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 4d 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.

Huang Y. F.;Dai Z. G.;Lu T.;Wei D. M.

Monthly Notices of the Royal Astronomical Society

1998

GRB 980519 is characterized by its rapidly declining optical and X-ray afterglows. Explanations of this behaviour include models invoking a dense medium environment, which makes the shock wave evolve quickly into the subrelativistic phase, a jet-like outflow, and a wind-shaped circumburst medium environment. Recently, Frail et al. found that the latter two cases are consistent with the radio afterglow of this burst. Here, by considering the transrelativistic shock hydrodynamics, we show that the dense medium model can also account for the radio light curve quite well. The potential virtue of the dense medium model for GRB 980519 is that it implies a smaller angular size of the afterglow, which is essential for interpreting the strong modulation of the radio light curve. Optical extinction arising from the dense medium is not important if the prompt optical-UV flash accompanying the γ-ray emission can destroy dust by sublimation out to an appreciable distance. Comparisons with some other radio afterglows are also discussed.

Wang X. Y.;Dai Z. G.;Lu T.

Monthly Notices of the Royal Astronomical Society

2000

Owing to some refinements in the dynamics, we can follow the overall evolution of a realistic jet numerically until its bulk velocity is as small as βc ∼ 10^-3c. We find no obvious break in the optical light curve during the relativistic phase itself. However, an obvious break does exist at the transition from the relativistic phase to the non-relativistic phase, which typically occurs at time t ∼ 10⁶-10^6.5 s (i.e. 10-30 d). The break is affected by many parameters, such as the electron energy fraction ξe, the magnetic energy fraction ξ²B the initial half-opening angle θ0 and the medium number density n. Increasing any of them to a large enough value will make the break disappear. Although the break itself is parameter-dependent, afterglows from jetted GRB remnants are uniformly characterized by a quick decay during the non-relativistic phase, with power-law timing index a α ≥ 2.1. This is quite different from that of isotropic fireballs, and may be of fundamental importance for determining the degree of beaming in γ-ray bursts observationally.

Huang Y. F.;Dai Z. G.;Lu T.

Monthly Notices of the Royal Astronomical Society

2000

Postburst evolution of adiabatic fireballs that produce γ-ray bursts is studied. Emphasis has been put on the transition from the highly relativistic phase to the non-relativistic phase, which, according to our calculation, should happen much earlier than previously expected. The theoretical light curves decline a little sharper at the non-relativistic stage than at early times, but still can fit the observations well. However, disagreements are obvious when t ≥ 100 d, implying a large initial energy E0, a low interstellar density n, or the possible existence of a persistent energy source at the center of the fireball.

Huang Y. F.;Dai Z. G.;Lu T.

Astronomy and Astrophysics

1998

The afterglow of a gamma-ray burst (GRB) is commonly thought to be the result of continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, i.e. next ∝ R^-k, we study the effects of the first-order radiative correction and the non-uniformity of the medium on a GRB afterglow analytically. We first derive a new relation among the observed time, the shock radius and the Lorentz factor of the fireball: t⊕ = R/4(4 - k)γ²c, and also derive a new relation among the comoving time, the shock radius and the Lorentz factor of the fireball: tco = 2R/(5 - k)γc. We next study the evolution of the fireball by using the analytic solution of Blandford & McKee. The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is p = 2.5, implied from the spectra of GRBs, the X-ray afterglow of GRB 970616 is well fitted by assuming k = 2.

Dai Z. G.;Lu T.

Monthly Notices of the Royal Astronomical Society

1998

Afterglows from jetted gamma-ray bursts are generally believed to be characterized by an obvious break in the light curve at the relativistic stage. We show that it is not the case. However, an obvious break does exist at the transition from the relativistic phase to the non-relativistic phase. Although this break itself is parameter-dependent, afterglows from jetted remnant are uniformly characterized by a quick decay during the non-relativistic phase.

Huang Yong-Feng;Dai Zi-Gao;Lu Tan

Chinese Physics Letters

2000

Assuming an adiabatic evolution of a gamma-ray burst (GRB) fireball interacting with an external medium, we calculate the hydrodynamics of the fireball with an energy injection from a strongly magnetic millisecond pulsar through magnetic dipole radiation, and obtain the light curve of the optical afterglow from the fireball by synchrotron radiation. The results are given both for an homogeneous external medium and for a wind ejected by GRB progenitor. Our calculations are also available in both ultra-relativistic and non-relativistic phases. Furthermore, the observed R-band light curve of GRB000301C can be well fitted in our model, which might provide a probe of the properties of GRB progenitors.

Wang Wei;Dai Zi-Gao

Chinese Physics Letters

2001

We derive light curves of the afterglow emission from highly collimated jets if the power-law index (p) of the electron energy distribution is above 1 but below 2. We find the following: (1) Below the characteristic synchrotron frequency, the light-curve index depends generally on p. (2) As long as the jet expansion is spherical, the light-curve index above the characteristic frequency increases slowly as the spectral index of the emission increases. (3) Once the jet enters the spreading phase, the high-frequency emission flux decays as proportional to t^-(p+6)/4 rather than proportional to t^-p. All these results differ from those in the case of p > 2. We compare our analytical results with the observations on the GRB 010222 afterglow and conclude that the jet model may be unable to explain the observed data. Thus, a more promising explanation for this afterglow seems to be the expansion of a relativistic fireball or a mildly collimated jet in a dense medium.

Dai Z. G.;Cheng K. S.

Astrophysical Journal

2001

We discuss the afterglow emission from a relativistic jet that is initially in the radiative regime, in which the accelerated electrons are fast-cooling. We note that such a 'semiradiative' jet decelerates faster than an adiabatic jet does. We also take into account the effect of strong inverse-Compton scattering on the cooling frequency in the synchrotron component and therefore on the light-curve decay index. We find that there are two kinds of light-curve break for the jet effect. The first is an 'adiabatic break', if the electrons become slow-cooling before the jet enters a spreading phase, and the second is a 'radiative break', which appears in the contrary case. We then show how a relativistic jet evolves dynamically and derive the overall temporal synchrotron emission in both cases, focusing on the change in the light-curve decay index around the break time. Finally, in view of our results, we rule out two cases for relativistic jets which do not account for the observed light-curve breaks in a few afterglows: (i) an adiabatic jet with strong Compton cooling (Y > 1) and with the cooling frequency vc locating in the observed energy range; (ii) a radiative jet with a significant fraction of total energy occupied by electrons (εe ∼ 1).

Li Zhuo;Dai Z. G.;Lu T.

Monthly Notices of the Royal Astronomical Society

2002

We numerically investigate optical afterglows from two-component jets under various configurations. Generally, the light curve is characterized by a rapid rebrightening when the observer is off-axis with respect to the narrow component, with the amplitude and peak time depending on detailed parameters. We further show that the optical afterglow of XRF 030723, especially its notable and rapid rebrightening, can be well explained by a typical two-component jet. This X-ray flash, together with GRB 030329, strongly hints toward the two-component jet model as a unified picture for X-ray flashes and gamma-ray bursts. With a narrow but ultra-relativistic inner outflow and a wide but less energetic outer ejecta, a two-component jet will be observed as a typical gamma-ray burst if our line of sight is within the angular scope of the narrow outflow. Otherwise, if the line of sight is within or slightly beyond the cone of the wide component, an X-ray flash will be detected.

Huang Y. F.;Wu X. F.;Dai Z. G.;Ma H. T.;Lu T.

Astrophysical Journal

2004