195 research outputs found
Extensive ground state entropy in supersymmetric lattice models
We present the result of calculations of the Witten index for a
supersymmetric lattice model on lattices of various type and size. Because the
model remains supersymmetric at finite lattice size, the Witten index can be
calculated using row-to-row transfer matrices and the calculations are similar
to calculations of the partition function at negative activity -1. The Witten
index provides a lower bound on the number of ground states. We find strong
numerical evidence that the Witten index grows exponentially with the number of
sites of the lattice, implying that the model has extensive entropy in the
ground state.Comment: 7 figure
Observational implications of gamma-ray burst afterglow jet simulations and numerical light curve calculations
We discuss jet dynamics for narrow and wide gamma-ray burst (GRB) afterglow
jets and the observational implications of numerical simulations of
relativistic jets in two dimensions. We confirm earlier numerical results that
sideways expansion of relativistic jets during the bulk of the afterglow
emission phase is logarithmic in time and find that this also applies to narrow
jets with half opening angle of 0.05 radians. As a result, afterglow jets
remain highly nonspherical until after they have become nonrelativistic.
Although sideways expansion steepens the afterglow light curve after the jet
break, the jet edges becoming visible dominates the jet break, which means that
the jet break is sensitive to the observer angle even for narrow jets. Failure
to take the observer angle into account can lead to an overestimation of the
jet energy by up to a factor 4. This weakens the challenge posed to the
magneter energy limit by extreme events such as GRB090926A. Late time radio
calorimetry based on a spherical nonrelativistic outflow model remains relevant
when the observer is approximately on-axis and where differences of a few in
flux level between the model and the simulation are acceptable. However, this
does not imply sphericity of the outflow and therefore does not translate to
high observer angles relevant to orphan afterglows. For more accurate
calorimetry and in order to model significant late time features such as the
rise of the counterjet, detailed jet simulations remain indispensable.Comment: 7 Figures. Replaced with accepted version. Significantly expanded,
including additional discussion of time scale
Off-Axis Afterglow Light Curves from High-Resolution Hydrodynamical Jet Simulations
Numerical jet simulations serve a valuable role in calculating gamma-ray
burst afterglow emission beyond analytical approximations. Here we present the
results of high resolution 2D simulations of decelerating relativistic jets
performed using the RAM adaptive mesh refinement relativistic hydrodynamics
code. We have applied a separate synchrotron radiation code to the simulation
results in order to calculate light curves at frequencies varying from radio to
X-ray for observers at various angles from the jet axis. We provide a
confirmation from radio light curves from simulations rather than from a
simplified jet model for earlier results in the literature finding that only a
very small number of local Ibc supernovae can possibly harbor an orphan
afterglow.
Also, recent studies have noted an unexpected lack of observed jet breaks in
the Swift sample. Using a jet simulation with physical parameters
representative for an average Swift sample burst, such as a jet half opening
angle of 0.1 rad and a source redshift of z = 2.23, we have created synthetic
light curves at 1.5 keV with artificial errors while accounting for Swift
instrument biases as well. A large set of these light curves have been
generated and analyzed using a Monte Carlo approach. Single and broken power
law fits are compared. We find that for increasing observer angle, the jet
break quickly becomes hard to detect. This holds true even when the observer
remains well within the jet opening angle. We find that the odds that a Swift
light curve from a randomly oriented 0.1 radians jet at z = 2.23 will exhibit a
jet break at the 3 sigma level are only 12 percent. The observer angle
therefore provides a natural explanation for the lack of perceived jet breaks
in the Swift sample.Comment: 4 pages, 3 figures. First of two contributions to proceedings GRB2010
Maryland conference. Editors: McEnery, Racusin and Gehrels. The data from
this paper is publicly available from http://cosmo.nyu.edu/afterglowlibrary
An on-line library of afterglow light curves
Numerical studies of gamma-ray burst afterglow jets reveal significant
qualitative differences with simplified analytical models. We present an
on-line library of synthetic afterglow light curves and broadband spectra for
use in interpreting observational data. Light curves have been calculated for
various physics settings such as explosion energy and circumburst structure, as
well as differing jet parameters and observer angle and redshift. Calculations
gave been done for observer frequencies ranging from low radio to X-ray and for
observer times from hours to decades after the burst. The light curves have
been calculated from high-resolution 2D hydrodynamical simulations performed
with the RAM adaptive-mesh refinement code and a detailed synchrotron radiation
code.
