Spectral evolution

Spectral evolution study can give more constraints to theoretical models. Models of GRBs and afterglow emissions are mainly based on mechanisms of dissipation of the kinetic energy of a relativistic expanding fireball ([Mészáros and Rees 1997,Wijers et al. 1997,Vietri et al. 1997]). The origin of the fireball - either merging of neutron stars (NS/NS), neutron star/black holes (NS/BH) ([Narayan, Paczynski and Piran 1992]), Helium Star/Black Hole (He/BH) ([Fryer and Woosley 1998]) or the collapse of a massive star (hypernova) ([Paczynski 1998]), or a type I supernova explosion ([Wang and Wheeler 1998]), or the adiabatic implosion of a supra-massive NS (supra-nova) ([Vietri and Stella 1998]) - is still unclear at this stage. In spite of that, the spectral properties of both GRBs and afterglows seem to be consistent with a shock synchrotron model ([Tavani 1996]), while Inverse Compton emission is expected in the early times ([Waxman 1997]). Many questions are still open, like those related to the 'engine' of the main event and its radiation production process (e.g., internal shocks, Kobayashi et al. 1997 , the evolution of the spectral properties during GRB, the rise time of the afterglow and its relation with the GRB emission ([Sari 1997]), the radiation emission process of the afterglow (e.g., radiative shock vs. adiabatic shock, [Sari, Piran and Narayan 1998]). All these issues require observations to constrain models.

The time profile in two energy bands (1.5-26 keV and 40-700 keV) of the GRBs investigated is shown in figures 5.14,5.15,5.16. In some cases the X-ray emission is observed to lead the rise of the GRB (e.g., GRB970111), while in other cases (e.g., GRB970508) it is the $\gamma$-ray emission to lead the event. Time duration and shape of the GRB time profiles change from one GRB to the other, even if some similarity is observed between GRB980329 and GRB980425.

  

Figure 5.14: Time profiles in the 1.5-26 keV (upper panels) and 40-700 keV (lower panels) energy bands of the GRBs included in our sample. Also shown are the temporal sections in which we performed the spectral analysis.

  

Figure 5.15: Time profiles in the 1.5-26 keV (upper panels) and 40-700 keV (lower panels) energy bands of the GRBs included in our sample. Also shown are the temporal sections in which we performed the spectral analysis - continued

  

Figure 5.16: Time profiles in the 1.5-26 keV (upper panels) and 40-700 keV (lower panels) energy bands of the GRBs included in our sample. Also shown are the temporal sections in which we performed the spectral analysis - continued

Each time profile was divided into a given number of temporal sections (see Fig. 5.14,5.15,5.16), and a spectral analysis in the 1.5-700 keV energy band was performed on the average spectrum of each section. The duration of the sections was chosen short during the rise of the burst and and then longer, also taking into account the statistical quality of the data. A simultaneous fit to the time averaged WFC and GRBM spectra was performed, by using as input model the Band form.

 

$$\Gamma_{X} \Gamma_{\gamma}$$   # GRB Sect. E_p^(b)

1 GRB960720 A -1.5 fixed 0.67 fixed > 700

B -1.5 fixed 0.67 fixed > 700

$$\pm$$ C 0.67 fixed 2.44 fixed

$$\pm$$ D 0.67 fixed 2.44 fixed

$$\pm$$ E 0.67 fixed 2.44 fixed

$$\pm$$ F 0.67 fixed < 2.

$$\pm \pm$$ 2 GRB970111 A > 700

$$\pm \pm$$ B > 149

$$\pm \pm$$ C > 111

$$\pm \pm \pm$$ D

$$\pm \pm \pm$$ E

$$\pm \pm$$ 3 GRB970228 A > 700

$$\pm \pm \pm$$ B

$$\pm \pm$$ C < 2

$$\pm \pm$$ D < 2

$$\pm \pm$$ E < 2

$$\pm$$ F > 0.6 < 2

$$\pm \pm$$ G < 2

$$\pm \pm$$ 4 GRB970402 A ?

$$\pm \pm$$ B ?

$$\pm \pm$$ 5 GRB970508 A > 700

$$\pm \pm$$ B ?

$$\pm$$ C > 1.4 < 24

$$\pm \pm$$ 6 GRB971214 A > 700

$$\pm \pm$$ B > 224

$$\pm \pm$$ 7 GRB980329 A > 285

$$\pm \pm$$ B > 223

$$\pm \pm$$ C > 175

$$\pm \pm \pm$$ D

$$\pm \pm \pm$$ 8 GRB980425 A

$$\pm \pm \pm$$ B

• [^(a)]The photon indices reported in columns 2 and 3 refer to fit with the smoothed broken power-law proposed by Band et al. (1993)
• [^(b)]E_p values are in keV; N_H values are in units of 10²¹ cm^-2

The fits were performed by fixing the N_H columns to the galactic values in the directions of the GRB.
The derived best fit parameters ( photon indices $-\Gamma_X$ and $-\Gamma_\gamma$, peak energy E_p of the logarithmic power per photon energy decade (the $\nu$F($\nu$) spectrum) are shown in Tab. 5.2 , for each of the temporal sections. The value of E_p is given by E$_p \,=\, E_0 (2-\Gamma_X)$, under the condition that $\Gamma_\gamma \gt 2$. The lower limits in passband, reported in Tab. 5.2, were obtained in the cases in which the $\nu$F($\nu$) spectrum showed a bending, with the value of $\Gamma_\gamma \gt-2$. The lower limit was obtained by deriving the value of E₀ that corresponds to a reduced $\chi^2 \ge 1.2$ for a number of degrees of freedom (dof) $\le$ 22 in the fit to the data, with $\Gamma_{X}$ frozen to the value obtained from the best fit and $\Gamma_{\gamma}$ assumed slightly lower than -2 (-2.1). The reduced $\chi^{2}$ values obtained from the best fits were always acceptable (less than 1.1 for 20 dof). Notice that $\Gamma_{X}$ is mainly determined by the WFC X-ray spectral data, while $\Gamma_{\gamma}$ by the GRBM data ($\gamma$-ray band).
We see how GRB spectrum evolves with energy and with time is apparent. The spectra are generally harder at lower energies or they exhibit the same slope at high and low energies. We do not find bursts with low energy excesses with respect to the Band law (see eq. 1) as found by other authors ([Preece et al. 1996,Strohmayer et al. 1998]) and only in one case (970111) we find a photon index $\Gamma_{X}$ significantly larger than -2/3 . Other authors find larger fractions of GRB with this feature ([Preece et al. 1998,Strohmayer et al. 1998]).
The spectra become generally softer during the tail of the GRB. A remarkable exception is observed in the spectrum of GRB970228 ([Frontera et al. 1998a]) discussed below.

In figures 5.17,5.18,5.19, we show the $\nu$F($\nu$) spectrum in each of the temporal sections in which we subdivided the time profile ($\nu$ is the photon energy in keV and F$_{\nu}$ is the specific energy flux in keV cm^-2 s^-1 keV^-1) for GRB960720, GRB970111 and GRB970228, some of the most interesting events from the point of view of spectral evolution.

  

Figure 5.17: $\nu$F$\nu$ spectrum of GRB960720

  

Figure 5.18: $\nu$F$\nu$ spectrum of GRB970111

  

Figure 5.19: $\nu$F$\nu$ spectrum of GRB970228