Correlation between Peak Energy and Peak Luminosity in Short Gamma-Ray Bursts

A correlation between the peak luminosity and the peak energy has been found by Yonetoku et al. as $L_{p}\propto E_{p,i}^{2.0}$ for 11 pre-Swift long gamma-ray bursts. In this study, for a greatly expanded sample of 148 long gamma-ray bursts in the Swift era, we find that the correlation still exists, but most likely with a slightly different power-law index, i.e., $L_{p}\propto E_{p,i} ^{1.7}$. In addition, we have collected 17 short gamma-ray bursts with necessary data. It is found that the correlation of $L_{p}\propto E_{p,i} ^{1.7}$ also exists for this sample of short events. It is argued that the radiation mechanism of both long and short gamma-ray bursts should be similar, i.e., of quasi-thermal origin caused by the photosphere and the dissipation occurring very near the central engine. Some key parameters of the process are constrained. Our results suggest that the radiation process of both long and short bursts may be dominated by thermal emission, rather than the single synchrotron radiation. This might put strong physical constraints on the theoretical models.Comment: 22 pages, 5 figures and 1 table, Accepted for publication in Ap

Vertex operator algebras and operads

Vertex operator algebras are mathematically rigorous objects corresponding to chiral algebras in conformal field theory. Operads are mathematical devices to describe operations, that is, $n$-ary operations for all $n$ greater than or equal to $0$, not just binary products. In this paper, a reformulation of the notion of vertex operator algebra in terms of operads is presented. This reformulation shows that the rich geometric structure revealed in the study of conformal field theory and the rich algebraic structure of the theory of vertex operator algebras share a precise common foundation in basic operations associated with a certain kind of (two-dimensional) ``complex'' geometric object, in the sense in which classical algebraic structures (groups, algebras, Lie algebras and the like) are always implicitly based on (one-dimensional) ``real'' geometric objects. In effect, the standard analogy between point-particle theory and string theory is being shown to manifest itself at a more fundamental mathematical level.Comment: 16 pages. Only the definitions of "partial operad" and of "rescaling group" have been improve

Gamma-ray bursts: postburst evolution of fireballs

The postburst evolution of fireballs that produce $\gamma$-ray bursts is studied, assuming the expansion of fireballs to be adiabatic and relativistic. Numerical results as well as an approximate analytic solution for the evolution are presented. Due to adoption of a new relation among $t$, $R$ and $\gamma$ (see the text), our results differ markedly from the previous studies. Synchrotron radiation from the shocked interstellar medium is attentively calculated, using a convenient set of equations. The observed X-ray flux of GRB afterglows can be reproduced easily. Although the optical afterglows seem much more complicated, our results can still present a rather satisfactory approach to observations. It is also found that the expansion will no longer be highly relativistic about 4 days after the main GRB. We thus suggest that the marginally relativistic phase of the expansion should be investigated so as to check the afterglows observed a week or more later.Comment: 17 pages, 4 figures, MNRAS in pres

Modeling Vacuum Arcs

We are developing a model of vacuum arcs. This model assumes that arcs develop as a result of mechanical failure of the surface due to Coulomb explosions, followed by ionization of fragments by field emission and the development of a small, dense plasma that interacts with the surface primarily through self sputtering and terminates as a unipolar arc capable of producing breakdown sites with high enhancement factors. We have attempted to produce a self consistent picture of triggering, arc evolution and surface damage. We are modeling these mechanisms using Molecular Dynamics (mechanical failure, Coulomb explosions, self sputtering), Particle-In-Cell (PIC) codes (plasma evolution), mesoscale surface thermodynamics (surface evolution), and finite element electrostatic modeling (field enhancements). We can present a variety of numerical results. We identify where our model differs from other descriptions of this phenomenon.Comment: 4 pages, 5 figure

Parton Distributions at Hadronization from Bulk Dense Matter Produced at RHIC

We present an analysis of $\Omega$, $\Xi$, $\Lambda$ and $\phi$ spectra from Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV in terms of distributions of effective constituent quarks at hadronization. Consistency in quark ratios derived from various hadron spectra provides clear evidence for hadron formation dynamics as suggested by quark coalescence or recombination models. We argue that the constituent quark distribution reflects properties of the effective partonic degrees of freedom at hadronization. Experimental data indicate that strange quarks have a transverse momentum distribution flatter than that of up/down quarks consistent with hydrodynamic expansion in partonic phase prior to hadronization. After the AMPT model is tuned to reproduce the strange and up/down quark distributions, the model can describe the measured spectra of hyperons and $\phi$ mesons very well where hadrons are formed through dynamical coalescence.Comment: 5 pages, 3 figures, two more paragraph added to address the referee's comment, figure updated to include the KET scale. Accepted version to appear in Phys. Rev.

Spin-phonon coupling and pressure effect in the superconductor LiFeAs : Lattice dynamics from first-principles calculations

The lattice dynamics and the effect of pressure on superconducting LiFeAs in both nonmagnetic (NM) and striped antiferromagnetic (SAF) phases are investigated using the plane-wave pseudopotential, density-functional-based method. While the obtained electron-phonon coupling $\lambda$ is very small for the NM calculation, the softening of phonon in the SAF phase may lead to a large increase in $\lambda$. In the SAF phase, strong anisotropy of the phonon softening in the Fe plane is found to arise from different spin orders in the $x$ and $y$ directions, indicating that the phonon softening is of spin-phonon coupling origin. For the SAF structure, the calculated variation trend of the electronic density of states and the phonon frequencies under pressure can explain a large negative pressure coefficient of $T_{c}$ in the LiFeAs compound.Comment: 2 figure