Gamma-ray bursts: post-burst evolution of fireballs

The post-burst evolution of fireballs that produce γ-ray bursts (GRBs) is studied, assuming the expansion of fireballs to be adiabatic and relativistic. Numerical results as well as an approximate analytic solution for the evolution are presented. Owing to the adoption of a new relation between t R and γ, our results differ markedly from previous studies. Synchrotron radiation from the shocked interstellar medium is carefully calculated, using a conventional set of equations. The observed X-ray flux of GRB afterglows can be reproduced easily. Although the optical afterglows seem much more complicated, our results can still present a rather satisfactory agreement with observations. We also find that the expansion will no longer be highly relativistic about 4 d after the main GRB. We thus suggest that the marginally relativistic phase of the expansion should be investigated so as to check the afterglows observed a week or more later.     

Spectral lag of gamma‐ray bursts caused by the intrinsic spectral evolution and the curvature effect

Assuming an intrinsic ‘Band’ shape spectrum and an intrinsic energy‐independent emission profile we have investigated the connection between the evolution of the rest‐frame spectral parameters and the spectral lags measured in gamma‐ray burst (GRB) pulses by using a pulse model. We first focus our attention on the evolution of the peak energy, E_0,p, and neglect the effect of the curvature effect. It is found that the evolution of E_0,p alone can produce the observed lags. When E_0,p varies from hard to soft only the positive lags can be observed. The negative lags would occur in the case of E_0,p varying from soft to hard. When the evolution of E_0,p and the low‐energy spectral index α₀ varying from soft to hard then to soft we can find the aforesaid two sorts of lags. We then examine the combined case of the spectral evolution and the curvature effect of fireball and find the observed spectral lags would increase. A sample including 15 single pulses whose spectral evolution follows hard to soft has been investigated. All the lags of these pulses are positive, which is in good agreement with our theoretical predictions. Our analysis shows that only the intrinsic spectral evolution can produce the spectral lags and the observed lags should be contributed by the intrinsic spectral evolution and the curvature effect. But it is still unclear what cause the spectral evolution (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

White dwarf stars as strange quark matter detectors – III

We continue the study of the properties of non-radial pulsations of strange dwarfs. These stars are essentially white dwarfs with a strange quark matter (SQM) core. We have previously shown that the spectrum of oscillations should be formed by several, well-detached clusters of modes inside which the modes are almost evenly spaced. Here, we study the relation between the characteristics of these clusters and the size of the SQM core. We do so assuming that, for a given cluster, the kinetic energy of the modes is constant. For a constant amplitude of the oscillation at the stellar surface, we find that the kinetic energy of the modes is very similar for the cases of models with Log Q _SQM=−2, −3 and −4, while it is somewhat lower for  Log Q _SQM=−5  (here   Q _SQM≡ M _SQM/ M ; M _SQM  and M are the masses of the SQM core and the star, respectively). Remarkably, the shape (amplitude of the modes versus period of oscillation) of the clusters of periods is very similar. However, the number of modes inside each cluster is strongly (and non-monotonously) dependent upon the size of the SQM core.
The characteristics of the spectrum of oscillations of strange dwarf stars are very different from the ones corresponding to normal white dwarfs and should be, in principle, observable. Consequently, the stars usually considered as white dwarfs may indeed provide an interesting and affordable way to detect SQM in an astrophysical environment.     

Scattered emission from a relativistic outflow and its application to gamma-ray bursts

We investigate a scenario of photon scattering by electrons within a relativistic outflow. The outflow is composed of discrete shells with different speeds. One shell emits radiation for a short duration. Some of this radiation is scattered by the shell(s) behind. We calculate in a simple two-shell model the observed scattered flux density as a function of the observed primary flux density, the normalized arrival time delay between the two emission components, the Lorentz factor ratio of the two shells and the scattering shell's optical depth. Thomson scattering in a cold shell and inverse Compton scattering in a hot shell are both considered. The results of our calculations are applied to the gamma-ray bursts and the afterglows. We find that the scattered flux from a cold slower shell is small and likely to be detected only for those bursts with very weak afterglows. A hot scattering shell could give rise to a scattered emission as bright as the X-ray shallow decay component detected in many bursts, on a condition that the isotropically equivalent total energy carried by the hot electrons is large, ∼10⁵²–10⁵⁶ erg. The scattered emission from a faster shell could appear as a late short γ-ray/MeV flash or become part of the prompt emission depending on the delay of the ejection of the shell.     

Tail emission of prompt gamma-ray burst jets

Tail emission of the prompt gamma-ray burst (GRB) is discussed using a multiple emitting sub-shell (inhomogeneous jet, sub-jets or mini-jets) model, where the whole GRB jet consists of many emitting sub-shells. One may expect that such a jet with angular inhomogeneity should produce spiky tail emission. However, we found that the tail is not spiky but is decaying roughly monotonically. The global decay slope of the tail is not so much affected by the local angular inhomogeneity but affected by the global sub-shell energy distribution. The fact that steepening GRB tail breaks appeared in some events prefers the structured jets. If the angular size of the emitting sub-shell is around 0.01–0.02 rad, some bumps or fluctuations appear in the tail emission observed frequently in long GRBs. If the parameter differences of sub-shell properties are large, the tail has frequent changes of the temporal slope observed in a few bursts. Therefore, the multiple emitting sub-shell model has the advantage of explaining the small-scale structure in the observed rapid decay phase.     

