# Formation of Coronal Mass Ejection and Post-eruption Flow of Solar Wind on
2010 August 18 event 111Released on ,,

Vladimir Slemzin P.N. Lebedev Physical Institute of the Russian Academy of
Sciences (LPI),53 Leninskiy Prospekt,119991, Moscow, Russia  Farid Goryaev
P.N. Lebedev Physical Institute of the Russian Academy of Sciences (LPI),53
Leninskiy Prospekt,119991, Moscow, Russia  Denis Rodkin P.N. Lebedev Physical
Institute of the Russian Academy of Sciences (LPI),53 Leninskiy
Prospekt,119991, Moscow, Russia

###### Abstract

The state of the space environment plays a significant role for forecasting of
geomagnetic storms produced by disturbances of the solar wind (SW). Coronal
mass ejections (CMEs) passing through the heliosphere often have a prolonged
(up to several days) trail with declining speed, which affects propagation of
the subsequent SW streams. We studied the CME and the post-eruption plasma
flows behind the CME rear in the event on 2010 August 18 observed in
quadrature by several space-based instruments. Observations of the eruption in
the corona with EUV telescopes and coronagraphs revealed several discrete
outflows followed by a continuous structureless post-eruption stream. The
interplanetary coronal mass ejection (ICME), associated with this CME, was
registered by PLAsma and SupraThermal Ion Composition (PLASTIC) instrument
aboard the Solar TErrestrial RElations Observatory (STEREO-A) between August
20, 16:14 UT and August 21, 13:14 UT, after which the SW disturbance was
present over 3 days. Kinematic consideration with the use of the gravitational
and Drag-Based models has shown that the discrete plasma flows can be
associated with the ICME, whereas the post-eruption outflow was arrived in the
declining part of the SW transient. We simulated the Fe-ion charge
distributions of the ICME and post-CME parts of SW using the plasma
temperature and density in the ejection region derived from the Differential
Emission Measure analysis. The results demonstrate that in the studied event
the post-ICME trailing region was associated with the post-eruption flow from
the corona, rather then with the ambient SW entrained by the CME.

Solar corona (1483) — Solar wind(1534) — Solar physics(1476) — Solar coronal
mass ejections(310)

##  1 Introduction

Interplanetary plasma consisting mainly of the slow moving solar wind (SW)
represents a medium, in which recurrent disturbances of SW associated with
fast quasistationary streams from coronal holes and non-periodic disturbances
associated with coronal mass ejections (CMEs) propagate (Lüst, 1963; Russell,
2001). Depending on their magnitude and direction, CMEs may give rise to
geomagnetic storms, scattering of galactic cosmic rays and produce other
perturbations of all near-Earth environment. Thus, detection of the CME
initiation in the solar corona and prediction of its propagation in the
heliosphere is one of the most important tasks of the space weather
forecasting. Commonly such prediction consists in estimation of arrival time
and speed of the CME frontal structure to the observation site without taking
into account the post-eruption effects. However, very often (see, e.g. Lugaz
et al., 2017; Rodkin et al., 2018), due to their large-scale structure,
successive CMEs may interact in the heliosphere, which results in a change of
their initial kinematic and magnetic parameters. A statistical study of Temmer
et al. (2017) in the time period 2011 – 2015 has shown that CMEs often are
followed by a trailing region behind its rear with declining speed with
duration up to several days which much longer than the average CME duration
itself (about 1.3 days). As a result, powerful CMEs can cause disturbances of
the interplanetary medium, which may led to significant deviations of the CME
arrival times and speeds from the initially predicted, especially, in the case
of slow CMEs (Möstl et al., 2014; Corona-Romero et al., 2017; Shugay et al.,
2018; Ravishankar & Michałek, 2019).

The aim of this work is to clarify the nature of the post-Interplanetary
Coronal Mass Ejection (ICME) perturbation of SW: whether it is associated with
entrainment of the interplanetary medium by the passed CME or with some post-
CME plasma flow from the eruption site. We consider the case of the large
eruption occurred on 2010 August 18 at the western solar limb, which was
observed by several space telescopes and coronagraphs, studied formation of
the eruption flows in the corona and in the heliosphere and established the
correspondence between the flows and the SW disturbances measured in situ. The
state of the coronal plasma during the eruption process was determined from
the differential emission measure (DEM) analysis performed on the base of the
multiwave EUV images.The DEM function describes the amount of thermal plasma
along the line of sight at a given electron temperature retrieved from
intensities in spectral bands with different temperature responces. By
separating emission in specific temperature ranges, DEM enables to discern the
spatial and temporal dynamics of coronal structures participating in the
eruption process (e.g., Grechnev et al., 2019; Saqri et al., 2020; Heinemann
et al., 2021). A number of algorithms have been developed to derive a coronal
DEM from SDO/AIA images in multiple bandpasses (e.g., Hannah & Kontar, 2012;
Plowman et al., 2013; Plowman & Caspi, 2020). Detailed comparison of different
algorithms is beyond the scope of this paper, and can be found, for example,
in Aschwanden et al. (2015). In our case of the limb eruption we use the
method and software described recently in Plowman & Caspi (2020). Using the
data determined by the DEM analysis (the plasma densities and emission-
weighted temperatures), we performed modeling of the Fe-ion charge
distribution of the plasma outflows “frozen-in” at the boundary of the corona
for several temporal intervals: in the quiet state before eruption, during the
CME formation and after it’s liftoff. A comparison of the modeled Fe-ion
charge states with the measured ones has shown that the post-ICME disturbance
of SW is associated with the post-eruption coronal flow.

##  2 Data

In the analysis of the eruption plasma in the inner corona at the distances up
to 1.7 $R_{\odot}$ we used the EUV multiwavelength images from the Atmospheric
Imaging Assembly telescope (AIA: Lemen et al., 2012) aboard the Solar Dynamic
Observatory (SDO), the images in the 174 Å band of the Sun Watcher with Active
Pixels and Image Processing (SWAP) telescope as a part of the Project for
Onboard Autonomy 2 (PROBA2) mission (Seaton et al., 2013) and the images in
195 Å band from the Extreme-Ultra-Violet Imager (EUVI) as a part of Sun Earth
Connection Coronal and Heliospheric Investigation (SECCHI: Howard et al.,
2008) aboard the Solar TErrestrial RElations Observatory (STEREO) spacecraft
(Kaiser et al., 2008). At the distances 2 – 30 $R_{\odot}$ we explore the CME
formation from the data of the LASCO C2 and C3 coronagraphs (Brueckner et al.,
1995) aboard the Solar and Heliospheric Observatory (SOHO: Domingo et al.,
1995). The SW data, including the Fe-ion charge distributions, magnetic field
and plasma parameters, were taken from observations with the PLAsma and
SupraThermal Ion Composition (PLASTIC: Galvin et al., 2008) and the In situ
Measurements of Particles And CME Transients (IMPACT: Luhmann et al., 2008)
instruments.

