Long-lived >100 MeV emission has been a common feature of most Fermi-LAT detected gamma-ray bursts (GRBs), e.g., detected up to ~10^3s in long GRBs 080916C and 090902B and ~10^2s in short GRB 090510. This emission is consistent with being produced by synchrotron emission of electrons accelerated to high energy by the relativistic collisionless shock propagating into the weakly magnetized medium. Here we show that this high-energy afterglow emission constrains the preshock magnetic field to satisfy 1(n/1cc)^{9/8} mG<B<10^2(n/1cc)^{3/8}mG, where n is the preshock density, more stringent than the previous constraint by X-ray afterglow observations on day scale. This suggests that the preshock magnetic field is strongly amplified, most likely by the streaming of high energy shock accelerated particles.
arXiv:1004.0791v3 [astro-ph.HE] 28 Apr 2011
Preprint typeset using LATEX style emulateapj v. 11/10/09
THE UPSTREAM MAGNETIC FIELD OF COLLISIONLESS GRB SHOCKS: CONSTRAINT BY FERMI-LAT
OBSERVATIONS
ZHUO LI1,2 AND XIAO-HONG ZHAO3,4
ABSTRACT
Long-lived > 100 MeV emission has been a common feature of most Fermi-LAT detected gamma-ray bursts
(GRBs), e.g., detected up to ∼103s in long GRBs 080916C and 090902B and ∼102s in short GRB 090510.
This emission is consistent with being produced by synchrotron emission of electrons accelerated to high
energy by the relativistic collisionless shock propagating into the weakly magnetized medium. Here we show
that this high-energy afterglow emission constrains the preshock magnetic field to satisfy 100n9/8
0 mG < Bu <
102n3/8
0 mG, where n0 is the preshock density in unit of 1 cm−3, more stringent than the previous constraint by
X-ray afterglow observations on day scale. This suggests that the preshock magnetic field is strongly amplified,
most likely by the streaming of high energy shock accelerated particles.
Subject headings: acceleration of particles — magnetic fields — shock waves — gamma-rays: bursts
1. INTRODUCTION
Diffusive (Fermi) shock acceleration is believed to play an
important role in gamma-ray burst (GRB) afterglow model,
where a shock propagating into the medium accelerates elec-
trons to high energy and then synchrotron/inverse-Compton
emission arises. Although the phenomenological afterglow
model works generally well with observational data, the shock
physics is not understood from first principle. One of the main
issues is how the magnetic field is amplified (see review by
Waxman 2006). Many groups have tried to address this issue
using numerical plasma simulations (see,e.g., Keshet et al.
2009, and references there in), but because the calculations
are extremely demanding numerically, the picture of field
growth is still not clear. Thus using observations to constrain
the shock physics parameters will be helpful in this issue. Af-
terglow observations were used to constrain the downstream
magnetic field and the accelerated electron energy distribu-
tion, at both high (Waxman 1997a; Freedman & Waxman
2001) and low (Waxman 1997b; Eichler & Waxman 2005)
energy. Li & Waxman (2006, hereafter LW06) had also used
X-ray afterglow observations on day scale to give a lower
limit to the preshock magnetic field amplitude, which sug-
gests either the shock propagates into a magnetized wind of
the GRB progenitor or strong preshock magnetic field ampli-
fication occurs, most likely due to the streaming of the ac-
celerated high-energy particles. LW06 further suggested that
observations in higher energy range and/or in later time may
post more stringent constraint on the preshock magnetic field.
Recently the Large Area Telescope (LAT) on board the
Fermi satellite revealed some new features in the GRB high-
energy emission. The onset of > 100 MeV emission is de-
layed compared to MeV emission, and lasts much longer,
as a decaying power-law, after the MeV emission already
ends.
For examples, in the bright GRBs, the extended >
1 Department of Astronomy, Peking University, Beijing 100871, China;
E-mail: zhuo.li@pku.edu.cn
2 Kavli Institute for Astronomy and Astrophysics, Peking University,
Beijing 100871, China
3 National Astronomical Observatories/Yunnan Observatory, Chinese
Academy of Sciences, P.O. Box 110, 650011 Kunming, China
4 Key Laboratory for the Structure and Evolution of Celestial Bodies,
Chinese Academy of Sciences, P.O. Box 110, 650011 Kunming, China
100 MeV emission was detected up to ∼103s in long GRBs
080916C and 090902B and ∼102s in short GRB 090510
(Abdo et al. 2009a,b,c), until the flux decreases to below
the LAT sensitivity. Kumar & Barniol Duran (2009a,b) pro-
posed that the whole high-energy burst, including the prompt
phase, is produced by synchrotron emission in the external
forward shock.
Other authors (Corsi, Guetta & Piro 2009;
Gao et al. 2009; Ghirlanda et al. 2010; Ghisellini et al. 2010;
De Pasquale et al. 2010; Pandey et al. 2010) also found that
the light curve slope, the spectral index and the flux level
of the extended high-energy emission are consistent with the
synchrotron afterglow model. Even though it may not be true
that the whole burst is dominated by forward shock emission
(see discussion in §6), for the 103s-scale emission the forward
shock emission is still most favored over other possible mod-
els (see a discussion in the introduction of Wang et al. 2010).
In this paper we show that if the extended > 100 MeV emis-
sion is produced by the synchrotron emission from afterglow
shock accelerated electrons, the 103s-scale > 100 MeV emis-
sion gives much more stringent constraint on the preshock
magnetic field, compared to that by X-ray afterglow obser-
vations. The paper is organized as follows: in §2 we list the
adopted preassumptions in our analysis; in §3 we derive the
maximum synchrotron photon energy limited by the radiative
(IC and synchrotron/
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