# Properties of the Sheath Regions of Coronal Mass Ejections with or without
Shocks from STEREO in situ Observations near 1 AU

Tarik M. Salman Space Science Center and Department of Physics
University of New Hampshire
Durham, NH 03824, USA  Noé Lugaz Space Science Center and Department of
Physics
University of New Hampshire
Durham, NH 03824, USA  Charles J. Farrugia Space Science Center and Department
of Physics
University of New Hampshire
Durham, NH 03824, USA  Reka M. Winslow Space Science Center and Department of
Physics
University of New Hampshire
Durham, NH 03824, USA  Lan K. Jian Heliophysics Science Division
NASA Goddard Space Flight Center
Greenbelt, MD 20771, USA  Antoinette B. Galvin Space Science Center and
Department of Physics
University of New Hampshire
Durham, NH 03824, USA

###### Abstract

We examine 188 coronal mass ejections (CMEs) measured by the twin STEREO
spacecraft during 2007-2016 to investigate the generic features of the CME
sheath and the magnetic ejecta (ME) and dependencies of average physical
parameters of the sheath on the ME. We classify the MEs into three categories,
focusing on whether a ME drives both a shock and sheath, or only a sheath, or
neither, near 1 AU. We also reevaluate our initial classification through an
automated algorithm and visual inspection. We observe that even for leading
edge speeds greater than 500 km s-1, 1 out of 4 MEs do not drive shocks near 1
AU. MEs driving both shocks and sheaths are the fastest and propagate in high
magnetosonic solar wind, whereas MEs driving only sheaths are the slowest and
propagate in low magnetosonic solar wind. Our statistical and superposed epoch
analyses indicate that all physical parameters are more enhanced in the sheath
regions following shocks than in sheaths without shocks. However, differences
within sheaths become statistically less significant for similar driving MEs.
We also find that the radial thickness of ME-driven sheaths apparently has no
clear linear correlation with the speed profile and associated Mach numbers of
the driver.

coronal mass ejections — sheath regions — shocks

††journal: apj

##  1 Introduction

In essence, coronal mass ejections (CMEs) are large-scale transient eruptions
of solar plasma and magnetic field into the heliosphere (e.g., Webb & Howard,
2012). CMEs are one of the most spectacular and energetic forms of solar
phenomena, with kinetic energies potentially exceeding 1032 ergs (Hudson et
al., 2006). The interplanetary manifestation of a fast CME typically involves
three distinct features: a shock wave compressing and deflecting the upstream
solar wind flow, the region of compressed solar wind bounded by the shock
front and the leading edge of the following magnetic ejecta (ME), termed as
the sheath, and a cold, magnetically-dominated region behind the sheath,
termed as the ME. However, sometimes the ME is preceded by a dense sheath even
in the absence of shocks, for example, the well-studied 12 December 2008 CME
(see DeForest et al., 2013) or the 17 January 2013 CME, studied by Lugaz et
al. (2016a). In addition, databases of CMEs measured near 1 AU (Jian et al.,
2018) and at 1 AU (Richardson & Cane, 2010; Nieves-Chinchilla et al., 2018)
include CMEs without shocks but with a start time several hours before the
beginning of the ME, corresponding to a period of dense and disturbed solar
wind which can be identified as the sheath region. Though MEs and their subset
magnetic clouds (MCs; Burlaga et al., 1981) are the primary drivers of intense
geomagnetic disturbances (Farrugia et al., 1997; Zhang et al., 2007;
Richardson & Cane, 2012), a substantial amount of moderate-intense geomagnetic
disturbances are associated with sheath plasma and magnetic field behind
shocks (Kamide et al., 1998; Richardson et al., 2001; Huttunen & Koskinen,
2004; Yermolaev et al., 2010; Echer et al., 2013). Geoeffective shocks/sheaths
(see Ontiveros & Gonzalez-Esparza, 2010; Lugaz et al., 2016b) provide even
shorter lead times for forecasts than MEs. ME-driven shocks and sheaths are
significant in solar-terrestrial studies as shocked plasma in the immediate
downstream of the shock may contribute in the acceleration of solar energetic
particles (Reames, 1999; Manchester et al., 2005) and significantly compress
and distort the magnetosphere (Joselyn & Tsurutani, 1990), enhancing the
geoeffective potential of MEs.

Throughout the rest of this manuscript, we define the sheath associated with a
ME as the region preceding the ME and driven by it, which contains compressed
plasma and magnetic field, regardless of the presence of a shock. This sheath
region is associated with the propagation and expansion of the ME and the
accumulation and compression of solar wind plasma and magnetic field in front
of it. When the leading edge speed of a ME relative to the ambient solar wind
is faster than the fast-magnetosonic speed of the medium, it produces a shock
(fast-forward) in the frame of the ME (Russell & Mulligan, 2002). In many
cases, MEs also expand at significant speeds, although the expansion is
typically slower than the local fast-magnetosonic speed (Klein & Burlaga,
1982). This expansion results in the continuous accumulation of solar wind
plasma and magnetic field upstream of the ME (Takahashi & Shibata, 2017). When
there is a fast-forward shock, the region consisting of this compressed and
heated plasma with stretched and turbulent magnetic field upstream of the ME
is identified as the sheath (Kaymaz & Siscoe, 2006). In this study, we extend
this definition of sheaths to MEs that do not drive fast-forward shocks but
for which there is compressed plasma and magnetic field upstream of it. While
both the sheath and ME feature elevated magnetic field signatures, the sheath
typically consists of a rapidly fluctuating magnetic field direction (Hietala
et al., 2014). ME-driven sheaths are often compared to planetary
magnetosheaths as the solar wind tries to flow around the magnetic obstacle,
just like the solar wind flows around the Earth’s magnetosphere. However, as
MEs not only propagate through interplanetary medium but also expand into it,
sheaths upstream of MEs significantly differ from planetary magnetosheaths
(Siscoe & Odstrcil, 2008; Démoulin & Dasso, 2009). The reduced lateral
deflection of the solar wind away from the nose of the ME may not be enough
for it to flow around, resulting in the pile up of solar wind in front of it
(Siscoe & Odstrcil, 2008; Owens et al., 2017). These layers are not simple
stacks of compressed solar wind along the radial line from the Sun because the
layers can also slide laterally by different amounts as they are compressed.
As a result, ME-driven sheaths are often associated with complex formations
and the sheath field appears to be highly variable and turbulent (Kataoka et
al., 2005), for example, the north/south direction of the magnetic field does
not present any clear relationship between the sheath region and ME (Jian et
al., 2018). This can make understanding their global configuration and
predicting their geoeffectivity particularly challenging (Palmerio et al.,
2016; Kilpua et al., 2017a).

Embedded magnetic fields in shock-driven sheath regions have significant
potential to impact the geomagnetic field (Tsurutani et al., 1988; Lugaz et
al., 2016b). Shock-driven sheath regions are often associated with prolonged
periods (several hours) of sustained and strong southward fields. Such out-of-
ecliptic fields in the sheath regions are a byproduct of two possible
mechanisms: compression of preexisting southward Bz at the boundary of a shock
with a normal close to the ecliptic (Lugaz et al., 2016b) or magnetic field
line draping upstream of the ME (McComas et al., 1989; Gonzalez et al., 1994).
Planar magnetic structures, where the magnetic field is ordered into laminar
sheets (Farrugia et al., 1991; Jones et al., 2002; Savani et al., 2011) are
commonly found within shock-driven sheath regions. Palmerio et al. (2016)
showed that these planar parts of the sheath in all likelihood are more
geoeffective than non-planar parts. Due to enhanced solar wind dynamic
pressure, sheath regions are capable of compressing the magnetosphere, pushing
the dayside magnetopause down to below geosynchronous orbit (Hietala et al.,
2014; Lugaz et al., 2015, 2016b; Kilpua et al., 2019). The quintessential
effect on the outer Van Allen radiation belts of such magnetospheric
compression involves the drastic depletion of relativistic electron fluxes
over a broad range of energy, equatorial pitch angle, and radial distance
(Pulkkinen et al., 2007; Turner et al., 2012; Hietala et al., 2014; Hudson et
al., 2014; Kilpua et al., 2015b; Alves et al., 2016; Lugaz et al., 2016b;
Xiang et al., 2017).

ME-driven sheath regions have only been studied for fast, shock-driving MEs
and all these results about sheath properties and geoeffectiveness have been
limited to sheaths associated with shocks. In addition, studies of such
sheaths, associated with shocks, come mostly from simplified numerical
simulations (often hydrodynamic) or similarities with Earth’s bow shock.
Though studies of ME-driven sheaths based on pure measurements have also been
carried out, focusing on the generic profile and/or correlation/comparison
with the driving ME (Mitsakou et al., 2009; Guo et al., 2010; Mitsakou &
Moussas, 2014; Kilpua et al., 2017b; Jian et al., 2018; Kilpua et al., 2019),
superposed epoch analysis (Kilpua et al., 2013; Masías-Meza et al., 2016;
Rodriguez et al., 2016; Janvier et al., 2019), radial evolution (Lugaz et al.,
2019; Good et al., 2020), to the best of our knowledge there has been no
specific study of sheaths driven by MEs not driving any shocks. In this study,
we examine ME-driven sheath regions measured by the twin STEREO (Solar
Terrestrial Relations Observatory; Kaiser, 2005) spacecraft from 2007-2016
focusing on all sheath regions, whether or not they are associated with
shocks. As described above, we define the sheath as a region with a
significant (see criteria in section 2.2) increase in density and magnetic
field strength for at least 2 hours above the background and directly
preceding a ME. Through this study, we aim to examine the distinctness of MEs,
especially the distinguishability of ME-driven sheaths with and without
shocks.