##  3 Description of the event and kinematics of eruption

We investigated the eruption in active region (AR) 11093 on 2010 August 18,
when it was seen from the Earth at the Western limb. During the preceding
days, when this AR crossed the solar disk, it produced a series of eruptions
studied by several researchers (Vemareddy et al., 2012; Tun & Vourlidas, 2013;
Lario et al., 2017; D’Huys et al., 2017). On August 18, the most powerful CME
(partial halo) was registered above the Western limb by LASCO C2 at 05:48 UT
and by STEREO-A/COR2 at 05:54 UT. The SolarDemon dimming detection system
(Kraaikamp & Verbeeck, 2015) determined that the eruption was accompanied by a
large dimming that appeared in the corona above the limb at 05:02 UT and
existed at least until 07:02 UT.

This eruption was observed in quadrature from two positions: from the Earth by
SDO/AIA and Proba 2/SWAP EUV telescopes, by SOHO/LASCO coronagraphs, and from
the STEREO-A position by the SECCHI/EUVI telescope. The ICME and subsequent
post-eruption SW flows were detected in situ by the STEREO-A/PLASTIC and
IMPACT instruments.

In Figure 1 the images of AR 11093 are shown before eruption on August 18 at
04:00 UT in the AIA 193 Å band (Figure 1a) and in the STA/EUVI 195 Å band
(Figure 1b). Figure 1c shows the PFSS-modeled magnetic field structure on 2010
August 14 at 07:00 UT, when the AR was on the solar disk, taken from the
Lockheed Martin Solar and Astrophysics Laboratory (LMSAL)
archive222https://www.lmsal.com/solarsoft/archive/sswdb-
new/packages/pfss/l1q_synop. The magnetic field structure included closed
coronal loops and a pseudostreamer (Wang, 2015), that separated a small
equatorial coronal hole near AR 11093 and the northern polar coronal hole.
Westward from the AR, a large filament F was seen, which later participated in
the eruption.

Figure 1: (a) Active Region 11093 seen on 2010 August 18 before eruption by
SDO/AIA in 193 Å at 04:00:07 UT; (b) by STEREO-A/EUVI in 195 Å at 04:00:30 UT.
(c) The magnetic field map of the Sun in the PFSS approximation for 2010
August 14, 07:00 UT (taken from the database
https://www.lmsal.com/solarsoft/archive/sswdb-new/packages/pfss/l1q_synop).
(d, e, f) The polar maps of the coronal structures during eruption in AIA 171
Å (2010 August 18, 05:00:48 UT), LASCO C2 (06:12:07 UT) and LASCO C3 (09:06:05
UT). The position angle counts out clockwise from the North. (g) The time-
distance (T-D) slice map of the eruption flows derived from the LASCO C2 polar
maps; (h) the same from the LASCO C3 maps; (i) the combined T-D plots of the
eruption flows including the AIA 171 Å and SWAP 174 Å (plus signs), C2
(crosses) and C3 (circles) data.

At the initial stage of eruption, below a distance of 2 $R_{\odot}$, when the
CME structure was not finally formed, the coronal loops started to move upward
(Figure 1d) ,which was seen by the EUV SDO/AIA (up to 1.3 $R_{\odot}$) and
PROBA2/SWAP (up to 1.7 $R_{\odot}$) telescopes. Then, from 2 to 5 $R_{\odot}$
(in LASCO C2 observations), during the solar flare (GOES C4.5, start at 04:45
UT, maximum at 05:48 UT, end at 09:30 UT), the eruption plasma was accelerated
and transformed from a system of loops to several successive compact
structures. At that period, the filament F seen in Figure 1a and 1b manifested
a draining towards the eruption site along the neutral magnetic line, so it
might enrich the eruption plasma by the cold filament material.

Figure 1d, 1e and 1f demonstrate the polar intensity maps of AIA 171 Å (2010
August 18, 05:00:48 UT), LASCO C2 (06:12:07 UT) and LASCO C3 (09:06:05 UT).
The position angle counts out clockwise from the North (it corresponds to the
ordinary LASCO position angle by the relation $360^{\circ}$ – PALASCO). The
apex of the coronal structure seen at the latitude angle of $73^{\circ}$ in
EUV below 1.3 $R_{\odot}$ shifted to $115^{\circ}$ at $R=2-5~{}R_{\odot}$ (C2)
and split into three parts above 10 $R_{\odot}$ (C3).

We identified the upward plasma flows by two methods. The confined plasma
flows were identified as bright ridges on the time-height maps (Figure 1g and
1h) created from the LASCO C2 and C3 (Figure 1e and 1f) polar maps.

To select the plasma flows that may contribute to SW, we integrated intensity
of the polar maps at each height on the C2 map within the position angles
$76.3^{\circ}-86.3^{\circ}$ and on the C3 map within $86.3^{\circ}\pm
2^{\circ}$. These ranges correspond to inclination of the eruption structure
with distance to the STA position near the equator (the HEEQ latitude of STA
for 2010 August 18 was equal to $3.7^{\circ}$). According to the WSA-ENLIL-
DONKI-HELCATS model 333http://helioweather.net/archive/2010/08/, in the
ecliptic plane the CME angular width is more than $60^{\circ}$, whereas the
STA position is declined from the CME apex on the angle less than
$10^{\circ}$. Thus, no corrections for the CME geometry and projection effect
have been needed. As a result, we obtained the time-distance maps shown on
Figure 1g (the C2 map) and Figure 1h (the C3 map). We distinguished 4 flows on
the C2 map and 5 flows on the C3 map which are combined together on Figure 1i.
The flows 1 and 2 seen in C2 and C3 are evidently match with the initial
upward moving structure seen in EUV below 1.3 $R_{\odot}$. The flows 3, 4 and
5 are seen only on the C2 and C3 maps, so they were originated above 2
$R_{\odot}$, probably at the streamer’s top. The visibility of all flows
diminishes with distance so, that they become indistinguishable from
background between 10 and 20 $R_{\odot}$ due to weakening of contrast.
Nevertheless, we expected that all flows may appear in SW.

All five flows were originated and accelerated in the corona during the
C-class flare up to 09:30 UT. After the end of the flare, the LASCO images
showed that the plasma outflow lasted as a continuous structureless stream. We
estimated the speed of this continuous flow by analysis of cross-correlation
between irregularities of intensity in the C3 polar maps at different heights
as a function of time between 11:18 UT and 12:54 UT. We found the mean speed
of this component to be $\backsim 530~{}km~{}s^{-1}$, which corresponds to its
startup from the solar surface at about 10:00 UT. We regard this component as
the sixth flow.

We suggested that after the end of the flare the flows were decelerated by two
forces: the gravitation force below 20 $R_{\odot}$ and the MHD drag force
above that distance (Shen et al., 2012; Grechnev et al., 2019). The
gravitational deceleration is described by the formula:

$v_{1}^{2}=v_{0}^{2}-2GM_{\odot}(\frac{1}{r_{0}}-\frac{1}{r_{1}})\,,$ (1)

with $v_{0}(v_{1})$ being a velocity of the flow at the distance of
$r_{0}(r_{1})$ from the Sun’s center, G is the universal gravity constant, and
$M_{\odot}$ is the mass of the Sun. In the Drag-based Model (DBM: Vršnak et
al., 2013; Vršnak, 2021) deceleration is defined by the magnetic drag force
between the flow and the ambient media according to the equation:

$dv/dt=-\gamma(v-w)|v-w|\,,$ (2)

where $v$ is the flow speed, $w$ is the speed of the ambient SW, $\gamma$ is
the MHD drag parameter. Integration of this equation along the path from the
initial point to the observer gives the arrival speed and time. As the initial
parameters, the model uses the flow speeds and times at $R=20~{}R_{\odot}$.

