Temporal Properties

One of the most apparent features of GRB time profiles is the variety of shapes and durations (fig. ): because of this, a rigorous classification based on the time profile shape is not feasible. Nevertheless, many bursts can be classified into some kinds based on rough criteria ([Ryde 1999], [Ryde & Svensson, 2001]): one such class collects the so-called FREDs, acronymous of Fast Rise Exponential Decay, for their typical single pulse profile, whose rise time is much shorter than the decay time (e.g. GRB010721, fig. ). Then, we can distinguish between the multi-peak bursts and those with only one or two peaks; the GRBs with no apparent signal among next pulses (GRB971110, GRB000115, GRB990913, fig. ) from those which do not show any ``gaps'' in the overall profile. No rule about the brightness of each pulse: the first pulses may be brighter (GRB990913) or fainter (GRB000115) than the following pulses. In some cases, a repetitive pattern seems to modulate the structure of the burst profile (GRB970831). Some bursts show time variability on ms timescales (GRB010412).

As to the time duration, from the BATSE sample there is some evidence for the existence of two classes: in fact, if the duration is evaluated in terms of $T_{90}$, which is calculated by taking the interval going from the time at which the total fluence is at 5% to the time at which it is at 95% of the overall burst fluence, then it comes out that the $T_{90}$ distribution (fig. ) is well described by a bimodal function, with the two peaks around $0.3$ s and $20$ s, respectively, and a minimum around 2 s ([Kouveliotou et al., 1993]). According to some papers ([Mukherjee et al., 1998,Horváth 1998,Balastegui et al., 2001]), a third intermediate class of GRBs might exist as well.

Figure: Duration ($T_{90}$) Distribution of 2704 BATSE bursts (from http://www.batse.msfc.nasa.gov/batse/grb/duration/).

From the $T_{90}$ distribution the GRBs are subdivided in two classes: short bursts (those with $T_{90}<2$ s) and long ones (those with $T_{90}>2$ s). An example of time profile of a short burst is given by GRB971230, fig. . According to [Cline et al., 1999], the short bursts seem to show more symmetrical profiles than the long ones.

In particular, in fig.  there is some evidence for a correlation betweeen spectral hardnesses and durations; the spectral hardness ratio is defined as the ratio between the BATSE channel 3 (100-300 keV) and channel 2 (50-100 keV) counts, while the duration is measured in terms of $T_{90}$.

Figure: HR-Duration ($T_{90}$) Correlation of GRBs. The squares spot the WFC/BeppoSAX bursts: to date, it has been possible to detect afterglows only from long bursts (from http://www.batse.msfc.nasa.gov/batse/grb/4bcatalog/.)

Another temporal property of GRBs which gives an insight into the progenitor nature is the time variability, which is significant on ms timescales ([Walker et al., 2000]): this suggests that the source should be compact, like neutron stars or black holes. Moreover, since at least some GRBs come from cosmological distances, there is a connected time dilation effect that should be taken into account; this time dilation also works differently, depending on the energy band.

An interesting property has been discovered by [Beloborodov, Stern & Svensson, 1998], from the study of the power density spectra (PDSs): according to this analysis, the average PDS seems to follow a power law with index -5/3 over almost two decades, with a break around $\sim$2 Hz; this property seems to be connected with the presence of developed turbulence. Some works ([Panaitescu et al., 1999], [Spada et al., 2000]) have tried to simulate bursts arising from internal shocks in relativistic winds (see the Fireball Model, next sections), in order to find out the most sensitive factors, that are consistent with the observed power law index -5/3; nevertheless, the interpretation of this feature is debated ([Chang & Yi, 2000]).

Figure: Direction distribution of 2704 bursts detected by BATSE (from http://www.batse.msfc.nasa.gov/batse/grb/skymap/).