Search

We explore the prospects for identifying differences in simulated gravitational-wave signals of binary neutron star (BNS) mergers associated with the way thermal effects are incorporated in the numerical-relativity modelling. We consider a hybrid approach in which the equation of state (EoS) comprises a cold, zero temperature, piecewise-polytropic part and a thermal part described by an ideal gas, and a tabulated approach based on self-consistent, microphysical, finite-temperature EoS. We use time-domain waveforms corresponding to BNS merger simulations with four different EoS. Those are injected into Gaussian noise given by the sensitivity of the third-generation detector Einstein Telescope and reconstructed using BayesWave, a Bayesian data-analysis algorithm that recovers the signals through a model-agnostic approach. The two representations of thermal effects result in frequency shifts of the dominant peaks in the spectra of the post-merger signals, for both the quadrupole fundamental mode and the late-time inertial modes. For some of the EoS investigated those differences are large enough to be told apart, especially in the early post-merger phase when the signal amplitude is the loudest., Comment: 15 pages, 8 figures, 3 tables

Neutron stars (NS) that are born in binary systems with a main-sequence star companion can experience mass transfer, resulting in the accumulation of material at the surface of the NS. This, in turn, leads to the continuous growth of the NS mass and the associated steepening of the gravitational potential. Supposing the central density surpasses the onset for the phase transition from nuclear, generally hadronic matter to deconfined quark-gluon plasma, which is a quantity currently constrained solely from an upper limit by asymptotic freedom in quantum chromodynamics (QCD), the system may experience a dynamic response due to the appearance of additional degrees of freedom in the equation of state (EOS). This dynamical response might give rise to a rapid softening of the EOS during the transition in the hadron-quark matter co-existence region. While this phenomenon has long been studied in the context of hydrostatic configurations, the dynamical implications of this problem are still incompletely understood. It is the purpose of the present paper to simulate the dynamics of NSs with previously accreted envelopes caused by the presence of a first-order QCD phase transition. Therefore, we employed the neutrino radiation hydrodynamics treatment based on the fully general relativistic approach in spherical symmetry, implementing a three-flavor Boltzmann neutrino transport and a microscopic model EOS that contains a first-order hadron-quark phase transition. The associated neutrino signal shows a sudden rise in the neutrino fluxes and average energies, becoming observable for the present generation of neutrino detectors for a galactic event, and a gravitational wave mode analysis revealed the behaviors of the dominant $f$ mode and the first and the second gravity $g$ modes that are excited during the NS evolution across the QCD phase transition., Comment: 16 pages, 14 figures,to be published in A&A Journal

We assess the impact of accurate, self-consistent modelling of thermal effects in neutron-star merger remnants in the context of third-generation gravitational-wave detectors. This is done through the usage, in Bayesian model selection experiments, of numerical-relativity simulations of binary neutron star (BNS) mergers modelled through: a) nuclear, finite-temperature (or ``tabulated'') equations of state (EoSs), and b) their simplifed piecewise (or ``hybrid'') representation. These cover four different EoSs, namely SLy4, DD2, HShen and LS220. Our analyses make direct use of the Newman-Penrose scalar $\psi_4$ outputted by numerical simulations. Considering a detector network formed by three Cosmic Explorers, we show that differences in the gravitational-wave emission predicted by the two models are detectable with a natural logarithmic Bayes Factor $\log{\cal{B}}\geq 5$ at average distances of $d_L \simeq 50$Mpc, reaching $d_L \simeq 100$Mpc for source inclinations $\iota \leq 0.8$, regardless of the EoS. This impact is most pronounced for the HShen EoS. For low inclinations, only the DD2 EoS prevents the detectability of such modelling differences at $d_L \simeq 150$Mpc. Our results suggest that the usage a self-consistent treatment of thermal effects is crucial for third-generation gravitational wave detectors., Comment: 9 pages, 3 Figures

The modelling of astrophysical systems such as binary neutron star mergers or the formation of magnetars from the collapse of massive stars involves the numerical evolution of magnetised fluids at extremely large Reynolds numbers. This is a major challenge for (unresolved) direct numerical simulations which may struggle to resolve highly dynamical features as, e.g. turbulence, magnetic field amplification, or the transport of angular momentum. Sub-grid models offer a means to overcome those difficulties. In a recent paper we presented MInIT, an MHD-instability-induced-turbulence mean-field, sub-grid model based on the modelling of the turbulent (Maxwell, Reynolds, and Faraday) stress tensors. While in our previous work MInIT was assessed within the framework of the magnetorotational instability, in this paper we further evaluate the model in the context of the Kelvin-Helmholtz instability (KHI). The main difference with other sub-grid models (as e.g. the alpha-viscosity model or the gradient model) is that in MInIT we track independently the turbulent energy density at sub-grid scales, which is used, via a simple closure relation, to compute the different turbulent stresses relevant for the dynamics. The free coefficients of the model are calibrated using well resolved box simulations of magnetic turbulence generated by the KHI. We test the model against these simulations and show that it yields order-of-magnitude accurate predictions for the evolution of the turbulent Reynolds and Maxwell stresses., Comment: 12 pages, 13 figures Accepted for publication in MNRAS

Core-collapse supernovae (CCSNe) are prime candidates for gravitational-wave detectors. The analysis of their complex waveforms can potentially provide information on the physical processes operating during the collapse of the iron cores of massive stars. In this work we analyze the early-bounce rapidly rotating CCSN signals reported in the waveform catalog of Richers et al 2017, which comprises over 1800 axisymmetric simulations extending up to about 10~ms of post-bounce evolution. It was previously established that for a large range of progenitors, the amplitude of the bounce signal, $\Delta h$, is proportional to the ratio of rotational-kinetic energy to potential energy, T/|W|, and the peak frequency, $f_{\rm peak}$, is proportional to the square root of the central rest-mass density. In this work, we exploit these relations to suggest that it could be possible to use such waveforms to infer protoneutron star properties from a future gravitational wave observation, if the distance and inclination are well known. Our approach relies on the ability to describe a subset of the waveforms in the early post-bounce phase in a simple form depending only on two parameters, $\Delta h$ and $f_{\rm peak}$. We use this template to perform a Bayesian inference analysis of waveform injections in Gaussian colored noise for a network of three gravitational wave detectors formed by Advanced LIGO and Advanced Virgo. We show that, for a galactic event, it is possible to recover the peak frequency and amplitude with an accuracy better than 10% for about 80% and 60% of the signals, respectively, given known distance and inclination angle. However, inference on waveforms from outside the Richers catalog is not reliable, indicating a need for carefully verified waveforms of the first 10 ms after bounce of rapidly rotating supernovae of different progenitors with agreement between different codes., Comment: 23 pages, 17 figures, accepted for publication in PRD

