Angular size and emission time scales of relativistic fireballs

The detection of delayed X-ray, optical and radio emission, ``afterglow,'' associated with gamma-ray bursts (GRBs) is consistent with models, where the bursts are produced by relativistic expanding blast waves, driven by expanding fireballs at cosmological distances. In particular, the time scales over which radiation is observed at different wave bands agree with model predictions. It had recently been claimed that the commonly used relation between observation time t and blast wave radius r, t=r/2\gamma^{2}c where \gamma(r) is the fluid Lorentz factor, should be replaced with t=r/16\gamma^{2}c due to blast wave deceleration. Applying the suggested deceleration modification would make it difficult to reconcile observed time scales with model predictions. It would also imply an apparent source size which is too large to allow attributing observed radio variability to diffractive scintillation. We present a detailed analysis of the implications of the relativistic hydrodynamics of expanding blast waves to the observed afterglow. We find that modifications due to shock deceleration are small, therefore allowing for both the observed afterglow time scales and for diffractive scintillation. We show that at time t the fireball appears on the sky as a narrow ring of radius h=r/\gamma and width 0.1h, where r and t are related by t=r/2\gamma^{2}c.Comment: Submitted to ApJL (11 pages, LaTeX

Gamma-Ray Burst Afterglow: Polarization and Analytic Light Curves

GRB afterglow polarization is discussed. We find an observable, up to 10%, polarization, if the magnetic field coherence length grows at about the speed of light after the field is generated at the shock front. Detection of a polarized afterglow would show that collisionless ultrarelativistic shocks can generate strong large scale magnetic fields and confirm the synchrotron afterglow model. Non-detection, at a 1% level, would imply that either the synchrotron emission model is incorrect, or that strong magnetic fields, after they are generated in the shock, somehow manage to stay un-dissipated at ``microscopic'', skin depth, scales. Analytic lightcurves of synchrotron emission from an ultrarelativistic self-similar blast wave are obtained for an arbitrary electron distribution function, taking into account the effects of synchrotron cooling. The peak synchrotron flux and the flux at frequencies much smaller than the peak frequency are insensitive to the details of the electron distribution function; hence their observational determination would provide strong constraints on blast wave parameters.Comment: 19 pages, submitted to Ap

Radiative Efficiencies of Continuously Powered Blast Waves

We use general arguments to show that a continuously powered radiative blast wave can behave self similarly if the energy injection and radiation mechanisms are self similar. In that case, the power-law indices of the blast wave evolution are set by only one of the two constituent physical mechanisms. If the luminosity of the energy source drops fast enough, the radiation mechanisms set the power-law indices, otherwise, they are set by the behavior of the energy source itself. We obtain self similar solutions for the Newtonian and the ultra-relativistic limits. Both limits behave self similarly if we assume that the central source supplies energy in the form of a hot wind, and that the radiative mechanism is the semi-radiative mechanism of Cohen, Piran & Sari (1998). We calculate the instantaneous radiative efficiencies for both limits and find that a relativistic blast wave has a higher efficiency than a Newtonian one. The instantaneous radiative efficiency depends strongly on the hydrodynamics and cannot be approximated by an estimate of local microscopic radiative efficiencies, since a fraction of the injected energy is deposited in shocked matter. These solutions can be used to calculate Gamma Ray Bursts afterglows, for cases in which the energy is not supplied instantaneously.Comment: 28 LaTeX pages, including 9 figures and 3 table

Extra galactic sources of high energy neutrinos

The main goal of the construction of large volume, high energy neutrino telescopes is the detection of extra-Galactic neutrino sources. The existence of such sources is implied by observations of ultra-high energy, >10^{19} eV, cosmic-rays (UHECRs), the origin of which is a mystery. The observed UHECR flux sets an upper bound to the extra-Galactic high energy neutrino intensity, which implies that the detector size required to detect the signal in the energy range of 1 TeV to 1 PeV is >=1 giga-ton, and much larger at higher energy. Optical Cerenkov neutrino detectors, currently being constructed under ice and water, are expected to achieve 1 giga-ton effective volume for 1 TeV to 1 PeV neutrinos. Coherent radio Cerenkov detectors (and possibly large air-shower detectors) will provide the >> 1 giga-ton effective volume required for detection at ~10^{19} eV. Detection of high energy neutrinos associated with electromagnetically identified sources will allow to identify the sources of UHECRs, will provide a unique probe of the sources, which may allow to resolve open questions related to the underlying physics of models describing these powerful accelerators, and will provide information on fundamental neutrino properties.Comment: 8 pages, 4 figures; Summary of talk presented at the Nobel Symposium 129: Neutrino Physics, Sweden 200

