A Radio-Selected Sample of Gamma Ray Burst Afterglows

We present a catalog of radio afterglow observations of gamma-ray bursts (GRBs) over a 14 year period from 1997 to 2011. Our sample of 304 afterglows consists of 2995 flux density measurements (including upper limits) at frequencies between 0.6 GHz and 660 GHz, with the majority of data taken at 8.5 GHz frequency band (1539 measurements). We use this dataset to carry out a statistical analysis of the radio-selected sample. The detection rate of radio afterglows has stayed unchanged almost at 31% before and after the launch of the {\em Swift} satellite. The canonical long-duration GRB radio light curve at 8.5 GHz peaks at 3-6 days in the source rest frame, with a median peak luminosity of $10^{31}$ erg s$^{-1}$ Hz$^{-1}$. The peak radio luminosities for short-hard bursts, X-ray flashes and the supernova-GRB classes are an order of magnitude or more fainter than this value. There are clear relationships between the detectability of a radio afterglow and the fluence or energy of a GRB, and the X-ray or optical brightness of the afterglow. However, we find few significant correlations between these same GRB and afterglow properties and the peak radio flux density. We also produce synthetic light curves at centimeter (cm) and millimeter (mm) bands using a range of blastwave and microphysics parameters derived from multiwavelength afterglow modeling, and we use them to compare to the radio sample. Finding agreement, we extrapolate this behavior to predict the cm and mm behavior of GRBs observed by the Expanded Very Large Array and the Atacama Large Millimeter Array.Comment: To appear in 20th Jan 2012 issue of ApJ, 26 pages in ApJ format, 48 figures, 6 table

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

A Beaming-Independent Estimate of the Energy Distribution of Long Gamma-Ray Bursts: Initial Results and Future Prospects

We present single-epoch radio afterglow observations of 24 long-duration gamma-ray burst (GRB) on a timescale of >100 d after the burst. These observations trace the afterglow evolution when the blastwave has decelerated to mildly- or non-relativistic velocities and has roughly isotropized. We infer beaming-independent kinetic energies using the Sedov-Taylor self-similar solution, and find a median value for the sample of detected bursts of about 7x10^51 erg, with a 90% confidence range of 1.1x10^50-3.3x10^53 erg. Both the median and 90% confidence range are somewhat larger than the results of multi-wavelength, multi-epoch afterglow modeling (including large beaming corrections), and the distribution of beaming-corrected gamma-ray energies. This is due to bursts in our sample with only a single-frequency observation for which we can only determine an upper bound on the peak of the synchrotron spectrum. This limitation leads to a wider range of allowed energies than for bursts with a well-measured spectral peak. Our study indicates that single-epoch centimeter-band observations covering the spectral peak on a timescale of ~1 yr can provide a robust estimate of the total kinetic energy distribution with a small investment of telescope time. The substantial increase in bandwidth of the EVLA (up to 8 GHz simultaneously with full coverage at 1-40 GHz) will provide the opportunity to estimate the kinetic energy distribution of GRBs with only a few hours of data per burst.Comment: Submitted to ApJ; 11 pages, 5 figures, 2 table

A Possible Explanation of the Radio Afterglow of GRB980519: The Dense Medium Effect

GRB{980519} is characterized by its rapidly declining optical and X-ray afterglows. Explanations of this behavior include models invoking a dense medium environment which makes the shock wave evolve quickly into the sub-relativistic phase, a jet-like outflow, and a wind-shaped circumburst medium environment. Recently, Frail {et al}. (1999a) found that the latter two cases are consistent with the radio afterglow of this burst. Here, by considering the trans-relativistic 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 due to the dense medium is not important if the prompt optical-UV flash accompanying the $\gamma$-ray emission can destroy dust by sublimation out to an appreciable distance. Comparisons with some other radio afterglows are also discussed.Comment: 5 pages, 1 figure, a few minor changes made and references up dated, MNRAS, in pres

Jets in GRBs: Tests and Predictions for the Structured Jet Model

The two leading interpretations of achromatic breaks that are observed in the light curves of GRBs afterglow are (i) the manifestation of the edge of a jet, which has a roughly uniform energy profile and a sharp edge and (ii) a line of sight effect in jets with a variable energy profile. The first scenario requires the inner engine to produce a jet with a different opening angle each explosion, while the latter requires a standard engine. The physical structure of the jet is a crucial factor in understanding GRB progenitors, and therefore discriminating the two jet scenarios is particularly relevant. In the structured jet case, specific predictions can be made for the distribution of observed break angles $\theta_{\rm break}$, while that distribution is arbitrary in the first scenario. We derive the theoretical distribution for the structured jet model. Specifically, we predict the most common angle to be about 0.12 rad, in rough agreement with the sample. If this agreement would hold as the sample size increases, it would strengthen the case for the standard jet hypothesis. We show that a prediction of this model is that the average viewing angle is an increasing function of the survey sensitivity, and in particular that a mission like {\em Swift} will find the typical viewing angle to be about 0.3 rad. The local event rate predicted by this model is $R_{\rm GRB}(z=0)\sim 0.5$ Gpc$^{-3}$ yr$^{-1}$.Comment: 14 pages, 3 figures; accepted to Ap

Gamma-Ray Burst Afterglows as Analogues of High Frequency-Peaked BL Lac Objects

The spectral properties from radio to optical bands are compared between the 18 optically bright Gamma-ray burst afterglows and well established power-spectrum sequence in Blazars. The comparison shows that the afterglows are well agreement with the well known Blazar sequence (i.e., the $\nu L_{\nu}(\mathrm{5GHz})$-$\alpha_{\mathrm{RO}}$ correlation, where $\alpha_{\mathrm{RO}}$ is the broad-band spectral slope from radio to optical bands). The afterglows are, however, clustered at the low luminosity end of the sequence, which is typically occupied by high frequency-peaked BL Lac objects. The correlation suggests that Gamma-ray burst afterglows share the similar emission process with high frequency-peaked BL Lac objects. We further identify a deviation at a significance level larger than 2$\sigma$ from the sequence for three typical optically "dark" bursts. The deviation favors a heavy extinction in optical bands for the "dark" bursts. The extinction $A_V$ is estimated to be larger than 0.5-0.6 magnitude from the $\nu L_{\nu}(\mathrm{5GHz})$-$\alpha_{\mathrm{RO}}$ sequence.Comment: 13 pages, 2 figures and 2 tables, to be published in ApJ

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

The prompt energy release of gamma-ray bursts using a cosmological k-correction

The fluences of gamma-ray bursts (GRBs) are measured with a variety of instruments in different detector energy ranges. A detailed comparison of the implied energy releases of the GRB sample requires, then, an accurate accounting of this diversity in fluence measurements which properly corrects for the redshifting of GRB spectra. Here, we develop a methodology to ``k-correct'' the implied prompt energy release of a GRB to a fixed co-moving bandpass. This allows us to homogenize the prompt energy release of 17 cosmological GRBs (using published redshifts, fluences, and spectra) to two common co-moving bandpasses: 20-2000 keV and 0.1 keV-10 MeV (``bolometric''). While the overall distribution of GRB energy releases does not change significantly by using a k-correction, we show that uncorrected energy estimates systematically undercounts the bolometric energy by ~5% to 600%, depending on the particular GRB. We find that the median bolometric isotropic-equivalent prompt energy release is 2.2 x 10^{53} erg with an r.m.s. scatter of 0.80 dex. The typical estimated uncertainty on a given k-corrected energy measurement is ~20%.Comment: Accepted to the Astronomical Journal. 21 pages (LaTeX) and 4 figure

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