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