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

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&

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

Probing Klein tunneling through quantum quenches

We study the interplay between an inhomogeneous quantum quench of the external potential in a system of relativistic fermions in one dimension and the well-known Klein tunneling. We find that the large time evolution is characterized by particle production at a constant rate which we derive analytically. The produced particles can be physically interpreted according to a semiclassical picture and the state reached in the long time limit can be classified as a non-equilibrium-steady-state. Such a quantum quench can be used in order to observe macroscopic effects of Klein tunneling in transport, raising the possibility of an experimental implementation.Comment: 15 pages, 8 figure