3D simulations of Einstein's equations: symmetric hyperbolicity, live gauges and dynamic control of the constraints

We present three-dimensional simulations of Einstein equations implementing a symmetric hyperbolic system of equations with dynamical lapse. The numerical implementation makes use of techniques that guarantee linear numerical stability for the associated initial-boundary value problem. The code is first tested with a gauge wave solution, where rather larger amplitudes and for significantly longer times are obtained with respect to other state of the art implementations. Additionally, by minimizing a suitably defined energy for the constraints in terms of free constraint-functions in the formulation one can dynamically single out preferred values of these functions for the problem at hand. We apply the technique to fully three-dimensional simulations of a stationary black hole spacetime with excision of the singularity, considerably extending the lifetime of the simulations.Comment: 21 pages. To appear in PR

Coherent Ro-vibrational Revivals in a Thermal Molecular Ensemble

We report an experimental and theoretical study of the evolution of vibrational coherence in a thermal ensemble of nitrogen molecules. Rotational dephasing and rephasing of the vibrational coherence is detected by coherent anti-Stokes Raman scattering. The existence of ro-vibrational coupling and the discrete energy spectrum of the rotational bath lead to a whole new class of full and fractional ro-vibrational revivals. Following the rich ro-vibrational dynamics on a nanosecond time scale with sub-picosecond time resolution enables us to determine the second-order ro-vibrational constant $gamma_e$ and assess new possibilities of controlling decoherence.Comment: submitted at Physical Review

Critical Phenomena in Neutron Stars I: Linearly Unstable Nonrotating Models

We consider the evolution in full general relativity of a family of linearly unstable isolated spherical neutron stars under the effects of very small, perturbations as induced by the truncation error. Using a simple ideal-fluid equation of state we find that this system exhibits a type-I critical behaviour, thus confirming the conclusions reached by Liebling et al. [1] for rotating magnetized stars. Exploiting the relative simplicity of our system, we are able carry out a more in-depth study providing solid evidences of the criticality of this phenomenon and also to give a simple interpretation of the putative critical solution as a spherical solution with the unstable mode being the fundamental F-mode. Hence for any choice of the polytropic constant, the critical solution will distinguish the set of subcritical models migrating to the stable branch of the models of equilibrium from the set of subcritical models collapsing to a black hole. Finally, we study how the dynamics changes when the numerically perturbation is replaced by a finite-size, resolution independent velocity perturbation and show that in such cases a nearly-critical solution can be changed into either a sub or supercritical. The work reported here also lays the basis for the analysis carried in a companion paper, where the critical behaviour in the the head-on collision of two neutron stars is instead considered [2].Comment: 15 pages, 9 figure

Operationally Invariant Measure of the Distance between Quantum States by Complementary Measurements

We propose an operational measure of distance of two quantum states, which conversely tells us their closeness. This is defined as a sum of differences in partial knowledge over a complete set of mutually complementary measurements for the two states. It is shown that the measure is operationally invariant and it is equivalent to the Hilbert-Schmidt distance. The operational measure of distance provides a remarkable interpretation of the information distance between quantum states.Comment: 4 page

Criticality and convergence in Newtonian collapse

We study through numerical simulation the spherical collapse of isothermal gas in Newtonian gravity. We observe a critical behavior which occurs at the threshold of gravitational instability leading to core formation. For a given initial density profile, we find a critical temperature, which is of the same order as the virial temperature of the initial configuration. For the exact critical temperature, the collapse converges to a self-similar form, the first member in Hunter's family of self-similar solutions. For a temperature close to the critical value, the collapse first approaches this critical solution. Later on, in the supercritical case, the collapse converges to another self-similar solution, which is called the Larson-Penston solution. In the subcritical case, the gas bounces and disperses to infinity. We find two scaling laws: one for the collapsed mass in the supercritical case and the other for the maximum density reached before dispersal in the subcritical case. The value of the critical exponent is measured to be $\simeq 0.11$ in the supercritical case, which agrees well with the predicted value $\simeq 0.10567$. These critical properties are quite similar to those observed in the collapse of a radiation fluid in general relativity. We study the response of the system to temperature fluctuation and discuss astrophysical implications for the insterstellar medium structure and for the star formation process. Newtonian critical behavior is important not only because it provides a simple model for general relativity but also because it is relevant for astrophysical systems such as molecular clouds.Comment: 15 pages, 8 figures, accepted for publication in PRD, figures 1 and 3 at lower resolution than in journal version, typos correcte

