Peak Energy-Isotropic Energy Relation in the Off-Axis Gamma-Ray Burst Model

Using a simple uniform jet model of prompt emissions of gamma-ray bursts (GRBs), we reproduce the observed peak energy--isotropic energy relation. A Monte Carlo simulation shows that the low-isotropic energy part of the relation is dominated by events viewed from off-axis directions, and the number of the off-axis events is about one-third of the on-axis emissions. We also compute the observed event rates of the GRBs, the X-ray-rich GRBs, and the X-ray flashes detected by HETE-2, and we find that they are similar.Comment: 11 pages, 2 eps figure

Cosmological X-Ray Flashes from Off-Axis Jets

The of the cosmological X-ray flashes detected by WFC/BeppoSAX is calculated theoretically in a simple jet model. The total emission energy from the jet is assumed to be constant. We find that if the jet opening half-angle is smaller than 0.03 radian, off-axis emission from sources at z<~4 can be seen. The theoretical is less than 0.4, which is consistent with the observational result of 0.27+/-0.16 at the 1-sigma level. This suggests that the off-axis GRB jet with the small opening half-angle at the cosmological distance can be identified as the cosmological X-ray flash.Comment: 4 pages, 3 figures aipTEX, contribution to the 2003 GRB Conference, held at Santa Fe, N

Delayed Flashes from Counter Jets of Gamma Ray Bursts

If X-ray flashes are due to the forward jet emissions from gamma ray bursts (GRBs) observed with large viewing angles, we show that a prompt emission from a counter jet should be observed as a delayed flash in the UV or optical band several hours to a day after the X-ray flash. Ultraviolet and Optical Telescope on Swift can observe the delayed flashes within ~13 Mpc, so that (double-sided) jets of GRBs may be directly confirmed. Since the event rate of delayed flashes detected by Swift may be as small as 6*10^{-5}events/yr, we require more sensitive detectors in future experiments.Comment: 15 pages, 4 eps figures, Accepted for publication in Ap

GRB980425 in the Off-Axis Jet Model of the Standard GRBs

Using a simple off-axis jet model of GRBs, we can reproduce the observed unusual properties of the prompt emission of GRB980425, such as the extremely low isotropic equivalent gamma-ray energy, the low peak energy, the high fluence ratio, and the long spectral lag when the jet with the standard energy of ~10^{51} ergs and the opening half-angle of \Delta\theta=~10-30 degree is seen from the off-axis viewing angle ~\Delta\theta+10/\gamma, where \gamma is a Lorentz factor of the jet. For our adopted fiducial parameters, if the jet that caused GRB 980425 is viewed from the on-axis direction, the intrinsic peak energy Ep(1+z) is ~2.0-4.0 MeV, which corresponds to those of GRB990123 and GRB021004. Our model might be able to explain the other unusual properties of this event. We also discuss the connection of GRB980425 in our model with the X-ray flash, and the origin of a class of GRBs with small E_\gamma such as GRB030329, GRB980329, GRB981226, and so on.Comment: 4 pages, 2 figures aipTEX, contribution to the 2003 GRB Conference, held at Santa Fe, N

A possible observational evidence for θ−2\theta^{-2} angular distribution of opening half-angle of GRB jets

We propose a method to estimate the pseudo jet opening half-angle of GRBs using the spectral peak energy (\Ep)--peak luminosity relation (so called Yonetoku relation) as well as the \Ep--collimation-corrected $\gamma$-ray energy relation (so called Ghirlanda relation). For bursts with known jet break times and redshifts, we compared the pseudo jet opening half-angle with the standard one and found that the differences are within a factor 2. We apply the method to 689 long GRBS. We found that the distribution function of the pseudo jet opening half-angle obeys $f(\theta_j)\propto\theta_j^{-2.2 \pm 0.2}$ with possible cutoffs for $\theta_j 0.3$ although the log-normal fit is also possible. $\theta^{-2}$ distribution is compatible with the structured jet model. From the distribution function we found that the beaming correction for the rate of GRBs is $\sim 340$, which means $\sim 10^{-5}$ yr$^{-1}$ galaxy$^{-1}$ or only one in $10^2$ type Ib/c supernovae. We also found the evolution of the distribution function as a function of the redshift.Comment: 5 pages, 5 figures, submitted to MNRA

Dimerizations in spin-SS antiferromagnetic chains with three-spin interaction

We discuss spin-$S$ antiferromagnetic Heisenberg chains with three-spin interactions, next-nearest-neighbor interactions, and bond alternation. First, we prove rigorously that there exist parameter regions of the exact dimerized ground state in this system. This is a generalization of the Majumdar-Ghosh model to arbitrary $S$. Next, we discuss the ground-state phase diagram of the models by introducing several effective field theories and the universality classes of the transitions are described by the level-$2S$ $\mathrm{SU}(2)$ Wess-Zumino-Witten model and the Gaussian model. Finally, we determine the phase diagrams of $S=1$ and $S=3/2$ systems by using exact diagonalization and level spectroscopy.Comment: 7 pages, 5 figure