2. Accretion onto a black hole as a driving engine of a GRB

1.2. Models of GRBs origin

16 Cosmic Rays

the order of GeV [18–20].

energy of a compact object with a stellar mass:

The gamma ray emission originates at rather large distances from the base of the jet. Therefore, the central engine driving the jets and forming its base are hidden from the observer and any studies of its structure must be grounded on the indirect analysis. The signal which would be emitted from the engine could be produced either in gravitational waves or in the neutrinos of MeV energies. Such neutrinos are rather impossible to be detected from cosmological distances. Much more promissing are neutrinos produced in the GRB jets which have energies in

The constraints which are based on the observed isotropic equivalent energy of the bursts suggested that the total energy released during the explosion is in the order of the binding

The burst durations are, however, much longer than the dynamical time, over which the matter can free fall onto such a star. The extended duration of the event must therefore be driven by a viscous process. The most plausible is the disk accretion process, which in addition provides a required collimation of the burst stream along the disk rotation axis. The appearance of a large amount of matter in the vicinity of a black hole, to be accreted with a few tens-hundreds of a

The scenario of a compact object merger [21] was able to explain the energies required for a detection of the event from a cosmological distance [22]. It was thought first that this scenario could be universal for all the types of GRBs; however, the observations of the GRB host galaxies, their active star formation rates in some cases, and the discoveries of GRB-supernova connection led to a different scenario for the long bursts. The currently accepted scenario for the long GRB progenitor is the collapsar, or hypernova model [23, 24]. In this model, the massive iron core of a rapidly rotating, evolved massive star (typically, the Wolf-Rayet type of star) quickly collapses to form a black hole. Most of the stellar envelope is expelled, but the remaining part is slowed down by the backward shocks and fall back. The material which posseses large angular momentum is concentrating in the equatorial plane of the star and forms an accretion disk. The non-rotating matter is falling radially along the axis of rotation into the black hole and the empty funnel forms there, to help collimate the subsequenltly launched jets [25]. They have to break out the stellar envelope, and accelerate up to ultrarela-

The hypernovae connected with long GRBs are a subgroup of the supernovae type I b/c (which do not exhibit neither hydrogen nor helium lines in their spectra) and constitute about 10% of this class [26]. Statistically, this should agree with the estimated rate of GRBs. Their occurrence rate is about 10�<sup>3</sup> of the supernova rate per galaxy per year [27]. The reason why not all the supernovae type I b/c (the core collapse supernovae) produce GRBs is most probably

connected with the extremely low metallicities and rotation of the pre-SN star [28].

second, implies an extremely violent process, most probably a birth of a new black hole.

tivistic velocities, with Lorentz factors in the order of Γ � 100.

<sup>R</sup> <sup>≈</sup> <sup>3</sup> � <sup>1054</sup> erg (1)

<sup>E</sup> <sup>¼</sup> GM<sup>2</sup>

The accretion tori surrounding black holes are ubiquitous in the universe. They occupy centers of galaxies, or reside in binary systems composed of stellar mass black holes and main sequence stars, being a source of power for their ultraviolet or X-ray emission. In these kinds of objects, frequently the black hole accretion is accompanied with the ejection of jets, launched along the accretion disk axis. Such sources are then observed as the radio-loud quasars, driven by the action of supermassive black holes, or the 'microquasars', which are driven by the stellar mass black holes. The jets of plasma are accelerated up to the relativistic speeds, and emit the high-energy radiation, measured over the entire energy spectrum.

Similarly, in the case of ultrarelativistic jets that are sources of gamma rays in GRBs, the driving engine is supposedly the stellar mass black hole surrounded by an accretion disk. However, since the GRB events are transients that last only up to several hundred seconds, and not for thousands, or millions of years, the accretion process should not be persistent and last not too long. The limiting time of the GRB engine activity is governed by the amount of matter available for accretion, and by the rate of this process (Figure 1).

From the computational point of view, the numerical model of any black hole accretion disk is based on standard equations of hydrodynamics (or MHD, if the magnetic fields are taken into account). The global parameters that enter the equations and act as scaling factors are the black hole mass, MBH, its angular momentum (called spin, a), and accretion rate, M\_ .

#### 2.1. Chemical composition of the accretion disk in GRB engine and the equation of state

The temperature and density in the accretion disk feeding the gamma ray busts are governed by a huge accretion rate. The physical conditions make the disk undergo onset of nuclear reactions, since <sup>r</sup> � 1010 � <sup>10</sup>12g cm�<sup>3</sup> and <sup>T</sup> � <sup>10</sup><sup>9</sup> � 1011K. The disk is composed from the free protons, electrons and neutrons, and its electron fraction, defined as the ratio of protons to baryons, which is typically less than Ye ¼ 0:5. This is because of the neutronisation reactions, which are established by the condition of β-equilibrium, and greatly reduce the number density of free protons (balanced by electrons to satisfy the charge neutrality), in the cost of increasing the neutron number density.

