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Analysis of Spherical Particle Distributions Observed on the WIND Spacecraft

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Analysis of Spherical Particle Distributions Observed on the WIND Spacecraft 2007:087 MASTER'S THESIS Analysis of Spherical Particle Distributions Observed on the WIND Spacecraft Katharina Nowak Luleå University of Technology Master Thesis, Continuation Courses Space Science and Technology Department of Space Science, Kiruna 2007:087 - ISSN: 1653-0187 - ISRN: LTU-PB-EX--07/087--SE Analysis of spherical particle distributions observed on the WIND spacecraft Katharina Nowak Wurzburg,¨ September 2007 Institut f¨ur Theoretische Physik und Astrophysik, Universit¨at W¨urzburg, Germany and Institutet f¨or rymdfysik, Lule˚atechniska universitet, Sweden Analysis of spherical particle distributions observed on the WIND spacecraft Katharina Nowak Wurzburg,¨ September 2007 Examiner: Prof. Dr. Wolfgang Droge¨ Institut fur¨ Theoretische Physik und Astrophysik, Universitat¨ Wurzburg,¨ Germany Second examiner (Sweden): Dr. Johnny Ejemalm Institutet for¨ rymdfysik, Lule˚a techniska universitet, Sweden Abstract WIND is a NASA spacecraft built to observe the solar wind. Since many phenomena like auroras are related to the solar wind and it has also an influence on all the spectra measured on Earth, therefore it is important to explore its behaviour. On board the spacecraft the SST, EESA and PESA instruments measure the electron and ion flux of the solar wind. These data have been further investigated. Access to existing data sets from the database of the WIND mission provided by University of Berkeley, USA, has been gained through some IDL library functions that have been specifically programmed for the purpose of preprocessing and presenting data. A statistical analysis of the present data is conducted using mostly Mathematica. After examining the data for false mea- surements and general characteristic attributes, like minima, maxima, mean value and variance, more sophisticated statistical derivations have been computed for gaining the knowledge about the spherical statistical behaviour which is thought to be describable by the von Mises-Fisher distribution or similar functional distributions. Therefore the data were examined first for the mean direction which defines one major part of the simulating, theoretical distribution expec- tation. It was found out that in the main solar events can be modelled by distributions defined on a sphere and therefore missing or wrong data can be reconstructed. i Contents 1 Introduction 1 1.1 Basicprinciples................................. .... 1 1.1.1 Thesunandthesolarwind . 1 1.1.2 Pitchangle ................................... 3 1.1.3 Thetransportequation . 4 1.2 WINDspacecraft.................................. 8 1.2.1 Instruments................................... 9 1.2.2 Datainformation............................... 11 1.3 Stereomission................................... 18 2 Analysis and Methods 21 2.1 Model .......................................... 21 2.1.1 von Mises-Fisher distribution . ...... 21 2.1.2 Kentdistribution.............................. 23 2.2 Simulationofsphericaldata . ....... 25 2.2.1 Calculating the mean, the major and the minor axis of the data separately 27 2.2.2 NMinimize ................................... 27 2.2.3 FindFit ..................................... 28 2.2.4 FindFitwithstartvalues . 28 2.2.5 Comparison of the results of the different methods . ......... 29 2.2.6 Reconstructionofdata. 35 2.3 Physicalmeaning................................. 37 3 Outcome 45 3.1 Issuesthatoccurred .............................. 45 3.2 Result .......................................... 45 3.3 Furtherwork ..................................... 46 Listoffigures....................................... 47 Listoftables ....................................... 51 References......................................... 52 ii CONTENTS CONTENTS A Appendix 58 A.1 Notations ....................................... 58 A.2 Mathematicanotebooks . 59 iii Chapter 1 Introduction 1.1 Basic principles 1.1.1 The sun and the solar wind The sun in the system of the Earth is the most interesting star in the whole universe even if it is an average star of the spectral class two. Due to the fact that is is just one astronomical unit (AU) away from the Earth, it is possible ”to study not only its electromagnetic radiation but also solar emissions of a different kinds - plasmas and energetic particles” ([1]). This is important to understand on the one hand other suns in the universe and on the other hand the effects of the Sun on the Earth, which can be seen in the atmosphere, in the weather on the Earth as well as for example in the field of biology. The chemical composition of this star is not different to other stars. About 92 % of the volume of the matter inside is hydrogen needed for the energy generation in the sun and nearly 8 % is helium, consisting of a leftover from the energy production due to nuclear fusion as well as originally