We present the results of hydrodynamical simulations of gamma-ray burst jets propagating through their stellar progenitor material and subsequently through the surrounding circumstellar medium. We consider both jets that are injected with constant properties in the center of the star and jets injected with a variable luminosity. We show that the variability properties of the jet outside the star are a combination of the variability injected by the engine and the variability caused by the jet propagation through the star. Comparing power spectra for the two cases shows that the variability injected by the engine is preserved even if the jet is heavily shocked inside the star. Such shocking produces additional variability at long time scales, of order several seconds. Our findings suggest that the broad pulses of several seconds duration typically observed in gamma-ray bursts are due to the interaction of the jet with the progenitor, while the short-timescale variability, characterized by fluctuations on time scales of milliseconds, has to be injected at the base of the jet. Studying the properties of the fast variability in GRBs may therefore provide clues to the nature of the inner engine and the mechanisms of energy extraction from it.
Gamma-ray bursts (GRBs) are extremely bright and highly variable sources of gamma-ray radiation. Their isotropic equivalent emitted energy can be as large as 10 55 erg (GRB080916C; Abdo et al. 2009). GRBs last between a fraction of a second and several thousand seconds and can be divided in two classes based on their duration and spectral characteristics (Kouveliotou et al. 1993). Short bursts last less than 2 s, while long bursts last between 2 and several thousand seconds. Even though some bursts seem hard to classify within this simple scheme (e.g., GRB 060505 and GRB 060614; Fynbo et al. 2006, Gal-Yam et al. 2006, Della Valle et al. 2006;GRB 060121, de Ugarte Postigo et al. 2006) it is widely believed that a substantial fraction of, if not all, long-duration GRBs are associated with the death of massive, rapidly spinning stars (Woosley 1993;MacFadyen & Woosley 1999;Stanek et al. 2003;Hjorth et al. 2003;Woosley & Bloom 2006).
Within the overall duration of the prompt phase, fast variability is commonly observed, with the shortest spikes lasting only a fraction of a millisecond (Schaefer & Walker 1999, Walker et al. 2000). Characterizing the burst variability has proved challenging, with each GRB seeming to have its own individual pattern. This is particularly frustrating since the variability can in principle carry information on the workings of the central engine, the energy dissipation processes, and the radiation mechanisms involved in the release of the burst emission. Fenimore & Ramirez-Ruiz (1999) showed that the variability time scale of GRB light curves does not evolve from the beginning to the end of the prompt emission. Their work placed a strong constraint on the dissipation process and proved that the variability in the GRB prompt emission is not due to the interaction of the fireball with the external medium (see Dermer et al. 1999;2000 for an alternative interpretation). Beloborodov et al. (1998Beloborodov et al. ( , 2000) ) analyzed the composite power spectrum of BATSE light curves, finding that it is well described by a power-law of the shape P DS(f ) ∝ f -5/3 , reminiscent of the Kolmogorov spectrum of fully developed turbulence.
The discovery of the association of GRBs with massive stars puts burst variability in a new light. There are two possible sources of variability in the outflow: the engine itself (MacFadyen & Woosley 1999;Aloy et al. 2000;Ouyed et al. 2003;Proga et al. 2003;McKinney & Narayan 2007;McKinney & Blandford 2009) and the interaction of the flow with the progenitor star material (Aloy et al. 2002;Gomez & Hardee 2004;Aloy & Obergaulinger 2007;Morsony et al. 2007). How these two sources of variability combine and interact to give rise to the variability in the light curve is unknown but of fundamental importance if any conclusion is to be drawn from the temporal properties of GRB light curves.
In this paper we present the results of 2D axisymmetric simulations of the propagation of baryonic GRB jets through their progenitor star material. We show simulations in which the engine is either constant or variable and compare the structure of the jets as they emerge from the progenitor star. This paper is organized as follows: in § 2 we describe our simulations, in § 3 we describe our results, and in § 4 we discuss their potential implications.
We present the results of four simulations, each of which has the same progenitor star and average jet properties, but with different injected luminosity histories. The first simulation has uniform injected luminosity and is analogous to that already presented in Morsony et al. (2007, hereafter MLB07) and Lazzati et al. (2009 hereafter LMB09). We call this simulation uniform. The second and third simulations (variable entropy and variable baryon load) represent an inner engine that releases a luminosity that varies in time. The time history was simulated as a random series of numbers convolved with a Gaussian, to yield a flat power spectrum (white noise) out to a cutoff at ∼ 0.1s. This represents a randomly varying energy input, with a cutoff such that all the variability is well resolved.
The energy input in a real GRB could, of course, have a different power spectrum, but for our purpose of determining how the variability is modified during propagation, this input is an adequate example. The difference between the simulation that we call variable entropy and the one that we call variable baryon load is that in the former the luminosity is varied by changing the entropy η = L/ ṁc 2 holding ṁ constant, while in the latter the luminosity is changed by changing the baryon load ṁ. Finally, a simulation was run with an on-off engine with a period of 0.2s (0.1s on, 0.1s off), in which the luminosity was changed by changing the baryon load ṁ. We identify this last simulation as step. The represents an extreme case of strong, fast variability but on a time scale that is well resolved in our simulation. A 3s section of the injected lumino
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