We present the results of two-dimensional magnetohydrodynamical numerical simulations of relativistic magnetic reconnection, with particular emphasis on the dynamics of Petschek-type configurations with high Lundquist numbers, S ~ 10^5-10^8. The nume
rical scheme adopted, allowing for unprecedented accuracy for this type of calculations, is based on high order finite volume and discontinuous Galerkin methods as recently proposed by Dumbser & Zanotti (2009). The possibility of producing high Lorentz factors is discussed, by studying the effects produced on the dynamics by different magnetization and resistivity regimes. We show that Lorentz factors close to ~4 can be produced for a plasma magnetization parameter sigma=20. Moreover, we find that the Sweet-Parker layers are unstable, generating secondary magnetic islands, but only for S>S_c~10^8, much larger than what is reported in the Newtonian regime.
We show the results of two dimensional general relativistic inviscid and isothermal hydrodynamical simulations comparing the behavior of co-rotating (with respect to the black hole rotation) and counter-rotating circumbinary quasi-Keplerian discs in
the post merger phase of a supermassive binary black hole system. While confirming the spiral shock generation within the disc due to the combined effects of mass loss and recoil velocity of the black hole, we find that the maximum luminosity of counter-rotating discs is a factor ~(2-12) higher than in the co-rotating case, depending on the spin of the black hole. On the other hand, the luminosity peak happens ~10 days later with respect to the co-rotating case, for a binary with a total mass M~10^6 M_odot. Although the global dynamics of counter-rotating discs in the post merger phase of a merging event is very similar to that for co-rotating discs, an important difference has been found. In fact, increasing the spin of the central black hole produces more luminous co-rotating discs while less luminous counter-rotating ones.
We investigate the conditions for radio emission in rotating and oscillating magnetars, by focusing on the main physical processes determining the position of their death-lines in the P-dot{P} diagram, i.e. of those lines that separate the regions wh
ere the neutron star may be radio-loud or radio-quiet. After using the general relativistic expression for the electromagnetic scalar potential in the magnetar magnetosphere, we find that larger compactness parameters of the star as well as larger inclination angles between the rotation axis and the magnetic moment produce death-lines well above the majority of known magnetars. This is consistent with the observational evidence of no regular radio emission from the magnetars in the frequency range typical for the ordinary pulsars. On the contrary, when oscillations of the magnetar are taken into account, the death-lines shift downward and the conditions necessary for the generation of radio emission in the magnetosphere are met. Present observations showing a close connection between the burst activity of magnetars and the generation of the radio emission in the magnetar magnetosphere are naturally accounted for within our interpretation.
We present the results of two-dimensional and three-dimensional magnetohydrodynamical numerical simulations of relativistic magnetic reconnection, with particular emphasis on the dynamics of the plasma in a Petschek-type configuration with high Lundq
uist numbers, Ssim 10^5-10^8. The numerical scheme adopted, allowing for unprecedented accuracy for this type of calculations, is based on high order finite volume and discontinuous Galerkin methods as recently proposed by citet{Dumbser2009}. The possibility of producing high Lorentz factors is discussed, showing that Lorentz factors close to sim 4 can be produced for a plasma parameter sigma_m=20. Moreover, we find that the Sweet-Parker layers are unstable, generating secondary magnetic islands, but only for S > S_c = 10^8, much larger than what is reported in the Newtonian regime. Finally, the effects of a mildly anisotropic Ohm law are considered in a configuration with a guide magnetic field. Such effects produce only slightly faster reconnection rates and Lorentz factors of about 1% larger with respect to the perfectly isotropic Ohm law.
We study the magnetosphere of a slowly rotating magnetized neutron star subject to toroidal oscillations in the relativistic regime. Under the assumption of a zero inclination angle between the magnetic moment and the angular momentum of the star, we
analyze the Goldreich-Julian charge density and derive a second-order differential equation for the electrostatic potential. The analytical solution of this equation in the polar cap region of the magnetosphere shows the modification induced by stellar toroidal oscillations on the accelerating electric field and on the charge density. We also find that, after decomposing the oscillation velocity in terms of spherical harmonics, the first few modes with $m=0,1$ are responsible for energy losses that are almost linearly dependent on the amplitude of the oscillation and that, for the mode $(l,m)=(2,1)$, can be a factor $sim8$ larger than the rotational energy losses, even for a velocity oscillation amplitude at the star surface as small as $eta=0.05 Omega R$. The results obtained in this paper clarify the extent to which stellar oscillations are reflected in the time variation of the physical properties at the surface of the rotating neutron star, mainly by showing the existence of a relation between $Pdot{P}$ and the oscillation amplitude. Finally, we propose a qualitative model for the explanation of the phenomenology of intermittent pulsars in terms of stellar oscillations that are periodically excited by star glitches.
We investigate the dynamics of a circumbinary disc that responds to the loss of mass and to the recoil velocity of the black hole produced by the merger of a binary system of supermassive black holes. We perform the first two-dimensional general rela
tivistic hydrodynamics simulations of textit{extended} non-Keplerian discs and employ a new technique to construct a shock detector, thus determining the precise location of the shocks produced in the accreting disc by the recoiling black hole. In this way we can study how the properties of the system, such as the spin, mass and recoil velocity of the black hole, affect the mass accretion rate and are imprinted on the electromagnetic emission from these sources. We argue that the estimates of the bremsstrahlung luminosity computed without properly taking into account the radiation transfer yield cooling times that are unrealistically short. At the same time we show, through an approximation based on the relativistic isothermal evolution, that the luminosity produced can reach a peak value above $L simeq 10^{43} {rm erg/s} $ at about $sim 30,{rm d}$ after the merger of a binary with total mass $Msimeq 10^6 M_odot$ and persist for several days at values which are a factor of a few smaller. If confirmed by more sophisticated calculations such a signal could indeed lead to an electromagnetic counterpart of the merger of binary black-hole system.
In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space dimensions. The non
linear system under consideration is purely hyperbolic and contains a source term, the one for the evolution of the electric field, that becomes stiff for low values of the resistivity. For the spatial discretization we propose to use high order $PNM$ schemes as introduced in cite{Dumbser2008} for hyperbolic conservation laws and a high order accurate unsplit time discretization is achieved using the element-local space-time discontinuous Galerkin approach proposed in cite{DumbserEnauxToro} for one-dimensional balance laws with stiff source terms. The divergence free character of the magnetic field is accounted for through the divergence cleaning procedure of Dedner et al. cite{Dedneretal}. To validate our high order method we first solve some numerical test cases for which exact analytical reference solutions are known and we also show numerical convergence studies in the stiff limit of the RRMHD equations using $PNM$ schemes from third to fifth order of accuracy in space and time. We also present some applications with shock waves such as a classical shock tube problem with different values for the conductivity as well as a relativistic MHD rotor problem and the relativistic equivalent of the Orszag-Tang vortex problem. We have verified that the proposed method can handle equally well the resistive regime and the stiff limit of ideal relativistic MHD. For these reasons it provides a powerful tool for relativistic astrophysical simulations involving the appearance of magnetic reconnection.
