Uniform External Medium Research Articles

Fast Standing Modes in Transversley Nonuniform Solar Coronal Slabs: The Effects of a Finite Plasma Beta

Abstract We examine the dispersive properties of linear fast standing modes in transversely nonuniform solar coronal slabs with finite gas pressure, or, equivalently, finite plasma beta. We derive a generic dispersion relation governing fast waves in coronal slabs, for which the continuous transverse distributions of the physical parameters comprise a uniform core, a uniform external medium, and a transition layer (TL) in between. The profiles in the TL are allowed to be essentially arbitrary. Restricting ourselves to the first several branches of fast modes, which are mostly interesting from an observational standpoint, we find that a finite plasma beta plays an at most marginal role in influencing the periods (P), damping times (τ), and critical longitudinal wavenumbers ( ), when both P and τ are measured in units of the transverse fast time. However, these parameters are in general significantly affected by how the TL profiles are described. We conclude that, for typical coronal structures, the dispersive properties of the first several branches of fast standing modes can be evaluated with the much simpler theory for cold slabs, provided that the transverse profiles are properly addressed and the transverse Alfvén time in cold MHD is replaced with the transverse fast time.

SIMULATIONS OF GAMMA-RAY BURST JETS IN A STRATIFIED EXTERNAL MEDIUM: DYNAMICS, AFTERGLOW LIGHT CURVES, JET BREAKS, AND RADIO CALORIMETRY

The dynamics of GRB jets during the afterglow phase is most reliably and accurately modelled using hydrodynamic simulations. All published simulations, however, have considered only a uniform external medium, while a stratified external medium is expected around long duration GRB progenitors. Here we present simulations of the dynamics of GRB jets and the resulting afterglow emission for both uniform and stratified external media with $\rho \propto r^{-k}$ for k = 0, 1, 2. The simulations are performed in 2D using the special relativistic version of the Mezcal code. The dynamics for stratified external media are broadly similar to those derived for expansion into a uniform external medium. The jet half-opening angle start increasing logarithmically with time once the Lorentz factor drops below 1/theta_0. For larger k values the lateral expansion is faster at early times and slower at late times with the jet expansion becoming Newtonian and slowly approaching spherical symmetry over progressively longer timescales. We find that contrary to analytic expectations, there is a reasonably sharp jet break in the lightcurve for k = 2 although the shape of the break is affected more by the viewing angle than by the slope of the external density profile. Steeper density profiles are found to produce more gradual jet breaks while larger viewing angles cause smoother and later appearing jet breaks. The counter-jet becomes visible as it becomes sub-relativistic, and for k=0 this results in a clear bump-like feature in the light curve. However, for larger k values the jet decelerates more gradually, causing only a mild flattening in the radio light curve that might be hard to discern when k=2. Late time radio calorimetry is likely to consistently over-estimate the true energy by up to a factor of a few for k=2, and either over-predict or under-predict it by a smaller factor for k = 0,1.

Smooth light curves from a bumpy ride: relativistic blast wave encounters a density jump

In the standard forward shock model for gamma-ray burst (GRB) afterglow, the observed afterglow emission is synchrotron radiation from a quasi-spherical, adiabatic, self-similar, relativistic blast wave, that propagates into the external medium. This model predicts a smooth light curve where the flux scales as a power law in time, and may at most smoothly transition to a different power law. However, some GRB afterglow light curves show significant variability, which often includes episodes of rebrightening. Such temporal variability had been attributed in several cases to a large enhancement in the external density, or a density ‘bump’, that is encountered by the self-similar adiabatic blast wave. Here we examine the effect of a sharp increase in the external density on the afterglow light curve in this scenario by considering, for the first time, a full treatment of both the hydrodynamic evolution and the radiation. To this end we develop a semi-analytic model for the light curve and carry out numerical simulations using a one-dimensional hydrodynamic code together with a synchrotron radiation code. Two spherically symmetric cases are explored in detail – a density jump in a uniform external medium (which is used to constrain the effect of a density clump) and a wind termination shock. We find that even a very sharp (modelled as a step function) and large (by a factor of a≫ 1) increase in the external density does not produce sharp features in the light curve, and cannot account for significant temporal variability in GRB afterglows in the forward shock model. For a wind termination shock, the light curve smoothly transitions between the asymptotic power laws over about one decade in time, and there is no rebrightening in the optical or X-rays that could serve as a clear observational signature. For a sharp jump in a uniform density profile, we find that the maximal deviation Δαmax of the temporal decay index α from its asymptotic value (at early and late times) is bounded (e.g, Δαmax < 0.4 for a= 10); Δαmax slowly increases with a, converging to Δαmax≈ 1 at very large a values. Therefore, no optical rebrightening is expected in this case as well. In the X-rays, while the asymptotic flux is unaffected by the density jump, the fluctuations in α are found to be comparable to those in the optical. Finally, we discuss the implications of our results for the origin of the observed fluctuations in several GRB afterglows.

