Reverse Shock Emission as a Probe of GRB Ejecta

We calculate the reverse shock (RS) synchrotron emission in the optical and the radio wavelength bands from electron-positron pair enriched gamma-ray burst ejecta with the goal of determining the pair content of GRBs using early time observations. We take into account an extensive number of physical effects that influence radiation from the reverse-shock heated GRB ejecta. We find that optical/IR flux depends very weakly on the number of pairs in the ejecta, and there is no unique signature of ejecta pair enrichment if observations are confined to a single wavelength band. It may be possible to determine if the number of pairs per proton in the ejecta is > 100 by using observations in optical and radio bands; the ratio of flux in the optical and radio at the peak of each respective reverse-shock light curve is dependent on the number of pairs per proton. We also find that over a large parameter space, RS emission is expected to be very weak; GRB 990123 seems to have been an exceptional burst in that only a very small fraction of the parameter space produces optical flashes this bright. Also, it is often the case that the optical flux from the forward shock is brighter than the reverse shock flux at deceleration. This could be another possible reason for the paucity of prompt optical flashes with a rapidly declining light curve at early times as was seen in 990123 and 021211. Some of these results are a generalization of similar results reported in Nakar & Piran (2004).Comment: 12 pages, 6 figures, 2 tables, accepted to MNRA

Pure and loaded fireballs in SGR giant flares

On December 27, 2004, a giant flare from SGR 1806$-$20 was detected on earth. Its thermal spectrum and temperature suggest that the flare resulted from an energy release of about $10^{47}$ erg/sec close to the surface of a neutron star in the form of radiation and/or pairs. This plasma expanded under its own pressure producing a fireball and the observed gamma-rays escaped once the fireball became optically thin. The giant flare was followed by a bright radio afterglow, with an observable extended size, implying an energetic relativistic outflow. We revisit here the evolution of relativistic fireballs and we calculate the Lorentz factor and energy remaining in relativistic outflow once the radiation escapes. We show that pairs that arise naturally in a pure pairs-radiation fireball do not carry enough energy to account for the observed afterglow. We consider various alternatives and we show that if the relativistic outflow that causes the afterglow is related directly to the prompt flare, then the initial fireball must be loaded by baryons or Poynting flux. While we focus on parameters applicable to the giant flare and the radio afterglow of SGR 1806$-$20 the calculations presented here might be also applicable to GRBs

Hydrodynamic Time Scales and Temporal Structure of GRBs

We calculate the hydrodynamic time scales for a spherical ultra-relativistic shell that is decelerated by the ISM and discuss the possible relations between these time scales and the observed temporal structure in $\gamma$-ray bursts. We suggest that the bursts' duration is related to the deceleration time, the variability is related to the ISM inhomogeneities and precursors are related to internal shocks within the shell. Good agreement can be achieved for these quantities with reasonable, not fined tuned, astrophysical parameters. The difference between Newtonian and relativistic reverse shocks may lead to the observed bimodal distribution of bursts' durations.Comment: 13 pages, uuencoed including two figures. UU encoded file or postcript files can also be obtained by anonymous ftp from ftp://shemesh.fiz.huji.ac.il or from http://shemesh.fiz.huji.ac.il/ . Revised version, Accepted for Publication in the Astrophysical Journal Letter

Radiative Efficiencies of Continuously Powered Blast Waves

We use general arguments to show that a continuously powered radiative blast wave can behave self similarly if the energy injection and radiation mechanisms are self similar. In that case, the power-law indices of the blast wave evolution are set by only one of the two constituent physical mechanisms. If the luminosity of the energy source drops fast enough, the radiation mechanisms set the power-law indices, otherwise, they are set by the behavior of the energy source itself. We obtain self similar solutions for the Newtonian and the ultra-relativistic limits. Both limits behave self similarly if we assume that the central source supplies energy in the form of a hot wind, and that the radiative mechanism is the semi-radiative mechanism of Cohen, Piran & Sari (1998). We calculate the instantaneous radiative efficiencies for both limits and find that a relativistic blast wave has a higher efficiency than a Newtonian one. The instantaneous radiative efficiency depends strongly on the hydrodynamics and cannot be approximated by an estimate of local microscopic radiative efficiencies, since a fraction of the injected energy is deposited in shocked matter. These solutions can be used to calculate Gamma Ray Bursts afterglows, for cases in which the energy is not supplied instantaneously.Comment: 28 LaTeX pages, including 9 figures and 3 table

