Properties of hypermassive neutron stars formed in mergers of spinning binaries

We present numerical simulations of binary neutron star mergers, comparing irrotational binaries to binaries of NSs rotating aligned to the orbital angular momentum. For the first time, we study spinning BNSs employing nuclear physics equations of state, namely the ones of Lattimer and Swesty as well as Shen, Horowitz, and Teige. We study mainly equal mass systems leading to a hypermassive neutron star (HMNS), and analyze in detail its structure and dynamics. In order to exclude gauge artifacts, we introduce a novel coordinate system used for post-processing. The results for our equal mass models show that the strong radial oscillations of the HMNS modulate the instantaneous frequency of the gravitational wave (GW) signal to an extend that leads to separate peaks in the corresponding Fourier spectrum. In particular, the high frequency peaks which are often attributed to combination frequencies can also be caused by the modulation of the m=2 mode frequency in the merger phase. As a consequence for GW data analysis, the offset of the high frequency peak does not necessarily carry information about the radial oscillation frequency. Further, the low frequency peak in our simulations is dominated by the contribution of the plunge and the first 1-2 bounces. The amplitude of the radial oscillations depends on the initial NS spin, which therefore has a complicated influence on the spectrum. Another important result is that HMNSs can consist of a slowly rotating core with an extended, massive envelope rotating close to Keplerian velocity, contrary to the common notion that a rapidly rotating core is necessary to prevent a prompt collapse. Finally, our estimates on the amount of unbound matter show a dependency on the initial NS spin, explained by the influence of the latter on the amplitude of radial oscillations, which in turn cause shock waves.Comment: 17 pages, 20 figures Updated to version published in PR

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.

Fundamental oscillation modes of neutron stars: validity of universal relations

We study the $f$-mode frequencies and damping times of nonrotating neutron stars (NS) in general relativity (GR) by solving the linearized perturbation equations, with the aim to establish "universal" relations that depend only weakly on the equations of state (EOS). Using a more comprehensive set of EOSs, we re-examine some proposed linearizations that describe the $f$-mode parameters in terms of mass and radius of the neutron star (NS), and we test a more recent proposal for expressing the $f$-mode parameters as quadratic functions of the effective compactness. Our extensive results for each equation of state considered allow us to study the accuracy of each proposal. In particular, we find that the damping time deviates quite considerably from the proposed linearization. We introduce a new universal relation for the product of the $f$-mode frequency and damping time as a function of the (ordinary) compactness, which proved to be more accurate. The relations using the effective compactness on the other hand also fit our data accurately. Our results show that the maximum oscillation frequency depends strongly on the EOS, such that the measurement of a high oscillation frequency would rule out several EOSs. Lastly, we compare the exact mode frequencies to those obtained in the Cowling approximation, and also to results obtained with a nonlinear evolution code, validating the implementations of the different approaches.Comment: 10 pages, 8 figures, v2: final version accepted for publication in Phys.Rev.

Numerical Inside View of Hypermassive Remnant Models for GW170817

The first multimessenger observation attributed to a merging neutron star binary provided an enormous amount of observational data. Unlocking the full potential of this data requires a better understanding of the merger process and the early post-merger phase, which are crucial for the later evolution that eventually leads to observable counterparts. In this work, we perform standard hydrodynamical numerical simulations of a system compatible with GW170817. We focus on a single equation of state (EOS) and two mass ratios, while neglecting magnetic fields and neutrino radiation. We then apply newly developed postprocessing and visualization techniques to the results obtained for this basic setting. The focus lies on understanding the three-dimensional structure of the remnant, most notably the fluid flow pattern, and its evolution until collapse. We investigate the evolution of mass and angular momentum distribution up to collapse, as well as the differential rotation along and perpendicular to the equatorial plane. For the cases that we studied, the remnant cannot be adequately modeled as a differentially rotating axisymetric NS. Further, the dominant aspect leading to collapse is the GW radiation and not internal redistribution of angular momentum. We relate features of the gravitational wave signal to the evolution of the merger remnant, and make the waveforms publicly available. Finally, we find that the three-dimensional vorticity field inside the disk is dominated by medium-scale perturbances and not the orbital velocity, with potential consequences for magnetic field amplification effects.Comment: 20 pages, 17 figure

First 100 ms of a long-lived magnetized neutron star formed in a binary neutron star merger

The recent multimessenger observation of the short gamma-ray burst (SGRB) GRB 170817A together with the gravitational wave (GW) event GW170817 provides evidence for the long-standing hypothesis associating SGRBs with binary neutron star (BNS) mergers. The nature of the remnant object powering the SGRB, which could have been either an accreting black hole (BH) or a long-lived magnetized neutron star (NS), is, however, still uncertain. General relativistic magnetohydrodynamic (GRMHD) simulations of the merger process represent a powerful tool to unravel the jet launching mechanism, but so far most simulations focused the attention on a BH as the central engine, while the long-lived NS scenario remains poorly investigated. Here, we explore the latter by performing a GRMHD BNS merger simulation extending up to ~100 ms after merger, much longer than any previous simulation of this kind. This allows us to (i) study the emerging structure and amplification of the magnetic field and observe a clear saturation at magnetic energy $E_\mathrm{mag} \sim 10^{51}$ erg, (ii) follow the magnetically supported expansion of the outer layers of the remnant NS and its evolution into an ellipsoidal shape without any surrounding torus, and (iii) monitor density, magnetization, and velocity along the axis, observing no signs of jet formation. We also argue that the conditions at the end of the simulation disfavor later jet formation on subsecond timescales if no BH is formed. Furthermore, we examine the rotation profile of the remnant, the conversion of rotational energy associated with differential rotation, the overall energy budget of the system, and the evolution of the GW frequency spectrum. Finally, we perform an additional simulation where we induce the collapse to a BH ~70 ms after merger, in order to gain insights on the prospects for massive accretion tori in case of a late collapse. We find that...Comment: 14 pages, 16 figures, matches published version in PR

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

Robust Recovery of Primitive Variables in Relativistic Ideal Magnetohydrodynamics

Modern simulation codes for general relativistic ideal magnetohydrodynamics are all facing a long standing technical problem given by the need to recover fundamental variables from those variables that are evolved in time. In the relativistic case, this requires the numerical solution of a system of nonlinear equations. Although several approaches are available, none has proven completely reliable. A recent study comparing different methods showed that all can fail, in particular for the important case of strong magnetization and moderate Lorentz factors. Here, we propose a new robust, efficient, and accurate solution scheme, along with a proof for the existence and uniqueness of a solution, and analytic bounds for the accuracy. Further, the scheme allows us to reliably detect evolution errors leading to unphysical states and automatically applies corrections for typical harmless cases. A reference implementation of the method is made publicly available as a software library. The aim of this library is to improve the reliability of binary neutron star merger simulations, in particular in the investigation of jet formation and magnetically driven winds.Comment: 18 pages, 6 figures, supplementary material at http://doi.org/10.5281/zenodo.407531