|
The prompt emission of gamma-ray bursts has yet defied any simple explanation, despite the presence of a rich observational material and great theoretical efforts. Here we show that all the types of spectral evolution and spectral shapes that have been observed can indeed be described with one and the same model, namely a hybrid model of a thermal and a non-thermal component. We further show that the thermal component is the key emission process determining the spectral evolution. Even though bursts appear to have a variety of, sometimes complex, spectral evolutions, the behaviors of the two separate components are remarkably similar for all bursts, with the temperature describing a broken power-law in time. The non-thermal component is consistent with emission from a population of fast cooling electrons emitting optically-thin synchrotron emission or non-thermal Compton radiation. This indicates that these behaviors are the fundamental and characteristic ones for gamma-ray bursts.
1. Introduction It was early recognized that the spectra of gamma-ray bursts (GRBs) have a non-thermal character, with emission over a broad energy range (e.g. Fishman & Meegan (1995)). This typically indicates emission from an optically-thin source and an initial proposal for GRBs was therefore an optically-thin synchrotron model from shock-accelerated, relativistic electrons (e.g. Katz (1994); Tavani (1996)). The number density of the radiating electrons is assumed to be typically a power law as a function of the electron Lorentz factor {tex}\gamma_e{/tex}above a minimum value, {tex}\gamma_{min}{/tex}, with index {tex} -p {/tex}. Such a distribution gives rise to a power-law photon spectrum with index {tex}\alpha = -2/3{/tex} below a break energy {tex}\large E\normal_p\propto\gamma\small^2_{min}{/tex} and a high-energy power-law with index {tex}\beta = -(p + 1)/2{/tex}. However, this model has difficulties in explaining the observed spectra of GRBs which show a great variation in {tex}\alpha{/tex} and {tex}\beta{/tex} (Preece et al. 2000). In particular, a substantial fraction of them have {tex}\alpha > -2/3{/tex}, which is not possible in the model in its simplest form, since {tex}\alpha = -2/3{/tex} is the power-law slope of the fundamental synchrotron function for electrons with an isotropic distribution of pitch angles (Pacholczyk 1970). The problem becomes even more severe for the case when the cooling time of the electrons is shorter than the typical dynamic timescale. In the typical setting of GRBs having a relativistic outflow with a bulk Lorentz factor {tex}\Gamma \sim 100{/tex}, the time scales for synchrotron and inverse Compton losses are {tex}\sim 10^{-6}s{/tex} (Ghisellini et al. 2000b), which is much shorter than both the dynamic time scale {tex}\large R/2\Gamma\small^2\large c \sim 1 s (R/10\small^{15}\large cm){/tex}, and the integration time scale of the recorded data, typically 64 ms to 1 s. In such a case the low-energy power law should be even softer, with {tex}\alpha = -1.5{/tex} (Bussard 1984; Ghisellini et al. 2000a), now contradicting a majority of the observed spectra. The spectra are also observed to evolve dramatically during the course of a burst, both in {tex}\large E\normal_p{/tex}, as well as in the power-law indices, in particular {tex}\alpha{/tex}. In approximately 60% of all bursts, {tex}\alpha{/tex} varies significantly, mainly by becoming softer (e.g. Crider et al. (1997)). Some bursts are found to have quasi-thermal spectra during the initial phases, before they become non-thermal (Ghirlanda et al. 2003; Kaneko et al. 2003; Ryde 2004). The peak energy from the above distribution of electrons is given by {tex}\large E\normal_p = \gamma\small^2_m\large B_\bot\Gamma{/tex}. In the external shock model {tex}\gamma_m{/tex} and {tex}\large B_\bot{/tex} are proportional to the bulk Lorentz factor, which makes {tex}\large E\normal_p\propto\large\Gamma\small^4{/tex}, which poses a problem in explaining the relative narrowness of the observed distribution of peak energies (Preece et al. 2000), even including the X-ray flashes. Similarly, for the internal shock model {tex}\gamma_m\propto\large\Gamma \small_{rel}{/tex}, the relative Lorentz factor between the two shells that collide, and {tex}\large E\normal_p\propto\large B_\bot\Gamma{/tex}, expected to give a larger scatter as well. A third complication arises in explaining the observed correlation between the burst's peak energy and luminosity, also known as the Amati relation (e.g. Lloyd-Ronning et al. (2000); Amati et al. (2002); Ghirlanda et al. (2004)); the peak energy is correlated with the isotropically equivalent energy {tex}\large E\normal_p\propto\large E\small^{0.40\pm 0.05}_{iso}{/tex}. For the synchrotron, internal-shock model one expects {tex}\large E\normal_p\propto\large\Gamma\normal^{-2}\large L\normal^{1/2}\large t\small^{-1}_v{/tex} (e.g. Zhang & M´esz´aros (2002)), where {tex}\large t\small_v{/tex} is the typical variability time scale. This requires that both {tex}\Gamma{/tex} and {tex}\large t\small_v{/tex} have to be quite similar for all bursts, which is difficult to imagine. In addition, assuming a typical {tex}\large L\propto\Gamma\normal^2{/tex} (e.g. Kobayashi et al. (2002)) would even lead to an anti-correlation (see also Ramirez-Ruiz & Lloyd-Ronning (2002)). Additional assumptions are needed to explain the positive correlation. Other variations of the synchrotron or/and inverse Compton model have been suggested (see e.g. Baring & Braby (2004); Lloyd-Ronning & Petrosian (2000); Stern & Poutanen (2004)), however, none have been able to describe all aspects of the observations in a convincing manner. To account for these aspects, I argue that GRBs, in general, have a strong thermal component, which is accompanied by a non-thermal component of similar strength. 