We present the results from a search for gravitational-wave transients associated with core-collapse supernovae observed optically within 30 Mpc during the third observing run of Advanced LIGO and Advanced Virgo. No gravitational wave associated with a core-collapse supernova has been identified. We then report the detection efficiency for a variety of possible gravitational-wave emissions. For neutrino-driven explosions, the distance at which we reach 50% detection efficiency is up to 8.9 kpc, while more energetic magnetorotationally-driven explosions are detectable at larger distances. The distance reaches for selected models of the black hole formation, and quantum chromodynamics phase transition are also provided. We then constrain the core-collapse supernova engine across a wide frequency range from 50 Hz to 2 kHz. The upper limits on gravitational-wave energy and luminosity emission are at low frequencies down to $10^{-4}\,M_\odot c^2$ and $6 \times 10^{-4}\,M_\odot c^2$/s, respectively. The upper limits on the proto-neutron star ellipticity are down to 3 at high frequencies. Finally, by combining the results obtained with the data from the first and second observing runs of LIGO and Virgo, we improve the constraints of the parameter spaces of the extreme emission models. Specifically, the proto-neutron star ellipticities for the long-lasting bar mode model are down to 1 for long emission (1 s) at high frequency., Comment: 20 pages, 11 figures; https://dcc.ligo.org/LIGO-P2200361

Core-collapse supernovae are predicted to produce gravitational waves (GWs) that may be detectable by Advanced LIGO/Virgo. These GW signals carry information from the heart of these catacylsmic events, where matter reaches nuclear densities. Recent studies have shown that it may be possible to infer properties of the proto-neutron star (PNS) via gravitational waves generated by hydrodynamic perturbations of the PNS. However, we lack a comprehensive understanding of how these relationships may change with the properties of core-collapse supernovae. In this work, we build a self-consistent suite of over 1000 exploding core-collapse supernovae from a grid of progenitor masses and metallicities combined with six different nuclear equations of state. Performing a linear perturbation analysis on each model, we compute the resonant gravitational-wave frequencies of the PNS, and we motivate a time-agnostic method for identifying characteristic frequencies of the dominant gravitational-wave emission. From this, we identify two characteristic frequencies, of the early- and late-time signal, that measure the surface gravity of the cold remnant neutron star, and simultaneously constrain the hot nuclear equation of state. However, we find that the details of the core-collapse supernova model, such as the treatment of gravity or the neutrino transport, and whether it explodes, noticeably change the magnitude and evolution of the PNS eigenfrequencies., Comment: 27 pages, 11 figures, submitted to ApJ

We present our study of stability of differentially rotating, axisymmetric neutron stars described by a polytropic equation of state with $\Gamma = 2$. We focus on quasi-toroidal solutions with a degree of differential rotation $\widetilde A=1$. Our results show that for a wide range of parameters hypermassive, quasi-toroidal neutron stars are dynamically stable against quasi-radial perturbations, which may have implications for newly born neutron stars and binary neutron stars mergers., Comment: Presented at the 8th Conference of the Polish Society on Relativity, submitted to Acta Physica Polonica B Proceedings Supplement

Some recent, long-term numerical simulations of binary neutron star mergers have shown that the long-lived remnants produced in such mergers might be affected by convective instabilities. Those would trigger the excitation of inertial modes, providing a potential method to improve our understanding of the rotational and thermal properties of neutron stars through the analysis of the modes' imprint in the late post-merger gravitational-wave signal. In this paper we assess the detectability of those modes by injecting numerically generated post-merger waveforms into colored Gaussian noise of second-generation and future detectors. Signals are recovered using BayesWave, a Bayesian data-analysis algorithm that reconstructs them through a morphology-independent approach using series of sine-Gaussian wavelets. Our study reveals that current interferometers (i.e. the Handford-Livingston-Virgo network) recover the peak frequency of inertial modes only if the merger occurs at distances of up to 1 Mpc. For future detectors such as the Einstein Telescope, the range of detection increases by about a factor 10.

Magnetars exhibit a variety of transient high-energy phenomena in the form of bursts, outbursts, and giant flares. It is a common belief that these events originate in the sudden release of magnetic energy due to the rearrangement of a twisted magnetic field. We present global models of a 3D Force-Free (FF) non-linear twisted magnetar magnetosphere. We solve the FF equations following the Grad-Rubin approach in a compactified spherical domain. Appropriate boundary conditions are imposed at the surface of the star for the current distribution and the magnetic field. Our implementation is tested by reproducing various known analytical as well as axisymmetric numerical results. We then proceed to study general 3D models with non-axisymmetric current distributions, such as fields with localised twists that resemble hotspots at the surface of the star, and we examine characteristic quantities such as energy, helicity and twist. Finally, we discuss implications on the available energy budget, the surface temperature and the diffusion timescale, which can be associated with observations., Comment: 12 pages, 10 figures, small typo corrections, removed Fig. 7 and relative discussion, new version of Fig. 8 (now 7) in v2

Insufficient numerical resolution of grid-based, direct numerical simulations (DNS) hampers the development of instabilitydriven turbulence at small (unresolved) scales. As an alternative to DNS, sub-grid models can potentially reproduce the effects of turbulence at small scales in terms of the resolved scales, and hence can capture physical effects with less computational resources. We present a new sub-grid model, the MHD-instability-induced-turbulence (MInIT) mean-field model. MInIT is a physically motivated model based on the evolution of the turbulent (Maxwell, Reynolds, and Faraday) stress tensors and their relation with the turbulent energy densities of the magneto-rotational (MRI) and parasitic instabilities, modeled with two partial differential evolution equations with stiff source terms. Their solution allows obtaining the turbulent stress tensors through the constant coefficients that link them to the energy densities. The model is assessed using data from MRI in-box DNS and applying a filtering operation to compare the filtered data with that from the model. Using the $L_2$-norm as the metric for the comparison, we find less than one order-of-magnitude difference between the two sets of data. No dependence on filter size or length scale of unresolved scales is found, as opposed to results using the gradient model (which we also use to contrast our model) in which the $L_2$-norm of some of the stresses increases with filter size. We conclude that MInIT can help DNS by properly capturing small-scale turbulent stresses which has potential implications on the dynamics of highly-magnetized rotating compact objects, such as those formed during binary neutron star mergers., Comment: 20 pages, 15 figures

