469 research outputs found
Gamma-ray burst afterglow plateau break time - luminosity correlations favour thick shell models over thin shell models
A number of correlations between observables have been found to exist for
gamma-ray burst (GRB) afterglows, linking ejecta energy to prompt and afterglow
energy release and linking early stage optical and X-ray luminosity to the end
times of these stages. Here, these correlations are compared to thick and thin
shell models for GRB afterglows. In the thick shell model, the time evolution
of the underlying relativistic blast wave is still influenced by the original
ejecta, while in the thin shell model most energy in the explosion has been
transferred to the external medium. It is shown here that the observed
correlations rule out basic thin shell models but not the basic thick shell
model. In the thick shell case, both forward shock and reverse shock dominated
outflows are shown to be consistent with the correlations, using randomly
generated samples of thick shell model afterglows.Comment: 11 pages, 4 figures. Expanded version, now matches MNRAS accepted
versio
Self-similar relativistic blast waves with energy injection
A sufficiently powerful astrophysical source with power law luminosity in
time will give rise to a self-similar relativistic blast wave with a reverse
shock traveling into the ejecta and a forward shock moving into the surrounding
medium. Once energy injection ceases and the last energy is delivered to the
shock front, the blast wave will transit into another self-similar stage
depending only on the total amount of energy injected.
I describe the effect of limited duration energy injection into environments
with density depending on radius as a power law, emphasizing optical / X-ray
Gamma-ray Burst afterglows as applications. The blast wave during injection is
treated analytically, the transition following last energy injection with
one-dimensional simulations. Flux equations for synchrotron emission from the
forward and reverse shock regions are provided. The reverse shock emission can
easily dominate, especially with different magnetizations for both regions.
Reverse shock emission is shown to support both the reported X-ray and optical
correlations between afterglow plateau duration and end time flux,
independently of the luminosity power law slope. The model is demonstrated by
application to bursts 120521A and 090515, and can accommodate their steep
post-plateau light curve slopes.Comment: Revised and corrected. Matches MNRAS accepted versio
Simulation and physical model based gamma-ray burst afterglow analysis
Advances in our numerical and theoretical understanding of gamma-ray burst
afterglow processes allow us to construct models capable of dealing with
complex relativistic jet dynamics and non-thermal emission, that can be
compared directly to data from instruments such as Swift. Because afterglow
blast waves and power law spectra are intrinsically scale-invariant under
changes of explosion energy and medium density, templates can be generated from
large-scale hydrodynamics simulations. This allows for iterative template-based
model fitting using the physical model parameters (quantifying the properties
of the burster, emission and observer) directly as fit variables. Here I review
how such an approach to afterglow analysis works in practice, paying special
attention to the underlying model assumptions, possibilities, caveats and
limitations of this type of analysis. Because some model parameters can be
degenerate in certain regions of parameter space, or unconstrained if data in a
limited number of a bands is available, a Bayesian approach is a natural fit.
The main features of the standard afterglow model are reviewed in detail.Comment: Invited contribution to Journal of High Energy Astrophysics special
issue "Swift: 10 years of discovery". Replaced with expanded version matching
JHEAP publicatio
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
Gamma-ray burst afterglow scaling relations for the full blast wave evolution
We demonstrate that gamma-ray burst afterglow spectra and light curves can be
calculated for arbitrary explosion and radiation parameters by scaling the peak
flux and the critical frequencies connecting different spectral regimes. Only
one baseline calculation needs to be done for each jet opening angle and
observer angle. These calculations are done numerically using high-resolution
relativistic hydrodynamical afterglow blast wave simulations which include the
two-dimensional dynamical features of expanding and decelerating afterglow
blast waves. Any light curve can then be generated by applying scaling
relations to the baseline calculations.
As a result, it is now possible to fully fit for the shape of the jet break,
e.g. at early time X-ray and optical frequencies. In addition, late-time radio
calorimetry can be improved since the general shape of the transition into the
Sedov-Taylor regime is now known for arbitrary explosion parameters so the
exact moment when the Sedov-Taylor asymptote is reached in the light curve is
no longer relevant.
When calculating the baselines, we find that the synchrotron critical
frequency and the cooling break frequency are strongly affected by the jet
break. The synchrotron break temporal slope quickly drops to the steep late
time Sedov-Taylor slope, while the cooling break first steepens then rises to
meet the level of its shallow late time asymptote.Comment: ApJL accepted. Some discussion of microphysics parameters added in
updated versio
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
Fitting Afterglows With Multi-Dimensional Simulations
We present preliminary data fit results of synthetic light curves computed
from numerical afterglow blast wave simulations. Our technique uses Markov
chain Monte Carlo (MCMC) in a new data analysis tool, ScaleFit. Scaling
relations in both the hydrodynamics and radiation equations allow light curves
to be parameterized by a small set of scale-invariant characteristic
quantities. These quantities have been calculated and tabulated from high
resolution two-dimensional hydrodynamic simulations. Producing a light curve
from the characteristics takes only a millisecond, allowing for the use of MCMC
data fitting techniques which can require millions of iterations. ScaleFit is a
portable, lightweight, python package which performs this analysis on afterglow
light curves. Using the set of Swift-XRT light curves from 2011 & 2012 with
known redshifts, we find ScaleFit can measure the jet opening angle, observer
angle, and spectral index of most afterglows. Globally we find gamma-ray burst
afterglows tend to be observed off axis, at a significant fraction of the jet
opening angle.Comment: 8 pages, 3 figures. 7th Huntsville Gamma-Ray Burst Symposium, GRB
2013: paper #30 in eConf Proceedings C130414
GRB Afterglow Blast Wave Encountering Sudden Circumburst Density Change Produces No Flares
Afterglows of gamma-ray bursts are observed to produce light curves with the
flux following power law evolution in time. However, recent observations reveal
bright flares at times on the order of minutes to days. One proposed
explanation for these flares is the interaction of a relativistic blast wave
with a circumburst density transition. In this paper, we model this type of
interaction computationally in one and two dimensions, using a relativistic
hydrodynamics code with adaptive mesh refinement called ram, and analytically
in one dimension. We simulate a blast wave traveling in a stellar wind
environment that encounters a sudden change in density, followed by a
homogeneous medium, and compute the observed radiation using a synchrotron
model. We show that flares are not observable for an encounter with a sudden
density increase, such as a wind termination shock, nor for an encounter with a
sudden density decrease. Furthermore, by extending our analysis to two
dimensions, we are able to resolve the spreading, collimation, and edge effects
of the blast wave as it encounters the change in circumburst medium. In all
cases considered in this paper, we find that a flare will not be observed for
any of the density changes studied.Comment: 7th Huntsville Gamma-Ray Burst Symposium, GRB 2013: paper 26 in eConf
Proceedings C130414
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