derived solar wind velocity. (f) Schematic representation of the trajectory of the spacecraft for the entire CR (red line starting from the smaller dot) relative to the source surface (black dot).

3.4. 9 June 1980

The Helios1 spacecraft was located at ≈0.39 AU from the Sun (Carrington latitude λ_C ≈ 6.8°) between ≈2:00 UT and ≈10:00 UT on 9 June 1980 during CR 1695. Looking at the SW parameters in Figure 7, at the beginning of the time interval we observe a very slow solar wind stream with proton number density roughly constant around ≈50 cm⁻³ and radial velocity that slowly rises from ≈270 to ≈310 km/s. The velocity components show strong fluctuations, highly correlated to the magnetic ones, that suddenly stop at ≈4:06 UT, when the number density suddenly raise to around ≈90 cm⁻³ and the magnetic field strength decrease to ≈8 nT. In addition, ≈4:06 UT marks a boundary of a transition into a SSW stream with strikingly different characteristic, most notably a steadier velocity and the beginning of a series of quasiperiodic density structures. These features and the fact that for the entire time interval the ratio T_∥/T_⊥ is roughly one (Figure 7o) suggest the transit of an isotropic solar wind stream with Alfvénic (before ≈4:06 UT) and non-Alfvénic (after ≈4:06 UT) plasma population (Stansby, Horbury, et al., 2018).

Figure 7.

The solar wind parameters as measured by Helios1 on 9 June 1980: (a) proton number density; (b) magnetic field strength; (c and d) θ_B and ϕ_B angle, the green and blue dashed lines represent, respectively, the outward and inward directions of the Parker spiral angle relative to the Sun; and (e–g) the velocity component in RTN coordinate system. The overlapping red lines are the corresponding 11 points running averages. (n) The parallel (blue), perpendicular (red), and total (black) proton temperature. (o) The parallel and perpendicular temperature ratio, the green dashed line indicates isotropic plasma. (p) The β_p value (black) and entropy per proton with γ = 1.5 (red). (q) The proton thermal (blue), magnetic (red), and total (gray shaded region between its minimum and the maximum value) pressure. The red shaded region corresponds to a flux rope. (h and i) The power spectral density and the F test relative to the proton number density; the vertical dashed lines indicate the frequencies of the relevant signals. (l and m) The same as before for the entire frequency range.

Right after the ϕ_B angle changes from inward to outward direction, indicating the crossing of the HCS (Figure 7d), the local enhancement of the magnetic field strength and the θ_B smooth variation from ≈78° to ≈ −40° (red shaded region in Figure 7) suggest the transit of a flux rope. We confirm the flux rope nature of this structure by applying the minimum variance analysis to the high resolution (6 s) magnetic field measurements shown in Figure 8d (although we obtain the same results using the averaged data). The three components of the magnetic field are rotated in the LMN system (Figure 8b) in which B_L, B_M, and B_N correspond, respectively, to the maximum (λ₁ ≈ 74), intermediate (λ₂ ≈ 20.5), and minimum (λ₃ ≈ 3.5) eigenvalues. We can observe the rotation of the magnetic field in the hodograms (Figure 8c) and in the B_L component which assumes values close to zero in concomitance with an increase of the intensity of the other two components and the strength of magnetic field.

Figure 8.

Minimum variance analysis of the high-resolution magnetic field measured by Helios1 between ≈4:10 and ≈4:46 UT on 9 June 1980. (a) The strength of the magnetic field. (b) The components of the magnetic field in the LMN coordinate system. (c) The hodograms of B_L versus B_M and B_M versus B_N. (d) The measured components of the magnetic field in the SSE coordinate system. The horizontal dashed lines represent the zero level.

Between ≈4:06 UT and ≈9:24 UT, we observed four density enhancements in subintervals of about ≈73, ≈79, ≈76, and ≈66 min (delimited in Figure 7 by red vertical dashed lines) that we associate with the transit of four structures. Each of them is composed of substructures (delimited by black vertical lines): four in the first (≈22, ≈19, ≈22, and ≈10 min), six in the second (≈16, ≈17, ≈13, ≈10, ≈11, and ≈13 min), five in the third (≈13, ≈17, ≈14, ≈15, and ≈17 min), and five in the fourth (≈13, ≈15, ≈14, ≈10, and ≈14 min). The solar wind speed, while slowly decreasing from ≈330 to around ≈310 km/s inside the four structures, has an enhancement up to ≈340 km/s. At the same time, the β_p value and the temperatures suddenly increase respective to the values of the surrounding plasma. The entropy per proton is stable between sharp variations corresponding to the beginning and the end of a single macrostructure containing all the four structures. The average periodicities of the density fluctuations identified by visual inspection correspond to ≈74 min (f ≈ 0.23 mHz) and ≈15 min (f ≈ 1.11 mHz).