The paper is organized as follows. In section 2, we explain the method of
classifying distinct MEs by using the STEREO CME list of Jian et al. (2018)
and implementing an “Automated Sheath Identification Algorithm” with visual
inspection. In section 3, we present our statistical results. A brief summary
and discussion of our results are in section 4.

##  2 Methodology

###  2.1 Initial Classification of MEs

We classify the MEs measured by the twin STEREO spacecraft, as reported in
Jian et al. (2018) into three main categories. For each ME, Jian et al. (2018)
lists the start time of the CME, start time of the ME, and end time of the ME
at the measuring spacecraft in this order. When the start time of the CME
differs from the start time of the ME, it means there is a sheath region
upstream of the ME. For MEs driving shocks, the CME start time corresponds to
the arrival of the shock at the measuring spacecraft. The first category
(Cat-I) includes MEs driving a shock near 1 AU and with a clear sheath region
upstream of the ME. We use the Heliospheric shock database of Kilpua et al.
(2015a), generated and maintained at the University of Helsinki (links for
this and all other sources used in this study are listed in the
acknowledgements section) and STEREO shock list for identifying shocks
associated with these MEs. We refer to the former shock database as IPshocks
database from now on. We only include shocks which are either listed in both
of the aforementioned databases or only listed in one of them but have
magnetosonic Mach numbers (Mms) greater than 1. For this category, we
initially identify 105 MEs. The second category (Cat-II) includes MEs with
associated sheath regions but with no shock signatures or sometimes associated
with a shock-like discontinuities. This category also includes MEs with shocks
listed in the IPshocks database with Mms<1\. We exclude 13 potential Cat-II
MEs as the sheath boundaries for these MEs were not properly defined due to
considerable data gaps. Therefore, initially through visual inspection, we
identify 17 Cat-II MEs. The third category (Cat-III) includes MEs driving no
sheaths. For this specific category, the CME and ME start times listed in Jian
et al. (2018) are the same. Initially, we identify 66 Cat-III MEs from the
STEREO CME list. We exclude 21 MEs through visual inspection as these MEs are
associated with “driverless shocks” or shocks which are not followed by their
drivers (see Gopalswamy et al., 2009). These “driverless shocks” are those for
which the start time of the CME corresponds to a shock and is listed as the
same time as the start of the ME, so that these CMEs have a shock and no
sheath or more reasonably a shock, a sheath but no driver (ME).

###  2.2 Automated Sheath Identification Algorithm

In addition to the visual search described above, we devise an Automated
Sheath Identification Algorithm (ASIA) for the identification of any possible
sheath region upstream of the ME. The algorithm is used to provide a
quantitative basis to confirm the initial classification and to reclassify as
needed a few unclear events. The sheath region in general features elevated
levels of density and magnetic field strength over the background. In our
approach, we approximate the sheath to be 1.5 times more compressed and 1.3
times more magnetized compared to the unperturbed solar wind. The rationale
for these specific ratios is that the weakest shocks measured near 1 AU have a
jump of $\sim$1.3 in the density and magnetic field strength at the shock but
the density in the sheath is often more elevated than just downstream of the
shock (Manchester et al., 2005), which led to our criteria of 1.5 for the
density and 1.3 for the magnetic field strength. Although enhancements in the
solar wind speed, temperature, and dynamic pressure are also considered
characteristic evidences for the identification of sheaths associated with
shocks, such enhancements are not universally associated with sheaths not
preceded by shocks. Therefore, for better optimization, we limit the ASIA to
only search for predefined enhancements in density and magnetic field strength
over the quiescent solar wind for the identification of sheaths.

We initially start with a preliminary sheath, extending up to the ME leading
edge and with a duration of 2 hours (blue shaded region in Figure 1) and we
approximate the 2-hr interval prior to this preliminary sheath as the
background solar wind (pink shaded region in Figure 1). The reason behind
starting with this predefined sheath interval of 2 hours is that $\sim$97% of
the sheaths in our database are longer than 2 hours in duration. Therefore, we
approximated a 2-hr interval to be the minimum threshold for any preliminary
sheath. However, this results in the algorithm inherently not identifying the
4 sheaths in our database that are shorter than 2 hours.

Then, for each following iteration of the ASIA, we extend this preliminary
sheath by 5-min steps but always limit the background solar wind as a 2-hr
interval prior to this. We carry out the iterations in a recursive manner and
extend this preliminary sheath up to 30 hours before the start of the ME
(allowing identification of extremely long sheaths) and each time compare the
average density and magnetic field strength in this preliminary sheath with
that of the background. As there can be substantial fluctuations of the solar
wind plasma and interplanetary magnetic field (IMF) within the sheath, it is
quite possible to have an interval that satisfies our average criteria, only
for the region enclosed by the immediate next time step to violate one or both
of them. To negate that, our goal is to find the time step after which for a
prolonged interval, both of the ratios are satisfied. The interval enclosed by
this specific time step upstream of the ME is identified as the probable
sheath. However, as our ratios are somewhat subjective, we do not entirely
rely on the ASIA for the identification of probable sheaths and no sheaths.
For disagreements between the initial classification of MEs, solely based on
the STEREO CME list of Jian et al. (2018) and ASIA, we visually inspect the
solar wind plasma and IMF profiles for each discrepancy. We run this algorithm
for each and every event of our database. For the Cat-III events, the
algorithm identified 20 events to have sheaths. We visually inspected these 20
events and identified them to have sheaths as well. We then looked for
upstream shock signatures within the previous 30-hr period prior to the start
of the ME in both of the shocks databases to determine whether to move these
events to Cat-I or Cat-II. Based on the findings, we moved 1 event to Cat-I
and 19 to Cat-II. In summary, the ASIA accurately identified 172 out of the
188 CMEs. Therefore, after the application of the ASIA along with thorough
visual insepection, our final database is composed of 106 Cat-I, 36 Cat-II,
and 46 Cat-III MEs.

Figure 1: Visual representation (selected iterations) of the ASIA based on the
average proton density and magnetic field strength criteria. The blue shaded
region is the approximated sheath for each iteration and the pink shaded
region is the approximated upstream solar wind. The horizontal red dotted
lines in each region indicate the averages within that region. The vertical
navy dashed line marks the start of the ME leading edge.

###  2.3 Example Events from Different Categories

Figure 2: IMF and plasma measurements of three example CMEs. The seven panels
show the magnetic field strength, components in RTN coordinates (red: radial,
green: tangential, blue: normal), solar wind speed, proton density, proton
temperature, dynamic pressure, and proton beta (from top to bottom). The two
vertical green dashed lines bound the sheath, with t=0 corresponding to the
start of the sheath and the vertical orange dashed lines denote the start of
the sheath, as identified by the ASIA (top panel). For the bottom panel, the
start of the ME is denoted by the green dashed line, with t=0 corresponding to
the start of the ME. Top left: STEREO-B measurements of the Cat-I CME starting
on 12 April 2014 at 2:27 UT, Top right: STEREO-B measurements of the Cat-II
CME starting on 29 October 2011 at 04:12 UT, Bottom: STEREO-A measurements of
the Cat-III CME starting on 28 April 2011 at 09:00 UT.

####  2.3.1 Cat-I (ME with an Associated Shock Structure and Sheath Region)

The Cat-I event presented here (see top left panel of Figure 2) is driven by
an expanding ME near 1 AU, with an expansion speed of 71 km s-1. The expansion
speed is taken as half the difference between the leading and trailing edge
speeds (see Owens et al., 2005). The shock propagates in an upstream solar
wind speed of 315 km s-1. The upstream fast-magnetosonic speed is 63 km s-1.
Here, the upstream solar wind and fast-magnetosonic speeds are taken as the
average of the 2-hr interval prior to the arrival of the shock at the
spacecraft. The associated shock is listed in both the IPshocks database (Mms
of 2) and the STEREO shock list (Mms of 2.6). The shock arrives at STEREO-B on
12 April 2014 at 2:27 UT. The spacecraft encounters the sheath for a
relatively long period of 18.32 hours, with the leading edge of the ME
arriving on 12 April 2014 at 20:46 UT. The ASIA also identified a sheath
region upstream of the ME. For this particular event, the sheath interval
identified by the ASIA is 17.25 hours, which is slightly shorter.

