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We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average disperse most efficiently in the form of extreme value statistics and flow anisotropy via the geometric properties of the convex hulls. We use the convex hull surface geometry to examine the anisotropy that occurs in turbulent convection. Applying extreme value theory, we show that the maximal square extensions of convex hull vertices are well described by a classic extreme value distribution, the Gumbel distribution. During turbulent convection, intermittent convective plumes grow and accelerate the dispersion of Lagrangian tracers. Convex hull analysis yields information that supplements standard Lagrangian analysis of coherent turbulent structures and their influence on the global statistics of the flow.
Context. radio spectra of many shell-type supernova remnants show deviations from those expected on theoretical grounds.
Aims. In this paper we determine the effect of stochastic reacceleration on the spectra of electrons in the GeV band and at lower energies, and we investigate whether reacceleration can explain the observed variation in radio spectral indices.
Methods. We explicitely calculated the momentum diffusion coefficient for 3 types of turbulence expected downstream of the forward shock: fast-mode waves, small-scale non-resonant modes, and large-scale modes arising from turbulent dynamo activity. After noting that low-energy particles are efficiently coupled to the quasi-thermal plasma, a simplified cosmic-ray transport equation can be formulated and is numerically solved.
Results. Only fast-mode waves can provide momentum diffusion fast enough to significantly modify the spectra of particles. Using a synchrotron emissivity that accurately reflects a highly turbulent magnetic field, we calculated the radio spectral index and find that soft spectra with index a alpha less than or similar to -0.6 can be maintained over more than 2 decades in radio frequency, even if the electrons experience reacceleration for only one acceleration time. A spectral hardening is possible but considerably more frequency-dependent. The spectral modification imposed by stochastic reacceleration downstream of the forward shock depends only weakly on the initial spectrum provided by, e.g., diffusive shock acceleration at the shock itself.
We perform two-dimensional relativistic magnetohydrodynamic simulations of a mildly relativistic shock propagating through an inhomogeneous medium. We show that the postshock region becomes turbulent owing to preshock density inhomogeneity, and the magnetic field is strongly amplified due to the stretching and folding of field lines in the turbulent velocity field. The amplified magnetic field evolves into a filamentary structure in two-dimensional simulations. The magnetic energy spectrum is flatter than the Kolmogorov spectrum and indicates that a so-called small-scale dynamo is occurring in the postshock region. We also find that the amount of magnetic-field amplification depends on the direction of the mean preshock magnetic field, and the timescale of magnetic-field growth depends on the shock strength.
We have investigated via 2D relativistic magnetohydrodynamic simulations the long-term evolution of turbulence created by a relativistic shock propagating through an inhomogeneous medium. In the post-shock region, magnetic field is strongly amplified by turbulent motions triggered by pre-shock density inhomogeneities. Using a long-simulation box we have followed the magnetic field amplification until it is fully developed and saturated. The turbulent velocity is subrelativistic even for a strong shock. Magnetic field amplification is controlled by the turbulent motion and saturation occurs when the magnetic energy is comparable to the turbulent kinetic energy. Magnetic field amplification and saturation depend on the initial strength and direction of the magnetic field in the pre-shock medium, and on the shock strength. If the initial magnetic field is perpendicular to the shock normal, the magnetic field is first compressed at the shock and then can be amplified by turbulent motion in the post-shock region. Saturation occurs when the magnetic energy becomes comparable to the turbulent kinetic energy in the post-shock region. If the initial magnetic field in the pre-shock medium is strong, the post-shock region becomes turbulent but significant field amplification does not occur. If the magnetic energy after shock compression is larger than the turbulent kinetic energy in the post-shock region, significant field amplification does not occur. We discuss possible applications of our results to gamma-ray bursts and active galactic nuclei.
