Operation of an archaeological lead PbWO$_4$ crystal to search for neutrinos from astrophysical sources with a Transition Edge Sensor

The experimental detection of the CE$ν$NS allows the investigation of neutrinos and neutrino sources with all-flavor sensitivity. Given its large content in neutrons and stability, Pb is a very appealing choice as target element. The presence of the radioisotope $^{210}$Pb (T$_{1/2}\sim$22 yrs) makes natural Pb unsuitable for low-background, low-energy event searches. This limitation can be overcome employing Pb of archaeological origin, where several half-lives of $^{210}$Pb have gone by. We present results of a cryogenic measurement of a 15g PbWO$_4$ crystal, grown with archaeological Pb (older than $\sim$2000 yrs) that achieved a sub-keV nuclear recoil detection threshold. A ton-scale experiment employing such material, with a detection threshold for nuclear recoils of just 1 keV would probe the entire Milky Way for SuperNovae, with equal sensitivity for all neutrino flavors, allowing the study of the core of such exceptional events.