arXiv subjects

Z. G. Dai

Publications and source records attributed to Z. G. Dai.

At least 235 records · Page 13Linked to original sources

arXiv2000

On the Optical Light Curves of Afterglows from Jetted Gamma-ray Burst Ejecta: Effects of Parameters

Due to some refinements in the dynamics, we can follow the overall evolution of a realistic jet numerically till its bulk velocity being as small as $βc \sim 10^{-3} c$. 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 $t \sim 10^6$ --- $10^{6.5}$ s (i.e., 10 --- 30 d). The break is affected by many parameters, such as the electron energy fraction $ξ_{\rm e}$, the magnetic energy fraction $ξ_{\rm B}^2$, the initial half opening angle $θ_0$, and the medium number density $n$. Increase of 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 $α\geq 2.1$. 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.

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arXiv2000

Overall Evolution of Jetted Gamma-ray Burst Ejecta

Whether gamma-ray bursts are highly beamed or not is a very difficult but important problem that we are confronted with. Some theorists suggest that beaming effect usually leads to a sharp break in the afterglow light curve during the ultra-relativistic phase, with the breaking point determined by $γ= 1 / θ_0$, where $γ$ is the Lorentz factor of the blastwave and $θ_0$ is the initial half opening angle of the ejecta, but numerical studies tend to reject the suggestion. We note that previous studies are uniformly based on dynamics that is not proper for non-relativistic blastwaves. Here we investigate the problem in more detail, paying special attention to the transition from the ultra-relativistic phase to the non-relativistic phase. Due to some crucial refinements in the dynamics, we can follow the overall evolution of a realistic jet till its velocity is as small as $βc \sim 10^{-3} c$. We find no obvious break in the optical light curve during the relativistic phase itself. However, an obvious break does appear at the transition from the relativistic phase to the Newtonian phase if the physical parameters involved are properly assumed. Generally speaking, the Newtonian phase is characterized by a sharp decay of optical afterglows, with the power law timing index $α\sim 1.8$ - 2.1. This is due to the quick lateral expansion at this stage. The quick decay of optical afterglows from GRB 970228, 980326, and 980519, and the breaks in the optical light curves of GRB 990123 and 990510 may indicate the presence of highly collimated $γ$-ray burst ejecta.

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arXiv2000

Could the Unusual Optical Afterglow of GRB 000301c Arise from a Non-relativistic Shock with Energy Injection?

Recent observations on the GRB 000301c afterglow show that three breaks appear in the R-band light curve, and in particular the decay slope at late times is as steep as -3.0. This unusual afterglow is clearly inconsistent with the standard afterglow shock model. Here we propose a non-standard model for the unusual R-band afterglow of GRB 000301c. In this model, an ultra-relativistic shock in a dense medium ("dirty environment")rapidly evolved to the non-relativistic phase in initial 1 day. During such a phase, the shock happened to be caught up with by two energetic shells ejected from the central engine at two different times, and the shock was refreshed, leading to two flattenings of the light curve. After each interaction between the shock and shell, the afterglow decayed as $\propto t^{-3.0}$ if the electron distribution index of the shocked medium, $p\approx 3.4$, derived from the optical spectrum. Therefore, this model can provide an excellent explanation for the flattening and steepening features of the GRB 000301c optical afterglow light curve. We further point out that the energy injection shells ejected from the central engine at later times may be material shells (e.g., in the massive star progenitor models related to black holes) or radiation shells (e.g., in the millisecond pulsar progenitor models).

