Carlo Alberto Graziani

Probing the Cosmic Gamma-Ray Burst Rate with Trigger Simulations of the Swift Burst Alert Telescope

The gamma-ray burst (GRB) rate is essential for revealing the connection between GRBs, supernovae, and stellar evolution. Additionally, the GRB rate at high redshift provides a strong probe of star formation history in the early universe. While hundreds of GRBs are observed by Swift, it remains difficult to determine the intrinsic GRB rate due to the complex trigger algorithm of Swift. Current studies of the GRB rate usually approximate the Swift trigger algorithm by a single detection threshold. However, unlike the previously flown GRB instruments, Swift has over 500 trigger criteria based on photon count rate and an additional image threshold for localization. To investigate possible systematic biases and explore the intrinsic GRB properties, we develop a program that is capable of simulating all the rate trigger criteria and mimicking the image threshold. Our simulations show that adopting the complex trigger algorithm of Swift increases the detection rate of dim bursts. As a result, our simulations suggest that bursts need to be dimmer than previously expected to avoid overproducing the number of detections and to match with Swift observations. Moreover, our results indicate that these dim bursts are more likely to be high redshift events than low-luminosity GRBs. This would imply an even higher cosmic GRB rate at large redshifts than previous expectations based on star formation rate measurements, unless other factors, such as the luminosity evolution, are taken into account. The GRB rate from our best result gives a total number of GRBs per year that are beamed toward us in the whole universe.

AN IMPROVED MULTIPOLE APPROXIMATION FOR SELF-GRAVITY AND ITS IMPORTANCE FOR CORE-COLLAPSE SUPERNOVA SIMULATIONS

Self-gravity computation by multipole expansion is a common approach in problems such as core-collapse and Type Ia supernovae, where single large condensations of mass must be treated. The standard formulation of multipole self-gravity in arbitrary coordinate systems suffers from two significant sources of error, which we correct in the formulation presented in this article. The first source of error is due to the numerical approximation that effectively places grid cell mass at the central point of the cell, then computes the gravitational potential at that point, resulting in a convergence failure of the multipole expansion. We describe a new scheme that avoids this problem by computing gravitational potential at cell faces. The second source of error is due to sub-optimal choice of location for the expansion center, which results in angular power at high multipole l values in the gravitational field, requiring a high—and expensive—value of multipole cutoff l max. By introducing a global measure of angular power in the gravitational field, we show that the optimal coordinate for the expansion is the square-density-weighted mean location. We subject our new multipole self-gravity algorithm, implemented in the FLASH simulation framework, to two rigorous test problems: MacLaurin spheroids for which exact analytic solutions are known, and core-collapse supernovae. We show that key observables of the core-collapse simulations, particularly shock expansion, proto-neutron star motion, and momentum conservation, are extremely sensitive to the accuracy of the multipole gravity, and the accuracy of their computation is greatly improved by our reformulated solver.

RADIATION TRANSPORT FOR EXPLOSIVE OUTFLOWS: A MULTIGROUP HYBRID MONTE CARLO METHOD

We explore Implicit Monte Carlo (IMC) and discrete diffusion Monte Carlo (DDMC) for radiation transport in high-velocity outflows with structured opacity. The IMC method is a stochastic computational technique for nonlinear radiation transport. IMC is partially implicit in time and may suffer in efficiency when tracking MC particles through optically thick materials. DDMC accelerates IMC in diffusive domains. Abdikamalov extended IMC and DDMC to multigroup, velocity-dependent transport with the intent of modeling neutrino dynamics in core-collapse supernovae. Densmore has also formulated a multifrequency extension to the originally gray DDMC method. We rigorously formulate IMC and DDMC over a high-velocity Lagrangian grid for possible application to photon transport in the post-explosion phase of Type Ia supernovae. This formulation includes an analysis that yields an additional factor in the standard IMC-to-DDMC spatial interface condition. To our knowledge the new boundary condition is distinct from others presented in prior DDMC literature. The method is suitable for a variety of opacity distributions and may be applied to semi-relativistic radiation transport in simple fluids and geometries. Additionally, we test the code, called SuperNu, using an analytic solution having static material, as well as with a manufactured solution for moving material with structured opacities. Finally, we demonstrate with a simple source and 10 group logarithmic wavelength grid that IMC-DDMC performs better than pure IMC in terms of accuracy and speed when there are large disparities between the magnitudes of opacities in adjacent groups. We also present and test our implementation of the new boundary condition.

Design and Performance of the Wide-Field X-Ray Monitor on Board the High-Energy Transient Explorer 2

The Wide-field X-ray Monitor (WXM) is one of the scientific instruments carried on the High Energy Transient Explorer 2 (HETE-2) satellite launched on 2000 October 9. HETE-2 is an international mission consisting of a small satellite dedicated to provide broad-band observations and accurate localizations of gamma-ray bursts (GRBs). A unique feature of this mission is its capability to determine and transmit GRB coordinates in almost real-time through the burst alert network. The WXM consists of three elements: four identical Xe-filled one-dimensional positionsensitive proportional counters, two sets of one-dimensional coded apertures, and the main electronics. The WXM counters are sensitive to X-rays between 2keV and 25keV within a field-of-view of about 1.5sr, with a total detector area of about 350cm 2 . The in-flight triggering and localization capability can produce a real-time GRB location of several to 30arcmin accuracy, with a limiting sensitivityof 10 −7 ergcm −2 . In this report, the details of the mechanical structure, electronics, on-board software, ground and in-flight calibration, and in-flight performance of the WXM are discussed.

