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\begin{document}
\begin{article}
\begin{opening}

\title{A Challenging Solar Eruptive Event of 18 November 2003
and the Causes of the 20 November Geomagnetic Superstorm.
IV.~Atypical Magnetic Cloud and Overall Scenario}


\author{V.V.~\surname{Grechnev}$^{1}$\sep
        A.M.~\surname{Uralov}$^{1}$~\sep
        I.M.~\surname{Chertok}$^{2}$\sep
        A.V.~\surname{Belov}$^{2}$\sep
        B.P.~\surname{Filippov}$^{2}$\sep
        V.A.~\surname{Slemzin}$^{3}$\sep
        B.V.~\surname{Jackson}$^{4}$}


\runningauthor{Grechnev et al.} \runningtitle{Magnetic cloud
responsible for the superstorm}


\institute{$^{1}$ Institute of Solar-Terrestrial Physics SB RAS,
                Lermontov St.\ 126A, Irkutsk 664033, Russia
                  email: \url{grechnev@iszf.irk.ru} email: \url{uralov@iszf.irk.ru}\\
           $^{2}$ Pushkov Institute of Terrestrial Magnetism,
                  Ionosphere and Radio Wave Propagation (IZMIRAN), Moscow, Troitsk, 142190
                  Russia
                  email: \url{ichertok@izmiran.ru}\\
           $^{3}$ P.N. Lebedev Physical Institute, Leninsky Pr., 53, Moscow, 119991,
                  Russia
                  email: \url{slem@lebedev.ru}\\
           $^{4}$ Center for Astrophysics and Space Sciences, University of California,
                  San Diego, La Jolla, California, USA
                  email: \url{bvjackson@ucsd.edu}}


\date{Received ; accepted }


\begin{abstract}

The geomagnetic superstorm on 20 November 2003 with Dst = $-422$
nT, one of the most intense in history, escapes understanding. The
superstorm was caused by a moderate solar eruptive event on 18
November, comprehensively studied in our preceding Papers
I\,--\,III. The analysis has shown a number of unusual and
extremely complex features, which presumedly led to the formation
of an isolated right-handed configuration. Here we analyze the
interplanetary disturbance responsible for the 20 November
superstorm, compare some of its properties with the extreme
28\,--\,29 October event, and reveal a compact size of the
magnetic cloud (MC) and its disconnection from the Sun. Most
likely, the MC had a spheromak configuration and expanded in a
narrow angle of $\leq 14^{\circ}$. A very strong magnetic field in
the MC up to 56 nT was due to the atypically weak expansion of the
disconnected spheromak in an enhanced-density environment
constituted by the tails of preceding ICMEs. Additional
circumstances favoring the superstorm were \textit{i})~the exact
impact of the spheromak on the Earth's magnetosphere and
\textit{ii})~the almost exact southward direction of the magnetic
field, corresponding to the orientation in a probable region of
its source near the solar disk center.

\end{abstract}
\keywords{Forbush Decreases; Geomagnetic Storms; Interplanetary
Coronal Mass Ejections; Magnetic Clouds; Solar Wind, Disturbances}


\end{opening}


\section{Introduction}
 \label{S-introduction}

A series of big eruptive flares in a complex of large super-active
regions 10484, 10486, and 10488 occurred late in October 2003
(see, \textit{e.g.}, \opencite{Veselovsky2004};
\opencite{ChertokGrechnev2005}; \citeauthor{Gopal2005a}
\citeyear{Gopal2005a,Gopal2005b}; \opencite{Grechnev2005}). The
`Halloween 2003 events' produced geomagnetic superstorms with Dst
$= -353$ and $-383$~nT\footnote{According to the Final data of the
Kyoto Dst index service,
\url{http://wdc.kugi.kyoto-u.ac.jp/dst_final/index.html}} on
29\,--\,31 October. A notable event on 18 November occurred in the
decaying active region (AR) 10501 during the second passage across
the solar disk of the former AR~10484. This event produced a still
stronger superstorm on 20 November 2003 with Dst $= -422$~nT, the
largest one during the solar cycle 23 (\textit{e.g.},
\opencite{Yermolaev2005}; \opencite{Gopal2005c};
\opencite{Yurchyshyn2005}; \opencite{Ivanov2006}; and others), and
one of the severest storms in history (probably, among top ten in
terms of the Dst index -- see \opencite{CliverSvalgaard2004}).

A number of studies addressed the 18 November 2003 event and its
interplanetary consequences, endeavoring to understand its extreme
geoeffective impact, but its causes remain unclear. The major
outcome of the studies is the oddness of the event, which strongly
deviated from established correlations between solar and
near-Earth parameters
\cite{Yermolaev2005,Yurchyshyn2005,Srivastava2005,Chertok2013}. In
particular, the magnetic cloud (MC) near the Earth carried an
exceptionally strong magnetic field of about 56~nT, while its
velocity was modest.

The extreme geomagnetic disturbances on 29\,--\,30 October and on
20\,--\,21 November (Figure~\ref{F-cosmic}e) were produced by
solar eruptions from nearly the same complex of active regions
(which evolved in the meantime), and therefore one might expect
the 18\,--\,20 November event to inherit the properties of the
Halloween events. However, it looks instead like their antipode.
For example, the 28 October solar event produced large and fast
CME and very strong flare emissions in soft X-rays (exceeded the
GOES saturation level of X17.2), hard X-rays, and gamma rays; huge
radio bursts in microwaves (RSTN radiometers saturated) and up to
submillimeters; strong SEP event (Figure~\ref{F-cosmic}a), and a
ground-level enhancement of the cosmic ray intensity, GLE~65. The
29 October event was similar to the 28 October event. On the other
hand, none of the listed extreme properties correspond to the 18
November event. It was medium in soft X-rays ($\lsim\,$M5), hard
X-rays, and microwaves. The enhancement of the near-Earth proton
flux was inconsiderable (but it could be reduced due to the
easterly position of the active region on 18 November). The
associated CMEs had a moderate speed, size, and brightness, and
did not exhibit any extreme features. The time intervals between
the solar eruptions and the geomagnetic storm onset/peak times
were 19/38~h on 29 October and much longer on 20 November,
48/61~h.

The peculiarities are also related to the MC, which reached the
Earth's magnetosphere on 20 November. The $B_z$ magnetic component
in the MC was pointed south (negative), although the MCs produced
by the eruptions from AR~10484 in October had $B_z > 0$. The
magnetic helicity of the MCs responsible for the Halloween
superstorms (from AR~10486) was negative, but it was positive in
the MC of 20 November. Moreover, the orientation and handedness of
the magnetic field in the 20 November MC mismatched those in its
presumable source region AR~10501 \cite{Moestl2008,Chandra2010}.

Thus, the 18\,--\,20 November extremely geoeffective event has
offered four major problems: \textit{i})~incomprehensible causes
of its extremeness, \textit{ii})~its enigmatic solar source, and
perplexing \textit{iii})~orientation and \textit{iv})~handedness
of the magnetic field in the MC. Despite several ideas proposed in
the listed studies to address these issues, satisfactory
explanations were still missing. This enigmatic event offers the
challenge in predictions of geomagnetic disturbances, which can
occur unexpectedly and be destructive for modern and future
high-technology systems.

These circumstances were the major causes, which inspired us to
undertake a comprehensive analysis of this event presented in our
Paper~I \cite{Grechnev2014_I}, Paper~II \cite{Grechnev2014_II},
and Paper~III \cite{Uralov2014}. The analysis has revealed an
extremely complex, unusual solar eruptive event. None of the
observed CMEs was an appropriate candidate for the source of the
MC, being only able to produce a glancing blow on the Earth due to
their rather large angles with the Sun\,--\,Earth line. However,
three different reconstructions of the MC \cite{Yurchyshyn2005,
Moestl2008, Lui2011} showed its central encounter with Earth.