The equation (2) is basically analogous to the aerodynamic drag considered by
Cargill (2004). The drag parameter can be expressed as:

$\gamma=\frac{c_{d}}{L\cdot(\frac{\rho}{\rho_{w}}+\frac{1}{2})}\,,$ (3)

where $c_{d}$ is the dimensionless drag coefficient (typically, $c_{d}=1$),
$L$ is the thickness of the ICME in the radial direction, $\rho$ and
$\rho_{w}$ are densities of the ICME and the ambient plasma. In the typical
conditions, $\gamma=0.2–2.10^{7}~{}km^{-1}$ (for details, see Vršnak et al.
(2013); Žic et al. (2015)).

As it follows from the definitions, the model was developed for a single
isolated CME propagated in the stationary ambient solar wind. The advanced
version of DBM – the Drag-Based Ensemble model (Dumbović et al., 2018) uses
the most probable model parameters based on the typical CME geometry and
ambient plasma conditions, which is important for operative forecasting.
Examples of application of DBM and comparison with other prediction models can
be found in Vršnak et al. (2014); Shi et al. (2015); Napoletano et al. (2018);
Vršnak (2021); Dumbović et al. (2021) and references herein. The drag-based
model for prediction of the CME fronts and sheaths directed to the Earth using
the height dependence and de-projected velocities with assistance of the
STEREO data was described by Hess & Zhang (2015). The DBM-based models for
prediction of the Earth-directed CMEs using the data from the STEREO
Heliospheric Imagers are recently developed, such as the elliptic model
ElEvoHI (Rollett et al., 2016) and ElEvoHI 2.0 elliptic front deformation
model (Hinterreiter et al., 2021).

In our case, the CME is formed from a series of consecutive flows followed by
the unstructured post-eruption flow propagated towards STA, so we cannot use
the STEREO data about their geometric shape and movement outside the corona.
However, we suggested that DBM can be used in this case taking into account
that the flows propagated along the same magnetic channel opened by the
frontal structure of the CME with the appropriate ambient plasma speed. By the
use of DBM, we aimed to check its applicability for this non-typical case and
determine the particular values of the model parameters for the best agreement
of the model results with the measurements. As the decisive parameter, we
consider matching of the modeled flow speed with the measured in situ speed of
the SW protons for the whole ensemble of flows.

Table 1 presents the initial data and the modeled times and speeds of the SW
flows calculated with the base version of DBM in comparison with the measured
in situ on STA. We have made a series of calculations and found that the
discrete flows 1 – 3 and 5 well correspond to the ICME density peak with
$\gamma=0.3\cdot 10^{-7}~{}km^{-1}$ for the first flow and $0.13\cdot
10^{-7}~{}km^{-1}$ for the others (the value averaged over the flows 2 – 5),
and the ambient plasma speed for all flows $w=445~{}km\cdot s^{-1}$. For the
unstructured flow we found $\gamma=0.13\cdot 10^{-7}~{}km^{-1}$ and the same
speed of the ambient plasma.

The spreads in the flow arrival times and speeds are summarized from two
parts: uncertainties from the time-distance maps due the data discretization
shown in the $T_{20}$ and $V_{20}$ columns of Table 1, and the model
uncertainties of DBM. Typically, DBM gives the CME arrival times with the
uncertainty of 9 – 14 hours (see the references cited above). However, our
investigation based on the data of 2010 – 2011 (Rodkin et al., 2018) has shown
that in the case of the single ICMEs (not interacted with other SW transients
in the heliosphere) the inaccuracy of the DBM results in the arrival time
amounts of 8 hours, in the speed – $65~{}km\cdot s^{-1}$. As a result, for all
flows, except flow 4, the difference between the modeled and measured times
and speeds did not exceed the final errors in $V_{STA}$ in Table 1. Flow 4 did
not fit to the SW data under any calculation parameters, probably, because it
was rather weak and merged to the main flows.

Table 1: Kinematic parameters of the CME and post-eruption flows

№ of | $R_{td}$ | $T_{td}$ | $T_{20}$ | $V_{20}$ | $T_{STA}$ | $V_{STA}$ | $V_{p}$
---|---|---|---|---|---|---|---
flow | $R_{\odot}$ | Aug 18 (UT) | Aug 18 (UT) | ($km~{}s^{-1}$) | (UT) | ($km~{}s^{-1}$) | ($km~{}s^{-1}$)
1 | 17.75 | 09:36 | $10:15\pm 0.22h$ | $670\pm 26$ | Aug 21 00:58$\pm 10h$ | $533\pm 66$ | 585
2 | 16.74 | 10:33 | $11:37\pm 0.24h$ | $599\pm 23$ | Aug 21 03:20$\pm 12h$ | $550\pm 69$ | 580
3 | 13.59 | 10:55 | $12:42\pm 0.28h$ | $686\pm 32$ | Aug 20 22:27$\pm 12h$ | $590\pm 70$ | 551
4 | 12.30 | 11:23 | $13:17\pm 0.33h$ | $872\pm 69$ | Aug 20 12:59$\pm 12h$ | $671\pm 75$ | 329
5 | 12.47 | 12:13 | $14:36\pm 0.37h$ | $606\pm 48$ | Aug 21 05:20$\pm 18h$ | $553\pm 80$ | 574
6 | 9.38 | 12:54 | $16:53\pm 0.40h$ | $508\pm 56$ | Aug 21 19:39$\pm 16h$ | $500\pm 77$ | 511

Note. — $R_{td}$ is a maximum distance in the time-distance map, $T_{td}$ is a
time at $R_{td}$, $T_{20}$ is a time at $20R_{\odot}$, $V_{20}$ is a speed at
$20R_{\odot}$, $T_{STA}$ is an arrival time at STA modeled by DBM, $V_{STA}$
is a speed at STA modeled by DBM, $V_{p}$ is a speed of protons measured at
STA

##  4 DEM diagnostics of plasma flows in the corona

We investigated variation of the plasma temperature and density in the
eruption region using the DEM distribution derived from the AIA EUV images.
Intensity fluxes in spectral bands are related to DEM via the expression:

$F_{i}=\int_{T}G_{i}(T)\mathrm{DEM}(T)\,dT\,,$ (4)

where $F_{i}$ is the intensity flux and $G_{i}(T)$ is the temperature response
function of the passband i.

