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We present a portable and highly-scalable framework that targets problems in the astrophysics and numerical relativity communities. This framework combines together the parallel Dendro octree with wavelet adaptive multiresolution and an automatic code-generation physics module to solve the Einstein equations of general relativity in the BSSNOK formulation. The goal of this work is to perform advanced, massively parallel numerical simulations of binary black hole and neutron star mergers, including Intermediate Mass Ratio Inspirals (IMRIs) of binary black holes with mass ratios on the order of 100:1. These studies will be used to study waveforms for use in LIGO data analysis and to calibrate approximate methods for generating gravitational waveforms. The key contribution of this work is the development of automatic code generators for computational relativity supporting SIMD vectorization, OpenMP, and CUDA combined with efficient distributed memory adaptive data-structures. These have enabled the development of efficient codes that demonstrate excellent weak scalability up to 131K cores on ORNL's Titan for binary mergers for mass ratios up to 100.

We present a highly-scalable framework that targets problems of interest to the numerical relativity and broader astrophysics communities. This framework combines a parallel octree-refined adaptive mesh with a wavelet adaptive multiresolution and a physics module to solve the Einstein equations of general relativity in the BSSN formulation. The goal of this work is to perform advanced, massively parallel numerical simulations of Intermediate Mass Ratio Inspirals (IMRIs) of binary black holes with mass ratios on the order of 100:1. These studies will be used to generate waveforms as used in LIGO data analysis and to calibrate semi-analytical approximate methods. Our framework consists of a distributed memory octree-based adaptive meshing framework in conjunction with a node-local code generator. The code generator makes our code portable across different architectures. The equations corresponding to the target application are written in symbolic notation and generators for different architectures can be added independent of the application. Additionally, this symbolic interface also makes our code extensible, and as such has been designed to easily accommodate many existing algorithms in astrophysics for plasma dynamics and radiation hydrodynamics. Our adaptive meshing algorithms and data-structures have been optimized for modern architectures with deep memory hierarchies. This enables our framework to have achieve excellent performance and scalability on modern leadership architectures. We demonstrate excellent weak scalability up to 131K cores on ORNL's Titan for binary mergers for mass ratios up to 100.

Observations of gravitational radiation from compact binary systems provide an unprecedented opportunity to test General Relativity in the strong field dynamical regime. In this paper, we investigate how future observations of gravitational radiation from binary neutron star mergers might provide constraints on finite-range forces from a universally coupled massive scalar field. Such scalar degrees of freedom are a characteristic feature of many extensions of General Relativity. For concreteness, we work in the context of metric $f(R)$ gravity, which is equivalent to General Relativity and a universally coupled scalar field with a non-linear potential whose form is fixed by the choice of $f(R)$. In theories where neutron stars (or other compact objects) obtain a significant scalar charge, the resulting attractive finite-range scalar force has implications for both the inspiral and merger phases of binary systems. We first present an analysis of the inspiral dynamics in Newtonian limit, and forecast the constraints on the mass of the scalar and charge of the compact objects for the Advanced LIGO gravitational wave observatory. We then perform a comparative study of binary neutron star mergers in General Relativity with those of a one-parameter model of $f(R)$ gravity using fully relativistic hydrodynamical simulations. These simulations elucidate the effects of the scalar on the merger and post-merger dynamics. We comment on the utility of the full waveform (inspiral, merger, post-merger) to probe different regions of parameter space for both the particular model of $f(R)$ gravity studied here and for finite-range scalar forces more generally., 22 pages, 8 figures. Typos fixed, references added. Updated to match the version accepted for publishing in PRD

We study the merger of binary neutron stars with different mass ratios adopting three different realistic, microphysical nuclear equations of state, as well as incorporating neutrino cooling effects. In particular, we concentrate on the influence of the equation of state on the gravitational wave signature and also on its role, in combination with neutrino cooling, in determining the properties of the resulting hypermassive neutron star, of the neutrinos produced, and of the ejected material. The ejecta we find are consistent with other recent studies that find that small mass ratios produce more ejecta than equal mass cases (up to some limit) and this ejecta is more neutron rich. This trend indicates the importance with future kilonovae observations of measuring the individual masses of an associated binary neutron star system, presumably from concurrent gravitational wave observations, in order to be able to extract information about the nuclear equation of state, 16 pages, 14 figures (some figures reduced in quality due to size constraints)

