arXiv subjects

Luciano Rezzolla

Publications and source records attributed to Luciano Rezzolla.

At least 145 records · Page 8Linked to original sources

arXiv2018

Conformal and covariant Z4 formulation of the Einstein equations: strongly hyperbolic first-order reduction and solution with discontinuous Galerkin schemes

We present a strongly hyperbolic first-order formulation of the Einstein equations based on the conformal and covariant Z4 system (CCZ4) with constraint-violation damping, which we refer to as FO-CCZ4. As CCZ4, this formulation combines the advantages of a conformal and traceless formulation, with the suppression of constraint violations given by the damping terms, but being first order in time and space, it is particularly suited for a discontinuous Galerkin (DG) implementation. The strongly hyperbolic first-order formulation has been obtained by making careful use of first and second-order ordering constraints. A proof of strong hyperbolicity is given for a selected choice of standard gauges via an analytical computation of the entire eigenstructure of the FO-CCZ4 system. The resulting governing partial differential equations system is written in non-conservative form and requires the evolution of 58 unknowns. A key feature of our formulation is that the first-order CCZ4 system decouples into a set of pure ordinary differential equations and a reduced hyperbolic system of partial differential equations that contains only linearly degenerate fields. We implement FO-CCZ4 in a high-order path-conservative arbitrary-high-order-method-using-derivatives (ADER)-DG scheme with adaptive mesh refinement and local time-stepping, supplemented with a third-order ADER-WENO subcell finite-volume limiter in order to deal with singularities arising with black holes. We validate the correctness of the formulation through a series of standard tests in vacuum, performed in one, two and three spatial dimensions, and also present preliminary results on the evolution of binary black-hole systems. To the best of our knowledge, these are the first successful three-dimensional simulations of moving punctures carried out with high-order DG schemes using a first-order formulation of the Einstein equations.

gr-qc↗

arXiv2018

The Current Ability to Test Theories of Gravity with Black Hole Shadows

Our Galactic Center, Sagittarius A* (Sgr A*), is believed to harbour a supermassive black hole (BH), as suggested by observations tracking individual orbiting stars. Upcoming sub-millimetre very-long-baseline-interferometry (VLBI) images of Sgr A* carried out by the Event-Horizon-Telescope Collaboration (EHTC) are expected to provide critical evidence for the existence of this supermassive BH. We assess our present ability to use EHTC images to determine if they correspond to a Kerr BH as predicted by Einstein's theory of general relativity (GR) or to a BH in alternative theories of gravity. To this end, we perform general-relativistic magnetohydrodynamical (GRMHD) simulations and use general-relativistic radiative transfer (GRRT) calculations to generate synthetic shadow images of a magnetised accretion flow onto a Kerr BH. In addition, and for the first time, we perform GRMHD simulations and GRRT calculations for a dilaton BH, which we take as a representative solution of an alternative theory of gravity. Adopting the VLBI configuration from the 2017 EHTC campaign, we find that it could be extremely difficult to distinguish between BHs from different theories of gravity, thus highlighting that great caution is needed when interpreting BH images as tests of GR.

astro-ph.GA↗

arXiv2018

Limits on Magnetic Field Amplification from the r-Mode Instability

At second order in perturbation theory, the unstable r-mode of a rotating star includes growing differential rotation whose form and growth rate are determined by gravitational-radiation reaction. With no magnetic field, the angular velocity of a fluid element grows exponentially until the mode reaches its nonlinear saturation amplitude and remains nonzero after saturation. With a background magnetic field, the differential rotation winds up and amplifies the field, and previous work where large mode amplitudes were considered suggests that the amplification may damp out the instability. A background magnetic field, however, turns the saturated time-independent perturbations corresponding to adding differential rotation into perturbations whose characteristic frequencies are of order the Alfvén frequency. As found in previous studies, we argue that magnetic- field growth is sharply limited by the saturation amplitude of an unstable mode. In contrast to previous work, however, we show that if the amplitude is small, i.e., of order 10^(-4), then the limit on the magnetic-field growth is stringent enough to prevent the loss of energy to the magnetic field from damping or significantly altering an unstable r-mode in nascent neutron stars with normal interiors and in cold stars whose interiors are type II superconductors. We show this result first for a toy model, and we then obtain an analogous upper limit on magnetic field growth using a more realistic model of a rotating neutron star. Our analysis depends on the assumption that there are no marginally unstable perturbations, and this may not hold when differential rotation leads to a magnetorotational instability.

