European Research Council Starting Grant

This project is funded by the **European Research Council**
through a 2007 Starting Grant.

The broad science objective of the project is to search for the root causes of solar magnetic activity by establishing physical relationships between internal solar properties and the various component of magnetic activity in the solar interior and atmosphere.

The physical processes inside the Sun are best studied with heliosesimology, i.e. the observation and interpretation of the solar seismic waves. Helioseismology is on the verge of a revolution with (1) the development of new techniques of data analysis and interpretation and (2) forthcoming observations by NASA's Solar Dynamics Observatory (SDO). SDO, scheduled for launch in 2009, represents a major technological step beyond the ESA/NASA Solar and Heliospheric Observatory (SOHO): higher spatial resolution, higher duty cycle, and a complete view of the solar disk and the corona.

The Sun is filled with seismic waves exscited by near-surface turbulent convection. These waves have periods in the range 2-10 minutes and can be recorded from the ground or from space by measuring motions on the solar surface. Two types of waves are used to probe the solar interior: acoustic waves (p modes) and surface-gravity waves (f modes).

Local helioseismology includes time-distance helioseismology (Duvall et al. 1997), which is the focus of the proposed work. The goal of time-distance helioseismology is to infer the three-dimensional structure of the solar interior using measurements of the travel times of seismic wave packets propagating between any two surface points through the Sun's interior. Travel times are measured with a cross-correlation technique. A travel-time measurement contains the seismic signature of buried inhomogeneities situated in the vicinity of the geometrical ray path of the wave packet. Different types of perturbations have different signatures. For instance, a flow will break the symmetry in travel time for waves propagating in opposite directions: waves move faster along the flow than against it. Time-distance helioseismology is the art of interpreting wave travel times in order to learn about flows, temperature, density, and other physical quantities inside the Sun.

Under the assumption that subsurface inhomogeneities are weak, it is possible to write a linear relationship between travel-time measurements and internal solar properties. This linear relationship is given by three-dimensional sensitivity kernel functions. We have developed the tools to compute travel-time sensitivity kernels for sound-speed perturbations and vector flows, using a single-scattering approximation (Gizon and Birch 2002, Birch and Gizon 2007). Because of finite-wavelength effects, kernel functions extend far beyond the theoretical ray path (as was shown first in terrestrial seismology). Sensitivity kernels, however, have not yet been computed for density, temperature, first adiabatic exponent, and weak magnetic perturbations. Without the kernels, we cannot have a proper understanding of the travel times or the subsurface structure of the Sun. An important objective of SISI is to compute sensitivity kernels to account for the effects of all types of physical perturbations.

The linear problem is quite well understood: solve a linear system of equations to retrieve the solar internal properties from the measurements. We have developed a linear inversion procedure, known as optimally localized averaging (Jackiewicz et al. 2007). This procedure has been successful in estimating the vector flows in the shallow subsurface layers. As the kernels for the other physical quantities become available, they will be incorporated into the inversion procedure. With the increasing number of sensitivity kernels, the inversion problem will grow dramatically and efficient algorithms will be required.

Unlike in the case of convective flows, the effect of the magnetic field on solar waves cannot be considered to be small near the solar surface. In sunspots, for example, the nature of waves is dramatically altered as they convert into magneto-acoustic waves. Such interactions cannot easily be studied using first-order perturbation theory and the procedures described above do not apply.

The best way to understand what is happening is through numerical modeling. We have recently developed a code, called SLiM (Semi-spectral Linear MHD), that computes the propagation of small-amplitude wave packets through a general 3D magnetized solar atmosphere (Cameron et al. 2007, 2008). SLiM has been tested and parallelized, and can be used to compute the seismic signature of model sunspots. The SISI compute cluster will provide the computational resources required to infer the main sunspot parameters within a few weeks of calculations. Over the time of the SISI project, we will be able to study a collection of sunspots.