Order out of Randomness : Self-Organization Processes in Astrophysics

Self-organization is a property of dissipative nonlinear processes that are governed by an internal driver and a positive feedback mechanism, which creates regular geometric and/or temporal patterns and decreases the entropy, in contrast to random processes. Here we investigate for the first time a comprehensive number of 16 self-organization processes that operate in planetary physics, solar physics, stellar physics, galactic physics, and cosmology. Self-organizing systems create spontaneous {\sl order out of chaos}, during the evolution from an initially disordered system to an ordered stationary system, via quasi-periodic limit-cycle dynamics, harmonic mechanical resonances, or gyromagnetic resonances. The internal driver can be gravity, rotation, thermal pressure, or acceleration of nonthermal particles, while the positive feedback mechanism is often an instability, such as the magneto-rotational instability, the Rayleigh-B\'enard convection instability, turbulence, vortex attraction, magnetic reconnection, plasma condensation, or loss-cone instability. Physical models of astrophysical self-organization processes involve hydrodynamic, MHD, and N-body formulations of Lotka-Volterra equation systems.Comment: 61 pages, 38 Figure

Towards a solution of the closure problem for convective atmospheric boundary-layer turbulence

We consider the closure problem for turbulence in the dry convective atmospheric boundary layer (CBL). Transport in the CBL is carried by small scale eddies near the surface and large plumes in the well mixed middle part up to the inversion that separates the CBL from the stably stratified air above. An analytically tractable model based on a multivariate Delta-PDF approach is developed. It is an extension of the model of Gryanik and Hartmann [1] (GH02) that additionally includes a term for background turbulence. Thus an exact solution is derived and all higher order moments (HOMs) are explained by second order moments, correlation coefficients and the skewness. The solution provides a proof of the extended universality hypothesis of GH02 which is the refinement of the Millionshchikov hypothesis (quasi- normality of FOM). This refined hypothesis states that CBL turbulence can be considered as result of a linear interpolation between the Gaussian and the very skewed turbulence regimes. Although the extended universality hypothesis was confirmed by results of field measurements, LES and DNS simulations (see e.g. [2-4]), several questions remained unexplained. These are now answered by the new model including the reasons of the universality of the functional form of the HOMs, the significant scatter of the values of the coefficients and the source of the magic of the linear interpolation. Finally, the closures 61 predicted by the model are tested against measurements and LES data. Some of the other issues of CBL turbulence, e.g. familiar kurtosis-skewness relationships and relation of area coverage parameters of plumes (so called filling factors) with HOM will be discussed also

The 3D MHD code GOEMHD3 for large-Reynolds-number astrophysical plasmas

The numerical simulation of turbulence and flows in almost ideal, large-Reynolds-number astrophysical plasmas motivates the implementation of almost conservative MHD computer codes. They should efficiently calculate, use highly parallelized schemes scaling well with large numbers of CPU cores, allows to obtain a high grid resolution over large simulation domains and which can easily be adapted to new computer architectures as well as to new initial and boundary conditions, allow modular extensions. The new massively parallel simulation code GOEMHD3 enables efficient and fast simulations of almost ideal, large-Reynolds-number astrophysical plasma flows, well resolved and on huge grids covering large domains. Its abilities are validated by major tests of ideal and weakly dissipative plasma phenomena. The high resolution ($2048^3$ grid points) simulation of a large part of the solar corona above an observed active region proved the excellent parallel scalability of the code using more than 30.000 processor cores.Comment: The revised versio

A Meshless Method for Magnetohydrodynamics and Applications to Protoplanetary Disks

This thesis presents an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. Local, third-order, least-squares, polynomial interpolations (Moving Least Squares interpolations) are calculated from the field values of neighboring particles to obtain field values and spatial derivatives at the particle position. Field values and particle positions are advanced in time with a second order predictor-corrector scheme. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is implemented to ensure the particles fill the computational volume, which gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. Particle addition and deletion is based on a local void and clump detection algorithm. Dynamic artificial viscosity fields provide stability to the integration. The resulting algorithm provides a robust solution for modeling flows that require Lagrangian or adaptive discretizations to resolve. The code has been parallelized by adapting the framework provided by Gadget-2. A set of standard test problems, including one part in a million amplitude linear MHD waves, magnetized shock tubes, and Kelvin-Helmholtz instabilities are presented. Finally we demonstrate good agreement with analytic predictions of linear growth rates for magnetorotational instability in a cylindrical geometry. We provide a rigorous methodology for verifying a numerical method on two dimensional Kelvin-Helmholtz instability. The test problem was run in the Pencil Code, Athena, Enzo, NDSPHMHD, and Phurbas. A strict comparison, judgment, or ranking, between codes is beyond the scope of this work, although this work provides the mathematical framework needed for such a study. Nonetheless, how the test is posed circumvents the issues raised by tests starting from a sharp contact discontinuity yet it still shows the poor performance of Smoothed Particle Hydrodynamics. We then comment on the connection between this behavior and the underlying lack of zeroth-order consistency in Smoothed Particle Hydrodynamics interpolation. In astrophysical magnetohydrodynamics (MHD) and electrodynamics simulations, numerically enforcing the divergence free constraint on the magnetic field has been difficult. We observe that for point-based discretization, as used in finite-difference type and pseudo-spectral methods, the divergence free constraint can be satisfied entirely by a choice of interpolation used to define the derivatives of the magnetic field. As an example we demonstrate a new class of finite-difference type derivative operators on a regular grid which has the divergence free property. This principle clarifies the nature of magnetic monopole errors. The principles and techniques demonstrated in this chapter are particularly useful for the magnetic field, but can be applied to any vector field. Finally, we examine global zoom-in simulations of turbulent magnetorotationally unstable flow. We extract and analyze the high-current regions produced in the turbulent flow. Basic parameters of these regions are abstracted, and we build one dimensional models including non-ideal MHD, and radiative transfer. For sufficiently high temperatures, an instability resulting from the temperature dependence of the Ohmic resistivity is found. This instability concentrates current sheets, resulting in the possibility of rapid heating from temperatures on the order of 600 Kelvin to 2000 Kelvin in magnetorotationally turbulent regions of protoplanetary disks. This is a possible local mechanism for the melting of chondrules and the formation of other high-temperature materials in protoplanetary disks

