The exact solution of the Riemann problem with non-zero tangential velocities in relativistic hydrodynamics

We have generalised the exact solution of the Riemann problem in special relativistic hydrodynamics for arbitrary tangential flow velocities. The solution is obtained by solving the jump conditions across shocks plus an ordinary differential equation arising from the self-similarity condition along rarefaction waves, in a similar way as in purely normal flow. The dependence of the solution on the tangential velocities is analysed, and the impact of this result on the development of multidimensional relativistic hydrodynamic codes (of Godunov type) is discussed.Comment: 26 pages, 4 figures. Accepted for publication in Journal of Fluid Mechanic

CCOs and the hidden magnetic field scenario

CCOs are X-ray sources lying close the center of supernova remnants, with inferred values of the surface magnetic fields significantly lower (less than about 1e11 G) than those of standard pulsars. In this paper, we revise the hidden magnetic field scenario, presenting the first 2D simulations of the submergence and reemergence of the magnetic field in the crust of a neutron star. A post-supernova accretion stage of about 1e-4-1e-3 solar masses over a vast region of the surface is required to bury the magnetic field into the inner crust. When accretion stops, the field reemerges on a typical timescale of 1-100 kyr, depending on the submergence conditions. After this stage, the surface magnetic field is restored close to its birth values. A possible observable consequence of the hidden magnetic field is the anisotropy of the surface temperature distribution, in agreement with observations of several of these sources. We conclude that the hidden magnetic field model is viable as alternative to the anti-magnetar scenario, and it could provide the missing link between CCOs and the other classes of isolated neutron stars.Comment: 7 pages, 7 figures, MNRA

Hyperbolic character of the angular moment equations of radiative transfer and numerical methods

We study the mathematical character of the angular moment equations of radiative transfer in spherical symmetry and conclude that the system is hyperbolic for general forms of the closure relation found in the literature. Hyperbolicity and causality preservation lead to mathematical conditions allowing to establish a useful characterization of the closure relations. We apply numerical methods specifically designed to solve hyperbolic systems of conservation laws (the so-called Godunov-type methods), to calculate numerical solutions of the radiation transport equations in a static background. The feasibility of the method in any kind of regime, from diffusion to free-streaming, is demonstrated by a number of numerical tests and the effect of the choice of the closure relation on the results is discussed.Comment: 37 pags, 12 figures, accepted for publication in MNRA

Triggering magnetar outbursts in 3D force-free simulations

In this letter, we present the first 3D force-free general relativity simulations of the magnetosphere dynamics related to the magnetar outburst/flare phenomenology. Starting from an initial dipole configuration, we adiabatically increase the helicity by twisting the footprints of a spot on the stellar surface and follow the succession of quasi-equilibrium states until a critical twist is reached. Twisting beyond that point triggers instabilities that results in the rapid expansion of magnetic field lines, followed by reconnection, as observed in previous axi-symmetric simulations. If the injection of magnetic helicity goes on, the process is recurrent, periodically releasing a similar amount of energy, of the order of a few % of the total magnetic energy. From our current distribution, we estimate the local temperature assuming that dissipation occurs mainly in the highly resistive outermost layer of the neutron star. We find that the temperature smoothly increases with injected twist, being larger for spots located in the tropical regions than in polar regions, and rather independent of their sizes. After the injection of helicity ceases, the magnetosphere relaxes to a new stable state, in which the persistent currents maintain the footprints area slightly hotter than before the onset of the instability.Comment: 6 pages, 5 figure

Modelling of the Surface Emission of the Low-Magnetic Field Magnetar SGR 0418+5729

We perform a detailed modelling of the post-outburst surface emission of the low magnetic field magnetar SGR 0418+5729. The dipolar magnetic field of this source, B=6x10^12 G estimated from its spin-down rate, is in the observed range of magnetic fields for normal pulsars. The source is further characterized by a high pulse fraction and a single-peak profile. Using synthetic temperature distribution profiles, and fully accounting for the general-relativistic effects of light deflection and gravitational redshift, we generate synthetic X-ray spectra and pulse profiles that we fit to the observations. We find that asymmetric and symmetric surface temperature distributions can reproduce equally well the observed pulse profiles and spectra of SGR 0418. Nonetheless, the modelling allows us to place constraints on the system geometry (i.e. the angles $\psi$ and $\xi$ that the rotation axis makes with the line of sight and the dipolar axis, respectively), as well as on the spot size and temperature contrast on the neutron star surface. After performing an analysis iterating between the pulse profile and spectra, as done in similar previous works, we further employed, for the first time in this context, a Markov-Chain Monte-Carlo approach to extract constraints on the model parameters from the pulse profiles and spectra, simultaneously. We find that, to reproduce the observed spectrum and flux modulation: (a) the angles must be restricted to $65\deg < \psi+\xi < 125\deg$ or $235\deg < \psi+\xi <295\deg$; (b) the temperature contrast between the poles and the equator must be at least a factor of $\sim6$, and (c) the size of the hottest region ranges between 0.2-0.7 km (including uncertainties on the source distance). Last, we interpret our findings within the context of internal and external heating models.Comment: 13 pages, 10 figures. Accepted for publication in MNRA

Evolution of Proto-Neutron Stars with Quarks

Neutrino fluxes from proto-neutron stars with and without quarks are studied. Observable differences become apparent after 10--20 s of evolution. Sufficiently massive stars containing negatively-charged, strongly interacting, particles collapse to black holes during the first minute of evolution. Since the neutrino flux vanishes when a black hole forms, this is the most obvious signal that quarks (or other types of strange matter) have appeared. The metastability timescales for stars with quarks are intermediate between those containing hyperons and kaon condensates.Comment: 4 pages including 4 figures. Version with minor revisions. To be published in Physical Review Letter