\subsection{Supernova neutrinos}
\label{sec:SN}

\subsubsection{Core-collapse}
The large mass of a MEMPHYS-type detector means that the sample of
events collected during a supernova explosion would outnumber that
of all other existing detectors. For instance, for a supernova at
10 kpc $\sim 2\times 10^5$ events would be observed,
whereas Super-Kamiokande (22.5 kt) will see only 9,000 events (see Figure
\ref{fig:SN}, from ref.~\cite{Fogli:2004ff}). 
These numbers
are to be compared with the 19 (11 for Kamiokande and 8 for IMB)
events coming from the SN1987A in the Large Magellanic Cloud (50 kpc).

\begin{figure}
\begin{center}
\epsfig{figure=./figures/snburst.eps,width=8cm,height=8cm}
\caption{\it % Figure to be redone for 440 kt! 
The number of events in a 400 kt water \v{C}erenkov detector (left scale)
and in SK (right scale) in all channels and in the individual
detection channels as a function of distance for a supernova
explosion \cite{Fogli:2004ff}.}
\label{fig:SN}
\end{center}
\end{figure}

An estimated number of $3\pm 1$ supernovae occur in our galaxy and
its satellites every century.
A MEMPHYS-type detector would also be sensitive to supernovae 
occurring throughout
the local group of galaxies. For a supernova explosion in Andromeda 
(730-890 kpc),
the proposed detector will collect roughly the same amount of neutrinos
detected for the SN1987A.
A handful of events might be seen even at a distance as large as 3 Mpc. 

One of the unsolved problems in astrophysics is the mechanism of supernova
core-collapse. 
Inverse beta decay events from the silicon burning phase preceding 
the supernova explosion have very low (sub-threshold) positron 
energies, and could only be detected through neutron capture by adding
Gadolinium \cite{Beacom:2003nk}, 
provided that they can be statistically distinguished from background
fluctuations. 
The silicon burning signal should then be seen with a statistical
significance of 2$\div$8 standard deviations at a reference distance of 1
kpc. Unfortunately, at the 
galactic center ($\sim$10 kpc) the estimated silicon burning signal would
be 100 times smaller and thus unobservable.

There are better prospects to observe the neutronization burst from a
galactic supernova 
by means of elastic scattering on electrons, including contributions
from all flavors: a 0.4 Mton detector might observe such signal with a
statistical significance at the level of 4 standard deviations.
At the distance of the Large Magellanic Cloud, however, the
sensitivity drops dramatically. 

Returning to the overall rate in the inverse beta channel, 
the high statistics available for a 
galactic supernova explosion will allow many possible spectral
analyses, providing insight both on the properties of the collapse
mechanism and on those of neutrinos. 

For the first topic, an example is given in~\cite{Fogli:2004ff} 
in the context of shock-wave 
effects, based on the comparison of arrival times in different energy bins.

Concerning the spectral properties which depend on neutrino
oscillation parameters, 
it has been shown in \cite{Minakata:2001cd} that a detector
like the proposed one, considering the inverse-beta channel alone with
the current best values of solar neutrino oscillation parameters,
would allow the determination of the parameter $\tau_E$, defined as
the ratio of the average energy of time-integrated neutrino spectra
$\tau_E=\langle E_{\bar\nu_\mu}\rangle /\langle E_{\bar\nu_e}\rangle$,
with a precision at the level of few percent, to be compared with a
$\sim$20\% error possible at Super-Kamiokande. This would make it possible to
distinguish normal from inverted mass hierarchy, if
$\sin^2\theta_{13}>10^{-3}$ \cite{Lunardini:2003eh}. 
In the region $\sin^2\theta_{13}\sim (3\cdot 10^{-6}-3\cdot
10^{-4})$, measurements of $\sin^2\theta_{13}$ are possible with a
sensitivity at least an order of magnitude better than planned
terrestrial experiments \cite{Lunardini:2003eh}.

Up to now we have investigate supernova explosions occurring in our galaxy,
however the calculated rate of supernova explosions within a distance of 
10 Mpc is about one per year. Although the number of events from
a single explosion at such large distances would be small, the signal
could be separated from the background with the
request to observe at least two events within a time window 
comparable to the neutrino emission time-scale ($\sim$10 sec),
together with the full energy and time distribution of the 
events \cite{Ando:2005ka}.
In a MEMPHYS-type detector,
with at least two neutrinos observed, a supernova could be identified 
without optical confirmation, so that the start of the light curve 
could be forecasted by a few hours, along with a short list of probable
host galaxies. This would also allow the detection of supernovae
which are either heavily obscured by dust  or are optically
dark due to prompt black hole formation.
Neutrino detection with a time coincidence could therefore act
as a precise time trigger for other supernova detectors 
(gravitational antennas or neutrino telescopes).