The transport of cosmic rays (CRs) is crucial for the understanding of almost all high-energy phenomena. Both pre-existing large-scale magnetohydrodynamic (MHD) turbulence and locally generated turbulence through plasma instabilities are important for the CR propagation in astrophysical media. The potential role of the resonant instability triggered by CR pressure anisotropy to regulate the parallel spatial diffusion of low-energy CRs (less than or similar to 100 GeV) in the interstellar and intracluster medium of galaxies has been shown in previous theoretical works. This work aims to study the gyroresonance instability via direct numerical simulations, in order to access quantitatively the wave-particle scattering rates. For this, we employ a 1D PIC-MHD code to follow the growth and saturation of the gyroresonance instability. We extract from the simulations the pitch-angle diffusion coefficient D-mu mu produced by the instability during the linear and saturation phases, and a very good agreement (within a factor of 3) is found with the values predicted by the quasi-linear theory (QLT). Our results support the applicability of the QLT for modelling the scattering of low-energy CRs by the gyroresonance instability in the complex interplay between this instability and the large-scale MHD turbulence.
A non-resonant cosmic ray (CR) current-driven instability may operate in the shock precursors of young supernova remnants and be responsible for magnetic-field amplification, plasma heating and turbulence. Earlier simulations demonstrated magnetic-field amplification, and in kinetic studies a reduction of the relative drift between CRs and thermal plasma was observed as backreaction. However, all published simulations used periodic boundary conditions, which do not account for mass conservation in decelerating flows and only allow the temporal development to be studied. Here we report results of fully kinetic particle-in-cell simulations with open boundaries that permit inflow of plasma on one side of the simulation box and outflow at the other end, hence allowing an investigation of both the temporal and the spatial development of the instability. Magnetic-field amplification proceeds as in studies with periodic boundaries and, observed here for the first time, the reduction of relative drifts causes the formation of a shock-like compression structure at which a fraction of the plasma ions are reflected. Turbulent electric field generated by the non-resonant instability inelastically scatters CRs, modifying and anisotropizing their energy distribution. Spatial CR scattering is compatible with Bohm diffusion. Electromagnetic turbulence leads to significant non-adiabatic heating of the background plasma maintaining bulk equipartition between ions and electrons. The highest temperatures are reached at sites of large-amplitude electrostatic fields. Ion spectra show supra-thermal tails resulting from stochastic scattering in the turbulent electric field. Together, these modifications in the plasma flow will affect the properties of the shock and particle acceleration there.
Understanding the formation of stars in galaxies is central to much of modern astrophysics. For several decades it has been thought that the star formation process is primarily controlled by the interplay between gravity and magnetostatic support, modulated by neutral-ion drift. Recently, however, both observational and numerical work has begun to suggest that supersonic interstellar turbulence rather than magnetic fields controls star formation. This review begins with a historical overview of the successes and problems of both the classical dynamical theory of star formation, and the standard theory of magnetostatic support from both observational and theoretical perspectives. We then present the outline of a new paradigm of star formation based on the interplay between supersonic turbulence and self-gravity. Supersonic turbulence can provide support against gravitational collapse on global scales, while at the same time it produces localized density enhancements that allow for collapse on small scales. The efficiency and timescale of stellar birth in Galactic gas clouds strongly depend on the properties of the interstellar turbulent velocity field, with slow, inefficient, isolated star formation being a hallmark of turbulent support, and fast, efficient, clustered star formation occurring in its absence. After discussing in detail various theoretical aspects of supersonic turbulence in compressible self-gravitating gaseous media relevant for star forming interstellar clouds, we explore the consequences of the new theory for both local star formation and galactic scale star formation. The theory predicts that individual star-forming cores are likely not quasi-static objects, but dynamically evolving. Accretion onto these objects will vary with time and depend on the properties of the surrounding turbulent flow. This has important consequences for the resulting stellar mass function. Star formation on scales of galaxies as a whole is expected to be controlled by the balance between gravity and turbulence, just like star formation on scales of individual interstellar gas clouds, but may be modulated by additional effects like cooling and differential rotation. The dominant mechanism for driving interstellar turbulence in star-forming regions of galactic disks appears to be supernovae explosions. In the outer disk of our Milky Way or in low-surface brightness galaxies the coupling of rotation to the gas through magnetic fields or gravity may become important.
