Light Curves from an Expanding Relativistic Jet

We perform fully relativistic hydrodynamic simulations of the deceleration and lateral expansion of a relativistic jet as it expands into an ambient medium. The hydrodynamic calculations use a 2D adaptive mesh refinement (AMR) code, which provides adequate resolution of the thin shell of matter behind the shock. We find that the sideways propagation is different than predicted by simple analytic models. The physical conditions at the sides of the jet are found to be significantly different than at the front of the jet, and most of the emission occurs within the initial opening angle of the jet. The light curves, as seen by observers at different viewing angles with respect to the jet axis, are then calculated assuming synchrotron emission. For an observer along the jet axis, we find a sharp achromatic `jet break' in the light curve at frequencies above the typical synchrotron frequency, at $t_{jet}\approx 5.8(E_{52}/n_1)^{1/3}(\theta_0/0.2)^{8/3}$ days, while the temporal decay index $\alpha$ ($F_{\nu}\propto t^{\alpha}$) after the break is steeper than $-p$ ($\alpha=-2.85$ for $p=2.5$). At larger viewing angles $t_{jet}$ increases and the jet break becomes smoother.