Estimation Prospects of the Source Number Density of Ultra-high-energy Cosmic Rays

We discuss the possibility of accurately estimating the source number density of ultra-high-energy cosmic rays (UHECRs) using small-scale anisotropy in their arrival distribution. The arrival distribution has information on their source and source distribution. We calculate the propagation of UHE protons in a structured extragalactic magnetic field (EGMF) and simulate their arrival distribution at the Earth using our previously developed method. The source number density that can best reproduce observational results by Akeno Giant Air Shower Array is estimated at about $10^{-5} {\rm Mpc}^{-3}$ in a simple source model. Despite having large uncertainties of about one order of magnitude, due to small number of observed events in current status, we find that more detection of UHECRs in the Auger era can sufficiently decrease this so that the source number density can be more robustly estimated. 200 event observation above $4 \times 10^{19} {\rm eV}$ in a hemisphere can discriminate between $10^{-5}$ and $10^{-6} {\rm Mpc}^{-3}$. Number of events to discriminate between $10^{-4}$ and $10^{-5} {\rm Mpc}^{-3}$ is dependent on EGMF strength. We also discuss the same in another source model in this paper.Comment: 19 pages, 8 figures, accepted for publication in Astroparticle Physic

Curves on a spacelike surface in three dimensional Lorentz-Minkowski space

In this paper we consider curves on a spacelike surface in Lorentz-Minkowski $3$-space.\ud We introduce new geometric invariants for these curves. As an application of the unfolding theory of functions, we investigate the local and global propereties of these invariants

Towards unravelling the structural distribution of ultra-high-energy cosmic ray sources

We investigate the possibility that near future observations of ultra-high-energy cosmic rays (UHECRs) can unveil their local source distribution, which reflects the observed local structures if their origins are astrophysical objects. In order to discuss this possibility, we calculate the arrival distribution of UHE protons taking into account their propagation process in intergalactic space i.e. energy losses and deflections by extragalactic magnetic field (EGMF). For a realistic simulation, we construct and adopt a model of a structured EGMF and UHECR source distribution, which reproduce the local structures actually observed around the Milky Way. The arrival distribution is compared statistically to their source distribution using correlation coefficient. We specially find that UHECRs above $10^{19.8}$eV are best indicators to decipher their source distribution within 100 Mpc, and detection of about 500 events on all the sky allows us to unveil the local structure of UHE universe for plausible EGMF strength and the source number density. This number of events can be detected by five years observation by Pierre Auger Observatory.Comment: 7pages, 4 figures, submitted to Ap

Probing the Structure of Gamma-Ray Burst Jets with Steep Decay Phase of their Early X-ray Afterglows

We show that the jet structure of gamma-ray bursts (GRBs) can be investigated with the tail emission of the prompt GRB. The tail emission which we consider is identified as a steep-decay component of the early X-ray afterglow observed by the X-ray Telescope onboard Swift. Using a Monte Carlo method, we derive, for the first time, the distribution of the decay index of the GRB tail emission for various jet models. The new definitions of the zero of time and the time interval of a fitting region are proposed. These definitions for fitting the light curve lead us an unique definition of the decay index, which is useful to investigate the structure of the GRB jet. We find that if the GRB jet has a core-envelope structure, the predicted distribution of the decay index of the tail has a wide scatter and has multiple peaks, which cannot be seen for the case of the uniform and the Gaussian jet. Therefore, the decay index distribution tells us the information on the jet structure. Especially, if we observe events whose decay index is less than about 2, both the uniform and the Gaussian jet models will be disfavored according to our simulation study.Comment: 21 pages, 10 figures, the paper with full resolution images is http://theo.phys.sci.hiroshima-u.ac.jp/~takami/research/achievements/papers/003_full.pd

Interaction and Localization of One-electron Orbitals in an Organic Molecule: Fictitious Parameter Analysis for Multi-physics Simulations

We present a new methodology to analyze complicated multi-physics simulations by introducing a fictitious parameter. Using the method, we study quantum mechanical aspects of an organic molecule in water. The simulation is variationally constructed from the ab initio molecular orbital method and the classical statistical mechanics with the fictitious parameter representing the coupling strength between solute and solvent. We obtain a number of one-electron orbital energies of the solute molecule derived from the Hartree-Fock approximation, and eigenvalue-statistical analysis developed in the study of nonintegrable systems is applied to them. Based on the results, we analyze localization properties of the electronic wavefunctions under the influence of the solvent.Comment: 4 pages, 5 figures, the revised version will appear in J. Phys. Soc. Jpn. Vol.76 (No.1