Sunspots are the most evident manifestations of solar magnetism, and oscillations are a fundamental physical process taking place in them. Despite the efforts over the last 50 years, a global picture about sunspot oscillations remains elusive. This project aims to perform a thorough analysis of sunspot waves, from the solar interior to the chromosphere. This goal will be addressed from a multidisciplinary approach, combining forward modeling, local helioseismology, ground- and space-based observations, plasma diagnostic methods, and machine learning.
Internal layers of stars are opaque to radiation and, therefore, inaccessible by optical imaging. Seismology offers a unique approach to analyze the solar interior, but significant disagreements still exist regarding the interpretation of helioseismic data in active regions due to the complexity of wave interactions with magnetic fields. One of the main objectives of this project is the development of a novel methodology to infer the subsurface structure of sunspots. Traditional approaches try to infer the interior of active regions by solving an inverse problem that recovers the subsurface solar stratification from travel-time measurements. However, inversions to date require the use of several assumptions:

1) the direct effect of the magnetic field is neglected;

2) sunspots are considered as weak perturbations; 

3) flows and sound speed changes are the only factors that generate the observed effects.

Neither of these assumptions holds for sunspots. Nowadays, there is a strong consensus that travel-time inversions do not reveal the true subsurface structure of sunspots.

We propose to develop a new technique that can bypass the limitations of current inversion methods. A neural network will be trained with the results of a large set of numerical simulations. It will associate the travel-time measurements with the properties of the sunspot interior. The main advantage of this approach is that it uses the solution of the full magnetohydrodynamics equations and, thus, it takes into account all the relevant physical processes.
In this project we will also address several unsettled questions about wave propagation at atmospheric heights. Sunspot waves are driven by external p-modes and/or by in-situ magnetoconvective motions. They show different manifestations at the umbral atmosphere, including oscillations with 5 minute period at the photosphere, 3 minute period at the chromosphere, and umbral flashes. However, a clear picture about the origin and nature of all these phenomena is still missing. There are several competing scenarios trying to explain the change in the wave period from the photosphere to the chromosphere, and all of them have recently found observational support. In addition, recent works have identified magnetic field oscillations and downward velocity flows associated to umbral flashes. These findings are in conflict with the most accepted model for umbral flashes, which considers that they are produced by the upward propagation of slow mode shock waves.

Our research team and working group have a broad experience in the study of waves in the internal layers of the Sun and the atmosphere. In this project we aim to link these two lines of research and perform a comprehensive study of the global process of wave propagation in sunspots. This goal will be accomplished by fostering the interaction of local helioseismic analyses, forward modeling, and spectropolarimetry.