A comparative study of resistivity models for simulations of magnetic reconnection in the solar atmosphere

II. Plasmoid formation^⋆

¹ Rosseland Centre for Solar Physics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
e-mail: o.h.farder@astro.uio.no
² Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
³ Instituto de Astrofísica de Canarias, 38205 La Laguna, Tenerife, Spain
⁴ Universidad de La Laguna, Dept. Astrofísica, 38206 La Laguna, Tenerife, Spain

Received: 22 September 2023
Accepted: 9 December 2023

Abstract

Context. Plasmoid-mediated reconnection plays a fundamental role in different solar atmospheric phenomena. Numerical reproduction of this process is therefore essential for developing robust solar models.

Aims. Our goal is to assess plasmoid-mediated reconnection across various numerical resistivity models in order to investigate how plasmoid numbers and reconnection rates depend on the Lundquist number.

Methods. We used the Bifrost code to drive magnetic reconnection in a 2D coronal fan-spine topology, carrying out a parametric study of several experiments with different numerical resolution and resistivity models. We employed three anomalous resistivity models: (1) the original hyper-diffusion from Bifrost, (2) a resistivity proportional to current density, and (3) a resistivity quadratically proportional to electron drift velocity. For comparisons, experiments with uniform resistivity were also run.

Results. Plasmoid-mediated reconnection is obtained in most of the experiments. With uniform resistivity, increasing the resolution reveals higher plasmoid frequency with weaker scaling to the Lundquist number, obtaining 7.9–12 plasmoids per minute for S_L ∈ [1.8 × 10⁴, 2.6 × 10⁵] with a scaling of S_L^0.210 in the highest-resolution resistivity cases, transcending into Petschek reconnection in the high-S_L limit (where the diffusive effects of the resistivity become small compared to the non-uniform viscosity) and Sweet-Parker reconnection in the low-S_L limit. Anomalous resistivity leads to similar results even with lower resolution. The drift-velocity-dependent resistivity excellently reproduces Petschek reconnection for any Lundquist number, and similar results are seen with resistivity proportional to current-density though with slightly lower reconnection rates and plasmoid numbers. Among the different resistivity models applied on the given numerical resolution, the hyper-diffusion model reproduced plasmoid characteristics in closest resemblance to those obtained with uniform resistivity at a significantly higher resolution.