Obtaining Potential Field Solution with Spherical Harmonics and Finite Differences

Potential magnetic field solutions can be obtained based on the synoptic magnetograms of the Sun. Traditionally, a spherical harmonics decomposition of the magnetogram is used to construct the current and divergence free magnetic field solution. This method works reasonably well when the order of spherical harmonics is limited to be small relative to the resolution of the magnetogram, although some artifacts, such as ringing, can arise around sharp features. When the number of spherical harmonics is increased, however, using the raw magnetogram data given on a grid that is uniform in the sine of the latitude coordinate can result in inaccurate and unreliable results, especially in the polar regions close to the Sun. We discuss here two approaches that can mitigate or completely avoid these problems: i) Remeshing the magnetogram onto a grid with uniform resolution in latitude, and limiting the highest order of the spherical harmonics to the anti-alias limit; ii) Using an iterative finite difference algorithm to solve for the potential field. The naive and the improved numerical solutions are compared for actual magnetograms, and the differences are found to be rather dramatic. We made our new Finite Difference Iterative Potential-field Solver (FDIPS) a publically available code, so that other researchers can also use it as an alternative to the spherical harmonics approach.Comment: This paper describes the publicly available Finite Difference Iterative Potential field Solver (FDIPS). The code can be obtained from http://csem.engin.umich.edu/FDIP

Buildup of Magnetic Shear and Free Energy During Flux Emergence and Cancellation

We examine a simulation of flux emergence and cancellation, which shows a complex sequence of processes that accumulate free magnetic energy in the solar corona essential for the eruptive events such as coronal mass ejections (CMEs), filament eruptions and flares. The flow velocity at the surface and in the corona shows a consistent shearing pattern along the polarity inversion line (PIL), which together with the rotation of the magnetic polarities, builds up the magnetic shear. Tether-cutting reconnection above the PIL then produces longer sheared magnetic field lines that extend higher into the corona, where a sigmoidal structure forms. Most significantly, reconnection and upward energy-flux transfer are found to occur even as magnetic flux is submerging and appears to cancel at the photosphere. A comparison of the simulated coronal field with the corresponding coronal potential field graphically shows the development of nonpotential fields during the emergence of the magnetic flux and formation of sunspots

Non-equilibrium Ionization Effects on Synthetic Spectra in the AWSoM Solar Corona

In this work we combined AWSoM's non-equilibrium ionization [NEI] calculations from (Szente:2022) with the synthetic spectral computations of SPECTRUM (Szente:2019), to predict non-equilibrium line intensities across the entire domain of the AWSoM 3D global model. We find that the resulting spectra are strongly affected by non-equilibrium effects in the fast wind regions and streamer edges and that these effects propagate to narrowband images from SoHO/EIT, SECCHI/EUVI and SDO/AIA. The dependence shows a different nature for each line observed resulting in significant changes in line intensity, which need to be accounted for during plasma diagnostics. However, we also find that these effects depend on the local plasma properties, and that no single correction can be developed to account for non-equilibrium effects in observed spectra and images. Comparing to observational data we saw that the changes due to NEI, while significant, are not sufficient to account for the differences between Hinode/EIS spectra and AWSoM/SPECTRUM predictions

Simulation of Flux Emergence from the Convection Zone to the Corona

Here, we present numerical simulations of magnetic flux buoyantly rising from a granular convection zone into the low corona. We study the complex interaction of the magnetic field with the turbulent plasma. The model includes the radiative loss terms, non-ideal equations of state, and empirical corona heating. We find that the convection plays a crucial role in shaping the morphology and evolution of the emerging structure. The emergence of magnetic fields can disrupt the convection pattern as the field strength increases, and form an ephemeral region-like structure, while weak magnetic flux emerges and quickly becomes concentrated in the intergranular lanes, i.e. downflow regions. As the flux rises, a coherent shear pattern in the low corona is observed in the simulation. In the photosphere, both magnetic shearing and velocity shearing occur at a very sharp polarity inversion line (PIL). In a case of U-loop magnetic field structure, the field above the surface is highly sheared while below it is relaxed

Solar wind modeling with the Alfven Wave Solar atmosphere Model driven by HMI-based Near-Real-Time maps by the National Solar Observatory

We explore model performance for the Alfven Wave Solar atmosphere Model (AWSoM) with near-real-time (NRT) synoptic maps of the photospheric vector magnetic field. These maps, produced by assimilating data from the Helioseismic Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO), use a different method developed at the National Solar Observatory (NSO) to provide a near contemporaneous source of data to drive numerical models. Here, we apply these NSO-HMI-NRT maps to simulate three Carrington rotations (CRs): 2107-2108 (centered on 2011/03/07 20:12 CME event), 2123 (integer CR) and 2218--2219 (centered on 2019/07/2 solar eclipse), which together cover a wide range of activity level for solar cycle 24. We show simulation results, which reproduce both extreme ultraviolet emission (EUV) from the low corona while simultaneously matching in situ observations at 1 au as well as quantify the total unsigned open magnetic flux from these maps