3. Numerical simulations

<sup>T</sup>μν <sup>¼</sup> <sup>T</sup>μν

<sup>u</sup><sup>μ</sup>u<sup>ν</sup> <sup>þ</sup> 1 2 b2

Tμν

Tμν EM <sup>¼</sup> <sup>b</sup><sup>2</sup>

2.4. Nucleosynthesis of heavy isotopes in GRB engines

nucleosynthesis theory) (Figure 3).

where

20 Cosmic Rays

Fermi gas.

<sup>g</sup>as <sup>þ</sup> <sup>T</sup>μν

<sup>g</sup>μν � <sup>b</sup><sup>μ</sup>b<sup>ν</sup>

where equation of state of gas in the adiabatic form, <sup>p</sup> <sup>¼</sup> <sup>K</sup>r<sup>γ</sup> <sup>¼</sup> ð Þ <sup>γ</sup> � <sup>1</sup> <sup>u</sup>, does not hold for the dense and hot plasma in the GRB flows. The EOS has to be therefore substituted with the

The subsequent isotopes after Helium are created in the outer layers of the accretion disk body, as well as in its ejecta. Synthesis of heavy isotopes can be computed by means of the thermonuclear reaction network simulations [33]. The code and reaction data (http://webnucleo.org) can be adopted to read the input data in the form of density, temperature, and electron fraction distribution along the distance radial coordinate in the accretion disk [34]. The numerical methods and algorithms in the network computations under the nuclear statistical equilibrium were described in Hix and Meyer [35] (see also Meyer [36] for a review of the r-process

The analysis of the integrated mass fraction distribution allows establishing the role of global parameters of the accretion flow model, such as the black hole mass and its spin, in forming the disk composition. We show here the resulting distribution of certain chosen isotopes synthesized

Figure 3. Profiles of the relative, height integrated mass fractions of the most abundant isotopes produced in the body of the accretion torus in GRB engine. The accretion rate is equal to about 0:1M⊙s�1. The black hole parameters are <sup>M</sup> <sup>¼</sup> <sup>3</sup>M⊙,

and a ¼ 0:98. Nucleosynthesis computations were based on the NSE condition.

gas <sup>¼</sup> <sup>r</sup>hu<sup>μ</sup>u<sup>ν</sup> <sup>þ</sup> pgμν <sup>¼</sup> ð Þ <sup>r</sup> <sup>þ</sup> <sup>u</sup> <sup>þ</sup> <sup>p</sup> <sup>u</sup><sup>μ</sup>u<sup>ν</sup> <sup>þ</sup> pgμν (7)

EM (6)

; b<sup>μ</sup> <sup>¼</sup> <sup>u</sup>νFμν (8)

The modeling of the emerging outflows in both types of GRBs is in general a very difficult task. Beyond the challenges of the various microphysical process participating and the general relativistic frameworks, it involves a wide range of spatial scales. For example, a simulation aimed to describe the whole extent of a jet originating from compact binaries needs a fine resolution of <sup>10</sup><sup>2</sup> points for a typical 10 km of NS radius, or even an order of magnitude shorter, in order to properly resolve hydromagnetic phenomena like turbulence, Kelvin-Helmholtz instability (see Zrake & MacFadyen [42]; Kiuchi et al. [43]), and the magnetorotational instability (see Hawley et al. [44] and references therein). However, it must be able to reach radial distances up to the 10<sup>2</sup> 106 rg where the terminating Lorentz factor might be achieved (e.g., Tchekhovskoy et al. [45]). An even more extended scale regime occurs in the long GRBs counterpart since the spatial scales involve the stellar envelope penetration phase and the propagation to the surrounding space (1010–10<sup>13</sup> cm). It is thus apparent that building a global simulation describing the whole outflow evolution is much beyond the present calculating capabilities and every specific effort is able to describe accurately a particular phase of the evolution, more or less extended depending on the use of adaptive mesh refinement techniques or a clever mesh selection.

#### 3.1. Full GRMHD scheme

The merging phase of the compact object binaries has to be performed by fully relativistic schema, that is, ones that beyond capturing the essential of the hydro- and magnetohydrodynamic aspects of the accretion evolves also the space-time. At present, the ambiguity for the precise nature of the members consisting the binary has not been clarified and the dominant research effort is oriented toward the BH-NS, NS-NS candidates. As a result, a number of codes were developed to solve the underlying equations for both types of progenitors, every of which presenting its own approximations and limitations (see Paschalidis [46] for a list on the codes and a more detailed review on the full GR findings).

Assuming the driving object of the burst is a black hole—torus system simulations must accomplish two challenges: create a viable disk that feeds the system for the burst duration and launch a jet which able to reach the Lorentz factor γ<sup>f</sup> ≥ 100 that satifies the fireball model requirements. None of these tasks are trivial to be obtained. Back of the envelope estimates for the accretion rate is <sup>M</sup>\_ � <sup>ε</sup>c<sup>2</sup> , where <sup>ε</sup> is the efficiency of converting the disk accretion to the observed γ-photons luminosity, for the typical values of the sGRB medium value duration <sup>t</sup> � <sup>0</sup>:3<sup>s</sup> [4] and energy of 10<sup>51</sup> erg result to a disk of � <sup>0</sup>:015M⊙. Foucart [47] examined a number of unmagnetized BHNS simulation and proposed the fit:

$$\frac{M\_{\rm disk}}{M\_{\rm NS}} = 0.42q^{1/3}(1 - 2\,\text{C}) - 0.148\frac{R\_{\rm ISCO}}{R\_{\rm NS}} \quad , \quad q = \frac{M\_{\rm BH}}{M\_{\rm NS}} \quad \text{C} = \frac{M\_{\rm NS}}{R\_{\rm NS}} \tag{9}$$

4. Ejection and acceleration of jets in gamma ray bursts

proposed.

than the short bursts.