We perform a spectral analysis (Figures 7h-7m) on the number density of the solar wind between ≈2:38 UT and ≈9:27 UT (number of points N = 607 and step in frequency Δf ≈ 0.04 mHz). As in the previous events, we assumed the background spectra as a power law (solid red line) fitted in the 0–10-mHz range to the running median of the spectra over bandwidths of ≈1.5 mHz (green line). We observed three relevant enhancements in the power spectral density at f ≈ 0.20 mHz (≈83 min), f ≈ 0.57 mHz (≈29 min), and f ≈ 1.55 mHz (≈11 min) corresponding to F values just below the 95% confidence level. The anticorrelation between n_p and B and between p_p and p_B (correlation coefficients, respectively, of −0.54 and −0.81 for the whole macrostructure) suggests that the structures are in pressure balance. The cross-correlation coefficients for each structure are −0.69, −0.60, −0.93, and −0.83 for n_p and B, and −0.70, −0.82, −0.86, and −0.87 for p_p and p_B.

The MWO maps were unavailable for this CR due to lack of data, so we used the photospheric field at 1 R_⊙ and the coronal field at 2.5 R_⊙ from the Wilcox Solar Observatory (WSO). Our event is mapped very close to the predicted HCS (red dot in Figure 9c) in accordance to the spacecraft observations (Figure 9d) in which the magnetic field for later times changes direction 2 times (on the left of the red vertical line), suggesting a double cross of the HCS. Between 120° and 180° of Carrington longitude, the ϕ_B angle manifests an inward direction in disagreement with the prediction (Figure 9c), but in accordance with the coronal field of the previous CR (Figure 6b) which show for the same region a coronal hole with inward direction extended to lower latitudes.

Figure 9.

(a) The photospheric field map from the Wilcox Solar Observatory for CR 1695 plus 30° of the previous and the next CR. (b) Schematic representation of the trajectory of the spacecraft for the entire CR (red line starting from the smaller dot) relative to the source surface (black dot). The red line in (c) represents the trajectory mapped ballistically to 2.5 R_⊙. The position of the solar wind stream that transits through the spacecraft on 9 June 1980 (bigger red dot in (b)) is mapped at 2.5 R_⊙ (c) to the red dot. (c) The coronal field at 2.5 R_⊙: the gray (black) region indicates the outward (inward) direction of the magnetic field. (c) The ϕ_B observed by Helios1 (black dots) as compared to the expected outward (green circles) and inward (blue crosses) direction respective to the Sun of the Parker spiral angle. The red dashed line marks the 9 June 1980 event date.

3.5. 4–13 June 1981

In the first four events, the Helios probes were all near or at the HCS. For our final event, we explicitly sought to identify an event that was in SSW well separated from the HCS and mapped far away from the streamer belt region back at the solar surface, as this is a direct test of the S-web model of SSW formation. This was a difficult task given the constraints of the Helios coverage (see supporting tables) coupled with the solar configuration during the rising phase of the solar cycle, such that the HCS was located very near to the ecliptic where Helios sampled for much of the time. Despite these limitations, we identified such an event and present it next.

