Miguel-Ángel Aloy

GENESIS: A High-Resolution Code for Three-dimensional Relativistic Hydrodynamics

The main features of a three-dimensional, high-resolution special relativistic hydro code based on relativistic Riemann solvers are described. The capabilities and performance of the code are discussed. In particular, we present the results of extensive test calculations that demonstrate that the code can accurately and efficiently handle strong shocks in three spatial dimensions. Results of the performance of the code on single and multiprocessor machines are given. Simulations (in double precision) with ≤7×106 computational cells require less than 1 Gbyte of RAM memory and ≈ 7×10-5 CPU s per zone and time step (on a SCI Cray-Origin 2000 with a R10000 processor). Currently, a version of the numerical code is under development, which is suited for massively parallel computers with distributed memory architecture (such as, e.g., Cray T3E).

Jet Stability and the Generation of Superluminal and Stationary Components

We present a numerical simulation of the response of an expanding relativistic jet to the ejection of a superluminal component. The simulation has been performed with a relativistic time-dependent hydrodynamical code from which simulated radio maps are computed by integrating the transfer equations for synchrotron radiation. The interaction of the superluminal component with the underlying jet results in the formation of multiple conical shocks behind the main perturbation. These trailing components can be easily distinguished because they appear to be released from the primary superluminal component instead of being ejected from the core. Their oblique nature should also result in distinct polarization properties. Those appearing closer to the core show small apparent motions and a very slow secular decrease in brightness and could be identified as stationary components. Those appearing farther downstream are weaker and can reach superluminal apparent motions. The existence of these trailing components indicates that not all observed components necessarily represent major perturbations at the jet inlet; rather, multiple emission components can be generated by a single disturbance in the jet. While the superluminal component associated with the primary perturbation exhibits a rather stable pattern speed, trailing components have velocities that increase with distance from the core but move at less than the jet speed. The trailing components exhibit motion and structure consistent with the triggering of pinch modes by the superluminal component. The increase in velocity of the trailing components is an indirect consequence of the acceleration of the expanding fluid, which is assumed to be relativistically hot; if observed, such accelerations would therefore favor an electron-positron (as opposed to proton rest mass) dominated jet.

High-Resolution Three-dimensional Simulations of Relativistic Jets

We have performed high-resolution three-dimensional simulations of relativistic jets with beam-flow Lorentz factors of up to 7, a spatial resolution of 8 cells per beam radius, and up to 75 normalized time units in order to study the morphology and dynamics of three-dimensional relativistic jets. Our simulations show that the coherent fast backflows found in axisymmetric models are not present in three-dimensional models. We further find that when the jet is exposed to nonaxisymmetric perturbations, (1) it does not display the strong perturbations found for three-dimensional classical hydrodynamic and MHD jets (at least during the period of time covered by our simulations) and (2) it does propagate according to the one-dimensional estimate. Small three-dimensional effects in the relativistic beam give rise to a lumpy distribution of apparent speeds like that observed in M87. The beam is surrounded by a boundary layer of high specific internal energy. The properties of this layer are briefly discussed.

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.

Radio Emission from Three-dimensional Relativistic Hydrodynamic Jets: Observational Evidence of Jet Stratification

We present the first radio emission simulations from high-resolution three-dimensional relativistic hydrodynamic jets; these simulations allow us to study the observational implications of the interaction between the jet and the external medium. This interaction gives rise to a stratification of the jet in which a fast spine is surrounded by a slow high-energy shear layer. The stratification (in particular, the large specific internal energy and slow flow in the shear layer) largely determines the emission from the jet. If the magnetic field in the shear layer becomes helical (e.g., resulting from an initial toroidal field and an aligned field component generated by shear), the emission shows a cross section asymmetry, in which either the top or the bottom of the jet dominates the emission. This, as well as limb or spine brightening, is a function of the viewing angle and flow velocity, and the top/bottom jet emission predominance can be reversed if the jet changes direction with respect to the observer or if it presents a change in velocity. The asymmetry is more prominent in the polarized flux because of field cancellation (or amplification) along the line of sight. Recent observations of jet cross section emission asymmetries in the blazar 1055+018 can be explained by assuming the existence of a shear layer with a helical magnetic field.

GRB 060121: Implications of a Short-/Intermediate-Duration γ-Ray Burst at High Redshift

Since the discovery of the first short-population γ-ray burst (GRB) afterglows in 2005, the handful of observed events have been found to be embedded in nearby (z 102). A photometric redshift for this event places the progenitor at a most probable redshift of z = 4.6, with a less probable scenario of z = 1.7. In either case, GRB 060121 could be the farthermost short-population GRB detected to date and implies an isotropic-equivalent energy release in gamma rays comparable to that seen in long-population bursts. We discuss the implications of the released energy on the nature of the progenitor. These results suggest that GRB 060121 may belong to a family of energetic short-population events, lying at z > 1 and whose optical afterglows would outshine their host galaxies, unlike the first short GRBs observed in 2005. The possibility of GRB 060121 being an intermediate-duration burst is also discussed.

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.

Numerical models of blackbody-dominated gamma-ray bursts – I. Hydrodynamics and the origin of the thermal emission

GRB 101225A is a prototype of the class of blackbody-dominated (BBD) gamma-ray bursts (GRBs). It has been suggested that BBD-GRBs result from the merger of a binary system formed by a neutron star and the helium core of an evolved star. We have modelled the propagation of ultrarelativistic jets through the environment left behind the merger by means of relativistic hydrodynamic simulations. In this paper, the output of our numerical models is post-processed to obtain the (thermal) radiative signature of the resulting outflow. We outline the most relevant dynamical details of the jet propagation and connect them to the generation of thermal radiation in GRB events akin to that of GRB 101225A. A comprehensive parameter study of the jet/environment interaction has been performed and synthetic light curves are confronted with the observational data. The thermal emission in our models originates from the interaction between the jet and the hydrogen envelope ejected during the neutron star/He core merger. We find that the lack of a classical afterglow and the accompanying thermal emission in BBD-GRBs can be explained by the interaction of an ultrarelativistic jet with a toroidally shaped ejecta whose axis coincides with the binary rotation axis. The spectral inversion and reddening happening at about 2 d in GRB 101225A can be related to the time at which the massive shell ejected in an early phase of the common envelope evolution of the progenitor system is completely ablated by the ultrarelativistic jet.

An efficient implementation of flux formulae in multidimensional relativistic hydrodynamical codes

Abstract We derive and analyze a simplified formulation of the numerical viscosity terms appearing in the expression of the numerical fluxes associated to several High-Resolution Shock-Capturing schemes. After some algebraic preprocessing, we give explicit expressions for the numerical viscosity terms of two of the most widely used flux formulae, which implementation saves computational time in multidimensional simulations of relativistic flows. Additionally, such treatment explicitely cancels and factorizes a number of terms helping to damp the growing of round-off errors. We have checked the performance of our formulation running a 3D relativistic hydrodynamical code to solve a standard test-bed problem and found that the improvement in efficiency is of high practical interest in numerical simulations of relativistic flows in Astrophysics.

On the maximum magnetic field amplification by the magnetorotational instability in core-collapse supernovae

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.