We analyze the anomalous wave structure appearing in flow dynamics under the influence of magnetic field in materials described by non-ideal equations of state. We consider the hyperbolic system of magnetohydrodynamics equations closed by a general equation of state (EOS) and propose a complete spectral decomposition of the fluxes that allows us to derive an expression of the nonlinearity factor as the mathematical tool to determine the nature of the wave phenomena. We prove that the possible formation of non-classical wave structure is determined by the thermodynamic properties of the material. The analytical expression of the nonlinearity factor allows us to determine the specific amount of magnetic field necessary to prevent formation of complex structure induced by phase transition in the material. We illustrate our analytical approach by considering two non-convex EOS that exhibit phase transitions and anomalous behavior in the evolution. We present numerical experiments validating the analysis performed through a set of one-dimensional Riemann problems. (Work in collaboration with Dr. Susana Serna, Phys. Fluids, vol. 26, 016101, (2014))

TBA

The astrophysical site for the production of r-process elements is still mysterious. Recent studies suggest that instead of the long favored core-collapse supernovae the outflows from compact binary (i.e. double neutron-star, NS-NS, or neutron-star black-hole, NS-BH) mergers could provide suitable conditions to allow for the r-process. In general, during each stage of the merger different types of outflows with individual nucleosynthesis signatures can be launched. I will present the results of our recent study in which we conducted a first comprehensive analysis of compact binary mergers that takes into account the prompt ejecta from both NS-NS and NS-BH mergers consistently together with their relic BH-torus systems.

Besides being among the most promising sources of gravitational waves, merging neutron star binaries also represent a leading scenario to explain the phenomenology of short gamma-ray bursts (SGRBs). Recent observations have revealed a large subclass of SGRBs with roughly constant luminosity in their X-ray afterglows, lasting 10–10^4 s. These features are generally taken as evidence of a long-lived central engine powered by the magnetic spin-down of a uniformly rotating, magnetized object. We propose a scenario in which the central engine powering the early X-ray afterglow emission is a differentially rotating hypermassive or supramassive neutron star (HMNS or SMNS). This emission is associated with a quasi-isotropic and baryon-loaded wind driven by the magnetic field, which is built-up through differential rotation. Our model is supported by long-term, three-dimensional, general-relativistic, and ideal magnetohydrodynamic simulations, showing that this isotropic emission is a very robust feature. We show that our results are compatible with the timescales and luminosities of the observed X-ray afterglows.

Short gamma-ray bursts (SGRBs) are among the most luminous explosions in the Universe and their origin still remains uncertain. Observational evidence favors the association with binary neutron star or neutron star-black hole (NS-BH) binary mergers. Leading models relate SGRBs to a relativistic jet launched by the BH-torus system resulting from the merger. However, recent observations have revealed a large fraction of SGRB events accompanied by X-ray afterglows with durations $10^2-10^5$ s, suggesting continuous energy injection from a long-lived central engine, which is incompatible with the short ($lt 1$ s) accretion timescale of a BH-torus system. The formation of a supramassive NS, resisting the collapse on much longer spin-down timescales, can explain these afterglow durations, but leaves serious doubts on whether a relativistic jet can be launched at merger. Here we present a novel scenario accommodating both aspects, where the SGRB is produced after the collapse of a supramassive NS. Early differential rotation and subsequent spin-down emission generate an optically thick environment around the NS consisting of a photon-pair nebula and an outer shell of baryon-loaded ejecta. While the jet easily drills through this environment, spin-down radiation diffuses outwards on much longer timescales and accumulates a delay that allows the SGRB to be observed before (part of) the long-lasting X-ray signal. By analyzing diffusion timescales for a wide range of physical parameters, we find delays that can generally reach $10^5$ s, compatible with observations. The success of this fundamental test makes this "time-reversal" scenario an attractive alternative to current SGRB models.

We use the Landau-Lifshitz Pseudotensor to measure the spin of Kerr black holes with arbitrary initial spin orientation in BBH simulations. We compare the method to measuring the spin in the quasi-local framework using an approximate Killing vector on the horizon and a method using flat space coordinate rotational Killing vectors for the calculation of the spin.

I will present simulations of collapsing gravitational waves obtained using two methods. First, using the moving puncture gauge, I show that it is possible to evolve certain types of initial data through apparent horizon formation. Secondly I will present a new pseudo-spectral code which we are using to tackle the same initial data.

