Tim Dietrich

Modeling the Dynamics of Tidally Interacting Binary Neutron Stars up to the Merger

The data analysis of the gravitational wave signals emitted by coalescing neutron star binaries requires the availability of an accurate analytical representation of the dynamics and waveforms of these systems. We propose an effective-one-body model that describes the general relativistic dynamics of neutron star binaries from the early inspiral up to the merger. Our effective-one-body model incorporates an enhanced attractive tidal potential motivated by recent analytical advances in the post-Newtonian and gravitational self-force description of relativistic tidal interactions. No fitting parameters are introduced for the description of tidal interaction in the late, strong-field dynamics. We compare the model energetics and the gravitational wave phasing with new high-resolution multiorbit numerical relativity simulations of equal-mass configurations with different equations of state. We find agreement within the uncertainty of the numerical data for all configurations. Our model is the first semianalytical model that captures the tidal amplification effects close to merger. It thereby provides the most accurate analytical representation of binary neutron star dynamics and waveforms currently available.

Modeling the Complete Gravitational Wave Spectrum of Neutron Star Mergers.

In the context of neutron star mergers, we study the gravitational wave spectrum of the merger remnant using numerical relativity simulations. Postmerger spectra are characterized by a main peak frequency f2 related to the particular structure and dynamics of the remnant hot hypermassive neutron star. We show that f(2) is correlated with the tidal coupling constant κ(2)^T that characterizes the binary tidal interactions during the late-inspiral merger. The relation f(2)(κ(2)^T) depends very weakly on the binary total mass, mass ratio, equation of state, and thermal effects. This observation opens up the possibility of developing a model of the gravitational spectrum of every merger unifying the late-inspiral and postmerger descriptions.

Numerical relativity simulations of neutron star merger remnants using conservative mesh refinement

We study equal- and unequal-mass neutron star mergers by means of new numerical relativity simulations in which the general relativistic hydrodynamics solver employs an algorithm that guarantees mass conservation across the refinement levels of the computational mesh. We consider eight binary configurations with total mass M=2.7M_⊙, mass ratios q=1 and q=1.16, four different equations of state (EOSs) and one configuration with a stiff EOS, M=2.5M_⊙ and q=1.5, which is one of the largest mass ratios simulated in numerical relativity to date. We focus on the postmerger dynamics and study the merger remnant, the dynamical ejecta, and the postmerger gravitational wave spectrum. Although most of the merger remnants are a hypermassive neutron star collapsing to a black hole+disk system on dynamical time scales, stiff EOSs can eventually produce a stable massive neutron star. During the merger process and on very short time scales, about ∼10^(−3) –10^(−2) M_⊙ of material become unbound with kinetic energies ∼10^(50) erg. Ejecta are mostly emitted around the orbital plane and favored by large mass ratios and softer EOS. The postmerger wave spectrum is mainly characterized by the nonaxisymmetric oscillations of the remnant neutron star. The stiff EOS configuration consisting of a 1.5M_⊙ and a 1.0M_⊙ neutron star, simulated here for the first time, shows a rather peculiar dynamics. During merger the companion star is very deformed; about ∼0.03M_⊙ of the rest mass becomes unbound from the tidal tail due to the torque generated by the two-core inner structure. The merger remnant is a stable neutron star surrounded by a massive accretion disk of rest mass ∼0.3M_⊙. This and similar configurations might be particularly interesting for electromagnetic counterparts. Comparing results obtained with and without the conservative mesh refinement algorithm, we find that postmerger simulations can be affected by systematic errors if mass conservation is not enforced in the mesh refinement strategy. However, mass conservation also depends on grid details and on the artificial atmosphere setup; the latter are particularly significant in the computation of the dynamical ejecta.

Binary neutron stars with generic spin, eccentricity, mass ratio, and compactness: Quasi-equilibrium sequences and first evolutions

Information about the last stages of a binary neutron star inspiral and the final merger can be extracted from quasiequilibrium configurations and dynamical evolutions. In this article, we construct quasiequilibrium configurations for different spins, eccentricities, mass ratios, compactnesses, and equations of state. For this purpose we employ the sgrid code, which allows us to construct such data in previously inaccessible regions of the parameter space. In particular, we consider spinning neutron stars in isolation and in binary systems; we incorporate new methods to produce highly eccentric and eccentricity-reduced data; we present the possibility of computing data for significantly unequal-mass binaries with mass ratios q≃2; and we create equal-mass binaries with individual compactness up to