On the other hand, indications were found of an additional
eruption, which probably occurred rather far from AR~10501, but
close to the solar disk center. The presumable erupted magnetic
structure was a right-handed pair of linked tori moving away from
the Sun, and slowly expanding with a radial (lateral) speed of
$\sim 100$~km~s$^{-1}$, \textit{i.e.}, within a narrow angle of
$\lsim 14^{\circ}$ (Papers II and III). It is not completely clear
into what structure the couple of tori evolved. Most likely, this
structure was disconnected from the Sun and developed into a
toroid or spheromak. Due to its weak expansion, the earthward
direction, and a presumedly small mass, the probability to detect
this eruption in coronagraph images was very low. Just this
eluding structure could evolve into the MC, which reached Earth on
20 November.

We will not list all the ideas proposed previously and follow
instead only those results and suggestions, which appear to be
consistent with these findings and promising to shed light on the
issues in question. The major reasons for the superstorm probably
were the strongest magnetic field in the MC (close to a record
value, while its speed was ordinary) and its orientation ($\theta
= -(49-87)^{\circ}$, see \opencite{Moestl2008}).
\textbf{\inlinecite{Qiu2007} demonstrated a quantitative
correspondence between the magnetic fluxes in nine MCs and their
solar source regions. Furthermore, \inlinecite{Chertok2013}
analyzed the major Solar Cycle 23 geomagnetic storms
(Dst~$<-100$~nT), whose sufficiently reliably identified solar
source regions were located in the central part of the disk. They
found that the intensity of the geomagnetic storms, as well as the
ICMEs' Sun--Earth transit times, were mainly governed by the
parameters of their solar sources, such as the total unsigned
magnetic flux at the photospheric level within the post-eruption
EUV arcades and dimming regions. For example, these magnetic
fluxes in the solar sources of the strongest Solar Cycle 23
geomagnetic storms with $\mathrm{Dst} < -200$~nT, the near-Earth
magnetic field $|{\bf B}| > 50$~nT, and large southern $B_z$
component, such as the 14--15 July 2000, 22--24 November 2001,
28--30 October 2003, and 13--15 May 2005 superstorms (see,
\textit{e.g.}, \opencite{Wu2005}; \opencite{Cerrato2012};
\opencite{Manchester2014}) were very large, $(240-870) \times
10^{20}$~Mx. The severity of the geomagnetic superstorm on 20
November 2003 appears to correspond to the near-Earth magnetic
field of $|{\bf B}|_{\max} \approx 56$~nT with a large southern
magnetic component up to $B_z \approx -45$~nT, while the total
unsigned magnetic flux in the eruption region was as low as $130
\times 10^{20}$~Mx, even including the flare arcade in active
region 10501 and all dimmings.} The only way to get an extremely
strong magnetic field with a modest magnetic flux is a small size
of the MC. This conjecture is consistent with the mentioned
reconstructions of the MC, all of which showed both its dimensions
in the ecliptic plane to be $< 0.3$~AU ($< 17^{\circ}$). One more
indication is that the Forbush decrease on 20 November was much
less than that after the 28 October event. Note also the idea
about the compression of the MC due to the interaction of CMEs
\cite{Gopal2005c,Yermolaev2005}.

The mentioned reconstructions were based on the fitting of
specific configurations such as a torus or cylinder
\cite{Yurchyshyn2005, Moestl2008, Lui2011, Marubashi2012} to the
observed rotating magnetic components in the MC. The fitted
components more or less resembled the observed ones within some
limited portions of the ICME, overlapping with each other, but
covering somewhat different parts of the ICME in different
reconstructions. On the other hand, considerations of the $\phi_B$
and $\theta_B$ angles led \inlinecite{KumarManoUddin2011} to the
idea that the MC occupied a longer part of the ICME along the
Sun--Earth line (see also \opencite{Gopal2005c} and
\opencite{Marubashi2012}). This possibility suggests that its
magnetic structure might be different from those considered
previously.

To verify these suggestions and shed further light on the
enigmatic 18\,--\,20 November 2003 event, we address in this paper
the corresponding ICME. In Section~\ref{S-icme} we revisit
\textit{in situ} measurements of the interplanetary disturbance,
analyze ground-based data on cosmic rays, and consider
heliospheric 3D reconstructions made from the observations of the
\textit{Solar Mass Ejection Imager} (SMEI, \opencite{Eyles2003};
\opencite{Jackson2004}). Then we discuss the results and their
implications in Section~\ref{S-discussion}. In particular, we
endeavor to understand the probable causes of the superstorm, to
follow the whole presumable chain from the solar eruption on 18
November up to the encounter of the MC with the Earth on 20
November, and to outline possible ways to diagnose such
anomalously geoeffective events.

\section{Properties of the ICME}
 \label{S-icme}

As mentioned, the 20 November geomagnetic superstorm was a
conspicuous exception to almost all established statistical
correlations (see, \textit{e.g.}, \opencite{Yurchyshyn2005};
\opencite{Srivastava2005}; \opencite{Chertok2013}). Being
surprising, this fact also promises an opportunity to find hints
at causes of the superstorm from its particularities. By comparing
the 28 October event and related interplanetary disturbances with
those on 18--20 November, we hope to understand the
incomprehensibly large geomagnetic effect of the 18 November
eruption.

\subsection{Interplanetary Data}

Data on \textit{in situ} measurements of the interplanetary
disturbance have been addressed in several studies (\textit{e.g.},
\opencite{Yurchyshyn2005}; \opencite{Yermolaev2005};
\opencite{Gopal2005c}; \opencite{Moestl2008};
\opencite{KumarManoUddin2011}; and \opencite{Marubashi2012}).
Nevertheless, some significant particularities were not discussed
previously. Here we consider the near-Earth ICME observations made
with Solar Wind Electron Proton Alpha Monitor (SWEPAM,
\opencite{McComas1998}) and Magnetometer Instrument (MAG,
\opencite{Smith1998}) on \textit{Advanced Composition Explorer}
(ACE). Figure~\ref{F-ace} shows records of the magnetic field
components $B_x$, $B_y$, and $B_z$ along with a magnitude $|{\bf
B}|$ (a), solar wind velocity (b), proton temperature (c) and
density (e), and plasma $\beta$ inferred from the above
parameters. The reasons for our identification of the boundaries
of the magnetic cloud are as follows.

 \begin{figure} % {1}
  \centerline{\includegraphics[width=0.85\textwidth]
   {ace_data.eps}
  }
  \caption{ACE data. a)~$B_x$, $B_y$, and $B_z$ components of the
magnetic field and its magnitude $|{\bf B}|$. Parameters of the
ejecta: velocity (b), proton density (c) and temperature (d), and
plasma $\beta$ (e). f)~Polytropic index $\gamma$ inferred from the
density and temperature in two intervals marked with the pink and
purple lines. g)~Pitch angle distribution of 272~eV electrons
(minimum blue, maximum red). h)~Same as (g) but with a moving
normalization (adopted from Marubashi \textit{et al.}, 2012). }
  \label{F-ace}
  \end{figure}

After arrival of the shock front at about 07:20 on 20 November,
the plasma velocity kept on increasing up to the contact surface
that is typical of a bow shock. This fact suggests significance of
the aerodynamic drag. The thick dashed line at 08:35 and the thin
dash-dotted line at 10:08 in Figure~\ref{F-ace} mark possible
arrival times of the MC frontal edge that is rather uncertain. The
earlier thick line roughly corresponds to the position of the
highest plasma velocity. Such a situation occurs at the forward
stagnation point of a supersonic body with fixed shape and size.
The later thin line approximately corresponds to the position
where the plasma beta and density underwent a seemingly sharpest
drop. This situation is expected for a typical MC. It is difficult
to choose between the two options of the MC leading edge for the
following reasons. On the one hand, the MC expanded with a
velocity of the order of 100~km~s$^{-1}$ which was appreciably
higher than the fast-mode speed in an undisturbed solar wind that
prevented a stationary flow around the ICME. On the other hand,
the nearly self-similar expansion of a MC that is often employed
implies conservation of the profile of the plasma beta formed at
the MC creation. As Paper~III showed, the MC hitting the Earth was
probably formed from magnetic structures with considerably
different temperatures, densities, and possibly plasma beta.
Therefore, sharp changes of beta without significant variations of
$|{\bf B}|$ in Figure~\ref{F-ace} might correspond to these
different parent structures.

