# Dropouts of Fully Stripped Ions in the Solar Wind: A Diagnostic for Wave
Heating versus Reconnection

John C. Raymond Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden
St., Cambridge, MA 02138, USA  M. Asgari-Targhi  Center for Astrophysics $|$
Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA  Maurice L.
Wilson  Center for Astrophysics $|$ Harvard & Smithsonian, 60 Garden St.,
Cambridge, MA 02138, USA  Yeimy J. Rivera  Center for Astrophysics $|$ Harvard
& Smithsonian, 60 Garden St., Cambridge, MA 02138, USA  Susan T. Lepri
Department of Climate and Space Sciences and Engineering, University of
Michigan, Ann Arbor, MI 48109, USA  Chengcai Shen  Center for Astrophysics $|$
Harvard & Smithsonian, 60 Garden St., Cambridge, MA 02138, USA

###### Abstract

The SWICS instrument aboard the ACE satellite has detected frequent intervals
in the slow solar wind and interplanetary coronal mass ejections (ICMEs) in
which C6+ and other fully stripped ions are strongly depleted, though the
ionization states of elements such as Si and Fe indicate that those ions
should be present. It has been suggested that these “outlier” or “dropout”
events can be explained by the resonant cyclotron heating process, because
these ions all have the same cyclotron frequency as He2+. We investigate the
region in the corona where these outlier events form. It must be above the
ionization freeze-in height and the transition to collisionless plasma
conditions, but low enough that the wind still feels the effects of solar
gravity. We suggest that the dropout events correspond to relatively dense
blobs of gas in which the heating is reduced because local variations in the
Alfvén speed change the reflection of Alfvén waves and the turbulent cascade.
As a result, the wave power at the cyclotron frequency of the fully stripped
ions is absorbed by He2+ and may not be able to heat the other fully-stripped
ions enough to overcome solar gravity. If this picture is borne out, it may
help to discriminate between resonant cyclotron heating and stochastic heating
models of the solar wind.

Sun: ion composition — Sun: coronal mass ejections, solar wind — Solar wind:
slow solar wind — Solar corona: Solar coronal heating

††journal: ApJ††software: plasmapy

##  1 INTRODUCTION

Models for heating and driving the solar wind generally emphasize either
dissipation of magnetohydrodynamic (MHD) wave energy or magnetic reconnection.
The wave models can naturally explain strong preferential heating of O and Mg
ions observed in the fast solar wind and at large heights in the slow wind
(Kohl et al., 1997; Cranmer et al., 1999; Frazin et al., 2003). The
reconnection models can naturally explain the observed density fluctuations
and some composition anomalies in the slow wind. Both models have some
difficulty reproducing the ionization states measured in the heliosphere (Oran
et al., 2015; Shen et al., 2017; Szente et al., 2022). We also note that while
coronal mass ejections (CMEs) are basically driven by simple MHD forces, the
ejected plasma continues to be heated after it leaves the Sun (Akmal et al.,
2001; Lee et al., 2009; Rakowski et al., 2007, 2011; Murphy et al., 2011;
Wilson et al., 2022), but the nature of that heating is difficult to
determine.

Composition anomalies in the solar wind provide a means to connect observed
structures in the wind to their coronal origins, and they constrain the
physical processes that drive the wind. The first composition changes to be
measured were variations in the He abundance correlated with solar wind speed
(Ogilvie & Hirshberg, 1974; Kasper et al., 2012; Alterman & Kasper, 2019). It
was later established that abundances of elements whose First Ionization
Potential (FIP) was below about 10 eV were enhanced in the slow solar wind
(Geiss et al., 1995; von Steiger et al., 2000). More recently, drastic
dropouts in the abundances of heavy elements, probably associated with clouds
of depleted gas released from the cusps of streamers, were reported (Weberg et
al., 2012, 2015).

Two recent papers have reported remarkable ionization state anomalies, which
they call “Outliers”, in the solar wind. Zhao et al. (2017) examined data from
the Solar Wind Ion Composition Spectrometer (SWICS) instrument aboard the
Advanced Composition Explorer (ACE) satellite, and they found intervals when
the ratio C6+/ C5+ was anomalously low by as much as an order of magnitude
compared with other measures of the ionization state, such as O7+/ O6+. Zhao
et al. (2017) examined the slow solar wind, and Kocher et al. (2017),
performed a similar study of interplanetary CMEs (ICMEs). Almost half of the
anomalies occurred in the slow wind and almost half in ICMEs, with only about
1% of the events occurring in the fast wind. More recently, Rivera et al.
(2021) extended that work to include magnetic field measurements and more
elemental composition data. Notably, Rivera et al. (2021) show changes in the
magnetic field direction and the electron strahl properties of the Outlier
wind indicating a strong connection with heliospheric current sheet crossings.

Zhao et al. (2017) and Kocher et al. (2017) list several other properties of
the outlier intervals. In both the slow solar wind and ICMEs, the fluxes of
N7+ and O8+, that is to say the ions that are stripped bare, are anomalously
low, along with the C6+. The ionization states of other elements, such as Ne,
Si, S and Fe, and their FIP fractionation seem to be the same as that of the
slow solar wind or CME in which the outliers are embedded. In the slow wind,
the outlier intervals occur about 10% of the time, and the densities during
the outlier intervals are about twice normal. The proton temperature is
somewhat lower than is typical for the slow wind, and perhaps bimodal. Under
normal circumstances, much of carbon would be in the C6+ state. The total
abundance of carbon is depleted, unlike the other elements. Thus it seems that
ions in the stripped ionization state are simply missing, rather than being
shifted to lower ionization states. On the other hand, Rivera et al. (2021)
find that the He/H ratios are enhanced relative to regions upstream and
dowstream of the outliers, and they discuss magnetic field variations
associated with the dropouts.

Here, we try to quantify the requirements on the fractionation mechanism. We
explore one mechanism, a lack of wave energy at the resonant frequency of the
fully stripped ions, in more detail. The large abundance of He2+ means that
He2+ can absorb all the available wave energy at that frequency if the heating
rate is sufficiently low. In many models for the origin of the solar wind,
Alfvén waves from the solar surface partially reflect from the Alfvén speed
gradient in the corona, and the interaction between inward- and outward-
propagating waves generates a turbulent cascade that can heat the ions.
Density fluctuations in the corona cause variations in the Alfvén speed and
the wave reflection, so they create significant variation in the wave local
heating rate. Some models for the observed preferential heating of ions such
as O VI and Mg X are based upon resonant absorption of wave power at the
cyclotron frequency (Cranmer, 2000; Hollweg & Isenberg, 2002). However, it is
problematic whether the turbulence can cascade to the resonant frequency.
Therefore, other models rely on stochastic heating by lower-frequency Kinetic
Alfven Waves at the scale of the ion gyroradius (Chandran et al., 2010). The
outlier events discussed here may offer a means to discriminate between these
two pictures.

From here on, we will take the term “Alfvénic waves” to mean Alfvén-like waves
including fast mode waves and Kinetic Alfvén Waves (KAWs). The paper is
organized as follows: Section 2 reviews the observed characteristics of the
Outlier wind, Section 3 summarizes the physical mechanisms that have been
discussed to explain them, and Section 4 lists constraints on the region where
the Outlier wind must be formed. In Section 5 we consider how wave-driven and
reconnection-driven winds might produce the dropouts, and in Section 6 we
discuss the different implications of dropouts in the slow solar wind and in
ICMEs. Section 7 summarizes our conclusions.

##  2 GENERAL CHARACTERISTICS

We first summarize the observed characteristics of the dropout regions as
determined by Zhao et al. (2017) for the slow wind, Kocher et al. (2017) for
ICMEs, and Rivera et al. (2021) for both the slow wind and ICMEs.

