Gamma-Ray Bursts (GRBs) are widely thought to originate from collimated jets
of material moving at relativistic velocities. Emission from such a jet should
be visible even when viewed from outside the angle of collimation. Using Monte
Carlo population synthesis methods and including the effects of this off-axis
beaming, we can compare various GRB jet models against the global properties of
observed bursts. We explore whether or not the X-Ray Flashes (XRFs) seen by
HETE-2 and BeppoSAX can be explained as classical GRBs viewed off-axis, and
begin to address the more general question of the importance of off-axis
beaming in current burst samples.Comment: 4 pages, 1 figure. Poster presented at the 4th Workshop Gamma-Ray
  Bursts in the Afterglow Era, Rome,18-22 October 2004. Editors: L. Piro, L.
  Amati, S. Covino, and B. Gendre. Il Nuovo Cimento, in pres

Donaghy, T. Q.

English

arXiv

Gamma-Ray Bursts (GRBs) arewide ly thought to originatefrom

collimated jets of material moving at relativistic velocities. Emission from such a jet should be visible even when viewed from outside the angle of collimation. Using

Monte Carlo population synthesis methods and including the effects of this off-axis beaming, we can compare various GRB jet models against the global properties of observed bursts. We explore whether or not the X-Ray Flashes (XRFs) seen by HETE-2 and BeppoSAX can be explained as classical GRBs viewed off-axis, and begin to address the more general question of the importance of off-axis beaming in current burst samples