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

Collapse and black hole formation in magnetized, differentially rotating neutron stars

The capacity to model magnetohydrodynamical (MHD) flows in dynamical, strongly curved spacetimes significantly extends the reach of numerical relativity in addressing many problems at the forefront of theoretical astrophysics. We have developed and tested an evolution code for the coupled Einstein-Maxwell-MHD equations which combines a BSSN solver with a high resolution shock capturing scheme. As one application, we evolve magnetized, differentially rotating neutron stars under the influence of a small seed magnetic field. Of particular significance is the behavior found for hypermassive neutron stars (HMNSs), which have rest masses greater the mass limit allowed by uniform rotation for a given equation of state. The remnant of a binary neutron star merger is likely to be a HMNS. We find that magnetic braking and the magnetorotational instability lead to the collapse of HMNSs and the formation of rotating black holes surrounded by massive, hot accretion tori and collimated magnetic field lines. Such tori radiate strongly in neutrinos, and the resulting neutrino-antineutrino annihilation (possibly in concert with energy extraction by MHD effects) could provide enough energy to power short-hard gamma-ray bursts. To explore the range of outcomes, we also evolve differentially rotating neutron stars with lower masses and angular momenta than the HMNS models. Instead of collapsing, the non-hypermassive models form nearly uniformly rotating central objects which, in cases with significant angular momentum, are surrounded by massive tori.Comment: Submitted to a special issue of Classical and Quantum Gravity based around the New Frontiers in Numerical Relativity meeting at the Albert Einstein Institute, Potsdam, July 17-21, 200

The Globular Cluster System in the Inner Region of M87

1057 globular cluster candidates have been identified in a WFPC2 image of the inner region of M87. The Globular Cluster Luminosity Function (GCLF) can be well fit by a Gaussian profile with a mean value of m_V^0=23.67 +/- 0.07 mag and sigma=1.39 +/- 0.06 mag (compared to m_V^0=23.74 mag and sigma=1.44 mag from an earlier study using the same data by Whitmore it et al. 1995). The GCLF in five radial bins is found to be statistically the same at all points, showing no clear evidence of dynamical destruction processes based on the luminosity function (LF), in contradiction to the claim by Gnedin (1997). Similarly, there is no obvious correlation between the half light radius of the clusters and the galactocentric distance. The core radius of the globular cluster density distribution is R_c=56'', considerably larger than the core of the stellar component (R_c=6.8''). The mean color of the cluster candidates is V-I=1.09 mag which corresponds to an average metallicity of Fe/H = -0.74 dex. The color distribution is bimodal everywhere, with a blue peak at V-I=0.95 mag and a red peak at V-I=1.20 mag. The red population is only 0.1 magnitude bluer than the underlying galaxy, indicating that these clusters formed late in the metal enrichment history of the galaxy and were possibly created in a burst of star/cluster formation 3-6 Gyr after the blue population. We also find that both the red and the blue cluster distributions have a more elliptical shape (Hubble type E3.5) than the nearly spherical galaxy. The average half light radius of the clusters is ~2.5 pc which is comparable to the 3 pc average effective radius of the Milky Way clusters, though the red candidates are ~20% smaller than the blue ones.Comment: 40 pages, 17 figures, 4 tables, latex, accepted for publication in the Ap

Stability criterion for self-similar solutions with a scalar field and those with a stiff fluid in general relativity

A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state $P=\rho$. A wide class of self-similar solutions turn out to be unstable against kink mode perturbation. According to the criterion, the Evans-Coleman stiff-fluid solution is unstable and cannot be a critical solution for the spherical collapse of a stiff fluid if we allow sufficiently small discontinuity in the density gradient field in the initial data sets. The self-similar scalar-field solution, which was recently found numerically by Brady {\it et al.} (2002 {\it Class. Quantum. Grav.} {\bf 19} 6359), is also unstable. Both the flat Friedmann universe with a scalar field and that with a stiff fluid suffer from kink instability at the particle horizon scale.Comment: 15 pages, accepted for publication in Classical and Quantum Gravity, typos correcte