Download Studying extended magnetic structures of ICMEs

Studying extended magnetic
structures of ICMEs
Using in situ detections of interplanetary shock fronts
Saida Milena Díaz Castillo
Departamento de Física
Universidad Nacional de Colombia
Advisor: Benjamín Calvo Mozo
Observatorio Astronómico Nacional
This dissertation is submitted for the degree of
Bachelor of Physics
December 2014
Para mi amada familia por toda su dedicación y empeño en formarme.....
Para mi amado quien me ha acompañado en la busqueda de mi sueño......
Acknowledgements
Cada día el Sol ilumina un mundo nuevo
Paulo Coelho
Apart from the efforts of myself, the success of any project depends largely on the
encouragement and guidelines of many others. In my paricular case, I would like to
express appreciation and thanks to my supervisor Professor Benjamín Calvo Mozo,
who have been a tremendous mentor for me. I would like to thank you for encouraging
my research and for allowing me to grow as a research scientist and as well as a integral
person. I would like to thank you very much for your support and understanding over
these past three years. I would like to thank Dr. Juan Carlos Martinez of University
of California at Berkeley and Professor Maxim Lyutikov of Purdue University as well
for his assistance and guidance in the develop of the thesis goals. I would like to
thank to Science Faculty of the Universidad Nacional de Colombia for give me the
opportunity to participate in the first academic exchange with Purdue University in
order to developing one of the objectives of this work. I would also like to thank all
of my friends and colleagues of the GoSA research group who supported me in my
training as a physicist.
A special thanks to my family. Words cannot express how grateful I am to my
mother, father and brothers for all of the sacrifices that you’ve made on my behalf.
Your prayer for me was what sustained me thus far. At the end I would like express my
special appreciation to my dear Wilmar Fajardo who have been incented me to strive
towards my goals and was always my support in the moments when I most needed. I
will be grateful forever for your love.
Abstract
The eruption of solar plasma into interplanetary medium known as coronal mass
ejection not only releases material to the environment; the ejection is accompanied by
a release of part of the solar magnetic field, magnetic structure known as flux rope.
These solar disturbances that propagate and expand in the interplanetary medium are
known as interplanetary coronal mass ejections (ICME), phenomena that is still one of
the basic problems in the areas of space physics, solar physics and geophysics.
In this paper, we present a partial study of the frontal and magnetic internal
structure of interplanetary coronal mass ejections using in-situ measurements provided
by the specialized missions: Wind and STEREO. In this frontal boundary, which
can extend to several solar radii, we can observe a particular heliospheric phenomena:
interplanetary shock fronts induced by a ICME transient. The study of these shock
fronts in different regions over the leading edge may characterize the physical properties
of the front structure of the ICME. With the aim of studying the magnetic cloud
structure associated to the ICME, we evaluate a model of magnetic structure derived
from force-free plasma configurations. Such magnetic confinement configurations are
usually used in astrophysical plasmas because they are considered to be spontaneous
and self-sustaining structures which may be created in nature.
In the observational study, we performed a review of all interplanetary shocks
detected by these two missions in two time periods: 2007-2010 and the first five months
of 2014, with the aim of finding ICME-driver shock detected in three or two different
regions. In that survey we find just one clear event that fulfill the conditions: the
ICME of 12-14 April, 2014. We report some shock parameters, the profiles of the
main physical features of the proton plasma, the radio emission and the electron beam
spectra for both spacecraft of STEREO mission, which detected the event. In the
theoretical study, we developed a code that models artificial magnetic field profiles
produced by a magnetic confinement structure with spherical symmetry: Spheromak.
We evaluate two boundary conditions for the system: non force-free and force-free.
viii
Also, we evaluate its static and self-similar expansion behavior. The magnetic cloud
detected at the event was compared to force-free model profile: magnetic field strength
and its three components in the RTN coordinate system of the spacecraft.
We determine that the region downstream of the detected interplanetary shock
corresponds to a turbulent and intense magnetic field region, where electrons flows
generate a radio emission that saturate the instrument . We conclude that the two
detection, over the two regions of the shock front, probably are associated to different
dynamical processes due to the particular interaction that take place there. With the
data obtain was imposible determine a foreshock zone on the upstream region of each
shock. In the case of the theoretical model, the correlation between the model and
STEREO-B data ensures a toroidal topology structure for the real magnetic cloud
without ensuring it spherical geometry. This type of correlation makes it impossible for
STEREO-A detects the same magnetic cloud due to the insufficient expansion, what
makes us think that the system may have a tubular geometry, in order to ensure the
fact that both spacecraft are detecting the same ICME transient.
Table of contents
List of figures
xi
List of tables
xiii
1 Intoduction
1
2 External solar structure
5
2.1
2.2
Solar corona . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
2.1.1
Magnetic field, density and temperature . . . . . . . . . . . . .
7
Solar wind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
3 Coronal Mass Ejection (CME)
15
3.1
Drivers and progenitors . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
3.2
Propagation: Interplanetary coronal mass ejection (ICME) . . . . . . .
20
4 Interplanetary shocks
23
4.1
Interplanetary Transients: SIR and ICME . . . . . . . . . . . . . . . .
24
4.2
Interplanetary type II radio burst . . . . . . . . . . . . . . . . . . . . .
26
5 Spacecraft detection
29
5.1
Wind Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
5.2
STEREO Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
5.3
Detected events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
33
6 ICME of April 11, 2014
39
6.1
Associated precursor . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
6.2
Interplanety shocks in-situ detection . . . . . . . . . . . . . . . . . . .
42
6.2.1
Radio emission detection . . . . . . . . . . . . . . . . . . . . . .
45
6.2.2
Magnetic cloud features . . . . . . . . . . . . . . . . . . . . . .
48
x
7 Theorical modeling
7.1 Magnetic models: Spheromaks Configurations .
7.1.1 Magnetic Cavity: Static case . . . . . . .
7.1.2 Magnetic Cavity: Self-similar expansion
7.1.3 Force-Free Spheromak . . . . . . . . . .
7.2 Physical System . . . . . . . . . . . . . . . . . .
7.2.1 Trajectory evaluation . . . . . . . . . . .
7.2.2 Magnetic field magnitude profiles . . . .
7.3 Observational Signature . . . . . . . . . . . . .
Table of contents
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8 Disscusion
69
References
73
List of figures
1.1
Sun structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
2.1
2.2
2.3
Solar corona features . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Plasma —-paramenter distribution . . . . . . . . . . . . . . . . . . . . .
Mission Ulysses results . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
9
11
3.1
Coronal mass ejection: STEREO view . . . . . . . . . . . . . . . . . .
16
4.1
4.2
Stream interaction regions . . . . . . . . . . . . . . . . . . . . . . . . .
Interplanetary shock radio emission from Pulupa 2008 . . . . . . . . . .
25
28
5.1
STEREO spacecraft . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
6.1
6.2
6.3
EUVI STEREO-A/B Images . . . . . . . . . . . . . . . . . . . . . . . .
Image sequence of SECCHI/COR2 in STEREO-A/B . . . . . . . . . .
STEREO/PLASTIC and STEREO/IMPACT in-situ Level 2 data:
Shocks events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Picture of the ENLIL-lowers + GONGb-WSADU + Cone-SWRC model
STEREO/WAVES dynamic spectra . . . . . . . . . . . . . . . . . . . .
STEREO/SWEA Level 1 data . . . . . . . . . . . . . . . . . . . . . . .
STEREO/PLASTIC and STEREO/IMPACT in-situ Level 2 data:
Magnetic cloud event . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
41
6.4
6.5
6.6
6.7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
Physical system of the model . . . . . . . . . . . .
Magnetic cavity: First static case . . . . . . . . . .
Magnetic cavity: Second static case . . . . . . . . .
Magnetic cavity: First self-similar expansion case .
Magnetic cavity: Second self-similar expansion case
Magnetic cavity: Third self-similar expansion case .
Spheromak: Static case . . . . . . . . . . . . . . . .
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xii
List of figures
7.8
7.9
7.10
7.11
7.12
Spheromak: First self-similar expansion case . . . . . . . . . .
Spheromak: Second self-similar expansion case . . . . . . . . .
Spheromak: Second self-similar expansion case . . . . . . . . .
Physical system considered in the simulation . . . . . . . . . .
Simulation results for the STEREO-B detection on 12-15 April
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2014
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List of tables
2.1
Physical variables in the solar corona . . . . . . . . . . . . . . . . . . .
5.1
Interplanetary shock events detected by Wind, STEREO-A (STA)
and STEREO-B (STB) for the 2007-2010 period . . . . . . . . . . . . .
Interplanetary shock events detected by Wind, STEREO-A (STA)
and STEREO-B (STB) for the 2014 period . . . . . . . . . . . . . . . .
5.2
8
35
36
Chapter 1
Intoduction
Our nearest star, the Sun, is considered a kind of ordinary star in our galaxy, brighter
than others but not exceptionally so. It is not a variable or active star, without
any enormous chemical or magnetic peculiarities and which is in its half-life time
currently. Nevertheless, our Sun is truly exceptional in many ways for us, mainly
because it is very close to the Earth, at just the right distance to make life as we know
it possible, and it furnishes us with the closest laboratory for astrophysical plasma
physics, magnetohydrodynamics (MHD), atomic physics, and particle physics [26] [3].
Our Sun, a self-gravitating gas sphere in hydrostatic equilibrium, is classified as a
G2-V spectral type star, with a radius of r§ ¥ 700.000 km, a mass of M§ ¥ 2 ◊ 1030
kg, an age of t§ ¥ 4, 6 ◊ 109 years and a luminosity of L§ ¥ 4 ◊ 1026 W [3], which is
comparable with the changing of four million tonnes of mass into energy every second.
That energy is produced in the central core where nuclear processes takes place, there
the 40% of the material is hydrogen which is almost completely consumed[3]. The
general chemical composition of the Sun consists mainly in 92, 1% of hydrogen atoms,
7, 8% of helium atoms and the other 0, 1% of atoms of heavier elements, in number of
atoms[41].
The study of the solar structure and dynamics has been become a challenge to the
current astrophysicists. The main ideas about, the internal structure is mostly established by theoretical models that are constrained by global physical quantities, by the
measurements of global oscillations or by measurements of neutrino flux (observational
features)[3]. Nowadays, we know that the solar interior consists of three main zones:
a central core, that has a central temperature and pressure of Tc ¥ 1, 5 ◊ 107 K and
Pc ¥ 2.5 ◊ 1011 atm, respectively. Then the radiative zone, which is the solar interior
2
Intoduction
second zone, where the hard X-ray photons, created by the nucleosynthesis process,
transport the energy by radiative diffusion. The outer third zone of the solar interior is
called the convective zone, where energy is transported mostly by convection [41][22].
Unlike the solar interior, the solar external layers have the benefit of direct observation of their characteristics, thanks to the emitted radiation that can travel freely,
after a random walk of ¥ 105 ≠ 106 years inside the Sun[3]. This has not ensured
full understanding of the processes that are produced there, but has provided tools to
discover new phenomenology and the physical processes involved that take place there.
The first outer layer that we found is the photosphere, which is the innermost
layer of the solar atmosphere. It is observed in white light and is considered as the
solar surface, with only about 300 ≠ 500 km thick and with an effective temperature
of 6400 K[41]. In the photosphere are observed granulation patterns, that are the
manifestation of the sub-photospheric convection. Each granule have a bright core
where the photospheric plasma is rising upward and a darker boundary where the
plasma flows down. The effects of photospheric magnetic field, which is generated by
the internal convection motion, as well as the granular dynamic produce solar activity
phenomena as: sunspots and faculaes (See 1.1), which has been study objects for the
understanding of the solar cycle[3][22]. Outside the photosphere there is a paticular
layer: the chromosphere where the temperature increases from 4500 K to about 6000
K in about 500 km, while the particle density decrease[41]. Depending on which
spectral line, wavelength or line position which is used to observe the chromosphere,
the fine-structure that is evidenced change dramatically, due to the sensitivity of the
observations to differents temperatures (altitudes) and velocity ranges. In general,
the chromospheric images are normally taken in UV spectral range, mainly showing
a bright network surrounding supergranulation cells, which coincide with the photospheric large-scale network. Also, there is observed very thin spaghetti-like elongated
fine structure in H– spectroheliograms knowing as fibrils (around the sunspots) or
mottles (on the disk)[3]. Other jet-like structure of plasma can be observed: spicules
which reach the temperature of 10000 K and the maximum height of 10000 km, close
to the transition region on the inner limit of the most external atmosphere structure:
the solar corona (See 1.1).[3]
The observation of solar atmosphere allowed the development of the theory of
radiative transfer in stellar cases, as well as the discovery of the element helium [22][66].
3
Fig. 1.1 Internal and external view of the sun showing the characteristics main zones
and also showing the most eruptive phenomenology in the outer layers. This eruptive phenomena are created by the external dynamics of the magnetic field emerging
from the photospheric region and cover the entire solar system.
4
Intoduction
Besides, due to the internal and external dynamics of the Sun is governed mainly by
the complex magnetic field structure; this one corresponds to the principal magnetohydrodynamic (MHD) laboratory for large magnetic Reynolds numbers, exhibiting
a totally unexpected, energetic and eruptive phenomena [66]. The most dramatic
events associated with solar activity are related to explosions in the atmosphere, which
generate energetic emissions across the entire electromagnetic spectrum: flares and
ejections of matter and magnetic field into space: Coronal Mass ejection CMEs.
Most of the above mentioned phenomena generate disturbances in the whole interplanetary space system, especially in our terrestrial environment that can adversely
affect certain important technologies (satellite and telecommunication systems, power
grid system, oil pipelines system and water supply systems) and threaten the health
and safety of astronauts. Thus, the fundamental goal of solar and space physics
research is to discover, explore, and ultimately to understand the solar activity and
the often complex effects of that activity on the interplanetary environment [58]. Due
to the direct interaction of the interplanetary medium with the solar activity, the
interplanetary environment includes many fundamental phenomena of physical nature
that are important for the understanding the Sun-Earth connection.
One of the most crucial phenomena in the study of the Sun-Earth connection, which
take place in space, is the Interplanetary coronal mass ejection (ICME). When an
eruption was generated in the Sun driving a solar ejecta, the formed structure which
propagates into the interplanetary medium is known as ICME[32]. That event changes
the dynamics of the solar corona and the interplanetary magnetic field structure. In
this work we provide a observational and theoretical study of the interplanetary coronal
mass ejection (ICME) as a magnetic confinement structure using multi-spacecraft
detection of ICME-driven interplanetary shocks. At the first part of this work, we
give an overview of the main knowledge of the external structure of the Sun and of
the interplanetary medium, developed in the last years in order to understand the
physical system studied. At the second part, we present a observational survey of the
interplanetary shocks that can be generated by ICME, looking for events detected by
two or more spacecraft (STEREO and Wind) over different regions of the shock front.