In the slow solar wind, the dropouts show depletions of C6+ by up to an order
of magnitude. The wind speeds of 350 to 450 $\rm km~{}s^{-1}$and the O7+/O6+
ratios and Fe charge states are normal for the slow wind. The dropouts occur
about 10% of the time, and they show density enhancements by factors of 1.2 to
2, with proton temperatures reduced by about 50%. Helium abundances are also
enhanced by factors of 1.2 to 2, and the FIP bias is normal for the slow wind,
except that Ne in the ICME outliers is enhanced relative to nearby regions in
the ICMEs. The magnetic field shows rotations or sudden changes in direction,
and enhanced magnetic field fluctuations are seen downstream of the dropouts.
Alfvén speeds are enhanced by a factor of 1.7 on average. Unidirectional
electron strahl is observed over half of the time.

In ICMEs, reductions of N7+ and O8+ are seen, though otherwise the ionization
state is similar to that of the surrounding plasma. Dropouts are seen in 72%
of the ICMEs studied by Rivera et al. (2021). The FIP enhancements are typical
of ICMEs, but Ne is enhanced, as in the slow solar wind.

Rivera et al. (2021) suggest a link between the dropouts seen in the slow wind
and in ICMEs, in that the magnetic field changes seen in slow wind dropouts
are similar to what is seen in the small interplanetary magnetic flux ropes
(SIMFRs) studied by Moldwin et al. (2000), Feng et al. (2008), Kilpua et al.
(2009) and Huang et al. (2020). In particular, they show strong rotation of
the magnetic field, and they are often associated with sector boundaries,
elevated He abundance, elevated $\rm<Q_{Fe}>$ and electron strahl. These point
to an association with reconnection events in the corona.

An important consideration is that the fractionation would not occur in a
steady flow. If the particle fluxes are set by the boundary condition at the
chromosphere and the plasma is in a steady flow, then the flux of each species
must remain constant. In principle, there could be variations between one
streamline and its neighbor. High density contrasts among magnetic flux tubes
over scales of a few thousand km were inferred from eclipse images (November &
Koutchmy, 1996) and from Atmospheric Imaging Assembly (AIA) observations of
Comet C/2011 (Lovejoy) by Raymond et al. (2014). Thus the relatively steady
flow in the fast wind may be part of the explanation for the lack of dropouts
in the fast wind.

Assuming that the outliers develop just above the freeze-in and
collisional/collisionless transition, we take 4 R☉ as the typical location. If
an Outlier lasts for two hours at a solar wind speed of 400 $\rm km~{}s^{-1}$,
the size scale is around $3\times 10^{10}$ cm, which corresponds to about
$6\times 10^{8}$ cm at 4 R☉. If the speed increases from 100 $\rm
km~{}s^{-1}$at 4 R☉ to 400 $\rm km~{}s^{-1}$at 1 AU and the area increases as
r2, a density of 10 $\rm cm^{-3}$ at 1 AU would correspond to a density of
$10^{5}$ $\rm cm^{-3}$ at 4 R☉.

Several characteristics of the source regions of the slow solar wind and CMEs
are likely to be relevant to the origin of the dropouts. In the case of the
slow wind, the acceleration is slow, reconnection is likely to be important,
and the heliospheric current sheet is present. The wind is unsteady and clumpy
in comparison with the fast solar wind, though the coronal holes where the
fast wind originates also show modest density inhomogenities (Cadavid et al.,
2019; Hahn et al., 2018). Both coronal holes and quiet Sun regions have low-
lying magnetic loops, but only the quiet Sun and active regions have high
coronal loops. In the case of ICMEs, the range of characteristics makes it
difficult of point to the important characteristics. They have complex
structures, including a leading edge, a flux rope (void), a prominence(core),
and an EUV dimming region. There can be a broad range of speeds and densities,
and reconnection plays an important role.

##  3 PHYSICAL CAUSES OF DROPOUTS

Zhao et al. (2017) consider several possible interpretations for the anomalous
C6+ dropouts in the slow solar wind. They raise the possibilities that 1)
resonant heating by MHD waves favors ions that are not fully stripped, 2)
closed magnetic loops depleted in fully stripped ions reconnect with open
field lines to release their plasma, or 3) fully stripped ions are depleted by
Coulomb collisions with energetic protons produced by magnetic reconnection.

Scenario 2, the opening of loops depleted in fully stripped ions, is
attractive because it is related to models for the FIP (First Ionization
Potential) effect (Schwadron et al., 1999; Laming, 2017; Laming et al., 2019),
and it fits in with the intermittent appearance of the anomalies in the slow
solar wind. However, the abundance of S suggests that solar wind FIP
fractionation does not happen on the same closed loops responsible for the
bulk of the coronal EUV and X-ray emission, but that magnetic structures
without strong resonances like open field regions may play a role (J.M. Laming
2022, private communication). Moreover, attributing the dropouts to opening
loops just shifts the problem from open to closed field regions without
offering a specific mechanism. Also, it is not obvious how many of the loop
openings would occur above the freeze-in height. Scenario 3 posits a source of
energetic protons. Simnett (1995) emphasized the role of energetic protons in
flares, and proton beams could be produced during reconnection between open
and closed magnetic field believed to be important in causing the FIP effect
in the slow solar wind (Schwadron et al., 1999; Laming, 2017). However, this
scenario has the difficulty that the cross-section for momentum transfer
between protons and C6+ is only about 44% larger than that for C5+, so that
C6+ would not be much more strongly depleted than C5+. Moreover, sufficiently
energetic protons would ionize C5+, producing an anomaly opposite to that
observed.

It therefore seems that the first scenario is the most likely because, as
pointed out by Zhao et al. (2017), all the missing ions have the same charge-
to-mass ratio and therefore share the same cyclotron frequency. Evidence for
the importance of preferential heating in driving the heavy element component
of the solar wind comes from the large velocity widths of O and Mg ions
observed in coronal holes and in streamers above 3 R☉ (Kohl et al., 1997;
Frazin et al., 2003), though the measured line profiles are not good enough to
distinguish between resonant and stochastic heating (Klein & Chandran, 2016).
Large variations in the $\rm{}^{3}He/^{4}He$ ratio observed across the solar
cycle (Gloeckler et al., 2016) may be compatible with either picture. If there
is a deficit of wave energy at that frequency, all the fully stripped ions
will experience less resonant heating. It is also conceivable that there is
excess energy at the resonant frequency of the fully stripped ions, so that
they are heated and driven out of a parcel of plasma. However, they would have
to be spread over a large volume to avoid producing regions with excess fully
stripped ions, and no such regions are reported by Zhao et al. (2017) or
Rivera et al. (2021).

Kocher et al. (2017) measured the ionization state anomaly in ICMEs. Much less
is known about the heating of CME plasma than about the heating of streamers.
It is generally assumed that the plasma in CMEs is ejected by purely MHD
forces, which would not naturally produce the fractionation observed. However,
observations of CMEs with UVCS (Kohl et al., 1995, 1997) show that the plasma
continues to be heated well after it is launched (Akmal et al., 2001;
Ciaravella et al., 2001; Lee et al., 2009; Murphy et al., 2011; Wilson et al.,
2022), and the ionization states of CME plasma at 1 AU with ACE and STEREO
also require heating at least to heights of several R☉ (Rakowski et al., 2007,
2011; Rivera et al., 2019). The nature of that heating is not fully settled,
but dissipation of magnetic energy, presumably via turbulence, is the most
viable option (Kumar & Rust, 1996; Landi et al., 2010; Murphy et al., 2011).
If that turbulence cascades to small enough scales, it could resonantly heat
the ions.

