Spectral Analysis of Large-Scale Solar Flows and Surface-Convection

Vigorous turbulent convection near the solar surface excites acoustic waves that propagate through the solar interior and form a large discrete set of resonant modes. High-precision measurements of these modes have been carried out for decades, enabling the imaging of the solar interior using helioseismology. Flows and deviations from purely radial stratification act as perturbations that modify these modes. Global helioseismic normal-mode coupling promises to be a modern tool that enables the estimation of all physical perturbations such as flows, structure and magnetic fields. Differential rotation, the dominant global-scale axisymmetric perturbation, which plays a crucial role in modulating the large-scale solar magnetic field, has been tightly constrained primarily using measurements of mode-frequency splittings. However, the frequency-splitting formalism invokes the approximation that modes are isolated, which becomes increasingly inaccurate for modes at high angular degrees. Such modes dominantly propagate in the shallow depths near the surface, thereby influencing the inferences of structure and rotation in this region. While the effects of coupling have been estimated to be reasonably small through analytical estimates, a full-blown analysis of the inaccuracy of the assumption was impracticable due to prohibitively expensive computing and can be historically attributed to legacy computing architecture, limited memory and inefficient algorithms. Using modern computing architecture with a massive memory bandwidth, we set up a parallel computation on large HPC compute nodes, to analyse eigenfunction corrections, which respect cross-coupling of modes across multiplets. A successful estimation of differential rotation establishes the method of normal-mode coupling as a valid probe for measuring large-scale flows, internal structure and dynamics. We show that, surprisingly, if structure perturbations are ignored, mode-coupling does not affect the inference of rotation. Consequently, we also demonstrate that, at shallow depths, mode-coupling breaks the selections rules that enabled a simple disentangling of flows, structure and magnetic fields from observations, highlighting the need for a simultaneous estimation of all these features. We also propose a framework for the measurement of meridional circulation through mode-coupling which is enabled by our modelling of the Center-to-Limb systematic.