We investigate the effects ultralight bosonic field dark matter may have on the dynamics of unstable differentially-rotating neutron stars prone to the bar-mode instability. To this aim we perform numerical simulations in general relativity of rotating neutron stars accreting an initial spherically symmetric bosonic field cloud, solving the Einstein-(complex, massive) Klein-Gordon-Euler and the Einstein-(complex) Proca-Euler systems. We find that the presence of the bosonic field can critically modify the development of the bar-mode instability of neutron stars, depending on the total mass of the bosonic field and on the boson particle mass. In some cases, the accreting bosonic field can even quench the dominant $\ell=m=2$ mode of the bar-deformation by dynamically forming a mixed (fermion-boson) star that retains part of the angular momentum of the original neutron star. However, the mixed star undergoes the development of a mixed bar that leads to significant gravitational-wave emission, substantially different to that of the isolated neutron star. Our results indicate that dark-matter accretion in neutron stars could change the frequency of the expected emission of the bar-mode instability, which would have an important impact on ongoing searches for continuous gravitational waves., Comment: 18 pages, 8 figures

Mixed fermion-boson stars are stable, horizonless, everywhere regular solutions of the coupled Einstein-(complex, massive) Klein-Gordon-Euler system. While isolated neutron stars and boson stars are uniquely determined by their central energy density, mixed configurations conform an extended parameter space that depends on the combination of the number of fermions and (ultra-light) bosons. The wider possibilities offered by fermion-boson stars could help explain the tension in the measurements of neutron star masses and radii reported in recent multi-messenger observations and nuclear-physics experiments. In this work we construct equilibrium configurations of mixed fermion-boson stars with realistic equations of state for the fermionic component and different percentages of bosonic matter. We show that our solutions are in excellent agreement with multi-messenger data, including gravitational-wave events GW170817 and GW190814 and X-ray pulsars PSR J0030+0451 and PSR J0740+6620, as well as with nuclear physics constraints from the PREX-2 experiment., Comment: 9 pages, 7 figures

Gravitational waves provide a unique and powerful opportunity to constrain the dynamics in the interior of proto-neutron stars during core collapse supernovae. Convective motions play an important role in generating neutron stars magnetic fields, which could explain magnetar formation in the presence of fast rotation. We compute the gravitational wave emission from proto-neutron star convection and its associated dynamo, by post-processing three-dimensional MHD simulations of a model restricted to the convective zone in the anelastic approximation. We consider two different proto-neutron star structures representative of early times (with a convective layer) and late times (when the star is almost entirely convective). In the slow rotation regime, the gravitational wave emission follows a broad spectrum peaking at about three times the turnover frequency. In this regime, the inclusion of magnetic fields slightly decreases the amplitude without changing the spectrum significantly compared to a non-magnetised simulation. Fast rotation changes both the amplitude and spectrum dramatically. The amplitude is increased by a factor of up to a few thousands. The spectrum is characterized by several peaks associated to inertial modes, whose frequency scales with the rotation frequency. Using simple physical arguments, we derive scalings that reproduce quantitatively several aspects of these numerical results. We also observe an excess of low-frequency gravitational waves, which appears at the transition to a strong field dynamo characterized by a strong axisymmetric toroidal magnetic field. This signature of dynamo action could be used to constrain the dynamo efficiency in a proto-neutron star with future gravitational wave detections., Comment: 18 pages, 13 figures, accepted for publication in MNRAS

The eventual detection of gravitational waves from core-collapse supernovae (CCSN) will help improve our current understanding of the explosion mechanism of massive stars. The stochastic nature of the late post-bounce gravitational wave signal due to the non-linear dynamics of the matter involved and the large number of degrees of freedom of the phenomenon make the source parameter inference problem very challenging. In this paper we take a step towards that goal and present a parameter estimation approach which is based on the gravitational waves associated with oscillations of proto-neutron stars (PNS). Numerical simulations of CCSN have shown that buoyancy-driven g-modes are responsible for a significant fraction of the gravitational wave signal and their time-frequency evolution is linked to the physical properties of the compact remnant through universal relations, as demonstrated in [1]. We use a set of 1D CCSN simulations to build a model that relates the evolution of the PNS properties with the frequency of the dominant g-mode, which is extracted from the gravitational-wave data using a new algorithm we have developed for our study. The model is used to infer the time evolution of a combination of the mass and the radius of the PNS. The performance of the method is estimated employing simulations of 2D CCSN waveforms covering a progenitor mass range between 11 and 40 solar masses and different equations of state. Considering signals embedded in Gaussian gravitational wave detector noise, we show that it is possible to infer PNS properties for a galactic source using Advanced LIGO and Advanced Virgo data at design sensitivities. Third generation detectors such as Einstein Telescope and Cosmic Explorer will allow to test distances of ${\cal O}(100\, {\rm kpc})$.

