Kilonovae of binary neutron star mergers leading to short-lived remnant neutron star formation

We study kilonova emission from binary neutron star (BNS) mergers for the case that a remnant massive neutron star (MNS) forms and collapses to a black hole within $20$ ms after the onset of the merger (which we refer to as "a short-lived case") by consistently employing numerical-relativity and nucleosynthesis results. We find that such kilonovae are fainter and last shorter than those for BNSs resulting in the formation of long-lived ($\gg 1\,{\rm s}$) MNSs, in particular in the optical band. The resulting light curves are too faint and last for a too short duration to explain the kilonova observation for the BNS associated with GW170817, indicating that the merger remnant formed in GW170817 is unlikely to have collapsed to a black hole within a short period of time ($\sim 20$ ms) after the onset of the merger. Our present result implies that early observation is necessary to detect kilonovae associated with BNSs leading to short-lived MNS formation in particular for the optical blue band as well as that kilonovae could be hidden by the gamma-ray burst afterglow for nearly face-on observation. We provide a possible approximate scaling law for near-infrared light curves with the given reference time and magnitude when the decline power of the ${\it z}$-band magnitude, $d M_{\it z}/d{\rm log}_{10}t$, reaches $2.5$. This scaling law suggests that the ${\it HK}$-band follow-up observation should be at least $1$ mag deeper than that for the ${\it z}$-band reference magnitude and earlier than 4 times the reference time.