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arXiv2000

Rapid fading of optical afterglows as evidence for beaming in gamma-ray bursts

Based on the refined dynamical model proposed by us earlier for beamed $γ$-ray burst ejecta, we carry out detailed numerical procedure to study those $γ$-ray bursts with rapidly fading afterglows (i.e., $\sim t^{-2}$). It is found that optical afterglows from GRB 970228, 980326, 980519, 990123, 990510 and 991208 can be satisfactorily fitted if the $γ$-ray burst ejecta are highly collimated, with a universal initial half opening angle $θ_0 \sim 0.1$. The obvious light curve break observed in GRB 990123 is due to the relativistic-Newtonian transition of the beamed ejecta, and the rapidly fading optical afterglows come from synchrotron emissions during the mildly relativistic and non-relativistic phases. We strongly suggest that the rapid fading of afterglows currently observed in some $γ$-ray bursts is evidence for beaming in these cases.

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arXiv2000

Environment and Energy Injection Effects in GRB Afterglows

In a recent paper (Dai & Lu 1999), we have proposed a simple model in which the steepening in the light curve of the R-band afterglow of the gamma-ray burst (GRB) 990123 is caused by the adiabatic shock which has evolved from an ultrarelativistic phase to a nonrelativistic phase in a dense medium. We find that such a model is quite consistent with observations if the medium density is about $3\times 10^6 {\rm cm}^{-3}$. Here we discuss this model in more details. In particular, we investigate the effects of synchrotron self absorption and energy injection. A shock in a dense medium becomes nonrelativistic rapidly after a short relativistic phase. The afterglow from the shock at the nonrelativistic stage decays more rapidly than at the relativistic stage. Since some models for GRB energy sources predict that a strongly magnetic millisecond pulsar may be born during the formation of GRB, we discuss the effect of such a pulsar on the evolution of the nonrelativistic shock through magnetic dipole radiation. We find that after the energy which the shock obtains from the pulsar is much more than the initial energy of the shock, the afterglow decay will flatten significantly. When the pulsar energy input effect disappears, the decay will steepen again. These features are in excellent agreement with the afterglows of GRB 980519, GRB 990510 and GRB 980326. Furthermore, our model fits very well all the observational data of GRB 980519 including the last two detections.

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arXiv1999

Energy Sources of Soft Gamma-Ray Repeaters

Quiescence and burst emission and relativistic particle winds of soft gamma-ray repeaters (SGRs) have been widely interpreted to result from ultrastrongly magnetized neutron stars. In this magnetar model, the magnetic energy and gravitational energy of the neutron stars are suggested as the energy sources of all the emission and winds. However, Harding, Contopoulos & Kazanas (1999) have shown that the magnetic field should be only ~ 3 x 10^{13} G in order to match the characteristic spin-down timescale of SGR 1806-20 and its SNR age. Here we argue that if the magnetic field is indeed so weak, the previously suggested energy sources seem problematic. We further propose a plausible model in which SGR pulsars are young strange stars with superconducting cores and with a poloidal magnetic field of ~ 3 x 10^{13} G. In this model, the movement of the flux tubes not only leads to crustal cracking of the stars, giving rise to deconfinement of crustal matter to strange matter, but also to movement of internal magnetic toruses with the flux tubes. The former process will result in burst and quiescence emission and the latter process will produce steady relativistic winds which will power the surrounding supernova remnants.

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arXiv1999

The polarization and beaming effect for GRBs

Both observations and theoretical models suggest that the emissions in gamma-ray bursts (GRBs) and the afterglows are beamed. We argue that the recent polarization measured in the afterglows gives further evidence of beaming in GRBs. In this approach, we adopted the polarization-magnitude relation of BL Lacertae objects to 4 GRBs with available polarization measurements and found that the data of the 4 GRBs are consistent with the relation of BL Lacertae objects. This result suggests that the emissions in GRBs are beamed and there are similarities between GRBs and BL Lacertae objects (or generally blazars). We suggest that the weak polarization of GRBs may result from low percentage of orderly magnetic field in the shock front.