The Helios1 spacecraft was located between ≈0.37 AU (Carrington latitude λ_C ≈ −5.9°) and ≈0.31 AU (Carrington latitude λ_C ≈ 0.5°) from the Sun between the 4 June 1981 and the 13 June 1981 UT during CR 1709. The corresponding SW parameters, reported in Figure 10, show the transit through fast and slow solar wind streams (green vertical lines), and slow wind separated from the HCS (delimited by red vertical lines). At the beginning, we observe a solar wind stream with density around ≈32 cm⁻³ and velocity ≈380 km/s; after ≈16:20 UT on 9 June the velocity goes down to ≈263 km/s (with a minimum of ≈216 km/s) and the density raises reaching a maximum of ≈285 cm⁻³. In this very slow stream, at ≈3:03 UT and ≈13:42 UT the variation of the magnetic field direction (ϕ_B angle from outward to inward direction), in concomitance with the intensity drop, denote the crossing of the HCS (blue lines). Approximately 29 hr after the crossing of the HCS, we observe a series of quasiperiodic density structures in the time interval identified by the red vertical lines at ≈18:55 UT on 10 June and ≈12:15 UT on 12 June in Figure 10. The number density enhancement, after a decrease down to ≈50 cm⁻³, together with the raise of radial velocity (to around ≈352 km/s) and temperature suggest that this is an independent SW stream different from the one that embeds the HCS. The gray shaded region identifies a stream interaction region caused by a fast SW stream of ≈500 km/s, observed at ≈19:11 UT on 12 June, catching up the slower stream. The ratio between the parallel and perpendicular proton temperature shows a clear distinction between the fast SW streams, at the beginning and the end of the time interval, characterized by T_⊥ > T_∥ (Marsch, Mühlhäuser, Schwenn, et al., 1982) and the SSW streams characterized by a roughly isotropic plasma. An interesting feature manifests in the proton temperature which start to fluctuate with a periodicity between 5 and 7 hr after a structure (red shaded region) transits past the spacecraft from ≈22:33 UT on 7 June to ≈8:41 UT on 8 June (about ≈10 hr). This structure is characterized by an enhancement in number density, a smooth rotation of the magnetic field, and a surprisingly low mean solar wind bulk speed of ≈233 km/s while all the other SW parameters show less variability than the surrounding plasma.

Figure 10.

The solar wind parameters as measured by Helios1 between 4 and 13 June 1981: (a) proton number density; (b) magnetic field strength; (c and d) θ_B and ϕ_B angle, the green and blue dashed lines represent, respectively, the outward and inward directions of the Parker spiral angle relative to the Sun; and (e–g) the velocity component in RTN coordinate system. The overlapping red lines are the corresponding 11 points running averages. (h–l) The parallel, perpendicular, and total proton temperature. (m) The parallel and perpendicular temperature ratio, the green dashed line indicates isotropic plasma. (n) The β_p value. (o) The entropy per proton with γ = 1.5. (p) The proton thermal (blue), magnetic (red), and total (gray shaded region between its minimum and the maximum value) pressure.

In Figure 11, for CR 1709, we show the output of the WSA model based on the photospheric field map from the Mount Wilson Observatory. The red line in Figures 11b and 11e represents the trajectory mapped ballistically to 5 R_⊙. The positions of the different solar wind streams that transit through the spacecraft between 4 and 13 June 1981 (Figure 11f) are mapped at 1 R_⊙ (Figures 11a and 11d) and 5 R_⊙ (Figures 11b and 11e) to dots with different colors corresponding to the ones of the vertical lines in Figure 10 with vertical dashed lines of the same colors. The magnetic field direction expected from the coronal field at 5 R_⊙ along the trajectory of the spacecraft (Figure 11b) agrees with the observed ϕ_B (Figure 11c). There is also a good accordance between the modeled and the observed position of the HCS (yellow line and blue dot in Figure 11b, respectively, at ≈217° and ≈211° of Carrington longitude and ≈ −3° of latitude). Unlike solar minimum, near solar maximum the HCS is highly inclined and it is far less ambiguous whether spacecraft are sampling near or far from the current sheet. The model also derives well the HCS near solar maximum because the contribution of the polar photospheric field (a region that is poorly observed) to the global field is significantly less (MacNeice, 2009). For this time period, the location and inclination of the HCS where Helios crossed was qualitatively in good agreement with the WSO-derived HCS. The green dots, corresponding to the two faster streams (first and last green lines in Figure 10), are, respectively, ≈17°−23° and ≈38°−44° in Carrington longitude far from the current sheet and mapped on two different coronal holes (Figure 11d). The mapped boundaries of the solar wind stream embedding quasiperiodic structures (red dots) are ≈18°−24° and ≈25°−31° in Carrington longitude far from the current sheet. The model-derived solar wind speed at 5 R_⊙ is reported in Figure 11e and for our event (red dots) it is ≈405 km/s.

Figure 11.