astro-ph.HE↗

arXiv2018

RAPTOR I: Time-dependent radiative transfer in arbitrary spacetimes

Observational efforts to image the immediate environment of a black hole at the scale of the event horizon benefit from the development of efficient imaging codes that are capable of producing synthetic data, which may be compared with observational data. We aim to present RAPTOR, a new public code that produces accurate images, animations, and spectra of relativistic plasmas in strong gravity by numerically integrating the equations of motion of light rays and performing time-dependent radiative transfer calculations along the rays. The code is compatible with any analytical or numerical spacetime. It is hardware-agnostic and may be compiled and run both on GPUs and CPUs. We describe the algorithms used in RAPTOR and test the code's performance. We have performed a detailed comparison of RAPTOR output with that of other radiative-transfer codes and demonstrate convergence of the results. We then applied RAPTOR to study accretion models of supermassive black holes, performing time-dependent radiative transfer through general relativistic magneto-hydrodynamical (GRMHD) simulations and investigating the expected observational differences between the so-called fast-light and slow-light paradigms. Using RAPTOR to produce synthetic images and light curves of a GRMHD model of an accreting black hole, we find that the relative difference between fast-light and slow-light light curves is less than 5%. Using two distinct radiative-transfer codes to process the same data, we find integrated flux densities with a relative difference less than 0.01%. For two-dimensional GRMHD models, such as those examined in this paper, the fast-light approximation suffices as long as errors of a few percent are acceptable. The convergence of the results of two different codes demonstrates that they are, at a minimum, consistent.

astro-ph.HE↗

arXiv2018

Using gravitational-wave observations and quasi-universal relations to constrain the maximum mass of neutron stars

Combining the GW observations of merging systems of binary neutron stars and quasi-universal relations, we set constraints on the maximum mass that can be attained by nonrotating stellar models of neutron stars. More specifically, exploiting the recent observation of the GW event GW 170817 and drawing from basic arguments on kilonova modeling of GRB 170817A, together with the quasi-universal relation between the maximum mass of nonrotating stellar models $M_{\rm TOV}$ and the maximum mass supported through uniform rotation $M_{\rm max}=\left(1.20^{+0.02}_{-0.05}\right) M_{\rm TOV}$ we set limits for the maximum mass to be $ 2.01^{+0.04}_{-0.04}\leq M_{\rm TOV}/M_{\odot}\lesssim 2.16^{+0.17}_{-0.15}$, where the lower limit in this range comes from pulsar observations. Our estimate, which follows a very simple line of arguments and does not rely on the modeling of the electromagnetic signal in terms of numerical simulations, can be further refined as new detections become available. We briefly discuss the impact that our conclusions have on the equation of state of nuclear matter.

astro-ph.HE↗

arXiv2017

Magnetic field amplification by the r-mode instability

We discuss magnetic field enhancement by unstable r-modes (driven by the gravitational radiation reaction force) in rotating stars. In the absence of a magnetic field, gravitational radiation exponentially increases the r-mode amplitude $α$, and accelerates differential rotation (secular motion of fluid elements). For a magnetized star, differential rotation enhances the magnetic field energy. Rezzolla et al. (2000--2001) argued that if the magnetic energy grows faster than the gravitational radiation reaction force pumps energy into the r-modes, then the r-mode instability is suppressed. Chugunov (2015) demonstrated that without gravitational radiation, differential rotation can be treated as a degree of freedom decoupled from the r-modes and controlled by the back reaction of the magnetic field. In particular, the magnetic field windup does not damp r-modes. Here we discuss the effect of the back reaction of the magnetic field on differential rotation of unstable r-modes, and show that it limits the generated magnetic field and the magnetic energy growth rate preventing suppression of the r-mode instability by magnetic windup at low saturation amplitudes, $α\ll 1$, predicted by current models.

astro-ph.HE↗

arXiv2017

Uniformly rotating, axisymmetric and triaxial quark stars in general relativity

Quasi-equilibrium models of uniformly rotating axisymmetric and triaxial quark stars are computed in general relativistic gravity scenario. The Isenberg-Wilson-Mathews (IWM) formulation is employed and the Compact Object CALculator (COCAL) code is extended to treat rotating stars with finite surface density and new equations of state (EOSs). Besides the MIT bag model for quark matter which is composed of de-confined quarks, we examine a new EOS proposed by Lai and Xu that is based on quark clustering and results in a stiff EOS that can support masses up to $3.3M_\odot$ in the case we considered. We perform convergence tests for our new code to evaluate the effect of finite surface density in the accuracy of our solutions and construct sequences of solutions for both small and high compactness. The onset of secular instability due to viscous dissipation is identified and possible implications are discussed. An estimate of the gravitational wave amplitude and luminosity based on quadrupole formulas is presented and comparison with neutron stars is discussed.

