Possible correlations between gamma-ray burst and its host galaxy offset

We collected the information of 304 gamma-ray bursts (GRBs) from the literature, and analyzed the correlations among the host galaxy offsets (the distance from the site of the GRB to the center of its host galaxy), $T_{\rm 90,i}$ (the duration $T_{\rm 90}$ in rest-frame), $T_{\rm R45,i}$ (the duration $T_{\rm R45}$ in rest-frame), $E_{\rm \gamma,iso}$ (the isotropic equivalent energy), $L_{\rm \gamma,iso}$ ($=E_{\rm \gamma,iso}/T_{\rm 90,i}$, the isotropic equivalent luminosity) and $L_{\rm pk}$ (peak luminosity). We found that $T_{\rm 90,i}$, $T_{\rm R45,i}$, $E_{\rm \gamma,iso}$, $L_{\rm pk}$ have negative correlation with ${\rm offset}$, which is consistent with origin of short GRBs (SGRBs) and long GRBs (LGRBs). On separate analysis, we found similar results for $\log E_{\rm \gamma,iso}$ - $\log {\rm (offset)}$ and $\log L_{\rm pk}$ - $\log {\rm (offset)}$ relations in case of SGRBs only, while no obvious relation for LGRBs. There is no correlations between offset and $L_{\rm \gamma,iso}$. We also put the special GRB 170817A {and GRB 060218A} on the plots. {The two GRBs both have low luminosity and small offset.} In the $\log ({\rm offset})- \log T_{\rm 90,i}$ plot, we found GRB 170817A locates in between the two regions of SGRBs and LGRBs and it is the outlier in the ${\rm offset}-E_{\rm \gamma, iso}$, ${\rm offset}-L_{\rm \gamma, iso}$ and ${\rm offset}-L_{\rm pk}$ plots. Together with GRB 060218A being an outlier in all plots, it indicates the speciality of GRBs 170817A and 060218A, and might imply more subgroups of the GRB samples.