Sensitivity kernels for inferring Lorentz stresses from normal-mode frequency splittings in the Sun

Abstract

Departures from standard spherically symmetric solar models, in the form of perturbations such as global and local-scale flows and structural asphericities, result in the splitting of eigenfrequencies in the observed spectrum of solar oscillations. Drawing from prevalent ideas in normal-mode coupling theory in geophysical literature, we devise a procedure that enables the computation of sensitivity kernels for general Lorentz stress fields in the Sun. Mode coupling due to any perturbation requires careful consideration of self- and cross-coupling of multiplets. Invoking the isolated-multiplet approximation allows for limiting the treatment to purely self-coupling, requiring significantly less computational resources. We identify the presence of such isolated multiplets under the effect of Lorentz stresses in the Sun. Currently, solar missions allow precise measurements of self-coupling of multiplets via "$a$-coefficients" and the cross-spectral correlation signal which enables the estimation of the "structure coefficients". We demonstrate the forward problem for both self-coupling ($a$-coefficients) and cross-coupling (structure coefficients). In doing so, we plot the self-coupling kernels and estimate $a$-coefficients arising from a combination of deep-toroidal and surface-dipolar axisymmetric fields. We also compute the structure coefficients for an arbitrary general magnetic field (real and solenoidal) and plot the corresponding "splitting function", a convenient way to visualize the splitting of multiplets under 3D internal perturbations. The results discussed in this paper pave the way to formally pose an inverse problem, and infer solar internal magnetic fields.

32 pages, 8 figures, Astrophysical Journal

References in corpus (29)

• Asteroseismology of Solar-Type and Red-Giant Stars
• Solar Interior Rotation and its Variation
• Prediction of the strength and timing of sunspot cycle 25 reveal decadal-scale space environmental conditions
• Changes in Solar Dynamics from 1995 to 2002
• Anomalously Weak Solar Convection
• Ring diagram analysis of near-surface flows in the Sun
• Helioseismology of Sunspots: A Case Study of NOAA Region 9787
• Turbulent small-scale dynamo action in solar surface simulations
• Helioseismology of Sunspots: Confronting Observations with Three-Dimensional MHD Simulations of Wave Propagation
• Efficient small-scale dynamo in solar convection zone
• A Comparative Study of Magnetic Fields in the Solar Photosphere and Chromosphere at Equatorial and Polar Latitudes
• Helioseismic Probing of Solar Variability: The Formalism and Simple Asses sments
• A Three-Dimensional Babcock-Leighton Solar Dynamo Model: Initial Results with Axisymmetric Flows
• Constructing semi-empirical sunspot models for helioseismology
• Using the Dipolar and Quadrupolar Moments to Improve Solar-Cycle Predictions Based on the Polar Magnetic Fields
• 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
• Sensitivity of Helioseismic Measurements of Normal-mode Coupling to Flows and Sound-speed Perturbations
• Modeling star-planet interactions in far-out planetary and exoplanetary systems
• Flows around Averaged Solar Active Regions
• The Effect of Toroidal Magnetic Fields on Solar Oscillation Frequencies
• Seismic probes of solar interior magnetic structure
• Seismic sensitivity of Normal-mode Coupling to Lorentz stresses in the Sun
• Moat flow system around sunspots in shallow subsurface layers
• The Direct Effect of Toroidal Magnetic Fields on Stellar Oscillations: An Analytical Expression for the General Matrix Element
• Solar Magnetic Fields
• On the magnetic field required for driving the observed angular-velocity variations in the solar convection zone
• Statistical analysis of acoustic wave power and flows around solar active regions
• Accurate Characterization of High-Degree Modes Using MDI Observations

Cited by in corpus (7)

• Unveiling complex magnetic field configurations in red giant stars
• Detectability of axisymmetric magnetic fields from the core to the surface of oscillating post-main sequence stars
• Inferring solar differential rotation through normal-mode coupling using Bayesian statistics
• Recipe for inferring sub-surface solar magnetism via local mode-coupling using Slepian basis functions
• Minuscule corrections to near-surface solar internal rotation using mode-coupling
• Asteroseismic detection of an internal magnetic field in the B0.5V pulsator HD 192575
• Magneto-Archeology of White Dwarfs. Revisiting the fossil field scenario with observational constraints during the red giant branch