Recent high-cadence transient surveys have discovered rapid transients whose light-curve timescales are shorter than those of typical supernovae (SNe). In this paper, we present a systematic search for rapid transients at medium-high redshifts among 3381 SNe candidates obtained from the Hyper Suprime-Cam Subaru Strategic Program transient survey. We developed a machine learning classifier to classify the SN candidates into four types (Type Ia, Ibc, II SNe and rapid transients) based on the features derived from the light curves. By applying this classifier to the 3381 SN candidates and by further applying the quality cut, we selected 14 rapid transient samples. They are located at a wide range of redshifts (0.34 ≤ z ≤ 1.85) and show a wide range of the peak absolute magnitude (−17 ≥ M ≥ −22). The event rate of the rapid transients is estimated to be ∼6 × 103 events yr−1 Gpc−3 at z ∼ 0.74, which corresponds to about 2% of the event rate of normal core-collapse SNe at a similar redshift. Based on the luminosity and color evolution, we selected two candidates of Type Ibn SNe at z ∼ 0.75. The event rate of Type Ibn SN candidates is more than 1% of Type Ib SN rate at the same redshift, suggesting that this fraction of massive stars at this redshift range eruptively ejects their He-rich envelope just before the explosions. Also, two objects at z = 1.37 and 1.85 show high luminosities comparable to superluminous SNe. Their event rate is about 10%–25% of superluminous SNe at z ∼ 2.
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