A study of gamma ray bursts with afterglow plateau phases associated   with supernovae
  The analysis of 176 gamma ray burst (GRB) afterglow plateaus observed by Swift from GRBs with known redshifts revealed that the subsample of long GRBs associated with supernovae (LONG-SNe) - 19 events - presents a very high correlation coefficient between the luminosity at the end of the plateau phase La and the end time of the plateau T*a, hereafter Dainotti relation. Furthermore, these SNe Ib/c associated with GRBs also obey the peak-magnitude stretch relation, similar to that used to standardize the SNe Ia. We here investigate a category of GRBs with plateau and associated with SNe to compare the Dainotti correlation for this sample with the correlation for long GRBs for which no associated SN has been observed (hereafter LONG-NO-SNe, 128 GRBs) and to check whether there is a difference among these sub-samples. We first adopted a non-parametric statistical method to take redshift evolution into account and to check if and how this effect may steepen the slope for the LONG-NO-SNe sample. Therefore, removing selection bias is the first step before any comparison among samples observed at different redshifts could be properly performed. Then, we applied the T-student test to evaluate a statistical difference between the slopes of the two samples. We demonstrate that there is no evolution for the slope of the LONG-NO-SNe sample and no evolution is expected for the LONG-SNe sample at small redshifts. The difference between the slope of the LONG-NO-SNe and the slope of LONG-SNe with firm spectral detection of SN components, is statistically significant. This possibly suggests that, unlike LONG-NO-SNe, LONG-SNe with firm spectroscopic features of the associated SNe might not require a standard energy reservoir in the plateau phase. Therefore, this analysis may open new perspectives in future theoretical investigations of the GRBs with plateau emission and that are associated with SNe. 
Maria G. Dainotti, Shigehiro Nagataki, Keichi Maeda, Sergey Postnikov   and Elena Pian
astro-ph.HE