On the energy of gamma-ray bursts

We show that gamma-ray burst (GRB) afterglow observations strongly suggest, within the fireball model framework, that radiating electrons are shock accelerated to a power-law energy distribution, with universal index p \approx 2.2, and that the fraction of shock energy carried by electrons, \xi_e, is universal and close to equipartition, \xi_e ~ 1/3. For universal p and \xi_e, a single measurement of the X-ray afterglow flux on the time scale of a day provides a robust estimate of the fireball energy per unit solid angle, \epsilon, averaged over a conical section of the fireball of opening angle \theta ~ 0.1. Applying our analysis to BeppoSAX afterglow data we find that: (i) Fireball energies are in the range of 4\pi\epsilon=10^{51.5} to 10^{53.5} erg; (ii) The ratio of observed $\gamma$-ray to total fireball energy per unit solid angle, \epsilon_\gamma / \epsilon, is of order unity, satisfying abs[log10(\epsilon_\gamma/\epsilon)]<0.5; (iii) If fireballs are jet like, their opening angle should satisfy \theta>=0.1. Our results imply that if typical opening angles are \theta ~ 0.1, a value consistent with our analysis, the total energy associated with a GRB event is in the range of 10^{50} erg to 10^{51.5} erg.Comment: 16 pages; Submitted to Ap

A simple empirical redshift indicator for gamma-ray bursts

We propose a new empirical redshift indicator for gamma-ray bursts. This indicator is easily computed from the gamma-ray burst spectral parameters, and its duration, and it provides ``pseudo-redshifts'' accurate to a factor two. Possible applications of this redshift indicator are briefly discussed.Comment: Final version, 4 pages, 3 figures, A&A, vol. 407, L

X-ray afterglow detection of the short gamma-ray burst 991014

GRB 991014 is one of the shortest gamma-ray bursts detected so far with the Wide Field Cameras aboard BeppoSAX, both in gamma-rays and X-rays. The duration is 9.6 sec in 2-28 keV and 3.2 sec in 40 to 700 keV (as measured between the times when 5 and 95% of the burst photons have been accumulated). We refine the InterPlanetary Network annulus of the burst, present the detection of the X-ray afterglow of GRB 991014 within this refined annulus, and discuss X-ray and gamma-ray observations of the prompt and afterglow emission. Except for the briefness of the prompt event, no other unusual aspects were found in the prompt and afterglow observations as compared to such measurements in previous gamma-ray bursts.Comment: accepted for publication in Astrophysical Journa

GRB990510: on the possibility of a beamed X-ray afterglow

We discuss the prompt emission of the gamma-ray burst (GRB) 990510 and its subsequent X-ray afterglow from 8.0 to 44.3 hrs after the prompt emission, using observations with the Gamma-ray Burst Monitor and Narrow Field Instruments on BeppoSAX. In the 40-700 keV band, GRB990510 had a fluence of \~1.9x10^{-5}erg cm^{-2}, whereas it reached a peak flux of ~2.4x10^{-6}erg cm^{-2} s^{-1}. The X-ray afterglow decay light curve can be satisfactorily described by a single power law with index of -1.42+/-0.07. Both the X-ray and optical behaviour of the afterglow can be explained by gamma-ray burst debris expanding as a jet; we find that the cooling frequency is (fixed) between the optical and X-ray wavelength bands.Comment: 16 pages, 4 figures, accepted for publication in the Astrophysical Journa

Weak solutions to problems involving inviscid fluids

We consider an abstract functional-differential equation derived from the pressure-less Euler system with variable coefficients that includes several systems of partial differential equations arising in the fluid mechanics. Using the method of convex integration we show the existence of infinitely many weak solutions for prescribed initial data and kinetic energy

BeppoSAX measurements of the bright gamma-ray burst 010222

We analyze the BeppoSAX measurements of the prompt and afterglow emission of the gamma-ray burst GRB010222. Among 45 GRBs detected with the Wide Field Cameras on BeppoSAX, the 40-700 keV fluence of (9.3+/-0.3)E-5 erg cm-2 is only surpassed by GRB990123. In terms of the isotropic 20-2000 keV energy output of 7.8E53 erg, it ranks third of all GRBs with measured distances. Since this burst is so bright, the data provide complete and valuable coverage up to 65 hr after the event, except for a gap between 3.5 and 8.0 hr. The 2-10 keV flux history shows clear signs of a break which is consistent with a break seen in the optical, and provides supporting evidence for the achromatic nature of the break. An explanation for the break in the context of a collimated expansion is not straightforward. Rather, a model is favored whereby the fireball is braked to the non-relativistic regime quickly (within a fraction of day) by a dense 1E6 cm-3 circumburst medium. This implies that, after a mild beaming correction, GRB010222 may be the most energetic burst observed thus far. The X-ray decay index after the break is 1.33+/-0.04, the spectral index 0.97+/-0.05. The decay is, with unprecedented accuracy, identical to that observed in the optical.Comment: Accepted on June 6 for publication in ApJ part I. Publication due in October 2001. Accepted version has only minor modification

Positronium Decay : Gauge Invariance and Analyticity

The construction of positronium decay amplitudes is handled through the use of dispersion relations. In this way, emphasis is put on basic QED principles: gauge invariance and soft-photon limits (analyticity). A firm grounding is given to the factorization approaches, and some ambiguities in the spin and energy structures of the positronium wavefunction are removed. Non-factorizable amplitudes are naturally introduced. Their dynamics is described, especially regarding the enforcement of gauge invariance and analyticity through delicate interferences. The important question of the completeness of the present theoretical predictions for the decay rates is then addressed. Indeed, some of those non-factorizable contributions are unaccounted for by NRQED analyses. However, it is shown that such new contributions are highly suppressed, being of order alpha^3. Finally, a particular effective form factor formalism is constructed for parapositronium, allowing a thorough analysis of binding energy effects and analyticity implementation.Comment: 34 pages, 13 figure

Intrinsic spectra and energetics of BeppoSAX Gamma-Ray Bursts with known redshifts

We present the main results of a study of spectral and energetics properties of twelve gamma-ray bursts (GRBs) with redshift estimates. All GRBs in our sample were detected by BeppoSAX in a broad energy range (2-700 keV). From the redshift estimates and the good-quality BeppoSAX time-integrated spectra we deduce the main properties of GRBs in their cosmological rest frames. All spectra in our sample are satisfactorily represented by the Band model with no significant soft X-ray excesses or spectral absorptions. We find a positive correlation between the estimated total (isotropic) energies in the 1-10000 keV energy range (E_rad) and redshifts z. Interestingly, more luminous GRBs are characterized also by larger peak energies E_p of their EF(E) spectra. Furthermore, more distant GRBs appear to be systematically harder in the X-ray band compared to GRBs with lower redshifts. We discuss how selection and data truncation effects could bias our results and give possible explanations for the correlations that we found.Comment: 10 pages, 5 figures, accepted for publication in Astronomy & Astrophysic