# Characteristics and Source Regions of Slow Alfvénic Solar Wind Observed by
Parker Solar Probe

Tamar Ervin Department of Physics, University of California, Berkeley,
Berkeley, CA 94720-7300, USA  Space Sciences Laboratory, University of
California, Berkeley, CA 94720-7450, USA  Kai Jaffarove Department of Physics,
University of California, Berkeley, Berkeley, CA 94720-7300, USA  Space
Sciences Laboratory, University of California, Berkeley, CA 94720-7450, USA
Samuel T. Badman Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden
Street, Cambridge, MA 02138, USA  Jia Huang Space Sciences Laboratory,
University of California, Berkeley, CA 94720-7450, USA  Yeimy J. Rivera Center
for Astrophysics $|$ Harvard & Smithsonian, 60 Garden Street, Cambridge, MA
02138, USA  Stuart D. Bale Department of Physics, University of California,
Berkeley, Berkeley, CA 94720-7300, USA  Space Sciences Laboratory, University
of California, Berkeley, CA 94720-7450, USA

###### Abstract

Using a classification scheme for solar wind type based on the heliocentric
distance of the observation, we look at near perihelion observations from
Parker Solar Probe Encounters Four to Fourteen to study the sources of the
slow Alfvénic solar wind (SASW). Through Potential Field Source Surface (PFSS)
modeling and ballistic mapping, we connect streams to their solar source and
find that a primary population of SASW comes from small coronal holes (CHs)
and their over-expanded boundaries, while a second population seems to emerge
from non-CH structures potentially through interchange reconnection with
nearby open field lines. This CH-like SASW shows larger expansion than the
FSW, potentially indicating additional heating below the critical point
leading to slower wind emerging from CH-like structures. We show that SASW
emerging from CH-like structures shows stronger preferential acceleration of
alpha particles (similar to the FSW) than the SASW emerging from non-CH
structures, and that this is a velocity dependent phenomena as found in
previous studies. To have additional confidence in our mapping results, we
quantify the error on both the PFSS model and ballistic mapping and discuss
how additional multi-point observations of plasma parameters and composition
would allow us to better constrain our models and connect the solar wind to
its source.

††software:  Astropy (Astropy Collaboration et al., 2013, 2018, 2022), heliopy
(Stansby et al., 2022), matplotlib (Hunter, 2007), numpy (Harris et al.,
2020), pandas (Wes McKinney, 2010), sunkit-magex (Stansby et al., 2020),
pySPEDAS (Angelopoulos et al., 2019), scipy (Virtanen et al., 2020), spiceypy
(Annex et al., 2020), SunPy (Community et al., 2020)

##  1 Introduction

The source regions of the solar wind have been a topic of interest to the
space physics community for decades, and while the source of the fast solar
wind (FSW) is well known to be coronal holes (CH) (McComas et al., 1998, 2008,
and others), the source of the slow solar wind is still unresolved. The solar
wind has traditionally been categorized by wind speed at 1AU: fast (speeds
above 500 $\mathrm{km\ s^{-1}}$ at 1AU) and slow (speeds below 500
$\mathrm{km\ s^{-1}}$), however more recent works have shown that the slow
solar wind can be further categorized into slow Alfvénic solar wind (SASW) and
classical slow solar wind (SSW) based on the Alfvénicity of the plasma
(D’Amicis & Bruno, 2015; Stansby et al., 2018, 2020b; Ervin et al., 2024b, and
others). This SASW shows similar properties to the fast solar wind
specifically in terms of Alfvénicity (D’Amicis & Bruno, 2015; Perrone et al.,
2020; D’Amicis et al., 2021), alpha particle abundances (Ohmi et al., 2004;
Ervin et al., 2024b), differential velocities (Stansby et al., 2020a), and
composition (Stakhiv et al., 2015; D’Amicis et al., 2018; Ervin et al., 2024b)
meaning that this wind likely has a similar source to the FSW (D’Amicis &
Bruno, 2015; D’Amicis et al., 2021, and others).

Since the FSW emerges from open field lines streaming from within CHs, some of
the SASW likely originates from CHs and/or their boundaries (Wang & Sheeley,
1990, and others). Expansion within these CH regions can play a role in the
speed of the emergent wind and perhaps lead to slower wind emerging from CH
regions. Specifically, heating above the critical point (where the wind
becomes supersonic) increases wind speeds (Leer & Holzer, 1980). Heating
concentrated near the coronal base leads to a larger mass flux and lower
energy available per particle which decreases the acceleration leading to
slower wind speeds (Wang et al., 2009). Therefore, rapidly diverging fields
with higher critical points and less energy deposited near the sonic point can
produce slower speed winds (Wang et al., 2012; Stansby et al., 2020b).

The magnetic expansion factor ($f_{s}$) is a measure of the divergence of the
magnetic field (Wang & Sheeley, 1990, 1997) and there is an empirically
established anti-correlation between the expansion factor and solar wind speed
(Wang & Sheeley, 1990). Small CHs and their boundaries have been shown to have
higher magnetic expansion (Wallace et al., 2020; Ervin et al., 2024b) and
could therefore be a source of slower wind due to higher critical points
leading to heating below the transition to supersonic wind speeds (Nolte et
al., 1976; Garton et al., 2018). It has been shown that the expansion factor
does not always follow this correlation with wind speed, but that the dynamic
boundary between open and closed magnetic field lines could be responsible for
this correlation or deviation from it (Riley et al., 2015; Wallace et al.,
2020).

In addition to the correlation between expansion factor and wind type,
different compositional characteristics have been shown to be associated with
different wind speeds and a potential tracer of the source region of the wind.
Due to the freeze-in process, composition ratios stay constant through the
radial evolution of the solar wind and are thus a good metric to evaluate the
source of the wind when compared with known properties of various source
regions (Buergi & Geiss, 1986; Chen et al., 2003; Landi et al., 2012). The
processes that lead to compositional variations occur in the solar atmosphere
itself, meaning that the amount of time spent in the corona will lead to
differences in compositional metrics, and plasma must stay in the corona long
enough (2-3 days) to experience these fractionation effects (Laming, 2015).
Therefore, plasma quickly escaping the corona on open field lines (such as
from CH structures) show more ‘photospheric’ like compositions in comparison
to plasma escaping from closed field lines or loop-like structures (Feldman &
Marsch, 1997; Laming, 2017). These plasma parcels would show an enhancement in
low first ionization potential (FIP) elements (high $\mathrm{Fe/O}$ ratio) and
enhanced ion ratios arising from the hotter source region (Geiss et al., 1995;
von Steiger et al., 2000).

The solar wind typically shows alpha particle (Helium; He) abundance ratios
($\mathrm{A_{He}}$) that are depleted compared with photospheric values
($\sim$8.4%, Asplund et al. (2021)) and are highly variable. Helium rich
periods are often associated with solar eruptions (Song et al., 2022; Feldman
et al., 2005; Johnson et al., 2024), streamer belt outflows, and other active
region structures (Kasper et al., 2016; Alterman et al., 2018; Alterman &
Kasper, 2019). There is some modulation of the abundance with the solar cycle
which could be due to variations in the structure of the solar wind source
regions throughout the solar cycle (Norton et al., 2023). Differences in
$\mathrm{A_{He}}$ can also be attributed to gravitational settling, another
process that shows solar cycle dependence (Rivera et al., 2022a). Therefore,
even though Helium is the highest FIP element, the ubiquitously observed
depletion of Helium within the ambient solar wind indicates that the
process(es) leading to its enhancement or depletion are likely different from
the FIP effect as described above (Johnson et al., 2024) and thus there is no
full picture to describe what we would expect in terms of alpha abundance
related to source region. Typically, $\mathrm{A_{He}}$ are expected to be
enhanced in plasma streaming from open field lines or CH-like structures,
however this does not always hold true (Ervin et al., 2024b).

In this study, we use Parker Solar Probe (Parker) observations within
40$\mathrm{R_{\odot}}$ from Encounters 4 to 14 to study the in situ
characteristics and source regions of the SASW in comparison with the FSW, as
the source region and characteristics of the FSW are well understood. We will
not make any definitive claims regarding the general source of the SASW, but
rather seek to highlight that they likely emerge from a variety of sources –
some similar to FSW, some different. In Section 3, we outline our data
selection and wind stream identification methods along with modeling methods
we use to identify the source regions of the SASW streams of interest
(additional details can be found in Appendix A). Section 4 discusses the in
situ and modeling parameters associated with the SASW and identified source
regions. We conclude in Section 5 with an overview of our results, the
limitations of this study, and future work necessary to fully understand the
source regions of the slow Alfvénic solar wind. In Appendix B we show
overviews of modeling results for specific streams, and in Appendix C discuss
uncertainty quantification on our modeling methods.