The WSA model output based on the photospheric field map (a) from the Mount Wilson Observatory for CR 1709. (b) The coronal field derived at 5 R_⊙: the gray (black) region indicates the outward (inward) direction of the magnetic field. (c) The ϕ_B observed by Helios1 (black dots) as compared to the expected outward (green circles) and inward (blue crosses) direction respective to the Sun of the Parker spiral angle. The red dashed line marks the 11 June 1981 event date. (d) Colored areas represent the coronal holes; the color scale indicates the corresponding solar wind velocity derived by the model. The light (dark) gray areas represent the outward (inward) direction of the magnetic field at 1 R_⊙. (e) Model-derived solar wind velocity. (f) Schematic representation of the trajectory of the spacecraft for the entire CR (red line starting from the smaller dot) relative to the source surface (black dot).

Figure 12 shows in detail the SW parameters for the time interval between ≈15:30 UT on 10 June and ≈21:30 UT on 12 June in which the Helios1 spacecraft was located at ≈0.31 AU from the Sun (Carrington latitude λ_C ≈ −1.0°). This slow speed stream manifests quasiperiodic fluctuations in the proton number densities as highlighted by the red vertical lines positioned in the boundaries of the corresponding subintervals identified by visual inspection as in the previous events. The first three density oscillations lasting ≈5.8, ≈5.9, and ≈5.2 hr are clearly seen also in the temperatures, β_p, and entropy per proton. In the fourth subinterval of ≈6.1 hr, the density increases, and the magnetic field strength sharply decreases. The seven subsequent subintervals last, respectively, for ≈131, ≈124, ≈154, ≈154, ≈146, ≈83, and ≈106 min (we excluded the interval with missing data). Again, as in the previous events, most of the boundaries correspond to sharp variations of the temperatures, β_p, and entropy per proton. The average periodicities are ≈5.8 hr (f ≈ 0.05 mHz) and ≈128 min (f ≈ 0.13 mHz); unfortunately, due to the large amount of missing data we were unable to perform a spectral analysis.

Figure 12.

The solar wind parameters as measured by Helios1 between 10 and 12 June 1981: (a) proton number density; (b) magnetic field strength; (c and d) θ_B and ϕ_B angle, the green and blue dashed lines represent, respectively, the outward and inward directions of the Parker spiral angle relative to the Sun; and (e–g) the velocity component in RTN coordinate system. The overlapping red lines are the corresponding 11 points running averages. (h–l) The parallel, perpendicular, and total proton temperature. (m) The parallel and perpendicular temperature ratio, the green dashed line indicates isotropic plasma. (n) The β_p value. (o) The entropy per proton with γ = 1.5. (p) The proton thermal (blue), magnetic (red), and total (gray shaded region between its minimum and the maximum value) pressure. The gray shaded region is the interaction region between the fast and the slow streams.

4. Summary and Discussion

We found, for the first time by in situ measurements, evidence of quasiperiodic density structures embedded in SSW streams between 0.3 and 0.6 AU. We presented five instances of trains of quasiperiodic density structures. In each instance, we began by visually identifying large (approximately hours) density structures and marking concurrent magnetic flux tube boundaries associated with the number density local minima. We used the average duration of these structures to provide an estimate of the period (T_o) of the oscillations. Then, performing a spectral analysis on n_p, we confirmed the periodic nature of the fluctuations defined as when a signal passed both the narrowband test and the F test with a 95% confidence level at a frequency close to f_o ≈ 1/T_o.

The periodicities of the structures identified here generally follow the trend of periodicities identified in situ at 1 AU. Kepko et al. (2002) and Kepko and Spence (2003) in an analysis of seven periodic density structure events at 1 AU found that 0.25, 0.6, and 1.4 mHz (70, 30, and 10 min) occurred often, similar to the periods identified in this paper. In a statistical study of the occurrence rate of periodic density structures between 0.5 and 5 mHz observed in 13 years of in situ data at 1 AU, Viall, Kepko, et al. (2009) showed that ≈0.6, 1.4, and 3.0 mHz, (30, 10, and 5 min) were indeed characteristic periodicities that occurred more often than others, consistent with the events found here. They also identified two additional occurrence peaks at 2.3 and 4.7 mHz (7 and 3.5 min), which we did not find here, as well as a solar cycle dependence of the frequency peaks, which highlights the need for more future measurements of the solar wind at these solar distances.