Protostellar birth with ambipolar and ohmic diffusion

The transport of angular momentum is capital during the formation of low-mass stars; too little removal and rotation ensures stellar densities are never reached, too much and the absence of rotation means no protoplanetary disks can form. Magnetic diffusion is seen as a pathway to resolving this long-standing problem. We investigate the impact of including resistive MHD in simulations of the gravitational collapse of a 1 solar mass gas sphere, from molecular cloud densities to the formation of the protostellar seed; the second Larson core. We used the AMR code RAMSES to perform two 3D simulations of collapsing magnetised gas spheres, including self-gravity, radiative transfer, and a non-ideal gas equation of state to describe H2 dissociation which leads to the second collapse. The first run was carried out under the ideal MHD approximation, while ambipolar and ohmic diffusion was incorporated in the second calculation. In the ideal MHD simulation, the magnetic field dominates the energy budget everywhere inside and around the first core, fueling interchange instabilities and driving a low-velocity outflow. High magnetic braking removes essentially all angular momentum from the second core. On the other hand, ambipolar and ohmic diffusion create a barrier which prevents amplification of the magnetic field beyond 0.1 G in the first Larson core which is now fully thermally supported. A significant amount of rotation is preserved and a small Keplerian-like disk forms around the second core. When studying the radiative efficiency of the first and second core accretion shocks, we found that it can vary by several orders of magnitude over the 3D surface of the cores. Magnetic diffusion is a pre-requisite to star-formation; it enables the formation of protoplanetary disks in which planets will eventually form, and also plays a determinant role in the formation of the protostar itself.Comment: 18 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

Magnetic fields in cosmic particle acceleration sources

We review here some magnetic phenomena in astrophysical particle accelerators associated with collisionless shocks in supernova remnants, radio galaxies and clusters of galaxies. A specific feature is that the accelerated particles can play an important role in magnetic field evolution in the objects. We discuss a number of CR-driven, magnetic field amplification processes that are likely to operate when diffusive shock acceleration (DSA) becomes efficient and nonlinear. The turbulent magnetic fields produced by these processes determine the maximum energies of accelerated particles and result in specific features in the observed photon radiation of the sources. Equally important, magnetic field amplification by the CR currents and pressure anisotropies may affect the shocked gas temperatures and compression, both in the shock precursor and in the downstream flow, if the shock is an efficient CR accelerator. Strong fluctuations of the magnetic field on scales above the radiation formation length in the shock vicinity result in intermittent structures observable in synchrotron emission images. Resonant and non-resonant CR streaming instabilities in the shock precursor can generate mesoscale magnetic fields with scale-sizes comparable to supernova remnants and even superbubbles. This opens the possibility that magnetic fields in the earliest galaxies were produced by the first generation Population III supernova remnants and by clustered supernovae in star forming regions.Comment: 30 pages, Space Science Review

MHD numerical simulations in a cosmological context

Magnetic fields in the Universe are found in almost all studied environments. In particular, their presence in the inter-galactic medium and in the intra-cluster medium is confirmed by diffuse radio emission as well as by observations of Faraday Rotation Measures towards polarized radio sources within or behind the magnetized medium. Besides the observations, their dynamical importance in astrophysical systems is poorly constrained, therefore there are still plenty of processes in which the role of magnetic fields are not fully understood. Astrophysical systems are complex and highly nonlinear. Therefore, numerical simulations have demonstrated to be a useful tool to study those problems. However, the inclusion of magnetic fields in numerical implementations is not easy to achieve. Mainly because of the difficulties to keep the ∇ · B constraint low, and to have a stable implementation in different circumstances. We study and developed a cosmological MHD code in SPH. We study different possible schemes to regularize the magnetic field, and avoid instabilities. Those schemes included the use of Euler potentials to build the magnetic field, as well as cleaning schemes for the numerical ∇ · B errors. We studied the magnetic field evolution in the context of cosmological structure formation of galaxy clusters. We compare different numerical schemes leading us to the conclusion that the ∇ · B terms do not drive the evolution and growth of the magnetic field in galaxy clusters. We made synthetic rotation measure maps and study the reversals of the magnetic field in comparison with observations. The comparison between observations and high resolution simulations, suggests that the physics may be described by a multi scale turbulence model. This means that the turbulent dynamo driven by the cosmological cluster formation process works effectively, reproducing basic properties from observations, even to details shown in structure functions and converging to the observation when we increase the resolution. We clearly demonstrates that using advanced schemes together with very high resolution allow to probe the properties of the ICM. Additionally, we investigate the magnetic fields and their relation with the cosmic structure in which they are embedded. In general, the observed rotation measure signal is strongly dominated by denser regions (e.g. those populated by galaxy clusters and groups), and in unclear how is their transition to low density regions, because there is difficult to acquire direct magnetic field information of those regions. Therefore statistical tools, such as correlation functions have to be used. To do so, we use cosmological simulations and try to mimic all the possible observation biases to constrain actual measurements. We find that the shape of the cross-correlation function using a normalized estimator (in absence of any noise or foreground signal) nicely reflects the underlying distribution of magnetic field within the large scale structure. However, current measurement errors suppress the signal in such a way that it is impossible to relate the amplitude of the cross-correlation function to the underlying magnetization of the large scale structur