##  2 Data Overview

This study uses observations from within 40$\mathrm{R_{\odot}}$ during
Encounters 4 to 14 (E4 - 14) of Parker Solar Probe (Parker) spanning January
2020 to January 2023, providing a good overview of the solar wind at the inner
heliosphere during solar minimum and into the rising phase of the solar cycle.
We use near perihelion magnetic field measurements from the Electromagnetic
Fields Investigation (FIELDS; Bale et al. (2016)) fluxgate magnetometer and
partial plasma moments of alphas and protons from the ion Solar Probe ANalyzer
(SPAN-I; Livi et al. (2022)) aboard the ‘Solar Wind Electrons, Alphas, and
Protons’ (SWEAP; Kasper et al. (2016)) suite. SPAN-I measurements are
available starting in Encounter 4 which is the reason observations from E1 to
3 are not used such that we can maintain consistency throughout our study, and
use the native quality flags to mitigate field-of-view (FOV) issues. An
important note is that the SPAN-I absolute abundance measurements (number
density) is likely an underestimate of the total density as they are computed
from partial moments (Livi et al., 2022).

As the lower boundary photospheric magnetic field observation to our potential
field source surface (PFSS) modeling (described in Section 3.2), we use ADAPT-
GONG magnetograms. These are high resolution, full disk photospheric
magnetograms from the Global Oscillation Network Group (GONG; Harvey et al.
(1996)) with the Air Force Data Assimilative Photospheric Flux Transport
(ADAPT; Worden & Harvey (2000); Arge et al. (2010, 2011, 2013); Hickmann et
al. (2015)) model applied. To compare footpoints estimated from PFSS method,
we use EUV observations from the Atmospheric Imaging Assembly (AIA; Lemen et
al. (2012)) aboard the Solar Dynamics Observatory (SDO; Pesnell et al.
(2012)), which takes high resolution and high cadence, narrow band full disk
images of the solar atmosphere. We look at SDO/AIA observations of 193Å
allowing us to probe EUV emissions in the corona with a characteristic
$\log{T}$ of 6.3 (Lemen et al., 2012).

##  3 Methods

###  3.1 Stream Identification

All usable (good field of view) E4 - E14 data within 40$\mathrm{R_{\odot}}$
was compiled and analyzed based on certain parameters. The objective of the
method is to classify observed wind as SSW, SASW, or FSW. We can detect all
three wind types simultaneously because the designated parameters are mutually
exclusive such that each observation can belong only to a specific wind
category.

It is common practice to identify slow solar wind as streams with mean speeds
below a threshold value (typically 400 to 500 $\mathrm{km\ s^{-1}}$ depending
on the heliocentric distance and study) for a specified time period. In this
case, due to Parker being so close to the Sun, we modified the traditional
classification scheme to account for solar wind acceleration. Using
observations over more than a full solar cycle (2004 to 2024) from the Wind
spacecraft (Lin et al., 1995) at 1AU, we looked at the fraction of the
observed wind that would be considered classically fast. We then narrow this
window to just the time period of the Parker observations we look at (January
2020 to January 2023) finding that $\sim 20\%$ was above 500 $\mathrm{km\
s^{-1}}$ and $\sim 50\%$ above 400 $\mathrm{km\ s^{-1}}$. Appendix A shows an
overview of this method and how these percentage thresholds stay consistent
throughout time. We applied the categorization thresholds to Parker data
observed at different radial distances.

Binning by radial distance in bins of 10$\mathrm{R_{\odot}}$ (10-20
$\mathrm{R_{\odot}}$, 20-30 $\mathrm{R_{\odot}}$, and 30-40
$\mathrm{R_{\odot}}$) gave different thresholds for the fast versus slow solar
wind cutoff depending on the radial distance. Wind is classified as ‘slow’
below 391 $\mathrm{km\ s^{-1}}$ from 10 - 20 $\mathrm{R_{\odot}}$, 370
$\mathrm{km\ s^{-1}}$ from 20 - 30 $\mathrm{R_{\odot}}$, and 388 $\mathrm{km\
s^{-1}}$ from 30 - 40 $\mathrm{R_{\odot}}$, as seen in Figure 1. Applying
these new thresholds for each radial bin, rather than the traditional
classification, attempts to account for potential slow wind acceleration into
fast wind beyond the location of Parker.

Figure 1: Distribution functions of solar wind speed binned by heliocentric
distance. The dashed lines indicate different threshold percentages based on
observations of wind speeds at 1AU (see section 3.1) as applied to Parker. The
red, purple, and blue lines signify the uppermost 19%, 35%, and 51% of the
wind respectively where 19% is the 500 $\mathrm{km\ s^{-1}}$ cutoff at 1AU,
51% is the 400 $\mathrm{km\ s^{-1}}$ cutoff, and 35% falls in between. In our
data stream identification, we use the red line, or the fastest 19% of wind
measured from Parker to differentiate slow and fast solar winds. The
velocities associated with each dashed line are listed. Panel (a): All Parker
solar wind velocity data below 40 $\mathrm{R_{\odot}}$ for Encounters 4-14
with associated dashed lines. Panel (b) - (d): All Parker solar wind velocity
data for radial bins (b): 10-20 $\mathrm{R_{\odot}}$, (c): 20-30
$\mathrm{R_{\odot}}$ and (d): 30-40 $\mathrm{R_{\odot}}$ with the associated
thresholds.

In addition to categorizing the wind by speed, we further categorize the slow
wind into classically slow and slow Alfvénic wind based on the cross helicity
($\mathrm{\sigma_{C}}$). $\mathrm{\sigma_{C}}$ is generally used as a proxy
for the Alfvénicity of the plasma where higher cross helicity measurements
($\mathrm{\sigma_{C}}$ values of 1 or -1) are indicative of pure Alfvén waves
propagating parallel or antiparallel to the magnetic field.
$\mathrm{\sigma_{C}}$ is calculated via Equation 1 where $E^{\pm}$ is the
energy associated with the Elsässer variables:
$\mathbf{z}^{\pm}=\delta\mathbf{v}\mp\mathrm{sign}\langle
B_{r}\rangle\delta\mathbf{b}$ such that $\mathrm{sign}\langle B_{r}\rangle$ is
the averaged polarity of the magnetic field. $<\cdot\cdot\cdot>$ represents a
time average over a 60-minute non-overlapping time window which is based on
the correlation times of Parker magnetic field fluctuations (Parashar et al.,
2020; Chen et al., 2020) and captures the full spectral features over the
inertial range (Ervin et al., 2024).

$\sigma_{C}=\frac{<E^{+}>-<E^{-}>}{<E^{+}>+<E^{-}>}$ (1)

We define slow wind to be Alfvénic (SASW) if every $|\sigma_{C}|$ value over a
30-minute time window is above 0.7, and considered classically slow (SSW) if
it is below. This categorization method leads to three subcategories of wind
based on the wind speed and $\mathrm{\sigma_{C}}$ value. We identify streams
of interest as time intervals lasting at least 30 minutes that fall into one
of these categories for the entire stream. Due to the trajectory of Parker,
the streams will traverse different longitudinal/spatial distances depending
on the portion of the trajectory to which the stream corresponds.

###  3.2 Source Region Connection

We use a combination of ballistic propagation (Snyder & Neugebauer, 1966;
Nolte & Roelof, 1973; Badman et al., 2020; Macneil et al., 2022; Koukras et
al., 2022) and potential field source surface (PFSS) modeling to connect the
plasma observed at Parker to its estimated footpoint on the photosphere. The
PFSS model is an efficient method to model the global coronal magnetic field
out to an equipotential surface (source surface - $\mathrm{R_{ss}}$) where the
magnetic field is assumed to be purely radial. The model assumes a
magnetostatic ($\nabla\times\mathbf{B}=0$) corona, with a photospheric radial
magnetic field observation as the inner boundary (Schatten et al., 1969;
Altschuler & Newkirk, 1969) to reconstruct the field out to the
$\mathrm{R_{ss}}$. We use the open source sunkit-magex
111https://github.com/sunpy/sunkit-magex package (Stansby et al., 2020) to
reconstruct the coronal field out to a $\mathrm{R_{ss}}$ height of
2.5$\mathrm{R_{\odot}}$ (Hoeksema, 1984) with ADAPT-GONG magnetograms as the
inner boundary condition. We determine the best PFSS model for each encounter
based on matching the observed neutral line (HCS) crossings at Parker with the
modeled HCS from the PFSS instantiation (Badman et al., 2020; Ervin et al.,
2024b).

