A New Jeans Resolution Criterion for (M)hd Simulations of Self-Gravitating Gas: Application to Magnetic Field Amplification by Gravity-Driven Turbulence

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, adaptivemesh 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 ≈ 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 Link Between Turbulence, Magnetic Fields, Filaments, and Star Formation in the Central Molecular Zone Cloud G0.253+0.016

“…The fact that we see turbulence thus leads us to conclude that it must be driven by some physical stirring mechanism. In general, potential driving mechanisms include supernova explosions and expanding radiation fronts and shells induced by high-mass stellar feedback (McKee 1989;Balsara et al 2004;Krumholz et al 2006;Breitschwerdt et al 2009;Goldbaum et al 2011;Peters et al 2011;Lee et al 2012), winds , gravitational collapse and accretion of material (Vazquez-Semadeni et al 1998;Elmegreen & Burkert 2010;Klessen & Hennebelle 2010;Vázquez-Semadeni et al 2010;Federrath et al 2011b;Robertson & Goldreich 2012;Lee et al 2015), and Galactic spiral-arm compressions of H I clouds turning them into molecular clouds (Dobbs & Bonnell 2008;, as well as magnetorotational instability (MRI) and shear (Piontek & Ostriker 2007;Tamburro et al 2009). Jets and outflows from young stars and their accretion disks have also been suggested to drive turbulence (Norman & Silk 1980;Matzner & McKee 2000;Banerjee et al 2007;Nakamura & Li 2008;Cunningham et al 2009Cunningham et al , 2011Carroll et al 2010;Wang et al 2010;Plunkett et al 2013Plunkett et al , 2015Federrath et al 2014;Offner & Arce 2014).…”

“…It is supersonic, magnetized turbulence that determines the density PDF and, in particular, its standard deviation (Padoan et al 1997b;Federrath et al 2008b;Padoan & Nordlund 2011;Price et al 2011;Konstandin et al 2012;Burkhart & Lazarian 2012;Molina et al 2012;Federrath & Banerjee 2015;Nolan et al 2015). A high-density power-law tail can develop as a consequence of gravitational contraction of the dense cores in a cloud (Klessen 2000;Federrath et al 2008aFederrath et al , 2011bKritsuk et al 2011;Federrath & Klessen 2013;Girichidis et al 2014). …”

“…By contrast, stellar feedback or gravitational infall would produce a shock, i.e., a discontinuity, but we see a rather smooth gradient, which is most likely associated with shear (Kruijssen et al 2016, in preparation). Such large-scale systematic motions must be subtracted in order to isolate the turbulent motions on scales smaller or equal to the size of the cloud (e.g., Burkert & Bodenheimer 2000;Sur et al 2010;Federrath et al 2011b). In order to isolate the turbulent motions, we fit the gradient with a plane, shown in the middle panel, and then subtract it from the original velocity map (shown in the top right-hand panel of Figure 4).…”

GMC Collisions as Triggers of Star Formation. II. 3D Turbulent, Magnetized Simulations

“…However, we note that for our magnetically supported gas the effective "magneto-Jeans mass" will be significantly larger than the thermal Jeans mass. While these refinement conditions do not necessarily capture the full turbulent cascade or dynamo amplification, which would require 30 cells per Jeans length (Federrath et al 2011), they should nonetheless provide approximations to real GMC structures while sufficiently avoiding artificial fragmentation.…”

SHOCKFIND - an algorithm to identify magnetohydrodynamic shock waves in turbulent clouds

“…High resolution threedimensional simulations of molecular clouds have shown that the star formation rate and efficiency depend on whether the turbulence is solenoidally or compressively driven (Federrath & Klessen 2012, and that the stellar initial mass function is sensitive both to non-ideal MHD effects such as ambipolar diffusion (McKee et al 2010) and to the driving and Mach number of the turbulence (Hennebelle & Chabrier 2009Hopkins 2013). The importance of stellar feedback (Krumholz et al 2007;Cunningham et al 2011;Myers et al 2014;Nakamura & Li 2007;Wang et al 2010; Price & E-mail: andrew.lehmann@mq.edu.au Bate 2008Bate , 2009Offner & Arce 2014;Federrath et al 2014;Federrath 2015;Padoan et al 2015), whether gravity drives turbulent motions (Elmegreen & Burkert 2010;Klessen & Hennebelle 2010;Vzquez-Semadeni et al 2010;Federrath et al 2011;Robertson & Goldreich 2012) and the role that turbulence plays in producing the ubiquitously observed filaments (Arzoumanian et al 2011;André et al 2014;Smith et al 2014Smith et al , 2016Federrath 2016;Kainulainen et al 2016;Hacar et al 2016) are big questions that continue to be studied. Rigorous observational effects distinctly revealing the presence or dominance of the various physical processes are strongly sought after.…”