Finally, we present the evaluation of a MHD magnetic confinement structure model
that can be ralated to the ICME structure (magnetic cloud), making a comparison of
artificial magnetic field strength profiles with the above mentioned observational data.
Chapter 2
External solar structure
In the course of a total solar eclipse when the solar disk is perfectly cover by the moon,
we can observe a pearly white, subtly structured halo extending to distance of several
solar radii beyond the photospheric limit[22]. This extended atmosphere is called the
corona (See 2.1). Due to the extreme radiation that is emitted at the photosphere,
the optical coronal emission produced by Thomson scattering, it is really faint to be
observed with the naked eye. Thanks to the impressive and exact coincidence in the
angular diameters of the Sun and Moon as seen from Earth, we were able to discover
the existence of the solar external structure in a total solar eclipse[4]. Currently, solar
observatories in spacecraft missions give us a broader perspective of external solar
atmosphere, where observations are no longer limited to the optical limit. Nowadays,
the observations are made in soft X-rays, hard X-rays, or radio wavelengths where the
brightest emission comes from the corona, while the photosphere becomes invisible
[22]. In the next sections, we present a review of the basic observational and physical
features of this external solar layer: the solar corona and the phenomenon known as
solar wind.
2.1
Solar corona
Depending on the type of coronal emission observed, result in the initial classification of
the solar corona (See 2.1). The inner part of the corona, the K corona, has a continuous
spectrum formed by the free scattering of the photospheric light by electrons at the
zone[41]. This spectrum is polarized with the electric vector parallel to the limb without
any contributions of absorption lines[22]. Further out, at about two solar radii from
the surface, is the F corona, which has a spectrum showing Fraunhofer absorption lines.
The light of the F corona is the photospheric light diffracted by the much slower moving
6
External solar structure
dust of the interplanetary medium. Unlike the visible coronal continuum, other layer
of the corona: L corona has a discrete spectrum at visible and ultraviolet wavelengths
originated by atomic radiations from hot plasma. Those spectral lines detected in
the visible region are all forbidden transitions between low-lying fine structure states
of heavy and multiply ionized atoms[22]. Much energy is needed to remove so many
electrons from the atoms to form that kind of ionized atoms, which proves the fact that
the entire corona has to be two orders of magnitude hotter than the photosphere. The
physical mechanism of injection of energy to the corona to maintain these temperature
values is still unknown. Currently, it is believed that the energy comes from acoustic
or magnetohydrodynamic shock waves generated at the solar surface by the convection,
or from electric currents induced by changing magnetic fields.
Fig. 2.1 Left: Image of a solar eclipse showing the halo of light. Nowadays the
corona can be studied continuously using a device called the coronagraph. Right:
Intensity of the emission coronal layers in function of height (Stenborg 2012 Solar
Astrophysics school at Bogotá)
Also, the solar corona can be seen in different ways depending on which region
over the Sun we observed. It is customary to subdivide the solar corona into three
zones, which all vary their size during the solar cycle: active regions, quiet Sun regions
and coronal holes. [3] Although covers up only a small potion of the total surface
area, the active regions are zones with strong magnetic field concentrations, being
2.1 Solar corona
7
the areas with the greatest energetic and eruptive activity. These areas coincide
spatially with sunspot areas in the photosphere. The constant magnetic activity, as the
magnetic flux emergence, flux cancellation, magnetic reconfigurations, and magnetic
reconnection processes, trigger a number of dynamic processes such as plasma heating,
flares, and coronal mass ejections, that occur in active regions. The active regions
have a bipolar nature, showing closed magnetic field line structures that are combined
with the chromospheric upflows into coronal loops. The numerous filled loops, which
are hotter and denser than the background corona, produce bright emission in soft
X-rays and extreme ultraviolet wavelengths (EUV)[4]. The remaining areas outside of
active regions are classified as quiet Sun regions and coronal holes. Basically, the main
dynamic processes in the quiet Sun region range from small-scale phenomena such as
network heating events, nanoflares, explosive events, bright points, and soft X-ray jets;
to large-scale structures, such as transequatorial loops or coronal arches.[4] The coronal
holes are regions that appear much darker than the quiet Sun region. Those areas
are dominated by open magnetic field lines, where flushing heated plasma is driven
efficiently from the corona into the solar wind. The coronal holes are empty of plasma
most of the time thanks to this efficient transport mechanism, so when the heated
plasma rises from the chromosphere, the plasma remain trapped until it cools down
and precipitates back to the chromosphere, showing the characteristic low emission. [4]
2.1.1
Magnetic field, density and temperature
Stellar atmospheres are generally characterized in lowest order by gravitational stratification in spherical shells, with a decreasing density as function of the radial distance
from the surface[4]. That simple assumption of pressure equilibrium and homogeneity
is useful to built the average density structure for portions of atmosphere that are
quasi-homogeneous[3][22]. Nevertheless, the solar corona is highly inhomogeneous due
to the magnetic field presence.
The coronal magnetic field is driven by an internal dynamo that modulates the
magnetic field in the surface, which is characterized by a high complexity and non-linear
behavior. That field controls the dynamics and topology of all coronal phenomena.
The coronal loops are arc-shaped structures filled with heated plasma, that follows
the geometry of the magnetic field. The energetic particles can only propagate along
magnetic field lines, thus cross-field diffusion is strongly inhibited[4]. It is also possible
to classify areas in the solar corona depending on the magnetic field configuration:
open-field and closed-field regions. The open-field regions exist permanently in the
8
External solar structure
Table 2.1 Ranges of magnetic field strength, density and temperature in different
zones in the solar atmosphere[4]
|B| [G]
ne [1/cm≠3 ]
T [MK]
Active regions Quiet Sun regions
Coronal holes
3000 ≠ 100
10 ≠ 50
0, 5 ≠ 0, 1
8
8
(2 ≠ 20) ◊ 10 .
(1 ≠ 2) ◊ 10
(0, 5 ≠ 1, 0) ◊ 108
2 ≠ 6, 3
1≠2
61
polar regions or in the coronal holes areas. In those, the solar surface is connected
with the interplanetary field being the source of the fast solar wind ¥ 800 km/s [4]. In
contrast, the close-field regions are characterized by closed structures as the coronal
loops, which can open up at higher altitudes and connect eventually to the heliosphere.
Those areas produce the slow solar wind component at ¥ 400 km/s[4]. Thanks to the
inhomogeneity of the magnetic field, different zones over the surface have different
ranges of magnetic field strength (See 2.1). Although topological structure of the
corona can be used to delineate the 3D coronal magnetic field due to the radiating
coronal plasma, the coronal magnetic field also is reconstructed by extrapolation from
magnetograms at the lower boundary, using a potential or force-free field model. However, the extrapolation through the chromosphere and transition region is poor due to
unknown currents and non-force-free conditions[4].
As previously mentioned, the magnetic field structure produces a highly inhomogeneous density and temperature structure that can not be modeled as a homogeneous
atmosphere. A large amount of dynamical processes warms the chromospheric plasma,
which is driven by the overpressure upward into the corona, forming over dense structures with densities and temperature in excess of the ambient quiet corona[4]. The
optically thin emission from the corona in soft X-rays or in EUV provides evidence of
the above mentioned. In the Table 2.1 there is a compilation of density and temperature
measurements that evidence the inhomogeneous nature of the solar corona. In general,
electron densities and temperature in the solar corona, range from ne ¥ 109 cm≠3
and Te ¥ 104 K in the quiet sun low corona (upper chromosphere) to ne ¥ 106 cm≠3
and Te ¥ 106 K at a height of one solar radius (upper corona)[3]. In the transition
region there is a discontinuity in the physical variables where the coronal density
decreases several orders of magnitude higher than chromospheric values and the coronal temperature increases several orders of magnitude higher than chromospheric values.
2.1 Solar corona
9
The crucial parameter, that quantifies that inhomogeneous nature of the solar
atmosphere is the ratio of the thermal pressure pth to the magnetic pressure pmag , also
called the plasma-— parameter[4].
—=
pth
2›ne kB Te
=
¥ 0, 07›n9 T6 /B12
pmag
B 2 /8fi
(2.1)
where › is the local ionization fraction, ne the electron number density and Te the
electron temperature, kB the Boltzmann constant; B1 = B/10 G the magnetic field
strength, n9 = ne /109 cm≠3, and T6 = T /106 K. For the corona › = 1 because the
coronal plasma is fully ionized. The value of the — parameter is less than unity in the
major part of the solar corona showing its magnetic regime. That case constitutes
a rigorous topological constraint, inasmuch as the thermal pressure is insufficient to
warrant horizontal stratification across the magnetic field (See 2.2)[4]. It is noteworthy
in figure 2.2 that the solar corona is sandwiched between the values — > 1 in the
chromosphere and outer corona. For the case of the outer corona, the magnetic field
strength has decreased enough to maintain a thermodynamic regime.
Fig. 2.2 Plasma — in the solar atmosphere for two assumed field strengths, 100 G
and 2500 G. (Gary 2011)
The values of the plasma-— parameter, in different locations of the solar corona,
strongly depends on the employed magnetic field model, mainly because the magnetic
10
External solar structure
field strength is the least known physical parameter in the corona, unlike the density
and temperature.
2.2
Solar wind
The solar wind corresponds to a constant flow of hot plasma which originates at the
base of the solar corona and propagates in the interplanetary medium. Due to the
increase in temperature of the corona as function of height, pressure drives the solar
wind outflow, accelerating the particles, that later becomes to super-Alfvénic plasma
within 10 ≠ 20 solar radii [53]. The flow momentum is comparable to the magnetic
pressure within a few solar radii, thus this drags the coronal magnetic field out into
the solar system, forming the heliospheric magnetic field (HMF), historically referred
to as the interplanetary magnetic field (IMF), which pervades the entire heliosphere
where the solar magnetic field dominance finally ends [52].
The solar wind composition is different from the composition of the solar surface
and shows variations that are associated with solar activity and solar features [9].
Basically, it is composed of approximately equal numbers of ions and electrons. The ion
component consists predominantly of protons (95%), with a small amount of doubly
ionized helium nuclei (–-particles) and trace amounts of heavier ions[66]. The helium
abundance is highly variable during energetic transient events. In general, the solar
wind velocity ranges between 350 km/s and 750 km/s 90% of the time measured over
the eplitic plane, with negligible absolute error. Its total plasma density lies between
3 and 20 particles per cm≠3 also measured over the eplitic plane[22]. The plasma
temperature can be found from the particle velocity dispersion in the frame of reference
of the plasma bulk motion. The mean values of temperature for proton and electron
components are both in ranges between 1 ◊ 105 and 1, 5 ◊ 105 K, while the –-particles
are four to five times hotter[22].
In addition to the measurements of basic physical variables of the solar wind,
detected by in-ecliptic spacecraft, the parameters profiles exhibit two main patterns:
slow solar wind and fast solar wind[48]. The main speed of slow solar wind ranges
between 250 and 400 km/s and for the fast solar wind ranges between 400 and 800 km/s.
The low-speed wind tends to be cool, dense and structured while the high-speed wind
is hotter, more tenuous and uniform [30] but both patterns have striking similarities
in the density, energy and momentum[57]. Currently, we know that fast wind arises
2.2 Solar wind
11
from the inactive solar regions, especially the large coronal holes surrounding each pole,
where the magnetic field has a constant polarity. The more turbulent slow solar wind
emerges from active near-equatorial regions, often associated with closed magnetic
structures, such as bipolar loop systems and helmet streamers[57].
Fig. 2.3 These radial plots of the solar wind speed combine data from all three of
Ulysses polar orbits of the Sun, each of which take six years to complete. The blue
coloured lines represent the outward interplanetary magnetic field; the red coloured
lines the inward IMF. Sunspot number (bottom panel) shows that the first and
third orbit occurred through the solar cycle declining phase and minimum while
the second orbit spanned solar maximum. From the center out, these images are
from the Solar and Heliospheric Observatory (SOHO) Extreme ultraviolet Imaging
Telescope (Fe XII at 195 Å), the Mauna Loa K-coronameter (700 ≠ 950 nm), and the
SOHO C2 Large Angle Spectrometric Coronagraph (white light). From Southwest
Research Institute
Till the launch of Ulysses in 1990, the scientists discovered the three-dimensional
structure of the solar wind. The spacecraft traveled in a perpendicular orbit to the
ecliptic plane, especially suitable for studying the heliosphere, passing three times
over the solar poles in periods of solar maximum and solar minimum [48]. The results
obtained by Ulysses are best summarised in 2.3, which shows how the speed changes
with latitude and with solar activity[48]. In near solar minimum, the solar wind reflects
a simple structure: the speed is nearly constant at all latitudes except in a narrow
band of ±20o around the equator, where the speed pattern resembles the two-state
12
External solar structure
structure seen by near-ecliptic spacecrafts. Also, the sign of the radial component of
the magnetic field remains constant within each hemisphere (See left panel of 2.3). The
solar wind structure near solar maximum activity is completely different of the above
mentioned. The solar wind structure reflects this complexity, with alternating fast and
slow streams of small scale observed at all latitudes. This complex structure is shared
by the magnetic field, whose polarity alternates, and by other properties (See central
panel of 2.3)[48].
The Ulysses observations bear out the simple picture of the heliospheric magnetic
field near solar activity minimum, that had already been hinted at from remote-sensing
observations, and from data of previous spacecrafts that had gone slightly outside the
ecliptic[48]. This simplest steady-state picture is when the coronal magnetic field is
closest to have a dipolar configuration extended over the heliosphere, typically with
the magnetic dipole axis tilted a few degrees to the solar rotation axis[52]. In that vain,
the solar wind geometry can be understood by considering that completely steady state
idealised structure with an exactly radial outflow of constant speed, independent of
radial and latitudinal position. The footpoints of the magnetic field lines are assumed to
be fixed in the photosphere and, hence, to rotate with the Sun. The magnetic field is assumed to be frozen in to solar wind plasma, without exert no force on it[52]. Under such
conditions, the heliospheric magnetic field becomes twisted into an Archimedean spiral
in the solar equatorial plane known as Parker spiral[53]. In the model, in a spatial region
approximately bounding the solar corona, the magnetic field dominates the plasma flow
and undergoes significant non-radial (or super-radial) expansion with height. There,
the quadrupole contribution of the solar magnetic field are sufficient to induce more
complex patterns in the region. In the external limit known as source surface, typically
in a few solar radii, the pressure-driven expansion of the solar wind dominates, and
both the field and flow become purely radial. In the heliosphere, rotation of the HMF
footpoints within a radial solar wind flow generates an azimuthal component of the field,
leading to a spiral geometry[52]. Even when the solar activity rises, the solar magnetic
field becomes more complicated and the large-scale solar magnetic field becomes rather
disorganised, the Parker model has been shown that describe the real HMF to a good
approximation over a wide range of heliocentric distance, in particular around 1 AU[52].
