Surface Flows From Magnetograms

TL;DR

This paper evaluates methods for estimating perpendicular surface flows from magnetogram data, crucial for understanding magnetic energy transfer in the solar atmosphere, by testing techniques on synthetic MHD simulation data.

Contribution

It compares the effectiveness of the induction equation's normal component and tracking methods in recovering perpendicular flows from magnetogram data using synthetic simulations.

Findings

Induction equation's normal component alone has limited ability to estimate flows.

Tracking methods can recover flow components perpendicular to B and along contours of Bz.

Synthetic MHD data provides a testbed for flow estimation techniques.

Abstract

Estimates of velocities from time series of photospheric and/or chromospheric vector magnetograms can be used to determine fluxes of magnetic energy (the Poynting flux) and helicity across the magnetogram layer, and to provide time-dependent boundary conditions for data-driven simulations of the solar atmosphere above this layer. Velocity components perpendicular to the magnetic field are necessary both to compute these transport rates and to derive model boundary conditions. Here, we discuss some possible approaches to estimating perpendicular flows from magnetograms. Since Doppler shifts contain contributions from flows parallel to the magnetic field, perpendicular velocities are not generally recoverable from Doppler shifts alone. The induction equation's vertical component relates evolution in $B_z$ to the perpendicular flow field, but has a finite null space, meaning some ``null'' flows, e.g., motions along contours of normal field, do not affect $B_z$. Consequently, additional information is required to accurately specify the perpendicular flow field. Tracking methods, which analyze $\partial_t B_z$ in a neighborhood, have a long heritage, but other approaches have recently been developed. In a recent paper, several such techniques were tested using synthetic magnetograms from MHD simulations. Here, we use the same test data to characterize: 1) the ability of the induction equation's normal component, by itself, to estimate flows; and 2) a tracking method's ability to recover flow components that are perpendicular to $\mathbf{B}$ and parallel to contours of $B_z$. This work has been supported by NASA Heliophysics Theory grant NNG05G144G.