####  2.3.2 Cat-II (ME with a Sheath but without a Shock)

Our example Cat-II event reveals an interesting discontinuity. The start of
this sheath coincides with a sharp decrease in the magnetic field strength
(see top right panel of Figure 2). The discontinuity, which probably is a slow
mode shock/wave, arrives at STEREO-B on 29 October 2011 at 04:12 UT. According
to the STEREO CME list of Jian et al. (2018), the spacecraft encounters the
sheath for an interval of 7 hours. The ASIA also identifies a sheath region,
extending out to 7.83 hours upstream of the ME. However, with visual
inspection, we approximated the sheath to start at 12.80 hours before the
start of the ME to accomodate the enhancements of the solar wind speed, proton
density, temperature, and dynamic pressure. The driving ME expands at a much
slower rate compared to the aforementioned Cat-I ME, with an expansion speed
of $\sim$47 km s-1. Here, the upstream solar wind speed of 357 km s-1 might be
an over-estimate because of the compression region right before the sheath.
The upstream fast-magnetosonic speed is 72 km s-1, which is slightly higher
than in the previous example. The region upstream of the ME is a typical
sheath-like structure as the physical parameters (proton density, temperature)
within the sheath are enhanced by a factor of 2 than the background solar
wind, while this factor is 3 for the dynamic pressure. The average speeds of
the structures (sheath and ME) are also comparable to each other, indicating
that the sheath is being driven by the ME.

####  2.3.3 Cat-III (ME with No Associated Sheath Region)

The example Cat-III ME presented in the bottom panel of Figure 2 arrives at
STEREO-A on 28 April 2011 at 9:00 UT. The spacecraft encounters the ME for an
interval of $\sim$35 hours before it ends on 29 April 2011 at 20:07 UT. The ME
propagates in a moderately fast solar wind of 440 km s-1. The upstream fast-
magnetosonic speed is 55 km s-1. This ME, with a leading edge speed of 441 km
s-1, is expanding near 1 AU with an expansion speed of $\sim$58 km s-1. The
ASIA identified no sheath region upstream of the ME. There are some notable
enhancements and fluctuations in the magnetic field upstream of the ME.
However, they do not coincide with any notable enhancements in the plasma
parameters and might correspond to Alfvén waves. The sharp increase in proton
density just before the start of the ME, coinciding with a simultaneous sharp
decrease in the magnetic field strength may be a product of magnetic
reconnection. Also, the change in proton beta across the boundary is small,
which is a condition favorable for reconnection (Phan et al., 2013). This
certainly is not an anomaly, as 8 out of the 46 Cat-III MEs exhibit such
signatures. The ME has low average proton denisty (3.3 cm-3) and temperature
(2.7$\times 10^{4}$ K) compared to the background solar wind (11.6 cm-3 and
3.2$\times 10^{4}$ K).

##  3 Results

In this study, we use 1-min resolution plasma data from the PLASTIC instrument
(Galvin et al., 2008) and 1/8 s high resolution magnetic field data from the
IMPACT instrument (Luhmann et al., 2008) on-board the twin STEREO spacecraft.

###  3.1 Proportion of Different Categories

Figure 3: Top panel: Normalized ratios of leading edge speeds (left) and
annual occurrence rates (right) of the three ME categories, Bottom panel:
Normalized ratios of “pseudo” Mach numbers (see section 3.3.1) of the three ME
categories.

####  3.1.1 Variation in terms of the Leading Edge Speed of the ME

We examine the proportion of different categories based on the leading edge
speed of the ME near 1 AU (see top left panel of Figure 3). We first arrange
all the MEs by the increasing order of leading edge speeds. We exclude 3 MEs
because the leading edge portions for these MEs have considerable data gaps.
The leading edge speeds range from 301 km s-1 (a Cat-III ME) to 949 km s-1 (a
Cat-I ME). Then, we bin the leading edge speeds into 8 intervals, each
containing 23 MEs except the last one which contains 24. For each interval, we
normalize the count from each category by the total number of MEs in that
interval. We observe that, for small leading edge speeds, the number of MEs
not driving shocks (Cat-II and Cat-III) outweigh the number of MEs driving
shocks (Cat-I). For leading edge speeds below 400 km s-1, only 42% of MEs are
able to drive shocks, confirming the results of the study by Lugaz et al.
(2017) based on Wind/ACE data. The normalized ratio of Cat-II MEs peak for
leading edge speeds around 340-371 km s-1, maybe indicating that they are in
the process of forming shocks. As expected, with increasing leading edge
speeds, the proportion of shock driving MEs starts outweighing the non-shock
driving ones. However, the proportion of non-shock driving MEs does not
immediately become negligible. Even for higher leading edge speed intervals,
we do find a nonnegligible amount of non-shock driving MEs. For example,
between leading edge speeds 590-710 km s-1, 26% of MEs still do not drive
shocks. According to our database, MEs with leading edge speeds >598 km s-1
all drive sheaths and MEs with leading edge speeds >701 km s-1 all drive
shocks near 1 AU and have associated sheaths.

####  3.1.2 Solar Cycle Variation

In this section, we examine the annual variation of ME counts of the three
categories. Different phases of two solar cycles are sampled: the solar
minimum of solar cycle 23 and transition to solar cycle 24 (2007-2008), the
rising phase of solar cycle 24 (2009-2011), and the double-peak solar maximum
(2012-2014). For improved statistics, we combine the ME counts from 2007-2009.
We then normalize the ME counts for each temporal bin (2007-2009: 28, 2010:
19, 2011: 38, 2012: 40, 2013: 36, 2014: 27, see top right panel of Figure 3).
We observe a gradual increase in the proportion of Cat-I MEs from 2009
onwards, coinciding with the rising phase of solar cycle 24 and peaking near
the solar maximum (75% of the MEs in 2012 are Cat-I). During solar maximum, a
large proportion of MEs originate from active regions near big sunspot groups.
Eruptive events associated with active regions usually give rise to fast MEs
(Manchester et al., 2017). Therefore, the increase in the occurrence rate of
Cat-I MEs (fastest among the three categories) during the rising phase of a
solar cycle is expected. In contrast, during solar minimum, a majority of MEs
originate from streamer blowouts and quiescent prominences, located far from
active regions. Such eruptions usually produce slow MEs (Manchester et al.,
2017). Therefore, as expected, the occurrence rate of Cat-II MEs (slowest
among the three categories, see Table 1 for comparison of average ME speeds of
the three categories) peak at solar minimum (33% of Cat-II MEs occur during
the solar minimum). The proportion of Cat-III MEs is relatively constant with
a peak in 2010 during the rising phase of solar cycle 24. These MEs propagate
in the fastest upstream solar wind and may be associated with slower MEs
propagating through stream interaction regions (SIRs) that are more likely to
occur outside of the solar maximum.

###  3.2 Superposed Epoch Analysis

We perform a superposed epoch analysis (SEA), also known as Chree analysis
(Chree, 1913) to derive the generic profiles of sheaths driven by MEs near 1
AU. For Cat-I and Cat-II MEs, we use two characteristic epoch times, the start
of the sheath and the start of the ME, so that all events with different
timescales but from the same category are perfectly aligned. We primarily use
the timings listed in Jian et al. (2018). Only for discrepancies between the
STEREO CME list and the ASIA, we use the timings identified with visual
inspection. For each event, the sheath and ME timescales are resampled to the
average timescales of each category (average sheath duration: Cat-I is 9.27h,
Cat-II is 8.32h). Then, the SEA is performed to statistically analyze the
temporal profiles of Cat-I and Cat-II sheaths. This allows the average
temporal profiles to be presented on the average timescales of the sheath and
ME. We use the average sheath to ME interval ratio (0.44 for both Cat-I and
Cat-II) to set up the typical timescale of the ME (typical ME duration: Cat-I
is 21h, Cat-II is 18.9h). Therefore, the typical ME durations used in the SEA
differ from the average ME durations listed in Table 1. The sheaths of both
categories are binned to 75 time bins and later averaged to get the same
number of data points in the sheath interval. As the average ratio between the
length of the sheath and ME intervals for both Cat-I and Cat-II MEs is 0.44,
we impose 170 time bins for the ME (for both categories) and 16 (for Cat-I) or
18 (for Cat-II) time bins for the upstream solar wind (by comparing the
average sheath duration of 9.27h for Cat-I and 8.32h for Cat-II with the
predefined 2 hour interval upstream of the shock/discontinuity/sheath as the
solar wind). Lastly, the averaged values from different events but of the same
bin number are averaged to determine the average profiles of the physical
parameters in the sheath and ME.

For Cat-III MEs, we present the average timescale in a slightly different
manner, as these MEs do not have associated sheath regions. We select an
extended 8.8h solar wind interval upstream of the ME (average of the typical
durations of Cat-I and Cat-II sheaths). Similar to Cat-I and Cat-II sheaths,
we require this extended pre-ME solar wind interval to have 75 time bins. 211
time bins for the ME (by comparing the average ME duration of 24.8h with the
8.8h extended pre-ME solar wind interval) and 17 time bins for the solar wind
(2 hour interval upstream of the extended pre-ME solar wind interval) are
taken and later averaged.

The goal of the extended 8.8h pre-ME solar wind is to identify, if it exists,
any signature in the SEA of Cat-III MEs that may have been missed by the
visual inspection. It is also used for visualization purposes to present all
three categories with a similar format, the ME, preceded by a period of
$\sim$8-9 hours and a 2 hour pristine solar wind.

