Geometrically motivated hyperbolic coordinate conditions for numerical relativity: Analysis, issues and implementations

We study the implications of adopting hyperbolic driver coordinate conditions motivated by geometrical considerations. In particular, conditions that minimize the rate of change of the metric variables. We analyze the properties of the resulting system of equations and their effect when implementing excision techniques. We find that commonly used coordinate conditions lead to a characteristic structure at the excision surface where some modes are not of outflow-type with respect to any excision boundary chosen inside the horizon. Thus, boundary conditions are required for these modes. Unfortunately, the specification of these conditions is a delicate issue as the outflow modes involve both gauge and main variables. As an alternative to these driver equations, we examine conditions derived from extremizing a scalar constructed from Killing's equation and present specific numerical examples.Comment: 9 figure

An ISH technique for the early detection of Enterospora nucleophila, an intranuclear microsporidian causing emaciative disease in gilthead sea bream

Enterospora nucleophila is a microsporidian parasite causing serious emaciative disease in cultured gilthead sea bream (GSB), Sparus aurata, and closely related to Enterocytozoon hepatopenaei from shrimp. The parasite can be found within the nuclei of enterocytes and rodlet cells of the fish intestinal epithelium, and occasionally in the cytoplasm of phagocytes in more advanced infections. However, spores are the only stage that can be unmistakably identified but even this may require thorough histopathological examination and use of chitin fluorescent stains for a proper confirmatory diagnosis, due to their minute size and intranuclear location. In the absence of spores, the infection can be suspected from a remarkable hypercelullarity and the presence of altered nuclei in the epithelial layer. This results in a very poor correlation of disease signs with diagnosis of E. nucleophila infection, and to current uncertainty about its real impact in GSB culture. This work describes the development and application of an in situ hybridization (ISH) technique as a powerful tool to overcome current diagnostic limitations for this species, and to decipher basic data on the infection and disease onset. We designed DIG-labelled oligonucleotide probes targeting unique regions of the (+) strand of E. nucleophila rDNA gene, and we developed an ISH protocol that results in good staining of infected host cells prior to the development of spores or other conspicuous stages. On clinically infected samples, numerous ISH-positive cells are present which are not stained with fluorescent whiteners that bind to parasite spores. In contrast, poor staining of spores was obtained with the DNA probes, due to their limited penetration in these stages and the low number of target gene copies that they harbour. These aspects might be improved using specific steps (e.g., chitinase or more aggressive permeabilization strategies) but they are not necessary in a clinical diagnostic context. Due to the relevance of E. nucleophila infections it is essential to decipher unknown aspects of the parasite\u2019s biology and course of infection using proper diagnostic tools. Their cryptic nature makes this a challenging task for microsporidians like E. nucleophila, which can benefit from the method hereby presented

Coherence Resonance in Chaotic Systems

We show that it is possible for chaotic systems to display the main features of coherence resonance. In particular, we show that a Chua model, operating in a chaotic regime and in the presence of noise, can exhibit oscillations whose regularity is optimal for some intermediate value of the noise intensity. We find that the power spectrum of the signal develops a peak at finite frequency at intermediate values of the noise. These are all signatures of coherence resonance. We also experimentally study a Chua circuit and corroborate the above simulation results. Finally, we analyze a simple model composed of two separate limit cycles which still exhibits coherence resonance, and show that its behavior is qualitatively similar to that of the chaotic Chua systemComment: 4 pages (including 4 figures) LaTeX fil

Simulating binary neutron stars: dynamics and gravitational waves

We model two mergers of orbiting binary neutron stars, the first forming a black hole and the second a differentially rotating neutron star. We extract gravitational waveforms in the wave zone. Comparisons to a post-Newtonian analysis allow us to compute the orbital kinematics, including trajectories and orbital eccentricities. We verify our code by evolving single stars and extracting radial perturbative modes, which compare very well to results from perturbation theory. The Einstein equations are solved in a first order reduction of the generalized harmonic formulation, and the fluid equations are solved using a modified convex essentially non-oscillatory method. All calculations are done in three spatial dimensions without symmetry assumptions. We use the \had computational infrastructure for distributed adaptive mesh refinement.Comment: 14 pages, 16 figures. Added one figure from previous version; corrected typo

EM counterparts of recoiling black holes: general relativistic simulations of non-Keplerian discs