The PFSS model only reconstructs the magnetic field out to the source surface
(2.5$\mathrm{R_{\odot}}$), and thus we need another method to connect the
spacecraft trajectory which varies between 11$\mathrm{R_{\odot}}$ and
40$\mathrm{R_{\odot}}$ to the model outer boundary. Assuming a Parker spiral
and varied wind speed (the in situ $v_{R}$ measurement), we propagate the
spacecraft trajectory down to the $\mathrm{R_{ss}}$ height to connect our
observations with the model. This allows us to connect the plasma observed at
Parker with its estimated footpoint location at the photosphere and identify
source regions based on comparison with EUV images and other parameters.

In Appendix C we discuss model validation and sources of error in both the
ballistic propagation and PFSS model. We find that the error in the estimated
footpoints due to ballistic propagation methods is velocity dependent
(impacting the slower wind more) and is on the order of $1^{\circ}$. For the
PFSS modeling results, we find that the source surface height has the largest
impact on the resulting footpoints, however this can be optimized by comparing
modeled polarity with magnetic field observations. The choice of input
magnetogram leads to an error of $\sim 2^{\circ}$ when using magnetograms
within a few days from the optimal input parameter. Neugebauer et al. (2002)
showed that expected uncertainties in PFSS source region footpoints are $\sim
10^{\circ}$ or less in longitude and while the error on the PFSS estimated
footpoints is larger than for the ballistic propagation, the resulting source
region is unaffected when using input parameters optimized to the observations
leading to confidence in the results.

We use these modeling methods to closely examine 10 SASW streams and their
sources in addition to the overall in situ characteristics of slow Alfvénic
wind observed at Parker. We look at the source region and source
characteristics of 5 FSW streams for comparison, as it has been well
established that these streams emerge from CH regions and thus provide a good
source of comparison for our modeled SASW streams (McComas et al., 1998,
2008).

In this paper, when we discuss coronal holes, we are referring to cool, low
density regions of coronal plasma with rapidly expanding open field lines and
low magnetic activity levels (Cranmer, 2009). This manifests as relatively
dark regions in EUV observations and low photospheric magnetic field values.
When we refer to active regions (ARs), we are referencing regions of
relatively high magnetic activity in the corona associated with strong
photospheric magnetic fields in connection to bright loops in EUV (Weber et
al., 2023).

##  4 Discussion

###  4.1 In Situ Characteristics

As discussed in Section 1, the SASW shows high levels of Alfvénicity yet slow
wind speeds. Along with the $\mathrm{\sigma_{C}}$ calculation, we can also
determine the residual energy ($\mathrm{\sigma_{R}}$) or the difference
between the energy in velocity and magnetic field fluctuations, indicating
which one is dominant in the plasma. $\mathrm{\sigma_{R}}$ $>0$ is kinetic
energy dominant plasma and $\mathrm{\sigma_{R}}$ $<0$ is magnetic energy
dominant. $\mathrm{\sigma_{R}}$ is calculated via Equation 2 where
$<\cdot\cdot\cdot>$ represents a time average over a 60-minute non-overlapping
time window (see Section 3.1). The Elsässer variables ($\mathbf{z^{\pm}}$) and
their associated energies ($E^{\pm}$) are described in Section 3.1.

$\sigma_{R}=\frac{2<\mathbf{z}^{+}\cdot\mathbf{z}^{-}>}{<E^{+}>+<E^{-}>}$ (2)

Due to the relationship between $\mathrm{\sigma_{C}}$ and
$\mathrm{\sigma_{R}}$, we expect $\sigma_{C}^{2}+\sigma_{R}^{2}\leq 1$
(Bavassano et al., 1998) meaning these measurements (as shown in Figure 2) are
bounded by a circle. A comparison of the three panels, each for a different
wind categorization, shows the stark differences in the turbulence parameters
between the types of wind. From panel (a), it is clear that the SSW shows
dramatically different properties than the SASW (panel (b)) and FSW (panel
(c)). The SSW shows a large variance in $\mathrm{\sigma_{R}}$ values, with the
majority of the distribution at $\mathrm{\sigma_{R}}$ $<$ 0, indicating the
SSW is magnetically dominated and the $\mathrm{\sigma_{C}}$ distribution is
concentrated between 0.5 and 0.7. We expect the cross helicity to be more
strongly concentrated at $\mathrm{\sigma_{C}}$ $>$ 0, as the solar wind at
these heliocentric distances is dominated by outward propagating modes.

The SASW and FSW distributions look quite similar: $\mathrm{\sigma_{R}}$ $<0$
and $|\sigma_{C}|\sim 1$, meaning that SASW and FSW are both magnetic energy
dominant and the turbulence is strongly imbalanced: i.e. the energy fluxes in
the inward and outward propagating wave modes ($E^{\pm}$) differ such that
$\mathrm{\sigma_{C}}$ $\neq 0$ (Sioulas et al., 2024a). The impact of
imbalance on higher-order turbulence statistics is an open area of
investigation. Recent work by Shi et al. (2023); Sioulas et al. (2024a, b) and
others have looked at the scaling of alignment angles, spectral indices, and
the impact on the principles of ‘critical balance’ (Goldreich & Sridhar, 1995,
1997) and ‘scale-dependent dynamic alignment’ (Boldyrev, 2006; Chandran et
al., 2015; Mallet & Schekochihin, 2017) based on the level of imbalance.

The turbulence and energy properties of the SASW are far more similar to the
FSW than the SSW, potentially indicating a similar source region and/or
acceleration mechanism as the FSW (D’Amicis & Bruno, 2015; D’Amicis et al.,
2018; Stansby et al., 2020b; Ervin et al., 2024b).

Figure 2: All usable E4 to E14 data (see Section 3.1) is compiled into
normalized histograms of cross helicity ($\mathrm{\sigma_{C}}$) against the
residual energy ($\mathrm{\sigma_{R}}$) to showcase the identification method.
The criteria for categorization of ‘high’ Alfvénicity and the radially
dependent velocity thresholding method are described in Section 3.1. Panels
(a), (b), and (c) plot the designated data for SSW, SASW, and FSW
respectively.

Classifying the solar wind into these categories allows us to study the
sources and compositional metrics of these wind types. The alpha particle
(Helium) abundance is the ratio of alpha particle and proton densities
($\mathrm{A_{He}=N_{\alpha}/N_{p}}$). Elemental composition is often used as a
tracer of source region due to the conservation of plasma composition
throughout the solar wind’s radial evolution. Therefore, this can provide a
helpful metric to compare between solar wind types in association with modeled
source region mapping results. Generally, alpha particle abundances are shown
to be solar cycle dependent in slow solar wind, ranging between
$\mathrm{A_{He}}$$\sim 1-4\%$, while abundances become less and less solar
cycle dependent with increasing solar wind speed, remaining consistently
around $\mathrm{A_{He}}$$\sim 4\%$ (Kasper et al., 2007). In particular, He
abundances exhibit the largest difference during periods around solar
minimum/rising phase, where faster speed wind is observed to contain
$\mathrm{A_{He}}$$\sim 4\%$ while the slowest speed observed near the Earth
contains 1%, making solar wind types the most distinguishable during this
phase of the solar cycle. In general, alpha abundances are depleted compared
with photospheric values, however, exhibit changes across solar wind values
and thus can be used for analysis. Therefore, in this study that focuses on
solar minimum and the rising phase, high $\mathrm{A_{He}}$ will likely be
associated with open field line or CH-like structures where fast speed wind
emanates from, however this is not always the case (see Section 1).

Figure 3 shows the proton and alpha particle composition for each wind type,
where panel (a) looks at the SSW, panel (b) the SASW, and panel (c) the FSW.
We include dashed lines at $\mathrm{A_{He}}$ = 0.015 and 0.045 to indicate the
‘low’ and ‘high’ abundance thresholds (Kasper et al., 2007, 2012) and to guide
the eye.

We see that the $\mathrm{A_{He}}$ for the SSW and SASW rarely cross the
typical ‘high abundance’ threshold of 0.045 and that the SASW distribution is
larger concentrated below the ‘low abundance’ boundary of 0.015. The SSW shows
both intermediate and low alpha particle abundance. The FSW distribution
clusters around the ‘high abundance’ threshold of 0.045 (as to be expected
from CH wind), with some anomalous fast wind showing lower alpha densities
than expected.

