Modulating magnetar emission by magneto-elastic oscillations

We present a new numerical tool to calculate the emission of highly magnetized neutron stars (magnetars) and apply it to describe the quasi-periodic oscillations (QPOs) observed in magnetar giant flares. In previous work we have developed a model of magneto-elastic oscillations of magnetars that allows to reproduce the observed frequencies. These QPOs can couple to the star's exterior through the magnetic field and induce currents in the magnetosphere that provide scattering targets for resonant cyclotron scattering of the photons. The scattering is calculated with a Monte-Carlo approach and it is coupled to a code that calculates the momentum distribution of the charge carriers as an one-d…

Non-linear axisymmetric pulsations of rotating relativistic stars in the conformal flatness approximation

We study non-linear axisymmetric pulsations of rotating relativistic stars using a general relativistic hydrodynamics code under the assumption of a conformal flatness. We compare our results to previous simulations where the spacetime dynamics was neglected. The pulsations are studied along various sequences of both uniformly and differentially rotating relativistic polytropes with index N = 1. We identify several modes, including the lowest-order l = 0, 2, and 4 axisymmetric modes, as well as several axisymmetric inertial modes. Differential rotation significantly lowers mode frequencies, increasing prospects for detection by current gravitational wave interferometers. We observe an exten…

Imprints of superfluidity on magnetoelastic quasiperiodic oscillations of soft gamma-ray repeaters.

Our numerical simulations show that axisymmetric, torsional, magnetoelastic oscillations of magnetars with a superfluid core can explain the whole range of observed quasiperiodic oscillations (QPOs) in the giant flares of soft gamma-ray repeaters. There exist constant phase QPOs at $f\ensuremath{\lesssim}150\text{ }\text{ }\mathrm{Hz}$ and resonantly excited high-frequency QPOs ($fg500\text{ }\text{ }\mathrm{Hz}$), in good agreement with observations. The range of magnetic field strengths required to match the observed QPO frequencies agrees with that from spin-down estimates. These results suggest that there is at least one superfluid species in magnetar cores.

3-D collapse of rotating stars to Kerr black holes

We study gravitational collapse of uniformly rotating neutron stars to Kerr black holes, using a new three-dimensional, fully general relativistic hydrodynamics code, which uses high-resolution shock-capturing techniques and a conformal traceless formulation of the Einstein equations. We investigate the gravitational collapse by carefully studying not only the dynamics of the matter, but also that of the trapped surfaces, i.e. of both the apparent and event horizons formed during the collapse. The use of these surfaces, together with the dynamical horizon framework, allows for a precise measurement of the black-hole mass and spin. The ability to successfully perform these simulations for su…

General Relativistic Simulations of Accretion Disks Around Tilted Kerr Black Holes

We simulate the dynamics of self-gravitating accretion disks around tilted Kerr black holes (BH) in full 3D general relativity. For this purpose we employ the EinsteinToolkit, using the thorn McLachlan for the evolution of the spacetime via the BSSN formalism of the Einstein equations and the thorn GRHydro for the evolution of the hydrodynamics, using a 3D Cartesian mesh with adaptive mesh refinement. We investigate the effects of the tilt angle between the disk angular momentum and BH spin vector on the dynamics of these systems as the disk evolves in the tilted spacetime. By evolving the spacetime and matter fields, we are able to observe how both BH and disk react and evolve in the tilte…

Numerical relativity simulations of thick accretion disks around tilted Kerr black holes

In this work we present 3D numerical relativity simulations of thick accretion disks around tilted Kerr BH. We investigate the evolution of three different initial disk models with a range of initial black hole spin magnitudes and tilt angles. For all the disk-to-black hole mass ratios considered (0.044-0.16) we observe significant black hole precession and nutation during the evolution. This indicates that for such mass ratios, neglecting the self-gravity of the disks by evolving them in a fixed background black hole spacetime is not justified. We find that the two more massive models are unstable against the Papaloizou-Pringle (PP) instability and that those PP-unstable models remain unst…

On the dynamics of tilted black hole-torus systems

We present results from three-dimensional, numerical relativity simulations of a {\it tilted} black hole-thick accretion disc system. The simulations are analysed using tracer particles in the disc which are advected with the flow. Such tracers, which we employ in these new simulations for the first time, provide a powerful means to analyse in detail the complex dynamics of tilted black hole-torus systems. We show how its use helps to gain insight in the overall dynamics of the system, discussing the origin of the observed black hole precession and the development of a global non-axisymmetric $m=1$ mode in the disc. Our three-dimensional simulations show the presence of quasi-periodic oscil…

Imprints of superfluidity on magneto-elastic QPOs of SGRs

Our numerical simulations show that axisymmetric, torsional, magneto-elastic oscillations of magnetars with a superfluid core can explain the whole range of observed quasi-periodic oscillations (QPOs) in the giant flares of soft gamma-ray repeaters. There exist constant phase, magneto-elastic QPOs at both low (f<150 Hz) and high frequencies (f>500 Hz), in full agreement with observations. The range of magnetic field strengths required to match the observed QPO frequencies agrees with that from spin-down estimates. These results strongly suggest that neutrons in magnetar cores are superfluid.

