On the event rate and luminosity function of superluminous supernovae

We calculate the rate per unit volume of hydrogen-poor superluminous supernovae (SLSNe-I) based on the 17 events discovered with the Pan-STARRS1 Medium Deep Survey (PS1 MDS). Two forms of the luminosity function (LF) are assumed : a log-normal form and a single power-law form, respectively. The rate of SLSNe-I is assumed to be proportional to the cosmic star formation rate with an additional redshift evolution of $(1+z)^{\alpha}$. Our results show that the single power-low form fits the data better than the log-normal form, and the event rate of SLSNe-I is proportional to the cosmic star formation rate directly (with $\alpha=0$). We measure the SLSNe-I rate to be about $40 ~\rm{yr^{-1}Gpc^{-3} }$ at a weighted mean redshift of $\overline z=0.89$, which is consistent with previous works.