Figure 3: All usable E4 to E14 data (see Section 3.1) is compiled into these
normalized histograms of alpha particle density ($N_{\alpha}$) against proton
density ($N_{p}$), each scaled by $R^{2}$. Particle measurements from the
SPAN-I instrument aboard Parker/SWEAP show the alpha-to-proton abundance
ratios. The dashed lines indicate the typical ‘high helium abundance’
threshold of 0.045 and the ‘low abundance’ boundary of 0.015 (Kasper et al.,
2007, 2012). Panels (a), (b), and (c) plot the designated data for SSW, SASW,
and FSW respectively.

While the categorization of the slow wind by cross helicity is useful in
creating to separate populations from potentially different sources, including
compositional characteristics in categorization schemes would be a useful
method to better categorize the wind by its source region. Additional
observations of heavy ions and molecular composition would aid in this process
allowing for better connection between in situ observations and sources, as
our understanding of alpha particle abundance and its relation to source
region is still convoluted and dependent on phase in the solar cycle.

The data highlighted above provides a strong rationale to study this
additional categorization of the SASW due to its unique properties in energy
and elemental composition in comparison to more classical fast and slow wind.
The SASW is seen to have similar properties to the FSW in terms of
$\mathrm{\sigma_{C}}$ and $\mathrm{\sigma_{R}}$, supporting the evidence that
at least some of SASW emerges from similar structures to the FSW. However, it
is noteworthy that the observed alpha abundance for the SASW is much lower
than that of the FSW and the observed proton abundance is larger than the FSW
(indicating additional mass flux), implying that some of this plasma likely
has a unique source region or acceleration mechanisms, warranting additional
study.

###  4.2 Source Region Characteristics

We use the PFSS and ballistic propagation methods for each Encounter to
compare results produced from the ‘estimated’ footpoints for the SASW to the
types of wind. We can calculate the expansion factor, photospheric magnetic
field value at the footpoint, and brightness in EUV. Due to the inherent
uncertainties in solar wind source modeling, doing this for one stream can be
inconclusive and therefore we look at a variety of streams from E4 to E14 to
have a more representative look at the potential sources of the SASW.

Based on the footpoint estimations, we can determine $B_{0}$ or the
photospheric magnetic field value at the estimated point of plasma emergence
by sampling GONG magnetograms at the footpoint locations. Additionally, we can
calculate the magnetic expansion factor ($f_{ss}$) between the photosphere
($R_{0}=$ 1.0$\mathrm{R_{\odot}}$) and another radial distance ($R_{1}$) based
on Wang & Sheeley (1990, 1997):

$f_{s}=\left(\frac{R_{0}}{R_{1}}\right)^{2}\frac{B_{R}(R_{0},\lambda_{0},\phi_{0})}{B_{R}(R_{1},\lambda_{1},\phi_{1})}$
(3)

such that expansion factor describes the divergence of the flux tube from
spherical expansion ($f_{s}=1$) meaning values of $f_{s}$ greater than 1
indicate a rapidly diverging flux tube (Wang & Sheeley, 1997). In this case,
$R_{1}$ = $\mathrm{R_{ss}}$, meaning our expansion factor is a measure of the
expansion to the source surface: $f_{ss}$, which is the quantity previously
correlation with heliospheric wind speed (Wang & Sheeley, 1990; Riley &
Luhmann, 2012; Riley et al., 2015).

In Tables 1 and 2, we show an overview of the SASW and FSW streams we model
and some of their associated characteristics.

Time Period | $\mathrm{\langle v_{r}\rangle}$ | $\mathrm{\langle|\sigma_{C}|\rangle}$ | $\mathrm{\langle M_{A}\rangle}$ | $\mathrm{\langle B_{r}R^{2}\rangle}$ | $\mathrm{\langle N_{p}R^{2}\rangle}$ | $\mathrm{\langle B_{0}\rangle}$ | $\mathrm{\langle f_{ss}\rangle}$ | $\mathrm{\langle I\rangle}$
---|---|---|---|---|---|---|---|---
| [$\mathrm{km\ s^{-1}}$] |  |  | [nT AU2] | [cm-3] | [G] |  |
2020-01-28 18:00:00 to 2020-01-29 01:00:00 (E4) | 284 | 0.86 | 2.06 | -1.95 | 7.47 | -4.27 | 236 | 30.9
2020-06-06 06:00:00 to 2020-06-06 09:00:00 (E5) | 306 | 0.87 | 2.19 | -2.03 | 6.77 | -1.55 | 31.7 | 7.68
2020-06-09 03:00:00 to 2020-06-09 22:00:00 (E5) | 217 | -0.92 | 2.45 | 2.01 | 12.7 | 2.28 | 27.5 | 11.4
2020-09-27 12:00:00 to 2020-09-27 16:00:00 (E6) | 306 | -0.92 | 1.51 | -2.12 | 7.54 | -3.13 | 48.2 | 10.3
2021-01-18 18:00:00 to 2021-01-19 06:00:00 (E7) | 231 | 0.86 | 2.29 | -2.58 | 4.20 | -5.86 | 27.7 | 23.6
2021-04-30 00:00:00 to 2021-04-30 05:00:00 (E8) | 155 | 0.86 | 1.23 | -1.99 | 20.6 | 37.8 | 105.7 | 395
2021-04-30 10:00:00 to 2021-05-01 00:00:00 (E8) | 192 | -0.95 | 1.70 | -1.99 | 18.7 | 3.43 | 11.4 | 96.5
2022-12-10 18:00:00 to 2022-12-10 19:00:00 (E14) | 187 | -0.92 | 0.94 | -2.65 | 17.9 | -118 | 354 | 64.9
2022-12-10 20:30:00 to 2022-12-10 22:00:00 (E14) | 178 | -0.92 | 0.79 | -2.81 | 16.7 | -146 | 4798 | 596
2022-12-12 12:00:00 to 2022-12-12 16:00:00 (E14) | 240 | -0.90 | 1.36 | 2.56 | 16.6 | -16.8 | 39 | 316
Table 1: Overview of the 10 SASW streams identified and modeled in this study. The $\langle\cdot\cdot\cdot\rangle$ refers to an average over these parameters for the entire stream. $\mathrm{v_{r}}$, $\mathrm{\sigma_{C}}$, $\mathrm{M_{A}}$, $\mathrm{B_{r}R^{2}}$ and $\mathrm{N_{p}R^{2}}$ are parameters derived from in situ Parker measurements, while $\mathrm{B_{0}}$, $\mathrm{f_{ss}}$, and $\mathrm{I}$ are determined from the model estimated footpoints of the streams. $\mathrm{B_{0}}$ is the photospheric footpoint field strength, $\mathrm{f_{ss}}$ is the magnetic expansion factor as defined by Equation 3, and $\mathrm{I}$ is the intensity of the footpoint from the corresponding AIA 193Å image. Time Period | $\mathrm{\langle v_{r}\rangle}$ | $\mathrm{\langle|\sigma_{C}|\rangle}$ | $\mathrm{\langle M_{A}\rangle}$ | $\mathrm{\langle B_{r}R^{2}\rangle}$ | $\mathrm{\langle N_{p}R^{2}\rangle}$ | $\mathrm{\langle B_{0}\rangle}$ | $\mathrm{\langle f_{ss}\rangle}$ | $\mathrm{\langle I\rangle}$
---|---|---|---|---|---|---|---|---
| [ $\mathrm{km\ s^{-1}}$] |  |  | [nT AU2] | [cm-3] | [G] |  |
2020-01-27 04:55:00 to 2020-01-27 05:15:00 (E4) | 412 | 0.86 | 2.30 | -2.18 | 3.78 | -5.43 | 34.6 | 14.5
2021-04-27 01:00:00 to 2021-04-27 04:00:00 (E8) | 436 | 0.86 | 1.54 | -2.51 | 2.70 | -15.1 | 75.5 | 81.7
2021-04-27 06:00:00 to 2021-04-27 08:30:00 (E8) | 443 | 0.85 | 1.67 | -2.45 | 3.25 | -15.0 | 75.8 | 88.6
2021-11-20 05:30:00 to 2021-11-20 10:30:00 (E10) | 563 | 0.88 | 1.48 | -2.10 | 2.91 | -12.9 | 34.4 | 34.8
2022-12-15 21:15:00 to 2022-12-15 22:15:00 (E14) | 473 | -0.80 | 2.21 | 3.47 | 3.36 | 17.0 | 15.9 | 126.7
Table 2: Overview of the 5 FSW streams identified and modeled in this study.
The $\langle\cdot\cdot\cdot\rangle$ refers to an average over these parameters
for the entire stream. $\mathrm{v_{r}}$, $\mathrm{\sigma_{C}}$,
$\mathrm{M_{A}}$, $\mathrm{B_{r}R^{2}}$ and $\mathrm{N_{p}R^{2}}$ are
parameters derived from in situ Parker measurements, while $\mathrm{B_{0}}$,
$\mathrm{f_{ss}}$, and $\mathrm{I}$ are determined from the model estimated
footpoints of the streams. $\mathrm{B_{0}}$ is the photospheric footpoint
field strength, $\mathrm{f_{ss}}$ is the magnetic expansion factor as defined
by Equation 3, and $\mathrm{I}$ is the intensity of the footpoint from the
corresponding AIA 193Å image.