Magneto-elastic oscillations of neutron stars: exploring different magnetic field configurations

We study magneto-elastic oscillations of highly magnetized neutron stars (magnetars) which have been proposed as an explanation for the quasi-periodic oscillations (QPOs) appearing in the decaying tail of the giant flares of soft gamma-ray repeaters (SGRs). We extend previous studies by investigating various magnetic field configurations, computing the Alfv��n spectrum in each case and performing magneto-elastic simulations for a selected number of models. By identifying the observed frequencies of 28 Hz (SGR 1900+14) and 30 Hz (SGR 1806-20) with the fundamental Alfv��n QPOs, we estimate the required surface magnetic field strength. For the magnetic field configurations investigated (dipole…

Magneto‐elastic oscillations modulating the emission of magnetars

Magneto-elastic oscillations of neutron stars are believed to explain observed quasi-periodic oscillations (QPOs) in the decaying tail of the giant flares of highly magnetized neutron stars (magnetars). Strong efforts of the theoretical modelling from different groups have increased our understanding of this phenomenon significantly. Here, we discuss some constraints on the matter in neutron stars that arise if the interpretation of the observations in terms of superfluid, magneto-elastic oscillations is correct. To explain the observed modulation of the light curve of the giant flare, we describe a model that allows the QPOs to couple to the stellar exterior through the magnetic field. In …

Three-dimensional relativistic simulations of rotating neutron-star collapse to a Kerr black hole

We present a new three-dimensional fully general-relativistic hydrodynamics code using high-resolution shock-capturing techniques and a conformal traceless formulation of the Einstein equations. Besides presenting a thorough set of tests which the code passes with very high accuracy, we discuss its application to the study of the gravitational collapse of uniformly rotating neutron stars to Kerr black holes. The initial stellar models are modelled as relativistic polytropes which are either secularly or dynamically unstable and with angular velocities which range from slow rotation to the mass-shedding limit. We investigate the gravitational collapse by carefully studying not only the dynam…

Numerical-relativity simulations of long-lived remnants of binary neutron star mergers

We analyze the properties of the gravitational wave signal emitted after the merger of a binary neutron star system when the remnant survives for more than a 80 ms (and up to 140ms). We employ four different piecewise polytropic equations of state supplemented by an ideal fluid thermal component. We find that the post-merger phase can be subdivided into three phases: an early post-merger phase (where the quadrupole mode and a few subdominant features are active), the intermediate post-merger phase (where only the quadrupole mode is active) and the late post-merger phase (where convective instabilities trigger inertial modes). The inertial modes have frequencies somewhat smaller than the qua…

Relativistic MHD simulations of stellar core collapse and magnetars

We present results from simulations of magneto-rotational stellar core collapse along with Alfven oscillations in magnetars. These simulations are performed with the CoCoA/CoCoNuT code, which is able to handle ideal MHD flows in dynamical spacetimes in general relativity. Our core collapse simulations highlight the importance of genuine magnetic effects, like the magneto-rotational instability, for the dynamics of the flow. For the modelling of magnetars we use the anelastic approximation to general relativistic MHD, which allows for an effective suppression of fluid modes and an accurate description of Alfven waves. We further compute Alfven oscillation frequencies along individual magneti…

Convective Excitation of Inertial Modes in Binary Neutron Star Mergers

We present the first very long-term simulations (extending up to ~140 ms after merger) of binary neutron star mergers with piecewise polytropic equations of state and in full general relativity. Our simulations reveal that at a time of 30-50 ms after merger, parts of the star become convectively unstable, which triggers the excitation of inertial modes. The excited inertial modes are sustained up to several tens of milliseconds and are potentially observable by the planned third-generation gravitational-wave detectors at frequencies of a few kilohertz. Since inertial modes depend on the rotation rate of the star and they are triggered by a convective instability in the postmerger remnant, t…

New horizons for fundamental physics with LISA

K. G. Arun et al.

Magneto-elastic oscillations and the damping of crustal shear modes in magnetars

In a realistic model of magneto-elastic oscillations in magnetars, we find that crustal shear oscillations, often invoked as an explanation of quasi-periodic oscillations (QPOs) seen after giant flares in soft gamma-ray repeaters (SGRs), are damped by resonant absorption on timescales of at most 0.2s, for a lower limit on the dipole magnetic field strength of 5 10 13 G. At higher magnetic field strengths (typical in magnetars) the damping timescale is even shorter, as anticipated by earlier toy-models. We have investigated a range of equations of state and masses and if magnetars are dominated by a dipole magnetic field, our findings exclude torsional shear oscillations of the crust from ex…

