Relationship between different channel light curves of gamma-ray burst pulses shown in aspects other than the pulse width

Abstract

In this paper, we employ the peak count rate{\bf \}$C_p$ and the total count $C_{total}$ of light curves to study in the corresponding aspects the relationship between different channel light curves. To make a direct comparison between count rates of different channel light curves we introduce a plot of $C(τ)$ versus $C_H(τ)$, where $C(τ)$ is the count rate of a channel and $C_H(τ)$ is the count rate of a definite cannel, channel H (see the text). According to the plot we define $ΔC_{\max}$ as the maximum deviation of the two count rate values of $C(τ)$ associated with a same count rate value of $% C_H(τ)$ and define $ΔS$ as the area confined by the close curve of $C(τ)$ in the plot to measure the difference of the rising and decaying portions of a light curve relative to the count rate of channel H. Under the assumption that some GRBs observed are in the stage of fireballs which expand relativistically, predictions on the relationships between the four quantities{\bf (}$C_p$, $C_{total}$, $ΔC_{\max}$, and $ΔS$) and energy within a wide band, calculated with different rest frame radiation forms and two typical Lorentz factors ($Γ=20$ and 200), are made and presented, which would make the test of our model with the coming Swift data easier. Interpretations to the relationships within the mechanism of fireballs are also presented.