Synchrotron radiation is commonly observed in connection with shocks of different velocities, ranging from relativistic shocks associated with active galactic nuclei, gamma-ray bursts or microquasars to weakly- or non-relativistic flows as those obse
rved in supernova remnants. Recent observations of synchrotron emission in protostellar jets are important not only because they extend the range over which the acceleration process works, but also because they allow to determine the jet and/or interstellar magnetic field structure, thus giving insights on the jet ejection and collimation mechanisms. In this paper, we compute for the first time polarized (synchrotron) and non polarized (thermal X-ray) synthetic emission maps from axisymmetrical simulations of magnetized protostellar jets. We consider models with different jet velocities and variability, as well as toroidal or helical magnetic field. Our simulations show that variable, low-density jets with velocities $sim$ 1000 km s$^{-1}$ and $sim$ 10 times lighter than the environment can produce internal knots with significant synchrotron emission, and thermal X-rays in the shocked region of the leading bow shock moving in a dense medium. While models with a purely toroidal magnetic field show a very large degree of polarization, models with helical magnetic field show lower values and a decrease of the degree of polarization, in agreement with observations of protostellar jets.
In this article we develop a numerical scheme to deal with interfaces between touching numerical grids when solving the second-order wave equation. We show that it is possible to implement an interface scheme of penalty type for the second-order wave
equation, similar to the ones used for first-order hyperbolic and parabolic equations, and the second-order scheme used by Mattsson et al (2008). These schemes, known as SAT schemes for finite difference approximations and penalties for spectral ones, and ours share similar properties but in our case one needs to pass at the interface a smaller amount of data than previously known schemes. This is important for multi-block parallelizations in several dimensions, for it implies that one obtains the same solution quality while sharing among different computational grids only a fraction of the data one would need for a comparable (in accuracy) SAT or Mattsson et al.s scheme. The semi-discrete approximation used here preserves the norm and uses standard finite-difference operators satisfying summation by parts. For the time integrator we use a semi-implicit IMEX Runge-Kutta method. This is crucial, since the explicit Runge-Kutta method would be impractical given the severe restrictions that arise from the stiff parts of the equations.
Context: We integrate the 2D MHD ideal equations of a straight slab to simulate observational results associated with fundamental sausage trapped modes. Aims: Starting from a non-equilibrium state with a dense chromospheric layer, we analyse the evol
ution of the internal plasma dynamics of magnetic loops, subject to line-tying boundary conditions, and with the coronal parameters described in Asai et al. (2001) and Melnikov et al. (2002) to investigate the onset and damping of sausage modes. Methods: To integrate the equations we used a high resolution shock-capturing (HRSC) method specially designed to deal appropriately with flow discontinuities. Results: Due to non-linearities and inhomogeneities, pure modes are difficult to sustain and always occur coupled among them so as to satisfy, e.g., the line-tying constraint. We found that, in one case, the resonant coupling of the sausage fundamental mode with a slow one results in a non-dissipative damping of the former. Conclusions: In scenarios of thick and dense loops, where the analytical theory predicts the existence of fundamental trapped sausage modes, the coupling of fast and slow quasi-periodic modes -with a node at the center of the longitudinal speed- occur contributing to the damping of the fast mode. If a discontinuity in the total pressure between the loop and the corona is assumed, a fundamental fast sausage transitory leaky regime is spontaneously produced and an external compressional Alfven wave takes away the magnetic energy.
