Exploring Solar Wind Origins and Connecting Plasma Flows from the Parker Solar Probe to 1 au: Nonspherical Source Surface and Alfvénic Fluctuations

The Parker Solar Probe (PSP; Fox et al. 2016) completed its first perihelion pass on 2018 November 6, reaching a distance of 35.7 R_⊙ from the Sun, closer by almost a factor of 2 than previous man-made explorations. Observations of the magnetic field and velocity show that PSP crossed the heliospheric current sheet multiple times (see Figure 1) and that the speed of the wind was predominantly very slow. Remarkably, the wind displayed a strongly dominant outward propagating spectrum of Alfvénic fluctuations throughout the encounter, a feature that is rarely seen in very slow solar wind streams at Earth and beyond.

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Here we use the simplest possible magnetic field extrapolation, namely Potential Field Source Surface (PFSS) model, to locate the solar footpoints of the solar wind seen by PSP throughout its first perihelion passage. We then explore possible connections with the solar wind seen at L1 and at Earth and discuss the different, evolved properties of the solar wind seen at much greater distances in conjunction with the source regions on the Sun. PFSS extrapolations provide a qualitatively correct model of the overall topology of the magnetic field at the source surface (SS), but may place the neutral line and pseudostreamers at slightly different latitudes with respect to what is seen in coronagraph data (see, e.g., Morgan & Habbal 2010; Morgan 2011). We therefore supplement the information provided by PFSS with coronagraph images and other plasma properties, such as the presence of Alfvén waves propagating away from the Sun and the corresponding magnetic field–velocity field correlation, to back up the correct determination of the neutral line crossings.

The first perihelion passages of PSP occurred during the minimum phase of the present solar cycle. During this phase, a spacecraft located in the ecliptic at 1 au would generally detect alternating streams of faster and slower wind. Beyond the speed differences, these two solar wind regimes show many other specific characteristics, from the large-scale structure (Schwenn 1990) to composition (Geiss et al. 1995), to the spectral properties of the embedded turbulent fluctuations (see reviews by Tu & Marsch 1995; Bruno & Carbone 2013) and last but not least, different origins on the Sun. In this regard, although it is well known that most of the fast solar wind streams originate from polar coronal holes, the origin(s) of the slow wind are still a mystery (e.g., Wang & Sheeley 1990; Antonucci et al. 2005; Abbo et al. 2016), and indeed, the classification of the solar wind outflow uniquely in terms of wind speed is probably too simplistic (e.g., von Steiger 2008; Zhao et al. 2009; Ko et al. 2018; D'Amicis et al. 2019; Stansby et al. 2019).

One important feature characterizing solar wind fluctuations, especially within the main portion of fast solar wind streams, is the presence of large-amplitude fluctuations showing an Alfvénic nature. The adjective Alfvénic refers to the presence in the wind of large-amplitude velocity and magnetic field fluctuations with the correlation between them corresponding to Alfvén waves propagating away from the Sun. In addition, relative density fluctuations are suppressed together with fluctuations in magnetic field magnitude, so that the magnetic field vector apex moves locally on the surface of a sphere (Matteini et al. 2015).

Based on this definition, fast wind is usually found to be more Alfvénic than slow wind (Belcher & Davis 1971; Belcher & Solodyna 1975). However, recent results (D'Amicis & Bruno 2015; D'Amicis et al. 2019) have shown that the slow solar wind can also sometimes show a high degree of Alfvénicity, with velocity and magnetic field fluctuations as large as those found in the fast wind. It is important to note that this kind of slow wind was studied using measurements at 1 au where one would expect a degradation of the Alfvénic correlation due to the solar wind expansion. In addition, the identification of this Alfvénic slow wind was found on a statistical basis over the maximum of solar cycle 23. D'Amicis et al. (2019) suggested the idea that a possible solar source for this Alfvénic slow solar wind would lie in low-latitude small coronal holes (in agreement with Wang 1994; Neugebauer et al. 1996; Wang & Ko 2019; Wang & Panasenco 2019) that were a ubiquitous feature of the solar surface during the maximum of solar cycle 23 (Platten et al. 2014).

