Sensitivity of the PICO-500 Bubble Chamber to Supernova Neutrinos Through Coherent Nuclear Elastic Scattering

Ton-scale direct dark matter search experiments should be sensitive to neutrino-induced recoil events from either $^8$B solar neutrinos or the brief but intense flux from a core collapse supernova in the Milky Way. These low-threshold detectors are sensitive to the very low recoil energies, of order 10 keV, deposited via coherent elastic scatters between supernova neutrinos and target nuclei. Large superheated fluid detectors like PICO-500, a bubble chamber to be initially filled with an active target of 1 t of C$_3$F$_8$, should see multiple-bubble events from CE$\nu$NS if the detector is live during a neutrino burst from a supernova at a distance up to 10 kpc. This paper discusses conditions under which bubble chambers could be used as an independent measurement in the event of a supernova similar to SN 1987A, with particular sensitivity to the currently less-constrained heavy-lepton $\nu_x$ channel.