2. Spectral Modeling Recently, in Ryde (2004) I identified bursts which are dominated by quasi-thermal emission throughout their duration. The temperature of the emitting matter exhibits a similar behavior for all of them, with an initially constant, or weakly decreasing, temperature (~100 keV, power-law index ~ 0 to -0.3) and a distinct break into a faster power-law decay with an index of approximately -0.6 to -1. I also suggested that bursts that are observed to be initially thermal, are similar to these but have an additional non-thermal component that varies in spectral slope and grows in relative strength with time. This category of bursts is illustrated in this paper by GRB980306 (all bursts discussed here were recorded by the BATSE detector on the Compton Gamma-ray Observatory). Spectra from three different times are shown in the lower-most panels in Figure 1. The model shown consists of a power law {tex}\propto\large E\normal^s{/tex}, representing the non-thermal emission, combined with a Planck function {tex}\propto\large (kT)\normal^2x^2/(e x p (x)-1){/tex} where {tex}x=\large E/kT{/tex}, k is Boltzmann’s constant and T is the temperature. It is clear that the relative strength of the non-thermal component increases with time and that the index s varies, in this particular burst from ~ -1.5 to ~ -3 (see Figure 2). This leads to the apparent softening below the peak energy. Figure 2 also shows that the temperature of the black body, for this burst, exhibits a similar evolution like the purely quasi-thermal bursts discussed by Ryde (2004), with a distinct break in the cooling curve. There is a total of 10 bursts that have been discussed in the literature from this category (Ghirlanda et al. 2003; Ryde 2004). We will now study the spectra of more typical bursts, bursts which do not have any exceptionally hard {tex}\alpha{/tex}-values, nor have any conspicuous spectral evolution, and therefore a thermal component is not required in a first appraisal. For this purpose we analyze the sample of the 25 strongest pulses in the catalogue of Kocevski, Ryde, & Liang (2003), which comprise a complete sample of pulses with a varying spectral shapes and evolution. We compare the results of the fits of the hybrid model to those of the most commonly used Band et al. (1993) model, which is an empirical function consisting of a low-energy powerlaw with index {tex}\alpha .{/tex} exponentially connected to a high-energy power-law with index {tex}\beta{/tex} at an energy {tex}\large E\normal_p{/tex}. We note that these two models have the same number of parameters; kT, s, and two amplitudes, compared to {tex}\alpha .{/tex}, {tex}\beta{/tex}, {tex}\large E\normal_p{/tex}, and one amplitude. The reduced {tex}X^2{/tex} values and the residuals of the fits indicate equally good fits for both models; the {tex}X^2{/tex}-values are in most cases indistinguishable statistically. The hybrid model was formally better (had a lower {tex}X^2_v{/tex} value) in 10 of the cases. The largest differences were for GRB950211 {tex}(X^2_{hyb};X^2_{band})=(1.03;1.10){/tex} for 540 degrees of freedom (d.o.f.) and GRB960530 {tex}(X^2_{hyb};X^2_{band})=(0.975;0.999){/tex} for 2071 d.o.f. and finally for GRB950818 {tex}(X^2_{hyb};X^2_{band})=(1.09;0.96){/tex} for 1819 d.o.f. If a hybrid model with a sharply broken power law with say {tex}\alpha\equiv-1.5{/tex} and {tex}\beta\equiv-2.1{/tex} (motivated in {tex}\S 3{/tex}) is used instead, the {tex}X^2_v{/tex} of the latter fit becomes lower: 1.02. This illustrates the obvious fact that the simple power-law model is an approximation of the actual non-thermal emission if the break energy is within the studied window for a significant fraction of the burst duration. In comparing the two models it should also be noted that the hybrid model is a physical model rather than an empirical model and that the fit results are reasonable from a theoretical point-of-view (see {tex}\S 3{/tex}). Figure 2 shows three of the studied bursts; GRB921207, GRB950624, which illustrate the most common behavior in which s evolves from -1.5 to ~ -2.1, and GRB960530 for which s is consistent of being constant ~ -1.5 even though a weak hardening is indicated. For all the cases the temperature again has a distinct break in its evolution. Three spectra from GRB950624 are also shown in Figure 1, illustrating the non-thermal character of the summed spectrum through out the pulse.  (0) Comments posted about this in the forum |
Gamma-Ray Bursts 
