Relative Helicity as a Topological Diagnostic of Three-dimensional Magnetic Null Reconnection Regimes
Year: 2026
Type: article
Abstract: Magnetic helicity is a fundamental topological invariant constraining magnetized plasmas, but its local behavior at magnetic null points—where reconnection is often localized—remains poorly understood, limiting diagnosis of coronal reconnection. We calculate relative magnetic helicity in a small spherical volume around a three-dimensional magnetic null for canonical torsional spine and fan reconnection regimes, using smooth, exponentially localized fields. A cylindrical gauge makes the vector potential regular and identical for twisted and potential reference fields. The helicity density becomes a simple algebraic expression, integrated analytically over the sphere. For torsional spine with physical parameters, the helicity density is odd in the axial coordinate, so the integral vanishes exactly; this holds for any even key exponent governing the azimuthal field. Torsional fan, however, has an even helicity density when a different exponent combination is odd, yielding finite, gauge-invariant local helicity. For standard fan parameters, this helicity is negative, scales as the ninth power of radius, and is proportional to the square of the reference field strength. This parity contrast provides a robust topological diagnostic distinguishing the two modes independent of detailed parameters. The presence or absence of a monopole helicity moment around a null is thus a topological signature of the reconnection regime. It can guide interpretation of circular flare ribbons, coronal jets, and simulations: Fan-driven reconnection produces net local helicity, while spine-driven reconnection leaves only odd-parity moments. The multipole framework offers a path to identify active reconnection modes and quantify the local reconnection electric field from observations.
Source: The Astrophysical Journal
Author: Mahboub Hosseinpour
Institution: University of Tabriz
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $4,499
OpenAlex ID: W7221773900