astro-ph.HE↗

arXiv2017

Effect of intense magnetic fields on reduced-MHD evolution in $\sqrt{s_{\rm NN}}$ = 200 GeV Au+Au collisions

We investigate the effect of large magnetic fields on the $2+1$ dimensional reduced-magnetohydrodynamical expansion of hot and dense nuclear matter produced in $\sqrt{s_{\rm NN}}$ = 200 GeV Au+Au collisions. For the sake of simplicity, we consider the case where the magnetic field points in the direction perpendicular to the reaction plane. We also consider this field to be external, with energy density parametrized as a two-dimensional Gaussian. The width of the Gaussian along the directions orthogonal to the beam axis varies with the centrality of the collision. The dependence of the magnetic field on proper time ($τ$) for the case of zero electrical conductivity of the QGP is parametrized following [Deng 2012], and for finite electrical conductivity following [Tuchin 2013]. We solve the equations of motion of ideal hydrodynamics for such an external magnetic field. For collisions with non-zero impact parameter we observe considerable changes in the evolution of the momentum eccentricities of the fireball when comparing the case when the magnetic field decays in a conducting QGP medium and when no magnetic field is present. The elliptic-flow coefficient $v_2$ of $π^{-}$ is shown to increase in the presence of an external magnetic field and the increment in $v_2$ is found to depend on the evolution and the initial magnitude of the magnetic field.

nucl-th↗

arXiv2017

Test-particle dynamics in general spherically symmetric black hole spacetimes

To date, the most precise tests of general relativity have been achieved through pulsar timing, albeit in the weak-field regime. Since pulsars are some of the most precise and stable "clocks" in the Universe, present observational efforts are focused on detecting pulsars in the vicinity of supermassive black holes (most notably in our Galactic Centre), enabling pulsar timing to be used as an extremely precise probe of strong-field gravity. In this paper a mathematical framework to describe test-particle dynamics in general black hole spacetimes is presented, and subsequently used to study a binary system comprising a pulsar orbiting a black hole. In particular, taking into account the parameterization of a general spherically symmetric black hole metric, general analytic expressions for both the advance of the periastron and for the orbital period of a massive test particle are derived. Furthermore, these expressions are applied to four representative cases of solutions arising in both general relativity and in alternative theories of gravity. Finally, this framework is applied to the Galactic Centre $S$-stars and four distinct pulsar toy models. It is shown that by adopting a fully general-relativistic description of test-particle motion which is independent of any particular theory of gravity, observations of pulsars can help impose better constraints on alternative theories of gravity than is presently possible.

gr-qc↗

arXiv2017

On the stability and maximum mass of differentially rotating relativistic stars

The stability properties of rotating relativistic stars against prompt gravitational collapse to a black hole are rather well understood for uniformly rotating models. This is not the case for differentially rotating neutron stars, which are expected to be produced in catastrophic events such as the merger of binary system of neutron stars or the collapse of a massive stellar core. We consider sequences of differentially rotating equilibrium models using the $j$-constant law and by combining them with their dynamical evolution, we show that a sufficient stability criterion for differentially rotating neutron stars exists similar to the one of their uniformly rotating counterparts. Namely: along a sequence of constant angular momentum, a dynamical instability sets in for central rest-mass densities slightly below the one of the equilibrium solution at the turning point. In addition, following Breu & Rezzolla (2016), we show that "quasi-universal" relations can be found when calculating the turning-point mass. In turn, this allows us to compute the maximum mass allowed by differential rotation, $M_{\rm max,dr}$, in terms of the maximum mass of the nonrotating configuration, $M_{_{\rm TOV}}$, finding that $M_{\rm max, dr} \simeq \left(1.54 \pm 0.05\right) M_{_{\rm TOV}}$ for all the equations of state we have considered.