Figure 4: Superposed epoch analysis profiles for the 106 Cat-I CMEs (top
left), 36 Cat-II CMEs (top right), and 46 Cat-III MEs (bottom). The purple
curves show the average values and shaded regions indicate the interquartile
ranges. The panels show distributions (from top to bottom) of the magnetic
field strength, total root-mean-square error of the magnetic field strength,
solar wind speed, proton density, proton temperature, and dynamic pressure.
The vertical green dashed lines (top panel) bound the sheath region. The
vertical green dotted lines (bottom panel) bound the extended pre-ME solar
wind interval. The region to the left of the vertical green dashed lines
represents the unperturbed solar wind and the region to the right of the
vertical green dashed/dotted lines represents the entire ME.

From the SEA profiles of Cat-I CMEs (see top left panel of Figure 4), as
expected, we observe an abrupt increase in the magnetic field strength,
magnetic field fluctuations, proton density, speed, temperature, and dynamic
pressure over the quiescent solar wind at the shock boundary. In the sheath
region, the IMF and plasma profiles remain relatively constant (except the
magnetic field fluctuations). We introduce a dynamic root-mean-square error of
the magnetic field strength (Brms) to quantify the magnetic field
fluctuations. For each 1-min time step, we determine the fluctuations in the
magnetic field strength within that time step by comparing the deviations of
each value from the corresponding average of this 1-min time step. Therefore,
the average Brms represents the arithmatic mean of the root-mean-square errors
for each 1-min time step that makes up the solar wind/sheath/ME. The field
fluctuations peak right at the shock arrival and then continuously decrease
throughout the sheath, consistent with the study of Masías-Meza et al. (2016),
before a second peak is observed at the leading edge of the ME. The piled-up
IMF and plasma in the sheath correspond to enhanced magnetic field and plasma
profiles over the background solar wind. The steady decline in the magnetic
field strength and lower levels of proton density and temperature in the ME
are direct consequences of the typical expansion undergone by the ME near 1
AU. In addition, the magnetic field strength inside the ME is asymmetric,
owing to the aging effect (see Démoulin et al., 2008). The magnetic field
fluctuations stabilise to lower typical solar wind levels in the ME, a feature
characteristic of MCs (Burlaga et al., 1981).

For Cat-II CMEs, at the start of the sheath, we also observe a jump in the
parameters compared to the unperturbed solar wind (see top right panel of
Figure 4). However, the jumps are significantly less pronounced than for Cat-I
CMEs. In addition, the jumps are more extended and smoother, not as abrupt and
sharp as Cat-I. Similar to Cat-I sheaths, the magnetic field and plasma
profiles stay roughly constant within the sheath. The magnetic field
fluctuations peak slightly after the start of the sheath and are more
symmetric compared to Cat-I fluctuations. Cat-II sheaths also correspond to
elevated IMF and plasma parameters over the background solar wind.

In the case of Cat-III CMEs (MEs), we observe an enhanced magnetic field in
the ME compared to the ambient solar wind (see bottom panel of Figure 4). The
magnetic field is roughly steady in the ME with relatively small fluctuations.
The proton density and temperature are also low compared to the background
solar wind.

###  3.3 Average Profiles of the Structures

####  3.3.1 Magnetic Ejecta Regions

In Table 1, we compare the average parameters within the ME for different
categories. We also introduce three different types of Mach numbers. The
“pseudo” Mach number (Mpseudo) represents the ratio of the leading edge speed
in the solar wind frame to the upstream fast-magnetosonic speed. The
“propagation” Mach number (Mpropagation) denotes the ratio of the average ME
speed in the solar wind frame to the upstream fast-magnetosonic speed. The
“expansion” Mach number (Mexpansion) is the ratio of the expansion speed to
the upstream fast-magnetosonic speed. The main results are as follows:

1) MEs driving Cat-I sheaths are the fastest among the three categories and
they have the fastest expansion speed. 50% of Cat-I MEs have an average speed
in the solar wind frame which is less than the upstream fast-magnetosonic
speed of 64 km s-1.

2) MEs driving Cat-II sheaths are the slowest among the three categories and
they have the slowest expansion speed as well. However, they also propagate in
the slowest solar wind and that with the lowest fast-magnetosonic speed, i.e.,
in conditions that would be ideal to drive a shock. In fact, the average
leading edge speed of MEs driving Cat-II sheaths is 416 km s-1, which is
almost identical to the minimum leading edge speed a Cat-II ME requires to
drive a perpendicular shock near 1 AU, which is 412 km s-1.

3) Cat-III MEs have almost the same average speed as those driving Cat-II
sheaths. However, they propagate in the fastest solar wind and that with the
highest fast-magnetosonic speed, i.e., in conditions that is the least ideal
to drive a shock. The leading edge speeds of Cat-III MEs are comparable to the
upstream solar wind speed, which is consistent with these MEs not driving any
shocks. In addition, faster solar wind is less dense and also the average
expansion speed of Cat-III MEs is moderate. As a result, it is easier for the
deflected solar wind at the nose of the ME to go around it, which is a
possible physical explanation as to why these MEs also do not drive sheaths.

4) Except for their faster speed, another major difference between MEs
associated with Cat-I and Cat-II sheaths is that Cat-I MEs are of longer
duration.

5) For Cat-I sheaths, the average magnetic field strength in the sheath (see
Table 2) is higher than that in the ME by 13% and the peak magnetic field
occurs 60% of the time in the sheaths. For Cat-II sheaths, the magnetic field
strength in the sheath is lower than that in the ME by 30% and the peak
magnetic field occurs only 25% of the time in the sheaths. Cat-III MEs have
the weakest average magnetic field strength.

6) While the leading edge speeds of the MEs organizes the three categories
fairly well (see top left panel of Figure 3), it is even better organized if
we examine the distribution based on Mpseudo (see bottom panel of Figure 3),
as defined above. We do the binning of Mpseudo in a similar way to section
3.1.1. It is clearly evident that leading edge speeds of Cat-III MEs in the
solar wind frame are considerably lower than the upstream fast-magnetosonic
speed (Mpseudo<1). The largest proportion of Cat-II MEs are found in the range
of 1<Mpseudo<1.2, whereas $\sim$57% of Cat-I MEs have Mpseudo>1.2.

Table 1: Averages and standard deviations of selected solar wind plasma and IMF parameters in the ME regions of different categories. The standard deviations represent 1-$\sigma$ uncertainty. The values in parentheses are of a subset of Cat-I MEs with leading edge speeds <516 km s-1. Parameter | Cat-I (Cat-I Subset) | Cat-II | Cat-III
---|---|---|---
$<t>$ (h) | 27$\pm$16(27$\pm$18) | 22$\pm$10 | 25$\pm$13
$<N_{p}>$ (cm-3) | 5.4$\pm$3.7(6.0$\pm$3.8) | 5.9$\pm$4.2 | 4.6$\pm$3.3
$<v>$ (km s-1) | 460$\pm$112(402$\pm$57) | 396$\pm$88 | 402$\pm$65
$<T>$ (104K) | 7.4$\pm$5.4(6.2$\pm$3.6) | 6.4$\pm$9.6 | 4.8$\pm$3.0
$<B>$ (nT) | 9.9$\pm$3.9(9.5$\pm$3.1) | 9.9$\pm$2.9 | 8.0$\pm$3.1
$<P_{dyn}>$ (nPa) | 2.2$\pm$1.7(2.0$\pm$1.4) | 1.9$\pm$2.1 | 1.5$\pm$1.1
$<v>_{Upstream-sw}$ (km s-1) | 382$\pm$81(345$\pm$44) | 364$\pm$68 | 421$\pm$82
$<v>_{Upstream-fms}$ (km s-1) | 64$\pm$26(53$\pm$18) | 48$\pm$18 | 73$\pm$35
$v_{LE}$ (km s-1) | 483$\pm$118(416$\pm$56) | 416$\pm$100 | 429$\pm$80
$v_{exp}$ (km s-1) | 26$\pm$38(12$\pm$26) | 12$\pm$26 | 17$\pm$30
$M_{pseudo}$ | 1.7$\pm$1.2(1.5$\pm$1.1) | 1.1$\pm$1.1 | 0.1$\pm$0.3
$M_{propagation}$ | 1.4$\pm$1.2(1.2$\pm$1.1) | 0.7$\pm$0.9 | -0.3$\pm$0.6
$M_{expansion}$ | 0.4$\pm$0.6(0.2$\pm$0.5) | 0.3$\pm$0.5 | 0.3$\pm$0.6
$<\beta>_{Proton}$ | 0.2$\pm$0.2(0.2$\pm$0.2) | 0.1$\pm$0.1 | 0.1$\pm$0.1

####  3.3.2 Sheath Regions

We list the average sheath parameters driven by Cat-I and Cat-II MEs in Table
2. Table 3 lists the results from the Welch’s t-test (with 95% confidence
level) to determine if differences between Cat-I and Cat-II sheaths are
statistically different. In this section, we focus on the main differences
between Cat-I and Cat-II sheaths, listing only those which are statistically
significant. We find the following results:

