explain the observed value from SN 1987A.

Another possible way to enhance neutrino luminosity is through rapid rotation. A nascent neutron star can be rotating rapidly shortly after the supernova explosion[@ls95], though we have little knowledge about how fast it rotates observationally and theoretically. The inner core of a rapid rotating proto-neutron star is usually more [*massive*]{} than that of a non-rotating one in order to compress the inner core to about the same supranuclear density at which the prompt shock wave occurs. When the proto-neutron star de-leptonizes, more neutrinos are emitted from a larger core, and the neutrino luminosity behind the stalled shock could be enhanced to explode the supernova successfully[^1]. Due to a larger centrifugal force from rapid rotation, the central density of the core could be much lower than the QCD phase transition density, so that a neutron star could exist after the explosion. However, such rapidly rotating neutron stars can not keep being there for a long time because of the fine-tuning problem, proposed by Glendenning[@glen97]. [*Only those neutron stars very close to the critical mass limit can rotate rapidly*]{} because they have the least radius and the greatest mass. These stars have much higher central 