Effect of Polarimetric Noise on the Estimation of Twist and Magnetic Energy of Force-Free Fields

TL;DR

This study assesses how polarimetric noise impacts the accuracy of estimating the twist parameter and magnetic energy in force-free magnetic fields, demonstrating that reliable measurements are achievable despite noise.

Contribution

It introduces a method to quantify the effects of polarimetric noise on magnetic parameter estimation using simulated profiles and inversion techniques.

Findings

Sign of alpha remains unaffected by noise.

Magnetic energy can be estimated with about 0.5% uncertainty.

Global twist values are accurately determined despite noise.

Abstract

The force-free parameter $\alpha$, also known as helicity parameter or twist parameter, bears the same sign as the magnetic helicity under some restrictive conditions. The single global value of $\alpha$ for a whole active region gives the degree of twist per unit axial length. We investigate the effect of polarimetric noise on the calculation of global $\alpha$ value and magnetic energy of an analytical bipole. The analytical bipole has been generated using the force-free field approximation with a known value of constant $\alpha$ and magnetic energy. The magnetic parameters obtained from the analytical bipole are used to generate Stokes profiles from the Unno-Rachkovsky solutions for polarized radiative transfer equations. Then we add random noise of the order of 10$^{-3}$ of the continuum intensity (I$_{c}$) in these profiles to simulate the real profiles obtained by modern spectropolarimeters like Hinode (SOT/SP), SVM (USO), ASP, DLSP, POLIS, SOLIS etc. These noisy profiles are then inverted using a Milne-Eddington inversion code to retrieve the magnetic parameters. Hundred realizations of this process of adding random noise and polarimetric inversion is repeated to study the distribution of error in global $\alpha$ and magnetic energy values. The results show that : (1). the sign of $\alpha$ is not influenced by polarimetric noise and very accurate values of global twist can be calculated, and (2). accurate estimation of magnetic energy with uncertainty as low as 0.5% is possible under the force-free condition.