Table 2: Averages and standard deviations of selected solar wind plasma and IMF parameters in the sheath regions of different categories. The standard deviations represent 1-$\sigma$ uncertainty. The values in parentheses are of a subset of Cat-I sheaths that are driven by MEs with leading edge speeds <516 km s-1. $<Ratio>$: Ratio of the average values within the sheath to that in the upstream solar wind. Parameter | Cat-I (Cat-I Subset) | Cat-II
---|---|---
$<t>$ (h) | 9.3$\pm$4.9(9.3$\pm$5.2) | 8.3$\pm$4.0
$<N_{p}>$ (cm-3) | 14.4$\pm$8.0(15.8$\pm$8.2) | 11.3$\pm$6.1
$<v>$ (km s-1) | 477$\pm$113(411$\pm$57) | 404$\pm$91
$<T>$ (105K) | 2.0$\pm$1.6(1.2$\pm$0.9) | 1.0$\pm$1.0
$<B>$ (nT) | 11.2$\pm$4.6(9.8$\pm$3.3) | 6.9$\pm$2.6
$<B_{rms}>$ (nT) | 0.3$\pm$0.2(0.3$\pm$0.2) | 0.2$\pm$0.4
$<P_{dyn}>$ (nPa) | 6.5$\pm$4.4(5.4$\pm$3.0) | 3.8$\pm$2.6
$<Ratio>_{N_{p}}$ | 3.8$\pm$2.3(4.0$\pm$2.1) | 2.2$\pm$1.4
$<Ratio>_{v}$ | 1.3$\pm$0.2(1.2$\pm$0.1) | 1.1$\pm$0.1
$<Ratio>_{T}$ | 3.4$\pm$2.6(3.1$\pm$2.4) | 2.1$\pm$1.5
$<Ratio>_{B}$ | 2.6$\pm$1.4(2.7$\pm$1.5) | 1.8$\pm$0.9
$<Ratio>_{P_{dyn}}$ | 6.4$\pm$4.7(6.0$\pm$4.2) | 2.8$\pm$2.0

1) The compression in density and magnetic field in the sheath as compared to
the background solar wind is significantly higher for Cat-I sheaths than Cat-
II sheaths. The level of compression ($\sim$4) in density for Cat-I sheaths is
unlikely to be explained only by the compression resulting from the associated
shock, since shock compression ratio for a typical ME-driven shock is
$\sim$2\. This indicates that there is follow-up compression after the shock,
consistent with the numerical simulation of Manchester et al. (2005).

2) Cat-I sheaths are made of denser (by 27%), hotter (by 100%), and more
magnetized (by 62%) plasma than Cat-II sheaths. The sheath plasma is faster
(by 18%) and has a higher dynamic pressure (by 71%) in Cat-I than Cat-II
sheaths. The level of fluctuations in the magnetic field is however not
statistically different.

3) The average sheath durations for Cat-I and Cat-II sheaths are similar, at
$\sim$8-9 hours. Because Cat-I sheaths are faster, their sizes are
statistically larger than Cat-II sheaths.

Table 3: Measure of statistical difference with 95% confidence level (p-values from the Welch’s t-test) between selected solar wind plasma and IMF parameters. P-values representing statistical difference are made bold. Parameter | Cat-I & Cat-II | Cat-I Subset & Cat-II
---|---|---
$<Size>_{Sheath}$ | 0.0020 | 0.1253
$<B>_{Sheath}$ | 4.2E-10 | 3.1E-06
$<N_{p}>_{Sheath}$ | 0.0134 | 0.0021
$<v>_{Sheath}$ | 0.0003 | 0.6806
$<T>_{Sheath}$ | 2.8E-05 | 0.2126
$<P_{dyn}>_{Sheath}$ | 2.1E-05 | 0.0067
$<B_{rms}>_{Sheath}$ | 0.1780 | 0.6056
$<v>_{Upstream-sw}$ | 0.2190 | 0.1326
$<v>_{Upstream-fms}$ | 0.0002 | 0.1724
$v_{LE}$ | 0.0016 | 0.9976
$v_{exp}$ | 0.0156 | 0.9134
$M_{pseudo}$ | 0.0065 | 0.0952
$M_{propagation}$ | 0.0007 | 0.0060
$M_{expansion}$ | 0.3111 | 0.8011

####  3.3.3 Comparison of Cat-II Sheaths and Cat-I Sheaths Driven by Slower
MEs

We next investigate if the differences between Cat-I and Cat-II sheaths are
due to the different speeds of the drivers or they are inherently different.
To do so, we create a subset of Cat-I MEs, where the leading edge speeds are
<516 km s-1 (average leading edge speed of Cat-II MEs is 416$\pm$100 km s-1).
We list the average values of this subset in parentheses in the Cat-I column
in Table 1 and Table 2. From the comparison of upstream conditions and ME
speeds, we can approximate that this subset of Cat-I sheaths and Cat-II
sheaths are driven by similar MEs, propagating in similar upstream solar wind
(see Table 3). We do see that the average properties of Cat-II sheaths and
sheaths of this subset are more similar to each other than Cat-I and Cat-II
sheaths. This is true for the sheath size, speed, and temperature (see Table
3). However, the sheath density, magnetic field strength, and dynamic pressure
remain more statistically elevated in Cat-I sheaths driven by slower MEs than
in Cat-II sheaths (see Table 2 and Table 3). This highlights intrinsic
differences in the compression (of the density and magnetic field) associated
with the presence or absence of a shock.

We expect the comparison between this subset of Cat-I sheaths and Cat-II
sheaths to be statistically less significant, as they are driven by MEs with
similar speeds. Except the sheath density and the upstream solar wind speed,
we indeed observe higher p-values for all other examined parameters (see Table
3). From these p-values, we can approximate that this subset of Cat-I sheaths
and Cat-II sheaths are similar in many aspects, even though their formation
mechanisms are supposed to be different, as Cat-I sheaths are driven by MEs
which also drive shocks and Cat-II sheaths are associated with MEs that do not
drive shocks.

###  3.4 Correlation Analysis between the Sheath and ME

We investigate any potential correlation between the average parameters of the
structures. We apply a linear least-squares regression technique to test the
correlation of the average parameters (proton density, solar wind speed, and
magnetic field strength) within the sheath with that of the driving ME. We use
the average ME speed in our correlation analysis to exclude the contribution
of the expansion speed, similar to Gopalswamy (2008). In the STEREO CME list,
Jian et al. (2018) ranks the MEs with a quality index ranging from 2 to 0. MEs
with an index of 2 are the closest to the MC criteria (enhanced magnetic field
strength, smooth rotation of the magnetic field vector, and low proton
temperature, see Burlaga et al., 1981). MEs with a quality index 1 are MC-
like, with the quality index 0 corresponding to non-MCs. Therefore, for each
category, we use two sets to examine the correlation of the sheath with its
driver ME. The first set considers all ME types (with quality index 0, 1, and
2) and the second set considers MEs with quality index 1 and 2 (see Table 4).

####  3.4.1 Correlation between Average Sheath and ME Properties

1) The average proton density of Cat-I sheaths show modest (Correlation
Coefficient or CC=0.50 - 0.75) positive correlation with the average proton
density (CC=0.55) and magnetic field strength (CC=0.57, see Figure 5) of the
ME, which mean that sheaths driven by denser and stronger MEs tend to be
denser as well. However, the average proton density of Cat-I sheaths does not
have any sort of relationship with how fast the ME is propagating. This is
surprising as the rate at which the ME accumulates solar wind material over
its propagation is assumed to be dependent on the speed of the ME. On the
other hand, density and speed of general solar wind are typically anti-
correlated, i.e., fast solar wind with lower density while slow solar wind
with higher density. Thus, the two effects may result in no clear correlation
between the sheath density and ME speed. For Cat-II sheaths, the average
proton density does not have any clear correlation with the average parameters
of the ME (see Figure 5 for the correlation with the average magnetic field
strength of the ME).

Table 4: Correlation coefficients of the linear least-squares regression between the average parameters of the structures (sheath and ME) for different categories. The values in parentheses refer to linear least-squares regression including MEs with quality index 1 and 2 only. + indicates positive correlation with CC<0.25. - indicates negative correlation with CC<0.25. CCs>0.50 are made bold. Parameter |  Average Np,Ejecta |  Average Np,Ejecta |  Average BEjecta |  Average BEjecta |  Average vEjecta |  Average vEjecta
---|---|---|---|---|---|---
|  Cat-I |  Cat-II |  Cat-I |  Cat-II |  Cat-I |  Cat-II
$<N_{p}>_{Sheath}$ |  0.55 (0.52) | \+ (+) |  0.57 (0.56) | 0.38 (0.37) | \- (-) | \- (-)
$<B>_{Sheath}$ | \+ (-) | \+ (-0.25) |  0.64 (0.62) |  0.54 (0.34) |  0.60 (0.63) |  0.62 (0.56)
$<v>_{Sheath}$ | -0.30 (-0.36) | \+ (-0.32) | \+ (+) | 0.31 (+) |  0.91 (0.93) |  0.93 (0.97)

2) The average magnetic field strength of Cat-I sheaths also shows a modest
relationship with the magnetic field strength (CC=0.64) and the average speed
(CC=0.60, see Figure 5) of the ME. Same is true for Cat-II sheaths. Sheaths of
both categories do not have any substantial correlation with the average
proton density of the ME.

