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Register a new userTime-implicit schemes in fluid dynamics? -- Their advantage in the regime of ultra-relativistic shock fronts
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Relativistic jets are intrinsic phenomena of active galactic nuclei (AGN) and quasars. They have been observed to also emanate from systems containing compact objects, such as white dwarfs, neutron stars and black hole candidates. The corresponding Lorentz factors, $Gamma$, were found to correlate with the compactness of the central objects. In the case of quasars and AGNs, plasmas with $Gamma$-factors larger than $8$ were detected. However, numerically consistent modelling of propagating shock-fronts with $Gamma geq 4$ is a difficult issue, as the non-linearities underlying the transport operators increase dramatically with $Gamma$, thereby giving rise to a numerical stagnation of the time-advancement procedure or alternatively they may diverge completely. In this paper, we present a unified numerical solver for modelling the propagation of one-dimensional shock fronts with high Lorentz factors. The numerical scheme is based on the finite-volume formulation with adaptive mesh refinement (AMR) and domain decomposition for parallel computation. It unifies both time-explicit and time-implicit numerical schemes within the framework of the pre-conditioned defect-correction iteration solution procedure. We find that time-implicit solution procedures are remarkably superior over their time-explicit counterparts in the very high $Gamma$-regime and therefore most suitable for consistent modelling of relativistic outflows in AGNs and micro-quasars.
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When galaxy clusters collide, they generate shock fronts in the hot intracluster medium. Observations of these shocks can provide valuable information on the merger dynamics and physical conditions in the cluster plasma, and even help constrain the nature of dark matter. To study shock fronts, one needs an X-ray telescope with high angular resolution (such as Chandra), and be lucky to see the merger from the right angle and at the right moment. As of this writing, only a handful of merger shock fronts have been discovered and confirmed using both X-ray imaging and gas temperature data -- those in 1E0657-56, A520, A754, and two fronts in A2146. A few more are probable shocks awaiting temperature profile confirmation -- those in A521, RXJ1314-25, A3667, A2744, and Coma. The highest Mach number is 3 in 1E0657-56, while the rest has M=1.6-2. Interestingly, all these relatively weak X-ray shocks coincide with sharp edges in their host clusters synchrotron radio halos (except in A3667, where it coincides with the distinct radio relic, and A2146, which does not have radio data yet). This is contrary to the common wisdom that weak shocks are inefficient particle accelerators, and may shed light on the mechanisms of relativistic electron production in astrophysical plasmas.
We investigate the symbiotic star BI Crucis through a comprehensive and self-consistent analysis of the spectra emitted in three different epochs: 60s, 70s, and late 80s. In particular, we would like to find out the physical conditions in the shocked nebula and in the dust shells, as well as their location within the symbiotic system, by exploiting both photometric and spectroscopic data from radio to UV. We suggest a model which, on the basis of optical imaging, emission line ratios and spectral energy distribution profile, is able to account for collision of the winds, formation of lobes and jets by accretion onto the WD, as well as for the interaction of the blast wave from a past, unrecorded outburst with the ISM. We have found that the spectra observed throughout the years show the marks of the different processes at work within BI Cru, perhaps signatures of a post-outburst evolution. We then call for new infrared and millimeter observations, potentially able to resolve the inner structure of the symbiotic nebula.
We have developed a one-dimensional code to solve ultra-relativistic hydrodynamic problems, using the Glimm method for an accurate treatment of shocks and contact discontinuities. The implementation of the Glimm method is based on an exact Riemann solver and van der Corput sampling sequence. In order to improve computational efficiency, the Glimm method is replaced by a finite differencing scheme in those regions where the fluid flow is sufficiently smooth. The accuracy and convergence of this hybrid method is investigated in tests involving planar, cylindrically and spherically symmetric flows that exhibit strong shocks and Lorentz factors of up to ~2000. This hybrid code has proven to be successful in simulating the interaction between a thin, ultra-relativistic, spherical shell and a low density stationary medium, a situation likely to appear in Gamma-Ray Bursts, supernovae explosions, pulsar winds and AGNs.
A class of explicit numerical schemes is developed to solve for the relativistic dynamics and spin of particles in electromagnetic fields, using the Lorentz-BMT equation formulated in the Clifford algebra representation of Baylis. It is demonstrated that these numerical methods, reminiscent of the leapfrog and Verlet methods, share a number of important properties: they are energy-conserving, volume-conserving and second order convergent. These properties are analysed empirically by benchmarking against known analytical solutions in constant uniform electrodynamic fields. It is demonstrated that the numerical error in a constant magnetic field remains bounded for long time simulations in contrast to the Boris pusher, whose angular error increases linearly with time. Finally, the intricate spin dynamics of a particle is investigated in a plane wave field configuration.
We present a formalism of the dynamics of internal shocks in relativistic jets where the source has a time-dependent injection velocity and mass-loss rate. The variation of the injection velocity produces a two-shock wave structure, the working surface, that moves along the jet. This new formalism takes into account the fact that momentum conservation is not valid for relativistic flows where the relativistic mass lost by radiation must be taken into account, in contrast to the classic regime. We find analytic solutions for the working surface velocity and radiated energy for the particular case of a step function variability of the injection parameters. We model two cases: a pulse of fast material and a pulse of slow material (with respect to the mean flow). Applying these models to gamma ray burst light curves, one can determine the ratio of the Lorentz factors gamma_2 / gamma_1 and the ratio of the mass-loss rates dot{m_2} / dot{m_1} of the upstream and downstream flows. As an example, we apply this model to the sources GRB 080413B and GRB 070318 and find the values of these ratios. Assuming a Lorentz factor gamma_1=100, we further estimate jet mass-loss rates between dot{m_1} ~ 10^{-5}-1 Msun.yr^{-1}. We also calculate the fraction of the injected mass lost by radiation. For GRB 070318 this fraction is ~7%. In contrast, for GRB 080413B this fraction is larger than 50%; in this case radiation losses clearly affect the dynamics of the internal shocks.
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