4. Ejection and acceleration of jets in gamma ray bursts

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 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> . The highenergy 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 proposed.

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 than the short bursts.

## 4.1. Jet launching

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:

material was so strong preventing even the launching of the wind.

ð Þ� <sup>1</sup> � <sup>2</sup><sup>C</sup> <sup>0</sup>:<sup>148</sup> RISCO

RNS

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

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

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.

, q <sup>¼</sup> MBH MNS <sup>C</sup> <sup>¼</sup> MNS RNS

(9)

Mdisk MNS

22 Cosmic Rays

BH spin, if a massive disk is to be created.

<sup>¼</sup> <sup>0</sup>:42q<sup>1</sup>=<sup>3</sup>

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:

$$
\dot{M}\_{\rm ign} = K\_{\rm ign} \left(\frac{\alpha}{0.1}\right)^{5/3} \quad \dot{M}\_{\rm trap} = K\_{\rm trap} \left(\frac{\alpha}{0.1}\right)^{1/3} \tag{10}
$$

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, 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 total energy ejected in neutrinos was calculated by Zalamea and Beloborodov [61] and in principle can reproduce the GRB energies, but for the higher accretion rates M\_ > 0:1M<sup>⊙</sup> s�<sup>1</sup> [62, 63], making the association with the longest duration bursts t > 30s is problematic [64]. Recent hydrodynamic simulations of Just et al. [65] assuming a black hole and torus accretion system gave negative conclusion for the neutrino annihilation applicability on the merger type progenitors. Specifically, the NS-NS merger tends to create heavier baryon loaded environments. Moreover, the efficiency of the mechanism is crucially depend on the fastly rotating central object which might be difficult to obtain in the case of the NS-NS mergers. The situation is more improved for the BH-NS progenitor, providing E<sup>I</sup>SO <sup>γ</sup>><sup>100</sup> � <sup>2</sup> � 1050erg, in a half cone opening around the axis θγ><sup>100</sup> > 8<sup>o</sup> which is only an order of magnitude lower than the medium of the observed GRBs [66]. Thus, the neutrino annihilation process can be applicable to the less energetic GRBS, but we still can exclude the case of its partial contribution to the rest class of short bursts (see, however, Levinson and Globus [67]).

axis of rotation (MAD, magnetically-arrested disk). Moreover in some specific initial configu-

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

accretion one Mc \_ 2, demonstrating the extraction of the rotational energy of the central object. As a conclusion, the high values of the emitted energy combined with the low baryon load currently set the BZ as the favorable mechanism applying on the GRB. Nevertheless, as mentioned before the whole picture is still incomplete and it will probably remain so, as long

The effects of the surrounding to the jet material are crucial for the dynamic evolution of the jet affecting both its acceleration and collimation. The build up of a large scale toroidal component in a magnetic dominated jet results to hoop stress that contributes to the jet collimation [76]. Nevertheless, this contribution proves to be less efficient in the relativistic regime and turns to be insufficient even for the cases where a very fast rotation is induced [77–79]. As a result, the contribution of the exterior environment pressure plays a fundamental role in the

In the long GRB framework, the outflow penetrates the stellar envelope, most likely a Wolf-Rayet star, and continues its propagation to the interstellar space. The propagation of the jet's head in the dense environment results to sideway motion of the stellar material and to the formation of a hot cocoon surrounding the jet. The accurate description of such a system is cyclic and both jet and stellar material must be described self consistently. The jet velocity depends crucially on the jet cross section, while it determines the amount of energy injected in the cocoon that in its turn defines the supporting exterior pressure of the jet. As a result, there exists a number of numerical simulations investigating the evolution of this phase both of hydrodynamic (e.g., Mizuta and Aloy [80]; Lazzati et al. [81]) as also of magnetic dominated outflows [82]. In addition, theoretical and semi-analytical models have also been developed to

interpret the underlying processes (e.g., Bromberg et al. [83]; Globus & Levinson [84]).