3) The average speeds of Cat-I and Cat-II sheaths do not have any clear
correlation with the average proton density and magnetic field strength of the
ME. The average speeds in the sheath for both categories only depend upon how
fast the driving ME is propagating (CC=0.91 for Cat-I, CC=0.93 for Cat-II, see
Figure 5), which means, as expected, a faster ME drives a faster sheath as
well.

Figure 5: Scatter plots of selected average parameters for Cat-I (left panels)
and Cat-II (right panels). Blue circles represent observations of MEs with
quality index 0. Orange (for Cat-I) and red (for Cat-II) circles represent
observations of MEs with quality index 1 and 2. The solid green line
represents the best linear least-squares fit of the data set for all ME
observations (with quality index 0, 1, and 2). The orange (for Cat-I) and red
(for Cat-II) lines represent the same but only for observations of MEs with
quality index 1 and 2.

####  3.4.2 Correlation of the Sheath Size with ME Properties

We also examined the linear relationship of the sheath size (in AU) of Cat-I
and Cat-II sheaths with the speed profile and associated Mach numbers of the
ME (see Table 5 and Figure 6). The sheath size is approximated as the product
of the average speed in the radial direction and the time interval through
which the spacecraft measures the sheath. Here, this approximation for the
sheath size is dependent on the location where the sheath is crossed with
respect to the nose of the ME.

Table 5: Correlation coefficients of the linear least-squares regression between the sheath size in radial direction (AU) with specific ME parameters for different categories and different combinations. (+) indicates positive correlation with CC<0.25, (-) indicates negative correlation with CC<0.25. CCs>0.50 are made bold. Parameter | Sheath Size (AU)
---|---
| Category | All MEs | MEs (Quality Index 1 & 2)
$v_{LE}$ (km s-1) |  Cat-I | 0.39 | 0.44
$v_{LE}$ (km s-1) |  Cat-II | (+) | 0.38
$v_{LE}$ \- $<v>_{Upstream-sw}$ (km s-1) |  Cat-I | (+) | 0.25
$v_{LE}$ \- $<v>_{Upstream-sw}$ (km s-1) |  Cat-II | 0.29 | 0.65
$<v>_{Ejecta}$ (km s-1) |  Cat-I | (+) | 0.28
$<v>_{Ejecta}$ (km s-1) |  Cat-II | (+) | 0.33
$v_{exp}$ (km s-1) |  Cat-I | 0.42 | 0.48
$v_{exp}$ (km s-1) |  Cat-II | (+) | 0.37
$M_{pseudo}$ |  Cat-I | (-) | (-)
$M_{pseudo}$ |  Cat-II | (+) | 0.41
$M_{propagation}$ |  Cat-I | -0.25 | (-)
$M_{propagation}$ |  Cat-II | 0.25 | 0.39
$M_{expansion}$ |  Cat-I | 0.30 | 0.35
$M_{expansion}$ |  Cat-II | (-) | 0.25

The sheath size for both Cat-I and Cat-II sheaths show weak linear correlation
with the speed profile of the driving ME. The best correlations for Cat-I MEs
are found with the leading edge speed and the expansion speed ($\sim$0.4). In
addition, both these correlations are positive, indicating that faster CMEs
have thicker sheaths. The correlations in general are poorer for Cat-II MEs.
There exist similar poor correlations between the sheath size and the three
aforementioned Mach numbers for both categories.

Figure 6: Scatter plots of the sheath size in radial direction (in AU) and
selected ME parameters for Cat-I (left panels) and Cat-II (right panels). Blue
circles represent observations of MEs with quality index 0. Orange (for Cat-I)
and red (for Cat-II) circles represent observations of MEs with quality index
1 and 2. The solid green line represents the best linear least-squares fit of
the data set for all ME observations (with quality index 0, 1, and 2). The
orange (for Cat-I) and red (for Cat-II) lines represent the same but only for
observations of MEs with quality index 1 and 2.

This poor correlation between the sheath size and the speed profile and
associated Mach numbers of the driving ME is unexpected compared to the
results of Russell & Mulligan (2002); Savani et al. (2011), where sheath
thickness is approximated to decrease with the shock Mach number, meaning
slower MEs tend to have thicker sheaths. On a similar note, Masías-Meza et al.
(2016) found slower MCs to have thicker sheaths on average at 1 AU owing to
the effect of drag during their propagation.

##  4 Discussion and Conclusions

In this manuscript, we have outlined solar wind plasma and IMF properties in
ME-driven sheath regions. We examined 142 sheaths and 188 MEs measured by the
twin STEREO spacecraft near 1 AU during 2007-2016. We classified these MEs
into three categories, based on whether a ME drives a shock and a sheath, or
only a sheath, or neither. We determined the statistical differences between
sheaths, with and without shocks. We also investigated the correlation between
the average properties of the sheath and ME.

As expected, MEs driving both shocks and sheaths are the fastest MEs (see
Gopalswamy, 2006), propagating through typical solar wind with moderately high
magnetosonic speed. MEs driving only sheaths are the slowest MEs, propagating
through slower solar wind with low magnetosonic speed. MEs without sheaths and
shocks are also slower MEs, propagating through faster solar wind with high
magnetosonic speed.

According to our findings, $\sim$56% of MEs drive shocks near 1 AU. This shock
rate varies in phase with solar cycle activity (e.g., Lindsay et al., 1994;
Gopalswamy, 2003; Jian et al., 2011, 2018). Significant proportion (92%) of
these faster MEs (who drive shocks near 1 AU) occur during the rising and
maximum phase of the solar cycle. In contrast, MEs that propagate with a speed
slightly higher than the ambient solar wind and expand slowly drive sheaths,
even if they are not fast enough to drive shocks. $\sim$43% of the MEs that
occur during the solar minimum are these slowest MEs. Their sheaths are about
as long as a typical sheath and have some similarities in properties with
sheaths preceded by shocks, once correcting for the leading edge speed of the
ME. Occurrence of MEs that do not drive sheaths is relatively constant through
the solar cycle and is slightly higher in the rising phase

In our database, we find that a ME with a leading edge speed as low as 316 km
s-1 drives a shock near 1 AU, whereas another one with a leading edge speed
701 km s-1 does not. Such scenarios were also reported by Chi et al. (2016).
According to them, these instances can be either subjected to the variation of
the background solar wind plasma and IMF conditions for individual cases
(e.g., Shen et al., 2007) or to the effect of drag during the propagation of
MEs in interplanetary space (e.g., Lugaz & Kintner, 2013; Vršnak et al.,
2013). Confirming Lugaz et al. (2017), we find that MEs need to have a leading
edge speed faster than 515 km s-1 to have clearly a >60% probability of
driving both a shock and a sheath near 1 AU.

From our statistical analysis, we find that ME-driven sheaths are
significantly more compressed and magnetized with higher dynamic pressure
compared to the quiescent ambient solar wind. Sheaths preceded by shocks are
on average hotter, faster, compressed, and magnetized with higher magnetic
field fluctuations and dynamic pressure compared to sheaths without shocks. In
addition, shock driving MEs are more magnetized than non-shock driving MEs
(see Wu & Lepping, 2016). Some of these differences in the sheath regions
become smaller when sheaths driven by MEs (with and without shocks) with
similar speed profiles are compared, though even in this case the average
proton density, magnetic field strength, and dynamic pressure still remain
statistically higher for sheaths with shocks than sheaths without shocks.
These properties are some of the most important ones to determine the effect
of solar wind structures on geospace, both in terms of reconnection and
compression. As such, we expect sheaths preceded by shocks to have a stronger
effect on the radiation belt and magnetosphere for a given speed than sheaths
not preceded by shocks.

From the investigated parameters, we find a strong correlation between the
average speed of the structures (sheath and ME) for any category of ME-driven
sheaths (with and without shocks), consistent with previous studies (Mitsakou
et al., 2009; Janvier et al., 2019). Such strong correlations confirm that
sheaths are indeed driven by these MEs, even in the absence of shocks. Kilpua
et al. (2019) found similar strong correlation between the average speed
within the sheath and the leading edge speed of the ME. The sheath magnetic
field strength is also moderately correlated with the average magnetic field
strength (see Chi et al., 2016) and speed of the ME for all sheaths (with and
without shocks). In the case of the average proton density in the sheath, it
has moderate correlation with the average magnetic field strength of the ME
for sheaths with shocks. There is no correlation between these parameters for
sheaths without shocks.

The lack of correlation we find between the radial thickness of sheaths and
the speed profile and associated Mach numbers of the driving ME, irrespective
of the type of sheath is surprising. However, it is in perfect agreement with
Salman et al. (2020) where we found that typical sheath durations throughout
the inner heliosphere are independent of the initial ME speed. This finding
runs contrary to the conventional wisdom of how these sheaths form and may
indicate that accumulation of the solar wind, before the ME drives a shock is
the dominant mechanism that forms sheaths near 1 AU, rather than the shock
compression, since for shock compression, the stand-off distance (the radial
separation between the magnetic obstacle boundary and the shock front) should
be related to the ME speed or the shock Mach number (Russell & Mulligan, 2002;
Savani et al., 2011). Important to note that, the time period concerning this
study primarily covers the significantly weak solar cycle 24 compared to solar
cycle 23 (McComas et al., 2013) where the fraction of fast CMEs is not
dominantly high (see Figures 7 and 18 in Jian et al., 2018). Further studies,
extending this for example with ACE or Wind data will allow for improved
statistics and the inclusion of more and faster CMEs from the more active
solar cycle 23.

