Afterglow Light Curves from Impulsive Relativistic Jets with an Unconventional Structure

The jet structure in gamma-ray burst (GRB) sources is still largely an open question. The leading models invoke either(1)aroughlyuniformjetwithsharpedgesor(2)ajetwithanarrowcoreandwidewingswheretheenergyper solid angle drops as a power law with the anglefrom the jet symmetry axis. Recently, a two-component jet model has also been considered, with a narrow uniform jet of initial Lorentz factor 0 k100 surrounded by a wider uniform jet with 0 � 10 30. Some models predict more exotic jet profiles, such as a thin uniform ring (i.e., the outflow is bounded by two concentric cones of half-opening anglec andc þ � , withTc )o r af an (a thin outflow withT1 along the rotational equator, � c ¼ � /2 þ � /2). In this paper we calculate the expected afterglow light curves from such jet structures, using a simple formalism that is developed here for this purpose and could also have other applications. These light curves are qualitatively compared to observations of GRB after- glows.Itisshownthatthetwo-componentjetmodelcannotproduceverysharpfeaturesintheafterglowlightcurve due to the deceleration of the wide jet or the narrow jet becoming visible at lines of sight outside the edge of the jet. We find that a ''ring''-shaped jet or a ''fan''-shaped jet produces a jet break in the afterglow light curve that is too shallowcomparedtoobservations,wherethechangeinthetemporaldecayindexacrossthejetbreakisabouthalfof that for a uniform conical jet. For a ring jet, the jet break is divided into two distinct and smaller breaks, the first occurring when � � � 1 2 and the second when �� c � 1 . Subject heading gs: gamma rays: bursts — gamma rays: theory — ISM: jets and outflows — radiation mechanisms: nonthermal — relativity