We investigate the rotational and thermal properties of star-forming molecular clouds using hydrodynamic simulations. Stars form from molecular cloud cores by gravoturbulent fragmentation. Understanding the angular momentum and the thermal evolution of cloud cores thus plays a fundamental role in completing the theoretical picture of star formation. This is true not only for current star formation as observed in regions like the Orion nebula or the ρ-Ophiuchi molecular cloud but also for the formation of stars of the first or second generation in the universe. In this thesis we show how the angular momentum of prestellar and protostellar cores evolves and compare our results with observed quantities. The specific angular momentum of prestellar cores in our models agree remarkably well with observations of cloud cores. Some prestellar cores go into collapse to build up stars and stellar systems. The resulting protostellar objects have specific angular momenta that fall into the range of observed binaries. We find that collapse induced by gravoturbulent fragmentation is accompanied by a substantial loss of specific angular momentum. This eases the "angular momentum problem" in star formation even in the absence of magnetic fields. The distribution of stellar masses at birth (the initial mass function, IMF) is another aspect that any theory of star formation must explain. We focus on the influence of the thermodynamic properties of star-forming gas and address this issue by studying the effects of a piecewise polytropic equation of state on the formation of stellar clusters. We increase the polytropic exponent γ from a value below unity to a value above unity at a certain critical density. The change of the thermodynamic state at the critical density selects a characteristic mass scale for fragmentation, which we relate to the peak of the IMF observed in the solar neighborhood. Our investigation generally supports the idea that the distribution of stellar masses depends mainly on the thermodynamic state of the gas. A common assumption is that the chemical evolution of the star-forming gas can be decoupled from its dynamical evolution, with the former never affecting the latter. Although justified in some circumstances, this assumption is not true in every case. In particular, in low-metallicity gas the timescales for reaching the chemical equilibrium are comparable or larger than the dynamical timescales. In this thesis we take a first approach to combine a chemical network with a hydrodynamical code in order to study the influence of low levels of metal enrichment on the cooling and collapse of ionized gas in small protogalactic halos. Our initial conditions represent protogalaxies forming within a fossil HII region -- a previously ionized HII region which has not yet had time to cool and recombine. We show that in these regions, H2 is the dominant and most effective coolant, and that it is the amount of H2 formed that controls whether or not the gas can collapse and form stars. For metallicities Z <= 10<sup>-3 Zsun, metal line cooling alters the density and temperature evolution of the gas by less than 1% compared to the metal-free case at densities below 1 cm<sup>-3 and temperatures above 2000 K. We also find that an external ultraviolet background delays or suppresses the cooling and collapse of the gas regardless of whether it is metal-enriched or not. Finally, we study the dependence of this process on redshift and mass of the dark matter halo.
Processes driving the production, transformation and transport of methane (CH4) in wetland ecosystems are highly complex. We present a simple calculation algorithm to separate open-water CH4 fluxes measured with automatic chambers into diffusion- and ebullition-derived components. This helps to reveal underlying dynamics, to identify potential environmental drivers and, thus, to calculate reliable CH4 emission estimates. The flux separation is based on identification of ebullition-related sudden concentration changes during single measurements. Therefore, a variable ebullition filter is applied, using the lower and upper quartile and the interquartile range (IQR). Automation of data processing is achieved by using an established R script, adjusted for the purpose of CH4 flux calculation. The algorithm was validated by performing a laboratory experiment and tested using flux measurement data (July to September 2013) from a former fen grassland site, which converted into a shallow lake as a result of rewetting. Ebullition and diffusion contributed equally (46 and 55 %) to total CH4 emissions, which is comparable to ratios given in the literature. Moreover, the separation algorithm revealed a concealed shift in the diurnal trend of diffusive fluxes throughout the measurement period. The water temperature gradient was identified as one of the major drivers of diffusive CH4 emissions, whereas no significant driver was found in the case of erratic CH4 ebullition events.
Bei Entscheidungen über abzulösende oder neue Anwendungssysteme kann mit Hilfe funktionaler Anforderungen immer nur der gegenwärtige oder vorhersehbare Bedarf ermittelt werden. In einem turbulenten Umfeld sind die Anwendungssysteme jedoch häufig langere Zeit im Einsatz als die Anforderungen gültig sind, mit Hilfe derer sie ausgewählt wurden. An der Universität Potsdam wird im Rahmen des BMBF-Projektes CHANGE eine Vorgehensweise zur Ermittlung der Zukunftsfähigkeit unternehmensweiter Anwendungssysteme entwickelt, deren wesentliche Merkmale in diesem Beitrag beschrieben werden.