Spectrum and Duration of Delayed MeV-GeV Emission of Gamma-Ray Bursts in Cosmic Background Radiation Fields

We generally analyze prompt high-energy emission above a few hundreds of GeV due to synchrotron self-Compton scattering in internal shocks. However, such photons cannot be detected because they may collide with cosmic infrared background photons, leading to electron/positron pair production. Inverse-Compton scattering of the resulting electron/positron pairs off cosmic microwave background photons will produce delayed MeV-GeV emission, which may be much stronger than a typical high-energy afterglow in the external shock model. We expand on the Cheng & Cheng model by deriving the emission spectrum and duration in the standard fireball shock model. A typical duration of the emission is ~ 10^3 seconds, and the time-integrated scattered photon spectrum is nu^{-(p+6)/4}, where p is the index of the electron energy distribution behind internal shocks. This is slightly harder than the synchrotron photon spectrum, nu^{-(p+2)/2}. The lower energy property of the scattered photon spectrum is dependent on the spectral energy distribution of the cosmic infrared background radiation. Therefore, future observations on such delayed MeV-GeV emission and the higher-energy spectral cutoff by the Gamma-Ray Large Area Space Telescope (GLAST) would provide a probe of the cosmic infrared background radiation.Comment: 5 pages, accepted for publication in Ap

Coupling between quasiparticles and a bosonic mode in the normal state of HgBa2_2CuO4+δ_{4+\delta}

We report a doping dependent study of the quasiparticles dynamics in HgBa$_2$CuO$_{4+\delta}$ via Electronic Raman Scattering. A well-defined energy scale is found in the normal state dynamics of the quasiparticles over a broad doping range. It is interpreted as evidence for coupling between the quasiparticles and a collective bosonic mode whose energy scale depend only weakly with doping. We contrast this behavior with that of the superconducting gap whose amplitude near the node continuously decreases towards the underdoped regime. We discuss the implications of our findings on the nature of the collective mode and argue that electron-phonon coupling is the most natural explanation.Comment: 5 pages, 4 figure

Semileptonic B decays into excited charmed mesons from QCD sum rules

Exclusive semileptonic $B$ decays into excited charmed mesons are studied with QCD sum rules in the leading order of heavy quark effective theory. Two universal Isgur-Wise functions \tau and \zeta for semileptonic B decays into four lowest lying excited $D$ mesons ($D_1$, $D_2^*$, $D'_0$, and $D'_1$) are determined. The decay rates and branching ratios for these processes are calculated.Comment: RevTeX, 17 pages including 2 figure

The Afterglow of GRB 990123 and a Dense Medium

Recent observations show that the temporal decay of the R-band afterglow from GRB 990123 steepened about 2.5 days after the burst. We here propose a possible explanation for such a steepening: a shock expanding in a dense medium has undergone the transition from a relativistic phase to a nonrelativistic phase. We find that this model is consistent with the observations if the medium density is about $3\times 10^6 {\rm cm}^{-3}$. By fitting our model to the observed optical and X-ray afterglow quantitatively, we further infer the electron and magnetic energy fractions of the shocked medium and find these two parameters are about 0.1 and $2\times 10^{-8}$ respectively. The former parameter is near the equipartition value while the latter is about six orders of magnitude smaller than inferred from the GRB 970508 afterglow. We also discuss possibilities that the dense medium can be produced.Comment: 12 pages, LaTeX, published in ApJ Letter

Gamma-Ray Burst Afterglows from Realistic Fireballs

A GRB afterglow has been commonly thought to be due to continuous deceleration of a postburst fireball. Many analytical models have made simplifications for deceleration dynamics of the fireball and its radiation property, although they are successful at explaining the overall features of the observed afterglows. We here propose a model for a GRB afterglow in which the evolution of a postburst fireball is in an intermediate case between the adiabatic and highly radiative expansion. In our model, the afterglow is both due to the contribution of the adiabatic electrons behind the external blastwave of the fireball and due to the contribution of the radiative electrons. In addition, this model can describe evolution of the fireball from the extremely relativistic phase to the non-relativistic phase. Our calculations show that the fireball will go to the adiabatic expansion phase after about a day if the accelerated electrons are assumed to occupy the total internal energy. In all cases considered, the fireball will go to the mildly relativistic phase about $10^4$ seconds later, and to the non-relativistic phase after several days. These results imply that the relativistic adiabatic model cannot describe the deceleration dynamics of the several-days-later fireball. The comparison of the calculated light curves with the observed results at late times may imply the presence of impulsive events or energy injection with much longer durations.Comment: 18 pages, 10 figures, plain latex file, submitted to Ap

Environment and Energy Injection Effects in GRB Afterglows

In a recent paper (Dai & Lu 1999), we have proposed a simple model in which the steepening in the light curve of the R-band afterglow of the gamma-ray burst (GRB) 990123 is caused by the adiabatic shock which has evolved from an ultrarelativistic phase to a nonrelativistic phase in a dense medium. We find that such a model is quite consistent with observations if the medium density is about $3\times 10^6 {\rm cm}^{-3}$. Here we discuss this model in more details. In particular, we investigate the effects of synchrotron self absorption and energy injection. A shock in a dense medium becomes nonrelativistic rapidly after a short relativistic phase. The afterglow from the shock at the nonrelativistic stage decays more rapidly than at the relativistic stage. Since some models for GRB energy sources predict that a strongly magnetic millisecond pulsar may be born during the formation of GRB, we discuss the effect of such a pulsar on the evolution of the nonrelativistic shock through magnetic dipole radiation. We find that after the energy which the shock obtains from the pulsar is much more than the initial energy of the shock, the afterglow decay will flatten significantly. When the pulsar energy input effect disappears, the decay will steepen again. These features are in excellent agreement with the afterglows of GRB 980519, GRB 990510 and GRB 980326. Furthermore, our model fits very well all the observational data of GRB 980519 including the last two detections.Comment: 21 pages, LaTeX, accepted for publication in ApJ, one paragraph adde

The equation of state for two-dimensional hard-sphere gases: Hard-sphere gases as ideal gases with multi-core boundaries

The equation of state for a two-dimensional hard-sphere gas is difficult to calculate by usual methods. In this paper we develop an approach for calculating the equation of state of hard-sphere gases, both for two- and three-dimensional cases. By regarding a hard-sphere gas as an ideal gas confined in a container with a multi-core (excluded sphere) boundary, we treat the hard-sphere interaction in an interacting gas as the boundary effect on an ideal quantum gas; this enables us to treat an interacting gas as an ideal one. We calculate the equation of state for a three-dimensional hard-sphere gas with spin $j$, and compare it with the results obtained by other methods. By this approach the equation of state for a two-dimensional hard-sphere gas can be calculated directly.Comment: 9 pages, 1 figur

A Hierarchical Emotion Regulated Sensorimotor Model: Case Studies

Inspired by the hierarchical cognitive architecture and the perception-action model (PAM), we propose that the internal status acts as a kind of common-coding representation which affects, mediates and even regulates the sensorimotor behaviours. These regulation can be depicted in the Bayesian framework, that is why cognitive agents are able to generate behaviours with subtle differences according to their emotion or recognize the emotion by perception. A novel recurrent neural network called recurrent neural network with parametric bias units (RNNPB) runs in three modes, constructing a two-level emotion regulated learning model, was further applied to testify this theory in two different cases.Comment: Accepted at The 5th International Conference on Data-Driven Control and Learning Systems. 201