An Alfvénic slow wind stream was observed in a portion of the wind preceding a fast stream during the perihelion passage of the Helios mission at solar activity minimum (Marsch et al. 1981). A detailed characterization of this kind of wind was developed recently by Stansby et al. (2020) and Perrone et al. (2020). In contrast to the findings of D'Amicis et al. (2019), the amplitude of the fluctuations was smaller in this case than that seen in typical fast wind but still larger than that of the typical slow wind. The solar wind seen by PSP over the first perihelion encounter appears to be an example of slow Alfvénic solar wind. In this case, the Alfvénic slow wind observed by PSP originated from a very rapidly expanding small equatorial coronal hole adjacent to a pseudostreamer configuration, i.e., a multipolar closed configuration opening into a unipolar field (Wang et al. 2007; Panasenco & Velli 2013; Panasenco et al. 2019). The corresponding solar wind at Earth showed this property only partially, providing evidence for the evolution and destruction of Alfvénicity in a slow solar wind stream as it traveled from the Sun to 1 au.

In the next section, the magnetic field measurements from the first PSP encounter and the connectivity from the solar coronal footpoints of PSP into the solar wind are discussed, and the SS height required to properly match the polarity transitions observed by the spacecraft and map them back to the Sun is determined. Although this height is lower than the "standard" accepted values, we show that it actually depends on the region above the Sun, along the lines of Levine et al. (1982). For clarity, we have labeled the polarities (P for positive, N for negative) and the transitions (T) we will discuss explicitly in Figure 1 (and further identified in Table 1). The choice of these transitions, seen in the figure as labeled green shadings over the 1 hr median field values plotted throughout the time intervals of the first (E1) and second (E2) encounters, was made to identify clear, reliable crossings of the heliospheric polarity inversion sheet, avoiding time-dependent disturbances such as blobs or coronal mass ejections (CMEs). For E1, we do not discuss the P3/N3 transition as there are multiple crossings within the 1 hr median time, and similarly for E2 we limit the discussion to the two transitions T6 and T7. E2 is discussed mainly to contrast the resulting SS height with the more surprising case of E1.

In our study, we use the PFSS model developed by Schrijver & De Rosa (2003). As a lower boundary condition, this PFSS model incorporates magnetic field maps produced by an evolving surface-flux transport model based on magnetic fields observed by the Helioseismic and Magnetic Imager (HMI; e.g., Scherrer et al. 2012; Schou et al. 2012) on the Solar Dynamics Observatory (SDO). The model evolves these fields in accordance with empirical prescriptions for differential rotation, meridional flows, and convective dispersal processes. In addition to SS height, PFSS extrapolation depends crucially on the effective resolution of the fields on the solar disk and the treatment of the polar fields, which are difficult to observe and often not used directly by the PFSS extrapolation model itself (in the present case, the magnetogram assimilation window is limited to the area within ±60° of disk center, and polar fields are determined by the large-scale transport processes). The effective magnetogram resolution used for the extrapolations here is 8'' (≃5800 km on the Sun, significantly less than a typical supergranule diameter). The PFSS model was updated in 2012 with polar flux transport modeling corrections to better fit the observed magnetic fields and neutral lines (Liu et al. 2012) of the next-to-last deep minimum. With a fixed resolution and the defined flux transport model, PFSS now depends only on the SS height. Again, the real coronal fields importantly involve dynamic layers, from the chromosphere through the transition region to the corona itself, where volume currents play a role and the PFSS model cannot be expected to reproduce the real solar coronal magnetic field precisely. It is for this reason that identifying the solar origin of solar wind parcels must rely on other factors as well, discussed further below.

