Search for the signatures of a new-born black hole from the collapse of a supra-massive millisecond magnetar in short GRB light curves

`Internal plateau' followed by a sharp decay is commonly seen in short gamma-ray burst (GRB) light curves. The plateau component is usually interpreted as the dipole emission from a supra-massive magnetar, and the sharp decay may imply the collapse of the magnetar to a black hole (BH). Fall-back accretion onto the new-born BH could produce long-lasting activities via the Blandford-Znajek (BZ) process. The magnetic flux accumulated near the BH would be confined by the accretion disks for a period of time. As the accretion rate decreases, the magnetic flux is strong enough to obstruct gas infall, leading to a magnetically-arrested disk (MAD). Within this scenario, we show that the BZ process could produce two types of typical X-ray light curves: type I exhibits a long-lasting plateau, followed by a power-law decay with slopes ranging from 5/3 to 40/9; type II shows roughly a single power-law decay with slope of 5/3. The former requires low magnetic filed strength, while the latter corresponds to relatively high values. We search for such signatures of the new-born BH from a sample of short GRBs with an internal plateau, and find two candidates: GRB 101219A and GRB 160821B, corresponding to type II and type I light curve, respectively. It is shown that our model can explain the data very well.