Estimating Electric Fields from Vector Magnetogram Sequences

TL;DR

This paper presents methods to estimate the solar photospheric electric field from vector magnetogram sequences using Faraday's Law, addressing the ill-posed inversion problem with PTD, iterative, and variational techniques, validated on synthetic and real data.

Contribution

It introduces a novel combination of PTD, iterative, and variational methods to accurately estimate electric fields from magnetogram data, improving upon previous approaches.

Findings

PTD, iterative, and variational methods produce consistent E-field estimates.

The techniques successfully recover known electric fields from synthetic data.

Application to real data demonstrates practical utility in solar physics.

Abstract

Determining the electric field (E-field) distribution on the Sun's photosphere is essential for quantitative studies of how energy flows from the Sun's photosphere, through the corona, and into the heliosphere. This E-field also provides valuable input for data-driven models of the solar atmosphere and the Sun-Earth system. We show how Faraday's Law can be used with observed vector magnetogram time series to estimate the photospheric E-field, an ill-posed inversion problem. Our method uses a "poloidal-toroidal decomposition" (PTD) of the time derivative of the vector magnetic field. The PTD solutions are not unique; the gradient of a scalar potential can be added to the PTD E-field without affecting consistency with Faraday's Law. We present an iterative technique to determine a potential function consistent with ideal MHD evolution; but this E-field is also not a unique solution to Faraday's Law. Finally, we explore a variational approach that minimizes an energy functional to determine a unique E-field, similar to Longcope's "Minimum Energy Fit". The PTD technique, the iterative technique, and the variational technique are used to estimate E-fields from a pair of synthetic vector magnetograms taken from an MHD simulation; and these E-fields are compared with the simulation's known electric fields. These three techniques are then applied to a pair of vector magnetograms of solar active region NOAA AR8210, to demonstrate the methods with real data.