Relativistic Hydrodynamics and Spectral Evolution of GRB Jets

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In this thesis we study the progenitor systems of long gamma-ray bursts (GRBs) using numerical models of their dynamics and the electromagnetic emission. Of all the possible classes of events, we focus on those showing a prominent component of thermal emission, which might be generated due to the interaction of a relativistic jet with the medium into which it is propagating. The main part of the thesis is devoted to modelling GRBs from two different clases of progenitors: ultra-long GRBs dominated by blackbody emission and GRBs associated with core-collapse supernovae (SNe). The study of GRB jets and their radiative emission has been basically divided into two steps. First, the dynamical evolution of relativistic jets can be simulated by means of multidimensional special relativistic hydrodynamic simulations which have been performed with the MRGENESIS code. Second, the synthetic emission from such jets is computed with the relativistic radiative transfer code SPEV in a post-processing stage assuming different radiative processes in which we follow the temporal and spectral evolution of the emitted radiation. An instrumental part of this project consisted in extending SPEV to include thermal processes, such as thermal bremsstrahlung, in order to account for the thermal signal that may arise in some GRBs. In the first part of this thesis, we extend an existing theoretical model to explain the class of blackbody-dominated GRBs (BBD-GRBs), i.e., long lasting events characterized by the presence of a notable thermal component trailing the GRB prompt emission, and a rather weak traditional afterglow. GRB 101225A, the "Christmas burst", is the most prominent member of this class. It has been suggested that BBD-GRBs could result from the merger of a binary system formed by a neutron star and the Helium core of an evolved, massive star. We model in 2D the propagation of ultrarelativistic jets through the environments created by such mergers. We outline the most relevant dynamical details of the jet propagation and connect them to the generation of thermal radiation in GRB events akin to that of the Christmas burst. A comprehensive parameter study of the jet/environment interaction has been performed and synthetic light curves are confronted with the observational data. The thermal emission in our models originates from the interaction between the jet and the hydrogen envelope ejected during the neutron star/He core merger. We find that the lack of a classical afterglow and the accompanying thermal emission in BBD-GRBs can be explained by the interaction of an ultrarelativistic jet with a toroidally shaped ejecta whose axis coincides with the binary rotation axis. We also find that the synchrotron emission of the forward shock of the jet is dominant during the early phases of the evolution, along which that shock is still moderately relativistic. The contribution of the reverse shock is of the same magnitude as that of the forward shock during the first 80 min after the GRB. Later, it quickly fades because the jet/environment interaction chokes the ultrarelativistic jet beam and effectively dumps the reverse shock. We highlight that, in agreement with observations, we obtain rather flat light curves during the first 2 days after the GRB, and a spectral evolution consistent with the observed reddening of the system. Besides, we obtain that this spectral inversion and reddening happening at about 2 days in the Christmas burst can be related to the time at which the massive shell, ejected in an early phase of the common-envelope evolution of the progenitor system, is completely ablated by the ultrarelativistic jet. In the second part of this thesis, we study more canonical progenitor systems of GRBs, namely single massive stars on the brink of collapse. Motivated by the many associations of GRBs with energetic SN explosions, we study the propagation of relativistic jets within the progenitor star and the circumstellar medium. Particular attention is paid to the interaction between the jets and a SN shock wave launched briefly before the jets start to propagate. We have followed the dynamical evolution in one spatial dimension (1D) of the SN ejecta alone. Employing 2D axisymmetric relativistic hydrodynamic simulations we have explored the dynamical evolution of jets running into the medium left behind by the SN shock. For completeness, we have studied also the case in which no SN has formed. Based on analytic considerations and verified with an extensive set of simulations, we have estimated a threshold intrinsic jet luminosity, L_j^{thr}. For the stellar model under consideration here it is L_j^{thr} ≳ 1E49 erg s^{-1}. The observed equivalent isotropic ɣ-ray luminosity, L_{iso,ɣ} ≃ 4 ϵ_ɣ L_j / θ_{BO}^2, crucially depends on the jet opening angle after breakout, θ_{BO}, and on the efficiency in converting the intrinsic jet luminosity into ɣ-radiation, ϵ_ɣ. Highly energetic jets can produce low-luminosity events if either their opening angle after the breakout is large, which is found in our models, or if the conversion efficiency of kinetic and internal energy into radiation is low enough. Beyond these theoretical analysis, we show how the presence of a SN shock wave modifies the jet propagation. One of the main goals of this chapter was studying the emission with SPEV at the breakout of the jet or the SN ejecta. However this part suffered from technical problems, in particular excessive numerical diffusion caused by a lack of numerical resolution. Due to computing time restrictions, we could not properly obtain long-time light curves and spectra and could only compute the thermal emission. Therefore, our conclusions have to be considered preliminary. We have obtained rather low luminosities inconsistent with previous calculations in the literature. We find that the SN flash of our models is ≲ 1000 times dimmer than that of one of the prototype examples of GRB/SNe (GRB 060218/SN 2006aj) or X-ray flashes (XRF) associated to SNe (XRF 080109/SN 2008D). However, observations of GRB/SNe show heterogeneous properties, with cases in which the bolometric luminosity is orders of magnitude smaller than in the previous examples. Besides, X-ray peak times of ~10 s are theoretically expected for compact WR progenitors. Both facts, make our models partly consistent with the existing phenomenology. From the analysis of the asymptotic Lorentz factor in the whole cavity blown by the different jets, we foresee that the high-energy transients we may produce will be more similar to XRF than to GRBs. Indeed, our jet events display their peak specific luminosity in the extreme UV band, rather than in the X-ray band, and clearly a fainter ɣ-ray luminosity (~2‒4 orders of magnitude smaller than in the X-ray band). Finally, we find that the very early observational signature of our different jet models (prior to the luminosity peak) below the ɣ-ray band is very similar comparing jets with the same intrinsic luminosity. This happens in spite of the substantially different hydrodynamic evolution of models which either interact with a pre-existing SN ejecta or propagate through the unmodified stellar progenitor. We expect this similarity lasting for time scales of the order of the light-crossing time of the transversal size of the emitting region (~1‒2 s). Thus, we shall continue our models for even longer evolutionary times and, as argued above, employing a finer grid resolution.
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