4.1. Jet launching

In both frameworks of the bursts, the plausible central engine refers to hyperaccreting solar mass black holes surrounded by a massive disk 0ð Þ :1 � 1 M⊙, while the energy released and the

Gamma Ray Bursts: Progenitors, Accretion in the Central Engine, Jet Acceleration Mechanisms

energy non-thermal photons received by the observers point for an ultrarelativistic outflow γ ≥ 100, most likely in jet geometry, that in turn implies baryon-clean outflow. Building a launching mechanism for such a jet is not trivial and beyond the Blandford Znajek proccess [55]. Therefore, an another type of mechanism namely the neutrino pair annihilation was

But beyond the enormous energetic constrains, our mechanism has to face another major challenge, namely, the great variability of the prompt emission lightcurves. Although long debated, two of the most widely accepted models for the origin of the γ-radiation, the internal shocks and the photospheric emission link the rapid variability directly with the properties of the central engine (see, however, Morsony et al. [56] and Zhang & Yan [57] for a source of additional variability due to the propagation inside the star and the effects of amplified local turbulence). As a consequence, the determination of the minimum time variability by the observational data is of primary importance, but that proves to be challenging since the corresponding time scales have power densities very close to the data noise. Nevertheless, some typical values can be obtained and MacLachlan et al. [58] using a method based on wavelets proved that both types of bursts present variability in the order of a few to few tenths of milliseconds, with the long GRBs exhibiting a longer time variability

The high density and temperature of the accreting flow result in a photon optically thick disk that cannot cool by radiation efficiently. On the other hand, the high temperature and density result in the intense neutrino emission from the inner parts of the disk, called NDAF (neutrino dominated accretion flow). The effects of neutrino outflow, if it is capable to produce a highly relativistic jet and what implications it imposes when it is combined with the Blandford-Znajek process, is a matter of intense debate, presently inconclusive. There exist two critical values of the accretion rate, M\_ ign and M\_ trapped, that determine the efficient neutrino cooling. If the accretion rate is lower, the temperature is not high enough to initiate the neutrino emission. If the accretion rate is higher, the disk becomes optically thick to neutrinos. Assuming an αviscosity in the disk [59], the values of the critical rates depend on both α and the spin of black

hole a. For example, the calculation by Chen and Beloborodov [60] provided the fit:

where Kign, Ktrap depend on the black hole's spin. For <sup>a</sup> <sup>¼</sup> 0, Kign <sup>¼</sup> <sup>0</sup>:071M⊙s�1, Ktrap <sup>¼</sup> <sup>9</sup>:3M⊙s�1,

<sup>M</sup>\_ trap <sup>¼</sup> Ktrap

α 0:1 <sup>1</sup>=<sup>3</sup>

α 0:1 <sup>5</sup>=<sup>3</sup>

<sup>M</sup>\_ ign <sup>¼</sup> Kign

while for <sup>a</sup> <sup>¼</sup> <sup>0</sup>:95, Kign <sup>¼</sup> <sup>0</sup>:021M⊙s�<sup>1</sup>, Ktrap <sup>¼</sup> <sup>1</sup>:8M⊙s�1.

. The high-

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prompt phase duration points to high accretion rates of order 0ð Þ :<sup>01</sup> � <sup>10</sup> <sup>M</sup>⊙s�<sup>1</sup>

which is applicable on a ≤ 0:9 [48], while a similar relationship has been proposed for the NS-NS and in the framework of the hydro simulations [49], but contrary to the one above the estimation is now EOS-dependent. Inspection of the above expression for a fixed value of q and assumed value of the compaction C provides the remnant disk mass as a function of the BH spin. The results of Foucart [47] and Lovelace et al. [48] point toward high initial values of the BH spin, if a massive disk is to be created.

Although the launch of jets was naturally obtained in the fixed space time simulations long before, that task proved to be non-trivial for the full GR ones. The NS-NS simulations by Rezzolla et al. [50] were until recently the only ones that demonstrated the emerging of a jet, while most of the simulations did not show a collimated outflow. For example, the BHNS of Kiuchi et al. [51], a wind was found, but for the NS-NS model of the pressure of the fall back material was so strong preventing even the launching of the wind.

All the above indicates that the magnetic field topology close to the vicinity of the black hole is of crucial importance and no matter of what process (Blandford and Payne [52]) is the one that drives the outflow acceleration and the resulting jet, a large scale poloidal component is crucial to drive the energy outflow outwards. But in the simulations, the field remaining outside the black hole is wounded to a toroidal configuration, while the poloidal component had an alternating orientation. Finally, the launching of the jets in the BHNS framework was achieved once a more realistic bipolar initial configuration was adopted [53]. The realization of such a configuration is a difficult task mostly because of the low density of the exterior medium. By adopting a specific set of initial condition to overcome code limitations on this regime, the authors managed to produce a configuration of enhanced magnetic field over the BH poles because of the magnetic winding. The field strength increased from 1013 to 10<sup>15</sup> G, which is a crucial value for the BZ process (see below), resulted in the launch of a 100 ms jet, a relatively short duration. A similar evolution was also obtained for the NS-NS framework, where once again the importance of the exterior magnetic field seems to be of crucial importance [54]. As a result, previous GRMHD results of Rezzolla et al. [50] have been confirmed, while in consistency with Kiuchi et al. [51], the jet was launched only after the density of the fall back material above the BH has decreased.