Coronal heating and solar wind acceleration lead to the stretching and opening of magnetic field lines into the solar wind. The simplest models for the magnetic expansion consist of the PFSS model and its variants: a height is specified at which all magnetic field lines become open and radial—the SS height—typically located at a height ${R}_{\mathrm{SS}}=2.5\,{R}_{\odot }$ from the center of the Sun, and the field from the photosphere to the corona is reconstructed, on the basis of the radial field at the surface, as a potential field. The radius of the SS is a free parameter of the model. By construction, because the magnetic field in the shell between the photosphere and SS is potential, the magnetic field in that region falls as 1/R³ or faster, depending on the multipolar expansion, i.e., on the strength and distribution of magnetic polarities. On the other hand, beyond the SS, the field becomes radial and decays as 1/R². As a consequence, adjusting the SS height changes both the total amount of open flux as well as the magnitude of the magnetic field at a given radius, and this can be done to fit the average values observed by different spacecraft. In addition, the location and shape of the heliospheric current sheet (HCS) will change. For example, Todd Hoeksema at Wilcox Solar Observatory has been producing HCS maps for two SSs: 2.5 and 3.25 R_⊙. Averaging over solar cycles, the best SS radius has been found to be at about 2.5 R_⊙, although ${R}_{\mathrm{SS}}=3.25\,{R}_{\odot }$ gave a slightly better result when comparing to the high-latitude Ulysses measurements during the 1994 polar pass in the middle of the declining phase. In this period, the Sun presents fewer sunspots but the global field may be stronger and more organized topologically. During the cycle 22 and 23 minimum periods, the SS radius values of 1.8 R_⊙ and 1.9 R_⊙ produced the best results (Lee et al. 2011). Badman et al. (2020) carries out an extensive investigation with PFSS reconstructions using different solar magnetic field sources (GONG, HMI). One of the main conclusions is that in order to accurately capture the relative magnitude of the radial magnetic field measured by PSP, and sufficiently open midlatitude and equatorial coronal holes, the SS must be placed at ${R}_{m\mathrm{SS}}\leqslant 2.0\,{R}_{\odot }$. Levine et al. (1977), using data for the entire Skylab period in 1973, found that extrapolation of an average magnetic field strength in the equatorial plane at 1 au, which is near the observed average value, requires an SS near 1.5 R_⊙ during the cycle 20 minimum. The present cycle 24 solar minimum is also very weak, and indeed as we shall see, the optimal SS height will also be quite low.

The PSP/FIELDS (Bale et al. 2016, 2019) observations of the radial magnetic field are summarized in Figure 1, showing the intensity and sign of the field expressed in terms of the modal field value from bins comprising 1 hr of data (i.e., each data point is the modal value of B_r  ±  30 minutes), so that all the rapidly varying transient structures are removed. In the figures, the label N is used to identify periods of negative polarity, P for different periods of positive polarity, and T for the transition periods (not all, but those of interest, as specified in Table 1). One can see that from October 18 through November 26 the polarity of the field changed at least seven times, while throughout the whole of the perihelion pass, from October 30 through November 15, PSP found itself in a region of negative polarity.

In the overall weak field of the current solar minimum during the first encounter, we can identify two specific areas on the Sun with a magnetic field stronger than average: the new active regions NOAA AR 12724 and AR 12725 at Carrington longitude ∼125°, and a decaying and heavily dispersed AR 12713 (first emerged five rotations earlier) at Carrington longitude ∼320°.

In the following, the footpoints of the wind seen by PSP will be traced down to their source regions on the Sun and compared with the magnetic field polarity at a height of 1.1 R_⊙ as obtained by PFSS extrapolation with different SS heights. In order to trace PSP observations to the sources back at the Sun, a ballistic extrapolation using the wind speed measured at PSP down to the SS height is carried out, at which point individual PFSS field lines are traced down toward the Sun. To analyze the robustness of this prediction, corrections up to ±80 km s⁻¹, in bins of 10 km s⁻¹, are added onto the measured solar wind velocity, and the ballistic tracing is repeated for all speeds. The result, for the transition period T1, is illustrated in Figure 2. The plots show magnetic pressure isocontours at $1.1\,{R}_{\odot }$, with shaded color indicating coronal holes with the respective polarity (blue, negative and red, positive). Overplotted is the direct radial projection of PSP, as a blue diamond, while the the ballistic extrapolations down to the SS are shown by the blue crosses on the plot.The crosses are then traced down to 1.1 R_⊙ using the PFSS field lines, and the results are plotted as open circles. The first thing to note is how irregular the neutral line (in bold) is, with large latitudinal excursions, the height of the SS notwithstanding (for the three panels, from left to right, R_SS goes from $1.4\,\mathrm{to}\,1.8\,{R}_{\odot }$). As the SS moves upward, coronal holes shrink in size, as seen from the decreasing areas shaded in blue and red moving from the left to the right panel. By inspecting the different panels, one can see that the SS height of 1.8 R_⊙ (right panel) cannot correctly identify the transition from one polarity to the other as seen in interval T1; rather, PSP then remains connected to the positive polarity of the low boundary of the polar coronal hole at higher latitudes. On the other hand, lower SS heights show that small changes in solar wind speed lead to a quick transition from one polarity to the other (left and center panels). The best fit for T1 is ${R}_{\mathrm{SS}}=1.6\,{R}_{\odot }$. Figures 3–7 provide analogous plots for the polarity transitions labeled T2–T7.