The footpoint field strength can be used to differentiate between CH and non-
CH regions. Stansby et al. (2021) studied the contribution of active regions
to the solar wind over four solar cycles using GONG magnetograms (the same
magnetograms used in this study). They set a lower limit on the field strength
of ARs by looking at the maximum magnetic field strength outside of AR
latitudes ($\pm$30° in the corona and $\pm$60° in the solar wind), finding it
to be 30G for GONG, well above the established noise level of 3G (Clark et
al., 2003). In Panel (a) of Figure 4, we look at the photospheric magnetic
field strength at the footpoints for wind identified as fast and slow Alfvénic
as described in Section 3.1. Using these methods, Ervin et al. (2024b, 2024)
looked at wind streams observed at Parker finding CH wind with
$\mathrm{B_{0}}$ $\sim$ 5-10G and AR wind with footpoint strengths $>$ 30G
reaching $\sim$ 73G. Similarly, Wang & Sheeley (2003) found that near solar
maximum, slow wind streams emerge from small sheared regions near open field
lines with high expansion factor ($f_{ss}>10$) and high footpoint field
strength ($B_{0}>$ 30G), while the fast wind streams come from regions of low
expansion factor ($f_{ss}\sim 5$) and low photospheric fields ($B_{0}\sim
5$G).

We find that the FSW streams show footpoint field strengths well below the 30G
CH threshold, as expected. The overall distribution of modeled SASW streams
also show footpoint field strengths below 30G, however when we look at the
average values across individual streams (Table 1), we find that there are
some streams where the average value exceeds (sometimes even dramatically)
this threshold. We then further sub-divide our SASW streams into CH-like
streams ($\langle\mathrm{B_{0}}\rangle$ below 30G) and non-CH streams
($\langle\mathrm{B_{0}}\rangle$ above 30G). With this reclassification, we now
see a dramatic difference in the overall spread in the photospheric field
strength, specifically the three ‘non-CH’ streams show $\mathrm{B_{0}}$ values
significantly higher than the CH threshold. The statistical separation of the
in situ data (which is independent from our modeling results) bolsters
confidence that the source mapping provides meaningful information, and
indicates that there might be multiple source regions for the SASW, some
similar to FSW sources (CHs and their boundaries) and some different.

Figure 4: Overview of parameters determined from PFSS modeling and the
associated estimated footpoints for the FSW. SASW, and the CH-like and non-CH
SASW sub-categories. The boxplot shows the inner quartile range (25 - 75%)
percentile and the solid line shows the median value. The dashed vertical
lines show the mean of each parameter for the type of wind stream. Panels (a),
(b), and (c) show the photospheric footpoint field strength
($\mathrm{B_{0}}$), intensity at the footpoint from AIA 193Å images, and
expansion factor based on Equation 3 respectively.

Identical to our methods of sampling the GONG magnetograms at the estimated
footpoint to determine $\mathrm{B_{0}}$, we can sample EUV observations
(SDO/AIA 193Å images) at these same footpoints to extract ‘intensity’ values.
Brightness in EUV channels is dependent on the electron temperature and
density, therefore hotter/denser ARs are brighter and cooler/tenuous CH
structures are darker. We choose EUV images for comparison based on the
estimated time the plasma left the photosphere which is determined based on
the speed of the stream of interest and position of Parker. In Figure 5, we
compare EUV intensity at the estimated footpoints of the 10 SASW streams we
studied in depth, with the distribution of intensity values from a variety of
AIA images corresponding to the two weeks around each of the studied SASW
streams to give an overview of ‘typical’ distributions of intensity values. We
find that the distribution of intensity values typically associated with SASW
streams falls on the ‘darker’ (cooler) end of the distribution when compared
with intensity values across many AIA images. Additionally, from Panel (b) of
Figure 4, we see that the non-CH SASW shows much higher intensity values in
comparison with the CH-like and FSW indicating a non-CH source.

Figure 5: Normalized histograms comparing intensity values from many AIA
images with intensity values sampled at the footpoints of the 10 identified
and modeled SASW streams. The AIA images chosen are images at a 24-hour
cadence for two weeks around each observation.

From the PFSS method, we can also calculate the magnetic expansion factor,
where a larger expansion factor implies more rapid divergence from spherical
expansion ($f_{ss}=1$). As discussed in the introduction, we would expect
higher magnetic expansion factors from slow wind emerging from the same
regions as fast wind, as rapid divergence of the flux tube leads to a higher
critical point and thus the majority of the heating occurs below the
transition to supersonic wind speeds (Leer & Holzer, 1980). In Panel (c) of
Figure 4, we find that in general the SASW has a higher expansion factor than
the FSW. With our additional classification into CH-like and non-CH SASW, we
find that the non-CH SASW has expansion factors an order of magnitude larger
than the CH-like SASW and FSW. As shown in Figure 6, the non-CH wind has
significantly larger mass flux which when coupled with the high expansion
indicating a rapidly diverging field with a higher critical point, means more
heating below the critical point leading to slower wind speeds. The same can
be said for th CH-like SASW with its slightly higher mass flux and expansion,
indicating that this is likely wind emerging from an overexpanded open field
line in a CH-like region with additional heating below the critical point
leading to slower wind speeds, but from the same structures as the FSW.

While anti-correlation between expansion factor and wind speed is expected
(Wang & Sheeley, 1990) and informs many current solar wind models such as the
Wang-Sheeley-Arge (WSA) Model (Arge & Pizzo, 2000; Arge et al., 2003, 2004)
there is not a one-to-one correlation between speed and $\mathrm{f_{ss}}$.
Other models, such as the distance from the coronal hole boundary (DCHB) model
(Riley et al., 2015) depend on the angular distance from a CH boundary to
determine the solar wind speed, rather than the expansion factor (Riley et
al., 2001). This indicates that our understanding of the expansion and
acceleration processes in the solar wind are incomplete, and relying solely on
the expansion factor to infer a final wind speed is not a fully accurate
description of the system.

Recent work by Yardley et al. (2024) combined spectroscopic observations with
in situ measurements of plasma parameters and composition to find the
emergence of wind streams from an AR-CH complex with an over-expanded magnetic
field. They claim that coronal plasma trapped within closed loops can be
released along open fan loops via interchange reconnection. Our observations
of high expansion factors associated with high EUV intensity and strong
footpoint magnetic field strength of these ‘non-CH’ streams alongside the long
lived fan structures seen in EUV observations supports this idea (Fisk, 2003).
This would allow for plasma with non-CH composition to be released from
coronal loop like structures after reconnection with open field lines leading
to in situ composition observations different from the FSW. If we had
measurements of heavy ion ratios and FIP bias from Parker, we would expect to
see enhanced heavy ion ratios ($\mathrm{O^{7+}/O^{6+}}$,
$\mathrm{C^{6+}/C^{4+}}$) and $\mathrm{Fe/O}$ ratios above typical
photospheric values.

In Section 4.1, we looked at the overall distribution of proton and alpha
particles from Parker observations. Now we will look at the composition of the
modeled FSW and SASW streams in more detail to compare in situ metrics with
potential sources. In Figure 6, we show an overview of the scaled proton
density ($\mathrm{N_{p}R^{2}}$), alpha particle abundance ($\mathrm{A_{He}}$ =
$N_{p}/N_{\alpha}$), and normalized differential streaming speed
($\mathrm{\Delta v_{\alpha p}}$ / $\mathrm{v_{A}}$) where $\mathrm{\Delta
v_{\alpha p}}$$\mathrm{=(v_{\alpha}-v_{p})/\cos{\theta}}$
($\cos{\theta}=|B_{R}/B|$ to account for magnetic polarity). We find that the
FSW streams have significantly lower proton densities and relatively higher
$\mathrm{A_{He}}$ than the SASW. The CH-like SASW shows a large range in
proton density and lower alpha particle abundance than the non-CH stream,
however both have mean values that fall within the ‘intermediate’ abundance
range (0.015 to 0.045 based on Kasper et al. (2007, 2012)). This is similar to
results for SASW previously observed at Parker by Huang et al. (2020); Ervin
et al. (2024b); Rivera et al. (2024) and others, contributing to the confusion
over source region of the SASW as there is not one abundance level that
corresponds to this wind type.