This type of magnetic structure present in the interplanetary medium together
with the dynamics of the solar wind plasma, generated a lot of physical phenomena
discovered in recent decades, which are key to understanding and forecasting space
2.2 Solar wind
13
weather. In the following chapters we will study deeply some specific phenomena that
occur in the interplanetary medium that are modulated by the interaction of the solar
wind, the HMD, and eruptive solar activity.
Chapter 3
Coronal Mass Ejection (CME)
Every star in the main sequence is losing mass, caused by dynamic phenomena in
its atmosphere that accelerate plasma or particles beyond the escape speed. In the
Sun, we observe two forms of mass loss: the already mentioned steady solar wind
outflow and the sporadic ejection of large plasma structures: Coronal mass ejections
(CMEs)[4]. A CME is a large eruption of plasma and magnetic field from the Sun
that contain a large mass and may achieve a speed of several thousand kilometres
per second [46][35]. The phenomenon of a CME occurs with an average frequency
of once a week at solar minimum, and three times per day at solar maximum, carrying typical mass of around 1011 ≠ 1013 kg and typical speed between 400 and 1000
km/s[32]. The transverse size of a normal CMEs can cover from a fraction up to
more than a solar radius spanning several tens of degrees of heliographic latitude (and
probably longitude)[32]. The estimated total energy for these events (kinetic plus
potential energy) ranges between 1022 J to some 1025 J which is similar to solar flares[64].
CMEs were first observed in the dynamic structure of the corona, initially when
eclipses occurs and later with coronagraphs (ground-based and space-borne), which is
a white-light sensing instrument provisioned with an artificial ellipse that blocks out
the photospheric light, detecting the relatively faint surrounding corona light (See 3.1).
According to the original definition, the CMEs are observable change in the coronal
structure that involve the appearance and outward motion of new, discrete, bright,
white-light feature in the coronagraph field of view, occurring on a time scale of a few
minutes to several hours[36]. As mentioned in the previous chapter, the white-light
emission of the corona comes from the photospheric radiation Thomson-scattered by
free electrons in the corona. Any enhanced brightness means that the coronal density
somewhere along the line of sight is increased. The Thomson-scattered radiation also
16
Coronal Mass Ejection (CME)
depends on the photospheric radiation incident and the angle between the incidence
and the line of sight, which makes CMEs favorably observed near the plane of the
sky[14].
Fig. 3.1 A composite image from the SECCHI instruments onboard the STEREO-A
and STEREO-B spacecrafts of the coronal mass ejection (CME) from December
of 2008. In the COR2 image, we can observe the CME three-part structure.(credit:
doi:10.1038/ncomms1077)
In white-light observations, CMEs present many different shapes and much of
the variety is believed simply due to the projection effects. However, fundamental
differences can be found between narrow CMEs and the others (sometimes called
normal CMEs). The narrow CMEs show jet-like motions probably along open magnetic
field, whereas normal CMEs are characterized by a closed frontal loop. The typical
morphology for normal CMEs is the so-called three-part structure[14]: a bright frontal
loop, which is immediately followed by a dark cavity with an embedded bright core
(See 3.1), although observations indicate that only ≥ 30% of CME events possess
all the three parts[65]. There is another kind of white-light observational structure
where CMEs show an outflow and expanding brightness around the Sun like a halo,
these are called halo CMEs. This does not correspond to a type of morphology, because it can be a normal one projected onto the line of sight, showing its particular
structure. Further observations indicate that CMEs can also be observed in other
wavelengths, such as soft X-rays, extreme ultra-violet, radio, and so on (For more details
3.1 Drivers and progenitors
17
[33]); in order to determine the true 3D configuration, which is still unclear due to the
difficulties of the optically thin coronal plasma and the highly dynamic nature of CMEs.
Some authors claim that there are two (or more) kinds of coronal mass ejections,
based on the CME velocity and acceleration profiles observed by SoHO spacecraft over
the distance range of 2 ≠ 30R§ [49]. The Gradual CMEs have balloon-like shapes that
in the initial stadium accelerate slowly and over large distances change their speeds
in the ranges from 300 to 600 km/s. The impulsive CMEs are often associated with
flares, with speeds in excess in ranges from 750 to 1000 km/s in the initial stadium,
and over distance of 2R§ keeps a constant velocity or decelerate. It is not clear yet
whether these are really fundamentally different processes or whether they represent
just the extrema of an otherwise continuous spectrum of CME properties.[4]
The composition of atoms and ions comprising the plasma in a CME remains
uncertain. The answer may lie in a complete understanding of the mechanism responsible for the CME launch. Assuming the CME launch near the Sun is magnetically
dominated, then it seems reasonable that the material dominant in the launch region
would comprise the bulk of the mass of the CME, such that can not interact with the
environment during its evolution[32]. There has been a suggestion that the CME is
probably a combination of material from many regions on the Sun, and some CMEs
may have different amounts of different solar components depending of its origins. In
the next section, we present the main theories of drivers and precursors that can be
responsible of the CME launch.
3.1
Drivers and progenitors
It is still a open question the reason for the CMEs eruptions. One explanation is
because the Sun is trying to do what all things in nature try to do: reduce its energy.
As the Sun evolves through its cycle, its coronal magnetic field becomes twisted and
entangled. It requires energy to sustain these complex structures, thus when the level
of complexity reaches a certain nonequilibrium state or a metastable state, a part of
the magnetic field can be released [32]. The result is an eruption of a field component.
Also, the natural state of the solar corona is one of expansion (Solar wind). Thus,
CMEs are originated as closed coronal magnetic field structures, which maybe act to
inhibit this expansion in certain regions. Hence, a CME launch may be initiated by
18
Coronal Mass Ejection (CME)
re-configuring the closed structure[32].
The cause of CMEs is the key for their physical understanding and should be
detectable in pre-CME conditions.[4] As any other eruptive phenomena, CMEs involve
the energy conversion from one kind to another, like the kinetic, potential, thermal,
and nonthermal energies. The only kind of energy that can fulfill such specification
is the magnetic energy for energetic CME events, which are the most interesting
in the spaceweather context. In those eruptive cases, the energy comes from the
partial release of the magnetic free energy[14]. The CME is believed to arise from
large closed magnetic field in the active regions, which generally exhibit a roughly
bipolar field. In order to provide conditions for eruptive phenomena such as flares
and CMEs, free magnetic energy needs to be stored in the form of a stressed and
sheared field[4]. The stress of the magnetic field with that photospheric shear motion
can be observationally determined from a vector magnetogram, which contains the
information of the full 3D magnetic field vectors at the photospheric boundary, in order
to evaluated the highly sheared segment of the neutral line[42]. Evidence for a highly
sheared magnetic configuration was found in filament eruptions and flares, without the
presence of a helmet streamer configuration[16]. Shearing and stressing of magnetic
field lines above the neutral line leads to helical S-shaped in projection, called sigmoid
structures[4]. When the helical twist exceeds some critical value, the structure becomes
susceptible to the kink instability, which produces a disruption of the magnetic field
leading to the expulsion of a filament or CME. Besides the helical structure, cavity patterns can be also observed in the pre-CME structures in Soft X-Rays: SXR sigmoids[14].
The SXR sigmoids is not the only signal of the initiation process just prior to the
eruption, CMEs also reveal thermal or nonthermal signatures before or during the
ejecta release. Mainly, the imaging and spectroscopic observations of the CME source
region are crucial to find out the possible precursors (For more details [14]):
1. Presence of flare and filaments in the zone: CMEs are often accompanied by
solar flares but many flares are not associated with CMEs. For instance, 70% of
C-class,44% of M-class, and 10% of X-class SXR flares are not associated with
CMEs. Unlike flares, Filament/prominence eruptions are strongly related with
CME eruption, such that a part of the erupting filament becomes the bright core
of the CME.
3.1 Drivers and progenitors
19
2. Helmet streamer swelling and/or slow rise of prominences: The CMEs can arise
from pre-existing helmet streamers, which is increased in brightness and size for
days before final eruption[34].
3. Reconnection-favored emerging flux: Erupted filaments can be associated with
emerging bipolar magnetic flux[19].
4. Type I and Type III radio burst: Due to the magnetic restructuring during CME
initiations and resulting from small-scale magnetic reconnection[38].
5. Long-term filament/prominence oscillations: Before the final eruption, the prominence oscillate almost 12 times the corresponding oscillation period[15].
6. Outward-moving blobs near the edge of streamers: Currently, it was identified
narrow rays comprised of a series of outward-propagating plasma blobs apparently
forming near the edge of the streamer belt prior to many CME eruptions[31].
It should be noted that none of the precursors is a necessary or sufficient condition for
CME eruptions. Therefore, the construct an empirical model for CME forecast have to
combine some or all of the above mentioned precursors together, in order to increase
the success rate.
A variety of models of CME initiation have been proposed, that would possibly
explain the eruption of a CME based of the precursors observation. One of these models
is the break-out model that was initially proposed by Antiochos in 1999[2]. In this
model, the initiation of a CME occurs in multipolar topological configuration wherein
reconnection between a sheared arcade and the neighboring flux system triggers the
eruption. Another model is the tether-cutting model proposed by Sturrock in 1984
[60], based on reconnection which occurs in initially sheared bipolar arcades, leading
to formation of a magnetic plasmoid, which is then ejected.
One of the most accepted generation models are those associated with the release
of a flux rope magnetic structure. A flux rope is a twisted or strongly sheared core
magnetic field, which may or may not hold a filament, kept in equilibrium by the
overlying envelope magnetic field lines which are line-tied to the solar surface[14]. The
pre-eruption configuration for this case consists of an infinitely long flux rope and a
overlying arcade which starts to rise in the initial phase. A set of magnetic field lines
then form an island through which goes the twisted flux rope, closing down below with
field lines reconnecting region, and finally a set of arcades close to the boundary. On the
20
Coronal Mass Ejection (CME)
other hand, the flux-injection model is such that the magnetic configuration of a CME
is that of a flux rope with footpoints anchored below the photosphere. The eruption
of such configuration can be brought by "flux injection" process or a rapid increase in
poloidal flux[66]. In Chapter 7, we describe and evaluate a model of magnetic structure
of CMEs, which unlike the flux rope model, considers a sun-disconnected entities with
spherical topology known as Spheromak model.
3.2
Propagation: Interplanetary coronal mass ejection (ICME)
The interplanetary coronal mass ejections or ICMEs are generally regarded as the
heliospheric counterpart of the CME, at much larger distances from the Sun. Like
CMEs, they have large masses and contain magnetic field, but generally are not as fast.
This can be due to the large deceleration imposed on fast CMEs by the surrounding
solar wind [32]. These interplanetary CMEs (ICMEs) can be observed both remotely
with white-light heliospheric imagers as density perturbations, with interplanetary
scintillation, with radio burst observations or directly with in situ magnetic field and
particle detectors.
There are a number of plasma, magnetic field, compositional and charge-state signatures used to identify ICMEs from in situ data. Direct measurements of ICMEs from
the early 1970s revealed a helium and high ionization states of oxygen and iron, such
as Fe10+ and even Fe16+ [32]. They contain cooler ions as well, such as singly-charged
helium, magnesium and neon. The high-temperature ions are generally regarded to
originate low in the solar corona or from heating during the launch of the CME, while
the low temperatures are probably associated with the filament material that erupted
behind the CME. While different ICMEs have different compositions, there do appear
to be some patterns, like He++/H+ and Fe16+ enhancements, that are common to
many ICMEs. Also, plasma density and pressure are usually lower than the bulk solar
wind, suggesting ICMEs undergo greater expansion than the bulk solar wind[32].
The magnetic structure inside an ICME, also detected in in-situ data, can be varied
but is typically greater in magnitude than the surrounding interplanetary magnetic
field. When the field is large enough, the structure is usually called magnetic clouds[52].
Magnetic clouds (MCs) are characterized by smooth rotation of the field vector in a
plane vertical to the propagation direction, mostly combined with very low beta plasma
3.2 Propagation: Interplanetary coronal mass ejection (ICME)
21
parameter, low plasma densities and a monotonous decrease of the plasma velocity,
giving evidence of a flux rope topology in expansion[47]. Those characteristics produce
the largest deviations of the Parker spiral magnetic field and are the primary source
of strong meridional HMF in the near-Earth solar wind, making ICMEs particularly
geoeffective [57].
Many ICMEs are supersonic or super-Alfvénic, this means that the structures have
speeds faster than the speed of sound and the Alfvén speed in the surrounding solar
wind[32]. Along to the other physical signatures of the ICMEs, they often cause shocks
in the interplanetary medium which are responsible for other secondary effects, such
as energetic particle acceleration and electromagnetic radio bursts[32]. In the next
chapter, we deeply discuss the characteristics of these shocks, their detection methods,
and how their interaction with the solar wind and with the heliospheric magnetic field
(HMF) is.
Chapter 4
Interplanetary shocks
As mentioned in the previous chapter, the solar wind extends throughout the interplanetary medium, filling the plasma and magnetic field all over the heliosphere. This
magnetohydrodynamic (MHD) medium can be characterized by physical quantities
that give evidence of its local state: density, temperature, magnetic field strength and
so on. In particular, a magnetized fluid exhibits three characteristic signal speeds:
the sound speed, the Alfven speed, and the magnetoacoustic speed[11]. Due to the
solar dynamics, many solar phenomena can move through the heliosphere at speeds
much greater than the above mentioned speeds. They can be therefore supersonic or
superalfvénic phenomena, and so give rise to collisionless shock waves. Shock waves in
the solar wind are to referred as Interplanetary shocks[32]. These events are of interest
in themselves, for example, in studying steepened nonlinear waves in a collisionless
plasma, and as consequences of solar events, such as ejected solar mass or strong
magnetic fields ramming into the upstream solar wind. They are also important as
accelerators of energetic particles, generators of radio waves and plasma waves, and
triggers of geomagnetic phenomena[43].
There are two basic types of MHD shocks in the solar wind: Fast shocks and Slow
shocks. The magnetic field strength increases across a fast shock and decreases across
a slow shock. A shock (either fast or slow) that is moving away from the sun relative
to the ambient medium is called a "forward shock". A shock (either fast or slow) that
is moving toward the sun relative to the ambient medium is called a "reverse shock."
