Search for Correlations and Study of Selection Effects When Analyzing a Sample of Supernovae Associated with Gamma-Ray Bursts

We present the most complete up-to-date sample of supernovae associated with gamma-ray bursts (GRB-SNe) for which the peak time of the SN light curve and the peak absolute magnitude have been found. The sample contains 44 SNe. We have searched for correlations between the parameters of the GRB-SN $$V$$ -band brightness peak (the rest-frame $$V$$ -band absolute magnitude $$M_{V}$$ ) and the rest-frame $$V$$ -band peak time $$T_{\textrm{max}}$$ as well as between them and GRB prompt emission parameters ( $$T_{90,i}$$ , $$E_{\textrm{iso}}$$ , $$E_{p,i}$$ ). Any correlations between any pairs of parameters cannot be confirmed at a statistically significant level. A separation into two groups is observed in the $$M_{V}{-}\log_{10}(E_{\textrm{iso}})$$ distribution. These two groups may correspond to significantly different initial or final parameters of the SN that is the progenitor of long GRBs. We discuss the selection effects that affect the detectability of GRB-SNe and the possible existence of correlations.