In our analysis, four events out of five show periodicities between ≈80 and ≈130 min (f_o ≈ 0.13–0.21 mHz). This periodicity is in the range of characteristic frequencies identified by Viall and Vourlidas (2015) in coronagraph data close to the Sun. The width of the occurrence enhancement they found was wide, ranging from ≈130 down to the 60-min Nyquist period of that data set. Periodic density enhancements with these time scales advect with the solar wind and are also observed at 1 AU (Kepko et al., 2002, 2016; Kepko & Spence, 2003). The present work shows the first observation of quasiperiodic structures with this characteristic time scale with in situ measurements at 0.3, 0.4, and 0.6 AU. In all cases, smaller quasiperiodic plasma structures were embedded within the larger ones. In the solar wind density of our events we observe additional periodicities at 30 min (two events), 10 min (three events), and 5 min (one event). The multiscale nature of the structures is a characteristic that has been observed previously in studies of in situ density structures at 1 AU (Kepko et al., 2002; Kepko & Spence, 2003; Viall et al., 2008; Viall, Kepko, et al., 2009; Sanchez-Diaz, Rouillard, Davies, Lavraud, Pinto, et al., 2017b).

In a similar way to Kepko and Spence (2003), we determined the scale size (L) of the observed quasiperiodic density structures. For each frequency f selected in our events, we evaluated L ± ΔL = (<v_r > ±σ_r)/(f ± Δf/2), in which <v_r> and σ_r are, respectively, the mean and the standard deviation of the solar wind radial velocity in the time intervals over which we performed the spectral analysis (Δf is the corresponding frequency resolution). For the last event f and Δf were derived from the mean and the standard deviation of the periodicity identified by visual inspection. The size of the structures, expressed in Earth's radii (R_E), and the other parameters are reported for each event in Table 1. The scale size of the solar wind density perturbations analyzed by Kepko and Spence (2003) fell within narrow band centered at L ≈ 23, 30, 45, and 80–100 R_E. Viall et al. (2008) identified an high occurrence of periodic number density structures in slow solar wind streams at radial length scales ≈73, 120, 136, and 180 Mm, that is ≈11, 19, 21, and 28 R_E. We found some similarity with the scale sizes of our smaller structures (L < 100 R_E) manifesting L ≈ 16, 31, 33, 38, and 85 R_E. The bigger density structures (L > 100 R_E) seem to possess a fundamental scale size of L_o ≈ 120 R_E; in fact, we found L ≈ 120 (L_o), 240 (≈2 L_o), 350, 360 (≈3 L_o), 460 (≈4 L_o), and 1,080 (≈9 L_o) R_E. Interestingly, the largest structure resembles the structures identified in coronagraph images by Sanchez-Diaz, Rouillard, Davies, Lavraud, Pinto, et al. (2017b) which manifest a typical radial length scale of ≈12 R_⊙, that is, ≈1,300 R_E.

The anticorrelation between n_p and B (p_p and p_B) on these many minutes to hours type of time scales that we observed in this paper is a representative signature of pressure balance structures, rather than slow-mode waves, because slow-mode waves on these large scales are expected to be strongly damped (Barnes, 1966, 1979). In addition, pressure balance structures have been observed throughout the inner heliosphere. For example, Roberts et al. (1987) and Roberts (1990) found a tendency for negative correlations of n_p and B with Helios data for 9-hr time intervals. Bavassano and Bruno (1991) observed frequently pressure-balanced structures between 0.3 and 1 AU at time scales from 1 to 6 hr, while Burlaga and Ogilvie (1970) at 1 AU found anticorrelation between magnetic and thermal pressures at the time scale of an hour. In similar time scales of a few hours or less, Klein et al. (1993) observed anticorrelations between n_p and p_p in slow streams observed by Helios2 from 0.3 to 1 AU corresponding to structures often not in a total pressure balance. In the inner heliosphere the number of pressure balance structures decreases moving away from the Sun and convert to compressive structures suggesting that they have a solar origin.