##  4 LOCATION OF DROPOUT FORMATION

###  4.1 Ionization Freeze-in

As pointed out by Zhao et al. (2017), the fractionation must occur above the
point where ionization states freeze-in. Otherwise, the C5+ would have time to
ionize to C6+ before the plasma leaves the low corona. The freeze-in height
depends on the density, temperature and velocity of the wind, so it varies
greatly among different coronal features. It also depends upon the ions being
considered, since the ionization and recombination rates of ions such as C5+
and C6+ are relatively slow compared with the Si and Fe ions with L-shell or
M-shell electrons at coronal temperatures. Therefore, the carbon ionization
state will freeze in first, at lower heights. The freeze-in occurs very low in
the fast solar wind because of its high speed and low density. We are
interested in the slow wind, where freeze-in typically occurs between about 2
R☉ and 3 R☉ in the pseudostreamer modeled by Shen et al. (2017), though it
varies within the pseudostreamer structure as the wind velocity increases and
the density decreases away from the neutral line. Landi et al. (2014) found
that the usual freeze-in picture cannot account for the full range of
ionization states in the fast solar wind, possibly due to non-Maxwellian
electron distributions (Ko et al., 1996), but perhaps due to the breakdown of
the assumption of steady flow in the models.

Figure 1: Flow parameters along a particular streamline in a pseudostreamer
computed with the MAS model, as presented on Shen et al. (2017) (solid lines).
The dashed lines show a clumpy AWT model similar to that of Asgari-Targhi et
al. (2021), but for the magnetic field expansion of Shen et al. (2017) and
fractional density inhomogeneities similar to those computed by Asgari-Targhi
et al. (2021) (dashed lines).

Figure 1 shows two models of the flow along a streamline in a pseudostreamer
modeled by Shen et al. (2017). The solid line shows the parameters for one
particular field line in the Magnetohydrodynamics on a Sphere (MAS) model
(Lionello et al., 2019) that was used by (Shen et al., 2017) to model a
pseudostreamer. In this model, the wind is heated and accelerated by
turbulence that is excited when outward propagating Alfvén waves interact with
Alfvén waves reflected higher in the corona. The dashed line shows the more
complex flow predicted by a model like that of Asgari-Targhi et al. (2021) for
the fast wind. It introduces modest density fluctuations and computes the
modified rate of Alfvén wave reflection and the dissipation heating rate,
which in turn affect the flow parameters and temperature. We will refer to
this as the clumpy Alfvén Wave Turbulence (AWT) model from now on.

Figure 2: C6+ over C5+ ionization fractions for one streamline of the MAS
model (solid line) and the MAS model with the temperature from the clumpy AWT
model (dashed line). The figure emphasizes the large range of possible
ionization states, but shows that for this streamline, the C6+ ionization
fraction freezes in below 3 R☉.

Figure 2 shows the ratios of C6+ and C5+ ion fractions for two models based on
a streamline along the pseudostreamer edge from Shen et al. (2017), one using
the temperature structure of that model, and one using the clumpy AWT model.
We note that although the temperature in the clumpy AWT model is higher, the
rapid acceleration and corresponding low density lead to a lower frozen-in
ionization state in this model. Time-dependent ionization states were computed
using ionization and recombination rates from CHIANTI (Dere et al., 2019) and
the PlasmaPy-NEI code in plasmapy of Shen et al. (2017) and Wilson et al.
(2022), as well as an older code of Raymond (1979). In both models for this
streamline, as well as for a dozen others we investigated, the C6+ ionization
fraction freezes in around 2 R☉, so we will use that value. We note that there
is a longstanding discrepancy between ionization states predicted by solar
wind models and charge states measured at 1 AU, in the sense that the models
predict lower ionization than are observed (Ko et al., 1996; Landi et al.,
2014; Oran et al., 2015; Shen et al., 2017; Lionello et al., 2019; Rivera et
al., 2020), suggesting that the freeze-in may be slightly higher than
indicated by the models.

The freeze-in conditions for ICMEs are much less clear because of their large
ranges of densities and outflow speeds, except that continued heating after
the material leaves the solar surface is required to match the ionization
states observed at 1 AU (Rakowski et al., 2007, 2011). It is not clear whether
the C6+ dropouts originate in prominence ejecta, leading edge material, the
flux rope void, or the EUV dimming regions that often accompany the CME
eruption. Prominence material is denser and it expands more slowly than the
surrounding material, and it is more likely to have an excess He abundance
(Del Zanna et al., 2004), though chromospheric evaporation can also lead to
enhanced He abundances (Fu et al., 2020). In the particular CME modeled by
Rivera et al. (2019), the prominence material C6+ was not yet frozen even at 8
R☉, though the hottest component freezes in by 4 R☉. Thus there is great
uncertainty as to the freeze-in height even within a single CME, and CMEs show
a wide range of velocity and density profiles. We will take 4 R☉ to be a
characteristic freeze-in height for CMEs, but we keep in mind that it will be
higher for dense prominence material, especially in slow CMEs.

Figure 3: Timescales computed for the models shown in Figure 1. For each
model, the flow time (taken to be 0.3 R/V; solid line), ionization timescale
for C5+ (1./(density $\times$ ionization rate); dashed line), Coulomb energy
loss timescale (dash-dot) and heating timescale (dotted) are given. The smooth
flow MAS model ((Shen et al., 2017) is shown in the left panel, and the clumpy
AWT model in the right panel.

###  4.2 Transition to collisionless heating

Collisionless plasmas behave differently than collisional ones in many ways.
For the purposes of this paper, the relevant condition is that cyclotron
resonant heating requires that the collision frequency for an ion to lose
energy be less than the cyclotron frequency (Hollweg, 1999). We assume that
the Coulomb collisional timescale (Spitzer, 1968) is most important. It
depends on the density and temperature of the plasma. Figure 3 indicates that
the plasma becomes collisionless above about 3 R☉ for this streamline. As
indicated by preferential heating of oxygen, roughly 2.5 to 3 R☉ is a
reasonable estimate for the height of the transition to collisionless
conditions in the slow wind (Frazin et al., 2003).

###  4.3 Gravitational Potential

The fractionation must occur close to the Sun because it is difficult for ions
to move very far relative to the wind in the highly supersonic flow at larger
radii. Turbulent heating occurs in ICMEs at 1 AU, but it is modest (Liu et
al., 2006). In addition, merely shifting the fully stripped ions within the
wind would create regions of overabundance of these ions as well as regions of
underabundance, and no such regions of overabundances are observed. In order
to separate C6+ from the other carbon ions, it is necessary to have both a
different heating rate, which we attribute to cyclotron resonant absorption,
and another force, such as gravity, which can act on all the ions, but is
countered to different degrees by the thermal content of different ions.
Carbon ions are 12 times heavier than protons, but once the wind becomes
supersonic, gravity can have only a modest effect on the overall flow. The
fractionation must occur where the solar gravity is still strong enough to
separate heavy ions such as C6+ from lighter protons and He2+ ions.

A rough criterion for the maximum height of the separation is

$E_{G}=E_{TH}+E_{KIN}$ (1)

where EG is the gravitational potential energy, ETH the thermal energy, and
EKIN the kinetic energy of the bulk flow. For carbon ions, these are 4000/R
eV, 90 T6 eV, and 600 V${}_{100}^{2}$ eV, respectively, where R is in solar
radii, T6 is the temperature in units of MK, and V100 is the wind speed in
units of 100 $\rm km~{}s^{-1}$. For the streamline shown in Figure 1, this
height is around 8 R☉if carbon is not preferentially heated. This estimate is
likely to be altered by other forces, including the ponderomotive force of
Alfvén waves, drag between carbon ions and protons, and Lorentz forces.
However, it gives a rough upper limit for the height at which the
fractionation takes place. Note that this height is below 3 R☉ in the fast
solar wind because of the rapid acceleration there (Cranmer et al., 1999).

##  5 Wave Dissipation or Reconnection?

Assuming that the dropouts are caused by deficits in the resonant cyclotron
heating rate, they could result from a deficit in wave power due to reduced
dissipation of wave energy, to absorption of wave power by excess He2+, or to
excess density, beyond the capacity of the wave power to provide enough heat.
These possibilities are not mutually exclusive. For instance, reduced wave
power could cause the He2+ outflow to stall, increasing the He2+ concentration
and further reducing the wave energy available per particle.

