A new Jeans resolution criterion for (M)HD simulations of self-gravitating gas: Application to magnetic field amplification by gravity-driven turbulence (1102.0266v2)

Abstract: Cosmic structure formation is characterized by the complex interplay between gravity, turbulence, and magnetic fields. The processes by which gravitational energy is converted into turbulent and magnetic energies, however, remain poorly understood. Here, we show with high-resolution, adaptive-mesh simulations that MHD turbulence is efficiently driven by extracting energy from the gravitational potential during the collapse of a dense gas cloud. Compressible motions generated during the contraction are converted into solenoidal, turbulent motions, leading to a natural energy ratio of E_sol/E_tot of approximately 2/3. We find that the energy injection scale of gravity-driven turbulence is close to the local Jeans scale. If small seeds of the magnetic field are present, they are amplified exponentially fast via the small-scale dynamo process. The magnetic field grows most efficiently on the smallest scales, for which the stretching, twisting, and folding of field lines, and the turbulent vortices are sufficiently resolved. We find that this scale corresponds to about 30 grid cells in the simulations. We thus suggest a new minimum resolution criterion of 30 cells per Jeans length in (magneto)hydrodynamical simulations of self-gravitating gas, in order to resolve turbulence on the Jeans scale, and to capture minimum dynamo amplification of the magnetic field. Due to numerical diffusion, however, any existing simulation today can at best provide lower limits on the physical growth rates. We conclude that a small, initial magnetic field can grow to dynamically important strength on time scales significantly shorter than the free-fall time of the cloud.

• The paper introduces a new Jeans resolution criterion, demonstrating that resolving the Jeans length with 30 cells is essential to capture dynamo-driven turbulence.
• It employs high-resolution, adaptive-mesh simulations to quantify gravitational energy conversion into solenoidal turbulence, with two-thirds of the energy in solenoidal motions.
• Findings imply that weak seed fields rapidly amplify during gas cloud collapse, significantly influencing star formation and cosmic structure evolution.

Magnetic Field Amplification by Gravity-Driven Turbulence

This essay reviews the paper "A new Jeans resolution criterion for (M)HD simulations of self-gravitating gas: Application to magnetic field amplification by gravity-driven turbulence" by Federrath et al. The paper employs high-resolution, adaptive-mesh simulations to investigate the process of magnetic field amplification within self-gravitating gas clouds, driven by turbulence induced by gravitational collapse.

The interplay of gravity, turbulence, and magnetic fields governs cosmic structure formation, but the mechanisms through which gravitational energy transitions into both turbulent and magnetic energy remain inadequately understood. This paper provides important insights into these processes by rigorously modeling the collapse of a dense gas cloud, demonstrating that magnetohydrodynamic (MHD) turbulence effectively grows by harnessing energy from the gravitational force during a cloud's contraction phase.

Key Findings and Numerical Results:

1. Energy Conversion and Scale: The contraction of gas clouds induces compressible motions which convert into solenoidal, turbulent motions, manifesting a natural energy partition. The energy injection scale aligns closely with the local Jeans scale. Solenoidal motions comprise approximately two-thirds of this energy balance.
2. Magnetic Field Amplification: If an initial seed for the magnetic field exists, it experiences exponential growth due to the small-scale dynamo. This dynamo is most effective on smaller scales, necessitating careful resolution in simulations to capture these phenomena. Specifically, about 30 grid cells per Jeans length are required for accurately resolving the turbulence and capturing the minimum dynamo amplification.
3. Numerical Diffusion: Current computational capabilities inherently limit accurate simulation; thus, present-day computational models can only establish lower boundaries on physical growth rates because of numerical diffusion. High-resolution simulations help ameliorate this issue, yet true physical growth rates remain an area for further exploration.
4. Resolution Criterion: A compelling aspect of this paper is the proposed new Jeans resolution criterion for simulations. Resolving the Jeans length with about 30 cells captures crucial dynamo processes and aligns with the solution's convergence regarding solenoidal energy and complete turbulence resolution.

Theoretical and Practical Implications:

The results have significant implications for the understanding of magnetic fields in various astrophysical contexts, from present-day accretion disks to primordial star formation. The findings suggest that small magnetic seeds can quickly evolve to dynamically important strengths much faster than collapsing gas clouds' free-fall timescales. This elevates the role of magnetic fields as essential contributors to the dynamics of star formation, potentially affecting gas fragmentation and star-forming region evolution.

Future Directions:

Future research leveraging enhanced resolution and computational resources may further delineate the growth rates of magnetic fields and refine the predictive power of MHD turbulence models. Additionally, integrating these models into larger scales and more complex environments might improve our understanding of magnetic fields in galaxy formation and structure development. Understanding the interactions between magnetic fields and self-gravitating media remains crucial.

This paper's findings represent a significant step in precisely characterizing the conditions under which turbulence and dynamo processes effectively energize magnetic fields during cosmic structure formation, broadening our grasp of magnetic phenomena in the universe.