gr-qc↗

arXiv2017

On r-process nucleosynthesis from matter ejected in binary neutron starmergers

When binary systems of neutron stars merge, a very small fraction of their rest mass is ejected, either dynamically or secularly. This material is neutron-rich and its nucleosynthesis could provide the astrophysical site for the production of heavy elements in the universe, together with a kilonova signal confirming neutron-star mergers as the origin of short gamma-ray bursts. We perform full general-relativistic simulations of binary neutron-star mergers employing three different nuclear-physics EOSs, considering both equal- and unequal-mass configurations, and adopting a leakage scheme to account for neutrino radiative losses. Using a combination of techniques, we carry out an extensive and systematic study of the hydrodynamical, thermodynamical, and geometrical properties of the matter ejected dynamically, employing the WinNet nuclear-reaction network to recover the relative abundances of heavy elements produced by each configurations. Among the results obtained, three are particularly important. First, we find that both the properties of the dynamical ejecta and the nucleosynthesis yields are robust against variations of the EOS and masses, and match very well the observed chemical abundances. Second, using a conservative but robust criterion for unbound matter, we find that the amount of ejected mass is $\lesssim 10^{-3}\,M_{\odot}$, hence at least one order of magnitude smaller than what normally assumed in modelling kilonova signals. Finally, using a simplified and gray-opacity model we assess the observability of the infrared kilonova emission finding, that for all binaries the luminosity peaks around $\sim1/2$ day in the $H$-band, reaching a maximum magnitude of $-13$, and decreasing rapidly after one day. These rather low luminosities make the prospects for detecting kilonovae less promising than what assumed so far.

gr-qc↗

arXiv2017

The kilo Hertz quasi-periodic oscillations in neutron star low-mass X-ray binaries as tori oscillation modes. I

There have been many efforts to explain the dynamical mechanisms behind the phenomenology of quasi-periodic oscillations (QPOs) seen in the X-ray light curves of low-mass X-ray binaries. Up to now, none of the models can successfully explain all the frequencies observed in the power density spectrum of the light curve. Here we perform several hydrodynamic simulations of non-self-gravitating relativistic axisymmetric thick tori applied to the neutron star in the low-mass X-ray binary 4U 1636-53 and show how the observed oscillation modes triggered by different velocity perturbations give rise to a set of variability features similar to what we see in the observational X-ray data. When we match pairs of frequencies from the simulations of constant angular momentum ($l$) tori with the observed kilo Hertz QPOs, we find that certain combinations of frequencies lie on top of the observed relation, provided we assume a smaller mass for the neutron star than is generally assumed. However, constant-$l$ tori cannot match the entire range of frequencies observed for 4U 1636-53 due to physical constraints set by the torus size. We show that our model is consistent with the observed shift in QPO frequency that accompany state transitions of the accretion disk.

astro-ph.HE↗

arXiv2017

On the use of tracer particles in simulations of binary neutron stars

In grid-based codes that provide the combined solution of the Einstein equations and of relativistic hydrodynamics, the history of the fluid is not simple to track, especially when compared with particle-based codes. The use of tracers, namely massless particles that are advected with the flow, represents a simple and effective way to solve this problem. Yet, the use of tracers in numerical relativity is far from being settled and several issues, such as the impact of different placements in time and space of the tracers, or the relation between the placement and the description of the underlying fluid, have not yet been addressed. In this paper we present the first detailed discussion of the use tracers in numerical-relativity simulations focussing on both unbound material -- such as the one leading to r-process nucleosynthesis in binary mergers of neutron stars -- and on bound material -- such as the one in the core of the object produced from the merger of two neutron stars. In particular, when interested in unbound matter, we have evaluated four different placement schemes that could be used to initially distribute the tracers and how well their predictions match those obtained when using information from the actual fluid flow. Countering our naive expectations, we found that the most effective method does not rely on the rest-mass density distribution nor on the fluid that is unbound, but simply distributes tracers uniformly in rest-mass density. This prescription leads to the closest matching with the information obtained from the hydrodynamical solution. When considering bound matter, we demonstrate that tracers can provide insight into the fine details of the fluid motion as they can be used to track the evolution of fluid elements or to calculate the variation of quantities that are conserved along streamlines of adiabatic flows.

gr-qc↗

arXiv2017

On the importance of viscous dissipation and heat conduction in binary neutron-star mergers

Inferring the properties of dense matter is one of the most exciting prospects from the measurement of gravitational waves from neutron star mergers. However, it will require reliable numerical simulations that incorporate viscous dissipation and energy transport if these can play a significant role within the survival time of the post-merger object. We calculate timescales for typical forms of dissipation and find that thermal transport and shear viscosity will not be important unless neutrino trapping occurs, which requires temperatures above about 10 MeV and gradients over lengthscales of 0.1 km or less. On the other hand, if direct-Urca processes remain suppressed, leaving modified-Urca processes to establish flavor equilibrium, then bulk viscous dissipation could provide significant damping to density oscillations observed right after the merger. When comparing with data from a state-of-the-art merger simulation we find that the bulk viscosity takes values close to its resonant maximum in a typical neutron-star merger, motivating a more careful assessment of the role of bulk viscous dissipation in the gravitational-wave signal from merging neutron stars.

