Constraint damping of the conformal and covariant formulation of the Z4 system in simulations of binary neutron stars

Following previous work in vacuum spacetimes, we investigate the constraint-damping properties in the presence of matter of the recently developed traceless, conformal and covariant Z4 (CCZ4) formulation of the Einstein equations. First, we evolve an isolated neutron star with an ideal gas equation of state and subject to a constraint-violating perturbation. We compare the evolution of the constraints using the CCZ4 and Baumgarte-Shibata-Shapiro-Nakamura-Oohara-Kojima (BSSNOK) systems. Second, we study the collapse of an unstable spherical star to a black hole. Finally, we evolve binary neutron star systems over several orbits until the merger, the formation of a black hole, and up to the ringdown. We show that the CCZ4 formulation is stable in the presence of matter and that the constraint violations are one or more orders of magnitude smaller than for the BSSNOK formulation. Furthermore, by comparing the CCZ4 and the BSSNOK formulations also for neutron star binaries with large initial constraint violations, we investigate their influence on the errors on physical quantities. We also give a new, simple and robust prescription for the damping parameter that removes the instabilities found when using the fully covariant version of CCZ4 in the evolution of black holes. Overall, we find that at essentially the same computational costs the CCZ4 formulation provides solutions that are stable and with a considerably smaller violation of the Hamiltonian constraint than the BSSNOK formulation. We also find that the performance of the CCZ4 formulation is very similar to another conformal and traceless, but noncovariant formulation of the Z4 system, i.e. the Z4c formulation.Comment: 15 pages, 11 figures; accepted for publication in Phys. Rev.

Dynamical damping terms for symmetry-seeking shift conditions

Suitable gauge conditions are fundamental for stable and accurate numerical-relativity simulations of inspiralling compact binaries. A number of well-studied conditions have been developed over the last decade for both the lapse and the shift and these have been successfully used both in vacuum and non-vacuum spacetimes when simulating binaries with comparable masses. At the same time, recent evidence has emerged that the standard "Gamma-driver" shift condition requires a careful and non-trivial tuning of its parameters to ensure long-term stable evolutions of unequal-mass binaries. We present a novel gauge condition in which the damping constant is promoted to be a dynamical variable and the solution of an evolution equation. We show that this choice removes the need for special tuning and provides a shift damping term which is free of instabilities in our simulations and dynamically adapts to the individual positions and masses of the binary black-hole system. Our gauge condition also reduces the variations in the coordinate size of the apparent horizon of the larger black hole and could therefore be useful when simulating binaries with very small mass ratios.Comment: 11 pages, 8 figure

Multi-state Boson Stars

Motivated by the increasing interest in models which consider scalar fields as viable dark matter candidates, we have constructed a generalization of relativistic Boson Stars (BS) composed of two coexisting states of the scalar field, the ground state and the first excited state. We have studied the dynamical evolution of these Multi-state Boson Stars (MSBS) under radial perturbations, using numerical techniques. We show that stable MSBS can be constructed, when the number of particles in the first excited state, N2, is smaller than the number of particles in the ground state, N1. On the other hand, when N2 > N1, the configurations are initially unstable. However, they evolve and settle down into stable configurations. In the stabilization process, the initially ground state is excited and ends in a first excited state, whereas the initially first excited state ends in a ground state. During this process, both states emit scalar field radiation, decreasing their number of particles. This behavior shows that even though BS in the first excited state are intrinsically unstable under finite perturbations, the configuration resulting from the combination of this state with the ground state produces stable objects. Finally we show in a qualitative way, that stable MSBS could be realistic models of dark matter galactic halos, as they produce rotation curves that are flatter at large radii than the rotation curves produced by BS with only one state.Comment: 14 pages. Extended discussion and new figures added. Conclusions unchanged. Accepted for publication in Physical Review

General-relativistic resistive magnetohydrodynamics in three dimensions: Formulation and tests

We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD) equations within the Whisky code. The numerical method adopted exploits the properties of implicit-explicit Runge-Kutta numerical schemes to treat the stiff terms that appear in the equations for large electrical conductivities. Using tests in one, two, and three dimensions, we show that our implementation is robust and recovers the ideal-MHD limit in regimes of very high conductivity. Moreover, the results illustrate that the code is capable of describing scenarios in a very wide range of conductivities. In addition to tests in flat spacetime, we report simulations of magnetized nonrotating relativistic stars, both in the Cowling approximation and in dynamical spacetimes. Finally, because of its astrophysical relevance and because it provides a severe testbed for general-relativistic codes with dynamical electromagnetic fields, we study the collapse of a nonrotating star to a black hole. We show that also in this case our results on the quasinormal mode frequencies of the excited electromagnetic fields in the Schwarzschild background agree with the perturbative studies within 0.7% and 5.6% for the real and the imaginary part of the l=1 mode eigenfrequency, respectively. Finally we provide an estimate of the electromagnetic efficiency of this process.Comment: 22 pages, 19 figure