Spinning bosonic stars (SBSs) can form from the gravitational collapse of a dilute cloud of scalar/Proca particles with non-zero angular momentum. In a recent work we found that the scalar stars are transient due to a non-axisymmetric instability which triggers the loss of angular momentum. We further study the dynamical formation of SBSs using 3-dimensional numerical-relativity simulations of the Einstein-(massive, complex)Klein-Gordon system and of the Einstein-(complex)Proca system. We incorporate a quartic self-interaction potential in the scalar case to gauge its effect on the instability; we investigate (m=2) Proca stars to assess their stability; we attempt to relate the instability of SBSs to the growth rate of azimuthal density modes and the existence of a corotation point. We show that: the self-interaction potential can only delay the instability in scalar SBSs; m=2 Proca stars always migrate to the stable m=1 spheroidal family; unstable m=2 Proca stars and m=1 scalar boson stars exhibit a corotation point. This establishes a parallelism with rotating neutron stars affected by dynamical bar-mode instabilities. We compute the gravitational waves (GWs) emitted and investigate the detectability of the waveforms comparing the characteristic strain of the signal with the sensitivity curves of a variety of detectors, computing the signal-to-noise ratio. By assuming that the characteristic damping timescale of the bar-like deformation in SBSs is only set by GWs emission and not by viscosity (unlike in neutron stars), we find that the post-collapse emission could be orders of magnitude more energetic than that of the bar-mode instability itself. Our results indicate that GW observations of SBSs might be within the reach of future experiments, offering a potential means to establish the existence of such stars and to place tight constraints on the mass of the bosonic particle., Comment: 16 pages, 11 figures. A longer version of the abstract in the pdf

State-of-the-art numerical simulations of core-collapse supernovae reveal that the main source of gravitational waves is the excitation of proto-neutron star modes during post-bounce evolution. In this work we derive universal relations that relate the frequencies of the most common oscillation modes observed, i.e. g-modes, p-modes and the f-mode, with fundamental properties of the system, such as the surface gravity of the proto-neutron star or the mean density in the region enclosed by the shock. These relations are independent of the equation of state, the neutrino treatment, and the progenitor mass and hence can be used to build methods to infer proto-neutron star properties from gravitational-wave observations alone. We outline how these measurements could be done and the constraints that could be placed on the proto-neutron star properties.

We study the coupling of the force-free magnetosphere to the long-term internal evolution of a magnetar. We allow the relation between the poloidal and toroidal stream functions - that characterizes the magnetosphere - to evolve freely without constraining its particular form. We find that, on time-scales of the order of kyr, the energy stored in the magnetosphere gradually increases, as the toroidal region grows and the field lines expand outwards. This continues until a critical point is reached beyond which force-free solutions for the magnetosphere can no longer be constructed, likely leading to some large-scale magnetospheric reorganization. The energy budget available for such events can be as high as several $10^{45}\,$erg for fields of $10^{14}\,$G. Subsequently, starting from the new initial conditions, the evolution proceeds in a similar manner. The time-scale to reach the critical point scales inversely with the magnetic field amplitude. Allowing currents to pass through the last few meters below the surface, where the magnetic diffusivity is orders of magnitude larger than in the crust, should give rise to a considerable amount of energy deposition through Joule heating. We estimate that the effective surface temperature could increase locally from $\sim 0.1\,$keV to $\sim 0.3 - 0.6\,$keV, in good agreement with observations. Similarly, the power input from the interior into the magnetosphere could be as high as $10^{35} - 10^{36}\,$erg/s, which is consistent with peak luminosities observed during magnetar outbursts. Therefore, a detailed treatment of currents flowing through the envelope may be needed to explain the thermal properties of magnetars., Comment: 9 pages, 9 figures; updated version accepted for publication by MNRAS

Improvements in ground-based, advanced gravitational wave (GW) detectors may allow in the near future to observe the GW signal of a nearby core-collapse supernova. For the most common type of progenitors, likely with slowly rotating cores, the dominant GW emission mechanisms are the post-bounce oscillations of the proto-neutron star (PNS) before the explosion. We present a new procedure to compute the eigenmodes of the system formed by the PNS and the stalled accretion shock in general relativity including spacetime perturbations. The new method improves on previous results by accounting for perturbations of both the lapse function and the conformal factor. We apply our analysis to two numerical core-collapse simulations and show that our improved method is able to obtain eigenfrequencies that accurately match the features observed in the GW signal and to predict the qualitative behaviour of quasi-radial oscillations. Our analysis is possible thanks to a newly developed algorithm to classify the computed eigenmodes in different classes (f-, p-, and g-modes), improving previous results which suffered from misclassification issues. We find that most of the GW energy is stored in the lowest order eigenmodes, in particular in the $^2g_1$ mode and in the $^2f$ mode. Our results also suggest that a low-frequency component of the GW signal attributed in previous works to the characteristic frequency of the Standing Accretion Shock Instability should be identified as the fundamental quadrupolar f-mode. We also develop a formalism to estimate the contribution of quasi-radial ($l=0$) modes to the quadrupolar component of the GW emission in the case of a deformed background, with application to rapidly rotating cores. This work provides further support for asteroseismology of core-collapse supernovae and the inference of PNS properties based on GW observations.

In the last decade there has been a remarkable increase in our knowledge about core-collapse supernovae (CC-SNe), and the birthplace of neutron stars, from both the observational and the theoretical point of view. Since the 1930's, with the first systematic supernova search, the techniques for discovering and studying extragalactic SNe have improved. Many SNe have been observed, and some of them, have been followed through efficiently and with detail. Furthermore, there has been a significant progress in the theoretical modelling of the scenario, boosted by the arrival of new generations of supercomputers that have allowed to perform multidimensional numerical simulations with unprecedented detail and realism. The joint work of observational and theoretical studies of individual SNe over the whole range of the electromagnetic spectrum has allowed to derive physical parameters, which constrain the nature of the progenitor, and the composition and structure of the star's envelope at the time of the explosion. The observed properties of a CC-SN are an imprint of the physical parameters of the explosion such as mass of the ejecta, kinetic energy of the explosion, the mass loss rate, or the structure of the star before the explosion. In this chapter, we review the current status of SNe observations and theoretical modelling, the connection with their progenitor stars, and the properties of the neutron stars left behind., Comment: To appear as a chapter in the White Book of "NewCompStar" European COST Action MP1304. 57 pages. 7 figures

The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress., Comment: White Paper for the COST action "Gravitational Waves, Black Holes, and Fundamental Physics", 272 pages, 12 figures; v4: updated references and author list. Overall improvements and corrections. To appear in Classical and Quantum Gravity

