Self‐Organization of Radio Lobe Magnetic Fields by Driven Relaxation

Abstract

In active galaxies, minimum energy estimates based on the observed radio emission suggest that 10% or more of the total gravitational energy released by the collapse of a supermassive black hole is deposited into lobe-scale magnetic fields and relativistic particles, roughly in equipartition. It is proposed here that the underlying physical process inside the lobe is magnetic self-organization by driven relaxation, rather than a traditional magnetohydrodynamic dynamo. There are two forms of magnetic self-organization. The extreme form of Taylor relaxation is similar to a driven harmonic oscillator, in which a resonance in spatial frequency constrains the input magnetic energy and helicity to the lowest order relaxation mode, commonly known as a spheromak in laboratory plasmas. The general form of magnetic self-organization takes into account the intrinsic nonlinearity of a driven plasma, which can access relaxed states beyond the spheromak resonance. This is a particularly useful physics description for radio lobe plasmas, which are likely overdriven. The degrees of self-organization can be quantified by a spectral energy analysis over the spatial distribution of the magnetic field. The preferred self-organized states can be characterized by a principal component analysis using a projection onto the fundamental relaxation modes that are unique to a given radio lobe morphology.

Structure of magnetic fields in intracluster cavities

“…Spheromaks are solutions of force‐free magnetic fields in axial symmetry (Chandrasekhar & Kendall 1957). They have been invoked before in the context of magnetic bubbles (Tang 2008). However, these solutions have one particular drawback that excludes them as reasonable solution for magnetic field structure in ICM cavities: they cannot have both poloidal components equal to zero on the surface.…”

Stabilizing effect of magnetic helicity on magnetic cavities in the intergalactic medium

“…a dynamo effect. The hypothesis of a helical magnetic field lying inside these bubbles appears justified also in light of results showing that AGN jets are characterized by helical magnetic fields (Li et al 2006;Tang 2008;Gabuzda 2018). If this field contains magnetic helicity, it is stable on diffusive times, i.e.…”

Numerical computation of the helical Chandrasekhar–Kendall modes

“…(15) is on the order of machine roundoffs, R b n;m / as defined in Eq. (16), is governed by the dicretization error of the finite difference scheme.…”

“…In fact, resonant coupling [9][10][11][12] is the physical mechanism underlying the self-organization of system-scale magnetic fields by magnetic relaxation in the laboratory formation of spherical tokamak [13,14], spheromak [15], and reversed field pinch by helicity injection. It is also thought to be a competing paradigm for the generation and sustainment of large scale magnetic fields in astrophysical radio lobes [16].…”

“…The primary result of the paper is a new formulation that numerically computes the helical CK modes as a standard matrix eigenvalue problem, which is suitable for numerical implementation in a torus of complex poloidal cross section. This capability can be of use for current and future design optimizations for reversed field pinch, spherical tokamak [14], and spheromak [15] experiments, and for astrophysical radio lobe analysis [16].…”