Accurate Simulations of Binary Black Hole Mergers in Force-free Electrodynamics

We provide additional information on our recent study of the electromagnetic emission produced during the inspiral and merger of supermassive black holes when these are immersed in a force-free plasma threaded by a uniform magnetic field. As anticipated in a recent letter, our results show that although a dual-jet structure is present, the associated luminosity is ~100 times smaller than the total one, which is predominantly quadrupolar. Here we discuss the details of our implementation of the equations in which the force-free condition is not implemented at a discrete level, but rather obtained via a damping scheme which drives the solution to satisfy the correct condition. We show that this is important for a correct and accurate description of the current sheets that can develop in the course of the simulation. We also study in greater detail the three-dimensional charge distribution produced as a consequence of the inspiral and show that during the inspiral it possesses a complex but ordered structure which traces the motion of the two black holes. Finally, we provide quantitative estimates of the scaling of the electromagnetic emission with frequency, with the diffused part having a dependence that is the same as the gravitational-wave one and that scales as L^(non-coll)_(EM) ≈ Ω^((10/3)–(8/3)), while the collimated one scales as L^(coll)_(EM) ≈ Ω^((5/3)–(6/3)), thus with a steeper dependence than previously estimated. We discuss the impact of these results on the potential detectability of dual jets from supermassive black holes and the steps necessary for more accurate estimates

On the black hole from merging binary neutron stars: how fast can it spin?

The merger of two neutron stars will in general lead to the formation of a torus surrounding a black hole whose rotational energy can be tapped to potentially power a short gamma-ray burst. We have studied the merger of equal-mass binaries with spins aligned with the orbital angular momentum to determine the maximum spin the black hole can reach. Our initial data consists of irrotational binaries to which we add various amounts of rotation to increase the total angular momentum. Although the initial data violates the constraint equations, the use of the constraint-damping CCZ4 formulation yields evolutions with violations smaller than those with irrotational initial data and standard formulations. Interestingly, we find that a limit of $J/M^2 \simeq 0.89$ exists for the dimensionless spin and that any additional angular momentum given to the binary ends up in the torus rather than in the black hole, thus providing another nontrivial example supporting the cosmic censorship hypothesis.Comment: 4 pages, 2 figures Version to appear in PRD Rapid Communication

Theoretical issues in Numerical Relativity simulations

In this thesis we address several analytical and numerical problems related with the general relativistic study of black hole space-times and boson stars. We have developed a new centered finite volume method based on the flux splitting approach. The techniques for dealing with the singularity, steep gradients and apparent horizon location, are studied in the context of a single Schwarzschild black hole, in both spherically symmetric and full 3D simulations. We present an extended study of gauge instabilities related with a class of singularity avoiding slicing conditions and show that, contrary to previous claims, these instabilities are not generic for evolved gauge conditions. We developed an alternative to the current space coordinate conditions, based on a generalized Almost Killing Equation. We performed a general relativistic study regarding the long term stability of Mixed-State Boson Stars configurations and showed that they are suitable candidates for dark matter models.En esta tesis abordamos varios problemas analíticos y numéricos relacionados con el estudio de agujeros negros relativistas y modelos de materia oscura. Hemos desarrollado un nuevo método de volúmenes finitos centrados basado en el enfoque de la división de flujo. Discutimos las técnicas para tratar con la singularidad, los gradientes abruptos y la localización del horizonte aparente en el contexto de un solo agujero negro de Schwarzschild, en simulaciones tanto con simetría esférica como completamente tridimensionales. Hemos extendido el estudio de una familia de condiciones de foliaciones evitadoras de singularidad y mostrado que ciertas inestabilidades no son genéricas para condiciones de gauge dinámicas. Desarrollamos una alternativa a las prescripciones actuales basada en una Almost Killing Equation generalizada. Hemos realizado también un estudio con respecto a la estabilidad a largo plazo de configuraciones de Mixed-State Boson Stars, el cual sugiere que estas podrían ser candidatas apropiadas para modelos de materia oscura

Towards a gauge-polyvalent Numerical Relativity code

The gauge polyvalence of a new numerical code is tested, both in harmonic-coordinate simulations (gauge-waves testbed) and in singularity-avoiding coordinates (simple Black-Hole simulations, either with or without shift). The code is built upon an adjusted first-order flux-conservative version of the Z4 formalism and a recently proposed family of robust finite-difference high-resolution algorithms. An outstanding result is the long-term evolution (up to 1000M) of a Black-Hole in normal coordinates (zero shift) without excision.Comment: to appear in Physical Review

Efficient implementation of finite volume methods in Numerical Relativity

Centered finite volume methods are considered in the context of Numerical Relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be interpreted as an 'adaptive viscosity' modification of centered finite difference algorithms. These points are fully confirmed by 1D black-hole simulations. In the 3D case, evidence is found that the use of a conformal decomposition is a key ingredient for the robustness of black hole numerical codes.Comment: Revised version, 10 pages, 6 figures. To appear in Phys. Rev.