  Recent discoveries of double neutron star (DNS) mergers and ultra-stripped
supernovae (SNe) raise the questions of their origin and connection. We present
the first 1D~model of a DNS progenitor system which is calculated
self-consistently until an ultra-stripped iron core collapse. We apply the
\texttt{MESA} code starting from a post-common envelope binary consisting of a
$1.35\;M_\odot$ NS and a $3.20\;M_\odot$ zero-age main-sequence helium star and
continue the modelling via Case~BB Roche-lobe overflow until the infall
velocity of the collapsing iron core exceeds $1000\;{\rm km\,s}^{-1}$. The
exploding star has a total mass of $\sim 1.90\;M_\odot$, consisting of a $\sim
0.29\;M_\odot$ He-rich envelope embedding a CO core of $\sim 1.61\;M_\odot$ and
an iron-rich core of $\sim 1.50\;M_\odot$. The resulting second-born NS has an
estimated mass of $\sim 1.44\;M_\odot$ and we discuss the fate of the post-SN
system, as well as the mild recycling of the first-born NS. Depending on the
initial conditions, this family of systems is anticipated to reproduce the DNS
mergers detected by the LIGO-network.

Solar and Stellar Astrophysics;High Energy Astrophysical Phenomena