Coherent magneto-elastic oscillations in superfluid magnetars

We study the effect of superfluidity on torsional oscillations of highly magnetised neutron stars (magnetars) with a microphysical equation of state by means of two-dimensional, magnetohydrodynamical- elastic simulations. The superfluid properties of the neutrons in the neutron star core are treated in a parametric way in which we effectively decouple part of the core matter from the oscillations. Our simulations confirm the existence of two groups of oscillations, namely continuum oscillations that are confined to the neutron star core and are of Alfv\'enic character, and global oscillations with constant phase and that are of mixed magneto-elastic type. The latter might explain the quasi-…

Magnetoelastic oscillations of neutron stars with dipolar magnetic fields

The Large Observatory For x-ray Timing

The Large Observatory For x-ray Timing (LOFT) was studied within ESA M3 Cosmic Vision framework and participated in the final down-selection for a launch slot in 2022-2024. Thanks to the unprecedented combination of effective area and spectral resolution of its main instrument, LOFT will study the behaviour of matter under extreme conditions, such as the strong gravitational field in the innermost regions of accretion flows close to black holes and neutron stars, and the supra-nuclear densities in the interior of neutron stars. The science payload is based on a Large Area Detector (LAD, 10 m 2 effective area, 2-30 keV, 240 eV spectral resolution, 1 deg collimated field of view) and a WideFi…

Magneto-elastic torsional oscillations of magnetars

We extend a general-relativistic ideal magneto-hydrodynamical code to include the effects of elasticity. Using this numerical tool we analyse the magneto-elastic oscillations of highly magnetised neutron stars (magnetars). In simulations without magnetic field we are able to recover the purely crustal shear oscillations within an accuracy of about a few per cent. For dipole magnetic fields between 5 x 10^13 and 10^15 G the Alfv\'en oscillations become modified substantially by the presence of the crust. Those quasi-periodic oscillations (QPOs) split into three families: Lower QPOs near the equator, Edge QPOs related to the last open field line and Upper QPOs at larger distance from the equa…

Modulating magnetar emission by magneto-elastic oscillations

THREE-DIMENSIONAL RELATIVISTIC SIMULATIONS OF ROTATING NEUTRON-STAR COLLAPSE TO A KERR BLACK HOLE

We present a new three-dimensional fully general-relativistic hydrodynamics code using high-resolution shock-capturing techniques and a conformal traceless formulation of the Einstein equations. Besides presenting a thorough set of tests which the code passes with very high accuracy, we discuss its application to the study of the gravitational collapse of uniformly rotating neutron stars to Kerr black holes. The initial stellar models are modeled as relativistic polytropes which are either secularly or dynamically unstable and with angular velocities which range from slow rotation to the mass-shedding limit. We investigate the gravitational collapse by carefully studying not only the dynami…

Constraining properties of high-density matter in neutron stars with magneto-elastic oscillations

We discuss torsional oscillations of highly magnetised neutron stars (magnetars) using two-dimensional, magneto-elastic-hydrodynamical simulations. Our model is able to explain both the low- and high-frequency quasi-periodic oscillations (QPOs) observed in magnetars. The analysis of these oscillations provides constraints on the breakout magnetic-field strength, on the fundamental QPO frequency, and on the frequency of a particularly excited overtone. More importantly, we show how to use this information to generically constraint properties of high-density matter in neutron stars, employing Bayesian analysis. In spite of current uncertainties and computational approximations, our model-depe…

Modulating the magnetosphere of magnetars by internal magneto-elastic oscillations

We couple internal torsional, magneto-elastic oscillations of highly magnetized neutron stars (magnetars) to their magnetospheres. The corresponding axisymmetric perturbations of the external magnetic field configuration evolve as a sequence of linear, force-free equilibria that are completely determined by the background magnetic field configuration and by the perturbations of the magnetic field at the surface. The perturbations are obtained from simulations of magneto-elastic oscillations in the interior of the magnetar. While such oscillations can excite travelling Alfv\'en waves in the exterior of the star only in a very limited region close to the poles, they still modulate the near ma…

Alfven QPOs in magnetars in the anelastic approximation

We perform two-dimensional simulations of Alfven oscillations in magnetars, modeled as relativistic stars with a dipolar magnetic field. We use the anelastic approximation to general relativistic magnetohydrodynamics, which allows for an effective suppression of fluid modes and an accurate description of Alfven waves. In addition, we compute Alfven oscillation frequencies along individual magnetic field lines with a semi-analytic approach, employing a short-wavelength approximation. Our main findings are as follows: a) we confirm the existence of two families of quasi-periodic oscillations (QPOs), with harmonics at integer multiples of the fundamental frequency, as was found in the linear s…