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Figure 3 illustrates the T2 transition from negative to positive and back, N1/P2/N2. An R_SS height of 1.6 R_⊙ was used to reproduce the negative–positive–negative jump, as PSP's trajectory moves leftwards on the plot. For the period T2, PSP magnetic footpoints were located mostly in the negative open field regions N1 and N2. To reproduce the observed short jump back to the positive polarity P2, the solar wind speed of 230 ± 80 km s⁻¹ was used, reproducing the short-lived magnetic connection back to the positive polarity region, which is the observed P2 result. The positive region P2 is the same as P1 in Figure 2.

Figure 4 illustrates transition T3 (N3/P4/N4), when the PSP magnetic footpoints moved across very weak magnetic field regions with ${B}_{r}$ = 0.4–1.3 G at 1.1 R_⊙, which is at least an order of magnitude smaller compared to the near-equatorial magnetic field observed during the solar maximum in cycle 24 in 2014 (Figure 5 in Janardhan et al. 2018). To reproduce the polarity transition observed by the PSP/FIELDS instrument, the R_SS height is reduced to 1.2 R_⊙. The left panel in Figure 4 illustrates the transition T3 (from negative to positive polarities): the PSP magnetic footpoints connected to the small equatorial coronal hole with negative polarity (blue shade) and to the open field area of the polar coronal extension of positive polarity (red shade). The right panel shows the transition P4/N4: the negative polarity region N4 is the western boundary of the big equatorial coronal hole above which PSP will spend the following two weeks: 2018 October 30–November 15. For the N3 negative polarity region, the SS was lowered to ${R}_{\mathrm{SS}}=1.2\,{R}_{\odot }$ and field lines projected from the SS down to B_r = 1.05 R_⊙. The transition N3/P4 is especially sensitive to the SS height and easily disappears for higher R_SS. However, the transition P4/N4 is captured for R_SS up to 1.6 R_⊙. This conclusion is also supported by Badman et al. (2020).

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Figure 5 illustrates the protracted transition period T4 (N4/P5), during which PSP leaves the corotation region above the negative open field area to which the spacecraft was connected for the two previous weeks. Figure 1 shows that the duration of the transition period T4 is 2 days and twice as long as all simple polarity transitions. To investigate the longer period transition, the PSP magnetic footpoint projections were modeled for two consecutive days 2018 November 14–15 and for three different R_SS heights of 1.6, 1.8, and 2.0 R_⊙. The goal was to find the R_SS height required to connect PSP to both polarities N4 and P5. The top-left panel in Figure 5 shows the moment when the PSP footpoints are located entirely in the negative area ${R}_{\mathrm{SS}}=1.6,\,{R}_{\odot }$: the beginning of the transition period T4. Twelve hours later (top-right panel), the transition is in progress and PSP connects to both polarities when including solar wind speed fluctuations up to ±80 km s⁻¹. To establish the best fit and the maximum fit, the SS was brought farther all the way up to ${R}_{\mathrm{SS}}=2.0\,{R}_{\odot }$ (Figure 5, bottom-left panel) and found that the transition was lost. Therefore, the bottom-right panel in Figure 5 shows the modeling for ${R}_{\mathrm{SS}}=1.8\,{R}_{\odot }$ made for the next day, 2018 November 15, the maximum workable SS height for this region.

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Figure 6 illustrates the transition T5 (P5/N5), which was fast (hr) and without polarity fluctuations. This can be explained by the fact that PSP was flying farther from the Sun, no longer in the quasi-corotation regime as it had been over T3 and T4, which are the beginning and end of the corotation. The simplicity of the transition period T5 allowed the straightforward modeling of the footpoint connection to opposite polarities of the relatively weak magnetic field area. The left panel shows the optimal PSP connection with both polarities for ${R}_{\mathrm{SS}}=1.4\,{R}_{\odot }$; the right panel shows how this transition nearly disappeared when the SS height increased up to ${R}_{\mathrm{SS}}\,=1.6\,{R}_{\odot }$.

