On the exact analytic expressions for the equitemporal surfaces in Gamma-Ray Burst afterglows

We have recently shown (see Bianco & Ruffini 2004) that marked differences exist between the EQuiTemporal Surfaces (EQTSs) for the Gamma-Ray Burst (GRB) afterglows numerically computed by the full integration of the equations of motion and the ones found in the current literature expressed analytically on the grounds of various approximations. In this Letter the exact analytic expressions of the EQTSs are presented both in the case of fully radiative and adiabatic regimes. The new EQTS analytic solutions validate the numerical results obtained in Bianco & Ruffini (2004) and offer a powerful tool to analytically perform the estimates of the physical observables in GRB afterglows.Comment: 3 pages, 1 figure, to appear on ApJ Letter

Exact versus approximate solutions in Gamma-Ray Burst afterglows

We have recently obtained the exact analytic solutions of the relativistic equations relating the radial and time coordinate of a relativistic thin uniform shell expanding in the interstellar medium in the fully radiative and fully adiabatic regimes. We here re-examine the validity of the constant-index power-law relations between the Lorentz gamma factor and its radial coordinate, usually adopted in the current Gamma-Ray Burst (GRB) literature on the grounds of an "ultrarelativistic" approximation. Such expressions are found to be mathematically correct but only approximately valid in a very limited range of the physical and astrophysical parameters and in an asymptotic regime which is reached only for a very short time, if any, and are shown to be not applicable to GRBs.Comment: 4 pages, 2 figures, to appear on ApJ Letter

Theoretical interpretation of GRB 011121

GRB011121 is analyzed as a prototype to understand the ``flares'' recently observed by Swift in the afterglow of many GRB sources. Detailed theoretical computation of the GRB011121 light curves in selected energy bands are presented and compared and contrasted with observational BeppoSAX data.Comment: 2 pages, 1 figure, to appear in the proceedings of "Swift and GRBs", Venice, 2006, Il Nuovo Cimento, in pres

Exact versus approximate beaming formulas in Gamma-Ray Burst afterglows

We present the exact analytic expressions to compute, assuming the emitted Gamma-Ray Burst (GRB) radiation is not spherically symmetric but is confined into a narrow jet, the value of the detector arrival time at which we start to "see" the sides of the jet, both in the fully radiative and adiabatic regimes. We obtain this result using our exact analytic expressions for the EQuiTemporal Surfaces (EQTSs) in GRB afterglows. We re-examine the validity of three different approximate formulas currently adopted for the adiabatic regime in the GRB literature. We also present an empirical fit of the numerical solutions of the exact equations, compared and contrasted with the three above approximate formulas. The extent of the differences is such as to require a reassessment on the existence and entity of beaming in the cases considered in the current literature, as well as on its consequences on the GRB energetics.Comment: 4 pages, 4 figures, to appear on ApJ Let

Decaying Majoron Dark Matter and Neutrino Masses

We review the recent proposal by Lattanzi & Valle of the majoron as a suitable warm dark matter candidate. The majoron is the Goldstone boson associated to the spontaneous breaking of ungauged lepton number, one of the mechanisms proposed to give rise to neutrino masses. The majoron can acquire a mass through quantum gravity effects, and can possibly account for the observed dark matter component of the Universe. We present constraints on the majoron lifetime, mass and abundance obtained by the analysis of the cosmic microwave background data. We find that, in the case of thermal production, the limits for the majoron mass read 0.12 keV<m_J<0.17 keV, and discuss how these limits are modified in the non-thermal case. The majoron lifetime is constrained to be larger than 250 Gyrs. We also apply this results to a given seesaw model for the generation of neutrino masses, and find that this constraints the energy scale for the lepton number breaking phase transition to be above 10^6 GeV. We thus find that the majoron decaying dark matter (DDM) scenario fits nicely in models where neutrino masses arise "a la seesaw" and may lead to other possible cosmological implications.Comment: 7 pages, 3 figures. Contribution to proceedings of the 4th Sino-Italian Workshop on Relativistic Astrophysics, Pescara, 20-30 July 200

Exact versus approximate equitemporal surfaces in Gamma-Ray Burst afterglows

By integrating the relativistic hydrodynamic equations introduced by Taub we have determined the exact EQuiTemporal Surfaces (EQTSs) for the Gamma-Ray Burst (GRB) afterglows. These surfaces are compared and contrasted to the ones obtained, using approximate methods, by Panaitescu & Meszaros (1998), Sari (1998), Granot et al. (1999).Comment: 4 pages, 4 figures, to appear on ApJ Let

