Spectral hardness evolution characteristics of tracking gamma-ray burst pulses

Employing a sample presented by Kaneko et al. (2006) [Kaneko, Y. et al., 2006. ApJS 166, 298 (Paper I)] and Kocevski et al. (2003) [Kocevski, D. et al., 2003. ApJ 596, 389], we select 42 individual tracking pulses (here we defined tracking as the cases in which the hardness follows the same pattern as the flux or count rate time profile) within 36 gamma-ray bursts (GRBs) containing 527 time-resolved spectra and investigate the spectral hardness, Epeak (where Epeak is the maximum of the νFν spectrum), evolutionary characteristics. The evolution of these pulses follow soft-to-hard-to-soft (the phase of soft-to-hard and hard-to-soft are denoted by rise phase and decay phase, respectively) with time. It is found that the overall characteristics of Epeak of our selected sample are: (1) the Epeak evolution in the rise phase always start on the high state (the values of Epeak are always higher than 50 keV); (2) the spectra of rise phase clearly start at higher energy (the median of Epeak are about 300 keV), whereas the spectra of decay phase end at much lower energy (the median of Epeak are about 200 keV); (3) the spectra of rise phase are harder than that of the decay phase and the duration of rise phase are much shorter than that of decay phase as well. In other words, for a complete pulse the initial Epeak is higher than the final Epeak and the duration of initial phase (rise phase) are much shorter than the final phase (decay phase). This results are in good agreement with the predictions of [Lu, R.J. et al., 2007. ApJ 663, 1110] and current popular view on the production of GRBs. We argue that the spectral evolution of tracking pulses may be relate to both of kinematic and dynamic process even if we currently can not provide further evidences to distinguish which one is dominant. Moreover, our statistical results give some witnesses to constrain the current GRB model.