Figure 1. The structure of the black hole accretion disk in the GRB central engine. Three values of the BH spin, a ¼ 0:6; 0:9, and a ¼ 0:98, are shown with blue, red, and green lines, respectively. The black hole mass is equal to 3M⊙. The model is computed for the mass of the disk equal to about 0:1M⊙. The mass accretion rate is varying, and is about 0:<sup>2</sup> � <sup>0</sup>:3M⊙s�1. Profiles show radial distribution of density and temperature in the disk equatorial plane.

Because the plasma may contain a certain number of positrons, which are also a product of the weak processes, the net value of the electron fraction must account for them, and is defined as:

$$Y\_{\ell} = \frac{n\_p}{n\_p + n\_n} = \frac{n\_{\ell^-} - n\_{\ell^+}}{n\_b} \tag{2}$$

The species in general are relativistic and may have an arbitrary degeneracy level (given by their chemical potential). They are therefore subject to the Fermi-Dirac statistics, as follows from the kinetic theory of gas, and hence the relations between pressure, density, temperature, and entropy in the gas will not obey the ideal gas equation of state. Typically, these quantities

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

The initial conditions for the structure of accretion disk should be specified in the fixed grid and the background metric most appropriate for the GRB problem is the Kerr spacetime. This is because the black hole is rapidly spinning. The initial condition evolves according to the

;<sup>ν</sup> ¼ 0 (4)

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19

<sup>ν</sup>;<sup>μ</sup> ¼ 0 (5)

ru<sup>μ</sup> 

Tμ

If the magnetic fields are taken into account, the energy tensor contains matter parts and electro-

Figure 2. Neutrino emissivity (left), electron fraction (middle), and gas to magnetic pressure ratio (right) in the 2 dimensional simulation of the innermost parts of accretion flow around black hole in the GRB central engine. Contours show the magnetic field configuration. Parameters of the model are black hole spin a ¼ 0:98, black hole mass M ¼ 3M⊙,

are computed numerically and stored in the EOS tables (Figure 2).

2.3. Accretion physics in general relativistic MHD framework

magnetic parts:

and disk mass M<sup>d</sup> ¼ 0:1M⊙.

continuity equation and the energy-momentum conservation equation:

#### 2.2. Neutrino cooling

The neutrino cooling in the GRB central engine is the most efficient mechanism of reducing the thermal energy of the plasma. The radiative processes involving photons are negligibly inefficient due to extremely large optical depths, such that the photons are completely trapped in the plasma.

The neutrino emission results from the following nuclear reactions:

$$\begin{aligned} p + e^- &\to n + \overline{v}\_e \\ n + \overline{v}\_e &\to p + e^- \\ p + \overline{v}\_e &\to n + \overline{e}\_+ \\ n + e\_+ &\to p + \overline{v}\_e \\ p + e^- + \overline{v}^\* &\to n \\ n &\to p + e^- + \overline{v}\_e \end{aligned} \tag{3}$$

and in certain large parts of the disk these processes lead to a fairly large neutrino emissivities. The equation of state is based on the equilibrium of nuclear reactions, which leads to establishing the balance between the rates of forward and backward processes, and on the ratio of number densities of protons to neutrons [32].

The species in general are relativistic and may have an arbitrary degeneracy level (given by their chemical potential). They are therefore subject to the Fermi-Dirac statistics, as follows from the kinetic theory of gas, and hence the relations between pressure, density, temperature, and entropy in the gas will not obey the ideal gas equation of state. Typically, these quantities are computed numerically and stored in the EOS tables (Figure 2).

#### 2.3. Accretion physics in general relativistic MHD framework

Because the plasma may contain a certain number of positrons, which are also a product of the weak processes, the net value of the electron fraction must account for them, and is defined as:

Figure 1. The structure of the black hole accretion disk in the GRB central engine. Three values of the BH spin, a ¼ 0:6; 0:9, and a ¼ 0:98, are shown with blue, red, and green lines, respectively. The black hole mass is equal to 3M⊙. The model is computed for the mass of the disk equal to about 0:1M⊙. The mass accretion rate is varying, and is about 0:<sup>2</sup> � <sup>0</sup>:3M⊙s�1.

The neutrino cooling in the GRB central engine is the most efficient mechanism of reducing the thermal energy of the plasma. The radiative processes involving photons are negligibly inefficient due to extremely large optical depths, such that the photons are completely trapped in

> p þ e� ! n þ ve n þ ve ! p þ e� p þ ve ! n þ e<sup>þ</sup> n þ e<sup>þ</sup> ! p þ ve <sup>p</sup> <sup>þ</sup> <sup>e</sup>� <sup>þ</sup> ve ! <sup>n</sup> n ! p þ e� þ ve

and in certain large parts of the disk these processes lead to a fairly large neutrino emissivities. The equation of state is based on the equilibrium of nuclear reactions, which leads to establishing the balance between the rates of forward and backward processes, and on the

<sup>¼</sup> ne� � ne<sup>þ</sup> nb

(2)

(3)

Ye <sup>¼</sup> np np þ nn

Profiles show radial distribution of density and temperature in the disk equatorial plane.

