Estudio de las propiedades de las ondas en simulaciones de magneto-convección

Abstract

The study of the sun was based on the analysis of images obtained using ground based telescopes and, later, using space based telescopes. Through these images we could analyze the observed structures (for example, sunspots), or also the polarization of the sun light using spectropolarimeters. Over the years, the telescopes and the tools for the analysis have been improving looking for a better spatial resolution and magnetic field sensitivity, allowing to solve the smallest structures observed to better determine their characteristics. The theoretical framework was developed, leading to the equations which define the movement, and its properties, of a plasma with a magnetic field, to result in the magnetohydrodynamics equations or MHD equations. This theoretical framework showed the existence of unknown features, like Alfv´en waves or the transformation between waves when passing through the equipartition layer with β=1. It was this frame, together with 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 sun and reproduce the observed structures.(Sec:2) In this work we have analyzed the result of a simulation made with the MANCHA 3D code (Khomenko & Collados, 2006), who solved the MHD equations with a realistic equation of state and radiative transfer in a grey atmosphere. The domain of the simulation covers 5, 8 × 5, 8 × 1, 6 Mm3 , located in such a way that the z axis covers from a depth 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 model based on the action of the Biermann battery effect. This effect generates a magnetic field due to the local imbalance of the electronic pressure in the partially ionized solar plasma. It is shown that the battery effect by itself is able, to create a seed magnetic field with a strength around µG, and together with the amplification of the dynamo mechanism, they allow the generation of a magnetic field with an average strength similar 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 the simulation, one 3D snapshot has been saved each 0,4 s, with a total time of 79 s. The grid has 20 km horizontally and 14 km vertically, with dimensions of 5, 8 × 5, 8 × 1, 6 Mm3 , 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 the interval between 100-200 mHz, while observations currently only reach up to 10-20 mHz. This type of waves have the property that they are not affected by the acoustic cut-off frequency, so they can spread to the upper layers of the atmosphere. Because they have a shorter wavelength, the theoretical models that are generally based on homogeneous 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 incompressible waves at a given height of z=0,31 Mm above the surface to avoid the contamination by the convection, through the Fourier temporal transform of ∇ × ~ ~v and ∇ · ~ ~v as representative magnitudes of the compressible and incompressible waves respectively. We have also analyzed the relation between these magnitudes and the physical magnitudes such as the magnetic field strength (B~ ), temperature (T) and azimuth (φ) in order to establish possible phase differences, useful to localized these kind of waves.(Sec:3) The simulation represents a region below and above the surface. With the data, we have calculated the value of β for the height of study and also in the surface, and in both layers, using a histogram we can see that the value of β is much greater than 1.(Sec:2.4) All the analysis has been carried out in two different intervals of frequency, low and high, (0,013-0,1 Hz y 0,11-0,2 Hz), chosen in such a way that there is a complementarity in temporal power, so that the distribution of power in the low frequency range is anticorrelated 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 the incompressible waves is defined by the fluctuation of the magnetic tension, but for the compressible waves the representative magnitude is the fluctuation of the total pressure.(Sec:4.2) In the last part, we have studied the differences between the phases of the Fourier transform of ∇ × ~ ~v and ∇ · ~ ~v, and those of B~ , T and φ. With this analysis, we want to determine which phase difference may be most useful to determine the existence of one or other kind of waves. So, for example if we want to study the differences between the compressible waves and the temperature, we begin by analyzing the difference in all 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 maps to 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 the temperature. 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 more effective and we obtained results which are different from zero, not only with T, but also with B~ and φ. In the “Mask”case, for the phase shift ΦI − ΦB, the histogram has two peaks around -30o and 40o , and in the one of ΦC − ΦB, 3 peaks appear at -80o ,0o and 70o . When comparing with φ, is representative the histogram of the phase shift ΦC − 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 characteristics are 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 shift ΦC − ΦT unfolds into two peaks, one near 0o and the other around 110o (Sec:4.3).