Stationary state after a quench to the Lieb-Liniger from rotating BECs

We study long-time dynamics of a bosonic system after suddenly switching on repulsive delta-like interactions. As initial states, we consider two experimentally relevant configurations: a rotating BEC and two counter-propagating BECs with opposite momentum, both on a ring. In the first case, the rapidity distribution function for the stationary state is derived analytically and it is given by the distribution obtained for the same quench starting from a BEC, shifted by the momentum of each boson. In the second case, the rapidity distribution function is obtained numerically for generic values of repulsive interaction and initial momentum. The significant differences for the case of large versus small quenches are discussed.Comment: 28 pages, 6 figures; v2) added proof and clarifications in the appendix; matches published versio

Polarization properties of turbulent synchrotron bubbles: an approach based on Chandrasekhar-Kendall functions

Synchrotron emitting bubbles arise when the outflow from a compact relativistic engine, either a Black Hole or a Neutron Star, impacts on the environment. The emission properties of synchrotron radiation are widely used to infer the dynamical properties of these bubbles, and from them the injection conditions of the engine. Radio polarization offers an important tool to investigate the level and spectrum of turbulence, the magnetic field configuration, and possibly the degree of mixing. Here we introduce a formalism based on Chandrasekhar-Kendall functions that allows us to properly take into account the geometry of the bubble, going beyond standard analysis based on periodic cartesian domains. We investigate how different turbulent spectra, magnetic helicity and particle distribution function, impact on global properties that are easily accessible to observations, even at low resolution, and we provide fitting formulae to relate observed quantities to the underlying magnetic field structure.Comment: 10 pages, 8 figures, to be published in MNRA

Modeling Radio Circular Polarization in the Crab Nebula

In this paper we present, for the first time, simulated maps of the circularly polarized synchrotron emission from the Crab nebula, using multidimensional state of the art models for the magnetic field geometry. Synchrotron emission is the signature of non-thermal emitting particles, typical of many high-energy astrophysical sources, both Galactic and extra-galactic ones. Its spectral and polarization properties allow us to infer key informations on the particles distribution function and magnetic field geometry. In recent years our understanding of pulsar wind nebulae has improved substantially thanks to a combination of observations and numerical models. A robust detection or non-detection of circular polarization will enable us to discriminate between an electron-proton plasma and a pair plasma, clarifying once for all the origin of the radio emitting particles, setting strong constraints on the pair production in pulsar magnetosphere, and the role of turbulence in the nebula. Previous attempts at measuring the circular polarization have only provided upper limits, but the lack of accurate estimates, based on reliable models, makes their interpretation ambiguous. We show here that those results are above the expected values, and that current polarimetric tecniques are not robust enough for conclusive result, suggesting that improvements in construction and calibration of next generation radio facilities are necessary to achieve the desired sensitivity.Comment: 5 pages, 2 figures, accepted for publication in MNRA

GRMHD in axisymmetric dynamical spacetimes: the X-ECHO code

We present a new numerical code, X-ECHO, for general relativistic magnetohydrodynamics (GRMHD) in dynamical spacetimes. This is aimed at studying astrophysical situations where strong gravity and magnetic fields are both supposed to play an important role, such as for the evolution of magnetized neutron stars or for the gravitational collapse of the magnetized rotating cores of massive stars, which is the astrophysical scenario believed to eventually lead to (long) GRB events. The code is based on the extension of the Eulerian conservative high-order (ECHO) scheme [Del Zanna et al., A&A 473, 11 (2007)] for GRMHD, here coupled to a novel solver for the Einstein equations in the extended conformally flat condition (XCFC). We fully exploit the 3+1 Eulerian formalism, so that all the equations are written in terms of familiar 3D vectors and tensors alone, we adopt spherical coordinates for the conformal background metric, and we consider axisymmetric spacetimes and fluid configurations. The GRMHD conservation laws are solved by means of shock-capturing methods within a finite-difference discretization, whereas, on the same numerical grid, the Einstein elliptic equations are treated by resorting to spherical harmonics decomposition and solved, for each harmonic, by inverting band diagonal matrices. As a side product, we build and make available to the community a code to produce GRMHD axisymmetric equilibria for polytropic relativistic stars in the presence of differential rotation and a purely toroidal magnetic field. This uses the same XCFC metric solver of the main code and has been named XNS. Both XNS and the full X-ECHO codes are validated through several tests of astrophysical interest.Comment: 18 pages, 9 figures, accepted for publication in A&

Magnetars and Gamma Ray Bursts

In the last few years, evidences for a long-lived and sustained engine in Gamma Ray Bursts (GRBs) have increased the attention to the so called millisecond-magnetar model, as a competitive alternative to the standard collapsar scenario. I will review here the key aspects of the {\it millisecond magnetar} model for Long Duration Gamma Ray Bursts (LGRBs). I will briefly describe what constraints, present observations put on any engine model, both in term of energetic, outflow properties, and the relation with the associated Supernova (SN). For each of these I will show how the millisecond magnetar model satisfies the requirements, what are the limits of the model, how can it be further tested, and what observations might be used to discriminate against it. I will also discuss numerical results that show the importance of the confinement by the progenitor star in explaining the formation of a collimated outflow, how a detailed model for the evolution of the central engine can be built, and show that a wide variety of explosive events can be explained by different magnetar parameters. I will conclude with a suggestion that magnetars might be at the origin of the Extended Emission (EE) observed in a significant fraction of Short GRBs.Comment: 8 pages; to appear in Proceedings of IAU 279 "Death of Massive Stars: Supernovae and Gamma-ray Bursts