Supernova pointing with low- and high-energy neutrino detectors

A future galactic SN can be located several hours before the optical explosion through the MeV-neutrino burst, exploiting the directionality of $nu$-$e$-scattering in a water Cherenkov detector such as Super-Kamiokande. We study the statistical efficiency of different methods for extracting the SN direction and identify a simple approach that is nearly optimal, yet independent of the exact SN neutrino spectra. We use this method to quantify the increase in the pointing accuracy by the addition of gadolinium to water, which tags neutrons from the inverse beta decay background. We also study the dependence of the pointing accuracy on neutrino mixing scenarios and initial spectra. We find that in the ``worst case'' scenario the pointing accuracy is $8^circ$ at 95% C.L. in the absence of tagging, which improves to $3^circ$ with a tagging efficiency of 95%. At a megaton detector, this accuracy can be as good as $0.6^circ$. A TeV-neutrino burst is also expected to be emitted contemporaneously with the SN optical explosion, which may locate the SN to within a few tenths of a degree at a future km$^2$ high-energy neutrino telescope. If the SN is not seen in the electromagnetic spectrum, locating it in the sky through neutrinos is crucial for identifying the Earth matter effects on SN neutrino oscillations.These e ects can be observed at a single detector through peaks in the Fourier transform of their \inverse energy" spectrum. The positions of these peaks are independent of the SN models and therefore the peaks can be used as a robust signature of the Earth matter e ects, which in turn can distinguish between di erent neutrino mixing scenarios. We analyze the strengths and positions of these peaks as a function of the location of the SN in the sky and explore their features at a large scintillation detector as well as at a megaton water Cherenkov detector through Monte Carlo simulations.