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

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.

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