T. A. Enßlin

Information field dynamics for simulation scheme construction

Information field dynamics (IFD) is introduced here as a framework to derive numerical schemes for the simulation of physical and other fields without assuming a particular subgrid structure as many schemes do. IFD constructs an ensemble of nonparametric subgrid field configurations from the combination of the data in computer memory, representing constraints on possible field configurations, and prior assumptions on the subgrid field statistics. Each of these field configurations can formally be evolved to a later moment since any differential operator of the dynamics can act on fields living in continuous space. However, these virtually evolved fields need again a representation by data in computer memory. The maximum entropy principle of information theory guides the construction of updated data sets via entropic matching, optimally representing these field configurations at the later time. The field dynamics thereby become represented by a finite set of evolution equations for the data that can be solved numerically. The subgrid dynamics is thereby treated within auxiliary analytic considerations. The resulting scheme acts solely on the data space. It should provide a more accurate description of the physical field dynamics than simulation schemes constructed ad hoc, due to the more rigorous accounting of subgrid physics and the space discretization process. Assimilation of measurement data into an IFD simulation is conceptually straightforward since measurement and simulation data can just be merged. The IFD approach is illustrated using the example of a coarsely discretized representation of a thermally excited classical Klein-Gordon field. This should pave the way towards the construction of schemes for more complex systems like turbulent hydrodynamics.

Detecting shock waves in cosmological smoothed particle hydrodynamics simulations

We develop a formalism for the identification and accurate estimation of the strength of structure formation shocks during cosmological smoothed particle hydrodynamics simulations. Shocks play a decisive role not only for the thermalization of gas in virializing structures but also for the acceleration of relativistic cosmic rays (CRs) through diffusive shock acceleration. Our formalism is applicable both to ordinary non-relativistic thermal gas, and to plasmas composed of CRs and thermal gas. To this end, we derive an analytic solution to the one-dimensional Riemann shock tube problem for a composite plasma of CRs and thermal gas. We apply our methods to study the properties of structure formation shocks in high-resolution hydrodynamic simulations of the Lambda cold dark matter (� CDM) model. We find that most of the energy is dissipated in weak internal shocks with Mach numbers M ∼ 2 which are predominantly central flow shocks or merger shock waves traversing halo centres. Collapsed cosmological structures are surrounded by external shocks with much higher Mach numbers up to M ∼ 1000, but they play only a minor role in the energy balance of thermalization. This is because of the higher pre-shock gas densities within non-linear structures, and the significant increase of the mean shock speed as the characteristic halo mass grows with cosmic time. We show that after the epoch of cosmic reionization the Mach number distribution is significantly modified by an efficient suppression of strong external shock waves due to the associated increase of the sound speed of the diffuse gas. Invoking a model for CR acceleration in shock waves, we find that the average strength of shock waves responsible for CR energy injection is higher than that for shocks that dominate the thermalization of the gas. This implies that the dynamical importance of shock-injected CRs is comparatively large in the low-density, peripheral halo infalling regions, but is less important for the weaker flow shocks occurring in central highdensity regions of haloes. When combined with radiative dissipation and star formation, our formalism can also be used to study CR injection by supernova shocks, or to construct models for shock-induced star formation in the interstellar medium.

Reviving fossil radio plasma in clusters of galaxies by adiabatic compression in environmental shock waves

We give for a plasma with a history of several expansion and contraction phases an analytical model of the evolution of a contained relativistic electron population under synchrotron, inverse Compton and adiabatic energy losses or gains. This is applied to different scenarios for evolution of radio plasma inside the cocoons of radio galaxies, after the activity of the central engine has ceased. It is demonstrated that fossil radio plasma with an age of even up to 2 Gyr can be revived by compression in a shock wave of large-scale structure formation, caused during the merging events of galaxy clusters, or by the accretion onto galaxy clusters. We argue, that this is a highly plausible explanation for the observed cluster radio relics, which are the regions of diffuse radio emission found in clusters of galaxies, without any likely parent radio galaxy seen nearby. An implication of this model is the existence of a population of diffuse, ultra-steep spectrum, very low frequency radio sources located inside and possibly outside of clusters of galaxies, tracing the revival of aged fossil radio plasma by the shock waves associated with large-scale structure formation.

A bayesian view on Faraday rotation maps - seeing the magnetic power spectra in galaxy clusters

We present a Bayesian maximum likelihood analysis of Faraday rotation measure (RM) maps of extended radio sources to determine magnetic field power spectra in clusters of galaxies. Using this approach, it is possible to determine the uncertainties in the measurements. We apply this approach to the RM map of Hydra A and derive the power spectrum of the cluster magnetic field. For Hydra A, we measure a spectral index of −5/3 over at least one order of magnitude implying Kolmogorov type turbulence. We find a dominant scale ∼3 kpc on which the magnetic power is concentrated, since the magnetic autocorrelation length is λB = 3 ± 0.5 kpc. Furthermore, we investigate the influences of the assumption about the sampling volume (described by a window function) on the magnetic power spectrum. The central magnetic field strength was determined to be ∼7 ± 2 µG for the most likely geometries.

