Fundamentación de la propuesta de una Multimedia como medio de enseñanza y

As has been discussed, the prompt emission properties are important for the classifi- cation of SGRBs based on their duration and hardness. In addition, throughout this thesis, the properties of SGRBs will be studied, in part based primarily on optical, infra-red and X-ray data of the afterglow emission. Below we outline how both the prompt and afterglow emission are thought to be generated along with the expected overall shape of the spectrum and lightcurve produced. The fireball model described in the following section is independant of the progenitor, as long as enough energy is provided, and is hence applicable to all progenitor models discussed in sections 1.4 and 1.5 (except perhaps for the proto-magnetar model).

1.6.1 Fireball model with internal and external shocks

To produce a GRB it is generally believed that an ultra-relativistic fireball of high energy photons is launched from some central engine. A small amount of entrained baryonic matter within the fireball can produce synchrotron emission via accelera- tion due to either internal (prompt emission) or external (afterglow emission) shocks (Rees and Meszaros, 1992).

An e+- e−γfireball is formed at initial radiusRindue to the huge energies de-

posited by the compact object central engine. As the fireball expands adiabatically, the bulk Lorentz factor Γ initially increases linearly with radius until a saturation

radius (Rsat) is reached at which point the fireball coasts at a constant value Γmax.

Before Rsat is reached the e+-e− pairs within the fireball start to fall out of equi- librium, producing a quasi-thermal emission spectrum. However, the optical depth is still high enough that this emission cannot escape. It is only beyond the photo- spheric radius,Rph, where the opacityτph= 1, that we can detect the non-thermal spectra produced first from internal shocks within the ejecta and then from the shock when the fireball decelerates due to coming into contact with the external medium surrounding the source.

The shocks which produce the GRB emission mainly accelerate the electrons associated with entrained baryonic matter. It is these accelerated electrons which then emit via synchrotron emission (and possibly inverse Compton scattering). Even a small amount of baryon loading (∼10−7−10−5M) would mean that the baryonic

matter would carry the bulk of the fireball energy. From repeated crossing of the shock, confined due to magnetic irregularities, the electrons at the shock front can be accelerated to very high energies resulting in an energy spectrum which is a power law distribution. We can define the electron energy spectrum based on Lorentz factorγe above a minimum Lorentz factor γm such that:

N(γe)∼γ_e−p forγe> γm (1.2) Most electrons will be atEmin =γmmec2, soγmcan be seen as the character-

isticγ. At higher frequencies there is a break in the spectrum known as the cooling break,νc≡νc(γc), and is characterised by the regime where the electrons lose a sig- nificant fraction of their energy to radiation. The resultant synchrotron spectrum is shown in Figure 1.6, adapted from Sari et al. (1998), and is dependant on whether

γm > γc (fast cooling) or γm < γc (slow cooling). For electrons with γ > γc they cool rapidly emitting most of their energy at their synchrotron frequency.

The characteristic lightcurve produced for high frequency emission is shown in Figure 1.7, also adapted from Sari et al. (1998).

1.6.2 Prompt emission

The prompt emission is explained by internal shocks and is generally in the fast cooling regime. If the output of the central engine is time-varying then multiple shells of material with different bulk Lorentz factors can be produced (Narayan et al., 1992; Rees and Meszaros, 1994). When faster shells overtake slower ones a shock front will be created. The presence of many of these shocks could explain the complexity and variety seen in the γ-ray lightcurves of the GRB (e.g. Daigne and

Figure 1.6: The synchrotron emission from shocked electrons in the ultra-relativistic jets of the GRB from Sari et al. (1998). The spectrum is characterised by two regimes: slow and fast cooling. The difference is based on the position of the cooling break νc above which the electrons lose significant energy from radiation. The top panel shows fast cooling, whereνm> νc, whereνm is the frequency associated with the characteristic Lorentz factor of the electron distribution, and the bottom panel shows slow cooling withνm < νc. The distribution will transition between these two regimes, most likely residing in the slow cooling regime for the majority of the afterglow emission. The lowest frequency emission is not dependant on the electron distribution and is affected by synchrotron self absorption, where the electrons re-absorb the synchrotron emission. This gives the regime belowνaa blackbody profile with Fν ∝ ν2_{. Above νa the flux density profile is Fν ∝ ν}1/3 _{where the emission}

is the sum of all the low energy tails of the electron distribution. At high frequencies the spectrum is dependant on the cooling regime and power-law index of electron distribution, p, as shown in the figure.

Figure 1.7: The canonical lightcurve produced for high frequency emission from the shocked electrons from Sari et al. (1998). The lightcurve seen is dependant on evolution of the break frequenciesνm(tm≡tm(νm)) and νc (tc ≡tc(νc)): the cooling break. Hence, a break seen in the lightcurve may be due to the evolution of the cooling break as it passes through the frequency regime being observed.

Mochkovitch 1998). The prompt emission itself reflects the activity of the central engine as well as the total duration telling us about its lifetime (Kobayashi et al., 1997).

1.6.3 Afterglow emission

Afterglow emission can be explained by external shocks when the fireball is decel- erated by the external medium. As the shell expands more and more of the ISM is shocked and heated. Beyond the deceleration radius, R > Rdec, the shocked gas

dominates, with the fireball reconverting the bulk kinetic energy into thermal energy (Kobayashi et al., 1999). Though two shocks are produced: the forward shock which propagates outwards into the external medium and the reverse shock which prop- agates into the ejecta, in the Standard Afterglow Model only the emission caused by the forward shock is considered. This is because the reverse shock is only mildly relativistic and most of the energy conversion takes place in the forward shock (Sari and Piran, 1995). However, it is predicted that the reverse shock will make a con- tribution to the afterglow emission producing a strong optical flash (Meszaros and Rees, 1997). When modelling the afterglow throughout this thesis the lightcurve and spectrum are treated as a series of power-laws, as shown in Figures 1.6 and 1.7, unless this is clearly a poor fit. However, we do also consider any deviations from this model such as flares.