Precursors and e± pair loading from erupting fireballs

Recent observations suggest that long-duration γ -ray bursts and their afterglows are produced by highly relativistic jets emitted in core-collapse explosions. As the jet makes its way out of the stellar mantle, a bow shock runs ahead and a strong thermal precursor is produced as the shock breaks out. Such erupting fireballs produce a very bright γ -ray precursor as they interact with the thermal break-out emission. The prompt γ -ray emission propagates ahead of the fireball before it becomes optically thin, leading to e^± pair loading and radiative acceleration of the external medium. The detection of such precursors would offer the possibility of diagnosing not only the radius of the stellar progenitor and the initial Lorentz factor of the collimated fireball, but also the density of the external environment.     

Gamma-ray burst precursors as the remnant of the thermal radiation initially trapped in the fireball

In the standard fireball model of gamma-ray bursts (GRBs), the fireball starts with an optically thick phase. As it expands, the fireball becomes optically thin at some stage. The thermal radiation trapped in the originally opaque fireball then leaks out, producing a transient event. The appearance of the event is investigated in the framework of a homogeneous, spherically symmetric and freely expanding fireball produced instantly by an explosive process without continuous injection of mass and energy. We find that, generally, the event has a time duration shorter than that of the main burst, which is presumably produced by the internal shock after the fireball becomes optically thin. The event is separated from the main burst by a quiescent time interval, and is weaker than the main burst at least in a high-energy band. Hence, the event corresponds to a GRB precursor. The precursor event predicted by our model has a smooth and Fast Rise and Exponential Decay (FRED) shaped light curve, and a quasi-thermal spectrum. Typically, the characteristic blackbody photon energy is in the X-ray band. However, if the distortion of the blackbody spectrum by electron scattering is considered, the characteristic photon energy could be boosted to the gamma-ray band. Our model may explain a class of observed GRB precursors – those having smooth and FRED-shaped light curves and quasi-thermal spectra.     

Can the bump in the composite spectrum of GRB 910503 be an emission line feature of gamma-ray bursts？

Appearing in the composite spectral data of BATSE, EGRET and COMPTEL for GRB 910503, there is a bump at around 1600 keV. We perform a statistical analysis on the spectral data, trying to find out if the bump could be accounted for by a blue-shifted and significantly broadened rest frame line due to the Doppler effect of an expanding fireball surface. We made an F-test and adopted previously proposed criteria. The study reveals that the criteria are well satisfied and the feature can be interpreted as the blue shifted 6.4 keV line. Prom the fit with this line taken into account, we find the Lorentz factor of this source to be P = 116-9+9 (at the 68% confident level,△x2 = 1) and the rest frame spectral peak energy to be E0,p- 2.96-0.18+0.24 keV. Although the existence of the emission line feature requires other independent tests to confirm, the analysis suggests that it is feasible to detect emission line features in the high energy range of GRB spectra when taking into account the Doppler effect of fireball expansion.     

A statistical study of gamma-ray burst afterglows measured by the Swift Ultraviolet Optical Telescope

We present the first statistical analysis of 27 Ultraviolet Optical Telescope (UVOT) optical/ultraviolet light curves of gamma-ray burst (GRB) afterglows. We have found, through analysis of the light curves in the observer's frame, that a significant fraction rise in the first 500 s after the GRB trigger, all light curves decay after 500 s, typically as a power law with a relatively narrow distribution of decay indices, and the brightest optical afterglows tend to decay the quickest. We find that the rise could be either produced physically by the start of the forward shock, when the jet begins to plough into the external medium, or geometrically where an off-axis observer sees a rising light curve as an increasing amount of emission enters the observers line of sight, which occurs as the jet slows. We find that at 99.8 per cent confidence, there is a correlation, in the observed frame, between the apparent magnitude of the light curves at 400 s and the rate of decay after 500 s. However, in the rest frame, a Spearman rank test shows only a weak correlation of low statistical significance between luminosity and decay rate. A correlation should be expected if the afterglows were produced by off-axis jets, suggesting that the jet is viewed from within the half-opening angle θ or within a core of a uniform energy density  θ_c  . We also produced logarithmic luminosity distributions for three rest-frame epochs. We find no evidence for bimodality in any of the distributions. Finally, we compare our sample of UVOT light curves with the X-ray Telescope (XRT) light-curve canonical model. The range in decay indices seen in UVOT light curves at any epoch is most similar to the range in decay of the shallow decay segment of the XRT canonical model. However, in the XRT canonical model, there is no indication of the rising behaviour observed in the UVOT light curves.