We present TEOBResumS, a new effective-one-body (EOB) waveform model for nonprecessing (spin-aligned) and tidally interacting compact binaries.Spin-orbit and spin-spin effects are blended together by making use of the concept of centrifugal EOB radius. The point-mass sector through merger and ringdown is informed by numerical relativity (NR) simulations of binary black holes (BBH) computed with the SpEC and BAM codes. An improved, NR-based phenomenological description of the postmerger waveform is developed.The tidal sector of TEOBResumS describes the dynamics of neutron star binaries up to merger and incorporates a resummed attractive potential motivated by recent advances in the post-Newtonian and gravitational self-force description of relativistic tidal interactions. Equation-of-state dependent self-spin interactions (monopole-quadrupole effects) are incorporated in the model using leading-order post-Newtonian results in a new expression of the centrifugal radius. TEOBResumS is compared to 135 SpEC and 19 BAM BBH waveforms. The maximum unfaithfulness to SpEC data $\bar{F}$ -- at design Advanced-LIGO sensitivity and evaluated with total mass $M$ varying between $10M_\odot \leq M \leq 200 M_\odot$ --is always below $2.5 \times 10^{-3}$ except for a single outlier that grazes the $7.1 \times 10^{-3}$ level. When compared to BAM data, $\bar{F}$ is smaller than $0.01$ except for a single outlier in one of the corners of the NR-covered parameter space, that reaches the $0.052$ level.TEOBResumS is also compatible, up to merger, to high end NR waveforms from binary neutron stars with spin effects and reduced initial eccentricity computed with the BAM and THC codes. The model is designed to generate accurate templates for the analysis of LIGO-Virgo data through merger and ringdown. We demonstrate its use by analyzing the publicly available data for GW150914., Comment: 39 pages, 36 figures. Extended appendix with discussion of the postmerger fits. Version accepted for publication in Phys. Rev. D

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-dependent Bayesian posterior estimates for SGR 1806-20 yield a magnetic-field strength $\bar B\sim 2.1^{+1.3}_{-1.0}\times10^{15}\,$G and a crust thickness of $\Delta r = 1.6^{+0.7}_{-0.6}$ km, which are both in remarkable agreement with observational and theoretical expectations, respectively (1-$\sigma$ error bars are indicated). Our posteriors also favour the presence of a superfluid phase in the core, a relatively low stellar compactness, $M/R<0.19$, indicating a relatively stiff equation of state and/or low mass neutron star, and high shear speeds at the base of the crust, $c_s>1.4\times10^8\,$cm/s. Although the procedure laid out here still has large uncertainties, these constraints could become tighter when additional observations become available., Comment: 14 pages, 8 figures, 6 tables, submitted to MNRAS

We extend our previous study of equilibrium solutions of non-rotating force-free magnetospheres of neutron stars. We show that multiple solutions exist for the same sets of parameters, implying that the solutions are degenerate. We are able to obtain configurations with disconnected field lines, however, in nearly all cases these correspond to degenerate higher energy solutions. We carry out a wide parametric search in order to understand the properties of the solutions. We confirm our previous results that the lower energy solutions have up to $\sim 25\%$ more energy than the vacuum case, helicity of the order of $\sim 5$ (in some defined units), maximum twist of $\sim 1.5$ rad, and a dipole strength that is up to $\sim 40\%$ larger than the vacuum dipole. Including the degenerate higher energy solutions allows for larger theoretical limits of up to $\sim 80\%$ more energy with respect to the vacuum case, helicity of the order of $\sim 8$, and a dipole strength that can now be up to four times that of the vacuum dipole, while the twist can be significantly larger and even diverge for configurations with disconnected domains. The higher energy solutions are probably unstable, therefore, it is unlikely that such magnetospheres exist under normal conditions in magnetars and high magnetic field pulsars., Comment: 12 pages, 9 figures; added missing reference; accepted for publication in MNRAS

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 this magnetosphere, the shaking magnetic field induces currents that provide scattering targets for resonant cyclotron scattering of photons, which is calculated with a Monte-Carlo approach and coupled to a code that calculates the momentum distribution of the charge carriers as a one-dimensional accelerator problem. We show first results of a simplified, but self-consistent momentum distribution, i.e. a waterbag distribution, and of the corresponding spectra., Comment: 7 pages, 4 figures, proceedings of stars2017 and 2017smfns

Gravitational waves from core-collapse supernovae are produced by the excitation of different oscillation modes in the proto-neutron star (PNS) and its surroundings, including the shock. In this work we study the relationship between the post-bounce oscillation spectrum of the PNS-shock system and the characteristic frequencies observed in gravitational-wave signals from core-collapse simulations. This is a fundamental first step in order to develop a procedure to infer astrophysical parameters of the PNS formed in core-collapse supernovae. Our method combines information from the oscillation spectrum of the PNS, obtained through linear-perturbation analysis in general relativity of a background physical system, with information from the gravitational-wave spectrum of the corresponding non-linear, core-collapse simulation. Using results from the simulation of the collapse of a 35 $M_{\odot}$ presupernova progenitor we show that both types of spectra are indeed related and we are able to identify the modes of oscillation of the PNS, namely g-modes, p-modes, hybrid modes, and standing-accretion-shock-instability (SASI) modes, obtaining a remarkably close correspondence with the time-frequency distribution of the gravitational-wave modes. The analysis presented in this paper provides a proof-of-concept that asteroseismology is indeed possible in the core-collapse scenario, and it may serve as a basis for future work on PNS parameter inference based on gravitational-wave observations.

We discuss the relevance of the magnetorotational instability (MRI) in core-collapse supernovae (CCSNe). Our recent numerical studies show that in CCSNe, the MRI is terminated by parasitic instabilities of the Kelvin-Helmholtz type. To determine whether the MRI can amplify initially weak magnetic fields to dynamically relevant strengths in CCSNe, we performed three-dimensional simulations of a region close to the surface of a differentially rotating proto-neutron star in non-ideal magnetohydrodynamics with two different numerical codes. We find that under the conditions prevailing in proto-neutron stars, the MRI can amplify the magnetic field by (only) one order of magnitude. This severely limits the role of MRI channel modes as an agent amplifying the magnetic field in proto-neutron stars starting from small seed fields., Comment: Proceedings in Acta Physica Polonica B, Proceedings Supplement, Vol. 10, No. 2, p.361, 4 pages, 1 figure

Extremely strong magnetic fields of the order of $10^{15}\,{\rm G}$ are required to explain the properties of magnetars, the most magnetic neutron stars. Such a strong magnetic field is expected to play an important role for the dynamics of core-collapse supernovae, and in the presence of rapid rotation may power superluminous supernovae and hypernovae associated to long gamma-ray bursts. The origin of these strong magnetic fields remains, however, obscure and most likely requires an amplification over many orders of magnitude in the protoneutron star. One of the most promising agents is the magnetorotational instability (MRI), which can in principle amplify exponentially fast a weak initial magnetic field to a dynamically relevant strength. We describe our current understanding of the MRI in protoneutron stars and show recent results on its dependence on physical conditions specific to protoneutron stars such as neutrino radiation, strong buoyancy effects and large magnetic Prandtl number., Comment: 6 pages, 4 figures, proceedings of IAUS 331

