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 similar to 0.05-0.20 M-circle dot of material and the formation of a low-mass neutron star (NS). 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 10(-3)-10(-2). Finally, we argue that the second explosion in some double NS systems (for example, the double pulsar PSR J0737-3039B) was likely associated with an ultra-stripped SN Ic.