Analytic Light-Curves of Gamma-Ray Burst Afterglows: Homogeneous versus Wind External Media

Assuming an adiabatic evolution of a Gamma-Ray Burst (GRB) remnant interacting with an external medium, we calculate the injection, cooling, and absorption break frequencies, and the afterglow flux for plausible orderings of the break and observing frequencies. The analytical calculations are restricted to a relativistic remnant and, in the case of collimated ejecta, to the phase where there is an insignificant lateral expansion. Results are given for both a homogeneous external medium and for a wind ejected by the GRB progenitor. We compare the afterglow emission at different observing frequencies, for each type of external medium. It is found that observations at sub-millimeter frequencies during the first day provide the best way of discriminating between the two models. By taking into account the effect of inverse Compton scatterings on the electron cooling, a new possible time-dependence of the cooling break is identified. The signature of the up-scattering losses could be seen in the optical synchrotron emission from a GRB remnant interacting with a pre-ejected wind, as a temporary mild flattening of the afterglow decay. The up-scattered radiation itself should be detected in the soft X-ray emission from GRB remnants running into denser external media, starting few hours after the main event.Comment: 11 pages, to be published in the ApJ, vol 54

Thermodynamics of a Higher Order Phase Transition: Scaling Exponents and Scaling Laws

The well known scaling laws relating critical exponents in a second order phase transition have been generalized to the case of an arbitrarily higher order phase transition. In a higher order transition, such as one suggested for the superconducting transition in Ba$_{0.6}$K$_{0.4}$BiO$_3$ and in Bi$_2$Sr$_2$CaCu$_2$O$_8$, there are singularities in higher order derivatives of the free energy. A relation between exponents of different observables has been found, regardless of whether the exponents are classical (mean-field theory, no fluctuations, integer order of a transition) or not (fluctuation effects included). We also comment on the phase transition in a thin film.Comment: 10 pages, no figure

Conversion of glassy antiferromagnetic-insulating phase to equilibrium ferromagnetic-metallic phase by devitrification and recrystallization in Al substituted Pr0.5{_{0.5}}Ca0.5_{0.5}MnO3{_3}

We show that Pr${_{0.5}}$Ca$_{0.5}$MnO${_3}$ with 2.5% Al substitution and La${_{0.5}}$Ca$_{0.5}$MnO${_3}$ (LCMO) exhibit qualitatively similar and visibly anomalous M-H curves at low temperature. Magnetic field causes a broad first-order but irreversible antiferromagnetic (AF)-insulating (I) to ferromagnetic (FM)-metallic (M) transition in both and gives rise to soft FM state. However, the low temperature equilibrium state of Pr$_{0.5}$Ca$_{0.5}$Mn$_{0.975}$Al$_{0.025}$O$_3$ (PCMAO) is FM-M whereas that of LCMO is AF-I. In both the systems the respective equilibrium phase coexists with the other phase with contrasting order, which is not in equilibrium, and the cooling field can tune the fractions of the coexisting phases. It is shown earlier that the coexisting FM-M phase behaves like `magnetic glass' in LCMO. Here we show from specially designed measurement protocols that the AF-I phase of PCMAO has all the characteristics of magnetic glassy states. It devitrifies on heating and also recrystallizes to equilibrium FM-M phase after annealing. This glass-like AF-I phase also shows similar intriguing feature observed in FM-M magnetic glassy state of LCMO that when the starting coexisting fraction of glass is larger, successive annealing results in larger fraction of equilibrium phase. This similarity between two manganite systems with contrasting magnetic orders of respective glassy and equilibrium phases points toward a possible universality.Comment: Highlights potential of CHUF (Cooling and Heating in Unequal Fields), a new measurement protoco