Another model for heating the ions by turbulence generated by dissipation of
Alvén waves was introduced in response to problems getting the turbulent
cascade to reach the relevant cyclotron freequencies. In this model, the
perpendicular cascade produces lower-frequency KAWs that can stochastically
heat the ions when they reach the scale of the ion gyroradii (Chandran et al.,
2010). This mechanism could also starve the fully-stripped ions of heating if
He2+ or protons absorb too much energy. Indeed, Chandran et al. (2010) found
that the wave power must exceed a critical value in order for irreversible
heating to occur. A difficulty arises from the relative gyroradii of
diffferent ions, however. The gyroradii scale as miv/qi, and if the ions are
in thermal equilibrium with each other at low heights where the heating must
begin to operate, they scale as m${}_{i}^{1/2}$/qi. The relative gyroradii of
H:He2+:C6+:O8+:Si10+:Fe11+ are thus 1.0:1:0.58:0.5:0.53:0.68. In other words,
He2+ and protons could absorb the cascading wave energy before it reached the
gyroradii of fully-stripped ions such as C6+, but they would also prevent the
cascade from reaching the gyroradii of most other coronal ions. It is possible
that stochastic heating could operate after some preferential heating has
occurred so that the ion velocities are similar to each other rather than
proportional to m${}_{i}^{-1/2}$, but it seems likely that the cyclotron
resonant heating must dominate the formation of the outliers.

###  5.1 Dissipation of Alfvénic waves

A popular mechanism for driving the solar wind is based on Alfvén waves
propagating up from the chromosphere. Left to themselves, Alfvén waves do not
dissipate efficiently in the corona. However, they can be partially reflected
by the gradient in the Alfvén speed in the corona, and the reflected waves
interact with the outward-going waves to produce turbulence and heating
(Verdini et al., 2010; Cranmer & van Ballegooijen, 2012). That mechanism is
the basis of the heating term in two successful MHD models of the global
corona and wind; AWSoM and MAS (van der Holst et al., 2014; Lionello et al.,
2019). In order for the turbulent energy to be dissipated, it must cascade to
small scales. Much of the energy may dissipate at the proton scale, but some
will be absorbed by resonant cyclotron heating of higher mass-to-charge ratio
ions before it reaches that scale.

There is observational evidence for wave heating of high m/q ions, though it
does not discriminate between resonant cyclotron absorption of MHD waves and
stochastic heating. The line widths of the Ly$\alpha$, O VI and Mg X
ultraviolet lines measured in coronal holes by UVCS imply kinetic temperatures
of the heavier ions that are more than mass-proportional; $T_{O}>16T_{p}$ and
$T_{Mg}>24T_{p}$ (Kohl et al., 1997; Cranmer et al., 1999). This requires
strong preferential heating of oxygen and magnesium, which is usually
attributed to absorption of wave energy at the cyclotron resonant frequencies
as the turbulent cascade transfers energy to small scales and high frequencies
(Cranmer et al., 1999; Hollweg, 2006), though it could also be explained by
stochastic heating by lower frequency waves (Chandran et al., 2010). A
cyclotron resonance heating process might also explain the factor of 100
variation in the 3He/4He ratio over the course of a Carrington rotation
reported by Gloeckler et al. (2016).

While the overall picture is attractive, the Alfvén wave reflection in a
smoothly accelerating wind is not strong enough to generate adequate
dissipation (van Ballegooijen & Asgari-Targhi, 2016; Asgari-Targhi et al.,
2021). One way to solve the problem is to introduce density fluctuations that
locally increase the reflection and dissipation. Density fluctuations of a few
percent to around 20 percent are known to exist in the 2 to 10 R☉ range
(Miyamoto et al., 2014; Hahn et al., 2018; Cadavid et al., 2019). The
reflection produces very localized heating, but the reflection coefficient
drops to zero where $dV_{A}/dr=0$ (Chandran & Hollweg, 2009; Cranmer, 2010),
so places where the density gradient equals the gradient in $B^{2}$ would be
places of minimal heating, while the heating would peak where the density
increases as B decreases.

Figure 4: Heating rate along the streamline shown in Figure 1 for the clumpy
AWT model. Excursions above and below the average by an order of magnitude
occur on small scales, especially below 5 R☉.

Figure 4 shows the time-averaged heating rate along the slow wind stream shown
in Figure 1 as computed by the code of Asgari-Targhi et al. (2021), with
similar modest (24%) random density fluctuations on scales of 0.05 R☉ (clumpy
AWT model). These Reduced MHD (RMHD) models start with a smooth solution to
the 1D flow in a flux tube with heating by Alfvén wave dissipation, then add
density fluctuations at the observed level, recompute the wave reflection and
heating, and obtain self-consistent time-steady solutions. The heating rate in
$\rm erg~{}cm^{-3}~{}s^{-1}$, that is to say the locally dissipated wave power
that drives the turbulent cascade, varies by orders of magnitude. The local
variations on short time scales span two orders of magnitude about the average
at the lower heights, though they diminish above about 7 R☉. Chandran et al.
(2010) found that the heating rates corresponding to Alfvén wave reflection in
a smooth outflow were roughly at the critical levels needed to preferentially
heat He2+ and O5+ in the stochastic heating model. Therefore, the strong
heating regions in the clumpy AWT models could easily produce preferential
heating, while the weak heating regions could not. Thus it is possible that
the dropouts correspond to places where the heating rate Q is unusually small.
In particular, the low heating region around 2 R☉ in this particular model is
a place where heating of bare ions could be greatly reduced.

As a hypothesis to explain the C6+ dropouts in the slow wind by a lack of
resonant cyclotron heating, we suggest that a blob of denser gas from the
chromosphere or a prominence, possibly rich in He and Ne, is lofted to the
height of ionization freeze-in and the transition from collisional to
collisionless conditions. It could be driven by either MHD or pressure forces,
but the former seems more likely. If it reaches that height but has not
reached escape speed, it will fall back unless Alfvénic waves can heat and
drive it onwards. Protons are light enough that their thermal energy might
still allow them to escape, and most other ions can be heated by cyclotron
resonance. However, if He2+ absorbs so much of the energy at its resonant
frequency that it falls below the critical value for irreversible heating
(Chandran et al., 2010), or if the heating rate is low because of the wave
reflection properties of the blob, then the heavier bare ions will be unable
to overcome gravity, and they will be left behind. Chandran et al. (2010)
indicate that level of turbulence in the steady-flow Alfvén wave reflection
models lies above the critical value for resonant heating for plausible
parameter choices, but the low points in the heating rate shown in Fig. 4
would not.

###  5.2 Reconnection

The idea that the dropouts are associated with reconnection is supported by
the magnetic field signatures similar to SIMFRs seen in dropout events and by
the frequent occurrence of dropouts in ICMEs (Rivera et al., 2021).
Reconnection plays a dominant role in solar flares, and it is observed at
larger heights as downflows and disconnection events (bifurcated flows) in CME
current sheets seen in white light (Savage et al., 2010) and especially near
sector boundaries in quiet Sun streamers (Wang et al., 1999a; Sheeley & Wang,
2014). The FIP effect in the slow solar wind is generally attributed to the
release of material from closed loops onto open field lines by reconnection
(Schwadron et al., 1999; Laming, 2017). Reconnection is also a fundamental
part of the S-web picture of pseudo-streamer winds (Higginson et al., 2017),
though it may occur at heights well below the freeze-in height. Scott et al.
(2022) have explored the ionization state signatures of interchange
reconnection at various heights. They predict regions of enhanced O7+/O6+, but
there is no reason to expect C6+ dropouts from time-dependent ionization in
those regions.

