Gamma-ray Bursts 080916C Research Articles

Energy Injection in Gamma‐Ray Burst Afterglow Models

We extend the standard fireball model, widely used to interpret gamma-ray burst (GRB) afterglow light curves, to include energy injections, and apply the model to the afterglow light curves of GRB 990510, GRB 000301C and GRB 010222. We show that discrete energy injections can cause temporal variations in the optical light curves and present fits to the light curves of GRB 000301C as an example. A continuous injection may be required to interpret other bursts such as GRB 010222. The extended model accounts reasonably well for the observations in all bands ranging from X-rays to radio wavelengths. In some cases, the radio light curves indicate that additional model ingredients may be needed.

Early re-brightenings in GRB afterglows as signatures of low-to-high density boundary

The association of long gamma-ray bursts (GRBs) with star forming regions and the idea of massive stars as progenitors of GRBs are widely accepted. Because of their short lifetimes, it is very likely that massive stars are still embedded in dense molecular clouds when they give birth to GRBs. Stellar winds from GRB progenitors can create low-density bubbles with sizes and densities strongly depending on the initial ambient density. A boundary between the bubble and the dense molecular cloud must exist with the density at the boundary increasing from that of the bubble to that of the outer cloud. We have calculated the lightcurves of the afterglows in such environments with three regions: the stellar wind region, the boundary, and the molecular cloud. We show that the interaction between the cylindrical jet and the density boundary can result in a re-brightening of the afterglow occurring as early as ∼1 day after the GRB. We compare our models with the optical afterglows of GRB 970508, GRB 000301C, and GRB 030226. We find that the values of our model parameters, including the radius of the wind bubble, the densities in the bubble and in the outer molecular cloud are within typical ranges.

Spectra and light curves of GRB afterglows

We performed accurate numerical calculations of angle-, time-, and frequency-dependent radiative transfer for the relativistic motion of matter in gamma-ray burst (GRB) models. Our technique for solving the transfer equation, which is based on the method of characteristics, can be applied to the motion of matter with a Lorentz factor up to 1000. The effect of synchrotron self-absorption is taken into account. We computed the spectra and light curves from electrons with a power-law energy distribution in an expanding relativistic shock and compare them with available analytic estimates. The behavior of the optical afterglows from GRB 990510 and GRB 000301c is discussed qualitatively.

Hydrodynamics of Relativistic Blast Waves in a Density-Jump Medium and Their Emission Signature

We analyze in detail the hydrodynamics and afterglow emission of an ultrarelativistic blast wave when it expands in a density-jump medium. Such a medium is likely to appear in the vicinity of gamma-ray bursts (GRBs) associated with massive stars. The interaction of the blast wave with this medium is described through a reverse shock and a forward shock. We show that the reverse shock is initially relativistic if the factor of a density jump (α) is much larger than 21 and Newtonian if 1 < α ≪ 21. We also calculate light curves of the afterglow emission during the interaction if the reverse shock is relativistic and find that the optical flux density initially decays abruptly, then rises rapidly, and finally fades based on a power law, which could be followed by an abrupt decay when the reverse shock has just crossed the originally swept-up matter. Therefore, one property of an afterglow occurring in a large density-jump medium is an abrupt drop followed by a bump in the light curve and thus provides a probe of circumburst environments. In addition, this property may not only account for the optical afterglows of GRB 970508 and GRB 000301C but may also explain the X-ray afterglow of GRB 981226.

Wind Interaction Models for the Afterglows of GRB 991208 and GRB 000301C

The simplest model of the afterglows of gamma-ray bursts (GRBs) envisions a spherical blast wave, with a power-law distribution of electron energy above some cutoff, running into a constant-density medium. A refinement involves a narrow jet, often invoked to explain the steep decline and/or steepening of light curves observed in some afterglows. The constant (ambient) density jet model has been applied to GRBs 991208 and 000301C, based to a large extent on radio observations. We show that, for these two sources, a spherical-wind model (with an r-2 density ambient medium) can fit the radio data as well as the jet model. The relatively steep decline and the fairly abrupt steepening of the R-band light curves of, respectively, GRB 991208 and GRB 000301C can be accounted for with a nonstandard, broken power-law distribution of electron energy. Our model predicts a slower late decline for the radio flux than does the jet model.

Could the unusual optical afterglow of GRB 000301c arise from a non-relativistic shock with energy injection?

Recent observations on the gamma-ray burst (GRB) 000301c afterglow show that one sharp break appears in the global optical/IR light curves, and in particular the decay slope at late times is as steep as about -3.0. This unusual feature is clearly inconsistent with the standard afterglow shock model. Here we propose a non-standard model for the afterglow of GRB 000301c, in which an initial ultra-relativistic shock in a dense medium (dirty environment) rapidly evolved to the non-relativistic phase in 1 day after the burst. During such a phase, the shock was refreshed by a strongly magnetized millisecond pulsar through magnetic dipole radiation. This refreshment led to flattening of the light curves. After the energy injection, 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, our model can provide a plausible explanation for the peculiar optical/IR afterglow light curves of GRB 000301c.

Resolving Gamma-Ray Burst 000301C with a Gravitational Microlens

The afterglow of the Gamma-Ray Burst (GRB) 000301C exhibited achromatic, short time-scale variability that is difficult to reconcile with the standard relativistic shock model. We interpret the observed light curves as a microlensing event superimposed on power-law flux decays typical of afterglows. In general, a relativistic GRB shock appears on the sky as a thin ring expanding at a superluminal speed. Initially the ring is small relative to its angular separation from the lens and so its flux is magnified by a constant factor. As the ring grows and sweeps across the lens its magnification reaches a maximum. Subsequently, the flux gradually recovers its unlensed value. This behavior involves only three free parameters in its simplest formulation and was predicted theoretically by Loeb & Perna (1998). Fitting the available R-band photometric data of GRB 000301C to a simple model of the microlensing event and a broken power-law for the afterglow, we find reasonable values for all the parameters and a reduced chi^2/DOF parameter of 1.48 compared with 2.99 for the broken power-law fit alone. The peak magnification of ~2 occurred 3.8 days after the burst. The entire optical-IR data imply a width of the GRB ring of order 10% of its radius, similar to theoretical expectations. The angular resolution provided by microlensing is better than a micro-arcsecond. We infer a mass of approximately 0.5 M_Sun for a lens located half way to the source at z_s=2.04. A galaxy 2'' from GRB 000301C might be the host of the stellar lens, but current data provides only an upper-limit on its surface brightness at the GRB position.