It is widely believed that the maximum energy of synchrotron photons when electrons are accelerated in shocks via the Fermi process is about 50 MeV (in plasma comoving frame). We show that under certain conditions, which are expected to be realized i
n relativistic shocks of gamma-ray bursts, synchrotron photons of energy much larger than 50 MeV (comoving frame) can be produced. The requirement is that magnetic field should decay downstream of the shock front on a length scale that is small compared with the distance traveled by the highest energy electrons before they lose half their energy; photons of energy much larger than 50 MeV are produced close to the shock front whereas the highest Lorentz factor that electrons can attain is controlled by the much weaker field that occupies most of the volume of the shocked plasma.
Synchrotron radiation mechanism, when electrons are accelerated in a relativistic shock, is known to have serious problems to explain the observed gamma-ray spectrum below the peak for most Gamma-Ray Bursts (GRBs); the synchrotron spectrum below the
peak is much softer than observed spectra. Recently, the possibility that electrons responsible for the radiation cool via Inverse Compton, but in the Klein-Nishina regime, has been proposed as a solution to this problem. We provide an analytical study of this effect and show that it leads to a hardening of the low energy spectrum but not by enough to make it consistent with the observed spectra for most GRBs (this is assuming that electrons are injected continuously over a time scale comparable to the dynamical time scale, as is expected for internal shocks of GRBs). In particular, we find that it is not possible to obtain a spectrum with alpha>-0.1 (f_{ u} propto u^{alpha}) whereas the typical observed value is alphasim0. Moreover, extreme values for a number of parameters are required in order that alphasim-0.1: the energy fraction in magnetic field needs to be less than about 10^{-4}, the thermal Lorentz factor of electrons should be larger than 10^6, and the radius where gamma-rays are produced should be not too far away from the deceleration radius. These difficulties suggest that the synchrotron radiation mechanism in internal shocks does not provide a self-consistent solution when alpha>-0.2.
Photons of energy larger than 100 MeV from long-GRBs arrive a few seconds after <10 MeV photons do. We show that this delay is a natural consequence of a magnetic dominated relativistic jet. The much slower acceleration of a magnetic jet with radius
(compared with a hot baryonic outflow) results in high energy gamma-ray photons to be converted to electron-positron pairs out to a larger radius whereas lower energy gamma-rays of energy less than ~10 MeV can escape when the jet crosses the Thomson-photosphere. The resulting delay for the arrival of high energy photons is found to be similar to the value observed by the Fermi satellite for a number of GRBs. A prediction of this model is that the delay should increase with photon energy (E) as E^{0.17} for E>100 MeV. The delay depends almost linearly on burst redshift, and on the distance from the central compact object where the jet is launched (R_0). Therefore, the delay in arrival of >10^2 MeV photons can be used to estimate burst redshift if the magnetic jet model for gamma-ray generation is correct and R_0 is roughly the same for long-GRBs.
Specific heat, dc- and ac-magnetic susceptibility are reported for a large single crystal of PrOs$_4$Sb$_{12}$ and, after grinding, its powder. The room temperature effective paramagnetic moment of the crystal was consistent with the Pr$^{3+}$ ionic
configuration and full occupancy of the Pr-sublattice. The crystal showed two distinct anomalies in the specific heat and an overall discontinuity in $C/T$ of more than 1000 mJ/K$^2$mol. The upper transition (at $T_{c1}$) was rounded, in an agreement with previous reports. The anomaly at $T_{c2}$ was very sharp, consistent with a good quality of the crystal. We observed a shoulder in $chi$ and two peaks in $chi$ below $T_{c1}$. However, there were no signatures in $chi$ of the lower temperature transition. PrOs$_4$Sb$_{12}$ is extremely sensitive to grinding, which suppresses the upper superconducting transition in both the specific heat and magnetic susceptibility. $Delta C/T_{c}$ was reduced to 140 mJ/K$^2$ mol in the powdered sample. Existing data on ground, polished, and sliced crystals suggests the existence of a length scale of order 100 $mu$, characterizing the higher temperature superconducting phase.