If we assume a frozen-in magnetic field, mass will be conserved along a flux
tube allowing for calculation of the proton mass density and energy flux at
the coronal base (Wang & Sheeley, 2003). The proton mass density $n_{0}v_{0}$
is calculated from the photospheric footpoint field strength determined from
the modeling alongside in situ parameters:
$n_{0}v_{0}=(B_{0}/B_{r})N_{P}v_{P}$. In Figure 6, we show the calculated
proton mass density, and find that the non-CH wind shows dramatically higher
mass flux than the CH-like SASW and FSW (similar to the results from Wang &
Sheeley (2003)). Higher mass flux is indicative of more heating below the
critical point, which is expected to produce wind with slower speeds (Wang et
al., 2012).

Figure 6: Box plot overviews of compositional parameters for the 10 SASW and 5
FSW streams we modeled. The dashed vertical lines indicate the mean for the
distribution with the corresponding color and the solid line shows the median.
Panel (a): Scaled proton density from SWEAP/SPAN-I. Panel (b): Proton mass
flux ($n_{0}v_{0}=(B_{0}/B_{r})N_{P}v_{P}$) calculated from in situ
observations and the photospheric footpoint field strength from modeling
results. Panel (c): Alpha abundance ratio ($\mathrm{A_{He}}$) using alpha and
proton measurements from SWEAP/SPAN-I. The dashed black lines indicate the
high (0.045) and low (0.015) $\mathrm{A_{He}}$ thresholds (Kasper et al.,
2007, 2012). Panel (d): Normalized differential streaming speed
($\mathrm{\Delta v_{\alpha p}}$ / $\mathrm{v_{A}}$).

In Figure 6 Panel (d), we show the normalized differential streaming speed
($\mathrm{\Delta v_{\alpha p}}$ / $\mathrm{v_{A}}$) and see that the FSW
streams show much higher differential speeds. Mostafavi et al. (2022) showed
correlation between $\mathrm{\Delta v_{\alpha p}}$ and $\mathrm{v_{sw}}$ and
we note that the CH-like SASW has higher differential speeds than the non-CH
SASW. This could point to a similar mechanism of preferential acceleration of
alpha particles between the FSW and CH-like SASW which would follow from these
streams having similar sources.

##  5 Conclusion

Through studying the in situ characteristics and parameters derived from
modeling the footpoints of slow Alfvénic wind streams, we find that some (if
not many) of these streams originate from coronal holes and their boundary
regions. These streams are characterized by high levels of Alfvénicity, slow
wind speeds, and intermediate alpha particle abundance in situ. From modeling
we find they have weak footpoint field strength (below 10G in most cases),
relatively large expansion factors, and low intensity in EUV (associated with
cold temperatures). These streams show higher differential speeds indicating
preferential acceleration of alpha particles.

However, we find another class of SASW streams for which identifying the exact
source likely requires additional study. These streams show high footpoint
field strength (up to 100s G), even larger expansion factors, and high
intensity in EUV. Their alpha particle abundance is relatively low and they
are associated with incredibly low differential speeds. When compared with EUV
observations, these wind streams look to be perhaps emerging from the
periphery of active regions or other closed loop structures. These non-CH like
streams might emerge from closed loop regions through interchange
reconnection, however additional work using composition metrics and other
observations is required for conclusive results.

While this work provides an overview of some slow Alfvénic solar wind streams
observed by Parker, their modeled sources and associated in situ parameters,
there are many caveats that must be considered when coming to conclusions
about the true source of the SASW due to the complexity associated with
modeling its origins. In this work, we use the potential field source surface
(PFSS) combined with ballistic propagation to estimate the footpoints
associated with wind observed in situ by Parker. This modeling method makes
huge (potentially unrealistic) assumptions about the magnetic topology of the
corona. Additionally, these modeling methods can only trace to sources
connected to field lines that are topologically ‘open’ at the source surface,
meaning that connecting to wind from the periphery of closed loops, or
streamer blobs is difficult with both aspects likely requiring time dependent
modeling. While PFSS can be validated, it is important to remember that these
are all ‘estimated’ footpoints and additional work such as looking at
elemental and charge state composition, and comparison with other modeling
methods such as magnetohydrodynamic (MHD) models to better capture the more
complicated physics in the corona would be useful to have additional
confidence in tracing of sources of the slow wind. However, we note that the
statistical approach we take here reveals robust trends in source region
properties. In particular, it is non-trivial that the properties inferred from
modeling and sampling remote observations are systematically distinct when
filtering wind of the same speed by cross helicity, an in situ property.

Solar Orbiter, through the Heavy Ion Sensor (HIS; Livi et al. (2023)) will
allow us to study the compositional characteristics of the wind in situ and
compare with its source region using Spectral Imaging of the Coronal
Environment (SPICE; SPICE Consortium et al. (2020)) instrument. Studies using
the combination of these instruments, alongside the other remote sensing and
in situ instrument aboard Solar Orbiter will support in our understanding of
the characteristics associated with wind emerging from various sources, but
are likely not enough.

To understand the full scope of the source, formation, evolution,
acceleration, and heating mechanisms at work in the solar wind we require
multi-point in situ observations at different radial and longitudinal
separations with complementary remote sensing observations of the wind’s
coronal origin. While existing fleets of heliophysics spacecraft including
Parker, Solar Orbiter, SDO, Hinode, STEREO, and others provide useful in situ
and remote sensing observations of varying wind types, the field still
struggles to connect remote and in situ observations because inter-spacecraft
coordination is limited and comparing in situ measurements and remote
observations of the Sun is difficult. Remote and in situ observations can be
better connected through multi-point compositional observations alongside the
typical plasma parameters measured throughout the heliosphere that offer a
robust method for model validation when connecting the solar wind to its
source region at the Sun. Remote observations of solar wind source can provide
the coronal temperature, density, outflow speeds, heavy ion composition, and
magnetic field properties that can be linked to situ measurements of the solar
wind, providing critical constraints to formation and acceleration by
interchange reconnection or other mechanisms (Rivera et al., 2022b). Large
scale studies using these sorts of observations will allow us to better probe
the source regions of the slow wind and understand the acceleration
mechanism(s) at work.

##  6 Acknowledgements

The FIELDS and SWEAP experiments on the Parker spacecraft was designed and
developed under NASA contract NNN06AA01C.

We acknowledge the NASA Parker Solar Probe Mission and the SWEAP team led by
J. Kasper for use of data. J. H. acknowledge support of NASA grant
80NSSC23K0737.

The authors would like to thank the individuals and institutions who
contributed to the Wind mission. Wind data come from SPDF/CDAWeb.

This work utilizes data produced collaboratively between Air Force Research
Laboratory (AFRL) & the National Solar Observatory (NSO). The ADAPT model
development is supported by AFRL. The input data utilized by ADAPT is obtained
by NSO/NISP (NSO Integrated Synoptic Program). NSO is operated by the
Association of Universities for Research in Astronomy (AURA), Inc., under a
cooperative agreement with the National Science Foundation (NSF).

This work utilizes GONG data obtained by the NSO Integrated Synoptic Program,
managed by the National Solar Observatory, which is operated by the
Association of Universities for Research in Astronomy (AURA), Inc. under a
cooperative agreement with the National Science Foundation and with
contribution from the National Oceanic and Atmospheric Administration. The
GONG network of instruments is hosted by the Big Bear Solar Observatory, High
Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory,
Instituto de Astrofísica de Canarias, and Cerro Tololo Interamerican
Observatory.

SDO/AIA and SDO/HMI data is courtesy of NASA/SDO and the AIA, EVE, and HMI
science teams.

This research used version 4.1.6 of the SunPy open source software package
(Community et al., 2020), and made use of HelioPy, a community-developed
Python package for space physics (Stansby et al., 2022). All code to replicate
figures can be found at Ervin et al. (2024a).

