Computational General Relativistic Force-Free Electrodynamics: II. Characterization of Numerical Diffusivity

Scientific codes are an indispensable link between theory and experiment; in (astro-)plasma physics, such numerical tools are one window into the universe's most extreme flows of energy. The discretization of Maxwell's equations - needed to make highly magnetized (astro)physical plasma amenable to its numerical modeling - introduces numerical diffusion. It acts as a source of dissipation independent of the system's physical constituents. Understanding the numerical diffusion of scientific codes is the key to classify their reliability. It gives specific limits in which the results of numerical experiments are physical. We aim at quantifying and characterizing the numerical diffusion properties of our recently developed numerical tool for the simulation of general relativistic force-free electrodynamics, by calibrating and comparing it with other strategies found in the literature. Our code correctly models smooth waves of highly magnetized plasma. We evaluate the limits of general relativistic force-free electrodynamics in the context of current sheets and tearing mode instabilities. We identify that the current parallel to the magnetic field ($\mathbf{j}_\parallel$), in combination with the break-down of general relativistic force-free electrodynamics across current sheets, impairs the physical modeling of resistive instabilities. We find that at least eight numerical cells per characteristic size of interest (e.g. the wavelength in plasma waves or the transverse width of a current sheet) are needed to find consistency between resistivity of numerical and of physical origins. High-order discretization of the force-free current allows us to provide almost ideal orders of convergence for (smooth) plasma wave dynamics. The physical modeling of resistive layers requires suitable current prescriptions or a sub-grid modeling for the evolution of $\mathbf{j}_\parallel$.Comment: 14 pages, 9 figures, submitted to A&

Computational General Relativistic Force-Free Electrodynamics: I. Multi-Coordinate Implementation and Testing

General relativistic force-free electrodynamics is one possible plasma-limit employed to analyze energetic outflows in which strong magnetic fields are dominant over all inertial phenomena. The amazing images of black hole shadows from the galactic center and the M87 galaxy provide a first direct glimpse into the physics of accretion flows in the most extreme environments of the universe. The efficient extraction of energy in the form of collimated outflows or jets from a rotating BH is directly linked to the topology of the surrounding magnetic field. We aim at providing a tool to numerically model the dynamics of such fields in magnetospheres around compact objects, such as black holes and neutron stars. By this, we probe their role in the formation of high energy phenomena such as magnetar flares and the highly variable teraelectronvolt emission of some active galactic nuclei. In this work, we present numerical strategies capable of modeling fully dynamical force-free magnetospheres of compact astrophysical objects. We provide implementation details and extensive testing of our implementation of general relativistic force-free electrodynamics in Cartesian and spherical coordinates using the infrastructure of the Einstein Toolkit. The employed hyperbolic/parabolic cleaning of numerical errors with full general relativistic compatibility allows for fast advection of numerical errors in dynamical spacetimes. Such fast advection of divergence errors significantly improves the stability of the general relativistic force-free electrodynamics modeling of black hole magnetospheres.Comment: 19 pages, 15 figures, submitted to A&

Self-consistent MHD simulation of jet launching in a neutron star - white dwarf merger

The merger of a white dwarf (WD) and a neutron star (NS) is a relatively common event that will produce an observable electromagnetic signal. Furthermore, the compactness of these stellar objects makes them an interesting candidate for gravitational wave (GW) astronomy, potentially being in the frequency range of LISA and other missions. To date, three-dimensional simulations of these mergers have not fully modelled the WD disruption, or have used lower resolutions and have not included magnetic fields even though they potentially shape the evolution of the merger remnant. In this work, we simulate the merger of a 1.4$M_\odot$ NS with a 1$M_\odot$ carbon oxygen WD in the magnetohydrodynamic moving mesh code \AREPO. We find that the disruption of the WD forms an accretion disk around the NS, and the subsequent accretion by the NS powers the launch of strongly magnetized, mildly relativistic jets perpendicular to the orbital plane. Although the exact properties of the jets could be altered by unresolved physics around the NS, the event could result in a transient with a larger luminosity than kilonovae. We discuss possible connections to fast blue optical transients (FBOTs) and long-duration gamma-ray bursts. We find that the frequency of GWs released during the merger is too high to be detectable by the LISA mission, but suitable for deci-hertz observatories such as LGWA, BBO or DECIGO.Comment: Accepted for publication in A&A. 13 pages, 11 figure