However, there is good reason to expect that very strong wave turbulence is
present in reconnection regions. Excess widths of spectral lines in the
current sheets that stretch between flare loop tops and CME flux ropes are
interpreted as turbulent velocities of order 100 $\rm km~{}s^{-1}$(Ciaravella
& Raymond, 2008; Bemporad, 2008; Warren et al., 2018), and velocity variations
are also observed (Freed & McKenzie, 2018). Cyclotron resonance interaction is
believed to be responsible for selective acceleration of 3He (Fisk, 1978) in
flares, and perhaps 22Ne (Mewaldt et al., 1979). Moreover, turbulence is
central to the acceleration process that produces the power-law distributions
of electrons seen in solar flares. On the theoretical side, turbulence is
produced by tearing modes or other instabilities, and it is crucial to rapid
reconnection (Lazarian & Vishniac, 1999; Loureiro et al., 2012; Shen et al.,
2013). Turbulence within the current sheet may generate waves that propagate
into surrounding plasma which does not pass through the current sheet itself,
but it is not clear how much turbulent energy would be available to this less
strongly heated and ionized gas (Ye et al., 2021).

Overall, it seems unlikely that a current sheet is a promising location where
a lack of wave power at the bare ion cyclotron frequency could cause dropouts.
However, it is entirely plausible that reconnection events inject high
density, high He abundance plasma into regions where the ionization state has
frozen-in, and where fractionation can occur.

##  6 Slow Wind, Fast Wind and ICMEs

We now ask how the Alfvénic wave scenario would play out in the fast and slow
solar winds and in ICMEs.

###  6.1 Fast Solar Wind

Since almost no Outlier events are observed in the fast solar wind, the
question becomes why the mechanism that fractionates the ions does not operate
there. Cadavid et al. (2019) and Hahn et al. (2018) showed that density
fluctuations are present, and Asgari-Targhi et al. (2021) showed that those
density fluctuations produce very large variations in the heating rate per
particle. Moreover, polar jets have been observed with EIT, UVCS and LASCO
(Gurman et al., 1998; Dobrzycka et al., 2002; Wang et al., 1998; Uritsky et
al., 2021). Perhaps the wave power is so large that even near minima in the
heating rate, the power at the cyclotron resonance remains above the critical
value described by Chandran et al. (2010). This would be compatible with the
rapid acceleration of the wind in coronal holes. Another possibility is that
the freeze-in radius could be near or above the sonic point, so that reduced
heating does not mean that the C6+ ions fail to escape. As mentioned above,
the rapid acceleration of the fast wind (Cranmer et al., 1999) means that $\rm
E_{g}=E_{KIN}+E_{TH}$ below 3 R☉, and dropouts may not be able to develop.

###  6.2 Slow Solar Wind

Cadavid et al. (2019) showed that density fluctuations are present in the
quiet corona as well as in coronal holes, and the quiet Sun and active regions
contain high coronal loops that could release plasma into the slow solar wind.
We have shown that the predicted fluctuations in the turbulent heating rate
are also large, particularly in the region around 3 R☉ where the ionization
freeze-in occurs. This is the region where resonant heating is particularly
important, in that Frazin et al. (2003) found that the thermal velocities of
O5+ gradually approach those of protons between 2.5 and 5 R☉ in streamers and
that the O5+ velocities seem to become anisotropic above about 4 R☉. Models
for the FIP effect that involve release of plasma from closed loops would
naturally provide the required density enhancements provided that the loops
are high or that the plasma is released at high enough speed to reach 3 to 4
R☉. The increase in magnetic fluctuations downstream of the outliers could
arise naturally from the reflection of Alfvénic waves traveling outwards from
the Sun.

Therefore the wave heating scenario suggested above, in which denser blobs of
gas are lifted to the freeze-in region, and all but the bare ions are heated
and driven by turbulence, would also fit in with the observed density
enhancements and the lower temperatures measured in the Outliers. Thus the
dissipation of Alfvénic waves seems well-suited as an explanation for the C6+
dropouts in the slow wind. The main feature of the Outliers that is not
explained easily in this picture is the rotation in magnetic field direction.
That might be explained if the blobs were launched by reconnection events and
the magnetic structure was preserved in the fractionation region.

An alternative picture for the origin of density enhancements is suggested by
Hahn et al. (2022). They propose that a parametric decay instability, in which
a high amplitude outward-propagating Alfvén wave decays to an inward-
propagating Alfvén wave and an outward-propagating acoustic wave, can account
for the density and velocity patterns they observe in the Si IV lines with
IRIS. Their observations pertain to the transition region at lower heights, so
it is not clear whether this instability is important where the ionization
state freezes in. It is also unclear how the process could produce the
magnetic and abundance signatures seen in the dropouts. Nevertheless, it
should produce density fluctuations of sufficient magnitude to drastically
alter the heating rate, and therefore the turbulent energy available to heat
the ions.

The reconnection scenario was invoked by Rivera et al. (2021). Blobs of gas
that detach from the cusps of streamers are believed to be created by
reconnection, then to accelerate up to slow solar wind speed (Wang et al.,
1999b; Sheeley et al., 1997). However, these LASCO blobs have been associated
with the heavy ion dropouts detected at 1 AU by ACE (Weberg et al., 2012,
2015) and interpreted as the release of material from the closed loops of the
streamer core that had undergone gravitational settling (Raymond et al.,
1997). No such elemental depletion is seen in the Outliers.

Brooks et al. (2020) invoke a two-component origin for the slow solar wind
based on Hi-C and AIA observations of an active region. They suggest that
reconnection between closed loops and open field lines injects FIP-enhanced
material, while the flow emerging from the active region plage has
photospheric abundances. The component injected by reconnection would perhaps
be subject to the ionic fractionation that produces Outliers. Scott et al.
(2022) predict regions of enhanced density just below regions of enhanced
O7+/O6+, and the high density regions could reflect upward-propagating Alfvén
waves before they reach the high ionization zone, thus starving that region of
wave heating and producing C6+ dropouts. The large percentage of the slow
solar wind that shows C6+ depletion, around 10%, would imply that a
significant fraction of this component has the right conditions above the
freeze-in height to become fractionated.

###  6.3 ICMEs

In the common picture of CME eruptions, a flux rope becomes unstable and is
launched by MHD forces. Magnetic reconnection accompanies the ejection, both
as a cause and an effect of the eruption, and some of the reconnecting field
lines form a flux rope or a sheath around an existing flux rope (Gosling et
al., 1995; Lin et al., 2004). The fractionation of bare ions indicates that
cyclotron resonant waves play a role, so that MHD forces are not the only
processes involved. As mentioned above, there is evidence from UV and EUV
spectra and from ionization states measured at 1 AU that the erupting gas
experiences continued heating at least up to several R☉. The nature of that
heating has not been firmly established, but relaxation of the expanding,
stressed magnetic field toward its minimum energy state (Lynch et al., 2004)
requires the release of energy, most likely by way of reconnection.

On the other hand, the EUV dimmings observed in many CMEs (Dissauer et al.,
2018) indicate that a large amount of material is launched as magnetic loops
straighten toward radial, and density inhomogeneities would be subject to the
Alfvénic wave mechanism described above. In some cases, material launched in
the eruption is observed to fall back to the solar surface when it is unable
to escape (Innes et al., 2016). Thus wave-driven fractionation is also
possible.