Even though our investigation focused on 10 years of data from the twin STEREO
spacecraft, some of our statistical results are constrained by the limited
sample sizes, especially when focusing on sub-categories. For example, there
are only 12 sheaths without shocks driven by MEs that are closest to true MCs.
However, this dataset with 142 sheaths was enough to shed some light on the
importance of the upstream solar wind conditions and the average properties of
the driving ME on the average sheath properties. In addition, measurements of
the same CME in radial conjunction close to the Sun by Parker Solar Probe (Fox
et al., 2016) or Solar Orbiter (Müller et al., 2013) and at or near 1 AU by
Wind or STEREO-A will allow us to better understand the evolution of the
sheath, especially given that previous work focusing on the radial evolution
of MEs and sheaths (e.g., Winslow et al., 2015; Good et al., 2019; Salman et
al., 2020) lacked plasma measurements in the innermost heliosphere.

T. M. S and N. L acknowledge support from NSF grant AGS1435785 and NASA grants
80NSSC17K0556, 80NSSC20K0431, NNX15AB87G, and 80NSSC20K0700. We also
acknowledge the use of Heliospheric shock database, which can be found at
http://ipshocks.fi/ and STEREO shock and CME lists, compiled by Dr. Lan K.
Jian and available at https://stereo-ssc.nascom.nasa.gov/. We are grateful to
the STEREO mission team and NASA/GSFC’s Space Physics Data Facility’s CDAWeb
service (available at https://cdaweb.gsfc.nasa.gov/index.html/) for providing
the data needed for this study. We also thank the anonymous reviewer for
critically reading the manuscript and suggesting substantial improvements.