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DOI 10.1393/ncc/i2005-10070-0IL NUOVO CIMENTO Vol. 28 C, N. 3 Maggio-Giugno 2005The importance of off-axis beaming in jet models(∗)T. Q. DonaghyDepartment of Astronomy & Astrophysics, University of Chicago5640 S. Ellis Ave., Chicago, IL, 60615, USA(ricevuto il 23 Maggio 2005; pubblicato online il 9 Settembre 2005)Summary. — Gamma-Ray Bursts (GRBs) are widely thought to originate fromcollimated jets of material moving at relativistic velocities. Emission from such ajet should be visible even when viewed from outside the angle of collimation. UsingMonte Carlo population synthesis methods and including the effects of this off-axisbeaming, we can compare various GRB jet models against the global properties ofobserved bursts. We explore whether or not the X-Ray Flashes (XRFs) seen byHETE-2 and BeppoSAX can be explained as classical GRBs viewed off-axis, andbegin to address the more general question of the importance of off-axis beaming incurrent burst samples.PACS 98.70.Rz – γ-ray sources; γ-ray bursts.PACS 01.30.Cc – Conference proceedings.1. – IntroductionThe importance of collimated jets in GRBs was highlighted by the extremely largeisotropic-equivalent energies of very bright events like GRB 990123 and by the observationof breaks in afterglow light-curves. [1] and [2] corrected the isotropic-equivalent energiesby the beaming fraction obtained from afterglow light-curves and found that the valuesof Eγ were clustered around 1051 ergs (although see [3]). Recent results from HETE-2 [4] have shown that XRFs [5, 6], X-Ray–Rich GRBs and GRBs lie along a continuumof properties and that XRFs with known redshift extend the Epeak ∝ E1/2iso relationpredicted by [7] and found by [8] to over 5 orders of magnitude in Eiso [9].Relativistic kinematics implies that even a “top-hat”-shaped jet will be visible whenviewed outside the angle of collimation, θ0 [10]. [11,12] used this fact to construct a modelwhere XRFs are simply classical GRBs viewed at an angle θv > θ0. The authors showedthat such a model could reproduce many of the observed characteristics of XRFs. [13]showed that in such a model, the distribution of both on- and off-axis observed burstswas roughly consistent with the Epeak ∝ E1/2iso relation.(∗) Paper presented at the “4th Workshop on Gamma-Ray Burst in the Afterglow Era”, Rome,October 18-22, 2004.c© Societa` Italiana di Fisica 407408 T. Q. DONAGHYIn this paper, we explore further the possibility that the XRFs observed by HETE-2and BeppoSAX are primarily off-axis GRBs. Using and extending the population synthe-sis techniques presented by [14] and [15], we present predictions for the global propertiesof bursts localized by HETE-2. We show that it is difficult to account for the observedproperties of XRFs by modelling them solely as regular GRBs viewed off-axis. However,since off-axis emission must exist solely on physical grounds, we seek to understand itsrelative importance in large burst populations. We revisit the model put forward in [14],now including the effects of off-axis beaming. We note that rough constraints on thebulk γ might be found by considering the fraction of bursts that are not consistent withthe Epeak ∝ E1/2iso relation. Finally, we consider some possible extensions to our model.2. – Simulations[11-13] work with a fairly detailed model of the burst emission; for this work, weadopt a simpler model of off-axis beaming in GRB jets. We make no assumptions aboutthe underlying physics generating the burst, and we make the approximation that thebulk of the emission comes directly from the edge of the jet closest to the viewing angleline-of-sight (i.e. we ignore all integrals over the surface of the jet and time-of-flighteffects). Our model focuses on the kinematic transformations of two important burstquantities, Eiso and Epeak, as a function of viewing angle.Frequencies in the rest frame of the burst material will appear Doppler shifted bya factor, δ = γ(1 − β cos θ), where β is the velocity of the bulk material and θ is theangle between the direction of motion and the source frame observer. The quantitiesEpeak and Eiso then transform as Epeak ∝ E′peakδ−1 and Eiso ∝ E′isoδ−3. For a burstviewed off-axis, these relations imply Epeak ∝ E1/3iso . [13] do not consider Eiso to be fullybolometric and so derive a slightly different prescription for the off-axis relation.We adopt an effective angular distribution of the emissivity, (θv), that is uniform forθv < θ0 and decreases for θv > θ0:(θv) =Eiso4π={A,A · (δ/δ0)−3 , and Epeak ={B, if θv ≤ θ0,B · (δ/δ0)−1 , if θv > θ0,(1)where in this expression, δ = γ[1− β cos(θv − θ0)], δ0 = γ(1− β) is the value of δ whenθv = θ0, A is a normalization constant described below, B = CA ·(Eiso/1052 ergs)1/2, andCA is drawn from a narrow lognormal distribution. Hence, Epeak obeys the Epeak ∝ E1/2isorelation inside the jet and Epeak ∝ E1/3iso outside the jet. We then define the “true”standard energy by integrating this emissivity over the entire sphere:Etrueγ = 2 · 2π∫ π/20(θv) sin θv dθv = 4πA [1− cos θ0 + I(γ, θ0)] .