The initial propagation, close to the launching point, is similar to the two extreme case of a hydro or Poynting dominated jet since the outflows internal pressure much exceeds the cocoon's one. The outflow's freely expansion is up to the collimation point defined by the equality of the above quantities, while after it the outflow evolution differs accordingly to its magnetic context (see Granot et al. [85] for a review). The Poynting dominated outflows result in a faster drilling breakout time in an order of magnitude 0.1 to ~10 s. Bromberg et al. [86] proposed a criterion to identify tb so that the burst T<sup>90</sup> duration is directly correlated with the central engine activity. As a result, there expected a plateau at the long GRB duration distribution for times lower than the break out one. Surprisingly, the analysis of the observational data from the three most dedicated satellites (BATSE, Swift, and Fermi) provided values that are in favor of the hydrodynamic propagation scenario. If the hydrodynamic launching mechanism is to be excluded for the above reasons, a process that dissipates the outflow energy inside the star has to be found. Lately, the progress has been made by the investigation of the 'kink instability' [82]. As a result, a typical Poynting dominated collapsar jet is able to achieve the

<sup>B</sup><sup>Z</sup> exceeded the

25

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

ration assumed, the time averaged power of the jet outflow efficiency E\_

as the neutrino effects will not be taken into account in a self-consistent manner.

GRB outflow evolution for the merging binaries and core-collapsing bursts.

4.2. Collimation mechanisms

The other mechanism that accounts for the launch of a low baryon loaded jet is the Blandford-Znajek process that might be resembled with a Penrose proccess of an ideally conducting plasma in the force free limit. According to it, the plasma is pushed via accretion to the ergospheric negative energy orbits, while the magnetic twist results in an outward propagating electromagnetic jet (see Komissarov [68] for an excellent explanation).

In general, the rotational energy of a black hole is

$$E\_{rot} = 1.8 \times 10^{54} f(a) \frac{M}{M\_{\odot}} \text{erg} \quad , \quad \text{f(a)} = 1 - \sqrt{\frac{1 + \sqrt{1 - a^2}}{2}} \tag{11}$$

where f að Þ¼ 0:29 for a maximally rotating BH (a ¼ 1). The rotational energy of the BH can be extracted through the lines threading the horizon forming a Poynting dominated jet of power

$$\dot{E}\_{\rm BZ} = 10^{50} a^2 \left(\frac{M}{M\_{\odot}}\right)^2 F(a) \left(\frac{B}{10^{15} G}\right)^2 \text{ ergs}^{-1} \tag{12}$$

where the spin dependent function is properly obtained under full GR framework. A familiar analytical approximation obtained by Lee et al. [69] and Wang et al. [70] is:

$$F(a) = \frac{1+q^2}{q^2} \left(\frac{1+q^2}{q^2} \arctan q - 1\right) \quad , \quad \mathbf{q} = \frac{\mathbf{a}}{1+\sqrt{1-\mathbf{a}^2}}\tag{13}$$

where 2=3 ≥ F að Þ ≥ ð Þ π � 2 for 0 ≥ a ≥ 1. A numerical investigation of the above estimation performed by Tchekhovskoy and McKinney [71] shows only small deviations at the very high rotation factors [72].

In the simulations under the fixed Kerr spacetime [71, 73], the central object is fed with a relatively large magnetic flux, that is, more than what the accreting plasma can push inside the horizon. The excessing part of the magnetic flow remains outside the horizon and forms a magnetic barrier [74, 75], saturating accretion and forming a baryon-clean funnel around the axis of rotation (MAD, magnetically-arrested disk). Moreover in some specific initial configuration assumed, the time averaged power of the jet outflow efficiency E\_ <sup>B</sup><sup>Z</sup> exceeded the accretion one Mc \_ 2, demonstrating the extraction of the rotational energy of the central object. As a conclusion, the high values of the emitted energy combined with the low baryon load currently set the BZ as the favorable mechanism applying on the GRB. Nevertheless, as mentioned before the whole picture is still incomplete and it will probably remain so, as long as the neutrino effects will not be taken into account in a self-consistent manner.

