The central engine of Gamma Ray Bursts is hidden from direct probing with photons mainly due to the high densities involved. Inferences on their properties are thus made from their cosmological setting, energetics, low-energy counterparts and variability. If GRBs are powered by hypercritical accretion onto compact objects, on small spatial scales the flow will exhibit fluctuations, which could in principle be reflected in the power output of the central engine and ultimately in the high energy prompt emission. Here we address this issue by characterizing the variability in neutrino cooled accretion flows through local shearing box simulations with magnetic fields, and then convolving them on a global scale with large scale dynamical simulations of accretion disks. The resulting signature is characteristic, and sensitive to the details of the cooling mechanism, providing in principle a discriminant for GRB central engine properties.
. The enabling cooling mechanism allowing accretion is neutrino emission, raising the usual Eddington rate for photons by sixteen orders of magnitude (Popham, Woosley & Fryer 1999;Narayan, Piran & Kumar 2001;Kohri & Mineshige 2002;Beloborodov 2003;Di Matteo, Perna & Narayan 2002;Setiawan, Ruffert & Janka 2004;Lee, Ramirez-Ruiz & Page 2005;Chen & Beloborodov 2007). This applies both to long and short GRBs, perhaps due to the collapse of massive rotating stars (Woosley 1993;MacFadyen & Woosley 1999) and compact binary mergers (Eichler et al. 1989;Paczyński 1991;Narayan, Paczyński & Piran 1992), respectively, or magnetized neutron stars (Usov 1992). The prompt gamma-ray emission originates at ≃ 10 14 -10 16 cm from this source, possibly from internal shocks in the relativistic outflow generated by the engine (Zhang & Mészáros 2004). The engine itself is hidden from view due to the high opacities, and can be potentially probed directly only through gravitational waves and neutrinos.
The observed time series in GRB prompt emission show diversity between events (see, e.g., Norris et al. 1996): some have a single peak, others multiple emission episodes, with correlations between the fluence of the active period and the length of the quiescent interval preceding it (Ramirez-Ruiz & Merloni 2001). On top of this, rapid (ms) fluctuations are routinely observed. Fourier analysis of the high-energy light curves of the prompt emission in GRBs in the source frame reveals power-law spectra (Beloborodov, Stern & Svensson 1998, 2000;Ryde et al. 2003), with index ≃ -5/3 and a break at ≃ 1 -2 Hz. Variability is likely due to a combination of several effects, allowing in principle an additional way to probe the central engine indirectly. Some are probably intrinsic to the progenitor: the distribution of angular momentum with radius inside the star in the case of a collapsar may lead to distinct episodes of energy release (Kumar, Narayan & Johnson 2008;Perna & MacFadyen 2010; Lopez-Camara, Lee & Ramirez-Ruiz 2010); the fall back at late times of material stripped from a tidally disrupted neutron star is capable of powering secondary accretion episodes (Rosswog 2007;Lee, Ramirez-Ruiz & Lopez-Camara 2009); hydrodynamical or magnetic instabilities in the accretion disk may result in intermittent accretion (Perna, Armitage & Zhang 2006;Proga & Zhang 2006;Taylor, Miller & Podsiadlowski 2010).
Others can come from the relativistic outflow: the interaction of a jet with high Lorentz factor with the stellar envelope before breakout can lead to irregularities and shocking (Morsony, Lazzati & Begelman 2010); the outcome of internal shocks between shells in the flow depends on the variation in mass and energy upon ejection (Panaitescu, Spada & Mészáros 1999;Ramirez-Ruiz, Merloni & Rees 2001;Bosnjak, Daigne & Dubus 2009;Mendoza et al. 2009). An additional factor, upon which we focus here, is related to the variability present in the accretion disk as a result of turbulent motions. The dissipation is related to the local hydrodynamical variables, and as these vary in time, so will the energy output.
The magnetorotational instability (MRI) (Balbus & Hawley 1998) is a possible mechanism that will allow for the transport of angular momentum in accretion disks with differential rotation. Its behavior under the physical conditions in neutrino cooled disks, which are similar to those occurring in supernovae, but different from the usual ones present in X-ray binaries and AGN, has come under scrutiny more recently (Thompson, Quataert & Burrows 2005;Masada et al. 2007;Rossi, Armitage & Menou 2008;Obergaulinger et al. 2009). One such difference lies in the sensitivity of the cooling rate to temperature and is at the heart of this work. Whereas, for example, the photon bremsstrahlung emissivity scales as q ∝ T 1/2 in the optically thin limit, for neutrinos q ∝ T β , where β ≃ 6 -9 depending on the cooling process. Further, while photon-cooled disks are typically optically thick, τ γ ≫ 1, for a wide range of relevant parameters their neutrino-cooled counterparts are optically thin, τ ν ≤ 1, tightly coupling the local conditions to the emitted luminosity.
In this Letter, we characterize the local variability in neutrino cooled disks through shearing box MHD simulations ( § 2), and then use the results of global disk simulations to scale the results for the central engine as a whole ( § 3). Prospects for placing constraints on GRBs are discussed in § 4.
The local flow in the disk is modeled by the shearing box approximation (Hawley, Gammie & Balbus 1995): a rectangular Cartesian coordinate system represents a local neighborhood inside the disk, at an arbitrary orbital radius R 0 with dimensions which are much smaller than R 0 . The x, y and z axes represent the radial, azimuthal and vertical directions in the disk, respectively. The radial component of the central object’s gravity is included, and differential rotation is replaced by a Keplerian she
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