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Figure 7 illustrates the transitions T6 and T7 during E2. Polarity transition T6 was also fast (hr) again because PSP was flying farther from the Sun and not in corotation. The left panel in Figure 7 shows the PSP connection with both positive and negative polarities calculated for ${R}_{\mathrm{SS}}=1.8\,{R}_{\odot }$. The right panel in Figure 7 shows the polarity transition T7 across the very strong active region NOAA AR 12738 on 2019 April 22. The SS height was found to be ${R}_{\mathrm{SS}}=2.5\,{R}_{\odot }$. This transition was preceded by multiple CMEs originating from the AR. These created a series of magnetic field inversions observed by PSP and indicated in Figure 1 (bottom panel). How CMEs influence PSP connections is discussed in the following Section 2.1.

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Table 2 summarizes results for the best estimates of the solar SS height R_SS above the polarity transition regions along PSP's trajectory during the first encounter. The best fit is defined as the height R_SS of the SS when the modeled magnetic polarity transition corresponds to that observed by PSP for the given T, even considering variations in the solar wind velocity. The upper limit value for R_SS is the height at which the calculated solar magnetic footpoints of PSP begin to deviate from the observed polarity values. B_1.1 in Table 2 is the photospheric magnetic field value B_r projected to 1.1 R_⊙ by PFSS modeling. B_1.1 is tabulated for the regions on the Sun where the corresponding polarity transitions (T1–T7) were taking place.

Table 2.  Source Surface Height above T1–T7 (in R_⊙)

	T1	T2	T3.1	T3.2	T4	T5	T6	T7
RSS	1.4	1.4	1.2	1.6	1.6	1.4	1.6	2.5
${{R}^{* }}_{{mSS}}$	1.6	1.6	1.3	1.8	1.8	1.5	1.8	2.5
B1.1, G	1.8–2.2	1.4–2	0.2–0.4	1.2–1.4	0.6–1.2	0.2–0.4	4.0	30 (sunspot)

Note. R_SS—best fit, ${{R}^{* }}_{{mSS}}$—max, B_1.1 is B_r at 1.1 R_⊙.

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During the current minimum, the optimal R_SS for PFSS reconstruction is found to be smaller right above polarity inversion regions, corresponding to dips in the overall nonspherical SS shape. The concept of a nonspherical SS was introduced by Schulz et al. (1978) and developed further by Levine et al. (1982). Using our results for the best-fit R_SS above the polarity transition regions T1–T7, a nonspherical SS shape was constructed in correspondence with the PSP solar encounter. The result is show in Figure 8, where the local minima in R_SS above T1–T7 are connected with continuity to the higher SS positions elsewhere using quadratic and cubic Bézier curve interpolations. The striking difference in the resulting shapes can be attributed to the different magnetic field magnitudes at the photosphere. The SS, contracted and wrinkled during E1, transformed into the nearly classical 2.5 R_⊙ SS during E2. Because these changes happened over a very short period of time between two encounters and cannot be attributed to different phases of the solar cycle, the explanation must lie in time-dependent changes in magnetic activity at the Sun in E2. During Encounter 2 in April 2019 the large-scale complex active region NOAA AR 12738 (with a sunspot) developed, together with a smaller but also relatively strong active region NOAA AR 12737. The active regions were separated by 120° in longitude. Such presence was sufficient to inflate the SS back to a nearly classic spherical shape with ${R}_{\mathrm{SS}}=2.5\,{R}_{\odot }$ except for two remaining dips. In Section 3, we use the best-fit R_SS height to find the solar sources of the Alfvénic slow solar wind observed at 1 au during the first PSP encounter and model how these regions were connected to PSP.

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2.1. Influence of CMEs on PSP Connectivity

During E2, and immediately preceding transition period T7, multiple polarity reversals were observed by PSP in conjunction with transient events and CMEs. Here we briefly discuss how the polarity changes associated with transient field openings from this type of event is influenced by the structure of the corresponding source filament channel on the Sun. Panasenco et al. (2013) found that the coronal cells observed and modeled by Sheeley & Warren (2012) do not cross the polarity reversal boundary within a filament channel at heights below the filament spine top. Coronal cells originate from the network field concentrations and show the same patterns as chromospheric fibrils because they follow the same filament channel magnetic topology, with a strong component of the field parallel to the photosphere. The direction of the axial field inside the filament channel and, therefore, its chirality can be deduced from the geometry of the chromospheric fibrils and coronal cells, as shown in Figure 9, illustrating active region NOAA AR 12738 and a filament channel that caused multiple CMEs. One of the CMEs is shown in Figure 10, captured by LASCO/C2. The chirality of CMEs then defines the polarity of the transient coronal hole formed on eruption and, therefore, the polarity of the field connecting to PSP during a CME passage. A dextral filament channel means that the direction of the axial magnetic field bears right when viewed from the positive polarity side. It means that the CME's axial magnetic field, when measured in situ by PSP, was directed from the positive to negative polarity parts of AR 12738. In other words, during the CME passages in 2019 April 15–22, PSP was momentarily connected to transient coronal holes with positive polarity. The number of positive polarity chunks in Figure 1 (bottom panel) corresponds to the number of CMEs crossing the PSP pass in this time period. PSP reaches the polarity transition period T7 only on April 22, when PFSS modeling connected PSP to the positive polarity of the northern corona hole extension (see Figure 7 for E2 connectivity).