We consider the first thick dashed line as the leading edge of the
MC because of \textit{i})~equality of the $B_z$ flux in a closed
magnetic structure (see below), \textit{ii})~a sharp density
increase of suprathermal electrons (Figure~\ref{F-ace}g) discussed
later; \textit{iii})~sharp changes of the proton temperature and
density. The conditions (\textit{i}) and (\textit{iii}) were also
used in identifying the rear edge of the MC.

One more feature deserving attention is a weak reverse shock in
Figure~\ref{F-ace} at 06:10 on 21 November. Its presence as well as
the presence of the forward shock indicates that expansion of the MC
was not free for all directions. A reverse shock can be due to two
reasons. One is overexpansion of a MC if its earthwards bulk
velocity is less than velocity of its own expansion. This is not the
case here. The second possibility for the development of the reverse
shock appears if a MC is pressed from behind by the faster flow of
the disturbed solar wind. The latter situation is favored if a MC is
disconnected from the Sun. In this situation the MC is not protected
from lateral disturbances such as shocks and related high-speed flow
which could come from expanding CME1, CME2, and CME3. If a magnetic
flux rope is connected to the Sun, then the extended magnetic
structure protects the top of the MC from such lateral disturbances.

The trend of the velocity in the MC (region B in
Figure~\ref{F-ace}a) is close to a linear one (dotted line), which
is an attribute of a self-similar expansion \cite{Low1984}. Such
expansion occurs if all forces affecting an ejecta (magnetic
forces, plasma pressure, and gravity; so far we neglect the
aerodynamic drag, whose effect is not self-similar) reduce with
distance by the same factor \cite{Low1982,Uralov2005}. This
condition is satisfied if the polytropic index $\gamma = 4/3$. Its
actual value in the MC interior can be estimated from the proton
density and temperature (Figure~\ref{F-ace}c,\,d) as $\gamma =
n/T\, \left( dT/dt \right) / \left( dn/dt \right) +1$ as shown in
Figure~\ref{F-ace}f. This expression is valid if the entropy
distribution inside the MC is uniform. Averaging of values
obtained in this way provides an average $\gamma$ inside the MC.
To bypass fluctuations in computations of the derivatives, we
fitted the trends within two intervals with smooth functions (pink
and purple). The actual $\gamma$ varies around $5/3$; the
difference from $4/3$ does not seem to be significant, because
$\beta \leq 0.1$ within this interval. [According to
\inlinecite{Farrugia1995}, the estimated value of $\gamma$
supports the spheromak configuration \textit{vs.} a flux rope.]
These circumstances allow us to calculate an expansion-corrected
`snapshot' of the ICME assuming its expansion to be exactly
self-similar. We infer the time-dependent expansion factor
$\xi(t)$ from the linear fit of the velocity profile. The
correction factor for the magnetic field strength in the snapshot
related to the $t_0$ moment is $[\xi(t_0)/\xi(t)]^2$ (from the
magnetic flux conservation), and the correction factor for the
density is $[\xi(t_0)/\xi(t)]^3$.

Figures \ref{F-ace_cor_spheromak}a and \ref{F-ace_cor_spheromak}b
show such `snapshots' for the magnetic field and density
distributions in the ICME along the Sun\,--\,Earth line
corresponding to the first contact with ACE spacecraft. The
expansion factor evaluated from the linear velocity profile in
Figure~\ref{F-ace}b was used in the second power for the magnetic
field strength and in the third power for the density. The total
length of the ICME in the Sun\,--\,Earth direction was $\approx
0.22$~AU and, according to the reconstructions of the MC
\cite{Yurchyshyn2005, Moestl2008, Lui2011}, its axis passed close
to ACE spacecraft.

  \begin{figure} % {2}
  \centerline{\includegraphics[width=\textwidth]
   {ace_corrected_spheromak.eps}
  }
  \caption{A `snapshot' of the magnetic field (a) and density (b)
distributions in the ICME along the Sun--Earth line according to
expansion-corrected ACE data. The ICME size corresponds to the
first contact with ACE. c,\,d)~A magnetic configuration of a
perfect spheromak with its axis shown perpendicular to the
ecliptic plane for simplicity. The brown ovals outline the regions
presumably belonging to the leading (A) and trailing (C) parts of
the MC. e)~The color scaling of the $B_z$ component in a prefect
spheromak shown in panels (c) and (d) and roughly corresponding to
$-B_z$ in Figure~15 of Lui (2011).}
  \label{F-ace_cor_spheromak}
  \end{figure}

The behavior of the $B_x$ component, which alternately reached
significant positive and negative values within the MC (see also
Figure~12 in \opencite{Lui2011}), rules out a glancing blow of a
flux rope connected to the Sun; otherwise, the sign of $B_x$ would
not change in the MC. Variations of the magnetic components in
regions A and C outlined with the brown ovals in
Figure~\ref{F-ace_cor_spheromak}a look like their regular
continuations from region B rather than pile-up fluctuations in
the sheath. To verify this conjecture, we estimated the total
magnetic fluxes of the $B_z$ component in region B, on the one
hand, and the corresponding sum in regions A and C, on the other
hand, assuming the ICME cross section to be circular. To take
account of the ICME asymmetry in the Sun--Earth direction, the two
estimates for each ICME half were averaged. The result shown in
Figure~\ref{F-ace_cor_spheromak}a demonstrates that the difference
between the magnetic fluxes in regions B ($-6.2 \times
10^{20}$~Mx) and A+C ($5.2 \times 10^{20}$~Mx) does not exceed
20\%. These values are close to the estimate of $5.5 \times
10^{20}$~Mx obtained by \inlinecite{Moestl2008}, despite the
coarseness of our approach. Hence, the magnetic field variations
in regions A and C were, most likely, not sporadic.

The presence of the opposite magnetic $B_z$ components and the
equality of their fluxes together with the same situation for $B_y$
(while $B_x$ was rather small) indicates their balance in the ICME,
\textit{i.e.}, a closed magnetic field in the MC. This is only
possible if the MC was not connected to the Sun, so that its
configuration was either an isolated toroid or a spheromak. In
either case, the angle between the MC axis and the ecliptic plane
must be large. We adopt the spheromak configuration and later
confirm this assumption by different indications considered in
Section~\ref{S-icme}.

A simplest 2.5-dimensional configuration which satisfies the
equality of magnetic fluxes is an infinitely long cylinder with a
linear force-free magnetic field inside: $B_z = J_0(\alpha r),
B_\varphi = \sqrt{(B_x^2+B_y^2)} = J_1(\alpha r)$ where $J_n$ is a
cylindric Bessel function of the first kind of order $n$. The
boundary of the cylinder is determined by the first root of the
equation $J_1(\alpha r) =0$. The total magnetic flux through a
normal cross section of such a magnetic flux rope is zero. A
3-dimensional analog of this situation is a spheromak whose total
magnetic flux equals to zero in both equatorial and meridional cross
sections. The boundary of a spheromak is determined by the first
root of the equation $j_1(\alpha r) = 0$ where $j_1$ is a spherical
Bessel function of the first kind. A transformation of a long
cylindric flux rope into a thin toroid does not significantly change
the inherent situation for an infinitely long flux rope. A
force-free flux rope whose small radius is determined by the
condition $J_1(\alpha r) =0$ cannot have bases frozen in the solar
surface. If it were so, then the total magnetic flux in each
photospheric base of the flux rope would be zero that obviously
disagrees with observations of eruptive coronal flux rope
structures. Thus, the MC was more probable a force-free self-closed
magnetic structure rather than that closed to the Sun, and the total
magnetic flux in its cross section was zero.

It is important to note that usually the boundary of a MC is
considered as a surface, at which the axial magnetic field of
either a loop-like flux rope or toroid is zero. To the linear
force-free approximation in this situation corresponds the
equation $J_0(\alpha r) =0$ whose first root determines the
boundary of a rope. In this case, the total flux of the axial
magnetic field in the flux rope's cross section is maximum but not
zero. At present this scheme is a basis of the technique to fit
the internal magnetic structure of many observed MCs (see,
\textit{e.g.}, \opencite{MarubashiLepping2007};
\opencite{RomashetsVandas2003}). \inlinecite{Marubashi2012} also
employed this technique to determine geometry of the 20 November
2003 MC. However, this technique does not permit the presence of
the opposite magnetic $B_z$ components with the equality of their
fluxes that we emphasize. The fitting technique usually employed
is not usable in the 20 November 2003 event exactly for this
reason.

