We examine the propagation of 2-dimensional relativistic jets through the stellar progenitor in the collapsar model for gamma-ray bursts. In agreement with previous studies, we find that relativistic jets are collimated by their passage through the stellar mantle. Interaction of these jets with the star and their own cocoons also causes mixing that sporadically decelerates the flow. We speculate that this mixing instability is chiefly responsible for the variable Lorentz factor needed in the internal shock model and for the complex light curves seen in many GRBs. In all cases studied, the jet is shocked deep inside the star following a brief period of adiabatic expansion. The jet that finally emerges from the star thus has a moderate Lorentz factor, modulated by mixing, and a very large internal energy. In a second series of calculations, we follow the escape of that sort of jet. Because of the large ratio of internal to kinetic energy in both the jet and its cocoon, the opening angle of the final jet is significantly greater than at breakout. A small amount of material emerges at large angles, but with a Lorentz factor still sufficiently large to make a weak GRB. This leads us to propose a "unified model" in which a variety of high energy transients, ranging from x-ray flashes to "classic" GRBs, may be seen depending upon the angle at which a standard collapsar is observed. We also speculate that the breakout of a relativistic jet and its collision with the stellar wind will produce a brief transient with properties similar to the class of "short-hard" GRBs. Implications of our calculations for GRB light curves, the luminosity-variability relation, and the GRB-supernova association are also discussed. (Abridged)Comment: 40 pages, 16 figures, To appear in vol. 586, ApJ, March 20, 200

The compact remnants of core collapse supernovae - neutron stars and black holes - have properties that reflect both the structure of their stellar progenitors and the physics of the explosion. In particular, the masses of these remnants are sensitive to the density structure of the presupernova star and to the explosion energy. To a considerable extent, the final mass is determined by the ``fallback'', during the explosion, of matter that initially moves outwards, yet ultimately fails to escape. We consider here the simulated explosion of a large number of massive stars (10 to 100 \Msun) of Population I (solar metallicity) and III (zero metallicity), and find systematic differences in the remnant mass distributions. As pointed out by Chevalier(1989), supernovae in more compact progenitor stars have stronger reverse shocks and experience more fallback. For Population III stars above about 25 \Msun and explosion energies less than $1.5 \times 10^{51}$ erg, black holes are a common outcome, with masses that increase monotonically with increasing main sequence mass up to a maximum hole mass of about 35 \Msun. If such stars produce primary nitrogen, however, their black holes are systematically smaller. For modern supernovae with nearly solar metallicity, black hole production is much less frequent and the typical masses, which depend sensitively on explosion energy, are smaller. We explore the neutron star initial mass function for both populations and, for reasonable assumptions about the initial mass cut of the explosion, find good agreement with the average of observed masses of neutron stars in binaries. We also find evidence for a bimodal distribution of neutron star masses with a spike around 1.2 \Msun (gravitational mass) and a broader distribution peaked around 1.4 \Msun.Comment: Accepted for publication in Ap

A pulsar wind nebula inside a supernova remnant provides a unique insight into the properties of the central neutron star, the relativistic wind powered by its loss of rotational energy, its progenitor supernova, and the surrounding environment. In this paper, we present a new semi-analytic model for the evolution of such a pulsar wind nebula. This model couples the dynamical and radiative evolution of the pulsar wind nebulae, traces the evolution of the pulsar wind nebulae throughout the lifetime of the supernova remnant produced by the progenitor explosion, and predicts both the dynamical (e.g. radius and expansion velocity) and radiative (radio to TeV γ-ray spectrum) properties of the pulsar wind nebula during this period. As a result, it is uniquely qualified for using the observed properties of a pulsar wind nebula in order to constrain the physical characteristics of the neutron star, pulsar wind, progenitor supernova, and surrounding interstellar medium. We also discuss the expected evolution for a particular set of these parameters, and show that it reproduced the large spectral break observed in radio and X-ray observations of many young pulsar wind nebulae, and the low break frequency, low radio luminosity and high TeV γ-ray luminosity, and high magnetization observed for several older pulsar wind nebulae. The predicted spectrum of this pulsar wind nebula also contains spectral features during different phases of its evolution detectable with new radio and γ-ray observing facilities such as the Extended Very Large Array and the Fermi Gamma-ray Space Telescope. Finally, this model has implications for determining if pulsar wind nebulae can inject a sufficient number of energetic electrons and positrons into the surrounding interstellar medium to explain the recent measurements of the cosmic ray positron fraction by PAMELA and the cosmic ray lepton spectrum by ATIC and HESS.

