Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 52 52 52 53 54 54 55 64 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 43 45 46 48 55 56 56 57 59 60 61 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 . . . . . . . . . . . . 2014 . . . . . . . . . . 62 63 64 65 68 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. References [1] E. Aguilar-Rodriguez, X. Blanco-Cano, C. T. Russell, J. G. Luhmann, L. K. Jian, and J. C. Ramírez Vélez. Dual observations of interplanetary shocks associated with stream interaction regions. Journal of Geophysical Research, 116(A12):A12109, December 2011. [2] S.K. Antiochos, C.R. DeVore, and J.A. Klimchuk. A model for solar coronal mass ejections. The Astrophysical Journal, 510:485–493, 1999. [3] Markus Aschwanden. Encyclopedia of the Solar System: Chapter 2: The Sun. Academy Press, Elsevier Science, second edition, 2005. [4] Markus Aschwanden. Physics of the Solar Corona. An introduction with Problems and Solutions. Springer-Praxis, 2006. [5] S D Bale, M J Reiner, L Bougeret, M L Kaiser, S Krucker, D E Larson, and R P Lin. The source region of an interplanetary type II radio burst. 26(11):1573–1576, 1999. [6] S. D. Bale, R. Ullrich, K. Goetz, N. Alster, B. Cecconi, M. Dekkali, N. R. Lingner, W. Macher, R. E. Manning, J. McCauley, S. J. Monson, T. H. Oswald, and M. Pulupa. The Electric Antennas for the STEREO/WAVES Experiment. Space Science Reviews, 136(1-4):529–547, November 2007. [7] P. Bellan. Spheromaks. A practical application of magnetohydrodynamic dynamos and plasma self-organization. Imperial College Press, 2000. [8] P. Bellan. Fundamentals of Plasma Physics. Cambridge University Press, 2006. [9] Peter Bochsler. Solar wind composition at solar maximum. Space Science Reviews, 97:113–121, 2001. [10] L Burlaga, E Sittler, F Mariani, and R Schwenn. Magnetic loop behind an interplanetary shock: Voyager, Helios, and IMP 8 observations. Journal of Geophysical Research, 86:6673–6684, 1981. [11] Leonard F. Burlaga. Interplanetary Magneto hydrodynamics. Oxford University Press, 1995. [12] H V Cane, N R Sheeley, and R A Howard. Energetic interplanetary shocks, radio emission, and coronal mass ejections. 92:9869–9874, 1987. 74 References [13] S Chandrasekhar and P.C. Kendall. On force-free magnetic fields. The Astrophysical Journal, 126, 1957. [14] P. F. Chen. Coronal Mass Ejections: Models and Their Observational Basis. Living Reviews in Solar Physics, 8, 2011. [15] P F Chen, D E Innes, and S K Solanki. SOHO/SUMER observations of prominence oscillation before eruption. 493:487–493, 2008. [16] C.C. Cheng, R Pallavicini, L.W. Acton, and E. Tandberg-Hanssen. Energy release Topolgy in a multiple-loop solar flare. The Astrophysical Journal, 298:887–897, 1985. [17] C J Farrugia. Recent work on modelling the global field line topology of interplanetary magnetic clouds. Geophysical Monographs, 1997. [18] C J Farrugia, V A Osherovich, and L F Burlaga. Magnetic flux rope versus the Spheromak as models for interplanetary magnetic clouds. Journal of Geophysical Research, 100:12293–12306, 1995. [19] J Feynman and S F Martin. The initiation of coronal mass ejections by newly emerging magnetic flux. Journal of Geophysical Research, 100:3355–3367, 1995. [20] Paul C Filbert and Paul J Kellogg. Electrostatic noise at the plasma frequency beyond the Earth’s bow shock. 