A quite different Grad\,--\,Shafranov reconstruction technique was
used by \inlinecite{Yurchyshyn2005}, \inlinecite{Moestl2008}, and
\inlinecite{Lui2011}. This technique allows one to reconstruct a
two-dimensional cross section of an MC and to evaluate the
inclination of its axis only if the MC is a nearly straight
portion of a magnetic flux rope with the curvature, plasma
pressure, and magnetic field slowly varying along the flux rope
axis. Regrettably, the reconstruction intervals in these papers
did not fully cover all the three intervals A, B, and C shown in
Figure~\ref{F-ace_cor_spheromak}. \inlinecite{Moestl2008}
considered a large portion of interval B starting from its left
boundary. \inlinecite{Yurchyshyn2005} included the same portion
and a half of interval A. \inlinecite{Lui2011} considered the
whole interval B and almost the whole interval C. Nevertheless,
Figure~15 from \inlinecite{Lui2011} shows that the direction of
the ${\bf B}_x + {\bf B}_y$ vector is practically constant in the
motion from the flux rope center to its periphery despite the
change of sign of $B_z$. The ecliptic cut of the spheromak in
Figure~\ref{F-ace_cor_spheromak}d shows the same situation. A cut
of a force-free magnetic cylinder with a boundary determined by
the condition $J_1(\alpha r) =0$ is similar. However, one should
be aware of the fact that the results of the Grad\,--\,Shafranov
reconstruction of outer parts of a MC can be distorted if all the
MC dimensions are comparable which is the case for a spheromak.
Possibly, this circumstance was responsible for the appearance of
an X point in the reconstruction of \inlinecite{Yurchyshyn2005}.


Figures \ref{F-ace_cor_spheromak}c and \ref{F-ace_cor_spheromak}d
show two views of a perfect non-distorted spheromak with its axis
perpendicular to the ecliptic for simplicity. The regions outlined
with the ovals correspond to regions A (dark brown ovals) and C
(bright brown ovals) in Figure~\ref{F-ace_cor_spheromak}a. The
pass of the spheromak across ACE spacecraft is expected to produce
a response, which is close to the observed one. The actual
front/tail asymmetry of the magnetic field indicates compression
of the leading half of the MC and stretch of the trailing one
suggesting a significant role of the aerodynamic drag. Note that
the toroidal (Figure~\ref{F-ace_cor_spheromak}d) and poloidal
(Figure~\ref{F-ace_cor_spheromak}c) magnetic fluxes in the
spheromak are transposed with respect to a torus (connected to the
Sun or disconnected).

For a spheromak configuration it is possible to estimate the total
mass of the ICME. We consider a simple three-layer spheroid
consisting of \textit{i}) a central core inside \textit{ii}) the
ICME surrounded by \textit{iii}) a sheath. The ICME cross section
is assumed to be an oval extended along the Sun-Earth line with an
eccentricity of 2 according to \inlinecite{Moestl2008}. The
estimates for the leading and trailing half of the MC are
averaged. The results are shown in
Figure~\ref{F-ace_cor_spheromak}b for the three layers separately.
The total ICME mass is estimated to be $\lsim 10\times 10^{14}$~g
and, since the sheath was acquired by the ejecta on the way to the
Earth, the initial mass of the CME was, most likely, $\lsim
5\times 10^{14}$~g. This estimate is consistent with the
conclusion of Paper~I that the major part, $(2-4) \times
10^{15}$~g, of the initial mass of the eruptive filament of $(4-6)
\times 10^{15}$~g remained on the Sun.

Figure~\ref{F-ace} shows that the standoff distance between the
ICME piston and the shock ahead was $\approx 0.02$ AU,
significantly less than a typical value of 0.1 AU
\cite{RussellMulligan2002}. According to the formulas from this
paper, the radius of curvature of the ICME nose in this case must
be $\lsim 0.1$ AU for each of the X and Y ICME dimensions with any
Mach number $M > 1$. This radius of curvature is consistent with
the ICME geometry discussed in the preceding paragraph and the
conclusion of \inlinecite{Vandas1997} related to a spheromak.

The spheromak configuration of the MC addresses the suggestions of
its small size mentioned in Section~\ref{S-introduction}. The
length of the MC along the Sun-Earth (the X direction) line was
about 0.2~AU (see Figure~\ref{F-ace_cor_spheromak}). The Y size
was close to the X size, as the reconstructions of the MC
presented by \inlinecite{Yurchyshyn2005}, \inlinecite{Moestl2008},
and \inlinecite{Lui2011} showed indeed. Considering all the facts,
we have to conclude that the whole spheromak-shaped ICME expanded
within a narrow cone of $\leq 14^{\circ}$. Therefore, the
corresponding CME could appear from behind the occulting disk of
LASCO/C2 at distances $\geq 16R_\odot$, where the
Thomson-scattered light was meager. Such a CME could only be
detected with LASCO if its mass were very large, which was not the
case. It is therefore not surprising that nobody has succeeded in
detecting this CME in LASCO images.

We have concluded that the magnetic configuration of the MC was
closed, \textit{i.e.}, the MC must be a trap for charged
particles. This suggestion can be verified by considering
pitch-angle distributions of suprathermal electrons.
Manifestations of bidirectional streams in pitch-angle maps are
sometimes considered as a support of the connection of a MC to the
Sun, as \inlinecite{Moestl2008} did. However, the argument of
bidirectional particles does not seem to certify their reflections
from bases of a magnetic flux rope anchored on the Sun being only
an indication of a magnetic trap. For example, closed isolated
torus or spheromak configurations are perfect magnetic traps, and
therefore bidirectional particles can also be present in such
configurations. Thus, we agree with the approach of
\inlinecite{Marubashi2012}, who revealed the presence of
counterstreaming electrons during more than half a day on
20\,--\,21 November and considered them among indications of a MC
structure. The pitch angle distribution of electrons in the 272 eV
channel calculated by \inlinecite{Marubashi2012} as 5-min averages
normalized to the maximum flux value in each time bin is shown in
Figure~\ref{F-ace}h. To understand the nature of the bidirectional
electron flows, let us consider the records of the $B_x$ and $B_y$
components in Figures \ref{F-ace}a and \ref{F-ace_cor_spheromak}b
(see also Figure~12 of \opencite{Lui2011}).

Before the arrival of the MC, the signs of these magnetic
components were $B_x <0, B_y>0$, and after the departure of the MC
$B_x >0, B_y<0$ suggesting that the MC passed ACE spacecraft when
it crossed a sector boundary of the heliospheric magnetic field
(anti-sunward before the MC and sunward afterwards; see also
\opencite{Ivanov2006}). This orientation corresponds to small
pitch angles of electrons flowing away from the Sun before the MC
and those close to $180^{\circ}$ after the MC pass as
Figure~\ref{F-ace}h confirms. The bidirectional electron flows
might appear due to reconnection of the MC with environment
magnetic fields that is supported by a nearly linear trend
separating the electron pitch-angle distribution. The trend
implies a gradual change of predominant reconnection at one MC
edge to the opposite one as the MC passed through the sector
boundary. Thus, the bidirectional electron flows might be absent
in the MC without reconnection and therefore should not be
considered in favor of the connection of the MC to the Sun.

An additional indication of the trap-like behavior of the MC can
be revealed from the pitch-angle
distribution\footnote{\url{http://www.srl.caltech.edu/ACE/ASC/DATA/level3/swepam/index.html}}
of the 272 eV electrons with an overall normalization presented in
Figure~\ref{F-ace}g. As we saw, region A of the ICME presumedly
belonged to the MC. Indeed, the SWEPAM-E plot shows a sharp
increase of the electron density at the leading MC boundary, which
we identified, and no drastic changes afterwards.