We study the merger of binary neutron stars using different realistic, microphysical nuclear equations of state, as well as incorporating magnetic field and neutrino cooling effects. In particular, we concentrate on the influence of the equation of state on the gravitational wave signature and also on its role, in combination with cooling and electromagnetic effects, in determining the properties of the hypermassive neutron star resulting from the merger, the production of neutrinos, and the characteristics of ejecta from the system. The ejecta we find are consistent with other recent studies that find soft equations of state produce more ejecta than stiffer equations of state. Moreover, the degree of neutron richness increases for softer equations of state. In light of reported kilonova observations (associated to GRB~130603B and GRB~060614) and the discovery of relatively low abundances of heavy, radioactive elements in deep sea deposits (with respect to possible production via supernovae), we speculate that a soft EoS might be preferred---because of its significant production of sufficiently neutron rich ejecta---if such events are driven by binary neutron star mergers. We also find that realistic magnetic field strengths, obtained with a sub-grid model tuned to capture magnetic amplification via the Kelvin-Helmholtz instability at merger, are generally too weak to affect the gravitational wave signature post-merger within a time scale of $\approx 10$~ms but can have subtle effects on the post-merger dynamics., 22 pages, 24 figures

A new algorithm for solving the general relativistic MHD equations is described in this paper. We design our scheme to incorporate black hole excision with smooth boundaries, and to simplify solving the combined Einstein and MHD equations with AMR. The fluid equations are solved using a finite difference Convex ENO method. Excision is implemented using overlapping grids. Elliptic and hyperbolic divergence cleaning techniques allow for maximum flexibility in choosing coordinate systems, and we compare both methods for a standard problem. Numerical results of standard test problems are presented in two-dimensional flat space using excision, overlapping grids, and elliptic and hyperbolic divergence cleaning.

The energy method can be used to identify well-posed initial boundary value problems for quasi-linear, symmetric hyperbolic partial differential equations with maximally dissipative boundary conditions. A similar analysis of the discrete system can be used to construct stable finite difference equations for these problems at the linear level. In this paper we apply these techniques to some test problems commonly used in numerical relativity and observe that while we obtain convergent schemes, fast growing modes, or ``artificial instabilities,'' contaminate the solution. We find that these growing modes can partially arise from the lack of a Leibnitz rule for discrete derivatives and discuss ways to limit this spurious growth., Comment: 18 pages, 22 figures

We present the first simulations of non-headon (grazing) collisions of binary black holes in which the black hole singularities have been excised from the computational domain. Initially two equal mass black holes $m$ are separated a distance $\approx10m$ and with impact parameter $\approx2m$. Initial data are based on superposed, boosted (velocity $\approx0.5c$) solutions of single black holes in Kerr-Schild coordinates. Both rotating and non-rotating black holes are considered. The excised regions containing the singularities are specified by following the dynamics of apparent horizons. Evolutions of up to $t \approx 35m$ are obtained in which two initially separate apparent horizons are present for $t\approx3.8m$. At that time a single enveloping apparent horizon forms, indicating that the holes have merged. Apparent horizon area estimates suggest gravitational radiation of about 2.6% of the total mass. The evolutions end after a moderate amount of time because of instabilities., Comment: 2 References corrected, reference to figure updated

Interferometric detectors will very soon give us an unprecedented view of the gravitational-wave sky, and in particular of the explosive and transient Universe. Now is the time to challenge our theoretical understanding of short-duration gravitational-wave signatures from cataclysmic events, their connection to more traditional electromagnetic and particle astrophysics, and the data analysis techniques that will make the observations a reality. This paper summarizes the state of the art, future science opportunities, and current challenges in understanding gravitational-wave transients., 33 pages, 2 figures

We expand on our study of the gravitational and electromagnetic emissions from the late stage of an inspiraling neutron star binary as presented in Ref. \cite{Palenzuela:2013hu}. Interactions between the stellar magnetospheres, driven by the extreme dynamics of the merger, can yield considerable outflows. We study the gravitational and electromagnetic waves produced during the inspiral and merger of a binary neutron star system using a full relativistic, resistive MHD evolution code. We show that the interaction between the stellar magnetospheres extracts kinetic energy from the system and powers radiative Poynting flux and heat dissipation. These features depend strongly on the configuration of the initial stellar magnetic moments. Our results indicate that this power can strongly outshine pulsars in binaries and have a distinctive angular and time-dependent pattern. Our discussion provides more detail than Ref. \cite{Palenzuela:2013hu}, showing clear evidence of the different effects taking place during the inspiral. Our simulations include a few milliseconds after the actual merger and study the dynamics of the magnetic fields during the formation of the hypermassive neutron star. We also briefly discuss the possibility of observing such emissions., 15 pages, 15 figures; Updated with spelling/grammar corrections, updated references, and better printing figures

The late stage of an inspiraling neutron-star binary gives rise to strong gravitational wave emission due to its highly dynamic, strong gravity. Moreover, interactions between the stellar magnetospheres can produce considerable electromagnetic radiation. We study this scenario using fully general relativistic, resistive magnetohydrodynamic simulations. We show that these interactions extract kinetic energy from the system, dissipate heat, and power radiative Poynting flux, as well as develop current sheets. Our results indicate that this power can (i) outshine pulsars in binaries, (ii) display a distinctive angular- and time-dependent pattern, and (iii) radiate within large opening angles. These properties suggest that some binary neutron-star mergers are ideal candidates for multimessenger astronomy.