Since the medium moves supersonically away from the Sun, both forward shocks and
reverse shocks move away from the Sun[11]. Thus, for the interplanetary medium case,
a forward shock, which is the most common type of shocks in the solar wind at 1 AU,
can easily be identified by a sudden increase in magnetic field strength, solar wind
24
Interplanetary shocks
plasma density, solar wind speed and temperature; in a similar manner, a reverse shock
can be identified by a sudden decrease in magnetic field and density but an increase in
solar wind speed and temperature[32].
Any kind of shock wave, being at a surface, has a characteristic vector normal ˛n,
which is assumed to point toward the upstream in the region with lower entropy [11]. In
MHD, some physical parameters related to the shock depends on the angle – between
˛ ‹ . If – = 90o , the shock is called a
˛n and the ambient magnetic field observation B
"perpendicular shock". If – is close to 90o it is called a "quasi-perpendicular shock". A
shock for which – = 0o is called a "parallel shock," and one for which – is close to 0o is
a "quasi-parallel shock". A shock for which – is neither close to 90o nor 0o is called
an "oblique shock." The discontinuities in the fields across a shock and the abrupt
change in the velocity across a shock depend on – as well as on —-parameter and on
the associated Mach number. The interplanetary magnetic field ahead of the shock and
behind it is never uniform, showing fluctuations whose nature and structure depend
on –. Also, the internal structure of a shock depends on – among other things[11].
In addition, the shock parameters of general interest that help to characterize the
shock include the following: the upstream magnetosonic Mach number and the alfvén
Mach number, which give a measure of the shock "strength", the ratio of the upstream
magnetic strength with the downstream magnetic strength, which gives a magnetic
compression measure, the upstream —-parameter and the sense of travel (forward or
reverse) to determine the move, generally "along with" or "against" the solar wind flow
direction.
4.1
Interplanetary Transients: SIR and ICME
Generally, the shocks are also separated according to their cause. Blast waves at
the Sun, solar wind corotating stream interactions, rapid gas clouds from the Sun
or fast-moving, strong, twisted magnetic field structures in the solar wind (magnetic
clouds or magnetic flux ropes), are all possible causes of interplanetary shock waves[43].
It is possible to identify two classes of shocks based on their origin: shocks driven by
the ejecta from solar eruptions or ICME ("transient shocks") and shocks associated
with corotating streams ("corotating shocks").
Due to the inclination of the solar magnetic axis, as well as warps in the streamer
belt, combined with the rotation of solar wind sources with the Sun, results in fast and
4.1 Interplanetary Transients: SIR and ICME
25
slow solar wind successively entering to the heliosphere[52]. In such instances, when a
fast solar wind stream overtakes a slower one, forms a region where the density and
temperature are enhanced because the slow solar wind is compressed and accelerated.
This interaction creates a pressure ridge between the two streams, slowing down the
fast stream, deflecting it, and speeding up the slow stream and deflecting it[1]. Those
regions are known as Stream Interaction Regions (SIRs) but when the medium is in a
quasi-steady state regime those SIRs will corotate with the Sun. In that cases, the SIR
are known as corotating interaction regions (CIRs)(See figure 4.1). Both CIRs and
SIRs are commonly bounded by fast forward-reverse corotating shock pairs which are
generally weak, to long distances from the Sun but detectable by spacecrafts[27]. CIRs
are most commonly observed during the declining phase of the solar cycle, when there
is typically quasi-stable dipolar corona with significantly inclination to the rotational
axis[52].
Fig. 4.1 Left: A sketch of a stream interaction region. Right: The magnetic axis, M,
and therefore the wind speed belts, are inclined to the rotation axis, R. The point in
the heliosphere at which fast wind is able to catch up to the slow wind ahead of it
is the stream interface. Both fast and slow wind flow in toward the stream interface.
As the interplanetary magnetic field is frozen to the plasma flow, neither fast nor
slow wind can pass through the stream interface and are defected along it.(From
[52])
For the case of transient shocks, fast ICMEs have been measured at speeds in
excess of v = 2000 km/s[4]. Since the fast solar wind has a typical maximum speed of
v ¥ 750 km/s , fast ICMEs are supersonic and super-Alfvénic. Thus, such fast CMEs
can drive interplanetary shocks[4]. Thanks to the front of a fast CME which overtakes
26
Interplanetary shocks
the slower solar wind, a strong presure gradient develops and pressure waves steepen
into a forward shock propagating into the ambient wind ahead, and occasionally a
reverse shock propagates back through the CME towards the Sun. For an ICME the
forward shock is stronger than the reverse, even a reverse shock is rarely seen at all,
unlike for a CIR where the reverse shock is stronger than the forward[1].
A large part of the knowledge about collisionless shocks comes from studies of
the Earth’s bow shock, where in situ measurements are obtained much of the time[1].
When the flow of fast solar wind collides with the earth’s magnetic field, is created
a shock wave. The wave is called the bow shock, wherein there is a jump in plasma
density, temperature, and magnetic field associated with the transition from supersonic
to subsonic flow. In that zone, it is formed the foreshock region upstream of the bow
shock, where energetic protons reflected from the shock back toward the sun helping
to heat, decelerate, and deflect the solar wind. In different parts of this structure are
different shock geometries. On the front point of the bow shock to the flow of the
wind shock is quasi-perpendicular instead on the flanks of the bow shock, the shock is
quasi-parallel[24].
To first approximation, the transient shocks within 1 AU are spherical[53], however
the dynamic structure of the shock is far from being spherical. Mesoscale distortions of
a transient shock shape, which can be caused by the interaction of shocks with streams,
deform the basic spherical form[11]. In addition, when a faster ICME catch up a slower
CME and interact, such interactions form compound streams in the inner heliosphere
distorting the shock front[11]. Since we know that the solar wind is not homogeneous
any shocks structure (transient or corotating) will not be spatially uniform[1]. Mainly,
one of our main objectives in this work is to use the Wind mission and STEREO
dual missions, which has the observation capabilities to investigate the characteristics
of shocks from the same ICME or magnetic cloud observed at two or three different
locations. We focus on the event detection that fulfill that condition and on the
evaluation of its physical variables associated, as well as the emission process that take
place there: Radio emission.
4.2
Interplanetary type II radio burst
There exist two sources of energetic particles in interplanetary space: flare-related
magnetic reconnection sites in the solar corona that are connected to interplanetary
4.2 Interplanetary type II radio burst
27
space via open field lines and shock acceleration sites associated with SIR or fast
ICME fronts that propagate through interplanetary space. Due to the collisionless
condition, suprathermal and high-energy particles can propagate unimpeded through
interplanetary space to form particle beams[4]. Such transient beams are unstable to
the bump-in-tail instability which active the Landau resonace over the beam. That
resonace generates Langmuir waves, which are believed to undergo nonlinear wavewave interactions that produce electromagnetic emissions at the local electron plasma
frequency (fpe ) and its second harmonic (2fpe ), which are related to the square root
of the electron plasma density (ne ) at the source region. That emission is generally
associated to type II radio bursts[4](See figure 4.2).
Solar radio bursts of type II are characterized by a narrow band of intense radiation
with a frequency drifts downwards in time and distance from the Sun over time scales
from a few hours to one or two days[4] (See figure 4.2). Type II radio bursts, that
occurs in the interplanetary space, are a primary method used to track the progress
CME-driven shocks through the heliosphere. That decrease of the frequency together
with a assumed radial electron density profile, can be used to determine the kinematic
features of the shock front[55]. Based on a canonical density model of the corona and
the heliosphere, the plasma frequency in the solar atmosphere starting at fp <≥ 1 GHz
in the transition region and steadily dropping to fp ¥ 30 kHz at 1 AU distance[4].
Many observations suggest that fast and slow interplanetary ICME-driven shocks
can generate type II radio emissions[12] [56] produced by the solar wind electrons
reflecting from the shock front. The accelerated solar wind electrons form a foreshock
region upstream of the shock, analogous to the electron foreshock region of the Earth’s
bow shock where the type II radio emission is also detectable[20]. In addition, if the
acceleration point is magnetically connected to the spacecraft, the spacecraft observes
an energetic electron beam aligned with the HMF[54]. It is belive that in the terrestrial
foreshock the electrons and ions from the solar wind are accelerated by a fast Fermi
process which gives evidence of a curved structure over the foreshock region[55].
On the other hand, Bale in 1999 describes the first interplanetary foreshock region in
the literature, where the observations suggest the inhomogeneous large-scale structure
of the shock front[5]. In the detection, before the arrival of the shock, electron beams
along the interplanetary magnetic field and associated Langmuir waves are detected,
suggesting magnetic connection to a quasi-perpendicular shock front acceleration site.
28
Interplanetary shocks
Fig. 4.2 Radio wave, magnetic field, and GOES X-ray data for three shock crossings seen by the Wind spacecraft. The type II emissions can be seen as slowly drifting features in the spectrum, and the spacecraft shock crossings are indicated by
abrupt jumps in the local plasma frequency and the magnetic field (Source: Pulupa
2008[54])
Moreover, based of the observation, the author affirms that the radio emissions mainly
will originate from the upstream edges of the observed foreshock region, but if the field
line connects to the shock in both ends, there exists the possibility of a radio emission
on the downstream region at a higher plasma frequency[5].
Prior to these observations, type II bursts were considered as a diffuse background
emission with sporadic intensifications and was suggested that some sporadic type II
emissions correspond to emission at multiple and distinct sites along the shock front,
showing for remote sensing[12][56]. Bale’s work helped to reaffirm these assumptions,
however, it is still an open question where on the ICME-driven shock surface, the type
II burst is being generated. The observation and detection of multiple spacecrafts is
the fundamental key for understand the process, in which we can know if the emission
is always at the "nose" of the shock, where the compression is the strongest, or if it can
also occur on the flanks or on the trailing edges. With the help of the STEREO and
Wind missions, scientists have been advancing the understanding of this phenomenon,
particularly in the multispacecraft detection of interplanetary shocks.
Chapter 5
Spacecraft detection
Space observatories are currently the main tool for certain studies in astrophysics,
because they have provided a vast knowledge of astronomical objects observed in
the regions of the electromagnetic spectrum that are blocked and absorbed by our
atmosphere. In addition, they do not present the difficulties presented in terrestrial
observatories such as light pollution or turbulence. These space-based missions are
particularly useful for characterizing the environment to which it is subject, especially
for the case of the spaceweather study. STEREO and Wind missions provide in
situ measurements of the properties of the surrounding plasma, which makes them
particularly useful for the development of our work. In the first part of this chapter,
we describe the properties of these spacecrafts and their main detectors. In the second
part, we present the results of the evaluation of a list of interplanetary shocks detected
by the mentioned spacecrafts, that can be related to a type II radio burst and to the
same interplanetary transients: ICMEs-driven.
5.1
Wind Mission
Wind spacecraft is the first of NASA’s Global Geospace Science (GGS) program, which
is part of the International Solar-Terrestrial Physics (ISTP) Science Initiative, a collaboration between several countries in Europe, Asia, and North America. The program
main aim is to understand the behavior of the solar-terrestrial plasma environment
in order to predict how the Earth’s atmosphere will respond to changes in solar wind
conditions. WIND was launched on November 1, 1994 and was positioned in a sunward,
multiple double-lunar swingby orbit with a maximum apogee of 250Re during the first
two years of operation. This will be followed by a halo orbit at the Earth-Sun L1 point.
It main objective is to measure the properties of the solar wind before it reaches the
30
Spacecraft detection
Earth.
The detector WAVES, inside Wind, provide comprehensive measurements of the radio and plasma wave phenomena which occur in the solar wind upstream of the Earth’s
magnetosphere and in key regions of the magnetosphere. The detector is able to measure
low-frequency electric waves and low-frequency magnetic fields, from DC to 10 kHz, the
electron thermal noise, from 4 kHz to 256 kHz and radio waves, from 20 kHz to 14 MHz.
The Wind’s 3-D Plasma and Energetic Particle Analyzer investigation measure ions
and electrons in the interplanetary medium with energies including that of the solar
wind and the energetic particle range. The detectors study the particles upstream
of the bow shock in the foreshock region and the transient particles emitted by the
Sun during solar particle events. Also, it is used to explore the interplanetary particle
population in the thermal and suprathermal energy, the transport of particles and
basic plasma processes in the interplanetary medium. The experiment is able to detect
the three dimensional distribution of plasma and energetic electrons and ions over the
particle energy range from few eV to several MeV. It have a energy resolution of 0.20
(”E/E) for particles energy from 3 eV to 30 keV; and energy resolution of 0.3 (”E/E)
from 20 keV to 11 MeV.
The Wind’s Magnetic Fields Investigation (MFI) investigates the large-scale structure and fluctuation characteristics of the interplanetary magnetic field. This detector
provide high resolution vector magnetic field measurements in near real time on a
continuous basis. The wide dynamic measuring range is from ±0.004 nT up to ±65536
nT, in eight discrete range steps. All information described above is based on the
information present at the official website of the mission: NASA Science Mission
http://science.nasa.gov/missions/wind/, NASA Goddard Space Flight Center: Wind
http://pwg.gsfc.nasa.gov/wind.shtml
5.2
STEREO Mission
STEREO (Solar TErrestrial RElations Observatory) is the third mission in NASA’s
Solar Terrestrial Probes program (STP) after Ulysses mission and Wind mission. It
employs two nearly identical space-based observatories, one ahead of Earth in its orbit
(STEREO-A) and the other trailing behind (STEREO-B), each at ≥ 1 AU distance
from the Sun. The twin STEREO spacecraft were launched on October 26, 2006, since
5.2 STEREO Mission
31
that time they have been separating between each other at approximately 44 to 45
degrees per year. The STEREO mission has as its primary science goal the study of the
generation, evolution, and propagation of Coronal Mass Ejections (CMEs) and its contraparts: ICMEs. Other objectives that has the mission is to discover the mechanisms
and sites of energetic particle acceleration in the low corona and the interplanetary
medium and to improve the determination of the structure of the ambient solar wind[40].
STEREO spacecrafts provides a unique and revolutionary view of the Sun-Earth
system thanks to their different positions over the Earth’s orbit (See 5.1). The satellites trace the flow of energy and matter from the Sun to Earth as well as reveal
the 3-D structure of coronal mass ejections[40]. STEREO also provides alerts for
Earth-directed solar ejections, from its unique side-viewing perspective adding it to
the fleet of space weather detection satellites. The STEREO science consists of four
measurement packages: SECCHI, IMPACT, PLASTIC and SWAVES; each of which
has several components totaling at least 18 individual detectors (See 5.1). Together,
this suite of instruments will characterize the CME plasma from the solar corona to
Earth’s orbit[40]. For our purposes, we describe only three of them in this review.
