RT info:eu-repo/semantics/masterThesis
T1 Determinación de los parámetros físicos de estructuras magnéticas solares
A1 Díaz Suárez, Sergio
A2 Máster Universitario en Astrofísica
K1 Astrofísica
AB The Sun is the nearest star for us. It is an almost perfect sphere of magnetizedplasma which emits radiation constantly and it is fundamental for the existence anddevelopment of life on Earth but at the same time, it can be a threat because weare dependent on electricity and eventually a solar storm could destroy our infrastructures,leaving us without access to technology, so it is important to understandhow the Sun is and predict its behaviour.In this Master thesis, we will focus on obtaining the thermodynamic and magneticconditions from the polarized light, that is to say from the Stokes parameters.We will use not only simulated conditions but real data from the solar photosphere,which is the nearest layer to the Sun’s surface. In order to do this, we will talkabout the Stokes parameters and about the Radiative Transfer Equation for fullPolarized Light. After that, we will solve this equation under the Milne-Eddingtonapproximation and we will explain its analytical solution. However, this isn’t theonly way to obtain a solution. In fact, nowadays this equation is solved numericallybecause when we consider the dependence of parameters with optical depth thereis not analytical solution although there are several programs to study the low atmosphereof the Sun like SIR, which we will explain how it works and its advantagesand disadvantages.To make this possible, once we have seen how analytical solution of the RadiativeTransfer Equation for full Polarized Light are, we will explain the method tosynthesize under the Milne-Eddington approximation or in other words, how to obtainthe Stokes parameters from 9 free parameters. These parameters are S0 and S1which are the associated coefficiens to the source function. η is the ratio betweenthe absorption on the line and on the continuum. a is the damping adimensionalizedparameter whereas wm is the line of sight velocity of the medium. Respect to ∆λD,B, θ and χ, they are the Doppler broadening in wavelength units, the intensity ofthe magnetic field in Gauss, the inclination of the magnetic field respect to the lineof sight in degrees and the azimuth of the magnetic field also in degrees. We willparticularize for the spectral line of Fe I at 6301.5 ˚A and maintaining an initial setconstant, we will change each parameter to observe and explain what happens. Usingthis method, we will study what occurs when we vary the intensity of magnetic field, the inclination of the magnetic field respect to the line of sight and its azimuth.After that, we will build up the response functions. Under the Milne-Eddingtonhypothesis, we will show you that the response functions are analytical and are thefirst derivative of Stokes parameters respect to the free parameters of the MilneEddingtonapproximation. In any case, we will also check these analytical responsefunctions by using a central difference method. Nevertheless, the response functions,numerical or analytical, tell us how Stokes parameters change because of linearperturbations on the parameters which we use for synthetizing the Stokes profiles.Now, in order to achieve the inversion of an observed Stokes profile under theMilne-Eddington approximation, one must introduce to the program a set of MilneEddingtonparameters to synthesize the Stokes parameters, compare between theobserved and synthetic Stokes profiles and change iteratively the parameters untila good fit is achieved. As the Radiative Transfer Equation for full Polarized Lightis not lineal, we have to do it iteratively until the difference between the observedand synthesized Stokes profiles are minimum or specifically, until χ2is minimum. Fortunately, there are algorithms to make non-linear fits from which LevenbergMarquardtalgorithm is selected for being standard and giving excellent results. Asa test, we can substitute the observed profile by a synthetic Stokes profile plus anoise. Applying our inversion code to this profile, we can check the behaviour of ourcode. In practice, we will use first a synthetic Stokes profile without noise to obtainthe 9 free parameters and later, the same profile but noise is added. However, inboth cases, we will simulate the spectral line of Fe I at 6301.5 ˚A.In addition to this, we are going to apply our Milne-Eddington inversion code onreal spectropolametric data, which are Stokes profiles versus wavelength. Particularly,we are going to use it on a granule near to the active region NOAA 10953which was observed by HINODE in 2007. But now, we are going to invert the line ofFe I at 6302.49 ˚A instead of the line of Fe I at 6301.5 ˚A because the first one is moresensitive to magnetic field as we will see. At the same time, we are going to compareour results from Milne-Eddington inversion code with those from SIR, whichdoesn’t have problems to invert multiple spectral lines simultaneously, and we willexplain why both programs agree with the values of magnetic field or the inclinationof magnetic field. Here, we will see the fundamental disadvantage of maintaining thequantities constant with optical depth because a Milne-Eddington inversion codecan’t explain the asymmetries on Stokes profiles or the ascent and the descent ofplasma in photospheric layers of granules. In addition to this, our Milne-Eddington inversion code can be used only for one spectral line whereas SIR inverts multiplespectral lines at the same time.Last of all, we are going to obtain the maps of temperature, microturbulence,velocity along the line of sight, intensity of magnetic field, inclination and azimuth of magnetic field for a section of the before mentioned active region, which includesthe quiet Sun, and a part of a sunspot with its penumbra and its umbra. Thosewill be obtained with SIR and we will discover that the values are concordant withthe literature. Also we will obtain the map of temperatures at a top layer and wewill check that this quantity decreases with height, which is expected in the solarphotosphere and we will relate the intensity of magnetic field to the temperature forthe different structures which appear on the section of the before mentioned activeregion.
YR 23/1
FD 23/11/2018 10:50
LK http://riull.ull.es/xmlui/handle/915/11595
UL http://riull.ull.es/xmlui/handle/915/11595
LA es
DS Repositorio institucional de la Universidad de La Laguna
RD 26-abr-2024