To determine DEM for the eruption plasma, we applied the method and software
developed by Plowman & Caspi (2020). The integral of DEM over the temperature
gives the total emission measure (EM) integrated along the line of sight:
$\mathrm{EM}=\int_{T}\mathrm{DEM}(T)\,dT$. Using the obtained DEM, one can
calculate the emission-weighted temperature (e.g., Cheng et al., 2012; Saqri
et al., 2020):

$T_{\mathrm{em}}=\frac{\int_{T}T\cdot\mathrm{DEM}(T)\,dT}{\mathrm{EM}}\,.$ (5)

Based on the EM structure, we can estimate the plasma density, assuming that
the depth of the structure along the line of sight ($L$) is approximately
equal to its visible width (the same method can be found, for example, in
Cheng et al., 2012). So the plasma density can be estimated as :

$N_{e}=\sqrt{\frac{\mathrm{EM}}{L}}\,.$ (6)

To retrieve DEM, we used the AIA/SDO images of the solar corona in six
channels (94 Å, 131 Å, 171 Å, 193 Å, 211 Å, 335 Å), that coverage a broad
temperature range (from $10^{5}$ to above $10^{7}K$). The input error of each
pixel in AIA images was calculated using $aia_{-}bp_{-}estimate_{-}error$
routine considering the data obtained during eclipses (Heinemann et al.,
2021).

Stray light in some cases can significantly disturb intensities of the AIA
images (Wendeln & Landi, 2018; Saqri et al., 2020; Heinemann et al., 2021) in
particular, above the limb, where intensities are fast weakening. In our case
no correction for stray light was needed within the typical error of the DEM
reconstruction (about 20 %).

The errors may occur in the DEM solution at high flow speeds (over
$800~{}km~{}s^{-1}$, see Grechnev et al. (2019)) due to non-simultaneity in
the registration of images in different AIA channels. In our case, it is
possible to compute the DEM without a compensation for its motion, since the
flow speeds at distances $1.2~{}R_{\odot}$ were about $100~{}km~{}s^{-1}$.

We analyzed DEM in the AIA field of view for the several moments on 2010
August 18: before the eruption at 04:01 UT, during the development of the
solar flare at 05:20 UT, 05:22 UT and 05:25 UT, when the plasma rose up in the
AIA field of view, and in the post-eruption stage at 10:00 UT, when the CME
leaved the corona.

In Figure 2, we show the EM polar maps at 05:20 UT in three temperature ranges
$5.5<\mathrm{log}_{10}T<6.3$ (A), $6.3<\mathrm{log}_{10}T<6.8$ (B), and
$6.8<\mathrm{log}_{10}T<7.2$ (C). The right panel shows variation of the DEM
temperature distribution in the indicated box before (04:01 UT), during (05:20
UT) and after (10:00 UT) eruption. The DEM profiles were averaged over the box
$1.15\pm 0.02R_{\odot}$ and $73^{\circ}\pm 1^{\circ}$ in the position angle,
which corresponds to the highest total EM during eruption. The DEM was
considered only up to $\mathrm{log}_{10}T=7.2$ because of the artifacts
appeared due to the low temperature sensitivity of the AIA channels at high
temperatures (Plowman & Caspi, 2020). To calculate the plasma density in the
hottest range ($\mathrm{log}_{10}T>6.8$), the value of EM integrated over the
temperature was doubled, since the DEM distribution at this temperature range
included only half of the peak.

Figure 2: Polar EM maps for 3 temperature ranges (A:
$5.5<\mathrm{log}_{10}T<6.3$, B: $6.3<\mathrm{log}_{10}T<6.8$, and C:
$6.8<\mathrm{log}_{10}T<7.2$) at 05:20 UT and the DEM temperature distribution
in the indicated box at three time moments. Red curve – 04:01 UT ($\chi^{2}$ =
0.99), black – 05:20 UT ($\chi^{2}$ = 0.95), green – 10:00 UT ($\chi^{2}$ =
0.94)

In Table 2 we show the mean values of plasma density and emission-weighted
temperature in three ranges: $5.5<\mathrm{log}_{10}T<6.3$,
$6.3<\mathrm{log}_{10}T<6.8$, and $6.8<\mathrm{log}_{10}T<7.2$. The mean
values at 05:20 UT, 04:01 UT, 10:00 UT were averaged over the box as described
above. The box was shifted to $1.17~{}R_{\odot}$ at 05:22 UT, and to
$1.20~{}R_{\odot}$ at 05:25 UT according to the plasma movement. In the quiet
conditions, before eruption (04:01 UT) and after eruption (10:00 UT),
densities in the hot temperature range ($6.8<\mathrm{log}_{10}T<7.2$) were
larger than those in the cold range ($5.5<\mathrm{log}_{10}T<6.3$), although
in the histograms of Figure 2 the relation between the corresponding EM values
is reverse. The cause is that in the quiet conditions the depth of the hot
structures was much less (more than one order) than of the cold ones. During
the eruption (05:20 – 05:25 UT), density in the hot range increases due to
inflow of the heated plasma of the reconnected surrounding loops with the
medium temperature $6.3<\mathrm{log}_{10}T<6.8$. After eruption (at 10:00 UT)
densities in all temperature ranges drop down due to liftoff of the CME.

Table 2: The mean values of plasma density and emission-weighted temperature for 5 time moments in three temperature ranges  | $5.5<\mathrm{log}_{10}T<6.3$ | $6.3<\mathrm{log}_{10}T<6.8$ | $6.8<\mathrm{log}_{10}T<7.2$
---|---|---|---
Time | $N_{e}~{}(10^{8})$ | $T_{\mathrm{em}}$ | $N_{e}~{}(10^{8})$ | $T_{\mathrm{em}}$ | $N_{e}~{}(10^{8})$ | $T_{\mathrm{em}}$
(UT) | $(cm^{-3})$ | $(MK)$ | $(cm^{-3})$ | $(MK)$ | $(cm^{-3})$ | $(MK)$
04:01 | $1.0\pm 0.1$ | $1.5\pm 0.4$ | $4.8\pm 0.5$ | $3.4\pm 0.7$ | $3.7\pm 0.2$ | -
05:20 | $1.3\pm 0.1$ | $1.4\pm 0.3$ | $3.3\pm 0.2$ | $3.6\pm 0.3$ | $5.2\pm 1.0$ | $10.6\pm 4.5$
05:22 | $1.1\pm 0.1$ | $1.4\pm 0.2$ | $3.1\pm 0.2$ | $3.6\pm 0.4$ | $4.6\pm 1.0$ | $10.5\pm 4.9$
05:25 | $1.0\pm 0.1$ | $1.4\pm 0.3$ | $2.5\pm 0.2$ | $3.5\pm 0.5$ | $3.8\pm 0.5$ | $10.6\pm 3.2$
10:00 | $0.8\pm 0.1$ | $1.4\pm 0.1$ | $2.0\pm 0.4$ | $3.3\pm 0.9$ | $2.5\pm 0.6$ | -

##  5 Solar wind parameters measured in situ

Figure 3 shows the SW parameters registered by IMPACT and PLASTIC at STA in
the period 2010 August 19 – 26: the magnetic field magnitude and its RTN
components, proton speed, density and temperature, and parameters q4, q8 and
q12 (see the definition of these parameters below in equation (7))
characterizing the Fe-ion charge distribution. The SW disturbance started with
the shock on 2010 August 20, 16:14 UT444http://ipshocks.fi/database, the ICME
on August 20, 16:14 UT – August 21, 13:14 UT (from the STEREO event catalog
555https://stereo-ssc.nascom.nasa.gov/data/ins_data/impact/level3/ICMEs.pdf)
followed up to August 25 by a long trailing region with the declining speed.
The arrivals of the plasma flows given in Table 1 are marked on the proton
speed chart. The flows 1, 2, 3 and 5 evidently correspond to the magnetic
cloud of the ICME. The forth flow (not shown on the chart) with the highest
speed according to Table 1 should arrive significantly ahead of the ICME, but
it was not observed in SW. Most likely, this weak flow decelerated and merged
with other discrete flows. The sixth post-eruptive flow arrived in the post-
ICME part of the transient. It is worth to mention, that the shock time well
agrees with the DBM modeling of the CME frontal structure indicated in the
LASCO Coordinated Database Analysis Workshops (CDAW) database (start at 05:48
UT, $V_{20}=1416~{}km~{}s^{-1}$) with $\gamma=0.3\cdot 10^{-7}$ and
$w=330~{}km~{}s^{-1}$.