\textbf{In contrast to the considered indications of the unusual
spheromak configuration of the 20 November 2003 MC, the Halloween
2003 MC showed the properties typical of a classical
croissant-like flux rope. The latter event and its solar source
were addressed by \inlinecite{Yurchyshyn2005}.}

\subsection{Data on Heavy Relativistic Particles}

The intensity of geomagnetic storms is known to strongly depend on
the parameters (the sign and value of the $B_z$ component, speed)
in a relatively local ICME part interacting directly with the
Earth's magnetosphere (see, \textit{e.g.},
\opencite{TsurutaniGonzalez1997}), while the depth of a Forbush
decrease (FD) is determined by global characteristics of an ICME,
particularly such as its magnetic field strength, size, and speed
(see, \textit{e.g.}, \opencite{Belov2009}). Figure~\ref{F-cosmic}e
shows that the geomagnetic effect from the 18 November event (in
terms of the Dst index) was stronger than that of the 28 October
event, but the FD from the 20 November interplanetary disturbance
was incomparably moderate with respect to the huge Halloween one
(Figure~\ref{F-cosmic}b). However, the correctness of the
comparison of FDs in the two events does not seem to be obvious.
In particular, the 29 October FD was a largest one ever observed
with neutron monitors \cite{Belov2009} and could acquire its value
only due to an extremely rare combination of circumstances.


  \begin{figure} % {3}
  \centerline{\includegraphics[width=0.8\textwidth]
   {cosmicr.eps}
  }
  \caption{Solar protons (a), galactic cosmic ray data (b\,--\,d, Courtesy V. Sdobnov),
and geomagnetic disturbances (e) during the late October through
November interval. The spherical harmonics of the galactic cosmic
ray pitch-angle anisotropy are shown in panel c (first, $A1$) and
d (second, $A2$). The dashed lines mark the 28 October and 18
November solar events.}

  \label{F-cosmic}
  \end{figure}

For comparison with other events we have used a data base on
interplanetary disturbances and Forbush decreases created in
IZMIRAN (\citeauthor{Belov2001}, \citeyear{Belov2001};
\citeyear{Belov2009}). The density variations of cosmic rays in
the data base refer to cosmic rays of 10 GV rigidity, which is
close to the effective one for the majority of ground-based
neutron monitors, so that cosmic ray variations around this
rigidity can be evaluated with a highest accuracy. The FD
magnitude determined in this way was 28.0\% for 29 October FD and
4.7\% for 20 November. The latter effect is probably
underestimated and needs correction for the following reason. An
unusually large magnetospheric variation of the cosmic ray
intensity observed over ground-based detectors on 20 November
\cite{Dorman2009} resulted in a decrease of the geomagnetic cutoff
rigidities at observation stations \cite{Belov2005} that decreased
the FD depth evaluated over the whole World's neutron monitor
network. Thus, the real magnitude of the 20 November FD was most
likely 6\,--\,7\% (this has been really confirmed by the most
recent estimate of 6.6\% by taking account of the magnetospheric
effect). This effect is generally large \cite{Belov2001}, but does
not seem to correspond to the parameters of the associated ICME.
With a strength of the total interplanetary magnetic field $|{\bf
B}|$ of up to 55.8 nT (hourly averages), one might expect a
considerably larger FD, because such a strong magnetic field was
additionally observed only two times over the whole history of the
solar wind observations. The two extra events occurred in November
2001, while the corresponding FDs were considerably larger, 9.2\%
and 12.4\%. All but one (31 March 2001) events with strongest
magnetic field exceeding 45 nT caused FDs larger than that on 20
November (pronouncedly larger, as a rule).

Besides the magnetic field strength in an ICME, the solar wind
speed should be taken into account in these comparisons. Unlike
the magnetic field, the solar wind speed on 20 November was
ordinary and increased only up to 703 km~s$^{-1}$ (hourly data).
The FD magnitude is known to correlate well with a product of
observed maximums of the magnetic field strength $|{\bf
B}|_{\max}$ and the solar wind speed $V_{\max}$ (\textit{e.g.},
\opencite{Belov2009}). In the 20 November 2003 event, the $|{\bf
B}|_{\max}V_{\max}$ product normalized to 5 nT and 400 km~s$^{-1}$
is 19.6, while the whole range of the product over the data base
is from 0 to 29.6. We have considered all the events with $|{\bf
B}|_{\max}V_{\max} > 15$ that were not influenced by preceding
events. Almost all the events (except for the mentioned 31 March
2001 event) produced deeper FDs than the 20 November 2003 one,
with an average value of $10.1 \pm 1.8\%$. This value is probably
underestimated, because data on the solar wind were incomplete or
absent during several largest FDs. Due to this reason, our sample
does not include such FDs as those in August 1972 (25\%) and in
October 2003 (28\%).

Thus, the ICME parameters observed on 20 November 2003 suggested
expectations of a larger FD. This fact implies that a smaller size
and/or an unusual structure of the CME in question can be a reason
for its lowered ability to modulate cosmic rays. It is possible
that two kinds of powerful CMEs/ICMEs exist whose probably
different structure and other properties determine the difference
between their influence on cosmic rays even with equal parameters
of the plasma velocity and magnetic field strength.

Both the geomagnetic effect and FD of an ICME are considered to
depend on parameters of a MC with the FD depth being independent
of $B_z$; thus, the inconsistency between the geomagnetic effect
and the FD depth provides further support to the small size of the
20 November MC. Indeed, its extent along the Sun\,--\,Earth line
was about three-times less than that of the Halloween MC, and
reconstructions of the MC \cite{Yurchyshyn2005,Moestl2008,Lui2011}
show its perpendicular size in the ecliptic to be even less than
the Sun\,--\,Earth extent. Thus, the area of the 20 November MC
cross-section was about one order of magnitude smaller than that
of the 28 October MC.

An additional indication can be revealed from the pitch-angle
anisotropy of relativistic protons. Their gyroradius is larger
than that of suprathermal electrons by a factor of $\sim 10^5$,
which considerably reduces effects on their pitch-angle anisotropy
due to factors irrelevant to trapping. Therefore, anisotropy of
relativistic protons promises still more reliable indication of a
large-scale magnetic trap connected to the Sun than low-energy
electrons do. Anisotropy appears in ground-level enhancements of
cosmic ray intensity (GLE events) and due to modulation of
galactic cosmic rays by magnetic clouds and corotating interacting
regions in the solar wind.

The spherical harmonics of the pitch-angle anisotropy computed by
\inlinecite{Dvornikov2013} from the data of the worldwide neutron
monitor network using the method of
\citeauthor{DvornikovSdobnov1997}
(\citeyear{DvornikovSdobnov1997,DvornikovSdobnov1998}) are shown
in Figures \ref{F-cosmic}c (first harmonic, A1) and
\ref{F-cosmic}d (second harmonic, A2). The percentage in the
figure shows the excess of the cosmic ray intensity over the
opposite direction (100\% correspond to a two-fold excess). The
second harmonic of the pitch-angle distribution of 4.1~GeV protons
indicating their trapping was absent just before 20 November,
while the first harmonic was well pronounced, unlike the end of
October, when both harmonics were distinct.

\inlinecite{Richardson2000} showed that significant increases of the
second harmonic of the cosmic ray anisotropy corresponding to
bidirectional particle flows are typical of MCs of large ICMEs. An
example is shown by the ICMEs of 29 and 30 October in
Figure~\ref{F-cosmic}. In addition to the incompatibly moderate FD
with respect to very large Dst, the absence of any increase in the
second harmonic on 20 November clearly indicates that this ICME was
atypical.


\subsection{Heliospheric 3D Reconstructions from SMEI observations}

While the CME of interest is not detectable in SOHO/LASCO images,
now we consider 3D reconstructions of heliospheric disturbances made
from white-light Thomson scattering observations with SMEI. Three
SMEI cameras allow to achieve a combined $\approx 160^{\circ}$ wide
field of view at a sufficiently high spatial resolution. The
tomographic reconstructions have been made by the Center for
Astrophysics and Space Sciences in University of California, San
Diego (CASS/UCSD).