Several pieces of evidence may favor one mechanism or the other. The magnetic
structure, electron strahl and overabundance of He and Ne in the Outliers
could be explained if the material originates in prominence flux ropes, since
there are observations of high He and Ne abundances in prominences (Spicer et
al., 1998; Del Zanna et al., 2004; Li & Yao, 2020). Prominence material is
also indicated by low charge states, such as singly ionized He (Yao et al.,
2010). On the other hand, to the extent that plasma is trapped in the dips in
a magnetic flux rope, it is difficult for fractionation to occur, though flows
along flux ropes can occur as the flux ropes straighten out. The generally
high ionization states seen in ICME Outliers (Kocher et al., 2017) suggest
that much of the material experienced heating in a reconnection current sheet.
The EUV dimmings can account for a large amount of mass, but it is uncertain
how much that material is heated and what ionization state would be expected.
Also, the material might lie outside the flux rope, and therefore not show the
observed magnetic structure, though it could show electron strahl. A large
percentage of ICMEs show Outliers, 72%, implying a substantial filling factor.
That could be consistent with gas from the EUV dimming regions. A large
filling factor would also be consistent with plasma from the main reconnection
current sheet, which fills the flux rope formed by reconnection itself.
However, a very large expansion factor between the current sheet and the outer
flux rope might lead to low densities, in contradiction to the observations.

##  7 Conclusions

Zhao et al. (2017); Kocher et al. (2017) discovered periods in the slow solar
wind and ICMEs when the bare ions of carbon and other elements were severely
depleted. The fact that the fully stripped ions of C, N and O all show drastic
depletions (Zhao et al., 2017; Kocher et al., 2017) strongly suggests that the
cyclotron frequency that they share with He2+is a key factor and that the
strong preferential heating of heavier ions (Kohl et al., 1997) is weakened,
while the magnetic field anomalies similar to SIMFRs (Rivera et al., 2021)
strongly suggest that reconnection plays a significant role. We therefore
hypothesize that reconnection injects cloudlets of relatively dense, perhaps
He-rich plasma into the corona, and that such cloudlets in the region above
ionization freeze-in and the collisional-collisionless transition, but below
the height where all the ions flow freely to 1 AU are the origin of the
dropouts. It is also possible that some other mechanism, such as parametric
decay instabilities (Hahn et al., 2022) produces the density fluctuations.

A plausible, but unproven, interpretation is that He2+ absorbs so much of the
resonant wave power that the heating rate of the bare ions falls below a
critical value for preferential heating (Chandran et al., 2010), and that the
bare carbon and heavier ions are unable to escape the Sun’s gravitational
potential. Density fluctuations and the resulting changes in Alfvén speed
would lead to large variations in Alfvén wave reflection and turbulent heating
rates (Asgari-Targhi et al., 2021). The clumpiness of the solar wind provides
some support for this idea. The analysis by Brooks et al. (2020) indicating
that the slow wind contains both material from opening active region loops and
material injected from the chromosphere is consistent with the general
picture, though the magnitudes of the density contrasts, the sizes of the
clumps, and the heights where the clumps occur are not well known.

Thus we suggest that density inhomogeneities between roughly 3 and 7 R☉ are
created by reconnection in the corona, chromosphere or prominences, and that
they produce regions where weakened preferential heating of bare ions is
unable to overcome gravity, and the bare ions fail to escape from the Sun. The
rapid acceleration of the fast solar wind might mean that region where such
weakened heating would prevent the escape is too close to the solar surface
for the mechanism to operate effectively. ICMEs have such a broad range of
temperatures, heating rates and accelerations that it is difficult to pin down
where such a mechanism would be most effective, but it is known that heating
continues after the initial ejection from the solar surface (Rakowski et al.,
2007; Murphy et al., 2011; Wilson et al., 2022).

If our hypothesis that the common cyclotron frequency of He2+ and the other
fully stripped ions accounts for the dropouts is correct, it supports the
resonant cyclotron absorption models (Hollweg & Isenberg, 2002) for coronal
heating over the models that invoke stochastic heating by lower frequency
waves (Chandran et al., 2010). It is therefore important to test this
hypothesis further. It is difficult to test with remote sensing observations,
because the bare ions have no spectral lines, and the dropouts probably form
well below the regions probed by PSP or Solar Orbiter. Therefore, those tests
are likely to be indirect or model-dependent.

We are far from a complete theory of the origin of the bare ion dropout
events, but we have attempted to constrain the region where they originate. In
particular, the observed density fluctuations are not quantitatively
understood, there are no secure numbers for the wave power spectrum, and we
have not considered the ponderomotive force or ion-ion drag. Transverse
density variations (Downs et al., 2013; Raymond et al., 2014) may severely
affect the Alfvén wave reflection computed from 1D models. Nevertheless, if
the general picture is correct, we might expect that Parker Solar Probe and
Solar Orbiter might measure density enhancements, He abundance enhancements
and magnetic signatures of flux ropes with timescales on the order of an hour
in the radial direction, though the transverse size scales are unknown. If
fully-stripped ions are detected, they might show lower velocities.

This work was carried out as part of NASA Grant 80NSSC19K0853 to the
Smithsonian Astrophysical Observatory. MAT is supported under contract
80NSSC18K1207 from the NASA Heliophysics Supporting Research program to the
Smithsonian Astrophysical Observatory (SAO) and Columbia University. YJR
acknowledges support from the Future Faculty Leaders postdoctoral fellowship
at Harvard University. STL acknowledges support from NASA Grants
80NSSC19K0853, 80NSSC20K0185, 80NSSC18K0645,80NSSC22K0204, and 80NSSC20K0192
to the University of Michigan. We thank the referee, Martin Laming, for
valuable insights that have strengthened the paper.

