Authors: Dennis Tilipman (University of Colorado, Boulder / NSO), Maria Kazachenko (University of Colorado, Boulder / NSO / LASP), Matthias Rempel (National Center for Atmospheric Research, HAO, Boulder, Colorado)

Estimates of photospheric electric fields and Poynting fluxes are crucial to our understanding of energy transport in the solar atmosphere. However, these quantities are not easily derived from observations, even with the data from the most advanced telescopes such as DKIST or SolO. Uncertainties arise from limited polarimetric sensitivity, limited spatial and temporal resolutions, with no instrument being able to optimize for all three of these simultaneously. The goal of our work is to characterize the propagation of these respective uncertainties, with a focus on spatial and temporal effects. Understanding these effects will allow us to design observation strategies optimized for reliable inversions of electric fields in a variety of settings, including the quiet Sun.

In addition, inversions of electric fields rely on spatial derivatives and vector products of magnetic and velocity fields. This presents a problem in observations, since v- and B-fields are observed on optical surfaces, but their derivatives and vector products are computed on geometrical surfaces. Thus, another component of our work is to explore the effect of this discrepancy at different spatial and temporal resolutions. We employ two electric field inversions: one that assumes idealized Ohm’s law E = −v × B, and another one which relies on uncurling Faraday’s induction equation (PDFI_SS, Fisher et al. 2020). The resulting electric fields are used to both evaluate how spatial and temporal effects change the field inductivity, as well as to estimate energy output in the form of Poynting flux.

As a ground truth, we use the outputs of MURaM 3-D MHD (Rempel 2017) simulations containing both an active and a quieter regions. These simulations are suitable for our purposes since they are computed on both geometrical and optical depth grids. We degrade the native MURaM spatial resolution and cadence using several methods that approximate instrumentation effects. In particular, we use spatial and temporal resolutions that mimic presently existing or soon-to-become-available instruments, such as SDO/HMI, SST, Sunrise/IMaX, and DKIST/VTF.

Our results indicate that spatial degradation effects result in a more inductive
electric field than what is observed in MURaM simulations at native resolution, whereas de-
graded cadence, on the contrary, decreases field inductivity. We also report that the effects
of computing electric fields on the optical rather than geometrical surfaces are outweighed by
degraded spatial resolution and cadence. We discuss the possible causes and implications of
these findings, as well as how these effects can be mitigated.