A detailed numerical and analytical examination of the evolution of stochastic magnetic fields between a putative magnetogenesis era at high cosmic temperatures T ∼ 100 MeV -100 GeV and the present epoch is presented. The analysis includes all relevant dissipation processes, such as neutrinoand photon-induced fluid viscosities as well as ambipolar-and hydrogen-diffusion. A simple and intuitive analytical model matching the results of the three-dimensional MHD simulations allows for the prediction of pre-recombination and present day magnetic field correlation lengths and energy densities as a function of initial magnetic field energy density, helicity, and spectral index. Our conclusions are multi fold. (a) Initial primordial fields with only a small amount of helicity are evolving into maximally helical fields at the present. Furthermore, the simulations show a selfsimilarity in the evolution of maximally helical fields implying a seemingly acausual amplification of magnetic fields on large scales is observed. (b) There exists a correlation between the strength of the magnetic field B at the peak of it's spectrum and the location of the peak, given at the present epoch by: B ≈ 5 × 10 −12 Gauss (L/kpc), where L is the magnetic field correlation length determined by the initial properties of the magnetic field. (c) Concerning studies of generation of cosmic microwave background (CMBR) anisotropies due to primordial magnetic fields of B ∼ 10 −9 Gauss on > ∼ 10 Mpc scales, such fields are not only impossible to generate in early causal magnetogenesis scenarios but also seemingly ruled out by distortions of the CMBR spectrum due to magnetic field dissipation on smaller scales and the overproduction of cluster magnetic fields. (d) The most promising detection possibility of CMBR distortions due to primordial magnetic fields may be on much smaller scales at higher multipoles l ∼ 10 6 where the signal is predicted to be the strongest (e) It seems possible that magnetic fields in clusters of galaxies are entirely of primordial origin, without invoking dynamo amplification. Such fields would be of (pre-collapse) strength 10 −12 − 10 −11 Gauss with correlation lengths in the kpc range, and would also exist in voids of galaxies.

Star formation is such a complex process that accurate numerical tools are needed to quantitatively examine the mass distribution and accretion of fragments in collapsing, turbulent, magnetized gas clouds. To enable a numerical treatment of this regime, we implemented sink particles in the adaptive mesh refinement (amr) hydrodynamics code flash. Sink particles are created in regions of local gravitational collapse, and their trajectories and accretion can be followed over many dynamical times. We perform a series of tests including the time integration of circular and elliptical orbits, the collapse of a Bonnor-Ebert sphere and a rotating, fragmenting cloud core. We compare the collapse of a highly unstable singular isothermal sphere to the theory by Shu (1977), and show that the sink particle accretion rate is in excellent agreement with the theoretical prediction.To model eccentric orbits and close encounters of sink particles accurately, we show that a very small timestep is often required, for which we implemented subcycling of the N -body system. We emphasize that a sole density threshold for sink particle creation is insufficient in supersonic flows, if the density threshold is below the opacity limit. In that case, the density can exceed the threshold in strong shocks that do not necessarily lead to local collapse. Additional checks for bound state, gravitational potential minimum, Jeans instability and converging flows are absolutely necessary for a meaningful creation of sink particles.We apply our new sink particle module for flash to the formation of a stellar cluster, and compare to a smoothed particle hydrodynamics (sph) code with sink particles. Our comparison shows encouraging agreement of gas properties, indicated by column density distributions and radial profiles, and of sink particle formation times and positions. We find excellent agreement in the number of sink particles formed, and in their accretion and mass distributions.

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.

We describe the first three-dimensional simulation of the gravitational collapse of a massive, rotating molecular cloud that includes heating by both non-ionizing and ionizing radiation. These models were performed with the FLASH code, incorporating a hybrid, long characteristic, ray tracing technique. We find that as the first protostars gain sufficient mass to ionize the accretion flow, their H ii regions are initially gravitationally trapped, but soon begin to rapidly fluctuate between trapped and extended states, in agreement with observations. Over time, the same ultracompact H ii region can expand anisotropically, contract again, and take on any of the observed morphological classes. In their extended phases, expanding H ii regions drive bipolar neutral outflows characteristic of high-mass star formation. The total lifetime of H ii regions is given by the global accretion timescale, rather than their short internal sound-crossing time. This explains the observed number statistics. The pressure of the hot, ionized gas does not terminate accretion. Instead the final stellar mass is set by fragmentationinduced starvation. Local gravitational instabilities in the accretion flow lead to the build-up of a small cluster of stars, all with relatively high masses due to heating from accretion radiation. These companions subsequently compete with the initial high-mass star for the same common gas reservoir and limit its mass growth. This is contrary to the classical competitive accretion model, where the massive stars are never hindered in growth by the low-mass stars in the cluster.Our findings show that the most significant differences between the formation of low-mass and high-mass stars are all explained as the result of rapid accretion within a dense, gravitationally unstable, ionized flow.

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