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Constraining the Beaming of Gamma- Ray Bursts with Radio Surveys Constraining the Beaming of Gamma- Ray Bursts with Radio Surveys The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Perna, Rosalba, and Abraham Loeb. 1998. “Constraining the Beaming of Gamma-Ray Bursts with Radio Surveys.” The Astrophysical Journal 509 (2): L85–88. https:// doi.org/10.1086/311784. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:41393210 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA The Astrophysical Journal, 509:L85±L88, 1998 December 20 q 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A. CONSTRAINING THE BEAMING OF GAMMA-RAY BURSTS WITH RADIO SURVEYS Rosalba Perna and Abraham Loeb Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 Received 1998 October 6; accepted 1998 October 22; published 1998 November 10 ABSTRACT The degree of beaming in gamma-ray bursts (GRBs) is currently unknown. The uncertainty in the g-ray±beaming / 2 / 22 angle, vb, leaves the total energy release (vbb ) and the event rate per galaxy (v ) unknown to within orders of magnitude. Since the delayed radio emission of GRB sources originates from a mildly relativistic shock and receives only weak relativistic beaming, the rate of radio-selected transients with no GRB counterparts can be 22 » used to set an upper limit onvb . We ®nd that a VLA survey with a sensitivity of 0.1 mJy at 10 GHz could * # 4 C 22 identify 2 10 (vb /10 ) radio afterglows across the sky if each source is sampled at least twice over a period of 1 month or longer. From the total number of *0.1 mJy sources observed at 8.44 GHz and the fraction * C of fading sources at 1.44 GHz, we get the crude limitvb 6 . Subject heading: gamma rays: bursts 1. INTRODUCTION ros, Rees, & Wijers 1998). The search for long-wavelength transients with no GRB counterparts can set important con- Gamma-ray burst (GRB) sources were discovered histori- straints on vb and hence on these models. cally in g-rays because they are rare and hence require con- In this Letter, we show that a 0.1 mJy radio survey at the tinuous monitoring of large areas of the sky. The necessary VLA1 (analogous to the FIRST survey; Helfand et al. 1996) all-sky monitoring program was ®rst made feasible in the g-ray can provide strong constraints on vb. The surveyed sources need regime, hence the name GRBs. By now, the prompt g-ray to be sampled at least twice over a timescale on the order of emission is known to be followed in most cases by delayed a month or longer, since short-term variability may also be emission in the X-ray (Costa et al. 1997), optical (van Paradijs caused by scintillations of steady pointlike sources. In our cal- et al. 1997; Fruchter et al. 1998a, 1998b), and radio (Frail 1998; culations, we assume that the GRB rate is proportional to the Frail et al. 1998) bands. Given the recent discovery of after- cosmic star formation rate and neglect the small fraction glows, it is now timely to explore the feasibility of searching (&10%) of GRBs that might be related to local radio super- for GRB sources at longer wavelengths than traditionally at- novae (Bloom et al. 1998). We model the time-dependent lu- tempted. The importance of complementary searches is high- minosity of the radio afterglows based on observational data lighted by the possibility that some sources might be g-ray and allow for a scatter in their peak luminosities. Our model faint for geometric or physical reasons. Such sources can only is described in detail in § 2. The number count of radio after- be found at long wavelengths, e.g., in radio surveys. Indeed, glows that it predicts for radio surveys is calculated in § 3. By if the g-ray emission is beamed, then there should be a pop- comparing this number with that of fading sources in existing ulation of radio afterglows that are g-ray faint (Rhoads 1997). radio surveys, we get a lower limit on vb. Finally, our main This follows from the fact that the bulk Lorentz factor of the conclusions are summarized in § 4. emitting material in GRB sources declines with time and is only of order unity when the late radio emission takes place (Waxman, Kulkarni, & Frail 1998), hence making the effect of relativistic beaming weak at that time. 2. STATISTICS OF RADIO GRB AFTERGLOWS The evolution of a jet resembles that of a spherical ®reball The isotropy of GRBs (Meegan et al. 1993; Briggs et al. (i.e., the jet behaves like a conical section of a spherical ®re- 1993) and the ¯attening of their number count distribution at ball), as