## Introducción a la espectropolarimetría solar

##### Author

Bonilla Mariana, Iván##### Date

2022##### Abstract

The first part of this report contains an introduction to what the Sun is like.
It reviews both the structure of the Sun (using the Standard model, it is formed
by 7 layers: the core, the radiative zone, the convective zone, the photosphere,
the chromosphere, the solar corona and the heliosphere) and the existence of
magnetic structures like the solar flares and the coronal mass ejections.
Later, the radiation field and the magnitudes that define it are described, as
well as the radiative transfer equation (RTE), and the main approximations
that usually are applied.
Then we talk about the mechanisms of formation of spectral lines and the
broadenings mechanisms, responsible of its shape which is a Voigt profile (or
function) resulting from three mechanisms: the natural broadening (which can
be ignored), the Doppler broadening (the most important) and the collisional
broadening. Additionally we speak about the polarization of light. For that the
Stokes parameters are presented and the radiative transfer equation for Stokes
parameters is written.
Later we see the Zeeman effect and how this effect produces polarization. Then
we describe the different approaches that are made to be able to solve the RTE,
among them, the most important for this work is the Milne-Eddington approximation in which, in order to obtain an analytical solution of the RTE in the case
of polarized light, it is imposed that the absorption matrix is constant with the
optical depth (which implies that all magnitudes will be constant with depth,
such as the magnetic field vector, the component of the velocity along the line of
sight and also the parameters that define the line, such as its intensity, Doppler
width and damping). Furthermore, it is necessary to assume that the source function (the ratio of emission to absorption) is a linear function of optical depth.
Making this approximation we get an analytical solution of the Stokes parameters (the Unno-Rachkovsky equations) as a function of the parameters that
define the line (such as the wavelength or the quantum numbers of the levels
involved in the bound bound transition) and of 9 free parameters: the two that
define the source function; the three that define the magnetic field; the one that
defines the velocity along the line of sight; the one that defines the strength of
the line; and finally the two that define the broadening of the line.
In this work, a python program has been designed and written that allows us
calculating the profiles of the Stokes parameters once the parameters that define
the spectral line are known, for any set of values of the 9 free parameters. It has been verified that the program has no errors and then the behavior of the
spectral lines has been studied by varying each of these 9 parameters independently.
In the final part of the memory, some data observed by the Hinode satellite
in a spot near the center of the Sun has been read and represented. The data
consists on a cube of 512x512 pixels observed in the 4 Stokes parameters along
112 wavelengths that include two spectral lines of Fe I around 6300 A.
Finally, some of these pixels have been chosen and their Stokes spectra have
been compared with those synthesized with our program.