Strong-field cyclotron scattering. I: Scattering amplitudes and natural line width

The introduction of resonance line width into the QED cyclotron scattering amplitudes is considered. It is shown that the width arises from loop corrections to the electron propagator, which also bring about shifts in the Landau energy levels. A formalism is developed that allows the dressed electron propagator to be derived. It is shown that the states of Herold, Ruder, & Wunner, and of Sokolov & Ternov, which diagonalize the component of the magnetic moment operator parallel to the external magnetic field, are appropriate for calculation of the scattering amplitudes, whereas the states of Johnson & Lippmann are not

Spectral-Lag Relations in GRB Pulses Detected with HETE-2

Using a pulse-fit method, we investigated the spectral lags between the traditional gamma-ray band (50–400 keV) and the X-ray band (6–25 keV) for 8 GRBs with known redshifts (GRB 010921, GRB 020124, GRB 020127, GRB 021211, GRB 030528, GRB 040924, GRB 041006, and GRB 050408), detected with the WXM and FREGATE instruments aboard the HETE-2 satellite. We found several relations for individual GRB pulses between the spectral lag and other observables, such as the luminosity, pulse duration, and peak energy, Epeak. The obtained results are consistent with those for BATSE, indicating that the BATSE correlations are still valid at lower energies (6–25 keV). Furthermore, we found that the photon energy dependence for the spectral lags can be reconciled with the simple curvature effect model. We discuss the implications of these results from various points of view.

GRBs as standard candles: There is no “circularity problem” (and there never was)

Abstract Beginning with the 2002 discovery of the “Amati Relation” of GRB spectra, there has been much interest in the possibility that this and other correlations of GRB phenomenology might be used to make GRBs into standard candles. One recurring apparent difficulty with this program has been that some of the primary observational quantities to be fit as “data” – to wit, the isotropic-equivalent prompt energy Eiso and the collimation-corrected “total” prompt energy Eγ – depend for their construction on the very cosmological models that they are supposed to help constrain. This is the so-called “circularity problem” of standard candle GRBs. This paper is intended to point out that the circularity problem is not in fact a problem at all, except to the extent that it amounts to a self-inflicted wound. It arises essentially because of an unfortunate choice of data variables – “source-frame” variables such as Eiso, which are unnecessarily encumbered by cosmological considerations. If, instead, the empirical correlations of GRB phenomenology which are formulated in source-variables are mapped to the primitive observational variables (such as fluence) and compared to the observations in that space, then all taint of circularity disappears. I also indicate here a set of procedures for encoding high-dimensional empirical correlations (such as between Eiso, E pk ( src ) , t jet ( src ) , and T 45 ( src ) ) in a “Gaussian Tube” smeared model that includes both the correlation and its intrinsic scatter, and how that source-variable model may easily be mapped to the space of primitive observables, to be convolved with the measurement errors and fashioned into a likelihood. I discuss the projections of such Gaussian tubes into sub-spaces, which may be used to incorporate data from GRB events that may lack some element of the data (for example, GRBs without ascertained jet-break times). In this way, a large set of inhomogeneously observed GRBs may be assimilated into a single analysis, so long as each possesses at least two correlated data attributes.

Numerical modeling of laser-driven experiments aiming to demonstrate magnetic field amplification via turbulent dynamo

The universe is permeated by magnetic fields, with strengths ranging from a femtogauss in the voids between the filaments of galaxy clusters to several teragauss in black holes and neutron stars. The standard model behind cosmological magnetic fields is the nonlinear amplification of seed fields via turbulent dynamo to the values observed. We have conceived experiments that aim to demonstrate and study the turbulent dynamo mechanism in the laboratory. Here, we describe the design of these experiments through simulation campaigns using FLASH, a highly capable radiation magnetohydrodynamics code that we have developed, and large-scale three-dimensional simulations on the Mira supercomputer at the Argonne National Laboratory. The simulation results indicate that the experimental platform may be capable of reaching a turbulent plasma state and determining the dynamo amplification. We validate and compare our numerical results with a small subset of experimental data using synthetic diagnostics.

Localization of GRBs by Bayesian Analysis of Data from the HETE WXM

We describe a new method of transient point source localization for coded‐aperture X‐ray detectors that we have applied to data from the HETE Wide‐Field X‐Ray Monitor (WXM). The method is based upon the calculation of the likelihood function and its interpretation as a probability density for the transient source location by an application of Bayes’ Theorem. The method gives a point estimate of the source location by finding the maximum of this probability density, and credible regions for the source location by choosing suitable contours of constant probability density. We describe the application of this method to data from the WXM, and give examples of GRB localizations which illustrate the results that can be obtained using this method.

Multiple-component analysis of the time-resolved spectra of GRB 041006: A clue to the nature of the underlying soft component of GRBs

GRB 041006 was detected by HETE-2 on 2004 October 06. The light curves in four different energy bands display different features. At higher energy bands several peaks are seen in the light curve, while at lower energy bands a single broader bump dominates. It is expected that these different features are the result of a mixture of several components, each of which has different energetics and variability. We analyzed the time-resolved spectra, which were resolved into several components. These components can be classified into two distinct classes. One is a component that has an exponential decay of Ep with a characteristic timescale shorter than � 30 s; its spectrum is well represented by a broken power-law function, which is frequently observed in many prompt GRB emissions, so it should have an internal-shock origin. Another is a component whose Ep is almost unchanged with a characteristic timescale longer than � 60 s, and shows a very soft emission and slower variability. The spectrum is characterized by either a broken power law or a black-body spectrum. By assuming that the soft component is a thermal emission, the radiation radius is initially 4:4� 10 6 km, which is a typical radius of a blue supergiant, and its expansion velocity is 2:4� 10 5 km s � 1 in the source frame.