The "Fireshell" model in the Swift era

We here re-examine the validity of the constant-index power-law relation between the fireshell Lorentz gamma factor and its radial coordinate, usually adopted in the current Gamma-Ray Burst (GRB) literature on the grounds of an "ultrarelativistic" approximation. Such expressions are found to be mathematically correct but only approximately valid in a very limited range of the physical and astrophysical parameters and in an asymptotic regime which is reached only for a very short time, if any.Comment: 3 pages, 1 figure, to appear on the Proceedings of the Eleventh Marcel Grossmann Meeting, Berlin (Germany), July 200

Boost symmetry in the Quantum Gravity sector

We perform a canonical quantization of gravity in a second-order formulation, taking as configuration variables those describing a 4-bein, not adapted to the space-time splitting. We outline how, neither if we fix the Lorentz frame before quantizing, nor if we perform no gauge fixing at all, is invariance under boost transformations affected by the quantization.Comment: 8 pages, to appear in the proceedings of'' 4th Italian-Sino Workshop on Relativistic Astrophysics'', AIP Conference Serie

Gravitational Stability and Bulk Cosmology

We present a discussion of the effects induced by bulk viscosity either on the very early Universe stability and on the dynamics associated to the extreme gravitational collapse of a gas cloud. In both cases the viscosity coefficient is related to the energy density $\rho$ via a power-law of the form $\zeta=\zeta_0 \rho^s$ (where $\zeta_0, s=const.$) and the behavior of the density contrast in analyzed. In the first case, matter filling the isotropic and homogeneous background is described by an ultra-relativistic equation of state. The analytic expression of the density contrast shows that its growth is suppressed forward in time as soon as $\zeta_0$ overcomes a critical value. On the other hand, in such a regime, the asymptotic approach to the initial singularity admits an unstable collapsing picture. In the second case, we investigate the top-down fragmentation process of an uniform and spherically symmetric gas cloud within the framework of a Newtonian approach, including the negative pressure contribution associated to the bulk viscous phenomenology. In the extreme regime toward the singularity, we show that the density contrast associated to an adiabatic-like behavior of the gas (which is identified by a particular range of the politropic index) acquire, for sufficiently large viscous contributions, a vanishing behavior which prevents the formation of sub-structures. Such a feature is not present in the isothermal-like collapse. We also emphasize that in the adiabatic-like case bulk viscosity is also responsible for the appearance of a threshold scale (equivalent to a Jeans length) beyond which perturbations begin to increase.Comment: 13 pages, no figur

The luminosity evolution over the EQuiTemporal Surfaces in the prompt emission of Gamma-Ray Bursts

Due to the ultrarelativistic velocity of the expanding "fireshell" (Lorentz gamma factor \gamma \sim 10^2 - 10^3), photons emitted at the same time from the fireshell surface do not reach the observer at the same arrival time. In interpreting Gamma-Ray Bursts (GRBs) it is crucial to determine the properties of the EQuiTemporal Surfaces (EQTSs): the locus of points which are source of radiation reaching the observer at the same arrival time. In the current literature this analysis is performed only in the latest phases of the afterglow. Here we study the distribution of the GRB bolometric luminosity over the EQTSs, with special attention to the prompt emission phase. We analyze as well the temporal evolution of the EQTS apparent size in the sky. We use the analytic solutions of the equations of motion of the fireshell and the corresponding analytic expressions of the EQTSs which have been presented in recent works and which are valid for both the fully radiative and the adiabatic dynamics. We find the novel result that at the beginning of the prompt emission the most luminous regions of the EQTSs are the ones closest to the line of sight. On the contrary, in the late prompt emission and in the early afterglow phases the most luminous EQTS regions are the ones closest to the boundary of the visible region. This transition in the emitting region may lead to specific observational signatures, i.e. an anomalous spectral evolution, in the rising part or at the peak of the prompt emission. We find as well an expression for the apparent radius of the EQTS in the sky, valid in both the fully radiative and the adiabatic regimes. Such considerations are essential for the theoretical interpretation of the prompt emission phase of GRBs.Comment: 11 pages, 5 figures, in the Proceedings of the 1st Galileo-Xu GuangQi Meeting, October 26-30, 2009, Shangha