Fig. 5.1 Left: STEREO-B spacecraft and detectors. Right: Orbital configuration of
the mission. Because the two spacecraft were in slightly different orbits, the "ahead"
(A) spacecraft was ejected to a heliocentric orbit inside Earth’s orbit while the "behind" (B) spacecraft remained temporarily in a high earth orbit. The A spacecraftsun-earth angle increases at 21, 650 degree per year. The B spacecraft-sun-earth
angle changes ≠21, 999 degrees per year[40]
32
Spacecraft detection
The In-situ Measurements of Particles and CME Transients (IMPACT) is a suite
of seven instruments that samples the 3-D distribution of solar wind plasma electrons,
characterizing the solar energetic particle and the local vector magnetic field. The
Solar Wind Electron Analyzer (SWEA) and the Suprathermal Electron Telescope
(STE) are designed to measure the distribution function of the solar wind core and
halo electrons with energies between below of few eV to 3 keV and measure the eletron
flux moving in the sunward and antisunward directions in the energy range ≥ 2 keV to
100 keV[44]. The response time of these instruments varies from 8 s to 30 s[44]. MAG
is a triaxial fluxgate Magnetometer built at Goddard Space Flight Center to measure
the vector magnetic field in two ranges up to 65, 536 nT and up to 500 nT with 0.1
nT accuracy[44]. IMPACT’s Solar Energetic Particle suite (SEP) is made up of the
Suprathermal Ion Telescope (SIT), the Solar Electron and Proton Telescope (SEPT),
the Low Energy Telescope (LET), and the High Energy Telescope (HET)[44]. The
SEP suite covers measurements of heliospheric electrons from 0.03 ≠ 6 MeV, protons
from 0.06 ≠ 100 MeV, Helium ions from 0.12 ≠ 100 MeV/nucleon, and heavier ions
from 0.03 ≠ 40 MeV/nucleon[44].
PLAsma and SupraThermal Ion Composition (PLASTIC) provides plasma characteristics of protons, alpha particles, and heavy ions. This experiment will provide
key diagnostic measurements of the form of mass and charge state composition of
heavy ions and characterize the CME plasma from ambient coronal plasma. PLASTIC
has nearly complete angular coverage in the ecliptic plane and an energy range from
≥ 0.3 to 80 keV/e, from which the distribution functions of suprathermal ions include
those ions created in pick-up and local shock acceleration processes[23]. The SWS
system in PLASTIC can measure the solar wind proton bulk parameters and the main
characteristic of the solar wind minor ions and the suprathermal ions[23].
S/WAVES is an interplanetary radio burst tracker that observes the generation and
evolution of traveling radio disturbances from the Sun to the orbit of Earth. S/WAVES
uses three mutually orthogonal monopole antenna elements, each six meters in length
[40]. The three monopoles were deployed anti-sunward, so they remain out of the fields
of view of Sun-facing instruments. The primary measurement goal of the S/WAVES
experiment is to resolve these IP type II bursts in frequency and time, to measure their
direction of arrival and use these measurements to infer CME speed and acceleration,
shock structure, and heliospheric density. S/WAVES will also measure the fast-drifting
radio emission from solar flare electrons, called “type III” radio bursts. Another science
5.3 Detected events
33
goal for STEREO/WAVES is the measurement in situ of the plasma waves involved in
the plasma radiation process and collisionless shock physics[6]. S/WAVES has four
radio receivers that cover the frequency ranges of 10 kHz to 16 MHz and another one
that cover 50 MHz as fixed frequency[40].
5.3
Detected events
Since the first detection of the source region of interplanetary type II radio burst
associated to a ICME-driven interplanetary shock made by Bale in 1999[5], scientists
have been developed a series of studies to determine the extended structure of these
shocks[54][55]. However, investigations were carried out considering a single region
on the shock structure, with the detection of only one spacecraft, limiting the real
study of the area. With the help of the above mentioned missions, we propose evaluate
and classify the interplanetary shock events detected by each spacecraft that can be
related with a type II radio burst and that could be associated each other to the same
transient event in order to detect multiple regions on the interplanetary shock front.
The Harvard-Smithsonian Center of Astrophysics (CfA) [59] provide an online
database of interplanetary shocks observed by the Wind and ACE spacecraft. These
page is maintained by Dr. Michael L. Stevens and Professor Justin C. Kasper, in
support of studies of shock physics and particle acceleration. This database offers
a complete description of the main features of the interplanetary shock from 19952014, including the shock normal angle –, the field change, the beta parameter, Mach
number, among others. Likewise, the Space Physics Center of the UCLA Institute
of geophysics and planetary science provide a database for Level 3 data Results of
STEREO: IMPACT/PLASTIC with the list of the interplanetary shocks detected by
the twin spacecrafts[62]. Also, this database offers a complete description of the main
features of the interplanetary shock from 2006-2013. The data was confirm checking
the 1-min PLASTIC data looking for the plasma features of the shock. The event list
is compiled by Dr. Lan Jian for reference purpose[39].
Based on the information from these databases, we compared the interplanetary
shock features detected by the three ships, which can be correlated both temporally and
spatially giving evidence of the same shock-driven event detected in multiple locations.
The study was conducted in the period from 2007 to 2010. The period begins one year
after the launch of STEREO and ends when the three ships are sufficiently separated
34
Spacecraft detection
such that there is a very low probability of spatial correlation. In the period mentioned,
we evaluated 220 isolates interplanetary shocks, of which only 25 are likely to be
appreciable correlated. Eleven shock-driven source were determined of these isolated
interplanetary shocks, which mostly correspond to SIR. In the table 5.1 we present the
results obtained for this classification reporting the characteristic parameters for each
shock, the associated spacecraft and source.
The selected period corresponds to the final stage of the 23 solar cycle approaching
to the solar minimum, which explain the high occurrence of interplanetary shock
associate to stream interaction regions SIR and the few events associate to ICMEdriven shock. Due to the low solar activity, most of the events have a low intensity with
respect to the magnetic field change (See Chapter 4). However, due to the variability
of the solar wind structure, there are a diversity of shock normal angles. Thanks to
the WAVES of Wind and S/WAVES of STEREO, was possible to determine whether
each is associated with Type II radio emission, for our case every reported event has a
radio emission temporally associated. Nevertheless, our particular purpose is to find
events of interplanetary ICME-driven shock to develop an appropriate characterization
of its extended structure, for which we only have four events reported for this period
(See table 5.1). This is not the only drawback, closer examination of the data provided
by the spacecrafts and the reports in the database, led us to conclude that none of
the four events is likely to have sufficient temporal and spatial correlations between
the respective detections. Therefore it is not possible to assert that these isolated
interplanetary shocks produced by the action of ICME-driven are associated with the
same event.
Due to the previous finding, we have evaluated a second time period in 2014.
Thanks to the orbital characteristics of the STEREO mission, the two spacecraft are
currently in the diametrically opposite region of the Earth relative to the Sun position
but relatively close each other, being this setup appropriate for our purposes, even if
the data from the Wind mission are not used this time (See Image 5.1). The selected
study period is from January 2014 to May 2014, for which the spacecrafts had an angle
of initial sepation of ≥ 55o in January , decreasing to a separation angle of ≥ 37o in
May. Later dates were not taken to account because, after of May, Level 2 PLASTIC
data were not available. For this period of time there is no documented record of interplanetary shocks detected by STEREO, since the database only reports shocks until
2013. For this reason, we have examined of the magnetic field strength, velocity and
density plasma profile data, looking for main features of interplanetary shocks in order
STA
Wind
STA
STB
Wind
Wind
STB
STB
STA
STB
Wind
STB
Wind
Wind
STB
Wind
STB
STB
Wind
STB
Wind
STB
STB
STB
Wind
Spacecraft
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2007
2008
2008
2009
2009
2009
2009
2009
2009
2010
2010
2010
2010
2
2
5
5
5
7
7
8
8
9
9
11
11
4
4
2
2
8
8
8
8
8
8
8
8
12
12
7
7
7
20
20
24
25
19
20
19
19
30
29
10
10
5
5
30
30
2
3
4
3
8
9
8
9
7
3
1
14
20
18
9
13
17
15
14
12
13
22
4
2
0
15
5
7
17
39
0
11
42
2
27
22
16
30
15
23
49
22
2
10
9
15
35
50
49
33
31
0
9
5
1,36
1,33
1,72
1,65
2,02
0.55
1,45
1,58
2,01
1,64
1,78
1,84
1,87
1,45
1,97
1,34
2
1,57
1,28
1,42
1,86
1,98
1,89
1,48
2,88
76,6
62.0
80,3
62,5
76,4
73,5
51,6
69,0
70,4
65,6
78,3
62,0
36,6
36.5
68,9
77,1
47,5
75,7
48
55,5
76,7
58,2
66,7
1,00
1,1
4,35
2,24
0,9
0.29
0,44
2,09
3,85
29,46
0,56
2,34
0,5
0.,89
0,25
1,19
1
4,69
2,48
1,44
1,18
0,10
0,07
0,2
Source
Forward/Reverse Shock
1,28
SIR
1,3
1,53
Forward
1,55
SIR
Forward
2,1
Forward
-0,8
Forward
SIR
1,38
Forward
1,45
Forward
ICME+SIR
1,83
Forward
1,52
Forward
SIR
1,6
1,84
Forward
ICME+SIR
1,8
Forward
1,3
ICME
1,86
Forward
1,2
SIR
1,62
Forward
ICME
1,34
Forward
ICME
0,9
1,94
F, up/downstream waves
1,74
F downstream waves
ICME+Fast Wind
1,38
Reverse
3,1
-
Time [UT]
Shock parameters
1 –2
3 M4
Year Month Day Hour Min Bdown /Bup
up
Bn —
report 11 transient source events that produce between 2 to 4 interplanetary shock detections for different spacecrafts. We report
the time occurrence of the shocks in UT, the magnetic field upstream and downstream ratio 1 , the normal shock angle 2 , plasma
—-parameter 3 and the upstream Mach number 4 as shock parameters. Also, we report if the shock is forward type or reverse type.
Table 5.1 Interplanetary shock events detected by Wind, STEREO-A (STA) and STEREO-B (STB) for the 2007-2010 period. We
5.3 Detected events
35
36
Spacecraft detection
Table 5.2 Interplanetary shock events detected by STEREO-A (STA) and STEREO-B
(STB) for the 2014 period. We report 7 transient source events with the interplanetary
shock detections for different spacecrafts. We report the time occurrence of the shocks in
UT, the magnetic field upstream and downstream ratio 1 and the plasma — parameter 2 as
shock parameters.
Spacecraft
STB
STA
STA
STB
STA
STB
STA
STA
STB
STA
STB
STA
STB
STA
STB
Time [UT]
Shock parameters
1
Year Month Day Hour Min Bdown /Bup
—1
2014
2014
2014
2014
2014
2014
2014
2014
2014
2014
2014
2014
2014
2014
2014
1
1
2
2
2
2
2
2
2
3
3
3
3
4
4
29
29
1
1
5
6
22
22
23
7
8
14
14
11
12
5
18
6
15
3
12
7
23
0
18
4
16
23
15
2
20
13
19
58
27
3
59
6
10
35
41
39
10
25
28
1,84
1,92
1,55
1,63
2,04
1,57
2,09
1,72
1,62
4,85
1,38
5,5
1,3
2,79
0,78
1,04
1,15
1,66
1,65
0,46
1,21
1,76
0,65
1,67
0,25
4,34
0,35
1,24
Source
SIR
SIR
ICME
SIR+ICME
SIR+ICME
ICME
5.3 Detected events
37
to find interplanetary shock events associated to transient sources. In the data analysis,
we find 27 isolated interplanetary shock events (for STEREO-A and STEREO-B) in the
five month period, but only 15 of these can be associated to multispacecraft detection
regions of a front shock produced by a single transient event. We find 7 differents transien sources of which 2 are SIR, 2 are ICME-driven and the others are a combination
of both sources or undetermined. The table 5.2 summarizes the results of these analyzes.
In the case of the 2014 period, we estimate only two parameters associated shock:
the magnetic field change ratio and the —-parameter. The calculation of normal angle
of shock and Mach number is left as a future work, because it is not possible calculate
them trivially (See references about Coplanarity Theorem [5]). Also, all the isolated
interplanetary shocks reported are forward shock wave type. A closer examination
of the data, led us to conclude that one of the two ICME-Driven events is likely to
have sufficient temporal and spatial correlations between the two spacecrafts detection
for correspond to the same event: The ICME-driven shock of April 11 and 12. The
correlation was confirmed by comparing the time difference of the shocks and the radial
distance of the two ships to the average speed of the ICME, and also with an external
source: ENLIL Solar Wind Prediction model.
Chapter 6
ICME of April 11, 2014
The interplanetary shock detected by STEREO-A and STEREO-B on April 11-12, 2014
is particularly useful for our purposes. Initially, it is associated to a CME-driven source
that propagates, forming a magnetic cloud structure of ICME. Also, the same structure
is detected by both spacecrafts in different locations over the shock front and over the
ICME front, in order to study its extended structure at first approximation. Finally,
a radio emission can be identify over the spectrum which is temporally correlated
with the shock detection showing specific characteristics of the shock in each region.
In this chapter, we exhibit all main features of this event since its generation in the
high corona until the in situ detection of the plasma parameters and particle emission
associated to the shock.
6.1
Associated precursor
On April 8, 2014, since 22:00 UT to 23:00 UT, STEREO mission detected an energetic
event in the solar corona. Thanks to the Extreme ultraviolet detector (EUVI) on
the SECCHI package, we have observed a clear active region and a filament rupture
that accelerated the plasma inward the Sun surface generating a flare emission. In
the external solar region, the magnetic field and plasma are released, generating an
energetic coronal mass ejection. The four SECCHI chanels detected the eruption and
emission but we report just three different channels where the the detection is clearest.
In the figure 6.1, are exhibited the 171 Å bandpass which is sensitive to the Fe IX and
Fe X ionization states, at a characteristic temperature of about 1.0 million degrees
Kelvin, and the 195 Å bandpass which is sensitive to the Fe XII ionization state, at a
characteristic temperature of about 1.4 million degrees Kelvin, both corresponding to
the middle corona region[40]. In addition, is exhibited the 304 Å bandpass which is
40
ICME of April 11, 2014
Fig. 6.1 EUVI STEREO-A/B Images in 171Å, 195Å and 304Å bandpass showing
the energetic emission region (white boxes). In the event the filament suddenly
becomes unstable and breaks, generating a "whiplash" which causes the emission of
the flare
6.1 Associated precursor
41
Fig. 6.2 Image sequence of SECCHI/COR2 in STEREO-A/B showing the CME
propagation through 15 solar radii which is the field of view of the instrument.
