The Nonlinear Magnetic Cascade

Abstract

The Galactic magnetic field has an energy density comparable to that of the interstellar medium turbulence and a coherence spanning the Galaxy. It is not known if this field was formed before, during, or after the Galaxy. However, it is often assumed to originate from a turbulent dynamo process. We investigate the early stages of a Galactic dynamo when the dynamics is well approximated by homogeneous turbulence. Our simulations show that homogeneous magnetized turbulence with large Prandtl number yields magnetic energy at the small, resistive scale rather than at the Galactic scale. Thus, additional phenomena-perhaps helicity generated from Galactic rotation, stratification, and the differential rotation of the disk-are needed to explain the observed field. We simulate the growth of magnetic energy in forced nonhelical turbulence from an initially weak value until it saturates with the same energy density as the turbulence. When the field is dynamically weak, the simulations agree with the kinematic theory. In the long-term saturated state, the magnetic field is strong enough to modify the turbulence. This is the magnetohydrodynamic (MHD) analog of the Kolmogorov problem for hydrodynamic turbulence. The nature of the back-reaction is to neutralize the net shear (stretching) in small-scale eddies that are less energetic than the magnetic field. Only the forcing-scale eddies remain energetic enough to shear and cascade the magnetic field. The magnetic field at all scales therefore forward-cascades at the forcing timescale through spectrally nonlocal interactions with the forcing-scale eddies. Furthermore, the magnetic field folds into a reduced-tension state where field-line curvature anticorrelates with intensity. Direct consequences of these statements are that the magnetic spectrum is largely independent of viscosity and that the magnetic energy is located at the small, resistive scale. For Edward Burns, 1970-2002.