We study the long-term quasi-steady evolution of the force-free magnetosphere of a magnetar coupled to its internal magnetic field. We find that magnetospheric currents can be maintained on long timescales of the order of thousands of years. Meanwhile, the energy, helicity and twist stored in the magnetosphere all gradually increase over the course of this evolution, until a critical point is reached, beyond which a force-free magnetosphere cannot be constructed. At this point, some large-scale magnetospheric rearrangement, possibly resulting in an outburst or a flare, must occur, releasing a large fraction of the stored energy, helicity and twist. After that, the quasi-steady evolution should continue in a similar manner from the new initial conditions. The timescale for reaching this critical point depends on the overall magnetic field strength and on the relative fraction of the toroidal field. The energy stored in the force-free magnetosphere is found to be up to $\sim 30\%$ larger than the corresponding vacuum energy. This implies that for a $10^{14}$ G field at the pole, the energy budget available for fast magnetospheric events is of the order of a few $10^{44}$ erg. The spindown rate is estimated to increase by up to $\sim 60\%$, since the dipole content in the magnetosphere is enhanced by the currents present there. A rough estimate of the braking index $n$ reveals that it is systematically $n < 3$ for the most part of the evolution, consistent with actual measurements for pulsars and early estimates for several magnetars., Comment: 10 pages, 8 figures; corrected typos; accepted for publication in MNRAS

We propose a simple ansatz for estimating the value of the numerical resistivity and the numerical viscosity of any Eulerian MHD code. We test this ansatz with the help of simulations of the propagation of (magneto)sonic waves, Alfven waves, and the tearing mode instability using the MHD code Aenus. By comparing the simu- lation results with analytical solutions of the resistive-viscous MHD equations and an empirical ansatz for the growth rate of tearing modes we measure the numerical viscosity and resistivity of Aenus. The comparison shows that the fast-magnetosonic speed and wavelength are the characteristic velocity and length, respectively, of the aforementioned (relatively simple) systems. We also determine the dependance of the numerical viscosity and resistivity on the time integration method, the spatial reconstruction scheme and (to a lesser extent) the Riemann solver employed in the simulations. From the measured results we infer the numerical resolution (as a function of the spatial reconstruction method) required to properly resolve the growth and saturation level of the magnetic field amplified by the magnetorotational instability in the post-collapsed core of massive stars. Our results show that it is to the best advantage to resort to ultra-high order methods (e.g., 9th-order Monotonicity Preserving method) to tackle this problem properly, in particular in three dimensional simulations., Comment: 36 pages, 35 figures, accepted for publication in ApJS

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-periodic oscillations observed in magnetar giant flares, since they do not suffer from the additional damping mechanism due to phase mixing, contrary to what happens for continuum oscillations. However, we cannot prove rigorously that the coherent oscillations with constant phase are normal modes. Moreover, we find no crustal shear modes for the magnetic field strengths typical for magnetars.We provide fits to our numerical simulations that give the oscillation frequencies as functions of magnetic field strength and proton fraction in the core., Comment: 16 pages, 12 figures, accepted by MNRAS

We present a detailed analysis of the properties of twisted, force-free magnetospheres of non-rotating neutron stars, which are of interest in the modelling of magnetar properties and evolution. In our models the magnetic field smoothly matches to a current-free (vacuum) solution at some large external radius, and they are specifically built to avoid pathological surface currents at any of the interfaces. By exploring a large range of parameters, we find a few remarkable general trends. We find that the total dipolar moment can be increased by up to $40\%$ with respect to a vacuum model with the same surface magnetic field, due to the contribution of magnetospheric currents to the global magnetic field. Thus, estimates of the surface magnetic field based on the large-scale dipolar braking torque are slightly overestimating the surface value by the same amount. Consistently, there is a moderate increase in the total energy of the model with respect to the vacuum solution of up to $25\%$, which would be the available energy budget in the event of a fast, global magnetospheric reorganization commonly associated with magnetar flares. We have also found the interesting result of the existence of a critical twist ($\varphi_{\rm max} \lesssim 1.5$ rad), beyond which we cannot find any more numerical solutions. Combining the models considered in this paper with the evolution of the interior of neutron stars will allow us to study the influence of the magnetosphere on the long-term magnetic, thermal, and rotational evolution., Comment: 17 pages, 9 figures; corrected typos; accepted for publication in MNRAS

Whether the magnetorotational instability (MRI) can amplify initially weak magnetic fields to dynamically relevant strengths in core collapse supernovae is still a matter of active scientific debate. Recent numerical studies have shown that the first phase of MRI growth dominated by channel flows is terminated by parasitic instabilities of the Kelvin-Helmholtz type that disrupt MRI channel flows and quench further magnetic field growth. However, it remains to be prop- erly assessed by what factor the initial magnetic field can be amplified and how it depends on the initial field strength and the amplitude of the perturbations. Different termination criteria leading to different estimates of the amplification factor were proposed within the parasitic model. To determine the amplification factor and test which criterion is a better predictor of the MRI termination, we perform three-dimensional shearing-disc and shearing-box simula- tions of a region close to the surface of a differentially rotating proto-neutron star in non-ideal MHD with two different numerical codes. We find that independently of the initial magnetic field strength, the MRI channel modes can amplify the magnetic field by, at most, a factor of 100. Under the conditions found in proto-neutron stars a more realistic value for the mag- netic field amplification is of the order of 10. This severely limits the role of the MRI channel modes as an agent amplifying the magnetic field in proto-neutron stars starting from small seed fields. A further amplification should therefore rely on other physical processes, such as for example an MRI-driven turbulent dynamo., Comment: 19 pages, 6 figures, accepted for publication in MNRAS

