33 research outputs found
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 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 analÃticos 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 simetrÃa 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 podrÃan 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.