Abstract 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 ) α . 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 α = 0 ). We measure the SLSNe-I rate to be about 40 yr − 1 Gpc − 3 at a weighted mean redshift of z ¯ = 0.89 , which is consistent with previous works.

中文翻译：

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关于超亮超新星的事件率和光度函数

摘要 我们根据 Pan-STARRS1 中等深度巡天 (PS1 MDS) 发现的 17 个事件计算了每单位体积贫氢超发光超新星 (SLSNe-I) 的速率。假设光度函数 (LF) 有两种形式：分别是对数正态形式和单一幂律形式。假设 SLSNe-I 的速率与宇宙恒星的形成速率成正比，另外还有 (1 + z ) α 的红移演化。我们的结果表明，单一功率低形式比对数正态形式更适合数据，并且 SLSNe-I 的事件率直接与宇宙恒星形成率成正比（α = 0）。我们在 z¯ = 0.89 的加权平均红移下测量 SLSNe-I 速率约为 40 yr - 1 Gpc - 3，这与之前的工作一致。