Turbulent dynamos with advective magnetic helicity flux

Abstract

Many astrophysical bodies harbor magnetic fields that are thought to be sustained by a dynamo process. However, it has been argued that the production of large-scale magnetic fields by mean-field dynamo action is strongly suppressed at large magnetic Reynolds numbers owing to the conservation of magnetic helicity. This phenomenon is known as catastrophic quenching. Advection of magnetic fields by stellar and galactic winds toward the outer boundaries and away from the dynamo is expected to alleviate such quenching. Here we explore the relative roles played by advective and turbulentdiffusive fluxes of magnetic helicity in the dynamo. In particular, we study how the dynamo is affected by advection. We do this by performing direct numerical simulations of a turbulent dynamo of α 2 type driven by forced turbulence in a Cartesian domain in the presence of a flow away from the equator where helicity changes sign.Our results indicate that in the presence of advection, the dynamo, otherwise stationary, becomes oscillatory. We confirm an earlier result for turbulent-diffusive magnetic helicity fluxes that for small magnetic Reynolds numbers (Rm 100...200, based on the wavenumber of the energy-carrying eddies) the magnetic helicity flux scales less strongly with magnetic Reynolds number (Rm −1/2 ) than the term describing magnetic helicity destruction by resistivity (Rm −1 ). Our new results now suggest that for larger Rm the former becomes approximately independent of Rm, while the latter falls off more slowly. We show for the first time that both for weak and stronger winds, the magnetic helicity flux term becomes comparable to the resistive term for Rm 1000, which is necessary for alleviating catastrophic quenching.

Convection-driven spherical shell dynamos at varying Prandtl numbers

“…Although the large-scale magnetic field amplitude does not decrease proportional to Re M in the cases when open boundaries are used, there is still a decreasing trend even at the highest currently studied Re M in local simulations of convection-driven dynamos (e.g., Käpylä et al 2010a). This, however, is compatible with mean-field models, which suggest that the magnetic helicity fluxes become effective only at significantly higher Re M Del Sordo et al 2013).…”

“…In astrophysical systems this would mean that magnetic helicity would be nearly conserved. However, astrophysical systems are not closed and magnetic helicity can escape, for example, through coronal mass ejections in the Sun (e.g., Blackman & Brandenburg 2003;Warnecke et al 2011Warnecke et al , 2012 or through winds from galaxies (Shukurov et al 2006;Sur et al 2007;Del Sordo et al 2013). In mean-field theory these physical effects are parameterized by fluxes, which lead to alleviation of catastrophic quenching in suitable parameter regimes (e.g., Brandenburg et al 2009).…”

Magnetic Helicity and Large Scale Magnetic Fields: A Primer

“…In the steady-state the divergence is invariant at every point so one can obtain the spatial dependence of the flux. These principles were also verified in Hubbard & Brandenburg (2010) and apply even to oscillatory dynamos by first identifying a gauge for which the helicity is steady (Del Sordo et al 2013), which eliminates the dependent terms and the divergence term emerges as gauge invariant.…”

“…The left panel shows the late time saturation value is increased with increasing λ and the right panel shows the tendency that for large enough λ the kinematic regime (the regime independent of RM ) can be extended. Del Sordo et al (2013) have studied numerically the relative role of advective and diffusive fluxes. Their generalized α 2 dynamos can become oscillatory with even a weak advective wind, due to the spatial dependence of the imposed kinetic helicity.…”

Dynamical quenching with non‐local α and downward pumping

“…Even though the domain may be closed, we must always expect there to be internal magnetic helicity fluxes resulting from the inhomogeneity of the model. Magnetic helicity fluxes between local extrema in the smallscale magnetic helicity density and across the equator have been detected in direct numerical simulations (Mitra et al 2010;Hubbard & Brandenburg 2010;Del Sordo et al 2013). Such fluxes might well be sufficient for alleviating catastrophic quenching without the need for invoking the non-locality of α.…”