Ultra-stripped Type Ic supernovae from close binary evolution
  Recent discoveries of weak and fast optical transients raise the question of
their origin. We investigate the minimum ejecta mass associated with
core-collapse supernovae (SNe) of Type Ic. We show that mass transfer from a
helium star to a compact companion can produce an ultra-stripped core which
undergoes iron core collapse and leads to an extremely fast and faint SN Ic. In
this Letter, a detailed example is presented in which the pre-SN stellar mass
is barely above the Chandrasekhar limit, resulting in the ejection of only
~0.05-0.20 M_sun of material and the formation of a low-mass neutron star. We
compute synthetic light curves of this case and demonstrate that SN 2005ek
could be explained by our model. We estimate that the fraction of such
ultra-stripped to all SNe could be as high as 0.001-0.01. Finally, we argue
that the second explosion in some double neutron star systems (for example, the
double pulsar PSR J0737-3039B) was likely associated with an ultra-stripped SN
Ic.