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2.2. Comparison of 3D PFSS Modeling with the LASCO/C2 Coronagraph Observations

This section compares the PFSS extrapolations during E1 and E2 with LASCO C2 images to show the direct link between the neutral lines and streamers (as well as pseudostreamer stalks). The PFSS magnetogram, superposed on the (occulted) solar disk, is also shown. Figure 11 shows results for E1: superposition of the neighboring streamers and pseudostreamers (left panel) resulted in the merging of these two structures in coronagraph observations. However, two separate pseudostreamer stalks may be seen in the coronagraph images as thin rays. Both pseudostreamers are leaning into the equatorial streamer. Stalks are curved in both the PFSS model and white-light LASCO/C2 images, due to their weak magnetic field, lower SS heights during E1, and the northern coronal hole superradial expansion. Figure 12 shows the PFSS extrapolation and LASCO/C2 images for period E2: the open coronal field of the small coronal hole of negative polarity originating near the center of the sunspot inside active region NOAA AR 12738 coincides with the area between the streamer and pseudostreamer stalk. The active region produced multiple CMEs erupting from under the streamer, as well as multiple transients and flares with plasma propagating into the open field in the pseudostreamer environment. This might explain the apparent asymmetry in the pseudostreamer appearance at the limb, where the northern half is illuminated with more dense plasma and the southern half appears to be completely empty.

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Throughout the first perihelion encounter, the solar wind as measured by PSP was dominated by large-amplitude Alfvénic fluctuations. This is well documented, e.g., in the papers by Badman et al. (2020) and Matteini et al. (2015). Quantitatively, if we define the Elsässer variables

$$\begin{eqnarray*}&&{{\boldsymbol{z}}}^{\pm }={\boldsymbol{v}}\mp \mathrm{sign}({B}_{r}){\boldsymbol{b}}/\sqrt{(4\pi \rho )},\end{eqnarray*}$$

where r denotes the radial component of the large-scale magnetic field B, while v and b denote velocity and magnetic field fluctuations, and ρ is the plasma density, purely outwardly propagating Alfvén waves have ${{\boldsymbol{z}}}^{-}=0$. In terms of the normalized velocity magnetic field correlation,

$$\begin{eqnarray*}&&{\rho }_{v\mbox{--}b}=\displaystyle \frac{{\boldsymbol{v}}\cdot {\boldsymbol{b}}}{| {\boldsymbol{v}}\cdot {\boldsymbol{b}}| };\end{eqnarray*}$$

this means that ρ_v–b = +1 for outwardly propagating Alfvénic fluctuations along a negative polarity magnetic field line anchored at the Sun, while ρ_v–b = −1 for outwardly propagating Alfvénic fluctuations along a positive polarity magnetic field line anchored at the Sun. A state with $| {{\boldsymbol{z}}}^{-}| \ll | {{\boldsymbol{z}}}^{+}|$ and $| {\rho }_{v\mbox{--}b}| \geqslant 0.5$ is called Alfvénic. Additional properties of Alfvénic fluctuations are that the fluctuations of the magnetic field magnitude are much smaller than the magnetic field fluctuation amplitudes, and that relative density fluctuations are strongly suppressed with respect to the typical value in a turbulence flow, i.e., the squared turbulent Mach number.