#### 4.2. Collimation mechanisms

The total energy ejected in neutrinos was calculated by Zalamea and Beloborodov [61] and in principle can reproduce the GRB energies, but for the higher accretion rates M\_ > 0:1M<sup>⊙</sup> s�<sup>1</sup> [62, 63], making the association with the longest duration bursts t > 30s is problematic [64]. Recent hydrodynamic simulations of Just et al. [65] assuming a black hole and torus accretion system gave negative conclusion for the neutrino annihilation applicability on the merger type progenitors. Specifically, the NS-NS merger tends to create heavier baryon loaded environments. Moreover, the efficiency of the mechanism is crucially depend on the fastly rotating central object which might be difficult to obtain in the case of the NS-NS mergers. The situation

opening around the axis θγ><sup>100</sup> > 8<sup>o</sup> which is only an order of magnitude lower than the medium of the observed GRBs [66]. Thus, the neutrino annihilation process can be applicable to the less energetic GRBS, but we still can exclude the case of its partial contribution to the rest

The other mechanism that accounts for the launch of a low baryon loaded jet is the Blandford-Znajek process that might be resembled with a Penrose proccess of an ideally conducting plasma in the force free limit. According to it, the plasma is pushed via accretion to the ergospheric negative energy orbits, while the magnetic twist results in an outward propagat-

erg , f að Þ¼ 1 �

F að Þ <sup>B</sup> 1015G � �<sup>2</sup>

where f að Þ¼ 0:29 for a maximally rotating BH (a ¼ 1). The rotational energy of the BH can be extracted through the lines threading the horizon forming a Poynting dominated jet of power

where the spin dependent function is properly obtained under full GR framework. A familiar

where 2=3 ≥ F að Þ ≥ ð Þ π � 2 for 0 ≥ a ≥ 1. A numerical investigation of the above estimation performed by Tchekhovskoy and McKinney [71] shows only small deviations at the very high

In the simulations under the fixed Kerr spacetime [71, 73], the central object is fed with a relatively large magnetic flux, that is, more than what the accreting plasma can push inside the horizon. The excessing part of the magnetic flow remains outside the horizon and forms a magnetic barrier [74, 75], saturating accretion and forming a baryon-clean funnel around the

<sup>γ</sup>><sup>100</sup> � <sup>2</sup> � 1050erg, in a half cone

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> ffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> � <sup>a</sup><sup>2</sup> <sup>p</sup> 2

ergs�<sup>1</sup> (12)

<sup>1</sup> � a2 <sup>p</sup> (13)

(11)

s

, <sup>q</sup> <sup>¼</sup> <sup>a</sup>

<sup>1</sup> <sup>þ</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffi

is more improved for the BH-NS progenitor, providing E<sup>I</sup>SO

class of short bursts (see, however, Levinson and Globus [67]).

In general, the rotational energy of a black hole is

Erot <sup>¼</sup> <sup>1</sup>:<sup>8</sup> � <sup>1054</sup>f að Þ <sup>M</sup>

E\_

F að Þ¼ <sup>1</sup> <sup>þ</sup> <sup>q</sup><sup>2</sup> q2

rotation factors [72].

24 Cosmic Rays

ing electromagnetic jet (see Komissarov [68] for an excellent explanation).

BZ <sup>¼</sup> <sup>10</sup><sup>50</sup>a<sup>2</sup> <sup>M</sup>

analytical approximation obtained by Lee et al. [69] and Wang et al. [70] is:

<sup>1</sup> <sup>þ</sup> <sup>q</sup><sup>2</sup>

M<sup>⊙</sup>

M<sup>⊙</sup> � �<sup>2</sup>

<sup>q</sup><sup>2</sup> arctan<sup>q</sup> � <sup>1</sup> � � The effects of the surrounding to the jet material are crucial for the dynamic evolution of the jet affecting both its acceleration and collimation. The build up of a large scale toroidal component in a magnetic dominated jet results to hoop stress that contributes to the jet collimation [76]. Nevertheless, this contribution proves to be less efficient in the relativistic regime and turns to be insufficient even for the cases where a very fast rotation is induced [77–79]. As a result, the contribution of the exterior environment pressure plays a fundamental role in the GRB outflow evolution for the merging binaries and core-collapsing bursts.

In the long GRB framework, the outflow penetrates the stellar envelope, most likely a Wolf-Rayet star, and continues its propagation to the interstellar space. The propagation of the jet's head in the dense environment results to sideway motion of the stellar material and to the formation of a hot cocoon surrounding the jet. The accurate description of such a system is cyclic and both jet and stellar material must be described self consistently. The jet velocity depends crucially on the jet cross section, while it determines the amount of energy injected in the cocoon that in its turn defines the supporting exterior pressure of the jet. As a result, there exists a number of numerical simulations investigating the evolution of this phase both of hydrodynamic (e.g., Mizuta and Aloy [80]; Lazzati et al. [81]) as also of magnetic dominated outflows [82]. In addition, theoretical and semi-analytical models have also been developed to interpret the underlying processes (e.g., Bromberg et al. [83]; Globus & Levinson [84]).

