## Síntesis de líneas espectrales de simulaciones numéricas de magnetoconvección

##### Date

2021##### Abstract

Nowadays, the studies carried out by the Sun are diverse and their purpose is simple: having a
better aknowledgement of our star.
Spectroscopy and spectropolarimetry are the most important observational techniques in this
field of Astrophysics, but in our case we will not use observational data. We will take a numerical
simulation of the Sun and we will compare the data provided by it with those obtained through
the observations to know how accurate is the simulation.
Studies of the Sun by numerical simulations provides numerous advantages. One of the most
important is that it allows to identify physical processes that occur there. When the synthetic
spectrum of the simulation is obtained, it is compared with those obtained with the observations,
but, previously, we have to ad the imperfections introduced by the telescope or spectrograph in
the data. If the comparison with the observations is good, we can infer that the properties and
phenomena given in the simulation occur as well in the Sun. Then we have the option to reproduce
this phenomenon every time we want and change it to study other posibilities.
In the presence of magnetic fields, the lines suffer modifications due to splitting of the energy
levels, resulting new transitions. This is known as the Zeeman effect. When the magnetic field
is weak (the splitting is lower than the width of the line), it may not have visible effects on the
intensity profiles. However we can see changes in the circular polarization profiles. This case is
characterized by the weak field equation, which is the solution of the radiative tranfer equation
(RTE) under these conditions. This is why under weak field conditions we do not obtain the
information of the field from the intensity profiles, we do it from the circular polarization profiles.
In this work we will synthesize the Fe 5247Å, 5250Å, 6173Å, 6301Å, 6302Å, 15648Å, 15652Å
lines from a simulation of the quiet Sun. The simulation will contain the values of magnetic field
components, speed or temperature in each point. We will have to do an interpolation to get a model
that is equidistant in tau on a logarithmic scale, instead of being equidistant in height. After this,
we will give the model to SIR and it will carry out the synthesis and it will return us the intensity,
linear polarization and circular polarization profiles.
SIR perform the synthesis solving the radiative transfer equation for τ = τ5 (optical depth
of the continuum at 5000Å), using a Hermite algorithm. It also works under conditions of Local
Thermodynamic Equilibrium (which allows to use Saha’s and Botzmann’s equation to compute
the populations) in order to calculate the absorption matrix and the source function. SIR assume
Hydrostatic Equilibrium in each iteration.
We will only work with circular intensity and polarization profiles since the simulation will
fulfill the weak field regime and there is no linear polarization. For the former, For Stokes I, we
will make a study of the displacement of the lines which will give us an estimation of the material
velocity at each point using the Doppler effect formula. Comparing with the intensity of the continuum, we see that for the intergranular lanes we obtain positive speeds (descending material)
whose absolute value is greater than the ones for granular zones, where we obtain negative speeds
(ascending material). This is because the gravity action support the descending movement while,
in the ascending one, it goes against.
We also do a study of the bisector of the lines but, in this case, we make a separation between the
intergranular lanes and granular areas. This separation is done using the intensity of the continuum.
We will calculate the mean value and defining the granules as those areas which exceed a sigma
of this average value. The intergranular lanes are defined as the areas which has associated an
intensity lower or equal than one sigma of the mean value. We obtain for the granules a bisector
that is blueshifted, as is expected, since as we have said, the speeds are negative, while for the
intergranular lanes, the bisector is redshifted (positive velocities).
To finish with this part, we will calculate the spatial average of the intensity profiles and
compare it with the lines of the atlas, obtaining a fairly similar fit with all lines.
Now, for the circular polarization profiles (Stokes V ), we will calculate their amplitudes and
asymmetries. Previously we will make a classification of all profiles and we will choose for the study
only those whose class will be 1, 2, or 3, according to this classification. We generate amplitude
histograms where we can see that for the seven lines most of the profiles have amplitudes between
0.001 and 0.01.
We have made an analysis of the amplitude and area asymmetries and with them we will
determine the gradients of speed and magnetic field. If we have very asymmetric profiles, these
gradients will be larger because they tend to cause a deformation in the circular polarization. On
the contrary, if they are not very asymmetric we will know that the gradients are smaller. We
found the first case in the higher energy visible lines because they are formed at higher altitudes,
while for infrared lines we have smaller asymmetries, because its formation occurs closer to the
continuum.
We will also calculate the spatial average of the circular polarization profiles and we study if
we are in a weak field regime. In order to do this, we will look for the proportionality coefficient
between the average Stokes V and the derivative of the average intensity minimizing residuals. If
we represent both, we can see that we are in a weak field regime since both profiles are proportional.
Some lines, specially infrared ones, are at the limit of the approach, but it is considered that, even
in the limit, we are in weak field regime. Using this comparison, we will calculate the average of
the longitudinal magnetic field and comparing it with the obtained from the simulation, we are
going to make an estimation of the height where the lines are formed.
Finally, using the classification that we have done previously, we will take the infrared lines
and we will do a study of the classes with the amplitude and with the intensity of the continuum.
From the first one, we conclude that the classes with a higher frequency predominate the larger
amplitudes and as they become less frequent, they are more significant at lower amplitudes. From
the study of the continuum we find that the most frequent class predominates in the granules
(higher intensities), the next one abounds in intergranular lanes (lower intensities) and the rest is
present everywhere.