Rapidly Rising Optical Transients from the Birth of Binary Neutron Stars.

We study optical counterparts of a new-born pulsar in a double neutron star system like PSR J0737-3039A/B. This system is believed to eject a small amount of mass of $\mathcal{O}(0.1M_{\odot})$ at the second core-collapse supernova. We argue that the initial spin of the new-born pulsar can be determined by the orbital period at the time when the second supernova occurs. The spin angular momentum of the progenitor is expected to be similar to that of the He-burning core, which is tidally synchronized with the orbital motion, and then the second remnant may be born as a millisecond pulsar. If the dipole magnetic field strength of the nascent pulsar is comparable to that inferred from the current spin-down rate of PSR J0737-3039B, the initial spin-down luminosity is comparable to the luminosity of super-luminous supernovae. We consider thermal emission arising from the supernova ejecta driven by the relativistic wind from such a new-born pulsar. The resulting optical light curves have a rising time $\sim 10$ days and peak luminosity $\sim 10^{44}$ erg/s. The optical emission may last for a month to several months, due to the reprocessing of X-rays and UV photons via photoelectric absorption. These features are broadly consistent with those of the rapidly-rising optical transients. The high spin-down luminosity and small ejecta mass are favorable for the progenitor of the repeating fast radio burst, FRB 121102. We discuss a possible connection between newborn double pulsars and fast radio bursts.