84(8), 1979. [21] T. G. Forbes, J. a. Linker, J. Chen, C. Cid, J. Kóta, M. a. Lee, G. Mann, Z. MikiÊ, M. S. Potgieter, J. M. Schmidt, G. L. Siscoe, R. Vainio, S. K. Antiochos, and P. Riley. CME Theory and Models. Space Science Reviews, 123(1-3):251–302, October 2006. [22] Peter V. Foukal. Solar Astrophysics. WIley_VCH, second edition, 2004. [23] a. B. Galvin, L. M. Kistler, M. a. Popecki, C. J. Farrugia, K. D. C. Simunac, L. Ellis, E. Möbius, M. a. Lee, M. Boehm, J. Carroll, a. Crawshaw, M. Conti, P. Demaine, S. Ellis, J. a. Gaidos, J. Googins, M. Granoff, a. Gustafson, D. Heirtzler, B. King, U. Knauss, J. Levasseur, S. Longworth, K. Singer, S. Turco, P. Vachon, M. Vosbury, M. Widholm, L. M. Blush, R. Karrer, P. Bochsler, H. Daoudi, a. Etter, J. Fischer, J. Jost, a. Opitz, M. Sigrist, P. Wurz, B. Klecker, M. Ertl, E. Seidenschwang, R. F. Wimmer-Schweingruber, M. Koeten, B. Thompson, and D. Steinfeld. The Plasma and Suprathermal Ion Composition (PLASTIC) Investigation on the STEREO Observatories. Space Science Reviews, 136(1-4):437–486, January 2008. [24] Peter Gary. Near the Earth’s Bow Shock. IGPPWorkshop Report, Los Alamos science, 2:124–126, 1981. [25] GMU. ENLIL Solar Wind Prediction. [26] Leon Golub and Jay M. Pasachoff. Nearest star. Harvard University Press, 2001. [27] J.T. Gosling and V.J. Pizzo. Formation and evolution of corotating interaction regions and their three dimensional structure. Space Science Reviews, 89(1-2):21– 52, 1999. References 75 [28] Konstantinos N Gourgouliatos and Maxim Lyutikov. Dynamics of rising magnetized cavities and UHECR acceleration in clusters of galaxies. Monthly Notices of the Royal Astronomical Society, 9(June):1–9, 2011. [29] Konstantinos Nektarios Gourgouliatos, Jonathan Braithwaite, and Maxim Lyutikov. Structure of magnetic fields in intracluster cavities. Monthly Notices of the Royal Astronomical Society, 409(4):1660–1668, December 2010. [30] Arnold Hanslmeier. The Sun and Space Weather. Springer, 2007. [31] Richard a. Harrison, Christopher J. Davis, and Jackie a. Davies. Pre-CME Onset Fuses – Do the STEREO Heliospheric Imagers Hold the Clues to the CME Onset Process? Solar Physics, 259(1-2):277–296, September 2009. [32] Timothy Howard. Coronal Mass Ejection: An Introduction. Springer, 2011. [33] H S Hudson and E W Cliver. Observing coronal mass ejections without coronagraphs. Journal of Geophysical Research, 106(A11), 2001. [34] A J Hundhausen. Sizes and locations of coronal mass ejections: SMM observations from 1980 and 1984-1989. Journal of Geophysical Research, 98:177–200, 1993. [35] A J Hundhausen, J T Burkepile, and O C St Cyr. Speeds of coronal mass ejections: SMM observations from 1980 and 1984-1989. Journal of Geophysical Research, 99:6543–6552, 1994. [36] A J Hundhausen, C B Sawyer, L House, R M E Illing, and W J Wagner. Coronal mass ejections observed during the Solar Maximum Mission: Latitude distribution and rate of occurrence. Journal of Geophysical Research, 89:2639–2646, 1984. [37] K.G. Ivanov and A. F. Harshiladze. Interplanetary hydromagnetic clouds as flare-generated spheromaks. Solar Physics, 98:379–386, 1985. [38] V. Jackson, K.V. Sheridan, G.A. Dulk, and D.J. McLean. A Possible Association of Solar Type III Bursts and White Light Transients. Proc. ASA, 3, 1978. [39] L. K. Jian, C. T. Russell, J. G. Luhmann, a. B. Galvin, and K. D. C. Simunac. Solar wind observations at STEREO: 2007 - 2011. 191(1):191–194, 2013. [40] M. L. Kaiser, T. a. Kucera, J. M. Davila, O. C. St. Cyr, M. Guhathakurta, and E. Christian. The STEREO Mission: An Introduction. Space Science Reviews, 136(1-4):5–16, November 2007. [41] Hannu Karttunen, Pekka Kröger, Heikki Oja, and Markku Poutanen. Fundamental Astronomy. Springer, fifth edition, 2017. [42] K.D. Leka and G. Barnes. Photospheric magnetic field properties of flaring versus flare-quiet active regions. II. Discriminant analysis. The Astrophysical Journal, 595:1296–1306, 2003. [43] R.P. Lepping. Encyclopedia of Astronomy and Astrophysics: Solar Wind Shock Waves and Discontinuities. Institute of Physics Publishing Bristol and Philadelphia, 2005. 