Figure~\ref{F-smei} presents 3D reconstructions from SMEI data of
the heliospheric response for two ICMEs ejected on 28 October
(upper row) and 18 November 2003, which we want to compare. The
images show heliospheric plasma density distributions as viewed
from 3\,AU $30^{\circ}$ above the ecliptic plane and $\sim
45^{\circ}$ west of the Sun--Earth line. The location of the Earth
is indicated by a blue circle with the Earth's orbit viewed in
perspective drawn as an ellipse. The Sun is indicated by a red
dot. An $r^{-2}$ density gradient is removed.

  \begin{figure}    %%%%%%%%%%%%%%%%%% FIGURE 4
%
   \centerline{\includegraphics[width=0.995\textwidth,clip=]{smei_29_oct.eps}}
%
   \centerline{\includegraphics[width=0.995\textwidth,clip=]{smei_20_nov.eps}}
%
   \centerline{\includegraphics[width=0.995\textwidth,clip=]{smei_ecliptic.eps}}
%
   \centerline{\includegraphics[width=0.995\textwidth,clip=]{smei_meridional.eps}}
%
\caption{SMEI 3D reconstructions made by the CASS/UCSD team.
a\,--\,d)~Large croissant\-shaped ICME observed on 29\,--\,30
October suggesting a flux rope connected to the Sun (from Jackson
\textit{et al.}, 2006). e\,--\,h)~Ejecta observed on 19\,--\,21
November: ICME1, ICME2, ICME3, and a probable compact source of
the geomagnetic storm (SGS). i\,--\,l)~ecliptic and
m\,--\,p)~meridional cuts corresponding to the remote views
(e)\,--\,(h). `IR' is a probable intrusion region of CME2 into
CME1. The scale bars on the left quantify the densities in the
corresponding rows.
        }
   \label{F-smei}
   \end{figure}

Figure~\ref{F-smei}a\,--\,d adopted from \inlinecite{Jackson2006}
shows four successive times of the heliospheric response to the 28
October CME. The images reveal a large croissant-shaped ICME
expanding from the Sun and suggest connection of the flux rope to
the Sun. The overall picture shows a presumable typical scenario: a
large expanding flux rope reached the Earth on 29 October and caused
(with its southern $B_z$) a severe geomagnetic storm.

The SMEI 3D reconstructions for the 18\,--\,20 November event in
Figure~\ref{F-smei}e\,--\,h present a very different picture,
which is more complex (see also the movie
\url{SMEI_19-20_11_2003.mpg} accompanying the electronic version
of the paper). To make it clearer, Figure~\ref{F-smei}i\,--\,l
also shows the corresponding ecliptic cuts, and
Figure~\ref{F-smei}m\,--\,p shows the meridional cuts. Comparison
of the heliospheric disturbances within a sector of $\sim
120^{\circ}$ embracing the Earth, on the one hand, with the CMEs
observed by LASCO on 18 November by taking account of their
directions and speeds (see Paper~II), on the other hand, allows
one to presumably identify visible ICMEs with the southeast CME1
and southwest CME2 addressed in Paper~II. They are labeled ICME1
and ICME2. An extended density enhancement labeled ICME3 in
Figure~\ref{F-smei}e appears to correspond to the fastest far-east
CME3.

A far-west Y-like feature resembles in shape the darkening
observed with CORONAS-F/SPIRIT at 304~\AA\ (see Paper~I). However,
the speed of the 304~\AA\ darkening was only $\lsim
100$~km~s$^{-1}$ that rules out their association.

A large inhomogeneous density enhancement IR south of the ecliptic
visible in meridional cuts (Figure~\ref{F-smei}m\,--\,p) as a
multitude of small blobs appears to correspond to the region where
CME2 intruded into CME1 (see Paper~II). The intrusion region
appears to have missed the Earth being south of it.

A feature of our major interest is a rather compact blob exactly
impacting the Earth. This is a moderate density enhancement
presumedly associated with a source of the geomagnetic storm
(SGS). The pass of the blob across the Earth temporally
corresponds to the ACE measurements (Figure~\ref{F-ace}c). The
maximum density in the lower-resolution SMEI two-dimensional cuts
passed through the Earth at about 00 UT on 21 November
(\textit{i.e.}, between Figures \ref{F-smei}k and \ref{F-smei}l)
that reasonably corresponds to the weighted center of the
expansion-corrected higher-resolution ACE record in
Figure~\ref{F-ace_cor_spheromak}b (before the density minimum at
the end of the ICME core, \textit{cf.} Figure \ref{F-ace}c). The
SGS dimensions correspond to expectations: the dotted lines in
Figure~\ref{F-smei}i\,--\,l delimit a sector of $14^{\circ}$,
where the bulk of the ICME mass was concentrated. The images do
not leave any doubt that just this blob was associated with the MC
responsible for the geomagnetic disturbance.

The density in the blob was moderate, peaking at 22~cm$^{-3}$
according to the SMEI tomography that it close to the ACE
measurements. The blob was surrounded by a larger enhanced-density
cloud suggesting a possible influence from the southwestern ICME2
and southeastern ICME1 as well as the southern intrusion region.
As all the three representations of the SMEI reconstructions show,
the shape of the blob does not suggest either a larger isolated
torus nearly perpendicular to the ecliptic plane or a croissant
connected to the Sun. The spheromak configuration appears to be
most appropriate. Thus, the SMEI data put the last missing point
in hunting out the mysterious source of the 20 November
superstorm.


\section{Discussion}
 \label{S-discussion}

All the observational facts and indications considered in
Section~\ref{S-icme} lead to a conclusion that the 20 November MC
was a spheromak of a small size disconnected from the Sun. These
particularities of the 20 November ICME must be reflected in its
propagation between the Sun and Earth. Let us compare the
corresponding properties of the 18 November and 28 October ICMEs.

\subsection{Propagation of the 18 November and 28 October ICMEs}

The average velocity of the 18\,--\,20 November ICME between the
Sun and Earth was about 865~km~s$^{-1}$, while its velocity at the
first contact of the ICME body with ACE was $v_1 \approx
700$~km~s$^{-1}$. This suggests its considerable deceleration.
Assuming that the disconnected 18\,--\,20 November ICME moved
almost in the free-fall regime, it is possible to estimate its
initial velocity $v_0$ from energy conservation, $v_0 =
\sqrt{v_1^2 + 2 G M_\odot\left[1/R_\odot - 1/(1\ \mathrm{AU})
\right]} \approx 930$~km~s$^{-1}$ (the initial velocity could be
still higher, if the aerodynamic drag was efficient). Conspicuous
deceleration of the 20 November ICME supports its disconnection
from the Sun.

The situation was different for the ICME which erupted on 28
October at about 11~UT and whose body reached ACE on 29 October at
about 08~UT according to the ACE/SWICS and ACE/MAG data
(ACE/SWEPAM did not operate because of a large particle event).
The average transit velocity of the ICME was $\approx
1980$~km~s$^{-1}$, while the frontal speed of the ICME body
slightly exceeded 1900~km~s$^{-1}$ (ACE/SWICS, He$^{++}$ bulk
speed). Thus, deceleration of the 28\,--\,29 October ICME was
inconspicuous as if it also moved in the free-fall regime (in this
case, $v_0 \approx 2000$~km~s$^{-1}$) despite its huge size and a
much higher speed relative to the 18\,--\,20 November ICME. With
such a high speed the gravitational deceleration is as small as
5\% of the speed so that it is not possible to reveal it reliably.
However, significant deceleration of the 28\,--\,29 October ICME
due to strong aerodynamic drag could be expected. This seemingly
inconsistency can be accounted for by a toroidal propelling force
of the 28\,--\,30 October flux rope connected to the Sun. The
toroidal propelling force dramatically decreased in expansion of
the ICME, but its influence probably was able to ensure the
observed velocity of the ICME, while the actual $v_0$ was probably
higher.

Some properties of the 20 November MC were atypical of magnetic
clouds. The inhomogeneous temperature distribution in the MC
(Figure~\ref{F-ace}d) provides a hint that the MC was possibly
formed from different-temperature structures, as we have concluded
in Paper~III.

The inclination of the 20 November MC axis to the ecliptic
estimated by different authors ranged within $\theta =
-(49-87)^{\circ}$ [see \inlinecite{Moestl2008}], which is
reasonably close to the orientation of the dipole at the eruption
site, $\alpha = -80^{\circ}$, evaluated in Paper~III. Thus, the
orientations of the dipole on the Sun, from which the spheromak
was formed, and the MC near the Earth were close to each other,
and no significant rotation of the ejecta was required (which was
among the problems discussed by \opencite{Moestl2008}).

