A critical shock Mach number for particle acceleration in the absence of pre-existing cosmic rays: M=5M=\sqrt 5

It is shown that, under some generic assumptions, shocks cannot accelerate particles unless the overall shock Mach number exceeds a critical value M > sqrt(5). The reason is that for M <= sqrt(5) the work done to compress the flow in a particle precursor requires more enthalpy flux than the system can sustain. This lower limit applies to situations without significant magnetic field pressure. In case that the magnetic field pressure dominates the pressure in the unshocked medium, i.e. for low plasma beta, the resistivity of the magnetic field makes it even more difficult to fulfil the energetic requirements for the formation of shock with an accelerated particle precursor and associated compression of the upstream plasma. We illustrate the effects of magnetic fields for the extreme situation of a purely perpendicular magnetic field configuration with plasma beta = 0, which gives a minimum Mach number of M = 5/2. The situation becomes more complex, if we incorporate the effects of pre-existing cosmic rays, indicating that the additional degree of freedom allows for less strict Mach number limits on acceleration. We discuss the implications of this result for low Mach number shock acceleration as found in solar system shocks, and shocks in clusters of galaxies.Comment: Accepted for publication in the Astrophysical Journal. 14 pages, 10 figures. (Minor corrections wrt last version.

Black holes in three-dimensional Einstein-Born-Infeld-dilaton theory

The three-dimensional static and circularly symmetric solution of the Einstein-Born-Infeld-dilaton system is derived. The solutions corresponding to low energy string theory are investigated in detail, which include black hole solutions if the cosmological constant is negative and the mass parameter exceeds a certain critical value. Some differences between the Born-Infeld nonlinear electrodynamics and the Maxwell electrodynamics are revealed.Comment: 10 pages LaTeX, 2 eps figures, accepted for publication in PR

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

Possibility of Ultra High-Energy Cosmic Rays from the Giant Flare in SGR 1806-20

On 2004 December 27, a giant flare from the soft gamma repeater 1806$-$20 was observed. The radiation mechanism of the initial peak of the flare would be controversial. In this letter we point out that very high-energy cosmic rays would be produced in the case that the flare was caused by internal shocks, as is usually considered for gamma-ray bursts. The highest energy of cosmic rays can reach $10^{19}$ eV, if the Lorentz factor of the shocks is sufficiently high. Future observations of cosmic rays will inform us about the mechanism of the giant flare.Comment: 8 pages, 2figure