CAN WE PROBE THE LORENTZ FACTOR OF GAMMA-RAY BURSTS FROM GeV-TeV SPECTRA INTEGRATED OVER INTERNAL SHOCKS?

Abstract

We revisit the high-energy spectral cutoff originating from the electron−positron pair creation in the prompt phase of gamma-ray bursts (GRBs) with numerical and analytical calculations. We show that the conventional exponential and/or broken power law cutoff should be drastically modified to a shallower broken power-law in practical observations that integrate emissions from different internal shocks. Since the steepening is tiny for observations, this "smearing" effect can generally reduce the previous estimates of the Lorentz factor of the GRB outflows. We apply our formulation to GRB 080916C, recently detected by the Large Area Telescope detector on the Fermi satellite, and find that the minimum Lorentz factor can be ∼ 600 (or even smaller values), which is below but consistent with the previous result of ∼ 900. Observing the steepening energy (so-called "pair-break energy") is crucial to diagnose the Lorentz factor and/or the emission site in the future observations, especially current and future Cherenkov telescopes such as MAGIC, VERITAS, and CTA.

An Up-Scattered Cocoon Emission Model of Gamma-Ray Burst High-Energy Lags

“…The observed flux and width of the second pulse of this burst indicate that the isotropic-equivalent luminosity of the jet L 10 55 erg s −1 and the angular spreading timescale of the pulse Δt i 2 s. The absence of a γ γ absorption cutoff in the spectra leads to a jet bulk Lorentz factor of Γ j 10 3 (Abdo et al 2009) (see also Aoi et al 2009). (A larger Γ j would make the internal shock radius larger than the deceleration radius of the shell.)…”

Multi-messenger Light Curves from Gamma-Ray Bursts in the Internal Shock Model

“…In the internal shock scenario, the shape of the GRB light curve is the result of shell collisions (Kobayashi et al 1997;Daigne & Mochkovitch 1998;Beloborodov 2000;Spada et al 2000;Kobayashi & Sari 2001;Daigne & Mochkovitch 2003;Aoi et al 2010). When shells collide, a gamma-ray pulse and a neutrino pulse are emitted.…”

“…In the internal shock model, d and l should be comparable. The simulations in Kobayashi et al (1997) set d=l, while Aoi et al (2010) …”

“…Instead, as in Aoi et al (2010), Abbasi et al (2012), we assume that its shape is that of observed GRB spectra. We parametrize the spectrum as a broken power law, i.e., , respectively (Aoi et al 2010). Pair production via gg  + -e e may limit the maximum energy of escaping photons; see Figure 9, right column.…”

Temporal Decomposition Studies of GRB Lightcurves

“…In addition, As pointed out by Granot et al (2008), due to the temporal evolution of τ γγ , the opacity cut-off in a time-integrated spectrum will be smoother than a sharp exponential decay: the cut-off transition will be close to a power-law steepening. This time evolution takes place within a given γ-ray pulse, and can be even stronger in a complex burst where the light curve is made up of many pulses (Aoi et al 2010). Hence a study of the evolution of Γ min would lead to a better understanding of the possible connection between the temporal structure of the light curve and the spectral evolution of the GRB.…”