Mergers of binary neutron stars with realistic spin

Simulations of binary neutron stars have seen great advances in terms of physical detail and numerical quality. However, the spin of the neutron stars, one of the simplest global parameters of binaries, remains mostly unstudied. We present the first, fully nonlinear general relativistic dynamical evolutions of the last three orbits for constraint satisfying initial data of spinning neutron star binaries, with astrophysically realistic spins aligned and anti-aligned to the orbital angular momentum. The initial data is computed with the constant rotational velocity approach. The dynamics of the systems is analyzed in terms of gauge-invariant binding energy vs. orbital angular momentum curves. By comparing to a binary black hole configuration we can estimate the different tidal and spin contributions to the binding energy for the first time. First results on the gravitational wave forms are presented. The phase evolution during the orbital motion is significantly affected by spin-orbit interactions, leading to delayed or early mergers. Furthermore, a frequency shift in the main emission mode of the hyper massive neutron star is observed. Our results suggest that a detailed modeling of merger waveforms requires the inclusion of spin, even for the moderate magnitudes observed in binary neutron star systems.

Collapse of nonlinear gravitational waves in moving-puncture coordinates

We study numerical evolutions of nonlinear gravitational waves in moving-puncture coordinates. We adopt two different types of initial data\char22{}Brill and Teukolsky waves\char22{}and evolve them with two independent codes producing consistent results. We find that Brill data fail to produce long-term evolutions for common choices of coordinates and parameters, unless the initial amplitude is small, while Teukolsky wave initial data lead to stable evolutions, at least for amplitudes sufficiently far from criticality. The critical amplitude separates initial data whose evolutions leave behind flat space from those that lead to a black hole. For the latter we follow the interaction of the wave, the formation of a horizon, and the settling down into a time-independent trumpet geometry. We explore the differences between Brill and Teukolsky data and show that for less common choices of the parameters\char22{}in particular negative amplitudes\char22{}Brill data can be evolved with moving-puncture coordinates and behave similarly to Teukolsky waves.

Simulations of inspiraling and merging double neutron stars using the Spectral Einstein Code

We present results on the inspiral, merger, and postmerger evolution of a neutron star-neutron star (NSNS) system. Our results are obtained using the hybrid pseudospectral-finite volume Spectral Einstein Code (SpEC). To test our numerical methods, we evolve an equal-mass system for ≈22 orbits before merger. This waveform is the longest waveform obtained from fully general-relativistic simulations for NSNSs to date. Such long (and accurate) numerical waveforms are required to further improve semianalytical models used in gravitational wave data analysis, for example, the effective one body models. We discuss in detail the improvements to SpEC’s ability to simulate NSNS mergers, in particular mesh refined grids to better resolve the merger and postmerger phases. We provide a set of consistency checks and compare our results to NSNS merger simulations with the independent bam code. We find agreement between them, which increases confidence in results obtained with either code. This work paves the way for future studies using long waveforms and more complex microphysical descriptions of neutron star matter in SpEC.

Solving the Hamiltonian constraint for 1+log trumpets

The puncture method specifies black hole data on a hypersurface with the aid of a conformal rescaling of the metric that exhibits a coordinate singularity at the puncture point. When constructing puncture initial data by solving the Hamiltonian constraint for the conformal factor, the coordinate singularity requires special attention. The standard way to treat the pole singularity occurring in wormhole puncture data is not generally applicable to trumpet puncture data. We investigate a new approach based on inverse powers of the conformal factor and present numerical examples for single punctures of the wormhole and 1+log-trumpet type. Additionally, we describe a method to solve the Hamiltonian constraint for two 1+log trumpets for a given extrinsic curvature with non-vanishing trace. We investigate properties of this constructed initial data during binary black hole evolutions and find that the initial gauge dynamics is reduced.

Simulations of rotating neutron star collapse with the puncture gauge: End state and gravitational waveforms

We reexamine the gravitational collapse of rotating neutron stars to black holes by new 3+1 numerical relativity simulations employing the Z4c formulation of Einstein equations, the moving puncture gauge conditions, and a conservative mesh refinement scheme for the general relativistic hydrodynamics. The end state of the collapse is compared to the vacuum spacetime resulting from the evolution of spinning puncture initial data. Using a local analysis for the metric fields, we demonstrate that the two spacetimes actually agree. Gravitational waveforms are analyzed in some detail. We connect the emission of radiation to the collapse dynamics using simplified spacetime diagrams, and discuss the similarity of the waveform structure with the one of black hole perturbation theory.