Curvature Effects in Gamma Ray Burst Colliding Shells

An elementary kinematic model for emission produced by relativistic spherical colliding shells is studied. The case of a uniform blast-wave shell with jet opening angle $\theta_j \gg 1/\Gamma$ is considered, where $\Gamma$ is the Lorentz factor of the emitting shell. The shell, with comoving width $\Delta r^\prime$, is assumed to be illuminated for a comoving time $\Delta t^\prime$ and to radiate a broken power-law $\nu L_\nu$ spectrum peaking at comoving photon energy \e_{pk,0}^{\prime}. Synthetic GRB pulses are calculated, and the relation between energy flux and internal comoving energy density is quantified. Curvature effects dictate that the measured $\nu F_\nu$ flux at the measured peak photon energy \e_{pk} is proportional to \e^3_{pk} in the declining phase of a GRB pulse. Possible reasons for discrepancy with observations are discussed, including adiabatic and radiative cooling processes that extend the decay timescale, a nonuniform jet, or the formation of pulses by external shock processes. A prediction of a correlation between prompt emission properties and times of the optical afterglow beaming breaks is made for a cooling model, which can be tested with Swift.Comment: 13 pages, 5 figures, added back-of-envelope estimate of curvature relation, minor corrections, ApJ, in press, v. 614, 10 Oct 200

Variability of sub-mJy radio sources

We present 1.4 GHz VLA observations of the variability of radio sources in the Lockman Hole region at the level of > 100 uJy on timescales of 17 months and 19 days. These data indicate that the areal density of highly variable sources at this level is < 0.005 arcmin^{-2}. We set an upper limit of 2% to the fraction of 50 to 100uJy sources that are highly variable (> 50%). These results imply a lower limit to the beaming angle for GRBs of 1deg, and give a lower limit of 200 arcmin^2 to the area that can be safely searched for GRB radio afterglows before confusion might become an issue.Comment: aastex 2 postscript figures. to appear in the Astrophysical Journa

The Angular Size and Proper Motion of the Afterglow of GRB 030329

The bright, nearby (z=0.1685) gamma-ray burst of 29 March 2003 has presented us with the first opportunity to directly image the expansion of a GRB. This burst reached flux density levels at centimeter wavelengths more than 50 times brighter than any previously studied event. Here we present the results of a VLBI campaign using the VLBA, VLA, Green Bank, Effelsberg, Arecibo, and Westerbork telescopes that resolves the radio afterglow of GRB 030329 and constrains its rate of expansion. The size of the afterglow is found to be \~0.07 mas (0.2 pc) 25 days after the burst, and 0.17 mas (0.5 pc) 83 days after the burst, indicating an average velocity of 3-5 c. This expansion is consistent with expectations of the standard fireball model. We measure the projected proper motion of GRB 030329 in the sky to <0.3 mas in the 80 days following the burst. In observations taken 52 days after the burst we detect an additional compact component at a distance from the main component of 0.28 +/- 0.05 mas (0.80 pc). The presence of this component is not expected from the standard model.Comment: 12 pages including 2 figures, LaTeX. Accepted to ApJ Letters on May 14, 200

Constraints on Off-Axis GRB Jets in Type Ibc Supernovae From Late-Time Radio Observations

It has been suggested that the peculiar properties of the luminous Type Ic supernova SN 1998bw and its low-energy gamma-ray burst GRB 980425 may be understood if they originated in a standard gamma-ray burst explosion viewed far from the axis of the relativistic jet. In this scenario, strong radio emission is predicted from the jet on a timescale 1 to 10 years after the explosion as it decelerates and spreads into our line of sight. To test this hypothesis we have carried out late-time radio observations of SN 1998bw at $t=5.6$ years, yielding upper limits which are consistent with the continued fading of the supernova. We find these limits to be consistent with an off-axis jet only if the progenitor mass loss rate is $\dot{M}\lesssim 4 \times 10^{-7}$ M$_\odot$ yr$^{-1}$ (for a wind velocity $v_w=1000$ km s$^{-1}$) or the fraction of the shock energy in magnetic fields is $\epsilon_B \lesssim 10^{-3}$. These values are low relative to those inferred for cosmological GRBs. We combine the SN 1998bw measurements with existing observations for a sample of 15 local Type Ibc supernovae to estimate that at most 6% produce collimated, relativistic outflows.Comment: Revised version, as it appears in ApJ

Efficiency and spectrum of internal gamma-ray burst shocks

We present an analysis of the Internal Shock Model of GRBs, where gamma-rays are produced by internal shocks within a relativistic wind. We show that observed GRB characteristics impose stringent constraints on wind and source parameters. We find that a significant fraction, of order 20 %, of the wind kinetic energy can be converted to radiation, provided the distribution of Lorentz factors within the wind has a large variance and provided the minimum Lorentz factor is higher than 10^(2.5)L_(52)^(2/9), where L=10^(52)L_(52)erg/s is the wind luminosity. For a high, >10 %, efficiency wind, spectral energy breaks in the 0.1 to 1 MeV range are obtained for sources with dynamical time R/c < 1 ms, suggesting a possible explanation for the observed clustering of spectral break energies in this range. The lower limit to wind Lorenz factor and the upper limit, around (R/10^7 cm)^(-5/6) MeV to observed break energies are set by Thomson optical depth due to electron positron pairs produced by synchrotron photons. Natural consequences of the model are absence of bursts with peak emission energy significantly exceeding 1 MeV, and existence of low luminosity bursts with low, 1 keV to 10 keV, break energies.Comment: 10 pages, 5 ps-figures. Expanded discussion of magnetic field and electron energy fraction. Accepted for publication in Astrophysical Journa

SN1998bw: The Case for a Relativistic Shock

SN1998bw shot to fame by claims of association with GRB980425. Independent of its presumed association with a GRB, this SN is unusual in its radio properties. A simple interpretation of the unusually bright radio emission leads us to the conclusion that there are two shocks in this SN: a slow moving shock containing most of the ejecta and a relativistic shock (Gamma=2) which is responsible for the radio emission. This is the first evidence for the existence of relativistic shocks in supernovae. It is quite plausible that this shock may produce high energy emission (at early times and by inverse Compton scattering). As with other supernovae, we expect radio emission at much later times powered primarily by the slow moving ejecta. This expectation has motivated us to continue monitoring this unusual SN.Comment: A&A (in press), Rome GRB Symposium, Nov. 199