The extraction of rotational energy from a spinning black hole via the Blandford-Znajek mechanism has long been understood as an important component in models to explain energetic jets from compact astrophysical sources. Here we show more generally that the kinetic energy of the black hole, both rotational and translational, can be tapped, thereby producing even more luminous jets powered by the interaction of the black hole with its surrounding plasma. We study the resulting Poynting jet that arises from single boosted black holes and binary black hole systems. In the latter case, we find that increasing the orbital angular momenta of the system and/or the spins of the individual black holes results in an enhanced Poynting flux., Comment: 7 pages, 5 figures

We investigate the merger of a neutron star (of compaction ratio $0.1$) in orbit about a spinning black hole in full general relativity with a mass ratio of $5:1$, allowing for the star to have an initial magnetization of $10^{12} {\rm Gauss}$. We present the resulting gravitational waveform and analyze the fallback accretion as the star is disrupted. The evolutions suggest no significant effects from the initial magnetization. We find that only a negligible amount of matter becomes unbound; $99%$ of the neutron star material has a fallback time of 10 seconds or shorter to reach the region of the central engine and that $99.99%$ of the star will interact with the central disk and black hole within 3 hours., Comment: Version updated to match published version (Phys Rev Letters V105, 111101; 2010.) 5 pages, 5 figures

We study the evolution of magnetized and rigidly rotating neutron stars within a fully general relativistic implementation of ideal magnetohydrodynamics with no assumed symmetries in three spatial dimensions. The stars are modeled as rotating, magnetized polytropic stars and we examine diverse scenarios to study their dynamics and stability properties. In particular we concentrate on the stability of the stars and possible critical behavior. In addition to their intrinsic physical significance, we use these evolutions as further tests of our implementation which incorporates new developments to handle magnetized systems., Comment: 12 pages, 8 figures

We simulate the possible emission from a disk perturbed by a recoiling super-massive black hole. To this end, we study radiation transfer from the system incorporating bremsstrahlung emission from a Maxwellian plasma and absorption given by Kramer's opacity law modified to incorporate blackbody effects. We employ this model in the radiation transfer integration to compute the luminosity at several frequencies, and compare with previous bremsstrahlung luminosity estimations from a transparent limit (in which the emissivity is integrated over the computational domain and over all frequencies) and with a simple thermal emission model. We find close agreement between the radiation transfer results and the estimated bremsstrahlung luminosity from previous work for electromagnetic signals above $10^{14}$ Hz. For lower frequencies, we find a self-eclipsing behavior in the disk, resulting in a strong intensity variability connected to the orbital period of the disk., 9 pages, 6 figures

In addition to producing gravitational waves (GW), the dynamics of a binary black hole system could induce emission of electromagnetic (EM) radiation by affecting the behavior of plasmas and electromagnetic fields in their vicinity. We here study how the electromagnetic fields are affected by a pair of orbiting black holes through the merger. In particular, we show how the binary's dynamics induce a variability in possible electromagnetically induced emissions as well as a possible enhancement of electromagnetic fields during the late-merge and merger epochs. These time dependent features will likely leave their imprint in processes generating detectable emissions and can be exploited in the detection of electromagnetic counterparts of gravitational waves., 4 pages, 4 figures. Updated to coincide with PRL version

The merger process of a binary black hole system can have a strong impact on a circumbinary disk. In the present work we study the effect of both central mass reduction (due to the energy loss through gravitational waves) and a possible black hole recoil (due to asymmetric emission of gravitational radiation). For the mass reduction case and recoil directed along the disk's angular momentum, oscillations are induced in the disk which then modulate the internal energy and bremsstrahlung luminosities. On the other hand, when the recoil direction has a component orthogonal to the disk's angular momentum, the disk's dynamics are strongly impacted, giving rise to relativistic shocks. The shock heating leaves its signature in our proxies for radiation, the total internal energy and bremsstrahlung luminosity. Interestingly, for cases where the kick velocity is below the smallest orbital velocity in the disk (a likely scenario in real AGN), we observe a common, characteristic pattern in the internal energy of the disk. Variations in kick velocity simply provide a phase offset in the characteristic pattern implying that observations of such a signature could yield a measure of the kick velocity through electromagnetic signals alone., Comment: 10 pages, 13 figures. v2: Minor changes, version to be published in PRD