Figure 3: Parameters of the magnetic field, proton speed, density, kinetic
temperature and Fe-ion distributions of SW from measurements by PLASTIC and
IMPACT at STA in comparison with the results of calculations of the flow
arrival times and speeds by the Drag-based model. The dotted lines designate
the start and end of the ICME according to the STEREO-A ICME catalog
(https://stereo-ssc.nascom.nasa.gov/data/ins_data/impact/level3/ICMEs.pdf).

The ionization state of the SW plasma is “frozen-in” in the inner corona at
heights where recombination/ionization timescales become dominant over the
plasma expansion timescale (see, e.g., Hundhausen et al., 1968; Ko et al.,
1997; Goryaev et al., 2020). Since the Fe ions freeze-in at the largest
heights than other abundant elements, the Fe-ion composition is the most
suitable for characterizing the state of the SW plasma. In the development of
the approach proposed in Goryaev et al. (2020), we introduce here three
relative parameters q4, q8, and q12 for characterizing the Fe-ion charge
distribution as follows:

$q4=\frac{\sum_{0\leq Z\leq 7}n_{z}}{\sum_{0\leq Z\leq
20}n_{z}},\>q8=\frac{\sum_{8\leq Z\leq 11}n_{z}}{\sum_{0\leq Z\leq
20}n_{z}},\>q12=\frac{\sum_{12\leq Z\leq 20}n_{z}}{\sum_{0\leq Z\leq
20}n_{z}},\;q4+q8+q12=1\,,$ (7)

where $n_{z}$ is the number density of the ion with charge $Z$. The parameters
q4, q8, and q12 correspond conditionally to the “cold”, “middle”, and “hot”
parts of the Fe charge distribution.

In contrast to the average charge $Q_{\mathrm{Fe}}$, the differentiation for
the parameters q4, q8, and q12 shown in Figure 3 allows one to derive a more
detailed information on conditions in the SW plasma.

In the period from August 19 to the shock time the Fe-ion charge distribution
was characterized by the largest value of q8$>$0.8 and the minor q4 and q12
values below 0.1, which corresponds to the slow SW. After the shock, the jump
of q4 to 0.3 indicated appearance of the sheath cold matter, then, in the ICME
part, arrival of the hot eruption plasma has led to intermittent rise up of
q12 to 0.2 – 0.3. The most interesting anomaly in the Fe-ion charge
distribution is seen in the period after the rear of the ICME, from August 21,
13:14 UT to August 23, 00:00 UT. During this post-ICME period, the values of
q4 were several times higher than that of q12, which means a significant
domination of the “cold” component in the SW plasma. Development of the
dimming in the period from the shock to August 23, 12:00 UT was indicated by a
decrease of the medium temperature parameter q8. After August 23, 12:00 UT all
charge distribution parameters returned to the slow SW values.

##  6 Fe-ion charge distributions of the flows in the corona and in SW around
the ICME event

For our analysis of the ICME event, we considered the four time intervals
designated as T1 – T4 in Figure 3: 2010-08-19 00:00 – 2010-08-20 14:00 (T1);
2010-08-20 18:00 – 2010-08-21 12:00 (T2); 2010-08-21 14:00 – 2010-08-22 20:00
(T3); and 2010-08-23 06:00 – 2010-08-25 06:00 (T4). The interval T1
corresponds to the pre-ICME SW, T2 is associated with the passage of the ICME,
T3 is related to the post-eruptive SW flows, and T4 is SW returned to pre-ICME
conditions. For each time interval we summed the 2 hour Fe-ion distributions
taken from the STEREO-A/PLASTIC database.

Figure 4a shows the number of counts of Fe ions with the charge $Z$ summed
over the intervals T1 – T4. The distributions for the intervals T1 (green) and
T4 (yellow) have similar shapes peaked at $Z=9$, because these are probably
associated with the slow component of SW. Though the distributions for T2
(red) and T3 (blue) intervals are associated with different SW types, these
are peaked at the same value $Z=8$. Also, T2 distribution has the noticeable
high charge tail with $Z\geq 12$, which is an evidence for the ICME event.

Figure 4: The Fe-ions distributions for four time intervals associated with
the ICME event as compared with modeled ones (in black). (a) The summed Fe-ion
distributions (number of counts of charged Fe ions) for four time intervals T1
– T4; (b) the relative (normalized to unity) distributions for time intervals
1 (green) and 4 (yellow); (c) the relative distribution for the time interval
2 (red); (d) the relative distribution for the time interval 3 (blue). The
vertical dashed lines separate the ranges of ionic charge Z corresponding to
the parameters q4 (left), q8 (middle), q12 (right).

We modeled the evolution of the Fe-ion charge state and “frozen-in” conditions
for the CME event on 2010 August 18 to compare with the in situ observations
of the associated ICME. To determine a “frozen-in” charge state, we solved a
system of balance equations with the preset profiles of plasma electron
temperature $T_{e}$ and density $N_{e}$, and bulk velocity $V$ as functions of
distance (see details in Rodkin et al., 2017; Grechnev et al., 2019). We have
performed three sets of calculations for the initial times from Table 2: 04:01
UT (hereafter case 1), 05:20 UT (case 2), and 10:00 UT (case 3). The bulk
velocities $V$ for three cases were derived from the kinematic measurements.
For the electron densities $N_{e}$ we used the plausible geometry of the
expansion of the SW plasma in the corona: $N_{e}\sim 1/h^{2}$ ($h$ is the
height above the solar surface) for the cases 1 and 3 (the slow SW flowing
from streamers), and $N_{e}\sim 1/r^{3}$ ($r$ is the heliocentric distance)
for the case 2 (CME flux rope). For the plasma temperatures we used the
initial measured values from Table 2 and performed a fit for the temperature
profile to have a good agreement with the in situ observations. A similar
procedure was applied by Landi et al. (2012) to the coronal hole and
equatorial streamer model. Our calculations have shown that our models for
plasma densities and temperatures agree well with the results of Landi et al.
(2012) for cases 1 and 3 and with numerical MHD simulations of Lynch et al.
(2011) for the CME flux rope (case 2).