76 References [44] J. G. Luhmann, D. W. Curtis, P. Schroeder, J. McCauley, R. P. Lin, D. E. Larson, S. D. Bale, J.-a. Sauvaud, C. Aoustin, R. a. Mewaldt, a. C. Cummings, E. C. Stone, a. J. Davis, W. R. Cook, B. Kecman, M. E. Wiedenbeck, T. von Rosenvinge, M. H. Acuna, L. S. Reichenthal, S. Shuman, K. a. Wortman, D. V. Reames, R. MuellerMellin, H. Kunow, G. M. Mason, P. Walpole, a. Korth, T. R. Sanderson, C. T. Russell, and J. T. Gosling. STEREO IMPACT Investigation Goals, Measurements, and Data Products Overview. Space Science Reviews, 136(1-4):117–184, June 2007. [45] Maxim Lyutikov and Konstantinos N Gourgouliatos. Coronal mass ejections as expanding force-free structures. 2011. [46] R.M. MacQueen. Coronal transients: a summary. Phil. Trans. R. Soc. Lond., 297(1433):605–620, 2014. [47] K Marubashi. Structure of the interplanetary magnetic clouds and their solar origins. Adv. Space Reseach, 6(6), 1986. [48] Nicole Meyer Vernet. Basic of the Solar Wind. Cambridge University Press, 2007. [49] Y. Moon, G.S Choe, W. Haimin, Y.D. Park, N Goplaswamy, Guo Yang, and S. Yashiro. A Statistical study of two classes of Coronal Mass Ejections. The Astrophysical Journal, 581(2001):694–702, 2002. [50] T Mulligan and C T Russell. Multispacecraft modeling of the flux rope structure of interplanetary coronal mass ejections: Cylindrically symmetric versus nonsymmetric topologies. Journal of Geophysical Research, 106:10581–10596, 2001. [51] V A Osherovich, J Farrugia, and L F Burlaga. Dynamics of aging magnetic clouds. Advances in Space Research, 13(6):57–62, 1993. [52] Mathew J. Owens and Robert J. Forsyth. The Heliospheric Magnetic Field. Living Reviews in Solar Physics, 10(5), 2013. [53] E.N. Parker. Interplanetary Dynamical Processes. Interscience monographs and texts in physics and astrophysics, 1963. [54] M Pulupa and S D Bale. Structure on interplanetary shock fronts: type ii radio burst source regions. The Astrophysical Journal, 676:1330–1337, 2008. [55] M. P. Pulupa, S. D. Bale, and J. C. Kasper. Langmuir waves upstream of interplanetary shocks: Dependence on shock and plasma parameters. Journal of Geophysical Research, 115(A4):A04106, April 2010. [56] M J Reiner, M L Kaiser, J Fainberg, and R G Stone. A new method for studying remote type II radio emissions from coronal mass ejection-driven shocks. 103:651– 664, 1998. [57] Rainer Schwenn. Space Weather: The Solar Perspective. Living Reviews in Solar Physics, 3(2006), 2010. References 77 [58] National Research Council Solar and Space Physics Survey Committee. The Sun to the Earth Solar —and Beyond: A Decadal Research Strategy Solar and Space Physics. National Academy of Sciences, 2002. [59] M.L. Stevens and J.C. Kasper. Harvard-Smithsonian Center of Astrophysics, Interplanetary Shock Database. [60] P.A. Sturrock, P. Kaufman, R.L. Moore, and D.F. Smith. Energy Release in solar flares. Solar Physics, 94:341–357, 1984. [61] S T Suess. Magnetic clouds and the pinch effect. Journal of Geophysical Research, 93:5437–5445, 1988. [62] UCLA. Level 3 Results of STEREO IMPACT/PLASTIC. [63] M Vandas, S Fischer, and A Geranios. Spherical and cylindrical models of magnetized plasma clouds and their comparison with spacecraft data. 39(8), 1991. [64] A. Vourlidas, D. Buzasi, R.A. Howard, and E. Esfandiari. Mass and energy properties of LASCO CMEs. European Solar Physics Meeting, 2002. [65] D.F. Webb and A.J. Hundhausen. Activity associated with the solar origin of coronal mass ejection. Solar Physics, 108:383–401, 1987. [66] National Workshop, Recent Advances, and Solar Physics. Physics of the Sun and its Atmosphere. World Scientific, first edition, 2006.