On the Shear Instability in Relativistic Neutron Stars

We present new results on instabilities in rapidly and differentially rotating neutron stars. We model the stars in full general relativity and describe the stellar matter adopting a cold realistic equation of state based on the unified SLy prescription. We provide evidence that rapidly and differentially rotating stars that are below the expected threshold for the dynamical bar-mode instability, beta_c = T/|W| ~ 0.25, do nevertheless develop a shear instability on a dynamical timescale and for a wide range of values of beta. This class of instability, which has so far been found only for small values of beta and with very small growth rates, is therefore more generic than previously found and potentially more effective in producing strong sources of gravitational waves. Overall, our findings support the phenomenological predictions made by Watts, Andersson and Jones on the nature of the low-T/|W|.Comment: 20 pages; accepted to the Classical and Quantum Gravity special issue for MICRA200

Magnetic Braking and Damping of Differential Rotation in Massive Stars

Fragmentation of highly differentially rotating massive stars that undergo collapse has been suggested as a possible channel for binary black hole formation. Such a scenario could explain the formation of the new population of massive black holes detected by the LIGO/VIRGO gravitational wave laser interferometers. We probe that scenario by performing general relativistic magnetohydrodynamic simulations of differentially rotating massive stars supported by thermal radiation pressure plus a gas pressure perturbation. The stars are initially threaded by a dynamically weak, poloidal magnetic field confined to the stellar interior. We find that magnetic braking and turbulent viscous damping via magnetic winding and the magnetorotational instability in the bulk of the star redistribute angular momentum, damp differential rotation and induce the formation of a massive and nearly uniformly rotating inner core surrounded by a Keplerian envelope. The core + disk configuration evolves on a secular timescale and remains in quasi-stationary equilibrium until the termination of our simulations. Our results suggest that the high degree of differential rotation required for $m=2$ seed density perturbations to trigger gas fragmentation and binary black hole formation is likely to be suppressed during the normal lifetime of the star prior to evolving to the point of dynamical instability to collapse. Other cataclysmic events, such as stellar mergers leading to collapse, may therefore be necessary to reestablish sufficient differential rotation and density perturbations to drive nonaxisymmetric modes leading to binary black hole formation.Comment: 11 pages, 5 figures. Minor changes, matches published versio

Neutron Star instabilities in full General Relativity using a Γ=2.75\Gamma=2.75 ideal fluid

We present results about the effect of the use of a stiffer equation of state, namely the ideal-fluid $\Gamma=2.75$ ones, on the dynamical bar-mode instability in rapidly rotating polytropic models of neutron stars in full General Relativity. We determine the change on the critical value of the instability parameter $\beta$ for the emergence of the instability when the adiabatic index $\Gamma$ is changed from 2 to 2.75 in order to mimic the behavior of a realistic equation of state. In particular, we show that the threshold for the onset of the bar-mode instability is reduced by this change in the stiffness and give a precise quantification of the change in value of the critical parameter $\beta_c$. We also extend the analysis to lower values of $\beta$ and show that low-beta shear instabilities are present also in the case of matter described by a simple polytropic equation of state.Comment: 16 pages, 16 figure

Accurate evolutions of inspiralling neutron-star binaries: prompt and delayed collapse to black hole

Binary neutron-star (BNS) systems represent primary sources for the gravitational-wave (GW) detectors. We present a systematic investigation in full GR of the dynamics and GW emission from BNS which inspiral and merge, producing a black hole (BH) surrounded by a torus. Our results represent the state of the art from several points of view: (i) We use HRSC methods for the hydrodynamics equations and high-order finite-differencing techniques for the Einstein equations; (ii) We employ AMR techniques with "moving boxes"; (iii) We use as initial data BNSs in irrotational quasi-circular orbits; (iv) We exploit the isolated-horizon formalism to measure the properties of the BHs produced in the merger; (v) Finally, we use two approaches, based either on gauge-invariant perturbations or on Weyl scalars, to calculate the GWs. These techniques allow us to perform accurate evolutions on timescales never reported before (ie ~30 ms) and to provide the first complete description of the inspiral and merger of a BNS leading to the prompt or delayed formation of a BH and to its ringdown. We consider either a polytropic or an ideal fluid EOS and show that already with this idealized EOSs a very interesting phenomenology emerges. In particular, we show that while high-mass binaries lead to the prompt formation of a rapidly rotating BH surrounded by a dense torus, lower-mass binaries give rise to a differentially rotating NS, which undergoes large oscillations and emits large amounts of GWs. Eventually, also the NS collapses to a rotating BH surrounded by a torus. Finally, we also show that the use of a non-isentropic EOS leads to significantly different evolutions, giving rise to a delayed collapse also with high-mass binaries, as well as to a more intense emission of GWs and to a geometrically thicker torus.Comment: 35 pages, 29 figures, corrected few typos to match the published version. High-resolution figures and animations can be found at http://numrel.aei.mpg.de/Visualisations/Archive/BinaryNeutronStars/Relativistic_Meudon/index.htm

