Hardness ratio evolutionary curves of gamma-ray bursts expected by the curvature effect

Abstract

Hardness ratio evolutionary curves of gamma-ray bursts expected by the curvature effect AbstractWe have investigated the gamma-ray bursts (GRBs) pulses with a fast rise and an exponential decay phase, assumed to arise from relativistically expending fireballs, and found that the curvature effect influences the evolutionary curve of the corresponding hardness ratio (hereafter HRC). We find, due to the curvature effect, the evolutionary curve of the pure hardness ratio (when the background count is not included) would peak at the very beginning of the curve, and then would undergo a drop-to-rise-to-decay phase. In the case of the raw hardness ratio (when the background count is included), the curvature effect would give rise to several types of evolutionary curve, depending on the hardness of a burst. For a soft burst, an upside-down pulse of its raw HRC would be observed; for a hard burst, its raw HRC shows a pulse-like profile with a sinkage in its decaying phase; for a very hard burst, the raw HRC possesses a pulse-like profile without a sinkage in its decaying phase. For a pulse-like raw HRC as shown in the case of the hard and very hard bursts, its peak would appear in advance of that of the corresponding light curve, which was observed previously in some GRBs. For illustration, we have studied here the HRC of GRB 920216, GRB 920830 and GRB 990816 in detail. The features of the raw HRC expected in the hard burst are observed in these bursts. A fit to the three bursts shows that the curvature effect alone could indeed account for the predicted characteristics of HRCs. In addition, we find that the observed hardness ratio tends to be harder at the beginning of the pulses than what the curvature effect could predict and be softer at the late time of the pulses. We believe this is an evidence showing the existence of intrinsic hard-to-soft radiation which might be due to the acceleration-to-deceleration mode of shocks.PACS numbers: 98.70. Rz,

Spectral Hardness Evolution of Gamma‐Ray Bursts Due to the Doppler Effect of Fireballs

“…Figure 1 illustrates the evolutions of E p of the observed spectrum corresponding to a constant rest-frame radiation spectrum for three different local pulses. From the figure, we find that, like the characteristic of the evolution of the pure hardness ratio seen in Qin et al (2006), the peak energy E p peaks at the very onset of the corresponding light-curve pulse and then undergoes a dropto-rise-to-decay evolution (the A, B, and C phases, respectively; see the figure) for the local pulses with a rising portion; but for the local pulse without a rising portion, the peak energy E p decreases monotonically from the onset of the corresponding light curve, which indicates that the B phase in the evolutionary curve of E p results from the contributions from the rising portion of its local pulse. Lu et al (2006bLu et al ( , 2007 pointed out that a GRB light-curve pulse could result from the combined contributions of both the rising and decaying portion of its corresponding local pulse.…”

“…First, we here only investigate a simple intrinsic mechanism, but the real intrinsic radiation mechanism may be more complicated, such as a combination of Comptonized and synchrotron spectra, or nonlinear evolution of the intrinsic spectrum, and so on. Second, as pointed out in previous literature (e.g., Qin et al 2006;Lu et al 2006bLu et al , 2006a, equations (1) and (2), derived based on simple cases, such as that of a fireball expanding isotropically with a constant Lorentz factor, are suitable both for the case of a spherical fireball and of a uniform jet. But GRBs might be associated with more complicated situations, such as structure jets.…”

“…Therefore, as Qin et al (2006) pointed out, the peak energy and the hardness ratio reflect different aspects of the spectral evolution of GRBs. Searching Figures 1-3 in Qin et al (2006), one would find that, due to the Doppler effect, different bulk Lorentz factors would give rise to several different types of evolutionary curve for the hardness ratio. But this is not the case for the peak energy.…”

“…Recently, Qin et al (2006) studied the evolution of the hardness ratio, defined as the ratio of a higher energy channel to that of a lower energy channel within GRB pulses with a fast rise and an exponential decay phase, based on the assumption of relativistically expanding fireballs, and found that due to the Doppler effect, the evolutionary curve of the pure hardness ratio (when the background count is not included ) would peak at the onset of the pulse and then undergo a drop to rise to decay evolution. When the background count is included, the Doppler effect gives rise to several types of evolutionary curve, depending on the bulk Lorentz factor of a burst.…”

The Full Curvature Effect Expected in Early X‐Ray Afterglow Emission from Gamma‐Ray Bursts

“…Taking all these factors into account, one may come to a full description of the so-called curvature effect (see also Qin et al 2006 for a detailed explanation). Consider a constantly expanding fireball shell emitting within a proper-time interval t 0, min t 0 t 0, max and over an area min max , where is the angle to the line of sight.…”