The neutrino emission results from the following nuclear reactions:

ratio of number densities of protons to neutrons [32].

2.2. Neutrino cooling

the plasma.

18 Cosmic Rays

The initial conditions for the structure of accretion disk should be specified in the fixed grid and the background metric most appropriate for the GRB problem is the Kerr spacetime. This is because the black hole is rapidly spinning. The initial condition evolves according to the continuity equation and the energy-momentum conservation equation:

$$(\rho u\_{\mu})\_{;v} = 0 \tag{4}$$

$$T\_{"\prime,\mu}^{\mu} = \mathbf{0} \tag{5}$$

If the magnetic fields are taken into account, the energy tensor contains matter parts and electromagnetic parts:

Figure 2. Neutrino emissivity (left), electron fraction (middle), and gas to magnetic pressure ratio (right) in the 2 dimensional simulation of the innermost parts of accretion flow around black hole in the GRB central engine. Contours show the magnetic field configuration. Parameters of the model are black hole spin a ¼ 0:98, black hole mass M ¼ 3M⊙, and disk mass M<sup>d</sup> ¼ 0:1M⊙.

$$T^{\mu\nu} = T^{\mu\nu}\_{\text{gas}} + T^{\mu\nu}\_{EM} \tag{6}$$

in the nearest vicinity of the accreting black hole (up to 500Rg). The computations were performed via postprocessing of the results of the accretion disk structure, as computed for the spinning stellar mass black hole in the collapsar center [34]. As was also shown by Banerjee & Mukhopadhyay [37], many new isotopes of titanium, copper, zinc, etc., are present in the outflows. Emission lines of many of these heavy elements have been observed in the X-ray afterglows of several GRBs by Chandra, BeppoSAX, XMM-Newton; however Swift seems to have not yet detected these lines. In principle, the evolution of the isotope distribution can be traced along the trajectories of the winds ejected from the disk surface to large distances. Such situation is more appropriate for ejecta launched from disks feeding short GRBS, which forms in addition to the dynamical ejecta from the NS-NS merger [38]. If the accretion disk wind is expanding faster than the preceeding ejecta, the signatures of heavy elements might be observable via their radioactive decay and subsequent optical and infrared emission [39] called a 'kilonova' (see review by Tanaka [40]). Theoretically, this problem was studied in the first computations by

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

http://dx.doi.org/10.5772/intechopen.76283

21

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

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

Janiuk [32] and also by Siegel and Metzger [41].

3. Numerical simulations

techniques or a clever mesh selection.

3.1. Full GRMHD scheme

where

$$T\_{\text{gas}}^{\mu\nu} = \rho h u^{\mu} u^{\nu} + p \mathbf{g}^{\mu\nu} = (\rho + \mu + p) u^{\mu} u^{\nu} + p \mathbf{g}^{\mu\nu} \tag{7}$$

$$T\_{EM}^{\mu\nu} = b^2 u^\mu u^\nu + \frac{1}{2} b^2 g^{\mu\nu} - b^\mu b^\nu; \;\; b^\mu = u\_\nu F^{\mu\nu} \tag{8}$$

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 Fermi gas.

#### 2.4. Nucleosynthesis of heavy isotopes in GRB engines

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 nucleosynthesis theory) (Figure 3).

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.

in the nearest vicinity of the accreting black hole (up to 500Rg). The computations were performed via postprocessing of the results of the accretion disk structure, as computed for the spinning stellar mass black hole in the collapsar center [34]. As was also shown by Banerjee & Mukhopadhyay [37], many new isotopes of titanium, copper, zinc, etc., are present in the outflows. Emission lines of many of these heavy elements have been observed in the X-ray afterglows of several GRBs by Chandra, BeppoSAX, XMM-Newton; however Swift seems to have not yet detected these lines. In principle, the evolution of the isotope distribution can be traced along the trajectories of the winds ejected from the disk surface to large distances. Such situation is more appropriate for ejecta launched from disks feeding short GRBS, which forms in addition to the dynamical ejecta from the NS-NS merger [38]. If the accretion disk wind is expanding faster than the preceeding ejecta, the signatures of heavy elements might be observable via their radioactive decay and subsequent optical and infrared emission [39] called a 'kilonova' (see review by Tanaka [40]). Theoretically, this problem was studied in the first computations by Janiuk [32] and also by Siegel and Metzger [41].