Gravitational waves from supernova matter

We have performed a set of 11 three-dimensional magnetohydrodynamical core collapse supernova simulations in order to investigate the dependencies of the gravitational wave signal on the progenitor's initial conditions. We study the effects of the initial central angular velocity and different variants of neutrino transport. Our models are started up from a 15 solar mass progenitor and incorporate an effective general relativistic gravitational potential and a finite temperature nuclear equation of state. Furthermore, the electron flavour neutrino transport is tracked by efficient algorithms for the radiative transfer of massless fermions. We find that non- and slowly rotating models show gravitational wave emission due to prompt- and lepton driven convection that reveals details about the hydrodynamical state of the fluid inside the protoneutron stars. Furthermore we show that protoneutron stars can become dynamically unstable to rotational instabilities at T/|W| values as low as ~2 % at core bounce. We point out that the inclusion of deleptonization during the postbounce phase is very important for the quantitative GW prediction, as it enhances the absolute values of the gravitational wave trains up to a factor of ten with respect to a lepton-conserving treatment.Comment: 10 pages, 6 figures, accepted, to be published in a Classical and Quantum Gravity special issue for MICRA200

Dynamical bar-mode instability in rotating and magnetized relativistic stars

We present three-dimensional simulations of the dynamical bar-mode instability in magnetized and differentially rotating stars in full general relativity. Our focus is on the effects that magnetic fields have on the dynamics and the onset of the instability. In particular, we perform ideal-magnetohydrodynamics simulations of neutron stars that are known to be either stable or unstable against the purely hydrodynamical instability, but to which a poloidal magnetic field in the range of $10^{14}$--$10^{16}$ G is superimposed initially. As expected, the differential rotation is responsible for the shearing of the poloidal field and the consequent linear growth in time of the toroidal magnetic field. The latter rapidly exceeds in strength the original poloidal one, leading to a magnetic-field amplification in the the stars. Weak initial magnetic fields, i.e. $\lesssim 10^{15}$ G, have negligible effects on the development of the dynamical bar-mode instability, simply braking the stellar configuration via magnetic-field shearing, and over a timescale for which we derived a simple algebraic expression. On the other hand, strong magnetic fields, i.e. $\gtrsim 10^{16}$ G, can suppress the instability completely, with the precise threshold being dependent also on the amount of rotation. As a result, it is unlikely that very highly magnetized neutron stars can be considered as sources of gravitational waves via the dynamical bar-mode instability.Comment: 18 pages, 13 figure

Simulating the Magnetorotational Collapse of Supermassive Stars: Incorporating Gas Pressure Perturbations and Different Rotation Profiles

Collapsing supermassive stars (SMSs) with masses $M \gtrsim 10^{4-6}M_\odot$ have long been speculated to be the seeds that can grow and become supermassive black holes (SMBHs). We previously performed GRMHD simulations of marginally stable magnetized $\Gamma = 4/3$ polytropes uniformly rotating at the mass-shedding limit to model the direct collapse of SMSs. These configurations are supported entirely by thermal radiation pressure and model SMSs with $M \gtrsim 10^{6}M_\odot$. We found that around $90\%$ of the initial stellar mass forms a spinning black hole (BH) surrounded by a massive, hot, magnetized torus, which eventually launches an incipient jet. Here we perform GRMHD simulations of $\Gamma \gtrsim 4/3$, polytropes to account for the perturbative role of gas pressure in SMSs with $M \lesssim 10^{6}M_\odot$. We also consider different initial stellar rotation profiles. The stars are initially seeded with a dynamically weak dipole magnetic field that is either confined to the stellar interior or extended from its interior into the stellar exterior. We find that the mass of the BH remnant is $90\%-99\%$ of the initial stellar mass, depending sharply on $\Gamma -4/3$ as well as on the initial stellar rotation profile. After $t\sim 250-550M\approx 1-2\times 10^3(M/10^6M_\odot)$s following the BH formation, a jet is launched and it lasts for $\sim 10^4-10^5(M/10^6M_\odot)$s, consistent with the duration of long gamma-ray bursts. Our results suggest that the Blandford-Znajek mechanism powers the jet. They are also in agreement with our proposed universal model that estimates accretion rates and luminosities that characterize magnetized BH-disk remnant systems that launch a jet. This model helps explain why the outgoing luminosities for vastly different BH-disk formation scenarios all reside within a narrow range ($\sim 10^{52 \pm 1} \rm erg/s$), roughly independent of $M$.Comment: 16 pages, 7 figures. Added references, matches published versio

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

By performing new, long and numerically accurate general-relativistic simulations of magnetized, equal-mass neutron-star binaries, we investigate the role that realistic magnetic fields may have in the evolution of these systems. In particular, we study the evolution of the magnetic fields and show that they can influence the survival of the hypermassive-neutron star produced at the merger by accelerating its collapse to a black hole. We also provide evidence that even if purely poloidal initially, the magnetic fields produced in the tori surrounding the black hole have toroidal and poloidal components of equivalent strength. When estimating the possibility that magnetic fields could have an impact on the gravitational-wave signals emitted by these systems either during the inspiral or after the merger we conclude that for realistic magnetic-field strengths B<~1e12 G such effects could be detected, but only marginally, by detectors such as advanced LIGO or advanced Virgo. However, magnetically induced modifications could become detectable in the case of small-mass binaries and with the development of gravitational-wave detectors, such as the Einstein Telescope, with much higher sensitivities at frequencies larger than ~2 kHz.Comment: 18 pages, 10 figures. Added two new figures (figures 1 and 7). Small modifications to the text to match the version published on Phys. Rev.