Simulations Of Magneto-rotational Core Collapse Research Articles

A new general relativistic magnetohydrodynamics code for dynamical spacetimes

We present a new numerical code which solves the general relativistic magneto-hydrodynamics (GRMHD) equations coupled to the Einstein equations for the evolution of a dynamical spacetime within the 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 hydrodynamics code and on its extension to accommodate weakly magnetized fluids (passive magnetic field approximation). The numerical code we present here is based on high-resolution shock-capturing schemes to solve the GRMHD equations together with the flux constraint transport method to ensure the solenoidal condition of the magnetic field. Since the astrophysical applications envisaged do not deviate much from spherical symmetry, the conformal flatness condition approximation is used for the formulation of the Einstein equations. 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, magneto-rotational core collapse simulations of a realistic progenitor are presented, comparing the results with our previous finding in the passive magnetic field approximation.

Magnetorotational Collapse of Population III Stars

Abstract We performed a series of two-dimensional magnetorotational core-collapse simulations of Population III stars. Changing the initial distributions of the rotation and magnetic fields prior to collapse in a parametric manner, we computed 19 models. By so doing, we systematically investigated how rotation and magnetic fields affect the collapse dynamics, and explored how the properties of black-hole formations and neutrino emissions could be affected. As for microphysics, we employed a realistic equation of state, and approximated neutrino transfer by a multiflavour leakage scheme. With these computations, we found that jet-like explosions are obtained by magneto-driven shock waves if the initial magnetic field is as large as $10^{12}$G. We point out that although the black-hole masses at formation decrease with the initial field strength, they increase with the initial rotation rates. As for the neutrino properties, we point out that the degree of differential rotation plays an important role in determining which species of the neutrino luminosity is more dominant than the others. Furthermore, we find that stronger magnetic fields make the peak neutrino luminosities smaller, because the magnetic pressure acts to halt collapse in the central regions, leading to a suppression of the releasable gravitational binding energies.

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.

Towards relativistic simulations of magneto-rotational core collapse

We present a new general relativistic hydrodynamics code specifically designed to study magneto-rotational, relativistic, stellar core collapse. 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 for the magneto-hydrodynamics equations. As a first step towards magneto-rotational core collapse simulations the code assumes a passive (test) magnetic field. The paper is focused on the description of the technical details of the numerical implementation, with emphasis on the magnetic field module. A number of code tests are presented and discussed, along with a representative core collapse simulation.

Axisymmetric simulations of magnetorotational core collapse: approximate inclusion of general relativistic effects

We continue our investigations of the magnetorotational collapse of stellar cores by discussing simulations performed with a modified Newtonian gravitational potential that mimics general relativistic effects. The approximate TOV gravitational potential used in our simulations captures several basic features of fully relativistic simulations quite well. In particular, it is able to correctly reproduce the behavior of models that show a qualitative change both of the dynamics and the gravitational wave signal when switching from Newtonian to fully relativistic simulations. For models where the dynamics and gravitational wave signals are already captured qualitatively correctly by a Newtonian potential, the results of the Newtonian and the approximate TOV models differ quantitatively. The collapse proceeds to higher densities with the approximate TOV potential, allowing for a more efficient amplification of the magnetic field by differential rotation. The strength of the saturation fields (∼10 15 G at the surface of the inner core) is a factor of two to three higher than in Newtonian gravity. Due to the more efficient field amplification, the influence of magnetic fields is considerably more pronounced than in the Newtonian case for some of the models. As in the Newtonian case, sufficiently strong magnetic fields slow down the core’s rotation and trigger a secular contraction phase to higher densities. More clearly than in Newtonian models, the collapsed cores of these models exhibit two different kinds of shock generation. Due to magnetic braking, a first shock wave created during the initial centrifugal bounce at subnuclear densities does not suffice for ejecting any mass, and the temporarily stabilized core continues to collapse to supranuclear densities. Another stronger shock wave is generated during the second bounce as the core exceeds nuclear matter density. The gravitational wave signal of these models does not fit into the standard classification. Therefore, in the first paper of this series we introduced a new type of gravitational wave signal, which we call type IV or “magnetic type”. This signal type is more frequent for the approximate relativistic potential than for the Newtonian one. Most of our weak-field models are marginally detectable with the current LIGO interferometer for a source located at a distance of 10 kpc. Strongly magnetized models emit a substantial fraction of their GW power at very low frequencies. A flat spectrum between 10 Hz and <100 kHz denotes the generation of a jet-like hydromagnetic outflow.

Axisymmetric simulations of magneto-rotational core collapse: dynamics and gravitational wave signal

Aims. We have performed a comprehensive parameter study of the collapse of rotating, strongly magnetized stellar cores in axisymmetry to determine their gravitational wave signature based on the Einstein quadrupole formula. Methods. We use a Newtonian explicit magnetohydrodynamic Eulerian code based on the relaxing-TVD method for the solution of the ideal MHD equations, and apply the constraint-transport method to guarantee a divergence-free evolution of the magnetic field. We neglect effects due to neutrino transport and employ a simplified equation of state. The initial models are polytropes in rotational equilibrium with a prescribed degree of differential rotation and rotational energy. The initial magnetic fields are purely poloidal the field strength ranging from 1010 G to 10 13 G. The evolution of the core is followed until a few ten milliseconds past core bounce. Results. The initial magnetic fields are amplified mainly by the differential rotation of the core giving rise to a strong toroidal field component with an energy comparable to the rotational energy. The poloidal field component grows by compression during collapse, but does not change significantly after core bounce. In large parts of the simulated cores the growth time of the magneto-rotational instability (MRI) is of the order of a few milliseconds. The saturation field strengths that can be reached both via a pure 12 dynamo or the MRI are of the order of 10 15 G at the surface of the core. Sheet-like circulation flows which produce a strong poloidal field component transporting angular momentum outwards develop due to MRI, provided the initial field is not too weak. Weak initial magnetic fields (≤10 11 G) have no significant effect on the dynamics of the core and the gravitational wave signal. Strong initial fields (≤10 12 G) cause considerable angular momentum transport whereby rotational energy is extracted from the collapsed core which loses centrifugal support and enters a phase of secular contraction. The gravitational wave amplitude at bounce changes by up to a few ten percent compared to the corresponding non-magnetic model. If the angular momentum losses are large, the post-bounce model. If the angular momentum losses are large the post-bounce equilibrium state of the core changes from a centrifugally to a pressure supported one. This transition imprints in the gravitational wave signal a reduction of the amplitude of the large-scale oscillations characteristic of cores bouncing due to centrifugal forces. In some models the quasi-periodic large-scale oscillations are replaced by higher frequency irregular oscillations. This pattern defines a new signal type which we call a type IV gravitational wave signal. Collimated bipolar outflows give rise to a unique feature that may allow their detection by means of gravitational wave astronomy: a large positive quadrupole wave amplitude of similar size as that of the bounce signal.