A NEW JEANS RESOLUTION CRITERION FOR (M)HD SIMULATIONS OF SELF-GRAVITATING GAS: APPLICATION TO MAGNETIC FIELD AMPLIFICATION BY GRAVITY-DRIVEN TURBULENCE

By Christoph Federrath, S. Sur, D. Schleicher, Robi Banerjee, Ralf Klessen. 2011

228 citations recorded by the source corpus.

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 Esol/Etot ≈ 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 timescales significantly shorter than the free-fall time of the cloud.

Subfields: Astronomy and Astrophysics, Instrumentation

View Paper: https://www.semanticscholar.org/paper/f99620adece78949e359d96a5406f3b6512609da

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Citations in the corpus

Feedback-regulated star formation and escape of LyC photons from mini-haloes during reionization (2016, background): “Although the use of the latter condition is computationally expensive, it makes our simulations more robust than previous simulations, as the turbulent properties of gas can be more accurately captured (Federrath et al. 2011; Turk et al. 2012; Meece et al. 2014).”
Magnetic Fields in the Large-Scale Structure of the Universe (2011, background): “Recent numerical MHD simulations suggest that the small-scale dynamo indeed operates during gravitational collapse, producing magnetic fields during the formation of the first structures (Sur et al. 2010; Federrath et al. 2011).”
THE GENERATION OF STRONG MAGNETIC FIELDS DURING THE FORMATION OF THE FIRST STARS (2010, background): “We address these questions in more detail in [24].”
THE STAR FORMATION RATE OF TURBULENT MAGNETIZED CLOUDS: COMPARING THEORY, SIMULATIONS, AND OBSERVATIONS (2012, background): “…on nonlinear dissipation properties, i.e., strengths of shocks and amount of vorticity generated, and thus on the Mach number of the turbulence (Federrath et al. 2011b), the time-averaged rms Mach number for a given forcing amplitude cannot be predicted a priori and must be adjusted…”
Black hole formation in the early Universe (2013, methodology): “Even though the presence of turbulence was reported in massive primordial haloes already by Wise et al. (2008), it was only realized by Federrath et al. (2011) that a minimum resolution of 32 cells per Jeans length is required to obtain converged turbulent energies during gravitational collapse.”
THE MASS SPECTRUM OF THE FIRST STARS (2014, methodology): “However, so far the sufficient amplification to affect the dynamics of the gas has not been shown starting from a very week seed field of ∼10−18–10−20 G by ab initio numerical simulations (Sur et al. 2010; Federrath et al. 2011; Turk et al. 2012; Latif et al. 2013).”
The First Stars (2012, background): “Federrath et al. (2011) show that in gravitationally collapsing regions that undergo adaptive mesh refinement, the effective Reynolds number scales with the number of grid zones per Jeans length as Reeff = (N/2)4/3.”
On the universality of interstellar filaments: theory meets simulations and observations (2015, background): “This resolution criterion is very conservative and computationally costly, but guarantees that we resolve turbulence on the Jeans scale (Federrath et al. 2011), potential dynamo amplification of the magnetic field in the dense cores (Sur et al. 2010), and capture the basic structure of accretion…”
The density variance–Mach number relation in supersonic turbulence – I. Isothermal, magnetized gas (2012, background): “Aside from these reports, if the magnetic flux is not conserved, but increases due to turbulent dynamo amplification during compression, α can become larger than the values quoted above, depending on the Reynolds numbers of the gas (Schleicher et al. 2010; Sur et al. 2010; Federrath et al. 2011).”
VERTICAL STRUCTURE OF A SUPERNOVA-DRIVEN TURBULENT, MAGNETIZED INTERSTELLAR MEDIUM (2012, methodology): “To test similar growth, we have run an additional model at 4 pc resolution, bx10, noting that Sur et al. (2010) and Federrath et al. (2011) have demonstrated effective dynamos with the HLL3R Riemann solver used in FLASH in this work.”
Simulating galaxy formation with the IllustrisTNG model (2017, background): “…has not been applied to any of the simulations of the present work. dynamics in such a cloud is complex, and it may be that the magnetic field surrounding or within a molecular cloud is amplified during star formation (Schober et al. 2012), likely through turbulence (Federrath et al. 2011).”
On the universality of supersonic turbulence (2013, methodology): “The effective Reynolds numbers of our simulations are of the order of Re ≈ N1+αres (Benzi et al. 1993; Federrath et al. 2011a).”
COLLAPSE OF MASSIVE MAGNETIZED DENSE CORES USING RADIATION MAGNETOHYDRODYNAMICS: EARLY FRAGMENTATION INHIBITION (2011, background): “Further work will imply detailed fragmentation and resolution studies (e.g., Federrath et al. 2011) and the introduction of sink particles to follow a longer dynamical range.”
ON THE STAR FORMATION EFFICIENCY OF TURBULENT MAGNETIZED CLOUDS (2012, methodology): “If all these criteria are fulfilled, the excess mass above the density threshold defined by Equation (1) is removed from the MHD system and added to the sink particle, such that mass, momentum and angular momentum are conserved by construction (see Federrath et al. 2010a, 2011a, for details).”
Inefficient star formation through turbulence, magnetic fields and feedback (2015, background): “This resolution criterion is very conservative and computationally costly, but guarantees that we resolve turbulence on the Jeans scale (Federrath et al. 2011), potential dynamo amplification of the magnetic field in the dense cores (Sur et al. 2010), and capture the basic structure of accretion…”
The difficulty of getting high escape fractions of ionizing photons from high-redshift galaxies: A view from the FIRE cosmological simulations (2015, background): “It is also motivated by much higher-resolution, direct simulations of dense, star-forming clouds (Padoan & Nordlund 2011; Vázquez-Semadeni et al. 2011; Federrath et al. 2011).”
Titans of the early Universe: The Prato statement on the origin of the first supermassive black holes (2018, background): “The magnetic energy density at saturation is thought to reach levels of 0.1% up to a few × 10% of the kinetic energy density (Federrath et al. 2011a, 2014).”
Primordial star formation under the influence of far ultraviolet radiation: 1540 cosmological haloes and the stellar mass distribution (2015, background): “Moreover, recent magnetohydrodynamic simulations show that even a small amount of turbulence can amplify magnetic fields by a dynamo mechanism (Sur et al. 2010; Federrath et al. 2011; Sur et al. 2012; Turk et al. 2012).”
FORMATION OF MASSIVE PRIMORDIAL STARS: INTERMITTENT UV FEEDBACK WITH EPISODIC MASS ACCRETION (2015, background): “…studies argue that even higher resolutions are needed to correctly capture the gravity-driven turbulence that generally appears in the star formation process (e.g., Federrath et al. 2011; Turk et al. 2012; Meece et al. 2014), suggesting that the Jeans length should be resolved with 32-64 cells.”