The initial propagation, close to the launching point, is similar to the two extreme case of a hydro or Poynting dominated jet since the outflows internal pressure much exceeds the cocoon's one. The outflow's freely expansion is up to the collimation point defined by the equality of the above quantities, while after it the outflow evolution differs accordingly to its magnetic context (see Granot et al. [85] for a review). The Poynting dominated outflows result in a faster drilling breakout time in an order of magnitude 0.1 to ~10 s. Bromberg et al. [86] proposed a criterion to identify tb so that the burst T<sup>90</sup> duration is directly correlated with the central engine activity. As a result, there expected a plateau at the long GRB duration distribution for times lower than the break out one. Surprisingly, the analysis of the observational data from the three most dedicated satellites (BATSE, Swift, and Fermi) provided values that are in favor of the hydrodynamic propagation scenario. If the hydrodynamic launching mechanism is to be excluded for the above reasons, a process that dissipates the outflow energy inside the star has to be found. Lately, the progress has been made by the investigation of the 'kink instability' [82]. As a result, a typical Poynting dominated collapsar jet is able to achieve the equipartition between thermal and magnetic energy at the so-called recollimation point (� 108 cm in the specific simulations) without being disrupted by the instability. Such a jet propagates more or less as a hydrodynamic jet [85].

provides a natural way to dissipate the bulk kinetic of the outflow by assuming the mutual collision of inhomogeneities existing at the main body of the outflow. One of the great advantage of this model is its simplicity, while back of the envelope calculations exhibits the beauty

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

Lets assume two cells with Lorentz factors γ1, γ<sup>2</sup> ≫ 1 and masses m1, m2, respectively, emitted with a time difference δt. As long as the latter is propagating faster, their mutual collision will

where γavg is the average Lorentz factor of the outflow. Using the conservation of the 4-

<sup>γ</sup><sup>f</sup> <sup>¼</sup> <sup>m</sup>1γ<sup>1</sup> <sup>þ</sup> <sup>m</sup>2γ<sup>2</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

where <sup>γ</sup><sup>r</sup> <sup>¼</sup> <sup>γ</sup>1γ<sup>2</sup> <sup>1</sup> � <sup>u</sup>1u2=c<sup>2</sup> � � is the Lorentz factor of the relative motion; in reality the collision

The observed time variability is given by Kobayashi et al. [92]; Daigne and Mochkovitch [93];

Rint 2c<sup>2</sup>γ<sup>2</sup> f

where the first term of the right hand is because of the injection time difference and the second because of the shock propagation. We notice that the variability of lightcurves traces in general the central engine activity, and as a result, the high variability of the prompt emission can be ascribed to the intrinsic variability of the source (BH-torus for short bursts, BH-torus plus the

The biggest problem for the internal shock model is the efficiency of the collisions. The

<sup>ε</sup>therm <sup>¼</sup> <sup>1</sup> � <sup>m</sup><sup>1</sup> <sup>þ</sup> <sup>m</sup><sup>2</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m2 <sup>1</sup> <sup>þ</sup> <sup>m</sup><sup>2</sup>

and is maximized for a given <sup>γ</sup><sup>r</sup> when the two cells are of equal mass <sup>ε</sup>therm,max <sup>¼</sup> <sup>1</sup>� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>q</sup> � �, e.g., if <sup>γ</sup><sup>r</sup> <sup>¼</sup> 10, <sup>ε</sup>therm,max <sup>¼</sup> <sup>0</sup>:28. Detailed analysis by the number of authors increases this limit up to 40% for thermally dominated outflows, but most of the times the corresponding efficiency is in the range 1ð Þ � 10 %, contrary to the observations that suggest

efficiencies exceeding 50% (see Kumar and Zhang [72] and references therein).