For deriving the final “frozen-in” Fe-ion charge distributions in three
mentioned cases we used the following procedure. According to Table 2, the SW
flow for each case consists of two (cases 1 and 3) or three (case 2) plasma
components, which hereafter are called “cold”, “middle”, and “hot” ones
according to temperature regimes. For each case, the “frozen-in” charge
distributions are then calculated separately for all components, and the final
total distribution ($n_{z}$ values for all $Z$ under consideration) is given
by mixing of plasma components:

$n_{z}=\frac{n_{z}^{(c)}N_{e}^{(c)}L^{(c)}+n_{z}^{(m)}N_{e}^{(m)}L^{(m)}+n_{z}^{(h)}N_{e}^{(h)}L^{(h)}}{N_{e}^{(c)}L^{(c)}+N_{e}^{(m)}L^{(m)}+N_{e}^{(h)}L^{(h)}}\,,$
(8)

for case 2 (CME plasma) and

$n_{z}=\frac{n_{z}^{(c)}N_{e}^{(c)}L^{(c)}+n_{z}^{(m)}N_{e}^{(m)}L^{(m)}}{N_{e}^{(c)}L^{(c)}+N_{e}^{(m)}L^{(m)}}\,,$
(9)

for cases 1 and 3 (without the hot components), where $n_{z}^{(c)}$,
$n_{z}^{(m)}$, $n_{z}^{(h)}$ are the partial final distributions for “cold”,
“middle”, and “hot” plasma components; $N_{e}^{(c)}$, $N_{e}^{(m)}$,
$N_{e}^{(h)}$ and $L^{(c)}$, $L^{(m)}$, $L^{(h)}$ are the corresponding plasma
densities and depths along the line of sight. We did not take into accont the
hot component for the pre and post-eruption conditions due to large
uncertaintes in the DEM hot wing at the temperatures $\mathrm{log}_{10}T>7$. A
similar two-plasma model was used by Gruesbeck et al. (2012) for possible
interpreting ICME observations with very low and high charge state ions.

Figures 4b, 4c, and 4d show the comparison of the calculated relative
(normalized to unity) Fe-ion distributions with the measured ones for the T1 –
T4 intervals. As it is seen, the modeled distributions agree well with the
measurements. Nevertheless, the modeled distributions overestimate the high
charge states with $Z\geq 16$ for all cases, especially for case 2 associated
with the ICME. It may be related to the overestimation of the high temperature
part of DEM distributions in the reconstruction procedure. The high charge
peak for Fe16+ ion is caused by the smaller recombination rates compared to
the ions in lower charge states (see Goryaev et al., 2020). The comparison of
q4, q8, q12 parameters for the modeled and measured Fe-ion distributions are
shown in Table 3. It is also seen that q4 and q8 parameters have a very good
agreement with the measured ones, while the modeled q12 values are
overestimated about 2 times.

Table 3: Measured parameters q4, q8, q12 for four time intervals 1–4
associated with the ICME event and post-ICME flow

Time | q4 | q8 | q12
---|---|---|---
interval № | measured | modeled | measured | modeled | measured | modeled
1 | $0.059\pm 0.020$ | $0.053\pm 0.013$ | $0.864\pm 0.207$ | $0.789\pm 0.094$ | $0.077\pm 0.041$ | $0.158\pm 0.107$
2 | $0.229\pm 0.035$ | $0.250\pm 0.112$ | $0.600\pm 0.083$ | $0.395\pm 0.019$ | $0.171\pm 0.040$ | $0.354\pm 0.130$
3 | $0.217\pm 0.049$ | $0.218\pm 0.016$ | $0.722\pm 0.144$ | $0.623\pm 0.095$ | $0.061\pm 0.028$ | $0.159\pm 0.111$
4 | $0.089\pm 0.028$ | - | $0.836\pm 0.199$ | - | $0.074\pm 0.038$ | -

Note. — The parameters for the time intervals 1–3 are compared with the
modeled ones.

Furthermore, the modeling enables to interpret the difference in behaviour of
the q4 and q12 parameters in the cases 1 (T1) and 3 (T3) (see Figure 3) as
follows. In the pre-eruption state (case 1) the mean values of q4=0.059 and
q12=0.077 corresponded to the “frozen-in” conditions, where the plasma
transforms from collisional to collisionless state. It occurred at the heights
of $h\approx 4-5~{}R_{\odot}$ with the plasma electron temperature of
$T_{e}\approx 1~{}MK$ typical for the quiet slow SW. In the post-eruption
state (case 3) q4 = 0.217, q12 = 0.061, and $T_{e}\approx 0.5~{}MK$, so the
“cold” plasma dominates. According to the model results, this increase of the
“cold” component is explained not only by depletion of the highly charged ions
after the CME liftoff, but also by the absence of heating after the flare
ending. The last panel in Figure 3 and data from Table 3 shows that finally
the SW plasma in the T4 interval returns to the pre-ICME state as in the T1
interval.

##  7 Discussion and Conclusion

The analysis of the eruption in AR 11093 occurred on 2010 August 18 and the
associated SW transient detected by STA on 2010 August 20 – 23 has yielded the
following results.

The CME flux rope was formed during the C-class flare from several discrete
plasma flows originated in the region of AR 11093 with the pseudostreamer
nearby. According to the AIA, SWAP EUV images and LASCO C2 – C3 time-height
maps, the first flow started at $R=1.15~{}R_{\odot}$, others at
$2.2~{}R_{\odot}$ and higher, probably, as the streamer blowout blobs like
those observed recently by Parker Solar Probe (Lario et al., 2020; Rouillard
et al., 2020). After the end of the flare, the plasma outflow transformed into
the unstructured stream, whose speed was determined by correlation of
irregularities at different heights. To predict the arrival times and speeds
of the flows at STA we applied the gravitation and DBM kinematic models. The
drag parameters and ambient plasma speed were found in grid calculations under
condition of minimal difference between the modeled flow speeds and the
measured in situ proton speeds at the arrival times. Then the optimal values
of the drag parameter and the ambient plasma speed were obtained by averaging
the values for all flows except the fastest flow 4, which, probably, was
decelerated and merged with other flows. As a result, we obtained that the
discrete flows started during the eruption appeared in SW as components of the
ICME, whereas the unstructured flow started after eruption appeared in the
ICME trailing region. Thus, we showed that DBM is well applicable to the
propagation of the multicomponent CME structure and also for the post-eruption
flow. The ambient plasma speed was found to be of $445~{}km~{}s^{-1}$ for all
flows (except flow 4), the $\gamma$ value was amounted to 0.3 for the frontal
flow 1 and 0.13 for other flows. Such difference in $\gamma$ means that the
drag force diminished for the flows passed behind the CME front along the same
open magnetic field lines. The open magnetic field structure in the ICME
trailing region was first described by Neugebauer et al. (1997).

