  General Relativity predicts that the passage of matter or radiation from an
asymmetrically-emitting source should cause a permanent change in the local
space-time metric. This phenomenon, called the \emph{gravitational memory
effect}, has never been observed, however supernova neutrinos have long been
considered a promising avenue for its detection in the future. With the advent
of deci-Hertz gravitational wave interferometers, observing the supernova
neutrino memory will be possible, with important implications for
multimessenger astronomy and for tests of gravity. In this work, we develop a
phenomenological (analytical) toy model for the supernova neutrino memory
effect, which is overall consistent with the results of numerical simulations.
This description is then generalized to several case studies of interest. We
find that, for a galactic supernova, the dimensionless strain, $h(t)$, is of
order $\sim 10^{-22} - 10^{-21}$, and develops over a typical time scale that
varies between $\sim 0.1 - 10$ s, depending on the time-evolution of the
anisotropy of the neutrino emission. The characteristic strain, $h_c(f)$, has a
maximum at a frequency $f_{max} \sim {\mathcal O}(10^{-1}) - {\mathcal O}(1)$
Hz. The detailed features of the time- and frequency-structure of the memory
strain will inform us of the matter dynamics near the collapsed core, and allow
to distinguish between different stellar collapse scenarios. Next generation
gravitational wave detectors like DECIGO and BBO will be sensitive to the
neutrino memory effect for supernovae at typical galactic distances and beyond;
with Ultimate DECIGO exceeding a detectability distance of 10 Mpc.