The library will contain both generic afterglow simulations as well as
specific case studies and will be freely accessible at
http://cosmo.nyu.edu/afterglowlibrary . The synthetic light curves can be used
as a check on the accuracy of physical parameters derived from analytical model
fits to afterglow data, to quantitatively explore the consequences of varying
parameters such as observer angle and for accurate predictions of future
telescope data.Comment: 4 pages, 2 figures. Second of two contributions to proceedings
GRB2010 Maryland conference. Editors: McEnery, Racusin and Gehrels. The data
from this paper is publicly available from
http://cosmo.nyu.edu/afterglowlibrary
From blast wave to observation
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 authors.
We also show the light curves resulting from a relativistic blast wave
encountering a wind termination shock. From high resolution calculations we
find that the observed transition from a stellar wind type light curve to an
interstellar medium type light curve is smooth and without short-time
transitory features.Comment: conference proceedings 6th Huntsville symposium, 20-23 October 2008.
Editors: C.A. Meegan, N. Gehrels, and C. Kouvelioto
Applying an accurate spherical model to gamma-ray burst afterglow observations
We present results of model fits to afterglow data sets of GRB970508,
GRB980703 and GRB070125, characterized by long and broadband coverage. The
model assumes synchrotron radiation (including self-absorption) from a
spherical adiabatic blast wave and consists of analytic flux prescriptions
based on numerical results. For the first time it combines the accuracy of
hydrodynamic simulations through different stages of the outflow dynamics with
the flexibility of simple heuristic formulas. The prescriptions are especially
geared towards accurate description of the dynamical transition of the outflow
from relativistic to Newtonian velocities in an arbitrary power-law density
environment. We show that the spherical model can accurately describe the data
only in the case of GRB970508, for which we find a circumburst medium density
consistent with a stellar wind. We investigate in detail the implied spectra
and physical parameters of that burst. For the microphysics we show evidence
for equipartition between the fraction of energy density carried by
relativistic electrons and magnetic field. We also find that for the blast wave
to be adiabatic, the fraction of electrons accelerated at the shock has to be
smaller than 1. We present best-fit parameters for the afterglows of all three
bursts, including uncertainties in the parameters of GRB970508, and compare the
inferred values to those obtained by different authors
No visible optical variability from a relativistic blast wave encountering a wind-termination shock
Gamma-ray burst afterglow flares and rebrightenings of the optical and X-ray
light curve have been attributed to both late time inner engine activity and
density changes in the medium surrounding the burster. To test the latter, we
study the encounter between the relativistic blast wave from a gamma-ray
burster and a stellar wind termination shock. The blast wave is simulated using
a high performance adaptive mesh relativistic hydrodynamics code, AMRVAC, and
the synchrotron emission is analyzed in detail with a separate radiation code.
We find no bump in the resulting light curve, not even for very high density
jumps. Furthermore, by analyzing the contributions from the different shock
wave regions we are able to establish that it is essential to resolve the blast
wave structure in order to make qualitatively correct predictions on the
observed output and that the contribution from the reverse shock region will
not stand out, even when the magnetic field is increased in this region by
repeated shocks. This study resolves a controversy in recent literature.Comment: 4 figures, submitted to MNRAS letter
Jet simulations and Gamma-ray burst afterglow jet breaks
The conventional derivation of the gamma-ray burst afterglow jet break time
uses only the blast wave fluid Lorentz factor and therefore leads to an
achromatic break. We show that in general gamma-ray burst afterglow jet breaks
are chromatic across the self-absorption break. Depending on circumstances, the
radio jet break may be postponed significantly. Using high-accuracy adaptive
mesh fluid simulations in one dimension, coupled to a detailed synchrotron
radiation code, we demonstrate that this is true even for the standard fireball
model and hard-edged jets. We confirm these effects with a simulation in two
dimensions. The frequency dependence of the jet break is a result of the angle
dependence of the emission, the changing optical depth in the self-absorbed
regime and the shape of the synchrotron spectrum in general. In the optically
thin case the conventional analysis systematically overestimates the jet break
time, leading to inferred opening angles that are underestimated by a factor
1.32 and explosion energies that are underestimated by a factor 1.73, for
explosions in a homogeneous environment.Comment: MNRAS submitted. 9 pages, 12 figure
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