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On the resilience of helical magnetic fields to turbulent diffusion and the astrophysical implications

The extent to which large scale magnetic fields are susceptible to turbulent diffusion is important for interpreting the need for in situ large scale dynamos in astrophysics and for observationally inferring field strengths compared to kinetic energy. By solving coupled equations for magnetic energy and magnetic helicity in a system initiated with isotropic turbulence and an arbitrarily helical large scale field, we quantify the decay rate of the latter for a bounded or periodic system. The energy associated with the non-helical magnetic field rapidly decays by turbulent diffusion, but the decay rate of the helical component depends on whether the ratio of its magnetic energy to the turbulent kinetic energy exceeds a critical value given by M_{1,c} =(k_1/k_2)^2, where k_1 and k_2 are the wave numbers of the large and forcing scales. Turbulently diffusing helical fields to small scales while conserving magnetic helicity requires a rapid increase in total magnetic energy. As such, only when the helical fields are sub-critical can they so diffuse. When super-critical, the large scale helical field decays slowly, at a rate determined by microphysical dissipation even when macroscopic turbulence is present. Amplification of small scale magnetic helicity abates the turbulent diffusion. Two implications are that: (1) Standard arguments supporting the need for in situ large scale dynamos based on the otherwise rapid turbulent diffusion of large scale fields require re-thinking since only the non-helical field is so diffused in a closed system. Boundary terms could however provide potential pathways for rapid change of the large scale helical field. (2) Since M_{1,c} <<1 for k_1 << k_2, the presence of long-lived ordered large scale helical fields, as in extragalactic jets, does not guarantee that the magnetic field dominates the kinetic energy.