Finally, one can notice that electron elastic scattering events would
provide a pointing accuracy on the supernova 
explosion of about $1^\circ$. 

\subsubsection{Diffuse Supernova Neutrinos}

An upper limit on the flux of
neutrinos coming from all past core-collapse supernovae 
(the Diffuse Supernova Neutrinos~\footnote{We 
prefer to denote these neutrinos as ``Diffuse'' rahter than ``Relic''
to avoid confusion with the primordial neutrinos produced one second
after the Big Bang.}, DSN) has been set by the
Super-Kamiokande experiment \cite{Malek:2002ns},
however most of the estimates are below this limit and therefore 
DSN detection thorough inverse
beta decay  appears to be feasible at a megaton scale water \v{C}erenkov
detector.

Typical estimates for DSN fluxes 
(see for example \cite{Ando:2004sb}) predict an event
rate of the order of 0.1$\div$0.5 cm$^{-2}$s$^{-1}$MeV$^{-1}$ 
for energies above 20 MeV, a cut 
imposed by the rejection of spallation events. 
After experimental selections analogous to the ones
applied in the Super-Kamiokande analysis, such events are retained with an
efficiency of about 47\% for energies between 20 and 35 MeV; this is
to be considered as a very conservative estimate at MEMPHYS, where the
bigger overburden will reduce the cosmic-muon induced background and
less stringent selection criteria can be applied. 
Two irreducible backgrounds remain: atmospheric $\nu_e$ and $\bar\nu_e$, 
and decay electrons from
the so called ``invisible muons'' generated by CC interaction of
atmospheric neutrinos and having an energy below threshold for
\v{C}erenkov signal. 

The spectra of the two backgrounds were taken from the 
Super-Kamiokande estimates
and rescaled to a fiducial mass of 440 kton of water, while the
expected signal was computed according to the model called LL
in \cite{Ando:2004sb}. 
The results are shown in Fig.~\ref{fig:snr}:
the signal could be observed with a statistical significance of about
2 standard deviations after 10 years.

\begin{figure}
\begin{center}
\epsfig{figure=./figures/snrelic.eps,width=13cm}
\caption{\it Diffuse Supernova Neutrino signal and backgrounds (left)
and subtracted signal with statistical errors (right) in a 440 kt
water \v{C}erenkov detector with a 10 years exposure. 
The selection efficiencies of SK were assumed; 
the efficiency change at 34 MeV is due to the spallation cut.}
\label{fig:snr}
\end{center}
\end{figure}


As pointed out in \cite{Fogli:2004ff}, 
with addition of Gadolinium \cite{Beacom:2003nk} 
the detection of the captured neutron
would give the possibility to reject neutrinos other than $\bar\nu_e$
from spallation events and from atmospheric origin, and the
detection threshold could be lowered significantly - to about 10 MeV -
with a large gain on signal statistics. 
The tails of reactor neutrino spectra would
become the most relevant source of uncertainty on the background. In
such condition, not only would the statistical significance of the
signal become much higher, but is would even be possible to
distinguish between different theoretical predictions. For example,
the three models considered in \cite{Ando:2004sb} 
would give 409, 303 and 172 events respectively above 10 MeV. 
An analysis of the expected DSN spectrum that would be observed
with a Gadolinium-loaded water \v{C}erenkov detector has been carried out
in \cite{Yuksel:2005ae}: the possible limits on the emission parameters of
supernova $\bar\nu_e$ emission have been computed for 5 years running of
a Gd-enhanced SuperKamiokande detector, which would correspond to 1 year 
of one MEMPHYS shaft, and are shown in Fig.~\ref{fig:sndpar}. 
Detailed studies on characterization of the backgrounds, however,
are needed.

\begin{figure}
\begin{center}
\epsfig{figure=./figures/sndpar.eps,width=8cm}
\caption{\it Possible 90\% C.L. measurement of the emission parameters
of supranova $\bar\nu_e$ emission after 5 years running of
a Gd-enhanced Super-Kamiokande detector, which would correspond to 1 year 
of one MEMPHYS shaft. The points corespond to different assumptions on
the average energy and integrated luminaosty: A,B,C are taken at the
edge of the region excluded by SK, D is often regarded aas the
canonical values for $\bar\nu_e$ emission before neutrino mixing. See
\cite{Yuksel:2005ae}. }
\label{fig:sndpar}
\end{center}
\end{figure}

%\subsubsection{Gravitational trigger and GRBs (???)}