<sup>2</sup> þ 2m1m2γ<sup>r</sup>

<sup>q</sup> (19)

<sup>c</sup>δ<sup>t</sup> � <sup>2</sup>γ<sup>2</sup>

<sup>2</sup> þ 2m1m2γ<sup>r</sup>

� <sup>1</sup> <sup>þ</sup> <sup>γ</sup><sup>1</sup> γ2

avgcδt (16)

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

27

� �δ<sup>t</sup> (18)

<sup>q</sup> (17)

1γ2 2

momentum, we can model a plastic collision that will provide a single cell propagating

m<sup>2</sup> <sup>1</sup> <sup>þ</sup> <sup>m</sup><sup>2</sup>

results in a pair of shocks that propagate at the slower and faster cell, respectively.

δtobs � δt þ

Rint <sup>¼</sup> <sup>2</sup>γ<sup>2</sup>

γ2 <sup>2</sup> � <sup>γ</sup><sup>2</sup> 1

and the essentials of the process.

and Kumar and Zhang [72].

2= 1 þ γ<sup>r</sup>

propagation inside the star for the long ones).

efficiency of the thermal energy production is easily obtained

occur at a distance

#### 5. Radiative processes in jets: emission of gamma rays

Although rich in models, the dynamics of the phase after the jet break out, that is, at the place where the prompt radiation is being produced, is still not well understood. Among the two models assuming matter or Poynting flux dominance, the hot fireball [22, 87] is the older and more widely used one. The matter dominated fireball is mainly constituted by baryons and radiation, with the latter being significantly larger by at least two orders of magnitude. The adiabatic expansion of the fireball accelerates the baryons to high Lorentz factor, while a fraction of this thermal energy is being radiated when the flow becomes transparent to the electron-positron pair creation, providing the so-called photospheric emission. In even higher distances, the outflow inhomogeneities endure mutual collisions leading to the formation of internal shocks that accelerate electrons and produce the non-thermal part of the observed radiation.

The location of the photospheric radius Rph, when we assume that acceleration has effectively completed (saturation radius) before the flow becomes transparent, was calculated by the number of models. Following, for example, Hascoët et al. [88] and references therein,

$$R\_{\rm pl} \simeq \frac{\kappa \dot{M}}{8\pi c \gamma^2} \sim 2.9 \times 10^{13} cm \left(\frac{k}{0.2 cm^2/g}\right) (1+\sigma)^{-1} \left(\frac{\mathcal{V}}{100}\right)^{-3} \left(\frac{\dot{E}\_{\rm iso}}{10^{53} erg/s}\right) \tag{14}$$

where σ is the magnetization parameter at the saturation radius. The corresponding observed temperature and luminosity are:

$$T\_{ph} \approx \frac{T\_0}{1+z} \left(\frac{R\_{ph}}{\gamma R\_0}\right)^{-2/3} L\_{ph} = 4\pi R\_0^2 \sigma\_T T\_0^4 \left(\frac{R\_{ph}}{\gamma R\_0}\right)^{-2/3} \tag{15}$$

where z is the redshift and T<sup>0</sup> is the temperature at the initial radius R0. The emerging radiation is called a modified black body [87] with the lower energy Raleigh-Jeans tail having a photon index of 0:4 instead of 1 in the usual black body lower energy limit, because of relativistic geometric effects. It is worth to mention here that if some sub-photospheric dissipation occurs before the photospheric radius then the above scaling does not hold and the low energy part of the spectrum will be modified (see, for example, Thompson [89] and Giannios and Spruit [90] for the reconnection implications).

Beyond the photospheric emission, the interpretation of the non-thermal prompt emission is much more challenging. Up to day, there is no definite answer for the precise place that the γradiation emerge, but the most popular model is the internal shock model [91]. This model provides a natural way to dissipate the bulk kinetic of the outflow by assuming the mutual collision of inhomogeneities existing at the main body of the outflow. One of the great advantage of this model is its simplicity, while back of the envelope calculations exhibits the beauty and the essentials of the process.

equipartition between thermal and magnetic energy at the so-called recollimation point

Although rich in models, the dynamics of the phase after the jet break out, that is, at the place where the prompt radiation is being produced, is still not well understood. Among the two models assuming matter or Poynting flux dominance, the hot fireball [22, 87] is the older and more widely used one. The matter dominated fireball is mainly constituted by baryons and radiation, with the latter being significantly larger by at least two orders of magnitude. The adiabatic expansion of the fireball accelerates the baryons to high Lorentz factor, while a fraction of this thermal energy is being radiated when the flow becomes transparent to the electron-positron pair creation, providing the so-called photospheric emission. In even higher distances, the outflow inhomogeneities endure mutual collisions leading to the formation of internal shocks that accelerate electrons and produce the non-thermal part of the observed