present matter. In terms of mass these are 75 % hydrogen, 23 % helium and about 2 % are heavy elements, which is in total more than 99.8 % of the mass of the whole solar system ([2]). The temperature on the surface of the sun is approximately 5500 K. Further basic properties are summarised in table 1.1. The sun consists of different zones. The nuclear burning zone, which is also known as the Table 1.1: Properties of the sun [1], [3] Radius 696000 km Mass 1.99 1030 kg · Mean distance from the Earth 1 AU=150 106 km · Average density 1.91 g/cm3 Effective blackbody temperature 5785 K Radiation emitted (luminosity) 3.86 1026 W · Mass loss rate 109 kg/s core of the sun, is the innermost part, where about 50 % of its mass is concentrated. Since the energy is transported by radiation the second one is named radiation zone. From about 0.74 1 1.1. Basic principles 1.1.1 solar radii to the surface lies the hydrogen convection zone while the visible part itself is known as the photosphere. The solar atmosphere consists of three different parts and is located above the photosphere. These parts are the chromosphere, the transition region and the corona. The outer boundary of the corona is not well-defined but more hackly structured. The atmosphere itself is not stable. It emits a particle flow called solar wind. This was first demonstrated by E. N. Parker in 1958 ([4]). One year after Parker’s predictions it was measured by Lunik II, one of the first Soviet satellites. The US Venus probe Mariner 2 analysed the particles afterwards more precise and studied the number density, the different velocities of the particles and the magnetic field strength between the Earth and Venus, which is about 5 10 9 T · − in average. This weak magnetic field is directed almost parallel to the ecliptic plane. The 2 B 11 3 related energy density in the solar wind yields to Umag = 2µ0 = 10− Jm− . The direction of the interplanetary magnetic field lines frozen-in in the solar wind is not radial due to the rotation of the sun. The sidereal rotation period of the sun is 27 days. Directly at the outer boundary of the sun the solar wind flows radially away from its origin. But then the plasma circles westward and forms an Archimedian spiral. The deformation of the field lines is known as the garden-hose effect ([1]). This shape of the field lines and therefore also of the solar wind is not as steady-going in reality as it was described. There are several reasons, which would cause this deviation. One factor might be the different velocities of the streams of the solar wind. But also a change in the polarity of the interplanetary magnetic field seen from a position, which is not rotating with the sun, caused by the sector structure of the magnetic field of the sun. Another reason could be that coronal mass ejections (CMEs) or co-rotating interaction regions (CIRs) produce shocks, which generate discontinuities themselves. There is also a forth influence that should be named. Alfv´en waves originated by the sun could be a reason for the discontinuities, plasma waves and magneto-hydrodynamic waves with low frequencies, which are causing fluctuations. Those have an influence on the magnetic field described above due to superposition ([5]). The solar wind itself consists roughly of an equal number of protons and electrons, also of some heavier ions. These particles travel from the Sun with supersonic velocities and carry away a mass of 1.6 1012 g/s. There are two distinct kind of plasma flow. One is called the fast solar · wind and the other one is called the slow solar wind. The first type has a speed of 400 km/s to 800 km/s and is generated in the so called coronal holes, the dark parts of the corona, which are dominated by open field lines. From these holes open field lines extend, which cannot restrict the speed of the solar wind. In contrast the speed of the second type is only 250 km/s to 400 km/s whereas the density of the slow solar wind is with 8 ions/cm3 higher than the one of the fast solar wind, which is only about 3 ions/cm3 at 1 AU. If there is a solar minimum the slow solar wind comes from regions at the magnetic equator of the sun but during a solar maximum it originates in the streamer belt as it is described in [1]. The coronal streamer belt is limited to a small region of about 20 degrees around the equator. The speed is limited by the closed ± magnetic field lines to which this type of the solar wind is associated to ([6], [7]). One effect on the interplanetary magnetic field emerging from the occurrence of the two different types of the solar wind can be depicted with picture 1.1. As it can be seen in the illustration the sun rotates counterclockwise. Therefore the Archmedian spiral arises. The arrows specify the velocity of 2 1.1. Basic principles 1.1.2 the solar wind. Due to the different velocities of the two types at the transition from the slow solar wind to the fast one a rarefaction of the plasma occurs while a compression results from the approach of the fast one with the slower type.
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