We present extensive multi-wavelength observations of the extremely rapidly declining Type Ic supernova, SN 2005ek. Reaching a peak magnitude of M_R = -17.3 and decaying by ~3 mag in the first 15 days post-maximum, SN 2005ek is among the fastest Type I supernovae observed to date. The spectra of SN 2005ek closely resemble those of normal SN Ic, but with an accelerated evolution. There is evidence for the onset of nebular features at only nine days post-maximum. Spectroscopic modeling reveals an ejecta mass of ~0.3 Msun that is dominated by oxygen (~80%), while the pseudo-bolometric light curve is consistent with an explosion powered by ~0.03 Msun of radioactive Ni-56. Although previous rapidly evolving events (e.g., SN 1885A, SN 1939B, SN 2002bj, SN 2010X) were hypothesized to be produced by the detonation of a helium shell on a white dwarf, oxygen-dominated ejecta are difficult to reconcile with this proposed mechanism. We find that the properties of SN 2005ek are consistent with either the edge-lit double detonation of a low-mass white dwarf or the iron-core collapse of a massive star, stripped by binary interaction. However, if we assume that the strong spectroscopic similarity of SN 2005ek to other SN Ic is an indication of a similar progenitor channel, then a white-dwarf progenitor becomes very improbable. SN 2005ek may be one of the lowest mass stripped-envelope core-collapse explosions ever observed. We find that the rate of such rapidly declining Type I events is at least 1-3% of the normal SN Ia rate.
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