GeV Photons from Ultra High Energy Cosmic Rays accelerated in Gamma Ray Bursts

Gamma-ray bursts are produced by the dissipation of the kinetic energy of a highly relativistic fireball, via the formation of a collisionless shock. When this happens, Ultra High Energy Cosmic Rays up to 10^20 eV are produced. I show in this paper that these particles produce, via synchrotron emission as they cross the acceleration region, photons up to 300 GeV which carry away a small, ~0.01, but non-negligible fraction of the total burst energy. I show that, when the shock occurs with the interstellar medium, the optical depth to photon-photon scattering, which might cause energy degradation of the photons, is small. The burst thusly produced would be detected at Earth simultaneoulsy with the parent gamma-ray burst, although its duration may differ significantly from that of the lower energy photons. The expected fluences, ~10^{-5}-10^{-6} erg/cm^2 are well within the range of planned detectors. A new explanation for the exceptional burst GRB 940217 is discussed.Comment: Accepted for publication in The Physical Review Letters. 4 pages, RevTeX needed, no figure

High Energy Neutrinos from Astrophysical Sources: An Upper Bound

We show that cosmic-ray observations set a model-independent upper bound to the flux of high-energy, > 10^14 eV, neutrinos produced by photo-meson (or p-p) interactions in sources of size not much larger than the proton photo-meson (or pp) mean-free-path. The bound applies, in particular, to neutrino production by either AGN jets or GRBs. This upper limit is two orders of magnitude below the flux predicted in some popular AGN jet models, but is consistent with our predictions from GRB models. We discuss the implications of these results for future km^2 high-energy neutrino detectors.Comment: Added discussion showing bound cannot be evaded by invoking magnetic fields. Accepted Phys Rev

The Gradient Expansion for the Free-Energy of a Clean Superconductor

We describe a novel method for obtaining the gradient expansion for the free energy of a clean BCS superconductor. We present explicit results up to fourth order in the gradients of the order parameter.Comment: 33 pages, Late

High energy cosmic-rays: puzzles, models, and giga-ton neutrino telescopes

The existence of cosmic rays of energies exceeding 10^20 eV is one of the mysteries of high energy astrophysics. The spectrum and the high energy to which it extends rule out almost all suggested source models. The challenges posed by observations to models for the origin of high energy cosmic rays are reviewed, and the implications of recent new experimental results are discussed. Large area high energy cosmic ray detectors and large volume high energy neutrino detectors currently under construction may resolve the high energy cosmic ray puzzle, and shed light on the identity and physics of the most powerful accelerators in the universe.Comment: 12 pages, 7 figures; Summary of review talk, PASCOS 03 (Mumbai, India

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

Implications of the γ\gamma-ray Polarization of GRB 021206

We compare two possible scenarios for the producing of high level of polarization within the prompt emission of a GRB: synchrotron emission from a relativistic jet with a uniform (in space and time) magnetic field and synchrotron emission from a jet with a random magnetic field in the plane of the shock. Somewhat surprisingly we find that both scenarios can produce a comparable level of polarization ($\sim 45-50$% for the uniform field and $\sim 30-35$% for a random field). Uniform time independent field most naturally arises by expansion of the field from the compact object. It requires a $10^{12}$G field at the source and a transport of the field as $\propto R^{-1}$. It {\it does not} imply Poynting flux domination of the energy of the wind. There is a serious difficulty however, within this scenario, accounting for particle acceleration (which requires random magnetic fields) both for Poynting flux and non-Poynting flux domination. Significant polarization can also arise from a random field provided that the observer is located within $1/\Gamma$ orientation from a narrow ($\theta_j \sim 1/\Gamma$) jet. While most jets are wider, the jet of GRB 021206 from which strong polarization was recently observed, was most likely very narrow. GRB 021206 is among the strongest bursts ever. Adopting the energy-angle relation we find an estimated angle of $<1/40$rad or even smaller. Thus, for this particular burst the required geometry is not unusual. We conclude that the RHESSI observations suggest that the prompt emission results from synchrotron radiation. However, in view of the comparable levels of polarizations predicted by both the random field and the homogeneous field scenarios these observations are insufficient to rule out or confirm either one.Comment: 14 pages, 4 figure