## References

  * Akmal et al. (2001) Akmal, A., Raymond, J. C., Vourlidas, A., et al. 2001, ApJ, 553, 922, doi: 10.1086/320971
  * Alterman & Kasper (2019) Alterman, B. L., & Kasper, J. C. 2019, ApJ, 879, L6, doi: 10.3847/2041-8213/ab2391
  * Asgari-Targhi et al. (2021) Asgari-Targhi, M., Asgari-Targhi, A., Hahn, M., & Savin, D. W. 2021, ApJ, 911, 63, doi: 10.3847/1538-4357/abe9b4
  * Bemporad (2008) Bemporad, A. 2008, ApJ, 689, 572, doi: 10.1086/592377
  * Brooks et al. (2020) Brooks, D. H., Winebarger, A. R., Savage, S., et al. 2020, ApJ, 894, 144, doi: 10.3847/1538-4357/ab8a4c
  * Cadavid et al. (2019) Cadavid, A. C., Miralles, M. P., & Romich, K. 2019, ApJ, 886, 143, doi: 10.3847/1538-4357/ab4d4e
  * Chandran & Hollweg (2009) Chandran, B. D. G., & Hollweg, J. V. 2009, ApJ, 707, 1659, doi: 10.1088/0004-637X/707/2/1659
  * Chandran et al. (2010) Chandran, B. D. G., Li, B., Rogers, B. N., Quataert, E., & Germaschewski, K. 2010, ApJ, 720, 503, doi: 10.1088/0004-637X/720/1/503
  * Ciaravella & Raymond (2008) Ciaravella, A., & Raymond, J. C. 2008, ApJ, 686, 1372, doi: 10.1086/590655
  * Ciaravella et al. (2001) Ciaravella, A., Raymond, J. C., Reale, F., Strachan, L., & Peres, G. 2001, ApJ, 557, 351, doi: 10.1086/321662
  * Cranmer (2000) Cranmer, S. R. 2000, ApJ, 532, 1197, doi: 10.1086/308620
  * Cranmer (2010) —. 2010, ApJ, 710, 676, doi: 10.1088/0004-637X/710/1/676
  * Cranmer et al. (1999) Cranmer, S. R., Field, G. B., & Kohl, J. L. 1999, ApJ, 518, 937, doi: 10.1086/307330
  * Cranmer & van Ballegooijen (2012) Cranmer, S. R., & van Ballegooijen, A. A. 2012, ApJ, 754, 92, doi: 10.1088/0004-637X/754/2/92
  * Del Zanna et al. (2004) Del Zanna, G., Chiuderi Drago, F., & Parenti, S. 2004, A&A, 420, 307, doi: 10.1051/0004-6361:20034267
  * Dere et al. (2019) Dere, K. P., Del Zanna, G., Young, P. R., Landi, E., & Sutherland, R. S. 2019, ApJS, 241, 22, doi: 10.3847/1538-4365/ab05cf
  * Dissauer et al. (2018) Dissauer, K., Veronig, A. M., Temmer, M., Podladchikova, T., & Vanninathan, K. 2018, ApJ, 863, 169, doi: 10.3847/1538-4357/aad3c6
  * Dobrzycka et al. (2002) Dobrzycka, D., Cranmer, S. R., Raymond, J. C., Biesecker, D. A., & Gurman, J. B. 2002, ApJ, 565, 621, doi: 10.1086/324431
  * Downs et al. (2013) Downs, C., Linker, J. A., Mikić, Z., et al. 2013, Science, 340, 1196, doi: 10.1126/science.1236550
  * Feng et al. (2008) Feng, H. Q., Wu, D. J., Lin, C. C., et al. 2008, Journal of Geophysical Research (Space Physics), 113, A12105, doi: 10.1029/2008JA013103
  * Fisk (1978) Fisk, L. A. 1978, ApJ, 224, 1048, doi: 10.1086/156456
  * Frazin et al. (2003) Frazin, R. A., Cranmer, S. R., & Kohl, J. L. 2003, ApJ, 597, 1145, doi: 10.1086/378558
  * Freed & McKenzie (2018) Freed, M. S., & McKenzie, D. E. 2018, ApJ, 866, 29, doi: 10.3847/1538-4357/aadee4
  * Fu et al. (2020) Fu, H., Harrison, R. A., Davies, J. A., et al. 2020, ApJ, 900, L18, doi: 10.3847/2041-8213/abb083
  * Geiss et al. (1995) Geiss, J., Gloeckler, G., & von Steiger, R. 1995, Space Sci. Rev., 72, 49, doi: 10.1007/BF00768753
  * Gloeckler et al. (2016) Gloeckler, G., Fisk, L. A., & Geiss, J. 2016, in 41st COSPAR Scientific Assembly, Vol. 41, D2.6–3–16
  * Gosling et al. (1995) Gosling, J. T., Birn, J., & Hesse, M. 1995, Geophys. Res. Lett., 22, 869, doi: 10.1029/95GL00270
  * Gurman et al. (1998) Gurman, J. B., Thompson, B. J., Newmark, J. A., & Deforest, C. E. 1998, in Astronomical Society of the Pacific Conference Series, Vol. 154, Cool Stars, Stellar Systems, and the Sun, ed. R. A. Donahue & J. A. Bookbinder, 329
  * Hahn et al. (2018) Hahn, M., D’Huys, E., & Savin, D. W. 2018, ApJ, 860, 34, doi: 10.3847/1538-4357/aac0f3
  * Hahn et al. (2022) Hahn, M., Fu, X., & Savin, D. W. 2022, arXiv e-prints, arXiv:2204.09559.  https://arxiv.org/abs/2204.09559
  * Higginson et al. (2017) Higginson, A. K., Antiochos, S. K., DeVore, C. R., Wyper, P. F., & Zurbuchen, T. H. 2017, ApJ, 840, L10, doi: 10.3847/2041-8213/aa6d72
  * Hollweg (1999) Hollweg, J. V. 1999, J. Geophys. Res., 104, 24781, doi: 10.1029/1999JA900300
  * Hollweg (2006) —. 2006, Journal of Geophysical Research (Space Physics), 111, A12106, doi: 10.1029/2006JA011917
  * Hollweg & Isenberg (2002) Hollweg, J. V., & Isenberg, P. A. 2002, Journal of Geophysical Research (Space Physics), 107, 1147, doi: 10.1029/2001JA000270
  * Huang et al. (2020) Huang, J., Liu, Y., Liu, J., & Shen, Y. 2020, ApJ, 899, L29, doi: 10.3847/2041-8213/abac18
  * Innes et al. (2016) Innes, D. E., Heinrich, P., Inhester, B., & Guo, L. J. 2016, A&A, 592, A17, doi: 10.1051/0004-6361/201527520
  * Kasper et al. (2012) Kasper, J. C., Stevens, M. L., Korreck, K. E., et al. 2012, ApJ, 745, 162, doi: 10.1088/0004-637X/745/2/162
  * Kilpua et al. (2009) Kilpua, E. K. J., Luhmann, J. G., Gosling, J., et al. 2009, Sol. Phys., 256, 327, doi: 10.1007/s11207-009-9366-1
  * Klein & Chandran (2016) Klein, K. G., & Chandran, B. D. G. 2016, ApJ, 820, 47, doi: 10.3847/0004-637X/820/1/47
  * Ko et al. (1996) Ko, Y. K., Fisk, L. A., Gloeckler, G., & Geiss, J. 1996, Geophys. Res. Lett., 23, 2785, doi: 10.1029/96GL02449
  * Kocher et al. (2017) Kocher, M., Lepri, S. T., Landi, E., Zhao, L., & Manchester, W. B., I. 2017, ApJ, 834, 147, doi: 10.3847/1538-4357/834/2/147
  * Kohl et al. (1995) Kohl, J. L., Esser, R., Gardner, L. D., et al. 1995, Sol. Phys., 162, 313, doi: 10.1007/BF00733433
  * Kohl et al. (1997) Kohl, J. L., Noci, G., Antonucci, E., et al. 1997, Sol. Phys., 175, 613, doi: 10.1023/A:1004903206467
  * Kumar & Rust (1996) Kumar, A., & Rust, D. M. 1996, J. Geophys. Res., 101, 15667, doi: 10.1029/96JA00544
  * Laming (2017) Laming, J. M. 2017, ApJ, 844, 153, doi: 10.3847/1538-4357/aa7cf1
  * Laming et al. (2019) Laming, J. M., Vourlidas, A., Korendyke, C., et al. 2019, ApJ, 879, 124, doi: 10.3847/1538-4357/ab23f1
  * Landi et al. (2014) Landi, E., Oran, R., Lepri, S. T., et al. 2014, ApJ, 790, 111, doi: 10.1088/0004-637X/790/2/111
  * Landi et al. (2010) Landi, E., Raymond, J. C., Miralles, M. P., & Hara, H. 2010, ApJ, 711, 75, doi: 10.1088/0004-637X/711/1/75
  * Lazarian & Vishniac (1999) Lazarian, A., & Vishniac, E. T. 1999, ApJ, 517, 700, doi: 10.1086/307233
