Recipe for inferring sub-surface solar magnetism via local mode-coupling using Slepian basis functions

Abstract

Direct seismic imaging of sub-surface flow, sound-speed and magnetic field is crucial for predicting flux tube emergence on the solar surface, an important ingredient for space weather. The sensitivity of helioseismic mode-amplitude cross-correlation to $p$- and $f$-mode oscillations enable formal inversion of such sub-photospheric perturbations. It is well-known that such problems are written in the form of an integral equation that connects the perturbations to the observations via ``sensitivity kernels". While the sensitivity kernels for flow and sound-speed have been known for decades and have been used extensively, formulating kernels for general magnetic perturbations had been elusive. A recent study proposed sensitivity kernels for Lorentz-stresses corresponding to global magnetic fields of general geometry. The present study is devoted to proposing kernels for inferring Lorentz-stresses as well as the solenoidal magnetic field in a local patch on the Sun via Cartesian mode-coupling. Moreover, for the first time in solar physics, Slepian functions are employed to parameterize perturbations in the horizontal dimension. This is shown to increase the number of data constraints in the inverse problem, implying an increase in the precision of inferred parameters. This paves the path to reliably imaging sub-surface solar magnetic features in, e.g., supergranules, sunspots and (emerging) active regions.

arXiv comment18 pages, 5 figures; Accepted for publication in the Astrophysical Journal

References in corpus (29)

• The Helioseismic and Magnetic Imager (HMI) Vector Magnetic Field Pipeline: Overview and Performance
• Radiative MHD simulation of sunspot structure
• Solar Interior Rotation and its Variation
• Magneto-convection in a sunspot umbra
• Numerical sunspot models: Robustness of photospheric velocity and magnetic field structure
• Spherical Slepian functions and the polar gap in geodesy
• MHD simulations of penumbra fine structure
• Solar supergranulation as a wavelike phenomenon
• Penumbral fine structure and driving mechanisms of large-scale flows in simulated sunspots
• Magneto-acoustic waves in sunspots: first results from a new 3D nonlinear magnetohydrodynamic code
• Helioseismology of Sunspots: A Case Study of NOAA Region 9787
• Modeling the Subsurface Structure of Sunspots
• Helioseismology of Sunspots: Confronting Observations with Three-Dimensional MHD Simulations of Wave Propagation
• Subsurface magnetic field and flow structure of simulated sunspots
• Spatiospectral concentration in the Cartesian plane
• Numerical simulations of sunspot decay: On the penumbra -- Evershed flow -- moat flow connection
• Seismic Halos Around Active Regions: An MHD Theory
• Helioseismic Probing of Solar Variability: The Formalism and Simple Asses sments
• Constructing semi-empirical sunspot models for helioseismology
• Helioseismology of sunspots: how sensitive are travel times to the Wilson depression and to the subsurface magnetic field?
• Evidence for Large-Scale Subsurface Convection in the Sun
• The Effect of Toroidal Magnetic Fields on Solar Oscillation Frequencies
• Evolution and wave-like properties of the average solar supergranule
• Characterization of magneto-convection in sunspots -- The Gough & Tayler stability criterion in MURaM sunspot simulations
• Measurement process and inversions using helioseismic normal-mode coupling
• Sensitivity kernels for inferring Lorentz stresses from normal-mode frequency splittings in the Sun
• The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element
• Analyzing supergranular power spectra using helioseismic normal-mode coupling
• Imaging the Sun's near-surface flows using mode-coupling analysis