(2)We define the Eγ value inferred via the method of [1] to be Einfγ = 4πA(1−cos θ0). Thepresence of beaming implies Einfγ = Etrueγ . We fix our normalization constant, A, to matchthe original prescription used by [1], by drawing values for Einfγ from a narrow lognormaldistribution centered at E0γ . We perform Monte Carlo simulations using the methodpresented in [14], and employing the detector thresholds from the WXM on HETE-2.THE IMPORTANCE OF OFF-AXIS BEAMING IN JET MODELS 409Fig. 1. – Distribution of bursts detected on-axis (black) and off-axis (gray) in the [θ0,θv]-plane(top row), [Eiso,Epeak]-plane (middle row) and [Eobspeak,SE(2 − 400)]-plane (bottom row) for themodels Y04 (left), VOAUJ1 (center) and VOAUJ2 (right). Bursts not detectable by the WXMare not shown.3. – ResultsHere we explore the relative importance of off-axis beaming for three variable opening-angle uniform jet models. The first (Y04) using the parameters from [13], assumesγ = 100 and draws θ0 values from a power-law distribution given by f0 dθ0 ∝ θ−20 dθ0,defined from 0.3 to 0.03 rad. The Y04 model attempts to explain classical GRBs interms of the variation of jet opening angles, while XRFs are interpreted as bursts viewedoff-axis. The other two models explain both GRBs and XRFs by a distribution of jetopening angles, following results presented in [14]. Here we add the presence of off-axisbeaming to this picture, considering both γ = 100 (VOAUJ1) and γ = 300 (VOAUJ2).As can be seen from the top row of fig. 1, the relative importance of off-axis eventsincreases for models with a population of very small opening angles. This is mainlydue to the fact that narrower jets with a constant Eγ will have larger Eiso values, andtherefore such bursts viewed off-axis will also be brighter. More importantly, the middleand bottom rows show that the HETE-2 XRFs are not easily explained as classical GRBsviewed off-axis. The two XRFs with known redshift lie along the Epeak ∝ E1/2iso relation,410 T. Q. DONAGHYand furthermore the larger sample of HETE-2 XRFs without known redshifts do not fallin the region of the [Eobspeak, SE]-plane expected for this model; they lie at lower, ratherthan higher, Eobspeak values for a given SE. Even given the model of the off-axis emissionin [13], these HETE-2 XRFs are difficult to explain.The other two models we consider generate XRFs that obey the Epeak ∝ E1/2iso relationby extending the range of possible jet opening-angles to cover five orders of magnitude(see [14] for details and discussion). Hence, XRFs that obey the Epeak ∝ E1/2iso relationare bursts that are seen on-axis, but have larger jet opening-angles. Nonetheless, thesemodels generate a significant populations of off-axis events, although increasing γ reducesthe fraction of off-axis bursts in the observed sample.4. – DiscussionBursts with known redshift have been found to obey the Epeak ∝ E1/2iso relation, anda large population of off-axis bursts is not readily apparent in the observed datasets. [16]found that the Epeak ∝ E1/2iso relation holds internally within a large sample of brightBATSE bursts without redshift. It is unknown whether fainter bursts might deviate fromthis relation or what fraction of bursts are inconsistent with the Epeak ∝ E1/2iso relation.The result may be an indicator of the bulk γ of the material.In future work we will investigate the effect of possible correlations between θ0 andγ. If narrower jets have larger bulk γ values, this could reduce the importance of off-axisbeaming even further. Secondly, off-axis beaming will be important for non-uniform jetsas well [17]. Gaussian and Fisher-shaped jets rely on the exponential falloff of the emis-sivity with viewing angle to match the wide spread of observed burst quantities [18,19].If off-axis beaming is important, the exponential falloff will be dominated at some angleby the power-law falloff due to beaming, thereby broadening the emissivity distribution.REFERENCES[1] Frail D. et al., ApJ, 562 (2001) L55.[2] Bloom J., Frail D. A. and Kulkarni S. R., ApJ, 588 (2003) 945.[3] Ghirlanda G., Ghisellini G. and Lazzati D., ApJ, 616 (2004) 331.[4] Sakamoto T. et al., submitted to ApJ, 2004 (astro-ph/0409128).[5] Heise J. et al., in Proceedings of 2nd Rome Workshop: Gamma-Ray Bursts in the AfterglowEra, edited by Costa E., Frontera F. and Hjorth J. (Springer-Verlag, Berlin) 2000,p. 16.[6] Kippen R. M. et al., in Gamma-Ray Burst and Afterglow Astronomy, edited by RickerG. R. and Vanderspek R. K., AIP Conf. Proc., 662 (2002) 244.[7] Lloyd-Ronning N., Petrosian V. and Mallozzi R. S., ApJ, 534 (2000) 227.[8] Amati L. et al., A&A, 390 (2002) 81.[9] Lamb D. Q. et al., submitted to ApJ, 2005.[10] Ioka K. and Nakamura T., ApJ, 554 (2001) L163.[11] Yamazaki R., Ioka K. and Nakamura T., ApJ, 571 (2002) L31.[12] Yamazaki R., Ioka K. and Nakamura T., ApJ, 593 (2003) 941.[13] Yamazaki R., Ioka K. and Nakamura T., ApJ, 606 (2004) L33.[14] Lamb D. Q., Donaghy T. Q. and Graziani C., ApJ, 620 (2005) 355.[15] Donaghy T. Q., Lamb D. Q. and Graziani C., to be submitted to ApJ, 2005.[16] Liang E. W., Dai Z. G. and Wu X. F., ApJ, 606 (2004) L29.[17] Graziani C., submitted to ApJ, 2005.[18] Zhang B., Dai X., Lloyd-Ronning N. M. and Meszaros P., ApJ, 601 (2004) L119.[19] Donaghy T. Q., Lamb D. Q. and Graziani C., in these proceedings.

The importance of off-axis beaming in jet models

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The Importance of Off-Axis Beaming in Jet Models

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