Small-scale dynamo with finite correlation times

Abstract

Fluctuation dynamos occur in most turbulent plasmas in astrophysics and are the prime candidates for amplifying and maintaining cosmic magnetic fields. A few analytical models exist to describe their behaviour but they are based on simplifying assumptions. For instance the well-known Kazantsev model assumes an incompressible flow that is delta-correlated in time. However, these assumptions can break down in the interstellar medium as it is highly compressible and the velocity field has a finite correlation time. Using the renewing flow method developed by Bhat and Subramanian (2014), we aim to extend Kazantsev's results to a more general class of turbulent flows. The cumulative effect of both compressibility and finite correlation time over the Kazantsev spectrum is studied analytically. We derive an equation for the longitudinal two-point magnetic correlation function in real space to first order in the correlation time $\tau$ and for an arbitrary degree of compressibility (DOC). This generalised Kazantsev equation encapsulates the original Kazantsev equation. In the limit of small Strouhal numbers $St\propto \tau$ we use the WKB approximation to derive the growth rate and scaling of the magnetic power spectrum. We find the result that the Kazantsev spectrum is preserved, i.e. $M_k(k)\sim k^{3/2}$. The growth rate is also negligibly affected by the finite correlation time; however, it is reduced by the finite magnetic diffusivity, and the DOC together.

arXiv comment19 pages, 3 figures

References in corpus (44)

• Astrophysical magnetic fields and nonlinear dynamo theory
• Strange Quark Matter and Compact Stars
• Cluster Magnetic Fields
• Simulations of small-scale turbulent dynamo
• Diffuse Radio Emission from Galaxy Clusters
• Primordial magnetogenesis
• Simulations of nonhelical hydromagnetic turbulence
• Strong magnetic fields in normal galaxies at high redshifts
• Small-scale dynamo action during the formation of the first stars and galaxies. I. The ideal MHD limit
• Current status of turbulent dynamo theory: From large-scale to small-scale dynamos
• Numerical demonstration of fluctuation dynamo at low magnetic Prandtl numbers
• Magnetic field amplification in turbulent astrophysical plasmas
• A model of nonlinear evolution and saturation of the turbulent MHD dynamo
• The Small-Scale Dynamo and Non-Ideal MHD in Primordial Star Formation
• A new interpretation of the far-infrared - radio correlation and the expected breakdown at high redshift
• The Turbulent Dynamo in Highly Compressible Supersonic Plasmas
• Magnetic Field Amplification by Small-Scale Dynamo Action: Dependence on Turbulence Models and Reynolds and Prandtl Numbers
• Spectra and Growth Rates of Fluctuating Magnetic Fields in the Kinematic Dynamo Theory with Large Magnetic Prandtl Numbers
• Saturation of the Turbulent Dynamo
• Magnetic Field Amplification in Young Galaxies
• Magnetic fields during the formation of supermassive black holes
• Magnetic field amplification in accretion discs around the first stars: implications for the primordial IMF
• A Cold Front in A3667: Hydrodynamics and Magnetic Field in the Intracluster Medium
• The small-scale dynamo: Breaking universality at high Mach numbers
• Magnetic fields in the Milky Way and other spiral galaxies
• The Role of Magnetic Fields in Spiral Galaxies
• Turbulent magnetic field amplification from the smallest to the largest magnetic Prandtl numbers
• Magnetic fields in primordial accretion disks
• Small-scale-field Dynamo
• Magnetic Fluctuations with a Zero Mean Field in a Random Fluid Flow with a Finite Correlation Time and a Small Magnetic Diffusion
• The far-infrared - radio correlation in dwarf galaxies
• Magnetic field amplification by the small-scale dynamo in the early Universe
• Fundamental scales in the kinematic phase of the turbulent dynamo
• Finite-Correlation-Time Effects in the Kinematic Dynamo Problem
• Dynamo effect in the Kraichnan magnetohydrodynamic turbulence
• Fluctuation dynamo at finite correlation times and the Kazantsev spectrum
• Magnetic dynamo action in random flows with zero and finite correlation times
• Kazantsev dynamo in turbulent compressible flows
• Dissipative magnetic structures and scales in small-scale dynamos
• Fluctuation dynamo at finite correlation times using renewing flows
• Finite memory time and anisotropy effects for initial magnetic energy growth in random flow of conducting media
• Magnetic energy spectrum produced by turbulent dynamo: effect of time irreversibility
• Mean field dynamo action in renovating shearing flows
• Mean field dynamo action in shear flows. I: fixed kinetic helicity