Bell correlation depth in many-body systems

We address the question of assessing the number of particles sharing genuinely nonlocal correlations in a multipartite system. While the interest in multipartite nonlocality has grown in recent years, its existence in large quantum systems is difficult to confirm experimentally. This is mostly due to the inadequacy of standard multipartite Bell inequalities to many-body systems: Such inequalities usually rely on expectation values involving many parties, usually all, and require individual addressing of each party. In addition, known Bell inequalities for genuine nonlocality are composed of a number of expectation values that scales exponentially with the number of observers, which makes such inequalities impractical from the experimental point of view. In a recent work [Tura et al., Science 344, 1256 (2014)], it was shown that it is possible to detect nonlocality in multipartite systems using Bell inequalities with only two-body correlators. This opened the way for the detection of Bell correlations with trusted collective measurements through Bell correlation witnesses [Schmied et al., Science 352, 441 (2016)]. These witnesses were recently tested experimentally in many-body systems such as Bose-Einstein condensate or thermal ensembles, hence demonstrating the presence of Bell correlations with assumptions on the statistics. Here, we address the problem of detecting nonlocality depth, a notion that quantifies the number of particles sharing nonlocal correlation in a multipartite system. We introduce a general framework allowing us to derive Bell-like inequalities for nonlocality depth from symmetric two-body correlators. We characterize all such Bell-like inequalities for a finite number of parties and we show that they reveal Bell correlation depth k <= 6 in arbitrarily large systems. We then show how Bell correlation depth can be estimated using quantities that are within reach in current experiments. On one hand, we use the standard multipartite Bell inequalities such the Mermin and Svetlichny ones to derive Bell correlations witnesses of any depth that involves only two collective measurements, one of which being the parity measurement. On the other hand, we show that our two-body Bell inequalities can be turned into witnesses of depth k <= 6 that require measuring total spin components in certain directions. Interestingly, such a witness is violated by existing data from an ensemble of 480 atoms

An improved formulation of the relativistic hydrodynamics equations in 2D Cartesian coordinates

A number of astrophysical scenarios possess and preserve an overall cylindrical symmetry also when undergoing a catastrophic and nonlinear evolution. Exploiting such a symmetry, these processes can be studied through numerical-relativity simulations at smaller computational costs and at considerably larger spatial resolutions. We here present a new flux-conservative formulation of the relativistic hydrodynamics equations in cylindrical coordinates. By rearranging those terms in the equations which are the sources of the largest numerical errors, the new formulation yields a global truncation error which is one or more orders of magnitude smaller than those of alternative and commonly used formulations. We illustrate this through a series of numerical tests involving the evolution of oscillating spherical and rotating stars, as well as shock-tube tests.Comment: 19 pages, 9 figure

TeV Neutrinos from Successful and Choked Gamma-Ray Bursts

Core collapse of massive stars resulting in a relativistic fireball jet which breaks through the stellar envelope is a widely discussed scenario for gamma-ray burst production. For very extended or slow rotating stars, the fireball may be unable to break through the envelope. Both penetrating and choked jets will produce, by photo-meson interactions of accelerated protons, a burst of neutrinos with energies in excess of 5 TeV while propagating in the envelope. The predicted flux, from both penetrating and chocked fireballs, should be easily detectable by planned cubic kilometer neutrino telescopes.Comment: Phys.Rev.Letters, in press, final version accepted 8/31/01 (orig. 3/17/01

Accurate evolutions of inspiralling neutron-star binaries: assessment of the truncation error

We have recently presented an investigation in full general relativity of the dynamics and gravitational-wave emission from binary neutron stars which inspiral and merge, producing a black hole surrounded by a torus (see arXiv:0804.0594). We here discuss in more detail the convergence properties of the results presented in arXiv:0804.0594 and, in particular, the deterioration of the convergence rate at the merger and during the survival of the merged object, when strong shocks are formed and turbulence develops. We also show that physically reasonable and numerically convergent results obtained at low-resolution suffer however from large truncation errors and hence are of little physical use. We summarize our findings in an "error budget", which includes the different sources of possible inaccuracies we have investigated and provides a first quantitative assessment of the precision in the modelling of compact fluid binaries.Comment: 13 pages, 5 figures. Minor changes to match published version. Added figure 5 right pane

Accurate evolutions of unequal-mass neutron-star binaries: properties of the torus and short GRB engines

We present new results from accurate and fully general-relativistic simulations of the coalescence of unmagnetized binary neutron stars with various mass ratios. The evolution of the stars is followed through the inspiral phase, the merger and prompt collapse to a black hole, up until the appearance of a thick accretion disk, which is studied as it enters and remains in a regime of quasi-steady accretion. Although a simple ideal-fluid equation of state with \Gamma=2 is used, this work presents a systematic study within a fully general relativistic framework of the properties of the resulting black-hole--torus system produced by the merger of unequal-mass binaries. More specifically, we show that: (1) The mass of the torus increases considerably with the mass asymmetry and equal-mass binaries do not produce significant tori if they have a total baryonic mass M_tot >~ 3.7 M_sun; (2) Tori with masses M_tor ~ 0.2 M_sun are measured for binaries with M_tot ~ 3.4 M_sun and mass ratios q ~ 0.75-0.85; (3) The mass of the torus can be estimated by the simple expression M_tor(q, M_tot) = [c_1 (1-q) + c_2](M_max-M_tot), involving the maximum mass for the binaries and coefficients constrained from the simulations, and suggesting that the tori can have masses as large as M_tor ~ 0.35 M_sun for M_tot ~ 2.8 M_sun and q ~ 0.75-0.85; (4) Using a novel technique to analyze the evolution of the tori we find no evidence for the onset of non-axisymmetric instabilities and that very little, if any, of their mass is unbound; (5) Finally, for all the binaries considered we compute the complete gravitational waveforms and the recoils imparted to the black holes, discussing the prospects of detection of these sources for a number of present and future detectors.Comment: 35 pages; small changes to match the published versio