## References

  * Alves et al. (2016) Alves, L. R., Da Silva, L. A., Souza, V. M., et al. 2016, Geophys. Res. Lett., 43, 978, doi: 10.1002/2015GL067066
  * Burlaga et al. (1981) Burlaga, L., Sittler, E., Mariani, F., & Schwenn, R. 1981, J. Geophys. Res., 86, 6673
  * Chi et al. (2016) Chi, Y., Shen, C., Wang, Y., et al. 2016, Solar Phys., doi: 10.1007/s11207-016-0971-5
  * Chree (1913) Chree, C. 1913, Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character, 212, 75, doi: 10.1098/rsta.1913.0003
  * DeForest et al. (2013) DeForest, C. E., Howard, T. A., & McComas, D. J. 2013, The Astrophysical Journal, 769, 43, doi: 10.1088/0004-637X/769/1/43
  * Démoulin & Dasso (2009) Démoulin, P., & Dasso, S. 2009, Astron. Astrophys., 498, 551
  * Démoulin et al. (2008) Démoulin, P., Nakwacki, M. S., Dasso, S., & Mandrini, C. H. 2008, Solar Phys., 250, 347, doi: 10.1007/s11207-008-9221-9
  * Echer et al. (2013) Echer, E., Tsurutani, B. T., & Gonzalez, W. D. 2013, J. Geophys. Res., 118, 385, doi: 10.1029/2012JA018086
  * Farrugia et al. (1997) Farrugia, C. J., Burlaga, L. F., & Lepping, R. P. 1997, Geophysical Monogr. Ser., 98, 91
  * Farrugia et al. (1991) Farrugia, C. J., Dunlop, M. W., & Elliott, S. 1991, Journal of Atmospheric and Terrestrial Physics, 53, 1039, doi: 10.1016/0021-9169(91)90050-H
  * Fox et al. (2016) Fox, N. J., Velli, M. C., & Bale, S. D. 2016, Space Science Reviews, 204, 7, doi: 10.1007/s11214-015-0211-6
  * Galvin et al. (2008) Galvin, A. B., Kistler, L. M., Popecki, M. A., et al. 2008, Space Science Reviews, 136, 437, doi: 10.1007/s11214-007-9296-x
  * Gonzalez et al. (1994) Gonzalez, W. D., Joselyn, J. A., Kamide, Y., et al. 1994, J. Geophys. Res., 99, 5771
  * Good et al. (2020) Good, S. W., Ala-Lahti, M., Palmerio, E., Kilpua, E. K. J., & Osmane, A. 2020, The Astrophysical Journal, 893, doi: 10.3847/1538-4357/ab7fa2
  * Good et al. (2019) Good, S. W., Kilpua, E. K. J., LaMoury, A. T., et al. 2019, Journal of Geophysical Research: Space Physics, 124, doi: 10.1029/2019JA026475
  * Gopalswamy (2003) Gopalswamy, N. 2003, Advances in Space Research, 31, 869, doi: 10.1016/S0273-1177(02)00888-8
  * Gopalswamy (2006) —. 2006, Space Science Reviews, 124, 145, doi: 10.1007/s11214-006-9102-1
  * Gopalswamy (2008) —. 2008, J. Atmos. Sol. Terr. Phys., 70, 2078, doi: 10.1016/j.jastp.2008.06.010
  * Gopalswamy et al. (2009) Gopalswamy, N., Mäkelä, P., Xie, H., Akiyama, S., & Yashiro, S. 2009, J. Geophys. Res., 114, A00A22, doi: 10.1029/2008JA013686
  * Guo et al. (2010) Guo, J., Feng, X., Zhang, J., Zuo, P., & Xiang, C. 2010, Journal of Geophysical Research: Space Physics, 115, doi: 10.1029/2009JA015140
  * Hietala et al. (2014) Hietala, H., Kilpua, E. K. J., Turner, D. L., & Angelopoulos, V. 2014, Geophys. Res. Lett., 41, 2258, doi: 10.1002/2014GL059551
  * Hudson et al. (2006) Hudson, H. S., Bougeret, J., & Burkepile, J. 2006, Space Science Reviews, 123, 13, doi: 10.1007/s11214-006-9009-x
  * Hudson et al. (2014) Hudson, M. K., Baker, D. N., Goldstein, J., et al. 2014, Geophys. Res. Lett., 41, 1113, doi: 10.1002/2014GL059222
  * Huttunen & Koskinen (2004) Huttunen, K., & Koskinen, H. 2004, Annales Geophysicae, 22, 1729, doi: 10.5194/angeo-22-1729-2004
  * Janvier et al. (2019) Janvier, M., Winslow, R. M., Good, S., et al. 2019, Journal of Geophysical Research: Space Physics, 124, doi: 10.1029/2018JA025949
  * Jian et al. (2011) Jian, L. K., Russell, C. T., & Luhmann, J. G. 2011, Solar Phys., 274, 321, doi: 10.1007/s11207-011-9737-2
  * Jian et al. (2018) Jian, L. K., Russell, C. T., Luhmann, J. G., & Galvin, A. B. 2018, The Astrophysical Journal, 885, 114, doi: 10.3847/1538-4357/aab189
  * Jones et al. (2002) Jones, G. H., Rees, A., Balogh, A., & Forsyth, R. J. 2002, Geophys. Res. Lett., 11, 1520, doi: 10.1029/2001GL014110
  * Joselyn & Tsurutani (1990) Joselyn, J. A., & Tsurutani, B. T. 1990, EOS Trans., 71, 1808, doi: 10.1029/90EO00350
  * Kaiser (2005) Kaiser, M. L. 2005, Advances in Space Research, 36, 1483
  * Kamide et al. (1998) Kamide, Y., Yokoyama, N., Gonzalez, W., et al. 1998, J. Geophys. Res., 103, 6917, doi: 10.1029/97JA03337
  * Kataoka et al. (2005) Kataoka, R., Watari, S., Shimada, N., Shimazu, H., & Marubashi, K. 2005, Geophys. Res. Lett., 32, L12103, doi: 10.1029/2005GL022777
  * Kaymaz & Siscoe (2006) Kaymaz, Z., & Siscoe, G. 2006, Solar Phys., 239, 437, doi: 10.1007/s11207-006-0308-x
  * Kilpua et al. (2017a) Kilpua, E. K. J., Balogh, A., von Steiger, R., & Liu, Y. D. 2017a, Space Science Reviews, 212, 1271, doi: 10.1007/s11214-017-0411-3
  * Kilpua et al. (2019) Kilpua, E. K. J., Fontaine, D., Moissard, C., et al. 2019, Space Weather, 17, 1257, doi: 10.1029/2019SW002217
  * Kilpua et al. (2013) Kilpua, E. K. J., Hietala, H., Koskinen, H. E. J., Fontaine, D., & Turc, L. 2013, Annales Geophysicae, 31, 1559, doi: 10.5194/angeo-31-1559-2013
  * Kilpua et al. (2017b) Kilpua, E. K. J., Koskinen, H. E. J., & Pulkkinen, T. I. 2017b, Living Reviews in Solar Physics, 14, doi: 10.1007/s41116-017-0009-6
  * Kilpua et al. (2015a) Kilpua, E. K. J., Lumme, E., Andreeova, K., Isavnin, A., & Koskinen, H. E. J. 2015a, Journal of Geophysical Research: Space Physics, 120, 4112, doi: 10.1002/2015JA021138
  * Kilpua et al. (2015b) Kilpua, E. K. J., Hietala, H., Turner, D. L., et al. 2015b, Geophys. Res. Lett., 42, 3076, doi: 10.1002/2015GL063542
  * Klein & Burlaga (1982) Klein, L. W., & Burlaga, L. F. 1982, J. Geophys. Res., 87, 613, doi: 10.1029/JA087iA02p00613
  * Lindsay et al. (1994) Lindsay, G. M., Russell, C. T., Luhmann, J. G., & Gazis, P. 1994, J. Geophys. Res., 99, doi: 10.1029/93JA02666
  * Lugaz et al. (2015) Lugaz, N., Farrugia, C. J., Huang, C. L., & Spence, H. E. 2015, Geophys. Res. Lett., 42, 4694, doi: 10.1002/2015GL064530
  * Lugaz et al. (2016a) Lugaz, N., Farrugia, C. J., Huang, C.-L., et al. 2016a, Nature Communications, 7, 13001, doi: 10.1038/ncomms13001
  * Lugaz et al. (2016b) Lugaz, N., Farrugia, C. J., Winslow, R. M., et al. 2016b, Journal of Geophysical Research: Space Physics, 121, doi: 10.1002/2016JA023100
  * Lugaz et al. (2017) —. 2017, The Astrophysical Journal, 848, 75, doi: 10.3847/1538-4357/aa8ef9
  * Lugaz & Kintner (2013) Lugaz, N., & Kintner, P. 2013, Solar Phys., 285, 47, doi: 10.1007/s11207-012-9948-1
  * Lugaz et al. (2019) Lugaz, N., Winslow, R. M., & Farrugia, C. J. 2019, Journal of Geophysical Research: Space Physics, 125, doi: 10.1029/2019JA027213
  * Luhmann et al. (2008) Luhmann, J. G., Curtis, D. W., Schroeder, P., et al. 2008, Space Science Reviews, 136, 117, doi: 10.1007/s11214-007-9170-x
  * Manchester et al. (2017) Manchester, W., Kilpua, E. K. J., Liu, Y. D., et al. 2017, Space Science Reviews, 212, 1159, doi: 10.1007/s11214-017-0394-0
  * Manchester et al. (2005) Manchester, W. B., Gombosi, T. I., De Zeeuw, D. L., et al. 2005, The Astrophysical Journal, 622, 1225
  * Masías-Meza et al. (2016) Masías-Meza, J. J., Dasso, S., Démoulin, P., Rodriguez, L., & Janvier, M. 2016, Astron. Astrophys., 592, doi: 10.1051/0004-6361/201628571
  * McComas et al. (2013) McComas, D. J., Angold, N., Elliott, H. A., et al. 2013, The Astrophysical Journal, 779, 10, doi: 10.1088/0004-637X/779/1/2
  * McComas et al. (1989) McComas, D. J., Gosling, J. T., Bame, S. J., Smith, E. J., & Cane, H. V. 1989, J. Geophys. Res., 94, 1465, doi: 10.1029/JA094iA02p01465
  * Mitsakou et al. (2009) Mitsakou, E., Babasidis, G., & Moussas, X. 2009, Advances in Space Research, 43, 495, doi: 10.1016/j.asr.2008.08.003
  * Mitsakou & Moussas (2014) Mitsakou, E., & Moussas, X. 2014, Solar Phys., 289, 3137, doi: 10.1007/s11207-014-0505-y
  * Müller et al. (2013) Müller, D., Marsden, R. G., St. Cyr, O. C., & Gilbert, H. R. 2013, Solar Phys., 285, 25, doi: 10.1007/s11207-012-0085-7
  * Nieves-Chinchilla et al. (2018) Nieves-Chinchilla, T., Vourlidas, A., & Raymond, J. C. 2018, Solar Phys., 293, doi: 10.1007/s11207-018-1247-z
  * Ontiveros & Gonzalez-Esparza (2010) Ontiveros, V., & Gonzalez-Esparza, J. A. 2010, J. Geophys. Res., 115, A10244, doi: 10.1029/2010JA015471
  * Owens et al. (2005) Owens, M. J., Cargill, P. J., Pagel, C., Siscoe, G. L., & Crooker , N. U. 2005, J. Geophys. Res., 110, A01105, doi: 10.1029/2004JA010814
  * Owens et al. (2017) Owens, M. J., Lockwood, M., & Barnard, L. A. 2017, Scientific Reports, 7, 4152, doi: 10.1038/s41598-017-04546-3
  * Palmerio et al. (2016) Palmerio, E., Kilpua, E. K. J., & Savani, N. P. 2016, Annales Geophysicae, 34, 313, doi: 10.5194/angeo-34-313-2016
  * Phan et al. (2013) Phan, T. D., Paschmann, G., Gosling, J. T., et al. 2013, Geophys. Res. Lett., 40, 11, doi: 10.1029/2012GL054528
  * Pulkkinen et al. (2007) Pulkkinen, T. I., Partamies, N., Huttunen, K. E. J., Reeves, G. D., & Koskinen, H. E. J. 2007, Geophys. Res. Lett., 34, L02105, doi: 10.1029/2006GL027775
  * Reames (1999) Reames, D. V. 1999, Space Science Reviews, 90, 413
  * Richardson & Cane (2010) Richardson, I. G., & Cane, H. V. 2010, Solar Phys., 264, 189, doi: 10.1007/s11207-010-9568-6
  * Richardson & Cane (2012) —. 2012, J. Space Weather Space Clim, 2, doi: 10.1051/swsc/2012001
  * Richardson et al. (2001) Richardson, I. G., Cliver, E. W., & Cane, H. V. 2001, Geophys. Res. Lett., 28, 2569, doi: 10.1029/2001GL013052
  * Rodriguez et al. (2016) Rodriguez, L., Masías-Meza, J. J., & Dasso, S. 2016, Solar Phys., 291, 2145, doi: 10.1007/s11207-016-0955-5
  * Russell & Mulligan (2002) Russell, C. T., & Mulligan, T. 2002, Planetary and Space Science, 50, 527, doi: 10.1016/s0032-0633(02)00031-4
  * Salman et al. (2020) Salman, T. M., Winslow, R. M., & Lugaz, N. 2020, Journal of Geophysical Research: Space Physics, 125, doi: 10.1029/2019JA027084
  * Savani et al. (2011) Savani, N. P., Owens, M. J., Rouillard, A. P., et al. 2011, The Astrophysical Journal, 732, 117, doi: 10.1088/0004-637X/732/2/117
  * Shen et al. (2007) Shen, C., Wang, Y., Ye, P., et al. 2007, The Astrophysical Journal, 670, 849
  * Siscoe & Odstrcil (2008) Siscoe, G., & Odstrcil, D. 2008, J. Geophys. Res., 113, A00B07, doi: 10.1029/2008JA013142
  * Takahashi & Shibata (2017) Takahashi, T., & Shibata, K. 2017, The Astrophys. Journ. Lett., 837, doi: 10.3847/2041-8213/aa624c
  * Tsurutani et al. (1988) Tsurutani, B. T., Gonzalez, W. D., Tang, F., & Akasofu, S. I. Smith, E. J. 1988, J. Geophys. Res., 93, 8519
  * Turner et al. (2012) Turner, D. L., Shprits, Y., Hartinger, M., & Angelopoulos, V. 2012, Nature Physics, 8, 208, doi: 10.1038/nphys2185
  * Vršnak et al. (2013) Vršnak, B., Žic, T., Vrbanec, D., et al. 2013, Solar Phys., 285, 295, doi: 10.1007/s11207-012-0035-4
  * Webb & Howard (2012) Webb, D. F., & Howard, T. A. 2012, Living Reviews in Solar Physics, 9, 3, doi: 10.12942/lrsp-2012-3
  * Winslow et al. (2015) Winslow, R. M., Lugaz, N., Philpott, L. C., et al. 2015, Journal of Geophysical Research: Space Physics, 120, 6101, doi: 10.1002/2015JA021200
  * Wu & Lepping (2016) Wu, C. C., & Lepping, R. P. 2016, Solar Phys., 291, 265, doi: 10.1007/s11207-015-0806-9
  * Xiang et al. (2017) Xiang, Z., Tu, W., Li, X., et al. 2017, Journal of Geophysical Research: Space Physics, 122, 9858, doi: 10.1002/2017JA024487
  * Yermolaev et al. (2010) Yermolaev, Y. I., Nikolaeva, N. S., Lodkina, I. G., & Yermolaev, M. Y. 2010, Annales Geophysicae, 28, 2177, doi: 10.5194/angeo-28-2177-2010
  * Zhang et al. (2007) Zhang, J., Richardson, I. G., Webb, D. F., et al. 2007, J. Geophys. Res., 112, A10102, doi: 10.1029/2007JA012321