Pablo Cerdá-Durán

Magnetoelastic oscillations of neutron stars with dipolar magnetic fields

By means of two dimensional, general-relativistic, magneto-hydrodynamical simulations we investigate the oscillations of magnetized neutron star models (magnetars) including the de- scription of an extended solid crust. The aim of this study is to understand the origin of the quasi-periodic oscillations (QPOs) observed in the giant flares of soft gamma-ray repeaters (SGRs). We confirm our previous findings which showed the existence of three different regimes in the evolution depending on the dipolar magnetic field strength: (a) a weak mag- netic field regime B 10 15 G, where magneto-elastic oscillations reach the surface and approach the behavior of purely AlfvQPOs. When the Alfv´ en QPOs are confined to the core of the neutron star, we find qualitatively similar QPOs as in the absence of a crust. The lower QPOs associated with the closed field lines of the dipolar magnetic field configuration are reproduced as in our previous simulations without crust, while the upper QPOs connected to the open field lines are displaced from the polar axis. The position of these upper QPOs strongly depends on the magnetic field strength. Additionally, we observe a family of edge QPOs and one new upper QPO, which was not previously found in the ab- sence of a crust. We extend our semi-analytic model to obtain estimates for the continuum of the Alfvoscillations. Our results do not leave much room for a crustal-mode interpreta- tion of observed QPOs in SGR giant flares, but can accommodate an interpretation of these observations as originating from Alfv´ en-like, global, turning-point QPOs (which can reach the surface of the star) in models with dipolar magnetic field strengths in the narrow range of 5 10 15 G. B. 1:4 10 16 G (for a sample of two stiff EoS and various masses). This range is somewhat larger than estimates for magnetic field strengths in known magnetars. The discrepancy may be resolved in models including a more complicated magnetic field structure or with models taking superfluidity of the neutrons and superconductivity of the protons in the core into account.

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 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

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´ 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 8 10 14 G and 4 10 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).

The transient gravitational-wave sky

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.

A new general relativistic magnetohydrodynamics code for dynamical spacetimes

We present a new numerical code that solves the general relativistic magneto-hydrodynamical (GRMHD) equations coupled to the Einstein equations for the evolution of a dynamical spacetime within a conformally-flat approximation. This code has been developed with the main objective of studying astrophysical scenarios in which both, high magnetic fields and strong gravitational fields appear, such as the magneto-rotational collapse of stellar cores, the collapsar model of GRBs, and the evolution of neutron stars. The code is based on an existing and thoroughly tested purely hydrodynamical code and on its extension to accommodate weakly magnetized fluids (passive magnetic-field approximation). These codes have been applied in the past to simulate the aforementioned scenarios with increasing levels of sophistication in the input physics. The numerical code we present here is based on high-resolution shockcapturing schemes to solve the GRMHD equations, which are cast in first-order, flux-conservative hyperbolic form, together with the flux constraint transport method to ensure the solenoidal condition of the magnetic field. Since the astrophysical applications envisaged do not deviate significantly from spherical symmetry, the conformal flatness condition approximation is used for the formulation of the Einstein equations; this has repeatedly shown to yield very good agreement with full general relativistic simulations of corecollapse supernovae and the evolution of isolated neutron stars. In addition, the code can handle several equations of state, from simple analytical expressions to microphysical tabulated ones. In this paper we present stringent tests of our new GRMHD numerical code, which show its ability to handle all aspects appearing in the astrophysical scenarios for which the code is intended, namely relativistic shocks, highly magnetized fluids, and equilibrium configurations of magnetized neutron stars. As an application, magnetorotational core-collapse simulations of a realistic progenitor are presented and the results compared with our previous findings in the passive magnetic-field approximation.

