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

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

Modeling the Optical Afterglow of GRB 030329

The best-sampled afterglow light curves are available for GRB 030329. A distinguishing feature of this event is the obvious rebrightening at around 1.6 days after the burst. Proposed explanations for the rebrightening mainly include the two-component jet model and the refreshed shock model, although a sudden density-jump in the circumburst environment is also a potential choice. Here we re-examine the optical afterglow of GRB 030329 numerically in light of the three models. In the density-jump model, no obvious rebrightening can be produced at the jump moment. Additionally, after the density jump, the predicted flux density decreases rapidly to a level that is significantly below observations. A simple density-jump model thus can be excluded. In the two-component jet model, although the observed late afterglow (after 1.6 days) can potentially be explained as emission from the wide-component, the emergence of this emission actually is too slow and it does not manifest as a rebrightening as previously expected. The energy-injection model seems to be the most preferred choice. By engaging a sequence of energy-injection events, it provides an acceptable fit to the rebrightening at $\sim 1.6$ d, as well as the whole observed light curve that extends to $\sim 80$ d. Further studies on these multiple energy-injection processes may provide a valuable insight into the nature of the central engines of gamma-ray bursts.Comment: 18 pages, 3 figures; a few references added and minor word changes; now accepted for publication in Ap

Optimization of synchronization in gradient clustered networks

We consider complex clustered networks with a gradient structure, where sizes of the clusters are distributed unevenly. Such networks describe more closely actual networks in biophysical systems and in technological applications than previous models. Theoretical analysis predicts that the network synchronizability can be optimized by the strength of the gradient field but only when the gradient field points from large to small clusters. A remarkable finding is that, if the gradient field is sufficiently strong, synchronizability of the network is mainly determined by the properties of the subnetworks in the two largest clusters. These results are verified by numerical eigenvalue analysis and by direct simulation of synchronization dynamics on coupled-oscillator networks.Comment: PRE, 76, 056113 (2007

Structure of the combinatorial generalization of hypergeometric functions for SU(n) states. II

In the construction of the general SU(5) states, the action of each individual lowering operators (raised to a power) operating on the semimaximal state leads to an operator‐valued polynomial which is shown to belong to the class of generalized hypergeometric functions in the sense of Gel'fand (namely, they are Radon transform of linear forms). Three new functions are found at the SU(5) level and their content in terms of known lower‐hierarchy functions are explicitly exhibited. The structure of the general SU(n) states due to the combined action of all lowering operators is quite complicated, but the action of each individual lowering operator taken one at a time may still be manageable for higher n, and, in the spirit of boson operator formalism, this may be one systematical way of producing high‐hierarchy generalized hypergeometric functions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69711/2/JMAPAQ-14-2-263-1.pd