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arXiv1999

A Two-Step Model for Gamma-Ray Bursts Associated with Supernovae

We here propose a two-step model for gamma-ray bursts (GRBs) associated with supernovae. In the first step, the core collapse of a star with mass $\ge 19M_\odot$ leads to a massive neutron star and a normal supernova, and subsequently hypercritical accretion of the neutron star from the supernova ejecta may give rise to a jet through neutrino annihilation and/or Poynting flux along the stellar rotation axis. However, because of too much surrounding matter, this jet rapidly enters a nonrelativistic phase and evolves to a large bubble. In the second step, the neutron star promptly implodes to a rapidly rotating black hole surrounded by a torus when the mass of the star increases to the maximum mass and meanwhile its rotation frequency increases to the upper limit due to the accreted angular momentum. The gravitational binding energy of the torus may be dissipated by a magnetized relativistic wind, which may then be absorbed by the supernova ejecta, thus producing an energetic hypernova. The rotational energy of the black hole may be extracted by the Blandford-Znajek's mechanism, leading to another jet. This jet is relatively free of baryons and thus may be accelerated to an ultrarelativistic phase because the first jet has pushed out of its front matter and left a baryon-free exit. We expect that the second jet generates a GRB and its afterglow. Our two-step model may alleviate the baryon-contamination problem suffered possibly from in the hypernova models. Furthermore, this model not only accounts for association of several GRBs with supernovae but also explains well the features of the afterglows of these bursts.

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arXiv1999

GRB: A Signature of Phase Transition to QGP?

It is suggested that the inner energetic engine of Gamma ray burst (GRB) may be the result of the transition of normal hadron to quark-gluon plasma (QGP) in rapidly-rotating and spin-down newborn neutron star. When such a nascent neutron star slows down through dipole electromagnetic and quadruple gravitational radiation, the increasing center density may reach the QCD transition density, i.e., 5-10 nuclear density. Such kind of energy release from the phase transition would be responsible for GRB and its possible beaming effect. The relative dense gaseous environment of GRB location and the iron line observed in the X-ray afterglow support this idea. Some predictions in this model are given. keywords: Gamma-ray Bursts, Supernova, Quark-gluon plasma

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arXiv1999

Overall Evolution of Realistic Gamma-ray Burst Remnant and Its Afterglow

Conventional dynamic model of gamma-ray burst remnants is found to be incorrect for adiabatic blastwaves during the non-relativistic phase. A new model is derived, which is shown to be correct for both radiative and adiabatic blastwaves during both ultra-relativistic and non-relativistic phase. Our model also takes the evolution of the radiative efficiency into account. The importance of the transition from the ultra-relativistic phase to the non-relativistic phase is stressed.

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arXiv1999

The Afterglow of GRB 990123 and a Dense Medium

Recent observations show that the temporal decay of the R-band afterglow from GRB 990123 steepened about 2.5 days after the burst. We here propose a possible explanation for such a steepening: a shock expanding in a dense medium has undergone the transition from a relativistic phase to a nonrelativistic phase. We find that this model is consistent with the observations if the medium density is about $3\times 10^6 {\rm cm}^{-3}$. By fitting our model to the observed optical and X-ray afterglow quantitatively, we further infer the electron and magnetic energy fractions of the shocked medium and find these two parameters are about 0.1 and $2\times 10^{-8}$ respectively. The former parameter is near the equipartition value while the latter is about six orders of magnitude smaller than inferred from the GRB 970508 afterglow. We also discuss possibilities that the dense medium can be produced.

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arXiv1999

A Generic Dynamical Model of Gamma-ray Burst Remnants

The conventional generic model is deemed to explain the dynamics of $γ$-ray burst remnants very well, no matter whether they are adiabatic or highly radiative. However, we find that for adiabatic expansion, the model could not reproduce the Sedov solution in the non-relativistic phase, thus the model needs to be revised. In the present paper, a new differential equation is derived. The generic model based on this equation has been shown to be correct for both radiative and adiabatic fireballs, and in both ultra-relativistic and non-relativistic phase.