Figure 13 (left panel) shows solar wind measurements at 1 au over the period encompassing the first PSP perihelion. The left-hand side shows an interval of the slow wind detected by the Three-Dimensional Plasma and Energetic Particle Investigation (3DP; Lin et al. 1995) at ∼24 s resolution and magnetic field measurements sampled by the WIND Magnetic Field Investigation (MFI; Lepping et al. 1995) interpolated to the time of the plasma measurements, both on board the WIND spacecraft, from 2018 October 20 to 25. The upper panel displays the solar wind speed profile, V_SW (in km s⁻¹); in the middle panel, the v–b correlation coefficient, ρ_v–b, is computed at the 1 hr scale typical of Alfvénic fluctuations; the bottom panel shows the magnetic field magnitude, B (in nT). One sees that the velocity magnetic field correlation fluctuates strongly, with very few periods in which it is stably strongly either positive or negative. This interval, 2018 October 20–25, is characterized by a slow solar wind with a speed ranging between 300 and 400 km s⁻¹, and it is described by a very low v–b correlation coefficient overall. The most Alfvénic part is from days 23 to 23.5 with an average value of −0.87, which corresponds also to a period of almost constant magnetic field magnitude. The right-hand side of Figure 13 shows, in the same format and for the same instruments, the time series of the same parameters from 2018 November 1 to 6. In this case, the speed profile shows a transition from a slow wind characterized by a speed around 350 km s⁻¹ to a stream interface followed by a faster stream at the end of the interval reaching values around 600 km s⁻¹. In this case, the v–b correlation coefficient moves from values around 0 in the stream interface, where we also observe a strong compression of the magnetic field magnitude, to values around −1, in the fast wind.

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To connect selected solar wind streams observed at 1 au to their sources at the Sun, we use the same method as in Section 2, when we found magnetic footpoints for the PSP observations of the magnetic polarity inversion periods: the spacecraft (i.e., WIND, or the Earth's) position to the SS is projected via the Archimedean spiral with the given solar wind velocity, and from the SS down to the selected height above the solar surface along PFSS magnetic field lines. For each stream, the SS height determined in Section 2 for the specific region in the low solar corona is used.

Figure 14 shows the source region for the Alfvénic slow wind (measured at 1 au) plotted for two different SS radii R_SS = 1.4 and 1.6 R_⊙—the best fit and the maximum possible fit for R_SS as estimated from Figure 2 for this region. The projection of Earth to the SS (green crosses) and down to the height $R=1.1.{R}_{\odot }$ (green circles) shows that Earth was connected over this time to positive and negative open field areas close to an activity region with a relatively strong magnetic field. As shown in Figure 13, the October 23 Alfvénic slow solar wind stream has negative ρ_v–b, which corresponds to a positive magnetic field. Therefore, the area from where this Alfvénic slow solar wind stream originated for this day was on the positive polarity side connecting to Earth. PSP observed solar wind from this area during transition period T1 in October 20 as was discussed previously in Section 2.

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Figure 15 shows the same measurements but for the second Alfvénic slow wind stream observed on 2018 November 2. This Alfvénic slow solar wind stream has positive ${\rho }_{v\mbox{--}b}$ and therefore originated from a negative magnetic polarity region on the Sun. The PSP magnetic footpoints were in the same area for nearly two weeks as well as on 2018 November 2, when Earth also remained connected to this area.

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Figure 16 shows PSP measurements during the interval 2018 October 15–November 18. The three panels from top to bottom plot wind speed, the correlation ρ_v–b, and the radial magnetic field, respectively. Yellow shading indicates periods of Alfvénic slow solar wind on October 20th that originated from the same region on the Sun (Figures 2 and 14) and propagated from PSP to 1 au, arriving on October 23rd (Figure 13, left panel) when it was seen at Earth. The wind appears to undergo only a slight acceleration, from 320 to 350 km s⁻¹ over the PSP–1 au distance. Green shading shows an Alfvénic slow wind stream at PSP and 1 au for 2018 November 2: this is wind from the same solar source (Figure 15), observed at the same time, and therefore different plasma parcels. A similar very slight acceleration is observed.

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The Alfvénic fast solar wind stream on 2018 November 5 shown in blue in Figure 13 has a negative correlation ρ_v–b, and the corresponding Earth magnetic footpoints were anchored inside a positive open field area as shown in Figure 17. Earth's position extrapolates backwards into the middle of the equatorial extension of the positive northern polar corona hole. The SS where the magnetic field becomes radial was selected in accordance with the "best-fit" results described in Section 2 and was selected to be R_SS = 1.6 R_⊙. Three-dimensional PFSS models in Figures 18–20 correspond to the two-dimensional magnetic pressure maps shown in Figures 14, 15, and17.