In this talk we present a general overview of path-conservative numerical schemes for balance laws and nonconservative hyperbolic systems introduced by Parés. In particular, we show the main difficulties related to the presence of nonconservative products concerning the definition of weak solutions and the derivation of numerical schemes. Next, we present a class of incomplete Riemann solvers, whose viscosity matrix are defined in terms of an appropriate real function $R(x)$, that approximates the function $|x|$. The resulting approximate Riemann solvers are incomplete, in the sense that we do not use the complete spectral decomposition of the system, and only some information about the maximum in absolute value of the characteristic speeds are needed. Finally, some numerical tests will be presented.

We present a new numerical tool to study the resonant cyclotron scattering to calculate the modulation of the emission of highly magnetized neutron stars (magnetars). The scattering of the photons is calculated with a Monte-Carlo approach. In order to obtain a realistic prescription for the scattering targets, i.e. electrons and positrons that are accelerated along the magnetic field lines, we need to follow their motion. We follow the particles with a particle-in-a-line code that calculates their trajectories by taking the interaction with the photons into account. Our final aim is to apply the new code to describe the quasi-periodic oscillations (QPOs) observed in magnetar giant flares.

We present 1D and 2D relativistic MHD simulations of the accretion of matter onto neutron stars. We study the consequences of the accretion process in the distribution of the magnetic field across the magnetosphere of the star. To this end we explore different accretion rates, fluid composition (through various equations of state) and magnetic field distributions, in order to test the viability of the hidden magnetic field model. Such model has been put forward to explain the evolution of X-ray sources with low values ($\lt 10^11$ G) of the magnetic field. In this scenario, the reverse supernova shock falling back onto the neutron star compresses the magnetic field, a process that can eventually bury the field inside the neutron star crust.

Previously there have been attempts to determine the structure of neutron stars in strong magnetic fields. However, there is no such study which simultaneously includes the effect of the magnetic field on the equation of state, general relativistic aspects as well as the pressure anisotropy caused by the breaking of spherical symmetry of the star by the field. We present a self-consistent study of the structure of a neutron star in strong magnetic fields, including all the magnetic field effects. We solve Einstein’s equations in an axisymmetric metric, which is determined self consistently from the axisymmetric energy-momentum tensor of the star, and solve it numerically.

The application of suitable numerical boundary conditions for hyperbolic conservation laws on domains with complex geometry has become a problem with certain difficulty that has been tackled in different ways according to the nature of the numerical methods and mesh type. We present an extrapolation technique on structured Cartesian meshes (which, as opposed to non-structured meshes, cannot be adapted to the morphology of the domain boundary) of the information in the interior of the computational domain to ghost cells. This technique is based on the application of Lagrange interpolation with a previous filter for the detection of discontinuities that permits a data dependent extrapolation, with higher order at smooth regions and essentially non-oscillatory properties near discontinuities.

In this talk I will present some Runge-Kutta methods, named as Minimally Implicit Runge-Kutta (MIRK) methods, designed to integrate in time the resistive (non ideal) relativistic magnetohydrodynamic equations. This system of equations contains stiff source terms in the evolution of the electric field. I will comment on the motivation behind these methods and the derived schemes for several orders of convergence.

Following the talk of I. Cordero-Carrión, I will show the numerical performance of the Minimally Implicit Runge-Kutta (MIRK) methods on the system of resistive relativistic magnetohydrodynamics.

TBA

Recently, a general relativistic and energy dependent M1 scheme has been developed for CoCoNuT. I will report on its current state and give some technical details.

The pre-collapse magnetic fields of a supernova core can, apart from compression during collapse, be amplified by hydrodynamic instabilities developing in the proto-neutron star and the post-shock region. As a consequence, complex field geometries can develop and, for significantly strong field, an explosion can be facilitated. I will present simulations of the evolution of magnetised cores including neutrino transport in the two-moment approach.

Finite temperature effects are expected to be important in several astrophysical scenarios (e.g. core-collapse supernovae, cooling of proto-neutron stars). In this talk, we will present a model for stationary axisymmetric stars with non-barotropic equations of state. We propose a numerical scheme to find exact solutions of the equilibrium equations for stars with non-constant entropy profiles. We will present preliminary results for a simple analytic equation of state. Finally, we will discuss the possible applications of this model.

I will report on the present status of CoCoNuT. I will focus in the development of a MPI-parallel version and the possibility of going to an open source model.