RT info:eu-repo/semantics/masterThesis
T1 Estudio de las propiedades de las ondas en simulaciones de magneto-convección
A1 Larrodera Baca, Carlos
A2 Máster Universitario en Astrofísica
K1 Astrofísica
AB The study of the sun was based on the analysis of images obtained using groundbased telescopes and, later, using space based telescopes. Through these images wecould analyze the observed structures (for example, sunspots), or also the polarizationof the sun light using spectropolarimeters. Over the years, the telescopes and the toolsfor the analysis have been improving looking for a better spatial resolution and magneticfield sensitivity, allowing to solve the smallest structures observed to better determinetheir characteristics.The theoretical framework was developed, leading to the equations which define themovement, and its properties, of a plasma with a magnetic field, to result in the magnetohydrodynamicsequations or MHD equations. This theoretical framework showed theexistence of unknown features, like Alfv´en waves or the transformation between waveswhen passing through the equipartition layer with β=1. It was this frame, togetherwith the computer development, which allowed the growing of the numerical simulations,which are able to solve the MHD equations to simulate the behavior of the sunand reproduce the observed structures.(Sec:2)In this work we have analyzed the result of a simulation made with the MANCHA3D code (Khomenko & Collados, 2006), who solved the MHD equations with a realisticequation of state and radiative transfer in a grey atmosphere. The domain of the simulationcovers 5, 8 × 5, 8 × 1, 6 Mm3, located in such a way that the z axis covers from adepth z=0,95 Mm below the surface to z=0,62 Mm above it.In the article that describes the simulation, Khomenko et al. (2017) analyze a modelbased on the action of the Biermann battery effect. This effect generates a magneticfield due to the local imbalance of the electronic pressure in the partially ionized solarplasma. It is shown that the battery effect by itself is able, to create a seed magneticfield with a strength around µG, and together with the amplification of the dynamomechanism, they allow the generation of a magnetic field with an average strengthsimilar to that obtained from the observations. The generated magnetic field represents,the distribution of the quiet sun with a average value of < B >= 100 G. During thesimulation, one 3D snapshot has been saved each 0,4 s, with a total time of 79 s. Thegrid has 20 km horizontally and 14 km vertically, with dimensions of 5, 8 × 5, 8 × 1, 6Mm3, creating 199 data cubes with a size of 180 GB.The importance of this type of simulations is the high frequency of saving the snapshots,in this case each 0,4 s, which allow to study the behavior of the waves in theinterval between 100-200 mHz, while observations currently only reach up to 10-20mHz. This type of waves have the property that they are not affected by the acousticcut-off frequency, so they can spread to the upper layers of the atmosphere. Becausethey have a shorter wavelength, the theoretical models that are generally based onhomogeneous or slightly stratified situations serve better to explain their behavior.The analysis of the data has been based on the study of the compressible and incompressiblewaves at a given height of z=0,31 Mm above the surface to avoid thecontamination by the convection, through the Fourier temporal transform of ∇ × ~ ~vand ∇ · ~ ~v as representative magnitudes of the compressible and incompressible wavesrespectively. We have also analyzed the relation between these magnitudes and the physicalmagnitudes such as the magnetic field strength (B~ ), temperature (T) and azimuth(φ) in order to establish possible phase differences, useful to localized these kind ofwaves.(Sec:3)The simulation represents a region below and above the surface. With the data, wehave calculated the value of β for the height of study and also in the surface, and inboth layers, using a histogram we can see that the value of β is much greater than1.(Sec:2.4)All the analysis has been carried out in two different intervals of frequency, low andhigh, (0,013-0,1 Hz y 0,11-0,2 Hz), chosen in such a way that there is a complementarityin temporal power, so that the distribution of power in the low frequency range isanticorrelated with the power in the high frequency range.(Sec:4.1)In the study of power maps, we have shown that the temporal evolution of theincompressible waves is defined by the fluctuation of the magnetic tension, but forthe compressible waves the representative magnitude is the fluctuation of the totalpressure.(Sec:4.2)In the last part, we have studied the differences between the phases of the Fouriertransform of ∇ × ~ ~v and ∇ · ~ ~v, and those of B~ , T and φ. With this analysis, we wantto determine which phase difference may be most useful to determine the existence ofone or other kind of waves. So, for example if we want to study the differences betweenthe compressible waves and the temperature, we begin by analyzing the difference inall the points of the maps of power distribution (from now on we call it “Total”case).Then we select those points where the power is larger than a threshold in both mapsto obtain the most representative points. We call this the “Mask”case.For the low frequencies, the magnitude that can serve as an indicator of waves is thetemperature. For the phase shift ΦI − ΦT , the histograms in both cases, “Mask”and“Total”, appear to be most different. For the high frequencies, this method seems moreeffective and we obtained results which are different from zero, not only with T, butalso with B~ and φ. In the “Mask”case, for the phase shift ΦI − ΦB, the histogram hastwo peaks around -30o and 40o, and in the one of ΦC − ΦB, 3 peaks appear at -80o,0oand 70o. When comparing with φ, is representative the histogram of the phase shiftΦC − Φφ in the “Total”case, where a peak appears in the positive part (around 20o)and a tail in the negative part, and when we study the “Mask”case, both characteristicsare reinforced. And for the comparison with T, we obtained significant differences in the“Total”case for both phase shift histograms, ΦI −ΦT and ΦC −ΦT . In the “Mask”case,the peak for the histogram of ΦI − ΦT is reinforced around 80o, while the phase shiftΦC − ΦT unfolds into two peaks, one near 0o and the other around 110o(Sec:4.3).
YR 2018
FD 2018
LK http://riull.ull.es/xmlui/handle/915/10860
UL http://riull.ull.es/xmlui/handle/915/10860
LA es
DS Repositorio institucional de la Universidad de La Laguna
RD 19-abr-2024