The location of the photospheric radius Rph, when we assume that acceleration has effectively completed (saturation radius) before the flow becomes transparent, was calculated by the

> k 0:2cm<sup>2</sup>=g � �

where σ is the magnetization parameter at the saturation radius. The corresponding observed

where z is the redshift and T<sup>0</sup> is the temperature at the initial radius R0. The emerging radiation is called a modified black body [87] with the lower energy Raleigh-Jeans tail having a photon index of 0:4 instead of 1 in the usual black body lower energy limit, because of relativistic geometric effects. It is worth to mention here that if some sub-photospheric dissipation occurs before the photospheric radius then the above scaling does not hold and the low energy part of the spectrum will be modified (see, for example, Thompson [89] and Giannios

Beyond the photospheric emission, the interpretation of the non-thermal prompt emission is much more challenging. Up to day, there is no definite answer for the precise place that the γradiation emerge, but the most popular model is the internal shock model [91]. This model

Lph <sup>¼</sup> <sup>4</sup>πR<sup>2</sup>

ð Þ <sup>1</sup> <sup>þ</sup> <sup>σ</sup> �<sup>1</sup> <sup>γ</sup>

0σTT<sup>4</sup> 0 Rph γR<sup>0</sup> � ��2=<sup>3</sup>

100

� ��<sup>3</sup> E\_

iso 1053erg=s !

(14)

(15)

number of models. Following, for example, Hascoët et al. [88] and references therein,

propagates more or less as a hydrodynamic jet [85].

5. Radiative processes in jets: emission of gamma rays

cm in the specific simulations) without being disrupted by the instability. Such a jet

(� 108

26 Cosmic Rays

radiation.

Rph <sup>≃</sup> <sup>κ</sup>M\_

temperature and luminosity are:

<sup>8</sup>πcγ<sup>2</sup> � <sup>2</sup>:<sup>9</sup> � <sup>1013</sup>cm

Tph <sup>≈</sup> <sup>T</sup><sup>0</sup> 1 þ z

and Spruit [90] for the reconnection implications).

Rph γR<sup>0</sup> � ��2=<sup>3</sup> Lets assume two cells with Lorentz factors γ1, γ<sup>2</sup> ≫ 1 and masses m1, m2, respectively, emitted with a time difference δt. As long as the latter is propagating faster, their mutual collision will occur at a distance

$$R\_{int} = \frac{2\chi\_1^2 \chi\_2^2}{\chi\_2^2 - \chi\_1^2} c\delta t \sim 2\chi\_{avg}^2 c\delta t \tag{16}$$

where γavg is the average Lorentz factor of the outflow. Using the conservation of the 4 momentum, we can model a plastic collision that will provide a single cell propagating

$$\gamma\_f = \frac{m\_1 \gamma\_1 + m\_2 \gamma\_2}{\sqrt{m\_1^2 + m\_2^2 + 2m\_1 m\_2 \gamma\_r}}\tag{17}$$

where <sup>γ</sup><sup>r</sup> <sup>¼</sup> <sup>γ</sup>1γ<sup>2</sup> <sup>1</sup> � <sup>u</sup>1u2=c<sup>2</sup> � � is the Lorentz factor of the relative motion; in reality the collision results in a pair of shocks that propagate at the slower and faster cell, respectively.

The observed time variability is given by Kobayashi et al. [92]; Daigne and Mochkovitch [93]; and Kumar and Zhang [72].

$$
\delta t\_{obs} \sim \delta t + \frac{R\_{int}}{2c^2 \mathcal{V}\_f^2} \sim \left(1 + \frac{\mathcal{V}\_1}{\mathcal{V}\_2}\right) \delta t \tag{18}
$$

where the first term of the right hand is because of the injection time difference and the second because of the shock propagation. We notice that the variability of lightcurves traces in general the central engine activity, and as a result, the high variability of the prompt emission can be ascribed to the intrinsic variability of the source (BH-torus for short bursts, BH-torus plus the propagation inside the star for the long ones).