A comparison of radio and X-ray morphologies of four clusters of galaxies containing radio halos

Clusters of galaxies may contain cluster-wide, centrally located, diuse radio sources, called halos. They have been found to show morphologies similar to those of the X-ray emission. To quantify this qualitative statement we performed a point-to-point comparison of the radio and the X-ray emission for four clusters of galaxies containing radio halos: Coma, Abell 2255, Abell 2319, Abell 2744. Our study leads to a linear relation between the radio and the X-ray surface brightness in two clusters, namely Abell 2255 and Abell 2744. In Coma and A2319 the radio and the X-ray brightnesses seem to be related with a sub-linear power law. Implications of these ndings within simple radio halo formation models are briefly discussed.

Simulating cosmic rays in clusters of galaxies – II. A unified scheme for radio haloes and relics with predictions of the γ-ray emission

The thermal plasma of galaxy clusters lost most of its information on how structure formation proceeded as a result of dissipative processes. In contrast , non-equilibrium distributions of cosmic rays (CR) preserve the information about their injection and transport processes and provide thus a unique window of current and past structure formation processes. This information can be unveiled by observations of non-thermal radiative processes, including radio synchrotron, hard X-ray, andγ-ray emission. To explore this, we use high-resolution simulations of a sample of galaxy clusters spanning a mass range of about two orders of magnitudes, and follow self-consistent CR physics on top of the radiative hydrodynamics. We model relativistic electrons that are accelerated at cosmological st ructure formation shocks and those that are produced in hadronic interactions of CRs with ambient gas protons. We find that the CR proton pressure traces the time integrated non-equilibriu m activities of clusters and is modulated by the recent dynamical activities. In contrast, the p ressure of primary shock-accelerated CR electrons resembles current accretion and merging shock waves that break at the shallow cluster potential in the virial regions. The resulting sync hrotron emission is predicted to be polarised and has an inhomogeneous and aspherical spatial distribution which matches the properties of observed radio relics. We propose a unified sch eme for the generation of giant radio halos as well as radio mini-halos that naturally arise s from our simulated synchrotron surface brightness maps and emission profiles. Giant radio h alos are dominated in the centre by secondary synchrotron emission with a transition to the radio synchrotron radiation emitted from primary, shock-accelerated electrons in the cluster periphery. This model is able to explain the regular structure of radio halos by the dominant contribution of hadronically produced electrons. At the same time, it is able to account for th e observed correlation of mergers with radio halos, the larger peripheral variation of the spe ctral index, and the large scatter in the scaling relation between cluster mass and synchrotron emission. Future low-frequency radio telescopes (LOFAR, GMRT, MWA, LWA) are expected to probe the accretion shock regions of clusters and the warm-hot intergalactic medium, depending on the adopted model for the magnetic fields. The hadronic origin of radio halos can be scrutinised by the detection of pion-decay inducedγ-rays following hadronic CR interactions. The high-energyγ-ray emission depends only weakly on whether radiative or non-radiative gas physics is simulated due to the self-regulated nature of the CR cooling processes. Our models predict aγ-ray emission level that should be observable with the GLAST satellite.

Cosmic ray transport in galaxy clusters: implications for radio halos, gamma-ray signatures, and cool core heating

We investigate the interplay of cosmic ray (CR) propagation and advection in galaxy clusters. Propagation in form of CR diffusion and streaming tends to drive the CR radial profiles towards being flat, with equal CR number density everywhere. Advection of CR by the turbulent gas motions tends to produce centrally enhanced profiles. We assume that the CR streaming velocity is of the order of the sound velocity. This is motivated by plasma physical arguments. The CR streaming is then usually larger than typical advection velocities and becomes comparable or lower than this only for periods with trans- and super-sonic cluster turbulence. As a consequence a bimodality of the CR spatial distribution results. Strongly turbulent, merging clusters should have a more centrally concentrated CR energy density profile with respect to relaxed ones with very subsonic turbulence. This translates into a bimodality of the expected diffuse radio and gamma-ray emission of clusters, since more centrally concentrated CR will find higher target densities for hadronic CR proton interactions, higher plasma wave energy densities for CR electron and proton re-acceleration, and stronger magnetic fields. Thus, the observed bimodality of cluster radio halos appears to be a natural consequence of the interplay of CR transport processes, independent of the model of radio halo formation, be it hadronic interactions of CR protons or re-acceleration of low-energy CR electrons. Energy dependence of the CR propagation should lead to spectral steepening of dying radio halos. Furthermore, we show that the interplay of CR diffusion with advection implies first order CR re-acceleration in the pressure-stratified atmospheres of galaxy clusters. Finally, we argue that CR streaming could be important in turbulent cool cores of galaxy clusters since it heats preferentially the central gas with highest cooling rate.

Ultrahigh energy cosmic ray probes of large scale structure and magnetic fields

We study signatures of a structured universe in the multi-pole moments, auto-correlation function, and cluster statistics of ultrahigh energy cosmic rays above

Impact of tangled magnetic fields on fossil radio bubbles

{10}^{19}\mathrm{eV}.

An improved map of the galactic Faraday sky

We compare scenarios where the sources are distributed homogeneously or according to the baryon density distribution obtained from a cosmological large scale structure simulation. The influence of extragalactic magnetic fields is studied by comparing the case of negligible fields with fields expected to be produced along large scale shocks with a maximal strength consistent with observations. We confirm that strongly magnetized observers would predict considerable anisotropy on large scales, which is already in conflict with current data. In the best fit scenario only the sources are strongly magnetized, although deflection can still be considerable, of order