In four of our events, the solar wind streams propagated ballistically to 5 R_⊙, mapped to regions close to the HCS. The current sheet could be filled with tangled and intermingled flux ropes, as suggested by Crooker et al. (1996, 2004). Indeed, during one subinterval in the 9 June 1980 event, the local enhancement of the magnetic field strength and the smooth rotation observed in θ_B suggest the transit of a small flux rope created through magnetic reconnection in the solar atmosphere. Sheeley and Rouillard (2010) selected at 1-AU time intervals associated with the transit of flux ropes characterized by magnetic field rotation with time scales of 2 to 13 hr, reduced magnetic field strength fluctuations, and a drop in β_p. Similar structures have been observed by Cartwright and Moldwin (2010) who identified small-scale flux tubes between 0.3 and 5.5 AU with a strong core field, duration from tens of minutes to several hours, and constant temperature profile similar to the surrounding plasma. However, the features of the plasma and the magnetic field in the flux ropes identified in all these previous investigations differ from those observed during the subintervals associated to the periodic density enhancements in our events, which are characterized by

1. the absence of a core field for most of them;

2. the increase of temperature with strong discrepancy respective to the surrounding plasma;

3. the enhancement of the β_p value;

4. the raise of the entropy per proton;

5. the increase of the ratio T_∥/T⊥;

6. the strong anisotropy (T_∥>T_⊥) during periods of low-density plasma (n_p ≤ 25 cm⁻³).

In situ observations of these structures between 0.3 and 0.6 AU are important for understanding their origin. To relate the origin of structures observed at 1 AU to the release of coronal plasma from closed-field regions, previous investigations used the concomitant variation of SW number density, plasma charge state, and composition (Kepko et al., 2016; Viall, Spence, et al., 2009). While the events studied here lacked composition and charge state measurements, they were observed closer to the region of solar wind release, and therefore retain more of a direct imprint of its formation state, such as temperature. Our results on periodic density structures agree with the properties of individual density structures (rather than a train of periodic structures) recently observed in the inner heliosphere by Stansby and Horbury (2018). The most striking result is that in both kinds of events, temperature changes were observed, consistent with interchange reconnection, and the S-web model of solar wind formation. In both instances, the observation of an increase in temperature at the same time as solar wind density enhancements without a change in velocity contradicts the predictions of the expansion factor model. However, the detailed analysis of quasiperiodic structures revealed a more complicated picture. In our events, we noticed that an individual density structure might be characterized by further substructures recognizable by temperature changes at smaller time scales, but we note that a clear temperature enhancement was not always observed in each individual structure.

Taking the previous 1-AU studies, the coronagraph studies, and the events identified here all together, we argue that these periodic density structures are fossils of processes that occurred in the solar corona. It remains to be seen if all of the periodicities, from many hours, down to many minutes, are created through a single process or not. For example, the smaller-scale structures could be the result of waves. In the Wave/Turbulence-Driven solar wind model the majority of heating comes from the turbulent dissipation of partially reflected Alfvén waves (Cranmer et al., 2007; Hollweg & Isenberg, 2002; Velli, 1993) whose power spectrum, determined empirically, is dominated by periods on the order of 5–10 min. On the other hand, the temperature changes, the flux rope, and magnetic boundaries of the larger scales all point to magnetic reconnection. It may be though that the reconnection is itself driven by waves. Pylaev et al. (2017) linked the periodicities near ≈90 min to the acoustic cutoff frequency in the solar corona driving magnetic reconnection that releases solar wind plasma.

The S-web model of the slow wind best accounts for the combined properties of the periodic density structures. As described above, the observed temperature changes and flux rope structure are consistent with reconnection in the solar corona, and are not explained by the expansion factor model. Interestingly, properties (I) and (III) of the flux rope agree with the S-web predictions of Higginson and Lynch (2018) inside plasmoids released at the HCS in a 3-D magnetohydrodynamic simulation of the solar corona and solar wind. Furthermore, the magnetic field lines of the plasmoids, although similar to those of flux ropes, are observed (Rouillard et al., 2011) and predicted (Higginson & Lynch, 2018) to have a complicated topology, possibly explaining why we identified the magnetic signatures of flux ropes in only a few locations.