The biggest problem for the internal shock model is the efficiency of the collisions. The efficiency of the thermal energy production is easily obtained

$$\varepsilon\_{therm} = 1 - \frac{m\_1 + m\_2}{\sqrt{m\_1^2 + m\_2^2 + 2m\_1 m\_2 \gamma\_r}} \tag{19}$$

and is maximized for a given <sup>γ</sup><sup>r</sup> when the two cells are of equal mass <sup>ε</sup>therm,max <sup>¼</sup> <sup>1</sup>� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2= 1 þ γ<sup>r</sup> <sup>q</sup> � �, e.g., if <sup>γ</sup><sup>r</sup> <sup>¼</sup> 10, <sup>ε</sup>therm,max <sup>¼</sup> <sup>0</sup>:28. Detailed analysis by the number of authors increases this limit up to 40% for thermally dominated outflows, but most of the times the corresponding efficiency is in the range 1ð Þ � 10 %, contrary to the observations that suggest efficiencies exceeding 50% (see Kumar and Zhang [72] and references therein).

Despite the great progress in the interpretation of the prompt GRB radiation, crucial issues still remain open and especially on how the mildly relativistic shocks accelerate particles. As a result, today no model that describes self consistently the whole process exists and most of the approach still uses the fractions εB, ε<sup>e</sup> of the internal energy that is dissipated on an enhanced magnetic field of the shocked gas and on some fraction of electrons accelerated to a non-thermal energetic distribution. Sequentially to the approximation of the shocked regime, the radiation models can be applied and used to examine all the intervening radiative and kinetic processes. An interesting point to notice is that the cell high magnetization, σ ≫ 1, leads to inefficient collisions preventing the dissipation of the energy [94, 95]. In such a case, the acceleration of the electron can be obtained through the reconnection process. Such a process can occur before or after the photospheric radius [96–98] and despite the extensive outgoing study of the process there are still even bigger ambiguities than the other two just mentioned [99]. For a review on the issue, the reader can refer Kagan et al. [100].

In the above framework, it is in principle possible that the observed events have two distinct peaks in the electromagnetic signal, separated by the gravitational wave emission. The reorientation of spin vector of the black holes and gravitational recoil of the burst engine is, however, possible. Therefore, the probability of observing two electromagnetic counterparts of

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

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

29

The electromagnetic signal is in general not expected from a BH-BH merger. However, the weak transient detected by Fermi GBM detector 0.4 s after GW 150914 has been generating much speculation [104, 105]. Despite the fact that other gamma ray missions claimed nondetection of the signal, several theoretical scenarios aimed to account for such a coincidence,

Finally, the binary neutron star merger GW170817, detected in gravitational waves, was connected with the gamma ray emission observed as a weak short burst [111]. Its peculiar properties pose constraints for the progenitor model [112]). Moreover, at lower frequencies, the follow-up surveys have shown the presence of a kilonova emission from the merger's dynamical ejecta. These ejecta masses are broadly consistent with the estimated r-process production rates, required before to explain the Milky Way isotopes abundances. It is possible that the magnetically driven winds launched due to the accretion in the GRB engine may also contrib-

Gamma ray bursts are known since almost 50 years now and are still an exciting field of research for both observers and theoretitians. Their energetic requirements proved the fundamental role of the stellar mass black hole formation and mass accretion in the production of

The details of this process are, however, far from being fully understood. In short GRBs, the process of black hole birth after the neutron star merger may proceed through different channels, with the possible presence of a transient hypermassive neutron star, depending on the EOS and rotation of the progenitors. In long GRBs, the properties of progenitor star, its envelope rotation, metallicity, etc., as well as the binarity of the whole system, may affect the core collapse in an even greater way. The question of binarity is of a great interest in the context of the fate of high mass X-ray binaries, such as Cygnus X-3, which in addition to the pre-

Such fundamental questions are now being attacked with the modern tools of numerical astrophysics, which involve relativistic magnetohydrodynamics and nuclear physics. With the discovery of gravitational waves, a new window has also opened from the observational point of view, especially since the gamma ray signal has been identified in connection with the compact object merger. The identification of the additional electromagnetic signal from the radioactive decay of the GRB ejecta provided a completely new way to probe the whole

hypernova star contains a companion which is most probably a black hole.

process and hopefully build a comprehensive picture in the near future.

the gravitational wave source would be extremely low.

ute to the kilonova emission from NS-NS merger.

7. Summary

ultrarelativistic jets.

whether detected, or to be found in the future events [106–110].
