A Note on Computation of Relative Magnetic Helicity Flux Across the Photosphere 

Yang Liu Submitted: 20121219 09:07
A number of investigations of the rate of relative magnetic helicity transport across the photosphere [ dH/dtS ] have reported differences in the estimates computed from two different formulations of the relativehelicity flux density proxy [ GA ] and [ G_theta ]. There have been suggestions that [ G_theta ] is a more robust helicityflux density proxy and that the differences in the estimates of [dH/dtS ] are caused by biases in [ GA ], noise, and/or the boundary conditions. In this note, we prove that the differences are caused by the inconsistent choice of boundary conditions in the explicit or implicit Green?s function [ G (x, x′) ] used for computing [ GA ] and [ G_theta ] when comparing the helicity flux estimates based on [ GA ] and [ G_theta ]. When the boundary conditions in [ G ] are chosen consistetently, the two helicityflux density proxies, [ GA ] and [ G_theta ], produce essentially identical results for the rate of helicity transport across the photosphere. They also yield essentially identical results for the rate of helicity transport of the shearing and advection terms separately. Using MHD simulation, HMI observational data, and Monte Carlo simulations of noise we show that this result is robust. Neither the shape of the active region, nor the shape of the boundary, nor data noise causes any difference in the rate of helicity transport computed via [ GA ] and [ G_theta ].
Authors: Yang Liu, Peter W. Schuck
Projects: SDOHMI

Publication Status: Solar Physics, Accepted.
Last Modified: 20121219 12:09