##  Appendix A Velocity Categorization

Using observations at 1AU from the Wind 3D Plasma Analyzer (3DP; Lin et al.
(1995)) at 1AU, we look at the distribution of velocities over a full solar
cycle and for just the time period of interest in this study (January 2020 to
December 2022) to look at the fraction of wind at 1AU that is considered
classically ‘fast’. We are interested in doing this to provide a more
quantitative cutoff for solar wind speed to differentiate between fast and
slow wind at closer heliocentric distances (see Section 3.1).

Figure 7 shows an overview of the distribution function of solar wind velocity
measured by Wind. In panel (a), we show a timeseries of the observations
spanning from January 2020 to January 2023 (the time period of Parker
Encounters 4 to 14). In panels (b), (c), and (d) we look at the distribution
functions over different time periods and the percentage of the wind that
falls above the 500$\mathrm{km\ s^{-1}}$ (red) and 400$\mathrm{km\ s^{-1}}$
(blue) thresholds. Panel (b) shows the last 20 years of observations by Wind,
we see that a bit over half of the wind is above 400$\mathrm{km\ s^{-1}}$ and
$\sim 22\%$ is above 500$\mathrm{km\ s^{-1}}$. Looking at just the
observations during Solar Cycle 24 (Jan 2008 to December 2019), $\sim 20\%$ is
above 500$\mathrm{km\ s^{-1}}$ and $\sim 52\%$ is above 400$\mathrm{km\
s^{-1}}$. Looking at just the period of the Parker observations used in this
study (panel (d)), we see that about $\sim$20% of the wind showed speeds above
500 $\mathrm{km\ s^{-1}}$ and $\sim$50% above 400 $\mathrm{km\ s^{-1}}$. These
are the percentage values that we use for our thresholding at described in
Section 3.1. Despite some variance in the solar cycle, these thresholds remain
consistent over time giving us confidence in these threshold methods.

Figure 7: Overview of solar wind velocity observations from the Wind 3DP
instrument from 2004 to 2024. Panel (a): Time series of solar wind velocity
from Wind at 1AU during the time period of this study. Panel (b): Distribution
of velocity measurements from 2004 to 2024 from Wind. Panel (c): Distribution
of velocity measurements during Solar Cycle 24 (January 2008 to December
2019). Panel (d): Distribution of velocity measurements from 2020 to 2023,
covering the time period in this study. In panels (b) to (d), the dashed red
and blue lines indicate the 500 $\mathrm{km\ s^{-1}}$ and 400 $\mathrm{km\
s^{-1}}$ speed cutoffs respectively. The legend shows the percentage of
observations that fall above that threshold for each period.

##  Appendix B Stream Overviews

In this section, we show an overview of the basic plasma parameters and
estimated footpoint mapping from PFSS for the main streams studied in this
paper. The AIA images used for comparison with the estimated footpoints are
chosen based on an estimation of the emergence time of the stream using
ballistic mapping of the Parker trajectory with the measured solar wind speed.

###  B.1 Slow Alfvénic Streams

An overview of the plasma parameters for each of the 10 SASW streams we more
closely examined in this study. Each Figure shows the solar wind speed
($v_{R}$), absolute cross helicity ($|\sigma_{C}|$), scaled radial magnetic
field ($B_{R}R^{2}$), and scaled proton density ($N_{P}R^{2}$). The right
panel shows a comparison of the estimated footpoints with EUV observations
from SDO/AIA.

Figure 8 shows an overview for the SASW stream spanning from 2020-01-28
18:00:00 to 2020-01-29 01:00:00 during Encounter Four. The wind here is seen
to emerge from the edge of a coronal at mid-latitudes. The scaled proton
density is slightly enhanced over typical 1AU values (5$\mathrm{cm^{-3}}$).

Figure 8: Comparison of in situ characteristics and footpoint estimates for
the SASW stream spanning from 2020-01-28 18:00:00 to 2020-01-29 01:00:00
during Encounter Four.

Figure 9 shows an overview for the SASW stream spanning from 2020-06-06
06:00:00 to 2020-06-06 09:00:00 during Encounter Five. The wind here is
emerges from a CH edge / small mid-latitude CH. The scaled proton density is
slightly enhanced over typical 1AU values (5$\mathrm{cm^{-3}}$).

Figure 9: Comparison of in situ characteristics and footpoint estimates for
the SASW stream spanning from 2020-06-06 06:00:00 to 2020-06-06 09:00:00
during Encounter Five.

Figure 10 shows an overview for the SASW stream spanning from 2020-06-09
10:00:00 to 2020-06-09 22:00:00 during Encounter Five. The wind here is seen
to emerge from a small, mid-latitude CH. The scaled proton density is enhanced
over typical 1AU values (5$\mathrm{cm^{-3}}$).

Figure 10: Comparison of in situ characteristics and footpoint estimates for
the SASW stream spanning from 2020-06-09 10:00:00 to 2020-06-09 22:00:00
during Encounter Five.

Figure 11 shows an overview for the SASW stream spanning from 2020-09-27
12:00:00 to 2020-09-27 16:00:00 during Encounter Six. The wind here is seen to
emerge from the edge of a coronal at mid-latitudes. The scaled proton density
is slightly enhanced over typical 1AU values (5$\mathrm{cm^{-3}}$).

Figure 11: Comparison of in situ characteristics and footpoint estimates for
the SASW stream spanning from 2020-09-27 12:00:00 to 2020-09-27 16:00:00
during Encounter Six.

Figure 12 shows an overview for the SASW stream spanning from 2021-01-18
18:00:00 to 2021-01-19 06:00:00 during Encounter Seven. The wind here is seen
to emerge from the edge of a coronal at mid-latitudes, with the footpoints
outlining the edge of an observed CH. The scaled proton density is enhanced
over typical 1AU values (5$\mathrm{cm^{-3}}$).

Figure 12: Comparison of in situ characteristics and footpoint estimates for
the SASW stream spanning from 2021-01-18 18:00:00 to 2021-01-19 06:00:00
during Encounter Seven.

Figure 13 shows an overview for the SASW stream spanning from 2021-04-30
00:00:00 to 2021-04-30 05:00:00 during Encounter Eight. This wind stream is
very smooth and seems to emerge from the periphery of an active region, with
an incredibly incompressible magnetic field, smooth wind speed and enhanced
proton density.

Figure 13: Comparison of in situ characteristics and footpoint estimates for
the SASW stream spanning from 2021-04-30 00:00:00 to 2021-04-30 05:00:00
during Encounter Eight.

Figure 14 shows an overview for the SASW stream spanning from 2021-04-30
10:00:00 to 2021-05-01 00:00:00 during Encounter Eight. This wind streams
emerges from the peripheries of a coronal hole and shows enhanced proton
density.

Figure 14: Comparison of in situ characteristics and footpoint estimates for
the SASW stream spanning from 2021-04-30 10:00:00 to 2021-05-01 00:00:00
during Encounter Eight.

Figure 15 shows an overview for the SASW stream spanning from 2022-12-10
18:00:00 to 2022-12-10 19:00:00 during Encounter Fourteen. This wind streams
shows a large amount of structure, indicative of non-CH wind. It seems to
emerge from the edges of a loop like structure at active latitudes and shows
structure and enhancement in the proton density.

Figure 15: Comparison of in situ characteristics and footpoint estimates for
the SASW stream spanning from 2022-12-10 18:00:00 to 2022-12-10 19:00:00
during Encounter Fourteen.

Figure 16 for the SASW stream spanning from 2022-12-10 20:30:00 to 2022-12-10
22:00:00 during Encounter Fourteen. This wind streams shows a large amount of
structure, indicative of non-CH wind. It seems to emerge from the edges of a
loop like structure at active latitudes and shows structure and enhancement in
the proton density.

Figure 16: Comparison of in situ characteristics and footpoint estimates for
the SASW stream spanning from 2022-12-10 20:30:00 to 2022-12-10 22:00:00
during Encounter Fourteen.

Figure 17 shows an overview for the SASW stream spanning from 2022-12-12
12:00:00 to 2022-12-12 16:00:00 during Encounter Fourteen. This wind streams
shows enhanced proton density and looks to emerge from the periphery of a
coronal hole near an active region structure. There is structure in the
velocity, magnetic field, and observed proton density.

Figure 17: Comparison of in situ characteristics and footpoint estimates for
the SASW stream spanning from 2022-12-12 12:00:00 to 2022-12-12 16:00:00
during Encounter Fourteen.

###  B.2 Fast Wind Streams

An overview of the plasma parameters and footpoint mapping for the 5 FSW
streams modeled for this study. These five streams all emerge from within or
near the boundaries of coronal hole structures.