When the filament was broken the open field lines drives the material into the exterior forming the coronal mass ejection
sensitive to the He II singly ionized state of helium, at a characteristic temperature of
about 80 thousand degrees Kelvin corresponding to the low corona region [40]. The
detection in STEREO-B was localized close to the solar disk center, but for STEREO-A
was localized eastward from the solar disk center. Unfortunately, it is not possible to
determine the GOES classification for this type of flare or other definitive characteristics
of the emission, because the event was not observed by near-Earth satellites. For our
particular case, we only have knowledge of the event thanks to the observation made
by STEREO. Nevertheless, the flare emission is temporally correlated with a Type III
radio burst emission detected by both spacecraft S/WAVES detector.
Hours after, the coronal mass ejection was detected by coronagraphs onboard
the STEREO spacecrafts. COR2 detector inside the SECCHI package recorded the
propagation of the structure on April 9 from 00:00 UT to 02:39 UT. The CME has an
approximate average velocity of ≥ 650km/s, estimated from the sequence of STEREO-
42
ICME of April 11, 2014
Fig. 6.3 STEREO/PLASTIC and STEREO/IMPACT in-situ Level 2 data from
April 11 to April 12, 2014. The panel shows the proton number density (Np ), proton
velocity (Vp ) and proton temperature(Tp ) respectively, and the bottom panel shows
the magnetic field strength. It is marked the time where each shock was detected
(black lines) be it a forward shock (FS) or a reverse shock (RS). Also, it is marked
the time of the magnetic cloud initial (SMC) and final detection (EMC) (red lines)
A images. In the figure 6.2 we can appreciate, in the STEREO-A images, a three-part
structure of CME showing clearly the flux-rope structure. In contrast to the STEREOB images where we can appreciate a halo CME structure. The projection effect is
evident in this sequence, which is useful for estimating the direction of propagation
of the structure. Knowing the position of the spacecraft at that time (See figure 6.4),
at first approximation we can affirm that the CME structure is directed toward to
STEREO-B.
6.2
Interplanety shocks in-situ detection
The CME expands in the interplanetary medium forming an ICME magnetic cloud
structure moving towards the STEREO spacecrafts. STEREO-A detects the first
signal of the coming structure on April 11 at 15:25 UT: a forward interplanetary shock,
detecting a sudden increase in the in-situ physical variables: proton number density
Np , proton velocity Vp and proton temperature Tp and a sudden increase in the in-situ
magnetic field strength |B|. Also, we can appreciate another two apparent shock
6.2 Interplanety shocks in-situ detection
43
Fig. 6.4 Picture of the ENLIL-lowers + GONGb-WSADU + Cone-SWRC model for
Solar Wind Prediction in a constant latitude plane on April 12 at 02:00 UT. The
image shows the solar wind structure in that time with the transient disturbances.
Also shows the radial velocity distribution over the entire area and in some particular spacecrafts. The simulation reports the ICME interaction with STEREO-A
and STEREO-B (yellow boxes in the plots) and in the dynamic interplanetary plane
(Black contour structure)
structure after the initial. At 18:20 UT, STEREO detects a increase in Np , Tp and
Vp but a decrease in |B|, similar to the characteristic features of a reverse type shock.
Later on 12 April at 03:10 UT, STEREO-A detects a less clear forward shock structure
with appreciate increase in Vp and Tp and minor increse in Np and |B| (See figure 6.3).
Thanks to the CME features observed in SECCHI/COR2, the ICME bulk structure is
likely directed toward STEREO-B, therefore it is expected an intense shock detection.
As expected, on April 12 at 02:28 UT, STEREO-B detects an intense forward shock
type showing a intense discontinuity increase on all proton physical variables and on
the magnetic field strength(See figure 6.3).
From the beginning of the first shock front detection, we can measure a time
range for which each of the spacecrafts detects the ICME magnetic cloud, which is
similar for both ships, of about ≥ 18 ≠ 19 hours. This makes us think that, the
44
ICME of April 11, 2014
ICME structure drags and accelerates the solar wind plasma making a high-density
and high-temperature downstream shock region that present a hydrodynamic regime
and that could be probably turbulent. For the STEREO-A detection, we can appreciated some shock features in the the above mentioned region, showing a particular
dynamics. For the case of STEREO-B, it is not evident another clear and intense
shock feature, that make us think a quasi-constant downstream structure. However,
due to the discontinuous structure of that downstream region, we can link multiple
shock events to weak features of apparent shocks, which will not be reported in this work.
To get an idea of the two-dimensional physical system studied, we compare the
STEREO in-situ detection with the daily ENLIL model for Solar Wind Prediction.
The ENLIL (Sumerian god of wind) code is a numerical model for simulations of the
ambient corotating solar wind as well as transient disturbances throughout the inner
and mid heliosphere. The model is based on ideal magnetohydrodynamic (MHD)
equations with the ratio of specific heats in the heliosphere[25]. The real-time ENLIL
application is driven by the IPSBD model data and the Wang-Sheeley-Arge (WSA)
model data using data sets of important heliospheric missions[25]. Fortunately, there
is a database[25] that has the ENLIL animations and temporal profiles in 2011-2014
for free. We compare the solar wind activity modeled for April with the in-situ shock
detections measured on April 11-12 .
In the figure 6.4, we can observe the ENLIL simulation on April 12 at 02:00 UT,
showing that STEREO-A detection could be caused by the interaction of two transient
events: first an isolated transient event and later our ICME magnetic cloud structure.
The interaction of these two structures can explain the high discontinuity in the profiles
detected by STEREO-A. Furthermore, the simulation would show that the initial shock
front could be the product of the isolated event due to its temporal correspondence with
in-situ data. However, the simulation also shows that the first signal of the magnetic
cloud in the profiles, measured by STEREO-A, corresponds to the magnetic cloud
structure under study (See figures 6.3 and 6.4). For STEREO-B detection, only the
ship interacts with our ICME, specifically with a portion of the magnetic cloud bulk
structure, as we suggested based on the coronographic images. Finally, it is important
to note that simulation shows the direct evidence that the two spacecrafts are detecting
different regions of the same structure, at least for the case of the magnetic cloud
detection. Apparently, STEREO-B detects an appreciable part of the bulk ICME
structure, unlike STEREO-A that detects one of its flanks. Although one of the
6.2 Interplanety shocks in-situ detection
45
Fig. 6.5 Dynamic spectra detected by STEREO/WAVES. The top panel is the
STEREO-A spectrum on 2014 April 11. The bottom panel is the STEREO-B spectrum on 2014 April 12. We can observe an increase in emission intensity in a wide
frequency range at the time of detection of the first shock front for each spacecraft.
shock front detection is influenced by an isolated event, it is possible to characterize
and study such fronts in the two regions, in order to understand a little more the
dynamic and physical process present in these situations, which are very common in
the interplanetary medium.
6.2.1
Radio emission detection
Another important in-situ detection, unlike the proton physical variables, is the measurement of electron flow in the shock, which could be the cause of the radio emission.
In the figure 6.5, we present the dynamic spectrum from STEREO/WAVES on April
11 for STEREO-A and on April 12 for STEREO-B. The spectra are restricted in the
frequency range of ≥ 5kHz to ≥ 200kHz, range in which is found the average value of
46
ICME of April 11, 2014
Fig. 6.6 STEREO/SWEA Level 1 data of 3D Electron intensity distribution depending on the energy of the electrons at selected azimuthal angles: 1o , 40o and 80o .
The selected time interval is set for detect the shock arrival for each spacecraft. Different variations of the electron distribution are highly correlated temporally with
the increase of the radio emission and with the discontinuities in the proton physic
variables profiles.
the electronic plasma frequency for solar wind at 1 AU (See chapter 4). In the case
of STEREO-A measurement, the emission intensity varies clearly two times, which
fit temporarily to the intense discontinuities of the proton physical variables profiles
aforementioned, specifically on the initial forward shock and of the apparent reverse
shock. For the STEREO-B case, the emission intensity also varies, features which are
not clearly seen in the STEREO-B profiles (See figure 6.3). Also, we noticed that the
intense radio emission stops when the spacecraft is hit by the magnetic cloud, i.e. the
spectra show a significant decrease in the emission intensity at the very time that the
spacecrafts detected the magnetic cloud.
On a visual inspection, we found no decisive characteristics of the existence of a
foreshock Langmuir wave activity, evidenced by strong plasma frequency radiation
immediately prior to shock arrival (upstream shock region) for both STEREO measurement. Not knowing the exact value of the electronic plasma frequency in the specific
region and time makes the search more complicated. Nonetheless, it is necessary to
conduct a more detailed inspection of the spectra because this type of activity can
occur in short burst lasting less that 1 minute and therefore cannot appear clearly
in the spectra. Besides, the most intense features in the spectra are a type III radio
emission probably originated by energetic solar events. These intense emissions, that
are not related to interplanetary shocks, can cause misidentification of radio waves or
6.2 Interplanety shocks in-situ detection
47
Langmuir waves.
In order to observe the velocity-dispersed electron beams occurred upstream shock,
we report the measurements of the in-situ electron intensity distribution for different
electron energies and different azimuthal angle detection when the shock event takes
place. (See figure 6.6). The STEREO/SWEA detector aboard SEP package provide us
the 3D measurements of distribution function of the solar wind core and halo electrons
from below an eV to several keV. Unfortunately, we report the Level 1 data for which
the intensity values are measured in units of counts and the detection is not in burst
mode, because burst mode electron flux data are not available for the date in matter.
The lack of burst mode data made the association between the plasma emission and
electron beams imposible to confirm in the upstream region. However, the variations of
electron distribution in the shock region can give us a rough overview of the structure
of the shock.
The SWAE detector has a wide field of view, which is particularly useful when
measuring electron beams which propagated in different directions. In our particular
case, we report detections made to three general azimuthal angles: quasi-parallel flow
(1o ), quasi-perpendicular flow (80o ) and oblique flow (40o ). Initially, the spectra show
a fundamental feature in the energy distribution of electrons in the interplanetary
plasma, either part of the solar wind or of some transient event. The electron flux
distributions are larger at low energies that at higher energies, indicating that the
interplanetary medium has appreciable concentration low energy electrons. Another
fundamental features in the spectra are related to the shock arrival, the downstream
structure and the magnetic cloud detection. As expected, the measurement conditions
do not demonstrate clear signs of a foreshock electron beams in the upstream region.
However, we observe a electron flux increase in all energy range at the time of arrival
of the shock for each spacecraft (See figure 6.6). Separately each spectrum has specific
characteristics, typical of the detection region where each spacecraft was. In the case
of STEREO-A, the increase of the electron distribution intensity over the energy range
from ≥ 1eV to ≥ 100eV after the beginning of shock, are correlated with the intensity
variations in the radio spectrum and the sudden changes in the proton physic variables
profiles. In particular, it shows an appreciable increase in intensity when is detected the
apparent reverse shock type. In the case of STEREO-B spectra, the strongest increase
in electron distribution intensity is temporally related to the arrival of the shock front
to the ship, variation that is also clearly distinguished in the spectrum radio emission.
48
ICME of April 11, 2014
Fig. 6.7 STEREO/PLASTIC and STEREO/IMPACT in-situ Level 2 data. Left
panel shows the measurements made by STEREO-A on April 12. Right panel shows
the measurements made by STEREO-A on a temporal range from April 12 to April
15, times at which the magnetic cloud goes through the ship. The top panels shows
the proton number density (Np ), proton velocity (Vp ) and proton temperature(Tp )
respectively, and the bottom panels shows the — plasma paramenter and the magnetic field strength. It is marked the time of the magnetic cloud initial (SMC) and
final detection (EMC) (red lines)
Likewise, both spectra show different behaviors depending on the azimuthal angle of
detection and a clear decrease when the spacecrafts detect the magnetic cloud.
In general, all the in-situ observations reported above demonstrate that the extended
structure followed by the detection of the shock front has a high plasma dynamics,
which may be the cause of the different emission processes, the different plasma flows
and the new events corresponding possibly to new interplanetary shocks.
6.2.2
Magnetic cloud features
For this case, the structure more clearly observed in the in-situ detections is the
magnetic cloud. As shown in the figure 6.7, the first signal of the magnetic cloud is
detected by STEREO-A. At 11:40 UT on April 12 a sudden decrease in Np , Tp and the
6.2 Interplanety shocks in-situ detection
49
—-parameter is appreciated, unlike the sporadic increase of the magnetic field strength
|B|. This detection takes place in a period of 8 hours and 50 minutes, in which the
transit of one of the flanks of the cloud is observed. Nine hours after the first detection,
STEREO-B reports the measurement of the magnetic cloud bulk structure. At 20:45
UT is detected a decrease in Np , Tp and —-parameter and a increase in |B| (See figure
6.7). Unlike STEREO-A, it is not possible to determine accurately the end of the
magnetic cloud in STEREO-B. For our case, we determine that the end corresponds
to the instant when the —-parameter changes to a hydrodynamic regime (— > 1) and
when the orientation of the magnetic field ceases to rotate smoothly This detection
takes place in a period of 59 hours, in which the transit of the large structure of the
cloud is observed.
As a main characteristic of a magnetic cloud, the profiles Vp , |B| and the —-parameter
have specific behaviors when the cloud passes right through the spacecraft. The speed of
the plasma has a smooth behavior, monotonically decreasing; the intensity of magnetic
field has the maximum before the geometric center of the cloud and the —-parameter
shows that the magnetic cloud has a magnetic regime — < 1. All the above mentioned
behavior are presented in the profiles measured by both spacecrafts. Thanks to the
physical characteristics of the magnetic cloud is possible to simulate such structures as
magnetic confinement schemes. In the next chapter, we present the evaluation of a
MHD magnetic structure model as a magnetic cloud, calculating artificial magnetic
field profiles for be compared with the observational data.
Chapter 7
Theorical modeling
The coronal mass ejection is a large-scale magnetic structure that can be study with
MHD models. This structure, that spreads out in the interplanetary medium, has been
studied based in models of expansion of magnetic clouds of two types: Magnetic flux
ropes tied to the Sun and disconnected entities of spherical topology: Spheromaks [45].
Since 1980, some autors had proposed different models of magnetic clouds configuration. It was thought in the possibility of magnetic field lines as family of circles
centered about an axis of a magnetic cloud and some others pinch configurations
[10][61]. Golstein in 1983 considered that magnetic clouds were force-free configuration,
and until now several solution for a static conditions were proposed [? ]. Observations
shows that the maximum of the magnetic field profile in this clouds is often displaced
towards the leading edge and also shows the existence of pressure gradients inside,
features that were not evidenced in the models listed above. To address this, current
models have been proposed other configurations as Spheromak and Toroidal solution
[37][63] that include effects of expansion and interaction with the ambient plasma
[51][18], force-free methods and non force-free methods [50].