long as the expansion Lorentz factor is larger than the faint ¯uxes suggest that most GRBs occur at cosmological 1 21 inverse of the jet opening angle,G vb . The smooth power- distances. This hypothesis has been con®rmed by the detection law decline of optical afterglows, observed over a timescale of Fe ii and Mg ii absorption lines at a redshift of z 5 0.835 of days to months for GRB 970508 and GRB 970228 (Livio in the optical spectrum of GRB 970508 (Metzger et al. 1997), et al. 1997; Sokolov et al. 1998), suggests that these ®reballs the inference of a redshiftz 5 3.42 for the host galaxy of GRB behaved as if they were spherically symmetric on angular scales 971214 (Kulkarni et al. 1998), and the detection of emission » 11» ranging from 1/G (1 day) 83to 1/G (1 month) (Rhoads and absorption lines atz 5 0.966 for the host of GRB 980703 1997, 1998; Waxman 1997a). However, there is still a missing (Djorgovski et al. 1998). » 53 gap in afterglow observations on the time window of minutes The energy scale of cosmological GRBs, 10 fb ergs (Kul- to several hours following a GRB. During this time, the ®reball karni et al. 1998), corresponds to the rest mass energy of a decelerates fromG » 100 toG » 10 , and so there is uncertainty fraction of a solar mass and implies a link between their energy about the structure of the ®reball on angular scales of »0.01±0.1 budget and compact stars. Indeed, the most popular models for rad. It is still possible that the highly relativistic expansion with the origin of GRBs relate them to compact stellar remnants, G » 10 2 is restricted only to a very small angular diameter, » 5 7 vb 1/G 0.6. In fact, the popular GRB scenarios of binary 1 The VLA is a facility of the National Radio Astronomy Observatory, which coalescence of compact stars or failed supernovae favor strong is operated by Associated Universities, Inc., under contract with the National collimation over spherical expansion (Woosley 1998; MeÂszaÂ- Science Foundation. L85 L86 PERNA & LOEB Vol. 509 ¼ such as neutron stars or black holes (see, e.g., Eichler et al. 980703 yield AFnm S 0.7 mJy. For the above cosmology, this ¼ # 31 22 21 21 1989; Narayan, PaczynÂski, & Piran 1992; Usov 1992; Woosley implies AL nm S 1.5 10 h 70 ergs s Hz . 1993; MeÂszaÂros et al. 1998). Since these remnants form out of The calculation of the afterglow number counts should also massive stars not long after their birth, it is reasonable to assume incorporate the fact that not all GRBs have afterglows at radio that the GRB rate traces the star formation rate without a sig- frequencies. The fraction fradio of radio-loud GRBs is still un- ni®cant delay. This scenario was investigated by Wijers et al. certain, but the observation that four out of »15±17 well- (1997), who derived a best-®t constant of proportionality be- localized GRBs (namely, GRB 970508, GRB 980329, GRB tween the GRB occurrence rate, R(z), and the star formation 980519, and GRB 980703) were detected in the radio (D. Frail . rate per comoving volume, r(z), based on the requirement that 1998, private communication) implies that fradio 25%. Also, the former ®ts the observed number count distribution of GRBs. the afterglow radio ¯ux might have a break in its power-law The cosmic star formation rate as a function of redshift has evolution and decay more rapidly than predicted by equation been calibrated based on observations of the U- and B-band (1) after a particular time (e.g., during the nonrelativistic phase luminosity density evolution in the Hubble Deep Field (Madau of the shock hydrodynamics). We arti®cially introduce a free et al. 1996; Madau, Pozzetti, & Dickinson 1998). The ®t made parameter, tcutoff, after which we set the emitted radio ¯ux to by Wijers et al. (1997) yields a local GRB rate of R(z 5 zero. Current data do not allow an empirical calibration of 5 5 # 29 23 21 5 5 0) (0.14 0.02) 10 Mpc yr in an Q 1, L 0, tcutoff, and so we leave it as a free parameter. We assume that 5 21 21 * and H0 70 km s Mpc cosmology. tcutoff 3 months since a simple power-law decline was ob- We model the frequency and time dependence of the after- served in GRB 970508 for over 3 months (Waxman et al. 1998). glow luminosity, L n(t), using the simplest unbeamed synchro- The late phase of the radio emission, several months after a tron model (see, e.g., Waxman 1997a, 1997b), with a luminosity GRB event, originates from semirelativistic material with per unit emitted frequency nÄ of G » 1 and receives only weak relativistic beaming.
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