SN 2016iet: The Pulsational or Pair Instability Explosion of a Low Metallicity Massive CO Core Embedded in a Dense Hydrogen-Poor Circumstellar Medium

We present optical photometry and spectroscopy of SN 2016iet, an unprecedented Type I supernova (SN) at $z=0.0676$ with no obvious analog in the existing literature. The peculiar light curve has two roughly equal brightness peaks ($\approx -19$ mag) separated by 100 days, and a subsequent slow decline by 5 mag in 650 rest-frame days. The spectra are dominated by emission lines of calcium and oxygen, with a width of only $3400$ km s$^{-1}$, superposed on a strong blue continuum in the first year, and with a large ratio of $L_{\rm [Ca\,II]}/L_{\rm [O\,I]}\approx 4$ at late times. There is no clear evidence for hydrogen or helium associated with the SN at any phase. We model the light curves with several potential energy sources: radioactive decay, central engine, and circumstellar medium (CSM) interaction. Regardless of the model, the inferred progenitor mass near the end of its life (i.e., CO core mass) is $\gtrsim 55$ M$_\odot$ and up to $120$ M$_\odot$, placing the event in the regime of pulsational pair instability supernovae (PPISNe) or pair instability supernovae (PISNe). The models of CSM interaction provide the most consistent explanation for the light curves and spectra, and require a CSM mass of $\approx 35$ M$_\odot$ ejected in the final decade before explosion. We further find that SN 2016iet is located at an unusually large offset ($16.5$ kpc) from its low metallicity dwarf host galaxy ($Z\approx 0.1$ Z$_\odot$, $M\approx 10^{8.5}$ M$_\odot$), supporting the PPISN/PISN interpretation. In the final spectrum, we detect narrow H$\alpha$ emission at the SN location, likely due to a dim underlying galaxy host or an H II region. Despite the overall consistency of the SN and its unusual environment with PPISNe and PISNe, we find that the inferred properties of SN\,2016iet challenge existing models of such events.