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arXiv1998

Gamma-ray burst afterglows and evolution of postburst fireballs with energy injection from strongly magnetic millisecond pulsars

Millisecond pulsars with strong magnetic fields may be formed through several processes, e.g. accretion-induced collapse of magnetized white dwarfs, merger of two neutron stars. During the birth of such a pulsar, an initial fireball available for a gamma-ray burst (GRB) may occur. We here study evolution of a postburst relativistic fireball with energy injection from the pulsar through magnetic dipole radiation, and find that the magnitude of the optical afterglow from this fireball first decreases with time, subsequently flattens, and finally declines again. This may provide a natural explanation for the behavior of the lightcurve of the afterglow of GRB970228 if this burst resulted from the birth of a strongly magnetic millisecond pulsar.

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arXiv1998

Gamma-Ray Bursts and Afterglows from Rotating Strange Stars and Neutron Stars

We here discuss a new model of $γ$-ray bursts (GRBs) based on differentially rotating strange stars. Strange stars in this model and differentially rotating neutron stars in the Kluźniak-Ruderman model can produce extremely relativistic, variable fireballs required by GRBs and then become millisecond pulsars. The effect of such pulsars on expansion of the postburst fireballs through magnetic dipole radiation is studied. We show that these two models can explain naturally not only various features of GRBs but also light curves of afterglows.

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arXiv1998

GRB afterglows: from ultra-relativistic to non-relativistic phase

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 $t \ge 100$ d, implying a large initial energy $E_0$, a low interstellar density $n$, or the possible existence of a persistent energy source at the center of the fireball.

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arXiv1998

Gamma-ray bursts: postburst evolution of fireballs

The postburst evolution of fireballs that produce $γ$-ray bursts 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. Due to adoption of a new relation among $t$, $R$ and $γ$ (see the text), our results differ markedly from the previous studies. Synchrotron radiation from the shocked interstellar medium is attentively calculated, using a convenient 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 approach to observations. It is also found that the expansion will no longer be highly relativistic about 4 days 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.

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arXiv1998

Gamma-Ray Burst Afterglows from Realistic Fireballs

A GRB afterglow has been commonly thought to be due to continuous deceleration of a postburst fireball. Many analytical models have made simplifications for deceleration dynamics of the fireball and its radiation property, although they are successful at explaining the overall features of the observed afterglows. We here propose a model for a GRB afterglow in which the evolution of a postburst fireball is in an intermediate case between the adiabatic and highly radiative expansion. In our model, the afterglow is both due to the contribution of the adiabatic electrons behind the external blastwave of the fireball and due to the contribution of the radiative electrons. In addition, this model can describe evolution of the fireball from the extremely relativistic phase to the non-relativistic phase. Our calculations show that the fireball will go to the adiabatic expansion phase after about a day if the accelerated electrons are assumed to occupy the total internal energy. In all cases considered, the fireball will go to the mildly relativistic phase about $10^4$ seconds later, and to the non-relativistic phase after several days. These results imply that the relativistic adiabatic model cannot describe the deceleration dynamics of the several-days-later fireball. The comparison of the calculated light curves with the observed results at late times may imply the presence of impulsive events or energy injection with much longer durations.

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arXiv1998

Gamma-Ray Burst Afterglows: Effects of Radiative Corrections and Nonuniformity of the Surrounding Medium

The afterglow of a gamma-ray burst (GRB) is commonly thought to be due to 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, viz., $n_{ext}\propto R^{-k}$, we analytically study the effects of the first-order radiative correction and the nonuniformity of the medium on a GRB afterglow. We first derive a new relation among the observed time, the shock radius and the fireball's Lorentz factor: $t_\oplus=R/4(4-k)γ^2c$, and also derive a new relation among the comoving time, the shock radius and the fireball's Lorentz factor: $t_{co}=2R/(5-k)γc$. We next study the evolution of the fireball by using the analytic solution of Blandford and McKee (1976). 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 GRB970616 is well fitted by assuming $k=2$.

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