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    Sensitivity to Supernovae Average νx\nu_x Temperature with Neutral Current Interactions in DUNE

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    We explore a novel method for measuring the average temperature of the νx\nu_x component in Type-II core-collapse supernovae. By measuring neutral current incoherent neutrino-Argon interactions in DUNE we can obtain spectral information for the combination of all active neutrino species. Combining this all-neutrino spectral information with detailed charged current measurements of the electron neutrino and electron anti-neutrino fluxes from DUNE and Hyper-Kamiokande, we can infer the average temperature for the remaining neutrino species in the νx\nu_x component to within a factor two for most cases and to 30% for a small range of average νx\nu_x temperatures. Due to the limited energy range of the emitted photons from incoherent neutral current interactions on Argon, the νx\nu_x temperature reconstruction demonstrates a degeneracy in the one and two sigma credible regions. Furthermore, while large uncertainties on the NC cross-section penalize this measurement, we examined the efficacy of constraining NC cross-section uncertainties on improving νx\nu_x measurements. We found that if additional measurements of B(M1\uparrow) 1+^+ excited state transitions in Argon are able to reduce correlated cross section uncertainties from 15% to 7%, the size of the 1σ1\sigma allowed regions for TνxT_{\nu_x} becomes sample size limited, and approaches the case where there are no uncertainties on the cross-section.Comment: 9 pages, 13 figure