To understand the origins of the SW flows, we analyzed the Fe-ion charge
distribution of SW and confronted it with parameters of the coronal plasma.
First, we determined the plasma emission measure in the eruption region with
the use of DEM in the time intervals corresponding to the pre-eruption,
eruption and post-eruption conditions. The largest emission measure in all
temperature bands was determined in the pre-eruption stage (at 04:01 UT).
During the eruption (05:20 – 05:25 UT), the emission measure underwent on
about one order in the middle temperature ($6.3<\mathrm{log}_{10}T<6.8$) and
in the hot temperature ($6.8<\mathrm{log}_{10}T<7.2$) channels because of the
uncompensated plasma outflow from the dimming region. In the cold channel
($5.5<\mathrm{log}_{10}T<6.3$) the EM value dropped down less than three
times. Such lesser decrease can be explained by an additional inflow of the
cold plasma by interchange reconnection of the cold loops seen in the AIA 171
Å and SWAP 174 Å with the open magnetic lines of the flux rope (Owens et al.,
2020) and by drainage of the cold filament matter to the eruption site.
Drainage of the filament mass before eruption was described by Martin et al.
(2008); Bi et al. (2014); Zhang et al. (2017); Jenkins et al. (2018).

Using the obtained plasma parameters, we have modeled the “frozen-in” Fe-ion
charge distributions in the studied coronal flows and calculated the values of
the q4, q8 and q12 parameters averaged over four time intervals T1 – T4. For
all the intervals, the modeled values agreed with the measured ones within the
errors. A small excess of the measured q8 with respect to the modeled values
may be related to contribution of the surrounding coronal structures not
associated with the eruption. The observed anomalous divergence between the q4
and q12 values in the post-ICME trailing region can be explained by inflow of
the cold plasma in absence of heating after the solar flare end. As a result,
the SW ion state in the post-ICME tail in the interval 2010 August 21, 14:00
UT – 2010 August 22, 20:00 UT significantly differs from the state of the slow
ambient SW before 2010 August 20, 14:00 and after 2010 August 23, 06:00 UT.

Concluding, the results demonstrate that in the studied CME event of 2010
August 18 – 23 the post-ICME SW disturbance was caused by the post-eruption
coronal flow from the dimming region and cannot be associated with the ambient
SW entrained by the CME.

The authors thank the STEREO/PLASTIC, GOES, SDO/AIA, PROBA2/SWAP research
teams for their open data policy. The PLASTIC investigation is an
international (USA, Switzerland, Germany) effort involving the University of
New Hampshire, the University of Bern, the Max-Planck-Institute for
extraterrestrial Physics, Christian-Albrecht-University Kiel, NASA/Goddard
Space Flight Center, and the University of California, Berkeley. The SDO image
data are available by courtesy of NASA and AIA science team. SWAP is a project
of the Central Spatial de Liege and the Royal Observatory of Belgium. This
paper also uses data of the CME catalog that is generated and maintained at
the CDAW Data Center by NASA and The Catholic University of America in
cooperation with the Naval Research Laboratory. SOHO is a project of
international cooperation between ESA and NASA. We are grateful for the
opportunity to use the results of the simulation obtained by the Drag-Based
Model.