The models’s big problem, that try to fulfill the observational requirements, is the
high numbers of free parameters in the solution, that provide limitations. On the other
hand, other problem with magnetic cloud models is that there is no independent way
to assess the errors of the fit. The access to data of multipoints measurements inside
the magnetic cloud could help in this regard. [21].
52
7.1
7.1.1
Theorical modeling
Magnetic models: Spheromaks Configurations
Magnetic Cavity: Static case
In order to describe the behavior of the ICME magnetic structure, it is necessary
evaluate some of models of magnetic clouds configuration. At first, we propose study
the magnetic field solution of a static cavity. The system is assumed as a magnetic
structure that contain plasma in equilibrium which is confined by some external, constant and uniform pressure. Gourgouliatos et al. in 2010 and 2011 show that it is
posible find analytical solutions without surface currents and deformations that allows
plasma pressures[29][28]. The important feature of those solutions are the static and
stable conditions under MHD instabilities. The aforementioned autor ensures that the
stability arguments require that the internal structure of the magnetic field should be a
combination of toroidal and poloidal components, which, in order to be in equilibrium
with a constant external pressure, must vanish on the boundary. This physical system
admit solution of an elliptical partial differential equation: the Grad-Shafranov equation that must satisfy both Dirichlet and Newmann boundary conditions simultaneously.
˛ = ÒP
The Grad-Shafranov equation is the mechanical equilibrium equation J˛ ◊ B
which can be transformed into one-dimensional scalar equation due to physical and
geometrical symmetries of the system . In general, the magnetic field that evidence
such simplification can be expressed in terms of toroidal and poloidal components:
˛ = Ò ◊ Ò„ + 2I( )Ò„[[28]]. The one-dimensional equation related a variable
B
which results to be the independent variable: poloidal flux ( ) and two functions that
depends linearly on : the poloidal current and the plasma pressure[8]. To determine
the exact form of that functions, it is necessary to use the over-constraining boundary
conditions that satisfies the solution, in where the magnetic flux and its derivative are
both zero at the boundary, these conditions lead to zero fields on the surface and a
smooth transition from the cavity to the external medium[29]
7.1.2
Magnetic Cavity: Self-similar expansion
The magnetic clouds are configuration in expansion and it should be considered as nonstationary objects. This behavior can be deducted in the in-situ velocity profiles and in
the in-situ magnetic field profiles. In the first one, the decrease in the overall velocity
profile indicates a time evolution due to radial expansion. For the total magnetic profile,
exist two asymmetries: the magnitude of the field is stronger towards the magnetic
7.1 Magnetic models: Spheromaks Configurations
53
cloud front than forwards the rear edge and the maximum value is shifted towards the
front of the cloud, so it is reached before the middle of the time interval[17]. For that
reason, we also evaluate a particular time dependence thought the self-similar expansion.
The self-similar condition is characterized by the radial expansion of concentric
shells with characteristic velocity: ˛v = r ––˙ r̂, in where the –-parameter is time-dependent
– = –(t) but still spatially independent. The –-parameter corresponds to the expansion
1
rate and has the form of the inverse of the length – ≥ R(t)
[45]. Gourgouliatos et
al. in 2011 describes the solution for the magnetic cavity case that is used in this
work[28]. In the derived solution, it is neglected the dynamical effects of the electric
field, in particular the displacement current and the electric charge density. Also,
for constraining the system in order to describe a uniform expansion without total
acceleration, it is necessary to use a specific functional form of the –-parameter, for this
case: –(t) = (v0 t+r0 )≠1 where v0 is the expansion velocity of the boundary of the cavity.
The above condition changes the Grad-Shafranov equation form due to the solution of
˛ = Ò ◊ Ò„ + –(t) Ò„,
this system has an alternate form of the magnetic field: B
in where the one of the main components is exhibited with the time-dependence of
the –-parameter. The boundary condition are the same to the static case, the only
0 r0
difference is that the boundary radii of the cavity has also a time-dependence: rc = ––(t)
.
7.1.3
Force-Free Spheromak
Spheromaks are magnetic field force-free confinement configuration in an axisymmetric
magnetohydrodynamic equilibrium [7]. In general, the force-free condition means that
the system is dominated by the magnetic field, in where the plasma pressure and inertia
˛ derived by the
terms are negligible[45]. This model satisfies the condition J˛ = –B
conservation of the magnetic helicity when the total magnetic energy decreases to its
minimum value [7], which shows that the configuration is indeed force-free : J˛ ◊ B = 0.
The magnetic field in a Force-Free Spheromak system is also determinate by the
solution of the Grad-Shafranov equation in spherical coordinates without the pressure
effects. Also, this solution has the feature of be stable over some MHD instabilities:
ideal instabilities and resistive instabilities[7]. Similarly to the magnetic cavity, the
poloidal current and the poloidal flux have a lineal dependence related with the proportionality constant –. In this case, the general solution of the Grad-Shafranov equation
has separable solutions in term of spherical Bessel functions jn (–r), in where is taken
the first order solution to solve the system [13]. Again, we neglected dynamical effects
54
Theorical modeling
of electric field, in particular displacement current and electric charge density, so the
force-free condition involves only magnetic field and electric current. This is indeed a
reasonable assumption for the solar system where the velocities are non-relativistic.
For the expansion case, it is also assumed a self-similar configuration, in which the
proportionality constant – depends directly on the time, having the form of the inverse
of the length. Thus, the system is analised in the same way as the magnetic cavity
model.
7.2
Physical System
Based on the characteristics of the above two models, we evaluate the possible profiles
of the magnetic field detecting by spacecraft when it is crossed by a magnetic cloud.
For this analysis, we consider a system where the spacecraft is static while the magnetic
cloud propagates in space with constant speed, crossing the spacecraft in some points in
the space. Likewise, for at analyzing a more realistic case, the magnetic cloud expands
radially as it propagates. To be sure, the analysis is purely numerical, so this first
study is done using the units given by the code, mainly for the case of temporal and
spatial steps. For this case the spatial and temporal units are initially arbitrary. In
the case of the magnetic field these units are determined by the units of magnetic flux,
i.e. the solution of the equation itself.
7.2.1
Trajectory evaluation
In order to evaluate the magnetic field profiles, initially we calculated the path of
the spacecraft inside the magnetic cloud. We considered the simple case where the
trajectory of the spacecraft is on a straight line which goes thought the spherical
geometry. To determine different trajectories inside the sphere, we develop a code that
calculate the points on a straight line (spherical coordinates) inside the structure with
four initial parameters: The two spherical angles ◊0 , „0 associated the initial point
on the sphere surface and other two spherical angles ◊v , „v associated to the vector
velocity of the spacecraft (See figure 7.1). The code was develop in the programming
language: Python.
7.2 Physical System
55
Fig. 7.1 Right: The red vector is related to the initial point on the sphere surface
which is determined by two angles ◊0 and „0 ; in that position the movement begins.
The blue vector determinate the direction of the spacecraft vector velocity which
also is characterized by two angles ◊v and „v Left: Evaluation of the developed code.
In this case ◊0 = 30o , „0 = 0o , ◊v = 150o and „v = 160o
7.2.2
Magnetic field magnitude profiles
Magnetic Cavity: Static case
Initially, the magnetic field magnitude, that a spacecraft should detect when passes
through a magnetic cloud, is modelled as a static cavity. The solution of the GradShafranov equation for the cavity gives the behavior of the poloidal flux, which is
related to the magnetic field components.
2
C
= sin ◊ C1
A
2 cos ◊
r2 sin2 ◊
1 ˆ
B◊ = ≠
r sin ◊ ˆr
–
B„ =
r sin ◊
Br =
B
sin(–r)
F0
– cos(–r) ≠
≠ 2 r2
r
–
D
(7.1)
In this case the solution is given for spherical coordinates. Enforced the specific
boundary conditions to a flux confined in a sphere of unit radius, the solution has
three free parameters which should satisfy the conditions. For the study case, these are
– = 5.76, F0 = ≠24.46 and C1 = ≠0.13, which are the smallest roots (Gourgouliatos
56
Theorical modeling
Fig. 7.2 Static Case. Right: Plot of five different trajectories parallel to equatorial
plane at different highs. Left: Magnetic field magnitude profiles for the trajectories
Fig. 7.3 Static Case. Right: Plot of five different trajectories perpendicular to equatorial plane at different highs. Left: Magnetic field magnitude profiles for the trajectories
7.2 Physical System
57
Fig. 7.4 Magnetic field profile for the self-similar expansion case where no translational movement of the magnetic cloud is taken to account. For this case r0 =
1[a.u.], vc = 1[a.u.] (expansion velocity) and spacecraft positions: First configuration:
r = 3, ◊ = 0o , „ = 0o , Second configuration r = 6, ◊ = 0o , „ = 0o
et al. 2011).
With the given parameters, we have calculated the magnetic field components
(Bfl , B◊ , B„ ) inside the static cavity for each point in the the straight line trajectory
and then calculated the magnitude. It is possible to compute many trajectories, in
this summary we show ten characterized trajectories (See figures 7.2 7.3). We can
appreciate some features in the profiles of magnetic field strength. At the start and end
movement points, the values of the field magnitude are zero (on the sphere surface),
which is consistent with the boundary conditions proposed. We must also say that in
this code was considered that the speed of the magnetic cloud is constant and equal to
unity over all trajectories, which implies that the time parameter is directly related to
the distance traveled by the spacecraft, which can be seen in the profiles.
Magnetic Cavity: Self-similar expansion
For the expansion case, the solution derived by the Grad-Shafranov equation is characterized by radial dependencies. it have the form à –(t)r, thus the poloidal flux that
58
Theorical modeling
results has a temporal dependence. (Gourgouliatos et al. 2012)
C
A
B
sin2 ◊
sin(–(t)r)
(–(t)r, ◊) =
C1
≠ cos(–(t)r) ≠ F0 (–(t))2 r2
–0
–(t)r
D
(7.2)
With the above, we found the components of the magnetic field using the same
relations that the static case (See 7.1). Applied the boundary condition to the system,
we determinate the values for the free parameters needed. Choosing –0 = 5.76 and
r0 = 1, in where –0 is the –-parameter value at the initial time and r0 is the radius of
the cavity at the initial time, we find that c1 = ≠25.59 and F0 = 0.735. [28]. With
this family of solutions, we evaluate some physical configurations showing chages in
the kinematical conditions. Initially, we study the case where the translational motion
of magnetic cloud is null, thus only the expansion is taken into account. In this, the
initial radius is equal to unity and the position of the detector or spacecraft is fixed.
(See figure 7.4) We notice that the maximum measured value is displaced to the left
with respect to the static case and also we notice a decrease in the overall magnitude
of the magnetic field thanks to the expansion process. As can be seen in the figure 7.4,
the maximum magnetic field value does not correspond to the value of magnetic field of
the center of the structure (geometrical middle), so this maximum corresponds to the
first layers of the structure that have not decreased its value because of the expansion.
Other studied configurations take into account the two movements: the self-similar
expansion and the translational movement of the magnetic cloud. We evaluate different
velocity directions of the cloud, which evidence different trajectories of the spacecraft
inside the geometry. Also, we consider changes in the propagation speed and different
starting positions for the magnetic cloud in expansion. (See figures 7.5 7.6)
Figure 7.5 clearly shows changes in the magnetic field profiles depending on the
spacecraft trajectory inside the cloud. The above is due to the interaction with the
different layers of the structure that changes in function of the radius. While the effect
of the expansion in the system is seen, i.e. the shift of the maximum value to the left,
we can observe a increase of the overall magnetic field strength. That is due to the
translational movement of the cloud, that makes the spacecraft reaches more internal
layers of the structure before the decrease of the total magnetic field.
Therefore we can say that the translational motion of magnetic cloud counteracts
the effect of the expansion, such that there exists an increase in the total magnetic field
profile. However, the structure can begin the process of expansion in a away position
7.2 Physical System
59
Fig. 7.5 Right: Plot of five different trajectories parallel inside the equatorial plane
in the initial time of the expansion. All trajectories begins in the same initial point.
Left: Magnetic field magnitude profile calculated in the different trajectories when
the magnetic cloud is propagated with different direction velocities (Right plot).
The CME speed in this case is v = 4[a.u.], the initial radius r0 = 1[a.u.] and the
expansion velocity vc = 1[a.u.]
of the spacecraft, and so it carry the effect of a previous expansion. This implies a
prior decrease of the total magnetic field. (See figure 7.6)
Force-Free Spheromak
As an alternative study, we calculate the profiles for Spheromak force-free configuration
without null boundary conditions, i.e. the fields have nonzero values at the surface.
Nevertheless, the structure is contained inside a spherical flux conserver of finite radius.
For this case R = 1, then the bonundary condition has to fulfill that the radial magnetic
field must vanish in r = R having the lowest energy state [7]. The solution of the
Grad-Shafranov equation gives again the behavior of the poloidal flux and the behavior
of the the magnetic field components. The –-parameter for the static case again is
related to the size of the structure, which is defined when the radial magnetic field is
60
Theorical modeling
Fig. 7.6 Right: Magnetic field profile when the magnetic cloud has different speeds.
The initial radius is r0 = 1[a.u.] and expansion speed is vc = 1[a.u] Left: Magnetic
field profile when the magnetic cloud has different initial position. In the previous
configuration the magnetic cloud has a fixed initial position (In spherical coordinates (1, 0, 0)), thus we alter this changing the radial coordinate. Again, the initial
radius is r0 = 1[a.u.], expansion speed is vc = 1[a.u.] and the CME velocity is
v = 4[a.u.]. The direction of the velocity for each case corresponds to a vector on
the equatorial plane which is directed towards to the center of the spherical geometry.
zero in the specific surface r = R. Finding the first zero of the spherical bessel funtion
j1 = 0, the –-parameter must be – = 4.493[45].
j1 (–r)
cos ◊
–r
j1 (–r) + –rj1Õ (–r)
B◊ = ≠B0
sin ◊
–r
B„ = B0 j1 (–r) sin ◊
Br = 2B0
(7.3)
With the given parameters, we calculated the magnetic field profiles inside the
structure. Again, It is possible to compute many trajectories, particulary we show the
same ten characterized trajectories evaluated for the static cavity (See figures 7.2, 7.3,
7.7). Clearly, the magnetic field profiles show the effects of electric currents on the
surface, i.e. the non-zero magnetic field values in the initial and final time points. With
the profiles, we determinate the first approximation of the magnetic field distribution
over the surface for this model. The solution shows null total magnetic field values on
the poles of the structure and a maximum total magnetic fiel values in the equatorial
7.2 Physical System
61
Fig. 7.7 Right: Magnetic field magnitude profiles for the trajectories (See figure 7.2)
Left: Magnetic field magnitude profiles for the trajectories (See figure 7.3)
region, instead of the null total magnetic field values over all surface for the first model
evaluated (See figure 7.7). Also, alike to the magnetic cavity, the maximum values in
the profiles are in the geometric center of the structure, which reasserts that the two
models have the same internal topology.
