Synchrotron radiation from ultra-high energy protons and the Fermi observations of GRB 080916C

📝 Abstract

Fermi gamma-ray telescope data of GRB 080916C with ~1e55 erg in apparent isotropic gamma-ray energy, show a several second delay between the rise of 100 MeV - GeV radiation compared with keV - MeV radiation. Here we show that synchrotron radiation from cosmic ray protons accelerated in GRBs, delayed by the proton synchrotron cooling timescale in a jet of magnetically-dominated shocked plasma moving at highly relativistic speeds with bulk Lorentz factor Gamma ~ 500, could explain this result. A second generation electron synchrotron component from attenuated proton synchrotron radiation makes enhanced soft X-ray to MeV gamma-ray emission. Long GRBs with narrow, energetic jets accelerating particles to ultra-high energies could explain the Auger observations of UHE cosmic rays from sources within 100 Mpc for nano-Gauss intergalactic magnetic fields. The total energy requirements in a proton synchrotron model are proportional to Gamma^(16/3). This model for GRB 080916C is only plausible if Gamma ~< 500 and the jet opening angle is ~ 1 degree.

💡 Analysis

Fermi gamma-ray telescope data of GRB 080916C with ~1e55 erg in apparent isotropic gamma-ray energy, show a several second delay between the rise of 100 MeV - GeV radiation compared with keV - MeV radiation. Here we show that synchrotron radiation from cosmic ray protons accelerated in GRBs, delayed by the proton synchrotron cooling timescale in a jet of magnetically-dominated shocked plasma moving at highly relativistic speeds with bulk Lorentz factor Gamma ~ 500, could explain this result. A second generation electron synchrotron component from attenuated proton synchrotron radiation makes enhanced soft X-ray to MeV gamma-ray emission. Long GRBs with narrow, energetic jets accelerating particles to ultra-high energies could explain the Auger observations of UHE cosmic rays from sources within 100 Mpc for nano-Gauss intergalactic magnetic fields. The total energy requirements in a proton synchrotron model are proportional to Gamma^(16/3). This model for GRB 080916C is only plausible if Gamma ~< 500 and the jet opening angle is ~ 1 degree.

📄 Content

Synchrotron Radiation from Ultra-High energy protons and the Fermi observations of GRB 080916C Soebur Razzaque1,2∗, Charles D. Dermer1† and Justin D. Finke1,2 1Space Science Division, U.S. Naval Research Laboratory, Washington, DC 20375, USA 2National Research Council Research Associate Abstract Fermi γ-ray telescope data of GRB 080916C with ∼1055 erg in apparent isotropic γ-ray energy, show a several second delay between the rise of 100 MeV – GeV radiation compared with keV – MeV radiation. Here we show that synchrotron radiation from cosmic ray protons accelerated in GRBs, delayed by the proton synchrotron cooling timescale in a jet of magnetically-dominated shocked plasma moving at highly relativis- tic speeds with bulk Lorentz factor Γ ∼500, could explain this result. A second gen- eration electron synchrotron component from attenuated proton synchrotron radiation makes enhanced soft X-ray to MeV γ-ray emission. Long GRBs with narrow, energetic jets accelerating particles to ultra-high energies could explain the Auger observations of UHE cosmic rays from sources within 100 Mpc for nano-Gauss intergalactic magnetic fields. The total energy requirements in a proton synchrotron model are ∝Γ16/3. This model for GRB 080916C is only plausible if Γ ≲500 and the jet opening angle is ∼1◦. Subject headings: gamma rays: bursts—gamma rays: theory—radiation mechanisms: nonthermal 1 Introduction An integrated fluence of 2.4 × 10−4 erg cm−2 was measured from GRB 080916C with the Large Area Telescope (LAT) and Gamma ray Burst Monitor (GBM) on the Fermi Gamma ray Space Telescope, with one third of this energy in the LAT [1]. At a redshift z = 4.35 ± 0.15 [2], GRB 080916C has the largest apparent energy release yet observed from a GRB. A significant ≃4.5 s delay between the onset of > 100 MeV compared to the ∼8 keV – 5 MeV radiation is found (the characteristic duration of the GBM emission is ≈50 s). The spectrum of GRB 080916C was fit by the smoothly connected double power-law Band function [3] to multi-GeV energies, though with changing Band spectral parameters and peak photon energy in different time intervals. The emergence of delayed spectral hardening is represented by a Band beta spectral index changing from β = −2.6 in the first 3.6 seconds following the GRB trigger to β = −2.2 at later times [1]. Here we show that a hard spectral component arising from cosmic-ray proton synchrotron radiation explains the delayed onset of the LAT emission. If GRBs accelerate UHECRs, then the delayed onset of the LAT emission after the GBM trigger should be a regular feature of GRB spectral evolution. ∗email: srazzaque@ssd5.nrl.navy.mil †email: charles.dermer@nrl.navy.mil 1 arXiv:0908.0513v4 [astro-ph.HE] 2 Sep 2010 2 Proton acceleration and radiation GRB blast wave calculations usually treat electrons [4, 5], but protons and ions will also be accelerated if they are present in the relativistic flows in black-hole jet systems. Here we consider protons accelerated in GRB blast waves to such energies that they can efficiently radiate hard ∼GeV – TeV photons by the proton synchrotron mechanism [6, 7, 8, 9, 10, 11]. The highest energy photons are reprocessed by γγ →e+e−opacity [12] to make an injection source of electrons and positrons that cool by emitting < GeV electron synchrotron radiation. Two delays arise, the first from the time it takes to accelerate protons to a saturation Lorentz factor where the acceleration rate equals the synchrotron rate. A second delay arises during which sufficient time passes to build up the spectrum of the primary protons so that they become radiatively efficient in the LAT band. Observations of GRB 080916C are consistent with the delayed onset between GBM and LAT emission being caused by the second delay where the evolving proton cooling synchrotron spectrum sweeps from higher energies into the LAT waveband. This radiation is emitted from a jet of magnetically-dominated shocked plasma with ζB > 1, where ζB is the ratio of magnetic- field to proton/particle energy density in the plasma. The rapid variability, large apparent luminosity, and detection of high-energy photons from GRBs can be understood if this radiation is emitted from jetted plasma moving with bulk Lorentz factor Γ ≫1 towards us. Detection of 3 GeV and 13 GeV photons from GRB 080916C suggests Γ3 = Γ/1000 ∼1 (Ref. [1] and below, Section 3). For variability times tv ∼1 s and instantaneous energy fluxes Φ = 10−5Φ−5 erg cm−2s−1, the internal radiation energy density in the fluid is u′ γ ≈4πd2 LΦ/(4πR2cΓ2) ≈(1 + z)2d2 LΦ/(Γ6c3t2 v), implying a characteristic jet magnetic field of B′(kG) ≈2 p ζBρbΦ−5 Γ3 3tv(s) ≈2ζ1/2 B ρ1/2 b t−1/2 v (s)E−1/2 1 (13 GeV), (1) where primes refer to the comoving frame, ρb is the baryon-loading parameter giving the relative energy in nonthermal protons compared to γ-rays. The last relation in equation (1) assumes Γ ≈Γmin from the opacity condition τγγ = 1, which can be written as Γmin ∼= σTd2 L(1 + z)2fˆϵϵ1 4tvmec4 1/6 , (2)

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