1. A RUNAVA B HADRA AND B HAKTA K UNWAR High Energy & Cosmic Ray Research Centre, University of North Bengal, Siliguri, WB, India Scattered radiation from gamma ray bursts in the GeV energy range 08/11/2011 1 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011

2. Introduction 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 2 Gamma-ray bursts (GRBs) are among the most energetic events in the Universe Originated either in massive stellar explosions (core- collapse supernovae) or through the coalescence of binary systems of neutron stars or a neutron star-black hole pair. No clear experimental evidence for either of the models Experimental indications for an association of GRBs with core-collapse hypernovae. Properties of host regions of some short GRBs favor the mergers of compact objects model of GRB origin.

3. 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 3 The properties of immediate neighborhood of GRBs may throw light on the origin of GRBs. For supernova explosion model of origin of GRB a shell of dense gas is expected to exist in the immediate neighborhood of a GRB. The radiation from GRB scattered off such an expanding circumstellar matter can give rise to time variable echoes of the GRB in different wave lengths. The scattered radiation, therefore, in principle should act as a probe for the models of origin of GRBs.

4. Aim of the present work 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 4 The Compton scattering of gamma rays with the surrounding matter is generally regarded as the underlying physical mechanism behind the formation of X-ray/gamma-ray halos [Madau,APJ,2000] Here we would show that the Delbrück scattering, the elastic scattering of a photon in the Coulomb field of a nucleus via a virtual electron pair, of GeV gamma ray photons by ambient matter may also lead to an extended image of the object in the GeV energy range particularly when the target medium consists of high Z atoms.

5. Delbrück scattering 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 5 Delbrück scattering is an observable high order nonlinear process of quantum electrodynamics without having any classical analogue. Experimentally the process has been investigated covering a wide range of gamma-ray energies (1-1000 MeV) over the last eight decades. This scattering process has allowed testing a single Feynman graph of the order Z 2 e 6 with an accuracy of 5%. Theoretically a reasonable understanding of the Delbrück scattering has been achieved so far, though there is still no general solution for arbitrary photon- energies & scattering-angles.

6. Scattered radiation due to Delbrück process 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 6 We consider a simple scenario in which the GRB site is at the center of a spherical circumstellar material of uniform density n and radius R as schematically shown in the figure below. The observer is assumed to be located on the axis of symmetry. The observable gamma ray flux will consist of a core (unscattered gamma rays coming directly from the source), and a halo component due to the scattering by circumstellar material. In comparison to the core component, the halo component i.e. the scattered gamma rays arrive at the observer with a time delay.

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8. 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 8 The gamma-rays from the GRB, elastically scattered by the circumstellar matter through an angle θ, will reach the observer O after time t whereas the gamma- rays without undergoing any scattering processes will be detected at t = 0. The locus of scattering centers making a constant delay will be a paraboloid with its focus at the GRB site as given by If the host galaxy is at a red shift z then the gamma ray echo will be observed at time t=t(1+z).

9. , 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 9 The points on the paraboloid, which make the same delay in time t, are constrained within ( r < R, θ < θ o ) and the corresponding constraint in terms of scattering angle is θ 1 < θ < θ o, where the critical angle θ o is the collimation angle. The flux of all scattered  rays will give rise to the halo component. The scattered and hence delayed  -ray flux reaching the observer after time t will be, S  is the γ -ray burst fluence in the concerned energy band.

10. 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 10 At GeV energies the scattering is in very forward direction. The typical angle ( θ ) of scattering of  -rays of energy E by a scatterer of size a is given by which becomes 0.35 arcsecond and 3.4 o respectively for scattering of a 1 GeV photon by the Fe atom (radius ~0.14 nm) and the Fe nucleus (radius ~4 fm).

11. 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 11 At very small angles (when, m is rest mass of an electron,  =2ESin  is the momentum transferred to the nucleus) the Delbrück scattering cross section is given by where For relatively larger scattering angles satisfying where

12. 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 12 Accordingly the scattered radiation due to Delbrück scattering where

13. Delayed radiation 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 13 Expressing in terms of elapsed time t the Delbrück scattered γ -ray flux will be

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15. Scattered radiation: Delbrück versus Compton 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 15 The differential cross section for Compton scattering, at small angles such that Cos θ ~ 1, can be approximated as where is the so called incoherent scattering function (ISF) and is a function of θ, E and Z. The curves showing the Delbrück and Compton scattering differential cross sections are plotted in Fig.1 below. The values of S are taken from [Hubbell et al. 1975].

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17. Conclusion 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 17 We demonstrate for the first time that the Delbrück scattering, a non-linear process of QED, may lead to development of gamma ray halo around a GRB (or around similar sources) under certain physically viable situations. The GRB halo due to Delbrück scattering should be more intense that that due to Compton scattering, particularly at very small angles. For Z=26, z=0.5, n = 10 3 cm -3, the ratio of scattered to unscattered flux is found about few times of 10 -6. It does not like to be detectable by Fermi, but there is a good possibility that the future generation gamma-ray telescopes would be able to detect such photons and thereby can test models of origin of GRBs.

18. 08/11/2011 32ND INTERNATIONAL COSMIC RAY CONFERENCE, BEIJING 2011 18 Thank you