GRB afterglows: deep Newtonian phase and its application

Gamma-ray burst afterglows have been observed for months or even years in a few cases. It deserves noting that at such late stages, the remnants should have entered the deep Newtonian phase, during which the majority of shock-accelerated electrons will no longer be highly relativistic. To calculate the afterglows, we must assume that the electrons obey a power-law distribution according to their kinetic energy, not simply the Lorentz factor.Comment: Poster at the 4th workshop "Gamma-Ray Bursts in the Afterglow Era" (Rome, 2004), accepted for publication in the proceedings. 4 pages, with 3 figures inserte

Beaming effects in GRBs and orphan afterglows

The overall dynamical evolution and radiation mechanism of $\gamma$-ray burst jets are briefly introduced. Various interesting topics concerning beaming in $\gamma$-ray bursts are discussed, including jet structures, orphan afterglows and cylindrical jets. The possible connection between $\gamma$-ray bursts and neutron star kicks is also addressed.Comment: 10 Pages, 4 figures, to appear in a special issue of ApSS. Oral report presented at "The Multiwavelength Approach to Unidentified Gamma-Ray Sources" (Hong Kong, June 1 - 4, 2004; Conference organizers: K.S. Cheng and G.E. Romero

Isothermal Shock Formation in Non-Equatorial Accretion Flows around Kerr Black Holes

We explore isothermal shock formation in non-equatorial, adiabatic accretion flows onto a rotating black hole, with possible application to some active galactic nuclei (AGNs). The isothermal shock jump conditions as well as the regularity condition, previously developed for one-dimensional (1D) flows in the equatorial plane, are extended to two-dimensional (2D), non-equatorial flows, to explore possible geometrical effects. The basic hydrodynamic equations with these conditions are self-consistently solved in the context of general relativity to explore the formation of stable isothermal shocks. We find that strong shocks are formed in various locations above the equatorial plane, especially around a rapidly-rotating black hole with the prograde flows (rather than a Schwarzschild black hole). The retrograde flows are generally found to develop weaker shocks. The energy dissipation across the shock in the hot non-equatorial flows above the cooler accretion disk may offer an attractive illuminating source for the reprocessed features, such as the iron fluorescence lines, which are often observed in some AGNs.Comment: 22 pages with 11 figures, presented at 5th international conference on high energy density laboratory astrophysics in Tucson, Arizona. accepted to Ap

Zero modes and charged Skyrmions in graphene bilayer

We show that the electric charge of the Skyrmion in the vector order parameters that characterize the quantum anomalous spin Hall state and the layer-antiferromagnet in a graphene bilayer is four and zero, respectively. The result is based on the demonstration that a vortex configuration in two broken symmetry states in bilayer graphene with the quadratic band crossing has the number of zero modes doubled relative to the single layer. The doubling can be understood as a result of Kramers' theorem implied by the "pseudo time reversal" symmetry of the vortex Hamiltonian. Disordering the quantum anomalous spin Hall state by Skyrmion condensation should produce a superconductor of an elementary charge 4e.Comment: 4+ pages, one table, one figure; (v2) improved pedagogy, new expression for the Pontryagin index derived, additional explanations; (v3) new and updated references, minor typos corrected, published versio

Beaming Effects in Gamma-Ray Bursts

Based on a refined generic dynamical model, we investigate afterglows from jetted gamma-ray burst (GRB) remnants numerically. In the relativistic phase, the light curve break could marginally be seen. However, an obvious break does exist at the transition from the relativistic phase to the non-relativistic phase, which typically occurs at time 10 to 30 days. It is very interesting that the break is affected by many parameters, especially by the electron energy fraction (xi_e), and the magnetic energy fraction (xi_B^2). Implication of orphan afterglow surveys on GRB beaming is investigated. The possible existence of a kind of cylindrical jets is also discussed.Comment: Minor changes; 10 pages, with 9 eps figures embedded. Talk given at the Sixth Pacific Rim Conference on Stellar Astrophysics (Xi'an, China, July 11-17, 2002). A slightly revised version will appear in the proceeding

Lattice model study of the thermodynamic interplay of polymer crystallization and liquid-liquid demixing

We report Monte Carlo simulations of a lattice-polymer model that can account for both polymer crystallization and liquid-liquid demixing in solutions of semiflexible homopolymers. In our model, neighboring polymer segments can have isotropic interactions that affect demixing, and anisotropic interactions that are responsible for freezing. However, our simulations show that the isotropic interactions also have a noticeable effect on the freezing curve, as do the anisotropic interactions on demixing. As the relative strength of the isotropic interactions is reduced, the liquid-liquid demixing transition disappears below the freezing curve. A simple, extended Flory-Huggins theory accounts quite well for the phase behavior observed in the simulations.Comment: Revtex, 7 pages, the content accepted by J. Chem. Phy

Global Dynamics of Advection-Dominated Accretion Revisited

We numerically solve the set of dynamical equations describing advection-dominated accretion flows (ADAF) around black holes, using a method similar to that of Chakrabarti (1996a). We choose the sonic radius of the flow $R_s$ and the integration constant in angular momentum equation $j$ as free parameters, and integrate the equations from the sonic point inwards to see if the solution can extend supersonically to the black hole horizon, and outwards to see if and where an acceptable outer boundary of the flow can be found. We recover the ADAF-thin disk solution constructed in Narayan, Kato, & Honma (1997, NKH97), an representative paper of the previous works on global ADAF solutions, although in that paper an apparently very different procedure was adopted. We obtain a complete picture in the form of $R_s-j$ parameter space which sums up the situation of ADAF solution at a glance. For comparison we also present the distribution of global solutions for inviscid flows in the $R_s-j$ space, which supports the view that there should be some similarities between the dynamical behavior of ADAF and that of adiabatic flows, and that there should be a continuous change from the properties of viscous flows to those of inviscid ones.Comment: 24 pages with 15 figures, to appear in ApJ Vol. 52