## References

  * Aschwanden et al. (2015) Aschwanden, M. J., Boerner, P., Caspi, A., et al. 2015, Sol. Phys., 290, 2733, doi: 10.1007/s11207-015-0790-0
  * Bi et al. (2014) Bi, Y., Jiang, Y., Yang, J., et al. 2014, ApJ, 790, 100, doi: 10.1088/0004-637X/790/2/100
  * Brueckner et al. (1995) Brueckner, G. E., Howard, R. A., Koomen, M. J., et al. 1995, Sol. Phys., 162, 357, doi: 10.1007/BF00733434
  * Cargill (2004) Cargill, P. J. 2004, Sol. Phys., 221, 135, doi: 10.1023/B:SOLA.0000033366.10725.a2
  * Cheng et al. (2012) Cheng, X., Zhang, J., Saar, S. H., & Ding, M. D. 2012, ApJ, 761, 62, doi: 10.1088/0004-637X/761/1/62
  * Corona-Romero et al. (2017) Corona-Romero, P., Gonzalez-Esparza, J. A., Perez-Alanis, C. A., et al. 2017, Space Weather, 15, 464, doi: 10.1002/2016SW001489
  * D’Huys et al. (2017) D’Huys, E., Seaton, D. B., De Groof, A., Berghmans, D., & Poedts, S. 2017, Journal of Space Weather and Space Climate, 7, A7, doi: 10.1051/swsc/2017006
  * Domingo et al. (1995) Domingo, V., Fleck, B., & Poland, A. I. 1995, Sol. Phys., 162, 1, doi: 10.1007/BF00733425
  * Dumbović et al. (2021) Dumbović, M., Čalogović, J., Martinić, K., et al. 2021, Frontiers in Astronomy and Space Sciences, 8, 58, doi: 10.3389/fspas.2021.639986
  * Dumbović et al. (2018) Dumbović, M., Čalogović, J., Vršnak, B., et al. 2018, ApJ, 854, 180, doi: 10.3847/1538-4357/aaaa66
  * Galvin et al. (2008) Galvin, A. B., Kistler, L. M., Popecki, M. A., et al. 2008, Space Sci. Rev., 136, 437, doi: 10.1007/s11214-007-9296-x
  * Goryaev et al. (2020) Goryaev, F. F., Slemzin, V., & Rodkin, D. 2020, ApJ, 905, L17, doi: 10.3847/2041-8213/abcc76
  * Grechnev et al. (2019) Grechnev, V. V., Kochanov, A. A., Uralov, A. M., et al. 2019, Sol. Phys., 294, 139, doi: 10.1007/s11207-019-1529-0
  * Gruesbeck et al. (2012) Gruesbeck, J. R., Lepri, S. T., & Zurbuchen, T. H. 2012, ApJ, 760, 141, doi: 10.1088/0004-637X/760/2/141
  * Hannah & Kontar (2012) Hannah, I. G., & Kontar, E. P. 2012, A&A, 539, A146, doi: 10.1051/0004-6361/201117576
  * Heinemann et al. (2021) Heinemann, S. G., Saqri, J., Veronig, A. M., Hofmeister, S. J., & Temmer, M. 2021, Sol. Phys., 296, 18, doi: 10.1007/s11207-020-01759-0
  * Hess & Zhang (2015) Hess, P., & Zhang, J. 2015, ApJ, 812, 144, doi: 10.1088/0004-637X/812/2/144
  * Hinterreiter et al. (2021) Hinterreiter, J., Amerstorfer, T., Temmer, M., et al. 2021, Space Weather, 19, e02836, doi: 10.1029/2021SW002836
  * Howard et al. (2008) Howard, R. A., Moses, J. D., Vourlidas, A., et al. 2008, Space Sci. Rev., 136, 67, doi: 10.1007/s11214-008-9341-4
  * Hundhausen et al. (1968) Hundhausen, A. J., Gilbert, H. E., & Bame, S. J. 1968, ApJ, 152, L3, doi: 10.1086/180165
  * Jenkins et al. (2018) Jenkins, J. M., Long, D. M., van Driel-Gesztelyi, L., & Carlyle, J. 2018, Sol. Phys., 293, 7, doi: 10.1007/s11207-017-1224-y
  * Kaiser et al. (2008) Kaiser, M. L., Kucera, T. A., Davila, J. M., et al. 2008, Space Sci. Rev., 136, 5, doi: 10.1007/s11214-007-9277-0
  * Ko et al. (1997) Ko, Y.-K., Fisk, L. A., Geiss, J., Gloeckler, G., & Guhathakurta, M. 1997, Sol. Phys., 171, 345
  * Kraaikamp & Verbeeck (2015) Kraaikamp, E., & Verbeeck, C. 2015, Journal of Space Weather and Space Climate, 5, A18, doi: 10.1051/swsc/2015019
  * Landi et al. (2012) Landi, E., Gruesbeck, J. R., Lepri, S. T., & Zurbuchen, T. H. 2012, ApJ, 750, 159, doi: 10.1088/0004-637X/750/2/159
  * Lario et al. (2017) Lario, D., Kwon, R. Y., Richardson, I. G., et al. 2017, ApJ, 838, 51, doi: 10.3847/1538-4357/aa63e4
  * Lario et al. (2020) Lario, D., Balmaceda, L., Alzate, N., et al. 2020, ApJ, 897, 134, doi: 10.3847/1538-4357/ab9942
  * Lemen et al. (2012) Lemen, J. R., Title, A. M., Akin, D. J., et al. 2012, Sol. Phys., 275, 17, doi: 10.1007/s11207-011-9776-8
  * Lugaz et al. (2017) Lugaz, N., Temmer, M., Wang, Y., & Farrugia, C. J. 2017, Sol. Phys., 292, 64, doi: 10.1007/s11207-017-1091-6
  * Luhmann et al. (2008) Luhmann, J. G., Curtis, D. W., Schroeder, P., et al. 2008, Space Sci. Rev., 136, 117, doi: 10.1007/s11214-007-9170-x
  * Lüst (1963) Lüst, R. 1963, Space Sci. Rev., 1, 522, doi: 10.1007/BF00225270
  * Lynch et al. (2011) Lynch, B. J., Reinard, A. A., Mulligan, T., et al. 2011, ApJ, 740, 112, doi: 10.1088/0004-637X/740/2/112
  * Martin et al. (2008) Martin, S. F., Panasenco, O., Engvold, O., & Lin, Y. 2008, Annales Geophysicae, 26, 3061, doi: 10.5194/angeo-26-3061-2008
  * Möstl et al. (2014) Möstl, C., Amla, K., Hall, J. R., et al. 2014, ApJ, 787, 119, doi: 10.1088/0004-637X/787/2/119
  * Napoletano et al. (2018) Napoletano, G., Forte, R., Moro, D. D., et al. 2018, Journal of Space Weather and Space Climate, 8, A11, doi: 10.1051/swsc/2018003
  * Neugebauer et al. (1997) Neugebauer, M., Goldstein, R., & Goldstein, B. E. 1997, J. Geophys. Res., 102, 19743, doi: 10.1029/97JA01651
  * Owens et al. (2020) Owens, M., Lockwood, M., Macneil, A., & Stansby, D. 2020, Sol. Phys., 295, 37, doi: 10.1007/s11207-020-01601-7
  * Plowman & Caspi (2020) Plowman, J., & Caspi, A. 2020, ApJ, 905, 17, doi: 10.3847/1538-4357/abc260
  * Plowman et al. (2013) Plowman, J., Kankelborg, C., & Martens, P. 2013, ApJ, 771, 2, doi: 10.1088/0004-637X/771/1/2
  * Ravishankar & Michałek (2019) Ravishankar, A., & Michałek, G. 2019, Sol. Phys., 294, 125, doi: 10.1007/s11207-019-1470-2
  * Rodkin et al. (2017) Rodkin, D., Goryaev, F., Pagano, P., et al. 2017, Sol. Phys., 292, 90, doi: 10.1007/s11207-017-1109-0
  * Rodkin et al. (2018) Rodkin, D., Slemzin, V., Zhukov, A. N., et al. 2018, Sol. Phys., 293, 78, doi: 10.1007/s11207-018-1295-4
  * Rollett et al. (2016) Rollett, T., Möstl, C., Isavnin, A., et al. 2016, ApJ, 824, 131, doi: 10.3847/0004-637X/824/2/131
  * Rouillard et al. (2020) Rouillard, A. P., Kouloumvakos, A., Vourlidas, A., et al. 2020, ApJS, 246, 37, doi: 10.3847/1538-4365/ab579a
  * Russell (2001) Russell, C. T. 2001, Washington DC American Geophysical Union Geophysical Monograph Series, 125, 73, doi: 10.1029/GM125p0073
  * Saqri et al. (2020) Saqri, J., Veronig, A. M., Heinemann, S. G., et al. 2020, Sol. Phys., 295, 6, doi: 10.1007/s11207-019-1570-z
  * Seaton et al. (2013) Seaton, D. B., De Groof, A., Shearer, P., Berghmans, D., & Nicula, B. 2013, ApJ, 777, 72, doi: 10.1088/0004-637X/777/1/72
  * Shen et al. (2012) Shen, F., Wu, S. T., Feng, X., & Wu, C.-C. 2012, Journal of Geophysical Research (Space Physics), 117, A11101, doi: 10.1029/2012JA017776
  * Shi et al. (2015) Shi, T., Wang, Y., Wan, L., et al. 2015, ApJ, 806, 271, doi: 10.1088/0004-637X/806/2/271
  * Shugay et al. (2018) Shugay, Y., Slemzin, V., Rodkin, D., Yermolaev, Y., & Veselovsky, I. 2018, Journal of Space Weather and Space Climate, 8, A28, doi: 10.1051/swsc/2018015
  * Temmer et al. (2017) Temmer, M., Reiss, M. A., Nikolic, L., Hofmeister, S. J., & Veronig, A. M. 2017, ApJ, 835, 141, doi: 10.3847/1538-4357/835/2/141
  * Tun & Vourlidas (2013) Tun, S. D., & Vourlidas, A. 2013, ApJ, 766, 130, doi: 10.1088/0004-637X/766/2/130
  * Vemareddy et al. (2012) Vemareddy, P., Maurya, R. A., & Ambastha, A. 2012, Sol. Phys., 277, 337, doi: 10.1007/s11207-011-9903-6
  * Vršnak (2021) Vršnak, B. 2021, Journal of Space Weather and Space Climate, 11, 34, doi: 10.1051/swsc/2021012
  * Vršnak et al. (2013) Vršnak, B., Žic, T., Vrbanec, D., et al. 2013, Sol. Phys., 285, 295, doi: 10.1007/s11207-012-0035-4
  * Vršnak et al. (2014) Vršnak, B., Temmer, M., Žic, T., et al. 2014, ApJS, 213, 21, doi: 10.1088/0067-0049/213/2/21
  * Žic et al. (2015) Žic, T., Vršnak, B., & Temmer, M. 2015, ApJS, 218, 32, doi: 10.1088/0067-0049/218/2/32
  * Wang (2015) Wang, Y. M. 2015, ApJ, 803, L12, doi: 10.1088/2041-8205/803/1/L12
  * Wendeln & Landi (2018) Wendeln, C., & Landi, E. 2018, ApJ, 856, 28, doi: 10.3847/1538-4357/aaaadf
  * Zhang et al. (2017) Zhang, Q. M., Li, T., Zheng, R. S., Su, Y. N., & Ji, H. S. 2017, ApJ, 842, 27, doi: 10.3847/1538-4357/aa73d2