General relativistic simulations of passive-magneto-rotational core collapse with microphysics

This paper presents results from axisymmetric simulations of magneto-rotational stellar core collapse to neutron stars in general relativity using the passive field approximation for the magnetic field. These simulations are performed using a new general relativistic numerical code specifically designed to study this astrophysical scenario. The code is an extension of an existing (and thoroughly tested) hydrodynamics code, which has been applied in the recent past to study relativistic rotational core collapse. It is based on the conformally-flat approximation of Einstein’s field equations and conservative formulations of the magneto-hydrodynamics equations. The code has been recently upgraded to incorporate a tabulated, microphysical equation of state and an approximate deleptonization scheme. This allows us to perform the most realistic simulations of magneto-rotational core collapse to date, which are compared with simulations employing a simplified (hybrid) equation of state, widely used in the relativistic core collapse community. Furthermore, state-of-the-art (unmagnetized) initial models from stellar evolution are used. In general, stellar evolution models predict weak magnetic fields in the progenitors, which justifies our simplification of performing the computations under the approach that we call the passive field approximation for the magnetic field. Our results show that for the core collapse models with microphysics the saturation of the magnetic field cannot be reached within dynamical time scales by winding up the poloidal magnetic field into a toroidal one. We estimate the effect of other amplification mechanisms including the magneto-rotational instability (MRI) and several types of dynamos. We conclude that for progenitors with astrophysically expected (i.e. weak) magnetic fields, the MRI is the only mechanism that could amplify the magnetic field on dynamical time scales. The uncertainties about the strength of the magnetic field at which the MRI saturates are discussed. All our microphysical models exhibit post-bounce convective overturn in regions surrounding the inner part of the proto-neutron star. Since this has a potential impact on enhancing the MRI, it deserves further investigation with more accurate neutrino treatment or alternative microphysical equations of state.

CFC+: Improved dynamics and gravitational waveforms from relativistic core collapse simulations

Received date / Accepted date Abstract. Core collapse supernovae are a promising source of detectable gravitational waves. Most of the existing (multidimensional) numerical simulations of core collapse in general relativity have been done using approxima- tions of the Einstein field equations. As recently shown by Dimmelmeier et al. (2002a,b), one of the most inter- esting such approximation is the so-called conformal flatness condition (CFC) of Isenberg, Wilson and Mathews. Building on this previous work we present here new results from numerical simulations of relativistic rotational core collapse in axisymmetry, aiming at improving the dynamics and the gravitational waveforms. The computer code used for these simulations evolves the coupled system of metric and fluid equations using the 3+1 formalism, specialized to a new framework for the gravitational field equations which we call CFC+. In this approach we add new degrees of freedom to the original CFC equations, which extend them by terms of second post-Newtonian or- der. The resulting metric equations are still of elliptic type but the number of equations is significantly augmented in comparison to the original CFC approach. The hydrodynamics evolution and the CFC spacetime metric are calculated using the code developed by Dimmelmeier et al. (2002a), which has been conveniently extended to account for the additional CFC+ equations. The corrections for CFC+ are computed solving a system of elliptic linear equations. The new formalism is assessed with time evolutions of both rotating neutron stars in equilibrium and gravitational core collapse of rotating polytropes. Gravitational wave signals for a comprehensive sample of collapse models are extracted using either the quadrupole formula or directly from the metric. We discuss our results on the dynamics and the gravitational wave emission through a detailed comparison between CFC and CFC+ simulations. The main conclusion is that, for the neutron star spacetimes analyzed in the present work, no significant differences are found among CFC, CFC+, and full general relativity, which highlights the suitability of the former.

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

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 < 150Hz) and high frequencies (f > 500Hz), 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.

Improved constrained scheme for the Einstein equations: an approach to the uniqueness issue

The fully constrained formulation (FCF) proposed by Bonazzola, Gourgoulhon, Grand‐clement, and Novak is one of the constrained formulations of Einstein’s equations. It contains as an approximation the conformal flatness condition (CFC). The elliptic part of the FCF basically shares the same differential operators as the elliptic equations in the CFC scheme. We present here a reformulation of the elliptic sector of CFC that has the fundamental property of overcoming local uniqueness problems, and an extension of these ideas to FCF.

Termination of the magnetorotational instability via parasitic instabilities in core-collapse supernovae

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 di erentially rotating proto-neutron 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 proto-neutron 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 9th order spatial reconstruction schemes, we find that at least 8 grid zones per MRI channel are necessary to simulate the growth phase of the MRI and reach an accuracy of 10% 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.