The magnetic flux conservation along with the almost exactly
southwards orientation of the magnetic axis determined the extreme
geomagnetic effect of the atypically slowly expanding MC in the
ICME. The causes of the unusually slow expansion of the ICME
deserve further study. We assume they might be due to the
following reasons.
\begin{itemize}
 \item
The major condition for the slow own expansion of the ICME was its
disconnection from the Sun. Otherwise, at least, two of ICME
dimensions must be $\geq 1$~AU near the Earth.
 \item
The maximum magnetic field strength in a spheromak is $\approx
20\%$ higher than in a cylinder or thin torus under the same outer
pressure at their boundaries.
 \item
 The own ICME expansion could be restrained by the enhanced-density
environment, almost fourfold with respect to nominal conditions.
This dense environment could be due to combined effects of the
tail of the preceding CMEs, the lateral pressures from the ICME2
and ICME1 (including the intrusion region) and, possibly, from the
flank of the shock ahead of ICME3.
 \item
The orientation of the magnetic axis of the spheromak nearly
perpendicular to the direction of its motion determined the drag
pressure at its surface to preserve the speromak configuration and
to prevent its transformation into a toroid expected for a freely
expanding spheromak \cite{Vandas1997}.
\end{itemize}
The combined effect of the last two factors disfavored a free
expansion of the ICME.


\subsection{Why the 18\,--\,20 November 2003 Event Escaped Understanding?}

The analysis presented in our Papers I\,--\,IV appears to
reconcile all the challenges of the 18\,--\,20 November 2003
event. Moreover, now it seems to be strange that some important
aspects of the event were not revealed previously. For example,
there were several indications of the small size of the MC:
incomparable Dst value and the depth of the Forbush decrease; the
extremely strong magnetic field \textit{vs.} suggestions of an
ordinary magnetic flux (\textit{cf.} \opencite{Qiu2007}); the
small reconstructed cross section of the MC \cite{Yurchyshyn2005,
Moestl2008, Lui2011}. Note that the reduced MC size also
corresponds to the initial idea of \inlinecite{Yermolaev2005} and
\inlinecite{Gopal2005c} about compression of the MC from other
CMEs.

The spheromak configuration could be understood if the magnetic
field distribution were considered entirely, without ignoring the
positive $B_z$ portions in the leading and trailing portions of
the ICME. The orientation of the spheromak nearly perpendicular to
the ecliptic significantly favored its identification from the
magnetic field records, while the spheromak configurations of MCs
have been extensively considered for a long time (\textit{e.g.},
\opencite{Ivanov1985}; \opencite{Farrugia1995};
\opencite{Vandas1997}; \opencite{Shiota2010}; \opencite{Zhou2012};
and many others). One of lessons of the 20 November MC is that an
idealized consideration of an MC as a smooth `magnetic reservoir'
of low-proton-temperature plasma is not always justified.

Comparison of the 3D reconstructions from SMEI white-light
observations in Figure~\ref{F-smei}f,\,g with those made from Ooty
observations of interplanetary scintillations (IPS) presented by
\inlinecite{KumarManoUddin2011} in their Figure~16 leaves an
impression that important ICMEs could be also recognized in those
images, although they look not as clear as the SMEI
reconstructions. The IPS Ooty images also show suggestions of a
compact blob hitting the Earth, a tail of the southwestern ICME2
and, possibly, the southeastern ICME1 as well as the intrusion
region IR in the velocity images. The conclusion of the authors
were possibly different from the idea about the two merged CMEs,
if the authors paid more attention to the indications of a small
size of the MC (3D reconstructions for a longer time interval
would be probably also useful).

\inlinecite{Moestl2008} suspected the mismatch between the
handedness of the MC and the presumed solar source region
AR~10501. \inlinecite{Chandra2010} have convincingly confirmed
this conjecture. This mismatch, along with the conclusion of
\inlinecite{Grechnev2005} that the eruptive filament had not left
the Sun, seems to be sufficient to warn against a simple scenario,
in which the MC is considered as a stretched magnetic rope
initially associated with the pre-eruption filament in AR~10501.
However, this circumstance was not noticed. Instead,
\inlinecite{Chandra2010} proposed a right-handed eruption from a
small part of AR~10501, although the CME onset times estimated by
\inlinecite{Gopal2005c} did not support this conjecture. The
cautious suggestion of \inlinecite{Chandra2010}, \textit{`Should
this injection} [of the positive helicity flux] \textit{occur over
six days at the same rate an accumulated helicity of the order of
$10^{26}$ Wb$^2$ will be injected, enough to explain the helicity
carried by the positive MC'}, was exaggerated up to an established
fact. It was not noticed that one of the severest storms in
history was attributed to a partial eruption from a minor region.

This is also related to the study by \inlinecite{Marubashi2012},
who presented an undoubtedly valuable method aimed at a general
understanding how the encounter of an MC with the Earth occurs.
Their consideration of the whole sequence of events starting from
the solar eruption on 18 November was based, in particular, on the
assumptions of \textit{i})~the correspondence between the MC and
the eruption region in AR~10501 in handedness and orientation of
the magnetic field, \textit{ii})~the constancy of the direction of
the axial magnetic field in the MC, and \textit{iii})~the
association of the MC with CME2 or, less probable, CME1. None of
these assumptions was confirmed. Moreover, because the authors
ignored the positive-$B_z$ regions in the MC (like all other
researchers), their consideration of its magnetic configuration
could not be perfect.

The solar eruptive event on 18 November was extremely complex and
unusual, so that it was very difficult to reveal its features,
which were important for understanding the actual solar source of
the geomagnetic superstorm. (Even being aware of the spheromak
configuration of the MC, it was difficult to understand how such
an exotic object could form on the Sun.) One more lesson of the 18
November solar event is that simplified considerations of
observations can be unsuccessful. The analysis, which allowed us
to approach a plausible consistent picture of the event and to
reconcile its various aspects, has required the four papers to
present the results. These results agree with a number of those
obtained in preceding studies; otherwise, incorrectness of
previous conclusions has been revealed. These circumstances
emphasize the importance of the attention to various observational
facts and even indirect indications, especially if an event or
phenomenon in question is challenging.

\subsection{Expansion Factor}

\textbf{The fact that the geomagnetic superstorm on 20 November
2003 was produced by the ICME with a total magnetic field up to
$|{\bf B}|_{\max} \approx 56$~nT and a southern $B_z$ up to
$-45$~nT does not contradict well-known patterns (\textit{e.g.},
\opencite{Burton1975}; \opencite{WuLepping2005}). Other Solar
Cycle 23 geomagnetic superstorms mentioned in
Section~\ref{S-introduction} were also caused by the ICMEs with
magnetic field strengths of $|{\bf B}|_{\max} > 50$~nT. The 20
November 2003 ICME had even a considerably lower speed ($\approx
700$~km~s$^{-1}$) than the other ICMEs responsible for the
superstorms (up to $ 1900$~km~s$^{-1}$). Therefore, the key to the
extremeness of the 18--20 November event was primarily related to
the retention of the strongest magnetic field up to the Earth
orbit.}

\textbf{Thus, one} more important outcome of our analysis is a
significant role of the expansion factor for a geomagnetic effect,
along with the strength and orientation of the magnetic field in a
MC as well as its speed (as follows from the results of
\opencite{Chertok2013}, the magnetic field and speed of a MC are
largely determined by the magnetic flux in the eruption region;
see also \opencite{Qiu2007}). The magnetic flux conservation leads
to an estimate of the total magnetic field in a MC of
$|B_{\mathrm{MC}}| \sim B_0 / (L_{\mathrm{MC}}/L_0)^2$ where $L$
is a size and the `0' indices are related to a solar source
region. While the sign and value of the $B_z$ component can reduce
the geomagnetic effect relative to an utmost possible situation of
$B_z \approx -|B|$, an atypically small expansion factor can
considerably strengthen the geomagnetic impact. The expansion
factor can be reduced due to either larger $L_0$ (typical of
quiescent filaments) or smaller $L_{\mathrm{MC}}$, which most
likely was the case on 20 November 2003. The whole range of
variations of the squared expansion factors
$(L_{\mathrm{MC}}/L_0)^2$ can probably exceed one order of
magnitudes.