gr-qc↗

arXiv2017

Rotational properties of hypermassive neutron stars from binary mergers

Determining the differential-rotation law of compact stellar objects produced in binary neutron stars mergers or core-collapse supernovae is an old problem in relativistic astrophysics. Addressing this problem is important because it impacts directly on the maximum mass these objects can attain and hence on the threshold to black-hole formation under realistic conditions. Using the results from a large number of numerical simulations in full general relativity of binary neutron star mergers described with various equations of state and masses, we study the rotational properties of the resulting hypermassive neutron stars. We find that the angular-velocity distribution shows only a modest dependence on the equation of state, thus exhibiting the traits of "quasi-universality" found in other aspects of compact stars, both isolated and in binary systems. The distributions are characterized by an almost uniformly rotating core and a "disk". Such a configuration is significantly different from the $j-{\rm constant}$ differential-rotation law that is commonly adopted in equilibrium models of differentially rotating stars. Furthermore, the rest-mass contained in such a disk can be quite large, ranging from $\simeq 0.03\,M_{\odot}$ in the case of high-mass binaries with stiff equations of state, up to $\simeq 0.2\,M_{\odot}$ for low-mass binaries with soft equations of state. We comment on the astrophysical implications of our findings and on the long-term evolutionary scenarios that can be conjectured on the basis of our simulations.

gr-qc↗

arXiv2017

Entropy-limited hydrodynamics: a novel approach to relativistic hydrodynamics

We present entropy-limited hydrodynamics (ELH): a new approach for the computation of numerical fluxes arising in the discretization of hyperbolic equations in conservation form. ELH is based on the hybridisation of an unfiltered high-order scheme with the first-order Lax-Friedrichs method. The activation of the low-order part of the scheme is driven by a measure of the locally generated entropy inspired by the artificial-viscosity method proposed by Guermond et al. Here, we present ELH in the context of high-order finite-differencing methods and of the equations of general-relativistic hydrodynamics. We study the performance of ELH in a series of classical astrophysical tests in general relativity involving isolated, rotating and nonrotating neutron stars, and including a case of gravitational collapse to black hole. We present a detailed comparison of ELH with the fifth-order monotonicity preserving method MP5, one of the most common high-order schemes currently employed in numerical-relativity simulations. We find that ELH achieves comparable and, in many of the cases studied here, better accuracy than more traditional methods at a fraction of the computational cost (up to 50 % speedup). Given its accuracy and its simplicity of implementation, ELH is a promising framework for the development of new special- and general-relativistic hydrodynamics codes well adapted for massively parallel supercomputers.

gr-qc↗

arXiv2017

The Black Hole Accretion Code

We present the black hole accretion code (BHAC), a new multidimensional general-relativistic magnetohydrodynamics module for the MPI-AMRVAC framework. BHAC has been designed to solve the equations of ideal general-relativistic magnetohydrodynamics in arbitrary spacetimes and exploits adaptive mesh refinement techniques with an efficient block-based approach. Several spacetimes have already been implemented and tested. We demonstrate the validity of BHAC by means of various one-, two-, and three-dimensional test problems, as well as through a close comparison with the HARM3D code in the case of a torus accreting onto a black hole. The convergence of a turbulent accretion scenario is investigated with several diagnostics and we find accretion rates and horizon-penetrating fluxes to be convergent to within a few percent when the problem is run in three dimensions. Our analysis also involves the study of the corresponding thermal synchrotron emission, which is performed by means of a new general-relativistic radiative transfer code, BHOSS. The resulting synthetic intensity maps of accretion onto black holes are found to be convergent with increasing resolution and are anticipated to play a crucial role in the interpretation of horizon-scale images resulting from upcoming radio observations of the source at the Galactic Center.

gr-qc↗

arXiv2017

Neutron-star Radius from a Population of Binary Neutron Star Mergers

We show how gravitational-wave observations with advanced detectors of tens to several tens of neutron-star binaries can measure the neutron-star radius with an accuracy of several to a few percent, for mass and spatial distributions that are realistic, and with none of the sources located within 100 Mpc. We achieve such an accuracy by combining measurements of the total mass from the inspiral phase with those of the compactness from the postmerger oscillation frequencies. For estimating the measurement errors of these frequencies we utilize analytical fits to postmerger numerical-relativity waveforms in the time domain, obtained here for the first time, for four nuclear-physics equations of state and a couple of values for the mass. We further exploit quasi-universal relations to derive errors in compactness from those frequencies. Measuring the average radius to well within 10% is possible for a sample of 100 binaries distributed uniformly in volume between 100 and 300 Mpc, so long as the equation of state is not too soft or the binaries are not too heavy.

gr-qc↗