New two-and three-dimensional calculations are presented of relativistic jet propagation and break out in massive Wolf-Rayet stars. Such jets are thought to be responsible for gamma-ray bursts. As it erupts, the highly relativistic jet core (3 to 5 ; À k 100) is surrounded by a cocoon of less energetic, but still moderately relativistic ejecta (À $ 15) that expands and becomes visible at larger polar angles ($10 ). These less energetic ejecta may be the origin of X-ray flashes and other high-energy transients, which will be visible to a larger fraction of the sky, albeit to a shorter distance than common gamma-ray bursts. Jet stability is also examined in three-dimensional calculations. If the jet changes angle by more than 3 in several seconds, it will dissipate, producing a broad beam with inadequate Lorentz factor to make a common gamma-ray burst. This may be an alternate way to make X-ray flashes.

Direct multi-dimensional numerical simulation is the most reliable approach for calculating the fluid dynamics and observational signatures of relativistic jets in gamma-ray bursts (GRBs). We present a two-dimensional relativistic hydrodynamic simulation of a GRB outflow during the afterglow phase, which uses the fifth-order weighted essentially non-oscillatory scheme and adaptive mesh refinement. Initially, the jet has a Lorentz factor of 20. We have followed its evolution up to 150 years. Using the hydrodynamic data, we calculate synchrotron radiation based upon standard afterglow models and compare our results with previous analytic work. We find that the sideways expansion of a relativistic GRB jet is a very slow process and previous analytic works have overestimated its rate. In our computed lightcurves, a very sharp jet break is seen and the post-break lightcurves are steeper than analytic predictions. We find that the jet break in GRB afterglow lightcurves is mainly caused by the missing flux when the edge of the jet is observed. The outflow becomes nonrelativistic at the end of the Blandford-McKee phase. But it is still highly nonspherical, and it takes a rather long time for it to become a spherical Sedov-von Neumann-Taylor blast wave. We find that the late-time afterglows become increasingly flatter over time. But we disagree with the common notion that there is a sudden flattening in lightcurves due to the transition into the Sedov-von Neumann-Taylor solution. We have also found that there is a bump in lightcurves at very late times (∼ 1000 days) due to radiation from the counter jet. We speculate that such a counter jet bump might have already been observed in GRB 980703.

We have developed a new computer code, RAM, to solve the conservative equations of special relativistic hydrodynamics (SRHD) using adaptive mesh refinement (AMR) on parallel computers. We have implemented a characteristic-wise, finite difference, weighted essentially non-oscillatory (WENO) scheme using the full characteristic decomposition of the SRHD equations to achieve fifth-order accuracy in space. For time integration we use the method of lines with a third-order total variation diminishing (TVD) Runge-Kutta scheme. We have also implemented fourth and fifth order RungeKutta time integration schemes for comparison. The implementation of AMR and parallelization is based on the FLASH code. RAM is modular and includes the capability to easily swap hydrodynamics solvers, reconstruction methods and physics modules. In addition to WENO we have implemented a finite volume module with the piecewise parabolic method (PPM) for reconstruction and the modified Marquina approximate Riemann solver to work with TVD Runge-Kutta time integration. We examine the difficulty of accurately simulating shear flows in numerical relativistic hydrodynamics codes. We show that under-resolved simulations of simple test problems with transverse velocity components produce incorrect results and demonstrate the ability of RAM to correctly solve these problems. RAM has been tested in one, two and three dimensions and in Cartesian, cylindrical and spherical coordinates. We have demonstrated fifth-order accuracy for WENO in one and two dimensions and performed detailed comparison with other schemes for which we show significantly lower convergence rates. Extensive testing is presented demonstrating the ability of RAM to address challenging open questions in relativistic astrophysics.

Starting as highly relativistic collimated jets, gamma-ray burst outflows gradually decellerate and become non-relativistic spherical blast waves. Although detailed analytical solutions describing the afterglow emission received by an on-axis observer during both the early and late phases of the outflow evolution exist, a calculation of the received flux during the intermediate phase and for an off-axis observer requires either a more simplified analytical model or direct numerical simulations of the outflow dynamics. In this paper we present light curves for off-axis observers covering the long-term evolution of the blast wave, calculated from a high resolution two-dimensional relativistic hydrodynamics simulation using a synchrotron radiation model. We compare our results to earlier analytical work and calculate the consequence of the observer angle with respect to the jet axis both for the detection of orphan afterglows and for jet break fits to the observational data. We find that observable jet breaks can be delayed for up to several weeks for off-axis observers, potentially leading to overestimation of the beaming corrected total energy. When using our off-axis light curves to create synthetic Swift X-ray data, we find that jet breaks are likely to remain hidden in the data. We also confirm earlier results in the literature finding that only a very small number of local Type Ibc supernovae can harbor an orphan afterglow.

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