Figure 18 shows an overview for the SASW stream spanning from 2020-01-27
04:55:00 to 2020-01-27 05:15:00 during Encounter Four.

Figure 18: Comparison of in situ characteristics and footpoint estimates for
the FSW stream spanning from 2020-01-27 04:55:00 to 2020-01-27 05:15:00 during
Encounter Four.

Figure 19 shows an overview for the SASW stream spanning from 2021-04-27
01:00:00 to 2021-04-27 04:00:00 during Encounter Eight.

Figure 19: Comparison of in situ characteristics and footpoint estimates for
the FSW stream spanning from 2021-04-27 01:00:00 to 2021-04-27 04:00:00 during
Encounter Eight.

Figure 20 shows an overview for the SASW stream spanning from 2021-04-27
06:00:00 to 2021-04-27 08:30:00 during Encounter Eight.

Figure 20: Comparison of in situ characteristics and footpoint estimates for
the FSW stream spanning from 2021-04-27 06:00:00 to 2021-04-27 08:30:00 during
Encounter Eight.

Figure 21 shows an overview for the SASW stream spanning from 2021-11-20
05:30:00 to 2021-11-20 10:30:00 during Encounter Ten.

Figure 21: Comparison of in situ characteristics and footpoint estimates for
the FSW stream spanning from 2021-11-20 05:30:00 to 2021-11-20 10:30:00 during
Encounter Ten.

Figure 22 shows an overview for the SASW stream spanning from 2022-12-15
21:15:00 to 2022-12-15 22:15:00 during Encounter Fourteen. This stream comes
from the center of a coronal hole and has scaled proton densities
$\mathrm{\sim 5cm^{-3}}$.

Figure 22: Comparison of in situ characteristics and footpoint estimates for
the FSW stream spanning from 2022-12-15 21:15:00 to 2022-12-15 22:15:00 during
Encounter Fourteen.

##  Appendix C Model Validation

This study uses the Potential Field Source Surface (PFSS) model alongside
ballistic propagation methods to estimate the footpoints of plasma streams of
interest. The PFSS model has two inputs that can lead to variance in the
overall results: the choice of input magnetogram and source surface height.
Similar to methods previously outlined in Badman et al. (2020, 2022); Ervin et
al. (2024b, 2024) we look at the effect of these two parameters to understand
the impact on our conclusions.

The ballistic propagation results depend on the in situ $v_{R}$ measurement
and methodology, and the results of this projection can impact the estimated
footpoints. We probe how variance in the input velocity effect our footpoint
estimations (Ervin et al., 2024b, 2024). We vary the inputted in situ $v_{R}$
used to calculate the source surface trajectory via ballistic propagation by
bootstrapping noise on at a level of 4% – the estimated systematic uncertainty
in the SPAN-I velocity moment (3%) plus some extra noise to account for random
sources of error (Livi et al., 2022). From these new source surface
trajectories, we calculate the estimated footpoint from PFSS with the ‘best’
magnetogram used for identifying the source region of each SASW and FSW
stream. There are a variety of source of noise and uncertainty in the SPAN-I
velocity measurements and this methodology aims to show how noise and
uncertainty in the velocity measurement affect the resulting source surface
trajectory and footpoints.

In Figure 23, we show an overview of the variance in the source surface
trajectory when adding noise of 4% to the in situ $v_{R}$. We choose three
streams to represent different characteristics speeds: fast, slow, and slower,
and show how the slower wind speeds are more affected by the inputted velocity
to the ballistic propagation. This is one contributing factor to the
difficulty in determining the sources of the slow wind in comparison to the
source of faster streams. Figure 23 shows how the uncertainty in the velocity
translates to ‘error’ on the estimated footpoints determined from PFSS. In the
top row we show the distribution of error on our estimated footpoints finding
it to be less than 1° for these periods. In panels (d) to (f) we show how the
error in ballistic propagation impacts the resulting source surface trajectory
and finally the footpoint estimation (panels (g) to (i)).

We see that while the exact coordinate position in terms of longitude/latitude
has some slight variance (see panels (a) to (c) and (g) to (i)), the overall
source region remains unaffected. There is an obvious correlation between the
speed of the wind stream and the effects on ballistic propagation, notably
that there is more error in slow wind streams than in fast, a contributor to
the issues surrounding modeling the true source of slow wind. Dakeyo et al.
(2024) found similar results noting that the estimated error was $\leq
5^{\circ}$ and that the error decreased with heliocentric distance and had an
inverse correlation with wind speed.

Figure 23: Overview of error on estimated PFSS footpoints due to noise in the
velocity measurement used for ballistic propagation. We use three streams of
different speeds to show how the effect varies based on $\mathrm{v_{sw}}$. The
top row (panels (a), (b), (c)) show the overall error on the latitude and
longitude of the footpoints. The middle row (panels (d), (e), (f)) show the
error on the source surface longitude as a function of time. The bottom row
(panels (g) to (i)) shows the error on the footpoints compared with the
associated AIA image.

In the PFSS model, the chosen source surface height can impact the outputted
footpoints as this height ($\mathrm{R_{ss}}$) determines that point at which
the field is forced to be purely radial. For each of the streams of interest,
we vary the height of the source surface between 2.0 $\mathrm{R_{\odot}}$ and
3.5 $\mathrm{R_{\odot}}$ to understand how this impacts the resulting
footpoints. We see in Figure 24 that changing the source surface height leads
to large variance in the location of the footpoints, we see from Figure 25
that the optimal $\mathrm{R_{ss}}$ is 2.5$\mathrm{R_{\odot}}$. Varying
$\mathrm{R_{ss}}$ impacts the exact position of the footpoint (especially in
latitude), however it does not impact the resulting source region. It does
have a larger effect on the resulting footpoints in comparison with the effect
of the error of the in situ $v_{R}$ measurement. We use a source surface
height of 2.5 $\mathrm{R_{\odot}}$ for our modeling as this produces the best
result in terms of matching the modeled polarity with the measured magnetic
field polarity from FIELDS. Similar to the error in the ballistic propagation,
we see that this most impacts slower wind streams.

Figure 24: Comparison of the error on the estimated footpoints due to changing
the source surface height for streams of varying speeds. Panels (a) to (c)
show the overall error on the footpoints as a box plot. Panels (d) to (f) show
the footpoints associated with different source surface heights on the
associated AIA image.  Figure 25: Validation of our choice of source surface
height ($\mathrm{R_{ss}}$) for the three different streams we have discussed
in this section. The rows corresponding to the streams from E7, E6, and E10
from top to bottom respectively. The trajectory of Parker at the source
surface is shown in blue (negative polarity) and red (positive polarity) based
on the measurements from Parker/FIELDS. The heliospheric current sheet from
the PFSS model is compared with the trajectory and we show the percentage of
correct polarity the model predicted in the legend.

The last user input to PFSS, the choice of input magnetogram, also impacts the
resulting footpoint. We choose a ‘best’ magnetogram by comparing the outputted
polarity from the PFSS model to the observed polarity by Parker and optimizing
such that the neutral line crossings match. To quantify the impact on the
estimated footpoints by this choice, we use magnetograms from $\pm$2 days
around our choice of magnetograms with a $\mathrm{R_{ss}}$ of 2.5
$\mathrm{R_{\odot}}$ and compare results. We find that this produces an error
on the estimated footpoint of $\sim$2° and thus is an important consideration
when validating the PFSS model.

Figure 26: Comparison of the effect of the choice of input magnetogram for the
lower PFSS boundary condition on the estimated footpoints for streams of
varied speeds. Panels (a) to (c) show the overall error on the estimated
footpoint for each of the wind streams of interest. Panels (d) to (f) show the
footpoints and their error on the associated AIA images.

Through this analysis of the ballistic propagation and PFSS processes required
to trace from the spacecraft down to estimated photospheric footpoints, we see
that there are a variety of error sources which can impact the results. Most
notably, the source surface height has the largest impact on the resulting
footpoints. Much work has been done looking at this height, comparing it with
other models, optimizing to reproduce the observed open flux, and considering
a non-spherical source surface to better reproduce observations. We see that
the impact of the errors in the ballistic propagation and PFSS are
considerably less impactful for the fast wind, further contributing to the
difficulties in determining the source of the slow wind. While we can validate
our models with magnetic field observations, multi point observations would
provide additional measurements for further constraints and confidence in our
results. In this work, we look at statistical distributions of parameters and
while overlaps in distributions could be attributable to the error sources
described above, it would not the systematic shift in source region properties
seen in Figure 4. This indicates that the observed differences are real and
due to variance source regions of the wind.

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