- icrc2007@icrc2007.unam.mx

### Support

# Contribution Oral

# Opacity Build-up in Impulsive Relativistic Sources

## Speakers

- Mr. JOHANN COHEN-TANUGI

## Primary authors

- Mr. JOHANN COHEN-TANUGI (SLAC/KIPAC - Stanford University)

## Co-authors

- Mr. Jonathan GRANOT (SLAC/KIPAC - Stanford University)
- Mr. Eduardo DO COUTO E SILVA (SLAC/KIPAC - Stanford University)

## Files

## Abstract content

Opacity effects in relativistic sources of high-energy gamma-rays,
such as gamma-ray bursts (GRBs) or Blazars, can probe the Lorentz
factor of the outflow as well as the distance of the emission site
from the source, and thus help constrain the composition of the
outflow (protons, pairs, magnetic field) and the emission
mechanism. The attenuation of high energy photons will be probed by
the Large Area Telescope (LAT) onboard the Gamma ray Large Area Space
Telescope (GLAST), the next generation gamma-ray observatory to be
launched in late 2007. While most previous works consider the opacity
in steady state, we study here the time dependence of the opacity to
pair production (\gamma\gamma \to e^+e^-), which may be especially
relevant for impulsive relativistic sources, such as flares in Blazars
or the prompt emission and flares in GRBs. We present a simple, yet
rich, semi-analytic model that describes the build-up of the (target)
photon field, and derive the time and energy dependence of the optical
depth $\tau_{\gamma\gamma}$. Our model features a thin spherical
shell that expands ultra-relativistically and emits isotropically in
its own rest frame over a finite range of radii ($R_0 \leq R \leq R_0
+ \Delta R$). We find that in an impulsive source ($\Delta R \lesssim
R_0$), while the instantaneous spectrum has an exponential cutoff
above the photon energy $\epsilon_1(t)$ where
$\tau_{\gamma\gamma}(\epsilon_1) = 1$, the time integrated spectrum
has a power-law high-energy tail above the photon energy
$\epsilon_{1*} \sim \epsilon_1(\Delta t)$ where $\Delta t$ is the
duration of the emission episode. Furthermore, photons with energies
$\epsilon > \epsilon_{1*}$ are expected to arrive mainly near the
onset of the spike in the light curve or flare, which corresponds to
the short emission episode. This arises since in such impulsive
sources it takes time to build-up the (target) photon field, and thus
the optical depth initially increases with time and $\epsilon_1(t)$
correspondingly decreases with time, so that photons of energy
$\epsilon > \epsilon_{1*}$ are able to escape the source mainly very
early on while $\epsilon_1(t) > \epsilon$. As the source approaches a
quasi-steady state ($\Delta R \gg R_0$), the time integrated spectrum
develops an exponential cutoff, while the power-law tail becomes
increasingly suppressed.

## Reference

Proceedings of the 30th International Cosmic Ray Conference; Rogelio Caballero, Juan Carlos D'Olivo, Gustavo Medina-Tanco, Lukas Nellen, Federico A. Sánchez, José F. Valdés-Galicia (eds.); Universidad Nacional Autónoma de México, Mexico City, Mexico, 2008; Vol. 3 (OG part 2), pages 1183-1186