Predictions for The Very Early Afterglow and The Optical Flash

According to the internal-external shocks model for $\gamma$-ray bursts (GRBs), the GRB is produced by internal shocks within a relativistic flow while the afterglow is produced by external shocks with the ISM. We explore the early afterglow emission. For short GRBs the peak of the afterglow will be delayed, typically, by few dozens of seconds after the burst. For long GRBs the early afterglow emission will overlap the GRB signal. We calculate the expected spectrum and the light curves of the early afterglow in the optical, X-ray and $\gamma$-ray bands. These characteristics provide a way to discriminate between late internal shocks emission (part of the GRB) and the early afterglow signal. If such a delayed emission, with the characteristics of the early afterglow, will be detected it can be used both to prove the internal shock scenario as producing the GRB, as well as to measure the initial Lorentz factor of the relativistic flow. The reverse shock, at its peak, contains energy which is comparable to that of the GRB itself, but has a much lower temperature than that of the forward shock so it radiates at considerably lower frequencies. The reverse shock dominates the early optical emission, and an optical flash brighter than 15th magnitude, is expected together with the forward shock peak at x-rays or $\gamma$-rays. If this optical flash is not observed, strong limitations can be put on the baryonic contents of the relativistic shell deriving the GRBs, leading to a magnetically dominated energy density.Comment: 23 pages including 4 figure

Do long-duration GRBs follow star formation?

We compare the luminosity function and rate inferred from the BATSE long bursts peak flux distribution with those inferred from the Swift peak flux distribution. We find that both the BATSE and the Swift peak fluxes can be fitted by the same luminosity function and the two samples are compatible with a population that follows the star formation rate. The estimated local long GRB rate (without beaming corrections) varies by a factor of five from 0.05 Gpc^(-3)yr^(-1) for a rate function that has a large fraction of high redshift bursts to 0.27 Gpc^(-3)yr^(-1) for a rate function that has many local ones. We then turn to compare the BeppoSax/HETE2 and the Swift observed redshift distributions and compare them with the predictions of the luminosity function found. We find that the discrepancy between the BeppoSax/HETE2 and Swift observed redshift distributions is only partially explained by the different thresholds of the detectors and it may indicate strong selection effects. After trying different forms of the star formation rate (SFR) we find that the observed Swift redshift distribution, with more observed high redshift bursts than expected, is inconsistent with a GRB rate that simply follows current models for the SFR. We show that this can be explained by GRB evolution beyond the SFR (more high redshift bursts). Alternatively this can also arise if the luminosity function evolves and earlier bursts were more luminous or if strong selection effects affect the redshift determination.Comment: 15 pages, 8 figures, accepted for publication in JCA

Observational Prospects for Afterglows of Short Duration Gamma-ray Bursts

If the efficiency for producing $\gamma$-rays is the same in short duration (\siml 2 s) Gamma-Ray Bursts (GRBs) as in long duration GRBs, then the average kinetic energy of short GRBs must be $\sim 20$ times less than that of long GRBs. Assuming further that the relativistic shocks in short and long duration GRBs have similar parameters, we show that the afterglows of short GRBs will be on average 10--40 times dimmer than those of long GRBs. We find that the afterglow of a typical short GRB will be below the detection limit (\siml 10 \microJy) of searches at radio frequencies. The afterglow would be difficult to observe also in the optical, where we predict R \simg 23 a few hours after the burst. The radio and optical afterglow would be even fainter if short GRBs occur in a low-density medium, as expected in NS-NS and NS-BH merger models. The best prospects for detecting short-GRB afterglows are with early (\siml 1 day) observations in X-rays.Comment: 5 pages, 2 figures, submitted to ApJ lette

Jets in GRBs

In several GRBs afterglows, rapid temporal decay is observed which is inconsistent with spherical (isotropic) blast-wave models. In particular, GRB 980519 had the most rapidly fading of the well-documented GRB afterglows, with t^{-2.05\pm 0.04} in optical as well as in X-rays. We show that such temporal decay is more consistent with the evolution of a jet after it slows down and spreads laterally, for which t^{-p} decay is expected (where p is the index of the electron energy distribution). Such a beaming model would relax the energy requirements on some of the more extreme GRBs by a factor of several hundreds. It is likely that a large fraction of the weak (or no) afterglow observations are also due to the common occurrence of beaming in GRBs, and that their jets have already transitioned to the spreading phase before the first afterglow observations were made. With this interpretation, a universal value of p~2.5 is consistent with all data.Comment: 4 page