The observation of several neutron stars in the center of supernova remnants and with significantly lower values of the dipolar magnetic field than the average radio-pulsar population has motivated a lively debate about their formation and origin, with controversial interpretations. A possible explanation requires the slow rotation of the proto-neutron star at birth, which is unable to amplify its magnetic field to typical pulsar levels. An alternative possibility, the hidden magnetic field scenario, considers the accretion of the fallback of the supernova debris onto the neutron star as responsible for the submergence (or screening) of the field and its apparently low value. In this paper we study under which conditions the magnetic field of a neutron star can be buried into the crust due to an accreting, conducting fluid. For this purpose, we consider a spherically symmetric calculation in general relativity to estimate the balance between the incoming accretion flow and the magnetosphere. Our study analyses several models with different specific entropy, composition, and neutron star masses. The main conclusion of our work is that typical magnetic fields of a few times 1e12 G can be buried by accreting only 1e-3 - 1e-2 solar mass, a relatively modest amount of mass. In view of this result, the Central Compact Object scenario should not be considered unusual, and we predict that anomalously weak magnetic fields should be common in very young (< few kyr) neutron stars., Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journal

We explore magnetic-field amplification due to the Kelvin-Helmholtz instability during binary neutron star mergers. By performing high-resolution general relativistic magnetohydrodynamics simulations with a resolution of $17.5$ m for $4$--$5$ ms after the onset of the merger on the Japanese supercomputer "K", we find that an initial magnetic field of moderate maximum strength $10^{13}$ G is amplified at least by a factor of $\approx 10^3$. We also explore the saturation of the magnetic-field energy and our result shows that it is likely to be $\gtrsim 4 \times 10^{50}$ erg, which is $\gtrsim 0.1\%$ of the bulk kinetic energy of the merging binary neutron stars., Comment: 13 pages, 10 figures, accepted to PRD

The magnetorotational instability (MRI) can be a powerful mechanism amplifying the magnetic field in core-collapse supernovae. Whether initially weak magnetic fields can be amplified by this instability to dynamically relevant strengths is still a matter of debate. One of the main uncertainties concerns the process that terminates the growth of the instability. Parasitic instabilities of both Kelvin-Helmholtz and tearing-mode type have been suggested to play a crucial role in this process, disrupting MRI channel flows and quenching magnetic field amplification. We perform two-dimensional and three-dimensional sheering-disc simulations of a differentially rotating protoneutron star layer in non-ideal magnetohydrodynamics with unprecedented high numerical accuracy, finding that Kelvin-Helmholtz parasitic modes dominate tearing modes in the regime of large hydrodynamic and magnetic Reynolds numbers, as encountered close to the surface of protoneutron stars. They also determine the maximum magnetic field stress achievable during the exponential growth of the MRI. Our results are consistent with the theory of parasitic instabilities based on a local stability analysis. To simulate the Kelvin-Helmholtz instabilities properly, a very high numerical resolution is necessary. Using ninth-order spatial reconstruction schemes, we find that at least eight grid zones per MRI channel are necessary to simulate the growth phase of the MRI and reach an accuracy of ~10 per cent in the growth rate, while more than ~60 zones per channel are required to achieve convergent results for the value of the magnetic stress at MRI termination., Comment: 21 pages, 14 figures, accepted for publication in MNRAS

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 magnetosphere by inducing a time-dependent twist between the foot-points of closed magnetic field lines that exit the star at a polar angle $\gtrsim 0.19\,$rad. Moreover, we find that for a dipole-like background magnetic field configuration the magnetic field modulations in the magnetosphere, driven by internal oscillations, can only be symmetric with respect to the equator. This is in agreement with our previous findings, where we interpreted the observed quasi-periodic oscillations in the X-ray tail of magnetar bursts as driven by the family of internal magneto-elastic oscillations with symmetric magnetic field perturbations., Comment: 9 pages, 5 figures, 2 tables, Accepted by MNRAS

We present numerical simulations in general relativity of collapsing stellar cores. Our initial model consists of a low metallicity rapidly-rotating progenitor which is evolved in axisymmetry with the latest version of our general relativistic code CoCoNuT, which allows for black hole formation and includes the effects of a microphysical equation of state (LS220) and a neutrino leakage scheme to account for radiative losses. The motivation of our study is to analyze in detail the emission of gravitational waves in the collapsar scenario of long gamma-ray bursts. Our simulations show that the phase during which the proto-neutron star (PNS) survives before ultimately collapsing to a black hole is particularly optimal for gravitational wave emission. The high-amplitude waves last for several seconds and show a remarkable quasi-periodicity associated with the violent PNS dynamics, namely during the episodes of convection and the subsequent nonlinear development of the standing-accretion shock instability (SASI). By analyzing the spectrogram of our simulations we are able to identify the frequencies associated with the presence of g-modes and with the SASI motions at the PNS surface. We note that the gravitational waves emitted reach large enough amplitudes to be detected with third-generation detectors as the Einstein Telescope within a Virgo cluster volume at rates ~< 0.1 /y., Comment: 6 pages, 4 figures. Shortened version

Interferometric detectors will very soon give us an unprecedented view of the gravitational-wave sky, and in particular of the explosive and transient Universe. Now is the time to challenge our theoretical understanding of short-duration gravitational-wave signatures from cataclysmic events, their connection to more traditional electromagnetic and particle astrophysics, and the data analysis techniques that will make the observations a reality. This paper summarizes the state of the art, future science opportunities, and current challenges in understanding gravitational-wave transients., Comment: 33 pages, 2 figures

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., Comment: 5 pages, 4 figures

In this work we present a new class of Runge-Kutta (RK) methods for solving systems of hyperbolic equations with a particular structure, generalization of a wave-equation. The new methods are {\it partially implicit} in the sense that a proper subset of the equations of the system contains some terms which are treated implicitly. These methods can be viewed as a particular case of the implicit-explicit (IMEX) RK methods for systems of equations with wave-like structure. For these systems, the optimal methods with the new structure are easier to derive than the IMEX ones, specially when aiming at higher-order (up to fourth-order in this work). The methods are constructed considering the classical strong-stability-preserving optimal explicit RK methods for the purely explicit part. The resulting partially implicit RK methods do not require any inversion of operators and hence their computational cost per iteration is similar to those of explicit RK methods. We analyse the stability and convergence properties and show their practical applicability in several numerical examples. Our results show that, compared with explicit RK methods, the new methods have better stability properties (larger steps are allowed) and in general show smaller discretization error., Comment: 39 pages, 10 figures

