\subsection {Supernovae}

The core collapse supernovae are spectacular events which have been
theoretically studied for more than three decades. After explosion the star
loses energy, mainly by neutrino emission, and cools down, ending as a
neutron star or a black hole. Many features of the collapse mechanism are
indeed imprinted in the neutrinos released during the explosion.

At the same time, a galactic supernova would give particle physicists the
occasion to explore the neutrino properties on scales of distance up to
$10^{17}$ km and of time up to $\sim 10^{5}$ years and at very high density.
The detected signal from a supernova explosion depends on the
structure of the neutrino mass spectrum and lepton mixing. Therefore, in
principle, studying the properties of a supernova neutrino burst one
can get information about the values of parameters relevant for the
solution of the solar neutrino problem, the type of the mass
ordering (the so-called mass hierarchy), 
the mixing parameter $\sin^2\theta_{13}$, the
presence of sterile neutrinos and new neutrino interactions.

It is generally believed that
core-collapse supernovae have occurred throughout the
Universe since the formation of stars. Thus, there should
exist a diffuse background of neutrinos originating from
all the supernovae that have ever occurred. Detection
of these diffuse supernova neutrinos (DSN) would offer 
insight about the history of star formation and supernovae
explosions in the Universe.

Now the requirements for a detector are to be very massive, located
underground, to stay in operation for at least 20 years and to be equipped
with a real time neutrino detection electronics with a threshold around
10 MeV. For those reasons a megaton water \v{C}erenkov detector with a
fiducial volume around 450 kt is a good choice. Such a detector would
detect $\sim 10^{5}$
events from a galactic stellar collapse, and of the order of 20 events from a
supernova in Andromeda galaxy, which is one of the closest to our Milky way.
The large mass of such a detector compared to other proposed and existing
facilities means that the sample collected will outnumber that of all other
detectors combined.
The general and relative performances are summarized in section \ref{sec:SN}.

%As an example for an explosion at the center of our galaxy, we expect
%$\sim 300$ events per kiloton of water. A megaton water \v{C}erenkov detector
%would be sensitive to three main neutrino signals

All types of neutrinos and anti-neutrinos are emitted
from a core-collapse supernova, but not all are equally
detectable. 
The $\bar{\nu_e}$ is most likely to interact in a water \v{C}erenkov detector.
Three main neutrino signals would be detected, each one yielding unique
information: 
\begin{enumerate}
\item Inverse beta decay events (89\%) allowing for a good
determination of the time evolution and energy distribution of the neutrino
burst. The potentials would be enhanced by the detection of the neutron
with the addition of a small mount of Gadolinium \cite{Beacom:2003nk}.
\item Neutral current events involving $^{16}O$ (8\%), which are sensitive
to the temperature of the neutrino spectrum.
\item Directional elastic scattering events from $\nu_{x}$ + $e^{-}$ and
$\bar{\nu}_{x}$ + $e^{-}$ ($\sim$ 3\%). These events provide the direction
of the supernova within $\pm 1$ degree.
\end{enumerate}
%Each one of these modes will yield unique information.