The most compelling evidence for the S-web model in the events presented here is the June 1981 event. In this event, we also found quasiperiodic density structures of ≈128 min in a solar wind stream that mapped far from the HCS (more than ≈18° of Carrington longitude). Although the limitations of the Helios data made it difficult to find much SSW far away from the HCS, this observation is a crucial test of the S-web model. It is well established that the HCS and helmet streamers are dynamic and produce a zoo of plasma structures, many of them through magnetic reconnection of previously closed loops in the helmet streamer. However, it is still highly controversial if the rest of the SSW is steady, as predicted by the expansion factor model (Cranmer et al., 2007; Wang & Sheeley, 1990), or if it also could have plasma of closed-field regions away from the HCS as predicted by interchange reconnection and the S-web model. The S-web predicts that the SSW away from the HCS should also contain signatures of closed-field plasma released by means of the interchange reconnection along quasi-separatrices that extend far away from the HCS (Antiochos et al., 2011). Higginson and Lynch (2018) predicted that the magnetic field signatures associated with these reconnection events may be different than those at the HCS. Interestingly, in our last event that mapped far away from the HCS we noticed a high variability at small time scales of the solar wind number density and the related proton pressure. The same parameters in the second and the fourth events, closer to the HCS and with a similar average density (n_p ≈ 100 cm⁻³), did not exhibit this high-frequency component.

5. Conclusions

The present work is the first in situ observation of quasiperiodic density structures in SSW streams close to the Sun (<0.6 AU). We have identified periodicities ranging from several minutes to several hours by visual inspection of the density profiles and by means of two statistical tests in the spectral analysis. In particular, we observe structures on time scales between ≈80 and ≈130 min, which have been shown in coronagraph images to be a characteristic time scale of plasma release at the helmet streamer (Viall & Vourlidas, 2015). The flux rope nature of one structure and the temperature increases associated with most of the structures suggest that the quasiperiodic density fluctuations are related to the transit of solar wind structures, formed by the periodic release of closed field coronal plasma by magnetic reconnection supporting the S-web model of the SSW. These features cannot be explained by the expansion factor model of the slow solar wind, although it does not rule it out as a contributing factor.

For one of the solar wind streams embedding quasiperiodic density fluctuations, the identification of the corresponding source region far away from the HCS suggests that the coronal plasma can be released in a periodic manner also away from the streamer belt region. This supports the idea of the S-web model that predicts the occurrence of interchange reconnection, and hence the release of coronal plasma from closed-field regions, along quasi-separatrices that may extend far away from the HCS. However, while sometimes this reconnection is quasiperiodic, enabling us to identify these features objectively and easily, a lack of periodicity should not be assumed to imply that plasma was not released by reconnection (Stansby & Horbury, 2018).

The importance of these structures is not limited to the understanding of the release and acceleration process of the coronal plasma but extends also to processes in the Earth's magnetosphere. In fact, solar wind density fluctuations compress and relax the entire magnetosphere through variations in the solar wind dynamic pressure. This “forced breathing” appears as ultralow frequency waves in the magnetosphere (Di Matteo & Villante, 2018; Kepko et al., 2002; Kepko & Spence, 2003; Viall, Kepko, et al., 2009; Villante et al., 2016) which play a fundamental role in the acceleration, loss, and transport of radiation belt electrons. This range of directly driven ultralow frequency pulsations include magnetospheric field oscillations in the Pc5 frequency band (1.7–6.7 mHz corresponding to ≈150–600-s periods), which are comparable to the trapped electron drift frequency. Wave-particle interactions at these time scales lead to the violation of the third adiabatic invariant and determine the acceleration and inward radial transport of electrons (Baker et al., 2018; Degeling et al., 2008; Elkington & Sarris, 2016; Mathie & Mann, 2001; Regi et al., 2015; Schulz & Lanzerotti, 1974; Zong et al., 2017). Recent works have shown the importance of ultralow frequency waves to the dynamics and location of the radiation belts (e.g., Mann et al., 2016; Ozeke et al., 2018).

The features observed in these case events could be probed when data from Parker Solar Probe become available, and after the launch of Solar Orbiter. The data from these spacecrafts will provide new in situ measurements of the solar wind properties in the inner heliosphere. Together with the information of the other interplanetary and magnetospheric probes, a more comprehensive study of this process will give a new insight on the origin of the solar wind and on the consequences of the impact of quasiperiodic solar wind density oscillations on the Earth's magnetosphere.

Key Points:

• Quasiperiodic solar wind density structures observed closer to the Sun than ever before by in situ data

• Concomitant density/temperature enhancements suggest the release of coronal plasma from closed-field regions by magnetic reconnection

• One occurrence of quasiperiodic structures maps to a region far from the heliospheric current sheet, supporting the S-web model of the slow solar wind