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\'en 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\'en QPOs, we estimate the required surface magnetic field strength. For the magnetic field configurations investigated (dipole-like poloidal, mixed toroidal-poloidal with a dipole-like poloidal component and a toroidal field confined to the region of field lines closing inside the star, and for poloidal fields with an additional quadrupole-like component) the estimated dipole spin-down magnetic fields are between 8x10^14 G and 4x10^15 G, in broad agreement with spin-down estimates for the SGR sources producing giant flares. A number of these models exhibit a rich Alfv\'en continuum revealing new turning points which can produce QPOs. This allows one to explain most of the observed QPO frequencies as associated with magneto-elastic QPOs. In particular, we construct a possible configuration with two turning points in the spectrum which can explain all observed QPOs of SGR 1900+14. Finally, we find that magnetic field configurations which are entirely confined in the crust (if the core is assumed to be a type I superconductor) are not favoured, due to difficulties in explaining the lowest observed QPO frequencies (f<30 Hz)., Comment: 21 pages, 16 figures, 6 tables, matched to version accepted by MNRAS with extended comparison/discussion to previous work

The Fully Constrained Formulation (FCF) of General Relativity is a novel framework introduced as an alternative to the hyperbolic formulations traditionally used in numerical relativity. The FCF equations form a hybrid elliptic-hyperbolic system of equations including explicitly the constraints. We present an implicit-explicit numerical algorithm to solve the hyperbolic part, whereas the elliptic sector shares the form and properties with the well known Conformally Flat Condition (CFC) approximation. We show the stability andconvergence properties of the numerical scheme with numerical simulations of vacuum solutions. We have performed the first numerical evolutions of the coupled system of hydrodynamics and Einstein equations within FCF. As a proof of principle of the viability of the formalism, we present 2D axisymmetric simulations of an oscillating neutron star. In order to simplify the analysis we have neglected the back-reaction of the gravitational waves into the dynamics, which is small (<2 %) for the system considered in this work. We use spherical coordinates grids which are well adapted for simulations of stars and allow for extended grids that marginally reach the wave zone. We have extracted the gravitational wave signature and compared to the Newtonian quadrupole and hexadecapole formulae. Both extraction methods show agreement within the numerical errors and the approximations used (~30 %)., Comment: 17 pages, 9 figures, 2 tables, accepted for publication in PRD

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 equator. Edge QPOs are called so because they are related to an edge in the corresponding Alfv\'en continuum. The Upper QPOs are of the same kind, while the Lower QPOs are turning-point QPOs, related to a turning point in the continuous spectrum., Comment: 6 pages, 1 figure, 1 table, Proceedings of NEB14, to appear in J. Phys.: Conf. Ser

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 x 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 explaining the observed low-frequency QPOs. In contrast, we find that the Alfv\'en QPO model is a viable explanation of observed QPOs, if the dipole magnetic field strength exceeds a minimum strength of about several times 10^14 G to 10^15 G. Then, Alfv\'en QPOs are no longer confined to the fluid core, but completely dominate in the crust region and have a maximum amplitude at the surface of the star., Comment: 5 pages, 3 figure, 2 table, to match accepted Letter by MNRAS, different EOS included, generally more focused on damping

This contribution summarizes the recent work carried out to analyze the behavior of the hyperbolic sector of the Fully Constrained Formulation (FCF) derived in Bonazzola et al. 2004. The numerical experiments presented here allows one to be confident in the performances of the upgraded version of CoCoNuT's code by replacing the Conformally Flat Condition (CFC) approximation of the Einstein equations by the FCF., Comment: 4 pages, 7 figures. Accepted for publication in Journal of Physics: Conference Series, Proceedings of the 8th Edoardo Amaldi Conference on Gravitational Waves

We present an alternative method to estimate the numerical viscosity in simulations of astrophysical objects, which is based in the damping of fluid oscillations. We apply the method to general relativistic hydrodynamic simulations using a spherical coordinates. We perform 1D-spherical and 2D- axisymmetric simulations of radial oscillations in spherical systems. We calibrate first the method with simulations with added bulk viscosity and study the differences between different numerical schemes. We apply the method to radial oscillations of neutron stars and we conclude that the main source of numerical viscosity in this case is the surface of the star. We expect that this method could be useful to compute the resolution requirements and limitations of the numerical simulations in different astrophysical scenarios in the future., Comment: Accepted for publication in Class. Quantum Grav. 15 pages, 3 figures

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 study of Sotani, Kokkotas & Stergioulas; b) the QPOs appearing near the magnetic axis are split into two groups, depending on their symmetry across the equatorial plane. The antisymmetric QPOs have only odd integer-multiple harmonics; c) the continuum obtained with our semi-analytic approach agrees remarkably well with QPOs obtained via the two-dimensional simulations, allowing for a clear interpretation of the QPOs as corresponding to turning points of the continuum. This agreement will allow for a comprehensive study of Alfven QPOs for a larger number of different models, without the need for time-consuming simulations. Finally, we construct empirical relations for the QPO frequencies and compare them to observations of known Soft Gamma Repeaters. We find that, under the assumptions of our model and if the magnetic field of magnetars is characterized by a strong dipolar component, and QPOs are produced near the magnetic pole, then one can place an upper limit to the mean surface strength of the magnetic field of about 3-8 10^15 G., Comment: Revised version to be published in MNRAS. 14 pages, 7 figures

Uniqueness problems in the elliptic sector of constrained formulations of Einstein equations have a dramatic effect on the physical validity of some numerical solutions, for instance when calculating the spacetime of very compact stars or nascent black holes. The fully constrained formulation (FCF) proposed by Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak is one of these formulations. It contains, as a particular case, the approximation of the conformal flatness condition (CFC) which, in the last ten years, has been used in many astrophysical applications. The elliptic part of the FCF basically shares the same differential operators as the elliptic equations in CFC scheme. We present here a reformulation of the elliptic sector of CFC that has the fundamental property of overcoming the local uniqueness problems. The correct behavior of our new formulation is confirmed by means of a battery of numerical simulations. Finally, we extend these ideas to FCF, complementing the mathematical analysis carried out in previous studies., Comment: 17 pages, 5 figures. Minor changes to be consistent with published version