Bruno Giacomazzo

The missing link: Merging neutron stars naturally produce jet-like structures and can power short Gamma-Ray Bursts

Short Gamma-Ray Bursts (SGRBs) are among the most luminous explosions in the universe, releasing in less than one second the energy emitted by our Galaxy over one year. Despite decades of observations, the nature of their “central-engine” remains unknown. Considering a generic binary of magnetized neutron stars and solving Einstein equations, we show that their merger results in a rapidly spinning black hole surrounded by a hot and highly magnetized torus. Lasting over 35 ms and much longer than previous simulations, our study reveals that magnetohydrodynamical instabilities amplify an initially turbulent magnetic field of 10 12 G to produce an ordered poloidal field of 10 15 G along the black-hole spin-axis, within a half-opening angle of 30 , which may naturally launch a relativistic jet. The broad consistency of our ab-initio calculations with SGRB observations shows that the merger of magnetized neutron stars can provide the basic physical conditions for the central-engine of SGRBs. Subject headings: Gamma-ray burst: general — black hole physics — stars: neutron — gravitational waves — magnetohydrodynamics (MHD) — methods: numerical

The exact solution of the Riemann problem in relativistic magnetohydrodynamics

As first formulated by Riemann more than a hundred years ago, the solution of the one-dimensional Riemann problem in hydrodynamics consists of determining the temporal evolution of a fluid which, at some initial time, has two adjacent uniform states characterized by different values of uniform velocity, pressure and density. These initial conditions completely determine the way in which the discontinuity will decay after removal of the barrier separating the initial ‘left’ and ‘right’ states. The Riemann problem has ceased to be merely academic and gained enormous importance when it was realized that its numerical solution can serve as the building block of hydrodynamical codes based on Godunov-type finite difference methods (Godunov 1959). In such methods, the computational domain is discretized and each interface between two adjacent grid zones is used to construct the initial left and right states of a ‘local’ Riemann problem. The evolution of the hydrodynamical equations is then obtained through the solution across the computational grid of the sequence of local Riemann problems set up at the interfaces between successive grid zones (see Godunov 1959, and also Mart´ ¨ 2003 and Font 2003 for the use of the Riemann problem in relativistic regimes). In general, the Riemann problem requires the solution of a nonlinear algebraic system of equations written as a function of a single unknown quantity (e.g. the total pressure at the contact discontinuity in purely hydrodynamical problems). With the exception of few trivial initial configurations, the solution of the Riemann problem cannot be obtained analytically but requires a numerical approach. The solution found in this way is referred to as the ‘exact’ solution of the Riemann problem, to distinguish it from the ‘approximate’ solution of the Riemann problem, which is instead obtained when the system of equations is reduced to a locally linear form (an exhaustive discussion of approximate Riemann solvers can be found in Toro 1999). It is therefore useful to stress that although named ‘exact’, the solution of the Riemann problem is necessarily obtained with a small but non-zero truncation error.

Accurate evolutions of unequal-mass neutron-star binaries: properties of the torus and short GRB engines

We present new results from accurate and fully general-relativistic simulations of the coalescence of unmagnetized binary neutron stars with various mass ratios. The evolution of the stars is followed through the inspiral phase, the merger, and the prompt collapse to a black hole, up until the appearance of a thick accretion disc, which is studied as it enters and remains in a regime of quasi-steady accretion. Although a simple ideal-fluid equation of state with Γ = 2 is used, this work presents a systematic study within a fully general-relativistic framework of the properties of the resulting black-hole–torus system produced by the merger of unequal-mass binaries. More specifically, we show that (1) the mass of the torus increases considerably with the mass asymmetry, and equal-mass binaries do not produce significant tori if they have a total baryonic mass Mtot 3.7 M⊙; (2) tori with masses Mtor ~ 0.2 M⊙ are measured for binaries with Mtot ~ 3.4 M⊙ and mass ratios q ~ 0.75–0.85; (3) the mass of the torus can be estimated by the simple expression , involving the maximum mass for the binaries and coefficients constrained from the simulations, and suggesting that the tori can have masses as large as for Mtot ~ 2.8 M⊙ and q ~ 0.75–0.85; (4) using a novel technique to analyze the evolution of the tori, we find no evidence for the onset of non-axisymmetric instabilities and that very little, if any, of their mass is unbound; (5) finally, for all the binaries considered, we compute the complete gravitational waveforms and the recoils imparted to the black holes, discussing the prospects of the detection of these sources for a number of present and future detectors.

Matter effects on binary neutron star waveforms

Using an extended set of equations of state and a multiple-group multiple-code collaborative effort to generate waveforms, we improve numerical-relativity-based data-analysis estimates of the measurability of matter effects in neutron-star binaries. We vary two parameters of a parameterized piecewise-polytropic equation of state (EOS) to analyze the measurability of EOS properties, via a parameter {\Lambda} that characterizes the quadrupole deformability of an isolated neutron star. We find that, to within the accuracy of the simulations, the departure of the waveform from point-particle (or spinless double black-hole binary) inspiral increases monotonically with {\Lambda}, and changes in the EOS that did not change {\Lambda} are not measurable. We estimate with two methods the minimal and expected measurability of {\Lambda} in second- and third- generation gravitational-wave detectors. The first estimate, using numerical waveforms alone, shows two EOS which vary in radius by 1.3km are distinguishable in mergers at 100Mpc. The second estimate relies on the construction of hybrid waveforms by matching to post-Newtonian inspiral, and estimates that the same EOS are distinguishable in mergers at 300Mpc. We calculate systematic errors arising from numerical uncertainties and hybrid construction, and we estimate the frequency at which such effects would interfere with template-based searches.

WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics

The accurate modelling of astrophysical scenarios involving compact objects and magnetic fields, such as the collapse of rotating magnetized stars to black holes or the phenomenology of γ-ray bursts, requires the solution of the Einstein equations together with those of general-relativistic magnetohydrodynamics. We present a new numerical code developed to solve the full set of general-relativistic magnetohydrodynamics equations in a dynamical and arbitrary spacetime with high-resolution shock-capturing techniques on domains with adaptive mesh refinements. After a discussion of the equations solved and of the techniques employed, we present a series of testbeds carried out to validate the code and assess its accuracy. Such tests range from the solution of relativistic Riemann problems in flat spacetime, over to the stationary accretion onto a Schwarzschild black hole and up to the evolution of oscillating magnetized stars in equilibrium and constructed as consistent solutions of the coupled Einstein–Maxwell equations.

Accurate evolutions of inspiralling and magnetized neutron-stars: equal-mass binaries

By performing new, long and numerically accurate general-relativistic simulations of magnetized, equal-mass neutron-star binaries, we investigate the role that realistic magnetic fields may have in the evolution of these systems. In particular, we study the evolution of the magnetic fields and show that they can influence the survival of the hypermassive neutron star produced at the merger by accelerating its collapse to a black hole. We also provide evidence that, even if purely poloidal initially, the magnetic fields produced in the tori surrounding the black hole have toroidal and poloidal components of equivalent strength. When estimating the possibility that magnetic fields could have an impact on the gravitational-wave signals emitted by these systems either during the inspiral or after the merger, we conclude that for realistic magnetic-field strengths B < or approx. 10{sup 12} G such effects could be detected, but only marginally, by detectors such as advanced LIGO or advanced Virgo. However, magnetically induced modifications could become detectable in the case of small-mass binaries and with the development of gravitational-wave detectors, such as the Einstein Telescope, with much higher sensitivities at frequencies larger than {approx_equal}2 kHz.

Late time afterglow observations reveal a collimated relativistic jet in the ejecta of the binary neutron star merger GW170817

The binary neutron star (BNS) merger GW170817 was the first astrophysical source detected in gravitational waves and multiwavelength electromagnetic radiation. The almost simultaneous observation of a pulse of gamma rays proved that BNS mergers are associated with at least some short gamma-ray bursts (GRBs). However, the gamma-ray pulse was faint, casting doubt on the association of BNS mergers with the luminous, highly relativistic outflows of canonical short GRBs. Here we show that structured jets with a relativistic, energetic core surrounded by slower and less energetic wings produce afterglow emission that brightens characteristically with time, as recently seen in the afterglow of GW170817. Initially, we only see the relatively slow material moving towards us. As time passes, larger and larger sections of the outflow become visible, increasing the luminosity of the afterglow. The late appearance and increasing brightness of the multiwavelength afterglow of GW170817 allow us to constrain the geometry of its ejecta and thus reveal the presence of an off-axis jet pointing about 30° away from Earth. Our results confirm a single origin for BNS mergers and short GRBs: GW170817 produced a structured outflow with a highly relativistic core and a canonical short GRB. We did not see the bright burst because it was beamed away from Earth. However, approximately one in 20 mergers detected in gravitational waves will be accompanied by a bright, canonical short GRB.

Collapse of differentially rotating neutron stars and cosmic censorship

We present new results on the dynamics and gravitational-wave emission from the collapse of differentially rotating neutron stars. We have considered a number of polytropic stellar models having different values of the dimensionless angular momentumJ/M 2 , where J and M are the asymptotic angular momentum and mass of the star, respectively. For neutron stars with J/M 2 1, i.e. “supra-Kerr” models, on the other hand, we were not able to fin d models that are dynamically unstable and all of the computed supra-Kerr models were found to be far from the stability threshold. For these models a gravitational collapse is possible only afte r a very severe and artificial reduction of the pressure, which then leads to a torus developing nonaxisymmetric instabilities and eventually contracting to a stable axisymmetric stellar configuration. While this does not exc lude the possibility that a naked singularity can be produced by the collapse of a differentially rotating star, it also suggests that cosmic censorship is not violated and that generic conditions for a supra-Kerr progenitor do not lead to a naked singularity.

Analytic modelling of tidal effects in the relativistic inspiral of binary neutron stars

To detect the gravitational-wave (GW) signal from binary neutron stars and extract information about the equation of state of matter at nuclear density, it is necessary to match the signal with a bank of accurate templates. We present the two longest (to date) general-relativistic simulations of equal-mass binary neutron stars with different compactnesses, C=0.12 and C=0.14, and compare them with a tidal extension of the effective-one-body (EOB) model. The typical numerical phasing errors over the ≃22   GW cycles are Δϕ≃±0.24   rad. By calibrating only one parameter (representing a higher-order amplification of tidal effects), the EOB model can reproduce, within the numerical error, the two numerical waveforms essentially up to the merger. By contrast, the third post-Newtonian Taylor-T4 approximant with leading-order tidal corrections dephases with respect to the numerical waveforms by several radians.

General-Relativistic Resistive Magnetohydrodynamics in three dimensions: formulation and tests

We present a new numerical implementation of the general-relativistic resistive magnetohydrodynamics (MHD)equationswithintheWHISKYcode.ThenumericalmethodadoptedexploitsthepropertiesofimplicitexplicitRunge-Kuttanumericalschemestotreatthestifftermsthatappearintheequationsforlargeelectrical conductivities. Using tests in one, two, andthree dimensions, we show that ourimplementation is robustand 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 approximationandindynamicalspacetimes.Finally,becauseofitsastrophysicalrelevanceandbecauseitprovidesa severe tested 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 ‘ ¼ 1 mode eigenfrequency, respectively. Finally we provide an estimate of the electromagnetic efficiency of this process.