Gamma-Ray Burst afterglow scaling coefficients for general density profile

Gamma-ray burst (GRB) afterglows are well described by synchrotron emission originating from the interaction between a relativistic blast wave and the external medium surrounding the GRB progenitor. We introduce a code to reconstruct spectra and light curves from arbitrary fluid configurations, making it especially suited to study the effects of fluid flows beyond those that can be described using analytical approximations. As a check and first application of our code we use it to fit the scaling coefficients of theoretical models of afterglow spectra. We extend earlier results of other authors to general circumburst density profiles. We rederive the physical parameters of GRB 970508 and compare with other authorsComment: 11 pages, 5 figures. Revised edition removes references to unphysical chromatic break and adds appendix on hot region directly behind shoc

Detailed study of the GRB 030329 radio afterglow deep into the non-relativistic phase

We explore the physics behind one of the brightest radio afterglows ever, GRB 030329, at late times when the jet is non-relativistic. We determine the physical parameters of the blast wave and its surroundings, in particular the index of the electron energy distribution, the energy of the blast wave, and the density (structure) of the circumburst medium. We then compare our results with those from image size measurements. We observed the GRB 030329 radio afterglow with the Westerbork Synthesis Radio Telescope and the Giant Metrewave Radio Telescope at frequencies from 325 MHz to 8.4 GHz, spanning a time range of 268-1128 days after the burst. We modeled all the available radio data and derived the physical parameters. The index of the electron energy distribution is p=2.1, the circumburst medium is homogeneous, and the transition to the non-relativistic phase happens at t_NR ~ 80 days. The energy of the blast wave and density of the surrounding medium are comparable to previous findings. Our findings indicate that the blast wave is roughly spherical at t_NR, and they agree with the implications from the VLBI studies of image size evolution. It is not clear from the presented dataset whether we have seen emission from the counter jet or not. We predict that the Low Frequency Array will be able to observe the afterglow of GRB 030329 and many other radio afterglows, constraining the physics of the blast wave during its non-relativistic phase even further.Comment: 9 pages, 2 figures; accepted for publication in Astronomy & Astrophysics after minor revisions; small changes in GMRT fluxes at 1280 MH

Quantum particle displacement by a moving localized potential trap

We describe the dynamics of a bound state of an attractive $\delta$-well under displacement of the potential. Exact analytical results are presented for the suddenly moved potential. Since this is a quantum system, only a fraction of the initially confined wavefunction remains confined to the moving potential. However, it is shown that besides the probability to remain confined to the moving barrier and the probability to remain in the initial position, there is also a certain probability for the particle to move at double speed. A quasi-classical interpretation for this effect is suggested. The temporal and spectral dynamics of each one of the scenarios is investigated.Comment: 5 pages, 6 figure

Retinal metric: a stimulus distance measure derived from population neural responses

The ability of the organism to distinguish between various stimuli is limited by the structure and noise in the population code of its sensory neurons. Here we infer a distance measure on the stimulus space directly from the recorded activity of 100 neurons in the salamander retina. In contrast to previously used measures of stimulus similarity, this "neural metric" tells us how distinguishable a pair of stimulus clips is to the retina, given the noise in the neural population response. We show that the retinal distance strongly deviates from Euclidean, or any static metric, yet has a simple structure: we identify the stimulus features that the neural population is jointly sensitive to, and show the SVM-like kernel function relating the stimulus and neural response spaces. We show that the non-Euclidean nature of the retinal distance has important consequences for neural decoding.Comment: 5 pages, 4 figures, to appear in Phys Rev Let

Stability of narrow beams in bulk Kerr-type nonlinear media

We consider (2+1)-dimensional beams, whose transverse size may be comparable to or smaller than the carrier wavelength, on the basis of an extended version of the nonlinear Schr\"{o}dinger equation derived from the Maxwell`s equations. As this equation is very cumbersome, we also study, in parallel to it, its simplified version which keeps the most essential term: the term which accounts for the {\it nonlinear diffraction}. The full equation additionally includes terms generated by a deviation from the paraxial approximation and by a longitudinal electric-field component in the beam. Solitary-wave stationary solutions to both the full and simplified equations are found, treating the terms which modify the nonlinear Schr\"{o}dinger equation as perturbations. Within the framework of the perturbative approach, a conserved power of the beam is obtained in an explicit form. It is found that the nonlinear diffraction affects stationary beams much stronger than nonparaxiality and longitudinal field. Stability of the beams is directly tested by simulating the simplified equation, with initial configurations taken as predicted by the perturbation theory. The numerically generated solitary beams are always stable and never start to collapse, although they display periodic internal vibrations, whose amplitude decreases with the increase of the beam power.Comment: 7 pages, 6 figures Accepted for publication in PR

Energy Injection in GRB Afterglow Models

We extend the standard fireball model, widely used to interpret gamma-ray burst (GRB) afterglow light curves, to include energy injections, and apply the model to the afterglow light curves of GRB 990510, GRB 000301C and GRB 010222. We show that discrete energy injections can cause temporal variations in the optical light curves and present fits to the light curves of GRB 000301C as an example. A continuous injection may be required to interpret other bursts such as GRB 010222. The extended model accounts reasonably well for the observations in all bands ranging from X-rays to radio wavelengths. In some cases, the radio light curves indicate that additional model ingredients may be needed.Comment: Accepted for publication in the Astrophysical Journa

Spectra and Light Curves of GRB Afterglows

We performed accurate numerical calculations of angle-, time-, and frequency-dependent radiative transfer for the relativistic motion of matter in gamma-ray burst (GRB) models. Our technique for solving the transfer equation, which is based on the method of characteristics, can be applied to the motion of matter with a Lorentz factor up to 1000. The effect of synchrotron self-absorption is taken into account. We computed the spectra and light curves from electrons with a power-law energy distribution in an expanding relativistic shock and compare them with available analytic estimates. The behavior of the optical afterglows from GRB 990510 and GRB 000301c is discussed qualitatively.Comment: 8 pages, 7 figure