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The first slow Alfvénic stream, observed on 2018 October 23 at 1 au, originated from a pseudostreamer configuration, more precisely from its southern coronal hole indicated by the black arrow in Figure 18. This is the same positive open field region shown in Figure 14 and to which Earth was magnetically connected (green circles). The very nonmonotonic expansion of the open magnetic field appears to have a funnel-like topology, similar to the geometry of the field described in Panasenco et al. (2019), which might explain its very low speed.

The second slow Alfvénic wind stream originated from an equatorial coronal hole with a relatively strong magnetic field. The very complicated topology near the base of this open field area includes multiple small-scale pseudostreamers whose branches converge and diverge in the direction perpendicular to the equator (Figure 19). On the other hand, the coronal hole from where the Alfvénic fast wind originated presented by a very smooth and monotonically expanding magnetic field (Figure 20). These results suggest that for the origin of slow Alfvénic streams, highly expanding open coronal fields are a requirement.

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PSP's trajectory over its first perihelion pass brought it to traverse different regions on the Sun with different solar wind sources. A range of the solar SS heights R_SS = 1.2–1.8 R_⊙ was required to correctly reproduce polarity transition periods during E1, and 1.6–2.5 for E2, showing that SS extrapolations generally require a nonspherical outer boundary, as illustrated in Figure 8. The SS heights above the polarity inversion regions are the local dips or minimums in the overall nonspherical SS shape during the current solar minimum.

Although the perihelion passage occurred during a time of deep solar minimum and the magnetic field on the Sun was globally very weak, different types of solar wind were observed. Around perihelion and inside corotation, PSP traversed a very small negative coronal hole (or coronal hole extension) prograde and retrograde, observing slow wind dominated by outwardly propagating Alfvénic turbulence throughout the encounter. It also saw faster Alfvénic wind streams before and after. The detailed properties of the waves, large-scale wave packets, including the so-called switchbacks and radial jets, are detailed elsewhere (Horbury et al. 2020; Matteini et al. 2015). Such fluctuations in the presence of extremely slow wind are not a common occurrence at greater heliocentric distances, where Alfvénic slow wind is seen more commonly at solar maximum appearing to originate from so-called magnetic funnels (Panasenco et al. 2019). Here we see that the open region crossed at perihelion also has very large expansion factors, while more standard radially expanding regions remain Alfvénic with faster winds.

Using the best fit for ${R}_{\mathrm{SS}}$, we also traced back to the Sun the short Alfvénic slow wind streams observed at 1  au, found their source regions, and created the 3D PFSS models for the coronal field in these regions. These models revealed the peculiar topology in both cases—coronal pseudostreamers at large and smaller scales. We found that only small regions of wind remained Alfvénic out to 1 au, one of which corresponded to the fast expanding open region at the PSP perihelion.

Our findings confirm an important property of the coronal magnetic field, namely that small regions in the corona, in the presence of complex field structures at the Sun (i.e., largely nondipolar fields) can expand superradially to occupy large regions of the heliosphere. Our findings also show that Alfvén waves may be an important part of most of the nascent solar wind, with the Alfvénicity decreasing rapidly with distance from the streams close to the equator and the heliospheric current sheet, and surviving out to greater distances only in the fast wind from dominant polar coronal holes or in the slow wind from rapidly superradially expanding small open "funnel" regions. Further research will show whether these regions, often presenting multipolar pseudostreamer configurations at their base, may be identified by other tracers, including compositional differences, in the solar wind. To this end, joint observations with the upcoming Solar Orbiter together with PSP will help to shed light on the generation and acceleration of different solar wind stream types.

O.P. was supported by the NSF EAGER grant No. 1853530. M.V. was supported by the NASA Parker Solar Probe Observatory Scientist grant No. NNX15AF34G. We would like to thank Marc DeRosa and Aram Panasenco for the helpful discussion on PFSS modeling. Parker Solar Probe was designed, built, and is now operated by the Johns Hopkins Applied Physics Laboratory as part of NASA's Living with a Star (LWS) program (contract NNN06AA01C). Support from the LWS management and technical team has played a critical role in the success of the Parker Solar Probe mission. Finally, we thank the referee for their careful reading of the manuscript and timely and constructive comments.