We considered a large intensity of the geomagnetic storm along
with a moderate Forbush decrease as an indication of a small size
of the MC that turned out to be justified in the 20 November 2003
event. A similar anomaly was also the case in the major
geomagnetic storms of 31 March 2001 (Dst $= -387$~nT, FD of 4.1\%)
and of 8 November 2004 (Dst $= -374$~nT, FD of 5.2\%). The latter
storm was followed by another one on 10 November 2004 (Dst $=
-263$~nT, FD of 8.3\%), for which the Dst \textit{vs.} FD anomaly
was not as challenging. It is possible to check the conjecture
about the small size of the ICME for the November 2004 events by
looking at SMEI reconstructions (SMEI observed during
2003\,--\,2011) available at
\url{http://smei.ucsd.edu/smeidata.html} and
\url{http://smei.ucsd.edu/test/index.php?type=smei3drecons}.
Indeed, on 8\,--\,10 November 2004 they show two earthward ICMEs
of a moderate size following each other and do not suggest their
connection to the Sun.

The implication of the expansion factor in the geomagnetic
importance of a solar eruption can probably be responsible for an
additional significant scatter in loose correlations between
parameters of solar eruptions and space weather disturbances (see,
\textit{e.g.}, \opencite{CliverSvalgaard2004};
\opencite{Yurchyshyn2005}; \opencite{Chertok2013}). The expansion
factor, which can be especially reduced for disconnected MCs,
might be probably implicated in such abnormal events as the
13\,--\,14 March 1989 superstorm (Dst $= -589$~nT) and that one
after the Carrington event on 1 September 1859
(\opencite{Carrington1859}; \opencite{Tsurutani2003}; estimated
Dst on the order of $-850$~nT according to
\opencite{SiscoeCrookerClauer2006}). Previous studies of such
events (\textit{e.g.}, \opencite{Tsurutani2003};
\opencite{CliverSvalgaard2004}) did not consider such a
possibility, while it seems to be qualitatively clear what could
occur if an event similar to the 18 November 2003 one involved an
eruption in much stronger magnetic fields like the 28 October 2003
event. Such a possibility should also be considered.

\subsection{Overall Scenario of the Event}

Although the whole event was extremely complicated, a key to its
overall scenario seems to be comprehended now. The eruption of the
left-handed main filament from AR~10501 was followed by a
collision with a topological discontinuity in a coronal null point
(whose projection was close to the solar disk center) on its way
that resulted in \textit{i})~disintegration of the filament, which
transformed into an inverse-Y-like cloud flying along the solar
surface and probably eventually landed on the Sun, \textit{ii})~a
forced eruption of CME2, and \textit{iii})~reconnection of the
filament's portion with a static closed coronal structure that led
to formation of a right-handed isolated couple of grappled tori
slowly expanding in its motion away from the Sun exactly
earthward. The couple of tori then evolved into a spheromak, whose
expansion was probably restrained by an enhanced-density
environment due to combined effects of neighbor CMEs. The
earthward direction of this ejecta along with its weak expansion
and a small mass prevented its detection with LASCO. Due to the
unusually slow expansion, the disconnected spheromak preserved
very strong magnetic field. In addition, this strong field was
pointed almost exactly south. As a result, its interaction with
the Earth's magnetosphere caused the surprisingly strong
geomagnetic storm on 20 November.

The source region of a compact ICME hitting the Earth obviously
must be close to the solar disk center. This was really the case.
The toroidal magnetic component of the MC was formed from the
axial magnetic field of the eruptive filament. The toroidal
magnetic flux of a perfect spheromak is about 3.5 larger than its
poloidal flux. The poloidal flux of the spheromak was $\approx 5.5
\times 10^{20}$~Mx according to \inlinecite{Moestl2008}, and their
estimate of the complementary magnetic flux of $(11-44) \times
10^{20}$~Mx is surprisingly consistent with the expectation for a
spheromak, although it was obtained for a flux rope geometry. The
large negative $B_z$ in the MC was due to its poloidal magnetic
field formed from the formerly static coronal structure, while the
inherited magnetic field of the filament was mainly responsible
for the $B_y$ component, which most likely was not crucial for the
extreme geomagnetic effect (although $B_y$ is implicated in the
Akasofu's $\epsilon$ parameter).


\subsection{Is It Possible to Forecast Such Superstorms?}

The outlined scenario along with complications of the solar event
considered in Papers I\,--\,III leave a pessimistic impression of
an erratic combination of accidental circumstances that is
impossible to predict. However, there are some promising
circumstances.
 \begin{itemize}
 \item
As the magnetic field extrapolation in Paper~III shows, the
pre-eruption filament was pointed exactly to the coronal null
point. Thus, the topological catastrophe was inevitable and
therefore predictable in principle.
 \item
An outer manifestation of the topological catastrophe was an
anomalous eruption. Such eruptions are manifest in the He{\sc ii}
304~\AA\ line (Paper~I; \opencite{Grechnev2011_AE}) and can be
indicators of potentially dangerous processes on the Sun.
 \item
The dangerous compact earthward CME was not detected by LASCO but
could be detected from a vantage point far from the Sun-Earth
line. Such a compact CME/ICME can be probably registered with
STEREO imagers.
 \item
The 3D reconstructions from SMEI data were very helpful in
recognizing the compact earthwards ICME. The SMEI observations
have been terminated in 2011, while the state-of-art would not
allow such reconstructions to be made in the near-the-real-time
regime. The fruitful employment of the SMEI data confirms that the
method of tomographic reconstructions of heliospheric disturbances
from white-light observations with a wide field of view deserves
further elaboration and implementation in future missions.
 \end{itemize}
The major challenge of the 18\,--\,20 November event was its
incomprehensibly large geomagnetic effect. Once a key to the
enigma has been found, investigations into its features could
hopefully make clearer its different manifestations.


\subsection{Concluding Remarks}
 \label{S-conclusion}

\textbf{Several researchers contributed to the study of the 18
November 2003 event and the 20 November magnetic cloud. These
efforts certainly have advanced, step by step, our understanding
of solar phenomena and their space weather outcome.}

Various observations reveal that the magnetic cloud responsible
for the 20 November 2003 superstorm was, most likely, a compact
spheromak disconnected from the Sun. We do not think that our
analysis puts a final point in the study of the 18\,--\,20
November 2003 event. The analysis has revealed several
particularities of different aspects of the event that were not
noticed previously. Our main purposes were to understand the
overall scenario of the event and to answer the major question,
why this seemingly ordinary eruptive event gave rise to the MC
with a very large southern magnetic component near Earth, $B_z
\approx -45$ nT, and eventually caused the strongest geomagnetic
storm. In this way our analysis has revealed, for example, an
anomalous eruption with a catastrophe of the filament in a coronal
null point; the transformation of the handedness of a pre-eruption
structure; the necessity to take account of the expansion factor
of an ICME that can be significantly different; possible
considerable differences of a real magnetic cloud from an
idealized concept, and others. These issues appear to deserve
further investigation, and we hope that our results would
highlight some ways for future studies to address them.


\begin{acks}

We thank V.~Sdobnov for useful discussions and the processed data,
which he kindly made available to us. We thank the ACE/MAG and
SWEPAM teams and the ACE Science Center for providing the solar
wind data. We are grateful to anonymous reviewers for useful
remarks. We thank the Center for Astrophysics and Space Sciences
in USD for heliospheric 3D reconstruction made from the SMEI,
which is a joint project of the University of California at San
Diego, Boston College, the University of Birmingham (UK), and the
Air Force Research Laboratory.

This study was supported by the Russian Foundation of Basic
Research under grants 11-02-00757, 11-02-01079, 12-02-00008,
12-02-92692, and 12-02-00037, the Program of basic research of the
RAS Presidium No.~22, and the Russian Ministry of Education and
Science under State Contracts 16.518.11.7065 and 02.740.11.0576.

\end{acks}


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\end{article}

\end{document}
