Quiet Sun flux rope formation via incomplete Taylor relaxation

¹ Rosseland Centre for Solar Physics (RoCS), University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
e-mail: rebecrob@uio.no
² Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029 Blindern, 0315 Oslo, Norway
³ Sorbonne Université, École Polytechnique, Institut Polytechnique de Paris, Observatoire de Paris – PSL, CNRS, Laboratoire de physique des plasmas (LPP), 4 place Jussieu, 75005 Paris, France

Received: 2 February 2023
Accepted: 9 March 2023

Abstract

Context. Low-altitude nanoflares are among the candidates for atmospheric heating in the quiet Sun’s corona. Low-altitude twisted magnetic fields may be involved in such events, as they are in larger flares. But for nanoflares, the exact role, topology, and formation mechanisms of these twisted fields remain to be studied.

Aims. In this paper, we investigate the formation and evolution of a preflare flux rope in a fully stratified, 3D magnetohydrodynamics simulation of the quiet Sun using the Bifrost code. This study focuses on the time period before the rope eventually reconnects with an overlying field, resulting in a nanoflare-scale energy on the order of 10¹⁷ J. One puzzle is that this modeled flux rope does not form by any of the mechanisms usually at work in larger flares, such as flux emergence, flux cancellation, or tether-cutting reconnection.

Methods. Using Lagrangian markers to trace representative field lines, we follow the spatiotemporal evolution of the flux rope. By focusing on current volumes (which we call current sheets) between these lines, we identify flux bundles and associated reconnecting field line pairs. We also analyze the time-varying distribution function for the force-free parameter as the flux rope relaxes. Lastly, we compare different seeding methods for tracing magnetic field lines, and discuss their relevance to the analysis.

Results. We show that the modeled flux rope is gradually built from the coalescence of numerous current-carrying flux tubes. This occurs through a series of component reconnections that are continuously driven by the complex flows in the underlying convection zone. These reconnections lead to an inverse cascade of helicity from small scales to larger scales. We also find that the system attempts to relax toward a linear force-free field, but that the convective drivers and the nanoflare event prevent full Taylor relaxation.

Conclusions. Using a self-consistently driven simulation of a nanoflare event, we show for the first time an inverse helicity cascade tending toward a Taylor relaxation in the Sun’s corona, resulting in a well-ordered flux rope that later reconnects with surrounding fields. This provides context clues toward understanding the buildup of nanoflare events in the quiet Sun through incomplete Taylor relaxations, when no relevant flux emergence or cancellation is observed.