We investigate the dynamics of a circumbinary disc that responds to the loss of mass and to the recoil velocity of the black hole produced by the merger of a binary system of supermassive black holes. We perform the first two-dimensional general relativistic hydrodynamics simulations of \textit{extended} non-Keplerian discs and employ a new technique to construct a "shock detector", thus determining the precise location of the shocks produced in the accreting disc by the recoiling black hole. In this way we can study how the properties of the system, such as the spin, mass and recoil velocity of the black hole, affect the mass accretion rate and are imprinted on the electromagnetic emission from these sources. We argue that the estimates of the bremsstrahlung luminosity computed without properly taking into account the radiation transfer yield cooling times that are unrealistically short. At the same time we show, through an approximation based on the relativistic isothermal evolution, that the luminosity produced can reach a peak value above $L \simeq 10^{43} \ {\rm erg/s}$ at about $\sim 30\,{\rm d}$ after the merger of a binary with total mass $M\simeq 10^6 M_\odot$ and persist for several days at values which are a factor of a few smaller. If confirmed by more sophisticated calculations such a signal could indeed lead to an electromagnetic counterpart of the merger of binary black-hole system.Comment: 17 pages, 11 figures, accepted by A&A, movies available at http://numrel.aei.mpg.de/Visualisations/Archive/BinaryBlackHoles/EMCounterparts/EMCounterparts.htm

On the Use of Multipole Expansion in Time Evolution of Non-linear Dynamical Systems and Some Surprises Related to Superradiance

A new numerical method is introduced to study the problem of time evolution of generic non-linear dynamical systems in four-dimensional spacetimes. It is assumed that the time level surfaces are foliated by a one-parameter family of codimension two compact surfaces with no boundary and which are conformal to a Riemannian manifold C. The method is based on the use of a multipole expansion determined uniquely by the induced metric structure on C. The approach is fully spectral in the angular directions. The dynamics in the complementary 1+1 Lorentzian spacetime is followed by making use of a fourth order finite differencing scheme with adaptive mesh refinement. In checking the reliability of the introduced new method the evolution of a massless scalar field on a fixed Kerr spacetime is investigated. In particular, the angular distribution of the evolving field in to be superradiant scattering is studied. The primary aim was to check the validity of some of the recent arguments claiming that the Penrose process, or its field theoretical correspondence---superradiance---does play crucial role in jet formation in black hole spacetimes while matter accretes onto the central object. Our findings appear to be on contrary to these claims as the angular dependence of a to be superradiant scattering of a massless scalar field does not show any preference of the axis of rotation. In addition, the process of superradiance, in case of a massless scalar field, was also investigated. On contrary to the general expectations no energy extraction from black hole was found even though the incident wave packets was fine tuned to be maximally superradiant. Instead of energy extraction the to be superradiant part of the incident wave packet fails to reach the ergoregion rather it suffers a total reflection which appears to be a new phenomenon.Comment: 49 pages, 11 figure

General relativistic radiation hydrodynamics of accretion flows. I: Bondi-Hoyle accretion

We present a new code for performing general-relativistic radiation-hydrodynamics simulations of accretion flows onto black holes. The radiation field is treated in the optically-thick approximation, with the opacity contributed by Thomson scattering and thermal bremsstrahlung. Our analysis is concentrated on a detailed numerical investigation of hot two-dimensional, Bondi-Hoyle accretion flows with various Mach numbers. We find significant differences with respect to purely hydrodynamical evolutions. In particular, once the system relaxes to a radiation-pressure dominated regime, the accretion rates become about two orders of magnitude smaller than in the purely hydrodynamical case, remaining however super-Eddington as are the luminosities. Furthermore, when increasing the Mach number of the inflowing gas, the accretion rates become smaller because of the smaller cross section of the black hole, but the luminosities increase as a result a stronger emission in the shocked regions. Overall, our approach provides the first self-consistent calculation of the Bondi-Hoyle luminosity, most of which is emitted within r~100 M from the black hole, with typical values L/L_Edd ~ 1-7, and corresponding energy efficiencies eta_BH ~ 0.09-0.5. The possibility of computing luminosities self-consistently has also allowed us to compare with the bremsstrahlung luminosity often used in modelling the electromagnetic counterparts to supermassive black-hole binaries, to find that in the optically-thick regime these more crude estimates are about 20 times larger than our radiation-hydrodynamics results.Comment: With updated bibliographyc informatio

Relativistic MHD with Adaptive Mesh Refinement

This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO method (CENO) in 3+1 dimensions, and the AMR is Berger-Oliger. Hyperbolic divergence cleaning is used to control the $\nabla\cdot {\bf B}=0$ constraint. We present results from three flat space tests, and examine the accretion of a fluid onto a Schwarzschild black hole, reproducing the Michel solution. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. Finally, we discuss strong scaling results for parallel unigrid and AMR runs.Comment: 24 pages, 14 figures, 3 table