On the same way, we study the self-similar, non-relativistic expansion of the
structure, where the rate of expansion gives the time dependence on the solution. The
induction equation and the magnetic flux conservation inside the structure establishes
that the time-dependence solution of the poloidal flux must be (t) = (–/–0 )2 0 ,
where –0 is the value at some initial time and 0 is a solution of a stationary force-free
problem [45]. Thereby, the components of the magnetic field in spherical coordinates
become:
j1 (–r)
cos ◊
–02 r
j1 (–r) + –rj1Õ (–r)
B◊ = ≠B0 –
sin ◊
–02 r
3 42
–
B„ = B0
j1 (–r) sin ◊
–0
Br = 2B0 –
(7.4)
As in the previous model, we evaluate various system configuration. Initially, we
calculated profiles for the case where the magnetic cloud is only expanding, without
any translational movement (figure 7.8). This profile has a similar behavior of the
above mentioned model (non force-free), unlike the non-zero magnetic field values on
62
Theorical modeling
Fig. 7.8 Magnetic field profile for the self-similar expansion case in where no
translational movement of the magnetic cloud is taken to account. For this case
r0 = 1[a.u.], vc = 1[a.u.] (expansion velocity) and spacecraft positions: First configuration: r = 3, ◊ = 10o , „ = 0o , Second configuration r = 6, ◊ = 10o , „ = 0o . Due
to the force-free condition the initial value i.e. over the surface, have a finite total
magnetic field value. This condition changes depending of the initial point over the
suface.
7.2 Physical System
63
Fig. 7.9 Right: Plot of five different trajectories parallel over the meridional plane
in the initial time of the expansion. All trajectories begins in the same initial point.
Left: Magnetic field magnitude profile calculated in the different trajectories when
the magnetic cloud is propagated with different direction velocities (Right plot).
The CME speed again is v = 2[a.u.], the initial radius r0 = 1[a.u.] and the expansion
velocity vc = 1[a.u.]
the surface. Thus, this configuration presents contributions of current sheet over the
surface due to the force-free condition. The other studied configurations take into
account the two movements: the self-similar expansion and the translational movement
of the magnetic cloud. Again, we evaluate different velocity directions of the cloud,
different propagation speed and different starting positions for the magnetic cloud in
expansion (See figures 7.9 and 7.11).
The current sheet condition over the surface is noticed in all profiles, but is dominant
over some cases, maily due to the changing on the profile behavior depending on the
dynamic configuration of the system, i.e. to the differents effects of the auto-similar
expansion in each case. For instans, trajectories that began in the geometry flanks
(figure 7.9, Trajectory 1) and when the translational speed is small compared with the
expansion speed (figure 7.11 , Left CME speed 0.1[a.u.]), the maximum magnetic field
value is found in the surface.
Besides, profiles evidenced the similar behavior of the non-force-free model, where
the maximum magnetic field is shifted to the left due to the expansion effect. Again
the different propagation speeds (figure 7.11, left) and the different initial positions
of the expansion (figure 7.11, right) generated profiles where the spacecraft detects
64
Theorical modeling
Fig. 7.10 Right: Magnetic field profile when the magnetic cloud has different speeds.
The initial radius is r0 = 1[a.u.] and expansion speed is vc = 1[a.u]. Left: Magnetic
field profile when the magnetic cloud has different initial position. In the previous
configuration the magnetic cloud has a fixed initial position (in spherical coordinates (1, 0, 0)) so we also alter this changing the radial coordinate. Again, the initial
radius is r0 = 1[a.u.], expansion speed is vc = 1[a.u.] and the CME velocity is
v = 4[a.u.]. The direction of the velocity for each case corresponds to a vector on
the equatorial plane which is directed towards to the center of the spherical geometry
internal magnetic layers that are influenced of different expansion stadiums, similar to
the previous model case.
7.3
Observational Signature
As we already have mentioned, it is usual to find this type of behavior of magnetic
field strength profiles detected by a spacecraft when a magnetic cloud passes through
it. In order to prove that the magnetic clouds can evidence this type of topological
structure, we compare the profiles of magnetic field detected by the STEREO mission
for the April 2014 event with the models. It was not only possible to compare the
magnetic field strength with artificial profiles, but also have data of the magnetic field
components in the spacecraft coordinate system RTN. On the system, R axis points
from Sun center to the spacecraft, the T axis follows the direction of the cross product
of the solar rotational axis and R, which lies in the solar equatorial plane (towards
the west limb), and the N axis complete the right-handed system. With the type of
comparison written above and using the orientation system, we can determine whether
the physical system has a toroidal topology of magnetic field, feature of the models
7.3 Observational Signature
65
Fig. 7.11 Physical system considered in the simulation. Left: Ecliptic plane of the
system showing the spatial distribution of the system. The RTN coordinate system
for each spacecraft and the coordinate system used in the simulation are specified
as well as the ICME direction of propagation. For this case the Z and N axis are
directed outwards from the sheet. Right: Magnetic cloud topological orientation
determined by the correlation of the model with the data. In this case the X axis is
directed inwards from the sheet
studied. In addition it is possible determine various physical parameters that may
account for the initial state of the system.
Before comparing artificial profiles with observational data is necessary to restrict
the theoretical solution to a set of solutions, because the model has many free parameters and some of them has to be constrain in order to determine the physical system
studied. Thanks to the observations of the two spacecraft (COR2 and in-situ data and
ENLIL simulation), we can estimate the direction of propagation of the structure. Also,
an initial inspection of the observed magnetic field profile, enable us to think that a probable consistent model is the Spheromak force-free model. The orientation of the toroidal
structure of the system is defined by the model; however we constrain the toroidal
axis (Z axis) as perpendicular to the plane of the ecliptic in order to simplified the math.
With that constraints we determine the initial parameters of the system depending
on the best fit of the artificial magnetic field profiles, either the magnetic field strength
or the magnetic field components, with the observational data. These parameters are
the average self-similar expansion speed v¯e and average propagation speed v¯p along the
entire path. It is also possible to determine the intensity of magnetic field B0 at the
expansion of a solar radius which may shows the intensity of magnetic field structure
66
Theorical modeling
released in the solar corona (See equations 7.4). In the simulation is considered the
coordinate system centered on the solar center, the Z axis parallel to the solar rotation
axis, the Y axis in the direction of propagation of the cloud and the X axis completes
the right-handed system. In our case the cloud starts its movement from the origin with
an initial solar radius, propagating in a straight line to a range of 8o ≠ 12o measured
counterclockwise from the position of STEREO-B. This configuration is based on the
ENLIL simulation (See figures 6.4 and 7.11).
The figure 7.12 shows the results of setting the spheromak model with observational
data from STEREO-B. Because the ship B detects a part of the bulk structure, the
analysis is based on this observation. The initial parameters found for the setting have
comparable values with in-situ data, so it is reasonable to think that corresponds to
real values. For the setting shown in the figure 7.12, the average propagation velocity
and average velocity of expansion values used are v¯p = 395 km/s and v¯e = 115 km/s
respectively. This average propagation speed is clearly different ot the propagation
speed value determined in the early stages of the cloud (measurement given by COR2),
which gives a direct evidence of acceleration or deceleration effects over the trajectory.
Likewise, the speed average expansion determined for the model is much higher than
the speed expansion value determined by the in-situ speed profile ≥ 75 km/s (See figure
6.7). That make us think that maybe in the early stages of the cloud the expansion
was accelerated. Also, the initial magnetic field intensity used is |B0 | = 1.5 Gauss,
characteristic value in the corona corresponding to quiet sun areas (See Chapter 2).
Unfortunately, the parameters used in the system make it impossible for STEREO-A to
detect any sign of the cloud, so this kind of model determines that the two detections
do not correspond to the same cloud.
The first thing we can report based on the comparison (See figure 7.12), is the fact
that the initial detection given by the model does not fit with the observational data.
Due to the different approximations of the initial conditions in the model as well as
the difficulty of determining the start and end of the magnetic cloud in observational
data, the initial and final detection moments should not perfectly fit with the model.
The profiles, both artificial and real, confirm the fact that the cloud expands while
it propagates, which may correspond to a kind of self-similar expansion. This can
be seen directly on the strength magnetic field profile , where the maximum value of
magnetic field is detected first that the geometric center of the structure (See top left
7.3 Observational Signature
67
panel 7.12).
Through the comparison of the profiles of the magnetic field components was
possible to demonstrate many properties of the real system studied. Initially, the
profile form of the R component of the field can be a evidence that the spacecraft do
not go through the geometric center of the structure. In addition, other components
may give evidence that the ship passes through the cloud in diagonal direction, i.e.
initially detected one hemisphere and then when is leaving the other one. In our
case, the trajectory of the spacecraft passes through the northern hemisphere of the
structure and is parallel to its equatorial plane. We must stress that the majority
of artificial profiles are adjusted least in functional form to observational data. This
suggests that the structure can evidence a kind of toroidal topological structure, but
without evidence of a clear spherical geometry. Finally, we determine the distribution
of toroidal and poloidal field that fits the observational data which is shown in figure
7.11.
68
Theorical modeling
Fig. 7.12 Simulation results for the STEREO-B detection on 12-15 April 2014. Top
left panel: Magnetic field strength profile measured by the spacecraft (blue) compared with the artificial profile (red). Top right panel: Field component R measured
by the spacecraft compared with the artificial profile. Bottom left panel: Field component T measured by the spacecraft compared with the artificial profile. Bottom
right panel: Field component N measured by the spacecraft compared with the artificial profile. Indeed we can observe a correlation at least in form, however, it is
clear that the observed structure cannot exhibit a spherical geometry.
Chapter 8
Disscusion
Present work was developed satisfactorily fulfilling the main objectives. It was possible
to find events of interplanetary shocks in two different regions, associated with the
propagation of the same interplanetary coronal mass ejection. Such event is interesting
in studying shock structures on a large scale (about hundreds of solar radii). Likewise,
the magnetic cloud structure associated with the event, is comparable to the structure
established in toroidal topology models used in estre work.
Although a single event has been reported, the review of events in the time periods
established were the basis for building a small database of events that can be useful,
especially with the aim of evaluating other types of shocks and transients with similar features. However, the April 11-12, 2014 event reported was particularly useful
for our purposes. Initially, we report several interplanetary shocks detected by the
two spacecraft STEREO-A and STEREO-B. Clearly, we affirm that the only shock
detected by STEREO-B is associated with the transit of the ICME bulk structure,
shock so intense that generates particles flow, which saturates the instrumentation of
the ship; apparently the intense emission is observed in the radio spectrum is due to
the activation of the control gain system. We believe that intense flow of particles at
the downstream shock region may be caused by the drag of the heliospheric plasma
by the leading edge of the ICME, creating a denser, hot and turbulent region. Unlike
STEREO-B, the STEREO-A measurement is characterized by a series of interplanetary
shocks detections, evidencing the great dynamic plasma in this region. We believe that
the interaction of two ICME that pass through spacecraft in this range temporal are
responsible for the diversity of phenomena that can occur in the region. This dynamic
also evidence in the radio spectrum and in beam electron spectrum. However there is
still an open question whether indeed we are seeing the same structure of ICME in
70
Disscusion
the two detections. We base our judgment on the report given by ENLIL simulation
on that date. Unfortunately, in this work was not possible to report any emission of
foreshock region located upstream of the shock. The emission of Langmuir waves was
not clearly observed, immediately before of the shock arrival for both radio spectra.
Also, with data reported of the electron flux is not possible to perform this type of
analysis.
The detection of magnetic cloud, meanwhile, gave us a good stage to make a direct
comparison with MHD models of confinement. It is usual to compare these structures
with flux rope systems that remain bound to the sun while are propagating. In our
case, we decided to use a model unbound of the Sun, a toroidal topological structure
wrapped in a spherical bubble: Spheromak structure. Due to its self-sustaining character may be generated naturally by which may be a good candidate for the magnetic
structure of the cloud. Other evidence that may support the idea that Spheromak
type models could describe the structure of magnetic clouds was provided by COR2
observations. We determine that the precursor event associated to the CME was due
to the breaking of a filament. We think that the CME released this composed of a
closed flux-rope structure, similar to a plasmoid. Due to the profile of magnetic field
observation, we decided to use the Spheromak force-free model for direct comparison.
It is very likely in this type of structures in a magnetic regime have a current sheet
structure at the boundaries, which can be seen in observational profiles. Indeed the
results of the comparison of force-free model with STEREO-B observational data
gives evidence of a structure with toroidal topology but without ensuring a spherical
geometry. This is to be expected due to the discontinuities and asymmetries that exist
in the interplanetary medium. What surprises us, is the adjustment on the functional
form of the theoretical profiles with observational profiles, giving evidence of a closed
structure. This lead us to think that indeed the magnetic clouds can be associated
with magnetic confinement systems. But even we wonder what happens in the initial
stage of propagation, where the CME crosses different regimes of plasma; Is the system
broken in the path? or confinement remains? This is still an open question in the area.
Another important result of this analysis is the fact that we can not ensure that the
system propagates or expands uniformly from the beginning, such assertion can be
verified in the literature. In the scenario proposed by the model, the magnetic cloud
detection made by STEREO-A does not correspond to the same event. This makes us
doubt about the fact the detection of the structure of ICME in different regions of the
leading edge. It is possible that the geometry of cloud was quite different to a sphere,
71
thus the detection of STEREO-A can correspon to the flank of the ICME in matter.
As future work we propose to perform a more thorough study of the event reported.
Initially, determine the shock parameters associated to the detections to characterize
the system completely. Also, get the missing data of electron flux and deeply analyze
the radio spectra, with the aim of finding the foreshock region or emission of Langmuir
waves close to the shock. We propose to conduct the review in a wider time range of
the radio spectra in the two missions Wind and STEREO, in order to find Langmuir
emission at various times that can be correlated with shocks. This will be confronted
with a complete modelling of the system, including the interplanetary environment:
HMF, solar wind, the transients observed, in order to find the different scenarios
where collisions can occur. For this case the transient ICME will have to satisfy the
specifications of magnetic cloud observed.
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