  * Lee et al. (2009) Lee, J. Y., Raymond, J. C., Ko, Y. K., & Kim, K. S. 2009, ApJ, 692, 1271, doi: 10.1088/0004-637X/692/2/1271
  * Li & Yao (2020) Li, D., & Yao, S. 2020, ApJ, 891, 79, doi: 10.3847/1538-4357/ab7197
  * Lin et al. (2004) Lin, J., Raymond, J. C., & van Ballegooijen, A. A. 2004, ApJ, 602, 422, doi: 10.1086/380900
  * Lionello et al. (2019) Lionello, R., Downs, C., Linker, J. A., et al. 2019, Sol. Phys., 294, 13, doi: 10.1007/s11207-019-1401-2
  * Liu et al. (2006) Liu, Y., Richardson, J. D., Belcher, J. W., Kasper, J. C., & Elliott, H. A. 2006, Journal of Geophysical Research (Space Physics), 111, A01102, doi: 10.1029/2005JA011329
  * Loureiro et al. (2012) Loureiro, N. F., Samtaney, R., Schekochihin, A. A., & Uzdensky, D. A. 2012, Physics of Plasmas, 19, 042303, doi: 10.1063/1.3703318
  * Lynch et al. (2004) Lynch, B. J., Antiochos, S. K., MacNeice, P. J., Zurbuchen, T. H., & Fisk, L. A. 2004, ApJ, 617, 589, doi: 10.1086/424564
  * Mewaldt et al. (1979) Mewaldt, R. A., Spalding, J. D., Stone, E. C., & Vogt, R. E. 1979, ApJ, 231, L97, doi: 10.1086/183012
  * Miyamoto et al. (2014) Miyamoto, M., Imamura, T., Tokumaru, M., et al. 2014, ApJ, 797, 51, doi: 10.1088/0004-637X/797/1/51
  * Moldwin et al. (2000) Moldwin, M. B., Ford, S., Lepping, R., Slavin, J., & Szabo, A. 2000, Geophys. Res. Lett., 27, 57, doi: 10.1029/1999GL010724
  * Murphy et al. (2011) Murphy, N. A., Raymond, J. C., & Korreck, K. E. 2011, ApJ, 735, 17, doi: 10.1088/0004-637X/735/1/17
  * November & Koutchmy (1996) November, L. J., & Koutchmy, S. 1996, ApJ, 466, 512, doi: 10.1086/177528
  * Ogilvie & Hirshberg (1974) Ogilvie, K. W., & Hirshberg, J. 1974, J. Geophys. Res., 79, 4595, doi: 10.1029/JA079i031p04595
  * Oran et al. (2015) Oran, R., Landi, E., van der Holst, B., et al. 2015, ApJ, 806, 55, doi: 10.1088/0004-637X/806/1/55
  * Rakowski et al. (2007) Rakowski, C. E., Laming, J. M., & Lepri, S. T. 2007, ApJ, 667, 602, doi: 10.1086/520914
  * Rakowski et al. (2011) Rakowski, C. E., Laming, J. M., & Lyutikov, M. 2011, ApJ, 730, 30, doi: 10.1088/0004-637X/730/1/30
  * Raymond (1979) Raymond, J. C. 1979, ApJS, 39, 1, doi: 10.1086/190562
  * Raymond et al. (2014) Raymond, J. C., McCauley, P. I., Cranmer, S. R., & Downs, C. 2014, ApJ, 788, 152, doi: 10.1088/0004-637X/788/2/152
  * Raymond et al. (1997) Raymond, J. C., Kohl, J. L., Noci, G., et al. 1997, Sol. Phys., 175, 645, doi: 10.1023/A:1004948423169
  * Rivera et al. (2019) Rivera, Y. J., Landi, E., Lepri, S. T., & Gilbert, J. A. 2019, ApJ, 874, 164, doi: 10.3847/1538-4357/ab0e11
  * Rivera et al. (2020) —. 2020, ApJ, 899, 11, doi: 10.3847/1538-4357/aba4a9
  * Rivera et al. (2021) Rivera, Y. J., Lepri, S. T., Raymond, J. C., et al. 2021, ApJ, 921, 93, doi: 10.3847/1538-4357/ac1676
  * Savage et al. (2010) Savage, S. L., McKenzie, D. E., Reeves, K. K., Forbes, T. G., & Longcope, D. W. 2010, ApJ, 722, 329, doi: 10.1088/0004-637X/722/1/329
  * Schwadron et al. (1999) Schwadron, N. A., Fisk, L. A., & Zurbuchen, T. H. 1999, ApJ, 521, 859, doi: 10.1086/307575
  * Scott et al. (2022) Scott, R. B., Bradshaw, S. J., & Linton, M. G. 2022, arXiv e-prints, arXiv:2206.06471.  https://arxiv.org/abs/2206.06471
  * Sheeley & Wang (2014) Sheeley, N. R., J., & Wang, Y. M. 2014, ApJ, 797, 10, doi: 10.1088/0004-637X/797/1/10
  * Sheeley et al. (1997) Sheeley, N. R., Wang, Y. M., Hawley, S. H., et al. 1997, ApJ, 484, 472, doi: 10.1086/304338
  * Shen et al. (2013) Shen, C., Lin, J., Murphy, N. A., & Raymond, J. C. 2013, Physics of Plasmas, 20, 072114, doi: 10.1063/1.4816711
  * Shen et al. (2017) Shen, C., Raymond, J. C., Mikić, Z., et al. 2017, ApJ, 850, 26, doi: 10.3847/1538-4357/aa93f3
  * Simnett (1995) Simnett, G. M. 1995, Space Sci. Rev., 73, 387, doi: 10.1007/BF00751241
  * Spicer et al. (1998) Spicer, D. S., Feldman, U., Widing, K. G., & Rilee, M. 1998, ApJ, 494, 450, doi: 10.1086/305203
  * Spitzer (1968) Spitzer, L. 1968, Diffuse matter in space (New York: Interscience)
  * Szente et al. (2022) Szente, J., Landi, E., & van der Holst, B. 2022, ApJ, 926, 35, doi: 10.3847/1538-4357/ac3918
  * Uritsky et al. (2021) Uritsky, V. M., DeForest, C. E., Karpen, J. T., et al. 2021, ApJ, 907, 1, doi: 10.3847/1538-4357/abd186
  * van Ballegooijen & Asgari-Targhi (2016) van Ballegooijen, A. A., & Asgari-Targhi, M. 2016, ApJ, 821, 106, doi: 10.3847/0004-637X/821/2/106
  * van der Holst et al. (2014) van der Holst, B., Sokolov, I. V., Meng, X., et al. 2014, ApJ, 782, 81, doi: 10.1088/0004-637X/782/2/81
  * Verdini et al. (2010) Verdini, A., Velli, M., Matthaeus, W. H., Oughton, S., & Dmitruk, P. 2010, ApJ, 708, L116, doi: 10.1088/2041-8205/708/2/L116
  * von Steiger et al. (2000) von Steiger, R., Schwadron, N. A., Fisk, L. A., et al. 2000, J. Geophys. Res., 105, 27217, doi: 10.1029/1999JA000358
  * Wang et al. (1999a) Wang, Y. M., Sheeley, N. R., J., Howard, R. A., Cyr, O. C. S., & Simnett, G. M. 1999a, Geophys. Res. Lett., 26, 1203, doi: 10.1029/1999GL900209
  * Wang et al. (1999b) Wang, Y. M., Sheeley, N. R., J., Howard, R. A., Rich, N. B., & Lamy, P. L. 1999b, Geophys. Res. Lett., 26, 1349, doi: 10.1029/1999GL900177
  * Wang et al. (1998) Wang, Y. M., Sheeley, N. R., J., Socker, D. G., et al. 1998, ApJ, 508, 899, doi: 10.1086/306450
  * Warren et al. (2018) Warren, H. P., Brooks, D. H., Ugarte-Urra, I., et al. 2018, ApJ, 854, 122, doi: 10.3847/1538-4357/aaa9b8
  * Weberg et al. (2015) Weberg, M. J., Lepri, S. T., & Zurbuchen, T. H. 2015, ApJ, 801, 99, doi: 10.1088/0004-637X/801/2/99
  * Weberg et al. (2012) Weberg, M. J., Zurbuchen, T. H., & Lepri, S. T. 2012, ApJ, 760, 30, doi: 10.1088/0004-637X/760/1/30
  * Wilson et al. (2022) Wilson, M. L., Raymond, J. C., Lepri, S. T., et al. 2022, ApJ, 927, 27, doi: 10.3847/1538-4357/ac4d35
  * Yao et al. (2010) Yao, S., Marsch, E., Tu, C.-Y., & Schwenn, R. 2010, Journal of Geophysical Research (Space Physics), 115, A05103, doi: 10.1029/2009JA014914
  * Ye et al. (2021) Ye, J., Cai, Q., Shen, C., et al. 2021, ApJ, 909, 45, doi: 10.3847/1538-4357/abdeb5
  * Zhao et al. (2017) Zhao, L., Landi, E., Lepri, S. T., et al. 2017, ApJS, 228, 4, doi: 10.3847/1538-4365/228/1/4