Study of GRB light curve decay indices in the afterglow phase

In this work we study the distribution of temporal power-law decay indices, $\alpha$, in the Gamma Ray Burst (GRB) afterglow phase, fitted for $176$ GRBs (139 long GRBs, 12 short GRBs {\it with extended emission} and 25 X-Ray Flashes (XRFs)) with known redshifts. These indices are compared with the temporal decay index, $\alpha_W$, derived with the light curve fitting using the \cite{willingale07} model. This model fitting yields similar distributions of $\alpha_W$ to the fitted $\alpha$, but for individual bursts a difference can be significant. Analysis of ($\alpha$, $L_a$) distribution, where $L_a$ is the characteristic luminosity at the end of the plateau, reveals only a weak correlation of these quantities. However, we discovered a significant regular trend when studying GRB $\alpha$ values along the \cite{dainotti2008} correlation between $L_a$ and the end time of the plateau emission in the rest frame, $T_a^*$, hereafter LT correlation. We note a systematic variation of the $\alpha$ parameter distribution with luminosity for any selected $T_a^*$. We analyze this systematics with respect to the fitted LT correlation line, expecting that the presented trend may allow to constrain the GRB physical models. We also attempted to use the derived correlation of $\alpha(T_a)$ versus $L_a(T_a)$ to diminish the luminosity scatter related to the variations of $\alpha$ along the LT distribution, a step forward in the effort of standardizing GRBs. A proposed toy model accounting for this systematics applied to the analyzed GRB distribution results in a slight increase of the LT correlation coefficient.