Possible neutrino signature of hadron-quark phase transition in failing core-collapse supernovae*

We study the consequence of a hadron-quark phase transition in failing core-collapse supernovae, which give birth to stellar-mass black holes. In models with a range of progenitor compactness, the protoneutron star collapses and bounces for a second time due to the phase transition. However, this second bounce cannot revive the supernova shock. Instead, the protoneutron star oscillates with the excess kinetic energy and emits a train of neutrino pulses with a period of $\sim$ms. Black-hole formation takes place in a third collapse. The periodic neutrino signal can be a strong indicator for the hadron-quark phase transition in failing core-collapse supernovae if detected in the future.