Swift and XMM-Newton observations of the dark GRB 050326

We present Swift and XMM observations of GRB 050326, detected by Swift-BAT. The fluence was 7.7x10^-6 erg cm^-2 (20-150 keV), and its spectrum was hard, with a power law photon index 1.25. The afterglow light curve did not show any break nor flares between ~1 hr and ~6 d after the burst, and decayed with a slope 1.70. The afterglow spectrum is well fitted by a power-law model, suffering absorption both in the Milky Way and in the host galaxy. The rest-frame Hydrogen column density is significant, N_H_z > 4x10^21 cm^-2, and the redshift of the absorber is z > 1.5. There was good agreement between the Swift-XRT and XMM results. By comparing the prompt and afterglow fluxes, we found that an early break occurred before the XRT observation. The properties of the GRB 050326 afterglow are well described by a spherical fireball expanding in a uniform external medium, so a further steepening is expected at later times. The lack of such a break constrains the jet angle to be >7 deg. Using the redshift constraints provided by the X-ray analysis, we also estimated that the beaming-corrected gamma-ray energy was >3x10^51 erg, at the high end of GRB energies. Despite the brightness in X rays, only deep limits could be placed by Swift-UVOT at optical/UV wavelengths. Thus, this GRB was "truly dark", with the optical-to-X-ray spectrum violating the synchrotron limit. The optical and X-ray observations are consistent either with an absorbed event or with a high-redshift one. To obey the Ghirlanda relation, a moderate/large redshift z>4.5 is required. (abridged)

Revealing the Jet Structure of GRB 030329 with High-Resolution Multicolor Photometry

We present multicolor optical observations of the nearby (z=0.1685) GRB 030329 obtained with the same instrumentation over a time period of 6 hours for a total of an unprecedented 475 quasi-simultaneous BVR observations. The achromatic steepening in the optical, which occurs at t~0.7 days, provides evidence for a dynamic transition of the source, and can be most readily explained by models in which the GRB ejecta are collimated into a jet. Since the current state-of-the-art modeling of GRB jets is still flawed with uncertainties, we use these data to critically assess some classes of models that have been proposed in the literature. The data, especially the smooth decline rate seen in the optical afterglow, are consistent with a model in which GRB 030329 was a homogeneous, sharp-edged jet, viewed near its edge interacting with a uniform external medium, or viewed near its symmetry axis with a stratified wind-like external environment. The lack of short timescale fluctuations in the optical afterglow flux down to the 0.5 per cent level puts stringent constraints on possible small scale angular inhomogeneities within the jet or fluctuations in the external density.

Implications of the Measured Image Size for the Radio Afterglow of GRB 030329

We use data on the image size of the radio afterglow of GRB 030329 to constrain the physical parameters of this explosion. Together with the observed broadband spectrum, this data overconstrains the physical parameters, thus enabling us to test different GRB jet models for consistency. We consider two extreme models for the lateral spreading of the jet: model 1, with relativistic expansion in the local rest frame, and model 2, with little lateral expansion as long as the jet is highly relativistic. We find that both models are consistent with the data for a uniform external medium, while for a stellar wind environment model 1 is consistent with the data but model 2 is disfavored by the data. Our derivations can be used to place tighter constraints on the dynamics and structure of GRB jets in future afterglows, following a denser monitoring campaign for the temporal evolution of their image size.

Synthetic X-ray light curves of BL Lacs from relativistic hydrodynamic simulations

We present the results of relativistic hydrodynamic simulations of the collision of two dense shells in a uniform external medium, as envisaged in the internal shock model for BL Lac jets. The non-thermal radiation produced by highly energetic electrons injected at the relativistic shocks is computed following their temporal and spatial evolution. The acceleration of electrons at the relativistic shocks is parametrized using two different models and the corresponding X-ray light curves are computed. We find that the interaction time scale of the two shells is influenced by an interaction with the external medium. For the chosen parameter sets, the efficiency of the collision in converting dissipated kinetic energy into the observed X-ray radiation is of the order of one percent.

The large-scale structure of FR-II radio sources

The large-scale flow produced by classical and relativistic jets in a uniform external medium is explored using a combination of general arguments and numerical simulations. We find that in both cases, jets with finite initial opening angles are recollimated by the high pressure in the cocoon and that the outer flow becomes approximately self-similar at large times. However, if the opening angle is significantly less than 20°, then there is an intermediate stage during which the working surface propagates at a constant speed, which is of the same order as that in the jet. The behaviour of the relativistic and classical jets is very similar, except that the relativistic jets generate lighter cocoons. Application of the model to Cygnus A gives estimates of the source age and advance speed which agree very well with spectral ageing observations. Quantitative estimates and general arguments suggest that the regularly spaced knots in the Cygnus A jet can be interpreted as shocks associated with reconfinement of an initially free jet, knot 3 of the Cygnus A jet being identified with the reflection point of the reconfinement shock. However, the model predicts too large an initial opening angle for the Cygnus A jets. It is possible that this discrepancy is due to our imposition of axisymmetry which allows the numerical jets to become much better collimated after the reconfinement than they would be in the three-dimensional case. Further study is needed to test this idea.