We solve the general relativistic magnetohydrodynamics equations using distributed parallel adaptive mesh refinement. We discuss strong scaling tests of the code, and present evolutions of Michel accretion and a TOV star., Comment: 3 Pages, Proceedings of the Marcel Grossmann Meeting XI

We investigate the influence of magnetic fields upon the dynamics of and resulting gravitational waves from a binary neutron star merger in full general relativity coupled to ideal magnetohydrodynamics (MHD). We consider two merger scenarios, one where the stars begin with initially aligned poloidal magnetic fields and one with no magnetic field. Both mergers result in a strongly differentially rotating object. In comparison to the non-magnetized scenario, the aligned magnetic fields delay the final merger of the two stars. During and after merger we observe phenomena driven by the magnetic field, including Kelvin-Helmholtz instabilities in shear layers, winding of the field lines, and transition from poloidal to toroidal fields. These effects not only produce electromagnetic radiation, but also can have a strong influence on the gravitational waves. Thus, there are promising prospects for studying such systems with both types of waves., Comment: Replaced with accepted PRL version. (Figures have been reduced in quality)

We model two mergers of orbiting binary neutron stars, the first forming a black hole and the second a differentially rotating neutron star. We extract gravitational waveforms in the wave zone. Comparisons to a post-Newtonian analysis allow us to compute the orbital kinematics, including trajectories and orbital eccentricities. We verify our code by evolving single stars and extracting radial perturbative modes, which compare very well to results from perturbation theory. The Einstein equations are solved in a first order reduction of the generalized harmonic formulation, and the fluid equations are solved using a modified convex essentially non-oscillatory method. All calculations are done in three spatial dimensions without symmetry assumptions. We use the \had computational infrastructure for distributed adaptive mesh refinement., 14 pages, 16 figures. Added one figure from previous version; corrected typos

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 tables

We use the overlapping grids method to construct a fourth order accurate discretization of a first order reduction of the Klein-Gordon scalar field equation on a boosted spinning black hole blackground in axisymmetry. This method allows us to use a spherical outer boundary and excise the singularity from the domain with a spheroidal inner boundary which is moving with respect to the main grid. We discuss the use of higher order accurate energy conserving schemes to handle the axis of symmetry and compare it with a simpler technique based on regularity conditions. We also compare the single grid long term stability property of this formulation of the wave equation with that of a different first order reduction., 20 pages, 12 figures

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 PRD

An orbiting black hole binary will generate strong gravitational radiation signatures, making these binaries important candidates for detection in gravitational wave observatories. The gravitational radiation is characterized by the orbital parameters, including the frequency and separation at the inner-most stable circular orbit (ISCO). One approach to estimating these parameters relies on a sequence of initial data slices that attempt to capture the physics of the inspiral. Using calculations of the binding energy, several authors have estimated the ISCO parameters using initial data constructed with various algorithms. In this paper we examine this problem using conformally Kerr-Schild initial data. We present convergence results for our initial data solutions, and give data from numerical solutions of the constraint equations representing a range of physical configurations. In a first attempt to understand the physical content of the initial data, we find that the Newtonian binding energy is contained in the superposed Kerr-Schild background before the constraints are solved. We examine some deficiencies with the initial data approach to orbiting binaries, especially touching on the effects of prior motion and spin-orbital coupling of the angular momenta. Making rough estimates of these effects, we find that they are not insignificant compared to the binding energy, leaving some doubt of the utility of using initial data to predict ISCO parameters. In computations of specific initial-data configurations we find spin-specific effects that are consistent with analytical estimates., 41 pages, 17 figures

It is expected that the realization of a convergent and long-term stable numerical code for the simulation of a black hole inspiral collision will depend greatly upon the construction of stable algorithms capable of handling smooth and, most likely, time dependent boundaries. After deriving single grid, energy conserving discretizations for axisymmetric systems containing the axis of symmetry, we present a new excision method for moving black holes using multiple overlapping coordinate patches, such that each boundary is fixed with respect to at least one coordinate system. This multiple coordinate structure eliminates all need for extrapolation, a commonly used procedure for moving boundaries in numerical relativity. We demonstrate this excision method by evolving a massless Klein-Gordon scalar field around a boosted Schwarzschild black hole in axisymmetry. The excision boundary is defined by a spherical coordinate system co-moving with the black hole. Our numerical experiments indicate that arbitrarily high boost velocities can be used without observing any sign of instability., 23 pages, 13 figures. Revised version

By writing the complete set of $3 + 1$ (ADM) equations for linearized waves, we are able to demonstrate the properties of the initial data and of the evolution of a wave problem set by Alcubierre and Schutz. We show that the gauge modes and constraint error modes arise in a straightforward way in the analysis, and are of a form which will be controlled in any well specified convergent computational discretization of the differential equations., Comment: 11pages LaTeX