971 research outputs found
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 -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
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